NBS MONOGRAPH 8

Mercuiy Barometers and Manometers

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTAIEXT OF COMAIERCE • Frederick H. Mueller, Secret, NATIONAL BUREAU OF STANDARDS . A. V. Astin, Director

Mercury Barometers and Manometers

W. G. Brombacher, D. P. Johnson, and J. L. Cross

National Bureau of Standards Monograph 8

Issued May 20, 1960

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 40 cents

Foreword

Preparation of this Monograph on mercury barometers and manometers

was undertaken to fill the need of manufacturers and users for information

which is now scattered thi-ough the literature and im some cases unpublished.

This mformation is primarily on the sources of error and methods for their

correction. Moderately extensive tables of corrections for temperatm-e, gravity,

capillarity, and other errors are included, mainly for application to portable

instruments. The various types of instruments are defined and design features

affecting the accuracy discussed in some detail. The preparation of this monograph is part of the work on pressure standards now in progress in the Mechanics Division, B. L. Wilson, Chief, imder

the direct supervision of E. C. Lloyd, Chief of the Mechanical Instruments

Section. A. V. AsTiN, Director.
Contents

Page

Foreword

1. Introduction 1

2. Definitions 1

3. Principle of measurement and standards 2

3.1. Principle of measurement 2

3.2. Standard conditions 3

3.3. Pressure units 3

4. Properties 4

4.1. Density of mercury 4

4.2. Vapor pressure of mercury 4

4.3. Surface tension of mercury 4

4.4. Compressibility of mercury 5

4.5. Purity and composition 5

4.6. Electrical resistance of mercury 6

5. Types of barometers and manometers 6

5.1. Fortin barometers. 6

5.2. U-tube barometers and manometers 7

5.3. Fixed cistern barometers and manometers. 7

5.4. Standard barometers 8

5.5. Recording mercury barometers 8

5.6. High pressure manometers 9

5.6.1. Single U-tube high pressure manometers 9

5.6.1. Multiple tube manometers .. 9

5.6.3. Ring balance 10

6. Design elements of barometers 10

6.1. Methods of detecting the mercury surface. 10

6.1.1. Sighting on the meniscus by eye.. 10

6.1.2. Sighting on an index 10

6.1.3. Mercury float 1 11

6.1.4. Sighting with a telescope 11

6.1.5. Photocell detector 12

6.1.6. Capacitance detector 13

6.1.7. Optical reflection detectors 13

6.1.8. Interference fringes 14

6.1.9. Resistance wire 14

6.1.10. Gamma-ray pickup 15

6.2. Measurement of mercury column height.. 15

6.2.1. Scale and vernier 15

6.2.2. Cathetometer and scale 15

6.2.3. Precision screw 16

6.2.4. Gage blocks 16

6.3. Illumination of the mercury surface 16

6.4. Vacuum above mercury column 17

6.4.1. Mercury sealed valve 17

6.4.2. Pump 18

6.5. Tubing 18

6.6. Alinement of scales and sighting devices.. 18

6.7. Instrument temperature 19

6.7.1. Measurement of temperature 19

6.7.2. Control of the temperature 19

6.8. Automatic compensation for temperature

and gravity error 20

6.9. Damping and lag 21

7. Sources of error 21

IV

Page

8. Scale errors 22

8.1. Zero error 22

8.2. Methods of test 23

8.2.1. Fortin barometers 24

8.2.2. Altitude barometers 24

8.2.3. Manometers 25

8.3. Barostat 25

9. Temperature errors 26

9.1. Basic formula 27

9.2. Fortin barometers, U-tube barometers and

manometers 28

9.2.1. Scale accurate at 0° C 28

9.2.2. Fortin barometers, scale accurate

at 62° F 28

9.2.3. Scale accurate at unknown temperature 29

9.2.4. Scale indicates pressure, instru- ment temperature not 0° C 29

9.3. Fixed cistern barometers and manometers. 29

9.3.1. Scale accurate at 0° C 30

9.3.2. Scale accurate at unknown temperature ^^ii

9.3.3. Scale indicates pressure, instru- ment temperature not 0° C 30

9.3.4. Fixed cistern barometers with an

altitude scale 31

9.4. Method of test 31

9.5. Temperature correction tables 32

10. Gravity errors 33

10.1. Basic relations . 33

10.2. Value of gravity at the instrument loca- tion 33

10.3. Variation of gravity error with latitude and

elevation 34

10.4. Gravity correction tables 34

11. Capillary errors 34

11.1. Tube 35

11.2. Cistern 35)

11.3. Correction table 36)

12. Return head and elevation correction 36

12.1. Definition of symbols 37s

12.2. Change in gas pressure with elevation— 37

12.3. Return head correction 38

1

12.4. Elevation correction, gas head 39

12.4.1. U-tube manometers 40

12.4.2. Cistern manometers 40

12.4.3. Barometers 40

1

12.5. Elevation correction, Uquid head 40 j 13. Vacuum error of barometers 41

14. Compression of mercury 41

15. Computation of corrections 42 r 15.1. Fortin barometer 42

15.2. Altitude barometer, fixed cistern 43 i 15.3. Manometer, U-tube 43

16. Testing at National Bureau of Standards 44

17. References 45
Mercury Barometers and Manometers

W. G. Brombacher, D. P. Johnson, and J. L. Cross

The various designs of mercury barometers and manometers are briefly described, with

a more extended discussion of the various design elements which may affect the achievable accuracy. Sources of error in measuring pressures are described in considerable detail, particularly for portable instruments, including scale, temperature, gravity, capillarity, vacuum

errors and return gas column. Methods of minimizing those errors and of making the corrections, including extensive tables, are presented. Standard conditions are defined and the pertinent properties of mercury given. The paper contains 65 literature references.

1. Introduction

. Mercury barometers and manometers are widely

;j used in aeronautics, meteorology, science, and

' industry. In aeronautics they are used to cali-

; brate a multitude of pressure measuring instrurnents, including altimeters, rate-of-climb meters,

airspeed indicators, manifold pressure gages and

, Mach meters, many of these instruments demanding continually increasing accuracy [581].^ In

, meteorology, mercury barometers are used to measure the atmospheric pressure. In industry

and industrial research laboratories barometers

^ are used principally to measure atmospheric pres-

, sure, whereas the mercury manometer has a

; multitude of applications.

The principal objectives in preparing this

Monograph are : (a) To outline the inherent errors

of mercury barometers and manometers and to provide information and tables for correcting these

errors; (b) to briefly describe the variety of design

elements of these instruments which are critical

in obtaining precision and accuracy; and (c) in some measure to contribute to national standardization of practices and methods of measuring

pressure with mercury columns.

A great deal of the material in this report reflects the experience of the National Bureau of Standards

in this field of pressure measurement. However,

a number of manufacturers have made substantial

contributions to the art. Present day needs are not only for increased

accuracy in pressure measurements, but also for an extension of the range of mercury barometers

and manometers. Mercury barometers and manometers up to 10 ft in height are now being

required but such instruments are relatively

awkward to transport and use. The reading diffi- culty is in a fair way of being eluninated by the use of the photocell detector coupled with automatic setting of the photocell to the mercury level.

2. Definitions

I 1. Pressure is the force per unit area exerted by

a gas, liquid, or solid.

1 2. Absolute pressure is the total pressure.

I 3. Differential pressure is the difference in presi sure of a fluid at any two levels or of two fluids

i at any two levels. The height of a liquid column,

! corrected to standard conditions, measures the

i differential pressure existing between the two

I menisci; when the pressure above one meniscus is

i zero, the absolute pressure is measured.

1 4. Gage pressure is differential pressure with

I respect to atmospheric pressure. Gage pressure

I plus the atmospheric pressure equals the absolute

i pressure.

I 5. Barometers (from haro—, weight +?w6^er,

I measure) are instruments for measuring the presI sure of the atmosphere. Manometers on the other

- hand (from mano—, thin, rare +meier) are instru-

! ments for measuring the pressures of gases or

I vapors. In both instruments the pressure may be

I balanced against a column of mercury in a tube or

I against the elastic force of a spring, an elastic

i diaphragm, or the like, as in an aneroid barometer.

> Fieures in brackets indicate the literature references on page 45.

Manometers are frequently used with other liquids

than mercury and often are used differentially in a U-tube with one end either open to the atmosphere

or to a gas under pressure. One authority [231]

considers all manometers to be differential manometers and says, "The barometer as generally understood, is a particular case of a manometer in which

one of the two pressures is zero." Thus, all of the instruments considered here are

strictly speaking, manometers, whether used to measure absolute or differential pressure. In course of application of barometers to other

purposes than given above, the definition of

barometers has been extended by common consent

to include many types of portable manometers

which measure absolute pressure. This distinction between barometers and manometers will be

followed in view of its convenience.

6. Aneroid barometers are barometers, the

pressure sensitive element of which is an evacuated

corrugated diaphragm capsule, a metal bellows or a Bourdon tube in contrast to mercury barometers

in which the height of a column of mercruy is a measure of the pressure.

1
7. U-tube manometers are those which have

two tubes the same in bore, commonl}^ having the

shape of an elongated U. The U-tube is filled with mercury or other liquid so that two liquid

sui'faces exist in the tube. The difference in pressure applied to the two liquid surfaces is measured by the difference in height of the two

liquid surfaces.

8. U-tube barometers are U-tube manometers

in which the pressure on one liquid surface, usually

mercury, is luaintained at essentially zero pressure, as by evacuating the space above the tube

and sealing the tube.

9. Cistern barometers or manometers are those

in which the diameter of one mercury column is much larger than the other to provide a reservoir

which is usually called a cistern. A single scale

mounted along the side of the tube is used to measure the height of the mercury column. There

are many forms of cistern barometers, some of

which have reasonably well accepted names, as indicated below.

(a) Fortin barometers are cistern barometers

in which the height of the mercury surface in the

cistern can be adjusted by eye to the level of a

fixed index, which insures a fixed zero reference

for the scale. These barometers are primarily

used to measure atmospheric or ambient absolute

pressure.

(b) Fixed cistern barometers usually have a

single scale ruled so as to compensate for the

change in zero position due to the rise and fall of

the mercury in the cistern with change in pressure.

(c) Fixed cistern barometers often are designed to measure only ambient pressure in which

case the space above the mercury in the cistern is not gas tight. The Kew barometer, developed in England and the Tonnelot, developed in France,

are of this type.

10. Altitude barometers are fixed cistern or U-tube barometers in which the design is such that

the absolute pressure in closed systems can be

measured. For this purpose the cistern of cistern

barometers is entirely sealed except for a connecting nipple. The U-tube barometer needs only a

suitable nipple. Altitude barometers of the fixed

cistern type, when used to calibrate althneters,

may sometmies have a scale calibrated in altitude

units corresponding to the altitude pressure rela-, tion of a standard atmosphere, in addition to aj,r' pressure scale. ^ 11. Standard, sometimes called normal, barom-J Jl' eters strictly speaking are barometers of the 'r* highest precision and accuracy. More loosely,T

they are barometers used to calibrate other ha,-r

rometers, to be suitable for which their errors must | be known, and their precision and accuracy should

be superior to that of the barometers to be tested.

12. The sign of an error in indication of an in- strument is determined by the relation ' ^ E^R-T

and of a correction by

C=T-R

where E is the error; R, the reading; T, the true* value; and C is the correction. It follows that

E=-C.

[ICOI

IlBt

13. Scale error is the error in the reading of a, barometer or manometer caused by errors inl, graduation of the seals and vernier. Practically

for portable barometers it is the residual error remaining after corrections normally made are applied for other errors.

j 14. Zero error is the error in reading of a

barometer or manometer when the differential! pressure applied to the two liquid surfaces is zero.

15. Correction for temperature is the correction

required to reduce the reading of the barometer or[|s

manometer to a reading corresponding to the

density of mercury and the length of the scale at

selected standard temperatures. See section 3.2 for the selected standard temperatures.

16. Correction for gravity is the correction

required to reduce the reading of the barometerj

or manometer to a reading corresponding to a^ selected standard gravity, discussed in section 3.2.,j 17. Capillary error is the amount that a mercury

meniscus is depressed below the height correspond-j

ing to the applied differential pressure of which thej

primary cause is the surface tension of mercury.

3. Principle of Measurement and Standards

3.1. Principle of Measurement where

In measuring pressure by the height of a liquid

column, the weight (not mass) of a column of unit area numerically equals the pressure difference.

For a liquid column in which the upper surface is subjected to a vacuum, the fundamental relation

for the pressure it exerts is P=pgh (1)

P is the absolute pressure in dynes per square |f

J

centimeter or pomidals per square inch at the

lower liquid surface, if '

p is the density of the liquid in g/cm^ or Ib/in.^;,

g is the acceleration of gravity in cm/sec^ or in./ sec^; and '

h is the height of the liquid column in centimeters

or inches.

Ml m
J If the pressure is desired at some other point in ^'the system differing in elevation from the lower

liquid surface, correction must be made for the

..I weight of the intervening column of gas or liquid.

X (See sec. 12). For manometers which measure

either the differential or gage pressure, the fundai mental relation is similar to eq (1)

f where

P=P2—Pi=pgh (2)

I j>= differential or gage pressm'e in dynes per

I square centimeter or poundals per square inch.

jPi and P2=the absolute pressures at the upper

I

! and lower hquid surfaces of the manometer.

The other terms have been defined.

Strictly speaking, the differential pressure

Ijidefined in eq (2) is the difference between the

.pressures impressed upon the upper and lower

liquid surfaces. At some other elevation or level,

correction must be made for the weight of the

intervening column of gas or liquid (see sec. 12).

u For both eq (1) and (2) pgh/gs is the pressm-e

Ifexpressed in grams per square centimeter or in •^pounds per square inch where Qs is standard

gravitv, 980.665 cm/sec^ or 386.088 in./sec^;

P OTp=

_ P9h

(1.1)

3.2. Standard Conditions

c In many cases the height of the liquid column

lis taken as a measure of the pressure, then

h=— or —

pg pg

(1)

Since both p and g are only approximately constant, some ambient condition must be selected

as standard so that this pressure imit bears a

.fixed relation to the metric or English unit pressure.

] The density of mercurj' at any one pressure is Ifixed by its temperature, hence it is general practice to use the density of mercury at 0° C subjected to a pressure of 1 atm. Since measure- ments are rarely made at 0° C, readings generally

require correction for deviation from 0° C. these

iare discussed in section 9. The height of mercury columns as a measure of

/pressure has been based for many years on a value

of the acceleration of gravity of 980.665 cm/sec^

1(32.1740 ft/sec^) by physicists and engineers

Oil]. While this value was selected because it

ikvas believed to be the value at 45 deg^ lat, there

iS little merit in tying a pressure standard to a

atitude, and imiform acceptance of a value is of

p-eater importance. Meteorologists have varied

ja their choice from time to time, using 980.62

bm/sec^ up to 1953, when the International

Meteorological Organization also adopted 980.665

cm/sec^ for this purpose [533, 534, and 556].

Corrections are usually necessary for deviation of

ambient gravity from the standard value, which

are discussed in section 10. Mercury manometers and barometers are often

calibrated to indicate the height of the mercury

column in terms of mercury at 0° C, when the

instrument is at another temperature, for example,

20° C, 25° C, 62° F, or 100° F.

3.3. Pressure Units

In cgs units the fundamental pressure unit is the dyne/cm^. By definition, 1 bar=10* dyne/

cm^, and accordingly the convenient unit, 1 mb= 1,000 dynes/cm^.

In English units, the primary pressure imit is the pomidal per square foot, but the practical

xmit is the pound per square inch (psi).

Another unit is the pressure of one atmosphere

defined for fLxed points on the International

Temperature Scale as 1013.250 mb [493]. This

definition provides for stability in the definition of

the pressure unit in atmospheres. This pressure

is equivalent to that exerted by a column of mercury 760 mm high, having a density of 13.5951

g/cm^ and subject to a gravitational acceleration

of 980.665 cm/sec.2 The value of 13.5951 g/cm^ was taken for the density of mercury at 0°C;

it differs only slightly from the value reported in a

recent determination at the National Physical

Laboratory [571], also table 4. Note that owing to the slight compressibility of

mercury under its own weight, multiples or submultiples of 760 mm of mercury do not precisely

correspond to the same multiples or submultiples of

1013.250 mb. Except for very precise pressure

measurements, this difference is neglected.

Conversion factors for a number of commonly

used pressure units are given in table 1. The

conversion factors for centimeters and inches of

water are based on a value of the density of water

at 20°C of 0.998207 g/cm. For values of the

primary units involved in computing table 1 (see ref. [551]), except for the value of the pound

in terms of the kilogram and the inch in terms of

the centimeter. Changes in the conversion factors

have recently been adopted, retaining as standard

the mass of 1 kg and the length of 1 cm. The

change is 2 parts per million in the length of the

inch (shorter) and 2 parts per 15 million in the

pound (smaller). Most of the table is also ac- curate for the obsolete units.

The units, gram per square centimeter, pound

per square inch, etc., involve a force of Ig or of

1 lb. This force is a mass of 1 g or 1 lb. subjected

to the standard value of gravity, 980.665 cm/sec^

or its equivalent, where required.

Other units often used are: (a) barye = l djme/cm^ (b) micron =0.001 mm of mercury;

(c) tor (or torr) = 1/760 of 1 atm, closely, 1 mm

of mercury; pieze (French) = 10 mb.
4. Properties of Mercury

Only the properties of mercury of importance

in manometrj^ will be discussed. The melting

point is —38.9°C and the boiling point at 1 atm,

about 357°C. For general information on mercury see ref. [421, 522, and 574].

4.1. Density of Mercury

A redetermination of the density of mercury is in progress at the National Physical Laboratory;

the density by one method of measurement [571]

is 13.5458924 g/cm^ at 20°C under a pressure of

1 atm. This value reduces to 13.5950889 g/cm^

at 0°C,avalue not significantly different from that

generally accepted, 13.5951 g/cm^.

Based on the value for the density of mercury

at 0°C, the density at other temperatures is obtained from the relations

V=Vo (1 +0.0001818 t), t in °C (4)

V=Vo (1+0.0001010 (^-32)), t in °F (5)

V

(6)

where V, specific volume at temperature t and at 0°C

p=the density.

Equations (4) and (5) apply primarily when

mercury is subjected to a pressure of 1 atm.

Practically they are useful up to the point where

the compression of mercury becomes significant,

certainly up to at least 1 atm.

The value of the coefficient of cubical expansion

m= 1,818 X 10~^ per ° C is a sufficiently accurate

approximation which is widely used, and standard

for most purposes. More accurate values, based

upon the relation,

mX10«=18144.01 + 0.7016t

+ 0.0028625^2+0.000002617^3

are given in ref. [413], where t is the temperature

in ° C, from 0° to 350° C. The exact mean values

of 'm—{Vt—Vo)/Vot are given below for a few

temperatures; for a more extended table see table

10 of ref. [413].

The value of the density of mercury at temperatures above 0° C is less than the true value

when computed using m= 1,818X 10""'^. It is seen

that for room temperatures, the approximate

value m is sufficiently accurate for use in manometry in all but the most precise work.

The ratio of the density of mercury at ^° C to that at 0° C are presented in table 2. These are taken from table 12 of ref. [413] and are based

4

Temperature True Error in density

coefficient using eq (4)

° C mX10» Parts per million 0 18, 144 0

1U_ 18, 151 2. 9 20 18, 159 4. 2 30 18, 168 3. 6 40 18, 177 1. 2 50 18, 187 3. 5

t

II

upon the precise value of the coefficient of expansion, not the average value 1,818X10"'' per ° C.

Values of the density of mercury are given in tables 3 and 4 for various temperatures. These

are based upon the ratios given in table 2 ; in table

3 upon the value of 13.5951 g/cm^ at 20° C, all when the mercury is under a pressure of 1 atm.

The density in g/cm^ is given in table 3A, and in

lb/in. ^ in table 3B. In table 3B the recently t adopted values for the inch and the pound given

in table 1 were used to obtain the density in Ib/in.^;

these densities are 5.9 parts per million smaller

than those based upon the previous values.

Tables of the specific volume of mercury at various temperatures and of the true temperature

coefficient of mercury, dV/Vodt, are given in ref. [413].

4.2 Vapor Pressure of Mercury

The vapor pressure of mercury is given in table

3A, computed from the equation

log P=11.0372-

3,204

where P is the vapor pressure in microns of mercury; and T is the absolute temperature in ° K.

This is an empirical equation derived by Ernsberger and Pitman [558] to fit the data of previous

investigators and fits their experimental values

within 1 percent in the temperature range 12° to 53° C. These values agree closely with the computed values given in ref. [516] and are about 2

percent lower than the computed values in ref.

[ [535]. The vapor pressures given in the Inter-; national Critical Tables and in ref. [531] are about

10 percent lower, and those in ref. [414], stilly

lower. See ref. [471] for data at temperatures

higher than listed in table 3A and for references to

earlier original work. i

4.3. Surface Tension of Mercury

The best value for the surface tension of mercury

[461] and [494] is 484 at 25° C, 479 at 50° C, and

' 474.5 dynes/cm. at 75° C. This refers to mercury

j in a vacuum. For mercury in contact with air no

[ valid data appears to exist [494] but is expected

I
to be somewhat less than for a vacuum. Impurities

and particularly oxidation will affect the surface

tension of mercury, probably lower it, but the

amount of change is speculative. See section 11

for a more detailed discussion.

4.4. Compressibility of Mercury

C. H. Meyers at the National Bureau of Standards, based on Bridgman's data, arrived at the

following values for constant a in eq (11), to cover

the pressure range up to 1,000 in. of mercury:

a= 1.36X10"'' for P in in. of mercury, and

0=5.36X10"' for P in mm of mercury. These

data are unpublished.

The decrease in volume, aF, per imit volume of

! mercm-v with increasing pressure P in bars at 25°

: C is [121, 542]:

AF=4.0391X10-« P-0.7817X10-'°P-

+0.191X10-^" (7)

For most manometer applications the approxi-

- mate relation given below is satisfactory

AV=aP-hrwhere

a=4.04X10-^ 6 =0.78X10-'° for P m bars

(8)

If a=4.09X10-^ 6=0.80X10-'° for P in atmospheres

|j|a=5.38X10-^ 6 =0.81X10-'« for P in milli-

' meters of mercury

a=137X10-^ 6 =89X10-'^ for P in -inches of

merciu-y

Computations based on eq (8) follow:

Pressure bars

0

1 10 100

1, 000

Decrease in unit volume

0

4. 04X10-6

40. 4 X 10-6

40. 3 X 10-6

3, 960 X 10-«

Density of mercury

gjcm ' 13. 59505

13. 5951

13. 59565

13. 60058

13. 6478

It follows that for pressures below 10 atm the

last term in eq (8) can usually be neglected, and

or

and

^V=aP

V={l-aP)V,

P=l3^=Po(l+aP),

(9)

(10)

(11)

where a is a constant with values given above for various units of pressure : V is the volume at unit

pressure P; po, p are respectively the density of

mercury at zero pressure and at P.

4.5. Purity and Composition

The possible variation of iso topic composition of

mercury from various sources and subject to vari- ous processes, primarily distillation, affects the

density and is therefore important in precise manometry. Estimates based upon some data indi- cate that the variation in the density of mercury

will not exceed one part in 30,000 due to extreme

variation in isotopic composition. However, exact data on isotopic composition of mercury secured

from different sources or subjected to various procedures in distilling are lacking to a large extent. See ref. [571] for a review of the present situation.

The effect and methods of removal of impurities

are of particular interest. All but traces of metals

dissolved in mercury can be removed by a procedure of distillation [574]. Methods of testing for purity of mercury are discussed in ref. [571], which

indicate that with isotope tracers one part in 10 ^ of base metals can be detected. Very small quantities of base metals which form an amalgam with

mercury, rise to the surface and are easily detected

by the surface contamination.

Air is not absorbed by mercury, as is indicated

by the fact that barometers have maintained a good vacuum above the mercury column for years. However, air bubbles may be trapped in the mercury, and should be removed, usually accomplished by subjecting the instrument to several

pressure cycles while jarring the instrument

sharply.

Water trapped in mercury can only be removed

by subjecting the mercury to a temperature above

100° C. Water in a barometer is particularly

troublesome since a satisfactory vacuum cannot be

obtained above the mercury column.

In general, mercury compounds are formed as a

result of contact of air and other gases with the

mercury surface, and remain there. Gases containing sulfur are particularly active in forming

such compounds. Detection of such compounds,

even in small amounts is simple; accurate observations on the mercury surface become difficult or

impossible.

On procedures for cleaning mercury, see refs. [531, 561, 571, 574, 591].

Experience indicates that mercury remains free from contamination when stored in bottles of soft

glass, at least more so than in containers of other

materials on which extended experience is available. 536771—60—2 5
4.6. Electrical Resistance of Mercury

The electrical resistivity K of mercury is: SB Kl (12)

where E is the resistance, I the length of the column

in centimeters and S the area of the cross section

in square centimeters.

At 0° C, K=M.Q1 and at 100° C, 103.25 I Mohm-cm [531]. These values are for a pressure of

1 atm and they decrease measurably as the pres- sure increases [191].

5. Types of Barometers and IManometers

Barometers and manometers are basically simple instruments where the primary measurement

to be made is the height of the mercury column.

Other measurements must be made also in order to convert the indicated height of the mercury col- umn to accepted or standard pressure units.

Many factors must be considered in the design

of a barometer or manometer such as portability,

range, accuracy, convenience and degree of automation in making readings, and usefulness for the

application. As a result many designs have been

evolved. The principal designs will be only briefly

considered, since the emphasis here is on perform- ance rather than design. The descriptions in this

section will be augmented in the next section by some design details of the means which are used to meet problems more or less common to all barometers and manometers.

The essential features and components of a first class barometer are indicated in figure 1 . Alternatives for detecting the position of the mercury

surface and for measuring the column height are indicated; these and the other components will be

discussed in this and the succeeding section . When

the accuracy required is not high, some of the

r

[PRESSURE SIDE

M G

VACUUM SIDE

]r_ _TE^1PERATUR^E _CONTROLLED_SPACE j

FiGUEE 1. Principal elements of a precise laboratory ba- rometer system.

T, barometer tube; DR, restriction in tube bore for damping; S, scale, or precision screw plus controls, or gage blocks; sighting device, not shown,

either telescope, photocell or other optical devices; MG, McLeod or other vacuum gage; CT, liquid air trap; DP, diffusion pump; FP, forepump;

F, filter; B, barostat; A, air supply; TP, vacuum pump; and P, line to point where pressure is to be measured.

components or accessories can be and are omitted,

but for highest accm^acy the function of all is significant and where selection is possible, those

producing the gi'eater accuracy must be chosen.

There are a large number of clever schemes for

amplifying the indicated height of a mercury

column, particularly in measuring small differ- ential pressm-es. The precision of reading is thereby increased, also the acciu-acy, but not to the same degree as the precision. Most of the

schemes require some extra manipulation. The

devices described in ref. [453, 513], are exceptions

in that they are automatic in operation. Another

device, not automatic but easily made so, is described in ref. [483]. See also ref. [391] for descriptions of a number of designs. These devices

all come under the general head of micromanometers, which include mechanical devices also; detailed consideration of these is in general outside

of the scope of this report.

5.L Fortin Barometers

The Fortin barometer is one of the oldest forms

of commercial barometers, having been used for

measuring atmospheric pressure by meteorological

services for about 100 years [301]. The barometer

tube is surrounded, except for reading slits, by

metal tubes one fixed to the cistern assembly and

another short one, movable up and down within

the first. The movable tube carries the vernier

and ring used for sighting on the mercury meniscus.

The fixed tube has the pressure scale, usually

plated brass, adjustably attached to it. The cistern has an index fixed to its top wall,

usually a thin ivory or bone rod, tapering to a

point at the lower end. The cistern is essentially a leather bag which can be raised or lowered by a metal plate at the end of a screw, which can be

turned by hand at the bottom of the cistern. To take a reading the mercury in the cistern is brought up until it is just in contact with the index,

thus bringing the mercury surface into alinement

with the zero of the scale. Valid readings are made only when the mercury level in the cistern

is so adjusted. Since the lower end of the scale

does not extend to the cistern, the distance from

the cistern mercury surface to a point on the

graduated scale must be determined, usually by

comparing at the same pressure the reading of

the Fortin barometer with that of a standard

barometer.

6
j The Fortin barometer can be used only to measI lire ambient pressui'e and is widely used by meteor-

' ological services and in laboratories to measure

I atmospheric pressure. Pressm-e equilibrimn with

I the ambient gas is obtamed in the cistern by a vent at its top or through the chamois seal above

the merciu-y.

The most common range of the Fortin barometer

is 28 to 31 in. of mercm-y (about 950 to 1,050 mb;

i about 710 to 790 mm of mercury). For use at

i stations well above sea level, barometers with

I ranges extending from 20 to 31 in. of mercury

have been built. With no great trouble the range

could be fi'om 4 to 5 in. of mercury upward to any value within reason, but in practice it is tailored to the range of pressures expected at its location.

The quality of Fortin barometers is measured

: practically by the bore of the tubing used, which

in large measure also determines the diameter of

I the cistern. Fortin barometers are commonly

made in this coimtry with tubing either 0.25, 0.6 •or 0.8 in. bores. For modest accm-acy measureI ments, which is for the most laboratory require-

, ments the irreducible limit, the tubing bore is 0.25

I in. (6.35 mm). For the highest accuracy reason- ably attainable with Fortin barometers, the tubing

bore is about 0.8 in. (20.3 mm). The slight inI crease in accuracy obtained with the 0.8 in. bore

is balanced by the greater degree of portability

of the 0.6 in. bore barometer.

!l The Fortin barometer is designed to 'be safely

portable in the upside down position. Before

slowly tipping it over, the cistern mercury level control is operated to force mercury up the tube

until the cistern is nearly filled. Thus splashing

; of the mercury is practically eliminated and the vacuum in the tube preserved. See [591] for detailed instructions.

5.2. U-tube Barometers and Manometers

In its simplest form the U-tube barometer or manometer consists of a U-tube containing mercury and a scale between the legs of the U for reading the position of the two mercury surfaces. If

! precision bore tubing is used, reading the position

' of the mercury surface in one leg may be sufficient. In manometers the pressure to be measured is applied to one leg and the other leg left open to the atmosphere if gage pressiu-e is to be measured,

I or connected to the reference pressure if differ-

' ential pressure is to be measured. In barometers

the space above the mercury sm'face in one leg is

I evacuated.

j The above described design of U-tube manomjeter is widely used; of barometers, less so. The

'described reading means are crude so that both

: the precision and accuracy are low. A big step

in improving the accuracy is to add a vernier and

a means for sighting on the mercury surfaces.

This and other reading means are discussed more

fully in sec. 6.

In order to reduce the error due to the capillary

depression in fixed cistern barometers, discussed

in a later section, barometers of the highest precision and accuracy are of the U-tube type.

Diverse reading means and additional accessories are used as discussed in sec. 6. U-tube manometers are used conveniently to measure gage pressures up to about 50 psi (about

3 to 3J^ atm); for this range the mercuiy column

is about 10 ft (3 m) high. Manometers for measuring differential pressures at high pressures are discussed below in section 5.5. Manometers may

be used to measure absolute pressures if the space

above one mercury surface is evacuated.

5.3. Fixed Cistern Barometers

and Manometers

Mercury barometers in which the mercury level in the cistern cannot be adjusted during the reading process are called fixed cistern barometers.

Here the barometer tube extends below the sur- face of the mercury in a cistern of much larger

cross section than the tube so that the rise and

fall of mercury level is small, but not negligible,

in comparison to that in the tube. The larger the

cross section of the cistern, within limits, the less the zero shift due to change in the meniscus height

of the cistern mercury.

To compensate for the rise and fall of the mercury level in the cistern with pressure, the scale graduations are foreshortened, that is 1 mm dif- ferences in reading on the scale are less than 1 mm apart. Thus

AR

''A+a (13)

where

D=the distance between two graduations

R=the indicated interval between two graduations

^=the cross sectional area of the mercury in the

cistern

a=the internal cross sectional area of the tube.

In practical designs D/R will vary from about 0.97

to 0.985.

In fixed cistern barometers used to measm'e only

ambient atmospheric pressure, the cistern is vented

to the atmosphere. This form of barometer, heavUy damped by a restriction in the tube bore, is commonly used on shipboard by the meteorological services of the world, but is being superseded

gradually by aneroid barometers because they are

less sensitive to acceleration. In Great Britain the

fixed cistern barometer of this type is called a Kew

pattern barometer and is the type chiefly used by

the British Meteorological Office. A French design

which has had, and probably stUl has, some application is known as the Tonnelot barometer. The

chief virtue of the Tonnelot barometer is that an

adjustment is provided for reducing the cistern

volume, as in the Fortin, so that the tube and

cistern can both be completely filled with mercury

to obtain safe portability.

ll
The fixed cistern barometer lends itself to securing a leak tight cistern so that gas pressures

in a closed S3^stem can be measured. It has been

and is widely used as a working standard for

calibrating altimeters and aneroid barometers.

For such use the cistern is made airtight except

for a nipple, to which a chamber or instruments

themselves are connected by tubing. Pressure

control means are connected to the system.

In earlier designs the cistern and barometer

tube were made coaxial. However, as lower and

lower absolute pressm-es have had to be measured,

it has been found necessary to have an offset cistern so that readings can be made down to zero pressure. Obviously, fixed cistern manometers have

also necessarily had to have offset cisterns if dif- ferential pressures below about 3 in. of mercury

were to be measured. Reasonable accuracy is difficult to attain at pressures below about 1 mm

of mercury in designs having a range to an atmosphere and above from either the cistern or Utube instruments. Measurements of absolute

pressures below 1 mm of mercury are in the realm

of vacuum measurement which is outside of the

scope of this report.

Fixed cistern barometers have generally been

constructed to measure pressures below about 1 atm. Barometers have been built to have a range

up to 2 or 2}^ atm, but these instriunents are bidky

and unwieldy to transport.

The scale is usually graduated in pressure units

but often has an added altitude scale based upon

the altitude-pressure relation of the standard at- mosphere. A vernier sensitivity as low as 0.05 mm

of mercury (0.002 in.) is sometimes provided with

the idea of realizing this accm-acy. However, the

accm-acy of a fixed cistern barometer is limited by

uncertainty m surface tension effects in the cis- tern to at least 0.1 mm of mercury, as discussed

in sec. 11.

5.4. Standard Barometers

A primary or standard barometer may be defined as a barometer which measures absolute

pressm-es with precision, and requires no comparison test with another barometer to determine its en'ors. Perhaps, and preferably, a standard barometer is an instrument which measures absolute

pressure with an accuracy greater than that of the

barometer or pressure gage under test. A better

term in many cases is working or secondary standard. Under the latter definition a calibrated

Fortin barometer with a tube bore of 0.6 in. is a

suitable standard for testing Fortin barometers

with a tube bore less than about 0.4 in. Also a

fixed cistern barometer when used to calibrate

altimeters and aneroid barometers is a standard

barometer.

Discussion here will be limited to standard

barometers the calibration of which is made in

terms of the basic standards of mass, length, and

time and thus require no calibration by comparison with another barometer. Highly precise and

,

accurate barometers or manometers have been;

constructed at the National Physical Laboratory

[333, 552], Massachusetts Institute of Technology,

[412], International Bureau of Weights and Measures [592], and the National Bureau of Standards

[545, 553]. In these a great deal of attention has

been given to the reduction insofar as possible, of

all sources of error and uncertainty in order to obtain an accuracy of at least 0.001 mm of mercury. Convenience in making readings, however,

has had to be sacrificed to accuracy.

The National Physical Laboratory standard

barometer [333] has also been constructed, with some modifications to extend its pressure range, by

the South African National Physical Laboratory

[557]. The Physikalisch-Technischen Bundesanstalt, Braunschweig, also has constructed a standard barometer with an accuracy of 0.005 mm of

mercury [576] (see sec. 6.1.2).

All of the above instruments are of the U-tube

type; other design details will be discussed in

sec. 6. A standard barometer constructed at the University of Helsinki [554], has an estimated accm'acy

of 0.01 mm of mercury.

For calibrating portable barometers the National Bm'eau of Standards has another standard

barometer of the U-tube tj''pe which can be read

to 0.01 mm of mercury, and has an accuracy of 0.02 to 0.03 mm of mercury. This accuracy is sufficient for most portable barometers submitted,

but improvements to increase accuracy are in- evitably becoming necessary as requirements for

portable barometers become stringent. This

barometer is briefly described in reference [491],

but many of the design features wiU be touched

upon in sec. 6.

5.5. Recording Mercury Barometers

A number of designs for recording atmospheric

pressiu-e based upon the mercury barometer were

developed in the period around 1900 [301]. These

never came into general use, in view of the greater

convenience and portability of the barogi'aph

based upon aneroid capsules, particularly since

the latter proved adequate in performance for

meteorologists. Principally, the primary designs were based upon: (a) The rise and fall of a float in the mercury of the barometer cistern; and (b)

the use of a beam balance to weigh either the

barometer tube or cistern which varies approximately as the atmospheric pressure. For relatively rough measm-ements, the height

of a mercury column has been recorded by recording the change in resistance or voltage of a fine wire extending through the mercury column. The

resistance or voltage drop varies regularly as the

length of wire immersed in the mercur}^ column

changes and thus is a measure of the pressure. (See ref [532] and sec. 6.1.6.)

A record can be obtained of the height of a mercury column if the position of a photocell is

til

ai

iio

8
i governed hr a precision screw or other means.

I Since power is available to drive the screw, its

II angular deflection can be recorded by various means. One such recorder is described by Haynes

" [511] for obtaining a record of the calibration of

'j the baroswitches of radiosondes.

5.6. High-Pressure Manometers

Mercury amalgamates with steel at high pressm'es, causing the failiire of steel vessels containing

mercury, more likely in the case of hardened than

• soft steel. Experiments [496] indicate that ulti-

• mate failure of steel tubes will occur at pressm'es

' in the range 4,000 to 6,000 atm. No data are

available on stainless steels. For practical reasons high pressiue mercury

; manometers have generally been hmited to about

= 60 ft, giving a pressure range of about 24 atm

(360 psi). To obtain higher pressures, two designs

are available. The first, practically useful only to calibrate piston gages, consists of a single U-tube

and requires in addition two piston gages in order

to transfer the measmements as the mercury

' colmnn is subjected to steps of absolute pressure

to the ultimate range desired, which may be

many times the difl^erential pressure measurable

with the U-tube manometer. See the next section

;';for additional details.

'I The second design is the multiple manometer

'= consisting of a series of U-tube mercury, columns,

i with the low pressiue side of one mercury column

' connected to the high pressure side of the next

'' mercury column. (See sec. 5.6.2.)

For measming small differential pressures at

i <| high pressure a ring balance has had some applicaIjl tion. (See sec. 5.6.3.)

5.6.1. Single l7-tube High Pressure Manometers

Keyes and Dewey [271], Michels [321], and Bett,

!v Hayes, and Hewitt [541] have constructed single

'\ U-tube mercury manometers for measuring differ-

! ' ential pressures at high pressure. AE were prif 1 marily used to calibrate piston gages. The essen1 1 tial features of the Bett et al., manometer are H typical and will be described.

The manometer is about 30 ft high, with the

ii' tubes water jacketed to maintain them at constant

' temperature. The two mercury surfaces are

' detected by fixed electrical contacts, requiring

' adjustment of both the pressure and volume of

' mercury in the system to obtain a valid reading.

! Keyes and Dewey also used electrical contacts to

t

j detect the mercury surfaces, but made them verti-

-

j cally movable with means to measure the movei ' ment. An invar tape is used to measure the

t

j differential in height between the electrical coni ' tacts, which is necessary since compression effects

1 can be expected to change this distance as the

• absolute pressure is increased. Elaborate provision is made for transferring the position of the

i|' electrical contacts horizontally to the measuring

3 tape.

The manometer can be used to calibrate piston

gages at pressure steps equal to its differential

pressure range. Two piston gages are required.

These, installed at levels between the mercury

surfaces, are connected to the manometer, alter- nately to the lower and higher pressure leg of the

manometer at each pressure step. The connecting lines are filled with a petroleum derivative

which has relatively good viscosity characteristics at high pressure. Valves are provided to connect

the piston gages to either leg of manometer, as

desired.

In operation, the pressure difference of each

step is determined from a knowledge of the height

of the mercury column, of necessity corrected to standard temperature and gravity, and corrected

for compressibility of the mercury. This pressure

difference must be transferred to the piston of the

piston gages, which requires a knowledge of the

difference in elevation between the mercury sur- face and the piston, and of the density and compressibility of the transmitting liquid. To obtain

pressure continuity so that the total pressure on

the piston gages can be determined, a reference

pressure must be established in passing from one

pressure step to the next. This is done by a pres- sure balance on one piston gage when connected

to the lower leg of the manometer (high pressure)

and then, without changing the weights, connecting it to the upper leg of the manometer (low pressure). The pressure in the low pressure side of

the manometer is then adjusted so the reference

piston is in balance. Except for some small rela- tively constant corrections involving the transfer

liquid column, the pressure continuity is preserved.

It is obvious that the sum of the differential

pressures (plus atmospheric pressure) equals the

total pressure. From the weight balancing the

pressures acting on the pistons at each step, the

effective area of the piston can be computed.

It is of interest to note that Bett and his co- workers plan to calibrate piston gages to 2,000

bars (nearly 2,000 atm, 30,000 psi) involving 175

transfers. Keyes and Dewey had a manometer

about 28 ft high and calibrated piston gages to nearly 600 atm (about 9,000 psi). Michels

avoided the labor of the continuous step-by-step

process and used his manometer to calibrate piston

gages against differential pressure only at selected

aboslute pressures, known only approximately.

An elaborate discussion of the sources and

amounts of the errors in high pressure U-tube

manometers is given by Bett et al. [541].

5.6.2. Multiple Tube Manometers

Multiple tube manometers have been extensively developed for use in measuring pressure in

physical experiments by Meyers and Jessup [311]

and Roebuck and his coworkers Grain, Miller, and

Ibser [371, 544]. The manometer of Jessup and

Meyers, using glass tubes, had a range of 1,000 psi

while that of Roebuck went to 3,000 psi (200 atm).

9
The Roebuck manometer will be briefly described. The instrument has U -tubes connected

in series so as to secure nine mercury columns.

The transmitting liquid from the top of one mercury column to the bottom of the next was toluene.

The tubes were of steel, Ks in. in bore, about

1,746 cm (57 ft) high. Electrical contacts were

first used to detect the position of the mercury

surfaces, and later advantageously changed to a

sighting device by using a section of transparent

material in the tubes. Invar measuring tubes were used to measure the column heights. Many

accessories were required to meet problems, not- ably a barostat, for details of which see ref. [544].

The differential pressure between the two terminal mercury surfaces is simply the sum of the

heights of the individual mercury columns (here

nine) times the difference in the densities of mercury and the transmitting liquid. Obviously the

liquid column heights must be individually re- duced to standard conditions which involves

applying corrections for deviations from standard

temperature and for compressibility of the two

liquids. Further correction is needed if the pres- sure is desired at a level differing from that of the

lower mercury surface.

5.6.3. Ring Balance

The ring balance has been applied to measuring

small pressure differences at high pressure [361].

This is a torus or hollow doughnut of small cross

section. At the top, the two sides of the hollow

space are sealed from each other; sufficient mercury is placed in the hollow to seal off each side

from the other. The gas at a slightly different

pressure is fed to each compartment of the ring

balance through entrances which wUl not affect the weighing operation to be described. The entire ring balance is hung from a knife edge placed

at a point just above the center of gravity of the

torus. A beam mounted on the outside of the

torus permits weights to be applied to rotate the

torus. When a small differential pressure exists

in the ring balance, the mercury is displaced,

upward on one side and downward on the high

pressure side. This causes the torus and beam

unit to rotate about the knife edge to a new equilibrium position. Weights are then added to the

beam until the beam is restored to the original

equilibrium position. The weights are a function

of the differential pressure.

6. Design Elements of Barometers and IVlanometers

Many new developments in mercury manometry

have been produced in the last few years and are

still being evolved as a result of needs in various

laboratories for greater accuracy and precision in measuring absolute and differential pressures. Such needs as greater speed and ease in measuring

and controlling pressures and safer portability

have also greatly stimulated development work.

The principal directions of development and its status will be briefly discussed.

6.1. Methods of Detecting the Mercury Surface

These methods cannot always be completely

separated from the means of measuring the height

of the column which however, insofar as feasible,

is considered separately in sec. 6.2. Quite a few

methods are used to detect the position of the

surface of the mercury in barometers and

manometers.

6.1.1. Sighting on the Meniscus by Eye

In sighting on the meniscus by unaided eye, if there is any pretense to accuracy, a sighting ring

is provided. The lower edge of the sighting ring,

in front and behind the meniscus, is used as a

reference and is lined up with the top of the meniscus. The sighting ring is usually attached to the

vernier and must bear a known relation with the

zero of the vernier in order to obtain a valid

reading. This relation offers no difficulty in determination if the barometer is calibrated or its zero correction determined. It is obvious that

the plane of the sighting ring should be horizontal

and not move with respect to the vernier. The

final adjustment of the sighting ring and vernier

combination is usually made with a control screw

of limited travel.

If the meniscus height is to be measured, the

sighting ring is also set upon the line of contact of

mercury to glass, usually with much less accuracy

than on the meniscus, due to the raggedness of

this line of contact and the difficulty of securing

good illumination. Tapping the tube helps if done

before making any settings on the mercury surface.

Illumination of the meniscus so as to sharply

define the crown of the meniscus is essential for accuracy. In some situations a miniature electric lamp behind a translucent screen illuminating the

mercury surface from behind has been found

helpful.

It is estimated that the precision of sighting by

eye probably is not better than 0.001 in. (0.025

mm). This estimate assumes optimum viewing

conditions as to illumination and sharpness of the

meniscus. In portable barometers and manometers the sighting precision is ordinarily not the

factor that limits the accuracy.

6.1.2. Sighting on an Index

An index, such as an ivory point, which can be

lowered to the mercury surface, or the mercury

raised to it, is with proper illumination a very precise detecting means. If the mercury is bright,

and parallel lines on paper are reflected from the

10
surface to viewer's eye, the point of contact can

be determined to 0.001 mm (ref. [141]).

The contact is judged to be made when a small

dimple in the mercmy just disappears as the

mercury level is lowered, or the index is raised.

! The use of an index has the disadvantage of an

extra operation, since it has to be adjusted before

making a reading. However, in some designs it is quite feasible to make the setting automatically.

The index makes an electrical contact with a small

i voltage output, which, amplified, can be used to

1 operate a mechanical device which adjusts the

mercury level. See ref. [453] for an example.

The index is used in the cistern of Fortin barometers to set the mercury level to a predetermined

height. It may be remarked that the cleanliness

of the mercury surface is preserved much longer if the index be kept above the mercury when readings

I are not being taken.

In some fLxed cistern barometers a fixed mdex is installed in the cistern and the pressure determined

when the index contacts the mercury. If subsequently this pressure is found to change, the

change may be incorporated into the scale correction, or the need of other corrective action is

Ij indicated; also it is used as an indicator of the

amount of mercury requu-ed for the barometer, if the barometer is sliipped dry and filled with mercury in the field. In general the use of an adjustable index on a mercury surface subject to a pressur'e differing

from atmospheric pressure requires a stuffing box.

One manufacturer, in order to increase the accuI racy of a fixed cistern barometer used as a working

j standard, installed an index in the cistern and

i adjusted it through a stuffing box with a micrometer head, in this way measuring the rise and fall of the cistern mercury. The cistern was made of

glass.

In the Braunschweig standard barometer [576], a fixed index is installed above the mercury surface

, in the vacuum space and a movable index above

I the lower mercury surface. Only atmospheric

pressure is measured. At any pressure in its

j range, the mercury is forced up the tubes by a plunger in an auxilliary cistern so the upper index

1 just touches the mercury; the lower index, together

I with a short scale, is then adjusted to contact with

I the mercury. Contact is observed with a microscope. The movement of the short scale is measured with reference to a fixed mark on the baromj eter support, the distance of which to each index

ij had been previously measured.

Another manufacturer, to facilitate calibration

I at fixed pressures (barometer thermostatted)

I installed tungsten contacts at selected intervals in

' a glass barometer tube [495]. These were adjusted

to within 0.001 in. of the desired values. By means

of a selection switch a selected contact was con-

•|| nected to a low voltage. When the proper pres- sure was attained by adjustment, an audible

buzzing signal was heard in earphones by the

operator. Probably visual observation was also

needed to make sure the contact did not dip into

the mercury. This system could also be made

automatic by adaptation of the means described

m ref [453].

When sighting by eye on an index the mercury

surface can be detected to a precision of at least 0.001 mm. With a fresh mercury surface detection by electrical contact has a precision of about

0.005 mm; this presicion falls markedly as the

mercury surface fouls.

6.1.3. Mercury Float

A float has been installed in the tube on the

mercury by one manufacturer. A horizontal mark

on the float is sighted on by eye. The barometer

requires comparison with a standard barometer to determine the relation of the mark to the meniscus

level. In another design the same manufacturer

mounts a thin steel disk on the float in the barometer tube. The movable sighting and vernier unit

carries with it a small magnet on a shaft free to rotate. Proper alinement of the sighting device

is indicated when a pointer attached to the shaft rotates to indicate zero on the vernier as a result

of the force of attraction between the magnet and

disk. When the sighting device is again moved

so that the vernier zero is alined with the next

scale division of the main scale, the pointer will indicate on the vernier the distance the sighting

device has moved. From scale and vernier readings, the pressure can be deduced. Again at least one barometer reading must be compared with

that of a standard barometer.

In another design by another manufacturer, the

float carries a piece of magnetically permeable

material. A differential transformer encircling the

tube can be moved up or down to detect the position of the core piece on the float. The signal

from the differential transformer is amplified to operate a servomotor to position automaticaUy the

differential transformer symmetrically with respect

to the core piece. The angular motion of the

servomotor is used to secure an indiction of the

pressure. For reproducible capiUary error the float should

be shaped so that the mercury surface always contacts the float at a fixed level. This can be se- cured by a sharp corner on the float where contact is made. If the mercury surface is nearly

level in the vicinity of the line of contact, the

depression of the float due to capillarity wiU be

of the same order as the capillary depression of

mercury in a tube having a radius equal to the

clearance between the float and the tube wall.

6.1.4. Sighting With a Telescope

As a matter of convenience manometers and

barometers are often read by cathetometers. To

push the accuracy to the limit requires attention

to the details discussed below.

In this method the observer views the mercury

surface with a telescope. The telescope is mounted

11
on a cathetometer so that it can be raised and

lowered as needed to view the mercury surface.

For convenience two telescopes are best used so that both legs of a U-tube instrument can be observed independently, and with greater simultaneity. If one telescope is used and the inability to measure low pressures is permissible, the two

mercury surfaces should be one directly above the

other. Preferably the scale should be installed

alongside of the barometer of manometer tubes,

and read at some optical distance through the

telescope; the need for this installation will be

discussed in section 6.2. If the scale is so read,

the vernier is provided by means of a reticule in the telescopes or a filar eyepiece. The reticule

requires that the magnification of the telescope

be fixed, so that the distance of the scale from the

telescope is fixed. The filar eyepiece with its screw requires an additional reading to transfer

the reading to a scale graduation.

To locate the meniscus top accurately and with

ease, it must be illuminated. For this purpose it has been found reasonably satisfactory to use miniature electric lamps with a green translucent

material between the lamp and mercury column.

The lamp units are mounted behind each mercury

column and are movable vertically by hand or preferably by small motors to the best position

with reference to the mercury surface. The meniscus must be sharply defined and be without highlights. A more elaborate method is described in

ref. [412].

The cathetometer must be rigidly built so as not

to flex appreciably when small torques are applied

which tend to turn it about a horizontal axis. The

cathetometer must be free to rotate about a vertical axis and for the angle of turn needed to view

the mercury surfaces and scale, must rotate truly

vertical. If the axis of rotation is off the vertical one degree of arc, a rotation of deg may change

the height sighted on at 2 m by as much as 0.9 mm. It must therefore be possible to plumb the

cathetometer. For essential details on the design

of a cathetometer for precision applications see ref. [351, 412]. For detads on the alinement errors see sec. 6.6. When the distances from the mercury meniscus

and from the scale to the telescope are the same

and the optical axes of the two telescopes are

parallel, it is not necessary that the telescope axes be precisely horizontal. In some cases, it may be

desirable to set the telescopes at a slight angle ofi^ horizontal to gain the maximum illumination. A

horizontal indication of the level bubble mounted

on the telescope may not necessarily indicate that

the optical axis of the telescope is horizontal. To

check this, the telescope is sighted on the scale

and the scale reading noted; the telescope is re- versed in its mounting, the cathetometer rotated

180° and the scale reading again observed. The

difference between the two readings is an indication of the deviation of the optical axis of the

telescope from horizontal.

Since in telescopic sighting the barometer and

sighting device are separated by distances up to 5 ft it is essential, for precision measurements, that

there be no relative motion of the parts while

readings are in process. If mounted on the concrete or wood floor of a building, walking in the

vicinity of the installation may cause measurable

changes in readings. Vibrations are also trouble- some. In general, for accuracy better than 0.1 mm of mercury it is necessary to install the unit ' in a basement room, on a foundation separate from I that of the budding. The working standard at the National Bureau of Standards is so installed on a separate cork-concrete platform. Other in- , stallations may be just as satisfactory; the barometer and associated apparatus described in ref. [412] is mounted on structural members of con-

' siderable rigidity.

The working standard barometer at the National

Bureau of Standards used to calibrate barometers

and precision aneroid barometers is of the U-tube

type, utilizing two telescopes on a cathetometer ^ for making the readings. The overall accuracy is now estimated at 0.02 to 0.03 mm of mercury

(0.0008 to 0.0012 in.) with a precision of reading i of 0.01 mm. The limitation, however, is probably

not in the sighting means which has a precision

of the order of 0.005 mm. ' The ultimate in developing the telescopic sighting method is perhaps in the MIT barometer [412],

where special attention was given to all sources of error or difficulty. The accuracy aimed for was

0.001 mm of mercury; that attained was estimated

at 0.005 mm of mercury.

Two micrometer microscopes are used in the

NPL standard barometer [333, 552], sighting on

the mercury surfaces through optical flats. The

settings are transferred to a line standard to obtain

the column height. Only atmospheric pressure is measured, with an estimated uncertainty of 0.01

mb (0.003 in. of mercury).

6.1.5. Photocell Detector

The essential features of detecting the position

of a mercury surface, with a photocell are: (a) A

light source to sflhouette or flluminate the mercury

surface; (b) one or more photoceUs in a circuit to provide an electrical signal dependent on the posi- < tion of the mercury surface; and (c) an indicator i that responds to the electrical signal. The electrical signal is a more or less invariable function of

the position of the optical system with respect to the mercury surface. The position indicator thus

reads zero when the photocell is at the desired position, goes to the left or right when the photocell

position is too high or low. The electrical signal,

amplified, may be used to drive a servomotor

which keeps the photocell at a position corre- sponding to the mercury surface. As an aid to detecting malfunctioning, provision is usually

made for visual sighting on the mercury surface.

Restricting comments to the mercury surface

12
I detecting system, it is seen that any change in

' characteristics of the hght source, or the photocell,

may affect the balancing position of the unit rela- tive to the mercury surface. In a barometer used

to calibrate radiosondes, [511] where photocell detection was used, a second photocell was used to compensate for changes in the characteristics of

the light source. Light from the light source was

permitted to fall upon the compensating photocell,

j the output of which was fed to one arm of the

i Wheatstone bridge so as to achieve compensation.

I This was believed necessary because it was doubtful whether the bright light source remained

constant. Fully as important, and probably less easy to eliminate, is the effect of film forming on

the inside tube surface. The change in intensity

I of the light reaching tlie photocell directly affects

I the position of the photocell, since it must move to

i a position admitting more light in order to secure

a balanced position. In at least one device, the

light passes through the barometer tube before

reaching the compensating photocell. If the film

is uniform in density, compensation for the effect of

I the film is thus achieved. If not uniform, the tube

, must be cleaned or replaced. However, with two

j photocells, any change in characteristics of either

' will affect the position of the photocells with refer- ence to the mercury surface at the balance point.

A photocell detector unit has been developed

I I [572] in which no compensation is used for the

light source variation. The photocell is primarily

sensitive to red and infrared so that the light source

is operated at low filament temperatures, and

Ij variations in characteristics are less likely to occur.

' However, changes in the balancing position of the

photocell detector with reference to the mercury

li surface can still occur if a film forms on the tube

surface.

Barometers and manometers of both the U-tube

and cistern types are being made with photocell

detectors. In the U-tube instruments, two photocell detectors each with its own accessories are

i-equired.

One advantage, perhaps doubtful, of the power

amplification possible with the photocell is that a

. selected pressure can be maintained. The photocell can be set to the position corresponding to a

selected pressure and, instead of positioning the

sighting device, the servomotor can operate a valve

to maintain the pressure constant. A barostat,

independent of the barometer, may be preferable

i for several reasons, as discussed in the section on

Scale Errors. The accuracy of commercially available barometers and manometers with clean mercury and

j tubes in setting the photocell detector is of the

order of 0.001 in. (0.025 mm). This accuracy or

precision is not realized over all. No data are

' available on the variation expected as the instruI ment and components age. One manometer [572]

[ is stated to have a repeatability of reading within

' 0.05 mm (0.002 in.) which includes all sources of error in the mechanical and electronic system.

6.1.6. Capacitance Detector Stimson [454, 553] used a capacitance type

pickup in the U-tube manometer designed to measure gas pressures accurately. A steel plate,

35 mm (1.38 in.) in diameter, electrically insulated was installed above the mercury surface in each

of two shallow cells 7.3 mm (2.87 in.) in diameter.

A reference capacitance was installed in a shielded

chamber above each cell. The electrical capaci- tance between the steel plate and the mercury

surface is a measure of the separation between

the plate and the mercury surface. A means for comparing the capacitance of the reference capacitor and the mercury capacitor is provided. One

of the two cells is wrung to a pile of Hoke gage

blocks (end standards) so its height can be

changed.

A description of the measuring procedure will aid in visualizing the design. First the pile of gage

blocks under the movable cell is found that will make height of the steel plates in both cells nearly

the same. The cells are evacuated and the

mercury level is adjusted so that the separation

between the mercury meniscus and the steel plates

is appi'oximately 0.15 mm. One reference capacitor is then adjusted slightly so that each reference

capacitor has a value equal to the capacitance

between its steel plate and the mercury surface.

The pressure to be measured is applied to the

mercury surface in one cell and the other cell

(still evacuated) is raised on a higher pile of gage

blocks. The quantity of mercury in the system

and the pressure are then adjusted so that the

capacitance of the mercury to the plate in each

cell is equal to its reference capacitance. The

change in height of the pile of gage blocks is the measure of the pressure applied.

The precision of detecting the vertical position

of the mercury surface in this manner stated to be

less than 0.0001 mm (4X10-Mn.).

Los and Morrison [513] used the capacitance

between an invar plate and a mercury surface to measure differential pressures in the range 0 to

2.5 mm of mercury (0.1 in.). The variation in beat frequency of two oscillators to which the

capacitances were singly connected served to measure the pressure. Column heights were not

measured directly, so that calibration was necessary, for which an improved design of McLeod

gage was used. Data are given to show the

nonlinearity of beat frequency with change in

height of the invar plates alaove the mercury

surface. In this design a precision of 0.1 to 0.2/x of mercury was claimed for the range 0 to 0.2 mm

of mercury, and 0.1 percent or better for the range

above 0.2 mm of mercury.

6.1.7. Optical Reflection Dectors An optical probe which is being apphed to a U-tube barometer has been developed by the

National Physical Laboratory [573]. The U-tube

barometer is vertical while the optical probe is hori5.36771—60 3 13
zontal, a right angle prism being used to transmit

reflections from the mercury sm'face to the probe.

Two horizontal tubes movable as a unit on a track

have their axes intersect at a selected angle.

A light source at the end of one tube passes

through a grid to the mercury surface. The light reflected from the mercury surface passes through

the second tube and through a grid exactly

similar to the first. If the mercury surface is precisely at the intersection of the two tube axes, maximum illrmiination is received at the exit of

the second grid. At any other position the

brightness of the light at the exit is less. The

accuracy of setting is stated to be about 0.5/x (20X10-' in.). For detection of brightness a photocell is placed

at the exit of the second grid. For reference a second photocell receives some of the reflected

light from a lightly aluminized glass plate placed

ahead of the second grid. The output of the two

photocells is amplified and passed thi'ough a Wheatstone bridge, which in the balanced condition indicates the maximum brightness of the

reflected light coming through the second grid.

The optical tubes are mounted on precision

ways for adjusting their position to that where

the light received by the grid exit photocell is a maximum. A fixed line standard, with optical

accessories for viewing, serves to measure the

position of the tubes on the ways. Alinement of

the ways must be held within close tolerances; the

errors introduced, and their amounts, are discussed

in ref. [573].

The barometer, not discussed in ref. [573],

consists of a stainless steel U-tube, 4 in. in di- ameter. The range is 1 atm or more. Any glass

plate between the light and mercury surface

should preferably be optically flat. In order to obtain observations on the two

mercury surfaces, the difference in height of which

is to be measured, two optical probe systems as described above are used. These can be coordinated by measurements made when both legs of the barometer are subjected to the same pressure. Another optical probe, described by Moser

[555, 575], detects equality in the meniscus

curvature. It was used to establish the equality

of two pressures and, while possibly applicable in detecting a mercuzy surface in connection with

precise pressure measurement, has not so far as is known been so applied. A brief description of the

probe as used may be of interest.

The operation of the probe depends upon the

fact that at a hole ending with a sharp edge the

mercury meniscus is captm-ed by the sharp edge.

Moser desired to obtain an equality of gas pressm'e

in two systems. The gas pressures from the two

systems were brought into two vertical chambers

about 3 mm in diameter and 15 mm high. The

bottom ends of these chambers ended in sharp

edges, at the same level, in a manifold filled with

mercury. The tops of the chambers were sealed

with glass windows. Gas pressures were adjusted

in the chambers till the menisci were nearly plane

at the sharp edges. Light from point sources above the chambers passed down through 45°

semireflecting plates, through the chamber windows to the mercm*y menisci, whence they were ; fc reflected back through the windows to the 45° i i plates, and out horizontally to telescopes. Small t ^ changes of pressure in the chambers changed the f

t( curvature of the menisci. When the radii of I m cmvature were equal to half the distance to the ; si point light sources the reflected light beams i « became parallel and the field was uniformly ) ffi illuminated. The uncertainty of equality in the [ 1 pressure settings was said to be ±0.002 mm of s

i| mercury. n

ii

6.1.8. Interference Fringes \ *

Terrien [592] describes three ways in which

interference fringes from two mercury surfaces can be used to detect the relative vertical distance I

i, apart of the mercury surfaces. In aU cases the

p length of the significant light paths must be equal. I j This is secured by a mechanical adjustment of the , position of a reflector or reflectors, the amount of [, {] which is used as a measure of the column height. « ij One of the methods originates in Japan, another !{ in Russia, and the third is due to Terrien. Briefly, ij in the design due to Terrien, a beam of white light ^ \^ is split by a half-sUvered surface. One beam j passes through a Michaelson interferometer, and \, j is reflected to one of the mercury surfaces. The i j other beam is reflected to the other mercury !( surface. Upon reflection the beams reverse their [ paths and are reunited as they issue from the

j j interferometer. If the optical path lengths are exactly equal, and if the mercury surface has

infinitesimal ripples, a condition difficult to pre-

^ vent, the observed fringes are white, not colored.

The fringes are detected by a photocell. To

' obtain exact equality in the light paths two

| horizontal prism reflectors are adjusted horizon-

^ tally as a unit. The amount of the horizontal

^ ^ motion is a measure of the height of the mercury

column.

J Both the Japanese and Russian interferometer

^ methods require two light sources. ,

6.1.9. Resistance Wire

One method of transducing a pressure to an i electrical quantity which can be easily recorded, : c or indicated as desired, is to stretch a wire through * a the mercury column. A voltage is applied to t the upper end of the wire and to the mercury. [ The electrical resistance of the wire must be j greater than that of the mercury column; sensi- i tivity increases with difference in resistance per t unit length. As the mercury column faUs, the re- i sistance of the circuit rises. s Either the resistance of the circuit is measmed

with a Wlieatstone bridge or the drop in potential i with a potentiometer. The use of a recording i ( potentiometer is discussed in ref. [532]. A ; j nichrome wire has been used [501, 532]; a carbon

14
rod [543] ; and in tandem, a 9H lead from a lead

I pencil and a steel wire to complete the electrical

I circuit [562].

; Apparently none of the experimenters with this

I form of pressure indication required high accm-acy,

since in most cases rather small bore tubing was

used. Variable capillary effects can be expected

to affect the acciu-acy, both at the glass and

mercury surface and at the wire and mercury

[! surface. About the latter boimdary not much

; can be done to effect an improvement beyond an

imcertainty of several tenths of a millimeter.

' This limitation seriously hmits the method in any

I application to really precise and accurate measurements. Its convenience merits its use when high

1 accuracy or precision are not required.

6.1.10. Gamma Ray Pickup

This method of detecting a mercmy surface is useful in measuring differential pressures at high

pressxu"e where a steel tube must be used to secm'e

1 adequate strength [514]. A narrow beam of

|: gamma rays from a radium source are projected

i; through the tube. On the other side of the tube

jj an ionization chamber is placed. The ionization

j| chamber and radium are moimted as a unit with an indicator of their position on a scale. A dis- continuity in the intensity of received gamma

radiation received by the ionization chamber is observed when the unit moves vertically by the

mercury surface. A precision of t.ji mm is

il claimed.

6.2. Measurement of Mercury Column Height

Methods of measuring the height of a mercury

j] column have been discussed to some extent in

i previous sections but some elaboration is needed,

j A simple, widely used, method is to visually esti-

' mate the height of the colimin by comparison

I'' with a scale alongside of the mercury column,

either with or without a sighting ring.

Refinements in measuring, to which further

||; discussion is limited, are: (a) the use of a scale and

vernier; (b) a cathetometer; (c) a precision screw; and (d) gage blocks.

6.2.1. Scale and Vernier

Ordinarily the scale is a separate member, more

convenient to cahbrate in this form, which is

^ attached to the structure supporting the glass

tubes containing the mercury. A sighting ring, free to slide or controlled in position by a rack and

' pinion arrangement, and a vernier with its zero alined with the sighting ring, form a unit. In

I taking a reading the bottom of the sighting ring

is alined with the top of the mercury meniscus

and its position determined on the scale. Verniers are customarily made with a least reading not below 0.05 mm or 0.002 in., since the

overall accuracy achievable does not warrant

greater precision.

j Scales on portable instruments are commonly

made of brass. In one design a plastic scale is used, which is discussed in sec. 6.8. For precise measurements of pressure the scale must be ruled on a first class ruling engine under

controlled conditions of temperature. If the

reference temperature for the scale is 0° C, a convenient, but not necessarily essential reference

temperature, the ruling engine can be manipulated

so that the scale is accurate at 0° C. This practice

is commonly followed, theoretically at least, for portable barometers, with one exception. This

exception is the Fortin barometer commonly used

in meteorology the scale of which when in inches

of mercury is graduated to be accurate at 62° F. The scale so graduated is becoming obsolete

because meteorologists now use the millibar as the

unit of measurement, and transition is well under

way to barometers so calibrated. The temperature at which scales may be graduated to be

accurate will be discussed in more detail in the

section on temperature errors. Scales attached to the barometer or manometer

have to be read by an observer so close to the

barometer, that he affects its temperature. Since

this aft'ect is normally a transient, some uncertainty

is introduced in the accuracy of the measured

temperature of the barometer, particularly since

in most instrument designs the thermal lag of the

thermometer, of the scale, and of the mercury all

dift'er measurably. This imcertainty can be

reduced, if the desired accuracy justifies it, by

obvious expedients, such as reading the thermometer before initiating the pressure measuring

process and by making the thermal lag of the

thermometer about the same as that of the mercury in the barometer. This effect is mentioned

here, because it is one of the principal reasons for

instrument designs in which readings are made by

an observer at a distance from the barometer or manometer [563].

6.2.2. Cathetometer and Scale In the preferred method, used as long ago as 1889

by Professor Morley in determining the density

of air, a scale is placed alongside of the mercury

tubes and is read through a telescope or telescopes

mounted on a cathetometer. The telescopes are from about a foot to six feet away from the scale and tubes in the various designs. The mercury

meniscus and scale should be at equal optical

distances from the focal plane of the objective

lenses of the telescope.

The other method is to locate the mercury

mensicus with the telescope mounted on the

cathetometer and determine its height by reading

the position of the telescope on the scale attached

to the cathetometer. This method is not usually

used in precise work unless the telescope is quite

close to the mercury column, in itself undesirable

because of uncertainties introduced in the mercury

and scale temperature. The objection to the

method is the necessity for maintaining the optical axes of the telescope or telescopes horizontal

15
within close limits. For example, if the telescope

objective is 1 m away from the scale, the telescope axes must be held horizontal within Sji min of arc in order to avoid errors up to 0.1 mm in measurement. This source of error is practically

eliminated in the preferred method.

Returning now to the preferred method, the

scales may be either of invar, stainless steel or other reasonably noncorrosive material with a Imown temperature coefficient of expansion and

stable in dimensions. They are graduated in

either 0.5 or 1.0 mm divisions. If the barometer

or manometer is of the U-tube type and is to be

used as a standard, it is only necessary to have the

scale calibrated against a standard scale and to establish or laiow its linear coefficient of expansion

in order to apply the correction for temperature.

If the scale is calibrated at a temperature close to that of its use, less accurate Imowlege of its coefficient of expansion is needed.

To determine subdivisions of the scale divisions,

that is fractions of 0.5 or 1.0 mm, two methods

have been followed. In the first, a sight is taken on the mercury meniscus, the telescope is rotated

about a vertical axis to sight on the scale and the

telescope raised or lowered until the sighting cross hair is coincident with a scale division. A micrometer screw is used to raise or lower the tele- scope and is read to give the fractional scale

division. Thus two adjustments of the cross hair

position are required. In the other method a

reticule is placed in the focal plane of the telescope,

and can be used as a vernier when the telescope is at the proper distance from the scale, a distance

which can be adjusted when installing the cath- etometer. In talcing a reading the cross hair in

the telescope is brought into coincidence with the

mercury meniscus, the telescope rotated to the

scale and the reading obtained similarly as on a

scale with a vernier.

From experience limited to one arrangement of a reticule it was found that considerable training

is required to obtain reliable readings and that some attention must be paid to the illumination

in order to distinguish clearly between the divisions of the scale and of the reticule. It does have

the advantage that only one adjustment of cross hair position is needed.

6.2.3. Precision Screw

Use of the rotation of a precision screw to measure

the height of a mercury column appears to be the

logical method if automatic indications are desired; particularly if mechanical means are used.

The lead screw, mounted in a vertical position, can be used to raise or lower the sighting mechanism. A counter connected to the screw by means

of a gear train may be used to count the revolutions of the screw and so provide a digital indication of the pressure. A photocell detector of the

mercury surface position, or other sensing device

which provides an electrical signal indicating the

position of the mercury surface may be used to

drive a servo system connected to the screw to achieve automatic positioning of the sighting

mechanism.

There is nothing to preclude the use of the precision screw as a means of manual measurement of

the height of the mercury column, though it may

not prove practical, except as a check on the auto- matic reading. It is merely necessary to have a

sighting ring adjusted by manually rotating the screw through gearing and read the rotations of

the screw on a suitable indicator.

The screw can be made to measure as precisely

as desired, possibly to a part in 100,000, for the

length required in barometers. The only barrier

is the expense in securing the precision, which of course increases as the length of screw increases.

Uniformity of pitch is highly desirable. The

pitch will vary with temperature for the materials

of which the screw would ordinarily be made, but

this efi'ect on the accuracy can be eliminated by

maintaining the barometer or manometer at constant temperature or by applying corrections. The

latter procedure in the present applications of the screw to manometry will prove inconvenient.

6.2.4. Gage Blocks

For high accuracy, Stimson [454, 553], has used

gage blocks, calibrated to two parts in a million, to measure the height of the mercury column in a manometer. The manometer is of the U-tube

type; it has articulate joints in one leg, and the

mercury menisci are in cells of large diameter in

order to minimize errors from capillary depressions.

The amount of the mercury and the pressure can

be adjusted to bring the mercury menisci to refer- ence positions in the cells. These reference positions are determined with the capacitance pickup,

described in sec. 6.1.6. The height of the pile of

gage blocks for the zero reference is obtained when

both cells are evacuated. When gage blocks are subsequently added and the pressure adjusted to bring the mercury to the same reference positions

in the cells, the added blocks give the direct measure of the height of the mercury column.

Obviously to realize the accuracy inherent in the use of the gage blocks, many precautions must

be taken. Principally, temperature control and

temperature equilibrium to about 0.01° C before

taking a reading are both necessary. Coupled

with the necessity of obtaining a zero reference

reading sometime before and after each pressure

determinations, it is seen that pressure measure- ments are a time-consuming operation. In the

present state of the development, realizing the

accuracy possible from gage blocks is essentially a research operation.

6.3. Illumination of the Mercury Surface

For sighting on the mercury meniscus by eye, guided by a sighting ring, only simple means of

illumination are justified. If the installation is such that the mercury meniscus is poorly defined

16
in daylight, it is only necessary to install a lowI wattage (flashlight) lamp behind the mercury

II meniscus with a ground glass, or better a green

I translucent paper, in front of the lamp. A similar

' arrangement helps with setting the index in the

cistern of Fortin barometers.

For more precise measurements made by sightI ing on the meniscus wdth a telescope, the above

! described lamp installation is often adequate.

The height of the lamp and diffuser assembly can

. be best adjusted by a small motor operated by the

observer. The adjustment of the lamp height may

be critical in order to obtain a well-defined meniscus repeatably the same. Highlights on the mercury meniscus from other sources of illumination

' can be troublesome but can be avoided by shielding or better by eliminating the sources while

' making a setting.

In order to secure the ultimate in precision in sighting on the meniscus through a telescope,

experimenters [333, 412], agree in the necessity

;i of having parallel or nearly parallel light on the

1 meniscus. A further refinement, [412], is to have

'!j the illumination nearly parallel in the vertical

I direction, but diffuse horizontally; this illumina-

!| tion can be secured with a cylindrical lens. In

i the end, experimentation is necessary to determine the invariant optical configuration associated with the meniscus on which to sight. This

I may be an outstanding reflection from the menis-

,1 cus, rather than the outline of the meniscus, which

I may be indefinite when a precision of the order of

0.001 mm is desired.

6.4. Vacuum Above Mercury Column

This discussion relates only to instruments

where a vacuum must be maintained above the

mercury column. In fixed cistern and Fortin

barmometers used only to measure atmospheric

pressure, no provision is made, beyond a careful

!| procedure in filling the barometer tube, for main-

' taining the vacuum. The design is usually such

that, following a precautionary procediu-e to pre- vent admitting air into the tube, the barometer

' can be tipped upside down, or better if the design

permits nearly horizontal with the upper end of

the tube lower than the cistern, and the air bubble removed by tapping the tube. This procedure

in the hands of experienced persons is usually

I reasonably effective. However, in practically all barometers a small gas bubble will be visible

• when the baromet'er is tipped just enough to fill

' the tube with mercury, in fact will also exist in

freslily filled barometers.

The situation is not serious in barometers used

solely to measure atmospheric pressure. Such

jl barometers are known to have maintained a sat-

! isfactory degree of vacuum for many years

^\^thout attention.

The procedure of fiUing a barometer tube may

be of interest. First, the tube must be clean. In filling the tube with mercury by any practical

procedure it is almost necessary that the mercury

be above 100° C in order to eliminate water vapor

entirely. In the end the only really satisfactory

method is to distill the mercury into the tube in a system which is kept evacuated, preferably with

a diffusion pump. The tube being filled should

be kept at a temperature somewhat above 100° C

and should be outgassed by well known procedures

before the filling operation.

The situatioQ is different in fixed cistern barometers which are more or less continuously used

to calibrate altimeters and aneroid barometers

where large cyclic changes in the pressure in the

cistern are required. In a relatively short time

of such use, the vacuum seriously deteriorates.

If the space above the mercury column is observed

in a darkened room while the pressure in the cis- tern is reduced, luminescence of the mercury vapor

in the tube will be seen, probably caused by the

discharge of an electrical charge on the walls of

the tube resulting from the contact difference of potential between the mercury and glass. This seems to accelerate the formation of gaseous products or promote outgassing of the glass. In any

event painting the outside waU of the glass tubing, but not where it would interfere with visibil- ity of the meniscus, with a metallic electrically

conducting paint greatly reduces the rate at which the vacuum deteriorates.

To facilitate removal of gas above the mercury

column, fixed cistern barometers are designed so that the open end of the glass tube is covered by

the mercury in the cistern, independent of its orientation, vertical, horizontal, or upside down.

This makes it possible to eliminate much of the

gas from the tube by a simple procedure. The

cistern is evacuated, the barometer is oriented

to an almost horizontal position with the open

end of the tube a little above the closed end,

thus tremendously increasing the volume of the

gas bubble by reducing the pressure. As mercury flowed back into the tube the gas bubble

moved up the tube and out. However, for complete removal the bore of the tube at the open

end has to exceed 3 mm.

Shipment of fixed cistern barometers has also been a problem. Usuall}^ the barometer has been

shipped in an upside down position, suspended in a box, but breakage of the tube due to rough

handling occurred frequently.

6.4.1. Mercury Sealed Valve

The situation just described led to the development of barometer tubes with a mercury sealed

valve at the top. Barometers with these tubes

are shipped unfilled with mercury, and thus more

safely, and the procedure of maintaining a vacuum

is much simplified. The valve is so designed that

it opens outward, but is normally kept closed by a

force, usually produced by its own weight. A

small cup around the seal holds a small amount

of mercury for a more positive seal. The gas that

accumulates above the mercury column may be

17
removed by evacuating the space above the seal while the mercury in the tube is forced up by

applying pressure to the system until it is forced

out through the mercuiy seal. It is sometimes

necessary to manually lift the valve slightly off

its seat to permit the gas bubbles to escape. Some

idea of the quantity of gas in the tube can be

obtained by observing the number of bubbles that come through the mercur}^ seal. With this valve, a barometer can be shipped free of mercury and the mercury added at the place

of installation. Securing a vacuum requires many

repetitions of the above described procedure at

intervals up to a week, and the procedure can be

repeated when there is any doubt about the vacuum.

6.4.2. Pump

The vacuum above the mercury column can be

maintained by the use of a vacuum pump, which

can produce a vacuum better than the accuracy

required for portable barometers. These pumps

are operated while the barometer is being used.

For standard barometers and where high precision in absolute pressure measurement is desired, more elaborate pumping systems are used. In its simplest form, the top of the tube is connected to a

diffusion pump backed up by a mechanical vacumn

pump. To prevent oil vapor from the diffusion

pump entering the barometer vacuum system,

a liquid air trap can be used. To measure the vacuum a McLeod gage or other type vacuum gage

may be connected to the system.

6.5. Tubing

At present for portable barometers, precision

bore Pyrex tubing is generally used. There is some evidence that less chemical interaction and

less scum develops at the mercury-glass interface

with some other Idnds of glass, but any defuiite

conclusion is probably debatable in the present

state of our Icnowledge.

Precision bore tubing apparently has satis- factory optical properties in the bore, but its external surface may have irregularities which

deviate the light rays as they pass from the

glass into the atmosphere. Thus the position of

the meniscus as seen may be up or down from its position. This deviation may be called a prismatic error since it is similar to the deviation of

rays passing through a prism. The deviation is generally kept within boimds by selection of the

tubing and in occasional cases by giinding the

outside of the precision bore tubing to uniformity.

Precision bore tubing is exceedingly useful in fixed cistern barometers and manometers and in U-tube instruments where the height of mercury

in only one leg is measured. Wlien using precision

bore tubing the scale contraction is a constant;

if the tubing were irregular in bore, the difference

in the two column heights would still be unchanged, but the scale error of the readings on a

single scale would fluctuate with the irregularity

in the bore.

18

As will be discussed in detail in sec. 11, the uncertaint}^ in capillary error can only be reduced i by increasing the bore of the tubing. Barometers I with any pretense to accuracy must have a tubing

bore of at least ji in.; the uncertainty in pressure

| measurement for this bore is about 0.01 in. of

mercury (0.25 mm). Increasing the bore to 0.6 |

: in. (15 mm) lessens the uncertainty to about 0.004 I in. (dzO.lO mm), if no capillary corrections are ' made to the readings. ' In precise measurements, if the mercmy menis- \

' cus is sighted upon through glass, the tubing is !

' enlarged at the sighting levels and optical flats '

' form part of the mercury container in the line of -

' sighting. (See ref. [333].) ' If metal tubing is used in whole or in part, steel ' or preferably stainless steel must be used. Most \

' other metals amalgamate with mercury. Barome- ' ter or manometer cisterns are generally made of .

' stainless steel or glass. \

'

1-

6.6. Alinement of Scales and Sighting Devices \

i In manometry it is necessary to measure the ; ^ vertical height of the mercury column. The |[j errors introduced by misalinement of the scale and j accessories, may be divided into two types, one | the cosine error, the other the sine error. I j The cosine error is caused by the scale not being | 1 vertical; it, in general, equals the scale readmg | i times 1-cos a, where a is the angle of tilt. An | ; error of one part in 10,000 is produced by the i scale tilting 49 min of arc. There is usuall}^ no j difficulty in reducing this error to practical limits, ( by adjustments provided in most portable barom- ; eters. Most barometers designed to hang from a ] hook do not hang vertically; their scales are ad- ) justed to be vertical by means of a separately j supported ring encircling the cistern, with screws ; to control its horizontal position. Platform ba- ! ( rometers and manometers are provided with level- ' ing screws. j The sine error is some function of the separation i of the mercury columns, or the distance of the [ scale from the mercury columns, or some other j distance significant in the measurement; all multiplied by the sine of the angle of misalinement. , It usually occui's when a measurement requires [ transfer from one vertical to another. In general, ; [ the sine error is a constant, independent of the ; f height of the mercury column, if the misalinement ( does not vary in amount. It is often corrected for f as part of the zero error, discussed in section 8.1, j and indistinguishable from other causes of it.

j In general the sine error equals the pertinent

distance times the sine of the angle of misaline- , ment; for an error of 0.1 mm, this angle is 34 min j of arc for 1 cm of distance, 17 min for 2 cm, or (j for an error of 0.01 in., 34 min of arc for 1 in. of

distance. Several examples of sources of this error are outlined below.

Some barometers, such as the Fortin, are ; equipped with a zero index in the cistern for setting t
the mercury surface in the cistern. If the scale does not hang vertically, both a sine and cosine

error are introduced. The sine error equals the

product of the distance of the index to the center

of the tube times the sine of the deviation angle.

To eliminate the sine error, the Fortin barometer

is adjusted to hang so that, upon rotating the

barometer, the relative vertical position of the

index and mercm-y smface in the cistern is invariant. If the scale is then vertical, the cosine error

is also eliminated.

In sighting upon the mercury meniscus with a

telescope, with the scale attached to the cathetometer, the sine error is proportional to the dis- tance of the scale to the mercury column. To re- duce the error to a reasonable amoimt, the optical

,1 axis of the telescope must be maintained horizonI tal within excessively close limits; therefore this

, location of the scale should be avoided, as disi cussed in section 6.2.2. In making readings with a telescope, where the

1 scale is in the preferred position along side of the

I merciiry column, a sine error may be introduced

if the cathetometer does not rotate about a true

vertical axis. If the cathetometer axis is displaced

I from the vertical at right angles to the vertical

I plane of sight, the sine error is a maximum; if

I tilted in the vertical plane of sight the sine error

' is zero. Assume, for example, that a scale is

I between the two legs of a U-tube barometer. To

transfer the observed level of one meniscus to the

' scale, assimie that the telescope sighting line runs

ij uphiU; to the other meniscus it runs downhill. If

i the maximum rotation of the cathetometer re-

' quired is over an arc I at the scale, and A is the

angle of tilt of cathetometer axis in the vertical

ii plane at right angles to the plane of sight, the rise

' r of the sighting line of the telescope is to a good

approximation I sin A. For the practical case of an arc length of 10 cm a total rise r, or an error, of 0.1 mm is obtained for a tilt of about 4 min.

: The large effect of small tilts indicates the necesJ sity of reducing the transfer distance I to the

minimum and most important, the need for a rugged, rigid cathetometer, since constancy in

|j axial alinement is a primary necessity.

If If the ways along which a sighting ring and

vernier unit of an instrument slide are not vertical

in the vertical plane of sighting, a sine error is introduced. If the scale is not vertical, a cosine

error is additionally introduced. The sine error equals the product of the distance of the scale from the center of the tube and the sine of the

angle of tilt. For a distance of 2 cm and an error

of 0.1 mm the tilt of the ways is 17 min of arc. Misalinement giving rise to the sine error which

I varies with the reading can be avoided to the

degree needed for the designed accura,cy by good

design and care in the construction of instrument.

6.7. Instrument Temperature

If the uncertainty in pressure measurement is to be held to 0.01 percent (0.1 mb at 1 atm) the

mercury temperature must be known within

±0.6° C, and proportionately smaller for better

accuracy. The scale temperature, if brass, needs

to be known to only approximately ten times this uncertainty (that is 6° C) for the same accuracy

limits (0.01%). For precise pressure measure- ments it is seen that the mercury temperature

must be known to very close limits, which in- volves both the measurement and control of

temperature.

6.7.1. Measurement of Temperature

In simple portable barometers the temperature

is measured by mercury thermometers, with their

bulbs imbedded in a metal shield. Thermal lag is thus introduced in the thermometer which it is hoped will equal that of the mercury in the barometer or manometer, but in the nature of things, can only approximate it. A better arrangement

sometimes used in laboratory instruments is to place the thermometer in a tube of mercury, more

or less simulating the barometer tube [576]. Since

at best the mercury thermometer cannot be depended upon for an accuracy better than 0.01° C,

resistance thermometer or thermocouples are preferable when better accuracy is needed.

It is generally assumed, probably without significant error, that the scale and mercury column

temperatures are identical. In view of the lower

temperature coefficient of the scale, the error is held to a minimum if the effort is directed to obtaining the mercury temperature.

In the absence of continual control of the instrument temperature, special attention must be given

to thermal lags if the ambient temperature is varying or has varied. It takes hours for an unventilated barometer or manometer to come to temperature equilibrium with its surroundings after an abrupt shift in the ambient temperature. See

ref. [563] for some data. The thermal lags of the

barometer and attached thermometers in spite of

all effort are unlikely to be the same. Within

limits the two temperatures, instrument and thermometer, are reasonably identical only if the

thermometer reading has not changed appreciably,

say a few tenths of a degree, over a period of time,

say at least hr. In portable barometers where the observer per- forms operations while standing close to the instrument the temperature is influenced if the barometer temperature differs from body temperature.

With care to reduce this time to the minimum,

and by reading the thermometer fu-st, this uncertainty can be reduced to manageable limits, say

of the order to 0.2° C.

6.7.2. Control of the Temperature

Two methods of controlling the temperature of

the instruments are in use. In the first, the

barometer is enclosed in a cabinet in which air

is circulated and thermostatted at a selected temperature above the expected ambient temperature.

This temperature should be as low as practical in

19
order to avoid evaporation of mercury into the

cooler lines where amalgamation of metal and mer- cmy may occur. Generally the cabinet is divided

vertically into two compartments except for neces- sary ducts ; the barometer or manometer is installed

in one and the electrical heater and circulating fan

,

in the other. The thermostat is in the same compartment as the barometer. The air is forced to flow in a circuit, down the heater compartment and

up the barometer compartment. Refinements are incorporated in order to eliminate temperature

differences along the length of the barometer, but

these cannot be eliminated entirely, since even

with no heat exchange the temperature falls nearly

0.01° C/m of elevation, i.e., adiabatic change.

The other method is to install the barometer in a room in which the temperature is maintained

constant. Primary standards and others where

high precision is required are usually so installed.

A subbasement room is desirable because its temperature will have a smaller diurnal variation.

Generally such a room will require a source of both

heat and cooling, thermostatically controlled.

Ventilation will be required, so directed as to eliminate vertical temperature gradients as far as practical. The closeness and stability of the

temperature control is determined by the accuracy

desired in the pressure measurements.

Controlling the instrument temperature with

reasonable accuracy must be continuous night and

day because securing thermal equilibrium of the

instrument with its surroundings requires many

hours.

6.8. Automatic Compensation for Temperature and Gravity Error

Both the corrections for deviation from standard

temperature and gravity are directly proportional

to the height of the mercury column, as discussed

in detad. in sees. 9 and 10. Mechanical means have

been developed so that readings on fixed cistern

barometers may be automatically compensated for

these errors. In one design a long auxiliary rod is hinged at the zero of the scale and is adjustable angularly

about a horizontal axis. Actually, the hinge is slightly below the scale zero in cistern barometers

in order to include a correction for the change in mercury height in the cistern with temperature.

Any change in angular position thus causes a

vertical displacement at any point along the rod

which is a function of the radius, i.e., the barometer

reading. The sighting device and vernier unit is connected to the rod through a lever system and

is free to slide up or down the rod as a unit during

adjustments needed to make a reading. The

arrangement is such that when the auxiliary rod

is vertical, the vernier position is unaffected by the

lever system. This corresponds to zero temperature and gravity correction. If the auxiliary rod

deviates angularly from its vertical position, the

vernier is moved up or down relative to the sighting device by the lever system. The amount of , motion of the vernier is proportional to the chord

defined by the deflection of the auxiliary rod from |

?' the vertical. This chord length is approximately ' proportional to the height of the mercury column. " Two additive adjustments of the angular position " of the auxiliary rod angle are provided, one for ^ gravity error and one for temperature error com- " pensation. The auxiliary rod can be manually set to the angular position corresponding to local

' gravity and then to an angular position determined i

| by the measured instrument temperature. A scale > J graduated in gravity units and one graduated in " temperature are provided to indicate the adjustment to be made [515]. " The permitted angular motion in one design is " about 2 deg, while about 6 deg is needed. This '- need is taken care of by amplification of the rod " motion by the lever system. '

Another design of mechanical automatic compensator for temperature and gravity error has

been developed. A fixed vertical rack is used

instead of the hinged rod. A gear forming part

of the vernier and sighting unit of the barometer c runs on this vertical rack. A screw on the same ' I shaft as the gear positions a wedge in contact ' t with a lever which controls the vertical position of

the sighting device. The rack makes this control |

, i proportional to the height of the mercury column 1 and thus to the temperature and gravity correc- i

! ( tion. The gravity and instrument temperature s for which correction is desired can be set into the j ( corrector by manual adjustment of the angle the ] [ control lever makes with the horizontal. i A variation of the design just described and

developed by the same manufacturer depends < upon a vertical wire extending the entire scale f length. A pulley attached to the sighting device ( and vernier unit has the wire looped around it, so \ that its angular motion, as the sighting device , moves up and down, is proportional to the height

of the mercury column, and thus to the gravity and

temperature correction. Through a system of

gears, a rack, and a lever the sighting device and j vernier position is controlled as a function of the

height of the mercury column. By this design

sliding contacts are eliminated. The effective

radius of the lever is adjustable, by which the

gravity and temperature for which correction is desired can be set into the corrector. | A novel method of automatic compensation for temperature error which is also commercially j available is the use of a plastic scale which is stretched between rigid supports to a length

determined by the mercury temperature and local gravity. As the scale is stretched the distance

between scale graduations is expanded proportional to its length starting at the bottom. This

gives readings corrected for temperature as required. A scale graduated in temperature units

indicates the degree of stretch necessary.

It is obvious that the extension of the plastic

scale between two temperatures is the sum of the

20

5
linear expansion of the scale support with increase

in temperature and an extension produced by the

adjustment of a screw. The total stretch must

be repeatable time after time, that is, the scale must be taut when in use. In the design now

available this condition is met for temperature

variations ordinarily experienced by the instruments.

The acciu-acy of automatic compensators need

be considered practically only for the range of

temperatures differing from the temperature at which the instrxmaent is calibrated. At the cali- bration temperatm-e of the instrument, the error

is automatically incorporated into the scale error, or adjustments made on the instrument to correct

it. The accuracy on this basis can be held to ±0.1 rrnn of mercury (0.004 in.), perhaps even

better, an amount which is well within uncertainties in measurement due to other causes.

6.9. Damping and Lag

Mercm-y column instruments have little application in making djTiamic pressure measurements.

However some remarks on the djmamic characteristics may be pertinent.

Damping is usually necessary and generally

incorporated in the form of a restriction or a short

length of capillary tubing between the two legs

of a U-tube mstrument or in between the tube

and cistern of a fixed cistern instrument. This

damping reduces the effect of xmdesired column

pulsations or piunping, such as would occm- on

an undamped barometer on a ship at sea. Consider a manometer consisting of a U-tube

connecting two cisterns of equal area. Assume it filled so that a mercm-y surface exists m both

cisterns. In oscillation the differential equation

governing the motion is, assuming laminar flow:

and the undamped free period Tq

pLAc X SttjLAc X A, A,'

^2pgx=0.

From which it follows that the period T is

2gAt 167r^r?n i/2

LA, p''A:-\

(13)

(14)

/2 (15)

For critically damped motion the two terms in the denominator of eq (14) are equal, achievable

by controlling At. Separating the variables with

which damping may be controlled from the

constants, this equality becomes

LA,.

At^ Sw'r,' (16)

When the column oscillates at about 0.8 of the

critical damping, it will return to rest in a time

equal to 67 percent of the free period Tq, which

appears to be an optimum value for the damping.

On this, eq (16) becomes

LA,^0.8p^g

A? ~ W

(17)

In the above equations:

X=length of the tubing connecting the

cisterns

-i4.c=area of each cistern

internal area of the tube

x= displacement or amplitude of the oscillation of the mercury in the cistern

from its equilibrium position

i; =velocity of the mercury in the tube

i, =acceleration of the mercury in the tube

p= density of mercury

77= viscosity of mercury

^=acceleration of gravity

T and To=period and undamped free period of

oscillation of the mercury column,

respectively.

Equation (15) shows that the undamped mercui*y column has a free period depending only upon

its length and the ratio of the areas of the cistern

and tubing. Ordinarily this period cannot be

found experimentally because of the viscous

damping of the flowing mercury, and the restric- tion offered to flow by the finite size of the tubing.

7. Sources of Error

Ordinarily the readings of portable barometers

and manometers are corrected only for scale errors and for deviations of the instrument from

the standard temperature and gravity. The scale error is determined by a calibration of the portable

barometer against a standard instrument. It includes a correction for many other factors,

including capiUarity and vacuum, which while

assumed to be constants, may change with time.

For measurements to the limit of accuracy of

most portable instruments this assumption is reasonably tolerable. The situation is quite dift'erent for instruments

from which a high degree of accuracy is required.

More corrections, and to higher accuracy, must

be made, and of course, greater care must be

exercised in designing the parts significantly

affecting the accuracy and in controlling the

.536771—60 4 21
environment of the barometer. The followmg

table illustrates the situation for barometers,

where corrections and controls are given to secure

in one case, an accuracy of 0.1 mm of mercur}^

and in the other, 0.01 mm of mercury in each

factor. Obviousl}'^ to increase the overall accuracy

of the measurement, each factor must have

a proportionately smaller tolerance.

The overall error can be easity held within 0.1 mm of mercury except for the temperature unThe tolerance for each factor is for an error in that factor of

either 0.10 or 0.01 mm of mercury.

Accui acy, mm of mercury

0. 10 0. 01 Inch of mercury

0. 004 0. 0004

Factor Tolerance Tolerance

1. Zero error (stability of zero) mm.. 0. 10 0. 01

2. Scale error (reliability of scale).. . mm. .10 .01

3. Sensitivity of vernier or detecting means.. mm.. .10 .01

4. Temperature uncertainty at 1 atm ° C. .8 .08

at H atm ° C. 1.6 . 16

5. Capillary depression en-or _. mm. 0. 10 .01

6. Alinement uncertainty (sec. 6.6):

(a) Cosine error, at 1,000 mm of Hg 0°49' 0°15'

(b) Sine error, in practical cases 4 to 10' 0. 4 to 1'

7. Vacuum uncertainty, mm of mercm v 0. 10 0.01

8. Gravity in cm/sec^ must be knovm at 45 ° lati- tude witbin at 1 atm _ .. .13 .013

at }4 atm .26 .026

9. Altitude difference in feet between measured and desired point, at 1 atm 3.6 .36

certainty, zero stability and capillary depression,

j

pii Some care is necessary to be certain that the >

(ir barometer temperature is known to an accuracy i « well within 0.8° C. The change in capillary error , is with time is such that in barometers with tubes , (li less than about 12 mm bore, calibration will be i, n frequently needed. For this a criterion is the |; lo degree of fouling of the mercury surface. For i ta fixed cistern barometers, particularly if the cistern \ Ib is opaque so the surface can not be seen, the zero j « shift in calibration due to volume changes in the

cistern meniscus probably limits the accuracy [I l)i at best to 0.1 mm of mercury. to On the other hand no portable barometer has , ai as yet been developed which can meet all of the , ij above tolerances for an accuracy of 0.01 mm of

mercury. Items 2, 3, 4, 5, and 7 require special , n design features in the barometer to secure an , qi accuracy sufficient to hold the overall error within - j 0.01 mm of mercmy. This can be achieved ap- n parently only in a precision type, laboratory |j instrument, not readily portable. j is A number of the errors of barometers for which tl corrections can be more or less readily made, , i particularly for portable barometers, are con- r is sidered in detail in the following sections. Other \l s( sources of error and methods and means for their j , correction for barometers of high precision are , si discussed in sec. 6. I' b

8. Scale Errors

Strictly speaking, scale errors are the errors in the graduation of the scale at the chosen standard

temperature. For standard barometers of high

accuracy this definition holds. The scale can be

checked against a standard meter bar and correc- tions are applied to the scale readings as found

needed as a result of the calibration.

While many manufacturers take no less care in

graduating the scales of portable barometers and

manometers, the accuracy required does not ordinarily justif}'^ the expense of testing the scale alone.

Uniformity in spacing the graduations which is absolutely essential, can be checked adequately by

using the vernier as a length standard at various

points on the scale. This practice leads to a more practical definition

of scale error. The portable instrument is cali- brated against a standard barometer or manomeeter, and its readings corrected for temperature

and gravity errors, zero error if obtainable, and

possibly for capillary errors. The difl^erence in the

reading so corrected, and the pressure determined

by the standard instrument is defined as the scale

error. The scale error thus derived may include errors:

(a) Caused by installing the scale so that its zero or zero projected is not at the zero pressure point;

(b) caused by overfilling or underfilling the instrument with mercury; (c) due to the effect in fixed

cistern instruments of a tube bore difi^erent from

that for which the scale is graduated (foreshorten ( ing constant is in error) ; (d) due to incorrect alinej ment of sighting ring and vernier zero; (e) due to ! j capillary error, if not separately corrected for;

j (f) due to sighting errors introduced by poor j optical quality of the tubing; (g) due to the im- : ( perfection in the vacuum above the mercury col- umn; and (h) due to temperature error if the

installed thermometer is in error. Naturally in

^ barometers and manometers of good design and

J where care is used in assemblj^, many of these , errors are insignificant. An exception is the cap- , illary error, which will change with time, as dis- cussed in sec. 12. The size, and more important, ' the uniformity at various readings, of the scale ' error, together with the precision of reading, is a

' measure of the quality of the barometer or | ! manometer. j ! 8.1. Zero Error '

'

( The difference in reading of a U-tube, and the i reading of a cistern, barometer or manometer when i both mercury surfaces are subjected to the same i pressm'e is defined as the zero error. The design ' i may be such that the zero error cannot be obtained, notably Fortin and cistern instruments , which do not have scales going to zero. It can be ] obtained on practically all U-tube instruments. | Usually the zero error in barometers is determined

when both mercury surfaces are subjected to a vacuum, but often when subjected to atmospheric

22
pressure. The value usually differs slightly in the

two procedm-es, if no correction is made for

j capillarity, because of variability in the capillarity

' in the two surfaces, or because of possible flexure

of the cistern of a fixed cistern barometer when

vacuum is applied. It is usually more convenient

to determine the zero error in barometers when

both merciu-y surfaces are subjected to a vacuum;

in manometers, when subjected to atmospheric

pressure.

; The zero error may include any error introduced

' by: (a) Failure to adjust the zero of the scale so as

I to indicate the height of the mercury column; (b)

j misalinement involving a sine error; and (c)

' capillary errors, to some degree.

If a U-tube barometer is installed; (a) To have

{ no cosine error of misalinement; (b) has an adeI quate vacuimi above the mercui'}'^ column; (c) has

I a constant value of the sine error of misahnement;

I and (d) has a scale known to have adequate accu-

! racy, a determination of the zero error, is all that

l| is theoretically necessary to calibrate it. All of

Ij these assumptions can be verified without serious

Ij difficulty, and in fact must be met if any calibration

J is to have validity. Actually, as a check, comparif son with a standard barometer at some pressure

'j weU above zero is advisable. The error thus fomid

, should agree, within the expected accuracy of the

' barometer, with the zero error. The foregoing discussion applies also to a Utube manometer, except of course, vacuum may

ij not be involved.

I' The accuracy of a barometer is no greater than

the accuracy with which its zero error can be

i determined. The probable error, and the average

j deviation and maximum deviation of a single

I observation of a number of independent observations of the zero error are all useful in determining

the accuracy.

Knowledge of the zero error is extremely

valuable to the ultimate user of the barometer or manometer, when it can be determined at any

time with little trouble. If it differs significantly

from the originally determined value, the instal- lation can be checked for misalinement, the

vacuum adequacy checked and the amount of mercury in cistern instruments corrected, as neces-

' sary. If a difference develops with time, capillarity

I change (dirty mercury) or loss of mercury from

fixed cistern barometers is probably the cause,

in which case the instrument tubing will need

cleaning, or mercury needs to be added. If the

change in zero error has some cause which it is

I not desired to correct, the calibration errors at all readings may be shifted by the amount of the

change.

It should be noted that the zero error for U-tube

instruments is not affected by normal changes in instrument temperature. The zero error of cistern

i barometers varies with temperature, in most

, practical designs, bv an amount which does not

; exceed 0.1 mm for a 10° C (18° F) shift frona the

j temperature at which it was originally determined.

8.2. Method of Test

The test for scale error at a single ambient

temperature is often called a calibration test. It, and the zero determination if possible, are usually

the only laboratory tests made on portable barometers or manometers. The test essentially

consists in comparing the readings of the instrument under test at controlled pressures within its range with those of a standard instrument when

both are subjected to the same pressure and to constant environmental conditions, mainly temperature.

Standard barometers or manometers are either

primary standards or working standards. The

primary standard has its precision and accuracy

fixed by the excellence of its design and workmanship and by the application of corrections determined either theoretically or by test of its components against standards of the requisite

accuracy. A working standard is one used to calibrate other instruments; in this sense a primary standard may also be a working standard.

A working standard should ideally have a precision and accuracy about ten times that of the

instrument under calibration ; actually this is often

of necessity violated in practice. In many cases the working standard of a manufacturer is a barometer or manometer of the same design as the

instrument under calibration but is one selected

for better quality which has been carefully cali- brated.

As indicated in the table in sec. 7, the uncertainty in the temperature of both the working

standard and the instrument under test must be

much less than 0.8° C at 1 atm of pressure if an

accuracy of 0.1 mm of mei'cury is to be obtained,

and less than 0.08° C for an accuracy of 0.01 mm

of mercury. These temperature uncertainties are proportional to the pressure, greater if the pressure

is greater, and less if the pressure is less. This

indicates the necessity of control of the ambient

temperature. Due to the large thermal lag of

barometers, the safest procedure is to maintain

the mstrument temperature constant withm the

necessary limits during the enthe period of the

test, and obviously during use afterwards also. Practically this requires installation in an air conditioned room, adequately ventilated, except

for the short time when the room pressure has to be measured, when the ventilation may introduce

undesh-able pressure gradients. The scale error

test is commonly made at a temperature between

22° and 25° C; at the National Bureau of Standards, 25° C.

In making readings the top of the mercury

meniscus is always sighted upon.

In computing the scale error, the reading of the

barometer under test is first corrected for zero, temperature and gravity error, which are discussed

in other sections. The difference, corrected barometer reading minus the pressure determined

from the reading of the standard barometer, is

23
the scale error. The scale correction is of the

opposite algebraic sign.

If ? correction is made for the capillary error, (see sec. 12) , which is rarely applied to the readings

of portable barometers, this correction is also applied to the reading, after applying the corrections for temperature and gravity error. The

scale error is then computed as outlined above.

The procedure given above for computing the

scale error is strictly speaking in error in that the

temperature correction has also been applied to the scale error. This procedure could be corrected

as follows: first determine an approximate scale error by the procedm^e outlined, then apply this scale correction to the reading and correct this reading for temperature and gravity error. The

scale error is the original reading minus the last obtained corrected reading.

This refinement is ordinarily unnecessary for portable barometers. For example, assume a

scale error of 4 mm of mercury (which is really

excessive), and a temperatm-e deviation of 15° C

from the test temperature, then the error introduced is 0.01 mm of mercury (0.0004 in.), an

insignificant amount. In effect this error is a measure of the undesired dependence of the scale error upon temperature.

8.2.1. Fortin Barometers

The distinguishing feature of barometers which

are designed to measiu-e atmospheric pressure

only is that the au'-space of the cistern is always

connected to the ambient air. This class includes

Fortin barometers and fixed cistern barometers,

such as the Kew-pattern and Tonnelot. The

construction of these barometers is such that the

zero error can not be determined by direct observation; consequently the zero error is incorporated

into the scale error. Normally, the barometers

are tested when subjected to ambient atmospheric

pressure. The readings of these barometers are compared

with those of a working standard for at least 10

days in order to obtain a valid correction. The

thermometer attached to each barometer is also read. The comparison readings should be made

when the atmospheric pressure is most free from

oscillations, and sudden changes, which can be

determined from the trace being made by a microbarograph. These atmospheric pressure oscilla- tions may occur suddenly and be 0.1 and more

millimeters of mercury and are most troublesome

when there is a high, gust}^ wind. Under these

conditions simultaneity in the readings of the

standard and the barometer under test is almost

impossible to obtain. In Washington the most

quiescent pressure period during normal working

hom-s is from about 4 to 5 p.m.; normaU}' valid

comparisons can be made at this time three or four

days each week.

The atmospheric pressure variation will almost never cover the pressure range of the barometer,

normally about 75 mm of mercury or 100 mb.

Actually for this pressure range a single correction

suffices, if the graduations of the scale are uniformly spaced, a condition which can be checked

independently by readings made with the vernier

at a number of positions on the scale. However, barometers which have to be used at high elevations have a measuring range up to 250

mm of mercury. These are generally Fortm

barometers. In these cases it is not entirely safe

to assume that the scale error can be represented

by a single number obtained in a test at sea level pressure. One way of testing these long-range

barometers requires that they be installed in a chamber the internal pressure of which can be controlled and measured, as discussed in sec. 9.4. Another way of obtaining a calibration of these

long-range barometers, if accuracy requirements

can be met, is to use as the working standard a

fixed cistern barometer with an airtight cistern

which has been tested as described in the next

section. The scale error test as above described

is then made at the high-altitude location of the

barometer. This procedure is practical for the

meteorological services, since the barometers at the various stations need to be tested from time to time, probably more conveniently done at the

barometer station.

In testing atmospheric pressure barometers

having a tubing bore of % in. (6.35 mm), a Fortin

barometer of laiown scale error having a tubing

bore of 0.6 in. (15 mm) or more is adequate as a working standard. Fixed cistern barometers

of the quality used to test aviation altimeters or

precision aneroid barometers are equally serviceable as a working standard if their scale errors have been determined.

The average of the scale errors determined by

the comparison readings is taken as the scale error

of the barometer, if all are considered equally valid

and there is no indication that the scale error

varies with the scale reading. Maximum deviations from the average and the probable error

of a single observation, if at least about ten comparisons are available, are computed, and are

indicators of the quality of the barometer.

8.2.2. Altitude Barometers

Testing altitude barometers requires a closed

system essentially such as sho^vn schematically in figure 2. Altitude barometers include all those in which the cistern is airtight except for a nipple, and

U-tube barometers. In figure 2, S is a standard

barometer of the U-tube type with its scale: Bl,

B2, and B3 are barometers to be tested; VP is a vacuum pump; is a filter; Mis a large volume

manifold; i? is a barostat; and A is an air supply.

The system must be leaktight in order to avoid

pressure gradients in the system which will affect the accuracy of the readings. Insofar as possible

metal or glass tubing should be used, using butjd

rubber or plastic tubing only to make short length

connections. Rubber tubmg can be used only if

24
M

Figure 2. Set up for testing altitude barometers.

S, standard barometer (see fig. 1); Bl, fixed cistern barometer; B2, U-tube

barometer; BS, high altitude range fixed cistern barometer; B, barostat; F, filter; M, large volume manifold or plenum chamber; A, air supply, VP, vacuum pump.

practically free from sulfur. Satisfactory tubing

of rubber or plastic is hard to find, since some give

up gasses which contaminate the mercmy and

others are permeable to air or water vapor to an

objectionable degi'ee. To test for tightness, the

system is subjected to the lowest pressure mdiI cated by the barometers. The barometers are

] read, and the procedure is repeated again the

next day. A rise in pressure of about a'centimeter

ti of mercury is considered excessive. To locate

Ij leaks, various parts of the system, including inI dividual barometers, can be isolated by pinch

clamps after making the initial readings,

ii The barostat, used to maintain the absolute

t pressure in the SA'stem at constant selected value,

I is a valuable accessory. It wUl be described in

i! sec. 8.3.

y The test procedure is simple in principle. The

I absolute pressure in the sj^stem is controlled by

I operating the vacuum pump, control valves and

setting the barostat if one is available. At each

pressure step, the standard barometer, barometers

under test, and the thermometers associated 'wath each barometer are read. It is preferable to make

readings on both the do^\Ti and up side of the

pressure cycle. From these readings the pressure

is obtained by apphing the necessary corrections

to readings made on the standard barometer.

The readings of the barometers under test are corrected for zero, temperatm-e and gravity errors.

I The scale errors are then computed. Obviously

if the barometer under test has an automatic cor- rector for temperatm-e and gravity errors, this is

' set to the coiTect ambient values of these quantities, and the scale error is the difference, barometer

reading minus the pressure. Again, if the barometer under test is maintained at a constant

temperature in its own chamber and its scale is graduated to read free from temperature error, only

the gravity correction need be applied to its reading.

UsuaUj^, due to the labor and expense involved,

only two tests on different days are ordinarily

made on a given instrument to determine the scale

errors. Several independent readings at each test point are a big aid in fixing limits to the accuracy,

as well as giving an average value to use as the

scale error.

8.2.3. Manometers

The apparatus and procedure for calibrating

differential mercury manometers are similar in

details to those for altitude barometers shown in figure 2. Since differential (usuall}" gage) pressure

is measm-ed, the standard manometer has no

evacuated space above the mercmy column.

Instead of the barostat, a pressure controller is used. A commercially' available diaphragm type

pump in combination with a ballast chamber and

pressure controller is convenient for the purpose.

Perhaps the most important difference is in the

range of the manometers now needed, which now

extends to 4 atm and more. Portability becomes

a problem, so that testing against a standard at some other laboratory becomes impractical. This means that the scale only can be checked for ac- curacy and the desired accuracy must be designed

into the manometer and its installation.

8.3. Barostat

The barostat designed and used at the National

Bureau of Standards is shown in cross section in figure 3. Plates B and H are fixed in relative

positions by four rods. Plates F and G are free to move between limit stops. Bellows E is sealed

gastight to plates F and H, and is evacuated.

Bellows A is sealed by plates B and G and has

three connections through plate B, one at P for an air intake, one at S for connection to a vacuum

pump, and one at T connecting into the system

the absolute pressure of which is to be controlled.

The pressure control valve consists of a ball V

attached to spring L. Spring controlled plunger

D operates the valve. The baU seats into a

conical opening. The plates F and G are con- nected to a scale pan on which weights M can be placed.

In operation weights, corresponding to a pres- sure approximately the value desired, are placed

upon the pan. If chamber A is originalh^ at atmospheric pressm'e the plates F and G remain

against the upper stop and the valve KVis conse- quently wide open. With au* entering tube P and

being evacuated thi-ough tube S, the pressure m

bellows A falls until the pressure therein balances

the weights. At this pressure the valve KVcloses

sufficienth' so that the air flowing in through P

equals that flowing out tlxrough S. Any deviation

in flow changes the upward force on FG and either

opens or closes valve KV, which changes the air- flow through S until the pressure in A again

balances the weights.

25
Figure 3. NBS harostat.

E, evacuated bellows; A, bellows maintained at desired pressure; Hand B, fixed mounting plates; F and G, fioating mounting plates; M, weights attached to F and G; D, spring controlled plunger; V, ball valve attached to spring L; K,

valve seat; P, pressure line; S, suction or vacuum line; N, a valve; T, line to system the pressure of which is controlled by the barostat.

The performance is dependent upon the flow of

air mto bellows A through P; for optimum pres- sure control this airflow is about 1 liter/min

secured by valve and a suitable rotameter in

line P, not shown in figure 3. The beUows are copper plated brass and are about 5% in. in diam. The weight required to balance at 1 atm is nominally 330 lbs. These

weights are applied manuaUy ; a mechanical weight

lifter would be a desirable improvement.

The barostat controls the pressure to within

0.01 mm of mercury during the time needed to make readings, about 10 min.

The barostat fails as an absolute pressure gage

by a few tenths of a millimeter of mercury, that is the pressure obtained at various times by a given

weight does not repeat by this amount. Perfection of the barostat in this respect has not been

undertaken.

9. Temperature Errors

It is evident that mercury barometers and manometers can read correctly at only one temperature principally because of the thermal expansion

of the mercury and the scale, but also of certain

other parts of the instrument. The height of the

mercury colimin in terms of the density of mercury

at 0° C (32° F) is desired. Deviations from the

selected standard temperature requires the application of corrections to the instrument readings.

GeneraUy the scale is graduated so that the

column height is indicated when the scale is at

0° C. Exceptions are that manometers frequently, and barometers more rarely, have scales graduated to incUcate the height of the mercury

colunm at 0° C when the instrument temperature

is at some selected value, commonly 20° or 25° C

(68° or 77° F). Also, an exception are the scales of Fortin barometers stfll in use in meteorology

graduated in inches, which are specified to indicate

inches accurately when the scale is at 62° F

(16.67° C). The requirement now is that the

scale be graduated to be accurate at 0° C

(32° F) [564].

The temperature correction for aU types of

26 %

I
barometers and manometers is generally computed from formulas derived from the pertinent

design constants of the instruments and the coeffi- cients of thermal expansion of the pertinent parts.

For any particular design, tests are essential in order to check the validity of the assumptions

made in deriving the correction formida; these

tests are particularly essential if the barometer or manometer temperature is much different from

that at which the zero and scale errors were

determined.

The thermometers attached to barometers and

manometers may be in error. If no correction is applied for such error, either during calibration or

service use of the barometer, and the error has a

small constant value at all temperatures experienced, the resultant error in the temperature cor- rection of the barometer will be almost entirely

absorbed in the scale en-or. Variable errors in the

attached thermometer over a few tenths of a degree may introduce significant errors in the

pressure determination, unless corrected. If there

are errors in the thermometer, any correction table

which is set up for the barometer should obviousl}"

be based upon the reading of the thermometer,

not the true temperature.

9.1. Basic Formula

The basic temperature correction formula is applicable to all portable barometers and manometers in which the height of the' column is measured with a scale not foreshortened. It is directly applicable to Fortin and U-tube barometers and U-tube manometers, and as will be dis- cussed later, with some modification to fixed

cistern instriunents.

The following terms are defined:

Ct= temperature correction of barometer reading to secure height of column at to

7?^ =barometer reading corrected for scale error

i?,= barometer reading corrected for scale and

temperature error

;=barometer temperature

^0= standard temperature for height of mercury

column, usually 0° C or 32° F

ii =temperature at which the scale indicates

the true height

rrt= cubical coefficient of thermal expansion of mercury per ° C or ° F as applicable

.s=linear coefficient of thermal expansion of

the scale per ° C or ° F, as applicable

/i,=height of the mercury colmnn at t

F=eL factor defined in eq (24) and (25).

The basic formula for the temperature correction wdl be derived for the general case where the

reference temperature for both the mercury

column and scale is unspecified.

First, to determine the height h of tlie mercury

column at temperature t, it is seen that as the

temperature of the scale decreases from t to U, the reading on the scale at the meniscus level increases. The height h of the colmnn at U is the

original reading plus the contraction of the

scale in going from t to U, or

(18)

The contraction of the mercury column from

temperature t to can now be written,

If

h=Bt[l+m{t-Q].

h follows from eq (18) and (19) that ^ (t-ti) — m(t —to) „

l+m(t-to) '

(19)

(20)

(21)

Ordinarily the coefficient of expansion s is fisted with reference either to 0° C or 32° F;

therefore s m eq (18) and (21) differs from the

ordinarily defined value if ti is not 0° C or 32° F. Let Si be the value of s at ti. Then

L2=Lo[l+sit-ti)] (22)

(22a)

where Lq, Li, and Lo are the scale lengths at 0° C,

ti, and t, respectively.

It follows that

1 (23)

Since Lo/Li is very nearly unit}', the approximation sLo/Li is justified; in fact with usually

insignificant error in all but precise manometry,

S =,S'i. The choice of the form of the above formulas is based upon the premise that it is more convenient

to apply a small correction, derived from con- venient tables than to make basic computations.

A constant value of the thermal expansion of

mercury, m, is assumed, which is sufficient^ accurate for all but precise manometry. (See sec. 4.1.) If an electric computer is available, a more

fundamental procedure is outlined in section 10.1,

eq (45), where the tempej-ature and gravity

corrections are made in one operation.

27
9.2. Fortin Barometers, U-tube Barometers

and Manometers

Since pressure in terms of the height of a mercury colunm is defined in terms of the density

of mercury at 0° C (32° F), ^ in eq (21) is either

0° or 32°, depending upon whether f is in degrees

Celsius (Centigrade) or Fahi-enheit.

Wliile generally scales are used or specified to have the indicated length at 0° C, exceptions exist. These cases will be discussed in the sections immediately following.

It is assiuned that the scales are graduated to indicate a length accurately, that is the scale is not foreshortened, as in the case of cistern instruments. It is also assumed that the scale, or metal

the same as the scale material, extends downward

to the level of the mercury in the cistern. This

assumption is usually violated in Fortin barometers to some degree in that diverse materials are used in the cistern. Thus the coefficient of ex- pansion s may not apply for a short length just

above the cistern mercury level. Only the differ- ence from the coefficient of expansion of the scale introduces an error. Neglect of these sources of error does not seriously affect the accuracy if the

ambient barometer temperatures do not differ greatly from the temperature at which the barometer was tested. The error in the applied temperature correction is completely absorbed by the

applied scale correction when the barometer is at the temperature at which the scale error test was

made, and to a major amount at other barometer

temperatures.

9.2.1. Scale Accurate at 0° C

where r=l + 6'^. The value of Y can be obtained from a computed table of Y against temperature t or table 7 as discussed in sec. 9.5. For portable barometers it is sufficiently accurate

to use a constant value of m, the cubical expansion

of mercury, over the temperature range normally

expected; if more precision is necessary, see sec.

4.1. The accepted value of m is 181.8X10"^ per

° C or 101.0X10-6 per ° F. The value of the linear coefficient of expansion

varies somewhat for a given scale material, depending upon its exact composition and the degree

of cold work. The exact value when required

must be determined experimentally. Average

values for a number of materials used either for

the scale or cistern are given in table 5. The

value for brass is taken from ref [512]; the others,

from other published data.

Commonly the scales of Fortin and other barometers are made of yellow brass for which the

value of s, the coefficient of linear expansion, is generally assumed to be 18.4 X 10"® per ° C. Using

this value of s and 181.8X10"^ for m, the cubical

expansion of mercury, eq (24) becomes

^_ 163.4X10-6^^,

' 1 + 181.8X10-6^ ^ ^

and eq (25) where ^ is in ° F, becomes

, 90.78X10-^^-32) i^,

1 + 101.0X10-6(^-32)

When the scale is graduated to be accurate at 0° C, tQ=tx. Equation (21) then becomes, when

t is in °C

C,=R,-R,=

^'~^l^\^'=FE, (24)

and when t is in degrees Fahrenheit

i + ^,(^_32) (25)

The factor F is identical in value in eq (24) and

(25) at the same temperature. It follows therefore

that a table of corrections against temperature in either ° C or ° F is equally applicable for all units

of pressure, including millibars, millimeters or inches of mercury, if entered with the temperature

in the unit for which the table was computed.

Note, however, that F is not identical in the two

equations if the scales are not accurate at 0° C

or 32° F. When a mechanical computer is available, the

following relation is useful, particidarly when many

readings are taken at the same temperature.

In these equations Ct, will be in the same unit of

pressure as E^, and apply equally for scales graduated in any pressure unit. The correction Ct is negative for temperatures above 0° C or 32° F,

and the correction is therefore to be subtractecl

from reading Bs, corrected for scale error. Correction tables based upon eq (27) are given

in table 6 of this report (see sec. 9.5. for discussion),

and also in ref [512]. If the barometer temperature is measured in °F, as indicated in eq (28),

these tables are equally applicable if they be

entered with the equivalent temperature in °C.

Tables based upon eq (28) are given in ref [591].

9.2.2. Fortin Barometers, Scale Accurate at 62° F

Fortin barometers graduated in inches of mercurv used in meteorology have the scale specified

graduated to be accurate at 62° F (16.67° C). In

view of the adoption of the millibar as the international standard unit of pressure by the meteorological services, Fortin barometers calibrated in inches of mercury are becoming obsolete ; however, some of these are still used in industry. It is advocated that in the future the scales of all 28
Fortin barometers be calibrated accurate at 0° C,

to secui'e agreement with the cahbration practice

followed for Fortin barometers calibrated in other

pressure units.

For barometer scales graduated to be accurate

at 62° F. formula (22) becomes, when t is in °F.

Cr- (t-Q2) s—(t-S2) m

l +m(<-32) (29)

Inserting the value of s for a brass scale, 10.2 X10~® per °F and m, the volume expansion

coefficient of mercmy, lOl.OX 10"^ per °F, eq (29)

becomes

„ _ (90.8 /-2599.6) 10"^ „

'~ l + 101X10-«(^-32)^ (30)

Here i is in °F and d and Bi are customarily ui

inches of mercurj* only.

The temperature correction is zero at all values

of Rs at 28.6° F and is negative at all temperature

above this value, meaning that the correction is to be subtracted from the barometer reading.

Correction tables based upon eq (30) are available [301, 512, 591].

9.2.3. Scale Accurate at Unknown Temperature

It is necessary to consider the case where the

temperature at which the scale is acciirate is \mknown. It is assimied that the scale is graduated

uniformly.

For U-tube instruments and Fortin barometers

with a thermometer graduated in °C, eq (22) can be modified to give

[s{t~U)~mt]R, (s—m)tR, sUR,

1+mt l+mi l-\-mt

(31)

where ti is the temperature at which the scale correctly indicates the height of the column.

The last member of the equation contains the

factor l-\-mt which affects the value of the last member only 0.7 percent at ^=40° C, and less at lower temperatures and Ct not more than 0.1 percent. Without significant error eq (31) then

becomes

{s—m)t Rs

1+mt stiRs (32)

The last term in eq (32) is therefore a constant

at a given reading Rs well within the accuracy of

barometers of this quality and therefore can be

incorporated into the scale correction. To do so may require determining the scale error against

reading over the range of indication. In determining the scale error, the temperature correction

applied is the same as that for the case when the

scale reads correctly at 0° C or 32° F given by eq

(24) or (25). The residual error, after applying

the usual gravity correction to the reading, is the

scale error. Thus, at the calibration temperature,

the term stiRs=0.

If the barometer has a brass scale, table 6 can be used to obtain the temperature correction.

9.2.4. Scale Indicates Pressure, Instrument Temperature Not 0° C

Assume that the scale indicates the height of

the mercury column at 0° C when the instrument

is at a temperature 4- This procedure is fairly

common for U-tube manometers and barometers

but rarelv for Fortin barometers. A temperature

between 20° to 25° C (68° to 77° F) is commonly

selected and it is here assmned that the temperatm'e of the barometer or manometer is not subsequently controlled.

When the ambient temperature, that is the

instrument temperature t, differs from t^, the temperature at which the barometer reads free from

temperature error, the temperature correction is (noting the discussion on the value of s in sec. 9.1.)

is-m)it-ts) Rs

1 + mt (33)

It is seen that table 6 can be used to obtain

approximate temperature corrections based upon

eq (33), if the scale is of brass, by entering the

table with Rs, the reading corrected for scale error and the temperature difference (t—ts) in degree

centigrade. Obviously, the correction is to be

subtracted from Rs if (t—ts) is positive; otherwise,

added. In the table the computation is for 1+m

(t—ts), instead of l-\-mt given in the equation;

the error in the correction is less than 0.3 percent

when ts=25° C and t—tg does not exceed 10° C.

Some manometers designed for relatively rough

measurements ha ve scales graduated as described.

With the advent of air conditioning for most laboratories, the need for any temperature correction

for manometers of this quality almost disappears.

In any event, corrections based upon eq (33) are

accurate. Many manometers and barometers of high

quality are installed in a temperature controlled room or in a cabinet the temperature within which

is controlled to give readings free from temperature

errors. The only temperature error which may

need to be applied is that for minor deviations, of

the order of 1° C, from the supposedly maintained

temperature. Greater temperature deviations in- dicate improper functioning which should be cor- rected. The temperature correction can be obtained without significant error from table 6, or computed accurately from eq (33).

9.3. Fixed Cistern Barometers and

Manometers

The temperature correction for fixed cistern

instruments differs only from that of U-tube in- struments in that the differential expansion of the

29
mercury in the cistern and of the cistern changes

the zero position of the mercury surface with

reference to the scale zero.

If the zero error of a fixed cistern instrument can be determined at several temperatures, as is the case for many modern designs, it is only neces- sary to apply the zero correction for the particular

barometer temperature. Only the temperature

correction as discussed for U-tube instruments

needs then to be applied.

9.3.1. Scale Accurate at 0° C

When the zero error can not be determined, the

temperature correction of fixed cistern barometers

and manometers is difficult to compute accurately

because simplifying assumptions must be made as

to the construction of the parts aff"ecting the change

in reading with temperature, in order to obtain

formulas practical to use. In the end it is essential to test each design of fixed cistern barometer at two or more temperatures in order to be able to compute a valid temperature correction.

Assume most simply that the fixed cistern in- strument is so designed that the scale extends

down to the level of the mercury in the cistern,

reads zero at zero pressure and 0° C and is graduated to be accurate at 0° C. Also assume that

the cistern is made of materials having the same

coefficient of expansion. In this simple case the

temperature correction C, is, neglecting second

order terms,

' l + mt .4o(l +m^+2.s,o'

The terms not previously defined are:

1^0 = the volume of mercury at zero pressure and

at 0° C

ylo=the effective area of the cistern at 0° C, as- sumed to be uniform

S(;=the linear coefficient of thermal expansion of the cistern material

i =barometer temperature in ° C.

If the cistern is made of diverse materials, s<. is not a simple constant, but is a function of several constants. For example if the cistern has a steel base and glass walls, 3.Sc becomes Sj+2Ss and 2sc

becomes 2ss where the subscripts g and s refer to

glass and steel, respectively.

With obvious modifications the formula applies

also if the temperature is measm-ed in degrees

Fakrenheit.

The first term of eq (34) is the same as the

temperatm-e correction for Fortin barometers;

the second term corrects for the rise of level of mercury in the cistern with temperature which

introduces an error because the scale, and its zero point, are in a fixed position.

The term FqMo in eq (34) equals the height of | the mercury in the cistern at zero pressure. More or less approximately, in eq (34)

{s—m) ^ 3s,—

m

1 + mt l + {m-2sc)t' ^ '

since in general Sc is much less than s and m. Approximately therefore eq (34) becomes

where ii^ is a constant approximately equal to Vq/Ao which can be added to the reading corrected

for scale eiTor Rs [231]. This simplifies computation and permits using table 6 if the ^cale is brass,

which is entered with Rs-\-K and the barometer

temperature.

In various designs of fixed cistern barometers

the computed K will vary from about 35 to 75

mm, with an uncertainty up to 20 percent due to deviations from the simple assumptions made. ' If K is determined by tests made at two or more

temperatm"es, the uncertainty of com"se disappears,

but some lack of constancy may remain, in the

practical case usually negligible. It is a matter of i convenience whether this deviation is incorpoiated \ in the temperature error or in the scale error; if i the latter, the scale error will vary with ! temperature. ; The difficulties in determining the exact temperature correction of fixed cistern barometers is a limitation upon the attainable accuracy. When

the accuracy must be better than about ±0.1 mm

of mercury (0.004 in.) it is necessary to mamtain

the barometer at constant temperatm^e, so that

the temperatm-e error can be incorporated once

for all into the scale error. This remark applies

particularly to altitude barometers.

9.3.2. Scale Accurate at Unknown Temperature

In some barometers and manometers of the

fixed cistern type of relatively low precision and

accuracy, scales, desired to be correct at 0° C, are ruled without care being taken to have them read

correctly at precisely 0° C. This case is discussed

in some detail for Fortin barometers in section j 9.1.2. For fixed cistern instruments the last term of eq (31) or (32) needs to be added to eq

(36). Again this approximately constant term

c^in be absorbed into the scale error with negligible error in the practical case.

9.3.3. Scale Indicates Pressure, Instrument Temperature Not 0° C

In this case the barometer or manometer is to be maintained at some constant temperature in

the range 25° to 45° C, and the scale is ruled so that the pressm-e is indicated, that is, no temperature (and no gravity) correction needs to be

30
applied. For small deviations in temperature

from the selected constant temperatiire, the

temperature correction, is with negligible error,

1+^^^ (I^s+K)- (37)

This relation is based upon eq (33) and (36) and

the assumptions made in their deviation also

apply. The equation should only be used if the

li zero error can not be measm-ed at the two tempera-

' tures t and ts. If it can, the procedure outlined

in section 9.3. is preferable and more accurate.

9.3.4. Fixed Cistern Barometers With An Altitude Scale

In calibrating altimeters it is often requii-ed

j that the altimeter be subjected to pressures

l! corresponding to definite pressure altitudes. The

barometer is always equipped with a pressm-e

scale and sometimes with an auxiliary scale gi-aduated at 1,000 or 500 ft intervals. Having

an altitude scale only is unpractical because the

graduations are nonuniform, making the use of a

vernier impractical.

On the above basis, it follows that accuracy in producing fixed pressure altitudes from an altitude

scale is obtainable only when the barometer is maintained at a constant temperature and has no

scale error. The altitude scale shoiild be graduated so that allowance is made for the temperature

error (and the gravity error at any one location).

If the barometer temperature is allowed to vary

with uncontrolled ambient temperature, the most

practical procedure is to precompute the barometer reading in pressure imits for the desired pres- sure altitudes. The pressure in the system is then

successively brought to correspond with these

readings. In precomputing, it must be remembered that the available corrections are to be

applied to the readings, not the pressure. Therefore, the temperature (and gravity) corrections

(with reversed signs) are first applied to the pressiu-e giving an approximate reading. Repeating

jl the process, using the approximate reading instead

' of the pressure usually gives a sufficiently accui'ate

reading. The process can be repeated if greater

accuracy is warranted. The scale (and zero, if determined,) corrections (with reversed signs) need

still to be applied to the reading corrected for

temperature (and gravity) to obtain the reading

corresponding to the pressure. Since pressure altitude varies as the logarithm of

the pressure, the limiting sensitivity or accuracy

in altitude units varies with pressure. Thus, if the accuracy of the barometer in measuring pres- sure is 0.1 mm of mercury, in pressure altitude

units this equals 3.6 ft at 0; 6.8 ft at 20,000 ft; 14.8

ft at 40,000 ft; and 39 ft at 60,000 ft of pressure

altitude.

Theoretically it is of interest that the temperature correction Cn of a fixed cistern barometer in pressure altitude units,

RT(m-s)t

' gP (l + mf) (38)

is almost constant at all values of the pressure,

since {Rs-\-K)T/P is almost constant in value.

Here R is the gas constant for air, T and P are respectively the temperature and pressure in the

standard atmosphere and g is the acceleration of

gravity.

9.4. Method of Test

The method of testing for temperature errors

differs only from that for scale error for the various

types of instruments described in sec. 8.1. in that

control of the temperature of the barometers and

manometers is required. The standard instrument is probably best maintained at its usual

operating temperature, but it is advantageous to operate working standards at the same temperature as the instrument under test. Generally U-tube instruments do not require

temperature tests. It is ordinaiily only necessary

to check their scales, or the precision screw if used, at several temperatures in order to determine its thermal coefficient of expansion, or its length at the temperature of use, if the instrument temperature is controlled. The temperature correction can then be accurately computed.

This makes it only necessary to test Fortin and

fixed cistern barometers, particularly the latter. The choice of temperature chamber lies between

a small one in which manipulation of the sightingmeans, sighting, and reading are done from the

outside and a temperature chamber large enough

for personnel to enter to make the adjustments

and reading. The large temperature chamber is definitely more advantageous for fixed cistern

instruments with airtight cisterns. Only temperature control is needed which ofl^ers no primary

difficulty.

For Fortin barometers and fixed cistern barometers which measure ambient pressure only, and

thus have cisterns which are not gastight, pressure

and temperature must both be simultaneously

controlled in the temperature chamber. This is more difficult in a large temperature chamber, but

the difficulty is balanced by the difficulty of adding means for operation and reading from the outside

of a small temperature pressure chamber. It is debatable which of the two sizes of chamber is preferable; experience indicates a preference for the large chamber.

It appears necessary to test instruments at least three temperatures if they will experience large

temperature differences in service. For computing, it is the aim to divide the overall error into a scale error constant at any one reading, and into a temperature error linear with the reading cor- rected for scale error. The temperature error so derived should be reasonably consistent with the

applicable equation for temperature correction,

after insertion of the values of the constants computed from the test results. Any other test

31
result gives rise to the suspicion that either the

test I'esults are unreHable or the design or construction of the barometer needs improvement.

A procedure is outlined in ref. [591] whereby the

temperature and scale errors of cistern barometers

can be determined from tests at three temperatures, if the pressure is adjusted so that the cistern

barometers have precisely the same readings at each temperature.

9.5. Temperature Correction Tables

As has been stated cori-ection tables are given in table 6, based upon the equation

' 1 + mt l-181.8X10-'^i'

The table covers the temperature range 0° to 50° C

and barometer readings (corrected for scale error)

from 100 to 1,195 in steps of 5. The table may be

entered with the barometer reading in any unit of pressure, ordinarily millibars, inches or milli- meters of mercury to obtain a correction in the same unit of pressure. The table applies only when the scale is graduated to indicate length accurately at 0° C and has a thermal coefficient of expansion of 18.4X10"^ per

degree Celsius (centigrade) which is closely that of yeUow brass. The volume coefficient of expansion

of mercury assumed is 181.8X10"^ per degree Celsius (centigi-ade).

All corrections given in table 6 are to be subtracted from the instrument reading, corrected for scale error. Temperature corrections can be obtamed with

sufficient accuracy from table 6 for practically all portable barometers which have brass scales. The

instruments for which it can be used are listed

below, together with a discussion of the limitations.

(a) The table applies to all Fortin barometers

and U-tube barometers and manometers which

have brass scales graduated to be accurate at 0° C

in any pressure unit, particularly millibars, inches, or millimeters of mercury, and when the instrument temperatm'e of which is measm'ed in, or converted to ° C.

(b) The table applies to all Fortm barometers

and U-tube barometers and manometers which

have brass scales graduated presumably to measure length, or a length proportional to pressure, accurately at 0° C but actually do so at some temperatm-e between about —10 to 25° C. The in- strument temperatm-e must be measured, or con- verted to, degrees Centigrade. Using the table

may necessitate applying a scale error determined

by test which will vary with the reading as in- dicated by eq (32). For example, if the scale is accurate at 20° C, the scale error will vary linearly

from 0.20 to 0.30 mm at readings varymg from 543

to 815 mm.

(c) The table can be used usually with negligible error to obtain the temperature correction of

U-tube barometers and manometers the scales of

which are graduated to read free from temperature

error at a selected temperature other than 0° C, if the temperature of the instrument differs only

slightly from the selected temperature. The scale must be brass and the temperatiu-e deviation must

be in deg Celsius (Centigi-ade) . The table is entered with the deviation in temperature and the

instrument reading corrected for scale error. The

resulting correction is subtracted if the instrument

temperature is greater than the selected temperatiu"e, and vice versa.

(d) The table can be used to obtam the temperatm-e corrections of fixed cistern barometers and

manometers with brass scales graduated m any

pressure unit, particularly millimeters or inches of mercury or millibars and the instrument temperatm-e is known in deg Celsius (Centigi-ade) . The

table is entered with the instrument temperatm-e

and with the sum of two quantities as indicated in eq (36), the bai-ometer reading corrected for scale

error, and the approximate constant K. This K is approximately the height at 0° C of the mercury

in the cistern at zero pressm-e difference in the

tube and cistern, but should be determined by

testing the instrument at several temperatures.

There is somewhat less uncertainty in the computed value of K if the brass scale is graduated to be accurate at 0° C and extends down to the mercury level m the cistern and if the cistern is made

of materials having a low value of the thermal

coefficient of expansion.

(e) The table can be used usuall}'' with negligible error to obtain the temperature corrections of

fixed cistern barometers and manometers, the

brass scales of which are calibrated to read free from temperature eiTor at a selected barometer

temperature other than 0° C, if the instrument

temperature differs only slightly from the selected

temperature. The table is entered with the deviation of the instrument temperature from the

selected temperature, instead of the instrument

temperature. With this exception the discussion

in (d) above applies. The correction obtained

from the table is subtracted from the reading

where the instrument temperature is higher than

the selected temperature, and vice versa.

It is perhaps unnecessary to add that for highly

precise measurements for which correspondingly

high quality instrumentation is required, table 6

is not sufficiently accurate. The temperature

errors of the scale may need to be determined more precisely and more accm-ate values of the

density of mercury as given in tables 2, 3, or 4

may need to be used.

The temperature correction factor F defined in

eq (24) and (25), that is

(s—m)t

(39)

is given in table 7 as a function of instrument

temperature and of the thermal coefficient of

32
expansion s of the scale. These are useful for making computations when table 6 does not apply.

The values are for a value of the thermal coeffi- cient of the volume expansion of mercm'v m of

181.8X10-^ per deg Centrigrade. Values of Y,

eq (26) can be obtained from table 6 bv addmg 1 to the value of F, if ti = to=0 in eq (26).

The factor F given in table 7 can be used for computing the temperature correction with an

accuracy sufficient for most portable barometers

and manometers having scales of the material

indicated. For greater accuracy the precise

value of the expansion coefficient s must be known

for the scale. If the corrections for the expansion of the scale and of mercury are determined separately, the

value of F in table 7 for invar (s =o) applies for the effect of the expansion of mercur^^

The factor F given for brass (.s= 18.4X 10"^) was used in computing table 6.

10. Gravity Errors

10.1 Basic Relations

It is necessary to coiTect the observed height of aU mercury columns for the deviation of the

i: acceleration of gi'avitv from the standard value,.

' 980.665 cm/sec- (32.1740 ft/sec^). The standard

I acceleration of gi-avity is assiuned in the definition

I of the inch and millimeter of mercur\^ as a imit of

Ij pressure and in the graduation of barometer scales

' in millibars.

The correction, derived from eq (1) is C,=^R,^F,R, (40)

E,^B,+C, ' (41)

where Cg is the gravit.v correction; g and gs, the

I

I acceleration of gravity at the location of the instru-

' ment and the standard value, respectively; Rt and

Rg, the instrument reading corrected for temperature and for gravity, respectively.

If no additional corrections are to be applied, as is often the case with portable instruments, Rg

is the pressure in any unit in which the instrimient

is calibrated.

With equal accuracy- C;=^' Rs=FgR. (42)

I Us

I R,g=R,+ Cg. (43)

Here R, is the instrument reading corrected for

' scale error and R^g is tlie same corrected for scale

'! and gravity error. The temperature correction is then obtained for R^g and applied to Rsg to obtain

tlie reading corrected for both temperature and

gravity errors. It may be preferable in precise measurements

to compute the temperature and gravity corrections in a single operation, particularly if corrections are first and separately made for the calibration and temperature errors of the scale. The

temperature error of the scale is given by eq (19).

From eq (1) PsgA=pgh (44)

and

Here ps and p are respectivel}^ the densities of mercury at 0° C and at the instrument temperatm'e; h is the true height of the mercury column

at the instrument temperatm-e and ambient

gravity; hs is the desired true height under standard

conditions, that is the pressure, if no other cor- rections are to be applied; and g and g,, have been

defined.

The ratio of the densities of mercury can be

obtained from table 2, or computed from table

3 or table 4.

10.2. Value of Gravity at the Instrument

Location

It remains to discuss how the acceleration of gravity g may be obtained. The U.S. Coast and

Geodetic Survey has determined the acceleration

of gravity at many points in the United States and

using these values, the U.S. Geological Survey

has made determinations at additional locations.

At the moment the gravity values are based upon

the Potsdam primary determination ; later primary

determmations indicate that the Postdam value is 0.013 cm/sec^ too high. The International Meteorological Organization has adopted the latest primary value; gravity data given in ref. [512] are

also based on the latest primary value. If the

location of the instrument is reasonably close to a point or points where the value is known, interpolation and application of the elevation correction

to be discussed below, may serve to obtain the

value of g to sufficient accuracy.

For precise work it is necessary to have the

value of gravity measured at the instrument location. When due to the lack of observed values, interpolation and computation can not be used to determine g, its value may be obtained by entering

table 9, discussed later, with the latitude of the

instrument location. The value so obtained is for sea level and requii-es a correction for elevation,

as also discussed below. The value of g so obtained

33
has a relatively low accurac}", particularly in mountainous regions where the elevation correc- tion is approximate and where anomalies in the

value of gi-avity in the United States may amount

to 0.110 cm/sec^ or 0.011 percent.

For a general discussion of the acceleration of gravity as applied to manometry and for pertinent

tables, see ref [512].

10.3. Variation of Gravity With Latitude

and Elevation

The value of gi-avity at sea level varies with

latitude as follows, based upon simple assumptions

and taking no account of anomalies:

^^=980.616(1 -.0026373 cos 2(^ +5.9X10-«cos2 20). (46)

Here is the value in cm/sec^ at latitude 4> and

980,616 cm/sec^ is the presently accepted value

at sea level and 45 deg lat. See ref. [512]. Values

of f/^, computed from eq (46) are given in table 9. The empirical relation for the value of gravity

g at elevations above sea level is

.'7=f/^-0.0003086/i. + . 0001118 {h-h') (47)

where g^=the acceleration of gTavit3' at sea level; ^=the elevation in meters of the instrument

above sea level; and h' = the elevation m meters

of the general terrain for a radius of 100 miles.

For further details and sample computations, see

ref. [591]. It is quite obvious that arriAdng at an accurate

value of h' is difficult in mountainous terrain.

For a relation similar to eq (47) but apptying

to a station under water, see ref [512].

10.4. Gravity Correction Tables

Gravity corrections are given in two tables,

Nos. 8 and 9. They are alike in that the corrections are given for selected values of gravity and

of instrument reading. The}' differ only in that in table 9 the selected values of gravity are associated with latitude.

Correction table 8 was computed from eq (40)

for various value of g and Bf The table is entered

with g and Rt to obtain the gravity coiTection

to be applied. The correction is subtracted from

Rt if the sign is minus, and added to Rt, if plus.

Table 8 can be entered equally well with R^,

the reading corrected for scale error only. The

correction is applied to Rg which gives Rg^, the

reading corrected for scale and gravity error. Table 5 can be entered with Rgs to obtain the

temperature error, which must however be applied

to Rgs. The final result is a reading corrected for

both temperatures and gravity errors. Table 8 can be entered with Rs in any pressure

unit, generally mifiibars, inches or millimeters of

mercury, to obtahi a correction in the same unit.

The correction varies linearly with Rg so that by

interpolation or other obvious numerical manipulation of Rs and the corrections, a correction for any

reading can be obtained. A table computed for a given location is more convenient, in the px'eparation of which table 8 may be helpful.

The values of gravity are given in table 8 in cm/sec^ If available in ft/sec^, multiply by

30.48006 (or 30.48 if the international inch is used)

to convert to cm/sec^.

Table 8 also includes the value of {g—gs)hs used

in making the calculations. This value when

algebraically added to unity gives the value of

gigs, needed if eq (45) is used in computing

corrections.

Table 9 dift'ers from table 8 only in that it is entered with latitude instead of g, the acceleration

of gravity. Tlie value of gravity, g, and the ratio

(g—gs)/gs are also given. The correction obtained

is applicable only if the instrument is at sea level; further correction for elevation may be necessary

using eq (47).

The value of g at a given latitude in table 9 was determined from eq (46). Otherwise, the

discussion of table 8 presented above applies.

11. Capillary Errors

The meniscus of mercury in containers, either

tubes or cisterns, is dra\vn do\vn at the line of

contact at the container wall. As a result the center of the meniscus is depressed somewhat

below the level of an infinite surface of mercurj'^.

The amount of the depression tends to vary with

the age of the barometer, with the direction of the

change in pressure, and with local differences in the condition of the surface of the container.

Theoretically, the amount of the depression is a function of the bore of the container, the meniscus

height and the value of the surface tension of

mercury. Foreign material on the container wall,

such as grease, and contamination of the mercury

surface, affect the meniscus height.

It has been reported that greater uniformity in

the meniscus height may be secured by putting mercurous nitrate at the interface [291] or coating

the container surface with a material to stabilize the meniscus height. Neither of these procedures

have found serious application in manometry.

A serious difficulty is lack of knowledge of the

surface tension of mercury, except in a freshly

distilled state under a vacuum. When in contact with air, it is known to be less than 484 dynes/cm

at 25° C, the value for freshly distilled mercury in a vacuum. Surface contamination, even apparently trivial, will affect the value of the surface

tension. Kistemaker, [451] in a series of careful

experiments deduces from measurements of the

capillary depression of mercury in a series of clean

tubes of various bores up to over 30 mm (1.2 in.)

34
that the surface tension of mercury in contact with

I air at about 18° C was 430 ± 5 d}Ties/cm. There is

I no certainty that this value holds for the mercmy

in other tubes.

Thus the capillary depression, a function of the

surface tension for a given bore of tube and

! meniscus height, can not be accurately determined.

Hopefully, the error in the determination of the

capillary depression is estimated to be less than — 20 percent but the error will exceed this amomit

in many cii'cumstances.

For highest accm'acy there is only one safe recourse for avoiding excessive capillar}' correcj tions, that is making the areas of the mercury

I surface large enough so that the capillary depres-

[i sion is negligible. In precision manometry and

i| barometry, if the capillary depression is not

I negligible, it is always considered desirable to

j measure the heights of the menisci and to apply

' the capillary correction.

It is common practice with ordinar.v barometers

and manometers to incorporate the capillary

depression into the zero correction (if one is applied). In the case of U-tube instruments it is

I often neglected on the assimiption that the

I capillary depression is the same within the acculi racy expected, for each mercmy surface. When

and if a correction is applied it is obtained from

tables (see sec. 11.3).

11.1. Tube

It is practical onh* to correct the indicated

\[ position of the mercury surface in transparent

" tubes for the capillary depression. If the correction is to be made, the height of the mercury

I meniscus must be measured, in effect requiring, in

I

i addition to the usual measurements, the measure- ment of the position of the mercmy-glass-gas

boundary'. This can be done only if the mercury

surface is clean. Also tapping of the barometer

or manometer is normally required to obtain a

continuous, level boundary to measure and to eliminate nonuniform sticking of mercmy to the

cistern wall. The capdlary depression is obtained

, from tables such as table 10, entered with the tube

'[ diameter and the meniscus height.

' In view of the lack of inherent accurac}^ in determining the capillary depression, it seems

hardly worthwhile to apply the correction for tubes

less than 10 mm in cliameter. In fact, the uncertainty in the capillary correction is such that

- if an accuracy of 0.1 mm of mercurj^ is desired, a

' tube of not less than 12 to 16 mm in diameter

should be used.

Kistemaker [452] describes a procedure for

I determining the capillary depression in tubes

which is of interest, but not often as practical as

f! using tubes of bore so large that the variations in

I the capillary depression can be neglected. An

additional tube of smaller bore is used in parallel

with the primary, subjected to the same pressure

J and of the same kind of glass and degree of

cleanliness. The measurements made are: d,

difference in heights of the mercury colimxn in the two tubes, which should be of the order of

1 nun, in effect the diflFerence in the capillary

depression of the two tubes; mi and m2, the

meniscus heights in the primary and secondary

tubes, respectively. Entering an accepted table, as described in sec. 11.3, with mi and m2 and the

applicable bore of the tubes, the capillary depressions Ci and C2 ai'e secured. The difference,

C2—Ci=dc is compared with d, the measured

difference. If the difference, dc—d, is significant,

the values given in the table 10 for the primary

tube are adjusted percentage-wise to give dc—d=o,

and then used to make the corrections for the

capillary corrections for that primary tube. One

obvious assumption is made that the condition

of the mercury surface in the two tubes is directly

comparable and that this relative condition

remains stable. It is claimed that, while the

method is theoretically an approximation, an

accuracy of ±2 percent in determining the

capillary correction is obtained.

11.2. Cistern

Corrections for the capillary depression of the

mercury in the cistern of manometers and barometers can not be applied because the meniscus

height can not be measured as a routine. The

cistern is usually, or should be, large enough in diameter so that the depression itself is negligible.

Ordinarily wdth time the- mercury surface in the

cistern, and the cistern walls, foul up so that the

meniscus height changes. In fixed cistern barometers or manometers where the scale zero is fixed,

there are two effects acting to give rise to errors

in measuring the pressure. First, the actual height

of the mercmy column falls hy the amount of the

capdlary depression. Second, a readjustment of

the volumes of mercmy in the cistern and tube

takes place which affects the relation between the

zero of the scale and the cistern mercury surface.

Due to the elimination of capillary depression,

when the meniscus flattens, a slight rise takes

place in the mercury level in the cistern; also as the meniscus flattens, the volume of the meniscus

decreases, which decrease must result in the lowering of the level of the mercury in both the cistern

and the tube. The latter, the volume effect, is predominant so that at constant pressure the

barometer reading on the fixed scale falls as the

meniscus flattens. The combination of these ef- fects can be reduced som^^ewhat by using cisterns

of large diameter. The error occurs at any pressure, and may vary \vith time, pressure and the manner in which the pressme is changed.

The capillary effects just described also occur

in the cistern of Fortin barometers. Since the

mercury level in the cistern is adjusted in height

to a fixed index, the residual error is only that due

to the change in the capiUary depresssion. Change

in the volume of the meniscus does not affect the

reading. In an extreme case of mercury foulmg

35
in the cistern of a Fortin barometer, with a ji in. bore tube, the change in reading of a good meniscus to no meniscus, was 0.02 in. (0.5 mm) of

mercury.

It is thus necessary to caHbrate botli Fortin

barometers and fixed cistern barometers and manometers more or less frequently.

11.3. Correction Table

The correction table for the capillary depression

in table 10 is given by Gould and Vickers [521];

it was computed from a mathematical development described in ref. [401]. It is seen that knowledge of the surface tension of mercury is needed,

as well as the meniscus height and bore of the

tube, in order to enter the table. Since it is not

practical to measure the surface tension of the

mercury in the barometer, some value must be

assumed.

Kistemaker [452] has computed a table of values

for the capillary depression based upon observations made on the depression of the mercury in

tubes of various bores and partly on the theory

given in ref. [401]. The menisci were in contact

with atmospheric air at 75 ±5 percent relative

humidity for 24 lir before the tests and the temperature was 19 ±1° C during the tests. These

data are compatible with a surface tension of 430

dynes/cm for mercury. On this basis the values

of the capillar}^ depression should be about 5 per- cent less than those given in table 10 for a surface

tension of 450 dynes. Actually for a 12 mm tube

the values in table 10 are higher, rismg from 10

to 20 percent for meniscus heights from 0.2 to 1.8 mm. Again, for a 19 mm tube, the values in the

capillary depression are practically identical up to a meniscus height of 1.0 mm; those in table 10

rise to 10 percent higher for meniscus heights from

1.2 to 1.8 mm. In general, the capUlary depressions given by Kistemaker are intermediate to

those for surface tensions of 400 and 500 dynes/cm

given in table 10; however, at high meniscus

heights and small bore tubes (10 mm and below),

Kistemaker's values are lower than those for 400

dynes/cm.

The capUlary depression given in table 10 for a

surface tension of 450 dynes/cm are from 5 to 10

percent lower than those of a much used correction

table [231], a discrepancy m^de greater by the

fact that the latter table was computed for a sur- face tension of 432 dynes/cm. Both tables were

prepared in the National Physical Laborator}'^ of

Great Britian.

Since there is no practical way to know the

applicable value of surface tension of the mercury

under the various conditions of use, in contact

with air or vacuum, and degree of surface cleanliness of the mercury, there is little to gain in choosing one set of tables over another. For the

moment, Gould's table (table 10), for 450 djmes/cm

seems as applicable as any.

For one important purpose any table is adequate, that is for the selection of a bore of tube

sufficiently large so that the variations in the

capillary depression will have negligible effect on

the required overall accuracy. In this connection

note that the percentage variation in the capillary

depression with surface tension at all meniscus

heights presented in table 10 is greater the larger

the bore of the tube. Thus for a change in sur- face tension from 400 to 500 dynes/cm the capillary depression varies as much as 100 percent.

Note that for Fortin and. fixed cistern barome-'

ters, the capillary depression givjen in the table

is added to the reading of the mercury barometer.

t

For U-tube barometers and manometers the capillary depression at the upper mercury surface is added to, and at the lower mercury surface subtracted from, the indicated height of the mercury

column.

12. Return Head and Elevation Corrections

Usually a differential pressure is measured

simply by the height of the mercury column.

Actually the differential pressure, measured at the

level of the mercury surface on the high pressure

side of a mercury manometer, is the difference of

the specific weight of the mercury column and of

the column of equal height of the gas or liquid on

the high pressure side. The specific weight of the

latter column is defined as the head correction.

Both differential pressure and absolute pressure

measured with any manometer or barometer,

liquid or mechanical, applies only to the elevation

at which made. In the case of mercury manometers this level is that of the mercury surface of the

high pressure side of the barometer. If pressures

are desired at any other level above or below, the

decrease or increase in absolute pressure with

elevation due to the intervening head of gas or

liquid in both legs of a manometer must be considered. The elevation correction is defined as the correction which needs to be applied to trans- i fer the pressure measured at an elevation to j another elevation.

Elevation corrections discussed in this section are mainly restricted to elevation differences of several hundred feet and pressures of several

atmospheres. These are conditions commonly

met with in laboratories and industry. Detei'-

mination of sea level pressure from readings of a barometer installed at elevations well above sea

level are outside the scope of this paper ; this computation is discussed in the publications of the | U.S. Weather Bureau.

36
12.1. Definition of Symbols

e=base of natiu'al logarithms=5

2.71828

^= acceleration of gravity. In this

section assumed to be the standard reference value, 980.665 cm/

sec^

/t =vertical height of the gas column

(see fig. 4)

Ao=the elevation with reference to the

level at zero differential pressure

of a barometer or a manometer

(see fig. 4)

hi =the height above or below a mercury

surface of a liquid used to trans- mit the pressure

H=scale height— RT/g

P=absolute pressure

Po= absolute pressure in a gas column

at elevation Aq (see fig. 4) Poo =absolute reference pressure, measured at some level other than ho Pi ,^2= absolute pressures at various levels on the low pressure side of the

system (see fig. 4)

Pio,Pii,Pi2 =absolute pressures at various levels on the high pressure side' (sfee fig. .4) ^ =differential pressure measured by

the mercury column (see fig. 4)

P=a constant for a gas

7"= absolute temperature of the gas at any level ; assumed to be constant

- at all levels of the gas colmnn

P=density of the gas at temperature T

and pressure P

P; =density of the liciuid which is used

to transmit pressure

12.2. Change in Gas Pressure with Elevation

The return head correction or the elevation

correction involves the computation of the change

in gas pressure in going from one level to another.

Since a gas compresses imder its own weight, its' density at a higher elevation is less than at a lower

elevation; this necessitates an integration.

The basic relation is

(51)

dP

dh~'^-

Substituting for p in eq (48) its value

there is obtained

dPP^

Pgdh

RT

(48)

(49)

(50)

Approximatel};-, with an accuracy within 0.1 mm

of mercury for h equal to several hundred feet and

Po equal to several atmospheres:

(52)

Here T is the temperature of the gas at pressure

P; and'Po and P are the absolute pressures of the

gas at the reference level A=0 and level h, respectively. If the level of P is above the level of Po, h

is plus; if below, h has a minus sign. See section

12.1 for other definitions.

The temperature of the gas column ordinarily can be assumed to be constant. If the gas temperature varies in the gas column an arithmetic

average of the temperature based on equal increments of log J) or here with sufficient accuracy, of equal increments of elevation, will give the temperature T to use in computing H. The factor H

is called "scale height" because it has the dimensions of a length.

Equations (51) or (52) are primary for computing the dift'erence in pressure at two elevations due

to a head of gas. In its derivation it has been as- sumed that the gas law given in eq (49) holds, and

of course that the gas does not condense anywhere

in the system.

For each gas a table of values of H against temperature will be useful. In computing H the gas

constant R, varies with the gas. It equals the universal gas constant, 8.31439X10'' erg/mole deg,

divided by the molecular weight of the gas. Values

of R for a few gases are given below [531]. Using

these values of R, g in cm/sec^ and T in degrees

Kelvin, gives ii/ in centimeters which can readily be

converted to be in the same unit as the elevation h.

Constant R Molecular

Gas cm2/sec2 °K weight

Air, dry 2. 8704X10" 28. 996 Carbon dioxide _ 2. 0800 XIO'-' 44. 01 Hydrogen _ _ 41. 242X106 2. 016

Helium 38. 910X106 4. 003

Nitrogen 2. 9673X10" 28. 02 Oxygen 2. 5982X10" 32. 00

Integrating eq (50)

From some points of view the method of computation to be presented is preferable, although it is an

approximation with about the same accuracy as eq

(52). In the absence of a mechanical computer it is definitely less laborious. This method will be

used in all of the examples given below ; if the use

of eq (51) or (52) is preferred, the substitutions to be made are straightforward.

In eq (48), dP/dh is the rate of change of pressure

per unit change in elevation. This rate varies

directly as the product of the gas density, inde37
pendent of its composition, and the acceleration of

gravity. The latter varies less than 0.3 percent over the surface of the earth, and, as will develop,

introduces an error of this amount in a small cor- rection term and therefoi'e can be assiuned to be a

constant. Thus, if precomputed values of dP/dh are available, changes in pressure with elevation can be

computed by the relation

rJP P=Po~AP=Po-^ h- (53)

In order to facilitate computation usmg eq (53),

tables 11 and 12 have been prepared. The value

of dP/dh, the rate of change of pressure per unit

change in height of the gas column, is presented in table 1 1 for selected values of the gas density and

for five different convenient units of measurement.

For convenience the absolute pressure for air only

is given for three air temperatures. Three as- sumptions underly table 11: (a) The value of

gravity is 980.665 cm/sec^; (b) the gas is dry and

does not condense in the system; and (c) tlae air temperature of the gas column is constant, usually

the case to a sufficient degree in laboratories. It should be noted that the gas density and the corre- sponding rates of change of absolute pressure given

in table 11 are independent of the composition of

the gas, pure or mixtures.

Table 12 is presented as an aid in determining

the density of dry air when the air pressure and

temperature are known. Air is assumed to have

an air density of 0.001293 g/cm^ at 0° C and a

pressure of 760 mm of mercury. The coefficient

of expansion of air is assumed to be 1/273; the

slight error thus introduced is inconsequential in the practical use of the table. An example will illustrate the utUity of the

tables in computing the pressure difference caused

by a head of gas. Assume the pressure of air to be 810 mm of mercury and the temperature 21° C,

to determine the pressure at a point 11 ft higher

in elevation. From table 12, the air density

corresponding to 810 mm of mercury and 21° C is, by interpolation, 0.001280 g/cm^. Entering table

11 with this value, it is found that dPldh=

0.02861 mm of mercury per foot. The difference

in pressure at the two levels is

dP Ap^—— A=-0.0286X11 = -0.31 mm Hg

and

P=810-0.31 =809.69 mm Hg.

It is seen that variations in gravity up to 0.3 percent affect the pressure decrease of 0.31 in. of mercury to an insignificant degree. Two sources

of error should be considered. First the density

itself and therefore dP/'dh, may be in error. An

error in temperature measurement of 1° C,

unlikely in practice, introduces roughly an error

of 0.3 percent in gas density or in dP/dh. This

error is usually insignificant. Second, the value

of dP/dh varies with gas density, so that its value

is not precisely the same at 810 and 809.69 mm of

mercury. The difference here is less than 0.04

percent, obviously insignificant. In this example

the method is accurate to at least 0.01 mm of

mercury.

In the second case the accuracy is about the same as the ratio of the pressure difference to the

reference pressure. If excessive, the error may be I reduced approximately one-half by two computations, first determining an approximate pressure

difference as outlined above, and finally, determining the pressure by using a value of dP/dh given

by the average of two values of dP/dh, one for the

j density at the measured pressure at h=0 and the

other for the density determined by the approximate pressure computed for level h.

12.3. Return Head Correction

I; In many cases the differential pressure at the

level of the lowest mercury surface is desired.

In figures 4 and 5 this differential pressure is 1'

Figure 4. Diagram illustrating coynputatiori of gas pressure

at two levels from differential pressure measured with Utube manometer.

H, system with unknown pressure at high level; L, system with unknown

level at lower level. A, tube connected to system the pressure of which is to be measured; B, manometer tube open to the atmosphere or connected to pressure reference; C, level at which pressure is desired; Pio, Pit, Pn, absolute [ pressure in system at various levels; Po, Pi, P2, absolute atmospheric or \ reference pressure at various levels, p, the measured differential pressures I

ft, Ao, differences in elevation.

38
Figure 5. Diagram illustrating computation of gas pressure

at two levels from gage pressure measured with cistern manometer.

See figure 4 for meaning of symbols.

P1Z—P3. The gas pressure impressed upon the

mercury surface at the upper level is Pi, figures

4 and 5, and must be knowTi or obtainable. The

problem reduces to the computation of P3 in terms

of Pi. The significant elevation here is h which

is also the height of the mercury column.

From eq (53)

P3=Pi+'^^ h- (54)

The absolute pressure P3 is greater than Pi,

therefore the correction is adchtive.

Pn^Pi+P . (55)

and

Pn-Pz=p-^-^ h- (56)

Alternatively, based upon eq (51) and (52)

or Piz~Ps=p+Piil-e''n (57)

=P-^P^ (58)

The terms- idP,/dh)h, P,(l-e''/«) and -h/HPi

are nearly equivalent various forms of the return head correction; only the term in eq (57) is strictly rigorous, but the accuracy of the others

is usually quite adequate.

For all practical purposes, in eq (56)

dPo^dPi

dh dh

a fact which often simplified computations.

Equations (56), (57), and (58) give the return

head correction for all forms of U-tube manometers

and for cistern manometers, wdth a change in

notation as indicated in figure 5. For mercury barometers of all forms, the return

head correction is zero. AU of the above discussion is for the case when

the low pressm-e side of manometer has a gas

above the mercmy sm'face. In some applications

this space is filled with a liquid, that is for example

the line from Pi to P2 in figure 4Z may be filled with a liquid of density pi. It is unlikely that

the differential pressure P13—P3 is of any interest,

but if so, it is Pri-Pz=V~Pigh (59)

where pigh is the return head correction. Here pi

is the density of the liquid at the pressm'e Pi and

at its temperatm'e. Compression effects can

ordinarily be neglected.

If pi is in grams per cubic centimeter, g in

centimeters per second squared in A in centimeters,

the head coiTection is in dynes per square centimeter, which can be converted to the units of p

with the aid of table 1.

12.4. Elevation Correction, Gas Head

The basic relations for pressm-e change with

elevation enable computation to be made of the

absolute pressure at the significant levels in any

pressure system. The difference in the absolute

pressm'es at a given level in the two legs of a manometer gives the requhed gage or dift'erential pressure. For barometers one of the absolute

pressures is essentially zero. The computations

will be made based only upon eq (53).

Generally, measurements of p, ho, and h as indicated in figiu-es 4 and 5 need to be available.

To compute dP/dh using table 11, it is necessary

to enter table 11 with the density of the gases

involved. This, most simply requires that measurements be made of the gas temperatm'e and the

absolute pressm-e of the two gas columns at the

zero reference level; absolute pressm'es at other

39
levels can be substituted without significant error

if these levels are within the height of the liquid

column.

In making computations a choice must be

made of the reference level from which elevations are measiu"ed. This zero elevation can be one of

the mercury surfaces but this choice has the

disadvantage that the zero reference level then

varies with pressm-e. Computations are often more conveniently made if the zero elevation of the gas column is chosen to be the level at which

the differential pressiu-e indicated by the barometer or manometer is zero. The height of the gas

column is then, as indicated in figure 4, ho±.h/2 for

U-tube instruments, or hozth for cistern instruments.

12.4.1 U-tube Manometers

Consider the pressure system figiu-e 411, where

one leg of the manometer is open to the atmosphere

and the other leg connected to a chamber at a

level above the manometer. It is required to determine the gage pressure P12—

In leg B of the manometer the absolute gas

pressures are:

(60)

(61)

If the atmospheric pressure is measured at some other elevation hoo than at the zero elevation

level,

dP

(62)

If the level of Pq is below that of Pqo, the minus

sign in eq (62) changes to plus.

In leg A of manometer H, the significant gas

pressures are, based upon eq (53) and (61).

(63)

Pl2=Pl3- ' dh (*•+!)

^1 p dP^h dPio

(64)

12.4.2. Cistern Manometers

For cistern manometers, figirre 5, the zero refer- ence level is at the mercury surface in the cistern,

which ordinarily can be assumed not to vary

significantly with pressure. Then for reference

absolute pressures in leg B,

p _p _(fPn 7 dh

^

dh ^°

and for absolute pressures in leg A,

jp

P,o=P+Pi=^P+Po-^ h

P12 —Pio' ho=p+Po — h —fio dh " ^ ' " dh dh

The differential pressure at level P12 is:

dPr,

dh

he,

(66)

(67)

(68)

(69)

(70)

Again, if the level of P2 is below the level of Pq,

eq (70) applies if the sign of ho is changed, as indicated in eq (65a) and (65b).

12.4.3. Barometers

In all cases tlie pressures Po=Pi =P2 =P3 = 0, since the space above the mercury column is evacuated.

In U-tube barometers the absolute pressure at an elevation dift'ering from tliat of Pio is simply,

using the notation in figure 4,

P,2=P:o±^/^o=Pi3-^(^±/.o)- (71)

In cistern barometers the absolute pressm-e at an elevation above or below the level of the mercury surface in the cistern, where the pressure

is Pio, is

Pi2 —Pioi

dP,n

dh

ho (72)

The gage pressure at level Aq is (eq 61 and 64)

^"-^-^+t(^'-|)-1^"(*«+l>

For cases, such as illustrated in figm-e 4i, where

the level at which the differential pressure is below

the level of Pq, it is only necessary to change the

sign of h'o. Equation (65a) becomes

12.5. Elevation Correction, Liquid Head

To consider this case, assume m figure 4P that

the tubing from both mercury surfaces to chamber

C are filled with the same pressure transmitting

liquid of density p. Assume that the pressures are low so that compression of the transmitting liquid

and of mercury can be neglected. It is then seen

in figure 4i that

40
P,,-P,=P,,-P,^P,,-P,=p-p,gh. (73)

Thus, the differential pressui'e at any level requires only a correction for the return head, as discussed in connection with eq (59).

To take care of compression of the transmitting

liquid it is only necessary to modify the value of the density pi in eq (73). It is unusual for the transmitting liquids to

to differ in the two legs of the manometer, so that

this case is not considered here.

13. Vacuum Error of Barometers

The vacuum above the mercmy colimm of barometers is never perfect; mercmy vapor and some air, and perhaps other gases are always

present. The pressm-e of the gases in the vacuimi

space results m an error in the measured pressure, and when known either by computation or meas- urement must be added to the measiu-ed pressme

to secure the pressure. In precise measiuements the vacuum is maintainecl below a value set by the desired precision

of measm'ement by means of a diffusion pump.

The vacumn can be checked "with a ]McLeod gage

to an acciiracy of the order of ±10 percent. In

this procedure however the eft'ect of the mercmy

vapor is neither eliminated nor measui'ed. If the

precision desired warrants, a correction must also

be apphed for the pressure of the mercmy vapor,

obtained from tables of observed values, as table 3. The operation schedule of the diffusion pump and

temperatme conditions must be such that equilibrium values of the mercmy vapor pressm^e exist at the time readings are made.

The precision in measm'ement desired may be

such that a less elaborate procedure than that just

described can be followed. The correction to be

applied is the sum of the mercmy vapor pressm'e at the barometer temperatme and of the pressm'e

measm-ed by the McLeod gage. The diffusion

pump is only operated when the vacuum has

deteriorated to a value where the uncertainty of the ^IcLeod gage measmement is of the same

order as the desu-ed precision in the measmed

pressure. It shoiJd be noted the vacuum cor- rection varies with the height of the mercmy

column, since the volume of the vacuum space

varies and the mass of the gas, except the mercury

vapor, is approximateh' constant. In portable barometers no correction is ordinarily made, or justified, for the back pressme in the vacumn space above the mercury column. If the barometer tube is equipped -svith a mercury

seal valve, the vacuum can be kept withm reqmi'ements for precision in pressm'e measm'ement by

periodic evacuation of the tube thi'ough the valve.

The frequency of evacuation needed can be determined only by experience; in general evacuation

is needed after subjecting the barometer to some

definite number of pressm'e cycles.

If the portable barometer is not eqmpped with

a valve in the top of the tube, a poor vacuum may

be detected by tipping the tube with suitable pre- cautions to avoid damage or uncovering the

bottom of the tube, so that the gas is subjected to about one-fom'th of an atmosphere. If the apparent size of the bubble is gi'eater than about two

or tlu'ee millimeters the vacuum needs improvement. In general barometers m the best of condition will have a bubble upon tipping, of the order

of about one miUimeter in size. Barometers

subjected only to ambient atmospheric pressm'e

have been known to maintain a satisfactory vacuum for years; on the other hand, altitude

barometers ia frequent use over a large pressm'e

range may maintaui a satisfactory vacuum only

for periods as short as a month. The vacuum is reestablished either b}' a complete overhaul job on the barometer, or ff the design permits, by

removing the gas withia satisfactory limits by the

procedme described in sec. 6.4.

14. Compression of Mercury

The compression of mercm-y with pressme

affects its density as discussed ia sec. 4.4. The

standard values of the density of mercury are generally for mercmy subjected to 1 atm of pres- sme. The compression of mercmy must be considered particularly in high pressm'e manometers

f sec. 5.6) and only in very precise measmements

at relatively low pressmes. In barometry and

for all portable barometers and manometers the

accmacy usually obtainable makes application of any correction for mercury compression insignifi- cant. Consider a manometer in which mercm'y sm'face

in the two legs are subjected to pressmes P and Pi.

Then

P-Pr=pgfr. (48)

The mercm'y at the lower mercm'y level is compressed by pressme P or Pi +pgh. Assuming that

the compression of mercmv is given bv p=po

(1 ±aP), eq (11), sec. 4.4

p=P,[l+a.{P^ +pgh)]. (74)

In a more acem'ate derivation for the compression effect due to a cokmm of mercury the relation

is 41
P = Po[l+ a (Pi + pQgh)]. (75) this case, eq (78) can be m-itten, since Pi =0.

Here p and po are respectively the densities of

mercury at pressm'e Pi-\-pgh and at zero pressure;

h is the height of the mercurj?' column; and a is the volume coefficient of compression per unit

pressure. The standard density Ps applies to mercury

under a pressure of one atmosphere. Therefore,

if as is the compression coefficient per atmosphere,

p,=Po(l +a,). (76)

Without significant error eq (75) now becomes

p = pJl-a, +a,(Pi +f)]. (77)

and eq (48) where in atmospheres P—Pi= ph/pshs

P-P, =^{l-a, +a, (Pi +

l)].

(78)

All of the quantities in the right hand side of

the equation are either constants or measured.

The pressure P—Pi is in atmospheres and hs is the height of the mercury column at 1 atm of

absolute pressure. Consider the case of the barometer where 1 atm

of pressure is defined as a mercury column 760

mm in height subjected to standard gravity with

the density of mercury equal to 13.5951 g/cm.^

This densit}^ is the commonly accepted value at 0° C and under a pressure of 1 atm. To consider

P=^[l-a,+a,h (79)

P At the bottom of the mercury column where the

mercury is subjected to 1 atm of pressure, eq (79)

gives P=unity. At the top of the column the

term ash/hs is practically zero and P=h(l~as)/hs.

Two conclusions can be derived. First, an interval of 1 mm will represent a higher pressure at the i bottom than at the top of the column, specifically I for 1 atm difference in compressing pressure, about

4 parts per million. Second, a pi'essure of 1 atm

is defined as 1,013.250 dynes/cm^, which when

converted to a mercury column of 760 mm implies

a mean density of mercury of 13.5951 g/cm^ at ' 0° C. Thus in a mercury column of 760 mm

representing 1 atm of absolute pressure, the density of mercury assumed is 2 parts per million

greater than 13.5951 g/cm^ at the bottom of the

column and the same amount less at the top of the

column. Thus the assumed density at 0° C and 3 at 1 atm differs from the presently accepted value

by about 2 parts per million. For most purposes , the point is academic.

In manometers measuring gage pressure (differential pressure with reference to atmospheric

pressure) the situation is the reverse of that for

barometers, since the mercury is generally subj ected

to pressures above atmospheric. A millimeter of

column height is equivalent to a pressure greater

than 1 mm of mercury under standard conditions,

roughly amounting to 4 parts per million per

atmosphere of applied pressure.

15. Computation of Corrections

Representative examples of the computation of

corrections as outlined in the previous sections

may be useful. For many types of portable barometers and manometers the only corrections ordinarily applied are for scale, temperature and

gravity errors. Two examples of such cases will be given.

One additional example will be presented where

higher accuracy is desired and corrections for the more significant errors will be applied. Some

errors will remain uncorrected, such as for the

compressibility of mercury, since the accuracy

attainable normally makes them insignificant.

The application of the corrections is based upon:

(a) adequate primary data; and (b) upon the use

of tables such as presented in this paper. It must

be emphasized that valid alternative methods of

computing the corrections exist and that the

methods here used are justified only by their

convenience.

15.1. Fortin Barometer

The following readings are taken:

Reading: 1021.15 mb

Barometer temperature: 23.2° C.

Other needed data or information are: Acceleration of gravity: 979.640 cm/sec^

Scale correction (includes correction for zero, capillary and vacuum errors) +0.35 mb

Brass scale calibrated to be accurate at 0° C.

(a) Scale Correction

Reading =1021.15

Scale correction = +0. 35

Rs =1021. 50 mb

(b) Temperature Correction.

Table 6 is entered with 1021.50 and 23.2° C to obtain by interpolation —3.86 mb for the temperature error C«. P,= 1021.50

Ct= -3.86 f

•

—• ) 1017.64 mb

Rt is the reading corrected for temperature error. I (c) Gravity Correction. I Table 8 is entered with 1017.64 mb and 979.640 { cm/sec^ to obtain by interpolation —1.06 mb for [ the gravity correction Cg. i 42
i?^=1017.64

C,= -1.06

P=1016.58mb

The pressure P is then 1016.58 mb at the level of

the mercury surface in the cistern.

15.2. Altitude Barometer, Fixed Cistern

This example is included as an illustration of the

application of the temperature correction. The

following readings are taken:

Reading: 352.7 mm of mercury

Barometer temperature: 23.6° C.

Other needed data or information are: Acceleration of gravity =979.640 cm/sec^

Constant K to be added to reading to obtain

the temperature correction: 65 mm

Scale correction (includes correction for zero, capiUary and vacuum errors): —0.5 mm of mercury at the reading.

Brass scale calibrated to be correct at 0° C or if not, error is absorbed in the scale correction,

(a) Scale correction

Reading i?=352.7

Scale correction (7s=— 0.5

Corrected reading i?s=352.2 mm of mercury

(b) Temperature correction

R, =352.2

Constant ^L= 65.0 (see eq (36) sec-. 9.3.1.)

Rg+K =417.2 mm of mercury.

Temperature correction table 6 is entered with

Rs+K and 23.6° C to obtain —1.6 mm as the

temperature correction Ct i?,=352.2

C,= -1.6

ii,=350.6 mm of mercury =reading corrected

for scale and temperature errors,

(c) Gravity correction

Gravity correction table 8 is entered with the

acceleration of gravity 979.640 cm/sec^ and Rt, to obtain —0.37 mm as the correction.

i?,=350.6

(7„=-0.4

P=350.2 mm of mercury.

Thus, the pressure at the level of the mercury

surface in the cistern is 350.2 mm of mercury.

15.3. Manometer, U-tube

In this example all corrections normally applied

will be made based upon an accuracy of 0.01 mm

of mercury in a pressure by a U-tube manometer.

The procedure is essentially the same for a Utube barometer, except for differences, easy to

I handle, due to the fact that the pressure above

1 one mercury surface is nominally zero in the

j barometer; this fact may however make a vacuum

correction necessary.

The following readings are taken on a manometer illustrated in figure 4L.

Reading on scale: upper mercury surface 1150.92 mm

lower mercury surface 130.27 mm

Manometer temperature: 23.21° C

Meniscus heights: upper 1.0 mm; lower 1.3 mm

Other needed data or information are: Bore of tube: 20 mm

Acceleration of gravity: 979.640 cm/sec^

Absolute pressure Pq, figure 4L: 380.22 mm of mercury

Elevation at which differential pressure is desired: 20 ft below the mercury surface at which the

differential pressure is zero (Aq in fig. 4L).

Zero correction: the reading at zero differential

pressure averages 0.02 mm higher in tube A, figure

4L (high-pressure side), after applying the capillary correction. While it is questionable if this correction is a constant independent of differential pressure, it will be applied.

Scales and vernier will be assumed to measm'e

colmun heights accm-ately at 0° C. Thermal coefficient of expansion of scale: 17.2X10-« per ° C

Alinenient errors are assumed to be zero.

(a) Nominal height of mercury colmnn

Pi= 1150.92

i?,= -130.27

Nominal height= 1020.65

(b) Zero correction

Since the reading tube A reads higher at zero

differential pressm-e, the nominal reading should

be increased 0.02 nma and becomes 1020.67 mm.

(c) Capillary correction

From table 10 the correction for a meniscus

height of 1.0 mm, tube bore, 20 mm= -|- 0.024 mm;

for a meniscus height of 1.3 mm= +0.030 mm.

The nominal reading, coiTected for capillarity is 1020.67 —0.030 +0.024 = 1020.66 mm, which is hi, the corrected scale reading at 23.21° C.

(d) Actual height of mercury colmnn at 23.21° C

To reduce the nominal height ht to the actual

height h at 23.21° C, a correction must be made

for the thermal expansion of the scale. In the

absence of tables.

1020.66

l+st 1 + 17.2X23.21X10"

: 1020.25 mm.

(e) Temperature and gravity correction

These corrections can be made in one of two

ways, both of which wUl be presented. In the first procedure a correction to be applied to h wiU be

computed. The sum of the temperature correction Ct and the gravity correction Cg is

The term mt/{l-\-'mt) is obtained from table 7, 43
the column headed invar, smce here the thermal

expansion of the scale is zero. For 23.21° C,

^=—0.0042018.

The term {g—gs)gs is obtained from table 8 from

the column headed "Correction factor". For

979.640 cm/sec- it equals —0.0010452.

Their sum gives

Ct+ -0.0052470(1020.25) = -5.35 mm.

The reading corrected for temperatiu'e and

gravity errors, the differential pressure p in figui'e

4L is then

p = 1020.25 —5.35 = 1014.90 mm of mercurj^

Alternatively, the differential pressui'e P can be

computed directly from

pgh

Psgs

(45)

Here Ps, and p are the density of mercur}' respectively at 0° C and 23.21° C, 13.5951 and 13.5380

(from table 3) gs/cm^; and f/^ and g are the standard

and ambient accelerations of gravity, 980.665 and

979.640 cm/sec^, respectively.

Inserting these values, and the value for h in (d)

above, m eq (45)

25= 13.5380X979.640X1020.25

13.5951X980.665= 1014.90 mm of mercm^.

A slight difference of the order of a few microns

(0.001 mm) in the values of p by the two methods

of computation can be expected from the fact that

m, the volume coefficient of thermal expansion of mercury is an average value. The latter value of p is the more accurate.

(f) Return head correction

If the differential pressure (fig. 4L)

P1Z—P3 is deshed:

(57)

Here ^ = 1014.90 mm of mercury and ^=1020.25

mm (3.347 ft). For an air pressui'e Po=380.22 mm of mercury

and temperature of 23.21° C, the air density is obtained by interpolation from table 12 to be

595.7 XlO-^'g/cy. From table 11, dPo/dh corre- sponding to this densitv is found to be 0.0133 mm

Hg/ft. Then

Pi3-P3= 1014.25-0.0133X3.347 = 1014.21 mm of mercur5^

The return head correction is 0.04 mm of mercui'y.

(g) Differential pressure at level 20 ft below

Po level In this case, referring to figure 4L:

f.-P.=l'-f(A.+|)+ff (*.-!) (65b)

Here p = 1014.25 mm of mercury; cJPo/c^^=0.0133

mm of mercury / ft;

Ao+^=20+ 1.673 ft.; and /i,o-^=18.327 ft.

To compute dPio/dh, Pio to sufficient accuracy =

2)-|-Po=1014.25-K380.2 = 1394.4 mm of mercury.

Following the procedui'e outlined above under (f) using tables 11 and 12, dPio/dh=0.04:89 mm of mercury / ft for p+Po and 23.21° C, therefore

Pj,-P2 = i014.25-0.0133X21. 7 + 0. 0489X18.3 = 1013.64 mm of mercur}".

The elevation correction is +0.61 mm of mercury

(P12-P2-P13+P3).

16. Testing at the National Bureau of Standards

For testing mercury barometers, the National

Bureau of Standards has a standard barometer

and barostat installed in a subbasement room the

temperature of which is maintained closely at 25° C. See sees. 5.4, 6.1.3, 6.2.2, and 8.2 for

details. The accuracy, now 0.02 to 0.03 mm of mercury, is not considered entirely adequate for testing portable barometers with accuracies approaching 0.05 mm of mercury. Continuing effort

is made to improve the accuracy.

For testing manometers the Bureau has a mercury manometer with a range of 50 psi (100 in. of mercury). Piston gages of the air type are under development for use as standards in order

to improve the accuracy and convenience of

operations.

The National Bureau of Standards accepts for

test mercury barometers and manometers which

are: (a) the reference standard or one working

standard of an organization or laboratory; and

(b) reference tests when the measurement of

pressure is in dispute. The accm-acy of the

instruments submitted must be at least ±0.1 mm

of mercury. See ref. [582] for details regarding

the acceptance of instruments for test. Listruments submitted for test should be sent to "National Bureau of Standards, Attn: Mechanical Instruments Section, Washington 25, D.C."

44
A piirchase order issued to the National Bureau

of Standards authorizing the test must be supplied. It is advisable to arrange for the test by

correspondence or telephone previous to shipping

the instrument. Tests fees are listed in the current NBS Test Fee Schedules which are based on cost. The experience of the Bureau is available to laboratories and manufacturers on the various

problems associated with the precise measurement

of pressure. Visits of technical personnel to discuss problems should be arranged in advance.

The authors are grateful to Dr. H. F. Stimson

and to L. F. Harrison, of the Weather Bureau for

many suggestions and correction.

17. References

The first two digits in each number are the j-ear of publication of the reference.

[Oil] Comptes rendus des seances de la troisieme confe- rence generale des poids et mesures, reunie a Paris en 1901. Travaux et memoires de Bureau Inter- national des Poids et Mesures.

[121] P. W. Bridgman, Mercury, liquid and solid under

pressure, Proc. Am. Acad. Arts Sci. 47, 347 (1912).

[141] M. H. Stillman, Note on the setting of a mercury

surface to a required height, BS Sci. Pap. 10, 371

(1914) S214.

[191] P. W. Bridgman, The measurement of high hydrostatic pressures; a secondary mercury resistance gauge, Proc. Am. Acad. Arts. Sci. 44, 221 (1919).

[231] F. A. Gould, Barometers and manometers, Diet. AppHed Physics 3, 140 (Macmillan & Co. London,

1923).

[271] F. G. Keyes and J. Dewey, An experimental study

of the piston pressure gage to 500 atmospheres,

J. Opt. Soc. Am. 14, 491 (1927).

[291] K. C. D. Hickman, The mercury meniscus, J. Opt.

Soc. and Rey. Sci. Instr. 19, 190 (1929).

[301] U.S. Weather Bureau, Barometers and the measure- ment of atmospheric pressure. Circular F, Instru- ment Diyision, reprinted (1930).

[311] C. H. Meyers and R. S. Jessup, A multiple manometer and piston gauges for precision measure-

; ments, BS J. Research 6, 1061 (1931) RP324.

' [321] A. Michels, The calibration of a pressure balance in absolute units, Proc. Krinkl. Akad. Wetenschap.,

Amsterdam 35, 994 (1932).

[331] F. E. Fowle, Smithsonian physical tables, 8th rev.

ed., (Smithsonian Inst., 1933).

[332] F. A. Gould and J. C. Evans, A new form of barostat, J. Sci. Instr. 10, 215 (1933).

[333] J. E. Sears and J. S. Clark, New standard barometer,

Proc. Roy. Soc. (A)139, 130 (1933).

[341] I. B. Smith and F. G. Keyes, Steam research. III A. Compressibility of liquid mercury from 30° to 300° C, Proc. Am. Acad. Arts Sci. 69, 313 (1934).

, [351] C. Moon, A precision cathetometer, J. Research

I NBS 14, 363 (1935) RP774.

I [361] E. Schmidt, Measurement of small pressure differ- ences at high pressure, VDI 80, 635 (1936). (In German)

.

[371] J. R. Roebuck and W. Cram, A multiple column

mercury manometer for pressures to 200 atmospheres. Rev. Sci. Instr. 8, 215 (1937).

[391] J. Reilly and W. N. Rae, Physico-chemical methods,

1, (D. Van Nostrand Co., N.Y., 1939).

[401] B. E. BlaisdeU, The physical properties of fluid interfaces of large radius of curvature. II. Numerical tables for capillary depressions and meniscus volumes, in moderately large tubes, J. Math,

and Phys. 19, 217 (1940).

[411] J. A. Beattie, B. E. Blaisdell, and J. Kaye, An

experimental study of the absolute temperature

scale. IX. The determination of the capillary

depression and meniscus volume of mercury in a manometer, Proc. Am. Acad. Arts Sci. 74, 389

(1941).

i [412] J. A. Beattie, D. D. Jacobus, J. M. Gaines, Jr.,

I M. Benedict, and B. E. Blaisdell, An experimental

study of the absolute temperature scale. VI. The

gas thermometer assembly and the experimental

method, Proc. Am. Acad. Arts Sci. 74, 327 (1941).

[413] J. A. Beattie, B. E. Blaisdell, J. Kaye, H. T. Gerry,

and C. A. Johnson, An experimental study of the

absolute temperature scale. VIII. The thermal

expansion and compressibility of vitreous silica and the thermal dilation of mercury, Proc. Am.

Acad. Arts Sci. 74, 370 (1941).

[414] G. W. C. Kaye, and T. H. Laby, Physical and chemical constants (Longman, Green & Co., 1941).

[421] E. Wickers, Pure mercury, Chem. Eng. News 20, nil (1942).

[451] J. Kistemaker, On the volume of mercury meniscus

and the surface tension of mercury and deduced

from them, Physica 11, 270 (1945).

[452] J. Kistemaker, The capillary depression of mercury

and high precision manometry, Physica 11, 277

(1945).

[453] D. J. LeRoy, An automatic differential manometer,

Ind. Eng. Chem. Anal. Ed. 17, 652 (1945).

[454] H. F. Stimson, The measurement of some thermal

properties of water, J. Wash. Acad. Sci. 35, 201

(1945).

[461] C. Kemball, On the surface tension of mercury,

Trans. Faraday Soc. 42, 526 (1946).

[471] D. R. Stull, Vapor pressure of pure substances, Ind. Eng. Chem. 39, 517 (1947). (References and data on vapor pressure of mercury.)

[481] D. P. Johnson, Calibration of altimeters under pres- sure conditions simulating dives and climbs,

NACA Tech. No. 1562, (1948).

[482] W. G. Bromacher and H. E. Ferguson, Manometer

tables, Inst. Soc. Am. RP2.1, 32 pp. (1948).

[483] I. E. Puddington, Sensitive mercury manometer,

Rev. Sci. Instr. 19, 577 (1948).

[491] W. G. Brombacher, Some problems in the precise measurement of pressure. Instruments 22, 355

(1949).

[492] H. Ebert, Establishment of a pressure scale and ex- perimental realization up to 20,000 atmospheres,

Z. angew. Phys. 1, 331 (1949). (In German.)

[493] H. F. Stimson, The international temperature scale

of 1948, J. Research NBS 42, 209 (1949) RP1962.

[494] R. S. Burden, Surface tension and the spreading of

liquids, (Cambridge Univ. Press, 2d ed., 1949).

[495] W. D. Wood, The development and maintenance of calibrating standards by an instrument manufacturer. Instruments 22, 1004 (1949).

[496] P. W. Bridgman, The physics of high pressure (G.

Bell & Sons, London, 1931 ed. with suppl., 1949).

[501] F. P. Price and P. D. Zemany, A simple recording manometer. Rev. Sci. Instr. 21, 261 (1950).

[511] S. Haynes, Automatic calibration of radiosonde baroswitches. Electronics 24, 126 (May 1951).

[512] R. G. List, Smithsonian Meteorological Tables 6th Rev. ed. (Smithsonian Instit., 1951).

[513] J. M. Los and J. A. Morrison, A sensitive differential manometer. Rev. Sci. Instr. 22, 805 (1951).

[514] R. Meaken, Determination of mercury level in steel- tube manometer. J. Sci. Instr. 28, 372 (1951).

[515] E. C. Hass, Correcting mechanism for mercury

column type measuring instruments, U.S. Patent No. 2,542,671 (Feb. 20, 1951).

45
[516] T. B. Douglas, A. F. Ball, and D. C. Ginnings, Heat

capacity of liquid mercury between 0° and 450° C;

calculation of certain thermodynamic properties

of the saturated liquid and vapor, J. Research

NBS 46, 334 (1951) RP2204.

[521] F. A. Gould and T. Vickers, Capillary depression in mercury barometers and manometers, J. Sci. Instr. 29, 85 (1952).

[522] J. B. Lawrence, Mercury, Instruments 25, 310

(1952) . [531] Charles D. Hodgman, ed. Handbook of physics and

chemistry (Chemical Publishing Co., 35th ed., 1953-54)'.

[532] H. J. Svec and D. S. Gibbs, Recording mercurial

manometer for pressure range 0-760 mm Hg, Rev.

Sci. Instr. 24, 202 (1953).

[533] World Meteorological Organization, Commission

for Instruments and Methods of Observation,

Abridged final report of the first session, Toronto,

1953. WMO No. 19, RP 9, p. 73, Secretariat of the WMO, Geneva, Switzerland, 1953.

[534] World Meteorological Organization, Fourth session

of the Executive Committee, Geneva, 1953. Abridged report with resolutions. WMO No. 20, RC5, p. 86, Secretariat of the WMO, Geneva, Switzerland, 1953.

[535] R. H. Busey and W. F. Giauque, The heat capacity

of mercury from 15 to 330°C. Thermodynamic

properties of solid, liquid and gas. Heat of fusion and vaporization, J. Am. Chem. Soc. 75, 806

(1953) . [541] K. E. Bett, P. F. Hayes, and D. M. Newitt, The

construction, operation and performance of a primary standard mercury column for the meas- urement of high pressure. Phil. Trans. 247, 59

(1954) . [542] K. E. Bett, K. E. Weale, and D. M. Newitt, The

critical evaluation of compression data for liquids

and a revision of the isotherms of mercury, Brit.

J. Appl. Phys. 5, 243 (1954).

[543] T. F. W. Embleton, A semi-automatic electrical manometer designed to calibrate a Mack-Zehnder

interferometer system for the recording of transient pressure changes. Rev. Sci. Instr. 25, 246 (1954).

[544] J. R. Roebuck and H. W. Ibser, Precision multiplemercury-column-manometer. Rev. Sci. Instr. 25, 46 (1954).

[551] L. V. Judson, Units of weight and measure; defini- tions and tables of equivalents, NBS Misc. Publ.

214, (1955).

[552] National Physical Laboratories, Teddington, Meas- urement of pressure with the mercury barometer. Notes on App. Sci. No. 9, (1955).

[553] H. F. Stimson, Precision resistance thermometry and

fixed points; Temperature, its measurement and

control. Am. Inst. Phys. 2, 141 (1955).

[554] E. T. Levanto, A new normal barometer, Ann. Acad.

Sci. Fennicae AI, No. 191, (1955).

1 atm

1 mb

1 mm mercury...

1 in. merom'y

1 g/cm^.. __- 1 lb/iii.2.

1 lb/ft2 1 cm water 20° C.

1 in. water 20° C.

1 atm=10332.3 Kg/m2=1.03323 Kg/cm2.

1 bar =1000 mb=108dynes/cm2.

1 in. =2.54 cm (old value, 2.54000508 cm; 2 parts per million greater).

1 lb = .45359237 Kg (old value, 0.45359243 Kg; 2 parts per 15 million greater).

[555] Helmut Moser, High temperature gas thermometry.

Temperature, its measurement and control, Am.

Inst. Phys. 2, 103 (1955).

[556] Second Congress of the World Meteorological Organization, Geneva, 1955. Final report, vol. II, Technical regulations. WMO No. 48, RCIO, p. 23, Secretariat of the WMO, Geneva, Switzerland,

1956.

[557] E. C. Halliday and H. J. Richards, The barometer

calibrating facilities at the South African National

Phvsical Laboratory. S. African J. Sci. 51, 217

(1955) . [558] F. M. Ernsberger and H. W. Pitman, New absolute manometer for vapor pressures in the micron range. Rev. Sci. Inst. 26, 584 (1955).

[561] N. Fuschillo, Improved method for cleaning mercury. Rev. Sci. Instr. 27, 410 (1956).

[562] M. Ross and E. E. Suckling, Permanent record from

a mercury manometer. Rev. Sci. Instr. 27, 409

(1956) . [563] E. C. Halliday, Temperature corrections for commercial barometers. S. African J. Sci. 52, 178

(1956).

[564] World Meteorological Organization Technical Regulations, Secretariat of the WMO, Geneva, Switzer- land 1, WMO No. 49, Bd 2 (1956).

[571] A. H. Cook and N. W. B. Stone, Precise measure- ments of the density of mercury at 20° C. I. Absolute displacement method. Phil. Trans. [A] 250, 279 (1957).

[572] J. Farquharson and H. A. Kermicle, Precise auto- matic manometer reader. Rev. Sci. Instr. 28, j' 324 (1957).

[573] K. W. T. Elliot and D. C. Wilson, An optical probe

for accurately measuring displacements of a re- flecting surface, J. Sci. Instr. 34, 349 (1957).

[574] C. L. Gordon and E. Wichers, Purification of mercury

and its physical properties, Ann. N.Y. Acad. Sci. 65, 369 (1957).

[575] H. Moser, J. Otto and W. Thomas, Gasthermometrische Messungen bei hohen Temperaturen, Z. Physik 147, 59 (1957).

[576] J. Gielessen, Ueber ein Normalbarometer neuerer Konstruktion, Z. Instrumentenk 65, 63 (1957).

[581] A. J. Eberlein, Laboratory pressure measurement

requirements for evaluating air data computer,

Aeronaut. Eng. Rev. 17, 53 (1958).

[582] Test for schedules of the National Bureau of Standards, Mechanics, Reprinted from Federal Register

23, No. 188, (1958).

[591] WBAN Manual of barometry. Published under

sponsorship of U.S. Weather Bureau, Dept. of the

Air Force, Air Weather Service and Dept. of the Navy, Naval Weather Service Division. Govt.

Printing Office 1 (1959). In press.

[592] Jean Terrien, Methodes optiques pour measurer la hauteur de mercure d'un manomfetre; noveau

manomfetre interferentiel. Rev. d'Optique 38, 24 (1959). Table 1. Conversion factors for various pressure units equivalent for unit value in first column

'ressm-e unit value mb mm mercury

0° C

in. mercury

0° C glcm^ lb/in-. IblfP cm water

20° C

in. water

20° C

1013. 25U

1

1. 3332

33. 864

0. 98066

68. 94752

0. 47880

. 97891

760. 000

0. 75006

1 25. 400

0. 73556

51. 715

0. 35913

. 73424

1. 8650

29. 9213

0. 029530

. 03937

0. 028959

2. 0360

0. 014139

. 028907

. 073424

1033. 23

1. 0197

1. 3595

34. 532

1 70. 307

0. 48824

. 99821

2. 5355

14. 69595

0. 014504

. 019337

. 49116

. 014223

0. 0069444

. 014198

. 036063

2116. 22

2. 088'

2. 7845

70. 727

2. 0482

144

1

2. 0445

5. 1930

1035. 08

1. 0215

1. 3609

34. 566

1. 0010

70. 376

0. 48872

1

2. 5400

407. 513

0. 40218

. 53577

13. 609

0. 39409

27. 707

0. 19241 .3937

46
Table 2. Ratio of the density of mercury at t° to the density at 0° C at 1 aim of pressure

c 0 2

o0 4 5 6 7 8 9

0 1. 0000 0000 0.9998 1859 0. 9996 3722 " 0. 9994 5591 0.9992 7465 0. 9990 9344 0. 9989 1229 0. 9987 3118 0. 9985 5012 0.9983 6911

10 0. 9981 8816 . 9980 0725 . 9978 2639 . 9976 4559 . 9974 6483 . 9972 8412 . 9971 0346 . 9969 2285 . 9967 4228 . 9965 6177

20 . 9963 8130 . 9962 0088 . 9960 2051 . 9958 4019 . 9956 5991 . 9954 7968 . 9952 9950 .9951 1936 . 9949 3927 . 9947 5923

30 . 9945 7923 . 9943 9928 .9942 1938 . 9940 3952 . 9938 5970 . 9936 7993 . 9935 0021 . 9933 2053 .9931 4089 . 9929 6130

40 . 9927 8175 . 9926 0225 .9924 2279 . 9922 4337 . 9920 6400 . 9918 8467 . 9917 0538 . 9915 2614 . 9913 4694 . 9911 6777

50 .9909 8866 . 9908 0958 . 9906 3054 . 9904 5155 . 9902 7260 . 9900 9369 .9899 1482 . 9897 3598 . 9895 5719 .9893 7844

T-\BLE 3A. Density and vapor pressure of mercury

The density is based upon the value 13.5951 g/cm^ at 0° C and the ratios of Table 2.

Temperature

" C

-20

-10

0

1

o p

-4

14

3233.8 35.6

37.4

39.2

4142.8

44.6

46.4

48.2

50

51.8 53.6

55.4 57.2

59

60.8

62.6

64.4

66.2

69.8

71.6

73.4

75.2

80.6

82.4 84.2

Density

Vapor

pressure

0.001 mm of mercury

13. 6446

13. 6198

13. 5951

13. 5926

13. 5902

13. 5877

13. 5852

13. 5828

13. 5803

13. 5779

13. 5754

13. 5729

13. 5705

13. 5680

13.5655

13. 5631

13. 5606

13. 5582

13. 5557

13. 5533

13. 5508

13.5484

13. 5459

13. 5435

13. 5410

13. 5385

13. 5361

13. 5336

13. 5312

13. 5287

13. 5263

13. 5239

0.024

.073

.203

.330

.540

.829

1.08

1.28

'ir52

1.80

"2."i2

2. .50

Temperature

87.8

89.6

91.4

93.2

9596.8

98.6

100.4

102.2

104 105.8

107.6

109.4 111.2

113

114.8

116.6

118.4

120.2

122 123.8

125.6

127.4 129.2

131 132.8

134.6

136.4

138.2

140

Density

13. 5214

13. 5190

13. 5165

13.5141 13.5116

13. 5092

13. 5067

13. 5043

13. 5018

13. 4994

13. 4970

13. 4945

13. 4921

13. 4896

13. 4872

iS. 4848

13. 4823

13. 4799

13. 4775

13. 4750

13. 4726

13. 4702

13. 4677

13. 4653

13. 4629

13. 4604

13. 4580

13. 4556

13. 4531

13. 4507

13. 4483

Vapor

pressure

0.001 mm of mercury

2. 94

6.32

9.26

13.26

18. 78

Table 4. Density of mercury

Based upon the value of 13.5458 925 g/cm^ at 20° C and the ratios of table 2

Temperature Density Temperature Density

°F

A

u 32. 00 13. 5950 QQQ Ooif OU 86.00 io. ozio you

1 33. 80 13. 5926 226 31 87. 80 13. 5189 466

2 35. 60 13. 5901 569 32 89.60 13. 5165 009

o 37. 40 13. .5876 919 33 9L 40 13 4 39. 20 13. 5852 277 93.20 1 t^l 1 R 1 1

A

5 41. uO 13. 5827 641 oO 95.00 13 ouy i D /

u

6 42.80 13. 6803 014 36 96.80 13. 5067 237

7 44. 60 13. 5778 392 37 98.60 13. 5042 809

8 46. 40 13. 5753 777 38 100. 40 13. 5018 387

9 48. 20 13. 5729 168 39 102. 20 13. 4993 971

10 50. 00 13. 5704 568 40 104. 00 13. 4969 561

11 51.80 13. 5679 973 41 105. 80 13. 4945 158

12 53. 60 13. 5655 385 42 107. 60 13. 4920 761 13 55.40 13. 5630 805 43 109. 40 13. 4896 368

14 57. 20 13. 5606 230 44 111. 20 13. 4871 983

15 59. 00 13. 5581 663 45 113. 00 13. 4847 603

16 60. 80 13. 5557 102 46 114 80 13 4823 228

17 62.60 13. 5532 548 47 116, 60 13. 4798 860

18 64 40 13. 5507 999 48 118. 40 13. 4774 498

19 66.20 13. 5483 459 49 120. 20 13 4750 139

20 68. 00 13 5458 924 50 122. 00 13 4725 789

21 69.80 13. 5434 395 51 123 80 13 4701 443 22 7L 60 13 5409 874 52 125. 60 13 4677 103 23 73. 40 13 5385 3.59 53 127. 40 13 4652 769 24 75. 20 13 5360 850 54 129. 20 13 4628 440

25 77.00 13 5336 347 55 131. 00 13 4604 117 26 78.80 13 5311 852 56 132 80 13 4579 800 27 80.60 13 5287 362 57 134. 60 13 4555 486 28 82.40 13 5262 878 58 136 40 13 4531 180

29 84 20 13 5238 402 59 138 20 13 4506 878

26.32

Table 3B. Density of mercury

The density is based upon the conversion factor: unit g/cm'=0.03612729

lb/in.3 in which 1 in.=2.54 cm and 1 lb=453.59237 g

Temperature Density

o F lb/in.' 0 0. 49274 13. 6391

10 .49225 13. 6253

20 . 49175 13. 6116 32 .491154 13. 5951 40 . 49076 13. 5841

50 . 49026 13. 5704

60 . 48977 13. 5568 • 70 .48928 13. 5431 80 . 48878 13. 5295

90 .48829 13. 5159

100 . 48780 13. 5023

110 . 48731 13. 4888

120 . 48683 13. 4753

130 . 48633 13. 4617

Table 5. Coefficients of linear expansion

Multiply all values by 10-'

Material

Aluminum _ Brass, yellow Cast iron Duralumin

Glass, soda lime

Glass, Pyrex

Invar Monel metal

Stainless steel (18+8)

Stainless steel, Carpenter No,

Steel, low carbon

Coefficient

per "C per "F

24. 5±0. 5 13.6

18 4±0. 8 10. 22

8 5±0. 5 4.7

23 5±1 13.

1

8 5±0. 5 4.7

3 0 1.7

0 to 5 0 to 3

14 ±0. 5 7.8

17 ±1 9.4

17 ±0. 5 9.4

11 5±0. 5 6.4

47
Table 6. Tem-perature corrections for Fortin barometer with brass scales

All corrections are to be subtracted from the reading.

Barometer reading, millibars, inches or millimeters of mercury Tempera- Correction

ture factor 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 186 190 195

° C %

0 CO 0.00 0. 00 0.00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0. 00 0. 00

5 . 081626 . 08 .09 . 09 . 09 . 10 . 10 . 11 . 11 . 11 . 12 . 12 . 13 . 13 . 13 . 14 . 14 . 15 . 15 . 16 .16

10 . 16310 . 16 . 17 . 18 . 19 . 20 . 20 . 21 . 22 . 23 . 24 . 24 . 25 . 26 . 27 . 28 . 29 . 29 . 30 . 31 . 32

11 . 17938 . 18 . 19 .20 .21 . 22 .22 .23 .24 .25 .26 .27 .28 .29 .30 .30 . 31 . 32 .33 .34 . 35

12 . 19565 . 20 . 21 . 22 .22 . 23 .24 .25 .26 .27 .28 .29 .30 .31 .32 .33 . 34 .35 . 36

' 37 . 38

13 .21192 .21 .22 .23 .24 .25 . 26 . 28 . 29 . 30 . 31 . 32 . 33 . 34 . 35 . 36 .37 .38 !39 !40 !41 14 . 22818 . 23 .24 .25 . 26 . 27 . 29 . 30 . 31 . 32 . 33 . 34 . 35 . 37 . 38 . 39 .40 .41 .42 .43 .44

15 . 24443 . 24 . 26 . 27 .28 . 29 . 31 . 32 . 33 . 34 . 35 . 37 . 38 .39 . 40 . 42 . 43 . 44 . 45 . 46 . 48

16 . 26068 . 26 .27 . 29 .30 . 31 .33 .34 .35 .36 .38 .39 .40 .42 .43 .44 . 46 . 47 . 48 . 50 . 51 17 . 27692 .28 .29 . 30 .32 .33 .35 .36 .37 .39 .40 .42 .43 .44 .46 .47 . 48 50 51 . 63 .64

18 .29316 .29 .31 .32 .34 .35 . 37 . 38 . 40 . 41 . 43 . 44 . 45 .47 . 48 . 60 .51 .63 .64 .56 .67

19 . 30939 .31 .32 .34 .36 .37 . 39 . 40 . 42 .43 . 45 . 46 . 48 . 50 . 51 . 53 . 54 .66 .57 .59 .60

20 . 32562 .33 .34 .36 .37 .39 . 41 . 42 . 44 . 46 . 47 . 49 . 60 . 62 . 54 . 56 . 57 . 59 . 60 . 62 . 63

21 .34183 .34 .36 .38 .39 .41 .43 .44 .46 .48 .50 .51 .63 .55 .56 .68 . 60 . 62 . 63 . 65 . 67

22 . 36805 .36 .38 .39 .41 .43 .45 .47 .48 .50 .52 .54 .55 . .57 .59 .61 .63 . 64 . 66 . 68 . 70

23 . 37426 .37 .39 .41 .43 .45 . 47 . 49 . 51 . 52 . 54 . 56 '. 68 . 60 . 62 . 64 .65 .67 .69 .71 .73 24 . 39046 .39 . 41 .43 . 45 .47 . 49 . 51 . 53 . 55 . 57 . 59 . 61 . 62 . 64 . 66 .68 . 70 .72 .74 .76

25 . 40665 . 41 .43 .45 .47 .49 . 51 . 53 . 55 . 57 . 59 . 61 . 63 . 65 . 67 . 69 . 71 .73 . 76 . 77 . 79

26 . 42284 . 42 .44 .47 .49 . 51 .53 .55 .57 .59 .61 .63 .66 .68 .70 .72 . 74 .76 . 78 . 80 . 82

27 . 43903 .44 .46 .48 .50 . 53 .55 .57 .59 .61 .64 .66 .68 .70 .72 .75 . 77 .79 .81 . 83 .86

28 . 45520 .46 .48 .50 .52 . 55 . 57 . 59 . 61 . 64 . 66 . 68 . 71 . 73 . 75 . 77 .80 .82 .84 .86 .89 29 .47137 .47 .49 .52 .54 . 57 . 59 . 61 . 64 . 66 . 68 . 71 . 73 . 76 . 78 . 80 .82 .85 .87 . 90 . 92

30 . 48754 .49 . 51 .54 .56 . 59 . 61 . 63 . 66 . 68 . 71 . 73 . 76 . 78 . 80 . 83 . 85 .88 . 90 . 93 . 95

31 . 50370 . 50 . 53 . 55 .58 .60 .63 .65 .68 .71 .73 .76 .78 .81 .83 .86 . 88 .91 .93 . 96 . 98

32 . 51986 . 52 . 55 . 57 . 60 . 62 .65 .68 .70 .73 .75 .78 .81 .83 .86 .88 . 91 .94 .96 .99 1. 01 33 . 536C0 .54 .56 .59 .62 .64 . 67 . 70 . 72 . 75 . 78 . 80 . 83 . 86 . 88 . 91 .94 .96 .99 1.02 1.05 34 . 55215 . 55 . 58 .61 .63 . 66 . 69 . 72 . 75 . 77 . 80 . 83 . 86 .88 . 91 . 94 . 97 .99 1. 02 1.06 1.08

35 . 56828 . 57 .60 .63 .65 .68 . 71 . 74 . 77 . 80 . 82 . 85 . 88 . 91 . 94 . 97 .99 1. 02 1.06 1. 08 1. 11

36 . 58442 . 58 . 61 .64 . 67 .70 .73 .76 .79 .82 .85 .88 .91 .94 .96 0. 99 1.02 1. 05 1.08 1. 11 1. 14 37 . 60054 . 60 .63 .66 . 69 . 72 .75 .78 .81 .84 .87 .90 .93 .96 .99 1.02 1. 05 1. 08 1. 11 1. 14 1. 17 38 .61666 .62 .65 .68 .71 .74 . 77 . 80 . 83 . 86 . 89 . 92 . 96 . 99 1. 02 1. 05 1.08 1.11 1.14 1.17 1.20 39 . 63277 .63 .66 . 70 .73 .76 . 79 . 82 . 85 . 89 . 92 . 95 . 98 1. 01 1. 04 1. 08 1. 11 1. 14 1. 17 1.20 1.23

40 . 64888 . 65 . 68 . 71 . 75 . 78 . 81 . 84 . 88 . 91 . 94 . 97 1.01 1. 04 1.07 1. 10 1. 14 1. 17 1. 20 1. 23 1. 27

41 . 66498 .66 . 70 .73 . 76 . 80 .83 .86 .90 .93 .96 1.00 1.03 1.06 1.10 1.13 1. 16 1. 20 1. 23 1. 26 1. .30 42 . 68108 . 68 . 72 . 75 .78 . 82 . 85 . 89 . 92 . 95 . 99 1. 02 1. 06 1. 09 1. 12 1. 16 1. 19 1. 23 1. 26 1.29 1. 33

43 . 69717 .70 .73 .77 .80 .84 .87 .91 .94 .98 1.01 1.05 1.08 1.12 1.15 1.19 1.22 1.25 1.29 1. 32 1.36

44 . 71325 .71 .75 .78 .82 .86 .89 .93 .96 1.00 1.03 1.07 1.11 1. 14 1.18 1.21 1.25 1.28 1.32 1. 36 1.39

45 . 72933 .73 .77 .80 .84 .88 .91 .95 .98 1.02 1.06 1.09 1.13 1.17 1.20 1.24 1.28 1.31 1. 35 1. 39 1.42

46 . 74541 .75 .78 .82 .86 .89 .93 .97 1. 01 1.04 1.08 1.12 1.16 1.19 1.23 1.27 1.30 1.34 1.38 1.42 1.45

47 . 76147 .76 .80 .84 .88 .91 .95 .99 1.03 1.07 1.10 1. 14 1.18 1.22 1.26 1.29 1.33 1.37 1.41 1.45 1.48 48 . 77744 .78 .82 .86 .89 .93 .97 1.01 1.05 1.09 1.13 1.17 1.21 1.24 1.28 1.32 1.36 1.40 1.44 1.48 1.52

49 . 79359 .79 .83 .87 .91 .95 .99 1.03 1. 07 1.11 1. 15 1.19 1.23 1.27 1.31 1.35 1.39 1.43 1.47 1.61 1.65

50 . 80964 .81 .85 .89 .93 .97 l.Cl 1.05 1.09 1.13 1.17 1.21 1.25 1.30 1.34 1.38 1.42 1.46 1.50 1.54 1.58

Temperature

Barometer readin g, millibars, inches or millimeters of mercury

200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295

° C

0 0.00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0. 00 0.00 0. 00 0.00 0. 00 0. 00 0.00 0.00 0 00 0 00 0.00

5 . 16 . 17 . 17 .18 .18 . 18 . 19 . 19 .20 .20 .20 .21 .21 .22 .22 .22 .23 23 24 .24

10 .33 .33 .34 .35 .36 .37 .38 .38 .39 .40 .41 .42 .42 .43 .44 .45 .46 46 47 .48

11 .36 .37 .38 .39 .39 .40 .41 .42 .43 .44 .45 .46 .47 .48 .48 .49 .60 51 62 .53

12 .39 .40 .41 .42 .43 .44 .45 .46 .47 .48 .49 .50 .51 .62 .53 .54 .55 56 67 .58

13 .42 .43 .45 .46 .47 .48 .49 .50 .51 .52 .53 .54 .55 .56 .57 .68 .59 60 61 .63

14 .46 .47 .48 .49 .50 .51 .52 .64 .65 .56 .57 .58 .59 .60 .62 .63 .64 65 66 .67

16 .49 . 50 .51 .63 . 54 .65 .56 .67 .59 .60 .61 .62 .64 .65 .66 .67 .68 70 71 .72

16 .52 .63 .55 .66 . 57 . 69 .60 .61 .63 .64 .66 .66 .68 .69 .70 .72 .73 74 76 .77 17 .66 .57 .58 .60 .61 .62 . 64 .65 .66 .68 .69 .71 .72 .73 .76 .76 .78 79 80 .82

18 .59 .60 .62 .63 .64 .66 .67 .69 .70 .72 .73 .75 .76 .78 .79 .81 .82 84 85 .86

19 .62 .63 .65 .67 .68 .70 .71 .73 .74 .76 .77 .79 .80 .82 .84 .85 .87 88 90 .91 20 .65 .67 .68 .70 .72 .73 .75 .77 .78 .80 .81 .83 .85 .86 .88 .90 .91 93 94 .96

21 .68 .70 .72 .73 .75 .77 .79 .80 .82 .84 .85 .87 .89 .91 .92 .94 .96 97 99 1.01 22 .72 .73 .75 .77 .79 .81 .82 .84 .86 .88 .90 .91 .93 .95 .97 .98 1.00 1 02 1 04 1.06 23 .75 .77 .79 .80 .82 .84 .86 .88 .90 .92 .94 .96 .97 .99 1.01 1.03 1.06 1 07 1 09 1. 10 24 .78 .80 .82 .84 .86 .88 .90 .92 .94 .96 .98 1. 00 1.02 1.03 1.05 1.07 1.09 1 11 1 13 1.15 25 .81 .83 .86 .87 .89 .91 .94 .96 .98 1.00 1.02 1. 04 1.06 1.08 1.10 1.12 1.14 1 16 1 18 1.20

26 .86 .87 .89 .91 .93 .95 0.97 .99 1.01 1. 04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1 21 1 23 1.25 27 .88 .90 .92 .94 .97 .99 1.01 1.03 1.06 1.08 1.10 1.12 1.14 1.16 1.19 1.21 1.23 1 25 1 27 1.30 28 .91 .93 .96 .98 1.00 1. 02 1.05 1.07 1.09 1.12 1.14 1.16 1.18 1. 21 1. 23 1.25 1.27 1 30 1 32 1.34 29 .94 .97 .99 1.01 1.04 1.06 1.08 1.11 1.13 1.15 1.18 1.20 1.23 1.25 1.27 1.30 1.32 1 34 1 37 1.39 30 .98 1.00 1, 02 1.05 1. 07 1.10 1. 12 1.15 1.17 1.19 1.22 1.24 1.27 1.29 1.32 1.34 1.37 1 39 1 41 1.44

48
Table 6. Temperature corrections for Fortin barometer with brass scales—Continued

All corrections are to be subtracted from the reading.

Barometer reading, millibars, inches or Tnil1imp.tp.rs of mercury

ature

200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295

C

31 1. 01 1 03 1. 06 1.08 1. 11 1.13 1.16 1. 18 1. 21 1. 23 1. 26 1.28 1. 31 1. 33 1.36 1.39 1 41 1.44 1.46 1.49 32 1. C4 1. 07 1. 09 1.12 1. 14 1.17 1.20 1. 22 1. 25 1. 27 1.30 1.33 1.35 1.38 1.40 1.43 1 46 1.48 1.51 1.53 33 1. 07 1. 10 1. 13 1. 15 1. 18 1. 21 1. 23 1. 26 1. 29 1. 31 1. 34 1. 37 1. 39 1. 42 1. 45 1.47 1 50 1. 53 1. 55 1. 58 34 1. 10 1 13 1 16 1. 19 1. 21 1. 24 1. 27 1. 30 1. 33 1. 35 1. 38 1. 41 1. 44 1.46 1. 49 1. 52 1 55 1. 57 1. 60 1. 63 35 1. 14 1 16 1 19 1 22 1 25 1. 28 1. 31 1. 34 1 36 1. 39 1. 42 1. 45 1.48 1.51 1. 53 1. 56 1 59 1. 62 1. 65 1. 68

36 1 17 1 20 1 23 1 26 1 29 1.31 1.34 1. 37 1 40 1 43 1.46 1.49 1.52 1.55 1.58 1.61 1 64 1.67 1.69 1.72 37 1 20 1 23 1 26 1 29 1 32 1.35 1.38 1 41 1 44 1 47 1.50 1.53 1. 56 1. 59 1.62 1.65 1 68 1.71 1.74 1.77 3S 1 23 1 26 1 29 1 33 1 36 1. 39 1. 42 1 45 1 48 1 51 1. 54 1. 57 1. 60 1. 63 1. 66 1.70 1 73 1.76 1. 79 1. 82 39 1. 27 1 30 1 33 1 36 1 39 1. 42 1. 46 1 49 1 52 1 55 1. 58 1. 61 1. 65 1. 68 1. 71 1.74 1 77 1. 80 1. 84 1. 87 40 1 30 1 33 1 36 1 40 1 43 1. 46 1. 49 1 52 1 56 1 59 1. 62 1. 65 1. 69 1. 72 1.75 1.78 1 82 1. 85 1.88 1. 91

41 1 33 1 36 1 40 1 43 1 46 1.50 1.53 1 66 1 60 1 63 1.66 1.70 1.73 1. 76 1.80 1.83 1 86 1.90 1.93 1.96

42 1 36 1 40 1 43 1 46 1 50 1. 53 1. 57 1 60 1 63 1 67 1 70 1 74 1 77 1. 80 1 84 1 87 1 91 1 94 1 98 2 01 43 1 39 1 43 1 46 1 50 1 53 1. 57 l!60 1 64 1 67 1 71 L74 l!78 l.Sl 1. 85 l!88 L92 1 95 L99 2. 02 2^06

44 1 43 1 46 1 50 1 53 1 57 J. 60 1.64 1 68 1 71 1 75 1.78 1.82 1.85 1. 89 1.93 1.96 2 00 2. 03 2. 07 2. 10 45 1 46 1 50 1 53 1 57 1 60 1.64 1.68 1 71 1 75 1 79 1.82 1.86 1.90 1 93 1.97 2. 01 2 04 2. 08 2. 12 2.15

46 1 49 1 53 1 57 1 60 1 64 1.68 1.71 1 75 1 79 1 83 1.86 1.90 1.94 1 98 2.01 2. 05 2 09 2. 12 2. 16 2.20 47 1 52 1 56 1 60 1 64 1 68 1.71 1.75 1 79 1 83 1 87 1.90 1.94 1.98 2 02 2.06 2. 09 2 13 2.17 2.21 2. 25 48 1 56 1 59 1 63 1 67 1 71 1. 75 1.79 1 83 1 87 1 90 1.94 1.98 2.02 2 06 2. 10 2.14 2 18 2. 22 2. 25 2. 29

49 1 59 1 63 1 67 1 71 1 75 1.79 1.83 1 86 1 90 1 94 1.98 2. 02 2. 06 2 10 2.14 2.18 2 22 2. 26 2. 30 2. 34

50 1 62 1 66 1 70 1 74 1 78 1.82 1.86 1 90 1 94 1 98 2. 02 2. 06 2.11 2 15 2.19 2.23 2 27 2.31 2. 35 2. 39

Barometer reading, mUlibars, inches or mQlimeters of mercm-y

perature

i 300 305 310 315 320 325 330 335 340 345 350 355 360 365 370 375 380 385 390 395

° C

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0. 00 0.00 0.00 0.00 0.00 0. 00 0.00 0. 00

5 .24 .25 .25 .26 .26 .27 .27 .27 .28 .28 .29 .29 .29 .30 .30 .31 .31 .31 .32 .32

10 . 49 . 50 . 51 . 51 . 52 . 53 . 54 . 55 . 55 . 56 . 57 . 58 . 59 . 60 . 60 . 61 . 62 . 63 . 64 . 64

11 .54 .55 .56 .57 .57 .58 .59 .60 .61 .62 .63 .64 .65 .65 .66 .67 .68 .69 .70 .71

12 .59 .60 .61 .62 .63 .64 .65 .66 .67 .67 .68 .69 .70 .71 .72 .73 .74 . 75 .76 .77

13 .64 .65 .66 .67 .68 .69 ..70 .71 .72 .73 .74 .75 .76 .77 .78 .79 .81 .82 .83 .84

14 .68 .70 .71 .72 .73 .74 . 75 .76 .78 .79 .80 .81 .82 .83 .84 .86 .87 .88 .89 .90

15 .73 . 75 .76 . 77 .78 .79 .81 .82 .83 .84 .86 .87 .88 .89 .90 .92 .93 .94 .95 .97

16 .78 .80 .81 .82 .83 .85 .86 .87 .89 .90 .91 .93 .94 .95 .96 .98 .99 1.00 1.02 1.03

17 .83 .84 .86 .87 .89 .90 .91 .93 .94 .96 .97 .98 1.00 1.01 1.02 1. 04 1. 05 1. 07 1.08 1.09

18 .88 .89 .91 .92 .94 .95 .97 .98 1.00 1.01 1.03 1.04 1.06 1.07 1.08 1. 10 1.11 1.13 1.14 1.16

19 .93 .94 .96 .97 .99 1.01 1.02 1.04 1.05 1.07 1.08 1.10 1. 11 1. 13 1. 14 1. 16 1.18 1. 19 1.21 1.22 20 .98 .99 1. 01 1.03 1.04 1.06 1.07 1.09 1.11 1.12 1. 14 1.16 1.17 1.19 1.20 1.22 1.24 1.25 1.27 1.29

21 1.03 1.04 1.06 1.08 1.09 1. 11 1. 13 1.15 1. 16 1.18 1.20 1.21 1. 23 1.25 1.26 1.28 1. 30 1.32 1. 33 1.35 22 1.07 1.09 1.11 1.13 1.15 1. 16 1. 18 1.20 1. 22 1.24 1.25 1.27 1.29 1.31 1. 32 1.34 1.36 1.38 1.40 1.41 23 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1. 25 1.27 1.29 1.31 1.33 1.35 1.37 1.38 1.40 1. 42 1.44 1.46 1.48 24 1. 17 1. 19 1.21 1.23 1.25 1.27 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1. 43 1.44 1.46 1.48 1.50 1.52 1.54 25 1.22 1.24 1. 26 1.28 1.30 1.32 1.34 1. 36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1. 52 1.55 1. 57 1.59 1.61

26 1.27 1.29 1.31 1.33 1.35 1.37 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.59 1.61 1.63 1.65 1.67 27 1. 32 1.34 1. 36 1.38 1.40 1.43 1.45 1.47 1.49 1.51 1.54 1.56 1.58 1.60 1.62 1. 65 1.67 1.69 1. 71 1.73 28 1. 37 1.39 1.41 1.43 1.46 1.48 1.50 1.52 1.55 1. 57 1.59 1.62 1.64 1.66 1.68 1.71 1.73 1. 75 1.78 1.80 29 1.41 1.44 1.46 1.48 1.51 1. 53 1.56 1.58 1.60 1.63 1. 65 1.67 1. 70 1.72 1.74 1.77 1.79 1.81 1.84 1.86 30 1.46 1.49 1.51 1.54 1. 56 1. 58 1.61 1.63 1.66 1.68 1.71 1.73 1.76 1. 78 1.80 1.83 1.85 1.88 1. 90 1.93

31 1. 51 1.54 1.56 1.59 1.61 1.64 1.66 1.69 1.71 1.74 1.76 1.79 1. 81 1.84 1.86 1. 89 1.91 1. 94 1.96 1.99 32 1.56 1.59 1. 61 1.64 1.66 1.69 1.72 1.74 1. 77 1.79 1.82 1. 85 1.87 1.90 1. 92 1.95 1.98 2. 00 2. 03 2. 05 33 1.61 1.63 1.66 1.69 1. 72 1.74 1.77 1.80 1.82 1.85 1.88 1. 90 1.93 1.96 1. 98 2.01 2.04 2. 06 2. 09 2. 12 34 1. 66 1.68 1.71 1.74 1.77 1.79 1. 82 1.85 1.88 1.90 1.93 1.96 1.99 2. 02 2.04 2. 07 2. 10 2. 13 2. 15 2.18

35 1.70 1.73 1.76 1.79 1.82 1.85 1.88 1.90 1.93 1.96 1.99 2. 02 2.05 2.07 2. 10 2. 13 2. 16 2. 19 2. 22 2. 24

36 1.75 1.78 1.81 1.84 1. 87 1.90 1.93 1.96 1. 99 2. 02 2. 05 2. 07 2. 10 2.13 2. 16 2. 19 2.22 2. 25 2. 28 2. 31 37 1.80 1.83 1.86 1.89 1.92 1.95 1.98 2.01 2.04 2. 07 2. 10 2. 13 2. 16 2. 19 2. 22 2. 25 2. 28 2. 31 2. 34 2.37 38 1.85 1.88 1.91 1.94 1.97 2.00 2.03 2. 07 2. 10 2. 13 2.16 2. 19 2.22 2. 25 2. 28 2. 31 2. 34 2.37 2.40 2. 44

39 1.90 1.93 1.96 1.99 2. 02 2.06 2.09 2. 12 2.15 2. 18 2.21 2. 25 2. 28 2.30 2. 34 2.37 2.40 2.44 2. 47 2.50

40 1.95 1.98 2. 01 2. 04 2. 08 2. 11 2. 14 2.17 2. 21 2.24 2. 27 2. 30 2. 34 2. 37 2.40 2. 43 2. 47 2.50 2. 53 2. 56

41 1.99 2. 03 2. 06 2.09 2.13 2. 16 2. 19 2. 23 2.26 2. 29 2. 33 2.36 2.39 2. 43 2. 46 2.49 2. 53 2. 56 2. 59 2.63

42 2.04 2. 08 2.11 2. 15 2. 18 2. 21 2. 25 2. 28 2.32 2.35 2. 38 2.42 2. 45 2. 49 2. 52 2. 55 2.59 2. 62 2. 66 2.69

43 2.09 2. 13 2. 16 2.20 2. 23 2.27 2. 30 2.34 2.37 2. 41 2.44 2. 47 2. 51 2. 54 2. 58 2.61 2. 65 2. 68 2. 72 2. 75

44 2. 14 2. 18 2. 21 2. 25 2. 28 2. 32 2. 35 2. 39 2. 43 2. 46 2. 50 2. 53 2.57 2. 60 2.64 2.67 2.71 2. 75 2. 78 2. 82

45 2. 19 2.22 2. 26 2.30 2. 33 2. 37 2.41 2.44 2. 48 2. 52 2. 55 2. 59 2.63 2.66 2.70 2.74 2. 77 2. 81 2.84 2. 88

46 2. 24 2.27 2.31 2. 35 2.39 2.42 2.46 2. 50 2. 53 2. 57 2. 61 2.65 2. 68 2. 72 2. 76 2. 80 2. 83 2. 87 2.91 2. 94

47 2. 28 2. 32 2. 36 2.40 2. 44 2. 47 2. 51 2. 55 2. 59 2.63 2.67 2.70 2.74 2.78 2. 82 2.86 2.89 2.93 2. 97 3.01

48 2. 33 2.37 2.41 2. 45 2.49 2. 53 2. 57 2.60 2, 64 2. 68 2.72 2.76 2. 80 2. 84 2. 88 2. 92 2. 95 2. 99 3. 03 3.07

49 2.38 2.42 2.46 2. 50 2. 54 2. 58 2. 62 2. 66 2.70 2.74 2.78 2. 82 2. 86 2.90 2. 94 2. 98 3.02 3. 06 3. 10 3. 13 50 2. 43 2. 47 2.51 2. 55 2.59 2. 63- 2. 67 2. 71 2. 75 2. 79 2. 83 2. 87 2. 91 2. 96 3.00 3.04 3.08 3. 12 3. 16 3.20
0

510

1112

13

14

15

16

17

18

1920

2122

23

2425

26

27

28

2930

3132

33

34

35

36

37

3839

40

4142

43

44

45

4647

48

49

50

mp

tur

' C

0

510

1112

1314

15

16

17

181920

21

22

23

24

25

26

27

28

2930

Table 6. Te^nperature corrections for Fortin barometer with brass scales—Continued

All corrections are to be subtracted from the reading.

Barometer reading, millibars, inches or millimeters of mercury

400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495

0.00 0. 00 0. 00 0.00 0. 00 0 00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0.00 0. 00 0. 00 0. 00 0.00 0.00 0. 00 0.00

.33 .33 .33 .34 .34 35 .35 .35 .36 .36 .37 .37 .38 .38 .38 .39 .39 .40 .40 .40

.65 .66 .67 .68 .69 69 .70 .71 .72 .73 .73 .74 .75 .76 .77 .77 .78 .79 .80 .81

. 72 . 73 . 74 . 74 . 75 76 . 77 . 78 . 79 . 80 . 81 . 82 . 83 . 83 . 84 . 85 . 86 . 87 . 88 . 89 !78 !79 '.SO '.SI ^82 83 !84 ^86 !86 !87 ^88 ^89 !90 .91 ^92 !93 ^94 !95 !96 !97

.85 .86 .87 .88 .89 90 .91 .92 .93 .94 .95 .96 .97 .99 1.00 1.01 1.02 1.03 1.04 1.05

.91 .92 .94 .95 .96 97 .98 .99 1.00 1. 02 1. 03 1.04 1.06 1.06 1.07 1.08 1.10 1. 11 1. 12 1.13 .98 .99 1.00 1.01 1.03 1 04 1.05 1.06 1.08 1.09 1.10 1.11 1.12 1. 14 1. 15 1.16 1. 17 1.19 1.20 1. 21

1. 04 1. 06 1. 07 1. 08 1. 09 1 11 1. 12 1. 13 1. 15 1. 16 1. 17 1. 19 1. 20 1. 21 1. 23 1. 24 1. 25 1. 26 1. 28 1 29

l] 11 l'l2 L 14 l!l5 l!l6 1 18 i. 19 l!20 1.22 L23 L25 L26 i. 27 L29 1. 30 L32 L33 L34 1! 36 L 37

1.17 1.19 1.20 1.22 1.23 1 25 1. 26 1.28 1.29 1.30 1.32 1.33 1.35 1.36 1.38 1.39 1.41 1.42 1.44 1.45 1.24 1.25 1.27 1.28 1.30 I 31 1.33 1.35 1.36 1.38 1.39 1.41 1.42 1.44 1.45 1.47 1. 49 1.50 1.52 1.53

1.30 1.32 1.34 1. 35 1.37 1 38 1.40 1. 42 1.43 1. 45 1.47 1.48 1.50 1.51 1. 53 1. 55 1.56 1.58 1.60 1.61

1. 37 1. 38 1. 40 1. 42 1. 44 1 45 1. 47 1. 49 1. 50 1. 52 1. 54 1. 56 1. 57 1. 59 1. 61 1. 62 1. 64 1. 66 1. 67 1. 69 L43 1^45 L47 1^49 1^50 1 52 l'54 L56 1^58 1^59 L61 1. 63 1.65 1. 66 1.68 L70 1.72 L74 L 75 L77

1.50 1.52 1.53 1.55 1.57 1 59 1.61 1.63 1.65 1.67 1.68 1. 70 1.72 1:74 1.76 1. 78 1.80 1.82 1. 83 1.85

1.56 1. 58 1.60 1.62 1.64 I 66 1.68 1.70 1.72 1.74 1. 76 1.78 1.80 1.82 1.84 1.85 1.87 1.89 1.91 1.93 1.63 1. 65 1.67 1.69 1.71 1 73 1. 75 1.77 1.79 1.81 1.83 1.85 1.87 1.89 1.91 1.93 1.95 1.97 1.99 2. 01

1. 69 1. 71 1. 73 1. 75 1 78 1 80 1. 82 1. 84 1. 86 1. 88 1. 90 1. 92 1. 95 1. 97 1. 99 2. 01 2. 03 2. 05 2. 07 2. 09

1. 76 1.78 1.80 1.82 L84 1 87 1.89 1.91 l. 93 1.95 L98 2.00 2. 02 2. 04 2. 06 2.09 2. 11 2. 13 2. 15 2. 17

1. 82 1.84 1. 87 1.89 1.91 1 93 1.96 1.98 2.00 2. 03 2. 05 2. 07 2.09 2. 12 2. 14 2. 16 2. 18 2. 21 2. 23 2. 25 1.89 1.91 1.93 1.96 1.98 2 00 2. 03 2. 05 2. 07 2. 10 2. 12 2.14 2.17 2. 19 2.22 2. 24 2. 26 2. 29 2. 31 2. 33

1.95 1.97 2. 00 2. 02 2. 05 2 07 2. 10 2. 12 2. 15 2. 17 2. 19 2. 22 2.24 2. 27 2.29 2. 32 2. 34 2. 36 2.39 2. 41

2. 01 2. 04 2. 07 2. 09 2. 12 2 14 2. 17 2. 19 2. 22 2. 24 2. 27 2. 29 2. 32 2. 34 2. 37 2. 39 2. 42 2. 44 2. 47 2. 49

2. 08 2. 11 2. 13 2. 16 2. 18 2 21 2. 24 2. 26 2^29 2.31 2. 34 2. 37 2. 39 2.42 2. 44 2. 47 2.60 2. 52 2. 56 2. 57

2. 14 2. 17 2.20 2.22 2. 25 2 28 2. 30 2.33 2.36 2. 39 2. 41 2.44 2. 47 2. 49 2.52 2. 65 2. 67 2. 60 2.63 2. 65

2. 21 2.24 2. 26 2. 29 2. 32 2 35 2. 37 2.40 2. 43 2.46 2. 48 2. 51 2. 64 2. 67 2.60 2.62 2. 65 2..68 2. 71 2.73

2. 27 2.30 2. 33 2. 36 2, 39 2 42 2. 44 2. 47 2.50 2.53 2. 56 2.59 2. 61 2. 64 2. 67 2.70 2. 73 2. 76 2.78 2. 81

2. 34 2. 37 2. 40 2. 43 2. 45 2 48 2. 51 2. 54 2. 57 2. 60 2. 63 2. 66 2. 69 2. 72 2. 75 2. 78 2. 81 2. 83 2. 86 2. 89 2.40 2. 43 2.46 2^49 2^52 2 55 2. 58 2. 61 2. 64 2. 67 2.' 70 2^73 2. 76 2' 79 2. 82 2. 86 2^88 2.91 2. 94 2. 97 2.47 2.50 2. 53 2. 56 2. 59 2 62 2. 65 2. 68 2. 71 2. 74 2. 77 2. 81 2. 84 2. 87 2. 90 2. 93 2. 96 2.99 3. 02 3. 05

2. 53 2. 56 2. 59 2. 63 2. 66 2 69 2. 72 2. 75 2. 78 2. 82 2.85 2. 88 2. 91 2. 94 2. 97 3.01 3. 04 3. 07 3. 10 3. 13 2.60 2. 63 2. 66 2, 69 2. 73 2 76 2.79 2. 82 2. 86 2.89 2. 92 2. 95 2.98 3. 02 3. 05 3. 08 3. 11 3.15 3. 18 3. 21

2. 66 2.69 2.73 2. 76 2. 79 2 83 2. 86 2.89 2. 93 2. 96 2. 99 3.03 3. 06 3. 09 3. 13 3. 16 3. 19 3.23 3. 26 3. 29

2. 72 2. 76 2. 79 2. 83 2. 86 2 89 2. 93 2. 96 3. 00 3. 03 3. 06 3. 10 3. 13 3. 17 3. 20 3. 24 3- 27 3. 30 3. 34 3. 37

2. 79 2. 82 2. 86 2. 89 2.93 2 96 3. 00 3, 03 3. 07 3. 10 3. 14 3. 17 3. 21 3. 24 3. 28 3. 31 3.35 3. 38 3. 42 3. 45

2. 85 2.89 2. 92 2. 96 3. 00 3 03 3. 07 3. 10 3. 14 3. 17 3. 21 3. 25 3. 28 3. 32 3.36 3.39 3.42 3. 46 3.49 3.53

2. 92 2. 95 2. 99 3.03 3. 06 3 10 3. 14 3. 17 3. 21 3. 25 3.28 3. 32 3. 35 3. 39 3. 43 3.46 3.50 3. 54 3. 57 3. 61

2. 98 3. 02 3. 06 3.09 3. 13 3 17 3. 21 3. 24 3. 28 3. 32 3. 35 3. 39 3. 43 3. 47 3.50 3. 54 3.58 3. 62 3. 65 3.69

3. 05 3. 08 3. 12 3. 16 3.20 3 24 3. 27 3.31 3.35 3. 39 3. 43 3.46 3. 60 3. 54 3. 58 3. 62 3.66 3.69 3. 73 3. 77

3. 11 3. 15 3. 19 3. 23 3. 27 3 30 3. 34 3. 38 3. 42 3.46 3. 60 3. 64 3.68 3.62 3. 65 3.69 3.73 3. 77 3. 81 3. 86 3.17 3. 21 3. 25 3. 29 3. 33 3 37 3. 41 3. 45 3.49 3. .53 3. 67 3. 61 3. 65 3.69 3. 73 3. 77 3. 81 3. 85 3.89 3.93 3.24 3.28 3.32 3. 36 3.40 3 44 3. 48 3.62 3. 56 3.60 3.64 3. 68 3. 72 3.76 3. 81 3.86 3 89 3.93 3. 97 4.01

Barometer reading, millibars. Inches or millimeters of mercury

500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595

0. 00 0.00 0. 00 0.00 0.00 0. 00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0. 00 0. 00 0. 00 0. 00 0.00 0.00

.41 .41 .42 .42 .42 43 .43 .44 .44 .44 .45 .45 .46 .46 .47 .47 .47 .48 .48 .49 .82 .82 .83 .84 .85 86 .86 .87 .88 .89 .90 .91 .91 .92 .93 .94 .95 .95 .96 .97

.90 .91 .91 .92 .93 94 .95 .96 .97 .98 .99 1.00 1.00 1.01 1.02 1. 03 1.04 1.05 1.06 1.07

.98 .99 1.00 1. 01 1. 02 I. 03 1.04 1.05 1.06 1.07 1. 08 1. 09 1. 10 1.11 1. 12 1. 12 1.13 1.14 1. 15 1. 16 1.06 1.07 1. 08 1.09 1.10 1. 11 1.12 1.13 1. 14 1. 15 1. 17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1. 25 1.26

1. 14 1. 15 1. 16 1. 18 1. 19 1. 20 1. 21 1. 22 1.23 1.24 1.25 1.27 1.28 1. 29 1.30 1.31 1.32 1. 33 1. 35 1. 36

1.22 1.23 1.25 1.26 1. 27 1. 28 1.30 1. 31 1.32 1. 33 1.34 1.36 1. 37 1.38 1.39 1. 41 1.42 1.43 1.44 1. 45

1.30 1. 32 1.33 1.34 1. 36 1 37 1. 38 1.39 1. 41 1.42 1.43 1. 45 1. 46 1.47 1.49 1.50 1. 51 1.52 1.54 1.55

1. 38 1.40 1.41 1.43 1.44 1. 45 1.47 1.48 1.50 1. 51 1.52 1.54 1.55 1.56 1.58 1.69 1.61 1. 62 1.63 1.65

1. 47 1.48 1.50 1.51 1. 52 1 54 1. 55 1. 57 1.58 1.60 1.61 1. 63 1.64 1.66 1.67 1.69 1.70 1. 71 1. 73 1.74

1. 55 1. 56 1.58 1.59 1.61 1. 62 1.64 1. 66 1.67 1.69 1.70 1. 72 1. 73 1.75 1.76 1.78 1.79 1.81 1.83 1.84

1.63 1.64 1.66 1.68 1.69 1. 71 1. 73 1. 74 1. 76 1.77 1.79 1.81 1.82 1.84 1. 86 1.87 1. 89 1.90 1.92 1.94

1.71 1.73 1.74 1.76 1.78 1 79 1.81 1.83 1. 85 1.86 1.88 1.90 1.91 1.93 1.95 1.97 1.98 2. 00 2.02 2.03

1. 79 1.81 1.83 1.84 1.86 1. 88 1. 90 1.92 1.93 1.95 1. 97 1.99 2.01 2. 02 2. 04 2. 06 2.08 2. 09 2. 11 2. 13 1.87 1.89 1.91 1.93 1.95 1. 96 1.98 2. 00 2. 02 2. 04 2.06 2. 08 2. 10 2. 11 2. 13 2. 15 2. 17 2. 19 2.21 2.23

1.95 1.97 1.99 2. 01 2. 03 2. 05 2. 07 2.09 2.11 2. 13 2. 15 2. 17 2. 19 2. 21 2.23 2.25 2. 26 2.28 2. 30 2.32

2. 03 2. 05 2.07 2.09 2.11 2. 13 2. 16 2. 18 2.20 2. 22 2.24 2. 26 2.28 2. 30 2. 32 2. 34 2. 36 2.38 2.40 2. 42

2.11 2.14 2. 16 2. 18 2. 20 2. 22 2.24 2. 26 2.28 2.30 2. 33 2. 35 2. 37 2. 39 2.41 2. 43 2. 45 2. 47 2.49 2.52

2.20 2. 22 2.24 2. 26 2.28 2. 30 2. 33 2. 35 2. 37 2.39 2.41 2.44 2. 46 2. 48 2. 50 2. 52 2. 55 2. 57 2.59 2.61 2.28 2. 30 2. 32 2. 34 2.37 2. 39 2.41 2. 44 2. 46 2. 48 2. 50 2. 53 2. 55 2. 67 2.59 2. 62 2.64 2.66 2. 69 2.71

2. 36 2.38 2. 40 2. 43 2. 45 2. 47 2. 50 2. 52 2. 55 2.57 2.59 2. 62 2.64 2. 66 2.69 2. 71 2. 73 2.76 2.78 2.80

2.44 2. 46 2. 49 2. 51 2.54 2. 56 2.68 2.61 2. 63 2. 66 2. 68 2. 71 2. 73 2. 75 2. 78 2. 80 2. 83 2.86 2.88 2. 90
3132

33

34

35

36

3738

3940

4142

4344

45

46

47

4849

50

mp

ituri

= C

0

510

11

1213

14

15

1617

18

1920

212223

2425

26

27

2829

30

3132

33

3435

36

37

38

39

40

4142

43

44

45

46

4748

49

Table 6. Temperature corrections for Fortin harometer with brass scales—Contiimed

All corrections are to be subtracted from the reading.

BarorQet.er reading, millibars, inches or millimeters of mercury

500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595

2.52 2.54 2. 57 2. 59 2. 62 2 64 2 67 2 69 2. 72 2. 75 2. 77 2.80 2.82 2. 85 2. 87 2. 90 2. 92 2. 95 2.97 3.00

2.60 2.63 2.65 2. 68 2. 70 2 73 2 76 2. 78 2. 81 2 83 2.86 2.89 2. 91 2. 94 2. 96 2. 99 3.02 3. 04 3.' 07 3.09

2. 68 2- 71 2. 73 2. 76 2. 79 2 81 2 84 2. 87 2. 89 2 92 2. 95 2. 97 3.00 3. 03 3. 06 3 08 3. 11 3. 14 3. 16 3.19

2. 76 2. 79 2. 82 2. 84 2. 87 2 90 2 93 2 95 2 98 3 01 3.04 3.06 3. 09 3 12 3. 15 3. \j 3.20 3 23 3. 26 3.29

2. 84 2.87 2. 90 2. 93 2. 96 2 98 3. 01 3 04 3. 07 3 10 3. 13 3. 15 3. IS 3! 21 3 24 3! 27 3. 30 3! 32 3. 35 3.38

2.92 2.95 2.98

1. 01 3. 04 3 07 3 10 3. 13 3. 16 3. 19 3.21 3.24 3.27 3. 30 3. 33 3. 36 3. 39 3. 42 3. 45 3.48 3.00 3.03 3.06 09 3. 12 3 15 3 18 3. 21 3. 24 3. 27 3. 30 3.33 3. 36 3. 39 3. 42 3. 45 3.48 3. 51 3.54 3.57 3.08 3, 11 3. 14 3 IS 3 21 3 24 3. 27 3. 30 3. 33 3. 36 3.39 3.42 3.45 3. 48 3. 51 3. 55 3. 58 3. 61 3.64 3.67

3. 16 3. 20 3. 23 3. 26 3 29 3 32 3 35 3. 39 3. 42 3 45 3. 48 3. 51 3. 54 3. 58 3. 61 3. 64 3. 67 3. 70 3.73 3.76

3. 24 3. 28 3. 31 3 34 3. 37 3 41 3 44 3. 47 3. 50 3 54 3. 57 3. 60 3.63 3. 67 3. 70 3. 73 3. 76 3. 80 3.83 3.86

3.32 3.36 3.39 3 42 3. 46 3 49 3 52 3 56 3. 59 3 62 3.66 3.69 3.72 3. 76 3. 79 3 82 3. 86 3. 89 3. 92 3. 96

3.41 3. 11 3. 47 3 51 3. 54 3 58 3 61 3 64 3. 68 3 71 3 75 0. io 3. 81 3. 85 3. 88 3. 92 3. 95 3. 98 4. 02 4. 05 3149 3.52 3! 56 3 59 3 63 3 66 3 70 3 73 3. 76 3 80 3^83 3. 87 3.90 3. 94 3. 97 4. 01 4. 04 4. 08 4.11 4.15 3.57 3.60 3.64 3 67 3 71 3 74 3 78 3. 82 3. 85 3 89 3. 92 3.96 3.99 4. 03 4. 07 4. 10 4.14 4. 17 4.21 4.24 3.65 3.68 3.72 3 76 3. 79 3 83 3 87 3. 90 3 94 3 97 4.01 4. 05 4.08 4. 12 4.16 4. 19 4.23 4. 27 4. 30 4.34

3.73 3.76 3.80 3 84 3. 88 3 91 3 95 3 99 4.03 4.06 4.10 4.14 4.17 4. 21 4. 25 4 29 4. 32 4.36 4.40 4.44

3. 81 3.85 3.88 3 92 3 96 4 00 4.04 4. 07 4 11 4.15 4.19 4.23 4.26 4. 30 4.34 4. 38 4.42 4. 45 4.49 4.53 3.89 3.93 3.97 4.00 4.04 4 08 4 12 4.16 4.20 4.24 4.28 4.32 4. 35 4. 39 4.43 4.47 4.51 4. 55 4.59 4.63

3.97 4.01 4.05 4.09 4.13 4 17 4.21 4.25 4.29 4.33 4. 36 4.40 4.44 4.48 4. 52 4.56 4.60 4.64 4.68 4.72

4.05 4.09 4.13 4 17 4 21 4 25 4.29 4.33 4.37 4. 41 4. 45 4.49 4.53 4 57 4 61 66 4.70 4. 74 4.78 4.82

Barometer reading, millibars, inches or millimeters of mercury

600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695

0.00 0.00 0.00 0. 00 0.00 0.00 0.00 0.00 0. 00 0.00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0.00 0.00 0. 00 0.00

.49 49 50 50 .51 .51 51 52 .52 .53 53 .53 54 .54 . 55 . 55 .56 56 56 . 57 .98 99 99 1.00 1.01 1.02 1.03 1.04 1.04 1.05 1.06 1.07 1.08 1.08 1.09 1. 10 1. 11 1.12 1! 13 1. 13

1.08 1.09 1.09 1. 10 1. 11 1. 12 1. 13 1.14 1.15 1. 16 1. 17 1. 17 1. 18 1. 19 1.20 1. 21 1.22 1.23 1.24 1.25

1. 17 1. 18 1. 19 1. 20 1. 21 1.22 1.23 1.24 1.25 1.26 1. 27 1.28 1. 29 1.30 1. 31 1.32 1.33 1.34 1. 35 1.36

1.27 1.28 1. 29 1. 30 1.31 1 32 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1. 45 1. 46 1.47

1.37 1.38 1. 39 1.40 1. 41 1.43 1. 44 1. 45 1.46 1.47 1. 48 1.49 1. 51 1.52 1.53 1.54 1. 55 1.56 1. 57 1.59

1.47 1.48 1. 49 1. 50 1. 52 1. 53 1. 54 1. 55 1.56 1.58 1. 59 1.60 1. 61 1.63 1.64 1. 65 1.66 1.67 1.69 1. 70

1.56 1. 58 1.59 1.60 1.62 1.63 1.64 1. 66 1. 67 1.68 1. 69 1.71 1.72 1.73 1.75 1.76 1.77 1. 79 1.80 1.81

1.66 1. 68 1. 69 1.70 1.72 1.73 1. 74 1.76 1.77 1.79 1. 80 1.81 1.83 1.84 1.86 1.87 1.88 1.90 1. 91 1. 92

1.76 1. 77 1. 79 1.80 1.82 1.83 1.85 1. 86 1.88 1.89 1. 91 1.92 1. 93 1.95 1.96 1.98 1.99 2. 01 2. 02 2.04

1.86 1. 87 1. 89 1. 90 1.92 1.93 1. 95 1. 96 1.98 2. 00 2. 01 2. 03 2.04 2.06 2. 07 2.09 2. 10 2. 12 2. 13 2. 15 1.95 1. 97 1. 99 2.00 2. 02 2.04 2. 05 2.07 2.08 2.10 2. 12 2. 13 2. 15 2. 17 2. 18 2.20 2. 21 2.23 2.25 2. 26

2.05 2. 07 2.09 2. 10 2.12 2.14 2. 15 2. 17 2.19 2.20 2. 22 2.24 2.26 2.27 2.29 2. 31 2.32 2. 34 2.36 2.38

2.15 2. 17 2. 18 2.20 2.22 2.24 2. 26 2.27 2.29 2.31 2. 33 2.35 2.36 2.38 2.40 2.42 2.43 2. 45 2. 47 2.49 2.25 2. 26 2. 28 2.30 2. 32 2.34 2. 36 2.38 2.40 2.41 2. 43 2.45 2. 47 2. 49 2. 51 2.53 2.54 2. 56 2. 58 2.60

2.34 2. 36 2. 38 2. 40 2.42 2.44 2. 46 2. 48 2.50 2.52 2. 54 2.56 2.58 2.60 2. 62 2.64 2. 66 2. 67 2. 69 2. 71 2.44 2. 46 2. 48 2. .50 2.52 2.54 2. 56 2. 58 2.60 2.62 2. 64 2. 66 2. 68 2.70 2.72 2.74 2. 77 2. 79 2. 81 2.83

2.54 56 2. 58 2. 60 2. 62 2.64 2. 66 2. 69 2.71 2.73 2. 75 2.77 2. 79 2.81 2.83 2. 85 2.88 2. 90 2. 92 2.94

2.63 1 66 2. 68 2. 70 2. 72 2.74 2. 77 2. 79 2.81 2.83 2. 85 2.88 2. 90 2.92 2.94 2.96 2.99 3. 01 3. 03 3. 05 2.73 2. 75 2. 78 2. 80 2.82 2.85 2 87 2. 89 2. 91 2.94 2. 96 2.98 3. 00 3. 03 3. 05 3. 07 3. 10 3. 12 3 14 3. 16 2.83 2. 85 2. 88 2. 90 2.92 2.95 2. 97 2. 99 3. 02 3.04 3 06 3. 09 3. 11 3. 13 3. 16 3. 18 3. 21 3 23 3. 25 3.28 2.93 2. 95 2. 97 3. 00 3.02 3. 05 3. 07 3. 10 3. 12 3. 14 3 17 3. 19 3. 22 3.24 3.27 3.29 3. 32 3 34 3. 36 3.39

3.02 3. 05 3. 07 3. 10 3. 12 3. 15 3. 17 3. 20 3.22 3.25 3 27 3.30 3. 32 3. 35 3.37 3.40 3.43 3. 45 3. 48 3.50 3.12 3 15 3. 17 3. 20 3.22 3.25 3 28 3. 30 3.33 3.35 3 38 3. 41 3. 43 3. 46 3.48 3. 51 3.54 3 56 3. 59 3.61

3.22 3 24 3. 27 3. 30 3.32 3.35 3. 38 3. 40 3.43 3.46 3 48 3. 51 3. 54 3.56 3. 59 3. 62 3.64 3 67 3 70 3.73

3.31 3 34 3. 37 3 40 3.42 3. 45 3 48 3. 51 3.53 3.56 3 59 3.62 3. 64 3.67 3.70 3.73 3.75 3 78 3. 81 3.84

3.41 3 44 3. 47 3. 49 3.52 3. 55 3 58 3. 61 3.64 3.67 3 69 3. 72 3. 75 3.78 3.81 3.84 3.86 3 89 3. 92 3.95

3.51 3 54 3. 56 3. 59 3.62 3.65 3 68 3. 71 3.74 3.77 3 80 3.83 3. 86 3. 89 3.92 3.94 3. 97 4.00 4. 03 4.06

3.60 3 63 3. 66 3 69 3.72 3.75 3 78 3. 81 3.84 3.87 3 90 3.93 3. 96 3.99 4.02 4. 05 4.08 4 11 4. 14 4.17

3.70 3 73 3. 76 3. 79 3.82 3.85 3 88 3. 92 3. 95 3.98 4 01 4.04 4. 07 4. 10 4. 13 4. 16 4. 19 4 22 4. 25 4.29 3.80 3 83 3. 86 3 89 3.92 3. 95 3 99 4. 02 4. 05 4.08 4 11 4. 14 4. 18 4. 21 4.24 4.27 4.30 4 33 4. 37 4.40 3.89 3 93 3. 96 3. 99 4.02 4.06 4. 09 4. 12 4.15 4.19 4 22 4.25 4. 28 4.32 4. 35 4.38 4.41 4 44 4. 48 4.51

3.99 4.02 4.06 4. 09 4.12 4. 16 4.19 4.22 4.26 4.29 4 32 4.36 4. 39 4.42 4. 46 4.49 4.52 4 56 4 59 4.62

4.09 4 12 4.15 4. 19 4.22 4.26 4.29 4.32 4.36 4.39 4 43 4.46 4.50 4.53 4.56 4.60 4.63 4 67 4 70 4.73 4.18 4.22 4.25 4. 29 4.32 4.36 4.39 4.43 4.46 4.50 4.53 4. 57 4.60 4.64 4. 67 4. 71 4.74 4 78 4. 81 4.85 4.28 4.32 4.35 4 39 4.42 4.46 4.49 4.53 4.56 4.60 4.64 4. 67 4. 71 4.74 4.78 4.81 4.85 4 89 4 92 4.96 4.38 4.41 4.45 4 49 4.52 4.56 4.59 4.63 4.67 4.70 4 74 4.78 4. 81 4. 85 4.89 4.92 4.96 5 00 5. 03 5.07

4.47 4 51 4. 55 4 58 4.62 4.66 4 70 4.73 4.77 4.81 4.85 4.88 4.92 4.96 4.99 5.03 5.07 5 11 5 14 5.18 4.57 4.61 4.64 4.68 4.72 4.76 4.80 4.84 4.87 4. 91 4.95 4.99 5.03 5.06 5.10 5.14 5.18 5 22 5 25 5.29 4.67 4 70 4.74 4 78 4.82 4.86 4.90 4.94 4.98 5.02 5 05 5.09 5. 13 5. 17 5.21 5.25 5.29 5 33 5. 36 5.40

4.76 4.80 4.84 4.88 4.92 4.96 5 00 5. 04 5.08 5. 12 5 16 5.20 5. 24 5.28 5.32 5. 36 5.40 5 44 5 48 5.52

4.86 4.90 4.94 4.98 5.02 5. 06 -5. 10 5. 14 5.18 5.22 5 26 5.30 5 34 5.38 5.42 5. 47 5. 51 5 55 5 59 5.63
0

510

1112

1314

15

1617

18

1920

2122

2324

25

2627

28

2930

313233

34

35

36

37

38

39

40

4142

43

44

45

4647

48

49

50

mpi

,tur

° C

0

510

1112

13

1415

16

17

18

1920

2122

23

2425

26

27

28

29

30

Table 6. Temperature corrections for Fortin barometer with brass scales—Continued AU corrections are to be subtracted from the reading.

Barometer reading, millibars or millimeters ot mercury

700 705 710 715 720 725 730 735 740 745 750 755 760 765 770 775 780 785 790 795

0. 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0.00 0. 00

57 58 58 58 59 59 60 60 60 61 .61 .62 .62 .62 .63 .63 .64 .64 . 64 . 65

l' 14 l' 15 l' 16 1 17 1 17 1 18 1 19 1 20 1 21 1 22 1.22 1. 23 1. 24 1.25 1. 26 1.26 1. 27 1.28 1. 29 1. 30

1. 26 1 26 1 27 1 28 1 29 1 30 1 31 1 32 1 33 1 34 1.35 1.35 1. 36 1. 37 1.38 1.39 1.40 1.41 1.42 1.43

1. 37 1. 38 1. 39 1 40 1 41 1 42 1 43 1 44 1 45 1 46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56

1. 48 1. 49 1. 50 1 52 1 53 1 54 1 55 1 56 1 57 1 58 1. 59 1. 60 1. 61 1. 62 1. 63 1. 64 1. 65 1. 66 1. 67 1. 68

1. 60 1. 61 1 62 1 63 1 64 1 65 1 67 1 68 1 69 1 70 1. 71 1. 72 1. 73 1. 75 1. 76 1. 77 1. 78 1. 79 1. 80 1. 81

1. 71 1. 72 1. 74 1 75 1 76 1 77 1 78 1 80 1 81 1. 82 1. 83 1.85 1.86 1. 87 1. 88 1. 89 1. 91 1.92 1. 93 1. 94

1. 82 1. 84 1. 85 1 86 1 88 1. 89 1 90 1 92 1 93 1. 94 1. 96 1. 97 1. 98 1. 99 2, 01 2. 02 2. 03 2. 05 2. 06 2. 07

1. 94 1. 95 1 97 1 98 1 99 2. 01 2 02 2 04 2 05 2. 06 2. 08 2. 09 2. 10 2. 12 2. 13 2. 15 2. 16 2. 17 2. 19 2. 20

2. 05 2. 07 2. 08 2 10 2 11 2. 13 2 14 2 15 2 17 2. 18 2. 20 2. 21 2. 23 2. 24 2. 26 2. 27 2. 29 2. 30 2. 32 2. 33

2. 17 2 18 2 20 2 21 2 23 2, 24 2 26 2 27 2 29 2. 30 2. 32 2. 34 2. 35 2. 37 2. 38 2. 40 2. 41 2. 43 2. 44 2. 46

2. 28 2. 30 2. 31 2. 33 2 34 2. 36 2 38 2 39 2 41 2. 43 2. 44 2. 46 2.47 2.49 2. 51 2. 52 2. 54 2. 56 2. 57 2. 59

2. 39 2 41 2 43 2 44 2 46 2 48 2 50 2 51 2 53 2 55 2. 56 2. 58 2. 60 2. 62 2. 63 2. 65 2 67 2. 68 2. 70 2. 72

2. 51 2 52 2 54 2 56 2 58 2 60 2 61 2 63 2 65 2. 67 2. 69 2. 70 2. 72 2. 74 2. 76 2. 77 2. 79 2. 81 2. 83 2. 85

2. 62 2 64 2 66 2 68 2 69 2 71 2 73 2 75 2 77 2. 79 2. 81 2. 83 2.. 84 2. 86 2. 88 2. 90 2. 92 2.94 2. 96 2. 98

2. 73 2 75 2 77 2 79 2 81 2. 83 2 85 2 87 2 89 2 91 2. 93 2. 95 2. 97 2. 99 3. 01 3.03 3. 05 3. 07 3. 08 3. 10

2. 85 2 87 2 89 2 91 2 93 2. 95 2 97 2 99 3 01 3. 03 3. 05 3. 07 3. 09 3. 11 3. 13 3. 15 3. 17 3. 19 3. 21 3. 23

2. 96 2 98 3 00 3 02 3 04 3 07 3 09 3 11 3 13 3 15 3. 17 3. 19 3. 21 3. 23 3. 26 3. 28 3. 30 3. 32 3. 34 3. 36

3 07 3 10 3 12 3 14 3 16 3 18 3 20 3 23 3 25 3. 27 3. 29 3. 31 3. 34 3. 36 3. 38 3. 40 3. 42 3. 45 3. 47 3.49

3 19 3 21 3 23 3 25 3 28 3 30 3 32 3 35 3 37 3. 39 3.41 3.44 3.46 3. 48 3. 51 3. 53 3. 55 3. 57 3. 60 3. 62

3. 30 3 32 3 35 3 37 3 39 3 42 3 44 3 46 3 49 3 51 3. 54 3. 56 3. 58 3. 61 3. 63 3. 65 3. 68 3. 70 3. 72 3. 75

3 41 3 44 3 46 3 49 3 51 3 53 3 56 3 58 3 61 3. 63 3. 66 3. 68 3. 71 3.73 3. 75 3. 78 3.80 3.83 3.85 3. 88

3 53 3 55 3 58 3 60 3 63 3 65 3 68 3 70 3 73 3 75 3. 78 3.80 3. 83 3. 85 3. 88 3. 90 3. 93 3.95 3. 98 4. 00

3 64 3 66 3 69 3 72 3 74 3 77 3 79 3 82 3 85 3 87 3. 90 3. 92 3.95 3.98 4. 00 4. 03 4, 05 4. 08 4. 11 4. 13

3 75 3 78 3 81 3 83 3 86 3 89 3 91 3 94 3 97 3 99 4. 02 4. 05 4. 07 4. 10 4. 13 4. 15 4. 18 4.21 4. 23 4. 26

3 87 3 89 3 92 3 95 3 98 4. 00 4 03 4 06 4 09 4 11 4. 14 4. 17 4. 20 4.22 4. 25 4. 28 4. 31 4. 33 4. 36 4. 39

3 98 4 01 4 03 4 06 4 09 4 12 4 15 4 18 4 21 4 23 4. 26 4. 29 4. 32 4. 35 4. 38 4. 40 4.43 4. 46 4. 49 4. 52

4 09 4 12 4 15 4 18 4 21 4 24 4 27 4 30 4 32 4. 35 4. 38 4. 41 4.44 4. 47 4. 50 4. 53 4. 56 4. 59 4, 62 4. 65

4 20 4 23 4 26 4 29 4 32 4 35 4 38 4 41 4 44 4. 47 4. 60 4. 53 4. 56 4. 59 4. 62 4. 65 4. 68 4. 71 4.74 4. 77

4 32 4 35 4 38 4 41 4 44 4 47 4 50 4 53 4 56 4 59 4.62 4. 66 4.69 4. 72 4. 75 4. 78 4. 81 4. 84 4. 87 4. 90

4 43 4 46 4 49 4 52 4 56 4 59 4 62 4 65 4 68 4. 71 4. 75 4. 78 4. 81 4.84 4. 87 4. 90 4. 94 4. 97 5. 00 5. 03

4 54 4 57 4 61 4 64 4 67 4 70 4 74 4 77 4 80 4. 83 4.87 4. 90 4. 93 4. 96 5.00 5. 03 5. 06 5. 09 5. 13 5. 16

4 65 4 69 4 72 4 75 4 79 4 82 4 85 4 89 4 92 4. 95 4. 99 5. 02 5. 05 5. 09 5. 12 5.15 5. 19 5. 22 5.25 5. 29

4 77 4 80 4 84 4 87 4 90 4 94 4 97 5 01 5 04 5. 07 5. 11 5. 14 5. 18 5. 21 5. 24 5. 28 5. 31 5. 35 5. 38 5 41

4 88 4 92 4 95 4 98 5 02 5 05 5 09 5 12 5 16 5 19 5. 23 5. 26 5. 30 5. 33 5. 37 5. 40 5.44 5. 47 5. 51 5^54

4 99 5 03 5 06 5 10 5 14 5 17 5 21 5 24 5 28 5 31 5. 35 5. 39 5. 42 5. 46 5. 49 5.53 5.56 5. 60 5. 63 5.67

5 11 5 14 5 18 5 21 5 25 5 29 5 32 5 36 5 40 5 43 5. 47 5. 51 5. 54 5. 58 5. 62 5. 65 5.69 5.73 5.76 5.80

5 22 5 26 5 29 5 33 5 37 5 40 5 44 5 48 5 52 5 55 5.59 5. 63 5. 67 5.70 5.74 5. 78 5. 81 5.85 5.89 5. 93

5 33 5 37 5 41 5 44 5 48 5 52 5 56 5 60 5 63 5 67 5.71 5. 75 5. 79 5. 83 5. 86 5. 90 5. 94 5. 98 6. 02 6. 05

5 44 5 48 5 52 5 56 5 60 5 64 5 68 5 71 5 75 5 79 5. 83 5.87 5. 91 5. 95 5. 99 6. 03 6. 06 6. 10 6. 14 6. 18

5 56 5 59 5 63 5 67 5 71 5 75 5 79 5 83 5 87 5 91 5. 95 5. 99 6. 03 6.07 6. 11 6. 15 6. 19 6. 23 6. 27 6.31

6 67 5 71 5 75 5 79 5 83 6 87 5 91 5 95 5 99 6 03 6. 07 6.11 6. 15 6. 19 6. 23 6. 27 6. 32 6. 36 6.40 6. 44

Barometer reading, millibars, inches or millimeters of mercury

800 805 810 815 820 825 830 835 840 845 850 855 860 865 870 875 880 885 890 895

0. 00 0 00 0. 00 0. 00 0.00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0.00 0. 00 0. 00 0.00 0.00 0. 00 0 00 0 00

65 66 66 67 67 67 .68 68 .69 .69 69 .70 .70 .71 .71 .71 .72 72 73 73

i! 30 l' 31 1. 32 i! 33 1. 34 l' 35 1.35 l! 36 1. 37 1. 38 1. 39 1. 39 1.40 1.41 1.42 1.43 1.44 l! 44 1 45 1 46

1 44 1 44 1 45 1.46 1. 47 1. 48 1. 49 1. 50 1.51 1.52 1. 62 1. 53 1. 54 1.55 1.56 1.57 1.58 1. 59 1 60 1 61

1 57 1 57 1 58 1. 59 1.60 1. 61 1. 62 1. 63 1. 64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1. 73 1 74 1 75

1 70 1 71 1 72 1. 73 1. 74 1. 75 1.76 1. 77 1. 78 1.79 1. 80 1.81 1.82 1.83 1.84 1.85 1.86 1. 88 1 89 1 90

1 83 1 84 1 85 1. 86 1.87 1. 88 1.89 1. 91 1. 92 1. 93 1.94 1.95 1.96 1.97 1.99 2.00 2. 01 2. 02 2 03 2 04

1 96 1 97 1 98 1. 99 2.00 2. 02 2. 03 2. 04 2. 05 2.07 2. 08 2. 09 2. 10 2. 11 2. 13 2. 14 2. 15 2. 16 2 18 2 19

2 09 2 10 2 11 2. 12 2. 14 2. 15 2. 16 2. 18 2. 19 2. 20 2. 22 2. 23 2.24 2. 25 2. 27 2. 28 2.29 2. 31 2 32 2 33

2 22 2 23 2 24 2. 26 2. 27 2. 28 2. 30 2. 31 2. 33 2. 34 2. 35 2. 37 2. 38 2. 40 2. 41 2. 42 2. 44 2. 45 2 46 2 48

2 35 2 36 2 37 2. 39 2. 40 2. 42 2. 43 2. 45 2. 46 2. 48 2. 49 2. 51 2.52 2.54 2. 55 2. 57 2. 58 2. 59 2 61 2 62

2 48 2 49 2 51 2. 52 2. 54 2. 55 2. 57 2. 58 2. 60 2. 61 2. 63 2. 65 2. 66 2. 68 2.69 2. 71 2.72 2. 74 2 76 2 77

2 60 2 62 2 64 2. 65 2. 67 2. 69 2. 70 2. 72 2.74 2. 75 2. 77 2. 78 2. 80 2. 82 2. 83 2. 85 2.87 2. 88 2 90 2 91

2 73 2 75 2 77 2 79 2. 80 2. 82 2.84 2. 85 2.87 2.89 2. 91 2. 92 2. 94 2. 96 2. 97 2. 99 3.01 3. 03 3 04 3 06

2 86 2 88 2 90 2 92 2 94 2 95 2. 97 2. 99 3.01 3.03 3 04 3. 06 3. 08 3. 10 3.12 3.13 3. 15 3. 17 3 19 3 20

2 99 3 01 3 03 3 05 3 07 3 09 3. 11 3 13 3. 14 3. 16 3 18 3.20 3.22 3.24 3. 26 3.27 3. 29 3. 31 3 33 3 35

3 12 3 14 3 16 3 18 3 20 3 22 3. 24 3 26 3. 28 3.30 3. 32 3. 34 .3. 36 3. 38 3. 40 3.42 3.44 3. 46 3 48 3 49

3 25 3 27 3 29 3 31 3 33 3 35 3.38 3 40 3.42 3.44 3 46 3. 48 3. 50 3.52 3. 54 3. 56 3.58 3. 60 3 62 3 64

3 38 3 40 3 43 3 45 3 47 3 49 3. 51 3 53 3. 55 3. 57 3 59 3.62 3.64 3. 66 3. 68 3.70 3.72 3. 74 3 76 3 78

3 51 3 53 3 56 3 58 3 60 3 62 3. 64 3 67 3. 69 3.71 3 73 3. 76 3. 78 3.80 3,82 3. 84 3. 86 3. 89 3 91 3 93

3 64 3 66 3 69 3 71 3 73 3 76 3. 78 3 80 3. 82 3.85 3 87 3.89 3.91 3. 94 3.96 3. 98 4.01 4. 03 4 05 4 07

3 77 3 79 3 82 3 84 3 87 3 89 3.91 3 94 3.96 3. 98 4 01 4. 03 4.05 4. 08 4. 10 4. 12 4. 15 4. 17 4 20 4 22

3 90 3 92 3 95 3 97 4 00 4 02 4. 05 4 07 4. 10 4. 12 4 14 4. 17 4. 19 4. 22 4. 24 4, 27 4. 29 4 31 4 34 4 36
' c

3132

33

3435

36

37

38

39

40

4142

43

44

45

4647

48

49

50

mp:

,tiir(

° C

0

510

1112

13

14

15

]6

17

18

1920

2122

23

24

25

26

27

28

29

30

313233

34

35

36

37

38

39

40

4142

43

4445

46

4748

49

50

Table 6. Temperature corrections for Fortin barometer with brass scales—Continued

All corrections are to be subtracted from the reading.

Barometer reading, millibars, inches or millimeter of mercury

800 805 810 815 820 825 830 835 840 845 850 855 860 865 870 875 880 885 890 895

4. 03 4. 05 4. 08 4.11 4. 13 4. 16 4. 18 4.21 4. 23 4. 26 4. 28 4.31 4. 33 4. 36 4. 38 4.41 4. 43 4. 46 4. 48 4. 51

4. 16 4. 18 4. 21 4. 24 4. 26 4. 29 4. 31 4. 34 4. 37 4. 39 4.42 4.44 4.47 4. 50 4. 52 4. 56 4.67 4. 60 4.63 4.66

4. 29 4. 31 4. 34 4. 37 4. 40 4. 42 4. 45 4. 48 4. 50 4. 53 4.56 4. 58 4.61 4. 64 4. 66 4. 69 4. 72 4.74 4. 77 4. 80 4.42 4.44 4.47 4. 50 4. 53 4. 56 4. 58 4. 61 4. 64 4. 67 4. 69 4. 72 4. 75 4. 78 4.80 4. 83 4. 86 4, 89 4. 91 4. 94

4. 55 4. 57 4. 60 4. 63 4. 66 4. 69 4. 72 4. 75 4. 77 4. 80 4.83 4.86 4. 89 4. 92 4. 94 4. 97 6. 00 5. 03 5. 06 5. 09

4. 68 4. 70 4. 73 4.76 4. 79 4.82 4. 85 4.88 4. 91 4.94 4. 97 5. 00 5. 03 5. 06 5. 08 6. 11 5. 14 6. 17 5. 20 5. 23

4.80 4.83 4. 86 4.89 4. 92 4. 95 4. 98 5. 01 5. 04 5. 07 5. 10 5. 13 5. 16 5. 19 5. 22 6. 25 5. 28 6. 31 5. 34 5. 37 4.93 4. 96 4. 99 5. 03 5. 06 5.09 5. 12 5. 15 5. 18 5. 21 5. 24 6. 27 5. 30 5. 33 6. 36 5. 40 5. 43 6.46 5. 49 5. 52

5. 06 5. 09 5. 13 5. 16 5. 19 5. 22 5. 25 5. 28 5. 32 5. 35 5. 38 5.41 5. 44 6. 47 6. 61 6. 54 6. 57 6. 60 5. 63 5. 66

5. 19 5. 22 5. 26 5. 29 5. 32 5. 35 5. 39 5. 42 5. 45 5. 48 5. 52 5. 55 5. 58 5. 61 5. 65 6. 68 6. 71 6. 74 6. 78 5. 81

5.32 5. 35 5. 39 5.42 5. 45 5.49 5. 52 5. 55 5.59 5. 62 5. 65 5. 69 5. 72 6. 75 6. 79 6. 82 5. 85 6. 89 5. 92 5. 95

5. 45 5. 48 5.52 5. 55 5. 58 5. 62 5. 65 5. 69 5.72 5. 76 5 79 6 82 5. 86 6 89 5 93 5. 96 6 99 6. 03 6. 06 6. 10 5^58 5. 61 5. 65 5] 68 5. 72 5! 75 5^79 5^82 5. 86 5. 89 5.93 5.96 6. 00 6! 03 6'. 07 6. 10 e! 14 6. 17 6. 20 6^24

5.71 5. 74 5. 78 5. 81 5. 85 5.88 5. 92 5.96 5. 99 6. 03 6.06 6. 10 6. 13 6. 17 6. 21 6. 24 6. 28 6. 31 6. 35 6. 38

5.83 5. 87 5. 91 5.94 5. 98 6. 02 6. 05 6. 09 6. 13 6. 16 6. 20 6.24 6. 27 6.31 6. 35 6.38 6. 42 6. 45 6. 49 6. 53

5. 96 6. 00 6. 04 6. 08 6. 11 6. 15 6. 19 6. 22 6. 26 6. 30 6. 34 6. 37 6. 41 6. 45 6.49 6. 62 6.56 6. 60 6. 63 6. 67

6. 09 6. 13 6. 17 6.21 6.24 6. 28 6. 32 6. 36 6. 40 6. 43 6.47 6. 51 6. 55 6.59 6. 62 6. 66 6.70 6. 74 6. 78 6.82

6.22 6. 26 6. 30 6. 34 6. 38 6.41 6. 45 6. 49 6. 53 6. 57 6. 61 6. 65 6. 69 6. 73 6.76 6. 80 6.84 6. 88 6. 92 6. 96

6. 35 6. 39 6. 43 6. 47 6. 51 6. 55 6.59 6. 63 6. 67 6. 71 6. 75 6. 79 6.82 6.86 6. 90 6. 94 6. 98 7. 02 7. 06 7. 10

6. 48 6.52 6. 56 6. 60 6.64 6. 68 6. 72 6. 76 6.80 6. 84 6.88 6. 92 6. 96 7. 00 7. 04 7. 08 7. 12 7. 17 7. 21 7. 25

Barometer reading, millibars, inches or millimeters of mercury

900 905 910 915 920 925 930 935 940 945 950 955 960 965 970 976 980 985 990 996

0. CO 0. CO 0.00 0.00 0.00 0. 00 0. 00 0. 00 0.00 0. 00 0.00 0. 00 0.00 O.CO 0 CO 0. 00 0. 00 0. 00 0. 00 0. 00

.73 74 74 .75 75 .75 .76 .76 77 77 .78 .78 78 .79 .79 80 .80 80 81 .81 1.47 1.48 1.48 1.49 1! 50 1.51 1.52 1.53 1! 53 1.54 1.65 1.56 1.57 1.57 1.68 1.69 1.60 1.61 1! 61 1. 62

1. 61 1. 62 1. 63 1. 64 1.65 1. 66 1. 67 1. 68 1. 69 1.70 1.70 1. 71 1.72 1. 73 1. 74 1.75 1.76 1.77 1. 78 1.78

l! 76 1.77 1. 78 l!79 1. 80 1. 81 1.82 l!83 1. 84 1. 85 1.87 1. 88 1. 89 1^90 1. 91 1.92 1. 93 1. 94 1.95

l! 91 1.92 1.93 1*94 1.95 1.96 1! 98 1. 99 2. 00 2. 01 2.02 2. 03 2. 05 2. 06 2. 07 2.08 2. 09 2 10 2. 11

2. 05 2. 07 2.08 2! 09 2. 10 2^11 2! 12 2! 13 2. 14 2.16 2^17 2. 18 2. 19 2. 20 2. 21 2. 22 2. 24 2. 25 2. 26 2. 27

2. 20 2. 21 2. 22 2. 24 2. 25 2.26 2.27 2.29 2. 30 2. 31 2.32 2. 33 2. 35 2.36 2. 37 2. 38 2. 40 2. 41 2.42 2. 43

2. 35 2. 36 2. 37 2. 39 2. 40 2.41 2.42 2.44 2. 45 2. 46 2. 48 2.49 2. 50 2. 52 2.53 2. 64 2. 55 2. 57 2. 58 2. 59 2.49 2. 51 2. 52 2. 53 2. 55 2. 56 2.58 2.59 2. 60 2.62 2. 63 2.64 2. 66 2.67 2.69 2. 70 2. 71 2. 73 2 74 2. 76 2.64 2. 65 2.67 2.68 2. 70 2. 71 2. 73 2. 74 2. 76 2. 77 2. 79 2.80 2.81 2. 83 2. 84 2. 86 2. 87 2. 89 2 90 2.92 2.78 2. 80 2. 82 2.83 2. 85 2. 86 2. 88 2. 89 2. 91 2 92 2. 94 2. 95 2. 97 2. 99 3. 00 3. 02 3.03 3. 05 3 06 3. 08

2. 93 2. 95 2. 96 2. 98 3.00 3. 01 3.03 3. 04 3. 06 3 08 3. 09 3.11 3 13 3.14 3. 16 3. 17 3.19 3. 21 3 22 3.24

3.08 3 09 3.11 3.13 3. 14 3.16 3.18 3. 20 3 21 3 23 3.25 3.26 3 28 3. 30 3. 32 3. 33 3.35 3. 37 3 38 3.40

3. 22 3 24 3. 26 3.28 3.29 3. 31 3.33 3. 35 3 37 3 38 3. 40 3.42 3 44 3.46 3. 47 3. 49 3. 51 3. 53 3 54 3. 56 3.37 3 39 3 41 3.42 3 44 3. 46 3. 48 3.60 3 52 3 54 3. 56 3.57 3 59 3. 61 3.63 3. 66 3. 67 3 69 3 71 3. 72

3. 51 3 53 3 55 3. 57 3. 59 3. 61 3. 63 3. 65 3 67 3 69 3. 71 3. 73 3 76 3. 77 3. 79 3 81 3. 83 3 86 3 87 3.89

3. 66 3 68 3 70 3. 72 3. 74 3. 76 3.78 3.80 3 82 3 84 3.86 3.88 3 90 3.92 3. 94 3 96 3. 99 4 01 4 03 4. 05

3.81 3 83 3 85 3.87 3. 89 3. 91 3.93 3. 95 3 97 4 CO 4. 02 4. 04 4 06 4. 08 4.10 4 12 4. 14 4 16 4 19 4.21

3. 95 3 97 4 00 4.02 4 04 4.06 4.08 4.10 4 13 4 15 4.17 4.19 4 21 4. 24 4.26 4 28 4. 30 4 32 4 35 4. 37

4.10 4 12 4 14 4.17 4 19 4. 21 4.23 4. 26 4 28 4 30 4.32 4. 35 4 37 4. 39 4. 42 4 44 4. 46 4 48 4 51 4.53

4. 24 4 27 4 29 4. 31 4 34 4. 36 4. 38 4. 41 4 43 4 45 4.48 4.50 4 53 4. 65 4. 57 4 60 4.62 4 64 4 67 4.69

4. 85 4. 39 4 41 4 44 4. 46 4 49 4. 51 4.53 4.56 4 58 4 61 4. 63 4. 66 4 68 4.70 4. 73 4 76 4. 78 4 80 4 83

4.53 4 56 4 58 4. 61 4 63 4.66 4.68 4. 71 4 73 4 76 4.79 4. 81 4 84 4.86 4.89 4 91 4.94 4 96 4 99

15

5. 01 4.68 4 70 4 73 4. 76 4 78 4.81 4.83 4. 86 4 89 4 91 4. 94 4. 96 4 99 5. 02 5.04 5 07 6. 09 5 12 6 5.17 4.82 4 85 4 88 4. 90 4 93 4. 96 4. 98 5. 01 5 04 5 07 5.09 5.12 5 16 5.17 5. 20 5 23 6. 25 5 28 5 31 6. 33

4.97 5 00 5 02 5.05 5 08 5.11 5.13 5.16 5 19 5 22 5. 25 5. 27 5 30 5. 33 5. 36 5 38 5.41 5 44 5 47 5.49

5.11 5 14 5 17 5.20 5 23 5. 26 5. 29 5. 31 5 34 5 37 5.40 5. 43 5 46 6. 48 5. 51 5 54 5. 57 5 60 5 63 5. 65

5. 26 5 29 5 32 5. 35 5 38 5. 41 5.44 5. 46 5 49 5 52 5. 55 5.58 5 61 5.64 5. 67 5 70 6. 73 5 76 6 79 5.81

5. 40 5 43 5 46 5. 49 5 52 5. 55 5.59 5.62 5 65 5 68 6. 71 5.74 5 77 5.80 5. 83 5 86 6.89 5 92 6 95 6.98

5. 55 5 58 5 61 5.64 5 67 5. 70 5. 73 5. 77 5 80 5 83 6.86 5. 89 5 92 6. 95 5.98 6 01 6,04 6 07 6 10 6.14 5.69 5 73 5 76 5. 79 5 82 5. 85 6. 88 5.92 5 95 5 98 6. 01 6. 04 6 07 6.11 6.14 6 17 6.20 6 23 6 26 6. 30

5.84 5 87 5 90 5. 94 5 97 6. 00 6. 03 6.07 6 10 6 13 6.16 6.20 6 23 6. 26 6. 29 6 33 6. 36 6 39 6 42 6. 46

5. 98 6 02 6 05 6. 08 6 12 6.15 6. 18 6.22 6 25 6 28 6. 32 6. 35 6 38 6.42 6.45 6 48 6.52 6 65 6 68 6. 62 6.13 6 16 6 20 6.23 6 27 6. 30 6. 33 6. 37 6 40 6 44 6. 47 6.50 6 64 6.57 6. 61 6 64 6. 67 6 71 6 74 6. 78 6.27 6 31 6 34 6.38 6 41 6. 45 6. 48 6.52 6 55 6 59 6. 62 6. 66 6 69 6. 73 6. 76 6 80 6. 83 6 87 6 90 6. 94 6.42 6 45 6 49 6.53 6 56 6.60 6.63 6. 67 6 70 6 74 6. 78 6. 81 6 85 6. 88 6.92 6 96 6. 99 7 03 7 06 7.10

6. 56 6 60 6 64 6. 67 6 71 6. 75 6.78 6.82 6 86 6 89 6.93 6. 97 7 00 7. 04 7. 07 7 11 7.15 7. 18 7 22 7. 26

6. 71 6 75896 78 6.82 6 86 6.90 6.93 6. 97 7 01 7 04 7.08 7.12 7 16 7.19 7. 23 7 27 7. 31 7 34 7 38 7.42

6.85 6 6 93

08 6.97 01 7. 04 7.08 7. 12 7 16 7 20 7.23 7.27 7 31 7. 36 7. 39 7 42 7. 46 7 60 7 54 7. 68 7.00 7 04 7 7.11 7 15 7.19 7. 23 7. 27 7 31 7 35 7. 39 7. 43 7 46 7. 60 7.64 7 68 7.62 7 66 7 70 7. 74

7.14 18 7 22 7. 26 30 7. 34 7.38 7. 42 7 46 7 50 7.54 7.58 7 62 7.66 7. 70 74 7.78 7 82 7 86

02 7.90

7.29 7 33 37 7. 41 7 45 7. 49 7, 53 7.57 7 61 7 65 7.69 7. 73 7 77 7. 81 7. 85 89 7. 93 7 97 8 8.06
0

510

1112

13

14

15

16

17

18

1920

2122

23

24

25

2627

28

29

30

3132

33

34

35

36

37

38

39

40

4142

4344

45

4647

48

49

50

mp

tur

"C

0

510

111213

14

15

1617

18

1920

2122

23

2425

2627

28

29

30

3132

3334

35

Table 6. Temperature corrections for Fortin barometer with brass scales—Continued

All corrections are to be subtracted from the reading.

Barometer reading, millibars, inches or miUimeters of mercm-y

1,000 1,005 1,010 1,015 1,020 1,025 1,030 1,035 1,040 1,045 1,050 1,055 1,060 1,065 1,070 1,075 1,080 1,085 1,090 1,095

0. 00 0 00 0 00 0 00 0.00 0 00 0 00 0 00 0 00 0.00 0 00 0.00 0.00 0. 00 0.00 0.00 0.00 0 00 0.00 0. 00

. 82 82 82 83 . 83 84 84 84 85 .85 86 . 86 . 86 .87 . 87 .88 .88 89 .89 .89

1. 63 1 64 1 65 1 66 1. 66 1 67 1 68 1 69 1 70 1.70 1 71 1.72 1.73 1.74 1.75 1.75 1.76 1 77 1. 78 1. 79

1.79 1 80 1 81 1 82 1.83 1 84 1 85 1 86 1 87 1.87 1 88 1.89 1.90 1.91 1.92 1.93 1.94 1 95 1.96 1.96

1.96 1 97 1 98 1 99 2. 00 2 01 2 02 2 03 2 03 2. 04 2 05 2. 06 2. 07 2.08 2.09 2. 10 2.11 2 12 2.13 2.14

2. 12 2 13 2 14 2 15 2. 16 2 17 2 18 2 19 2 20 2. 21 2 23 2. 24 2.25 2.26 2. 27 2. 28 2. 29 2 30 2.31 2.32

2. 28 2 29 2 30 2 32 2. -33 2 34 2 35 2 36 2 37 2. 38 2 40 2. 41 2. 42 2.43 2. 44 2. 45 2. 46 2 48 2. 49 2. 60

2. 44 2 46 2 47 2 48 2. 49 2 51 2 52 2 53 2 54 2. 55 2 57 2. 58 2.59 2. 60 2. 62 2.63 2.64 2 65 2. 66 2. 68

2. 61 2 62 2 63 2 65 2.66 2. 67 2. 69 2 70 2 71 2. 72 2 74 2. 75 2. 76 2. 78 2. 79 2.80 2.82 2 83 2.84 2. 85

2. 77 2 78 2 80 2 81 2. 82 2 84 2 85 2 87 2 88 2.89 2 91 2.92 2.94 2. 95 2. 96 2. 98 2. 99 3 00 3. 02 3.03

2. 93 2 95 2 96 2 98 2. 99 3 00 3 02 3 03 3 05 3. 06 3 08 3. 09 3. 11 3. 12 3. 14 3. 15 3. 17 3 18 3. 20 3. 21

3. 09 3 \l 3 12 3 14 3. 16 3 17 3 19 3 20 3 22 3.23 3 25 3. 26 3.28 3. 30 3. 31 3. 33 3. 34 3 36 3. 37 3. 39

3. 26 3 27 3 29 3 31 3. 32 3 34 3 35 3 37 3 39 3.40 3 42 3.44 3. 45 3.47 3. 48 3.50 3. 52 3 53 3. 55 3. 57

3. 42 3 44 3 45 3 47 3. 49 3 50 3 52 3 54 3 56 3. 57 3 59 3. 61 3.62 3.64 3.66 3. 67 3.69 3 71 3. 73 3. 74 3.58 3 60 3 62 3 63 3. 65 3 67 3 69 3 71 3 72 3. 74 3 76 3. 78 3. 80 3. 81 3. 83 3. 85 3.87 3 88 3.90 3. 92

3. 74 3 76 3 78 3 80 3. 82 3 84 3 85 3. 87 3 89 3. 91 3 93 3. 95 3. 97 3. 99 4.00 4. 02 4.04 4 06 4.08 4. 10

3. 90 3 92 3 94 3 96 3. 98 4 00 4 02 4 04 4 06 4.08 10 4. 12 4. 14 4. 16 4. 18 4.20 4. 22 4 24 4.26 4.28

4. 07 4 09 4 11 4 13 4. 15 4. 17 4 19 4 21 4 23 4.25 4 27 4. 29 4. 31 4. 33 4. 35 4. 37 4. 39 4 41 4.43 4. 45

4. 23 4 25 4 27 4 29 4. 31 4 33 4 36 4 38 4 40 4. 42 4 44 4. 46 4. 48 4.50 4.52 4. 55 4. 57 4 59 4. 61 4.63

4. 39 4 41 4 43 4 46 4. 48 4 50 4 52 4 54 4 57 4. 59 4 61 4.63 4.65 4.68 4.70 4.72 4. 74 4 76 4. 79 4. 81

4. 55 4 57 4 60 4 62 4. 64 4 67 4 69 4 71 4 73 4. 76 4 78 4. 80 4. 83 4. 85 4. 87 4. 89 4. 92 4 94 4. 96 4.98

4. 71 4 74 4 76 4 78 4.81 4 83 4 86 4 88 4 90 4. 93 4 95 4. 97 5.00 5.02 5.04 5. 07 5. 09 11 5. 14 5. 16

4. 88 4 90 4 92 4 95 4. 97 5 00 5 02 5 05 5 07 5.09 5 12 5. 14 5. 17 5. 19 5.22 5. 24 5.27 5 29 5. 31 5. 34

5. 04 5 06 5 09 5 11 5.14 5 16 5 19 5 21 5. 24 5. 26 5. 29 5. 31 5. 34 5. 36 5. 39 5. 41 5. 44 5 47 5.49 5.52 5.20 5 22 5 25 5 28 5.30 5 33 5 35 5 38 5 41 5. 43 5 46 5.48 5. 51 5. 54 5.56 5. 59 5. 61 5 64 5.67 5.69

5. 36 5 39 5 41 5 44 5. 47 5 49 5 52 5 55 5 57 5.60 5 63 5. 65 5.68 5. 71 5. 74 5. 76 5. 79 5 82 5. 84 5.87

5. 52 5 55 5 58 5 60 5. 63 66 69 71 74 5. 77 80 5. 83 5. 85 5.88 5. 91 5. 94 5. 96 5 99 6.02 6. 05

5. 68 5 71 5 74 5 77 5. 80 5 82 5 85 5. 88 5 91 5. 94 5 97 6.00 6.02 6. 05 6. 08 6.11 6.14 6 17 6. 19 6. 22

5. 84 5 87 5 90 5 93 5. 96 5 99 6 02 6 05 6 08 6. 11 6 14 6. 17 6. 19 6. 22 6. 25 6.28 6. 31 6 34 6.37 6.40

6.01 6 04 6 07 6 10 6.13 6 16 6 19 6 22 6 25 6. 28 6 31 6. 34 6. 37 6. 40 6. 43 6. 46 6.49 6 52 6.65 6.68

6. 17 6 20 6 23 6 26 6. 29 6 32 6 35 6 38 6 41 6. 44 6 47 6. 51 6. 54 6. 57 6. 60 6. 63 6. 66 6 69 6. 72 6. 75

6. 33 6 36 6 39 6 42 6. 45 6 49 6 52 6 55 6 58 6. 61 6 64 6. 68 6. 71 6. 74 6. 77 6.80 6.83 6 87 6. 90 6.93

6. 49 6 52 6 55 6 59 6.62 6 65 6 68 6 72 6 75 6.78 6 81 6. 85 6.88 6. 91 6.94 6.98 7. 01 7 04 7. 07 7. 11

6. 65 6 68 6 72 6 75 6. 78 6 82 6 85 6 88 6 92 6. 95 6 98 7.02 7. 05 7.08 7. 12 7.15 7.18 7 22 7.25 7.28

6. 81 6 84 6 88 6 91 6. 95 6 98 7 02 7 05 7 08 7. 12 7 15 7. 19 7.22 7. 25 7. 29 7.32 7.36 7 39 7. 42 7. 46

6. 97 7 01 7 04 7 08 7. 11 7 15 7 18 7 22 7 25 7.29 7 32 7. 36 7.39 7. 42 7. 46 7. 49 7. 53 7 56 7.60 7.63

7.13 7 17 7 20 24 7. 28 7 31 7 35 7 38 7 42 7. 45 7 49 7.52 7. 56 7.60 7.63 7. 67 7.70 7 74 7. 77 7.81

7. 29 7 33 7 37 7 40 7.44 7 48 7 51 7 55 7 59 7.62 7. 66 7. 69 7.73 7. 77 7.80 7. 84 7. 88 7 91 7. 95 7.99

7.45 7 49 7 53 7 57 7.60 7 64 7 68 7 71 7 75 7.79 7 83 7. 86 7. 90 7. 94 7. 98 8.01 8. 05 8 09 8.12 8.16

7. 61 7 65 7 69 73 7. 77 7 81 7 84 7 88 7 92 7.96 8 00 8.03 8. 07 8.11 8. 15 8.19 8. 22 8 26 8. 30 8.34

7. 78 7 81 7 85 7 89 7. 93 7 97 8 01 8 05 8 09 8. 13 8 16 8.20 8. 24 8.28 8. 32 8. 36 8.40 8 44 8. 48 8. 51

7. 94 7 98 8 02 8 05 8. 09 8 13 8 17 8 21 8 25 8. 29 8 33 8. 37 8.41 8. 45 8.49 8. 53 8. 57 8 61 8. 65 8.69

8.10 8 14 8 18 8 22 8.26 8 30 8 34 8 38 8 42 8. 46 8. 50 8. 54 8.58 8.62 8.66 8.70 8.74 8 78 8.83 8.87

Barometer reading, millibars, inches or millimeters of mercury

1,100 1,105 1,110 1,115 1,120 1,125 1,130 1,135 1,140 1,145 1,150 1,155 1,160 1,165 1,170 1,175 1,180 1,185 1,190 1,195

0 00 0.00 0 00 0 00 0 00 0 00 0 00 0.00 0. 00 0. 00 0. 00 0.00 0. 00 0. 00 0 00 0 00 0. 00 0 00 0 00 0 00

90 90 91 91 91 92 92 .93 .93 93 .94 .94 95 .95 95 96 .96 97 97 98

1 79 1. 80 1 81 1 82 1 83 1 84 1 84 1.85 1.86 1.87 1.88 1.88 L 89 1.90 1 91 1 92 1.92 1 93 1 94 1 95

1 97 1 98 1 99 2 00 2 01 2 02 2 03 2. 04 2. 04 2 05 2. 06 2. 07 2 08 2.09 2 10 2 11 2. 12 2 13 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2. 22 2. 23 2. 24 2. 25 2.26 2. 27 2. 28 2 29 2 30 2. 31 2 32 2 33 2 34

2. 33 2. 34 2 35 2 36 2 37 2 38 2 39 2. 41 2. 42 2.43 2. 44 2. 45 2. 46 2. 47 2 48 2 49 2. 50 2 51 2 52 2 53

2. 51 2. 52 2 53 2 54 2 56 2 57 2 58 2.59 2.60 2. 61 2.62 2.64 2. 65 2. 66 2 67 2 68 2.69 2 70 2 72 2 73

2. 69 2. 70 2 71 2 73 2 74 2 75 2 76 2. 77 2.79 2. 80 2.81 2. 82 2. 84 2. 85 2 86 2 87 2.88 2 90 2 91 2 92

2 87 2. 88 2 89 2 91 2 92 2 93 2 95 2. 96 2. 97 2.98 3. 00 3. 01 3. 02 3. 04 3 05 3 06 3.08 3 09 3 10 3 12

3. 05 3. 06 3 07 3 09 3 10 3 12 3 13 3. 14 3. 16 3. 17 3. 18 3. 20 3. 21 3. 23 3 24 3 25 3.27 3 28 3 30 3 31

3. 22 3. 24 3 25 3 27 3 18 3 30 3 31 3. 33 3. 34 3. 36 3. 37 3. 39 3. 40 3. 42 3 43 3 44 3.46 3 47 3 49 3 50 3 40 3. 42 3 43 3 45 3 47 3 48 3 50 3. 51 3.53 3. 54 3.56 3. 57 3. 59 3.60 3 62 3 64 3. 65 3 67 3 68 3 70

3 58 3. 60 3 61 3 63 3 65 3 66 3 68 3. 70 3. 71 3.73 3.74 3.76 3. 78 3.79 3 81 3 83 3. 84 3 86 3 87 3 89

3. 76 3. 78 3 79 3 81 3 83 3 85 3 86 3.88 3. 90 3 91 3.93 3. 95 3. 97 3.98 4 00 4 02 4.03 4 05 4 07 4 08

3 94 3 96 3 97 3 99 4 01 4 03 4 05 4. 06 4,08 4 10 4. 12 4. 14 4. 15 4.17 4 19 4 21 4. 22 4 24 4 26 4 28

4 12 4 14 4 15 4 17 4 19 4 21 4 23 4. 25 4. 27 4 29 4.30 4.32 4. 34 4. 36 4 38 4 40 4.42 4 43 4 45 4 47

4 30 4 31 4 33 4 35 4 37 4 39 4 41 4. 43 4. 45 4 47 4.49 4. 51 4. 53 4. 55 4 57 4 59 4. 61 4 63 4 65 4 67

4 47 4 49 4 51 4 53 4 55 4 57 4 60 4.62 4.64 4 66 4.68 4. 70 4. 72 4.74 4 76 4 78 4.80 4 82 4 84 4 86

4 65 4 67 4 69 4 71 4 74 4 76 4 78 4.80 4.82 4 84 4. 86 4. 88 4. 90 4. 93 4 95 4 97 4.99 5 01 5 03 5 05

4 83 4 85 4 87 4 90 4 92 4 94 4 96 4.98 5.00 5 03 5. 05 5. 07 5 09 .5. 11 5 14 5 16 5. 18 5 20 5 22 5 25

5 01 5 03 5 05 5 08 5 10 5 12 5 14 5.17 5. 19 5 21 5.23 5. 26 5 28 5.30 5 33 5 35 5. 37 5 39 5 42 5 44

5 19 5 21 5 23 5 26 5 28 5 30 5 33 5. 35 5. 37 5 40 5.42 5.44 5 47 5.49 5 52 5 54 5. 56 5 59 5 61 5 63

5 36 5 39 5 41 5 44 5 46 5 48 5 51 5.53 5.56 5 58 5. 61 5.63 5 66 5.68 5 70 5 73 5.75 5 78 5 80 5 83

5 54 5 57 5 59 5 62 5 64 5 67 5 69 5. 72 5.74 5 77 5.79 5.82 5 84 5. 87 5 89 5 92 5.94 5 97 5 99 6 02

5 72 5 74 5 77 5 80 5 82 5 85 5 87 5. 90 5. 93 5 95 5. 98 6. 00 6 03 6.06 6 08 6 11 6. 13 6 16 6 19 6 21 5 90 5 92 5 95 5 98 6 00 6 03 6 06 6.08 6. 11 6 14 6. 16 6, 19 6 22 6.24 6 27 6 30 6.32 6 35 6 38 6 41 6 07 6 10 6 13 6 16 6 18 6 21 6 24 6. 27 6. 29 6 32 6. 35 6. 38 6 40 6. 43 6 46 6 49 6.52 6 54 6 57 6 60

6 25 6 28 6 31 6 34 6 36 6 39 6 42 6. 45 6. 48 6 51 6.54 6.56 6 59 6.62 6 65 6 68 6. 71 6 73 6 76 6 79
Table 6. Temperature corrections for Fortin barometer with brass scales—Continued AU corrections are to be substracted from the reading.

I Barometer reading, millibars, inches or millimeters of mercury Temper- 1 atiire 1,100 1,105 1,110 1,115 1,120 1,125 1,130 1,135 1,140 1,145 1,150 1,155 1,160 1,165 1,170 1,175 1,180 1,185 1,190 1,195

" C

36 6. 43 6. 46 D. -ay D. 6. 55 D. 0/ ft RH 6. 63 6. 66 6. 69 6. 72 6. 75 6. 78 6. 81 6. 84 6. 87 6. 90 6. 93 6. 95 6. 98 37 6.61 6.64 6. 67 6.70 6.73 6.76 6.79 6.82 6. 85 6.88 6.91 6.94 6. 97 7.00 7.03 7.06 7.09 7. 12 7. 15 7. 18 3S 6.78 6.81 6.84 6.88 6. 91 6.94 6. 97 7.00 7.03 7.06 7.09 7. 12 7. 15 7.18 7.21 7.25 7.28 7. 31 7.34 7.37 39 6.96 6.99 7.02 7.06 7.09 7.12 7. 15 7. 18 7.21 7.25 7.28 7. 31 7. 34 7.37 7.40 7.44 7.47 7.50 7.53 7. 56 40 7.14 7.17 7.20 7.24 7.27 7.30 7.33 7.36 7.40 7.43 7.46 7.49 7.53 7.56 7.59 7.62 7.66 7.69 7.72 7. 75

41 7.31 7.35 7.38 7.41 7.45 7.48 7.51 7. 55 7.58 7.61 7.65 7.68 7.71 7.75 7.78 7.81 7.85 7.88 7. 91 7.95 42 7.49 7.53 7. 56 7. 59 7.63 7. 66 7. 70 7. 73 7. 76 7. 80 7. 83 7.87 7. 90 7.93 7.97 8.00 8.04 8. 07 8. 10 8. 14

43 7.67 7.70 7.74 7.77 7.81 7.84 7.88 7.91 7.95 7.98 8.02 8. 05 8.09 8.12 8.16 8. 19 8.23 8. 26 8.30 8.33 44 7.85 7.88 7.92 7.95 8.99 8.02 8.06 8. 10 8. 13 8.17 8.20 8.24 8. 27 8.31 8. 35 8.38 8.42 8. 45 8.49 8.52

45 8.02 8.06 8. 10 8. 13 8. 17 8.20 8.24 8.28 8.31 8. 35 8. 39 8.42 8. 46 8.50 8.53 8. 57 8. 61 8.64 8.68 8.72

46 8.20 8.24 8.27 8. 31 8. 35 8.39 8.42 8.46 8.50 8.53 8. 57 8. 61 8. 65 8.68 8.72 8.76 8. 80 8.83 8. 87 8. 91 47 8.38 8.41 8.45 8.49 8.53 8. 57 8.60 8.64 8.68 8.72 8.76 8.79 8.83 8. 87 8. 91 8. 95 8. 99 9.02 9.06 9. 10 48 8.55 8.59 8.63 8. 67 8.71 8. 75 8.79 8.83 8.86 8.90 8. 94 8.98 9.02 9. 06 9.10 9. 14 9.17 9. 21 9. 25 9.29

49 8.73 8.77 8.81 8.85 8.89 8.93 8. 97 9. 01 9. 05 9.09 9. 13 9.17 9. 21 9. 25 9.29 9. 32 9. 36 9.40 9.44 9.48

50 8. 91 8. 95 8.99 9.03 9. 07 9.11 9. 15 9. 19 9.23 9. 27 9. 31 9. 35 9. 39 9. 43 9. 47 9. 51 9. 55 9. 59 9.63 9.68

Table 7. Temperature Correction factor Xumbers under scale material are values of expansion coefficient s, all of which must be

multiplied by 10-=

l+wii

Factor F (minus sign omitted) in percent

Temperature Aluminum Brass Stainless Steel Pvrex Invar

24.5 18.4 steel 17 n.5 3.0 0

" C °F

0 32.0 0 0 0 0 0 0 2 35.6 0. 0314 0.03267 0.0329 0.0340 0. 0357 0.03635 4 39.2 .0629 .06531 .0659 .0681 .0715 . 07267

6 42.8 .0943 .09793 .0988 .1021 .1072 .10896 8 46.4 .1257 .13053 .1316 .1360 .1428 .14523

10 50.0 .1570 .16310 .1645 .1700 .1785 . 18147

12 53.6 .1883 .19565 .1973 .2039 .2141 .21768

14 57.2 .2197 .22818 .2301 .2378 .2497 .25387

16 60.8 .2510 .26068 .2629 .2717 .2853 .29004

18 64.4 .2822 .29316 .2955 .3055 .3208 . 32617 20 68.0 .3135 .32562 .3284 .3394 .3563 .36228

22 71-6 .3447 .35805 .3611 .3732 .3918 .39837 24 75.2 .3759 .39046 .3938 .4069 .4273 .43442 28 78.8 .4071 .42284 .4265 .4407 .4627 .47046 28 82.4 .4382 .45520 .4591 .4744 .4981 .50646 30 86.0 .4693 .48754 .4917 .5081 .5335 .54244

32 89.6 .5004 . 51986 .5243 .5418 .5689 .57840 34 93.2 .5315 . 55215 .5569 . 5755 .6042 . 61432 36 96.8 .5626 .58442 .5894 .6091 .6395 .65022 38 100.4 .5936 .61666 .6219 .6427 .6748 .68610 40 104.0 .6247 .64888 .6544 .6763 .7100 . 72195

42 107.6 .6557 .68108 .6869 .7098 .7453 . 75778 44 111.2 .6866 .71325 .7194 .7434 .7805 . 79357 46 114.8 .7176 .74541 .7518 .7769 .8157 .82934

48 118.4 .7485 .77744 .7842 .8104 .8508 .86509 50 112.0 .7794 .80964 .8166 .8438 .8859 .90081

55
Table 8. Gravity correction

C^^ij^gMl^F.R, or F,R.

Correction for height of mercury column R, or Ri in any unit of pressure

Gravity

cm/sec^ 978.0

.1.2.3

.4.5

.6

.7

979.0

.1.2.3

.4

.5

980.0

.12!3.4

.5.6

.665

981.0

.1.2.3

.4

.5

.6

.7

982.0

. 1 .2.3

.4

.5

.6

983.0

.1.2

.3.4

.5

Correction

factor Fg %

-0. 27175

. 26156

.25136 .24116

. 23097

. 22077

. 21057

. 20037

.19018

. 17998

. 16978

. 15959

. 14939 .13919

. 12899

. 11880

. 10860

. 08821

. 07801

. 06781

. 05761 .04742

. 03722

. 02702

. 01682

. 00663

0+. 00357

.01377

. 02396

. 03416

. 04436

. 05455

.06475

. 07495

.08515

. 09534

. 10554

. 11574

. 12593

. 13613

. 14633

. 15653

.16672

. 17692 .18712

. 19732

. 20751

.21771

. 22791

. 23810

. 24830

. 25850

. 26870

. 27889

. 28909

100

-0. 272 -.262

-.251

-.241

-.231

-.221

-.211 -.200

-.190

-.180

-.170

-.160

-.149

-.139

-.129

-.119

-.109 -.098

-.088

-.078

-.058

-.047

-.037 -.027

-.017 -.007

0+. 004 +.014

+.024

+.034

+.044 +.055

+.065

+.075 +. 085 +.095 +. 106 +.116 +. 126 +. 136 +. 146 +.157

+.167 +.177

+.187

+.197 +.208

+.218

+.228

+.238

+.248 +.258

+.269

+. 279 +.289

200

-0. 544 -.523

-.503

-.482

-.462 -.442

-.421

-.401 -.380

-.360

-.340

-.319

-.299

-.278

-.258

-.238

-.217

-.197

-.176 -.156

-.136

-.115

-.095

-.074

-.054 -.034

-.013

0+.007 +.028

+. 048 +. 068 +.089

+.109 +. 130 +.150

+.170

+.191 +.211

+.231 +.252

+.272

+.293

+.313 +. 333 +.364

+. 374 +.395

+.415

+.435

+.456 +.476

+.497

+.517 +. 537 +.558

+. 578

oOO 400 500 600 700 800 900 1,000 1,100 1,200 1,300

—0. 815 —1. 087 —1. 359 —1. 631 —1. 902 —2. 174 —2. 446 —2. 718 -2. 989 -3. 261 -3. 533 —. 785 —1. 046 —1. 308 — 1. 569 — 1. 831 —2. 092 —2. 354 —2. 616 -2. 877 -3. 139 -3.400 —. 754 —1. 005 —1. 257 —1. 508 —1. 760 —2. Oil —2. 262 -2. 514 -2. 765 -3. 016 -3. 268 —. 724 —0. 965 —1. 206 — 1. 447 —1. 688 —1. 929 —2. 170 —2. 412 -2. 653 -2. 894 -3. 135 —. 693 —. 924 —1. 155 —1. 386 —1. 617 —1. 848 —2. 079 —2.310 -2. 541 -2. 772 -3. 003 —. 662 —. 883 —1. 104 —1. 325 —1. 545 —1. 766 —1.987 -2. 208 -2.428 -2. 649 -2. 870 —. uo^ —. 842 —1. 053 —1. 263 —1. 474 —1. 685 —1.895 —2. 106 -2. 316 -2. 627 -2. 737 —. 601 —. 801 —1. 002 —1. 202 —1. 403 —1.603 —1.803 —2. 004 -2. 204 -2. 404 -2. 605 —. 571 — . 761 —0. 951 —1. 141 —1. 331 —1. 521 —1. 712 —1.902 -2. 092 -2. 282 -2. 472 -.540 -.720 -.900 -1.080 -1.260 —1. 440 —1. 620 —1. 800 —1. 980 —2. 160 —2. 340 —. 509 —. 679 —. 849 —1. 019 — 1. 188 —1.358 —1. 528 -1. 698 -J. 868 -2. 037 -2. 207 —. 479 — .638 — .798 —0. 958 —1. 117 — 1.277 -1. 436 -1. 596 -1.755 -1.915 -2. 075 —. 448 —. 598 —. 747 —. 896 —1. 046 —1. 195 —1.345 —1. 494 -1. 643 -1. 793 -1.942 —. 418 —. 557 —. 696 —. 835 —0. 974 —1. 114 —1.253 —1.392 -1. 531 -1.670 -1.809 —. 387 —. 516 —. 645 —. 774 —. 903 —1. 032 —1. 161 — 1.290 -1.419 -1. 548 -1.677 —. 356 —. 475 —. 594 —. 713 —. 832 —0. 950 —1.069 —1. 188 -1.307 -1.426 -1.544 —. 326 —. 434 —. 543 —. 652 —. 760 —.869 -0. 977 -1.086 -1.195 -1.303 -1.412 —, 295 —. 394 —. 492 —. 590 —.689 —.787 -.886 -0. 984 -1.082 -1.181 -1.279 —. 265 —. 353 —. 441 —. 529 —. 617 —.706 —. 794 -. 882 -0. 970 -1.059 -1.147 —. 234 —. 312 —. 390 —. 468 —. 546 —. 624 —. 702 —.780 —.858 -0. 936 -1.014 -.203 -.271 -.339 -.407 -.475 -.542 -.610 -.678 -.746 -.814 -0. 882 — . 173 —. 230 —. 288 —. 346 —. 403 —.461 -. 518 —. 576 —. 634 -.691 -.749 —. 142 —. 190 —.237 — .285 —. 332 —. 379 —. 427 -.474 -.522 -.569 -.616 —. 112 —. 149 —. 186 —. 223 —. 261 —.298 -.335 —.372 —.409 -.447 -.484 —. 081 —. 108 —. 135 —. 162 —. 189 —.216 -.243 —. 270 -.297 -.324 -.3.51 —. 050 —. 067 —. 084 —. 101 — . 118 —. 135 —. 151 -. 168 -. 185 -.202 —.219 —. 020 —. 027 —. 033 —. 040 — .046 —.053 -. 060 —.066 -.073 -.080 -.086

0 0 0 0 0 0 0 0 0 0 0 +. Oil +. 014 +. 018 +. 021 +. 025 +. 029 +.032 +. 036 +.039 +.043 +.046 +. 041 +. 055 +. 069 +.083 +.096 +. 010 +. 124 + 138 +. 151 +. 165 +. 179 +.072 +.096 +. 120 +.144 +.168 +.192 +.216 +. 240 +.264 +. 288 +. 311

-f-. 102 +. 137 +. 171 +.205 +. 239 +. 273 +. 307 +. 342 +. 376 +. 410 +. 444 +. 133 +. 177 +. 222 +. 266 +. 311 +. 355 +. 399 +. 444 +. 488 +. 532 +.577

+. 164 +. 218 +.273 +. 327 +. 382 +. 436 +. 491 +. 546 +. 600 +.655 +. 709

-|-. 194 +. 259 +. 324 +. 389 +. 453 +. 518 +. 583 +. 648 +. 712 +. 777 +.842

+. 225 +. 300 +. 375 +. 450 +. 525 +. 600 +.675 +. 749 +.824 +.899 +.974 +. 255 +. 341 +. 426 +. 511 +. 596 +. 681 +. 766 +.851 +.937 +1.022 +1. 107 +. 286 +. 381 +. 477 +. 572 +. 667 + 763 +. 858 +. 953 +1.049 +1.144 +1.239 +. 317 +. 422 +. 528 +. 633 +. 739 +. 844 +. 950 +1.055 +1. 161 +1.266 +1. 372 +. 347 +. 463 +. 579 +. 694 +. 810 +. 926 +1.042 +1. 157 +1. 273 +1. 389 +1. 505 +. 378 +.504 +. 630 +.756 +.882 +1.007 +1. 133 +1. 259 +1- 385 +1. 511 +1. 637 +. 408 +. 545 +. 681 +. 817 +.953 +1. 089 +1.225 +1.361 +1.497 +1. 634 +1. 770 +. 439 +. 585 +. 732 +. 878 +1. 024 +1. 171 +1.317 +1. 463 +1. 610 +1. 756 +1.902 +. 470 +• 626 +. 783 +. 939 +1. 096 +1.252 +1.409 +1. 565 +1.722 +1. 878 +2. 035 +. 500 +. 667 +. 834 +1.000 +1. 167 +1. 334 +1. 500 +1. 667 +1. 834 +2. 001 +2. 167 +. 531 +. 708 +. 885 +1. 062 +1. 238 +1.415 +1.592 +1. 769 +1. 946 +2. 123 +2. 300 +.561 +.748 +. 936 +1.123 +1.310 +1. 497 +1.684 +1.871 +2. 058 +2. 245 +2. 433 +. 592 +. 789 +. 987 +1. 184 +1. 381 +1. 579 +1. 776 +1. 973 +2. 171 +2. 368 +2. 565 +.623 +. 830 +1. 038 +1.245 +1. 453 +1.660 +1.868 +2. 075 +2. 283 +2. 490 +2. 698 +.653 +.871 +1.089 +1. 306 +1. 524 +1. 742 +1. 959 +2.177 +2. 395 +2. 613 +2. 830 +.684 +. 912 +1. 140 +1.367 +1. 595 +1.823 +2. 051 +2. 279 +2. 507 +2. 735 +2. 963 +. 714 +. 952 +1.191 +1. 429 +1. 667 +1.905 +2. 143 +2. 381 +2. 619 +2. 857 +3. 095 +.745 +. 993 +1.242 +1.490 +1.738 +1.986 +2. 235 +2. 483 +2. 731 +2. 980 +3. 228 +.775 +1.034 +1.292 +1.551 +1. 809 +2. 068 +2. 326 +2. 585 +2. 843 +3. 102 +3. 360 +. 806 +1.075 +1. 343 +1.612 +1.881 +2. 150 +2. 418 +2. 687 +2. 956 +3. 224 +3. 493 +.837 +1.116 +1. 394 +1.673 +1. 952 +2. 231 +2. 510 +2. 789 +3. 068 +3. 347 +3. 626 +. 867 +1.156 +1. 445 +1. 735 +2. 024 +2. 313 +2. 602 +2. 891 +3. 180 +3. 469 +3. 758

56
Table 9. Gravity corrections at variom latitudes at sea level

Correction=?—^ E,=F,E, or F^Rt

Correction for height of meretuy colanm i?, or iJi in any unit of pressure measurement

Latitude Gravity Correction

factor F[

100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300

cm/safl %

0 97S.036 —0.26808 —0.268 —0.536 —0.SO4 —1. 072 —1.340 —1.608 —1.877 —2- 145 —2.413 —2. 681 -2.949 -3. 217 -3-485

2 &7S. 042 .26747 —.267 —- 535 —.802 —1. 070 —1.337 —1.605 —1. 872 —2. 140 —2.407 —2. 675 —2.942 —3. 210 —3-477

4 978,061 .26553 —.266 —.531 —.797 —1.062 —1.328 —1.593 —1- 859 —2.124 —2.390 —2. 655 —2-921 —3. 186 —3. 452 6 978.092 .26237 —.262 —. 525 —.787 —1.049 —1.312 —1.574 —1.837 —2-099 —2. 361 —2. 624 —2. 886 —3. 148 —3. 411 s 978.135 .25799 —.258 —.516 —.774 —1-032 —1.290 —1- 548 —1.806 —2-064 —2.322 —2. 5S0 —2.838 —3.096 —3. 354

10 978.191 .25228 -.252 —.505 —. 757 -1.009 -1.261 -1- 514 -1.766 -2. 018 -2-271 -2-523 -2- 775 -3.027 -3! 280

12 978.258 .24545 —.245 —.491 —.736 —0.982 —1.227 —1.473 —1.718 —1.964 —2.209 —2.454 —2.700 —2.945 —3- 191

14 978.337 .23739 —.237 —.475 —.712 —.950 —1.187 —1.424 —1.662 —1.899 —2. 137 —2. 374 —2- 611 —2.849 —3.086

16 978.427 .22821 —.228 —.456 —.685 —. 913 —1.141 —1. 369 —1. 597 —1.826 —2.054 —2-282 —2- 510 —2. 739 —2.967

18 978.528 .21791 —.218 —.436 —.654 —.872 —1.090 —1.307 —1. 525 —1.743 —1.961 —2- 179 —2- 397 —2. 615 —2.833

20 978.638 .20670 -.207 -.413 -.620 -.827 -1.033 -1.240 —1.447 -1.654 -1.S60 -2.067 —2- 274 -2.480 -2.687

22 978.759 . 19436 —.194 —.389 —.583 —.777 —0.972 —1- 166 —1- 361 -1 555 —1. 749 —1.944 —2-138 —2.332 —2. 527 24 978.888 .18120 —.181 —.362 —.544 —.725 —.906 —1.087 —1.268 —1. 450 —1-631 —1. 812 —1-993 —2. 174 —2.356

26 979.026 .16713 -.167 -.334 -.501 -.669 -.836 -1-003 -1. 170 -1.337 -1-504 -1.671 -1-838 -2-006 -2. 173 28 979.172 .15224 —. 152 —.304 —.457 —.609 —.761 —0- 913 —1.066 —1. 218 —1-370 —1.522 —1- 675 —1.827 —1. 979 30 979.324 .13674 -.137 —.273 —.410 -.547 -.684 -.820 -0.957 -1.094 -1.231 -1.367 -1.504 -1.641 -1.778

32 979.483 .12053 —. 121 —.241 —.362 —.482 —.603 —.723 —.844 —0.964 —1.085 —1.205 —1.328 —1.446 —1. 567 34 979.648 .10371 —.104 —.207 —.311 —.415 —.519 —.622 —.726 —.830 —0.933 —1.037 —1. 141 —1.244 —1.348

36 979.817 .08647 -.086 -. 173 -.259 -.346 -.432 —.519 -.605 -.692 -.778 -0.865 -0. 951 -1.038 -1.124

38 979.991 .06873 —.069 —. 137 —.206 —.275 —.344 —.412 —.481 —.550 —.619 —.687 —.756 —0.825 —0.893

40 980.167 .05078 —.051 —.102 —. 152 —.203 —.254 —. 305 —- 355 —-406 —.457 —.508 —. 559 —.609 —.660

42 9S0.346 .03253 —.033 —.065 —0.098 —.130 —.163 —. 195 —.228 —.260 —.293 —.325 —.358 —.390 —.423

44 980.526 . 01417 —.014 —.028 —0.043 —.057 — 071 —.085 —.099 —. 113 —.128 —.142 —. 156 —.170 —. 184 45 980.616 .00500 -.005 -.010 -0.015 -.020 -.025 -.030 -.035 -.040 -.045 -.050 —.055 -.060 -.065

980.665 0 0 0 0 0 0 0 0 0 0 0 0 0 0

46 980.706 +.00418 +.004 +.008 +.013 +.017 +. 021 +.025 +.029 +.033 +.038 +.042 +.046 +.050 +. 054 4S 980 886 .02254 + 023 + 045 +.068 +.090 +. 113 +.135 +. 158 +. 180 +.203 +.225 +.248 +.270 +.293

50 981.065 .04079 +.041 +.082 +.122 +.163 +.204 +.245 +.286 +.326 +.367 +.408 +.449 +.489 +.530

52 981.242 .05884 +.059 +.118 +.177 - +.235 +.294 +0.353 +.412 +.471 +.530 +.588 +.647 +.706 +.765

54 981.416 .06658 +.077 +.153 +.£30 +.306 +.383 +0.459 +.536 +.613 +.689 +.766 +.842 +.919 +.996

56 981.586 .09392 +.094 +. 188 +.282 +.376 +.470 +0- 564 +.657 +.751 +.845 +.939 +1.033 +1.127 +1- 221 58 98l! 751 . 11074 +. Ill +.221 +.332 +.443 +- 544 +0. 664 +. 775 +.886 +.997 +1. 107 +1. 218 +1.329 +1-440

60 981. 911 .12706 +.127 + .254 +.381 +.508 +-635 +0.762 +.889 +1.016 +1.144 +1.271 +1.398 +1.525 +1.652

62 982.064 . 14266 +.143 +.285 +.428 , -j^ +.713 +0.856 +.999 +1.141 +1.284 +1.427 +1.569 +1.712 +1. 855 64 982.210 . 15755 +] 158 +.315 +.473 +.630 +. 788 +0.945 +1.103 +1.260 +1. 418 +1. 575 +1-733 +1.891 +2.048

66 982.349 . 17172 +. 172 +.343 +.515 +.687 +.859 +1.030 +1.202 +1. 374 +1. 545 +1. 717 +1-8S9 +2. 061 +2.232

68 982.479 . 18198 -L 185 +.370 +.555 +.740 +.925 +1. 110 +1.295 +1.480 +1.665 +1.850 +2-035 +2.220 +2.405

70 982.601 ! 19742 +:i97 +. 395 +.592 +.790 +.987 +1.185 +1.382 +1.579 +1.777 +1.974 +2. 172 +2.369 +2.566

72 982.712 .20874 +.209 +. 417 +.626 +.835 +1.044 +1.252 +1.461 +1. 670 +1.879 +2.087 +2.296 +2.505 +2.714

74 982.813 .21904 +.219 +.438 +.657 +.876 +1-095 +1. 314 +1.533 +1.752 +1.971 +2.190 +2.409 +2-628 +2.848

76 982.904 .22831 +.228 +.457 +.685 +.913 +1-142 +1. 370 +1.598 +1.826 +2.055 +2.283 +2. 511 +2-740 +2.968

78 982.983 .23637 +.236 +.473 +.709 +.945 +1. 182 +1.418 +1.655 +1.891 +2.127 +2-364 +2.600 +2-836 +3.073

80 983.051 .24330 +.243 +.487 +.730 +.973 +1. 217 +1.460 +1.703 +1-916 +2.190 +2.433 +2-676 +2.920 +3. 163

82 983.107 .24901 +.249 +.498 +.747 +.996 +1.245 +1.494 +1.743 +1.992 +2.241 4-2.490 +2.739 +2.988 +3.237

84 983.151 .25-350 +.254 +.507 +.761 +1. 014 +1.268 +1. 521 +1- 775 +2-028 +2.282 +2.535 +2.789 +3.042 +3.296

86 983.183 .25676 +.257 +.514 +.770 +1.027 +1.284 +1.541 +1.797 +2- 051 +2.311 +2.568 +2. 824 +3.081 +3.338

88 983.202 .25870 +.259 +. 517 +.776 +1.035 +1-294 +1.552 +1. 811 +2- 070 +2-328 +2.587 ^-2.846 +3.104 +3.363

9<5 983.208 .25931 +.259 +. 519 +.778 +1.037 +1.297 +1- 556 +1. 815 +2. 074 +2-334 +2.593 +2.852 +3. 112 +3. 371

57
Table 10. Capillary depression of mercury column

Millimeters of mercury at 20°C and under standard gravity.

Meniscus height in mm

77i77i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.

1

1.2 1.3 1.4 1.6 1.6 1.7 1.8 1.9 2.0

Surface tension, 400 dynes/cm

8 0. 0.54 0. 108 0. 162 0.214 0.265 0.315 0. 363 0. 409 0. 453 0. 494 0. 533 0. 569 0.603 0.633 0. 660 0. 684 0. 705 0.723 0. 737 0. 749

10 .029 .058 .087 .115 .143 . 170 .196 .222 .247 .270 .292 .314 .333 .352 .369 .384 .398 .410 .421 .430

16 .006 .011 .016 .022 .027 .032 .037 .042 .047 .052 .056 .060 .065 .068 .072 .076 .079 .082 .084 .086

22 .001 .002 .003 .004 .005 .006 .008 .009 .010 .010 .011 .012 .013 .014 .014 .015 .016 .016 .017 .018

Surface tension, 450 dynes/cm

6 0.128 0. 254 0. 379 0.600 0. 617 0. 729 0. 836 0. 937 1.03 1. 12 1.20 1.27 1. 33 1.38 1.43 1.47 1.50

7 .088 .176 .263 .348 .430 .510 .587 .661 0. 730 0. 794 0. 855 0.910 0. 961 1.01 1.05 1.08 1.11 1.14 1.16

8 .063 .126 .189 .250 .310 .368 .424 .478 .530 .679 .626 .668 .708 0. 744 0. 777 0.807 0. 833 0.866 0.874 0.890

9 .046 .093 .138 .183 .228 .271 .313 .353 .392 .429 .464 .498 .629 .567 .684 .608 .630 .649 .665 .679

10 .035 .069 .103 .137 .170 .202 .234 .264 .294 .322 .349 .375 .399 .422 .443 .462 .480 .495 .509 .522

11 .026 .052 .078 .104 .128 .153 .177 .200 .223 .246 .266 .285 .304 .322 .338 .354 .368 .380 .392 .402

12 .020 .040 .059 .079 .098 .117 .135 .153 .170 .187 .203 .218 .233 .247 .260 .272 .283 .293 .303 .311

13 .015 .030 .045 .060 .075 .089 . 104 .117 .131 .144 .156 .168 .180 .190 .200 .210 .219 .227 .234 .241 14 .012 .023 .035 .046 .058 .069 .080 .090 .101 . Ill . 120 .130 .139 .147 .166 .163 . 170 .176 .182 .187

15 .009 .018 .027 .036 .045 .053 .062 .070 .078 .086 .093 .101 .108 .114 .120 .126 .132 .137 .141 .146n

16 .007 .014 .021 .028 .035 .041 .048 .054 .060 .067 .072 .078 .083 .089 .093 .098 .102 .106 .110 .113

17 .006 .011 .016 .022 .027 .032 .037 .042 .047 .062 .056 .061 .065 .069 .073 .076 .080 .083 .086 .088

18 .004 .008 .013 .017 .021 .025 .029 .033 .036 .040 .044 .047 .050 .054 .057 .059 .062 .064 .067 .069

19 .003 .006 .010 .013 .016 .019 .022 .026 .028 .031 .034 .037 .039 .042 .044 .046 .048 .060 .062 .054 20 .003 .005 .008 .010 .013 .015 .017 .020 .022 .024 .026 .029 .030 .032 .034 .036 .037 .039 .040 .042

21 .002 .004 .006 .008 .010 .012 .014 .015 .017 .019 .020 .022 .024 .025 .027 .028 .029 .030 .031 .032 22 .002 .003 .005 .006 .008 .009 .011 .012 .013 .015 .016 .017 .018 .020 .021 .022 .023 .024 .024 .025

Surface tension, 500 dynes/cm2

8 0. 072 0. 143 0.215 0. 286 0.354 0.421 0. 485 0.647 0.607 0. 663 0.716 0. 766 0. 813 0. 865 0.894 0. 929 0.961 0. 989 1.01 1.03

10 .040 .080 . 120 .159 .197 .235 .272 .308 .342 .375 .407 .436 .464 .491 .517 .542 .563 .582 .600 .615 16 .009 .017 .026 .034 .043 .051 .059 .067 .075 .082 .090 .097 .104 .110 .116 .122 .128 .133 .138 .142 22 .002 .004 .006 .008 .010 .012 .014 .016 .018 .020 .021 .023 .025 .026 .028 .029 .031 .032 .033 .034

Table 11. Rate of change of absolute pressure with height of a gas column of any composition at various densities

The rate of pressure change is negative; the absolute pressure increases for levels below, and decreases for levels above, the reference density

Density Absolute air pressure Rate of change of absolute pressure, dP/dh

glcm?X10^ 20''Cmm Hg SS°Cmm Hff SO°Cmm Hg mblft mm Hqljt in. Hg/ft psilft mbim

500 315. 6 321.0 326.4 0.01490 0. 01118 0. 0004400 0. 0002012 0. 04903

600 378. 7 385.2 391.6 . 01788 . 01341 . 0005280 . 0002415 .05884

700 441. 9 449.4 457.0 . 02086 . 01565 . 0006160 . 0002817 . 06865

800 605. 0 513. 6 522.2 . 02384 . 01788 . 0007040 . 0003219 .07846

900 568. 1 577. 8 587.6 . 02682 . 02012 . 0007920 . 0003622 .08826

1000 631. 2 642.0 662. 7 . 02980 . 02236 . 0008800 . 0004024 .09807

1100 694. 4 706.2 718. 1 . 03278 . 02469 . 0009680 . 0004427 . 1079 1200 757. 6 770.4 783. 4 . 03576 . 02682 . 001056 . 0004829 .1177

1300 820 6 834. 6 848. 6 . 03874 . 02906 . 001144 . 0005231 .1276

1400 883. 7 898. 8 913. 9 . 04172 . 03129 . 001232 . 0005634 .1373

1500 946. 8 963. 0 979. 1 . 04470 . 03353 . 001320 . 0006036 .1471 1600 1010. 0 1027. 2 1044. 5 . 04768 . 03576 . 001408 . 0006439 .1569

1700 1073. 1 1091. 4 1109. . 05066 . 03800 . 001496 . 0006841 .1667 1800 1136 2 1155. 6 1175. 0 . 06364 . 04023 . 001584 . 0007243 .1765

1900 1199. 3 1219. 8 1240. 2 . 06662 .04247 . 001672 . 0007646 .1863

2000 1262 6 1284. 0 1305 6 . 05960 .04470 . 001760 . 0008048 .1961 2500 1578 1 1605. 0 1632 0 . 07450 . 06588 . 002200 . 001006 .2452 3000 1893 7 1926 0 1958. 3 . 08940 . 06708 . 002640 . 001207 .2942 3500 2209 3 2247. 0 2284. 7 .1043 . 07823 . 003080 . 001408 .3432 4000 2524 9 2668 0 2611. 1 .1192 . 08941 . 003520 . 001610 .3923

4600 2840 5 2889. 0 2937. 5 . 1341 .1006 . 003960 .001811 .4413 5000 3156 2 3210. 1 3263. 9 . 1490 . 1118 . 004400 . 002012 .4903 5500 3471 8 3531. 0 3590. 3 .1639 . 1229 . 004840 . 002213 .5394

6000 3787 4 3852. 0 3916. 7 .1788 .1341 . 005280 .002415 .5884

58
Table 12. Air density at various absolute pressures and temperatures based on air density at 760 mm of Hg and 0° C of 0.001293 gjcm^

Absolute pressure Air density, g/cm3X10» mm Hg in. Hg mb pai 20° C 22° C 2;° C 26° C 28° C 30° C

300 11.81 400.0 5. 801 475.5 472.3 469.

1

465.9 462.8 459.8

350 13. 78 466 6 6. 768 554.

8

551 0 547 2 543. 6 540. 0 536. 4 400 15'. 75 533! 3 7^735 634! 0 629] 7 625. 4 621.3 617.

1

613.1 450 17. 72 599.9 8.702 713.2 708.4 703.6 698.9 694.2 689.7

500 19.68 666.6 9.668 792.6 787.1 781.8 776.6 771.4 766.3

550 21. 65 733.3 10.64 871.8 865.8 860.0 854.2 848.6 842.9 600 23. 62 799.9 11. 60 951.0 944.5 938.

1

931.9 925.7 919.6

650 25. 59 866.

6

12. 57 1030 1023 1016 1010 lUUo 996.

2

700 27] 56 933! 3 13! 54 1110 1102 1094 1087 1080 1073 750 29.53 999.9 14. 50 1189 1181 1173 1165 1157 1149

760 29. 9213 1013. 25 14. 696 1204.

6

1196.

4

1188.

3

1180.

4

1172.

5

1164.

8

800 31.50 1067 15. 47 1268 1259 1251 1243 1234 1226 850 33. 46 1133 16.44 1347 1338 1329 1320 1311 1303 900 35.43 1200 17. 40 1426 1417 1407 1398 1388 1379

950 37. 40 1267 18. 37 1506 1495 1485 1476 1466 1456 1000 39. 37 1333 19. 34 1585 1574 1564 1553 1543 1533

1050 41. 34 1400 20. 30 1664 1653 1642 1631 1620 1609 1100 43. 31 1467 21.27 1744 1732 1720 1708 1697 1686

1150 45.28 1533 22.24 1823 1810 1798 1786 1774 1763

1200 47.24 1600 23. 20 1902 1889 1876 1864 1851 1839

1250 49. 21 1667 24. 17 1981 1968 1954 1941 1928 1916 1300 51. 18 1733 25. 14 2060 2046 2033 2019 2006 1992

1350 53. 15 1800 26. 10 2140 2125 2111 2097 2083 2069

1400 55." 12 1866 27! 07 2219 2204 2189 2174 2160 2146

1450 57. 09 1933 28.04 2298 2283 2267 2252 2237 2222

1500 59.06 2000 29.01 2378 2361 2345 2330 2314 2299 1600 62. 99 2133 30. 94 2536 2519 2502 2485 2468 2452

1700 66! 93 2266 32! 87 2694 2676 2658 2640 2623 2605

1800 70. 87 2400 34. 81 2853 2834 2814 2796 2777 2759

1900 74.80 2533 36.74 3012 2991 2971 2951 2931 2912 2000 78. 72 2666 38. 67 3170 3148 3127 3106 3086 3065

2100 82. 68 2800 40. 61 3328 3306 3283 3262 3240 3219 2200 86'. 60 2933 42.54 3487 3463 3440 3417 3394 3372 2300 90. 55 3066 44.48 3646 3621 3596 3572 3548 3525 2400 94. 49 3200 46. 41 3804 3778 3753 3728 3703 3678

2500 98.42 3333 48.34 3962 3936 3909 3883 3857 3832

2600 102.4 3466 50.28 4121 4093 4065 4038 4011 3985

2700 106.3 3600 52. 21 4280 4250 4222 4194 4165 4138

2800 110. 2 3733 54. 14 4438 4408 4378 4349 4320 4291 2900 114.2 3866 56. 08 4596 4565 4534 4504 4474 4445

3000 118.

1

4000 58.01 4755 4723 4691 4659 4628 4598 3100 122.0 4133 59.94 4914 4880 4847 4815 4783 4751 3200 126.0 4266 61.88 5072 5037 5003 4970 4937 4904

3300 129.9 4400 63.81 5230 5195 5160 5125 5091 5058 3400 133.9 4533 65. 75 5389 5352 5316 5281 6245 5211 3500 137.8 4666 67. 68 5548 5510 5472 5436 5400 5364

Washington, D. C, April 2, 1959.

U.S. GOVFRNMENT PRINTING OFFICE: 1960

59

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