U. S. DEPARTMENT OF COMMERCE

W. AVERELL HARRIMAN, Secretary NATIONAL BUREAU OF STANDARDS

E. U. CONDON, Director

NATIONAL BUREAU OF STANDARDS MISCELLANEOUS PUBLICATION M177

TESTS OF INSTRUMENTS FOR THE DETERMINATION,

INDICATION, OR RECORDING OF THE

SPECIFIC GRAVITIES OF GASES

By

FRANCIS A. SMITH, JOHN H. EISEMAN, AND E. CARROLL CREITZ

Issued January 20, 1947

UNITED STATES

GOVERNMENT PRINTING OFFICE WASHINGTON : 1947

For sale by the Superintendent of Documents, U. S. Government Printing Office Washington 25, D. C. - Price $1.00
PREFACE

At the request of the American Society for Testing Materials, a

critical study was made of the commercial instruments for the determination of the specific gravities of gases. Eleven different instruments were studied with the use of 15 test gases of known specific

gravities. Determinations were made of the accuracy and reproducibility, of the effects of changes of temperature, relative humidity and

water content of the surrounding air, and of sources of error and

applicable corrections. It is believed that the results herein presented

will be of considerable value to those requiring accurate data on the

specific gravities of gases. E. U. Condon, Director.

ii
TESTS OF INSTRUMENTS FOR THE DETERMINATION,

INDICATION, OR RECORDING OF THE SPECIFIC

GRAVITIES OF GASES

By Francis A. Smith, John H. Eiseman, and E. Carroll Creitz

ABSTRACT

At the request of the American Society for Testing Materials, the National Bureau of Standards completed in 1941 a critical study of instruments available

to industry for the determination, indication, or recording of the specific

gravities of gases. Instruments were submitted for test by all interested manufacturers. The study of 11 instruments, with 15 test gases of known specific gravities,

comprised • determinations of accuracy and reproducibility, of the effects of changes of temperature, relative humidity and water content of the surrounding

air, and of sources of error and applicable corrections. The test gases ranged . in specific gravity from helium (0.15), in steps of approximately 0.15, to butane

(2.06). The probable errors in the values of the specific gravities of the test gases and mixtures used as standards of reference averaged ±0.00004, which

made it possible to fix the errors of the instruments to 0.0001 specific gravity

unit. No attempt was made to evaluate the instruments (which differ markedly in type and applicability) relative to one another, but the error of each instrument

with each test gas, with and without the application of corrections, is presented

in tables and graphs. With the aid of these, the prospective user may determine

from the characteristics exhibited the instrument best adapted to his specific- purpose. Suggestions for the improvement of the instruments made to the manufacturers

may indicate to the reader the direction in which improvement may be anticipated

when restrictions imposed by the war are removed. CONTENTS Page Preface n

I. Introduction 4

1. History of the project 4

2. Definitions 5

II. Equipment 6

1. Laboratory facilities 6

(a) Storage of the test gases 6

(b) Air-conditioned laboratory 7

(c) Reference air „ 7

2. Test gases 8

(a) Preparation 8

(b) Accurate determination of reference specific gravity 8

(c) Apparatus employed and its accuracy 9

(d) Constant-temperature bath 10

(e) Specific gravities of test gases 11

3. Instruments studied ' 12

III. Plan of the tests _ _ ___ 12

1. Methods 12

(a) Treatment of the results 13

1
2 Miscellaneous Publications, National Bureau of Standards

III. Plan of the tests—Continued Page

2. Corrections applicable and their evaluation 15

(a) Reference air 15

(b) Adjustment of observations for humidity and carbon

dioxide __: 15

(c) Pressure corrections 19

(d) Correction for deviation from ideal gas 20

(e) Chart corrections 20

IV. Results of tests of individual instruments 21

1. Pressure balances 22

(a) Construction and operation 22

(1) Edwards gas density balance 22

(A) Description 22

(B) Modifications for testing 23

(C) Method of operation 24

(2) Ac-Me balances 26

(A) Description 26

(B) Modifications for testing 28

(C) Method of operation 28

(b) Results of observations 29

(c) Sources of error 35

(1) Temperature coefficients 35

(2) Variations of temperature 36

(3) Material tested 38

(4) Measurement of absolute pressure 39

(5) Balancing the beam 41

(A) Edwards balance 41

(B) Ac-Me Junior balance No. 4041 42

(C) Ac-Me balance No. 3511 43

(6) Leveling 44

(d) Suggestions for improvement of instruments 44

(1) Edwards balance _- 45

(2) Ac-Me Junior balance No. 4041 46

(3) Ac-Me balance No. 3511 46

2. Anubis portable gas balance 47

(a) Description 47

(b) Method of operation 49

(c) Reference air 50

(d) Numerical results 52

(e) Mechanical action of the Anubis balance 52

(f) Leveling the balance 56

,(g) Temperature coefficient 57

(h) Other probable sources of error 58

(1) Air-check correction 58

(2) Calibration 58

(3) Purity of material tested 59

(4) Determination of balance point of beam 59

(5) Pressure determinations 60

(6) Temperature determinations 60

(7) Gas-law corrections 61

(i) Comments on operation and some suggestions for improvement 61

3. Ac-Me recording gravitometer No. 271 62

(a) Description 62

(b) Modifications for purposes of tests 64

(c) Method of operation 65

(d) Correction for effect of relative humidity on chart paper 67

(e) Reference air _'l 67

(f) Correction for water vapor and carbon dioxide in ref- erence air 67

(g) Sources of error 68

(1) Temperature coefficient 68

(2) Humidity coefficient 72

(3) Accuracy of readings 73

(4) Material tested 73
Specific Gravities of Gases 3

IV. Results of tests of individual instruments—Continued

3. Ac-Me recording gravitometer No. 271—Continued

(g) Sources of error—Continued Page

(5) Sealing liquid 73

(6) Volume of float 73

(7) Calibration 74

(8) Temperature changes 74

(9) Temperature and pressure compensator 74

(10) Mechanical effects 75

(h) Comments on operation and some suggestions for improvement 75

4. Anubis recording gas gravitometer 76

(a) Description 76

(b) Modifications for purposes of tests 78

(c) Method of operation 79

(d) Sources of error 82

(1) Accuracv of reading 82

(2) Calibration 82

(3) Effects of gravitational forces which change

with the position of the mechanism 84

(4) Gas column 85

(5) Leveling of instrument 86

(6) Weight of ink in pen 86

(7) Temperature coefficient 87

(8) Temperature lag 88

(9) Properties and changes of the sealing oil 89

(10) Humidity coefficient 90

(11) Effect of relative humidity on chart 92

(12) Barometric pressure 92

(13) Reference air 92

(e) Comments on operation and suggestions for improvement 93

5. Sigma recorder No. 7 for specific gravity 95

(a) Description 95

(b) Modifications for testing 97

(c) Method of operation 97

(d) Correction for composition of reference air 98

(e) Correction for effect of humidity on chart 99

(f) Temperature coefficient 99

(g) Humidity coefficient 102

(h) Other sources of erro^ 103

(1) Accuracv of readings 103

(2) Position of chart 103

(3) Material tested 103

(4) Effect of flame 104

(5) Height of gas column 104

(6) Rate of sampling 105

(7) Temperature lag 105

(8) The test weight 105

(9) Sealing oil _ 105

(10) Oil level 106

(11) Immersion error 106

(12) Pendulum weight 106

(13) Oil in pneumatic compensator 106

(i) Comments on operation and suggestions for improvement 106

6. Metric indicating gravitometer 107

(a) Description 107

(b) Modifications for testing 109

(c) Method of operation 109

(d) Correction for composition of reference air 110

(e) Temperature coefficient 112

(f) Humidity coefficient 113
4 Miscellaneous Publications, National Bureau of Standards

IV. Results of tests of individual instruments—Continued

6. Metiic indicating gravitometer—Continued Page

(g) Other sources, of error 114

(1) Readings 114

(2) Water level in manometers 115

(3) Material tested 115

(h) Comments on operation and suggestions for improvement 116

7. Ranarex specific gravity recorder No. A2360 and portable

specific gravity indicator No. P1284 116

(a) Description 116

(b) Modifications for testing 120

(c) Method of operation , 120

(d) Sources of error 122

(1) Temperature coefficient 122

(2) Pressure differences 127

(3) Purging 128

(4) Leaks 128

(5) Calibration 128

(6) Viscositv 128

(7) Readings 129

(8) Effect of relative humidity on the chart 129

(e) Comments on operation and suggestions for improvement 129

8. Fisher densimeter (experimental model) 130

(a) Introduction • 130

(b) Description 132

(c) Method of operation 133

(d) Sources of error 136

(1) Temperature coefficient 136

(2) Pressure changes 137

(3) Absolute pressure 138

(4) Changes of water temperature 138

(5) Material tested 139

(6) Errors in timing 140

(7) Errors of the observer 141

(e) Comments on the operation and some suggestions for improvement 142

V. Discussion 1 143

1. Interpretation of the results of tests 143

I. INTRODUCTION

1. HISTORY OF THE PROJECT

At the request of the American Society for Testing Materials, the

National Bureau of Standards undertook a study of instruments avail- able to industry for the determination, indication, or recording of

the specific gravity of gases. E. F. Schmidt, chairman of the ASTM

Subcommittee D-3-IV (on specific gravity of gaseous fuels), negotiated the loan of instruments to be tested, and the National Bureau of

Standards furnished the equipment and personnel and conducted the

tests. Announcement of the proposed tests was made in the Technical

News Bulletin of the. National Bureau of Standards in November

1938, inviting all interested manufacturers to submit instruments for

the tests. This was done to avoid the possibility of excluding any

interested manufacturer from participation and to secure as complete a collection of representative instruments as possible.
/Specific Gravities of Gases 5

After all preparations had been made for the testing, but before

the tests were actually started, each manufacturer was invited to send

a representative to inspect the installation and testing program and

to offer suggestions particularly, of course, regarding his own instru-

' ment. Three of the seven availed themselves of this opportunity.

A copy of the report on the instrument or instruments submitted

by him was sent to each of the cooperating manufacturers on October

18, 1941, with the request that he indicate any errors which he found

in the report. Replies were received from the manufacturers of all the

instruments except the Sigma.

A complete report of 240 typewritten pages was made on February

2, 1942, to ASTM Committee D-3 on Gaseous Fuels. This report, al- though accurate and complete, was somewhat hastily compiled from

the seven separate reports previously made to manufacturers, and

was full of repetitions and otherwise unsuitable for printing. In the

meantime, the authors of the report had become fully engaged in war

work and were unable to spare the time for a satisfactory revision

until recently.

Although the experimental work was completed in August 1941,

it is doubted that much has been done on the further development of

the instruments by their manufacturers, who also have had other

things to do. The information is probably not seriously out of date

for this reason. Numerous suggestions were made to the manufacturers in the re- ports sent to them individually in 1941, and almost without exception, they indicated that the recommendations would be accepted. Although the changes suggested should considerably improve convenience and minimize minor random errors in nearly all instruments, they

probably will not result in important changes in the accuracy generally attainable, except in the case of the Anubis instruments, bal- ance and recorder, in both of which the changes are expected to elimi- nate the sources of relatively large systematic errors in otherwise

excellent instruments.

2. DEFINITIONS

For the purposes of this report, the following definitions are used

Density is the mass per unit volume of the substance considered (gas

or air).

Gas is the material to be tested, as sampled, without change of

composition by drying, or otherwise.

Specific gravity of a gas is the ratio of the density of the gas, under

observed conditions of temperature and pressure, to the density of air

(dried and freed from carbon dioxide) at the same temperature and

pressure (usually 1 atm) as the gas. In this report, unless otherwise stated, no corrections are made for

deviations from the temperature arid pressure relations of ideal gases

hence, the specific gravity of a gas at one temperature and pressure is considered to be the same as at any other temperature and pressure. For purposes of convenience in maintaining a test mixture of constant specific gravity and in determining that specific gravity by the

independent method described later, (section II, 2) the test gases were all dry. In actual practice, the gas to be tested may contain
5 Miscellaneous Publications, National Bureau of Standards more or less water vapor as distributed and used. The specific gravity

of such gases should be determined without drying the gas. Or, if drying is necessary to avoid condensation, the water content should be

determined and the specific gravity of the dried gas corrected by computation to the value it would have had if the gas had not been dried.

(It is impracticable to determine the specific gravity of any gas at a temperature below the temperature of saturation of any of its vapor

constitutents. In general, therefore, before entering the testing ap- paratus a fuel gas from either a manufacturing plant or a natural

source must be exposed to a lower temperature or higher pressure, or

both, than will exist in the testing equipment. It may be necessary

to filter out fog at the condenser.)

In order to provide a reproducible and unchanging standard of

reference by which all specific-gravity data may be placed on a com- mon basis for comparison, Avhatever their source, the specific gravity

of each test gas was determined with reference to air that is dry and

free from carbon dioxide.

II. EQUIPMENT

1. LABORATORY FACILITIES

(a) STORAGE OF THE TEST GASES

All the test gases were stored in a steel tank of approximately

35-cu-ft capacity, tested to 500 lb/in.2

, and withdrawn as needed

Figure 1.

Diagram of mixing and storage tank.

(fig. 1) . A motor and fan within the tank provided good circulation

well directed by a 6-in. pipe arranged as a "wind tunnel." Four thermocouples in parallel were distributed in the air stream between the

rim of the funnel and the fan to measure the temperature of the gas. Spark plugs with long center terminals conducted the electric leads to the motor and thermocouples through the cover plate. The tank was mounted horizontally, and needle valves were located at the top and

bottom of each end, from which to sample the mixture for analysis

by a gas interferometer (Zeiss 1 m) to determine when mixing was

complete.
Specific Gravities of Gases 7

Gas was introduced and withdrawn through a single opening in

the end of the tank above the cover plate. This opening was fitted with

a tee connected to two diaphragm packless valves, one for discharging

the discarded residue of a mixture and the other connected to the line

to the laboratory.

All connections for the evacuation of the tank and for drying, in- troducing, and withdrawing gases and distributing them to testing

equipment and individual specific-gravity instruments were of copper

tubing with soldered fittings and "packless" diaphragm valves or needle valves with vacuum-tight packing, except that instruments

equipped by their manufacturers with hose-nipple inlets were con- nected to the system with minimum lengths of heavy rubber tubing.

After the tank and lines had been tested to establish freedom from

leaks, they were repeatedly evacuated and filled with air dried over calcium chloride until the tank was thoroughly dry. The tank was

then evacuated. The gases used in making the test mixtures were as pure as could be obtained without undue expense, and were introduced

from cylinders at one of the manifold connections. As the gases were

introduced they were dried, to avoid the possible condensation of water

in the storage tank, by passing them through a dehydrator containing 1.13 lb of freshly activated alumina, at a rate not in excess of

10 cu ft/hr. Before samples were withdrawn from the tank for the

tests, the alumina was removed from the line to avoid any change

of composition that might have resulted from selective absorption of

any constituent of the mixtures.

(b) AIR-CONDITIONED LABORATORY

In order to avoid variations of possible importance during testing

and to determine the effects of both temperature and humidity on

the specific-gravity measurements, the laboratory was air conditioned.

In order to place the results obtained over an extended period of time on a common basis, all the instruments were tested at 25° C (77° F),

and those affected by the water content of the laboratory air were

tested with the air containing 1.1 percent of water vapor, corresponding to a relative humidity of 35 percent at 77° F. Other temperatures and humidities were employed when some of the test gases were

used to establish the effect of the changes. In all cases, ample time was allowed for the temperature and water content of the air of the

laboratory to become steady and for the instruments to reach equilibrium with them before testing was started.

(c) REFERENCE AIR Several of the instruments used the air surrounding them as a standard of reference, and several discharged the gas sample into the

surrounding air. It was therefore necessary to prevent the contamination of the air in the laboratory by gas discharged from the in- struments. For this purpose an exhaust fan was provided, with

ducts arranged to pick up the gas at the point of discharge from the

instruments involved. No direct connections to the instruments were made, and dampers in the ducts were adjusted to provide ample flow

without affecting the indications of the instruments. For instru-
8 Miscellaneous Publications, National Bureau of Standards

ments purged by evacuation, the gas was discharged from a vacuum pump located in the adjoining laboratory, and the reference air was drawn through a copper tube from the outside, on the (normally)

windward side of the building.

2. TEST GASES

(a) PREPARATION

The test gases, which consisted of more than one constituent, were

prepared as follows : The constituents were successively passed

through the dryer and into the tank to predetermined pressures and

thoroughly mixed. Completeness of mixing was checked after each

addition by interferometer readings of gas from the four sampling

points. The temperature and pressure of the gas in the tank were

then observed and used to make one calculation of the composition

of the mixture. Interferometer readings, usually in comparison with

carbon dioxide, of each constituent and of the mixture in the tank

before and after its addition provided independent data for computing the composition of each successive mixture. An evacuated cylinder was filled from the final mixture and reserved for chemical

analysis. The three methods of analysis usually checked reasonably

satisfactorily.

(b) ACCURATE DETERMINATION OF REFERENCE SPECIFIC GRAVITIES

The specific gravity of the mixture from the tank was determined

by differential weighing in glass globes of about 1 -liter capacity, the

method and equipment described below being used.

Two glass bulbs of very nearly equal weight and volume were filled, one with air and the other with the gas under consideration, at the same temperature and pressure, and their difference in weight deter- mined by placing one on each pan of a sensitive balance. The bulbs were again evacuated and filled; the bulb that previously contained

air was filled with gas and vice versa. The difference in weight was

again determined.

The above procedure offered the following advantages : The differ- ence in weight, which is a measure of specific gravity, was doubled,

enabling a higher degree of accuracy to be attained ; corrections for

buoyancy effects on the bulbs were eliminated; the weights of the

bulbs became of secondary importance; and temperature and pressure

effects were minimized. The results were computed as follows: Let

2?i = weight of bulb 1 B2 — weight of bulb 2

V± =volume of gas in bulb 1 at 760 mm of mercury and the

temperature of the bath

V2 = volume of gas in bulb 2 at 760 mm of mercury and the

temperature of the bath

Da = density of 'air at 760 mm of mercury and the temperature

of the bath

Dg = density of the gas at 760 mm of mercury and the temperature

of the bath.
Specific Gravities of Gases 9

The same bulb was always weighed, on the same balance pan,

regardless of its contents. In general, it was necessary to add weights to one pan or the other

to produce a balance. Let

(Wr)i =weight on right pan

(Wi) x =weight on left pan.

The gas and air were then interchanged in the bulbs and

(Wr )x= weight on right pan

(Wi) 2 =weight on left pan.

At the prevailing barometric pressure, P, and the constant temperature of the bath, the quantity of gas in bulb 1 (reduced to units

of volume at 760 mm) was (P/760)Fi, and the quantity in bulb 2 was (P/760)F2 . Assume bulb 1 to contain gas and bulb 2 to contain

air, both at a pressure of P1 mm of mercury. The weight of gas in

bulb 1 is (Pi/760) V^Dg. Likewise, the weight of the air in bulb 2 is (Pi/760) V2Da . Assume also that bulb 1 is placed on the left balance

pan and bulb 2 is placed on the right. When a weight equilibrium

has been established, the following is true

B1 + ^V1 D! +(Wl ) 1 =B2 +^V2Da +(Wr ) 1 . (1)

The gas and air are interchanged in the bulbs, the temperature of

the bath remaining constant, while the atmospheric pressure may have

changed so that both bulbs are now at a pressure P2

. As before, with

bulb 1 on the left pan and bulb 2 on the right pan, an equilibrium is established.

B1 +^Vl Da +(Wt ) 2 =B2 +7^V2D,+ (Wr h. (2)

Subtracting eq 2 from eq 1 and solving for Dg/Da,

Two assumptions are involved in this derivation: (1) The temperature remains constant, and (2) it is permissible to make a linear

extrapolation from prevailing barometric pressure to 760 mm of

mercury with both air and gas.

(c) APPARATUS EMPLOYED AND ITS ACCURACY

Six 1-liter ring-neck, round-bottom, mold-blown flasks of approximately equal weight were selected from stock. The necks were re- moved and 7-mm (inside diameter) glass tubing substituted. The

flasks were then adjusted to approximately the same volume by softening the glass and expanding or shrinking the bulb near the neck.

Final adjustment was made by weighing into each bulb the same

weight of water and, after adjustment to a previously selected temperature, marking the position of the meniscus in the tubular neck.

Stopcocks were similarly treated. The same measured volume of
10 Miscellaneous Publications, National Bureau of Standards

water was introduced into one lead of each cock (the plug being in

the "off" position) and the position of the meniscus marked. The

stopcock lead and the tubular neck of each corresponding flask were

then cut off at the marks, and the cock was joined to the flask in such

a way that no appreciable change in volume occurred at the joint.

Standard-taper ground-glass connectors to fit the filling apparatus were cut to the proper length for sealing. Excess tubing was removed

from the stopcocks, and flasks and connectors weighed. Glass rod was

added to the lighter bulbs at the point where the connector was sealed

to the cock until all flasks were of equal weight.

The weights and volumes of the six bulbs, as finally adjusted, are shown below.

Bulb number Weight Volume at 25° C

1 238. 08

g± 0. 004

238. 02 ±0. 004

238. 12 ±0. 004

238. 10 ±0. 004

238. 02 ± 0. 004

238. 00 ± 0. 004

ml 1082. 22 ±0. 04

1081. 84 ±0. 04

1082. 30 ±0. 04 - 1082. 28 ±0. 04

1082. 24 ±0. 04

1082. 15 ±0. 04

2

34 ___

56

(d) CONSTANT-TEMPERATURE BATH

A well-insulated water bath, in which both bulbs were immersed

at the same time, was controlled by a system capable of maintaining

a temperature constant to about 0.002 deg. C over an extended period,

as measured with a resistance thermometer and Mueller bridge ac- curate to 0.001 deg. C. No differences between parts of the bath were found when it was explored with a differential thermocouple capable

of indicating, a difference of 0.005 deg. C. An uncertainty of 0.002 deg. C is reflected as an uncertainty of 0.00001 in the density of air. A permanent glass manifold to which the bulbs were attached

while in the thermostat permitted either bulb to be evacuated or

filled with either gas (the gas to be measured and purified outdoor air) or to be connected to the atmosphere through a guard tube that could

also be flushed with either gas and which prevented the diffusion

of room air into the flask when the connection was open. Each

flask connected to the manifold was evacuated and filled with the

gas to be weighed in it three times, again evacuated, filled to slightly more than atmospheric pressure, and given time to reach the temperature of the bath. Both bulbs were then opened to the air through

their guard tubes long enough to establish equality of pressure and

closed. Atmospheric pressures were read with a barometer capable of

measuring pressures to 0.05 mm. When the gas in question has a

specific gravity near 1.0, errors in pressure of this magnitude are

entirely insignificant. When the gas has a specific gravity as far
Specific Gravities of Gases 11

removed from 1.0 as that of hydrogen, an uncertainty of ±0.05 mm

of mercury appears in the specific gravity as ±0.00002.

Temperature and barometric pressure were read as promptly as possible after the bulbs were closed. They were then removed from

the bath, washed with pumice soap, wiped with damp and dry towels,

and the lubricant was removed from the ground-glass connectors.

It was found that during periods of extremely low humidity the bulbs

acquired a static charge. To eliminate errors from this source, the

bulbs, after being cleaned, were held in the steam from boiling distilled water until a light film of condensate had collected. This

apparently reduced the charges to negligibility. The bulbs were hung in the balance case for an hour before weighing.

Without doubt, some changes in the weight of the bulbs must have

occurred during all this handling. The magnitude of the changes

added to variations in the process of weighing itself were determined

by putting the bulbs through 10 cycles as above described but without

turning the stopcocks. There was thus no change in quantity or composition of the inclosed gas, and the reproducibility of results was

that of the entire cleaning and weighing process. The results of

the weighings were as shown in table 1. Table 1.

Reproducibility of the process of cleaning and weighing the bulbs

Date Difference

in weight Deviation from

average

August 24, 1939 mg15. 83

15. 78

15. 97

15. 56

15. 50

. 15. 85

15. 71

15. 74 15.64

16. 03

mg

+0. 07 +.02 + 21 -.20

-.26

+. 09 -.05 -.02

-. 12 +. 27

Do

Do

August 25, 1939 Do

DoDo

Do

August 26. 1939 Do

Average _ 15. 764 ±0. 13 The probable error of a single determination was ±0.11 mg. This

represents a probable error of ±0.00004 in the calculated specific

gravity.

If the errors discussed in this section are all of the same sign, a re- producibility of ±0.00007 can still be expected.

(e) SPECIFIC GRAVITIES OF TEST GASES

The approximate composition of the test gases and their specific

gravities, determined by 10 weighings of each, are shown in table 2. The probable errors listed are those computed in the usual manner

from the agreement among the observations on an individual gas. The

gases are listed in the table in the order of their specific gravities.

They are numbered in the order in which they were prepared and used.
12 Miscellaneous Publications, National Bureau of Standards

Table 2.

Compositions of the test gases, and their specific gravities, as deter- mined by weighing

Mixture number Test gas Approximate composition Specific gravity Probable

error

Helium

Helium-nitrogen dodo

Hydrogen-carbon dioxide.. Synthetic typical manufactured gas. Synthetic typical natural

gas. Helium-nitrogen Nitrogen

Nitrogen-carbon dioxide. do

do Carbon dioxide Propane

ft-Butane

Percent He, 98.3; Nj, 1.7 He, 80.0; N2 , 20.0 He, 65.9; N2 , 34.1 He, 44.5; N2 , 55.5 . H2 , 63.1; C02 , 36.9 CH4 , 9.11; CO, 29.96; H2 , 34.59; 2 , 0.55; N2 , 5.74; C02 , 4.44; C2 H6 , 2.64; C2 H4 , 12.96. CH4 , 79.4; C2 H6 , 14.7; C3 H8, 2.9; N2 , 2.4; C02 , 0.5. He, 21.1; N2 , 78.9 Atmospheric, fractionated, water pumped. • N2 , 76.4; C02 , 23.6 N2 , 44.1; C02 , 55.9 N2 , 22.9; C02 , 77.1 Commercial

Phillips, cp, reputed 100

Phillips, cp, reputed fra-butane 99.5 to be. lisobutane 0.5

0. 15262 ±0. 00006

. 3048o ±. 00004

. 42226 ±. 00003

. 6007o =1=. 00007

. 6080s ±. 00009

» . 6475 ±. 00007

. 6820o ±. 00005

. 79626 ±. 00001

. 96664 ±. 00001

1. 0982 ±. 00002

1. 2791 5 ±. 00005

1. 39839 ±. 00003

1. 5268o ±. 00002

1. 54609 ±. 00003

2. 06444 ±. 00007

» Mixture 1 was used in the determination of temperature and relative-humidity coefficients and con- sequently was stored for more than 3 months. Its specific gravity was therefore redetermined at the end of that period. The other mixtures were stored for very much shorter periods, and their specific gravities were

not redetermined. The value determined for mixture 1 on January 17, 1940, was 0.6475o. On April 26 the redetermination gave 0.6472g ±0.00007. Assuming the change to be uniform and continuous, reference values

for intervening dates were determined by interpolation.

3. INSTRUMENTS STUDIED

Seven manufacturers provided 11 instruments for the tests. It

is believed that all types of instruments in common use are repre- sented. The list of manufacturers and the instruments supplied by

them follows

:

Company

American Meter Co., Metric Metal

Works, Erie, Pa. American Recording Chart Co., 3113 East Eleventh Street, Los Angeles,

Calif. Fisher Scientific Co., 711-23 Forbes

Street, Pittsburgh, Pa. The Permutit Co., 330 West FortySecond Street, New York, N. Y. The Refinery Supply Co., 621 East Fourth Street, Tulsa, Okla. Sigma Instrument Co., Letchworth,

Herts, England.

Arthur H. Thomas Co., West Washington Square, Philadelphia, Pa.

Instrument

Metric Indicating Gravitometer. Anubis Portable Gas Balance No. 115. Anubis Recording Gas Gravitometer. Fisher Densimeter (experimental

model )

.

Ranarex Portable Specific Gravity In- dicator No. P 1284. Ranarex Specific

Gravity Recorder No. A 2360. Ac-Me Recording Gravitometer No. 271. Ac-Me Gravity Balance No. 3511. Ac-Me Jr. Gravity Balance No. 4041. Sigma Recorder No. 7 for Specific

Gravity.

Edwards Gas Density Balance No. 763.

III. PLAN OF THE TESTS

1. METHODS

Each instrument was tested with each of the test gases that fell within its range of specific gravity, at the "normal" temperature

of 77° F (25° C) and, where applicable, in air having the "normal"

water content of 1.1 percent.
Specific Gravities of Gases

Test gases 1 and 2 also were used to test the instruments at lower

and at higher temperatures than 77° F, in order to determine their

temperature coefficients. Similarly, these gases also were used to test the instruments in air having a lower and a higher water content than 1.1 percent in order to determine experimentally their humidity

coefficients. Test gases 1 and 2 were used for these purposes because

they were typical fuel gases with specific gravities between 0.6 and

0.7, the range most commonly encountered.

The possibility that the results obtained with two of the instruments might be dependent to some extent on the viscosity of the gas,

as well as its specific gravity, was investigated.

Test gas 8 was prepared to have a specific gravity very close to that

of test gas 6 but a considerably different viscosity, so that a comparison of results obtained with the two gases would indicate the effects of viscosity on the readings of the instruments.

A satisfactory technic was worked out for each instrument in pre- liminary tests> and the same procedure was followed throughout the

entire series of tests with a given instrument. The few cases in which

circumstances necessitated deviations from the "standard" procedure

are noted in the discussion of the individual instrument to which they

apply.

Each test of an instrument consisted of 10 determinations of specific

gravity, of which five determinations were made by one observer and

five by another, in order to minimize any effects of the personal equation. In every case an effort was made to determine the best per- formance of which the instrument was capable, after carefully con- sidering all factors which might influence the results.

(a) TREATMENT OF THE RESULTS

In making a test of an instrument under a given set of conditions,

and with a given test gas, the 10 determinations with their mean were

treated by the method of least squares to determine the probable error

of the mean and that of a single determination. As these figures

represent the variability, or uncertainty, of the results obtained with

the instrument when using a test gas of constant specific gravity under

substantially constant conditions of operation, they serve as a measure

of the reproducibility, or "precision" of the instrument.

The mean of the 10 determinations has been compared with the

known specific gravity of the test gas to obtain the ""error" of the

instrument under the conditions of the test, the error serving as a measure of accuracy. The following data obtained with the Edwards gas density balance,

using test mixture 1 at an average temperature of 77.7° F., are used to

illustrate the method of computation of probable error by means of

the formula (from Merriman, Method of Least Squares, p. 72) : Probable error of mean ^ / v 6745

\ n(n— 1)

—, -T 0.6745V^, n(n—l) *
14 Miscellaneous Publications, National Bureau of Standards

where V is the deviation of a single determination from the mean, and n is the number of determinations.

Determination No. Observed specific gravity Deviation from mean, V

Square of deviation,

1 0. 6433 0035 0000122^

2

.' 6496 . 0028 784

3 . 6486 . 0018 324

4 . 6475 . 0007 49

5 . 6532 . 0064 4096

6 . 6418 . 0050 2500

7 . 6489 . 0021 441

8 . 6452 . 0016 256

9 . 6451 . 0017 289

10 . 6447 . 0021 441 Mean 0. 6468 0. 00010405 =

2F2 (sum of V2

)

2?V 0.00010405 = _ 000001156

n(n-l) 10(10-1)

/ ?V2,.0.6745 =0.001075X0.6745 =0.000725, probable error of n(n—l)

mean. v lX 0.6745Vl0 =0.000725X3. 162 =0.00229, probable error of a

71(71—1)

single determination.

"Observed" specific gravity, mean 0.6468. Specific gravity of text mixture 1 0.6474 1 Uncorrected error of instrument — 0. 0006

Uncorrected error, percentage of standard

specific gravity — 0.09.

1 See footnote of table 2. The. "uncorrected" results of the observations were next "corrected"

to take account of certain conditions involved in testing, the effects of which were known quantatively. Some of these corrections were common to more than one of the instruments and will be discussed in the next section. Others applied to only one instrument and will be

described in connection with it. After the "corrections" had been made there still remained certain "sources of error", the effects of which were not known, independently

of the observations themselves, definitely enough to justify the application of numerical corrections for them. The observed and "corrected"

specific gravities for each of the gases used in the investigation are tabulated for each instrument. The "corrected" results are also plotted, as are other data relating to the sources of error, from which

it may be possible, in some cases, to apply additional corrections to the observed results.
Specific Gravities of Gases 15

2. CORRECTIONS APPLICABLE AND THEIR EVALUATION

(a) REFERENCE AIR The composition of outdoor air unmodified by products of combustion from nearby furnaces or other apparent sources of probable con- tamination is so constant with respect to all constituents except water

vapor that its density when dried does not change within the limits

of accuracy with which we are concerned in this investigation. However, contamination of laboratory air by products of combustion or by air exhaled by the occupants of the laboratory is so insidious a source of error that it is safest to base the most accurate determinations

of specific gravity on air from which both carbon dioxide and water

vapor have been removed. In the routine operation of specific-gravity

apparatus, particularly of the recording type, it may be impracticable

to make the comparison with carbon dioxide-free air. Specific gravities measured with respect to dry air of normal carbon dioxide content may be converted to specific gravities of dry air free from carbon

dioxide by multiplying by the factor 1.00016, in the case of such in- struments as the Metric portable gravitometer, the two Ac-Me balances

and the Edwards balance.

(b) ADJUSTMENT OF OBSERVATIONS FOR HUMIDITY AND CARBON DIOXIDE

The following applies to such instruments as the Fisher densimeter,

the Metric portable gravitometer, and the Ac-Me and Edwards

balances.

The conditions of humidity of gas or air existing at the time observations of density or specific gravity are made are not always the conditions under which it is desired to know the results. For example,

in the use of the effusion method of determining specific gravity, both

gas and air are usually confined over water and are saturated with

water vapor at the temperature which happens to exist in the apparatus

when the test is made. The square of the ratio of the times required

for efflux of gas and air is the ratio of the density of saturated gas to the density of saturated air at the temperature of observation. We

are less likely to be interested in this ratio than in the specific gravity

(ratio to dry air) of the dry gas or the gas as sampled, or even the gas

when saturated at a "standard" temperature. Similarly, in the use

of an Edwards balance or other apparatus depending on the same principle, it may be inconvenient to change the humidity of either gas

or air, and the ratio found by direct observation may be that of gas

of one humidity to air of another, in neither of which are we immediately interested.

The formulas that follow are easily derived by expressing the

densities of gas and air under each condition of humidity in terms of

their densities when dry, the density of water vapor, and the partial

pressure of each component of the mixtures. They permit the ready

calculation of the relative densities of gas and air for any conditions

of either from observations made under any other conditions. (These

corrections do not apply, however, to types of instruments such as the Anubis balance and the Sigma, Anubis, and Acme recorders,

which are discussed later.)

The symbols used are

R = ratio of density of gas to density of air under any definite

conditions of humidity in each.

719265—47 2
1 5 Miscellaneous Publications, National Bureau of Standards

Rs =the particular value of R when both gas and air are saturated.

S =the specific gravity of dry gas; that is, it is the particular

value of R when both gas and air are free from water

vapor.

#2=the specific gravity of gas containing a partial pressure, g, of water vapor : that is, it is the value of R when the air

is dry and the gas is not. a =the partial pressure of water vapor in the air. g =the partial pressure of water vapor in the gas. w =the pressure of water vapor at saturation. (When air is saturated, a=w\ when the gas is saturated, g =w).

h =the barometric pressure. h = the average head of water during a determination, in

millimeters of mercury.

p =the total pressure at which gas or air is saturated +

0.622 is the specific gravit}^ of water vapor, that is, it is the ratio of

the density of pure water vapor to the density of dry air at the same

temperature and pressure. The specific gravity, S, of a dry gas in terms of the ratio, R, of the

density of gas containing a partial pressure, g, of water vapor to the

density of air containing a partial pressure, of water vapor is \p-gJ p-g

The specific gravity, $, of a dry gas in terms of the ratio, i?s , of the

density of saturated gas to that of saturated air is +

0.62^(^.-1)

p — w

This is a special case of equation 3. The specific gravity, Ss , of gas containing a partial pressure of

water vapor, g, in terms of the specific gravity, of the dry gas is ^=(S£Z£+ 0^2£. VP (5)

For the special case of gas under the conventional "standard" conditions for expressing the heating value of fuel gases in the publicutility industry, p is 30 in. of mercury, and g is the vapor pressure of

water at 60°F. In this case ^=0.9826^+0.0108.

Under the standard conditions of gas measurement of the American

Society of Mechanical Engineers, p, is 760 mm of mercury, and g is the vapor pressure of water at 68° F. In this case

' ^=0.9769^+0.0144.

The ratio R of density of gas to that of air containing a partial

pressure, a, of water vapor, in terms of the specific gravity, Sg, of the

gas, is ^= ^^(l-0.622)

=

%-o!s78a- (6)
Specific Gravities of Gases 17

To facilitate the evaluation of these corrections, curves were plotted

from which the corrections could be read off when the relative humidity was known (for the water vapor) and when the percentage of carbon

dioxide was known. These curves are presented for the convenience

, of the manufacturers and users to whose instruments they are applicable. The corrections for water vapor and carbon dioxide that are applicable to the results obtained with the Ac-Me recording gravitometer, the Anubis recording gravitometer, and the Sigma specific

gravity recorder may be evaluated by means discussed in the reports on those instruments.

The relative humidity having been determined with any suitable

psyehrometer, the corresponding percentage of water vapor at the

existing dry bulb temperature may be read off from the family of curves presented in figure 2.

Figure 2.

Percentage of water vapor from percentage of relative humidity at

existing dry-bulb temperature.
18 Miscellaneous Publications, National Bureau of Standards

Corrections for water vapor applicable to the results obtained with

the Metric portable gravitometer may be obtained from the family of curves presented in figure 3. Corrections applicable to the results obtained with the Fisher densimeter, in which both gas and air are

saturated, are discussed in the report on that instrument.

SPECIFIC GRAVITY Figure 3.

Correction for water vapor in the reference air. Corrections applicable to the results obtained with the Anubis portable gas balance (if the carbon dioxide is not removed as well as the

water) are discussed in the report on that instrument.

On account of the method of calibration, and since both gas and air are saturated, no corrections for water vapor or carbon dioxide are applicable to the results obtained with the Ranarex recorder or Ranarex

portable indicator.

Corrections for carbon dioxide applicable to the results obtained

with the Metric portable gravitometer, the two Ac-Me balances, and

the Edwards balance may be obtained from the family of curves pre- sented in figure 4, which were derived from the equation

S=B (1.529 [C02 ]+1-[C02 ]),

where

S= specific gravity with respect to dry air free from carbon

dioxide

R=observed value uncorrected for carbon dioxide in the

reference air

[C02 ] = concentration of C02 in reference air expressed as a

fraction of the total 1.5290 = specific gravity of C02 .
Specific Gravities of Gases 19

(c) PRESSURE CORRECTIONS

For the Edwards and Ac-Me balances a correction of the pressure

is applicable at temperatures other than 32° F (0° C) to take account

of the expansion of mercury.

CORRECTION FOR CO2 IN REFERENCE AIR

op

J,2°'° r— U 08%

04%

0.2 04 0.6 8 1.0 12 14 1.6 1.8 2.0 SPECIFIC GRAVITY Figure 4.

Correction for carbon dioxide in the reference air.

2.2

In making a determination of the absolute pressure at which the

beam balances, the difference in pressure between inside and outside

of the balance case is read on the scale of a manometer containing

mercury at the existing temperature. This difference in pressure is added (algebraically) to the existing barometric pressure to obtain

the absolute pressure. The barometeric pressure reading usually is, and during these tests always has been, corrected to a mercury temperature of 32° F (0° C). In order to obtain a correct value for the

absolute pressure, the pressure difference should also be corrected to the value it would have if the mercury in the manometer were at 32° F (0° C). At first glance this correction would appear to have

a negligible effect on the specific gravity, but the correction increases

with the temperature and with the pressure difference involved. As

the correction is applied to the observed pressure difference, it must

be applied each time the beam is balanced, and the corrected specific

gravity computed from the corrected absolute pressures. For the Edwards balance, the linear temperature coefficient of the

maple scale, parallel to the grain, is approximately 0.000005 mm per

mm per deg C. This amounts to about one-fortieth of the linear coefficient of mercury and is negligible by comparison.

For the Ac-Me balances, the scales are made of aluminum or an aluminum alloy. The linear temperature coefficient of aluminum is
20 Miscellaneous Publications, National Bureau of Standards

0.00002313 mm per mm per deg C, which may or may not have been

very nearly that of the scale. This amounts to about one-eighth of

the coefficient (0.00018186) of mercury, and may be neglected without

appreciable error. The corrections, therefore, have been computed

from the expansion of the mercury alone. The pressure differences involved in the tests with these balances

have been corrected by means of the formula

G=aR%

the correction in millimeters of mercury

0.00018 mm per mm per deg C

the pressure difference in millimeters of mercury

the temperature in deg C.

(d) CORRECTION FOR DEVIATION FROM IDEAL GAS

As is well known, deviations from ideality of the material tested may

be a source of error. By the usual definition, specific gravity is the

ratio of the density of gas to the density of air at the same temperature

and pressure. If the density of the gas does not have the same coeffi- cients of temperature and pressure as air, the specific gravity according

to this definition is a function of those conditions of measurement.

When balances of the Edwards and Ac-Me types are used, it is cus- tomary to assume ideality in both air and gas by using the above rela- tion in the form : specific gravity is the ratio of the absolute pressure

of air to the absolute pressure of gas, when they are made to have the same density at the same temperature. Balancing the beam in each

brings the densities to equality.

From the results obtained in this study it appears that the gases

up to and including carbon dioxide do not depart from ideality enough

to affect their measurement significantly. The densities of propane

and butane, however, increase so much more rapidly than their pres- sures that their specific gravities are significantly dependent on the

absolute pressures at which the beam is balanced in them.

If the specific gravity is desired at an absolute pressure of 760 mm,

as it was in the present case, for comparison with the specific gravity

determined for the test gas at that pressure, it may be possible to make

a sufficiently accurate determination by balancing the beam in the gas

at two different pressures (by adjusting counterweight or rider)

preferably one above and one-below 760 mm. The two values of specific

gravity, after correction, are plotted against the absolute pressures, a straight line drawn through the two points and the desired specific

gravity read off at the absolute pressure of 760 mm.

(e) CHART CORRECTIONS

For recording instruments, a correction is applicable for changes

in the dimensions of the paper with changing relative humidity. The

effects of an 80-percent change of relative humidity on charts for each

instrument were measured by the Paper Section of the Bureau and

ranged from 0.60 to 0.72 percent in the "machine direction" of the

paper and 1.43 to 1.66 percent in the "cross direction." All the cir- cular charts are printed with the 6-o'clock diameter in the machine

where

C-- RP
Specific Gravities of Oases 21

direction, and to minimize the effects of humidity, all tests were made

with the pen close to that diameter. All readings were also corrected

to a relative humidity of 35 percent by multiplying the difference between 35 and the observed relative humidity by the distance from the

pen to the center and by the predetermined change of dimensions

per unit change of relative humidity. A typical numerical example

follows.

The chart of the Ac-Me gravitometer was found to expand 0.62 percent for an increase of relative humidity of 80 percent. With

mixture 2 and a relative humidity of 37.8 percent, the chart reading was 0.6900. The distance from the center of the chart to the pen was

65.5 mm. If the relative humidity were reduced to the standard of

35 percent, the paper would move inward under the pen (in the

direction of a higher specific gravity).

0.0062 X (37.8-35.0) X65.5

^ —- '- = Am/)0 0.0142 mm,

ou which is equivalent to 0.00008 specific gravity. This is the number

to be added to the original reading to correct to 35 percent relative

humidity.

Readings of the instrument are subject to correction on account

of the effect of relative humidity on the chart under all conditions ex- cept that in which the instrument is calibrated, and the record is made

with the chart exposed to air of the same relative humidity as that

existing at the time the chart was printed. At any other relative

humidity the circles on the chart are no longer circles, and their radii are different in different directions. A change of relative humidity

of 47.4 percent (which is not excessive) from that at calibration re- sulted in a correction of 0.0014 on the 6-o'clock axis. A correction of

approximately 0.0037 would have been required on the 12-o'clock axis

with this gas, and one of 0.0065 with a gas of 1.0 specific gravity.

There would have been an additional uncertainty in the reading unless

the relative humidity at calibration was known to be the same as that

at printing. IV. RESULTS OF TESTS OF INDIVIDUAL INSTRUMENTS

To facilitate the presentation of the data, the instruments have been

arranged in groups based on the type of instrument and the types of

corrections that are applicable to them.

Three balances, the Edwards, Ac-Me Junior No. 4041, and Ac-Me

No. 3511, are identical in principle. In each of them, a beam carrying

a bulb is brought to balance in the same position, successively in air

and in gas, by adjusting the pressure within the balance case; the

absolute pressures are determined by means of a barometer and a

mercury-filled manometer, and the specific gravity is computed from

their ratio. The instruments differ in size, method of supporting the

balance beam, sealing the balance case, and other minor details of

construction, but they are subject to corrections and errors of the same

kinds though not necessarily of the same magnitude.

Four instruments, the Anubis balance, Anubis recording gravitometer, Ac-Me recording gravitometer, and Sigma recorder, in princi-
22 Miscellaneous Publications, National Bureau of Standards

pie, balance the weight of a given volume of gas at atmospheric

pressure by a displacement of the center of gravity of a balance beam,

and the amount of this displacement, or "deflection," subject to corrections, measures the specific gravity. This group of instruments in- cludes much greater differences than the first in construction, methods

of compensating for changes of atmospheric conditions, etc., and does

not permit as much generalization with regard to corrections and

sources of error. Three instruments, the Metric indicating gravitometer, the Ranarex recorder, and the Ranarex indicator, depend on the pressure developed in stopping the movement of the gas that has been set in

motion by a rotary blower. Very different constructions are employed

by the two manufacturers represented.

One instrument, the Fisher densimeter, depends on a comparison

of the rates of efflux of air and gas through an orifice.

1. PRESSURE BALANCES

(a) CONSTRUCTION AND OPERATION

(1) Edwards Gas Density Balance. (A) Description.—The Edwards balance is approximately 9% in. long, 4 in. wide, and 5y2 in. high (Fig. 5). The manometer, mounted on a tripod stand, is 38 in. high. The instrument is supplied in a wooden case 39% by 12 by 5%

in. with a handle for carrying it. The total weight, including the case,

is 36 lb. This instrument (described briefly in Technological Service Bulletin 5980, of the Arthur H. Thomas Co., Philadelphia, Pa.) consists of

a balance beam, one end of which is cemented into a glass tube sealed

in a cylindrical glass bulb, and the other end, threaded, carries a counterweight, which consists of two knurled nuts locked together

and on its tip a circular target bearing two adjacent horizontal . lines on a white background. At its center of balance, the beam is clamped

between two cross bars, through which are screwed two steel points, one on either side of the beam. These- points are the pivots on which

the beam balances, and are seated, one in a cone and the other in a groove (at right angles to the beam) in an agate support mounted on

a metal part that fits snugly inside a cylindrical gastight chamber.

This chamber, or balance case, has a glass window at each end, is inclosed in a water jacket, and is fitted with a needle valve at each

end for connection to the sample and to vacuum and has a connection

to a mercury-filled manometer to measure the pressure difference

between the inside and outside of the balance case. The case is fitted with a base consisting of a single foot at the rear and a cross bar at the front carrying two leveling screws, one at each side, but no spirit

level, either longitudinal or transverse. On the cross bar at the front

is mounted an arm supporting a lens with which to observe the position of the target on the balance beam with respect to a single horizontal black line on a small circular glass window mounted on the end

of the beam support inside the window of the balance case. On the

under side of the cross bar of the beam is a pendulum screw and nut

with which to make fine adjustments of the height of the center of

gravity of the beam with respect to its points of support.
Specific Gravities of Gases 23

In operation, the balance case and manometer connections are filled with dry air and the pressure is gradually reduced until the beam is balanced. The pressure indicated by the manometer is noted, and

the balance is evacuated and filled with gas, the beam balanced as

1 before, and the pressure noted. The specific gravity of the gas -is the

Figure 5.Edwards gas density balance No. 163. ratio of the absolute pressure required to balance the beam in air to the absolute pressure required to balance it in gas. (B) Modifications for Testing.—A leak at the ball joint of the

manometer connection on the balance case, caused by imperfections in

the surface of the ball, was stopped by coating the ball with beeswaxrosin cement.
24 Miscellaneous Publications, National Bureau of Standards

The balance case, beam support, and beam were carefully freed of

dust. The steel points appeared to be in good condition, as were the cone and slot in the agate bearing. The nut for adjusting sensitivity was very loose and to make it more secure, as well as to increase sensitivity, it was turned as high as possible against the end of the thread.

With the nut near the center of the screw, the period of swing was

only 7.7 seconds. The period could not be increased beyond 8.0 seconds without changing the adjustment of the needle bearings. As

the directions for use stated, "The beam has already been adjusted

for high sensitivity and should not be changed unnecessarily," no

other change of sensitivity was made.

In order to use the balance over as wide a range of specific gravity

as possible with the least possible disturbance of the balance beam by

adjusting the counter weight to make it balance at different pressures, the beam was adjusted to balance in dry air at 1475 mm absolute.

An accessory rider was made of aluminum sheet, which, when slipped

into the groove in the counterweight, caused the beam to balance in

dry air at 388 mm absolute. The beam could thus be made to balance

above or below atmospheric pressure, for use with gases lighter or

heavier than air, merely by opening the case and placing or removing

the rider, and a return to approximately the original balancing pres- sure was assured without the necessity of hunting for the proper loca- tion of the counterweight on each occasion.

A small hole was bored in the wing of the plug to the water jacket

for the insertion of a thermocouple to measure the temperature of the

instrument.

An intermittent leak having been traced to the rear needle valve,

it was opened and a smeared brass chip was removed from the needle

point and cone. The needle and seat were cleaned, and the valve then

held satisfactorily.

Air was found to leak into the evacuated balance through the packing in the rear needle valve while filling the balance with gas, unless

the gas pressure on the needle valve was kept above atmospheric pressure. A diaphragm pressure regulator was installed in the main gas

line and set at 20 lb so that all the lines to the various instruments

could be maintained at that pressure and the flow controlled by the

valve on the balance.

(C) Method or Operation.—The directions for use of the Edwards

gas density balance, No. 5980, supplied with the instrument, were fol- lowed with various extensions during the testing with 14 of the gas

mixtures of known specific gravity.

In purging the instrument in preparation for a determination of

the pressure at which the beam balanced, the balance case was evac- uated to an absolute pressure of about 40 mm, then filled to atmospheric pressure with air taken through copper tubing from outside on the windward side of the building, and dried over calcium chloride

just before entering the balance. Evacuation and filling was repeated

a second and a third time. The needle valve was then opened slightly

to the vacuum, and the pressure reduced until the beam balanced.

If the residual pressure after each evacuation were always exactly

40 mm, the specimen would contain 5.3 percent of the previous contents after one evacuation and filling, 0.28 percent after the second,
Specific Gravities of Gases 25

and 0.015 percent after the third. Contamination to this extent would

result in an error of 0.00013 for helium at one extreme and of 0.00016

for butane at the other. As these errors would be only about twice

the uncertainty involved in the "standard" specific gravities of the test gases, and very minor fractions of the errors actually found, they were

considered sufficiently small for the purpose of these tests. As in any

case, the direction and amount of error from failure to purge completely can be determined after a specific-gravity test, a correction can and should be made if it is large enough to be significant. In this

case, the "errors" given above should be subtracted from the observed

density of helium and added to that of butane, but they cannot be

considered significant.

A test for leaks was always made before each series of determinations of specific gravity.

The directions do not state clearly whether the "balance" of the

beam shall be observed while it is oscillating or stationary. However, the character of the target and lines is unfavorable for accurately

estimating the amplitude of oscillation on the two sides of a balance

point, damping is rapid, and the precision with which the pressure

may be controlled by means of the needle valve makes it possible

to adjust the position of the beam gradually and with practically no oscillation. Previous knowledge indicated also that a static bal- ance has generally been used with this instrument, and this method

was followed throughout the tests. The means for evacuating the

balance is not provided with it. If a hand pump had to be used, adjusting the beam to a stationary balance might present more difficulty.

The beam was brought to balance by removing gas or air from the

balance until the beam started to oscillate, slowing down the flow as the swings damped out, until by the time the reference mark reached

one of the two parallel marks on the target, no oscillation was perceptible and the beam moved continuously and slowly to a position

where the reference mark was between the two marks of the target,

and an equal width of white showed on either side of the reference

mark between it and the adjacent target mark. The valve was then

closed, the manometer tapped alternately twice on each side at the

meniscus, and the position of the meniscus read to an estimated 0.1 mm.

The beam was then again observed to verify the balance point. If

any change had occurred while the manometer was being read, the

beam was rebalanced.

While changing the short rubber-hose connection to the gas and

air lines, care was taken to hold the balance firmly against the stone bench top by resting the left wrist and fingers on the front and rear

needle-valve knobs, respectively, and to avoid any slightest jar to the

balance during a series of determinations.

Occasional small permanent (for the time) shifts in the balance

point have been traced to such disturbances or to tapping the balance

case. Contact with the balance case itself was avoided to prevent

disturbance of its temperature.

In making a single determination of specific gravity, the beam

was balanced in air after purging three times, then in gas after purging three times, and then in air again after purging three times. Each

time the beam was balanced, the manometer readings, the tempera-
26 Miscellaneous Publications, National Bureau of Standards

ture of the instrument, the corrected barometric pressure, and the

time were recorded. If the instrument temperature changed in such

a way that the mean of the temperature at the two balance points in

air was not the same as the temperature at the intermediate balance

point in gas, the resulting value for the specific gravity was corrected

by multiplying it by the ratio of absolute temperatures required to bring the average of the air temperatures to the gas temperature.

(2) Ac-Me Balances. (A) Description.—The two Ac-Me gravity

balances, Junior No. 4041, and 3511, differ in size, method of suspending the balance beam, and minor details of construction. Both bal- ances are mounted on wooden bases, 14 by 6 in. and 22 by 7y2

in., re- spectively, and are about 8 and 11 in. high (fig. 6). The bases are provided with leveling screws and circular levels, and may be supported either on a table or on a tripod stand 37 in. high. A manometer,

provided for attachment to the stands, brings the total height to

63^/2 in. With the needed accessories, tripod, manometer, air dryer,

pump, and hose connections, the Junior No. 4041 balance weighs 50

lb. and No. 3511, 76 lb. In both balances the beams are suspended from frames attached

to face plates. The frames slide into cylinders, to the open ends

of which the face plates are attached by cap screws. Rubber gaskets

serve to make the cases gaslight when assembled. Plastic windows

in the face plates permit the observation of scales attached to the

beams and of thermometers attached to the frames inside the cases. Connections are made from the balance cases through needle valves

and heavy rubber tubing with metal union fittings to the source of

gas or air to the pump in both balances. The connection to the

manometer is also through a needle valve on balance No. 3511, and

a fourth needle valve permits the controlled discharge of excess pressure to the outside without disconnecting the balance from the

pump or gas supply. These two valves are missing on the Junior

balance (No. 4041).

A hand pump of the reciprocating plunger type is provided with

each balance. It is fitted with check valves to permit operation as the plunger moves in either direction and serves for either pressure or vacuum. The mercury manometer supplied has tubes of 3.5- to 4.0-mm bore

mounted in a channel 2 in. wide made of cast aluminum alloy, with

a removable sliding cover and metal plugs to prevent spilling mercury during transit. A millimeter scale with the zero at the center

is stamped on an adjustable strip of thin metal mounted between

the glass tubes and overlaps both a little. The air dryer uses calcium chloride and is fitted with brass plug

cocks for connection to the metal hose fittings.

In each balance, the balance beam is a metal rod with a bulb at one end and large and small adjustable counterweights with lock nuts at the other. On the tip of the balance beam is a scale which is observed through the window in the face. A cross arm at the center of gravity has screw clamps for attaching

metal suspension strips and a short vertical rod threaded for a weight

with which to adjust the sensitivity. Four thin metal suspension

strips, two at each end of the cross arm, are used in each balance,
Specific Gravities of Gases 27

but their arrangements are different. Viewed from the side, the pair

of suspensions in the Junior balance form a narrow V. In balance

No. 3511, they form a narrow-topped X, a true Cardan suspension,

though one of rather extreme form. In the Junior balance, the

Figure (5.

Ac-lie, gravity 'balance No. 3511 (left) ; Ac-Me Junior gravity balance No. 40U (right).

springs are of steel 0.001 in. thick and one-sixteenth in. wide. Phosphor bronze springs 0.001 in. thick and one-eighth in. wide are used

in balance No. 3511. The suspension in the Ac-Me Junior balance

does not entirely prevent lateral motion that may be caused by the
28 Miscellaneous Publications, National Bureau of Standards

manipulation of valves. The suspension of the Ac-Me No. 3511 bal- ance does prevent lateral motion. In each balance, the weight of the

beam can be lifted from the suspensions and locked rigidly in position for transportation by a cam on a shaft running through a packing in the face plate to a handle.

\~B) Modifications For Testing.—An aluminum clip to serve

as a holder for a rider was attached to the beam of each balance by

clamping it between the small counterweight and its locknut. The

counterweights were adjusted to balance inair, with the clip in place, at absolute pressures of about 1,500 mm. Eiders, made of Nichrome

wire, cause the beams to balance in air at about 100 mm when placed on the holders. The use of these riders permitted the quick adjustment of the balances for use with air above or below atmospheric pressure, with a minimum of disturbance of the mechanism.

The hand pump was used only for the introduction of air at pres- sures above atmospheric. Evacuation was accomplished by means

of a motor-driven rotary pump.

The supply of test gas was delivered through the diaphragm pres- sure regulator set to deliver 20 lb/in.2 so that the flow of gas could

be controlled by the needle valve on the balance case. Leakage of

air into the evacuated balance through valve packings and hose con- nections was thus prevented with certainty.

(C) Method of Operation.—The directions for use supplied with

the instruments were followed, with various extensions, during the

testing with 14 of the gas mixtures of known specific gravity with both

balances.

During purging, the balance was evacuated to an absolute pressure

of about 82 mm, then filled with dry air from outside the building.

This was done three times. The same procedure was followed in the

case of gas. Purging three times was found to reduce the previous

content of the gas to a negligible fraction of the sample.

A test for leaks was always made before each series of determinations of specific gravity. No leakage into or out of balance No. 3511 was detected during more than 2 years of use, but some trouble was

encountered from leakage where the rods pass through the plastic

window of the Junior balance when the pressure was above atmospheric, but not when it was below. Tests for leakage were thereafter

made with the balance under both pressure and vacuum. The level of the balances was verified each time before balancing

the beam, but no adjustment of the level of balance No. 3511 was found

necessary after the initial adjustment made before starting the tests. In both balances it was found that the balancing pressure was af- fected a little by the amplitude of oscillation of the balance beam, and

if the amplitude was too great the decrements were irregular, particularly with the Junior balance. The decrements were small and

fairly uniform if the beam oscillated only about one scale division.

For these reasons, the final balancing pressure was always determined

with oscillations of about this magnitude. With practice, it was possible to control the oscillation of the beam by timing small changes

of pressure while approaching the balance point.

The distance between the cross hair on the window and the scale on the balance beam and the curvature of the scale introduced uncer-
Specific Gravities of Gases 29

tainties into the readings until a single light bulb was placed several

feet behind and to the right of the observer to throw a shadow of the

cross hair onto the scale. The use of the shadow instead of the cross hair as an index completely eliminated parallax.

Following an adjustment of pressure to balance the beam, the

manometer was tapped and read to the nearest quarter millimeter.

In making a single determination of specific gravity, the same

sequence of repeated observations with gas and air was employed as with the Edwards balance. Similar data were recorded, and computations and corrections for changes of temperature were made in

the same way.

(b) RESULTS OF OBSERVATIONS

In conducting a test of each instrument at a given temperature,

with a given test gas, two observers each made a series of five determinations by balancing the beam alternately six times in air and five times in gas, beginning and ending with air. The absolute pressures

for air, before and after each absolute pressure for gas were averaged

and used with that for the intermediate gas for the computation of

the five values of the specific gravity.

The 10 determinations of specific gravity obtained by the 2 observers were then averaged for the test. The temperature reported

with each test is the average of all the observations of instrument temperature recorded during the test, and was used to correct the absolute

pressures in the manner described in section III, 2(c). The corrected

specific gravities were computed from the corrected absolute pressures, and averaged.- For test mixture 1 in the Edwards balance, the

average temperature was 77.7° F.

Specific gravity as observed 0. 6468

Specific gravity corrected for expansion of mercury . 6485 Correction for expansion of mercury 4-0. 0017 As may be seen, the correction, even with pressure differences under

350 mm, is not negligible. Had greater differences of pressure been

involved, the correction would have been greater.

In the tests with pressure balances, the air for reference was dried

as it entered" the balance. The concentration of carbon dioxide in the

air from outside the building was probably about 0.04 percent.2 This

would cause the specific gravity indicated by the balance to be low

by 0.00014. See section III, 2, (b).

Summarizing the observations and corrections for test mixture 1

Correction for expansion of mercury in manometer above

0° C +0.0017

Correction for 0.04 percent of carbon dioxide in air 4-. 0001 Net correction +0. 0018 Observed specific gravity, mean . 6468 Corrected specific gravity 0. 6486

Specific gravity of test mixture 1 . 6474 Error of instrument 4-0. 0012 Error of instrument, percentage of standard specific

gravity +. 19

2 The correct figure is 0.03 percent of C02 in most locations. The difference is purely of academic interest, since it would alter the correction by only 0.0001 in the most extreme

case, that of butane.
30 Miscellaneous Publications, National Bureau of Standards

Each instrument was operated with different types of gases of dif- ferent specific gravities, at different temperatures, and with the beam

balanced in air both below (mixtures 1 to 9) and above (mixtures 10

to 15) atmospheric pressure. The data have been treated in the manner described above in each case, and summaries of the numerical re- sults are presented in tables 3, 4, and 5.

010 005

5

jr.005

010

o£005

005

MIXT. NO. SYMBOL COMPOSITION

1 « MFD. GAS

2 a NAT'L " 4,5,6,7 o He-N2 8 a H2 -C02 9 • NITROGEN

10,11,12 a N 2 -C02 13 C02 14 & PROPANE

15 O BUTANE

AS OBS ERVE D

A.

a > -a

1 T3

< e H

a

a »

< -a

1 AFTER COR 3ECT

e ON

a

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 SP GR OF TEST GAS Figure 7.

Error of the Edwards gas density balance determined with each

test gas, as observed and after the application of 'corrections for the temperature of the mercury in the manometer and for carbon dioxide in the reference

air. The errors of the instruments, uncorrected and after corrections

for the temperature of the mercury in the manometer and for carbon

dioxide in the reference air were applied, have been plotted for each

test gas in figures 7, 8, and 9. For test mixtures 14 and 15 (propane and butane, respectively) the

instruments were tested with the beam balanced in gas both above

and below atmospheric pressure, and the errors for these gases given
Specific Gravities of Gases 31

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32 Miscellaneous Publications, National Bureau of Standards

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Specific Gravities of Gases 33

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34 Miscellaneous Publications, National Bureau of Standards

in the tables and plotted in the figures are "as observed" at the following average absolute pressures

:

Balance

Pressure Propane Butane

Edwards

mm.

937.

983. 8

958. 7

mm.

708. 8

725. 6

722. 6 Ac-Me Junior No. 4041 _ Ac-Me No. 3511 _

+ .010 O05

°.005

q:g

UJ .005 -.010

MIXT NO SYMBOL COMPOSITION

1 © MFD. GAS

2 A. NAT'L » 4,5,6,7 3 He-N2 8 B H 2 - C0 2 9 • NITROGEN

(0,11,12 a N 2 -C02

13 C02 14 A PROPANE

15 BUTANE

A —

c _a

1 9 > ir -a—

AS OBSE.RVED

-a

a * i * c AF"l"ER c ORREC;tion a

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 SP GR OF TEST GAS Figure 8.

Error of the Ac-Me Junior specific gravity balance No. JfOJ^l deter- mined with each test gas, as observed and after the application of corrections

for the temperature of the mercury in the manometer and for carbon dioxide

in the reference air. The errors, after correction, given in the tables are for the same pressures, but the errors, after correction, plotted in the figures for these

gases were determined after interpolating between (or extrapolating

from) the values for specific gravity obtained at the above absolute

pressures and those obtained at absolute pressures below atmospheric

in order to arrive at a value of specific gravity at an absolute pressure

of 760 mm, the pressure, at which the standard specific gravities of

the test gases were determined.

In the case of propane, the error of each instrument was reduced

in the manner just described to a value comparable with those ob-
Specific Gravities of Gases 35

+ .010 t-.005 z

LJ

CC£.005 o

-.005

MIXT NO SYMBOL COMPOSITION

1 9 MFD. GAS

2 A NAT'L " 4,5,6,7 » He-N2 8 B H 2 — C02 9 • NITROGEN

10,11,12 O N 2 -C02

13 C02

14 A PROPANE

15 Q BUTANE

a

c . e

a 1 , ^ «

. AS 3SERV ED

IP* r -O-J LJ&.

AFTER COR RECT ON

.2 .4 .6 .8 1.0 12 1.4 1.6 1.8 2.0 2.2

SP. GR OF TEST GAS Figure 9.

Error of the Ac-Me specific gravity balance No. 3511 determined with

each test gas, as observed and after the application of corrections for the temperature of the mercury in the manometer and for carbon dioxide in the reference air. tained with the gases whose supercompressibilities (above that of air) were of negligible effect. The method was not so effective with butane

except in the larger Ac-Me balance (No. 3511). The failure of the

method in the case of the Ac-Me Junior (No. 4041) is believed to be

attributable to the contamination of the reference air with butane

that had been absorbed by the rubber hose and gasket, an effect that

will be discussed later. Why the specific gravity remained low after

the correction of the observations with the Edwards balance has not

been satisfactorily explained. If the range of the manometer is sufficient to accommodate the air pressure required, it would be desirable in the routine measurement of the more compressible gases to adjust the counterweight on the beam so that the gas tested will balance

the beam at just about normal pressure.

(c) SOURCES OF ERROR

(1) Temperature Coefficients.—Except for differences between the

thermal expansions at constant pressure of the gases themselves and

' that of air and the effect of temperature on the manometer, there is no

apparent reason why the measurements made with specific gravity

balances of this group should be affected by temperature. The first

ji of the two effects mentioned is known to be very small in the case of

the usual gases, and corrections have already been made for the second.
36 Miscellaneous Publications, National Bureau of Standards

It was, therefore, to be expected that no appreciable effect of temperature on the corrected specific gravity would be found. To make sure of this, however, tests, consisting of 10 determinations of specific

gravity of the same test gas (mixture 1), were made after adjusting

and maintaining the temperature of the room to give instrument temperatures 10 or 12 deg on each side of the temperature at the time

of the original test. The results, as observed and after correction for the temperature of

the mercury in the manometer and for carbon dioxide in the air, have

been plotted against temperature in figures 10, 11, and 12. Straight

lines, determined by the method of least squares, have been passed

through the three points of each plot, and the slopes of the lines,

constituting the temperature coefficients, have been indicated thereon.

The radius of the circle around each observed point is equal to the

60 70 INSTRUMENT 80 90 TEMPERATURE Figure 10.

Temperature coefficient of the Edwards gas density balance de- termined with text mixture 1, as observed and after the application of corrections

for the temperature of the mercury in the manometer and for carbon dioxide in the reference air. probable error of the mean of the 10 determinations which that point

represents.

It may be noted that after corrections have been made for the temperature of the manometer, no residual temperature effects are greater

than can be accounted for by random errors in the observations equal

to the probable error of the series. (2) Variations of Temperature.—If the temperature of the balance

changes irregularly, so that the mean of the two air temperatures is not the same (within a few tenths of a deg F) as the intermediate

gas temperature, correction of the specific gravity by an appropriate

ratio of the absolute temperatures to bring the mean air temperature

to the gas temperature is required. The variation to be permitted

without correction is determined by the allowable error in the specific

gravity. A difference of 0.1 deg F between the mean of the air
Specific Gravities of Gases 37

5.65

.64

io AS OBSERVED

I- ALL CORRECTIONS

000£64__

.000030

^ TEST MIXT JRE

""""" I o

PER F

INSTRUMENT TEMPERATURE Figure 11.

Temperature coefficient of the Ac-Me Junior specific gravity balance No. 4041 determined ivitli test mixture 1, as observed and after the application of corrections for the temperature of the mercury in the manometer

and for carbon dioxide in the reference air.

>

.64

io AS OBSERVED

H« ALL CORRECTIONS

TEST MIXTl

n 0.00 0013 PER °F

RE —

-—

1 00

t 0025 PER ° F

50 60 70 80 90 100 110 INSTRUMENT TEMPERATURE °F Figure 12.

Temperature coefficient of the Ac-Me specific gravity balance No.

3511 determined tvith test mixture 1, as observed and after the application of corrections for the temperature of the mercury in the manometer and for carbon

dioxide in the reference air.
38 Miscellaneous Publications, National Bureau of Standards

temperatures and the gas temperature changes by 0.0001 the specific

gravity of a gas of 0.6475 specific gravity. Handling of the balance

case causes such changes, and even changes in radiation from the

operator or nearby electric lights, etc. may nullify careful control of

the room temperature.

(3) Material Tested.—The possible effects of deviations of the gas

tested from the ideal gas laws has been well illustrated by the errors

in the "observed" specific gravities of propane and butane and their

correction. The errors were of considerable magnitude, although the

absolute pressures differed from atmospheric by not more than 224 mm

for propane and —51.2 mm for butane.

An uncertainty of the composition of the material tested, as a result

of incomplete purging, may be a source of error. If the beam is balanced after purging three times by evacuation to 40 mm or less and

filling to 760 mm or more (absolute) , as was done with the Edwards

balance, the error in the case of helium would amount to 0.00013 or

less. If the beam is balanced after purging three times by evacuation

to 110 mm or less and filling to 1,410 mm or more (absolute), as recommended by the manufacturer of the Ac-Me balances, the error for helium, assuming complete mixing, would amount to 0.0005 and

for butane to 0.0015, which may or may not be considered negligible.

In the case of gases with specific gravities nearer air, the error would

be correspondingly less. If the pressure in the gas line connected to the needle valve is not

kept above atmospheric, air may enter through the valve packing or any other possible leak in the line between the source of supply and the

valve seat. It will then enter the balance case when the valve is opened for purging and filling.

A leak anywhere in the balance case would, of course, be a source

of error through contamination of the gas sample with air while the

pressure in the balance case is less than atmospheric. It was found

necessary to replace the rubber gasket sealing the front cover of the

Ac-Me Junior balance, and on four occasions leaks were found where

the plastic window is penetrated to permit attachment of the mechanism to the front cover. Detection was by soap solution applied to the face of the balance, with the container above atmospheric pressure. Three of the leaks were evidenced by bubbles at the edges of the openings in the metal face. One appeared where the body of the packing

gland for the locking device is screwed through the face. The recom- mendation of the manufacturer to make a test for leaks before using

the instrument should not be disregarded.

A nearly, but incompletely, sealed dead space in communication

with the inside of the balance case may be a source of error through

contamination of the sample by slow interchange during and following changes of pressure. If the space in question is a part of or is the entire bulb on the beam, an error may also arise through a change

in the weight of the bulb. The Edwards balance is fitted with a

glass bulb which, in the absence of pin holes, it is probably easier to make permanently tight than a bulb of another material. On

the other hand, the glass bulb is attached to the beam by inserting

the end of the beam into a glass tube sealed into one end of the bulb

and fastening it in place with cement. Needless to say, the space
Specific Gravities of Gases 39

between the beam and the tube should be either sealed completely

and permanently, or be made to communicate freely and completely

with the interior of the balance case so that they can be purged to- gether.

The composition of the sample, especially that of the reference air,

may be uncertain because rubber absorbs gases while in contact with

them, and then gives them up again to contaminate a different gas

which has displaced the first. Especially is this true of water vapor,

carbon dioxide, and the hydrocarbons. Of the gases used in this

study, butane is absorbed more rapidly and in larger quantities than

the others. It is also given off again rapidly when displaced by air. The Ac-Me balances as furnished by the manufacturer are connected

to the manometer with 30 in. of rubber hose and to the supply of gas

and air by another hose 67 in. long. To determine whether butane

absorbed by the rubber hose and the rubber gasket which seals the

face to the container was contaminating the air when the balance was filled with air, the rubber hose of the Ac-Me Junior was replaced

by copper tubing. Five determinations of the specific gravity of

butane were then made at an average absolute gas pressure of 715.4

mm and five determinations at 204.9 mm. When plotted and extra- polated to a pressure of 760 mm, the error was only —0.0013 as compared to —0.0065 when the rubber tubing was used. It is possible

that it might have been still smaller if the quantity of gasket rubber

exposed to the gas had also been reduced to a minimum.

A similar replacement of the rubber hose of the Ac-Me No. 3511

balance with copper did not produce a corresponding reduction in the

error of the tests. The results of three tests when copper tubing was

used were all within the spread of the values obtained in the regular

testing, and their average was slightly lower. If there had been any

contamination of the reference air by butane from the hose, the values

obtained when the copper tubing was used should have been higher.

In the tests with propane and butane, the purging of both Ac-Me

balances had been increased. In purging with gas, the balance was

evacuated and filled four times to atmospheric pressure, instead of

filling it three times to considerably more than atmospheric pressure. When purging with air, the balance was evacuated and filled to a pres- sure of about 700 mm above atmospheric pressure each time. This

resulted in passing about 450 cu in. of air through the hose in purging the Junior and 1,500 cu in. in purging the No. 3511 balance. It seems probable that the effect of replacing the hose with metal on the

readings of the Junior balance and the absence of any such effect in

the No. 3511 balance resulted from the threefold difference in purging. If so, the fact that the tests with the Junior balance remained

low after correcting for the effect of compressibility, while the larger

balance gave excellent agreement with the standard, is also accounted

for by absorption and release of butane from the rubber.

(4) Measurement of Absolute Pressure.—Uncertainties in the value

of the absolute pressure at which the beam has been balanced may

arise from uncertainty as to either the barometric pressure or the

pressure difference.

Uncertainties in the barometric pressure arising from lack of nec- essary corrections, or from scale errors, or errors in reading may cause
40 Miscellaneous Publications, National Bureau of Standards

errors in the specific gravity. Corrections for temperature of a mercurial barometer often amount to 2 mm or more. Assuming every- thing else correct, failure to make such a correction (of 2 mm) in the

case of initial air, gas, and final air pressure readings of one of the

determinations made with mixture 1 would result in the numerical

value being higher by 0.0011 than it should have been. Such an error of course becomes larger as the absolute pressure involved becomes

smaller.

Uncertainties in the pressure difference may arise in a number of

ways. Probably the most frequent and perhaps the largest error is the result of failure to correct the observed pressure difference to that

of mercury at 0° C. In the determination of the specific gravity of

mixture 1, referred to in the preceding paragraph, the correction

amounted to 1.6 mm for the air and 0.6 mm for the gas, and changed

the specific gravity by 0.0014. This error, of course, becomes larger

with higher temperatures and larger pressure differences. If neither

the barometer nor the pressure difference are corrected to their readings at 0° C, the error resulting may be smaller. In the present

illustration the specific gravity obtained without correction of barometer or pressure difference would be too low by 0.0002. The correc- tion to the barometer will not change very markedly if the temperature is nearly the same at all times, but the correction to the pressure

difference, depending on the magnitude of that difference, varies

greatly with different gases, and, while the two corrections may cancel

in some circumstances, the only certain way to avoid the errors in- volved is to apply the corrections to both at all times.

In the case of the pressure difference, still other errors may be in- volved. The scale of the manometer supplied with the Edwards bal- ance is made of wood, and wood expands and contracts with changes

in relative humidity. The reference mark on the slide may not be

accurately parallel to the horizontal marks on the scale. In the case of this instrument, there was a difference of about 0.2 mm from one

side to the other. The slide is set out in front of both scale and

manometer, with nothing to guide the observer in avoiding errors of

parallax.

The scales of the Ac-Me instruments are etched on metal tapes

which lie between the arms of the manometer but not even with the

centers of the meniscus. The readings therefore involve a mental

extrapolation of the end of one of the lines on the scale to the top of

the meniscus in addition to front-and-back parallax. Although the

background is dull white, it is difficult to illuminate the meniscus so that it stands out sharply, which makes it still harder to obtain accurate

readings.

It is, of course, desirable to conserve weight and expense in construction, and the small bore of the manometer tubes is probably the result of efforts in this direction. In tubes less than 8-mm bore, differences

in capillarity between one meniscus and the other, especially where

one is open to the outer air and the other is not, may lead to errors of

several tenths of a millimeter even though the tubes are tapped before

reading. Even an apparently clean mercury surface in an apparently

clean glass tube wets the surface of the glass to an extent that varies

markedly from one position to another in the tube. The errors of
Specific Gravities of Gases 41

parallax will probably be nearly random and may have opposite signs on the two sides of the manometer, thus doubling the effect. (5) Balancing the Beam.—Variations in the pressure at which

the beam is judged to be balanced involves errors of two kinds: (1)

, uncertainty as to when the positions of the beam are identical in suc- cessive tests with air and gas, and (2) mechanical effects which result in the beam assuming the same position under different forces. The

magnitudes of both types of error depend mainly on peculiarities of

construction of the individual balance; it is therefore necessary to discuss the three balances separately.

(A) Edwards Balance.—The beam of the Edwards balance carries a small "target" ruled with two closely spaced horizontal lines and is viewed, with the aid of a lens, through a window ruled with a

single horizontal line, the "reference mark." If the beam is balanced

with the reference mark opposite the upper mark on the target and

then balanced with the reference mark opposite the lower mark on the

target, the difference between the respective pressures amounts to about

8 mm. If the operator succeeds in balancing the beam in the same

position to one-tenth the distance between the lines on the beam target,

he still has an uncertainty in the corresponding pressure of ±0.8 mm

from this source alone (and this difference may be in opposite directions during the measurements of gas and air)

.

Variations in the pressure difference required to produce apparently

identical settings may result from slight and often unnoticed mechanical disturbances. When the beam had been brought to balance by a steady drift without oscillation, a tap with the finger on top of the

front needle valve caused a slight oscillation. After oscillation

ceased, the beam was found balanced at a different position than before, with no change of pressure.3 Although the presence of dust or moisture on the bearing surfaces or on the parts of the beam assembly, or imperfections in the agate

bearings or on the points are recognized causes of such irregular behavior, thorough cleaning and examination with a glass disclosed no

L cause of this kind. The behavior continued with no other indication

than a sudden change in the pressure at which the beam balanced.

The change sometimes persisted for several determinations and in- volved both gas and air. Nothing was found loose on the beam

assembly. The greatest care was taken to avoid the slightest jar and

to prevent dust from entering the balance. Nevertheless, such

; changes, amounting to several millimeters of pressure, sometimes

occurred two or three times in the course of the 10 successive deterI minations that constituted a "test" with one gas. When such changes

I were known to have occurred, the pressure measurement involved was discarded and the testing continued on the new basis until another

such shift in the balance point of the beam occurred. Shifts un- doubtedly occur which involve changes too small to be definitely

ascribed to this cause, and which therefore enter as a variability in the results of the tests. In the illustration given of the treatment of

the data, the 10 determinations of specific gravity involved balancing

the beam 12 times in air. There was no known variation in the air,

3 To restore as closely as possible the original position of the balanced beam required

a change of pressure as great as 4 mm.

I!
42 Miscellaneous Publications, National Bureau of Standards

but the extreme values of the absolute pressures involved were 9 mm

apart. This variability is reflected in the high value of ±0.0023 for

the probable error of a single determination.

If the beam is balanced repeatedly in air, the balance point being

approached alternately from opposite directions without displacing

it far enough to touch the stop in either direction, no significant difference in the balance point results. In normal use, however, purging

the balance involves displacing the beam until it comes in contact with

the stop. If care is taken that this contact is very gentle, the balancing

pressures are usually reproducible. If the pressure is changed too rapidly or if the beam rebounds appreciably from contact with the

stop, the balancing pressures are much more valiable. Undoubtedly

this result and the shifts in the balancing pressures discussed above

are caused by small shifts in the position of the points on the bearings

and as these are not plane surfaces, the slope of the bearing surface

changes with position. Changing the slope of the surface on which

the bearing points rest might be expected to change the pressure at which the beam balances.

(B) Ac-Me Junior Balance No. 4041.—The elimination of er- rors of parallax in reading the position of the cross hair on the beam

scale is essential. . This may be accomplished by using a light in a

fixed position and reading the position of the shadow of the cross hair on the scale as previously described.

The position of the shadow can be estimated to about one-tenth of

a division on the scale ; the divisions are about 1 mm apart. To avoid

errors resulting from failure to secure exact balance, the sensibility

of the balance was determined. The pressure was set to balance the

beam with the cross hair near one end of the scale. Starting with a swing five or more divisions up and down, readings on the scale were

taken each time the direction of swing reversed, while the amplitude

decreased to less than one division up and down. Choosing a group

of readings where the decrements were uniform, the mean reading of

the cross hair was determined as in the case of the pointer of an

analytical balance. This process was repeated at a series of pressures. The differences between successive absolute pressures were then

divided by the corresponding differences between the readings on the

scale to determine the number of millimeters corresponding to one

division on the scale attached to the beam. The intention was to bring

the beam to an approximate balance, determine the reading on the

scale and on the manometer, and then correct the latter, using the

sensibility, to what it would have been had the reading on the beam

scale been exactly zero. It was found, however, that the values for

sensibility were quite variable. For air at absolute pressures from 322

to 382 mm, the sensibility varied from 10.5 mm per division to 7.25 mm

per division, and averaged 8.9 mm per division. In the case of mixture 1 at absolute pressures from 505 to 626 mm, the sensibility varied

from 11.4 mm per division to 13.1 mm per division, but the 13.1 oc- curred in the middle of the range, the average being 12.3. During this

work it was also observed that when the reading on the beam scale was near zero, the mean reading was different when the amplitude was two or three divisions than when it was one division, although the

pressure remained the same.
Specific Gravities of Gases 43

It was noticed early in the testing that as the pressure was reduced

to approach the balance point with the beam swinging with small

amplitude, the beam could be balanced at a particular pressure. Then,

if the amplitude of the swing were increased by vibration incident to closing the valve so that the reading of the cross hair reached several

divisions below the zero, or if the vibration occurred while the reading was several divisions below zero, the beam would oscillate on either

side of a reading which was about two-tenths of a division below zero

instead of zero, thus causing the beam to balance at zero at a higher

pressure than before the vibration occurred. The suspension was

suspected and new springs installed, with the same result. The

mechanism was checked and everything found tight. The action of

each spring was observed with a lens while the beam was moved re- peatedly from one extreme position to the other, but all appeared

perfectly flat, and bending was smooth and without any perceptible

twist or kink. Care was taken during testing to see that the beam

was balanced on the same side of this "hump." Failure to recognize and guard against such behavior may result in errors or variations of several millimeters in the balancing pressures.

It would appear that a determination of sensibility would be a good test of proper functioning of the suspension. It would also appear that 9 to 12 mm per division is a rather large value, for considerable variations in the absolute pressure might be expected as .

a

result of failure to secure exact balance at zero on the beam scale by

the means provided by the manufacturer, as was indeed the case. Such variations are reflected in the variations observed in the series of ten determinations which constitute a test. During the testing with mixture 6 (in December 1940), a tendency was noticed for the absolute pressure at the balance point to increase

slightly during the series of ten determinations, which required a full

da}?-, although there was no corresponding drift of temperature to account for it. This tendency was noted from time to time, and with

the heavier gases it became more pronounced. Mixtures 1 to 9, in- clusive, were all balanced below atmospheric pressure, so the effect,

corresponding to a gradual increase in the weight of the bulb, could

not be accounted for on the basis of gas entering the bulb through a leak or by deformation of the bulb in such a way as to lengthen the

lever arm of the beam on that end. For butane, the effect had be- come so pronounced that increases in the absolute pressure at successive air balances amounting to several millimeters occurred several

times during the series of determinations. Condensation of butane on the bulb was unlikely, because the pressure was never above 880

mm absolute, and its reeyaporation into the air would have caused

the balance in the contaminated air to occur at a lower instead of at a higher pressure. The effect of such behavior on the resulting

specific gravity is probably not very great. An adequate explanation

for this behavior has not been found.

(C) Ac-Me Balance No. 3511.—The elimination of parallax in

reading the scale on the beam of this instrument was as necessary

as for the smaller Ac-Me balance and was accomplished in the same

way, by suspending a light in front of the balance and reading the

position on the scale of the shadow of the cross hair.
44 Miscellaneous Publications, National Bureau of Standards

Scale divisions are of about the same length, 1 mm, as in the Ac-Me

Junior balance and can likewise be read to about one-tenth division.

The sensibility of the balance was again tested at different parts of

the scale with different amplitudes of vibration and with both air and

mixture 1 in the balance. For air at absolute pressures from 381 to 406 mm, the values of the sensibility were 1.26, 1.81, 2.35, 1.82, and

1.24 mm per division. Although these values are quite symmetrical,

the value 2.35 was found at 2.2 mm below the zero of the scale. With

test mixture 1 at absolute pressures from 586 to 627 mm, the sensibilities were 2.02, 2.84, 3.39, and 3.96 mm per division, increasing con- tinuously from six divisions above to eight divisions below the zero of the scale. The average values, 1.7 and 3.0, in the two cases are, however, of a size likely to insure good reproducibility.

(6) Leveling.—If the level of the balance changes during a determination of specific gravity, the result may be in error. The

Edwards balance does not carry a level and, as has already been stated

is subject to the effects of comparatively slight shocks, which make

necessary the checking of the air reading before and after balancing

with gas. If the check readings are the same, it is probably safe to assume that the observed specific gravity has not been affected by a change of level. The Ac-Me Junior balance was removed from the tripod and leveled

up on a bench. The beam was then balanced in air at 1448.3 mm

absolute. The front of the balance was then lowered by turning the

two front leveling screws one complete turn, which tilted the balance

through an angle of 10.1 minutes of arc. The beam then balanced at 1445.05 mm absolute. The change in balancing pressure was thus

3.25 mm for 10.1 minutes of arc. Successive determinations of the

balancing pressure during the tests with test gases sometimes varied

by 3.25 mm or more with the balance level. The intentional tilt was

sufficient to move the bubble of the spirit level from the center until

its edge nearly reached the reference circle; hence, errors from in- accurate leveling should not be significant in comparison with other

uncertainties unless the tilt is easily noticeable on the spirit level. During the application of similar tests to the larger Ac-Me balance,

tilting the balance from the level position through 10.1 minutes of arc (by one turn of the leveling screw) changed the manometer reading

by 4.25 mm, from 1491.75 mm absolute to 1496.0 mm absolute, when

the beam was balanced in air. Variations of successive determinations of the balancing pressure during the tests with test gases did not

average much more than one-tenth of 4.25 mm. One turn of the level- ing screws caused the bubble in the spirit level to move from the center

until its rim nearly reached the reference circle, but one-tenth of a turn produced only a barely perceptible change in the position of the

bubble. A careful verification of the level is therefore desirable before

each determination of the balancing pressure if the highest accuracy

of which the balance is capable is to be obtained.

(d) SUGGESTIONS FOR IMPROVEMENT OF INSTRUMENTS

As one result of the investigation, certain suggestions for the improvement of each instrument were made to its manufacturer. In some cases these can be incorporated by the user of an instrument.
Specific Gravities of Gases 45

These suggestions have been, given careful consideration by the manufacturers, and some of them have since been adopted, as have other

improvements originated by the manufacturers. The suggestions

made for each instrument are stated below, but it should be recognized

that after an instrument has been in use for a period of years, it is difficult to suggest improvements that may not already have been tried

and discarded. In any case, improvements in performance and con- venience must be balanced against increased complexity and cost. (1) Edwards Balance.—(1) In view of the apparent susceptibility of the instrument to changes of balance point with slight

mechanical disturbance, it might be desirable to eliminate the most

frequent source of such disturbances, the changing of a rubber-hose

connection at the rear needle valve when changing from air to gas

and the reverse. Separate needle valves for gas and air might be

used. Metal unions, cone and cylinder rather than ball and socket,

would probably give less trouble than rubber-tube connections. Connections could then be made to both gas and air and left undisturbed

for as long as desired.

(2) Some provision for anchoring the balance firmly to a solid

foundation, free enough from vibration to avoid migration of the

points on the supporting surfaces, and massive enough to resist move- ment by accidental contact, would probably result in a marked improvement in reproducibility.

(3) It might also be desirable to include in the directions some warningn of the effect of changing the pressure too rapidly, while purging, on the reproducibility.

(4) It might be desirable to provide some sort of reflecting sur- face behind the manometer tubes, and to bring the glass slide closer to the tubes and scale so that the operator could more easily avoid

errors of parallax in reading the position of the meniscus, and at the same time make it easier to see the meniscus.

(5) If the nut for adjusting sensitivity is intended to be moved to

different positions on its screw and left there, some means of keeping it in the desired position should be provided. The effect on the

period of swing of moving the nut the full length of the screw is very small. Perhaps a heavier nut could be used, so that any reasonable changes of sensitivity might be made without the necessity of

changing the position of the points. An 8-second period seems rather

short, and the fact that changing the point of balance from one line to the other on the target involves a pressure change of 8 mm, would

seem to indicate that increasing the sensitivity might decrease the

variability, and probable error of single determinations.

(6) As the effect on the specific gravity of correcting the pressure

difference to 0° C to correspond with most barometer readings is not negligible, it would be advisable to call attention to this in the

directions for use.

# It might also be helpful to state in the directions

what period of swing is considered suitable for ordinary work, and

what period is suitable for high sensitivity capable of yielding re- sults concordant to ±0.0005.

(7) It might be a convenience to operators who use the balance

to test gases of widely different specific gravities to provide some

means, such as a set of calibrated riders, which might be attached to
46 Miscellaneous Publications, National Bureau of Standards

the counterweight or other suitable holder in such a way as to be

kept from moving while the balance is in use, but which would permit

them to be interchanged conveniently to eliminate the necessity of

adjusting the counterweight between tests. The range of the in- strument might be changed in such a way, in three or four. steps, so that it would accommodate all gases within the range of the manometer. Correspondence with the manufacturer indicates that most

of the suggestions made can and will be incorporated in future

models.

(2) Ac-Me Junior Balance No. 4-04-1-—(1) Some means of casting

a shadow of the cross-hair on the beam scale might be incorporated to advantage. An adjustable mirror mounted on the base might be a

possible solution for use in the field, provided it did not reflect direct

sunlight into the case and cause trouble from temperature changes.

(2) A wider tongue on the open end of the case would not tend to cut the rubber gasket as readily and might decrease the chance of

leaks at this point.

(3) A window separated from the attachments of the mechanism

to the face and reducing to a minimum the number of openings

through the face would reduce the opportunities for leaks. (4) A sensibility nearer 2- or 3-mm pressure per scale division

would improve the reproducibility of the results. This could probably only be accomplished by increasing the sensitivity and period of

swing (if the size of the bulb and case are not increased), and this

may cause other difficulties. (5) Some means of leveling other than by adjusting the clamps on

the legs of the tripod would be an added convenience.

(6) The end of the manometer that is open to the outer air might

be equipped with a dust cap, which would help keep the mercury

clean and still permit flow of air. (T) The manometer tubes might be of larger and certainly should

be of more uniform bore to decrease errors of capillarity and permit

the measurement of 760 mm above and below atmospheric pressure

without adjustment of the quantity of mercury. The whole mercury

column is 45 mm shorter when most of it is in the closed side than

when in the open side. With the present tubes, the slots in the scale are not long enough to accommodate the difference in bore.

(8) It might be well, in the instructions, to direct the user to tap

the manometer on both sides before reading either meniscus.

(9) The hand pump does not work well on vacuum, and pumps

effectively only on the down stroke on pressure. This may be the

fault of this individual pump.

(10) Same as suggestion (7) on Edwards balance.

(11) A filter of some sort over the calcium chloride in the air

dryer would be desirable to prevent dust from being blown into the

balance case. A wad of absorbent cotton was used during these tests. Evidences of calcium chloride having been in the case were found

before starting the tests. (12) It would be desirable, if the balance is to be used with the

hydrocarbon gases, to eliminate the rubber hose and minimize the

exposure to gas of the rubber gasket.

(3) Ac-Me Balance No. 3511.—Suggestions (1) and (6 to 11) for
Specific Gravities of Gases 47

the Ac-Me Junior No. -ICMrl balance apply equally to the larger balance

and were repeated for it. It was also stated that "some means for

determining the temperature (and temperature changes) of the gas

in the container more accurately than can be done with the present

thermometer might be desirable, although perhaps not practicable''

in the case of this balance.

2. ANUBIS PORTABLE GAS BALANCE

(a) DESCRIPTION

The Anubis portable gas balance No. 115 (fig. 13) is described in Care

and Operation Bulletin Xo. 106 of the American Recording Chart Co.

The balance consists essentially of a gas chamber, within which a spherical bulb of spun brass is mounted on an invar beam provided with

a cross head, in the under side of which are set two specially finished

and very hard chrome-steel balls. These balls (used instead of the

knife edges of an ordinary balance) rest on the highly polished and

Figure 13.

Anubis portable gas balance No. 115. 719265—47 4
48 Miscellaneous Publications, National Bureau of Standards

optically plane surfaces of two sapphires. The bulb is counterbalanced by a weight near the opposite end of the beam, and a small cali- brating weight is directly below the center of gravity of the beam

assembly. The front of the gas chamber is closed by a disk of plate

glass, through which the oscillations of the beam are observed. The

back head of the gas chamber is hemispherical, incloses the bulb, and

is fitted with a purge valve consisting of a cap sealed with a sheet

rubber gasket. The chamber is supported by a single ball-shaped foot

under the back and by a cross bar at the front with two leveling screws. Two large transit levels, one longitudinal and the other transverse, are mounted rigidly on the chamber, and a thermometer in a metal

sheath is mounted on top of the chamber with its bulb projecting

through to the inside. A lever is fastened to the end of a shaft that

projects through the transverse mounting of the chamber at the front,

extends through a special rubber "torsion-tube" packing, and operates

a toggle mechanism that raises two lifter forks. These forks engage

the cross head of the beam on either side and lift the beam assembly

and lock it against a locking pin which projects downward from the

top of the chamber against the center of the cross head. A fixed scale,

graduated in tenths from 0.5 to 1.5, is mounted inside the front window

at one side, and a movable index scale is mounted on the end of a movable arm at the other side. The movable arm is bent at right

angles and passes through another special rubber "torsion-tube" packing in the side of the chamber near the back to form a shaft on which

is mounted, outside the chamber, a toothed sector in mesh with a worm. The worm is rotated by a micrometer wheel at the front of the gas

chamber and serves to raise or lower the movable index scale until,

during a measurement, the beam pointer oscillates equally above and

below the center of the scale. The micrometer wheel is divided into

100 equal parts for interpolation between the tenths on the fixed

scale. It is possible to estimate tenths of a division on the wheel, so the specific gravity may be read to the third and estimated to the

fourth decimal place. The gas chamber is provided with a fitting to which a manometer may be attached for use at pressures other than

atmospheric, but this is not usually necessary and no manometer was

furnished with the instrument tested. When used at atmospheric

pressure, problems of leakage are eliminated. The sample is introduced through a plug cock mounted on the gas chamber near the front

and provided with a fitting for rubber hose. The beam assembly is calibrated by the manufacturer by adjusting

the center of gravity with respect to the point of support to produce

a fixed sensibility. This sensibility is such that the segment of arc subtended by the movable index scale when the micrometer wheel is rotated a given number of unit^ on the specific-gravity scale corre- sponds to the same number of specific-gravity units between air and a gas of known specific gravity. It is thus calibrated to a deflection of

arc that is directly proportional to the density of the gas. The con- version of density to specific gravity is made by correcting the observed reading of the instrument to the temperature and pressure at calibration, which was 30 in. and 60° F, by application of the gas laws.

The correction factors may be read from a chart supplied with the

instrument.
Specific Gravities of Gases

(b) METHOD OF OPERATION

49

The directions and illustrations in Instruction Bulletin No. 106,

supplied with the balance, are good and are clearly presented. They

were followed, with a few minor modifications and extensions, during the testing with nine of the gases of known specific gravity. The

other gases used in the study were outside the range of the instrument.

Each test of the instrument with a test gas was preceded by an

"air check," which involved purging the instrument with room air

dried over calcium chloride for 5 minutes, making a reading, and

repeating the purge and reading until no further drift in the readings was apparent. When the variations in the readings had become

random, the instrument was then alternately purged and read as before, five times by each of two observers. The temperature and

corrected barometric pressure at the time the balance was closed for

each reading were recorded, and the level of the instrument checked

or adjusted. The reading that should have been obtained with air is the reciprocal of the "correction factor" for the same temperature and

pressure read from the chart supplied with the instrument. The

difference between this "correct" value for air and the reading actually

obtained is one value of the "air-check correction." The data for the

first-such air-check correction will show how all of them, were obtained.

Corrected barometer : 29. 22 Instrument temperature 78. 5 Factor / from chart 1.0635

Ten independent settings of the scale were made for air before

introducing a test gas and the 10 corresponding values of the air- check correction were averaged. As this instrument does not measure

the ratio of the density of the gas to that of the reference air but measures the difference between them, the average air-check correction was added (algebraically) to each of the readings obtained with

the test gas. The air check and the determination of the air-check correction were made just before each test with gas because the correction had

been found to drift by a significant amount over a period as short as 2 weeks. When the correction had reached —0.0087, the balance-adjusting rod was shifted, bringing the correction to +0.0038. This

effect will be discussed further in the section on sources of error. Each test of the instrument with a test gas involved, purging the

instrument for one-half hour or more if the rate of flow approximated that used with air, or for 5 or 10 minutes if higher rates,

sufficient to be felt by a moistened finger at the purge valve, were

used. A reading was then taken, and the balance was alternately

purged for 10 to 15 minutes and read until variations in the reading

became random, as in the case of the air check. The balance was

then left closed, and the temperature and pressure recorded for the

reading last taken were considered to be the temperature and pressure

during a series of five readings by each of two observers. The aver- age air-check correction, previously determined, was applied to each

l/f Instrument reading

Air-check correction.

0. 9403

. 9456 —0. 0053
50 Miscellaneous Publications, National Bureau of Standards

of the 10 readings on gas, and the resulting value was then multiplied

by the pressure and temperature correction factor taken from the

chart, to give 10 values for the specific gravity. These 10 values of

specific gravity obtained by the two observers were then averaged for

the test. Disregarding the changes of temperature and barometric pressure

that may occur during the series of 10 readings is justified for these

tests for the following reasons : The values of temperature and pres- sure used were those existing at the time the balance case was closed, at atmospheric pressure. The series of 10 readings required less than

one-half hour. Barometric changes during this time are usually

small, and could not produce any significant leak in a balance case tight enough to be used at pressures other than atmospheric. The

temperature of the room was automatically controlled, and observed

variations in the temperature of the balance rarely exceeded 0.5 deg F

in a period of 2 hours. Except for leakage, the only possible error from changes of pressure or temperature during the observations is that caused by a change in the relative volumes of the balance case and

the bulb. As both are made of brass, they should expand alike if subject to equal changes of temperature. If the case Were 1 deg F

warmer than the bulb, the apparent specific gravity would be diminished by 0.003 percent. As the bulb is very thin, a difference of even

1 deg between its temperature and that of the surrounding case could

not occur except with a very rapidly changing temperature.

In making a reading, the beam was lowered gently to the jewels and

released entirely when the beam pointer reached the lower edge of the

movable index. The micrometer wheel having been turned counter- clockwise somewhat below the anticipated reading, it was turned only

clockwise during the approach to the balance reading. Because the

balance point usually tends to shift toward a higher reading as the

amplitude of swing decreases, the reading was always taken at the

point at which the beam pointer having swung four divisions up then

swung four divisions down. The reading of the pointer on the

movable-index scale was noted at the top of the swing and again at the bottom of the swing, when, if not equal, an adjustment of the

micrometer wheel was made immediately. If not equal by the time

the swing had decreased to four up and four down, the beam was

raised from the jewels and restarted without readjusting the micrometer wheel unless the reading had been overshot.

When testing was started with mixtures having specific gravities

greater than 1.0, and with the movable index in approximately the

right position, it was found that the pointer could not be lowered to the bottom of the movable index with the beam release lever. A swing

of satisfactory amplitude was produced by lowering the pointer with

the release lever to a suitable point (determined by experiment in

the case of each gas) and then releasing the beam while in motion.

(c) REFERENCE AIR The air used for reference with the Anubis balance was dried as it entered the balance, but only in later determinations was carbon

dioxide removed. The concentration of carbon dioxide in the air of
Specific Gravities of Gases 51

the room was found to average about 0.10 percent, as the room was

not large, was not well ventilated, and contained two and sometimes

three observers.

To take account of the error introduced by the presence of carbon

dioxide in the air with which the air check was determined and to indicate how corrections for it may be applied if and when circumstances require it. the results as observed have been corrected for 0.1 percent of carbon dioxide in the reference air in those cases in which

it was not removed by Ascarite. The correction cannot be applied to the mean observed value of the specific gravity in the same way in

which it was done for the instruments that measure the ratio of the

density of the gas to that of the reference air, because this instrument measures the difference between them. The correction must be applied by including it in the air-check correction. The reading that

the balance should give with air free from water vapor and carbon

dioxide at the observed temperature and pressure (the reciprocal of

the factor taken from the chart) was corrected to what it would have

been had the chart been computed with air containing the quantity of

carbon dioxide found in the reference air, by means of the equation

& =R (1.5290 [C02 ] +1 -[C02 ]) ? where

S =the reading which the balance should give with pure

air at the observed temperature and pressure. 8=* (1//. where / is the factor from the chart.)

i?=the reading that the balance should give with air con- taining the observed concentration.

[COo] =0.0010 by volume: the observed concentration and

1.5290 =the specific gravity of carbon dioxide.

The data previously used to illustrate the determination of the air- check correction will be used to illustrate the evaluation of an air- check correction that takes account of 0.1 percent of carbon dioxide

in the reference air. The value of 1/f previously used, 0.9-L03. was

substituted for 8 in the above equation, which was then solved for R.

0.9403=/? ( 1.5290x0.0010 + 0.9990)

R 0.9398 Instrument reading . 9456

Air-check corrections (corrected for 0.1 percent of C02 ) —0. 0058 Previous air-eheck correction —. 0053

Difference in applied correction because of 0.1 percent

of C02 —0.0005

The correction for carbon dioxide was applied by subtracting 0.0005

from each ''air check*' made with room air. The value —0.0005 applies only to the temperature 78.5° F and barometric pressure 29.22,

for it depends on the value of / from the chart corresponding to these

conditions. At appreciably different temperatures and pressures, it may have a different value.

The specific gravity of test gas 1, corrected for 0.1 percent of carbon
52 Miscellaneous Publications, National Bureau of Standards

dioxide in the air, was determined as follows from the data obtained

during the first of the 10 readings on gas

:

Corrected barometer 29. 86 Instrument temperature : 78. 2 Instrument reading 0. 6124 Average air-check correction —. 0057 Instrument reading corrected for air check 0. 6067 Factor f from chart 1. 0574

Specific gravity (0.6067X1.0574) 0.6415 Each of the other nine instrument readings on test gas 1 was treated

in the same manner, and when averaged gave a value of specific gravity

(corrected for 0.1 percent of carbon dioxide) of 0.6422. The observed results of the tests with mixtures 1, 2, and 6 have been

corrected as indicated above. In all the other tests the carbon dioxide was removed by Ascarite before drying the air, and consequently no

correction for carbon dioxide was applicable.

The error of the instrument with test gas 1 was computed as follows

:

Specific gravity, corrected for C02 in air 0. 6422

Specific gravity of test mixture 1 . 6474 Error of instrument — 0. 0052

Error, percentage of standard — . 80 The data for each of the nine test gases aud for the first test gas

at three different temperatures have been treated in the same way.

(d) NUMERICAL RESULTS

A summary of the numerical results obtained from the tests of the

balance with the series of test gases employed in the investigation

(except the tests made for determining a temperature coefficient) is given in table 6, and in figure 14 the instrumental errors are plotted

with respect to the specific gravities of the test gases. It is quite

evident that the errors are not primarily dependent on the chemical

makeup of the gas or the order in which they were measured, but that

they tend to approximate some continuous function of the specific

gravity. At specific gravities of 0.56 and 1.00, which represent cali- bration points, there are no appreciable errors, but at other densities

the errors are too systematic and far too great to be considered the

result of random causes. A consideration of the mechanics of the

balanced system provided an adequate explanation.

(e) MECHANICAL ACTION OF THE ANUBIS BALANCE

In the following discussion, the true specific gravity of gas in the

balance case is represented by S and the scale reading obtained when

the beam is balanced by R. S—R is the error of the reading, of course. The forces acting on the balance beam (including everything attached

to it) may be resolved into a supporting force exerted by the agate

plane and the "apparent" weight, m, of the beam (the weight in vacuum minus the buoyant force exerted by the gas in the balance

case). When the beam is in equilibrium, these forces are equal in

magnitude and act in opposite directions in the same vertical line. If the buoyant force is changed, one end of the beam is affected much
Specific Gravities of Gases 53

THE NUMBERS IDENTIFY THE TEST GAS, AND INDICATE THE

ORDER IN WHICH THE TESTS WERE MADE.

MIXT. NO. SYMBOL COMPOSITION

1 9 MFD. GAS

2 * NAT'L - 6,7 9 He - N 2 8 B H 2 -C02 9 • NITROGEN

10,11,12 a N 2 ~C02 + .030

.025 H

.020 z

UJ5.015

o:£.010 u

.005 o

S

gj.005

.010 -.015

.5 .6 .7 .8 .9 1.0 I.I 1.2 1.3 1.4 SP GR OF TEST GAS Figure 14.—Error of the Anubis portable gas balance No. 115 determined with

each test gas after correction for carbon dioxide in the reference air. Table 6.

Specific gravities of test gases as determined by the Annbis portable gas balance No. 115 at the ''normal" temperature of 77° F.

[Average time required for a single determination, 4.2 minutes]

No. Test gas

Specific gravity

Standard

Corrected reading Error

Percent- age of stand- ard

Reproducibility

Probable

error of mean

Probable

error

of single determination

12

3

456

7

8

910

1112

1314

15

Synthetic typical manufactured

gas 0. 6474

.6820

.1526

.3048 .4222

.6007

.7963

.6080

.9666

1. 0982

1. 2792

1. 3984

1. 5268

1. 5461

2. 0644

0. 6422

.6751 -0. 0052 -.0069

-0. 80 -1.01

±0. 00014 ±. 00007 ±0. 00045 Synthetic typical natural gas ±. 00022 Helium a Helium-nitrogen a do a do _ .5986

.7849

.6024

.9672

1. 1017

1. 2907

1. 4269

-. 0021 -.0114

-. 0056 +. 0006 +. 0035 +. 0115 +. 0285

-0. 35 -1.43

-0. 92 +.06

+.32

+.90

+2. 04

±. 00025 ±. 00029 ±. 00013 ±. 00014 ±. 00016 ±. 00012 ±.00011±. 00079 ±. 00092 ±. 00042 ±. 00044 ±. 00051 ±. 00039 ±. 00033

do Hydrogen-carbon dioxide, . Nitrogen _ . ._ Nitrogen-carbon dioxide... .. do

do Propane a ... Butane a . ..... .. Averages 0. 0084 0. 87 ±0. 00016 ±0. 00050

c i

—a

n

9O

d i

7

<

a The range of the instrument was such that the specific gravities of these gases could not be determined.
54 Miscellaneous Publications, National Bureau of Standards more than the other, with the result that the apparent center of

gravity (the point of application of m) is shifted, and to bring this

point again into vertical alinement with the point of support and thus

restore equilibrium, the beam must rot-ate through a certain angle.

The scale of the balance is graduated so that equal angles are marked

with equal increments of specific gravity, and the counterweight and

weight for adjusting sensitivity are fixed by the manufacturer so that

the reading is correct with air (£=1) and with some other gas of

known specific gravity,

A somewhat involved consideration of simple mechanical principles

leads to the equation

in which N is the distance of the apparent center of gravity below the

center of the bearing balls when the beam is in equilibrium, A is the

weight of air displaced by the bulb, L is the distance from the center of volume of the beam (nearly the center of the bulb) to its center of

gravity (nearly the center of the bearing balls) , a is the angle between

the equilibrium position of the beam in the gas being tested and the

equilibrium position in air, and ax is the corresponding angle between

the equilibrium positions in the calibrating gas and in air. S—R is the error in the determination of specific gravity inherent in the

mechanics of the system, and would be the same for a balance of any

kind in which equal angles are graduated to represent equal increments of specific gravity. Actually, a balance operates to make S~l

proportional to the tangent of the angle of displacement from the

position of equilibrium in air, not directly to that angle, and this is the source of the error. Unfortunately, the scale cannot be made

proportional to the tangents of angles without abandoning the present

very convenient micrometer head and worm gear as a reading device.

Each of the quantities on the right-hand side of eq 7 can be determined approximately. the distance of the center of gravity below

the center of the ball, is subject to adjustment and determines the

"sensitivity," the angle of displacement corresponding to a given

change in specific gravity; it can be computed from the two last- mentioned quantities.

In the Anubis balance, the sensitivity is such that a change of

specific gravity of 0.1 causes a deflection of about 2.5°. The calibrating gas was reported to have had a specific gravity of 0.56. The errors inherent in the scale have been computed and are represented in figure

15 by the curve marked 2.5°. As a matter of interest, the errors that

would have resulted had adjustments been made to give higher sensitivities of 3.5° and 5.0° per 0.1 unit of specific gravity have been added

to the figure.

The observed errors were much greater than those calculated by eq

9 for a balance of the observed sensitivity, and their plot can be con- sidered to resemble the curves of figure 15 only in a general way.

However, the balance beam is supported on balls resting on a plane,

and if the plane is tilted the balls tend to roll downhill. This ten- dency modifies the curve of errors decidedly. In the following dis-

(7)
Specific Gravities of Gases 55

cussion, the angle between the bearing plane and the horizontal will

be represented by e and the radius of the bearing balls by r. The point

of support of the beam is no longer directly below the line connecting

the center of the balls, and neither is the apparent center of gravity.

The angle between the vertical and a perpendicular from the apparent

center of gravity to the line connecting the centers of the balls will be

represented by e' . The other symbols have the same meanings as in

eq 7.

+ .025 ^.020

or .015

cro

£,0!0

UJQ.005

UJ

I—2 o o

°.005

.010

COMPUTED ERRORS OF BALANCE INDICATING SPECIFIC GRAVITY BY DEFLECTION

/

ANGLE OF DEFLECTION FOR A CHA

SPECIFIC GRAVITY OF 0.1 NGE C _5.0°_ 5.0°

3.5°

3.5°

2.5" <

\^

_2.5° >

2.5°

3.5°

3.5°

5.0°

5.0°

.7 .8 9 1.0 I.I 1.2 SPECIFIC GRAVITY

1.3 14 1.5 1.6 Figure 15.

Computed errors of a balance indicating specific gravity by deflection. Again, by considering simple mechanical principles, it is found that

(8)

, r . sm e sm e and that o j-\ a..mr sm e ax AL cos ax fsin Q'+O t l

L sin e' J mr sm

AL cos

in e j~sin (e'-\-a) _ ^"1 os a L sin e

r J"

(9) Again, putting approximate values for the Anubis balance into the

equation, the curves shown in figure 16 were obtained for various

angles of tilt. The curve marked 0' is the same as the curve marked

2.5° in figure 15. The small circles represent the observed errors previously shown in figure 14. Figure 16 appears to offer a complete

explanation for the general trend of the observed errors if the bearing

planes were tilted about 0.5° with respect to the level on the balance

case at the time of calibration. This tilt apparently remained unaltered, as the curve of errors appears to pass through 1.0 and 0.56,

the calibration points, within the limit of experimental error.
56 Miscellaneous Publications, National Bureau of Standards

+.035

.030

.025

"5/5.020

a. ~.0I5

cco

£.010

UJ~005

2

8.005

.010

.015 •020

COMPUTED ERRORS RESULTING FROM TILTED BEARING PLANES

FIGURES ON CURVES INDICATE TILT IN MINUTES OF ARC

CIRCLES REPRESENT OBSERVED ERRORS Vr

t -30

/ o -15 /

>

c VH5

7 .8 .9 1.0 II 1.2 SPECIFIC GRAVITY A 1.5 1.6 Figure 16.

Computed errors resulting from tilted tearing planes.

Figures on curves indicate tilt in minutes of arc. Circles indicate errors observed for Anubis portable gas balance No. 115.

(f) LEVELING THE BALANCE

The errors discussed in the preceding section were computed under

the assumption that the instrument is used in exactly the position in

which it was calibrated ; they are inherent in the mechanics of the

instrument and have nothing to do with its manipulation. A dis- placement of the longitudinal level after the air check is made in- troduces another set of errors that is much greater than that resulting

from an inclined support at the time of calibration. The effect can

be computed from eq. 8, in which e is the angle of tilt and e' the error

(in terms of angle) resulting from it. For the Anubis balance with a

sensitivity of 2.5° per 0.1 unit of specific gravity, it is found that a change of level of 0.1° after the air check will affect the following

measurement of specific gravity by 0.145. This extraordinary sensitivity to a change of level makes serious

the slightest disturbance between the time of the air check and the

reading of the specific gravity of the gas. The most probable cause

of such a disturbance is the accidental movement of the balance during connecting or disconnecting from the gas lines or air dryer or during manipulation of the valves. If after the balance has been

moved the spirit level is depended on to restore the condition of the

last air check,- the leveling must be done within an angle of about

0.0007° if the next reading is to be accurate to even 0.001 specificgravity unit. This is an almost impossible requirement.

During the experiments with the balance, it rested on a heavy stone laboratory table top supported on wooden cabinet work. The effect of inaccuracies of leveling the instrument were studied experimentally by placing a weight of 25 lb on the edge of the stone table top

in front of the balance. This caused the bubble in the spirit level to move toward the back of the instrument by about one tenth of a
Specific Gravities of Gases

division on the scale etched on the level. A series of 10 observations

of the balance reading on a single sample of air were made alternately

with and without the weight on the table. The average of five observations with the level displaced differed by 0.0.018 from the average

of the five taken with the instrument level. This means that variations of 0.0002 in specific gravity may result from variations of the

level of 0.01 division, which is entirely imperceptible. Perceptible

variations result when the arm is rested on the edge of the table while

adjusting the micrometer wheel, indicating that care should be taken

to see not only that the instrument is level when observed but that

it is not displaced from level during the process of making the adjustment to the balance point.

(g) TEMPERATURE COEFFICIENT

Tests, consisting of 10 determinations of specific gravity with the same test gas (mixture 1), were made at 65.0° and 90.1° F in addition to that at 78.2° F, for which the results have been given in detail. During these tests at a lower and at a higher temperature than

normal, the temperature of the room was maintained substantially

•66| 1 11 1

1 1

>

><

50 60 70 80 90 100 HO

INSTRUMENT TEMPERATURE °F Figure 17.

Temperature coefficient of the Anubis portable gas balance No. 115 determined with test mixture 1, after oorrection for carbon dioxide in the

reference air. constant by automatic control, and several hours were allowed for

the balance to come to temperature equilibrium before starting the

est. The air check was, of course, made at the same temperature

s the test with the gas. The results have been plotted against temperature in figure IT. A

straight line, determined by the method of least squares, has been

passed through the three points, and the slope of the line, constituting

he temperature coefficient, is indicated thereon. The radius of the

ircle around each observed point is equal to the probable error of the ean of the 10 determinations which that point represents. The fact
58 Miscellaneous Publications, National Bureau of Standards

that the observed differences between the specific gravities at the three

temperatures are not greatly in excess of their probable errors and that

they vary in a somewhat improbable manner leaves some doubt as to whether the balance has an appreciable temperature coefficient. Any

inaccuracy in the construction or use of the correction chart and dif- ferences in the deviations of test gas and reference air from the ideal

gas laws, as well as changes in dimensions of the balance itself, would

appear as part of the "temperature coefficient," As to changes of

dimensions within the balance, anj^ change that shifts the center of

gravity or the center of volume of the parts attached to the beam horizontally, would produce the same temperature coefficient for all gases. If the changes affected the vertical distance between the center of

gravity and the bearing surface, the temperature coefficient would be

proportional to the difference between the specific gravity of the gas

and 1.0.

(h) OTHER PROBABLE SOURCES OF ERROR

(1) Air-Check Correction.—If the instrument is so calibrated that

its reading on dry carbon dioxide-free air at 30 in. and 60° F is 1.0000,

it will indicate directly the specific gravity of a gas sample at the same temperature and pressure. It is impracticable to set the reading

exactly on 1.0000 under these conditions, or on the exact reading

corresponding to this at any other temperature and pressure, after

ascertaining the correct reading by use of the gas law factor in the

chart supplied with the instrument. The procedure recommended in

Bulletin 106 is to determine the reading of the instrument on air, and

then to determine the difference between this and the reading which

the instrument should give at the temperature and pressure observed,

as determined by use of the chart. This difference is then applied as a correction to the observed reading on gas before correction to standard conditions. If the air used were dry and free from carbon dioxide,

if temperature and pressure determinations were accurate, if suffi- ciently precise leveling were possible, and if no mechanical changes were to occur in the balance mechanism, a single determination of the

air-check correction would suffice. If accuracy is important, however,

the correction should be determined after moving to a new location or support and thereafter at intervals sufficiently frequent to demonstrate the permanence of the correction or insure that it is known to the required limit of uncertainty. It has been suggested that the

shift in the air-check correction for balance 115 may have been the

result of gradual relief of mechanical strains in the arm carrying

the movable index, introduced when it was shaped.

Individual determinations of the air-check correction vary suffi- ciently to necessitate the use of the average of a series of determinations rather than a single one. In the case of the test used as an

illustration above, the probable error of the mean of 10 determinations was 0.00013, while that of a single determination was 0.00042.

(2) Calibration.—The instrument is calibrated by the manufacturer, and its accuracy thereafter depends on the accuracy with which

the calibration is made and the absence of subsequent changes which

may affect it. It is important to follow the instructions in Bulletin

106 with regard to changes of any part of the beam assembly, since
Specific Gravities of Gases 59

any vertical change of the center of gravity of the beam with respect

to the point of support will change the calibration. Such effects may

arise from careless handling, or possibly from the gradual relief of

mechanical strains in the invar beam. They may manifest themselves

in changes in the air-check correction, if not obscured by larger effects such as those discussed above, but they will be accompanied by changes

of calibration which can only be detected by testing the instrument

with a gas of accurately known specific gravity. It should be stated,

however, that the balance is ruggedly made and that no effects were

observed which could be attributed to a change in "calibration."

The accuracy with which the manufacturer knows the specific

gravity of the gas used for calibration is important, for an uncertainty

of 0.001 at a specific gravity of 0.750 may amount to an error of 0.002

at a specific gravity of 0.500 and 1.500. At specific gravity 1.000, cali- bration errors become unimportant as compared with those resulting

from errors in level, pressure, temperature, correction chart, and

determination of the balance point.

(3) Purity of Material Tested.—An uncertainty of the composition

of the material tested, as a result of incomplete purging, may be a source of error. Purging should be rapid enough to produce some

turbulence inside the balance case which will keep the contents stirred

up and clean out corners. A filter may be necessary, as suggested in

Bulletin 106, if the gas carries dust. Alternate purging and reading

until the variations in the readings become random may be required to establish the time required at the rate used. In the case of air, the

rate should not be so high that incomplete drying results. Air from a compressed supply may contain vapors or other gases. Air from the

laboratory may be similarly objectionable. The balance is not provided with means for purging with air from other than a compressed

supply, but means for drawing air from the laboratory are not difficult to provide. If the laboratory air is not free from carbon dioxide, as will usually be the case, this should be removed before drying the air

during purging, or corrected for, as has been done in the case of the

test described above. Air from outside, unless contaminated with

measurable amounts of foreign gases, would be preferable. The carbon

dioxide content of outdoor air may be as high as 0.04 percent, which

would affect the specific gravity by 0.00014. The 0.10 percent of

carbon dioxide found in the air of the laboratory necessitated a cor- rection of 0.0005 in the specific gravity, which is somewhat larger than

the probable error of a single determination and may not be negligible.

As long as the balance is operated at atmospheric pressure, con- tamination of the sample by leaks is eliminated as a source of error, but, to prevent diffusion of air into the balance, care must be taken to

close the purge valve as soon as the balance has reached atmospheric

pressure after the gas flow is stopped.

(4) Determination of Balance Point of Beam.—The determination

of the balance point of the beam, and consequently the reading on the

scale, is subject to errors or uncertainties from several sources, most

of which are covered or implied in the directions for operation. The

reading is lower when the pointer swings five divisions up and five down on the movable index scale, than when it swings four up and

four down. The damping also seems to be more rapid and less regular.
60 Miscellaneous Publications, National Bureau of Standards

The reading continues to increase as the amplitude decreases. As indicated in Bulletin 106, best results are attained by taking the reading

when the amplitude is four divisions up and four down.

The method by which the pointer is determined to be swinging four

divisions up and four down makes a difference in the reading. If the

reading of the pointer on the movable index scale is observed at the

top of its swing and again the next time the pointer reaches the bottom

of its swing and the adjustment is made immediately thereafter, the

reading on the micrometer wheel will differ by about 0.004 from that

obtained if the adjustment follows observations made in the reverse

order. The first procedure gives the better results, when the index

scale is being adjusted downward, because it permits the observer to follow the highest positions of the pointer downward with the chosen

index line until the desired amplitude is reached. This results in

fairly accurate adjustments during a larger number of swings and is nearly equivalent to slowing down the rate of damping. In any case,

it is necessary to use the same procedure with the gas as with the pre- ceding air check.

The error in reading the scale on the micrometer wheel may be 0.0001 or 0.0002, since the fourth place is estimated. Of course continuous

clockwise motion of the micrometer wheel during the setting of

the balance point is essential to avoid errors caused by backlash in the

mechanical parts, as has been pointed out in Bulletin 106. For some reason not fully explained the displacement of the beam

produced when it is released by the arresting mechanism depends on

temperature. It is about 4.5 divisions at 65° F, 5.5 divisions at 78°

and beyond the end of the scale at 90°. At the lower temperatures

there is not enough time to make a good adjustment of the scale before

the oscillation becomes less than the prescribed 8 divisions. When this occurs it is necessary to release the beam several times before a good

setting can be obtained.

(5) Pressure Determinations.—An error in determining the barometric pressure, whether as the result of using a faulty instrument, an error in reading, or failure to make needed corrections, makes a proportional error in the specific gravity. For example, an error of

0.1 inch of mercury as the result of failure to correct the barometric

column for temperature would make the determination of the specific

gravity of test mixture 1 too high by 0.0021 if the air check was based on a correct barometric pressure, and too low by 0.0012 if the air check

involved the same barometric error as the gas.

(6) Temperature Determinations.—Uncertainties in reading the

thermometer scale, errors in the indication of the thermometer, and

lack of equilibrium between thermometer bulb and the gas in the

balance case may give rise to errors in the specific gravity. The scale on the thermometer of balance 115 is graduated in intervals of 1 deg F,

and one may attempt to estimate tenths of a degree. It can probably

be read to ±0.2 deg F with certainty.

Thermometers, even when they prove to have no correction on cali- bration, should be tapped before reading if they are to indicate correctly, and one hesitates to tap sharply a thermometer attached to the

balance case. In addition to this, the thermometer may have a cali- bration correction of a few tenths of a degree.
/Specific Gravities of Gases 61

Although the bulb of the thermometer does not project entirely into

the balance case, it is surrounded by a metal casing in good thermal

contact with the heavy-brass case. The gas will not require much

time to come to the temperature of the balance, and the thermometer

is likely already to be very near the temperature of the balance.

Handling, lights, observer, etc. all affect the balance temperature. A

varying temperature indicates possible uncertainties.

It seems easily possible that a combination of errors, such as the

above, might amount to a total of 0.5 deg F. Assuming everything

else correct, however, a thermometer reading that is too high by 0.5 deg

F will result in the value obtained for the specific gravity being too low by only 0.0006 in the case of test mixture 1 if the error was only

in the temperature of the gas, and by 0.0003 if the same error oc- curred during both the measurement of the gas and the air check.

Consequently, small uncertainties in the temperature are of little moment.

(7) Gas-Law Corrections.—The chart provided with the instrument appears to be accurately prepared with coordinates that can

be read as accurately as it is possible to read the thermometer and

barometer. Significant errors resulting from its use are likely only

in case the operator makes an error in the interpolation between the

steps to which the correction factor is given, which are 0.005 apart.

The Anubis balance is much less affected by deviations from ideality

of the gases tested than are balances in which adjustments of pressure

are used to produce the same position of balance with different gases, because changes which occur in barometric pressure are relatively

small and the Anubis balance is usually operated only at atmospheric

pressure.

(i) COMMENTS ON OPERATION AND SOME SUGGESTIONS FOR IMPROVEMENT

Suggestions made to the manufacturer for the improvement of the

instrument, some of which may be incorporated by the user, were as follows

Suggestion 1: While a three-point support is, in general, preferable

to one of four points, in the present case it might improve the stability

of the instrument to have a cross support more nearly under the center

of mass. Suggestion 2 : For convenience in purging with air, a hose connection

and cock in place of the purge valve would permit drawing air from

the best source, uncontaminated by passage through pumps, storage

tank or pipes, and dried and freed from carbon dioxide.

Suggestion 3: It might be worthwhile, for the peace of mind of the new user, to provide closer correspondence between the tenths on the

reference scale and the revolutions of the micrometer wheel. When

set to correspond at 1.000, the reference scale is off by 0.03 at 0.600. Suggestion 4 - Reading the position of the beam pointer on the movable index might be made easier if the pointer' were made to contrast more sharply with the scale. Suggestions : It might be desirable to amplify the printed directions

to include the following points : Careful lighting is necessary, and

the position of the light is important. The advisability of noting the

reading of the beam pointer at the top of its swing and again at
(32 Miscellaneous Publications, National Bureau of Standards

the bottom and making the adjustment of the micrometer wheel while

the pointer is moving upward. The great importance of doing this

the same way every time.

Suggestion 6: The greatest improvement could be made by supplying a correction chart for the systematic errors involved in the leveling

of the balance planes. If these are level, the fact can be determined

by calibrating with gases near both extremes of the range of the instrument. Carbon dioxide would probably be satisfactory for the heaviest

gas if the sensitivity of the instrument were reduced a little to accom- modate it. The entire calibration curve could be rather easily worked

out mathematically from three calibration points, for carbon dioxide,

air, and methane, for example, even if it is not practicable to make the

bearing planes exactly parallel to the level.

3. AC-ME RECORDING GRAVITOMETER NO. 271

(a) DESCRIPTION

This instrument (fig. 18) is described in the manufacturer's instruction booklet only by means of sectional drawings, with a key to identify

the numbered parts. The booklet gives adequate instructions for

installation, calibration, maintenance, and care. The instrument is not portable (weighs 157 lb.) and is inclosed

in a sheet metal case 4A in. high, 25 in. wide, and 15.5 in. deep, with

the top and right side hinged to provide access to the mechanism. It

is essentially a balance, the beam (forked at one end) consisting of a

cross member forming the base of the fork supported on knife edges

at each end of the cross member, and balanced by a rod (corresponding to the handle of a fork) , screwed into the cross member on the

side opposite the two arms. The float, a cylindrical tank of light sheet

aluminum about 27 in. high by 10 in. in diameter, is supported between

the two arms of the beam from hardened steel hooks on knife edges

placed on the ends of the arms. The float is counterbalanced by an

adjustable balancing weight held in place by a lock nut on the threaded

end of the rod that forms the rest of the beam.

The float has a conical top surmounted by a pin to hold the small

test weights, and a conical bottom opening into a short cylindrical

outlet 2 in. in diameter and 5 in. long. The outlet tube dips into liquid

in an oil-seal cup that is fitted with a large concentric tube to carry

the discharged sample outside the case at atmospheric pressure, and

a smaller tube in its axis running up nearly to the top of the float carries the sample into the float from the control valve and flow meter

mounted on the outside of the case at the top of the left side near the

front. The cross member of the beam carries a vertical rod at one end, near the front of the case, which is attached by means of a link to the

pen mechanism. The length of this rod and the relative length of the

pen arm as compared to the short rod, to which the link is connected,

serve to magnify the motion of the beam.

The circular 24-hour chart is driven by a spring clock located inside

the upper front of the case, and is accessible through a glass door on

the front.

The chart is 10 in. in diameter, graduated from 0.5 near the center
Specific Gravities of Gates 63

Figi'ee IS.

Ac-Me recording gravitometer No. 271.

719265—47
(34 Miscellaneous Publications, National Bureau of Standards

to 1.0 near the outer edge in intervals of 0.01. The 0.01 intervals are

a little more than one-sixteenth in. wide, and the reading can be esti- mated to about ±0.001.

The working force which operates the instrument is the difference

between the weight of the gas contained in the float and an equal

volume of the surrounding air. This working force is opposed by a pendulum which carries an adjustable weight and is attached to the

cross member of the beam in a manner which permits the angle between the pendulum rod and the longitudinal axis of the beam to be

adjusted.

The instrument is compensated for changes of temperature and at- mospheric pressure by the action of a volume of air contained within

a coiled metal tube mounted on the back of the case. One end of the

coil is closed b}^ means of a valve which permits adjustment of the

pressure of the air in the compensator coil. The other end connects with one side of what is, in effect, a flexible mercury manometer, the other side of which is attached to the balance

beam. The flexible link between the two parts is a small rubber tube

parallel to but below the bearings of the balance beam. A scale on

the arm of the manometer attached to the case assists in adjusting

the amount of mercury and the pressure of air in the compensator.

The arm of the manometer attached to the beam terminates in a bulb

above the bearings of the balance. The action of the compensator

is as follows : Changes of temperature or barometric pressure cause changes in the volume (and density) of air in the compensator coil. These changes of volume cause equal changes in the A

Tolume of mercury in the bulb attached to the balance beam. Hence, the effect of

a change of atmospheric temperature or pressure is to add to an upward extension of the beam a weight of mercury proportional to the

effect of the change on the density of air. When the float is filled with air and the pen indicates 1.000 the beam is level and the mass of

mercury is directly above the bearing, where it does not affect the

balance in either direction. But when gas of another specific gravity

fills the float and the beam is not level, the mass of mercury is at one

side of the support and tends to tilt the beam farther by an amount

proportional to the deflection. Thus there is added a correction to the reading of the balance which is proportional to the effect of atmospheric conditions on the density of gas and at the same time proportional to the difference between the density of the test gas and that

of air. This is the relation needed for compensation. The design

further ' involves the provision of a volume of compensating gas

and a weight and position of mercury that will make the compensating

force not only proportional to but equal to the correction desired.

(b) MODIFICATIONS FOR PURPOSES OF TESTS To avoid contamination of the surrounding air, the gas discharged

from the instrument at atmospheric pressure at the bottom of the case was collected and discharged from the room by means of the 3-in. exhaust duct with dampers previously mentioned and an adjustable

sleeve that fitted closely over but did not make contact with the top

of the downdraft diverter on the discharge outlet of the instrument.
Specific Gravities of Gases 65

The dampers were so adjusted that stopping or starting the exhaust

fan produced no change in the indication of the instrument.

Thermocouples were located inside the case, one mounted adjacent

to the thermometer near the top on the left side of the case and another

'< near the center of the compensator coil, so the temperature at these

points could be determined while the instrument was in operation

without opening the case. The feet of the instrument were fixed in position on the floor by

melting wax around and under the edges of the flanges.

The instructions call for filling the oil seal with "a very light oil, preferably mineral seal oil. If this is not available, kerosine may be

used." The oil seal was filled with kerosine of 0.81 specific gravity.

This evaporated rapidly and crept freely over the surrounding parts.

After evidence was obtained that changes in its level had a marked

effect on the indication of the instrument and that its vapor con- taminated the reference air inside the closed case, also affecting the

indication, the kerosine was replaced by Markol, a sharp petroleum

fraction having a specific gravity of 0.846 and a viscosity of 0.245 poise at 25° C, but a vapor pressure of about 0.0001 mm of mercury

at 25° C. In addition, it did not creep. The instructions call for filling the mercury container from the

bottle marked "exact amount of mercury for Ac-Me Gravitometer

Serial No. 271, 573.5 grams." When this was done the level of the

mercury in the gage glass was not exactly at zero, although the instrument case was level according to the spirit levels. Since it is necessary

that the mercury level in the gage be at zero when the compensator

valve is open, the quantity of mercury was adjusted to bring the level to zero.

(c) METHOD OF OPERATION

The directions supplied for the installation, calibration, and operation of the instrument were followed with a few minor modifications

and extensions during the testing with nine of the gases of known

specific gravity. It was after some preliminary operation and following the tests with mixture 1 that the kerosine in the seal cup was

replaced by Markol to prevent the various adverse effects attending the

use of a more volatile oil. Before admitting the test gases, the instrument was calibrated

according to the instructions. Air from the laboratory was drawn

through the float in reverse by applying suction at the gas connection.

The case of the instrument was open. The room was adjusted as nearly as possible to a relative humidity of 35 percent and a temperature of 77° F for calibration and for each test with a standard mixture,

in order that the chart might have the same dimension from test to

test as at calibration. The air check was made, as well as the subsequent calibration and tests with the standard mixtures, using the

portion of the chart at or near the 6-o'clock axis, the direction in which

the chart paper shows the least change of dimensions with changes of

relative humidity.

After purging the float with air, the flow was stopped and

I the case closed. The side door was opened during adjustments

. of compensator and weights but was kept closed but unlatched

during the rest of the time. Great care was taken to avoid
66 Miscellaneous Publications, National Bureau of Standards

jars to the case and movement of the knife edges on the supports during adjustments. . The beam was held in contact with

the limit stop at one end or the other of the gap while adjusting the

weights. The compensator gage was set at 0.00 and the counterweight

adjusted to bring the pen to 1.000. The adjustment of the pendulum

rod was checked by changing the compensator gage reading to + 1.00 and —1.00 successively, without change of indication on the chart. The compensator gage was again set at 0.00, all the five test weights were removed at the same time, 20 minutes was allowed for drainage,

and the pendulum weight was adjusted to bring the pen to 0.500. When all five test weights were replaced at the same time, the pen

again read 1.000. This result was accomplished only after several

successive adjustments of the counter- and pendulum weights with

varying departures of the pen from the desired readings. When the

test weights were replaced one at a time, the record of the pen was

never at the correct mark. The following, after setting the pen on

0.500 ±0.0005, is a typical series: 0.5985, 0.699, 0.799, 0.899, 0.9975. Considerable difficulty was encountered in adjusting the counter- and

pendulum weights as it was impossible to move the lock nut without some movement of the weight, and this could not be detected because

there is no mark on the weight and no reference point to which a mark

might be referred. In addition to this trouble, the pendulum weight

appeared to be eccentric, so that it was often impossible to predict

the direction of the effect of moving it. There were also indications

that the rubber tube connecting the mercury reservoir to the compensator gage sometimes slipped slightly on or off the end of the metal

tube as a result of stretching when the beam moved from one end to the other of its travel, and this resulted in the failure of the pen to return to 1.000 after having been set at 0.500. After succeeding in

the attempt to get a reading at 1.000 after a return from 0.500, the

barometer and temperature of the instrument thermometer were read,

the compensator gage reading was determined from the chart inside

the cover, and the compensator gage set at that reading.

Before subsequent tests, the barometer and instrument temperature were read, and the compensator gage was read without jarring

the case. The gage was then tapped and again read and both readings recorded, together with the reading from the chart. If correc- tion was required, the gage was reset at the reading from the chart. The level of the oil in the seal cup was checked and adjusted if necessary. The instrument case was opened to be sure that it was filled with room air at 35 -percent relative humidity and at 77° F. After the calibration which preceded testing with mixture 2, no

check of the calibration was made until after testing with mixture 9 (sp gr 0.9666). The range of the instrument was then changed by

adjusting the pendulum rod to the vertical position with the pen at 0.500 and checking by adjusting the compensator gage to +1.00 and — 1.00 as before. A single brass weight that had the same weight as the combined five test weights was placed on the float during the above

adjustment. The five test weights were then also placed on the float for the adjustment of the pen at 1.000 (sp gr 1.500). The instrument was then recalibrated, as previously described, for tests with the

mixtures having specific gravities between 1.000 and 1.500.
Specific Gravities of Gases 67

Each test of the instrument with a test gas involved purging until

the reading and record had been constant for at least 15 minutes.

The indication and record were then displaced by removing one of

the five test weights, which allowed the float to rise out of the oil. After about 7 minutes the weight was replaced with care to avoid

immersing the bell below its former position and so that no displacement of the reading would result from the presence of oil on the float and no time for drainage would be needed. The reading became constant again almost immediately.

During the 13-minute test period, a record was made of the chart

reading, the temperature shown by the two thermocouples, the room

temperature, the barometric pressure, the relative humidity and drybulb temperature, and the time at which the record was started. This

procedure was repeated until 10 records had been made with the test gas. The position of the center of the record line in each case was

then measured with an ocular-scale microscope. These 10 values

of specific gravity were then averaged for the test. The temperatures,

barometric pressure, and relative humidity reported with each test are the averages of the values recorded for the 10 determinations.

(d) CORRECTION FOR EFFECT OF RELATIVE HUMIDITY ON CHART PAPER

All readings were corrected, for the effect of humidity on the dimensions of the charts, to a relative humidity of 35 percent by the method

described for all instruments in section III, 2 (e) (p. 20)

.

(e) REFERENCE AIR The air inside the instrument case is used as a standard of reference,

and uncertainties as to its composition caused by contamination with

the vapor of a volatile seal oil or by variations in the carbon dioxide

and water content of the air cause errors in the specific gravity in- dicated by the instrument. Contamination with the vapor of a volatile

seal oil causes a reading that is too low, and the higher the temperature the greater is the error. Leaks of gas in the vicinity, inadequate

disposition of the sample discharged from the instrument, as well

as carbon dioxide from laboratory burners, power-plant stacks, etc., may cause errors of this kind. Although the case is not gastight,

there is little opportunity for interchange with the air outside.

Humidity and carbon dioxide determinations for the purpose of ap- plying corrections will result in corrections that may be wrong if the

air inside the case is not of the same composition as that outside.

In this case, as the air in the laboratory that surrounded the

instrument and filled the case and served as the standard of reference was neither dry nor free from carbon dioxide, corrections to the

observed reading were required to place the indication of the instrument on the same basis as the standard specific gravity of the test mixture.

(f) CORRECTION FOR WATER VAPOR AND CARBON DIOXIDE IN REFERENCE AIR The instrument is mechanically calibrated by the use of weights,

each of which has one-tenth the weight of "standard" air ( free from

water and carbon dioxide) which would fill the float at a temperature

of 60° F and a pressure of 14.4 lb in.2 (equivalent to a barometric
68 Miscellaneous Publications, National Bureau of Standards

pressure of 29.3 in.), which had been taken as standard conditions

in the manufacturer's calibration.

The compensator is designed to eliminate the effects of changes of

the buoyant force of the "reference" air surrounding the float, caused

by changes of temperature and pressure, but it does not compensate

for changes of its composition. Neglecting the volume of metal in

the thin-walled float, the volume of the outside air is equal to that

of the gas being tested. Then, if we take as the unit of force the

weight of that volume of gas of specific gravity 1.0000, it is apparent

that water vapor and carbon dioxide each affects the buoyant force

and the indication of specific gravity by an amount equal to the fraction in the outer air and to the difference between the specific gravity

of the contaminant and unity. That is, S=R— 0.378w + 0.529c, where

S is the specific gravity of the gas being tested, R is the reading of

the instrument, w is the fraction of water vapor, and c is the fraction

of carbon dioxide in the reference air. The average of the "observed" determinations of the specific gravity

of test gas 2 was 0.6900. After correction for the changes of dimensions of the chart, it was 0.6901. The average moisture content of

the air was 1.15 percent, and the average carbon dioxide content was

about 0.1 percent. Substituting these values in the above equation,

8=0.6901 - 0.378 X 0.0115 + 0.529 X 0.001 =0.6901-0.0043 + 0.0005 =0.6863. Summarizing the observations and corrections for mixture 2

:

Correction for effect on chart of departure of relative humidity from 35 percent +0. 0001

Correction for effect of water vapor in air on buoyancy —. 0043 Correction for effect of carbon dioxide in air on buoyancy— +. 0005 Net correction —0. 0037 "Observed" specific gravity, mean . 6900 Indicated specific gravity 0. 6863

Specific gravity of text mixture 2 . 6820 Error of instrument +0. 0043 Error of instrument, percentage of standard— +. 63 A summary of the numerical results obtained from the tests of the

instrument with the series of test gases (except the tests made to determine temperature and humidity coefficients) is given in table 7, and

the errors of the instrument uncorrected and after corrections for

the effect of relative humidity on the chart, and for water vapor and

for carbon dioxide in the reference air have been applied, have been

plotted for each test gas in figure 19.

(g) SOURCES OF ERROR

(1) Temperature Coefficient.—If the temperature and pressure

compensator operates satisfactorily, the specific gravity indicated by

the instrument, after calibration and operation by the methods described above, should be independent of the temperature of the in- strument. To determine whether this was the case, a series of tests
Specific Gravities of Gases 69

at different temperatures, each consisting of 10 readings of the specific gravity of a single test gas (mixture 2) was made as described

under "method of operation." Two of these tests at 77.6° F and one

at 92.6° F were made with substantially the same percentage (1.15)

by volume of water vapor in the reference air. In another test, at

67.9° F, the relative humidity was practically the same as in the tests at 77.6° F (36.9 percent), but the percentage of water by volume was

different of course. In still another test, at 80.1° F, neither the relative humidity nor the persentage of water by volume was duplicated.

The observed results have all been corrected for the departure of the

+ .015

.010

l—1.005 3

crz

^.005 o

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MIXT. NO. SYMBOL COMPOSITION

1 © MFD. GAS

2 * NAT'L " 6,7 O He — N2 8 a H2 -C02 9 • NITROGEN

10,11,12 a N 2 -C02

e

c b • a

AS BSERV ED

e

1 i

(

i AFTER CORRECTI ON •

a

5 .6 .7 .8 .9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 SP GR OF TEST GAS Figure 19.

Error of the Ac-Me recording gravitometer No. 271 determined with

each test gas, as observed and after the application of corrections for the ef- fect of relative humidity on the chart, and for water vapor and carton dioxide

in the reference air. chart paper from 35-percent relative humidity and to dry carbon

dioxide-free reference air. (The laboratory air was assumed to contain 0.1 percent of carbon dioxide.) The results, as observed and after

all corrections have been applied, have been plotted against temperature m figure 20. A straight line, determined by the method of least squares, has been passed through the three points representing tests made with gas containing the same percentage of water, another

through the three points representing tests with gas of the same relative humidity, and a third line through all five points after they have

been brought to a common basis by the application of the corrections

discussed above. The slopes of these lines, constituting the temperature coefficients, are indicated thereon.
70 Miscellaneous Publications, National Bureau of Standards

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Specific Gravities of Gases 71

The radius of the circle around each observed point is equal to the

probable error of the mean of the 10 determinations which that point

represents.

It may be noted that the circles are small as compared with the differences which appear between tests on successive days under nearly

the same conditions. Even when all the corrections that have been

evaluated have been applied, the difference appears to be approximately

0.0035 in one case. If one considers that the uncertainty of a particular test may be more accurately evaluated by comparing that test with

another made under the same conditions than by computing the probable error of the mean of the 10 determinations which constitute the

single test, then it is seen that an uncertainty of 0.0035 could suffice to bring all five of the solid points to a straight line at a specific gravity

as low as 0.6833 and eliminate any residual temperature coefficient.

70

.69

I-o- AS OBSERVED a$ ;«

HE* ALL CORRECTIONS

VARIABLES TEMP, REL. HUMID. % H 2 O !

CONSTANT % H 2 IN AIR (1.15%) REL. HUMID. (36.9%) — a °- £

TEST MIXTURE ^000095

50 60 70 INSTRUMENT 80 90

TEMPERATURE

I00 no Figure 20.

Temperature coefficients of the Ae-Me recording gravitometer No.

271 determined with test mixture 2, as observed (-0- at constant percentage of water vapor in the reference air {1.15 percent) ; $ at constant relative humidity of the reference air (36.9 percent)), and • after the application

of all corrections. Had this temperature coefficient been determined while the seal cup

contained kerosine, it could have been attributed to the kerosine, for

the contamination of the reference air with kerosine vapor would cer- tainly have been higher at higher temperatures. The gas would probably have been contaminated only slightly, if at all, because the flow of

sample would carry the heavier vapor out immediately. The gas, referred to a reference heavier than normal air, would then appear to be lighter than it actually was and thus could account for a residual

negative temperature coefficient. As this explanation can not apply when the seal cup was filled with

Markol, it must be concluded either that the temperature compensation of this instrument is inaccurate to the extent of about 0.0001/degF, or that its reproducibility is of the order of 0.0035.
72 Miscellaneous Publications^ National Bureau of Standards

(2) Humidity Coefficient.—Variations of relative humidity from

10 to 70 percent in the same place at different times of year are easily

possible. At a temperature of 77° F, this range corresponds to a range of water-vapor concentration of from 0.3 to 2.2 percent. The

uncorrected reading could be too high by as much as 0.0083 if the

water-vapor concentration were 2.2 percent.

In order to determine experimentally the effect on the indicated

reading of variations in the water content of the surrounding refer- ence air, a test, consisting of 10 determinations of the reading, was made in the manner previously described, with the reference air con- taining 2.78 percent in addition to two tests with air containing 1.15 percent and 1.19 percent of water, which correspond nearly to 35-per-

>

.68

lo AS OBSERVED !• ALL CORRECTIONS

VARIABLES % H 2 0, % REL HUMID Constant TEMP (78.4 °F)

JO'

—

—O- \^

©

• 00*20

' 5f.R % H 2

TEST MIXT URE

•

0.5 1.0 1.5 2.0 2.5 3 VOL % H 2 IN REFERENCE AIR Figure 21.

Humidity coefficient of the Ac-Me recording gravitometer No. 271 determined at constant temperature (78.4° F) with test mixture 2; O as ob- served, and • after the application of all corrections. cent relative humidity at 77° F, the conditions chosen as "normal"

for the purpose of these tests. During the tests the instrument was maintained at as near the same temperature as possible. The average temperature was 78.4° F,

and temperatures during individual tests differed from this by 1.7° F

or less. The results as observed and after correction to a chart reading at 35 percent relative humidity and to dry carbon dioxide-free reference

air have been plotted in figure 21 against percentage of water vapor

in the reference air. Straight lines, determined by the method of

least squares, have been passed through the three points, and the slopes

of the lines, constituting the humidity coefficients, are indicated

thereon.

The slope of the line through the solid points is still 29 percent of

the slope of the line through the uncorrected points, but it may be

noted that, as in the case of the temperature coefficient, an uncertainty

of 0.0032 would suffice to bring all the solid points to a horizontal line
Specific Gravities of Gases 73

at a specific gravity as low as 0.6835, and so eliminate any residual

slope. In this case the effect of water vapor on the readings is believed

to have been eliminated by the corrections. It must therefore be con- cluded that there is an uncertainty in the individual tests of at least 0.0032.

(3) Accuracy of Readings.—The position of the record mark on

the chart may be read to 0.01 and estimated to 0.001, which is small

as compared with some probable errors from other sources.

(4) Material Tested.—Uncertainty as to the material being tested

may be a source of error if insufficient time for purging is allowed.

Several tests indicated that from 8 to 10 cu ft of sample were required

to purge the float completely. The displacement of a heavier gas by

a lighter one is more readily accomplished than the reverse, as the

sample enters the float near the top. A heavier gas entering at the

top will tend to fall through a lighter one without displacing it so completely. The rate of purging should be kept relatively high to

facilitate mixing the entering gas with the contents of the float. This

seems feasible, as the rate of purging, from 4 to 12 cu ft/hr, caused no

perceptible change in the reading. Purging appears to approach

completeness asymtotically with time, and approximately the same

degree of completeness should be reached after a given length of time,

regardless of the difference between the specific gravity of the enter- ing gas and that already present. But the smaller the difference in

specific gravity, the smaller will be the departure from the reading

which would be reached after purging is complete. If the specific

gravity of the sample varies, rising and falling, the reading at a particular time will lag behind the specific gravity of the entering gas, and the uncertainty will be larger, the larger the variations and the

lower the purge rate. As the sample flows downward over the oil seal and directly out,

there is no likelihood of serious contamination of the sample with

vapor from a volatile oil in the seal cup.

(5) Sealing liquid.—In addition to the contamination of air in

the case with its vapor, a volatile seal oil can cause an error if its level in the cup is not maintained the same as at calibration. As the level

is lowered by evaporation, the buoyant force of the liquid on the

immersed neck of the float becomes less, causing the reading to be

high. At the same time the volume of the float is increased. With a

gas lighter than air this would cause the reading to be low. The

effect of the change in weight of seal oil displaced by immersed metal

is considerably larger than the change in the difference between the

weights of gas and air. With the float filled with air, a change of

one-eighth inch in the level of the liquid produced a change of 0.005

in the reading.

(6) Volume of float.—As the float rises, the volume of the float and, consequently, the working force are changed. The instrument

is placed in mechanical balance during calibration with the float at both extreme positions. It is filled with air and no buoyant force

is exerted by gas. With the float at its upper limit when rilled with

; a gas of 0.500 specific gravity, the volume of the float will be increased

by 1.37 cu in. which is 0.08 percent of the valume of the float (1,728 cu in.) . This would cause the reading to be too low by 0.0004.
74 Miscellaneous Publications, National Bureau of Standards

(7) Calibration.—As stated in the instructions, the pendulum rod

(which carries the mercury reservoir for temperature and pressure

compensation) should be exactly vertical when the float is filled with

air, so that the quantity of mercury in the reservoir will not affect the reading. Even though this condition is met and the pen reads

1.000 with the test weights on the float and also reads 0.500 without

the weights, the readings are slightly low by varying amounts when

the weights are added singly and low by from 0.002 to 0.010 when all have been added. The reading always was nearer 1.000 after a return from 0.500 when all the weights were added at once. No

reason for this behavior has been discovered other than the possible

displacement of the rubber tubing mentioned in the discussion of

calibration in section IV, 3 (c). The float is lowered into the seal

oil during this process, so no drainage is involved.

(8) Temperature Changes —-The relative lengths and arrangement

of lever arms in the beam and linkages connecting it to the pen appear

to have been so designed that there will be little residual effect on

the reading as a result of the changes in length of metal parts with

temperature, although the residual temperature coefficient shown by

the lowest curve of figure 20 may have resulted from this cause if the

effect is real. (9) Temperature and' Pressure Compensator.—An error in the loca- tion of the compensator gage on the instrument case, in the quantity

of mercury contained in the system, or in the volume of the air reservoir

could cause an error in the compensation of the instrument for temperature changes. For gases having a specific gravity less than 1.000,

overcompensation, causing too low a reading at higher temperatures,

would result if the system contained too much mercury, if the gage were set too high, or if the air reservoir were too large. For gases having a specific gravity greater than 1.000, overcompensation, causing

too high a reading at higher temperatures, would result from the same

errors. These possibilities are recognized by the manufacturer, and

while this instrument appears to be slightly overcompensated, the

error, if any, is not larger than the differences observed between readings on the same gas after an interval of 4 days.

However, when the temperature of the air surrounding the instrument was changed at a rate between 5° and 10° F/hr, the temperature

of the compensator air reservoir lagged behind the temperature at the

location of the mercury thermometer by about 3° F. This would be

expected to result in errors of compensation as well as errors resulting

from corresponding differences between the temperature of the gas

inside the float and the air surrounding it inside the case of the instrument. The net effect was that the readings rose with rising temperature as much as 0.003 above the reading at constant temperature and

fell as much as 0.0025 below with falling temperature.

When the mercury in the compensator system moves up or down

gradually as a result of temperature or pressure changes, it tends to hang up in the tubing. Tapping the gage caused the mercury to move

an average of 0.03 to 0.04 division or less ; 0.03 to 0.04 division could

account for an error in specific gravity of about 0.001. When the gage was tapped before each reading, the reading of the gage corresponded
Specific Gravities of Gases 75

satisfactorily over a period of several months with the reading from

the chart. The mercury meniscus in the gage was lubricated with a small drop

of w-dibutylphthalate, which was effective as long as the mercury was

in frequent motion but was not effective for slow changes. • (10) Mechanical Effects.—Errors may result, of course, from vari- ous mechanical sources, mainly friction. The action of the beam appeared to be sluggish with the pen near 1.00. Part of the difficulty

encountered during calibration may be from such a source. Sometimes slight tapping of the case will cause a shift in reading. This was noted at the beginning of the tests, and was quite marked during

the test with mixture 9, (0.9666) . After the displacements mentioned

in section IV, 3 (c), the pen was allowed to approach the equilibrium

reading from both directions. The readings as a result of approach

from above were consistent, as were those resulting from approach

from below, but the two sets were about 0.003 apart.

The bearings had been cleaned and oiled, as recommended in the

instructions, before calibration about 6y2 months before. During

this period the case was kept closed, and there was no indication of

dust or dirt inside the case. The constancy of volume of the rubber tubing connecting the parts

of the compensator is doubtful, and the constancy of the forces which

the tube exerts on the beam when in the same place at different times

is even more doubtful. The magnitude of the possible error from

these effects was not determined.

(h) COMMENTS ON OPERATION AND SOME SUGGESTIONS FOR IMPROVEMENT

The instrument appears to have been well designed and constructed,

and the following suggestions made to the manufacturer are in the

nature of refinements. Some of them pertain to convenience in cali- bration and adjustment, which is likely to be relatively infrequent, and

in practice may not be worth the trouble involved in incorporating

them in the instrument.

1. Comparing the apparent effects of the rubber tubing connecting

the compensator gage to the moving parts on the beam, it is sug- gested that, instead of the tube projecting from the side of the pendulum rod below the line of the knife edges, the pivot bearing of the

pendulum assembly be used as the tube. The yoke in the cross member of the beam could be extended, the pendulum bearing could pass

through a web across the center of the yoke, and the rubber tube could

be placed in the line of the bearings so that no lateral flexing or

stretching of the tubing would occur as the beam moves. This might

eliminate some of the sluggishness of the action and some uncertainty

as to reproducibility.

2. It is suggested that greater care in drilling and tapping the

pendulum weight might eliminate the eccentricity that has proved

troublesome in the present instrument.

3. The chart paper fits the short cylindrical hub rather snugly, so that the paper must be stretched slightly, and there is a possibility

of introducing a slight eccentricity in the position of the chart. It is suggested that the hub be tapered slightly, so that the paper can be

started easily and stretching minimized and distributed uniformly.
76 Miscellaneous Publications, National Bureau of Standards

4. It might be advantageous to provide for some more definite inter- change of air between the inside and outside of the instrument case, so that the composition and temperature of the air surrounding the

float will follow more closely that of the room. In some locations,

however, where changes may be rapid and considerable, louvres near

top and bottom of the case might not be an advantage.

5. A gage outside the seal cup, marked so that the level of the seal

oil could be easily observed and adjusted to the mark might be helpful.

6. To avoid inadvertent movements of the knife edges while adjusting weights during calibration, some means of locking the beam or

lifting it from the bearings might be an advantage.

7. If checking the calibration or adjustment of the weights is at all frequent, it would be helpful to substitute for the lock nuts some means

of holding the weights against inadvertent movement, but which

would permit them to be moved when desired. An index to indicate

in which direction and how much a weight had been moved would

also be helpful.

8. If checking the position of the pendulum rod or changes of range

is at all frequent, a point on the lower end of the pendulum rod, and

a corresponding reference point mounted vertically below the knife

edge on the back of the case would be helpful in setting the pendulum

rod in a vertical position while the beam is clamped with the pen at the desired reading.

4. ANUBIS RECORDING GAS GRAVITOMETER

(a) DESCRIPTION

The Anubis recorder (fig. 22), which weighs 41 lb, is adequately

described by the manufacturer in "Care and Operation," Bulletin No.

105, and instructions are given for installation, calibration, maintenance, and care. The instrument consists of a balance beam with arms of equal length,

at the ends of which are suspended two bells in sealing liquid con- tained in two interconnecting tanks. One bell is open to the air through holes in its crown, the other through a "gas column," a verti- cal tube connected to the space under the bell. The mechanism of the

balance is mounted on the column and protected by a wooden case 25 in. high, 18% in. wide and 11 in. deep, with a glass window in the

door. The working force that operates the instrument is the differ- ence in the pressures on the top and on the underside of the crown of

the second bell, and is equal to the difference in weight between a column of gas 6 in. in diameter and about 59 in. high and a column

of the surrounding "reference" air of the same dimensions. This

working force is opposed by a pendulum weight mounted on a horizontal arm (with a bimetallic strip to vary its distance below the

balance beam and compensate the instrument for temperature

changes) and by a difference in buoyant forces equal to the difference

in weight of sealing liquid displaced by the submerged metal of the

two bells. The motion of the beam is transmitted by a connecting

rod to a pen mechanism, and the specific gravity is recorded on a clock-driven circular chart graduated from 0.5 to 1.0 in intervals of

0.01. The first yz meter of the gas column is contained within the

78 Miscellaneous Publications, National Bureau of Standards

case, the upper section is removable and is attached at the top of the

lower section, which projects through the top of the case. At the

top of the gas column is a movable cap by means of which the height

of the column can be adjusted to compensate for changes in the

barometric pressure, or set to the height for the average pressure at the location of the instrument. A scale attached to the cap is marked

to correspond to different barometric pressures, and the adjustment

for each pressure is made by setting the corresponding scale reading

opposite a "barometric index" adjustably attached to the column.

The sensitivity of the instrument and its corresponding "calibration"

depend on the correct setting of the barometric index in relation to the combined effects of the pendulum weight and the buOyance of

the sealing liquid.

The gas sample is admitted to the bell through an orifice at constant pressure. The flow into the apparatus as a whole is approximately controlled by the manual adjustment of a valve, and excess pressure is relieved through a tube dipping into a water seal and vented

outside the balance case. Within the bell, the sample is distributed

through a T-tube and passes out through the gas column at the

rate of about 0.7 cu ft/hr. The bell that is open to the air serves to balance the weight of the working bell and to compensate for surface

tension of the sealing liquid on the working bell.

(b) MODIFICATIONS FOR PURPOSES OF TESTS To avoid contamination of the surrounding air, the gas from the

gas column was collected and discharged from the room by means of

the 6-inch exhaust duct with dampers previously mentioned and an

adjustable sleeve ending a short distance above the gas column. The

dampers were so adjusted that stopping or starting the exhaust fan

produced no change in the indication of the instrument. The dis- charge of the overflow gas from the seal bottle was inside this duct

also. For convenience in reading the temperature of the instrument during operation, a thermocouple was introduced through one of the vents in the back of the case and the junction located near the bimetallic

temperature compensator. The interconnecting tanks were at first filled with kerosine of 0.81 specific gravity. After some preliminary

operation and the tests on mixture 1, it was found that 120 ml of kerosine had evaporated from the tanks in 1 month at a temperature of

about 77° F. A distinct odor of kerosine was noticed whenever the

door of the case was opened. It was felt that contamination of the

reference air and of the flowing sample was probable, and as the tests with mixture 1 showed a small positive residual temperature coefficient, it was considered possible that this resulted from an increased

contamination of the sample with kerosine vapor at the higher temperatures. In addition, the kerosine crept over the surfaces of the

bells and over the rims of the tanks.

To eliminate probable sources of error from such causes, the kerosine was replaced by Markol, which had a vapor pressure of about

0.0001 mm of mercury at 25° C. In addition, it did not creep. Before further testing, however, a representative of the manufacturer stated that the design of the instrument had been based on the
Specific Gravities of Gases 79

use of kerosine of 0.78 specific gravity. Consequently, the Markol

was replaced by Varsol, or Stoddard solvent, another readily available petroleum fraction, which had a specific gravity of 0.78 and a minimum flashpoint of 100° F, as compared with that of 115° F for

the kerosine originally used. Its vapor pressure was probably about

2 to 3 mm at 25° C. Unfortunately, if one chooses a kerosine of a particular specific gravity, the vapor pressure that accompanies it is not subject to choice. They cannot be selected independently. This

material also had a tendency to creep. As the design of the instrument had been based on a specific gravity

of 0.78 for the sealing liquid, Varsol was used throughout the remaining tests. It will be noted, however, that when the determination

of the temperature coefficient was repeated when testing with mixture 2 (after recalibration), the coefficient which remained (after all corrections had been applied) was +0.0004/deg F? while that obtained with mixture 1 and kerosine of 0.81 specific gravity was + 0.0003. The effect of contamination of the sample with kerosine

vapor will be discussed further in the section on Sources of Error.

(c) METHOD OF OPERATION

The directions supplied for the installation and operation of the

instrument were followed, with a few minor modifications and ex- tensions during the testing with nine of the gases of known specific

gravity.

Before admitting the test gases, the instrument was checked with

air according to the instructions, air from the laboratory being drawn

through, with the upper section of gas column removed. During the

air check, as well as the subsequent tests on the standard mixtures,

the portion of the chart at or near the 6-o'clock axis, the direction in

which the chart paper showed the least change of dimensions with

changes of relative humidity was used.

The room was adjusted as nearly as could be to a relative humidity

of 35 percent at a temperature of 77° F for calibration and for each

test with a standard mixture, in order that the chart might have the same dimension from test to test as at calibration.

After the air check, the upper gas column was replaced and the

test mixture introduced. The movable cap of the gas column was

adjusted to bring the pen as near as possible to the specific gravity

of the test mixture (in this case mixture 2, sp gr 0.6820). The cor- rected barometric pressure was then ascertained, and the barometric

index of the gas column set at the point on the cap scale corresponding to this reading.

' Before each test of the instrument with a test gas, the oil level was

checked and adjusted to the proper level. (About 100 ml of Varsol

evaporated per month from the tanks, although gas flowed through

the instrument only about 1 percent of the time. The liquid level

is not of primary importance in this instrument because the two res- ervoirs are connected, and a change of level affects both sides of

the balance alike.) The case was opened to establish equilibrium of

air and chart with room conditions, after which the case was closed,

except for the two vents, which were left open at all times.

719265—47 6
80 Miscellaneous Publications, National Bureau of Standards

Each test of the instrument with a test gas involved purging until

the reading and record had been constant for at least 15 minutes.

The indication and record were then displaced about 0.03 specific gravity unit by placing a small piece of metal on the balance bell, which

lowered it into the oil and raised the working bell an equal distance.

After about 7 minutes the displacement weight was removed and

the immersion of the bells reversed momentarily so that as nearly

as possible the same drainage of oil would occur from both bells. The reading became constant again in about 3 minutes. During the

15-minute test period, a record was made of the chart reading, in- strument temperature, room temperataure, barometric pressure, rel- ative humidity, and dry-bulb temperature, and the time at which the

record was started. During the 7-minute displacement period the

gas-column cap was adjusted to the existing barometric pressure. This procedure was repeated until 10 determinations of the reading

of the instrument on the test gas had been made. The position of the

center of the record line for each reading and for the calibrating set- ting (with mixture 2) was measured with respect to printed lines on

the chart with the aid of an ocular-scale microscope. The 10 values of

specific gravity were then averaged for the test. The temperatures,

barometric pressure, and relative humidity reported with each test are the averages of the values recorded for the 10 determinations.

After the calibration with mixture 2, no further calibrations were made until that on mixture 10, which was made after the range of the

instrument was changed for operation with gases having specific

gravities from 1.0 to 1.5. The change of the range of the instrument from 0.5 to 1.0 to the

range 1.0 to 1.5 was accomplished in the manner indicated in the

instructions. The pendulum clamp screw was loosened, and while the

pendulum was still held vertically by the zero stop the balance beam

was moved until the pen read 0.5 instead of 1.0. Final adjustment was made by means of the sliding weight on the balance beam as in the

case of the previous air checks. Purging with air and the other neces- sary steps incident to the air check were conducted as previously

described. The calibration was attempted with test mixture 10 as described with mixture 2. The instrument could not, however, be brought to the correct reading with mixture 10 (sp gr= 1.0982) . The reading being too high and

the specific gravity greater than 1.0, the reading was decreased by

lowering the gas column cap. At its lowest possible position, the

reading was still too high, probably because in the process of changing

the range (making the pen read 0.5 with air) the working bell had

been brought to its lowest position, thus increasing the length of the

gas column more than it could be shortened by lowering the gas-column

cap.Various considerations connected with the preparation of the test mixtures made necessary their preparation in the order of increasing

specific gravity. Consequently, no mixture of known and higher specific gravity was available for calibration at a point farther from air

before testing with mixtures nearer air. Calibration with mixture 11 (sp gr= 1.2792) was successful and

tests were continued through mixture 13.
Specific Gravities of Gases 81

Corrections were applied in all cases for the effect of relative

humidity on the dimensions of the chart (as described in section III,

2 (e), p. 20) and for the effects of water vapor on the density of the

air of the laboratory, which was considered to be "reference air,"

because the instrument is not tightly inclosed. No corrections were

applied for temperature or pressure because the instrument is designed

to compensate for temperature by the action of the bimetallic element on the height of the center of gravity of the pendulum and for barometric pressure by the setting of the cap at the top of the gas column.

The effect of a change in the amount of carbon dioxide and water

vapor in the laboratory air on the indications of the instrument are exactly the same as in the case of the Ac-Me gravitometer. That is, if the instrument were set to record the true specific gravity, 89 in dry,

carbon dioxide-free air, the equation

£=i?-0.378w + 0.529c

given for the other instrument would apply. (B is the reading in

contaminated air, w is the fraction of water vapor, and c is the fraction

of carbon dioxide by volume in the reference air.) In this case, however, the measurement of specific gravity of the test gas is really

based on the difference between the reading with the test gas and

that with the calibrating gas of known specific gravity. Hence (7, the correction to be applied in this instrument, is given by the equation

0=S-R- (S -B ) = -0.378 (w-w ) +0.529 (c-c ), in which /S is the true specific gravity of the calibration gas, R the

scale reading at the time of calibration, and w and c the fractions

of water vapor and carbon dioxide in reference air at that time.

It was found impracticable, if not impossible, to set the pen exactly

at the specific gravity of the standard gas during calibration. The

position on the chart of the record made by the pen during calibration was measured with the ocular-scale microscope and compared with the

known specific gravity of the calibrating gas to obtain a "calibration

correction", which was thereafter applied to the average of tests with each of the other gases. In the calibration with mixture 2, this

correction was —0.0006.

The corrections for the results obtained with test mixture 2 have

then been combined as follows

Chart correction for departure of relative humidity from

35 percent +0.0001

Calibration correction —.0006 Correction of reference air to 1.10 percent water vapor —.0002 Correction of reference air to 0.1 percent carbon dioxide .0000 Net correction to observed specific gravity —0.0007

Observed specific gravity, mean .6822 Net correction —.0007

Indicated specific gravity 0.6815

Specific gravity of test mixture 2 .6820 Error of instrument —0.0005

Error, percentage of 'standard specific gravity — .07
82 Miscellaneous Publications, National Bureau of Standards

The data have been treated in the same manner in the case of each

of the other test gases which had specific gravities within the range of

the instrument, and a summary of the numerical results is presented

in table 8. The errors of the results "as observed" and after the cor- rections noted above have been applied are plotted for the various test gases in figure 23.

£.005

toz

~

.015

MIXT. NO. SYMBOL COMPOSITION

1 • MFD. GAS

2 A NAT'L

6,7 H«-N2 8 S Ht - COt 9 • NITROGEN

11,12 a N,-COi

13 COt

• t•

a.

! 1

IS

NUMBE RED P0IN7 S IN DICATE. VAL UES AS BSERV ED; UNNUMBERED POINTS, VALUES AFTER CORRECTION

1 111 I I 1 1 1 1 .2 .3 .4 .5 .6 .7 .8 9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 SP GR- OF TEST GAS Figtjke 23.

Error of the Anubis recording gas gravitometer determined with

each test gas. The numbered point of each pair indicates the error as observed and the unnumbered

point the error after the application of all corrections.

(d) SOURCES OF ERROR

(1) Accuracy of Beading.—The position of the record mark on the

chart can be read to 0.01 and estimated to 0.001. A mistake of 0.001

is small as compared with possible errors from some other sources.

(2) Calibration.—Failure to set the pen exactly at the specific

gravity of the known gas by the manipulation of the height of the gas

column will, of course, introduce an error into the record. The set- ting is not an easy one to make because the temperature of the column

is somewhat altered and the "steady state" otherwise somewhat dis- turbed, and the instrument must be left to "settle down" for a con- siderable time before it can be determined how accurately the setting was accomplished.

Any error or uncertainty in the specific gravity of the "known" gas

used to calibrate the instrument will result in error in the record with

gases of unknown specific gravity, and this fact is perhaps the worst

feature of the procedure recommended by the manufacturer of the

instrument. Very few laboratories have or can easily obtain a sufficient quantity of gas of known composition or properties, particularly

within the range of specific gravity 0.5 to 1.0, and probably very few

have facilities for determining the specific gravity of gas with the

accuracy that the excellent qualities of this instrument justify.
/Specific Gravities of Gases

Specific

gravity

Percentage 4

1

+0. 02

-.07 +.80

+1.47 +0. 48 5 : SZZ , 0.

56

1

5 +0.

0001

-.0005 +

.

0048

+.0117 +.

0029 1 ! Ill

+ ; + r r

j

Corrected I

0.

6476

.6815 N III

;

.

9779

1.2800 1.

3909 1.

5163

Chart,

air

for C02

and n

2

0,

calibration

(net)

-0.

0004

-.

0007

-.

0007

-.

0006

-.0009 Mi O 1 O 1 OOO 1 O ' O O O 1 31 O O 1

' '++ |

Reproducibility

Probable

error

of

single

determi- nation ±0.

00041 ±.

00025 ±.

00042 ±.00038 ±.00107 l! III!

-H : -H-H-H

|

±0.00065 J

Probable

error

of

mean ±0.

00013 ±.

00008

±.

00013

±.00012 ±.

00034

±.

00UU9

±.

00016

±.

00055

±.

00024

±0.00020

1I|

+0.08 +.03 +.92

+1.51 +0. 62

+1.

19 +0.06

-.54 0.63

I

+0.

0005 +.

0002 +.0055 +.

0123 +.

0038

+.0115 +.

0008

-.

0076

0109 I

d

If

11! .6062 .8086 .6118

.

9/81 1.

2800 1.

3908 1.

5159

I

mil inn inn

Test

gas

Synthetic

typical

manufactured

gas

Synthetic

typical

natural

gas

-

Helium

a

_

do« do

__

do

Hydrogen-carbon

dioxide..

.

.

_

iNitrogen

__.

.

Nitrogen-carbon

dioxide

b

_

.

....-do

-----

Carbon

dioxide

.

...

_

.

Propane

a

.

.

_

!

i

<

^cncotjoo cor^oooso 1-1 cn co 10
84 Miscellaneous Publications, National Bureau of Standards

The calibration is essentially an adjustment of relation of the height

of the column and the position of the counterweight so that the curve

of displacement with respect to specific gravity will have the correct

slope. As the slope is determined equally by the two fixed points,

any error in the setting of the counterweight to give a zero reading

for air is of as much importance as the column height, and if the

calibrating gas has a density too close to that of air, the errors in

either setting are multiplied for other gases. (3) Effects of Gravitational Forces That Change With the Position

of the Mechanism.—A complete analysis of the moments that tend to

deflect the balance beam involves any unbalance of the pen arm and

its attachments that is transmitted through the connecting rod, the

far from negligible weight of the rod itself, and the forces it produces

at its points of attachment to the beam and the pen arm, and the

force of gravity on the beam itself. The directions and magnitude

of these forces with respect to the axis of the beam are all changing

as the beam is deflected, and to determine their magnitude would re- quire that the balance be taken apart and its parts weighed. It seemed

better, therefore, to measure directly the forces applied to the bells and the deflections they caused than to calculate them, as was done

for the Anubis balance. A hook (made of a large paper clip) was

attached to the metal suspension of one of the bells and balanced by

a similar clip on the other bell. A large number of small paper clips were then weighed individually to 0.1 mg on an analytical balance and

placed one at a time on the improvised support. After each addition

of weight, approximately 15 minutes was allowed to permit the seal- ing fluid to drain and a state steady in other respects to be reached.

The record was read under the microscope as before. Plotting the

reading with respect to the weight added produced very nearly a

straight line. The equations of the straight line and of a curve of the

second degree that best fitted the observations were computed by the

method of least squares and were adjusted slightly to make them coincide exactly at the assumed calibration points of 1.0 and 0.5. (This

would be done in practice with as much accuracy as possible by shift- ing the counterweight and the calibration weight.) The curve of the

second degree, which undoubtedly agreed with the actual observations more accurately than did the straight line, then showed readings at various parts of the range of specific gravities, which were higher

than the straight line by the following amounts

:

Specific gravity Reading from sec- ond-degree curve minus reading

from straight line

sp gr 0. 5

. 6

. 7

. 8

. 9 1.0

0. 00000

. 00082

. 00103

. 00094

. 00017

. 00000
Specific Gravities of Gases 85

These departures from a straight line, the greatest of which is only

one-tenth of a division of the chart, are within the limit of accuracy

with which the chart can ordinarily be read with the unaided eye, and

the movements of the pen can be considered, for most purposes, to be

accurately proportional to the forces applied to the beam.

(4) Gas Column.—The height of the gas column is, of course, the

distance from the top of the working bell to the top of the gas- column cap. (The top of the bell is conical, and the force exerted on it by the inclosed gas is the same as would be exerted on a bell with a flat top located at one-third the distance from the base to the apex of the cone.) When the column cap was adjusted to the

index mark of 30 in. the height of the column was 149.7 cm when

the pen was at the top of its range, and the bell moved 2.35 cm

when the pen traveled across the chart, making the column 152.05

cm long when the bell was at its lowest position. As the working

bell rises when the specific gravity of the gas increases, the height

of the gas column is less than at calibration for gases of greater

specific gravity than that of the gas used for calibration (in case the

calibrating gas is lighter than air) and the reading is too high.

With gases of lower specific gravity than that used for calibration,

the height of the gas column will be greater than at calibration and

the reading will be too low. If the instrument is calibrated with a gas of 0.500 specific gravity (the instructions state that the calibration

should be made with a gas having as low a specific gravity as possible), it is necessary to lower the gas-column cap until the pen reads

0.500, which process brings the total height of the gas column to 152.05 cm (assuming a 30-in. barometer, to indicate that the barometric index is set at 30, the midpoint of the scale, and left there).

If gases of specific gravities 0.6, 0.7, 0.8, and 0.9 were then successively

introduced, the height of the gas column would be progressively decreased by the displacement of the bell, and consequently the dif- ference between the weight of air and gas would be decreased, but

at a different rate than it would if the height of the gas column had

remained constant. The errors have been computed for various specific gravities with an instrument calibrated with gas of specific gravity 0.5 and plotted

as the upper curve of figure 24. Corresponding errors computed in

the same way are shown for calibrations made with gases of other

specific gravities. The minimum error within the range 0.5 to 1.0 would occur if the instrument is calibrated with a gas of specific

gravity about 0.58. Applying the same reasoning to calibrations made for the specific

gravity range 1.0 to 1.5 (with air the position of the pen is made to coincide with the lowest line on the chart by keeping the pendulum

vertical and shifting the beam and counterweight) , it was computed

that after calibration with a gas of specific gravity 1.28, gases of

specific gravities 1.4 and 1.5 would read low by 0.0015 and 0.0034,

respectively. The computation was made for a calibrating gas of

specific gravity 1.28, because that was the gas actually used for the

purpose. The error introduced by the changing height of the column

accounts for about one-third of the observed error in the case of the

other test gases that were heavier than air.
S5 Miscellaneous Publications, National Bureau of Standards

(5) Leveling of instrument.—A change of level of the instrument

has a decided effect on the reading, and there is no provision for

determining when the instrument case is level. The principal effect results from the displacement of the supporting and recording mechanism with respect to the vertical position of the "pendulum. This

effect is partially counteracted by the flow of oil from one seal pot to the other. The magnitude of the resultant effect was computed and

checked experimentally by slipping a 1-mm shim under one edge of

the balance case. This change of level (through an angle of about

7") resulted in an apparent change of specific gravity of about 0.02,

which was in good agreement with the calculated value. Probably

the manufacturer intended that the effect of placing the instrument on a support not exactly level should be compensated for in the cali- bration, along with other effects. But without specifying the support, which may be subject to settling, warping, etc, no one can an-

+ .004| 1 1 1

1

1

1

1 1 1 1 1—^-| 1 1 .003

.5 .6 7 .8 .9 10 I.I I 2 SP GRAVITY OF GAS Figure 24.

Computed errors of the Anubis recording gas gravitometer resulting

from changes in the height of the gas column which accompany deflection. Numbers on the curves indicate the specific gravity of the gas used for calibration. ticipate the changes that may take place in its level after the instrument is calibrated. One should not have to make another calibration

to check the level. (6) Weight of Ink in Pen.—When the reading was approximately

1.0, the ink was removed nearly completely from the pen with the

aid of a narrow strip of blotting paper, and the chart was turned

under the pen to make a record. The pen was then filled normally

with ink and the paper turned in the opposite direction. The distance

between the two records was then measured with the aid of the microscope and found to correspond to a difference of 0.004 specific gravity.

The same gas in the upper part of the recorder range may, therefore,

show differences as great as this at different times, depending on the

amount of ink in the pen. In all tests not involving the study of this

point, the pen was carefully filled to the same extent as nearly as prac-
Specific Gravities of Gases 87

ticable before a critical reading was taken. In spite of this precaution, the amount of ink in the pen may have been one of the factors

that caused variations not otherwise accounted for, and it must cer- tainly appreciably affect readings in practice.

(7) Temperature Coefficient.—The specific gravity indicated by

the instrument after calibration and operation by the methods pre- viously described should be independent of the temperature of the

instrument if the means provided for temperature compensation is satisfactory. A test, consisting of 10 determinations of the specific

gravity reading with a single test gas (mixture 2) was made as described in the method of operation at each of the temperatures 67.7°,

78.5°, 79.1°, 80.1°, and 92.9° F. Three of these tests were made at substantially constant water content of the reference air (average 1.15 percent, equivalent to 36.5-per- cent relative humidity at 77° F) , and three were made at substantially

80 90 TEMPERATURE Figure 25.

Temperature coefficients of the Anubis recording gas gravitometer

determined, with test mixture 2, as observed (-O- at constant percentage of water vapor in the reference air (1.15 percent) ; Oat constant relative humidity

of the reference air (36.9 percent) ), and • after the application of all corrections. constant relative humidity (average 36.9 percent). The observed

results have all been corrected for the departure of the chart paper

from 35.0-percent relative humidity, for the calibration error, and to

1.1 percent of water vapor and 0.1 percent of carbon dioxide in the

reference air. The results as observed and after the above corrections

have been applied, have been plotted against temperature in figure

25. A straight (broken) line determined by the method of least squares has been passed through the five points as observed, and an- other (solid) line through the five points obtained after having been

brought to the same basis by application of the above corrections.

The slopes of these lines, constituting the temperature coefficients, are indicated thereon. The radius of the circle around each of the ob-
88 Miscellaneous Publications, National Bureau of Standards

served points is equal to the probable error of the mean of the 10 determinations that point represents.

It may be noted that the circles are small as compared with the dif- ferences that appear between tests on successive days at nearly the same

temperature. Even when all the corrections that have been evaluated

have been applied, the difference in one case is still 0.003, and a large

positive temperature coefficient still remains.

The sealing liquid, of 0.78 specific gravity, had been under suspicion on account of its rapid rate of evaporation. Consequently, approximate values of 4.4 and 5.9 mm for its vapor pressure at 77° and 90° F,

respectively, were derived from correlations of its properties. An

approximate molecular weight of 138, derived similarly, gave for its vapor a specific gravity of 4.76. These vapor pressures are about onesixth those of water, and assuming that the sample is saturated with

the vapor, it would contain 0.58 percent of the vapor at 77° F and 0.78 percent at 90° F. The test gas, 0.6820 specific gravity, mixed with

0.58 percent of solvent vapor, 4.76 specific gravity, then had a specific

gravity of 0.7056, which was made to read 0.6820 by the method of

calibration described. At 90° F, the specific gravity of the mixture

of test gas and 0.78 percent of vapor was 0.7138, or 0.0082 higher than

at 77°. If at 90° F the correction of -0.0082 is subtracted from the

position of the solid line, while it remains in the same place at its calibration temperature of 77° F, the line representing the positive

temperature coefficient is rotated through zero to a negative slope.

Although the values derived in the above computations are obviously rough approximations, it is seen that the degree of contamination of the sample arrived at by this means is ample to account

for the large temperature coefficient. Even though the mechanical

compensation for temperature changes were perfect, such a residua]

temperature coefficient could result from the use of a sealing liquid

with a vapor pressure as high as that of Varsol or Stoddard solvent

(sp gr 0.78). The kerosine (sp gr 0.81) originally used would have

been preferable to the Varsol had it been a nearly pure compound,

which it probably was not. The Markol (sp gr 0.846) had a vapor

pressure of approximately 0.0001 mm of mercury at 25° C, which is too low to affect the fourth decimal place in the specific gravity of

the sample at any temperature encountered in a laboratory.

The fact that the solvent vapor is more than sufficient to account

for the residual temperature coefficient may be explained either on

the basis of uncertainties in estimating its vapor pressure or on lack

of complete saturation of the test gas with the vapor or partial saturation of the reference air inside the case, or a combination of all three

effects. (8) Temperature Lag.—When the temperature of the air surrounding the instrument was changed at a rate between 5 and 10° F/hr, the

temperature at a point near the bimetallic compensator lagged behind the room temperature by nearly 2 deg F. This caused errors of compensation, as well as errors resulting from corresponding differences between the temperature of the gas inside the bell and gas

column and the air inside the case and surrounding the gas column

outside. The net effect was that with rising temperature the readings
Specific Gravities of Gases 89

rose as much as 0.014 above the reading at constant temperature, and

with falling temperature fell as much as 0.008 below.

(9) Properties and Changes of the Sealing Oil.—The properties of

the liquid used for sealing the bells are of great importance. The

> liquid must be able to "wet" the surface of the metal with certainty

and uniformity to prevent irregular errors as the result of surface

tension, but it is possible for the oil to be too "good" in this respect.

The kerosine in the tanks tends to creep over the surface of the bells and dust may collect on their tops. This can be a source of error only if the weight of the kerosine and dust is greater on one bell than

on the other. The equality of dimensions of the two bells reduces to a minimum the probability of significant error from this source but does

not eliminate it entirely. The oil should have a low viscosity in order

that it may drain promptly from the bell that is raised partly out of

the liquid by any change of specific gravity.

Kerosine of specific gravity 0.78, recommended by the manufacturer, is almost ideal in respect to the properties mentioned. However, a petroleum oil of so low a specific gravity usually has a high

vapor pressure and produces a high temperature coefficient, as al- ready described. In addition, a commercial kerosine is never a pure

compound and its composition and properties, including vapor pressure, change as the liquid evaporates.

The liquid exerts a buoyant force on each of the bells equal to the

product of the volume of submerged metal and the specific gravity

of the oil. When the specific gravity changes from 0.5 to 1.0, the

measuring bell rises 2.35 cm and the other falls a like amount. The

thickness of the metal of the bells is about 0.25 mm and their diameter 15 cm. The buoyant force (in grams) on each bell then changes

about

0.025 X 2.35 X15ttX^= 3d grams,

where d is the density of the oil. As there are two bells and their

buoyancies change in opposite directions, the net effect is equal to

a change of load produced by the gas column of about 6d g. If the

specific gravity of the oil does, not change, these buoyant forces are among the several that are taken into account by the calibration,

and therefore introduce no error. At the specific gravity of the gas

at which the buoyant forces are equal, that is, when the beam is level, their equality is not affected by a change of specific gravity of

the oil. But in other positions an error is introduced which is equal

to about

where S is the specific gravity of the gas, Si is the specific gravity at which the bells are equally submerged, and d and dx are, respectively,

the specific gravities of the liquid when the measurement and the

calibration are made. In this instrument, when calibrated for the

range of specific gravities 0.5 to 1.0, Sx is about 0.625. Assume, for

example, that the specific gravity of the liquid at the time of calibra-
90 Miscellaneous Publications, National Bureau of Standards

tion was 0.78 and that later it was 0.80. Then, with a gas of specific

gravity 0.80, the instrument would read low by about

0.15(0.80-0.625)(0.78-0.80) =0.0005.

This error is in addition to that caused by the effect of the changing

content of vapor on the actual specific gravity of the gas in the

column.

If kerosines possessing such characteristics as two samples tested

at this Bureau for purchase by the Government are used in the

instrument, they will gradually fractionate (more completely even than at higher temperature), and as the residue is replenished from

time to" time but never drained, the vapor pressure will fluctuate but

gradually become less. Differences between the vapor pressure at the time of calibration and later use may easily reach 0.0025 atm if a commercial kerosine is used as a sealing liquid. For the purpose

of computing the approximate errors that may result from fractional

distillation of the sealing oil, it was assumed that the average of

these two kerosines was used in the instrument. It was also assumed,

for the purpose of computing the changes in properties which ac- company the change in boiling point, that the oil consisted of a mixture of 67 mole percent of naphthene hydrocarbons and 33 mole

percent of paraffin hydrocarbons and that all properties follow the

"law of mixtures." Data for the properties of the hydrocarbons were taken from the monograph of the American Chemical Society on this subject. The data derived from these assumptions are stated

in table 9. Table 9.

Properties of kerosine assumed to be used as a sealing oil

Beginning of vaporization

10 percent evaporated

50 percent evaporated

Boiling point ... _ . C__

Specific gravity. . — . . 16977^3

139

0. 0035

4. 83

199.5 78.5

154

0. 0014

5. 34

223.5

79.6

175

0. 0007

5. 97

Molecular weight . . . . . .....

Vapor pressure at 25° C ... . atm..

Specific gravity of vapor. _ . . .... .. True specific gravity of gas Specific gravity of saturated gas

0.50 0. 5152

1.0134

1. 5117

0. 5061

1. 0053

1. 5046

0. 5038

1. 0034

1. 5031

1.00

1.50

0.50 .

Error caused by change of vapor pressure of sealing fluid

0. 0000

.0000 .0000

0. 0091

.0081 .0061

0. 0114

.0100

.0086

1.00 j 1.50The errors listed in the table are derived from the assumption that

the calibration will make the reading exactly right at the time the

sealing liquid is first added. Subsequent readings will be too low

by the amounts indicated.

(10) Humidity Coefficient.—In order to determine experimentally

the effect on the indicated reading of variations in the water content
Specific Gravities of Gases 91

of the surrounding air, a test consistng of 10 readings of the specific

gravity of the same gas was made in the manner previously described,

with the water content of the reference air at 2.78 percent in addition

to two tests at 1.15 and 1.19 percent, which correspond nearly to

35.0 percent relative humidity at 77° F, the conditions chosen as "normal" for the purposes of these tests. During these tests the instrument was maintained as near as possible to the same temperature. The average temperature was 79.2° F, and temperatures during individual tests differed from this by

0.9 deg F or less. The results, as observed and after all the corrections had been

applied, have been plotted against "percentage of water in reference

air" in figure 26. Straight lines, determined by the method of least squares have been passed through the three points, and the slopes

68

io AS OBSERVED

II* ALL CORRECTIONS

VARIABLES % H20, %REL HUMID CONSTANT

TEMP (79.2°F)

TEST MIXT URE— ^ ooo\e

" 0.5 1.0 1.5 2.0 2.5 30

VOL. % H 2 IN REFERENCE AIR Figure 26.

Humidity coefficient of the Anubis recording gas gravitometer deter- mined at constant temperature (79.2° F) with test mixture 2; O as observed and • after the application of all corrections. of the lines, constituting the humidity (or percentage of HX>) coeffi- cients, are indicated thereon.

It may be noted that although the effect of variations in the per- centage of water in the air has been reduced to about 37 percent of

the original effect by applying all the corrections, the coefficient has

not been reduced to zero as it should have been.

The correction for the 1.68 percent of water vapor in excess of

the 1.1 percent present at calibration amounts to —0.0064, which is 70 percent of the entire coefficient as observed. The residual coeffi- cient which is still to be accounted for is equivalent to an error of

0.90 percent of water vapor. The uncertainty in the observations of

relative humidity is sufficient to account for only about 0.04 percent

of water, or 4.4 percent of this amount. However, if one admits the

possibility of an uncertainty in the individual tests amounting to

0.003, as is indicated by the solid points used to determine the tern-
92 Miscellaneous Publications, National Bureau of Standards

perature coefficient, this would suffice to bring all the points to a horizontal line. Since any known dependence on water vapor has been

eliminated by the application of the corrections, it must be concluded

that such an uncertainty actually exists.

( 11 ) Effect of Relative Humidity on Chart.—Tests of the paper used on this instrument show that a change of 80 percent in the relative

humidity changes by 0.60 percent the dimension of the paper in the

6-o'clock axis and by the 1.43 percent in the 12-o'clock axis. Headings of the instrument are subject to correction on account of this

effect under all conditions except that in which the instrument is cal- ibrated, and the record made with the chart exposed to air of the same relative humidity as that existing at the time the chart was

printed.

At any other relative humidity, the circles on the chart are no longer

circles and their radii are different. A relative humidity change of

47.4 percent (which is not excessive) from that at calibration resulted

in a correction of 0.0012 on the 6-o'clock axis with test mixture 2 (sp gr

0.6320). A correction of approximately 0.0028 on the 12-o'clock axis

would have been required with an additional uncertainty in the reading unless it were known that the relative humidity at calibration was

the same as that at printing.

(12) Barometric Pressure.—If the calibration is done according to the manufacturer's instructions, the reading is correct at the barometric pressure assumed (when the calibration was made) to be aver- age for the testing station. The reading at any other pressure is in

error by an amount that is proportional to the calibrating pressure,

to the difference between the actual pressure and the assumed average,

and to the difference between the specific gravity of the gas and that of

air. That is,R-S=BX (B-B,) (l-£)=(|--l)(l-£),

where R is the reading of the instrument ; S is the true specific gravity

of the gas ; B is the barometric pressure at the time the reading is made,

and Bt is the barometric pressure at which the correct specific gravity

would be recorded. However, a correct reading of specific gravity can

be obtained by shifting the cap from the position representing the

average barometric pressure to a position representing the actual pres- sure at the moment. The cap was shifted in this way when making

tests with the various standard gas mixtures.

(13) Reference Air.—Uncertainties as to the composition of the

surrounding air, used as a standard of reference, caused by contamination from various sources, will cause errors in the specific gravity indicated by the instrument. Leaks of gas from points within the instrument case, especially from loose joints in the stopper of the seal bottle or rubber-tube connections, cracked rubber tubing, permeability of even good rubber to some gases, diffusion through the liquid in the seal tanks, etc., may contaminate that portion of the reference air that is inside the case. Lack of adequate disposition of the gas flowing from

the seahbottle vent and from the top of the gas column, may cause contamination of the reference air outside the case. Such contamination by the sample will result in an indicated specific gravity that is
Specific Gravities of Gases 93

nearer 1.000 than it should be, giving a high reading for gases having a

specific gravity lower than air and a low reading for gases having a

specific gravity higher than air. The vapor of the liquid in the seal tanks will contaminate the refer

1 ence air inside the case to an extent, depending on the degree of ventilation of the case. The effect of such vapors has just been discussed in

connection with the contamination of the gas sample. In the case of

the reference air, the effect will be to give an indicated specific gravity

that is too low. The magnitude of the effect will be much more variable

in this case because of the variability of concentration of the vapor as

a result of variations in ventilation, principally perhaps from opening

the door of the case. The effects of water vapor.and carbon dioxide have been discussed

in section III 1 (a) and IV 4 (d) (10). Variations of relative humidity from 10 to 70 percent in the same place at different times of

year are easily possible. At a temperature of 77° F this range corre- sponds to a range of water-vapor concentration of from 0.3 to 2.2 percent. Even if the calibration were made with the water content

of the air in the middle of this range, the uncorrected reading could

be in error by as much as ±0.0036 as a result of variations up to 0.95 percent of water vapor from the mean value of 1.25 percent. The

effects of carbon dioxide are produced only by variations of the carbon

dioxide content of the air from that existing at the time of calibration,

and will be negligible except for unusual changes in ventilation or occupancy of the room, or the operation of burners.

(e) COMMENTS ON OPERATION AND SUGGESTIONS FOR IMPROVEMENT

It was found that this instrument could be dismantled to the extent of lifting the bells from the oil and the beam from its bearings and

reassembled without readjustment and without change of reading.

This fact and the quick and accurate response of the instrument to mechanical loading shows that the action of the instrument as a balance is remarkably free from mechanical trouble. Inaccuracies

must arise almost wholly from conditions (of which the vapor of the

sealing liquid is an outstanding example) that affect the loads that

the gravitometer, as a balance, has to weigh.

Such an instrument deserves much more careful consideration in

the matter of calibration and sealing liquid than was provided for in

the recommendation of the manufacturer. The major changes needed,

therefore, had to do with the manufacturer's provisions for these two

most important items, and not with the construction of the balance

itself.

1. Instead of vaguely specifying (by density only) an extremely

variable commercial product as the sealing liquid, the manufacturer

should purchase and supply with the instrument a sealing fluid of

satisfactorily low vapor pressure and viscosity. This should be a nearly pure compound, so that its properties do not change appreciably.

An oil such as that sold under the name Markol (specific gravity

0.846) has a negligible vapor pressure and appears to be suitable in

other respects.

2. Instead of leaving the fundamental relation of column height

and the position of the center of gravity of the instrument to determi-
94 Miscellaneous Publications, National Bureau of Standards

nation by the user by a difficult and uncertain method as is done at present, the manufacturer should take the full responsibility for this

and should fix the index by which the column height is judged. Then

the cap can be graduated and numbered so that the reading of the

index will be 30 when the height is actually 30 in. ; then other graduations should be made and marked as a reciprocal scale. Then the user will simply set the cap to the mark reading his average barometer.

Checking of the calibration can be done, with much greater accuracy

than by the present method, with no trouble, and without the need

of using a gas of known specific gravity by adding a weight supplied

by the manufacturer to one side of the balance following an air check.

This check will not involve the height of the gas column. The weight

can be made conveniently in the form of a thumbscrew to be inserted

into a threaded hole in the strip by which the bell is suspended, and

adjusted in the company's laboratory with the aid of an analytical

balance.

3. The range of the instrument can be changed with accuracy and

ease by the same method, that is, by adding to one side or the other

of the balance a predetermined weight after shifting the position of

the beam. Again the thumbscrew in the suspension strip is suggested. This would probably be preferable to a shifting of the counterweight, as at present practiced.

4. If the final setting of the pen on 1.000 with air is to be left to the user, as it probably should be, a more accurate means than the

sliding of the counterweight should be provided. It is difficult to move this heavy weight by the necessary small amounts. A fine adjustment in the form of a screw entering the end of the counterweight,

which would probably be differently shaped than at present, would

be satisfactory and would involve a minimum of change in the present

instrument. A sleeve nut threaded directly on the balance beam, to- gether with a fixed counterweight providing most of the compensation

for the pen-arm connections might be equally satisfactory.

5. A simple means of correcting for the effect, on the chart, of

relative humidity changes that occur subsequent to calibration would

be to mount a fixed pen, adjusted to read 1.000 on the chart (or to fol- low a line outside the regular chart by perhaps the same space as that between lines of the chart) at the time of calibration and left there until the next calibration. The readings could then be corrected

by the amount of the departure of the record of this pen from 1.000,

multiplied by the proportionate distance of the reading of the movable

pen from the center of the chart.

6. Leaks inside the balance case from the seal bottle and its connections might be made less likely by using a bottle with a metal

screw cap and gasket. The metal tubes could then be soldered through

the cap and the rubber tubing replaced by metal tubing.

7. It has been suggested that the instrument might be made in- dependent of changes of the water vapor and carbon dioxide content of the surrounding air, which occur subsequent to calibration, by

closing the balance bell and fitting it with a reference air column opening through a replaceable cartridge containing Ascarite and calcium

chloride. The column could be purged at calibration and maintain
Specific Gravities of Gases 95

a standard of reference that would be dry and free from carbon

dioxide.

8. A humidity-correction chart could be supplied with the instrument for the use of those interested in momentary readings. Automatic correction for humidity does not appear practicable except

by the means suggested in the preceding paragraph.

9. It would be worthwhile to attach a spirit level or at least a plumb

bob to the column inside the case to make it possible to level the bal- ance easily and accurately.

10. The wooden case has shown some signs of warping and loosening at the joints at the bottom. It might be desirable to use a metal

case with louvres for ventilation. A metal case would provide better

conduction of heat and consequently reduce differences in temperature between inside and outside that occur during changes of the temperature of the surroundings.

5. SIGMA RECORDER NO. 7 FOR SPECIFIC GRAVITY

(a) DESCRIPTION

The Sigma recorder (fig. 27) is approximately 14 in. wide, 13y2 in. deep, and 19 in. high. The burner at the top of the gas column is 6 ft 7y2

in. above the table. The entire instrument weighs 68 lb. This instrument (described very briefly in the three pages of

description and instructions which accompany it) is nonportable and

consists of a heavy cast-iron reservoir and a housing, mounted on four

short legs. In the reservoir, filled with mineral seal oil, a bell float 10

in. in diameter and about 2 in. high is suspended from one end of a balance beam by a link passing through the cover. The bell is counterbalanced by an adjustable weight at the other end of the

beam. The clock, chart mechanism, pen linkage, and bell float for

compensating for temperature and pressure are mounted inside a

cast-iron housing that forms a part of the cover of the reservoir. An

air reservoir for the compensating device is mounted outside on the

back of the housing and connects with the compensator bell float inside. The large bell float is connected by a magnifying lever linkage to a cam, marked with the gas volume factors from 0.90 to 1.10 in the

intervals of 0.01. The cam follower magnifies and transmits the

motion of the bell to the pen arm, and the position of the rider on

the cam is adjusted automatically through linkages, by the motion

of the compensator bell float, which rises and falls as the air in the

compensating air reservoir expands or contracts with changes of

atmospheric temperature and pressure. The sample is introduced

under the 10-in. bell float through a valve, and passes out through the

gas column, where according to directions, it is to be disposed of by

burning. A rubber hose connects the bell float to a burner, the port

of which is adjusted to be 6 ft above the top of the bell. The burner

and its connections thus comprise a pressure column similar to that

of the Anubis gravitometer, and the force which actuates the instrument is equal to the buoyancy of a column of gas 6 ft high and 10 in. 719265—47 7
96 Miscellaneous Publications, National Bureau of Standards

in diameter. The burner is shielded to prevent extinction by drafts. The chart is calibrated in specific gravity from 0.40 to 0.65 in intervals of 0.01, which are five-thirty-seconds in. wide, permitting visual

estimation of the reading to 0.001 or a little better. The 14-day chart

Figure 27.Sigma recorder No. 7 for specific gravity.

is driven at the rate of y2 in./hr by a 14-day clock and is marked at hourly intervals.

The range of specific gravities over which the instrument operates,

although adequate for an English gas works, is too narrow to find

wide application among the diverse gases of the United States.
Specific Gravities of Gases 97

(b) MODIFICATIONS FOR TESTING

The burner, instead of being fastened to a wall, was mounted on a clamp sliding on a rod. A collar was adjusted on the rod under the

clamp so that the burner .was located at the specified height shown in

the blueprint. This permitted the determination of the effect of the

flame in terms of height of gas column.

A hood, consisting of 6-in. galvanized iron smoke pipe, was mounted

over the burner and connected to the exhaust fan. An adjustable

sleeve over the burner and dampers were provided so that the dis- charged gases could be removed from the room without affecting the

indication of the instrument. This permitted operation of the instrument with or without a flame on the burner and prevented contamination of the air of the room (which was used as a reference) with

products of combustion or unburned or noncombustible gases.

(c) METHOD OF OPERATION

The directions supplied for the installation and operation of the

instrument were followed, with a few minor modifications and extensions, during the testing with four of the gases of known specific

gravity.

According to the directions, the large reservoir was to be filled with

an oil of "low viscosity." "Paraffin" was said to be suitable, but

should it evaporate, "a very thin oil'" was to be used. "Spindle oil" and "gas oil" were said to be suitable. The small compensator reser- voir was to be filled with "spindle oil or common machine oil." Kerosine of specific gravity 0.81 first was used, but this evaporated

and crept over the rim of the small reservoir and over the adjacent

movable parts. Its level was difficult to maintain, its vapor probably

contaminated the gas sample, and the creeping liquid may have af- fected the reading of the instrument. It was therefore replaced in

both reservoirs with Markol (sp gr 0.846 and viscosity 0.245 poise

at 25° C). as was done in other cases previously mentioned.

Before admitting the test gases to the instrument it was calibrated

according to the instructions. The burner having been set at the

specified height, the instrument was purged with air from the laboratory (adjusted to 35-percent relative humidity) by drawing it clown

through the gas column, through the bell, and out through the inlet valve. The compensator air reservoir was opened to the air and the cam follower raised until it was above the 1.00 mark on the cam, and

the valve closed. By cracking the valve, air was allowed to escape

until the cam follower read 1.000; then the valve was closed tightly.

The cover disk over the large bell was removed, and the test weight

placed on the pin. The flow of purge air was stopped, the chart

adjusted with the left edge touching its guide, and the pen made to read 0.500 on the chart by adjusting the counterweight on the balance

beam. The test weight was then removed from the large bell and the

small cover disk replaced. The temperature of the instrument was

determined by means of a thermocouple located near the compensating

air reservoir, and the barometer was read and corrected. The gas- volume factor, representing the volume at the measured temperature

and pressure of a unit volume at 60° F and 30 in., was determined

from a table or computed by means of the gas laws. The valve to
98 Miscellaneous Publications, National Bureau of Standards

the compensating air reservoir was again opened and the cam fol- lower raised somewhat above the reading desired, the reading of the

follower on the cam adjusted to the gas volume factor just computed

by allowing air to escape as before, and the valve was again tightly

closed. Before each test of the instrument with a test gas the oil levels were

checked, and if necessary adjusted, the temperature and pressure were

determined, the correct gas volume factor computed, and if necessary

the cam follower was reset to that reading on the cam, and the reading

of the cam follower recorded before and after readjustment, as a test of the ability of the compensating mechanism to maintain a correct reading. The test gas was then admitted at a rate of 0.33 cu ft/hr,

resulting in a velocity of flow from the burner of 0.5 in./sec, and a flame about % in. high. (This rate had been determined by trial to be about that at which the indication of the instrument was least affected by small changes of rate of flow. The directions state : "The

smaller the flame at the burner, the more accurate will the reading

be, as a large flame causes a suction at the outlet of the burner which

will suck the bell down and give a reading of specific gravity which

is too low." Accordingly, the instrument was tested with no flame on the burner, but the effect of the flame was determined and will be

discussed under sources of error.)

Each test of the instrument with a test gas involved purging the

instrument until the reading and record had been constant for approximately 15 minutes. The indication and record were then displaced

by placing a wire rider over the counterweight, moving the pen by

about 0.04 specific gravity. This displacement raised the bell out of

the oil slightly, so that when the rider was removed after about

5 minutes, the bell returned to its former position in the oil, and no

drainage of oil from the bell interfered with the prompt resumption

of the equilibrium of the parts. While making the 15-minute record,

the chart reading, instrument temperature, room temperature, barometric pressure, relative humidity, and dry-bulb temperature, and the

time at which the record was started were all noted. After the dis- placement period of 5 minutes, another 15-minute record was made

as before, until 10 determinations of the reading of the instrument on

the test gas had been made.

The reading on the chart of the center of each of the 10 record lines was then determined with an ocular-scale microscope. These 10

values of specific gravity were averaged for the test. The temperatures, barometric pressure, and relative humidity reported with each

test are the averages of the values recorded for the 10 determinations.

(d) CORRECTION FOR COMPOSITION OF REFERENCE AIR The air surrounding the balance is again the reference air, and its composition affects the reading of the instrument to the same extent

as the reference air in the Ac-Me and Anubis recorders, that is, the

equation

#=i?-0.378w+0.529c

again applies, S being the true specific gravity, R the reading of the

instrument, and w and c, respectively, the fractions of water vapor

and carbon dioxide in the air.
Specific Gravities of Gases 99

(e) CORRECTION FOR EFFECT OF HUMIDITY ON CHART

In the case of the paper used on this instrument, tests indicated that

a change of 80 percent in the relative humidity changes any horizontal

dimension by 1.66 percent, or, for a change of each 1.0 percent in rela- tive humidity, the paper changes its horizontal dimension by 0.021

percent.

The record is made on a continuous strip of paper between guides

that are too far apart to prevent all lateral movement. If the specific

gravity indicated happened to be near one side of the paper and the

fixed chart guide on the other side, and if the relative humidity

changed by 30 percent, as it might from day to day, it would be possible

to have a difference from this cause as large as 0.0017. The mean of the 10 determinations constituting a test has in each

case been corrected to obtain the reading that would have been indicated had the relative humidity been exactly 35.0 percent, by the

method employed for other charts. (See section III, 2 (e).) The

only difference is that the distance from a fixed point to the recorded

line is measured from the guided edge instead of from a center. Summarizing the observations and corrections of mixture 5

Correction for effect on chart of departure of relative humidity from 35 percent +0. 0001

Correction for effect of water vapor in air on buoyancy —. 0039

Correction for effect of carbon dioxide in air on buoy- ancy +. 0005 Net correction —0. 0033 "Observed" specific gravity, mean . 4437

Indicated specific gravity 0. 4404

Specific gravity of test mixture 5 . 4222 Error of instrument +0. 0182 Error of instrument, percentage of standard specific gravity 4. 31 The data have been treated in the same manner in the case of the

other test gases whose specific gravity was within the range of the

instrument, and a summary of the numerical results is presented in

table 10. The errors of the results "as observed" and after the corrections noted above have been applied are plotted in figure 28.

(f) TEMPERATURE COEFFICIENT

A test consisting of 10 determinations of the specific-gravity reading with a single test gas (mixture 2) was made as described in the

method of operation at each of the temperatures 66.9°, 77.5°, 78.8°,

79.8°, and 92.6° F to determine whether the temperature and pressure

compensator operates satisfactorily.

Three of these tests were made at substantially constant water content of the reference air (average 1.15 percent, equivalent to 36.5 percent relative humidity at 77° F) and three were made at substantially constant relative humidity (average 36.9 percent). The observed results have all been corrected for the departure of the chart

paper from 35-percent relative humidity and to dry carbon dioxidefree reference air. The results as observed and after all corrections
100 Miscellaneous Publications, National Bureau of Standards

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Specific Gravities of Gases 101

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MIXT NO. SYMBOL COMPOSITION 5ond6 • He — N 2 8 S H2 — C02 NUMBERED POINTS INDICATE VALUES AS OBSERVED; UNNUMBERED POINTS, VALUES AFTER CORRECTION

6

asB

.5 .6 7 .8 .9 1.0 SP GR OF TEST GASI.I 1.2 1.5 Figure 28.

Error of the Sigma recorder No. 7 determined with each test gas. The numbered point of each pair indicates the error as observed, and the un- numbered point, the error after the application of all corrections.

I-o- AS OBSERVED 3» ALL CORRECTIONS

VARIABLES TEMP, REL. HUMID. % H2

CONSTANT % H2 IN AIR (1.15%) REL HUMID (36.9%) %—-V^ H -0.0000194 PER 3

F. V

s —1

v . 50 60 70 80 90 1 00 HO INSTRUMENT TEMPERATURE °F Figure 29.

Temperature coefficients of the Sigma recorder No. 7 determined

with test mixture 2, as observed ( -r> at constant percentage of water vapor

in the reefrence air (1.15 percent) ; q at constant relative humidity of tlie reference air {36.9 percent)), and • after the application of all corrections.
102 Miscellaneous Publications, National Bureau of Standards were applied have been plotted against temperature in figure 29. A

straight line, determined by the method of least squares, has been

passed through the three points of each of the two groups mentioned

above and another through all five points after they have been

brought to a common basis by the application of the corrections dis- cussed above. The slopes of these lines, constituting the temperature

coefficients, are indicated thereon.

The radius of the circle around each observed point is equal to the

probable error of the mean of the 10 determinations that point represents. It may be noted that the circles are small as compared with the dif- ferences that appear between tests on successive days under nearly

the same conditions. Even when all the corrections that have been

evaluated have been applied, the differences are still very large and a large negative temperature coefficient still remains.

The variations may in part be caused by failure to reproduce exactly

the rate of flow of the test gas and consequently the size of the flame on the burner. These had been adjusted to a minimum at the outset,

when it had been determined that extinguishing the flame could be

compensated by raising the burner 80 mm higher. An attempt was made to set the same rate for each test, using the height of the flame

as an indicator, and it is believed that this was accomplished to a far

greater extent than the instructions indicate is required.

The variations do not appear to result from malfunction of the

actuating portion of the compensating mechanism, because, while

temperature and pressure varied, the reading indicated by the cam

follower on the scale differed from the correct factor for that temperature and pressure by less than four-tenths division, whereas the factor

changed nearly five divisions. A fraction, about 5.2 percent of the

apparent residual negative temperature coefficient, may be accounted

for by expansion of the mechanical members of the mechanism.

If one considers that the uncertainty of a particular test may be more accurately evaluated by comparing that test with another made

under the same conditions than by computing the probable error of the mean of the 10 determinations that constitute the single test, then it is seen that an uncertainty of 0.0023 would suffice to bring all five of the

solid points of figure 29 to a straight line having a slope of about

-0.000154/°F. This is still about 47.5 percent of the slope -0.00032

which was found. It appears, therefore, that the instrument is over- compensated as a result of setting the center of curvature of the cam

too far from the pin by which the cam follower link is attached to the

pen mechanism.

(g) HUMIDITY COEFFICIENT

To determine experimentally the effect on the indicated reading of

variations in the water content of the surrounding air, which is used

as a reference, a test consisting of 10 determinations of the reading- was made in the manner previously described, with the water content

of the reference air at 2.78 percent in addition to two tests at 1.15 and 1.19 percent, which correspond nearly to 35.0-percent relative

humidity at 77° F, the conditions chosen as "normal" for the purposes

of these tests.
Specific Gravities of Gases 103

During these tests the instrument was maintained at as near the same temperature as possible. The average temperature was 78.7° F,

and the temperatures during individual tests differed from this by

1.2° F or less. The results as observed, and after correction to a chart reading at 35-percent relative humidity, for 0.1 percent of C02 in the air, and

to dry reference air, have been plotted against "water vapor in the

reference air," in figure 30. Straight lines, determined by the method

of least squares, have been passed through the three points, and the

slopes of the lines, constituting the humidity (or percentage of water)

coefficients, are indicated thereon.

It may be noted that the effect of variations in the percentage of

AS OBSERVED

ALL CORRECTIONS

.53

VARIABLES % H 2 0, % REL. HUMID. CONSTANT TEMP (78.7 °F.)

,.o°J

I O.OOOI2 , PER % H 2

0.5 1.0 1.5 2.0 2.5 3.0 VOL. % H 2 IN REFERENCE AIR Figure 30.

Humidity coefficient of the Sigma recorder No. 7 determined at constant temperature (78.7° F) with test mixture 2; O as observed, and •

after the application of all corrections. water in the air has been reduced practically to zero by applying all the corrections, the slight residual coefficient being easily accounted

for by the uncertainty in the individual tests. The results, when cor- rected for water vapor in the reference air, are independent of the

concentration of that water vapor.

(h) OTHER SOURCES OF ERROR

(1) Accuracy of Readings.—The position of the record mark on

the chart can be read to 0.01 and estimated to 0.001, in some cases perhaps to ±0.0005, which is small compared with errors from other

sources. (2) Position of Chart.—The guides for the chart paper are farther

apart than the width of the chart by about 1.1 mm, and consequently,

movement of the chart from contact on one side to contact on the

other would correspond to an uncertainty of 0.0027 in specific gravity.

(3) Material Tested.—With continuous purging, contamination of

the sample with air is unlikely unless there is a bad leak at some point

between the throttling valve and the lower end of the hose leading to
104 Miscellaneous Publications, National Bureau of Standards

the burner. Samples with specific gravities less than air cause the

pressure between those points and in the hose to be below atmospheric,

but by too small an amount to result in contamination with air unless the opening is large.

A possible source of contamination of the gas sample is the seal oil used in the reservoir to seal the bell float. The use of oil having an

appreciable vapor pressure will result in the contamination of the

sample with oil vapor. For example, a kerosine of specific gravity 0.81 (molecular wt about 180) such as that originally used in the in- strument would have a vapor of specific gravity about 6.2. Its vapor

pressure at 77° F is approximately 2 mm. If one assumes that it would evaporate into the sample at a rate which would bring the proportion of vapor in the sample to about one-half that at saturation,

the proportion present would be about 0.13 percent vapor. 0.13 per- cent of vapor of specific gravity 6.2 mixed with 99.87 percent sample

of specific gravity 0.5000 would yield a mixture of specific gravity

0.5074, and thus cause an error of + 0.0074 in the specific gravity of the

sample. If one assumes that the sample is saturated with kerosine

vapor, the error is twice as great.

The Markol, which has been used as a seal liquid in all the tests with this instrument, will not affect the fourth decimal place of the

specific gravity even though its vapor saturates the gas sample.

(4) Effect of Flame.—A statement in the directions that "The

smaller the flame at the burner, the more accurate will the reading

be, as a large flame causes a suction at the outlet of the burner which

will suck the bell down and give a reading of specific gravity which

is too low", indicates that the flame is recognized as a source of error. The magnitude of the error was determined by adjusting the sampling' rate with the flame burning, noting the indicated specific

gravity, and then extinguishing the flame. After the burner had

cooled to room temperature, the reading had increased by 0.014. Raising the burner 80 mm restored the indication to the original

reading by increasing the height and consequently the buoyancy of

the gas column. Another determination, however, indicated that an

increase in height of 100 mm was necessary to compensate for the

absence of the flame. The determination is obviously not of high

accuracy. The tests of the instrument with nonflammable gases made the

presence of a flame impossible, but when the test was completed in

each case, the burner was raised 80 mm and an additional determination made. The effect produced on the indicated specific gravity was

to decrease the reading in all cases, but the amount was found to vary

from 0.014 to 0.022. It is obvious that the flame, or its equivalent, is a source of a considerable and quite variable error, one that is several times that

required to account for the behavior with respect to temperature and

humidity coefficients. The desirability of eliminating the flame is distinctly indicated.

(5) Height of Gas Column.—The height of the gas column is the

distance between the top of the bell and the rim of the burner. When

gases of different specific gravity are introduced the bell moves upward or downward and thus changes the height of the gas column
Specific Gravities of Gases 105

by 0.1 in. for each 0.1 of specific gravity. The reading will thus be

in error by a corresponding amount at specific gravities other than

0.5, the calibration point. At 0.65 the error from this source would

be about —0.2 percent, and at 0.4 the error would be about —0.13

percent.

(6) Rate of Sampling.—The indication is affected by the rate of

sampling, as might be expected. The optimum rate is the lowest that

will keep the bell and gas column purged. If the rate is decreased

below this, air tends to spill into the top of the column and a higher

reading results. If the rate is increased above the optimum, the

pressure required to produce the increased flow through column and

burner increases the reading. At the optimum rate, the indication

is affected little or not at all by small changes in rate. The optimum

rate was determined by measurement to be 0.33 cu ft/hr for this

instrument, and when the gas is combustible results in a flame of the

size used in the determinations of temperature and humidity

coefficients. (7) Temperature Lag.—When the temperature of the room was

changed at a rate between 5 and 10 deg F/hr, the temperature at a point beside the compensator air reservoir lagged behind the room

temperature by between 3 and 4 deg F. This would result in errors of compensation, as well as errors resulting from corresponding dif- ferences between the temperature of the gas inside the bell and gas

column and the air surrounding them. The net effect was that w

T ith

rising temperature the readings rose as much as 0.0075 above the

reading at constant temperature, and with falling temperature, fell as much as 0.0100 below.

(8) The Test Weight.—Any inaccuracy in the determination and

adjustment of the proper mass of the test weight used in the cali- bration would result in an error of displacement at specific gravity

0.5, which appears to be constant over the entire range. The proper

weight is 0.5 times the weight of air (dry and free from C02 and at 60° F and 30 in. Hg) in a column having the height of the gas column

nd the diameter of the inside of the bell. Errors in the estimation

of these dimensions are involved in the determination of the proper

eight. If the dimensions given by the manufacturer are correct,

he weight should weigh 56.47 g. It was found to weigh 56.72 g. which is 0.5022 times the weight of the air. The pen being set to read

".5000, the indicated specific gravity is 0.0022 too low in the case of

his particular test weight.

(9) Sealing Oil.—Unless an oil of low viscosity and specific gravity

s used (which carries with it a vapor pressure higher than desirble), an appreciable weight of oil may be held upon the sides of the

ell after a change in specific gravity causes the bell to be immersed

and then withdrawn from the oil. About the same proportion of

the weight held up will drain off in a given length of time, regardless of viscosity or specific gravity of the oil. That which remains

tends to give a low reading, but should cause no serious lag or inaccuracy unless the changes are marked and rapid. If the sealing-oil

"reeps, the weight of the film formed tends to give a still lower reading, and no counterbalancing bell offers hope that the effect will be
106 Miscellaneous Publications, National Bureau of Standards

canceled. As Markol has little tendency to creep, the tests were not

much affected, but some kerosines might cause serious error by creeping.

(10) Oil Level.—The level of the oil in the reservoirs should be

carefully and regularly inspected and adjusted, especially if an oil of appreciable vapor pressure is being used. At calibration a portion of the bell is immersed in the oil, and subsequent readings are

subject to an error to the extent that the immersion of the bell changes

thereafter. There is no counterpoise bell to cancel the immersion

effect ; therefore, the reading becomes lower as the oil level drops.

(11) Immersion Error.—At calibration the reading is set at 0.5. Consequently, the immersion error is zero at specific gravity 0.5000. At lower specific gravity the bell will be immersed more deeply, the

buoyant force will be greater, and the reading will tend to be too high on this account. At higher specific gravities the reading will

tend to be too low.

(12) Pendulum Weight.—A pendulum weight attached to the ful- crum rod of the balance beam, its position adjustable by loosening

a setscrew, produces an effect opposite to that required for compensation of the immersion of the bell. Neither its purpose, its cor- rect position, nor its existence are mentioned in the instructions. Its weight is about 60 g, and it is suspended about 5 cm below the ful- crum, so that an incorrect position might account for an appreciable

systematic error. (13) Oil in Pneumatic Compensator.—Accidental movement of the

small balance beam carrying the compensator bell and counterweight

may result in the oil in the reservoir being raised to the rim of the

inner cylinder of the annular reservoir and some of it finding its way into the air reservoir. Some may collect in and partially close the tube connecting the reservoir to the bell and thus cause faulty

operation of the compensator. This small balance beam is not adequately protected from accidental contact when replacing or adjusting

the chart roll, which is located immediately in front of it. The oil level in the compensator reservoir must be kept at the same point

(!/4 in. from rim) in order to maintain the correct reading on the

compensator cam corresponding to a given temperature and pressure.

(i) COMMENTS ON OPERATION AND SUGGESTIONS FOR IMPROVEMENT

While the instrument is, as described by its manufacturer, rugged

and sensitive, it is believed that its reproducibility, accuracy, and

susceptibility to derangement would be improved by the following

modifications.

(1) Some sort of flow indicator should be provided, by means of

which the flow of the gas sample could be maintained at the same rate. (2) The error introduced by the presence of the flame on a burner

is much greater than that which might be caused by contamination of

the reference air by the effluent gas sample in a reasonably well ventilated laboratory. Means should be provided for the elimination of

the discharged sample, and the burner and flame should also be eliminated.

(3) The adjustable valve with the notch in the plug, as provided on

the instrument tested, leaked badly to the outside unless closed as
Specific Gravities of Gases 107

tightly as possible. As a leak here contaminates the reference air, a better type of gas inlet valve is desirable.

(4) The directions for installation, calibration, and care are in- complete and do not assure the user that he has performed certain

adjustments as the manufacturer intended.

(5) An adjustable guide at one side of the chart paper would be

desirable to keep the paper from wandering back and forth between

guides too far apart.

(6) The main balance beam and counterweight should be inclosed

in a housing to protect them from dirt and accidental contact, which

can change the adjustment and impair accuracy.

(7) Some sort of beam-arresting device to hold the beam while

adjusting the counterweight would be a help during calibration.

(8) If it is impossible to make a permanent adjustment of the

eccentricity of the cam to accomplish the proper compensation for

temperature and pressure changes, a thumbscrew (or screw and lock

nut) and hinge, or the equivalent, might be provided to make it possible for the user to eliminate temperature coefficients found to remain

after corrections for effects dependent on temperature have been

applied. This would not be worthwhile unless other equally serious sources of error are also eliminated.

(9) Some means of compensation for variations in the buoyant

force resulting from immersion of the bell to different depths at different specific gravities should be provided.

(10) The rubber hose might be replaced by a metal tube that could

be attached rigidly to the base of the instrument.

6. METRIC INDICATING GRAVITOMETER

(a) DESCRIPTION

The Metric indicating gravitometer (fig. 31) (described in

Bulletin E-21, of the American Meter Co.) consists of a motor, or

turbine, driven by compressed gas or air, and two centrifugal blowers

mounted directly on the shaft, one on each side of the motor. Each

blower is connected to a vertical water manometer that indicates the

static pressure produced by the blower to which it is connected. The

inlet of one blower is permanently open to the surrounding air, and

its case is provided with an orifice that allows air to escape at a rate

to insure that the case is continuously purged with fresh air. This

blower and manometer serve as a speed indicator for the motor and

the other blower. The inlet to the other blower is connected through

a valve to the supply of gas to be tested. When the gas is shut off, the

surrounding air is admitted automatically to the blower casing

through a small orifice. The casing is provided with an orifice to allow the air or gas to escape and keep the blower casing purged with

a fresh sample. The manometer, which indicates the pressure developed in the casing, will be referred to as the "test manometer."

When gas is admitted, the pressure on a third manometer at the inlet

orifice is kept slightly above ( +0.15 in. or less) atmospheric pressure

to prevent the entrance of air; air enters if the pressure falls below

atmospheric.
108 Miscellaneous Publications, National Bureau of Standards

Figure 31.

Metric indicating gravitometer.
Specific Gravities of Gases 109

The instrument is supplied with two diaphragm regulators in series to reduce the gas pressure nearly to atmospheric, as the instrument was designed to be driven by the gas supply that is being tested. In

the case of the instrument supplied for test, the regulators would

accommodate pressures between 25 and 100 lb/in.2 In making a test, the motor speed is increased (with gas shut off) until the test manometer indicates approximately 10 in. of static pressure, the position of the meniscus in the speed-indicating manometer

is marked by moving the adjustable marker, and the test manometer

read. Gas is then admitted and the speed regulated to bring the

meniscus of the speed-indicating manometer to the marked pressure

and the test manometer again read. The gas pressure divided by the

air pressure (both indicated on the test manometer) is the specific

gravity.

The Metric indicating gravitometer, although rather heavy, may be

classed as a portable instrument. The mechanism, mounted on a metal base is inclosed in a wooden case (with handle) 19!/2 in. high,

14 in. wide, and 12 in. deep. The case has a door at the front hinged

at the bottom and supported by chains for use as a shelf. The whole

is mounted on a detachable tripod stand with extensible wooden legs

having a minimum length of 30 in. A length of armored high-pressure rubber hose is supplied for connection to the gas line. The three

pieces combined weigh 51 lb.

(b) MODIFICATIONS FOR TESTING

For the purpose of these tests some modifications in the gas connections were necessary. The supply of test gas was limited, so the

motor was driven by a supply of compressed air at about 75 lb./in.2

, the cock at the motor controlling the gas supply to the inlet of the

first gas-pressure regulator was closed permanently, and the line dis- connected from the regulator. As the pressure of the test gas was

often above 100 lb./in. 2

, a high-pressure diaphragm regulator was in- stalled with a gage, from which the test gas was supplied to the inlet of the gas regulator on the instrument.

The wooden case was removed from the instrument to make the

parts more accessible and insure adequate ventilation so that the test gas discharged into the surrounding air would be less likely to con- taminate the reference air. A thermocouple was located near the test blower with which to measure the temperature of the instrument during operation.

(c) METHOD OF OPERATION

In making a single determination, the motor speed was adjusted

until the test manometer read exactly 10 in., and the position of the

meniscus in the speed-indicating manometer was marked by adjusting

the slide. Gas was then admitted by adjusting the outlet pressure on

the high-pressure regulator to give a positive pressure of from 0.05

to 0.10 in. on the manometer at the air-inlet orifice of the test blower.

The motor speed was then readjusted to bring the speed-indicating

manometer to the mark previously set, and the specific gravity read

off directly on the test manometer by multiplying the reading in
1 10 Miscellaneous Publications, National Bureau of Standards

inches by 0.1. During these operations another observer read and

recorded the temperature of the room, the instrument temperature,

the barometric pressure, and the relative humidity, as well as the time

when the specific-gravity reading was taken.

A test of the instrument with a given test gas, at a given temperature and relative humidity, consisted of a continuous series of 10

determinations of the specific gravity, as described above. The 10

values obtained were then averaged. The temperature, barometric

pressure, and relative humidity reported with each test are each the

average of the observed readings recorded during the 10 determinations. The temperature and relative humidity of the air of the room

were controlled, so that the effects of these variables on the indication

of the instrument might be determined.

When the specific gravity of the test gas reached 1.3, the motor

speed was adjusted until the test manometer read exactly 5 in. with

air instead of 10 in., and the manometer readings with gas were multiplied by 0.2 to obtain the specific gravity.

(d) CORRECTION FOR COMPOSITION OF REFERENCE AIR As the reference air that enters the blower when the speed is determined is neither dried nor freed from carbon dioxide, the observed

readings change with changes in the content of water and carbon

dioxide in the reference air. The specific gravity, is the product

of the reading R and the true specific gravity (referred to standard

air) of the reference air. That is, if water and carbon dioxide are

the only impurities,

S=R (l-0.378w + 0.529c),

where iv and c are the fractions of water vapor and carbon dioxide

respectively, in the reference air. Each observation of specific

gravity was corrected for the presence of these substances in the air

of the room, as indicated by the equation.

The corrections for the results obtained with test mixture 1 have

then been combined as follows

:

Correction of reference air to dry basis —0. 0027 Correction of reference air to freedom from C02 4-. 0003 Net correction to observed specific gravity —0. 0024 Observed specific gravity, mean — . 6501 Net correction —. 0024

Corrected specific gravity 0. 6477

Specific gravity of test mixture No. 1 . 6472 Error of instrument +0. 0005

Error, percentage of standard specific gravity -f . 7 The data have been treated in the above manner for each of a variety

of test gases and test conditions, and a summary of the numerical

results is presented in table 11. The errors of the results "as observed" and after the corrections

noted above have been applied are plotted in figure 32.
Specific Gravities of Gases 111

4i ^ gos

O CU ^

-So

o w

O O ~ O O O 3 3 o o c o o coo

<?+ f r r r r r

NNC-H CM O O O O O 25

I I I I III ^^(Ng O O O O O o o o

o o o o o o o o o :++++ +++

OS (M Ir^ CM CM O i—I i—

o o o o o Till ill

x: o <» a a g ^60 S.2 -Q o c 3

*i is cc « a

£ fc: S

*-< fc£ N

(2

03 «

O ^

O O O ( O I O O O : fl -H-H-H -H-H-H

S o o o o 3 -H -H-H-H coo coo coo

-H-H-H

OSNOOM ©N! cm «: x io i-i —. t -fill III C o 00 1ON >~ X — o — coo CO <© i-H CO lONCO

+ ++++

CO r-C CN i-H t~-

LO iO oo coco coco

S Scoo

s ssss

+ ++++

I I I I I

-H -H -H-H-H

o coco

4 4444

CO CO CO *C CT> ++++

4- ++++

CM O CO 00 CM

CM CM ^ CM

Tji 00 lO O CM

CO CO i-l CO »*<

CO O O CM

a 3

B a

aa

a a- mm*

it i. cj o att >jop

s>>.-s.-s

719265—47-

&jo a

c3 g Msg
1 12 Miscellaneous Publications, National Bureau of Standards

+ .055 .050

.045 040

g-035

lr. 030

co^.025 O.020 §015

crw.010

.005

.005 -.010

MIXT. NO. SYMBOL COMPOSITION

1 © MFD. GAS

2 A NAT'L - 3 O HELIUM

4,5,6,7 O He~N2 8 B H2 ~C02 10,11,12 a N,-C02 13 C02

14 & PROPANE

14

1 1 1 1

I NUMBERED POINTS INDICATE VALUES AS OBSERVED; UNNUMBERED POINTS AFTER CORRECTION

, VALUES

13

2

a

1 9

2 10

s -4-5

a 7

38

9

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 SP GR OF TEST GAS Figure 32.

Error of the Metric indicating gravitometer determined with each

test gas. The numbered point of each pair indicates the error as observed and the unnumbered

point the error after the application of all corrections.

(e) TEMPERATURE COEFFICIENT

To determine whether the numerical result obtained by following

the method of operation described above was independent of the temperature of the instrument, a test consisting of 10 determinations of

"specific gravity", using the same test gas (mixture 1), was made at 72.2° and at 96.2^ F, in addition to that at 82.1° F described in the

illustration discussed previously, and one at 83.5° F, which was made

as a check at normal conditions after the other tests. During these tests at a lower and a higher temperature than normal,

the water content of the reference air was maintained as nearly constant as possible. The average water content was 1.1 percent (35-

percent relative humidity at 77° F) and the water content during in- dividual tests deviated from this by 0.07 percent or less. The results, as observed and after correction to the basis of dry

reference air, have been plotted against temperature in figure 33. Straight lines, determined by the method of least squares, have been

passed through the four points, and the slopes of the lines, constituting the temperature coefficients, are indicated thereon.

The radius of the circle around each observed point is equal to the

probable error of the mean of the 10 determinations that point represents.
Specific Gravities of Gases 113

.66

65

.64

io AS OBSERVED

H> ALL CORRECTIONS

VARIABLES TEMP, REL. HUMID. TEMP

CONSTANT % H 2 IN AIR (1.1%) 0.0 % H 2 AND C02

__oi__-0 000053 r err wp

TEST MIX

J TURE

1 "O.OOi )040 per °F

50 60 70 80 90

INSTRUMENT TEMPERATURE

100 110 Figure 33.

Temperature coefficient of the Metric indicating gravitometer deter- mined with test mixture 1 : O as observed at constant percentage of water vapor

in the reference air (1.1 percent) and • after the application of all corrections. It may be noted that the temperature coefficient shown by the cor- rected values is only three-quarters of that shown by the values as observed, and that the error of the instrument has been greatly decreased by correcting the observed values to the basis of dry reference

air and 0.0 percent carbon dioxide.

(f) HUMIDITY COEFFICIENT

To determine experimentally the effect on the numerical result of

variations in the water content of the surrounding air, which is used

as a reference, a test consisting of 10 determinations of "specific

gravity" was made with the water content of the reference air at 0.52 percent and at 2.29 percent in addition to two at 1.09 percent, which

corresponds nearly to 35-percent relative humidity at 77° F, the conditions chosen as normal for the purposes of these tests. During these

tests at a lower and higher water content than normal, the instrument was maintained at as near the same temperature as possible. The

average temperature was 82.4° F, and the temperatures during in- dividual tests deviated from this by 1.1° F or less. The results, as observed and after correction to the basis of dry

reference air and for 0.1 percent C02 , have been plotted in figure 34

against the percentage of water vapor in the reference air. Straight

lines, determined by the method of least squares, have been passed

through the four points, and the slopes of the lines, constituting the

humidity (or percentage of water) coefficients, are indicated thereon.

It will be noted that the application of the corrections has slightly more than accounted for the effect of the water shown in the results

as observed. However, all the corrected values now fall within 0.001 of the specific gravity of mixture 1. 7192G5—47 9
1 14 Miscellaneous Publications, National Bureau of Standards

.66 1° AS OBSERVED H« ALL CORRECTIONS

TEST MIXTURE

VARIABLES % H 2 0, % REL. HUMID. CONSTANT TEMP (82.4 °F.)

.64

' 0.5 ~" 1.0 " 1.5 2.0 2.5 3.0 VOL. % H 2

IN REFERENCE AIR Figuee 34.

Humidity coefficient of the Metric indicating gravitometer determined

at constant temperature (82.4° F) with test mixture 1; O as observed, and%

after the application of all corrections. As may be seen from a study of figure 34, reference air containing

0.5 percent of water vapor by volume gives an indicated specific

gravity that is less by 0.0035 than reference air containing 2.5 per- cent of water vapor." These variations correspond to a range of variation of the relative humidity of from 13 to 67 percent at 82.4° F, a

variation not unlikely to be encountered.

At a relative humidity of 35 percent and at 77° F (chosen as nor- mal conditions) the indicated specific gravity of 0.6500 is higher by

0.0028 than it would be if the reference air were dry.

The magnitude and sign of the errors from this source are, of course, dependent on the specific gravity of the gas being tested.

(g) OTHER SOURCES OF ERROR

(1) Readings.—The position of the meniscus in the manometers

can be estimated to ±0.01 in., which would correspond to an uncertainty of ±0.001 in the specific gravity, if there were no other sources

of error. As it is necessary in making a determination to set one meniscus

to a mark and to read the position of the other as nearly simultaneously as practicable, equal errors of opposite sign are possible,

producing an uncertainty of ±0.002. As the test also depends on a preliminary setting with air, which involves the same chance of error

in reading, the total error that may be made is again doubled to

0.004. Although it is highly desirable that the test manometer be read

at the time the reference meniscus is set on the mark, this is impossible

because the two manometers are too far apart and the menisci are

usually at different levels. Relatively rapid variations in the positions
Specific Gravities of Gases 115

of the menisci and the irregularity of the interval between changes

add to the uncertainty that the readings of the two manometers

correspond to exactly the same speed.

The difficulty just mentioned may appear as a source of constant

error, rather than as a random one, in the process of setting the ref- erence marker to the meniscus while the test manometer reads 10.00 in. It is difficult to estimate the magnitude of errors of this kind, but

it appears possible that they might be larger than 0.004. (2) Water Level in Manometers.—As the right-hand manometer

is used only as a reference and speed indicator, the water in the reser- voir need not be set at zero on the scale with the motor stationary. In

the case of the test manometer, however, if the water level is not so adjusted that the meniscus reads zero when the motor is not running,

a small error may be introduced. For example, suppose the meniscus

read —0.1 in. instead of zero and apparent readings on air and gas were 10.00 and 6.80, respectively. The specific gravity would be sup- posed to be 0.680. The actual pressures would be 10.10 and 6.90, and

the corresponding specific gravity would be 0.683. The error of — 0.003 is the result of an easily noticeable maladjustment of the water

level and is not likely to occur unless its possibility is not recognized.

(3) Material Tested.—Errors of several types may arise from uncertainties as to the material being tested, either gas or air. After setting the speed-reference marker with the test meniscus

at 10.00 in., if insufficient time is allowed for the test blower to be

purged with gas, or if the pressure indicated by the gage on the gas

manifold is not greater than atmospheric, the material tested may be a mixture of gas and air instead of gas, and the indicated specific

gravity will be nearer that of air than would be the case if purging was complete.

During a test of gas, purging of the test blower results in a con- tinuous discharge of gas through the purge orifice, and also through

the larger orifice in the gas manifold. The discharge through this

orifice serves to relieve any excess of pressure at the entrance to the

blower and at the same time to prevent the entrance of air. This gas

is discharged into the air that surrounds the instrument, a portion of

which is drawn into the air blower, which indicates the motor speed.

If the air is contaminated with gas, the motor speed will be set faster

to bring the meniscus to the mark, and the indicated specific gravity

will again be nearer to air than it would be without contamination.

Errors from this cause may be minimized by keeping the manifold

manometer pressure positive but small and by making sure of good

positive ventilation of the instrument.

During a test of air with the motor running on gas or a test of gas

with the motor running on air, the pressure inside the motor casing

is greater than atmospheric and will tend to cause gas or air to flow

along the bearings from the motor case into the blowers. If, and to the extent to which such a flow takes place, contamination of the

material in the test blower and the speed-reference blower may be the

source of errors, causing the indicated specific gravity to be nearer air

than it should be.
1 16 Miscellaneous Publications, National Bureau of Standards

(h) COMMENTS ON OPERATION OF METRIC GRAVITOMETER AND SUGGESTED

MODIFICATIONS

Several suggestions for the improvement of the instrument have

been made to the manufacturer.

( 1

) A more positive means of insuring good ventilation of the instrument case might be provided to minimize contamination of air by gas

discharged through purge and manifold orifices. (1.0 percent of water

vapor (specific gravity 0.6221) in the reference air produces an error of 0.0025 when testing a gas of 0.647 specific gravity. Contamination

to the same extent with a gas of specific gravity near 0.622 would have

a like effect.) (2) Unless the pressure of the line from which the motor is driven

is quite steady, it is difficult to adjust and hold the motor speed constant long enough to read the test manometer. Perhaps a little more

inertia in the form of a flywheel on the motor shaft might help.

(3) It would seem to be possible, and very desirable, to bring the two

glass tubes close enough together so that the eye could observe both

at once. With an adjustable marker, there is no real need for a scale behind the gage on the speed-indicating blower, and the tube could be

placed alongside the scale of the test blower. There appears to be no

simple mechanical way to bring the two menisci to the same level,

except when both blowers operate on air. It might be done optically

by means of two small plane mirrors mounted on light frames ar- ranged with spring clamps to slide on the reference-gage tube and

form a periscope of variable length. The meniscus in the test gage

tube could then be read while observing the other meniscus at the

marker of the reference gage.

(4) In the case of mixture 9, the reading was obscured by the metal

marker on the test gage glass. Markers of transparent plastic might

be used to prevent such a difficulty.

(5) The legs of the tripod are hinged independently at their junc- ture with the head, and there is no bracing between the legs. The

weight of the instrument combined with these factors makes initial leveling difficult and sometimes precarious. A somewhat more rigid

tripod would be advantageous.

7. RANAREX SPECIFIC GRAVITY RECORDER NO. A2360 AND PORTABLE

SPECIFIC GRAVITY INDICATOR NO. P1284

(a) DESCRIPTION

The Ranarex specific gravity recorder (fig. 35) is designed to be

hung on a wall or mounted flush on a panel in a permanent location. It is rugged, compact, inclosed in a metal case occupying a space ap- proximately 26y2 by 11% by 1034 in. and weighs about 903/4 lb. The

Ranarex indicator (fig. 36) is portable, rugged, and compact. It is inclosed also in a metal case, occupies a space approximately 9 by 9 by

17 in., and weighs about 32 lb. Both instruments operate on 110-volt

alternating current, but instruments are supplied for other voltages

and types of current when desired, including 6- and 12-volt direct

(storage battery) current. The charts of alternating-current instruments are driven by Telechron motors ; those of direct-current instruments by spring-wound movements.
Specific Gravities of Gases 117

Figure 35.

Banarex specific gravity recorder No. A2360.
118 Miscellaneous Publications, National Bureau of Standards
Specific Gravities of Gases 119

They are made and sold by the Permutit Co., 330 West 42d St., New York, N. Y., and a description and directions for installation and

operation are given in booklets supplied with the instruments.

The two instruments are identical in principle. A rotating motion

is imparted to the gas by means of a motor-driven fan running in a chamber. The fan drives the gas against the blades of a similar fan

(or impulse wheel) located opposite the fan in the same chamber

and thus produces a torque on the shaft of that impulse wheel, the

torque being assumed to be proportional to the specific gravity of the

gas. In order to eliminate the influence of changes in fan speed,

temperature, humidity, and atmospheric pressure, a comparing torque

is produced by air on another impulse wheel to which a similar motion

is imparted by means of a second fan driven by the same motor and

a single belt rotating in the opposite direction in a second chamber.

The instruments are designed to saturate both gas and air with water

vapor before whirling them. The shafts of the two impulse wheels

are coupled together by means of a lever on each and a connecting link. The coupling system prevents complete rotation of the impulse wheels,

but the difference between the two opposing torques causes a limited

movement of the system that is transmitted to a pointer mounted on

the shaft of the impulse wheel operating in gas. The pointer indi- cates the ratio of the gas torque to air torque, in terms of specific

gravity, on a scale reading from 0.2 to 1.0 in the case of the lower

range, which was tested with mixtures 1 to 9, inclusive. The higher

range of the recorder extended from 0.6 to 1.6' and was tested with

mixtures 10 to 14, inclusive. The higher range of the indicator was from 0.5 to 1.5, and test mixture 14 was not used.

In the recorder the pointer shaft is extended on the opposite side

of its hub and is fitted with a hinge on which is mounted a pen shaft

that records the indication on a chart driven by a Telechron motor.

The scales of both instruments and the recorder chart are graduated

in intervals of 0.02, and the reading may be estimated to about ±0.002

at midrange and to about ±0.004 at the ends, where the divisions are about half as far apart. (The manufacturer states that the instruments may be furnished with a variety of shorter ranges for specific

purposes and that the shorter ranges are capable of being calibrated

and read more accurately than the longer ones.)

The case of the recorder is hinged in two places so that access may be had to the front and back of the center portion containing

the mechanism.

Tests indicated that the reading of the recorder will reach a constant value in about 2 minutes after admitting the gas and return

in about 1 minute to a constant reading on air. The indicator is somewhat faster—constant readings are obtained in about 30 seconds

after admitting gas or air to the measuring chamber.

The instructions call for operating the instrument with the gas

inlet valve adjusted so that the driving fan in sampling gas reduces

the gas pressure to between 14 in. and % in. of water below atmospheric

pressure as indicated by a manometer at the gas inlet. At y2

in. below

atmospheric, the instruments sample gas at about 6 cu ft/hr. At %

in., the rate is about 10 cu ft/hr.
120 Miscellaneous Publications, National Bureau of Standards

(b) MODIFICATIONS FOR TESTING

Thermocouples were used to measure temperatures. One couple was

immersed in the water of the air saturator, inserted through a rubber

stopper, which was used to close the water filler opening in place of

the screw plug. Another couple was inserted through a puncture in

the rubber hose at the outlet of both the gas and air chambers.

(c) METHOD OF OPERATION

During the testing with 13 gases of known specific gravity (12

only were used with the indicator), the directions for the installation

and operation of the instruments have been followed with only a few

minor modifications and extensions.

The rates of flow of gas and air through the instruments were such

as to give readings on the inlet gages of about minus one-quarter inch

or a little more, as recommended by the manufacturer. They were

first observed by connecting a laboratory gas meter to the outlet. However, the meter restricts the flow ; hence, in the tests of the action

of the saturators, the outlet of the meter was connected to vacuum

and the suction adjusted to make the flow the same, as indicated

by gage reading, as it was before the meter was connected. As first measured, with the meter driven by the pressure from the blowers,

the rates of flow were 6 to 10 cu ft/hr. When the resistence of

the meter was eliminated by applying suction, rates of 16.5 and 12.6 cu ft per hour were obtained for the recorder and the portable

instruments, respectively.

The instruments were tested in a room adjusted to a "normal"

temperature of 77° F, except during the determination of the effect of temperature, when one test was made at a lower and one at a higher temperature than this. Before each test of the instrument

with a test gas, the water level in the two saturator reservoirs was

adjusted to the full mark, and the instrument was then operated on

air for from 3 to 4 hours so that it reached temperature equilibrium. Tests showed that the temperature was still rising slightly at the end

of 4 hours. The reading of the recorder on air required slight readjustment to 1.0 during the first part of this period. When the air reading was set to 1.0 before each test with gas, the gas reading rose by 0.002 during the first hour but showed no change with temperature thereafter. No change of reading of the indicator could be

detected during the period of heating up. Each test of each instrument with a test gas involved observing

the reading on air for several minutes and, if necessary, setting the

pointer to 1.000 by means of the adjusting nut. The instrument was

then purged with the gas for approximately 10 minutes, during

which time the reading of the pointer was observed and recorded.

A record was made of the temperatures of the room, of the water

in the air saturator, and of the gas and air at the respective outlets. The barometric pressure, relative humidity, and the time of day were

also recorded. This entire process was repeated until 10 determinations had been made. The 10 readings of specific gravity read on

the scale of the indicator were averaged for the test of that instrument. In the case of the recorder, the reading on the chart of the
Specific Gravities of Gases 121

middle of each recorded line while operating on gas and on air was

determined with an ocular-scale microscope. These 10 values of

specific gravity after correction of each for the displacement of the

preceding air reading from 1.000, were then averaged for the test. The temperatures and other data reported with each test are the

averages of the values recorded for the 10 determinations.

After the completion of the testing with gases having specific

gravities less than 1.000, the recorder was cleaned, fitted with an

indicating mechanism designed for the range from 0.6 to 1.6, and its calibration checked by a representative of the manufacturer, so that

tests could be made with gases having specific gravities greater than

1.000. The indicating instrument was sent to the factory, where it was cleaned and fitted with an indicating mechanism designed for

the range from 0.5 to 1.5, and returned. In all cases the instruments were adjusted to indicate directly the specific gravity of the dry gas

with respect to dry air, and consequently no corrections should be

required to place the reading on the same basis as that of the test gas if the calibration was carried out at a room temperature of 77° F. As the temperature of the room during the original factory calibrations is not known, no attempt to compute corrections has been made,

and the results are reported as observed so far as the water-vapor

contents of the gas and air are concerned.

The data have been treated in the manner described in Section III,

1, under "Treatment of results" in each case. A summary of the

numerical results obtained with the recorder is presented in table 12. Table 12.

Specific gravities of the test gases as determined by the Ranarex

specific gravity recorder No. A2360 at the "normal" room temperature of 77° F.

Xo. Test gas

Specific gravity

Stand- ard Chart

read- ing Error

Percent- age

of stand- ard

Pointer

reading Error

Percent- age of stand- ard

Reproducibility

Probable

error

of mean

Probable

error

of single deter- mination

10

Synthetic typical manufactured gas. Synthetic typical nat- ural gas. Helium*

Helium-nitrogen DoDo

Do

Hydrogen-carbon di- oxide. Nitrogen

Xitrogen-earbon dioxide.

0. 6475

.6820 .1526

.3048

.4222

0. 6437 -0. 0038 +. 0140

-0. 59 0.

+2.05 .1

3i ins

. 7963' . 795^1

. 6080 . 607' .9714

1. 0991 Do

Do

Carbon dioxide. Propane Butanea

1. 2792

1. 3984

1. 5268

1. 5461

2. 0644

1. 2794

1. 3901

1. 5069

1. 5281

Average.

-.0040

-.0136

-. 0109 -. 0006 -.0001 +. 0048 +. 0009

+. 0002 -.0083

-.0199

-.0180

-1.31

-3. 22 -1.81 -.08

-.02

-f-50 +. 08

+. 02 -1.30 -1.16

0. 0076

-0. 0029 +. 0158

-0. 45 +2. 32

±0. 00029 ±. 00018

±0. 00091 ±. 00055

.3020 .4124

.5898 .7942 .6034

.9710

1. 1004

1. 2786

1. 3925

1. 5077

1. 5301

-.0028

-.0098

-. 0109 -. 0021 -.0046 +.0044

+. 0022

-. 0006 -. 0059 -.0191 -.0160

-.92

-2. 32 -1.81 -.26

-.76

+. 46 +.20

-.05

-.42

-1.25

-1.03

±. 00028 ±. 00027 ±. 00047 ±. 00023 ±. 00036 ±. 00013 ±. 00017

±. 00028 ±. 00018 ±. 00035 ±. 00029

±. 00089 ±. 00085 ±. 00150 ±. 00074 ±. 00113 ±. 00042 ±. 00053

±. 00088 ±. 00057 ±00111

±. 00091

0. 0075 0. 92 ±0. 0002' ±0. 00085

a The range of the instrument was such that the specific gravities of these gases could not be determined.
122 Miscellaneous Publications, National Bureau of Standards

The figures given for reproducibility apply only to the readings from

the chart. The value of specific gravity and error given for the

pointer is in each case the mean of the 10 pointer readings with that

test gas. The errors of the instrument, for the chart and for the

pointer, have been plotted for each test gas in figure 37. The readings of the indicating instrument have been treated in the same way. They are recorded in table 13 and plotted in figure 38.

.015

.010 .005

.005

.010 2.015

en

U..0I5 o

or .010 o

tr£.005

.005

.010 015

-.020

T

CHA a -s

a ( 9

a

I

m a |mixt no. symbol composition

1 9 MFD. GAS

2 A NAT'L " 4,5,6,7 • He-N2 8 O H 2 -C02 9 • NITROGEN

0,11,12 a n2 -co2

13 C02 Dm 14 A PROPANE k TCD

•

a

a

1 1

t S

( 1

.8 10 1.2 1.4 1.6 1.8 2.0 2.2 SP GR OF TEST GAS Figure 37.

Errors of the Ranarex specific gravity recorder No. A2360 deter- mined with each test gas as found for the chart and the pointer. No corrections are applicable.

(d) SOURCES OF ERROR

(1) Temperature Coefpcent.—In order to determine whether the

indications of the instruments, obtained by following the methods of

operation previously described were independent of the temperature

of the room, tests, consisting of 10 readings, were made with the same

test gas (mixture 1) after adjusting and maintaining the temperature

of the room at various constant temperatures. The recorder was

tested at 55.2°, 67.3°, twice at 91.8° F, and a check test was made at 77.3° F in addition to that at 77.2° F previously described. The

indicator was tested at 67.4° and 91.8° F in addition to the tests made

at 77.2° F.
Specific Gravities of Gases 123

+ 050 045 040

.035

i_ 030 z

iii 5 025

z>

a.£.020 z

-015

g.010

CT

crui.005

.005 010

.015 -.020

MIXT NO SYMBOL COMPOSITION

1 © MFD. GAS

2 A NAT'L » 4,5,6,7 3 He-N2 8 g h 2 -co2 9 • NITROGEN

io;m,i2 a n 2 -co2 13 C02

a

icp

> 9 •

a

a

B i

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 SP GR OF TEST GAS Figure 38.

Errors of the Ranarex portable specific gravity indicator No. PI284 determined with each test gas. No corrections are applicable.

Table 13.

Specific gravities of the test gases, as determined by the Ranarex

portable specific gravity indicator at the "normal" room temperature of 77° F.

Test gas

Synthetic typical manufactured

gas Synthetic typical natural gas Helium a Helium-nitrogen

..-_do

Hydrogen-carbon dioxide. Nitrogen

Nitrogen-carbon dioxide „ do

do Carbon dioxide- Propane a Butane a Average

Specific gravity

Standard

0. 6475

.6820

.1526

.3048

.4222 .6007

.7963

1.0982

1. 2792

1. 3984

1. 5268

1. 5461

2. 0644

Observed

reading Error

0. 6585

.7189 .3002

.4360

.6379

.8425

.6473

.9812

1. 1040

1. 2905

1. 4028

1. 5100

+0. 0110 +. 0369 -.0046 + 0138 +. 0372 +. 0462 +. 0393 +. 0146 +. 0058 +.0113

+. 0044 -.0168

0. 0202

Percent- age of standard

+1.70

+5. 41 -1.51

+3. 27 +6.20

+5. 80 +6. 46 +1. 51 +.53 +.96

+.31

-1. 10

2. 90

Reproducibility

Probable

error of mean

±0.00011

±. 00057 ±. 00013

d=. 00014 ±. 00029 ±. 00021 ±. 00018 ±. 00009 ±. 00000 ±. 00023 ±. 00009 ±. 00000

±0. 00017

Probable

error of single de- termination

±0. 0003'.

J=.flfJl81 ±. 00043 ±. 00045 ±. 00092 ±. 00066 ±. 00056 ±. 00028 ±. 00000 ±. 00073 ±. 00028 ±. 00000

±0. 00054 The range of the instrument was such that the specific gravities ot these gases could not be determined.
124 Miscellaneous Publications, National Bureau of Standards

The results from the chart readings of the recorder have been

plotted against temperature in figure 39. The readings of the indi- cator are plotted in figure 40. In each case, a straight line, determined

by the method of least squares, has been passed through the six points,

and the slope of the line constituting the temperature coefficient is

.661 1 1 1 1 1 1

50 60 70 80 90 100 no ROOM TEMPERATURE °F Figure 39.

Temperature coefficient of the Ranarex specific gravity recorder determined with test mixture 1.

66

65

°F

TEST MIXT URE

50 60 70 80 90 100 10 ROOM TEMPERATURE °F Figure 40.

Temperature coefficient of the Ranarex portable specific gravity in- dicator determined with test mixture 1. indicated thereon. The radius of the circle around each point is equal

to the probable error of the mean of the 10 readings which that point

represents.

The heat generated during the operation of the instruments, primarily by the electric motors, raises their temperatures above that of
Specific Gravities of Gases 125

the room. The temperature of the water in the air saturator and of the

gas and air at their respective outlets was determined after steady

conditions had been reached at the various room temperatures employed in the tests. The results have been plotted in figures 41 and 42. Supplementary tests indicated that the temperature of the water in the

gas saturator was practically the same as that in the air saturator

in each instrument.

70 80 ROOM TEMPERATURE Figure 41.

Equilibrium temperatures in the Ranarex specific gravity recorder

No. A2360 at the gas outlet, air outlet and of the water in the air saturator

as related to the temperature of the room.

The temperature of the chart is indicated by the solid circle.

50

<>

60 70 ROOM

80 TEMPERATURE

90 100 110 Figure 42.

Equilibrium temperatures in the Ranarex portable specific gravity

indicator No. P1284 at the gas outlet, air outlet, and of the water in the air saturator, as related to the temperature of the room.
126^ Miscellaneous Publications, National Bureau of Standards

The manufacturer has stated that the temperature of the room at calibration might have been as low as 70° or as high as 80°, and was

probably about 75° F, which differs so little from the 77° chosen as "normal" for these tests that no great error will result from assuming

calibration at 77° for the purpose of the following discussion. It may be seen from figure 41 that when the room was at 77°, the

water in the recording instrument was at 91°, at which temperature

its vapor pressure is 37.2 mm. The barometric pressure averaged

750 mm, and if saturated at this temperature, both air and gas would

contain 4.96 percent of water vapor. However, tests showed that

the instrument sampled gas at the rate of 16.5 cu ft/hr as compared

to 4.34 cu ft/hr for the air, and that the gas was only 65-percent sat- urated with water as compared to 96-percent saturation of the air. Consequently, gas containing 0.65X4.96, or 3.22 percent, of water

vapor was compared with air containing 0.96X4.96, or 4.76 percent,

of water vapor, and the adjustment of the instrument made it read

the specific gravity of the dry gas compared with dry air. When the room temperature was changed to 55°, the temperature

of the water was 75.7° F. If we assume the same degrees of saturation as at calibration, the gas contained 1.98 percent of water vapor

and the air 2.92 percent. Similarly, at a room temperature of 92°,

the water was at 104° and the gas, if saturated to the same degree as before, would contain 4.8 percent of water vapor and the air 7.08 percent.

When a dry gas of specific gravity 0.6475 with respect to dry air is mixed with 3.22 percent of water vapor of specific gravity 0.6221,

the ratio of its density to that of dry air is 0.6467. If it is referred

to air containing 4.76 percent of water vapor, the ratio is 0.6589. If the instrument was calibrated with this gas at 77°, it must have

been made to read 0.6475, less than the ratio of the density of the gas

to that of the air actually in the instrument by 0.0114. When the gas contains 1.98 percent of water vapor and the air contains 2.92 percent, the ratio of density of the wet gas to that of

the wet air is 0.6542, but as the instrument has been set to read 0.0114

less than the ratio of the actual densities, the reading should be

0.6542-0.0114=0.6428, which is less than the specific gravity of the

dry gas referred to dry air by 0.0047. When the gas contains 4.8 percent of water vapor and the air contains 7.08 percent, the ratio of density of the wet gas to that of the

wet air is 0.6640. Deducting the 0.0114 introduced in calibration,

the instrument should read 0.6526, which is too high by 0.0051. Likewise, it may be seen from figure 41 that when the room was

at 77°, the air at its outlet was at 96.3°, and the gas at its outlet was at 100.4° F. By definition, the specific gravity is the ratio of

the densities of gas and air at the same temperature and pressure. Taking into account the direct effects of the differences of temperature at calibration and during the experiments at different temperatures in the same way that vapor pressures were taken into account,

it was found that, within the temperature range investigated, the

maximum error that can result directly from temperature differences

will be of the order of 0.001, which is a small fraction of the effect caused by differences in water vapor content.
Specific Gravities of Gases 127

As has been noted, certain assumptions were made in the computations of the effect of water vapor when the temperature of the room

in which the instrument operates is different from that at the time of

calibration. In many cases, perhaps in most, the gas will be partially

saturated before reaching the instrument, and a higher degree of

saturation during the measurement will result. There was some uncertainty whether in making corrections at one temperature with the

aid of data observed at another the corrections should be assumed

to be a constant additive or a constant proportional quantity.

Actually, it makes little difference which is assumed. The available

observations seemed to be in a little better agreement when a constant

correction was added. Although the errors computed are not exact,

they indicate that the temperature coefficient shown in figure 39 is less than might have been expected and may be accounted for on

this basis alone. The observed data relating to moisture content and temperature

of gas and air at the temperature of calibration of the indicating

instrument and during subsequent tests were considered in the same

way. When the room was at 77°, the water in this instrument was

at 95.6°. Gas was sampled at the rate of 12.6 cu ft/hr; air at 4.1 cu ft/hr. The gas was 75-percent saturated and contained 4.29 per- cent of water vapor; the air was 98-percent saturated and contained

5.6 percent of water vapor. If these had represented the actual conditions of calibration, the ratio of density of the gas to that of the

air in the instrument would have been 0.6604, but the instrument

would have been made to read 0.6475, the specific gravity of dry gas

referred to dry air, less than 0.6604 by 0.0129. Assuming, as in the

case of the other instrument, that the degrees of saturation of gas

and air remained unchanged at other temperatures, the actual ratio

of density of gas to air in the instrument should have been 0.6580

when the room temperature was 67° and 0.6671 when room temperature was 91.8°. Subtracting 0.0129 in each case, we should expect

readings of 0.6451 and 0.6542 at the two temperatures for the specific

gravity of the gas. The first of these figures is less than the specific

gravity of dry gas referred to dry air by 0.0024, and the second is too high by 0.0067. From the computations made, therefore, we should

have expected the reading of specific gravity to increase with an

increase of room temperature. The observed effect was a decrease,

which has not been accounted for. It may be that the conditions

of calibration and of saturation assumed in the discussion did not

correspond closely enough to the fact, or that some factor that has

not been considered affected the result. When the disagreement be- tween observed and computed temperature effect was discovered, it was too late to supplement the original observations with more complete data.

(2) Pressure Differences.—The operator adjusts the pressure of the

gas in the gas chamber, according to the directions supplied by the

manufacturer, by opening the valve on the sample line until the gage

at the gas inlet shows from one-fourth to one-half in. in negative

water pressure. The pressure of the air in the air chamber depends on the suction produced by the impeller and on the size of the orifice
128 Miscellaneous Publications, National Bureau of Standards

that limits its flow into the saturator. The difference between the

pressure of the gas and that of the air usually will not be more than

one-fourth in. of water, which would introduce an error of about

0.06 percent, which is negligible in comparison with other sources of

error.

(3) Purging.—If the gas chamber is incompletely purged, the sample may be contaminated by air, which will cause the specific gravity

indicated to be nearer 1.00 than it should be. It was found necessary

to purge at a hi-gher rate than the directions called for in the case of gases of very low specific gravity. The negative pressure at the

gas inlet was reduced to near zero to obtain a minimum steady

reading.

(4) Leaks.—Leaks of any sort will cause the indicated specific

gravity to be nearer 1.00 than it should be. Directions are given by

the manufacturer for testing for leaks, and periodic tests should be

made.

A leak, which had escaped attention in the laboratory, was dis- covered in the indicating instrument by the manufacturer when it was

returned for readjustment to the higher range. Larger errors were found with the indicating than the recording instrument ; generally,

they were in the direction that would have been caused by leakage,

and they were greater before than after the readjustment. It is probable that the errors of this instrument resulted, in part at least,

from this undiscovered leak. Unfortunately, it was not possible to repeat the tests with the gases of low specific gravity after the leak was discovered, and it is impossible to say definitely how many tests were affected, or to what extent. Eegarding the cause of the leak, the manufacturer stated that it "probably developed during the testing and was probably caused by

the fact that the instruments were shipped so lon^ before being tested,

during which interval the gaskets lost their resilience." (5) Calibration.—Any uncertainty as to the specific gravity of the

gases with which the instrument is calibrated will cause corresponding

errors in the subsequent indications of the instrument.

(6) Viscosity.—In order to determine whether the indication of

the instrument was dependent on the viscosity of the gas, two of the

test mixtures were prepared with specific gravities as nearly the same

as practicable, but with viscosities that differed as much as possible.

Mixture 6 consisted of 44.5 percent of helium and 55.5 percent of

nitrogen, with a specific gravity of 0.6007. Mixture 8 consisted of

63.1 percent of hydrogen and 36.9 percent of carbon dioxide, with a

specific gravity of 0.6080. Although the relative viscosities of these

mixtures are not known, the viscosities of both helium and nitrogen

are relatively high, and those of both hydrogen and carbon dioxide

are relatively low.

The numerical results, given in tables 12 and 13, show that in the

recording instrument the error was —0.0109 with mixture 6 and — 0.0001 with mixture 8. With the indicator, the errors were +0.0372

and +0.0393, respectively. On the face of these results alone it might

be concluded that viscosity appreciably affects the recorder but not

the indicator.
Specific Gravities of Gases 129

However, there are three reasons for doubting the validity of such

a conclusion: (1) The mechanisms of the two instruments are so nearly identical that such a difference seems decidedly improbable,

(2) the apparent effect on the recorder judged from these two mixtures is in a direction opposite to that anticipated, and (3) there is, in the case of test gases 9 to 13 with the recorder, a consistent trend

of error in the direction we should expect from the differences in vis- cosity which is opposite to that observed with test gases 6 and 8. Probably the observed difference between the errors in the last two

cases was caused by something other than viscosity, in which case the

trend in mixtures 9 to 13 may be significant. With one exception, the

trend with the same mixtures in the indicator was in the same direction, but in view of the observations with test gases 6 and 8, the trend

cannot be ascribed with certainty to the effect of viscosity.

(7) Readings.—The positions of the pointers and the recording

pen on the scales are in continuous fluctuation, the range of which,

at the middle of the scale, was initially about 0.015 specific gravity

unit in the recorder and about 0.003 in the indicator. After the range

of the recorder was changed for tests with the gases of specific gravities greater than 1.0, the fluctuation in the recorder, as shown by the

width of the line on the chart was nearly 0.025. Because of the smaller

width of the scale intervals, all the above figures, in terms of scale

units, are approximately doubled near the ends of the scale. Errors in the recorder may also result from lack of correspondence

of the readings of pen and pointer. These were adjusted as nearly

as possible to correspond at the beginning of the tests, and after changing the range of the instrument. Although the readings did not re- main identical, there was no consistent difference that could be

ascribed to a mechanical displacement.

The width of the pointer and of the marks on the scale make the

estimation of the third decimal difficult. (8) Effect of Relative Humidity on the Chart.—Tests of the chart

paper used on the recorder showed that a change of 80 percent in the

relative humidity will change the dimension of the paper by 0.72 percent in the 6-o'clock axis, and by 1.66 percent in the 12-o'clock axis. Small errors, under 0.001, for a range of relative humidity from 25 to 55 percent, will result on this account if the instrument is calibrated or used at relative humidities other than that existing when the chart was printed. At other relative humidities the circles on the chart will no longer be exact circles, and their radii will be different.

(e) COMMENTS ON OPERATION AND SUGGESTIONS FOR IMPROVEMENT

The following suggestions for improvement were made to the

manufacturer.

1. The temperature coefficient might be reduced by the use of driers

instead of saturators, but resistance to flow through a drier might be a problem as the pressure differences are low, and rapid purging is necessary. If the flow is not through a drier but over its surface (as in

the case of the saturator), drying might be as uncertain as is the

saturation. There is also the trouble and expense of constantly re- newing the drying agent. If complete saturation is desired, a more
130 Miscellaneous Publications, National Bureau of Standards

effective saturator might be devised, without introducing much more

resistance to flow.

2. It might be an improvement to open up the orifice controlling the entrance of air so that the flow of air would be approximately the same as that of the gas. Although saturation would be less complete,

it would be more nearly the same in the two cases.

3. In the indicating instrument, the knob of the zero adjustment

gets very hot after several hours of operation, especially if the temperature of the room is high. Although this knob is octagonal in

shape, it is smooth and is difficult to turn. A deep knurl might be

better than the smooth octagonal shape.

4. In the recorder, the spring bar over the chart, which raises the

pen off the paper, should be located far enough from the chart that

the paper cannot touch it and smear the record. This was accomplished by bending in the present case.

8. FISHER DENSIMETER (EXPERIMENTAL MODEL)

(a) INTRODUCTION

The apparatus called a densimeter by its manufacturer (fig. 43)

is of the type also called an effusiometer, but is more commonly re- ferred to as a "Schilling apparatus". The intervals of time required

for identical volumes of gas and air to flow through a small orifice are observed, and the square of their ratio is the approximate specific

gravity of the gas. The method was developed nearly a century ago

by Bunsen and Schilling. It has been studied at the Bureau of Standards by Edwards 4 and by Buckingham and Edwards 5 much more

completely than has been possible in connection with the present in- vestigation and was found to be inherently incapable of giving very

accurate determinations of specific gravities of gases of all compositions. A variety of physical effects are involved, which may, in a given

case, lead to compensating errors so that a highly accurate result is obtained, but the same apparatus may not give good measurements

with another gas or under slightly changed conditions. The conditions that cause error include changes in the orifice by minute dust

particules or condensed films of liquid, usually water, but the most

important effects involve thermal changes in the gas stream through

expansion, friction, and turbulence, and these are greatly influenced

by microscopic variations in the small orifices used.

It was found that the inherent accuracy of the method is improved

by increasing the difference of pressure on the two sides of the orifice and by increasing the size of the orifice, but both changes decrease the

time required for the efflux of a given volume of gas or air, and the

impracticability of accurately measuring short intervals of time be- comes the limiting factor in determining specific gravity unless the

volume of gas is correspondingly increased.

This fact supplies the answer to a natural question. A knowledge

of the specific gravity of gas is useful principally in connection with

the measurement of the flow of gas through orifices ; then why is not

the rate of flow through an orifice the best measure of the property

4 J. D. Edwards, Effusion method of determining gas density, BS Tech. Pap. T94 (1917).

5 Edgar Buckingham and J. D. Edwards, Efflux of gases through small orifices, BS Sci. Pap. 15, 573 (1920), S359.
Specific Gravities of Gases 131

with which we are concerned in metering? The reason is that orifice meters are used almost exclusively for the measurement of very large

rates of flow; the orifices are many thousand times the area of those

in the effusion apparatus, and they are usually under considerably

Figure 43.

Fisher densimeter (experimental model).

greater pressure. If slightly increasing the size of orifice and the

driving pressure in an effusion apparatus decidedly improves the

accuracy of determinations of specific gravity, it is evident that the

relative rates of flow of different gases through commercial orifice 719265—47—10
132 Miscellaneous Publications, National Bureau of Standards

meters must correspond much more closely to their true specific gravities than to i he erroneous specific gravities deduced from the rate of flow through the tiny orifice of an effusion apparatus.

In comparison with other instruments of its type, the Fisher Densimeter employs unusually large reservoirs and, for a water-sealed apparatus, an unusually high pressure, which certainly contribute to its accuracy. It also incorporates improvements of mechanical construction that add to its ruggedness and convenience. The accuracy of

the determinations made with this apparatus have been surprisingly

high. In the light of previous experience with instruments of the

effusion t}^pe, judgment must be reserved as to whether duplication

of the equipment (particularly the orifice) and conditions of testing

will be practicable to the extent of insuring equally good results with

all "densimeters" of this model.

(b) DESCRIPTION

The Fisher densimeter consists of a tall cylindrical Pyrex jar with

a flat disk of Bakelite for a cover. The under side is grooved to fit over the rim of the jar, and thumbscrews are set through the edge to clamp against the outside of the glass to hold the cover in place. A

metal tube is arranged to slide through a smooth bushing fixed in the center of the Bakelite cover, and passes through a glass globe attached

to the lower end of the tube by compression between rubber gaskets

at the top and bottom. The upper end of the tube is fitted with a cross to which are connected three Hoke needle valves for controlling

air, sample, and flow to the orifice, which is mounted, inclosed in a

fitting, above the upper needle valve. Stops are provided to limit

the motion of the tube, which is raised to allow water to drain out and air to flow into the reservoir, and lowered to a fixed position to provide a reproducible head of water to expel air or sample through

the orifice. The jar is marked to indicate the height of water in it when the reservoir is lowered against the stop and filled with water. Blackened etch marks run entirely around the tubes above and below

the reservoir to serve as markers in timing the flow of gas through

the orifice. A small accessory reservoir below the lower mark provides

space for partial compression of the gas when the filled reservoir is lowered into the water. The water flows in and out of the reservoir

through holes around the lower rim of this accessory reservoir. A

thumbscrew is provided in the side of the smooth bushing on the cover

to hold the movable tube and reservoir at the raised position if desired.

Gas flows in and out of the reservoir through a hole in the metal tube

placed close enough to the upper rubber gasket so that no gas is trapped when the reservoir and tube fills with water. The portion

of metal tube below this hole is drained by a similar hole in the tube

below the lower reference mark, and a small hole in the bottom cap, which holds the lower rubber gasket. The glass tubes carrying the

reference marks above and below the reservoir are of approximately

the same size, and slightly larger than the concentric metal tube, so that the moving water surface passing the mark is about the same

size in both cases. The jar contains about 8 lb of water, which jackets the reservoir
Specific Gravities of Gases 133

and serves to minimize fluctuations of temperature and to make any

changes in temperature slow and reasonably uniform.

No provision had been made for a thermometer, so a hole was drilled

in the cover, through which a thermometer could be inserted between

the reservoir and the jar to about the level of the center of the

reservoir.

(c) METHOD OF OPERATION

The directions for the operation of the instrument supplied with

it were followed, with various extensions, during the testing with

15 mixtures of known specific gravity.

In purging the instrument in preparation for a determination of

effusion time, the reservoir was filled three times, and the determination made after the third filling. The volume of gas in the metal

tube not displaced by water was estimated to be about 14 ml, which

is 2.G4 percent of the total estimated volume of 530 ml when filled to the lower mark. The specimen to be measured would contain this

proportion of the previous contents if the determination were made

without purging. If the determination were made on the second

filling, the specimen would still contain 0.07 percent of the original

contents, which was not considered negligible for the purposes of these

tests. The determinations were made after the third filling when the

specimen timed contained only a negligible proportion (0.002 percent) of the original contents. Before starting the flow, about 30 seconds was allowed for water

to drain from the walls of the bulb, and for the gas to become sat- urated with water vapor. When the flow was started as soon as practicable, about 15 seconds, after all water had drained from the bulb,

the effusion time was between 0.2 and 0.3 second shorter than when

1 minute had elapsed after the water had drained out before starting

the flow. Longer delay in starting the flow, up to 10 minutes, showed

no further increase in effusion time. It was concluded that drainage

and saturation were complete, at least as far as any measurable effect on the effusion time is concerned, within 45 seconds after the last water drained out, or 30 seconds after it would have been possible

to start the flow. During the manipulation of the instrument care was taken to avoid

unnecessary contact of the hands with the metal parts above the cover,

so that the temperature of the water might represent as nearly as

possible the temperature of the orifice as well as that of the gas in

the glass bulb.

A single determination of specific gravity consisted of three successive determinations of the time of effusion of the air of the labrat ory, followed immediately by purging the instrument with the

st gas and three successive determinations of the time of effusion,

gain followed immediately by purging with air and three more determinations of the effusion time of air. The average of each set of

three effusion times was computed, and the mean of the averages for

air was used with the average for the gas in computing the specific

gravity.

Observations of the temperature of the water and of the corrected

arometric pressure were made during each determination of effusion
1 34 Miscellaneous Publications, National Bureau of Standards

time. The temperature of the room was automatically controlled.

Consequently, changes in temperature were very small, and as the

times for air were taken before and after those for the gas, the necessity for any correction for temperature changes during a determination are obviated. In the absence of relatively sudden reversals of

direction in barometric changes, corrections for changes in barometric

pressure likewise are obviated..

In making a test of the instrument at a given temperature, with a given test mixture, two observers each made a series of five determinations of specific gravity by taking the effusion times of air and gas

alternately, finishing with air, and using the effusion times of air

obtained before and after each of the five effusion times for gas for the

computation of the five values of specific gravity. The 10 values of

specific gravity obtained by the two observers were then averaged.

The temperature and barometric pressure reported with each test is the average of all the observations of water temperature and of barometric pressure recorded during the test. In this apparatus both gas and air are saturated with water vapor

during the observations. The quantities directly observed are the

time, Tg, of efflux of gas and the time, Ta , of efflux of air. If we let

± a R is the "observed" ratio of the density of saturated gas to that of

saturated air. The ratio, i?, is not the specific gravity of the gas, which is the ratio

of the density of the gas as sampled (dry, in this case) to the density

of dry air. (See sec. I, 2, for definitions.) The ratio, R, can be con- verted to the specific gravity, by the use of equation 4, given in

section III, 2 (b), under the heading "adjustment of observations of

gas density for humidity and carbon dioxide." The equation is 0.622 w(g-l)

in which b is the barometric pressure, A is the head of water, and w the

vapor pressure of water at the temperature of observation, all in milli- meters of mercury.

Substituting the observed value of R, the average values of the

barometric pressure (753.6 mm Hg), the average head of water (9.4

mm Hg) and water-vapor pressure under the conditions of observation

(24.75 mm Hg),

S=0. 6542 +°^|^ft7^=0.6542-0.0072

£=0.6470.

Corrected specific gravity = 0. 6470

Specific gravity of test mixture 1 =0. 6474

Error of instrument = — 0. 0004

Error, percentage of standard specific gravity = — 0. 06

As the accuracy and reproducibility of the instrument might be ex- pected to differ with different conditions of temperature and with test gases of different specific gravity and different chemical constitution,

the data have been treated in the above manner for each of the test gases, and a summary of the results is presented in table 14.
Specific Gravities of Gases 135

gSfcSS

1+4-1 < ' ill ' 777+?

IIIII IIIII Hill

=j>++ I lllll I I I ++'

IIIII IIIII IIIII

lllll Hill lllll

° I I I I 1111+ +++++ urn mil urn

%M44 -H-H-H-H-H -fi -H 4i -H -H urn urn urn

^j-H-H-H-H -H -H -H -H +i -H -H -H -K -H gSSSSS sssss Wfff ++ri , 777+;

lllll IIIII lllll

^++++ ++' I I I I I I ++ mil mil mil

urn mil mil

in*

111

I

'2 £222:2
136 Miscellaneous PubUcations, National Bureau of Standards

The errors of the instrument, as observed, and after corrections for

the water vapor in both gas and air have been applied, are plotted in

figure 44. + .040 035

.030 .025 020 5 015 c 010 ^.005

Ulo

O 005

<rtr".OlO

015 020

025 030 -035

1KlIXT. NO. SYMBOL COMPOSITE

1 O MFD. GAS

2 A NAT^L " 3 O HELIUM

4,5,6,7 9 He-N2 6 S He-C02 9 • NITROGEN

10,11,12 a Nt -C02

13 C0 2 14 £ PROPANE

15 D BUTANE

J

3O

b

4

5 o

i J*

o

» 81 c t aa

10 _ a

NUMBERED POINTS INDICATE VALUES AS OBSERVED; 1

i i 1 1 1 a

UNN

AFT JMBERER C ED P DRREC

DINTS, TION VALUES

" e i

t i "

2

4 6 .8 1.0 1.2 1.4 1.6 1.8 2.0 SP GR OF TEST GAS Figure 44.

Error of the Fisher densimeter {experimental model) determined

with each test gas, The numbered point of each pair indicates the error as observed, and the unnumbered

point the error after the application of corrections for the water vapor in both gas and air.

(d) SOURCES OF ERROR

The various data that should be recorded during any determination

of specific gravity with the effusiometer are all potential sources of

error, as errors in the determination of any variable will affect the

final result. Variables are barometric pressure, temperature, material tested, effusion time, and the observer, in addition to more constant sources of error, such as the characteristics of the orifice, which

may differ from one to another. Figure 45 shows an enlarged outline

of the orifice supplied in the densimeter, with a scale from which its size may be estimated.

(1) Temperature Coefficient.—A test consisting of 10 determinations

of "specific gravity" by two observers using the same test mixture,

No. 1, was made at 67.2° F and another at 91.8° F, in addition to that

at 78.2° F described in the illustration discussed previously. The

results, as observed, and after correction to the dry basis, have been

plotted against temperature in figure 46. Straight lines, determined

by the method of least squares, have been passed through the three
Specific Gravities of Gases 137

points, and the slopes of the lines, constituting the temperature coeffi- cients, are indicated thereon.

It will be noted that the correction of the observed results to the

basis of dry air and gas have practically eliminated the large temperature coefficient, as well as the error of the instrument, which increased

rapidly with increasing temperature.

If M| f Ml

0.1 mm

Figure 45.

Enlarged outline of the orifice supplied with the Fisher densimeter

(experimental model).

66

\

TEST MIX"rURE n - 0.00 D0078 PE:r °f

I AS OBSERVED

II CORRECTED TO DRY GAS AND AIR

50 60 70 80 90 100 l!0 INSTRUMENT TEMPERATURE oc Figure 46.

Temperature coefficient of the Fisher densimeter (experimental

model) determined with test mixture 1, O as observed, and • after correction to the dry basis. The radius of the circle around each observed point is equal to the

probable error of the mean of the 10 determinations which that point

represents.

(2) Pressure Changes.—Barometric pressure errors will produce

small and usually negligible effects on the numerical result. The effects of uniform pressure changes that take place during a determination are
1 38 Miscellaneous Publications, National Bureau of Standards

eliminated by taking an air time before and after the gas time, and

using the average. However, a significant error may occur if the

change is of the order of 1 mm and is not uniform ; for example, a case

in which the barometric pressure varies as follows : During first air 760,

during gas 760, during second air 759, the average barometric pressure

during the two air times would differ by 0.5 mm from the pressure

during the gas time. This is 1/1520, or 0.66 percent. The effect of a change of pressure would be to change the density of the reference

air by 0.066 percent, and cause a difference in the observed specific

gravity of 0.0004, with a gas of approximately 0.65 specific gravity.

(3) Absolute Pressure.—An equal error in the determination of the

barometric pressure has less effect because it affects gas and air almost

alike. Specific gravity is independent of pressure, as long as the pres- sure of gas and air are the same, but the barometric pressure affects the

proportion of water vapor and so enters the formula for correcting

observed results to the dry basis. An error of 10 mm in the barometric

pressure would affect the correction of a gas of 0.65 specific gravity by

only about 0.00007.

(4) Changes of Water Temperature.—Temperature errors, as in the

case of barometric pressure, are significant largely in the form of

temperature changes that occur during a determination. The effects on the numerical result of uniform temperature changes are eliminated by timing the air both before and after the gas. Nonuniform changes of temperature of the water are unlikely in an instrument containing as much water as this one does, except when

hot gas is introduced, when excessive time elapses between timing the

two air samples, or when the temperature of the room is changing very

rapidly. If, as in the case of the barometric change illustrated above,

the first air and the gas are timed at the same temperature (77.0°F)

and the second air at a water temperature 1° F lower, two effects will

result. The average air temperature will be 0.5° lower than the gas

temperature, which will increase the average air density by 0.5/460, or 0.11 percent, which will make the observed specific gravity lower

than it should have been by 0.0007. The average vapor pressure of

the water in the air will be lower by 0.38 mm than its vapor pressure

in the gas. The effect of this is in the opposite direction to the first and amounts to 0.0001. Both effects together would yield a specific

gravity, corrected to the dry basis, which would be too low by 0.0006. Absolute errors in measuring the water temperature affect only

the correction to the dry basis, if the temperature is constant during

a complete determination of specific gravity. If the thermometer

reads 77.0° F when the temperature is actually 76° F, the vapor pres- sure of the water in both gas and air will be less than supposed by

0.78 mm. This will make the actual specific gravity greater than

supposed by 0.0002. As temperature affects the density, and consequently the time of 1

effusion, it is important that the temperature of the orifice be constant, as well as the temperature of the water, during a determination of specific gravity. It is necessary during the raising and

lowering of the bulb and the manipulation of the needle valves to handle the metal parts to which the orifice is attached. No attempt

has been made in this study to measure the temperature of the orifice, !
Specific Gravities of Gases 139

but care has been taken to make contact only with the handle of the

valves, and to keep the time of contact between the hands and the

metal parts as short and as uniform as possible so as to minimize

temperature variations from this source.

It is likewise important that the orifice should never be at a lower

temperature than the water, and that such adiabatic cooling as takes

place as the sample flows through the orifice never reduces the temperature of the sample below the water temperature. Otherwise,

condensation of water in the orifice may change the time of effusion

in the same way that dust adhering to the orifice would change it. (5) Material Tested.—An uncertainty as to the material being

tested, either air or gas, may arise through incomplete purging of

the instrument before effusion. If the apparatus is purged only

twice, with either gas or air, 0.07 percent of the previous contents remain. In the case of a gas of 0.6500 specific gravity, the effect of

the lack of complete purging is that the air actually used for comparison has a specific gravity of 0.99975 instead of 1.0000 and the gas

has an actual specific gravity (referred to pure air as unity) of

1.00025. When the impure air is compared with the impure gas the

observed specific gravity is 0.6505. Another possible source of error in material is the possibility of

starting the effusion of the sample before allowing sufficient time to insure equilibrium with water vapor. At 77° F and 30 in. Hg the

sample, when saturated, is composed of 3.1 percent water vapor and

96.9 percent of gas or air. Correction of the observed result to the

dry basis assumes complete saturation. Tests have indicated that if effusion is started as soon as possible after filling the bulb, the time of

effusion is shorter, in the case of air, by 0.2 second than the time obtained if effusion is started 30 seconds or more later. This is the limit

to which many stopwatches may be read, and perhaps as close as many

observers may be expected to repeat.

It should be noted that with all other instruments tested, except

the Eanarex indicator and recorder, the specific gravity obtained is that of the gas as sampled, including the water vapor contained in it. In the "effusiometer" and the Eanarex instruments the gas is saturated

or nearly saturated with water vapor before testing and its specific

gravity subsequently computed to a dry basis. No information is available as to the specific gravity of the gas containing water, unless an independent determination of its water content is made and a

correction applied. This fact did not affect the results of tests in

this study, since all test gases were dry to begin with.

The material tested is a source of more serious errors, however,

In that physical properties, other than specific gravity, have various

effects upon the flow of the gases through the orifice. These properties

include compressibility, thermal conductivity, and viscosity, and have

been discussed, along with the effects of the individual orifice, by

Edwards and Buckingham in Scientific Paper S359 issued by the

National Bureau of Standards in 1920. The effects of these variables

may be seen by an examination of the errors observed when the present series of 15 gases were tested with the single orifice in the instrument supplied (fig. 44).
140 Miscellaneous Publications, National Bureau of Standards

The following comment on errors from solubility and condensation was submitted by the manufacturer of the instrument

:

"It would appear that the errors of corrected values up to a specific

gravity of 0.9 are very small indeed. However, almost immediately

after the specific gravity rises above 0.9, the errors are progressively

greater. I believe we can explain this readily on the basis of solubility or compressibility of the gases. For instance, the greatest negative

error is that of pure carbon dioxide, while various concentrations of

carbon dioxide in nitrogen produce negative errors of lesser magnitudes. I believe the propane and butane values are in error probably

because of compressibility or condensation. It has always been said

that diffusion methods should not be used on the more imperfect gases, and I presume we can almost call propane and butane vapors, rather

than gases."

(6) Errors in Timing.—Such errors include lack of reproducibility

of the reaction time of the observer and various possible defects of the

stop watch.

In order to minimize the former, in this study, three successive

times have been averaged, before changing from gas to air or the

reverse. The stop watch may be an unsuspected source of error in several

ways. The hand may fail to return accurately to zero sometimes,

but not always. The watch may run fast on one side of the dial and

slow on the other, usually on account of the eccentricity of the dial. The magnitude and sign of the error would thus depend on the portion of the dial at which the hand was stopped. As this is almost

always different as between the time for air and for the gas being

tested, this will usually cause an error in the specific gravity. The

watch may tend to stick or hesitate at some point or points during a revolution, sometimes but not always, and a number of times this

happens during the timing of a sample, and its severity will vary

and introduce errors. The hand may jump at the start, always or only at times, with its consequent effect on the result. The effect on the specific gravity of errors in timing are magnified

by reason of the fact that the times of effusion of air and gas are squared before taking the ratio. The effect may be illustrated by

the following assumed case of two consecutive determinations consisting of three effusion times for air alternating with two for gas, with

the temperatures and pressures constant throughout.

Effusion time for Average effu- sion time for

air Time2 for air Time2 for gas Gas time 2 Air time 2

Air 120.0 Gas 97.0 Air 120.0 Gas 97.2

Air 119.8

| 120.

} 119.9

14400.

14376.

9409.

9447. 8

0. 6534

. 6572
Specific Gravities of Gases 141

Although the two average times for air are within 0.1 second of

each other, and the two times for gas are within 0.2 second of each

other, the resulting difference in the specific gravity in the two cases

is 0.0038. Of course, the assumption that the time for air fell 0.2 second and

that for gas rose 0.2 second in the second determination accentuated

the effect, but the situation is entirely possible with random errors of 0.2 second. Such large differences between the two gas times and

between the two average times for air may be decreased by substituting for each individual time the average of two or more times taken

successively. If the individual times show an extreme variation of

0.2 second, as the}7 well may, the differences between their averages will

decrease as the number of observations increases, with a corresponding reduction in the variation of the resulting specific gravity.

Even when three observations are averaged, as was the case in this

study, the variations in the resulting specific gravity may be large, as can be seen in the table illustrating the method of treating the data

in an earlier portion of this report.

It may be mentioned that the watch used in obtaining the data

in this study was compared over a complete revolution with an audible

signal from a standard clock and that none of the various defects mentioned above was detected.

(7) Errors of the Observer.—In the absence of defects in the

watch, the variations in time observed at constant temperature and

pressure with successive determinations on the same material may be

ascribed to either or both of two causes. They may be the result of

actual differences in time of effusion between the marks, they may

be the result of differences in the reaction time of the observer, or they may be the result of both. In all probability the observer carries the most of the burden.

During three tests, of 10 determinations each, a total of 70 sets of

three consecutive effusion times each were involved. The differences

between the longest and shortest time in each set are tabulated to show

the number of times each difference occurred in the 70 sets. Difference (sec) 0.0 0.1 0.2 0.3 0.4 0.5 Number of times found 14 16 27 6 6 1 Total, 70 Percentage of 70 20 23 38.6 8.6 8.6 1.4 It will be noted that 81.6 percent of the 70 differences were 0.2 sec- ond or less. The observations were divided equally between two observers. The observer may decrease the variations in the time observed also by practice, or '•education'', as illustrated by the same data. In the

following table the three tests have been separated to show the de- crease in frequency of the larger variations.

Difference (sec) 0.0 0.1 0.2 0.3 0.4 0.5 Total

( 1st test 6 5 3 4 5 1 24

No. of times found I 2nd test_ 6 5 8 2 1 22

1 3rd test 2 6 16 24
142 Miscellaneous Publications, National Bureau of Standards

(e) COMMENTS ON THE OPERATION AND SOME SUGGESTIONS FOR IMPROVEMENT

The following suggestions for the improvement of the Fisher densimeter, which was an experimental model, were transmitted to the

manufacturer.

If the instrument is used in a place where changes of temperature

of several degrees may occur, or if the screws are turned up too tight,

the screws bearing directly on the glass rim may start cracks in the

jar. Such a crack occurred in the model tested after the temperature

had been changed over a range of about 30 deg F.

(1) An opening in the cover for a thermometer would be desirable

since for accurate work it is necessary to know that the temperature

is constant or that it is drifting at a uniform rate. In addition it

is necessary to know accurately what the temperature is during a determination if the result is to be corrected to a dry basis. For ac- curate work this correction cannot be neglected, for at 77° F the

correction to a dry basis changes the specific gravity by approximately 0.007. (2) The clearance between the metal tube and the glass tube at the

upper mark might be increased sufficiently so that all water will drain

out when the reservoir is filled with gas. Water is sometimes held

up by capillary attraction unless the gas is admitted very slowly at

first. No difference in effusion time has been definitely traced to

this variable in the volume of gas, but the presence of the water at

this point produces an irregular surface as the water surface passes the upper mark and may decrease the precision of timing the flow. (3) When filling with air, the water level rises in the overflow bulb

to a point so near the mark that disturbance of the water surface

incident to opening the needle valve sometimes persists as the water

passes the lower mark. Also the time which elapses between opening

the needle valve and starting the watch is so short that starting the

watch at exactly the right time is made more difficult than is desirable.

These difficulties might be more or less completely overcome by

lengthening the lower tube between reservoir and overflow bulb about an inch.

(4) A rim of metal or other suitable material might be cemented

to the rim of the glass jar, against which the thumb screws holding

the cover in place could bear. A groove or depressions might be

ground in the glass near the rim to key the cement to the glass if necessary.

(5) Access to the thumbscrew that holds the bulb and tube secure seems somewhat obstructed by the handles of the gas and air needle

valves when in the lowered position. There is no certainty that anything can be done about this to advantage for it probably would not

be wise to lengthen the tube until the valves are above the screw, or to change the orientation of the valves. Locating the thumb screw on the back of the collar by rotating the cover 180° does not seem to be much less inconvenient.

(6) The metal tube frequently binds in the collar in the cover while

being raised. No lubricant would seem desirable on account of con- tamination of the water, and it is doubtful whether it would be desirable to make the fit any looser. No simple unobjectionable substitute

has suggested itself.
Specific Gravities of Gases 143

(7) The rubber gasket at the top of the bulb swelled gradually, so that after immersion in water for about 2 years it trapped a bubble,

and failed to fill completely with water at the exit hole as gas is displaced. The rubber might be replaced by some plastic material

which would not swell after prolonged immersion in water. V. DISCUSSION

1. INTERPRETATION OF THE RESULTS OF TESTS

The instruments submitted for test are all supposedly stock instruments as sold to the industry, with the exception of the Fisher densimeter, which is an experimental model. One instrument might be

expected to exhibit the same kind of behavior and give the same kind

of results as another that is apparently identical. But it is obviously

impossible to make two instruments that are exactly alike and that will

give identical results under the same conditions.

It should be kept in mind, then, that although one may expect the

results of the tests described above to give a valid indication of the

performance in general of other instruments of the same kind, the

results of the tests apply quantitatively only to the one instrument of

each kind on which the tests were performed.

It should also be kept in mind that these tests were performed under

optimum conditions, designed to determine the best of which each

instrument was capable. Variations in the conditions of use, especially

in the field, as well as less care in manipulation on the part of the

operator may be expected to result in less accurate and less reproducible measurements than those indicated in this report.

The instruments vary widely in the character of service and functions they are designed to perform. Some are designed for permanent

installations, some for portability, some for quick results, some for the

highest accuracy, some for recording, some for indicating, and others

for measurements from which the results are computed.

It seemed best, in this report, to express no opinions regarding the

relative merits of the instruments but to present all the facts observed

during their testing so that the characteristics of each may be con- sidered in connection with the individual requirements of a particular

user. It is to be expected that in the long time that has elapsed since the

various instruments were manufactured numerous improvements have

been made. Some of these may be the result of "suggestions for improvement," which were made to the manufacturers after this in- vestigation and which have been recorded in this paper because some

of them are known to have been adopted, whereas others probably

indicate the direction, at least, in which improvement is to be anticipated. It is not to be expected that everything suggested will be

found practicable or even desirable or that improvements will be

limited to them.

Washington, October 9, 1944. o