U. S. DEPARTMENT OF COMMERCE

R. P. LAMONT, Secretary BUREAU OF STANDARDS

GEORGE K. BURGESS, Director

MISCELLANEOUS PUBLICATION, No. 117

UNITS USED

TO EXPRESS THE WAVE LENGTHS

OF ELECTROMAGNETIC WAVES

BY

HENRY D. HUBBARD

November 24, 1930

UNITED STATES

GOVERNMENT PRINTING OFFICE WASHINGTON : 1930

For sale by the Superintendent of Documents, Washington, D. C. Price 5 cents

UNITS USED TO EXPRESS THE WAVE LENGTHS OF

ELECTROMAGNETIC WAVES

By Henry D. Hubbard

ABSTRACT

The closing up of the gaps in the wave gamut of electromagnetic radiations makes it opportune to systematize the units and unit usages to cover the entire range. A well-selected series of units connected with the c. g. s. unit by the "powers-of-10 notation" will facilitate computation and conversion, and aid in visualizing, comparing, and correlating widely differing wave magnitudes. This paper aims to give the best existing usages including the trend toward the units which have a multiple or submultiple relation of 1,000 connected by the powers

of 10 equivalents.

CONTENTS

I. Need for standard usages 1 II. Use of wave-length reciprocal—frequencv 2

1. Radio 1 2

2. Spectroscopy 2

III. Use of wave lengths 2

IV. Usages for expressing wave lengths 2

1. Spectroscopy 3

2. Rontgen or X rays and gamma rays 3

3. Radiometry 3

4. Colorimetry 3

5. Radio communication 3

6. Multiples of 1,000 as ratio of units 4

7. Powers of 10 notation 4

I. NEED FOR STANDARD USAGES

Tha established continuity 1 of the spectrum of electromagnetic

radiation from the shortest experimentally measured wave lengths to beyond the 25-cycle, alternating-current waves (12,000 kilometers)

brings the need for a unified system of units for measuring and

expressing the wave lengths throughout a suggested gamut of more

than 60 octaves. A well-chosen set of units will facilitate computation and conversion, and will aid in visualizing, comparing, and correlating widely differing wave magnitudes. The closing up of the

gaps in the wave gamut makes it opportune to set forth a systematic

series of units and usages to cover all ranges.

> Nichols and Tear, Astrophys. J., 61, p. 17; 1925. 20081°—30 1
2 BUREAU OF STANDARDS

II. USE OF WAVE-LENGTH RECIPROCAL—FREQUENCY

1. RADIO

In radio communication the use of wave frequency (number of waves per second) is growing on account of distinct advantages in measurement and computation. As frequency is the reciprocal of a time period it is directly calculated if the oscillation period alone is known. The oscillation period is usually known for the standard

circuit or may be computed approximately from the constants of the radio circuit. Bureau of Standards Miscellaneous Publication

No. 67, Kilocycle-Meter Conversion Table,2 gives a list of radio-frequencies from 10 to 10,000 kilocycles, with equivalents for interconverting frequencies (per second) and wave lengths (meters).

2. SPECTROSCOPY

In spectroscopy the frequency is usually computed from the wave

length (in vacuum). Atomic physics, however, in some cases permits

computing the true frequency by the formula E= hv, where E= energy

(in ergs), h = Planck's unit quantum 3 of action (6.554 X 10"27 erg

second), and v is the number of waves per second. However, the

"wave number"4 (waves per centimeter, l/\cm ) is much used in

spectroscopy and atomic physics.

III. USE OF WAVE LENGTHS

The use of wave lengths is essential, especially in using light waves

as standards of length, in measuring the radial velocity of stars and

other celestial objects, in measuring space lattices by the use of known

Kontgen (or X-ray) waves, and elsewhere. For converting wave

lengths in air from 2,000 to 10,000 angstroms into "wave numbers"

in vacuum the best tables are those of H. Kayser, Tabelle der

Schwingungszahlen." 5 Since the wave lengths of the gamut involve in all some 24 significant figures (from 10~14 to 10+1° centimeters) the "powers-of-10 nota- tion" is advocated for use wherever facile comparison or translation

is desirable. Equivalents in this notation are given in this paper for

the various units cited. The c. g. s. units are fundamental, and the

specialized usages adopted for convenience are directly correlated to the c. g. s. units through the "powers-of-10 notation" which permits

simple expression of all orders of wave magnitudes in terms of the

basic c. g. s. units, the centimeter and the second.

IV. USAGES FOR EXPRESSING WAVE LENGTHS

The formulation of practice herein presented is approved standard usage for the Bureau of Standards with respect to units, subdivisions, abbreviations, and equivalents for all ranges of wave lengths

within the entire electromagnetic wave gamut.

* This publication may be purchased for 5 cents by addressing the Sunerintendenf of Documents. Washington, D. C.

s International Critical Tables, 1, p. 17; 1926.

* Sometimes incorrectly designated "frequency." The true or absolute frequency v is the ratio of tha

velocity of light c to the wave length in vacuum. The wmvo number is therefore equal to the ratio vie.

5 Printed by S. Hirzel, Leipzig; 1925.
UNITS USED TO EXPRESS WAVE LENGTHS

The "angstrom" is denned in terms of cadmium red wave length

measurements bv Benoit, Fabry, and Perot, the relation being that

this wave length equals 6438.4696 angstroms (0.00064384696 milli- meter) in dry air, at 15° C. on the international hydrogen scale of

temperature, at a pressure of 760 millimeters of mercury at the value

of gravity equal to 980.67 cm/sec 2 (45° north latitude).

This value is in essential agreement with the previous determination

made (1892) by Michelson, when reduced to the same basis. It is the value adopted (1907) and thereafter used by the International

Union for Cooperation in Solar Research (now the International Astronomical Union), and it is in world-wide use in spectroscopy and astro- physics.

The meter might thus be defined as equal to 1,553,164.13 wave

lengths of the red radiation of cadmium under the above standard

conditions.

1. SPECTROSCOPY

"Angstrom" (abbreviate A)

1 angstrom = 0.0000001 millimeter, or = 1,000 milliangstroms.

2. RONTGEN OR X RAYS, AND GAMMA RAYS * "Milliangstrom" (abbreviate mA)

1 milliangstrom = 0.0000000001 millimeter.7 = 0.001 angstrom.

"Microangstrom" (abbreviate /xA)

1 microangstrom = 0.000001 angstrom. = 0.0000000000001 millimeter.

3. RADIOMETRY

"Micron" (symbol pi); or any of above-named units.

1 micron = 0.000001 meter. = 0.001 millimeter. = 1,000 millimicrons. = 10,000 angstroms.

4. COLORIMETRY

"Millimicron" (symbol nnz)

1 millimicron = 0.000000001 meter. = 0.000001 millimeter = 10 angstroms.

5. RADIOCOMMUNICATION

"Meter" (abbreviate m)

1 meter = fundamental unit of length = 1,000 millimeters. = 10,000,000,000 angstroms.

"Millimeter" (abbreviate mm) for waves under 1 meter

1 millimeter = 0.001 meter. = 10,000,000 angstroms.

Wave lengths of ultra-penetrating rays notably shorter than gamma ray waves may be expressed in terms of the "microangstrom" (symbol ptA).

7 One X-unit=l milliangstrom.
4 BUREAU OF STANDARDS

6. MULTIPLES OF 1,000 AS RATIO OF UNITS

The units above denned conform to the growing practice of using

units having multiple interrelations of 1,000 or 0.001; for example, m> mm, m, km; or mg, g, kg, metric ton. The entire range of electro- magnetic waves may conveniently be expressed in the following

units: Meter, millimeter; micron, millimicron; angstrom, milliangstrom, microangstrom.

7. POWERS-OF-10 NOTATION

In general, to facilitate the intercomparison of wide ranges of elec- tromagnetic wave lengths and to simplify computation, the "powersof-10 notation" may be used to great advantage. The numerical

interrelation in this notation for the above-defined units are given in

the following table:

Units Powers-of-10 equivalent of units listed in column 1

Name Symbol M A mA mA

C. g. 8. unit cm mm m

Micron __ n 1 10* 10* 10' 1010 io-4 10-3 io-« Millimicron m/i io-3 1 10 10* 10" 10"7 io-e io-» Angstrom A io-* 10"1 1 10s 106 IO"8 io-7 10-10 Milliangstrom _ mA io-7 io-< io-s 1 103 10"11 10 -io 10"1! Microangstrom !0-io 10" io-6 IO"3 1 10-" IO"13 !0-ie

Washington, October 7, 1930.

o