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'r.3lC2 UollnliY

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THE

PHYSICAL REVIEW

A Journal of Experimental and
Theoretical Physics

CONDUCTED BY

THE

American Physical Society

BOARD OF EDITORS
F. BEDELL, Managing Editor

E. P. LEWIS N. E. DORSEY G. K. BURGESS

W. C. SABINE WM. DUANE A. D. COLE

A. TROWBRIDGE O. M. STEWART A. C. LUNN

Vol. XL, Series II.

The Physical Review
Lancaster, Pa., and Ithaca, N. Y.

1918

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PRESS OF

THE NEW ERA PRINTINO COMPANY

LANCASTER, PA.

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CONTENTS OF VOL XL, SECOND SERIES.

JANUARY. 1918.

Th.e Geometry of Image Fonnation in X-Ray Analysis. Horace Scudder Uhler i

The Ratio of the Intensities of the D Lines of Sodium. Vivian Voss 21

On the Thermodynamics of Fluorescence. E. H. Kbnnard 29

Kathodo-Fluorescence of Crystals. Thomas B. Brown 39

The Necessary Physical Assumptions Underlying a Proof of the Planck Radiation Law.

F. Russell v. Bichowsky 58

On Certain Absorption Bands in the Spectra of the Uranyl Salts. H. L. Howes 66

Resonance Radiation of Sodium Vapor Excited by One of the D Lines. R. W. Wood

and Fred L. Mohler 70

FEBRUARY, 1918.

The Brightness Sensibility of the Retina. Julian Blanchard 81

The Moment of Momentum Accompanying Magnetic Moment in Iron and Nickel.

John Q. Stewart 100

A Study of the Fluorescence of Certain Uranyl Salts at Room Temperature. Frances

G. Wick 121

Proceedings of the American Physical Society. 130

Minutes of the Rochester Meeting; The Nature of the Ultimate Magnetic Particle,
Arthur H. Compton and Oswald RognUy; The Production and Measurement of High
Vacua. /. E. Skrader and R. G. Sherwood; On the Residual Rays of Rock Salt, Herbert
P. Hollnagel; The Mathematical Structure of Band Series, II, Raymond T. Birge;
Images on Silvered Photo-Plate, C. W. Wagonner; Emulsions: (A) A New Method for
Making Emulsions, (B) Properties of Emulsions, Wheeler P. Davey; Note on a Com-
parison of High-Temperature Scales, E. P. Hyde and W. E. Forsythe; Methods of
Temperature-Control in Glass-Melting Furnaces, Clarence N. Fenner; On Certain
Absorption Bands in the Spectra of the Uranyl Salts, H. L. Howes; A New Hydrate
of Uranium Nitrate; Complete Achromatization of a Two-Piece Lens, C W, Moffitt;
A Self- Recording Evaporometer, Alexander McAdie; An Instrument for Continuously
Recording the Percentage of Saturation and the Weight of the Water Vapor per Unit
Volume in the Free Air, Alexander McAdie; Rotation of the Pulley in Melde's Ex-
periment, Arthur Taber Jones; Comparative Accuracy of Whirled Psychrometer,
Assmann Aspiration Psychrometer, Porous Cup Atometers, Hair Hygrographs.
Piche Evaporimeter Saturation Deficit Recorder, Open Water Surface Evaporimeter,
and Dry and Wet Bulb Thermometers, Alexander McAdie; Measurement of Heat
Conductivities of Metals at High Temperatures, Robert W. King; Bohr's Atom, Zee-
man's Effect and the Magnetic Properties of the Elements, Jakob Kunz; The In-
fluence of Temperature Upon the Crushing Strength of a Dental Amalgam, Arthur
W. Gray and Paris T. Carlisle, 4th; A New Formula for the Temperature Variation
of the Specific Heat of Hydrogen, Edwin C. Kemble.
New Books 159

MARCH, 1918.

The Magnetization of Iron in the Absence of Hysteresis. Winthrop R. Wright 161

The Ionization Potential of Mercury Vapor. T. C. Hbbb 170

On Equilibrium under Non-Hydrostatic Stress. P. W. Bridgman 180

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iv CONTENTS.

EUsticity of Impact of Electrons with Gas Molecules. J. M. Bbnadb and K. T. Compton 184

The Use of Mercury Droplets in Millikan's Experiment. John B. Deribux 203

The Optical Properties of Rubidium. J. B. Nathanson 227

The Theory of Ionization by Collision. IV. Cases of Elastic and Partially Elastic Im-
pact. K. T. Compton and J. M. Benade 234

Proceedings of the American Physical Society. 241

Vacuum Gauges of the Radiometer Type, R. G. Sherwood; Further Verification of
Knudsen's Equations for Resistance to Molecular Flow, L. E. Dodd; Rectification of
Alternating Curren*- by the Corona, J. W, Davis; A Mono- Wave-Length X-Ray
Concentrator, Elmer Dershem; Wave-lengths of the Tungsten X-Ray Spectrum,
Elmer Dershem; A Megaphone with a Rectangular Aperture. F. R, Watson; A New
Hydrate of Uranium Nitrate; Uranium Nitrate Icositetrahydrate, Frank E. E,
Germann; A Correction in the Theory of Ionization by Collision, Jakob Kum; Mo-
bility of Ions in Air, Hydrogen, and Nitrogen, Kia-Lok Yen; The Determination of
Organic Compounds by an Optical Method, Thomas E. Doubt and B. B. Freud;
The Analysis of Polarized Light Reflected from Small Opaque Crystals, Leroy D.
Weld,
New Books 251

APRIL. 1918.

The Breakdown Effort in Boron Conductors. F. W. Lyle 253

A General Theory of Energy Partition with Applications to Quantum Theory. Richard

C. Tolman 261

Photoelectric Effects on Mercury Droplets. John B. Derieux 276

On the Unpolarized Fluorescence and Absorption of Four Double Chlorides of Uranyl.

Edward L. Nichols and H. L. Howes 285

Young's Modulus of Drawn Tungsten and Its Variation with Change of Temperature,

including a Determination of the Coefficient of Expansion. H.L.Dodge 3x1

A New Method of Positive Ray Analysis. A. J. Dempster 3x6

Proceedings of the American Physical Society. 326

Minutes of the Ninety- first Meeting; Note on a Phosphorescent Caldte, E. L. Nichols
and H. L. Howes; The Visibility of Radiation in the Blue End of the Visible Spec-
trum, L. W. Hartman; Theory of Thermal Conductivity in Metals, Edwin H. Hail;
The Size and Shape of the Electron, Arthur H. Compton; Characteristic Curves of
Various Types of Audions, A. D. Cole; The Eflfect Produced upon Audion Character-
istic Curves by Various Kinds of Signals (Buzzer, Electron Relay and 6o-cycle, A.
C). A. D. Cole; Report of the Construction of Certain Mathematical Tables, C. E.
Van Orstrand; The Optical Properties of Rubidium, /. B, Nathanson.
New Books 335

MAY. 1918.

The Mobilities of Gaseous Ions. Kia-Lok Yen 337

Effect of Hydrogen on the Electrical Resistivity of Carbon. T. Peczalski 363

The Variation in the Blackening of a Photographic Plate with Time of Exposure, Total

Energy Remaining Constant. P. S. Helmick 372

Is a Moving Mass Retarded by the Reaction of its Own Radiation? Leigh Page 376

An Experimental Investigation of the Energy in the Continuous X-Ray Spectra of Certain

Elements. Clayton T. Ulrby 401

On the Second Postulate of the Theory of Relativity: An Experimental Demonstration

of the Constancy of the Velocity of Light Reflected by a Moving Mirror. Q. Ma-

JORANA 4IX

JUNE. 1918.
A Preliminary Study of the Luminescence of the Uranyl Salts under Cathode Ray Ex-
citation. Frances G. Wick and Louise S. McDowell 421

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OKNKRAI. ■OOKUNOINQ CO.

STGT

OOAUTT CONTROL MARK

— ^-

CONTENTS. V

Note on the Grating Space of Calcite and the X-Ray Spectrum of Gallium. Arthur H.

COMPTON 430

Characteristic X-Ray Emission as a Function of the Applied Voltage. Bergen Davis. . 433

On the Formation of Negatively Electrified Rain Drops. Fernando Sanford 445

The Air-Damped Vibrating System: Theoretical Calibration of the Condenser Trans-
mitter. I. B. Crandall 449

Waye-Lengths of the Tungsten X-Ray Spectrum. Elmer Dershbm 461

American Physical Society. 477

Minutes of the Ninety-Third Meeting; Minutes of the Ninety-Fourth Meeting; Ther-
mo-couples for Student Use in Calorimetric WorkiRalph S. Minor; An Harmonic Syn-
thesizer Having Components of Incommensurable Period and any Desired Decre-
ment. William J. Raymond; Variation of Velocity of Waves due to Motion of the
Source, Dinsmore Alter; Photograph of an Aurora Model. C. C. Trowbridge; On the
Observation of the Apparent Focus of Auroral Streamers. C. C. Trowbridge; Meteor
Train Spectra and Probable Erroneous Conclusions of the Observers. C. C. Trow-
bridge, The Photo-Luminescence and Katho-Luminescence of Calcite, E. L. Nichols,
H. L. Howes and D. T. Wilber; A Method for the Quantitative Study of Gases in
Metals, H. M. Ryder; The Resonance and Ionization Potentials for Electrons in
Thallium Vapor, Paul D, Foote and Fred L. Mohler; Electronic Frequency and
Atomic Number, Paul D. Foote; On the Relation between the K X-Ray Series
and the Atomic Numbers of the Chemical Elements, William Duane and Kang-
Fuk Hu; On the Critical Absorption and Characteristic Emission X-Ray Fre-
quencies, William Duane and Kang-Fuh Hu; The Relation between the General
X-Radiation and the Atomic Number of the Target, William Duane and Takeo
Shimisu; The Influence of Amalgamation Variables upon the Mercury Content and
the Crushing Strength of a Dental Amalgam, Arthur W, Gray and Paris T. Carlisle,
Fourth; Increase in Length of Life of Tribolium Confusum, Due to X-Rays. Wheeler
P. Davey; The Spectral Photoelectric Sensitivity of Molybdenite, W. W, Coblentz,
M. B. Long and H. Kahler; The Influence of Amplitude of Electromagnetic Driving
on the Frequency of Tuning Forks, Dayton C. Miller; The Law of Symmetry of the
Visibility Function, Irwin G. Priest; A Precision Method for Producing Artificial
Daylight, Irwin G. Priest; Transparency of Certain Carbon Compounds to Waves
of Great Length, H. P. Hollnagel; Some Preliminary Results in a Determination of
the Maximum Emission Velocity of the Photoelectrons from Metals at X-Ray Fre-
quencies, Kang-Fuh Hu.
Erratum 508

Index 509

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Second Series. January, igi8. Vol. XI., No. i

THE

PHYSICAL REVIEW.

THE GEOMETRY OF IMAGE FORMATION IN X-RAY

ANALYSIS.

By Horace Scuddbr Uhlbr.

Introduction, — ^The theory of diffraction as applied to ordinary surface
gratings and to the design of apparatus used in the spectroscopy of
radiations having wave-lengths much greater than those of JT-rays has
been thoroughly worked out, and the most important results obtained
are clearly presented in various places, for example, in Kayser's Hand-
buch der Spectroscopic. The theory of plane space-gratings (rigid
crystals) has also been investigated by Laue and Bragg. On the other
hand, as far as I have been able to ascertain, from a fairly complete search
of the accessible literature of the subject, very littie has been published
on the general theory upon which the construction of JT-ray spectrom-
eters and spectrographs should be based. Accordingly, it may not
be superfluous to present the results of my analytical study of some of
the questions which arose both during the time when Dr. C. D. Cooksey
and I were working on the high frequency spectrum of gallium and later
when we were engaged in designing a new JT-ray spectrograph for the
accurate determination of the wave-lengths of characteristic radiations.
Since these wave-lengths are too short to produce diffraction patterns of
sensible dimensions, the problems fall within the domain of geometrical
optics. As the interference and reflection methods used respectively
by Laue and by Bragg lead, of necessity, to the same conclusions, and
since the second point of view is the more advantageous for the present
purposes, the crystals will be treated as aggr^ates of reflecting planes
throughout the paper. The grating-space of the crystal, the wave-length
of the rays, and the order of the spectrum will be considered as constants
so that the glandng-angle y will also be constant, conformably to the
well-known relation wX = 2d sin y.

General Eguations. — ^Since a material space-lattice consists of a number

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HORACE SCUDDER UHLER,

Sbooiid

of parallel planes of r^^ularly spaced atoms, a first approximation to the
case of a real crystal may be made by studying the properties of a single
plane of unlimited area which reflects rays of a given wave-length at a
constant glandng-angle y. Accordingly, the first question for con-
sideration will be: To find the general equations of a ray reflected from
a perfectly selective mirror when the position and direction of the incident
ray are given in terms of certain convenient parameters.

Let the incident ray 57 (Fig. i) be determined by the point S (xu yu Zi)

and the angles a and fi.
a is the angle which the
orthogonal projection of
the incident ray on the
plane XOY makes with the
negative direction of the
axis OY. P is the angle
which the ray 57 forms
with this projection.
Hence, a and P may be
looked upon as giving the
azimuth and altitude of the
incident ray, respectively.

The mirror MO may rotate

around OZ as axis. 6 is the angle made by any normal to the mirror
(such as ON) with the co5rdinate plane XOZ. I'{x\ y, 2!) denotes the
point of incidence, and 72? indicates the reflected ray. The equation of
the reflector is

cos B'X + sin B^y = o. (i)

By spherical trigonometry (or otherwise) it is easy to show that the
direction cosines of the incident ray are sin a cos /S, — cos a cos /S, and
sin /5. Hence, the equations of this ray are

Fig. 1.

X — xi __ y — y\ g — gi

sin a cos fi cos a cos fi sin /9 '

(2)

From equations (i) and (2) the coordinates of the point of incidence 7
are found to be

{xi cos a + yi sin a) sin B

y = -

g' = gi +

sin {B — a) '

{xi cos g + yi sin a) cos B
sin {B - a) '

{x\ cos d + yi sin B) tan /5

sin (d — a).

(3)

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Vot. XL!
Nax. J

GEOMETRY OP IMAGE FORMATION.

Let /, m, and n denote the direction cosines of the reflected ray so that
the equations of this line may be written

X — x' y " y' z ^ ^

(4)

Since directions alone are now involved, expressions for /, m, and n
in terms of a, fi, and 6 may be obtained by moving all necessary lines
parallel to themselves until they radiate from the center of an auxiliary
sphere.

In Fig. 2, 01, OR, and ON are parallel respectively to the incident

Fig. 2.

ray, the reflected ray, and the normal to the mirror. The law of re-
flection requires that Z QOR = Z POI (= /S). Arcs of great circles
are drawn through the various points as shown in the diagram. Z Y'OP
= a, Z XON = 6. Let Z QOX s {. Z lOR = 27 = deviation of
ray.

In the rt. A QNR,

cos I y) = cos P cos (6 + i).

In the rt. A PNI,

cos ("+71 = COS P cos I d H aft

hence

sin y = cos /5 sin {$ — a) ;

{ = - _ (2« - «).

(5)

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In the rt. A QXR,

In thert. AQYR,

HORACE SCUDDER UHLER, [^SSS

/ = COS fi COS {

/ = COS /5 sin (2$ — a) ; (6)

= cos/5cos^^+ f j

m = — cos P cos {2$ — a), (7)

n = sin /5. (8)

In general, being given a, /5, and 7 relation (5) furnishes two supple-
mentary values for 6 — a. Hence the values of 6 corresponding to the
two possible angular positions of the reflecting plane are determined.
Having chosen the value of 6 which is required, or which is compatible
with the position of the point 5 (Fig. i), / and m are given by formulae
(6) and (7), respectively. Since the codrdinates Xu yu and Zi are also
supposed to be known, the values of x\ 3/, and s' may be computed at
once from (3). Therefore the six parameters of equations (4) have been
theoretically evaluated from the assigned data.

The preceding analysis is pertinent to the theory of the design of
JC-ray spectrometers in two respects: (a) it facilitates the actual calcu-
lation of the position and direction of the reflected ray so that its inter-
section with a photographic plate, or its path in an ionization chamber,
can be predicted from the hypothetical positions of slits, diaphragms,
etc. — ^in particular, spurious images and stray rajrs can be anticipated
and eliminated; and (ft) the numbered formulae may be combined in
various ways leading to conditional equations having useful interpre-
tations. It may also be remarked that, as far as my information goes,
all the papers which relate to the geometry of " image " formation with
plane crystals restrict the problem to two dimensions, or more precisely,
to pencils of rays lying in one plane perpendicular to the axis of rotation
of the crystal (/5 = o). Although these uniplanar problems are un-
doubtedly the simplest and most important, nevertheless they afford no
information as to what happens when the angular altitude of the rays is
not equal to zero. As will appear later, images may be widened un-
synmietrically and appreciably, under special circumstances, due to the
fact that P is not sufficiently small.

Complete Ray Determined by Two Points, — ^A solution of the following
problem will now be outlined: To find a formula for 6 being given the
value of the glancing-angle y and the two independent conditions that

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Na"if^'] GEOMETRY OP IMAGE FORMATION, 5

the incident and reflected rays shall pass through the fixed points {xu yu
Zi) and (xj, ytt Zt), respectively. Equations (4) already satisfy the first
condition hence they will involve both conditions when written as

fn(xi - x') = l{yi - y),

n{xi — jcO = /(«! — 20«

Substitution, in the first equation, of the expressions for x', y, /,
and m given by (3), (6), and (7) leads to

(xi sin 26 — yi cos 26 + yt) sin (26 — a)

+ (xi cos 2$ + yi sin 26 + xj) cos (26 — a) = o. (9)

Similarly, the second equation when combined with (3), (6), and (8)
reduces to

Xi tan p cos 26 + yi tan fi sin 26 + xt tan p

+ («i — «i) sin (26 — a) = o. (10)

Assuming, for the time being, that the trinomial coefficients in (9)
do not vanish simultaneously and that (10) is not satisfied by having
j3 = o and 21 — 21 = o, the elimination of a and fi from formulae (5),
(9), and (10) may be effected by the following operations. The square
of (5) may be transformed into

tan* P = [sin* (^ — a) — sin* 7] esc* 7,

which is then equated to the expression for tan* p obtained directly
from (10). Since ^ — a is identically the same as (2$ — a) ^ $ it
follows that

sin* (d — a) = i(^ + T* cos 2^ — 2r sin 2^ + I — cos 2^)(i + T*)"^

where r s tan (2O — a). Consequently the equation resulting from the
elimination of tan* p may be written as a rational function of r, sin 26,
and cos 26. Elimination of r is accomplished at once by substitution of
r from (9). The equation finally obtained is of the form

2i4 sin 2d + 5 cos 2d + C = o,
where

A s Xiyi + xtyt + («iyi + x^yi) cos 27,
JB s xi* + Xt* — yi* — ^2* + 2(xiX2 — yiyt) cos 27,
C s 2x1X2 + 2yiy2 - (21 - 22)*

• + [xi* + Xi* + yi* + V + (21 - 2i)*] cos 27,

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6 HORACE SCUDDER UHLER. [^S

Since sin 29 = 2/(1 + ^)-* and cos 2^ = (i — ^)(i + /»)-*, where
m tan ^, the last equation may be transformed into the following
quadratic in the single unknown quantity t

afi + 2bt + c ^ o,

a s Cvi + yi)* cos* y - [(xi - «,)« + («i - ««)*] sin* 7,

& = («! + *«)Cyi + y«) — 2(xi3f, + xtyi) sin* 7,

c s (xi + xj)* cos* 7 - [Cvi - yt)* + («i - 2«)*] sin* 7. .

(II)

It should be remarked, in passing, that formula (11) may also be
derived by making use of the fact that the reflected ray (extended back-
ward) must pass through the virtual image of the point (xi, yi, «i).
As formula (11) is of the second degree, the conclusion may be drawn
that, in general, not more than two rays can be constructed when one point
on the incident segment, one on the reflected segment, and the glancing-angle
are given. In applying the quadratic to numerical data it sometimes
happens that one of the roots corresponds to a position of the mirror
for which the points {xu yi, zi) and (xj, yt, Zt) are on opposite sides of
the reflecting plane, thus causing one of the points to play the rdle of a
virtual image. By equation (i), a necessary and sufficient condition
for the points to lie on the same side of the plane is that xi + tyi and
Xt + tyt shall have like signs.

In the special case where both of the given points lie in a plane per-
pendicular to the axis of rotation («i = Zt), the roots of (11) may be
reduced to the following rational form

^ ^ ^ (xi + Xt) cos 7 =F (yi - yt) sin 7 .,.

"^ (xi - xs) sin 7 ± Cvi + ys) cos 7 '

in which the upper signs, or the lower ones, must be taken together.*

Point Source and Negligibk Penetration. — ^The special case of rays
lying in a plane perpendicular to the axis of rotation of the mirror will
next be considered. This condition is represented by /9 = o and Zt — z%
= o, hence formula (10) is satisfied irrespective of the (finite) values of
xi, Xs, yu a. and 0. The admissible solutions of (5) are now di ^ a + y
and ^t = X — (7 — a). Equation (9) reduces to

(x ^ yi sin 27) cos (27 dt a) db (y + yi cos 27) sin (27 ± a) = o, (12)
in which the subscripts 2 have been suppressed, Xi has been put equal
to zero for sake of simplicity, and the upper and lower signs correspond
respectively to Oi and Ot. As may be seen at a glance, the lines repre-
sented by the upper and lower equations of (12) always pass respectively

* The order of the signs corresponds to < ■» ( — 6 ± V?— ac)la.

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NoI"x!^'*] GEOMETRY OP IMAGE FORMATION. J

through the points (db yi sin 27, — yi cos 27) independently of a.
Therefore, aU rays lying in a plane perpendicular to the axis of rotation of a
plane selective mirror — the axis coinciding with the mirror (pure rotation) —
and radiating frofjt a single point will, after reflection ^ pass through two focal
points each of which is at the same distance from the axis a^ the radiant point,
the angles of deviation of the aodal or principal rays of the pencils being
numerically equal to twice the constant glancing-angle. This fundamental
theorem is not new, since demonstrations involving only elementary,
non-analytic geometry have been given by Bragg, E. Wagner, and others.
Nevertheless I have not seen a published proof which involves a concise,
formal statement of the special conditions under which the theorem is
valid. The limitations may have been fully appreciated, but they seem
to have been tacitly assumed.

By taking the sum of the squares of the corresponding members of the
equations

— «t =» «i cos 2^ + yi sin 2^,

— yi = Xi sin 2^ — yi cos 26,
it will be found immediately that

x^ + yi? = X? + y?.

Therefore as 7 varies, the image point {xt, yi) describes the circumference
of the focal circle having the radius ^x? + yi*.

Point Source and Appreciable Penetration. — ^The qualifying remark,
between the dashes in the last italicized sentence, will now receive atten-
tion. The pertinence of the question depends on the fact that, in general,
X-TBys penetrate to a finite depth into the diflfracting crystal, so that
rigorously not more than one plane of atoms can contain the axis of
rotation. If this plane is the mean effective one then the parallel active
planes must be situated on both sides of the axis and at different distances
from the same. The problem is, accordingly: To investigate the proper-
ties of rays lying in a plane perpendicular to the axis of rotation when
this axis is parallel to the reflecting surface, but does not coincide with
the surface.

In Fig. 3, 5 (a, o) is the radiant point. The axis of rotation and the
plane of the mirror are both perpendicular to the plane XOY, and they
intersect it in the point 0 and the line MN, respectively. Let p sjon-
bolize the length of the normal OF* dropped from 0 on Af JV, and let this
perpendicular make an angle a' with the direction OX. The equation
of the mirror is

cos a!'X + sin a'^y — p = o.

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HORACE SCUDDER UHLER.

fSSOOMO

LSsmiBs

The equation of the line joining 5 to its virtual image S' is

• y = (x — a) tan a'

hence, the co5rdinates of the foot of the perpendicular F dropped from 5
on MN are

Fig. 3.

oc* ^ p cos a' + a sin* a\

y' = (/> — a cos a') sin a\

Since S'F = FS the codrdinates of 5' are found to be

x" = 2p cos a' — a cos 2a\

y" ^ 2{p — a cos a') sin a'.

The angle which the reflected ray makes with OX equals (t/2) + a' — 7.
Therefore the equation of the reflected ray IR is

cos (a' — 7) '* + sin (a' — 7) •> + a cos (a' + 7) — 2/> cos 7 = 0. (13)
Differentiation of equation (13) with respect to a' gives

sin (a' — y)*x ^ cos (a' — 7)-y + a sin (a' + 7) = O. (14)

The envelope of the reflected ray is found at once by eliminating a! from
the last two equations. (13) and (14) may be written as

and
where

A sin a' + B cos a! ^ C

B sin a' — A cos a! = o,

A s sin yx + cos yy — a sin 7,
B aa cos 7»x — sin yy + a cos 7,

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No*?'*] GEOMETRY OP IMAGE FORMATION. g

and

C ^ 2p COS y.

On squaring and adding the abbreviated equations, it is found that

(x + a cos 27)* + (y — a sin 27)* = {2p cos 7)*. (15)

Accordingly, the complete envelope is the circumference of a circle having
the radius 2p cos 7 and its center at the point Cy (— a cos 27, a sin 27),
which is identical in position with the focal point corresponding to
p = o. Formula (15) suflFers no modification when the source S and the
axis of rotation are on the same side of the mirror, that is, when the axis
is in front of the reflecting plane instead of behind it.

The general nature and rational form of the preceding equations,
together with the unlimited area of the reflecting surface, enable the
analytical conditions to be fulfilled by points situated on reversed pro-
longations of the lines. Such points are formally correct but they do
not correspond to the actual paths of the ^-rays. As some portions of
the envelope may also fail to satisfy the practical requirements of the
problem, and since the radius of the circle is not negligible for pene*
trating radiations, it becomes necessary to examine in detail the prop-
erties of this locus.

The co5rdinates of the point of contact 2? of the reflected ray with the
circle are easily derived from (13) and (15). They are

Xe - " a cos 2y + 2p cos y cos (a' — 7) 1 . ^.

yc — a sin 27 -f 2p cos 7 sin (a' — 7) [ *

Let 0 denote the angle made by the radius to the point of contact C-R
with the direction OX. Then

Vi, — a sin 27

tan 6 = ^^ :

Xc + a cos 27

hence, by (16), tan 0 = tan (a' — 7); therefore

0 = a' - 7.

This simple relation is very helpful in following the motion of the point
R when that of the point F' is known.

Now let another reflecting plane M'N\ which is parallel to MN and
at the same numerical distance p from 0, be taken into consideration.
Assuming 7 to have the same value for the plane M'N' as for MN, the

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lO HORACE SCUDDER UHLER. [j

codrdinates of the point of contact R' may be found either by changing
a' to T + a' or /> to ^ pin formulae (i6). Consequently

i(«« + «/) « - a cos 27,
iCy. + y*) = a sin 27,

and these are the co5rdinates of the center (X of the envelope. In other
words, under the specified conditions, the points of contact are situated
at the extremities of the same diameter. It is easy to show that the
points 5, /, and /' are collinear, so that both reflected rajrs arise from
one incident ray.

A fair approximation to the circumstances pertaining to a real crystal
may be made by imagining the space between MN and M'N' to be
filled with pairs of symmetrically situated reflecting planes for which p
varies continuously (grating-spaces are of the order 3 X lO"* cm.) from
zero to a maximum value. To each pair of planes will correspond a
little circular envelope, so that the entire area enclosed by the largest
circumference will be crossed by the ^-rays. It is therefore evident
that, when the medial effective reflecting plane of the crystal coincides
with the axis of rotation, the image of a point source will not be displaced
laterally with respect to the ideal image C, which corresponds to negli-
gible penetration. On the other hand, if the average reflecting plane is
sufficiently eccentric, the image may be displaced enough to influence
very accurate experimental work. Obviously, this displacement may
be on either side of the axial ray OC.

Attention should also be called to the radius of the envelope 2p cos 7.
As the -Y-rays become harder (shorter wave-length), not only does the
maximum value of p become greater but the glancing-angle 7 decreases,
thus causing cos 7 to increase. Hence, the radius is increased by both
of its variable factors. Theoretically, therefore, this is unfortunate
since the images become broader as the experimental difficulties inherent
in the usual methods of determining glancing-angles increase.

The preceding analysis and deductions are subject to such qualifica-
tions as may arise from the finite width of the aystal face, the distance
of the source 5 from 0, etc. For example, by combining the equation
of the mirror with formula (13), the co5rdinates of the point of incidence
/ are found to be

Xi ^ [p sin (a' + 7) — a sin a' cos (a' + 7)] esc 7,
yi = (a cos a' — p) CSC 7 cos (a' + 7).

The point F' being (J> cos a', p sin a'), the distance from .P' to / is given

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Vol. XI-l
Naz. J

GEOMETRY OP IMAGE FORMATION.

5 = [/> cos 7 — a cos (a' + 7)] esc 7.

(17)

Evidently the rotation of the crystal must not cause this quantity to
vary over a greater range than the width of the face of the crystal.

Broadening of Image by Oblique Rays. — ^As the effect of the altitude
angle P can be illustrated in a very large number of ways it becomes
necessary to choose some specific case when quantitative data are
desired. Accordingly, the following special problem has been selected
for the reasons that it is relatively simple, and that it conforms closely
to the experimental conditions which obtain when the ionization method
is used, or when the photographic plate is placed normal to the axis of
the beam of ^-rays.

In Fig. 4, the line ST, parallel to OZ, may be looked upon as a slit of
negligible width. Let the point S be (o, yi, — h). P indicates any
point on the focal circle (assum-
ing no penetration and no ec-
centricity) having the radius
OT = yi. By hypothesis, the
reflected ray IR is required to
pass through P (xj, yj, o). In
general, as the angle P varies,
the point P will move around
the circumference of the focal
circle, and the arc passed over
will correspond to the width of
the image which would be re-
corded on a photographic film
wrapped in the form of a circular cylinder, having OZ for axis and yi as
radius. Before proceeding to numerical quantities, two simple algebraic
relations must be derived.

Since Xi = «, = o and Si = — A, formula (10) reduces to

Xt = heat P sin {26 — a) — yi sin 2$
which, when substituted in equation (9), leads to

yt = yi cos 2^ — A cot P cos {2$ — a).
Substitution of these expressions in the equation of the focal circle

xt* + yt^ = yi*

Fig. 4.

gives

h = 2yi cos a tan p.

(18)

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HORACE SCUDDER UHLER.

.Sbrxbs.

In order to compare different positions of the point P, as this inter-
section moves along the circular arc, it is necessary to find a connection
between the angle Y'OP (ri) and known quantities. Replacing h cot P
by its equal 2yi cos a in the preceding simplified formulae for Xt and ytt
and noting that 2$ = {26 ^ a) + a, it will be found that

Xt = yi sin 2(6 — a),
^ yt — yi cos 2{B — a).

But

hence

tan 71 =

-yt
ri - 2{fi — a).

Therefore, under the given conditions, iy is equal to the deviation of
the orthogonal projection on the plane XOY of the ray SIR. (See
Z POQ, Fig. 2).
Finally, by formula (5),

sin 7

sin iiy =

cos P

(19)'

This equation shows that 17 has a minimum value when /3 = o, hence,
for slits of zero widths settings should be made on the inferior edge of a
photographic image in order to obtain the correct value of the glancing-
angle (i;o = 27, /3 = o).

The data for i/oi and A, in Table I., were calculated from the arbitrary
values of Po given in the first column, a being assigned the value zero
throughout. In all cases 7 = 15* and yi = 10 cm.

Table I.

00-

no-

A (mm.) .

0^ 0'

30''

0° 30'

30**

1.745

1* 0'

30*

17"

3.491

1* 30'

30**

38"

5.237

20 Q,

30**

6.984

2° 30'

30**

45"

8.732

3^ 0'

30*'

32"

10.482

^ It is interesting to note that this equation is identical in form and meaning with the
relation sin §Z? « sin §E cos lyi which occurs in the theory of oblique refraction through
prisms. Therefore, it is an expression of the single fact common to the laws of reflection and
single refraction, which is. that the angles of incidence and reflection or refraction lie in the
same plane containing the normal. See. H. S. Uhler, On the Deviation Produced by Prisms.
Amer. Jour. Science. Vol. 35, p. 389 (1913).

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Vol. XI,
No. I.

]

GEOMETRY OF IMAGE FORMATION.

The second column shows quantitatively how the point P (Fig. 4)
moves along the circumference as fio receives equal increments, a re-
maining unchanged. The second differences for 170 are practically
constant. The third column^ indicates the point on the slit through
which the ray must pass in order to give the corresponding value of 170.

If the image on a photographic film were of uniform density from one
edge to the other, and if settings were made on the middle of the image,
the error in the glancing angle would amount to + 0.03 per cent., for
Pa = 2° o' and 7 = 15°. Since o.oi per cent, seems to be attainable,
the angular subtense of the total length of the slit at the center of the
crystal should not exceed 3° when very accurate data are sought experi-
mentally.

Table II.

A (mm.).*

* a.

•♦-

•_.

1.048156

15*

10"

30*

31"

0' 11"

1.049

14^

50'

47"

29*

52'

10' 34"

1.050

14**

38'

21"

29*

39'

42"

23' 1"

1.060

120

22'

44"

27*

24'

38' 38"

1.070

36'

37"

24*

37'

58"

24' 45"

1.080

5«

37'

37"

20*

38'

59"

23' 44"

1.085

10'

43"

16*

12'

13*

50' 39"

1.0852

25'

24"

15*

26'

45"

14*

35' 57"

Table II. is intended primarily to illustrate the fact that, as the crystal
is rotated, different points along the slit send rays through a given point
on the focal circle- Since, in formula (18), a is operated on by the
cosine its sign cannot aflfect the values of the remaining quantities. In
other words, two rays, having the same angular altitude fi, can come
from a given point of the slit and pass, after reflection, through a properly
chosen, fixed point on the focal locus. The rays of such a pair have
numerically equal values of a but diflferent arithmetical values of 6,
the position angle of the reflecting plane. As fi changes sign so also will
h do likewise [by (18)] so that two points on the slit and equidistant
from the center of the same will simultaneously send two rays through
the chosen focal point. Hence, for a given numerical value of /3, four
rays can diverge from the slit and, as the crystal is rotated, eventually
converge to a single point on the focal circumference. It should be
emphasized, however, that only finite segments of the slit can come
into play in any actual case, since the angular positions of the re-
flector are theoretically limited by the condition that both the radiant
point and the image point must lie on the same side of the crystal. (In

^ Units are given to fix the ideas. The angles only determine the ratio hfyu

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14 HORACE SCUDDER UHLER. [^S^

general, the horizontal width of the crystal would restrict the length of
the effective slit segment more than the formal limiting condition just
mentioned.) If the rays be reversed, so as to treat the fixed point on
the focal circle as source and the slit as an image locus, then the properties
under discussion amount to a sort of astigmatism.

In Table II., yi = lo cm., Xt = 5.00683 cm., yi = — 8.65631 cm.,
i8 = 3° 6' 21", 7 = 15"^ o' o", and 17 = 30° 2' 43".

In applying photographic processes to the accurate determination of
the glancing-angles (with respect to a definite kind of crystal) of char-
acteristic -Y-rays it is not always convenient or desirable to place the
plate either normal to the axis of the beam of rays or as a mean chord
for a narrow region' of wave-lengths. (Photographic films are unreliable
for quantitative work.) Instead, the plate is placed normal to the line
which passes through the center of the slit and intersects the axis of
rotation at right angles. For sake of brevity, this line will be called
the '' collimation line." In this method care is usually taken to have the
distance from the axis to the latent image equal to the distance from the
slit to the axis, in order to take advantage of the uniplanar focal proper-
ties discussed above. For this case also, I have investigated, both
analytically and arithmetically, the broadening of the photographic
impressions due to the angular altitude fi. Even when a is kept equal
to zero the datum finally required depends upon the solution of a cubic.
It would be superfluous, therefore, to reproduce the analysis and numeri-
cal data in this place. Suffice it to state that, as might be expected, the
displacement of the center of the image is greater here than in the hypo-
thetical case of a cylindrical film previously treated. The relative in-
crease in displacement is primarily due to the changing azimuthal ob-
liquity of the rays with respect to the normal to the photographic plate.
An approximate idea of the conditions prevailing in the present problem
may be formed by referring to Fig. 4 and imagining the plate to be repre-
sented by a plane parallel to XOZ and passing through the point P,
when 1; has its least value 27. In all cases, the effect of /9 is to give too
large a value for the apparent glancing-angle and hence to produce a
positive error in the computed wave-length.

In all of the preceding cases the hypothesis was made that the reflecting
planes were parallel to the axis of rotation. Even when the incident
rays lie in the plane YOZ (Fig. i) and^are parallel to YO, an effective
obliquity is produced when the normal ON describes, during the rotation
of the crystal, a cone having OZ as axis. As a consequence of the
canting of the crystal the line on the spectrogram lacks parallelism to the
central image formed by the undeviated rays. Even if it were possible

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No'if^*] GEOMETRY OP IMAGE FORMATION. 1 5

to measure the plate along the line in which it was intersected by the
plane containing the collimation line and normal to the axis of rotation,
the distance obtained would not be exactly correct, so that a slight
error might be introduced in the calculated value of the glandng-angle.
The equation of the spectral line corresponding to the ideally simple
conditions specified in 'the preceding paragraph will now be given with-
out proof. It is

(1—2 cos* B cos* 4>')x' — cos $ sin 20'-s' + sin 2^-cos* 0'-yo = o. (20)

The plane of the plate is expressed by y = — yo. (Reference may be
made to Fig. i.) The origin of codrdinates is taken on the collimation

line^ The axes of x' and s' lie in the plate and are parallel respectively

to OX and OZ, if denotes the angle which the normal ON makes with
its orthogonal projection on the plane XOY. It is counted positive
when the complementary angle ZON is acute, that is, when the top of

the crystal is tilted back from the axis of rotation^ B symbolizes the

angle which this projection makes with the axis OX, Formula (20)
may be freed from the auxiliary angle B by virtue of the relation

sin ^ = sin 7 sec it.

The linear equation may be employed in two diflferent ways, (a) By
properly superposing two spectrograms, so as to magnify the angular
error, an approximate value of the slope of the spectral line can be ob-
tained. Equating the numerical value of this " slope " to its algebraic
expression derived from (20), an estimate of 0' may be gotten at once
by solving the resulting quadratic in cos 20\ (&) The intercept on the
axis of x\ derived from formula (20), may be employed in calculating the
order of magnitude of the error introduced by the maladjustment of the
crystal.

Assuming yi = 10 cm., 7 = 15*, and if = 1°, the values of the re-
maining quantities were computed to be: oco = 5 cm., y© = 5 V3 cm.,
B = 15** o' 8", slope angle = 92° 13' 51", and intercept on x' axis = 5.0027
cm. Therefore, the spectral image slants in the same general direction
as the crystal face and makes an angle of 2° 13' 5T" with the vertical.
This angle exceeds 20' by 11.5 per cent. The linear displacement along
the plate equals 0.027 mm. The calculated glancing-angle would be
15® o' 24", which corresponds to an error of + 0.045 P^r cent. My
short practical experience with the determination of glancing-angles
leads me to believe that, in the vicinity of 15^, it is possible to attain an
appreciably higher d^jee of accuracy than 1/22 per cent.

Practical Deductions, — In the first place, the preceding discussion of

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1 6 HORACE SCUDDER UHLER. [^22

the asymmetric broadening of spectral images due to obliquity in angular
altitude leads to the conclusion that, when the highest attainable ac-
curacy is required, diaphragms should be used so as to limit the vertical
height of the incident beam of ^-rays. Probably the most advantageous
location of one of the diaphragms would be (in the case of primary rays)
on the side of the anticathode itself. Although all the cases treated
analytically involved the assumption that the slits were of zero width,
it seems obvious that the various errors will not be decreased when the
slits have the finite horizontal aperture necessary for the practical trans-
mission of energy. In the following paragraphs, therefore, the hypothesis
will be made that the rays do not depart appreciably from planes per-
pendicular to the axis of rotation.

In the usual photographic method of determining glancing-angles it is
necessary to measure the perpendicular distance from the axis of rotation
to the plate. It is very difficult, if not impossible, so to adjust the
apparatus as to satisfy the definition of this distance, for, in the case of
rays of sensible penetration, the mean effective reflecting plane, which
should contain the axis of rotation, lies at a depth from the front face of
the crystal that involves uncertainty. Even if the crystal were in
perfect adjustment for one particular wave-length it would not remain
so for rays of appreciably different penetration. Doubt also arises as to
whether the gelatin side of the plate alwa3rs clamps at the same distance
from the axis of rotation, no matter how rigid the plate-holder itself
may be. (Gelatin is compressible, commercial dry plates are very often
curved and twisted, etc.)

The errors arising from these, and from many other, causes may be
largely, if not entirely, eliminated by the " Method of Displacement."
As far as I can find from the literature of the subject this simple idea is
new. It consists in taking one exposure when the plate is at a certain
distance from the crystal and then a second exposure when it is at a
different distance from the reflector. The displacement of the spectral
image, corresponding to some one wave-length, is a function of the
distance through which the plate has been translated parallel to the
coUimation line. The form of the function and the details of the calcu-
lation of the glancing-angle depend respectively upon the value of the
constant angle between the normal to the plate and the coUimation line,
and upon whether the measurements are absolute or are based upon
adjacent images pertaining to known wave-lengths. The interval of
translation may be determined with ease and great accuracy, whereas
only an approximate value of the distance between the plate and the
axis of rotation is required in any case. The plate can be pressed suf-

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NoI"if'*] GEOMETRY OP IMAGE FORMATION. I7

fidently flat by strong springs and, as it cannot move relative to its
holder, no doubt can arise concerning the distance through which the
plate has been translated. On the other hand, the method of displace-
ment involves the fundamental assumption that the images of the same
spectral line are sensibly identical in the two positions of the plate-
holder. As far as I have been able to find, both theoretically and experi-
mentally, this assumption is fulfilled by using hvo narrow slits of exactly
the same width. (Obviously, both slits must be completely filled by the
beam of ^-rays.)

The formation of a beam of ^-rays of constant cross-section, by two
slits of identical opening, will now be explained. As stated before, it
will be assumed that diaphragms have been interposed in the path of the
beam in such a manner as practically to eliminate any asymmetric
broadening of the images due to the angular altitude fi. For the time
being, the hypotheses will also be made that there is no penetration and
that the reflecting plane contains the axis of rotation. On the contrary,
the assumption that the slits are of zero width will no longer be retained.

The plane of the diagram (Fig. 5) is taken normal to the mutually

Fig. 5.

parallel long-axes of the slits S\ and 5s, but it does not have to contain
the collimation line. Now, by the fundamental theorem of the focal
circle (or cylinder), any ray which passes through the incidence edge £1
of slit Si will, aft?er reflection from the crystal at the given glancing-
angle 7 (monochromatic radiation being assumed), pass through the
point I\. The point /i is at the same distance from the axis of rotation 0
as the point £1, and the deviation of the line OIi with respect to the
line E\0 equals 27. The ray in question is not required to strike the
crystal at the point 0. If the ray also passes through the emergence

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1 8 HORACE SCUDDER UHLER. [^SSS

edge Et of slit St it will, after reflection, pass through a point It. This
point is likewise determined by the conditions Olt = EtO and Z EtOIt
= T — 27. Hence, one extreme diagonal ray EiEt takes the direction
It'll after reflection. Similarly the incident rays EiEt, -Ei-Ei, and
Ei'Et will become the reflected rays Itli, Itlu and /2'//, respectively.
In general, therefore, a ray which passes through any point P within
the rectangle EiE%EtEi will, after selective reflection, pass through the
homologous image point P', such that OP' = PO and z POP' = x — 27.
Since all rays that pass between the jaws of both slits are confined
between the parallel segments EiEt and E\Et it follows at once that
the reflected beam cannot escape through the sides Iti\ and Itl\ of
the rectangle Iiltlt'Ii- Consequently as long as the gelatin side of a
plate is moved parallel to itself .(along the collimation line or in some
other direction), and is kept within the limits set by the condition that
the sensitized surface shall not intersect the reflected beam at any point
outside of the rectangle Ixltltli, the images will be of constant width,
and their relative shifts will be directly proportional to the displacement
of the plate. As the length of the rectangle Itl\ is equal to the constant
distance EiEt between the slits it is independent of the glancing-angle
involved. Hence, the length Itl\ is dependent neither upon the wave-
length of the ^-rays nor upon the grating-space of the crystal. On the
contrary, the projection of Ith on the collimation line is a function of the
glancing-angle. In particular, if the photographic plate is kept normal
to this line the interval of translation is a little less than Itli cos 27.

If all the incident rays were strictly parallel to EiEt then all of the
reflected rays would be exactly parallel to /t/i, the beam would experi-
ence reflection for only one angular position of the crystal (assuming
that the curve of reflection is extremely steep on both sides of the maxi-
mum), and nothing would be gained by rotating the crystal. These
conditions would be fulfilled quite independently of penetration and of
any eccentricity of the mean effective reflecting plane. By drawing
lines, representing traces of planes, parallel to the lines which pass
through 0 (Fig. 5) and which indicate three positions of the single non-
eccentric reflecting plane, it is easy to see that the effects of symmetrical
penetration and of eccentricity would be respectively to increase the
cross-sections Iili and Ith'y and to shift the principal axis of the reflected
beam parallel to itself. [The rays IR and I'R! (Fig. 3) are parallel and
arise from the single incident ray SIV] Simple displacement without
alteration either in direction or in constancy of cross-section would
have no influence on the present method of determining glancing-angles.
Hence, all restricting conditions, save fi negligible, have been removed.

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Na'if^*] GEOMETRY OF IMAGE FORMATION. 1 9

The method has been tested experimentally, by Dr. C. D. Cooksey*
and myself, for the fairly soft rays of the K series of gallium and of the
L series of tungsten, and found to be very convenient and accurate.
We have not had time, as yet, to try it with very penetrating -Y-rays.
If, for some unforeseen reason, the scheme of using two equal slits simul-
taneously should eventually be found unsatisfactory for very hard rays,
the method of displacement may still be applied by using slit 5i alone
when the plate is near the focal spot /i//, and then employing slit 5i
alone with the plate near /1/2'. The last application of the general
method might require especially accurate construction and adjustment
of the spectrograph, but it would retain all the desirable features (such
as intensity) of the usual method of experimentation together with the
great advantage of knowing precisely how far the plate has been trans-
kted.

Summary.

1. The general equations of incident and reflected rays have been
derived.

2. It has been demonstrated that, in general, not more than two
rays are determined by one point on the incident segment, one point on
the reflected segment, and the glancing-angle.

3. The special theorem of the focal circle has been stated and proved
in a perfectly general manner.. It has been shown that this theorem
involves the following assumptions: (a) The rays of a pencil must all
lie in one plane perpendicular to the axis of rotation of the crystal,
(b) the rays must not penetrate the crystal to a finite depth, (c) the
reflecting plane must contain the axis of rotation, and (d) the slit must
act as a mathematical line source.

4. It has been shown analytically that a circular envelope arises when
the reflecting plane is parallel to the axis of rotation, but does not contain
this axis. Special properties of this locus have been demonstrated.

5. It has been proved that rays having finite angular altitude produce
asymmetric broadening of the spectral images even when the azimuth
is zero. It has been shown that, when the angular altitude is constant
and the azimuth is finite and variable, the bundles of rays have astigmatic
properties. The fact that this broadening is alwaj^ in such a direction
as to lead to too large a value of the glancing-angle has been demon-
strated. The special case of a photographic plate normal to the line of
collimation has been discussed.

6. The results obtained from an analytical study of the alteration in

» Sec " The K Series of the X-Ray Spectrum of Gallium," by H. S. Uhler and C. D.
Cookiey, Phy. Rbv.. N.S., p. 645, vol. X., Dec, 1917.

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20 HORACE SCUDDER UHLER. [^5^

the slope and intercepts of a spectral line, due to tilting the reflecting
planes of atoms with respect to the axis of rotation, have been given.

7. Whenever possible, the practical bearing of the theoretical con-
siderations has been discussed. In particular, the theoretical and experi-
mental aspects of a supposedly new method for the accurate determina-
tion of glancing-angles have been presented at some length. In so doing,
slits of finite width and rays of sensible penetration have been considered.
The general method involved has been styled the ** Method of Dis-
placement," and two ways of applying it have been suggested. One of
these ways has been tested experimentally^ and found very convenient
and accurate.

Sloans Physical Laboratory.
Yalb Univbrsity,
August 17* 191 7*

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nS"!^^'] intensities of d lines of sodium. 21

THE RATIO OF THE INTENSITIES OF THE D LINES OF

SODIUM.

By Vivian Voss.

TT has been known for a long time that the ratio of the intensities of
^ the D lines varies with the intensity of the sodium flame.

Gouy^ found the ratio Dt/Di to vary from 1.3 for a strong flame to 2
for a weak flame.

An investigation by Brotherus^ showed that the ratio varied from 1.25
to 1.53.

Some observations made by Wood' indicated that, for an exceedingly
weak flame, the ratio attained a value as high as 3 or 3.5. The estimate
was made by comparing photographs made with different times of
exposure, and it was assumed that the blackening of the photographic
plate was directly proportional to the time of exposure.

This large value of the ratio was questioned in a recent paper by
Ladenburg,* and so, at the suggestion of Professor Wood, a more careful
investigation was made.

In the present work, three methods have been employed:

(a) A photographic method, based on the use of a sectored disc.

(b) A visual method in which the intensities were made equal by a

polarization method.

absorption, were used.
We shall consider first the photographic method. — ^A sectored disc (Fig. i)
was prepared, for which the ratio of the time of exposure of any element
to that of the next adjacent element was 5/4. The
disc was backed by a large flame from a Meker r^^^^
burner, and an image of the upper portion of the y V
disc sharply focused on the slit of a large plane- ^
grating spectrograph. The flame was charged with ^ —
sodium and the slit of the spectrograph opened pjg j

until the rectangular images representing the two
wave-lengths Dt and Di just touched. If, now, the disc was set in rota-

I G. Gouy, Ann. de Chem. et de Pbys., 18, 5, 1879.

* Hj. v. Brothenis, Ann. der Pbys., 38, 397, 19x2.
» R. W. Wood. Phys. Zeit.. 15, 382, 1914.

* R. Ladenburg, Ber. der Deut. Pbys. Ges., 12, 765, 1914.

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2 2 VIVIAN VOSS. [sSm^

tion by a small motor, the lines were cut into seven horizontal strips
of varying, int^rated intensity.

To obtain the maximum value of the ratio, it is necessary to work
with a flame of much less intensity than any commonly employed in
the laboratory. The easiest method of obtaining such a flame is to
charge the air of the room with sodium by operating a rather intense
sodium flame for a few minutes. As the work was carried out in a large
room, and the doors and windows were kept shut, it was possible to
obtain in this way a very feeble flame which remained practically constant
for an hour or more. It is important to have the grid of the Meker
burner perfectly clean, and the air should be* free from dust, for if this
is present the particles make bright flashes of sodium light as they pass
through the flame. These flashes are many times brighter than the
feeble flames with which the large ratios are obtained. By avoiding
unnecessary movement in the room after the dust particles had been
allowed to settle, the number of flashes could be reduced. With a very
intense flame the plate was exposed for three seconds, while forty minutes
were required in the case of a very feeble flame. This makes the ratio
of the extreme flame intensities somewhat less than i : 800. The
intensity ratio Dt/Di was determined for a given plate by picking out
the two exposures (horizontal strips) for one of which Z>j showed the
same photographic density as that of Di on the other.

The sectored disc was rotated at a very slow speed,^ and it was at first
assumed that the density of the image on the photographic plate was
directly proportional to the time of exposure. On the above assumption,
the ratio D2ID1 could be immediately determined as the inverse ratio of
the times of exposure which made Dt and Z>i equally black on the plate.

As no Hartmann photometer was available the comparisons were
made by cutting the plate in two at the dotted line, Fig. i , superposing
the two halves, film to film, and matching Dt on one piece gainst Di
on the other, with the aid of a magnifying lens. This method is fairly
accurate, as by carefully fitting the plates the dividing line between the
two patches under examination can be made to disappear as in a photom-
eter.

Preliminary work showed that an exposure ratio 5 : 4 could be easily
detected in this way, and this ratio was accordingly adopted in making
the sectored disc.

The intensity ratios that could be determined in this way were as
follows:

I, 1.25, 1.56, 1.95, 2 44, 3.05, and 3.81.

* K. Schwarzschild, Astrophys. Jl., XL. 92, 1900.

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No*!^^] INTENSITIES OF D LINES OF SODIUM. 23

Care was taken to avoid having any of the horizontal strips either under
or over exposed.

With a very intense flame the ratio D2/D1 = 1.25 was obtained and
with the feeblest flame Dt/Di = 3. This maximum value 3 was later
shown to be too large, owing to a source of error in the photographic
method which has not as yet been explained.

The decrease in the ratio with increasing flame intensity is due to the
more powerful absorption of the D2 light. That absorption may fully
account for the effect was shown in the following way: The slit of a
spectroscope was illuminated by a feeble sodium flame and opened, as
before, until the two rectangles corresponding to Z>i and Dt just touched.
A glass bulb, highly exhausted and containing some sodium, was inter-
posed between the flame and the slit, and the sodium was vaporized by
playing a flame over the bulb. The large ratio for the weak flame
immediately dropped to the smaller value found for a more intense
flame. To get the maximum value of the ratio we should abolish absorp-
tion completely. We of course approximate this condition in a flame
very lightly tinted with sodium, but if we could powerfully excite a very
thin layer of the gas, the conditions would be still more favorable. Ac-
cordingly, a canal ray tube,^ Fig. 2, was
made. The cathode consisted of an
aluminum disc, punched with numerous
holes. The copper wire leading to this
was insulated by a piece of thin glass
tubing. The canal rays issuing from the
holes in the cathode struck the lump of
rock salt R, and in this way a highly
luminous and exceedingly thin layer of

sodium vapor was obtained. The ratio Dt/Di was no larger than for a
very weak flame.

The same value of D2/D1 as for a feeble flame was also obtained by
passing an electrodeless discharge through a vacuum tube containing
sodium vapor. An image of the central capillary portion, which was
about two millimeters in diameter, was thrown by a lens upon the slit
of the spectrograph. The tube was heated to allow the discharge to

* If the tube is made of sodium glass, in the absence of the rock salt R 2l bright sodium
fluorescence is obtained on the end of the tube on which the canal rays impinge. It was
suspected that the extreme shallowness of the glowing layer might result from the circumstance
that a thin layer of glowing sodium vapor is imprisoned by a layer of adsorbed air, and a
test of this hypothesis was made by heating a small portion of the bulb, thus driving off the
adsorbed air at that point. This region ceased [to fluoresce though the rest of the bulb
fluoresced brightly. On admitting air into the tube and allowing this to cool, the portion
which had been heated gradually recovered its power of fluorescing.

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24 VIVIAN voss. [iS»

pass, and a photograph of the D h'nes taken. An exposure of five minutes
was necessary. The Z>j line on this plate was matched with a Dt strip
on one of the plates taken with the rotating sector and a weak flame.
The Z>i line was found to match with the Z>i strip showing that the ratio
was that obtained with a weak sodium flame.

Polarization Method, — ^The polarization method was next tried. Pro-
fessor Wood's quartz block,^ 32 mm. thick and cut parallel to the optic
axis, was used.

If a beam of sodium light polarized in a plane making an angle of 45^
with the optic axis (which is vertical) is passed through the block, the
rays Z>i and Z>2 on emergence will be polarized in mutually perpendicular
planes. Either Z>i or Dt can be extinguished by a Nicol prism properly
oriented, and with the Nicol in some intermediate position Di and Dt
can be made of the same intensity. By observing the position of the
Nicol when this condition obtains, the original intensity ratio can be
computed.

For a full description of the block and its uses the reader is referred
to Professor Wood's original paper. Light from a sodium flame was
made parallel by a lens and passed through a Nicol prism, so that on
emerging its direction of vibration made an angle of 45® with the vertical.
It was then passed through the quartz block, through a second Nicol,
and brought to a focus on a slit of the spectrograph by a lens.

The quartz block was first removed and the second Nicol crossed ac-
curately with the first. The reading on the graduated circle of the
second Nicol was then taken. The block was now introduced and rotated
slightly about a vertical axis until Di was cut out. On turning the second
Nicol through 90®, Dt was cut out. Between these two positions there is
one position for which the intensities of Di and Dt can be made equal.
If B is the angle between this direction and the direction of vibration
of £>j, then the ratio of the intensity of Da to that of Di is tan* 6, To
obtain large values of the ratio, however, feeble flames must be used,
and after passing through the Nicols the light is much reduced in intensity.

Some difficulty was experienced at first in making settings for the
position of equality, but after much practice settings could be made
which differed by less than two degrees. The mean of many readings
was taken. The chief source of error lay in the setting of the first Nicol
so that the light incident on the block was polarized in a plane making
an angle of 45** with the optic axis. If this angle was less than 45**,
on emerging from the block D% made an angle less than 90° with Di as
can be seen from Fig. 3.

» R. W. Wood. Phil. Mag- 27, 524, 1914.

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Na'x^^'] INTENSITIES OF D LINES OF SODIUM, 25

ODi represents the condition of vibration of incident light. It is
analyzed by the block into OX and OY. On emergence the direction
of vibration of Z>i is parallel to its original direction, but in the case of Pj,
OX is rotated through 180** to 0X\ and the resultant direction of vibra-
tion is now parallel to ODi, also making an angle ^ with the optic axis.
If <t> is less than 45** the angle between ODi and OD2 is less than 90®,
and similarly if 4> is greater than 45°, the angle is greater than 90®.

Now the ratio of the intensities D^/Di is given by tan' d, where 6 is
the angle between the position of equality of the second Nicol and the
direction of vibration of D2.

In Fig. 4, ODi and OD2 represent the directions of vibration of Di
and Di respectively. OP represents that position of the second Nicol
for which Di and Di on emergence are of equal intensity. OQ is per-
pendicular to ODi.

If < 2<f> (Fig. 3) is less than or greater than 90°, < 2f (Fig. 4) is greater
than or less than 90**.

If, as in Fig. 4, < 2f is greater than 90® the true value of the ratio
Di/Di is cos* a/cos* d, while the measured ratio is

and is larger than the true ratio. Similarly, if < 2^ is less than 90° the
measured ratio is too small. After the first Nicol had been set approxi-
mately, and the quartz block put in position, the second Nicol was turned
until Di was cut out. It was found difficult to make this setting ac-
curately owing to the small intensity of the light. The observed values
of Di/Di increased rapidly as 2f became greater than 90** and diminished
rapidly for values of 2^ less than 90°.

Values in the neighborhood of 2 were obtained for the ratio, with a
flame colored only by the sodium in the air when the air was heavily
charged with sodium vapor. Such a flame is fairly bright, though con-
siderably less bright than a flame colored by an asbestos wick dipped in
brine. As will be shown later, the value 2 was also obtained for such a
flame by the third (most accurate) method employed.

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VIVIAN VOSS,

[Sboomd
Sbubs.

For the feebler flames, burning in air only lightly charged with sodium,
it was extremely difiicult to make accurate settings. From one set of
readings a value 2.3 was obtained for the ratio, while another set, under
apparently identical conditions, gave a value 2.6. The readings of this
latter set are given below:

Second Nicol Crossed with Pint.

Di Extinguished by Second
Nicol.

Position of Eauelity of
Diandl>i.

-21^

70**

37^3

-22

36.2

-21

68 .

36.8

-21.5

37.6

-21

-21.8

37.5

Means - 21^4

68^7

37M

From these, 2^ = 90".! and B = sS'-S

I>i

= tan* e = 2.6.

Fig. 5.

This method can be used therefore for flames varying from very bright
to fairly weak, but is unsuitable for the feeble flames.

The largest accurate value given by this method is 2 and is obtained
for a flame burning in air strongly charged with sodium.

Visual Method. — ^The third method will now be discussed. Some gray
gelatin films, whose coefficients of transmission had
been determined to a tenth of one per cent., were
supplied through the courtesy of Dr. Mees, of
the Eastman Kodak Co. Narrow strips of these
were cut and put across the plateholder of the
large plane-grating spectrograph (Fig. 5). The
strip a let through 33^ per cent, of the incident light, 6, 40 per cent, and
c, 50 per cent.

The slit of the spectrograph illuminated with sodium light was opened
until the two rectangles corresponding to Dt and Z>i just touched. By
sliding the plateholder along, Z>a could be covered successively by a,
6, or c, and values 3, 2^ and 2 distinguished for the ratio Dt/Di. When
the air of the room was charged with sodium vapor, and the flame of a
Meker burner put before the slit, Dt and Di appeared of exactly the
same intensity when Z>2 was covered by c, the 50 per cent, screen. This
was true for the fairly bright flames obtained in this way (and even these
are considerably weaker than the flames colored by an asbestos wick
dipped in brine), and also for the weaker, down to the very feeble flames.
In every case the match was perfect.

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Vol XI.j INTENSITIES OF D LINES OF SODIUM. 2y

Since it was easily possible to distinguish the difference in ratio when
Dt was covered by the 40 per cent, and by the 50 per cent, screens, it
was estimated that the value 2 for the ratio Dt/Di was correct to within
10 per cent. This direct method is certainly the most reliable of the
three.

Investigation of Apparent Inconsistency of Results of the First and
Third Methods, — It was now necessary to investigate the inconsistency
in the value 2 given in this method for the ratio in the weaker flames and
the value 3 given by the first (photographic) method.

An oblong slit, 24 X 6 mm., was cut in a sheet of cardboard and
covered with a yellow screen which cut off everything below the D lines.
Half of this slit was covered with a strip of the 50 per cent, gelatin screen.
This was backed first by a sodium flame and between the flame and the
slit was placed a piece of uniformly diffusing ground glass. Photographs
of the slit were now taken with varying times of exposure by means of
an ordinary box camera. The photographs were all taken on the same
plate by sliding the plate along in the plateholder between exposures.
One set of times of exposure were as follows: 4, 8, 12, 16, 24, 36, and 4
seconds. The last exposure of 4 seconds was taken to determine whether
the intensity of the flame had changed during the experiment. A con-
stant flame was obtained by putting a small piece of sodium glass tubing
on the grid of a Meker burner. The times of exposure were determined
by the swings of a seconds pendulum. The plate was cut lengthwise,
the two parts placed film to film, and the darker half of one strip was
matched against the light half of another. In every case it was found
that the ratio of the times of exposure of two half-images that matched
was 3:1, exactly as had been obtained in the photographs with weak
flames for Z>i and D2 in the first method.

Great care was taken to have the density of the image uniform through-
out the length of the strip, as otherwise an error would be made in
matching the strips unless the match was made exactly at the dividing
line.

The slit was now backed by a tungsten lamp placed behind a diffusing
screen made of two sheets of ground glaiss and a set of exposures again
made. The ratio of the times of exposure of the strips that now matched
was 2:1. The difference in the effects obtained with a sodium flame
and with a tungsten lamp cannot be due to a difference in the coefficient
of transmission of the gelatin film for sodium light, for the yellow film
placed over the artificial slit cut off everything below the D lines, and
the sensitivity of the Cramer isochromatic plates used falls off rapidly
above the D lines. This was further verified by illuminating the slit

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28 VIVIAN VOSS, j^SS!

with a very sharp continuous spectrum in the region of the D lines,
obtained from a monochromator. In this case also the ratio of the times
of exposure was 2:1.

It is also impossible to explain the difference by a variation with the
wave-length, in the quantity k in Schwarzschild's equation for the
blackening of the photographic plates, 5 = //* (5 is the density of the
image, / the intensity of the light, / the time of exposure, and k a quantity
varying slightly with the plate used and the wave-length of light),
owing to the very narrow range of wave-lengths used.

These results made it appear as if a curious difference existed between
the behavior of the photographic plate towards white light and mono-
chromatic light. This would bring the results obtained by the first
method into perfect agreement with those obtained by the other two
methods. For a ratio 3 for the times of exposure obtained with the
sectored disc means a ratio of Di/Di = 2.

A large number of experiments were made, all of which gave very
nearly the same results. Dr. Mees has however failed to confirm them
in the research laboratory of the Eastman Co. and the source of the
discrepancy has not been located at the present time.

Summary.

By three independent methods it has been shown that the maximum
value for the ratio of the intensities of the D lines of sodium is Dt/Di = 2,
correct to within 10 per cent.

In conclusion the author wishes to express his hearty thanks to Pro-
fessor R. W. Wood for suggesting the problem to me and for the many
suggestions made throughout the course of the investigation.

Johns Hopkins University,
June. 191 7.

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No*!?^] THERMODYNAMICS OF FLUORESCENCE, 29

ON THE THERMODYNAMICS OF FLUORESCENCE.

By E. H. Kennard.

THE relationship between thermodynamics and fluorescence does not
seem to have been investigated hitherto in as thorough a manner
as the subject deserves. In the present paper the conclusions that can be
obtained without adopting special hypotheses are first carried a littie
further than is done by Pringsheim^ in his discussion of the subject, and
a plausible hypothesis concerning the properties of the fluorescent process
is then advanced and is found to lead to an interesting relationship
between fluorescence and the black body spectrum which appears to
be confirmed by experiment.

Throughout the paper it will be assumed that fluorescence is a rever-
sible process, so that thermodynamic equilibrium is possible in a system
containing a fluorescent substance. .

Let us first consider an isothermal enclosure containing an isotropic
fluorescent substance. In the latter there will be set up the usual
flux of radiation corresponding to the temperature of the enclosure;
let /i denote the normal flux per unit of wave-length at wave-length Xi.
(/i is therefore the flux in vacuo multiplied by the square of the refractive
index.) The existence of equilibrium now requires as usual that the
radiant energy emitted by the substance shall be equal to that absorbed
for each wave-length separately; but in the present case the emission
consists in part of fluorescence. The latter may be denoted by

'■=P-

/jrfX,, (i)

where /12 is the "coefficient of fluorescence," i. «., the fluorescent emission
per unit volume and per unit wave-length at Xi which is excited by unit
normal flux of wave-length X2; Fi is thus the fluorescent emission excited
by black body radiation at the temperature of the enclosure and may be
called the full fluorescent emission corresponding to that temperature.

Hence, denoting by £1 the intensity of thermal emission per unit
volume at Xi and by ai the coefficient of absorption,

Ei + Fi= aiJi. (2)

» E. Prin^heim, P. Z. S.. XIV.. p. 129. 1913.

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30 E. H, KENNARD, [i

Instead however of concluding, with Pringsheim, that Kirchhoff's law
fails for fluorescent substances, it seems preferable to generalize the law
itself as follows : In different substances at the same temperature the absorp-
tion is proportional to the sum of the thermal and the full fluorescent emissions
at each wave-length.

It is more convenient, however, to think of the absorption as con-
sisting of two parts :

Oi = ai + ft,
where

ai = Ey/A (3)

and is the coefficient of the ** thermal absorption" which equilibrates
the thermal emission, while

ft = Fi/Ji (4)

and is the coefficient of the "fluorescence absorption** which equilibrates
the fluorescent emission in the enclosure. The distinction seems likely
on general grounds to be a real one, but it may not be; nor can we say
a priori whether the fluorescence absorption should be affected by the
action of the exciting light — an effectwhich has been looked for repeatedly
but without success.

We may now deduce certain conclusions applicable to an isolated
fluorescing body. Let us suppose first that the exciting light is so
adjusted that its spectrum is proportional in intensity at all wave-lengths
to the black-body spectrum corresponding to the temperature of the
fluorescing body. Let us assume further as an experimental fact that
proportionality holds between fluorescence and exciting intensity. Then
if F' denotes the intensity of fluorescent emission per unit volume, and
/', the intensity of flux of the exciting light, the former will bear to full
fluorescence the same ratio that the latter bears to black-body radiation,
and by (4) we shall have for any wave-length Xi

Fi' = ft//, (5)

where all quantities are taken for the same wave-length.

Such a distribution in the exciting spectrum never occurs in practice,
but we may utilize our result as follows: let us choose that wave-length
X2 at which the flux of exciting light, J2, bears the greatest ratio to the
black body flux, and let Ji in (5) be taken to bear this same ratio to
black body radiation at wave-length Xi; then clearly the value of Fi
given by (5) sets an upper limit to the intensity of fluorescent emission
obtainable. For the fluorescent emission would have this value if the
exciting intensity were increased until it stood in the same ratio to black

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Na*!^'*] THERMODYNAMICS OF FLUORESCENCE. 3 1

body radiation at all other wave-lengths as it does at X2. Substituting
such a value of Ji in (5) and letting Fi denote the intensity of fluores-
cence actually obtained, we have

F/^/3iy'//, (6)

where J\ and J% refer to black body radiation at Xi and X2 resp. If
Planck's law holds,

J, \\i)

or, taking T = 293° abs. and Xi of the order of 5-10"* cm., roughly

A''
and therefore

F/ ^ Pie ' ^ //. (7)

Observational material for an exact test of (7) is lacking; but certain
qualitative conclusions can be drawn. If the exciting light at the
wave-length X2, where it differs most from black body radiation, is of
shorter wave-length than the fluorescence (X2 < Xi), the exponential will
be greater than unity and usually very large, yet fluorescence is at best
relatively weak: thus the fluorescence absorption ft may easily be
exceedingly small and impossible to detect, which is in harmony with the
fact that fluorescent substances commonly show no unusual absorption
in the region where the fluorescence is strongest. But where Stokes's
law is violated (X? > Xi), the exponential becomes very small, and either
Pi must increase greatly or the intensity of fluorescent emission per
unit volume must become very small, and in either case the fluorescence
would be difficult to observe. Stokes's law should therefore in practice
be nearly true; and as a matter of fact violations of it have not been
observed for a value of (X2 — Xi)/X2 much exceeding .03, for which the
exponential in (7) becomes .034. But even over this restricted range the
fluorescence can hardly be of visible intensity unless ft is of appreciable
magnitude; and it is noteworthy that in solids and liquids, at least,
violations of Stokes's law seem to be observable only where the fluores-
cence band is known to overlap an absorption band.

Apparently no further results can be obtained with complete rigor.
But it is a characteristic feature of thermodynamics that further con-
clusions of great interest can often be obtained by adding certain more
or less plausible assumptions; in other words, it is often possible to find

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32 £. H. KENNARD, |^S.

a special set of assumptions which taken together are incompatible
with the second law; and while thermodynamics does not tell us which
assumption is the faulty one, yet we can often decide this point with
good probability on other grounds. An instance of this is afforded by
Stokes's law, which can be deduced theoretically only if the fluorescence
absorption is ignored.

Similarly, absorption of the exciting light can probably not be inferred
with rigor from thermodynamical considerations — the fluorescent energy
might be derived from the heat energy of the substance. But the
additional assumptions required in this case are so plausible and the
general likelihood of the conclusion is so strong that the occurrence of
such an absorption is highly probable. Its existence will accordingly
be assumed in the second part of the paper.

II.

The general argument thus leaves undecided the double question,
what is the source of the fluorescent energy, and what becomes of that
part of the absorbed energy which corresponds to the fluorescence and
is determined by the coeflficient /3; further progress is possible only on
the basis of special hypotheses. We shall accordingly assume, first,
that thermal emission and fluorescence are thermodynamically inde-
pendent so that the thermal emission and its equilibrating absorption,
determined by the coefficient a, may be left out of account without
affecting our conclusions touching the fluorescence; and, second, that
the energy of fluorescence is under all circumstances derived entirely
from the energy of the exciting light. The latter assumption seems
especially plausible in view of the fact that the fluorescent process leaves
(by the general hypothesis underlying the present paper) no permanent
change in the substance and should therefore be accompanied by no net
heat change; the immediate action of the exciting light, if it consists
in a chemical transformation or in the liberation of electrons, may well
be accompanied by a reversible heat change, but the latter should be
exactly reversed during the occurrence of recombination with the emission
of fluorescent light.

These two assumptions lead at once to the conclusion that the energy
absorbed from each monochromatic component of the exciting light in
consequence of the fluorescence absorption /3 is equal to the energy of
fluorescent emission excited by that component. For when fluorescence
is excited by an isolated monochromatic beam the absorption cannot be
less than the emission, there being by hypothesis no other source of
energy available for the latter. But then, if the absorption exceeded the

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Na*x?^'] THERMODYNAMICS OF FLUORESCENCE. 33

excited emission for certain wave-lengths, the absorption from full
radiation would exceed full fluorescence, whereas for equilibrium (since
we may ignore thermal absorption and emission) these two quantities
are equal.

Expressing the conclusion just stated in symbols, we have, for any
spectral intensity of flux Ji' of the exciting light,

ft/i' = J*/2i/i'rfX,.

where /n denotes as before the intensity of fluorescent emission at Xi
excited in unit volume by unit flux at Xi, so that the right-hand member
denotes the total fluorescent emission per unit volume and per unit of
wave-length of the exciting light.
Hence

?i = I ftidXit

ft = J ftidk^. (8)

which states simply that at any wave-length the coefficient of fluorescence
absorption is equal to what we may conveniently call the "exciting
power," viz., the total fluorescent emission per unit volume excited by
unit flux of that wave-length. This gives us a definite indication of the
magnitude of the fluorescence absorption which we were not able to
obtain without the aid of our special hypotheses. Since in practical
cases the exciting power is always very small, the same will be true of
the fluorescence absorption.
We may now combine this result with (i) and (4), obtaining

I /u/idXj = /i I /n(fX,, (9)

«/o «/o

where Ji and /j refer now to black-body radiation. This may be re-
garded as an int^ral equation for the determination of the coefficient
of fluorescence /(Xi, Xa). The range of possible solutions is too broad
to allow of any rigorous conclusions, but a solution whose simplicity
commends it as physically probable is:

/12/2 = /21/1. (10)

If we may assume that fluorescence is proportional to the intensity of
excitation, so that /is independent of the latter, then this equation would
assert that the spectral intensity of fluorescence at Xi excited by unit
flux of wave-length X2 bears to the reverse intensity at X2 excited by unit
flux at Xi the same ratio as the intensities in the black body spectrum

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34 ^- B, KENNARD, [gjj^

at Xi and X2 resp. If this conclusion is correct, the reason for the ap-
proximate validity of Stokes's law becomes very evident.

Equation (10), assuming proportionality, lends itself readily to an
experimental test even in the case of a line spectrum. Let two narrow
wave-length intervals be selected, AXi and AX2, each including one or
more lines, and let the specimen be illuminated with portions of a con-
tinuous spectrum confined in turn to each of the chosen intervals but
having in both cases the same uniform spectral intensity of flux, /'.
Then the total fluorescent energy in the interval AX2 emitted per unit
volume when the exciting light lies in AXi will be

Ft' ^ J' ( ( /nrfXidX,,

while that in AXi when AXj is excited will be

Fx' ^r f f /i2rfXi(fX,.

Now throughout these small intervals the black body intensity Ji and
Ji in equation (10) may be supposed constant, so that we can substitute
in the second integral

and treat the ratio JilJt as a constant. We then obtain

that is, the total fluorescent emissions excited in these two intervals of
wave-length under the conditions stated are proportional to the corre-
sponding intensities in the black-body spectrum. This conclusion could
easily be tested by using a mechanical photometer such as a photo-
electric cell.

Further theoretical progress is, however, possible, without loss of
rigor, if we assume, as has in certain cases been found to be true, that
the distribution of intensity within a fluorescence band is independent
of the wave-length of excitation. We may then write

/(Xi, X,) = f(Xi)^(X2), (12)

where ^(Xj) is the "exciting power" or total fluorescent emission excited
in unit volume by unit flux at Xj, while f (Xi)dXi is the fraction of this

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Na"x^^*] THERMODYNAMICS OP FLUORESCENCE. 35

emission included within dXi at Xi. (9) then takes the form

f (Xi) I <p{\t)J(\2)d\2 = ^(Xi)/(Xi) r f (X2)dX2.
«/o «/o

This may be written

f(Xi) = C^(Xi)/(Xi),

where C is a fixed number; substitution shows that the value of C may
be assigned artbirarily, so that this is the general solution of the integral
equation. But in the physical case by definition

f(Xi)(fXi = I,

whence

= C J* <p(\i)J{\i)d\i = C#.

where # stands for the last integral and represents the total full fluorescent
emission per unit volume irrespective of wave-length.
Hence

ri = ^^/i (13)

and

/l2=^^^/l. (14)

In words, (13) states that the intensity at any point in a homogeneous
fluorescence band is proportional to the intensity in the black body spectrum
at that point multiplied by the power of light of that wave-length to excite
the band.

All of these results hold, strictly, only for excitation by radiation
of the same temperature as the fluorescing substance. In seeking an
extension to other temperatures there appear to be two plausible paths
along which we may proceed.

If the fluorescent process consists in the ejection of electrons from the
atom with subsequent recombination accompanied by the emission of
light, then, by analogy with the photo-electric effect, we should expect
the rate of ejection of electrons and hence also the rate of fluorescent
emission' to be proportional to the exciting intensity, while the form of
the spectrum should be independent of it; f and <p will then depend
only on the temperature of the substance and 7 is to be taken for that
temperature.

If, on the other hand, the fluorescence is due to some kind of resonance

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36 E, H. KENNARD, [ISSS

within the atom, then it seems quite possible that equations (lo), (13)
and (14) will hold when J is taken for the temperature of the exciting
light, the temperature of the substance affecting the phenomenon only
indirectly by altering the properties of the resonators. But then a
change in the temperature of the exciting light will alter 7, so that if
(10) holds, / must change with a change of temperature; while if (13)
and (14) hold, then either f or <p, or both, must change with a change of
temperature, since the change in J does not consist in multiplication by
a constant factor. Now a change in the intensity of the exciting light
may or may not change its temperature: if the intensity is varied by
moving the source parallel to the beam the temperature remains un-
altered; while if the intensity is altered by interposing a diffusing screen
the temperature will be lowered. Accordingly, in the former case we
should expect the coefficient/ to remain constant, i, «., proportionality
should hold for all wave-lengths of excitation and emission ; while in the
latter case / would, in general, be altered and proportionality between
excitation and emission could not hold for all wave-lengths, the change
occurring either in f or in ^, or in both, in the simple case characterized
* by (12).

It is interesting to note that if J obeyed the Rayleigh-Lorentz law
its form would not change with a change of temperature and this break-
down of proportionality would not be required by our equations. If the
latter really occurs, therefore, it will probably find its ultimate explana-
tion in the factors which lead to the failure of equipartition, whatever
these may turn out to be.

Let us in conclusion turn to the comparison of the last results obtained
with observation. The fluorescence of gases exhibits peculiarities
strongly suggestive of resonance, but unfortunately no quantitative
data seem here to be available. On the other hand, in liquids and solids
the close connection usually found between fluorescence and phosphores-
' cence suggests the first alternative described above, viz., the production
of some intermediate change such as ionization or a chemical change,
so that the fluorescence ought to be related to the temperature of the
substance rather than to that of the exciting light.

Two substances which possess an isolated unitary band and which
should therefore, if the theory developed here is correct, obey equation
(13), are eosih and resorufin, and fortunately the necessary data are
available in a paper by Nichols and Merritt^ in the Physical Review.
In their Table I. they give what they call the ** specific exciting power"
for eosin, meaning the excitation per unit of absorbed energy; hence this

1 E. L. Nichols and E. Merritt, Phys. Rev., XXXI., p. 381, 1910.

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Vol. XI-l
NO.X. J

THERMODYNAMICS OP FLUORESCENCE.

quantity multiplied by the coefficient of absorption, given in the same
table, gives values of <p, which is here called the exciting power and
represents the excitation per unit of light flux. For resorufin, numbers
proportional to ip are obtained by multiplying the ordinates of the crosses
and circles in their Fig. (93) by the corresponding ordinates of the
absorption curve A in the same figure.

The experimental values of <p thus obtained are shown by the circles
on the annexed plots (Figs, i and 2). The distribution in the fluorescence
spectrum,^ which is known to be independent of the exciting light, is
shown by the curves marked f . We may suppose the temperature of
the specimens to have been about 20** C. ; the black body curve for this
temperature is shown by the curves marked / (the slight variation of
the refractive index with wave-length is left out of account.) Finally,
the theoretical values of ip given by equation (13) in the form

are shown by the curves marked ^, the single constant k being adjusted
for a good fit. [By (8) above, ^ = /9, so that the latter curve represents
also the coefficient of fluorescence absorption.]

The agreement between observed and calculated values of <p is about
as good as could be expected under the circumstances. The slope of
the theoretical curve over its central portion is almost exactly right and
it shows indications of a maximum in the right place; it fails chiefly

,t,

•

\ /

.54 ^5

Fig. 1.
Eosin.

56 M .57

• •

t /

• •

JSB .38

Fig. 2.
Resorufin.

.60 \i ja

at the ends, where either the fluorescence or the exciting power is small
and therefore not known with certainty. A change of 10 per cent, in
the slope would result from a change of 30** in the temperature or of
0.03 fi in the wave-length employed in calculating 7. The final test of
the theory must wait however until the region in which both quantities
are experimentally known shall have been considerably extended.

» E. L. Nichols and E. Merritt, Phys. Rev., XXX.. p. 345, 1910.

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38 £. H. KENNARD, [i

It is a pleasure to acknowledge a debt to Professor E. Merritt for his
obliging assistance as critic during the development of this paper.

Summary.

By applying thermodynamics to fluorescent substances a relationship
is deduced between the coefficient of fluorescence absorption, the inten-
sity of fluorescence and the intensity of black body radiation.

Adding the assumptions that fluorescence and thermal radiation are
thermodynamically independent and that the energy of fluorescence is
derived from that of the exciting light, it is concluded that in the case
of an isolated unitary band

where f = relative intensity in the fluorescence spectrum, <p = exciting
power, and / = intensity in the black body spectrum for the tempera-
ture of the substance, all being taken for the same wave-length; and
this equation appears to be confirmed by observed data.
Cornell University,
March. iQi?-

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Vol. XI.l
Nai. J

KATHODO-PLUORESCENCE OF CRYSTALS.

KATHODOFLUORESCENCE OF CRYSTALS.

By Thobias B. Brown.

Part I. — ^A Quantitative Investigation of the Kathodo-Fluorescence of '\^Ilemite, Kunzite

and Soda Glass. (A description of the results obtained by J. A. Veazey.)
Part II. — ^A Further Investigation of Willemite by the writer.

Introduction.

THE intensity of the fluorescence excited by the impact of kathode
rays upon a fluorescent substance depends, for a given substance
at a constant temperature, upon the velocity of the rays, and upon their
rate of impact. To a lesser degree it may be affected by other factors
as yet undetermined.
The experimental study naturally divides into two parts:

1. A determination of the relation between the intensity of the fluores-
cent light L and the kathode ray current / at constant discharge poten-
tials.

2. A determination of the relation between L and the discharge
potential V at constant current values.

The earliest investigation was made by Lenard.^ Lenard had only a
secondary interest in the phenomenon, as a means of detection of kathode
rays. He investigated several substances, making on each substance
only a few observations through the limited range he was interested in ;
from the results he postulated the relation

L = C/(7- 7o),

where Vo is a minimum potential below which no fluorescence can occur.
No experimental proof of the existence of this minimum is given; and
it seems, in the light of later investigation, an unjustifiable extrapolation.

a • I. 4 tcT. & a • « s^CT.

Fig. 1.
Plotted from data of Lenard. The lines drawn represent the equation he gives for them:

L - CI(V - Vo).
» P. Lenard, Ann. d. Phys.. 12, 1903, pp. 44^490.

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THOMAS B. BROWN.

(Sbcond
ISbribs.

The points plotted in Fig. i represent his observations on several sub-
stances, and the straight lines drawn, his interpretation of them.

The next observer in this field was Leithauser,^ who likewise wished
to use the phenomenon as a means of detecting kathode rays. Working
with calcium-sulphide, he found an exact proportionality between L
and / at constant V, but found the non-linear relation between L and V
at constant / which is given by Fig. 2, plotted from his data. It is to
be noted that, curiously enough, this curve, if extended backward, would
cut the intensity axis!

a »

Fig. 2.

Intensity-potential curve obtained
by Leithauser for CaS.

Fig. 3.
Diagram of connections.

Directly following a brief preliminary investigation by Nichols and
Merritt,' in connection with a study of the spectrum of kathodo-fluores-
cence as influenced by the velocity of the exciting rays, J. A. Veazey
took up, at their suggestion, an extended investigation of the problem.
His untimely death in the summer of 1912 cut his work short. To the
present writer, whose good fortune it had been to act as Veazey's assistant
the previous year, fell not only the continuance of the work, but also the
editing for publication of Veazey's work. This paper is accordingly in
two parts, as indicated in the heading above.

Part I. — The Kathodo-Fluorescence of Willemite, Kunzite and
Soda Glass. (Describing the Measurements by J. A. Veazey.)

After extended preliminary experiments which led to the elimination
of several important sources of error, the apparatus was finally arranged
as shown in diagram in Fig. 3.

Current is supplied to the discharge tube T through the high-tension
reversing switch MN from the large Holtz machine ff. An alcohol
rheostat R in shunt with the Holtz machine regulates the current through
the tube, and Kelvin electrostatic voltmeters V\ and Vj, having over-

* G. E. Leith&user, Ann. d. Phys.. 15. 1904. pp. 383-306.

> E. L. Nichols and E. Merritt, Phys. Rev.. 28, 1909. pp. 349-360.

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VOL. XI.l

No. I. J

KATHODO-FLUORESCENCE OF CRYSTALS,

lapping ranges, measure the potential difference across the tube. A
sensitive Sullivan galvanometer d measures the current carried to the
crystal by the kathode rays, and the galvanometer d measures the total
current passing through the tube. Ironless inductances Li and Lj are
inserted to prevent oscillations.

The tube is shown in section in Fig. 4. Kathode rays projected from
the kathode K along the axis of the
tube strike the crystal W, causing
fluorescence. The cylindrical box
anodes Ci and d shield off all but the
central portion of the bundle of kath-
ode rays, and receive all the current
passing through the tube except that
carried by this central portion of the
rays. For reasons explained later, the
lower box Cj may , when desired, be
maintained at a potential of — 55
volts with respect to the inner box
3f, by throwing over the switch 5.
The crystal W is surrounded by the
aluminum box Jlf, whose purpose it
is to receive the current carried to
the crystal by the kathode rays and
to conduct it to the galvanometer Gj.

The tube is evacuated by a Pfeif-
fer-Wetzlar rotary mercury pump and
a Fleuss oil pump in series. The vacuum system was so tightly closed
and so free from vapor that pumping at intervals sufficed to maintain any
desired potential difference across the tube.

Through holes in the sides of the boxes Ct and M photometric measure-
ments are made. The photometer used was designed especially for the
work. A Lummer-Brodhun cube matches the illumination of two
transmission-diffusion screens; one of these is illuminated by the fluores-
cence of the crystal, the other by a constant comparison source. By a
suitable variation of these calibrated screens, any range of visible fluores-
cence may be measured. The small central portion of a large acetylene
flame as seen through a circular hole in a diaphragm placed directly in
front of it and covered with a suitably colored glass or liquid screen to
give a visual color match with the fluorescent light, is used as the com-
parison source. The gas pressure was kept constant, and the outline
of the flame, as observed in a flame gauge, remained constant. The

h£>-1'-'

Fig. 4.

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42 THOMAS B. BROWN. [toiS

distance from the crystal to its diflfusion screen is fixed, while the com-
parison source is movable along a photometer bar. Since Nichols and
Merritt* have shown that the spectral distribution for the substances
examined is independent of the electrical conditions of the discharge
(or indeed, of the method of excitation), ordinary photometric measure-
ment is sufficient.

It was found upon trial with willemite that, for potentials below 1.5
K.V., with the box Cj earthed, the galvanometer d reads zero, and no
light is given off by the crystal; but as the potential is raised, it b^an
to deflect when the crystal b^an to fluoresce. At any discharge poten-
tial, a deflecting magnetic field reduced the galvanometer reading to zero
at the same time as it stopped all fluorescence of the crystal. These
tests seem to indicate that the current represented by the galvanometer
reading is exclusively kathode ray current. They do not prove, however,
that all of the impinging electrons contribute to the current read by this
galvanometer; since the rays suffer reflection, a part of the reflected
rays may escape through the openings in the box M and carry then-
charges to the cylinder Cj. But if the loss by reflection is independent
of the potential and of the gas pressure, the data will still give the true
, relation between the intensity of the fluorescence, the current, and the
potential. L. Austin and H. Starke* find the reflecting power of metals
for kathode rays at normal incidence independent of the gas pressure
and the potential within the limits of 3 to 30 K.V. No statement of
work covering the case at hand has been found. Here the crystal is
non-conducting, and the rays are incident at an angle of forty-five degrees.
It will be assumed, however, that the reflecting power in this case also
is independent of the potential and gas pressure.

Experiments with Willemite

The first crystal examined was a specimen of willemite (zinc ortho-
silicate) having an area of about one square centimeter ground smooth.
A circular area about 0.80 cm. in diameter was bombarded by the kathode
rays.

Curve I, Fig. 5, represents data taken at the constant potential of
3.50 K.V., with the cylindrical box C^ earthed. Curve 2 was taken
with this box charged to a small negative potential (—55 volts). These
results seem to indicate that with C^ earthed not all of the reflected
electrons are caught by the box M\ while with d at a small negative
potential, more if not all of the electrons are caught and their charge

1 E. L. Nichols and E. Merritt, Phys. Rev., 28, 1909, pp. 349-360.
« L. Austin and H. Starke, Ann. d. Phys., IX., p. 271, 1902.

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Vol. XI.l
No. X. J

KATHODO-FLUORESCENCE OF CRYSTALS.

measured by the galvanometer Gj. For all subsequent observations Cj
was kept at the potential of — 55 volts.

Fig. 5. Fig. 6.

Potential constant at 3.50 K.V.

Curve I. Cylinder C» grounded.

Curve 2. Cylinder C» at potential of — 55 volts.

Potential constant at 3 -50 K.V.

Curve I. Taken March 4th. Pressure maintained low previously.
Curve 3. March 4th. After admission of air and reSxhaustion.
Curve 3. March 8th. Same conditions as No. 2.

Fig. 6 shows the effect of admitting fresh air into the tube. Curve i
was taken after low gas pressures had been maintained for several days'
use of the tube. Curve 2 was taken the same day after admitting air
to the tube to atmospheric pressure, and reexhausting. Curve 3 was
taken a few days later, conditions similar to those of 2 having been
maintained approximately in the interim. As a result of the admission
of fresh air it is to be noticed that (a) for a given kathode ray current
there is a marked increase of the intensity of fluorescence, and (6) with
the same external circuit conditions, a much greater kathode ray current
may be obtained. The first of these results may be due to some change
in the surface condition of the crystal; perhaps to its oxidation by the
freshly admitted air. The subsequent bombardment of the crystal,
together with the removal of the gases of decomposition by pumping,
may again reduce the surface. Villard^ found in his experiments that
the portion of an oxidized copper plate exposed to the action of kathode
rays became bright, and he considered this a reduction of the surface
due to the bombardment.

> J. J. Thompson. Cond. of Elec. through Gases, p. 496*

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THOMAS B, BROWN.

fdlCOND
ISSKIBt.

The second result may be explained by assuming that the walls of the
tube become conducting when bombarded with kathode rays. Many

observations show that after low gas pres-
sures and high potentials have been main-
tained for several days, the discharge is
much less concentrated along the axis of the
tube; a greater portion of it being deflected
toward the wall of the tube above the anode,
as is shown by the increased fluorescence of
the glass walls, by the lower reading of the
galvanometer Gj, and by the occasional
snapping of sparks from the kathode to the
nearest portion of the walls. With the tube
freshly exhausted, the glass walls are but
slightly fluorescent, and the path of the
rays, as marked out by the blue glow, is
along the axis of the tube.

The curves shown in Fig. 7 are a part of
a series of constant potential curves taken
under conditions of maintained low pres-
sures. These, as well as the others not
shown, are all straight lines within the
limits of experimental error, and show a
direct proportionality between the inten-
sity of fluorescence and the kathode-ray
current. A great number of other curves,
taken both before and since, likewise verify this linear relation.
This is so far in agreement with the Lenard formula

L = C/(7- 7o).

In order that complete agreement obtain, data taken at constant current
should plot as straight lines for the intensity-potential relation, with an
intercept on the potential axis equal to Vq. Figs. 8, 9, 10, 11 repre-
sent the data obtained for the constant current values indicated. None
of these curves are straight lines, and all of them show decided hysteresis
effects for increasing and decreasing potentials. These curves might
possibly be considered straight lines with the superimposed effects of
changes of temperature, of change of reflecting power with change of
potential, and of fatigue and hysteresis. The lowest potential at which
fluorescence of willemite could be detected was 1.40 K.V. The curves
do not approach the axis close enough to determine an intercept ac-
curately.

I in /I^».*16*

Fig. 7.

Constant potential curves for
willemite, taken under conditions
of maintained low pressures.

No. I. 8.30 K.V.
No. a. 12.20 K.V.
No. 3. 14.20 K.V.
Area bombarded, 0.5 cm.«
O Ascending values.
X Descending values.

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Vol. XI.I
Nai. J

KATHODO-FLUORESCENCE OF CRYSTALS.

Curve 2, Fig. ii, illustrates another method of obtaining the relation
between intensity and potential at constant current. It was plotted
from the series of constant potential curves, a part of which are shown

•

10
C.P.

•

fcu

!•■

•0 M

0 •

» i

1 UIB.V.

e.r.

!••

s 1

s ir

1 1.«.». , ^^^

Constant Current Curves for Willbmite.

Fig. 8.
Current value of 0.65 • io« Amp.

Fig. 9.

Current value of 1.30' 10 Amp.

Fig. 10.

Current value of 3.20 • 10 Amp.
Figs. 8. 9, and 10, illustrate different tsrpes of hysteresis.

Fig 11.

Current value of 1.30 • 10 Amp.
Curve I was taken directly.

Curve 3 was obtained from the series of constant potential curves of which the curves in
Fig. 7 are a part.

in Fig. 7, using values read from those curves corresponding to the
current of 1.3 "lO"* amperes. It is to be recalled that this series of con-
stant potential curves was taken under conditions of maintained low
gas pressures, so that the bending of the upper part of this curve toward
the horizontal may be due to a slow deterioration of the fluorescent power
with time.

Experiments with Kunzite.

A crystal of kunzite (a variety of spodumene, LiAl(SiOt)2) was next
examined. Kunzite is fluorescent only under spark or kathode ray

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THOMAS JB. BROWN,

'Sbcohd

excitation, with an amber or reddish yellow fluorescence. This crystal
was less permanent under kathode ray bombardment than willemite,
giving off decomposition vapors much more rapidly, and exhibiting other
fatigue or decomposition phenomena to be described later.

The curves for kunzite are very similar to those for willemite in form,
but the relative intensity is considerably less. The constant potential
curves, of which Fig. 12 is an example, all show a good proportionality

M ao 9€

•.

Fig. 12.
Kunzite. Potential. 17.15 K.V. Area bombarded, 0.2 cm.*

Fig. 13.
Kunzite. Current, 3.88 • lO"* Amp.

Fig. 14.
Kunzite. Appearance of bombarded area. A , Low potentials. B, High potentials.

between the intensity of fluorescence and the current; while the constant
current curves, of which Fig. 13 is an example, are non-linear, much
resembling the corresponding ones for willemite, and show a considerable
hysteresis between the ascending and descending values.

Direct observation of the fluorescing crystal discovered that the
fluorescing area was not uniformly bright, but appeared as a luminous
ring surrounding a darker central area, with a very dark spot near its
center. At low potentials this ring grew to greater diameter, but became
narrower, and scallops appeared, extending into the ring from the center.
Fig. 14 illustrates this. These phenomena lead to the supposition that
the kathode ray bundle incident upon the crystal is not homogeneous,
but is more or less hollow, depending upon the potential. Such a hollow-
ness has been reported by Swinton.^

» C. Swinton, Proc. Roy. Soc., LXL, p. 79, 1897.

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Vol. XI.l
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KATHODO-FLUORESCENCE OF CRYSTALS.

Examination after removal from the tube found the surface of the
crystal to be discolored where it had suffered
bombardment; there being a dark spot near
the center surrounded by a discolored ring.
Several, hours' heating at several hundred
d^^rees Centigrade completely removed this
discoloration, together with the natural lilac
color of the crystal, so that it now appeared
as clear glass. The fluorescent properties were
but little changed, as Fig. 15, taken after
heating, shows. The noticeable change is the
absence of any hysteresis effect. For these
observations the distribution of the rays was
rendered more uniform by placing a plate of
aluminum drilled full of fine holes over the
opening in the cylinder Cj.

1 M

Fig. 15.

Kunzite, after heating. Cur-
rent value. 0.634' !<>-• Amp.

Experiments with Glass. (Soda glass of German manufacture.)

A piece of glass taken from a broken discharge tube was next examined.
The fluorescence is a greenish color, and much weaker than that of either
of the substances previously examined. The results obtained, shown in
Figs. 16 and 17, indicate the same general relation between the variables

Ie.tO-*ia».

Fig. 16.
Glass. Potential. 19. i K.V.

(

e 1

« K

Fig. 17.

Glass. Current, 3. 88* I o-« Amp. Area
bombarded. 0.2 cm.*

as holds for the other substances: a direct proportionality between
intensity and current at constant potentials, and a non-linear relation
between intensity and potential at constant currents. There is little
if any hysteresis. Direct observation discovered the same phenomena
of non-uniform luminosity as observed for kunzite, when the opening in
the top of the cylinder C% was uncovered.

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48 THOMAS B. BROWN.

<W»J^

Conclusions.

1. For potentials not too small, the constant potential curves obtained
for willemite and kunzite show a direct proportionality between the
intensity of fluorescence and the kathode ray current, and so far verify
the relation postulated by Lenard

L = CI{V - Vo).

The single curve for glass agrees approximately.

2. If precautions are taken to prevent loss ot charge by reflection, the
curves obtained for willemite and kunzite for small discharge potentials
likewise show this proportionality; except that, for the same potential,
a much steeper line is obtained in a freshly exhausted tube than is ob-
tained after the vacuum has been maintained at a low gas pressure, and
discharge passed at a high potential, for some time previously.

3. The constant current curves for willemite, kunzite, glass, and the
heat-treated kunzite, do not agree with the Lenard formula, although
they come closer to it than do the results of Leith^user. The constant-
current curves for willemite and native kunzite show marked hysteresis
effects, while the glass and the colorless (heat treated) kunzite do not.

4. The crookedness of the constant current curves may be due to the
effect of changes of temperature upon the fluorescent power of the crystal,
or to changes of the reflecting power of the crystal, with changes of
potential.

Some means must be provided to insure these conditions are constant
before the exact relation between the intensity of fluorescence and
discharge potential can be found.

Part 1 1. — ^A Further Investigation of Willemite.

If L is known to be a function of / and V, and it is found that for V
constant, L is directly proportional to /, then it follows that the ratio
L/I is a function of V alone. The results of all investigators agree that,
at a constant discharge potential 7, the intensity of fluorescence L is
directly proportional to the kathode-ray current /. Particularly con-
clusive evidence seem the abundance of curves verifying this relation
obtained by Veazey. This continuation of the work is concerned with,
first, checking the apparatus used by determining whether or not it will
give this same relation between L and / at constant potential, and then
determining the form of the relation between L/I and V.

Willemite was chosen for further investigation as typical of these
substances and also as being the most brilliantly fluorescent of them,
and the most stable under the kathode-ray bombardment. The speci-

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Vol. XI.l
NO.Z. J

KATHODO-PLUORESCENCE OP CRYSTALS.

men was used in powdered form, the crystals being chipped away from
the quartz with which they occurred, powdered, and then heated to
redness to drive off any volatile or gaseous impurities present. After
heating the color was almost white, but the fluorescent properties re-
mained unchanged. This specimen never gave evidence of the hysteresis
and tiring effects found by Veazey in his specimen; and this fact is
probably due to the preliminary heating.

It is to be recalled that for these substances at room temperature the
spectral distribution is the same for all discharge potentials.^ The
effect of temperature upon the spectral distribution has been investigated
by Nichols,* and is found to be inappreciable in the range of ordinary
room temperatures.

The discharge tube used is shown in vertical section in Fig. i8. This
tube is similar to the one used by Veazey, but much larger. The upper
part of the tube A is about 13 cm. in diameter and stands 24 cm. high.
The height over all is about 55 cm. and
the volume approximately 3.3 liters. The
kathode K is 2.7 cm. in diameter. The
anode, the two concentric cylindrical alu-
minum boxes M and N, occupies a major
portion of the tube. The distance be-
tween the top of the box M and the kath-
ode is 2.4 cm. The outer box M is
earthed and receives all the discharge
except that part carried by the central
portion of the kathode stream which en-
ters the inner box N through the circular
oj)enings a, ft, and c, and bombards the
fluorescent powder at d. N is insulated
from M by the glass plate which supports
it, and the charge carried to d by the rays
is conducted through C to the galvanom-
eter G and thence to the earth. The area
of powder surface bombarded is about one
centimeter in diameter. The upper open-
ing a was covered with a multi-perforated
plate, as this was found desirable by Veazey. A sixty-degree prism 0,
sheathed with aluminum except for openings as shown, reflects the
fluorescent light through holes in the sides of the boxes M and JV, and

» E. L. Nichols and E. Merritt, Phys. Rev., 28, 1909, p. 349-360.
' E. L. Nichols, Proc. Amer. Phil. Soc., 196, 1910, pp. 267-280.

- -f* rk«t«Mi«r.

Fig. 18.
Vertical section of discharge tube.

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THOMAS B. BROWN.

[ Second
Sxum.

the tube s (placed here to prevent any stray discharge reaching iV),
and thence into the photometer. In this form of anode the possibility of
loss of charge due to reflection is very much smaller than in the form
used by Veazey, and it was unnecessary to give the outer anode a negative
potential to prevent loss.

The pumping system is the same as that used by Veazey, and the
electrical system likewise (see Fig. 3), except for a few minor connections,
and the addition of a third static voltmeter, built by the author, to
cover a lower range of potentials than the others. All permanent con-
nections are soldered. The voltmeters were calibrated and checked
against an attracted disc electrometer. The photometer used is a modi-
fied form of the one used by Veazey, with an entirely new set of calibrated
comparison screens. By means of a contrast photometer comparison
was made with a laboratory standard, so that the intensity values are
given in approximate visual candle power.

First to be considered is the relation between the intensity of fluores-
cence L and the kathode ray current / at constant potentials; *. e.
testing for this apparatus the relation L = jfe/ at constant potential,
where fe is a function of the potential V.

Figs. 19 and 20 show the way in which the results were plotted. Since

§6

frmm u

MfVMtt

cir

«roHi

iMtafl.

£00

MJK

i i

• «

Figs. 19 and 20.
Method of plotting intensity-current curves.

in most cases it was difficult to hold the potential absolutely constant,
and since in the same cases the change of L for a small change of V is
relatively great, readings were made of a series of corresponding values
of L, V, and / in the neighborhood of the desired potential; this data is
plotted as in Fig. 19. Then by interpolation from these curves corre-
sponding values of L and / at a constant potential are obtained and
plotted as in Fig. 20, Fig. 21 shows the collection of curves obtained

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Vol. XL!

0.1. J

No.

KATHODO-PLUORESCENCE OP CRYSTALS.

to show the relation between L and / at constant potentials; they are
all straight lines within the limits of experimental error. They cover

Fig. 21.

Intensity-current curves for different potentials.

fairly well the range of potentials investigated hereafter, and are con-
sidered a satisfactory agreement with the relation i = ifeJ at constant
potential, which has already been pretty exactly verified by Veazey and
others.

Having established the direct proportionality between L and / at
constant F, *. e., the relation L = F{V)I, it is now possible to proceed
to investigate the form of the relation F{V) between L/I and V. Typi-
cal results of this investigation are shown in Figs. 22, 23, and 24. Be-
cause of the great range of intensities, it was necessary to plot the results

•

i — I

•

/
/.

T fBMVMI

t
1 1

Fig. 22.

April I. To read the values of LI I in candle power per ampere, multiply the ordinates
of curve A by 10*; of curve B by lo*; and of curve C by io«. O indicates increasing values;
Xf decreasing values.

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THOMAS B. BROWN.

rSSCOND

LSbkibs.

of a single run (often around a hundred observations) on two sheets, and
to three different scales of intensities. The results as represented by
these curves are in general agreement with the results obtained by Veazey ,
and with those obtained by Leithauser, with the exception pointed out
e otore. In addition, in the present work, successive observations

ave been made much closer together than in any previous work, and
the results present a greater degree of uniformity and extend the investi-
gation to a region of much lower potentials. The results are not in
agreement with the conclusions of Lenard i. e., that the relation would
a linear one, with a minimum potential existing below which no

uorescence could occur, but seem to be in good agreement with his data.

omparing Figs, i and 23, Curve A: It is easy to see how Lenard, having

) 1

Fig. 23.

April 7. Values of LI I are read as indicated under Fig. 22, O indicates ascending values*
and X> descending values, taken in the morning. + indicates ascending values taken in
the afternoon.

only a few observations in a region of potentials corresponding to the
nearly straight portion of Fig. 23 (between 4 and 13 K.V.) could conclude
them to represent a linear relation. It is very evident from the present
work that the relation is not linear. Fig. 24 shows better than the others
the marked curvature at the foot of these curves. As low down as the
fluorescence could be observed the curve is bending nearer and nearer
towards the horizontal. There was measurable fluorescence at 0.75 K.V. ;
and at even lower potentials fluorescence could be detected by viewing
the crystal directly. A transverse magnetic field would stop it, and at
the same time bring the deflection of the galvanometer to zero, thus
proving that the excitation was by the bombarding kathode electrons.
However, the fluorescence for the low potentials is so faint that the
results obtained below i.oo K.V. are not accurate; especially as a small
amount of light from the now luminous discharge in the top of the tube

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Vol. XI.l
Nai. J

KATHODO-FLUORESCENCE OF CRYSTALS,

illuminates the specimen enough to introduce between five and twenty
per cent, error for observations below one kilovolt potential. Above
this, the effect becomes inappreciable, since most of the luminous dis-
charge is then driven from the tube, and its illumination becomes a
negligible amount of the total brightness, which increases rapidly.

** 1 1 1 — »7^

I /*

ft o7^

T "7 •

I J" ***

•

e
*

a
i 1

Fig. 24.

April 8. Values of L// for curves A , B, and C are read as indicated under Fig. 22. Multi-
ply ordinates of curve C by 10.

The lower values of L\I are imdoubtedly too low; due to absorption,
by the relatively greater amounts of gas present, of a part of the measured
energy of the exciting electrons, and to scattering, by the same agent,
of a part of the electrons, whose charges are measured, but which do not
strike the crystal. There is nothing about the results obtained to indi-
cate that, if this absorption, etc., could be eliminated, the fluorescence
would not be present for all potentials down to zero potential. Certainly,
if there exists a minimum potential below which no fluorescence would
be produced, it is htlow the lowest value investigated here, and the data
gives no evidence of its existence. If the fluorescence of such substances
as willemite may be compared to the " characteristic ** X-radiation of
metals, computations based upon the conclusions of Duane and Hunt,^
who found that the minimum potential for that radiation is given by the
equations Fo = hv (where Fo is the minimum potential for X-radiation
of frequency v, and t and A are the electronic charge, and the Planck
radiation " quanta ** constant, respectively) give about 4 volts as the
minimum for the middle of the fluorescent spectrum. It is doubtful if
that value can be reached experimentally.

A slight change of temperature occurred during the bombardment,
and was measured during some of the later runs. For example, in the
case of the data of April 7, a temperature change of 19^ C. occurred.
This is hardly sufficient to affect the phenomena.

» W. Duane and F. L. Hunt. Phys. Rev., N.S.. VI., Aug., 1915, p. 166.

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TBOMAS B. BROWN.

Sbcowb

The results of the diflFerent runs, when compared (Fig. 25), instead of
coinciding, as might have been reasonably expected, scatter considerably ;

Fig. 25.

Combined results. Values of Ljl are read as indicated under Fig. 22. Different runs are
ndicated as follows: January 21 +> February 10 p, March 18 -0, April i .April 7 O 0
land April 8 X.

but in general, they fall into two groups, represented by the two lines
drawn in the figures. These two lines correspond to the data of April 7,
and of April 8, which are typical of the two groups respectively. A key
to the cause of these two groups of values is found in the results of
April 7 (Fig. 23). The longer curve was obtained in the morning; the
vacuum was poor, and the potential was raised by pumping, running
up to a maximum. After being once thoroughly exhausted, the tube
had an excessively slow rate of leak, so that after lunch hour the potential
was still up to 3.25 K.V. and rose steadily, due to the discharge alone
and without pumping, to 5.45 K.V., when pumping was begim. Through-
out the region where the potential rise was automatic the points repre-
senting these data fall considerably below those obtained in the morning;
approaching them after pumping is begun. The next day the potential
had fallen to 0.78 K.V., but the rise of potential was slow and automatic
up to 5.45 K.V., where pumping was begun. This curve also falls below
the first of those taken the day before, but it coincides with the second.
Examination of the data reveals that all those of the second (lower)
group of values (those of Jan. 21, Apr. 7 (P.M.), and Apr. 8) were taken
under conditions of automatic potential rise; and that all those of the
first (upper) group were obtained by pumping to raise the potential.
The January 21 values start out in good agreement with the lower group,
but fall increasingly below them above 3.3 K.V. Since this case is a

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Na^i^^*] KATHODO-FLUORESCENCE OF CRYSTALS. 55

" freak "; *. e., it has occurred in the data but the once, it will have to
be disregarded until some later work may throw some light upon it.

It seems more probable that the difference in these two sets of curves,
which seems to correspond to the difference that Veazey observed as a
difference between a freshly obtained vacuum and a long maintained
one, is not due to the causes he suggests (an oxidation or other change
of the surface of the specimen) but to a difference in the state of the
residual gas in the tube; either a difference in the pressure imder the-
different conditions of discharge, or a difference in the character of the
gas, due to vapors, or to formerly surface occluded gas, or both. The
differences are most marked in the lower range of values, where the
difference of absorption and scattering of the electrons due to the differ-
ences of the gas state might be sufficient to account for the lowering of
the values in the case of the second group.

At the time, no observations were made of the gas pressure conditions^,
except those indications gotten by observation of the discharge; and
these were not reliable, since the form of the tube was so different from
the usual one. Since then, a McLeod gauge has been attached and the
gas pressure observed under the conditions of taking the first group of
values (potential raised by pumping) and the characteristic pressure-
potential curves were obtained. Between the potentials i.oo and 13.00
K.V. the pressure varied between outside limits of 100 and iom (thous-
andths of mm. of mercury). To a crude approximation, the pressure is
inversely proportional to the potential through this range. The seal
of the new vacuum system was not sufficiently perfect to obtain the
conditions of the second set of values. Indications of the pressure con-
ditions of this set were obtained, however, in that a measurable rise of
potential was observed during an appreciable rise of pressure. The
suspicion is that the ** automatic " rise of potential occurred with at
the most only a slight decrease of pressure. The greater gas density
would cause a greater absorption of energy, etc., and this would explain
why the curves obtained in this manner lie below the others.

Only fragmentary data concerning absorption and scattering of kathode
rays are available. Extrapolation of values from a table given by
Lenard indicates that for the values obtained in group one (upper),
LI I at I K.V. is about seven times too small, while LI I at 4 K.V. is about
II per cent, low, and above 4 K.V. the losses are negligible. This does
not affect the conclusions drawn from the shape of the curves: As seen
m Fig. 22, where the values based on the extrapolation are represented
by the dash line, the curvature is just as pronounced, and the existence
of an appreciable *' minimum " potential is still less evident. Also,

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56 THOMAS B. BROWN. [i5SS?s

the magnitude of the losses is such that, taken together with the assump-
tion that the " automatic " rise of potential is accompanied by but a
slight change of gas pressure, it could quite well account for the difference
between the two groups of curves. Later work with this apparatus may
be undertaken to obtain more complete data on the absorption and
scattering losses. But a much simpler method of .obtaining the exact
relation between the variables is to use a modem hot kathode discharge
tube, since in such a tube the gas density is so small as to cause but an
immeasurable amount of loss. This work is now under way.

There will still be present another cause of error to consider; namely,
the static potential which accumulates on the specimen and results in
causing a reduction of the velocity of the electrons as they approach it.
Since the L — / curves at constant V are straight, this static potential
would seem to be dependent only upon the gas pressure, if indeed it is a
.variable. So that in the new apparatus it should be a constant. It
seems probable that the appearance of the fluorescent area, reported by
Veazey and illustrated in Fig. 14, is due to this static potential. It
would be naturally greater at the center, where the chance for leakage is
the less, and hence cause a greater decrease in the velocity of the electrons
striking there, and also deflect some of the approaching electrons towards
the outer annular ring.

The processes of fluorescent radiation are too complex and too little
understood to permit the derivation of any theoretical equation against
which to check these results. The results themselves suggest vaguely a
number of qualitative theoretical explanations, and several empirical
(expotential) equations have been tried in an attempt to arrive at some
definite conclusions. But the net result of it all is the conclusion that
further work is necessary, along lines suggested by the experimental
results and by these theoretical speculations, before any definite theory
can be developed that will stand rigid scrutiny.

Conclusion.

This investigation of the kathodo-fluorescence of willemite has had as
its purpose a determination of the relation between the intensity of
fluorescence L, the rate of impact of the kathode electrons (measured by
the kathode ray current /), and the electronic kinetic energy (measured
by the discharge potential V).

A direct proportionality is found between L and / at constant values
of F, confirming the results of previous investigators.

The relation between L/I and V (which corresponds to the relations
obtained by Veazey and others between L and V at constant values of /)

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No*!!^'] KATHODO-FLUORESCENCE OP CRYSTALS. 57

is found to be non-linear, of the form shown by the curves plotted; these
curves having an increasing slope as the potential is raised, which ap-
proaches a constant value for higher potentials, and possibly falls oflF for
values still higher (as indicated by Veazey's results, which are in fair
agreement with the present ones). There is no indication of a minimum
potential below which no fluorescence would be produced.

The results have been shown to be in general agreement with the
data obtained by Lenard for similar substances, but to be not in agree-
ment with the empirical relation postulated by him. Indeed, they may
be considered as a very definite disproof of that relation.

Certain discrepancies observed by Veazey have been observed in
greater detail, under conditions that permit them to be explained as
most probably due to the effects of absorption and scattering of the
energy of the kathode electrons by the residual gas in the tube.

Static potentials acquired by the specimen are suggested as explaining
the uneven appearance of the fluorescence, noticed by Veazey.

Sources of error are recognized in the two paragraphs above: losses
due to absorption and scattering, and to static potentials on the speci-
men. Means for their elimination are being considered.

While the present work has furnished some very promising germs for a
theoretical explanation, yet it is but idle speculation to attempt to develop
them into any concrete form without first planting them in a very much
more fertile soil of experimental investigation. Suffice they now to
point the way to that investigation.

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58 RUSSELL V. BICHOWSKY, [SSSiI

THE NECESSARY PHYSICAL ASSUMPTIONS UNDERLYING
A PROOF OF THE PLANCK RADIATION LAW.^

By p. Russell v. Bxchowsky.

TT is usually assumed that in order to prove the Planck radiation law
^ it is necessary to assume some sort of quanta, that is, that it is
necessary to assume that some at least of the quantities connected with
the distribution of energy in the spectra of a black body have physical
significance only for the values £, 2£, 3JS, etc., all intermediate values,
say J£, being impossible. There is, however, considerable disagreement
as to just what the quantities are which thus occur in quanta. Einstein*
assumes that radiant energy itself is atomic in structure, Planck* that
matter (oscillators) is such that it can only give out energy in quanta,
while Larmor* makes the physically somewhat indefinite assumption of
equal regions of probability. But in spite of these differences of detail
almost everyone assumes that quanta of some sort are necessary for a
proof of Planck's law. Indeed, Jeans* and also Poincar6* have under-
taken to prove as much. However, their proof of this point, and indeed
all possible proofs connecting the quantum hypothesis with the Planck
law are vitiated by the fact that they all make a far more dubious assump-
tion than the one they attempt to justify. For in the course of their
proof they assume, as indeed it can be proved they must assume, that
the radiating system has the statistical properties of a perfect gas, for
once one accepts at the same time both Planck's law and the quantum
hypothesis, Maxwell's distribution law (which may be considered the
definition of the statistical properties of a perfect gas) follows directly.
Putting Planck's equation for the distribution of energy among the
different degrees of freedom in any given system in the form

(i) ^« = ^^^"- I '

where Ea is the average energy per degree of freedom for any frequency

* Read at the Washington meeting of the American Physical Society, April 21, 191 7.
•Ann. d. Physik. IV.. 556 (1901).

* Dynamical Theory of Gases, Cambridge, 191 6. p. 405.

* Roy. Soc. Proc., Ser. A, 83* 92 (1909)-

* Ann. d. Physik. 17, 132 (1905); 20. 197 (1906); 22. 180 (i907).

* Journ. de Phys. [5I. 2, 5 (191 2). Demierds Penseds, Paris. Ch. VI.. *' L'hypothdse det
Quanta."

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Vol. XL
No. I.

] THE PLANCK RADIATION LAW. 59

(v«) and the constant £o replaces the hv of the more familiar form (£© is
of course only constant for a given frequency v^) and expanding by long
division we get:^

(la) Ea = ^^"^ + ^«^^ + • • • + ^-^^

But we have the condition

(2) iV = («' + n" + n'" + . . . n(»>)

(where N is the total number of degrees of freedom and «', n'\ etc., are
the number of degrees of freedom having respectively the energies yE',
yE", etc., 7 being an arbitrary constant) and also the condition

(3) ■ £a = EaN = a{n'E' + n"£" +•••),

where £. as before is the average energy, JSa the total energy. (This
equation asserts that the total energy equals the sum of the energies
of its parts.) (£^*»^ does not necessarily have the dimensions of energy
though of course a£^*»^ does.)

Now if we assume the quantum theory it is equivalent to assuming
that the values £', E'\ etc., equal respectively £oi 2£o, 3-Eo, etc., and
hence we have from equation (3) (/* being another arbitrary constant)

(4) EaN = M(n'£o + n"2£o + »'"3£o +•••).

But n\ n'\ n"\ etc., are in general some function of £', £", etc., and
since our system will be supposed to be large enough so that the law of
distribution does not depend on the size of the system n\ n'\ etc., will
always be the same function (/) of £', E'\ etc., hence

(3) NEa = m{£o/(£o) + 2£o/(2£o) + • • • + fiE^inEo) }
and

(4) N = /(£o) + /(2£o) + • • • /(n£o).

But the solution for fitiEo) consistent with equations (la), (3) and (4)
turns out to be

(5) W^^^^ ^!t^^f(nEo)^e'^^^.

But this is merely the familiar form of the Maxwell distribution law
where W^^^^ represents the probability of a degree of freedom having the

^ It is impossible to consistently carry any of the usual quantum theory proof of the
radiation law beyond the derivation of equation (i) or (la). To evaluate Ea or Ua {Ua
-« EJV) requires counting up the total number of degrees of freedom in a black body, and
this can only be done by using Fourier's analysis, but Fourier's analysis is explicitly based on
the assumption of continuous energy radiation, and cannot be applied to radiation in quanta.

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60 RUSSELL V, BICHOWSKY. [iSSS

value n£oi which shows that instead of the quantum theory being a
necessary consequence of the Planck law one cannot prove Planck's
law from the single assumption of the quantum hypothesis but must
necessarily make the further and arbitrary assumption that Maxwell's
law holds for the local distribution of values of those coordinates fixing
the distribution of radiant energy in a black body at steady state. If
you fail to make the Maxwell assumption the radiation law can not by
any mathematical process be derived from the quantum theory. Or
putting our result in other terms, the three propositions: (a) Planck's
law represents the facts, (b) the quantum theory is true, (c) Maxwell's
law holds for the system in question ; are not independent. If you assume
any two the other follows. The establishment however of the truth (or
falsity) of only one of these statements implies nothing whatsoever about
either the truth or falsity of the others.

Now most of the criticism that has been rained on the Planck equation
has had to do not with the Maxwell's law assumption but with the
quantum hypothesis. But this, at least in my opinion, has simply con-
fused the issue. The really doubtful part of the present derivation of
the Planck law is the assumption that Maxwell's law holds. That is,
the assumption that the distribution of the values of the coordinates is a
function only of the single variable nfiEo (which we may speak of as the
generalized energy per wave-length). If this assumption were true it is
easy to show that the radiation in a black body should obey the perfect
gas laws. This being the case, since we know both theoretically and
from actual experiment that equipartition must hold for a perfect gas,
and since we have (if Maxwell's law holds) in a radiating system a con-
dition exactly analogous to the distribution of momenta in a perfect gas;
it is quite inconceivable that equipartition and hence the Rayleigh-Jeans
distribution law, should not hold for radiation. It is the assumption of
the truth of Maxwell's law as applied to the case of a radiating system,
and not the assumption of quanta that contradicts classical mechanics
and this in a far more grievous manner than has usually been assumed,
for after all the basis of the Hamiltonian equations and hence of the
equipartition law for a perfect gas is nothing more or less than the
assumption that the dynamical system can be reduced to parts whose
motions obey the law of the simple pendulum, i. e,,

dp, _ _^E
dt " 5g,

and if this assumption is not true for the system '* Radiation in equi-
librium with a black body " by what juggling is the vibratory theory

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VOL.XI.J j,jj^ PLANCK RADIATION LAW. 6l

of light to be justified? If one wishes further confirmation of the fact
that the fairly innocuous though quite needless assumption of quanta
does not by itself contradict classical mechanics he should observe an
automatic weighing machine. It is obvious that, given the proper
kind of a system to produce them, quanta of energy or anything else
could exist. My objection to the Planck law is that the kind of system
assumed is not a proper kind of system.

Obviously a system which is going to act as a weighing machine must
have certain properties. If you are going to transfer a continuous
variable into a discontinuous variable, you must have some sort of a
reserve stock. If energy comes in a continuous stream and goes out in
quanta there must be between periods of discharge a heaping up of
energy. Thus it is necessary to assume some sort of reserved or bound
energy different from the free energy of radiation.

But this Maxwell's law does not allow. The physical bases for Max-
well's law or any law of that form are the two definitions:

(i) The system is in a steady state.

(2) The property distributed according to Maxwell's law is con-

servative
(with which we will not be greatly interested) and the physical assumption :

(3) No restrictions hold other than (i) and (2).
In mathematical form this condition is:

*^" = Miv.'iv."ivl"'.-.)=°-

It is this condition to which your attention is invited, for it forms the
Achilles' heel of the quantum argument. If no other conditions hold in a
radiating system than (i) and (2) the distribution of energy is a function
only of the energy density of the system. This besides requiring equi-
partition makes it impossible to explain the mechanism of quantum
emission as that mechanism requires a distinction between the bound
energy of the system and the total energy (without which, by the way,
transfer of energy from wave-length to wave-length could not take place).
In other words it requires that W^ be a function not only of E but of
some other variable, say ^. Unfortunately, due to our lack of experi-
mental data in regard to mechanism of radiation transfer, it is not possible
to give an absolute solution for this function. Gibbs, however, with
almost preternatural foresight has given us the simplest form that such a
function may take in his formula for canonical distribution, namely.

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62 RUSSELL V. BICHOWSKY. [i

This form corresponds to the assumption, say that codrdinates deter-
mining energy values between 0 and E determine the total energy of
the system and co6rdinates fixing energy values between 0 and some
values less than £, say £©, fix the bound energy of the system (the energy
associated with ankylosed co6rdinates). In other words Gibbs's assump-
tion is for the radiation case equivalent to assuming that radiation (free
energy) of a system cannot be generated until the magnitude of the
co5rdinates reach a certain value, say Eq. From here on, however,
radiation will be continuous. And thus in the proper sense of the
word no quantum theory is needed. If we make Gibbs's assumption
it is easy to show, as indeed Ratnowsky^ has already shown, that the
Planck radiation law follows directly and this without the assumption
of quanta (you assume instead a threshold value), without the assumption
of discontinuities, without necessitating the giving up of infinitesimal
analysis (as of course the quantum theory requires), without contra-
dicting classical mechanics, without contradicting the very cogent
experimental evidence of Duane and others that shows very plainly
that quanta have no physical existence, and with the very great ad-
vantage that the one physical assumption made, namely, that radiation
is given oflF only when the energy of the system has become greater
than a given threshold value £© and from there on is given off continu-
ously, is of itself very probable.*

Appendix.

The Entropy Equation of Solid Bodies and Ga^es and the Universal
Quantum of Activity.*

By Simon Ratnowsky.

Let qu qtf ' ", qn equal the generalized coordinates which determine the state and con-
figuration of the system, and let qi, gs. • • * , q/ be the generalized velocities, then

de de

represent the generalized momenta where e is the total energy of the system, the value.
91, . . ', qm» pi, .... Pm fix a particular state (phase) of the system. It is, therefore, possible
to plot the state of such a system by means of a single point in a 2n-dimensional space.

» Ber. d. D. Phy. Gcs., i6, 232 (19x6); see appendix for a translation.

* Appended to this article is a translation of a part of Ratnowsky's original proof. It is
possible to make a more direct and perhaps more rigorous derivation of the Planck equation
on this basis than Ratnowsky has given, but since Ratnowsky's article has, because of the
war, become practically inaccessible to American readers it has been thought worth while
to republish the proof in its original form.

• Ber. d. D. Phy. Ges., itf, 232 (1916). Translated by F. Russell v. Bichowsky. Only
the mathematical part of Ratnowsky's paper is given here. The last part of the proof has
been greatly abbreviated.

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NoI"i^''l ^^^ PLANCK RADIATION LAW. 63

Following Gibbs a totality (N) of syttems is canonically distributed when the number of
ssrstems in an element of the phase space dX ■> dqi, • • • , dqn* dpu * ** • dPn is given by the
equation

Izi

tip, q)d\ - iV • rfX(t - distribution density). (i)

where 8 and ^ are two constants which have a definite thermodynamic meaning. The
constant, 8, which after Gibbs will be called the modulus of the distribution, is proportional
to the absolute temperature, (8 -> kT, where k -> 1.347 X lo-i*), and ^ is the statistical
free energy which is identical with the thermodynamic free energy of any actual system.

Since sdX is the number of systems in an element, </X, of phase space it follows that sdX
integrated over the whole phase space must give the total number of systems (N), that Is

♦-t

fsdX ^N J , "',fe ^' dqu '",dqn,dpu '",dpn -^ N

(2)

and ^, therefore is defined by the equation,

J , ••• , J • • dqu '",dPn - I
or.

<"• - J , '"»J e-^dqw", dpn.

From this equation ^ may be calculated whenever f is given specifically as a function of
qu " * , pM' If, for instance, c is given by the equation

2 am

we can write:

If the integration limits of the variables

(qupi)* (qupt), •••. (q»,pn)
are independent by pairs this multiple integral can be factored into

and

♦ - - 8 log // e~»(» ^^ *S^*) dqidpi 'ff e'^f '"'"^ Sip-* hqndpn.

If the integration is carried out over all possible values of the variables between — * eo and
+ 00 the total free energy of the system can be calculated and this totally independent of
what the nature of this energy is and of from what energy reservoirs it is drawn.

Now. without further inquiring about the inner mechanism of the system we will make the
purely formal assumption that the energy of the system is of a two-fold nature: the one kind
the energy which is the so-called heat energy (except that borrowed from the energy reservoirs),
the other kind of energy, the proper energy of the system. Since the total energy (heat
energy plus proper energy) can have all possible values and since in order to calculate ^ by
means of equation (3). the integration must be taken over all possible phases, therefore, if
we are to calculate that part of ^(^0) which corresponds to the proper energy, the phase
space must be limited by some special assumption. This limitation must of course agree
with the hypothesis of proper energy and must indeed follow as its consequence, we will.

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64 RUSSELL V. BICHOWSKY, [SSS£

therefore, further define our assumption of proper energy. That is, we will make a special
hypothesis in regard to the proper energy, namely, that the amount of proper energy of any
degree of freedom cannot be more than a certain fixed amount, say c«, or in other words we
will assume that for every degree of freedom there is a limiting value for the proper energy.
If we take for the variables of equation (3) instead of qu pu • • • . 9». ^1.. the energy of a
single degree of freedom

2 am

we will get the total free energy of the system if we integrate between o and 4- * • On the
other hand, we will get that part of the " free energy " of the system which belongs to the
proper energy of the system if we carry out the integration only over the possible variations
of the proper energy, that is, if we carry out the integration not over the entire phase space
(which is unlimited) but only over that part of the phase space which we have limited by
our restriction. In the light of this restriction we can define ^0 as follows:

= { // *-5(i''+»v )d,ip Y (4)

where we make the simplification that the limiting value of the proper energy is the same
(co) for each degree of freedom.

For the heat energy, (*i). then * - *9 - *i. *i is also defined from (3) and (4)

* ® ■» «

f fe h.dqv "dPn I //_^ e e(2*'+2m ^) dqdp |

where we have placed n = 32V". Now. if we take as the variable, e. we can write

where e/0 ■» jc. and also

« «=-, -r--:^-. V7Z' (4«)

If we carry out this simple integration, we have

e e

where

€0

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Xaxf^'J THE PLANCK RADIATION LAW. 65

and hence

(l -« ^).

♦i - zNQ log
or since 9 - *r

*i ^zNkT log

The quantity ^1 has the meaning of free energy, therefore, we can make the usual calcu*
latlon of total energy, pressure and entropy from the well-known equations of thermodynamics,
namely:

S-— ----: U'^F-T—i P'm-T—i
ST ST' dT* SV

from these equations we obtain for the entropy

•9
5 - 3Nk -^ log (i - e"^)

•2.
kT
e — I

and for the energy U

From (4) and (4a)

t« r . \m (^ . ^^

where «• - €»/*r; 6 - *r and iT-^im/f) - i/f. Therefore,

and

kT ^

♦p - - zNkT log— (I -e'^T);

from this since So - — (6^9/iT) we get

«o
5« - zNk

-log (I -e'^T^^klog-^+sNk.

But from (7) if kT ^ «o

5« -3*Ariog-.

(S)

^-3iNr ,/ . (6)

(e--x)

Now if €$/kT is very small, that is, if i^T ^ c»

S* - 3iV* 1 1 - log^l - 3i^ log r + 3il - 3ii log^'

where

U ^kN,

Now according to the classical thermodsmamics

S "ZRlogT •^S'.

Therefore <o/r » a universal constant ■> h and

<• - Ar. (8)

Gbophtsical Laboratory,

Carnbgis Institution op Washington,
Washington, D. C.

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66 H, L. HOWES, ISiMW.

ON CERTAIN ABSORPTION BANDS IN THE SPECTRA
OF THE URANYL SALTS.

By H. L. Howes.

OROBABLY Mr. G. C. Stokes^ was the first investigator to notice
A that the fluorescence and absorption spectra of the uranyl salts
are sh'ghtly overlapped.

Morton and Bolton* also noticed coincidences in the position of several
fluorescence and absorption bands of the uranyl salts.

J. Becquerel and Onnes* working at low temperature found several
coincidences in the positions of the narrowed bands.

Nichols and Merritt^ found that the ** reversing region " was of con-
siderable length; in the case of uranyl potassium sulphate they were
able to reverse the brilliant fluorescence band at 5,130 A. u. whereas
previously the reversals had been limited to the region beyond 5,000
A. u.

In our study of the uranyl double chlorides Prof. E. L. Nichols and the
writer found it possible to reverse a complete group of fluorescence bands
lying between 5,080 A. u. and 4,880 A. u. The desire to extend this
" reversing region " towards the red led the writer to undertake the
present investigation. A theory of luminescent radiation very recently
proposed by Dr. E. H. Kennard also made the investigation of interest.

Since the crystals are of a greenish yellow color they become rapidly
transparent as the light admitted is changed from blue to yellow. This
necessitates the use of crystals of increasingly thicker layers to bring
out the dimmer absorption bands. To a certain extent the crystal acts
as a screen to absorb the blue light which would cause fluorescence,
nevertheless it was found necessary to interpose orange or yellow screens
of different densities to eliminate fluorescence in a region where ordi-
narily it is at a maximum. At first the colored glasses made by the
Corning Glass Company were used as filters; later, solutions of potassium
bichromate of varying concentration. It is evident that the screening
must be constantly changed when light from the arc is used as a back-

» G. C. Stokes, Phil. Trans.. 1852, p. 463.

« Morton and Bolton, Chem. News, pp. 47. 113. etc. (1873).

* J. Becquerel and Onnes, Leiden Communications, No. no, 1909.

* Nichols and Merritt, Phys. Rev., Vol. 33, Nov.. 191 1. p. 354.

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Vol XL!
Nai. J

SPECTRA OF URANYL SALTS.

ground for bands of increasingly longer wave-length. It was thought
that a beam of monochromatic light could be used as a background and
thus obviate exciting the crystal to fluorescence, but a preliminary study
by Dr. D. T. Wilber and the writer indicated that such a beam of dis-
persed light could not be made of sufficient intensity to bring out the
dimmer bands.

In Fig. I is pictured a portion of the fluorescence and absorption

I I

■ I ■ ■ -I 1 l.l.i.l I I h ! Ill

-1 —

"i '

rrt

' i I i" i '

-V^rh

' n I III \t 1 1 hitllilihi^

' M Uh I II UHl'l!

-4-\

i 1 I ! ' I i

Fig. 1.

Fluorescence bands are indicated by lines above the horizontal. Old absorption bands
are indicated by dotted bands below the line; new absorption bands by solid bands below
the horizontal.

The plot shows only a portion of the complete spectra of the following salts at + 20® C.

1. Potassium uranyl chloride.

2. Ammonium uranyl chloride.

3. Rubidium uranyl chloride.

4. Caesium uranyl chloride.

spectrum of each of the double chlorides studied. Fluorescence bands
are designated by heavy lines above the horizontal line. The older,
well-established absorption bands are designated by dotted lines below
the horizontal and the new bands by solid lines below the horizontal.
The relative positions of the fluorescence and absorption bands are
readily seen. An examination of Table I. will indicate more definitely,
in frequency numbers, the agreement or lack of agreement in position.
In the third and fourth columns are given the well-established fluores-
cence and absorption band series. At + 20** almost all of the new bands
fall into fluorescence series while at — 185° the new bands generally
fall in the absorption band series. Table II. gives the new bands at
- I85^

The r61e played by these new bands in producing fluorescence is a
minor one, because they are excessively dim. No doubt if special

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B. L. HOWES.

Sboomd

crystals of great size and exceptional clearness were formed the bands
would appear stronger, and more bands could be discovered. The
present study has added the reversals of two complete groups to the
original group mentioned. For some reason the bands can not be traced
as far into the red when the crystal is cooled to — 185®. It is evident
that Stokes's law does not hold and it may be that every fluorescence
band has an absorption band of the same wave-length.

Table I.

New Absorption Bands at -f 20^ C.

Potassium Uranyl Chloride.

Ammonium Uranyl Chloride.

Absorption.

Fluores-
cence.

Fluores-
cence
Series.

Absorp-
tion
Series.

Absorption.

Fluores-
cence.

Fluores-
cence
Series.

Absorp-
tion
Series.

1802.1
1820.2
1836.5
1846.0

1801.4
1819.3
1837.6

B
C
D

"d'

1802.5
1820.8
1838.9
1848.8
1857.8
1869.2
1871.8
1886.5
1906.2
1924.2
1942.3
1957.4

1803.1
1820.7
1839,7

B
C
D

1855.3
1865.0

1855.3

1856.9

1869.4
1879.0

1869.6

1871.8
1886.8
1904.6
1923.2
1940.5
1956.3

A
B

D
E
A

1885.1
1902.2
1920.9
1937.6
1954.7

1884.7
1901.5
1920.1
1938.3
1953.5

D
E
A

........

Rubidium Uranyl Chloride.

Crnium Uranyl Chloride.

Absorption.

Fluores-
cence.

Fluores-
cence
Series.

Absorp-
tion
Series.

Absorption.

Fluores-
cence.

Fluores-
cence
Series.

Absorp-
tion
Series.

1740.0

1778.7
1789.5
1806.1
1823.2

1741.6
1777.8
1789.4
1806.1
1822.8

C
E
A
B

d
e?

1791.5
1808.0
1829.2
1843.0
1846.4
1861.2
1873.0
1890.7
1911.1
1923.8
1944.4
1957.8

1789.7
1808.6
1827.5
1840.5

A
B

1834.9

1859.1
1873.1
1891.1
1910.4
1923.6
1942.7
1955.7

E
A
B
C
D
E
A

1841.6
1859.8
1872.0
1889.0
1907.2
1926.7
1941.7?

1841.5
1859.8
1873.1
1890.0
1905.5
1925.0

D
E
A
B
C
D

1944.0
1952.0?

1943.5

1958.7

1957.1

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Vol. XI.1
Naz. J

SPECTRA OP URANYL SALTS.

Table II.

New Absorption Bands at — 185'^ C.

Potassium Uranyl Chloride.

Ammonium Uranyl Chloride.

Absorption.

Fluores-
cence.

Fluores-
cence
Series.

Abiorp-

tion
Seriei.

Absorption.

Fluores- <
cence.

Fluores-
cence
Series.

Absorp-
tion
Series.

1941.7
1947.6

1940.0

£t'

ex'
W
ai
bt
h,
cr'
c."

1945.9
1953.5
1956.6
1963.5
1967.7
1973.6
1977.1
1981.0
1984.9
1992.0
1996.8
2002.8
2006.8
2014.1

1945.0
1953.7

1954.7

1960.4

et"

1965.8
1972.4

1963.9
1972.3
1977.8

Bi
Bt
B,

1968.7

1977.5
1984.9

1977.9

bt
bt''

1989.3

b»

1998.0
2008.8

1997.2
2007.4

1992.7

di'

di"

dt"

Rubidium Uranyl Chloride.

Caesium Uranyl Chloride.

Absorption.

Fluores-
cence.

Fluores-
cence

Series.

Absorp-
tion
Sorie*.

Absorption.

Fluores-
cence.

Plaoret-
cenc.
Seric

Absorp-
tion
Series.

1944.4

dt"

1953.9
1956.6
1958.9
1967.0
1970.8
1974.3
1978.2
1982.9
1987.7
1991.3
1997.6
2005.6
2009.6
2016.1
2022.2

dt''

1952.4

1954.7

et'

1958.1

1957.9

a.'
W
bt

ax'

1963.9

1973.9

bi!

1981.0

bi"

1985.7

bt'

1995.6

dx
dt'
dt"

bt"

2005.2

2003.7

2010.1

1997.6

2016.1

2008.5
2014.9

Dt
Dt'

d,
dt'
dt"

Physical Laboratory of Cornell University.
August 31, 1917-

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70 R^ W. WOOD AND FRED L. MOHLER. [i

Sboomd
Swrntt

RESONANCE RADIATION OF SODIUM VAPOR EXCITED BY
ONE OF THE D LINES.

By R. W. Wood and Frsd L. Mohler.

Introduction.

THE purpose of this investigation was to study the resonance spec-
trum of sodium vapor when the resonance was excited by a single
D line. In a paper on " Resonance Radiation of Sodium Vapor "*
published by one of us in 1905, it was shown that if a bulb containing
pure sodium vapor was illuminated by light from a sodium flame, the
vapor emitted a yellow light which spectroscopic analysis showed to
be identical with the exciting light, in other words, the two D lines.
It was suggested at this time that it would be interesting to see if both
D lines appeared when the vapor was illuminated by a single D line.
This would determine whether the mechanisms that give rise to the
D lines are separate or in some way connected.

In 1914 this experiment was tried by Wood and Dunoyer.* This
experiment was made possible by the discovery of a polarization method
of separating close spectral doublets that eliminated the great loss of
light involved in a high-power monochromator, but even with this
method the resonance light is very faint. The spectrum of resonance
excited by D2 was photographed with exposures varying from 10 to 15
hours. The majority of the plates showed only the Da line, but owing
to under exposure Di would not have been visible if it was less than one
fourth of the intensity of Dj. Some plates indeed showed both Di
and D2, but the presence of Di in the exciting light was judged to be
the cause of this. Imperfections in the optical system made it impossible
to entirely remove Di from the exciting light and as it was sensitive to
temperature changes the nature of the transmitted light sometimes
changed during an exposure. It was concluded that sodium resonance
excited by D2 consisted of D2 alone, but the results admit of two other
possibilities. Di light may always be present though much fainter than
D2, or it may only appear under certain conditions.

Other resonance phenomena show that the radiation centers in sodium
are not entirely independent. One of us^ showed in 1905 that excitation

1 R. W. Wood, Phil. Mag. (6). lo, 513. 1905.
*Wood and Dunoyer, Phil. Mag. (6), 27, 1018, 1914.
' Wood, Phil. Mag. (6), 10, 408. 1905.

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X^j^^] RESONANCE RADIATION OF SODIUM VAPOR. 7 1

of sodium vapor by blue-green light, in the region of the band spectrum,
gives rise to the D lines, or, at least, to a band in that region.

Strutt^ in 1915 found that resonance radiation consisting of the D lines
could be excited by the 3300 doublet of sodium, the second doublet in
the principal series of which the D lines are the first. When only one
line of the 3300 doublet was excited by a coincident zinc line both the D
lines again appeared. This remarkable discovery, indicating clearly
some connection between the emission centers of the doublets of the
principal series of sodium, made a further study of the excitation of
resonance by one of the D lines seem desirable. In view of results which
will be mentioned further along, it may be well to point out that Strutt's
results may have been due to the presence of hydrogen in his bulb of
sodium vapor.

The arrangement of the apparatus and the method used in the present
work differ only in minor details from the method of Wood and Dunoyer.

The chief requirements for the investigation are:

1. A method of completely separating Di and D2 in the exciting light

with the least possible reduction in the intensity of the light.

2. The preparation of bulbs containing sodium vapor that will give

brilliant resonance during a prolonged heating.
J. The analysis of the light by a spectroscope giving the greatest possible
intensity of light commensurate with the dispersion necessary to
clearly resolve the D lines.

The Method of Separating the D Lines.

The polarization method of separating close spectrum lines was
described by one of us* in 1914. Briefly the method is as follows: If
plane-polarized monochromatic light is passed through a doubly refracting
crystal with its direction of vibration making an angle of 45° with the
optic axis of the crystal, it will in general emerge elliptically polarized,
but for certain thicknesses of the crystal it will be plane polarized either
in the same direction as the incident light or at 90** to this direction. If,
now, we have light of two wave-lengths in the incident beam, the emerg-
ing beam will be in two different states of polarization due to the difference
in refractive index for the two wave-lengths. It is possible to find a
thickness of the crystal such that the emergent light consists of two
monochromatic beams plane polarized at right angles to each other.
By the use of an analyzing nicol either wave-length may be cut out
and monochromatic light secured.

» R. J. Strutt, Proc. of Royal Soc. Series A, 91. P- 5".
' Wood, Phil. Mag. (6). 27, 524, 1914.

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72 R. W, WOOD AND FRED L. MOHLER, [tow?

To cut out one of the D lines with quartz a plate about 32 mm. thick
is required. The thicicness can vary considerably for the precise optical
length of path required can be secured by tilting the plate. To secure
intense illumination a large plate of quartz must be used in parallel
light and the faces must be optically plane, or nearly so.

Since half of the light is cut out if it is polarized by a nicol, large
double-image prisms were used to polarize and analyze the light. They
were placed so that only two images of the source were formed. When
the quartz block was placed between them and properly oriented three
images appeared, the central image consisting of two superposed images
containing only Ds light and two lateral ones containing only Di light.
A slight tilting of the quartz plate changed the central image to Di and
the lateral ones to Ds.

The large quartz block measuring 85 X 60 X 32 nrnis., prepared for
the experiment of Wood and Dunoyer, was refigured and supported
rigidly in a brass frame arranged to rotate on an axis parallel to the optic
axis of the crystal, and inclined at an angle of 45° to the vertical. It was
placed between two large Iceland-spar prisms of about the same size
as the block of quartz and mounted with their edges (optic axes) vertical.
The lenses of a large Dunoyer condenser made the light passing through
the prisms parallel, and brought it to a focus on the bulb of sodium vapor.

This optical system was enclosed in a wooden box, which was kept
at a constant temperature to within 0.1° C. by a benzene thermostat.
This precaution is necessary for a change in temperature of a d^ree or
two will completely change the nature of the light transmitted by the
quartz block. A long handle fastened to the supporting rod of the
quartz block made it possible for an observer at the spectroscope to turn
the block and adjust the apparatus for the extinction of one of the D
lines.

The Spectroscope.

For analysis of the resonance radiation a large two-prism spectroscope
furnished with portrait objectives of 3 inch aperture and 24 inch focus,
loaned by the psychology department of this university, was found to
give the best results. With this instrument brilliant illumination and
clear resolution of the D lines were secured with a fairly wide slit, though
the definition was not perfect. This spectroscope had been arranged
for use as a monochromator, with the second slit mounted on a screw,
so that it could be moved along the spectrum. For the present work the
photographic plates were simply clamped against the second slit mount-
ing. This offered a very convenient method of taking a series of ex-
posures on the same plate, side by side instead of one above the other, as
in the ordinary plateholder.

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Vol. XI.l
No. I. J

RESONANCE RADIATION OP SODIUM VAPOR.

Light Source.

The source of light was a Maker burner surrounded by a chimney
provided with a rectangular aperture measuring about 2X5 cms.
The image of this rectangle, formed by the polarizing separator, was
thrown on the bulb of sodium vapor. A disk of asbestos soaked in salt
solution touched the edge of the flame and this disk was revolved once
in twelve hours by the hour hand gear of a clock. This device kept the
sodium flame at about the proper intensity to give the maximum brilli-
ancy of resonance. It is very important, however, to have the disk
graze the flame on the side furthest removed from the lens, as by this
arrangement reversal of the D lines is obviated. This is of fundamental
importance since the resonance radiation is excited by the core of the
line only.

Heating Device.

The bulb containing the sodium was supported above an asbestos
chinmey about two feet high and five inches in diameter, below which
was placed a nest of Bunsen burners. The bulb was supported by a
wire frame in such a way that it could be turned about a vertical axis,
and a firmly supported pin point touched the front surface to detect
any possible displacement when the bulb was rotated.

Fig. 1.

Arrangement of Apparatus.

Fig. I shows a plan of the apparatus. The light source asbestos disk
and surrounding chimney is at i4. B is the optical system for separating
the D lines with the long handle C to turn the quartz block Q between
the spar prisms PP. The bulb of sodium vapor is at Z>, placed in the
position shown so as to prevent directly reflected light from falling on
the slit of the spectroscope. At E is the plateholder of the spectroscope
mounted on a horizontal screw.

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74 R, W, WOOD AND FRED L. MOHLER. ]SSm,

The improvements over the apparatus previously used are in the
device for separating the D lines and in the spectroscope. The spectro-
scope gave better illumination and the system for separating the D lines
gave almost perfect extinction of Di, though the extinction of Dt was
not quite so good, as Dj has double the intensity of Di in the case of the
comparatively feeble flame used for the excitation.

Preparation of the Bulbs.

The method used in preparing the sodium bulbs is practically that
previously described by Dunoyer and Wood.^ A bulb about 5 cm. in
diameter is made as shown in Fig. 2. A piece of sodium, weighing about
^ of a gram, is put in the tube at the left,
the tube immediately sealed at A and the
bulb connected to the pump and exhausted.
The bulb is heated for about half an hour
to free the glass from occluded water and p. 2

the sodium is then distilled into it and
the side tube sealed off. The sodium is then distilled from one side
of the bulb to the other many times by heating opposite sides alter-
nately with a Bunsen burner, while the pump is kept running and the
pressure read from time to time on a McLeod gauge.

The preliminary heating prevents or at least retards the reaction of
the sodium with the glass which at temperatures above 200** reduces the
silicon oxide and makes the glass brown and finally opaque. Bulbs of
Pyrex glass, which proved to be far superior to ordinary glass in this
respect, prepared in the way described, showed scarcely any color after
twelve hours* heating at 220°, and were quite transparent, though brown,
after heating twelve hours at 300°.

The repeated distillation of the sodium was to drive off the hydrogen
which is occluded by it in large quantities. If, after distilling the
sodium into the bulb the pump was cut off and the sodium driven from
one side of the bulb to the other two or three times the pressure gauge
indicated a rise of about .3 mm., and repeated distillation with the
pump maintaining a vacuum of about .002 mm., only removed this
hydrogen very slowly. The sodium vapor seemed to carry most of the
hydrogen with it as it was distilled from side to side of the bulb, for when
the pump was stopped and the bulb heated the pressure alwa3r8 increased
several hundredths of a millimeter. In the preparation of one bulb the
sodium was distilled back and forth across the bulb 170 times in a high
vacuum after which the pump was stopped and .01 mm. of gas was

1 Dunoyer and Wood, Phil. Mag. (6), 27, 1027, 1914.

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Vol. XL!
No. X. J

RESONANCE RADIATION OF SODIUM VAPOR,

given off by the sodium when it was heated. In cases in which it was
desirable to have some hydrogen present the pump was cut off as soon
as the sodium distilled into the bulb. The bulb was then heated, the
pressure measured, and the bulb sealed off. To test whether prolonged
heating increased the amount of gas some bulbs were opened under
mercury after they had been used, but the amount of gas present was
not noticeably different.

The careful removal of all the hydrogen is not necessary to secure
brilliant resonance, but it does affect the character of the resonance
spectrum, as will be explained later.

Procedure.

To facilitate the adjustment of the apparatus for extinction of one of
the D lines a patch of magnesium oxide was put on the surface of the
bulb by burning magnesium wire below it and then removing all the
oxide except a small rectangular strip. To adjust the apparatus the
bulb is placed in position and turned until the light from the sodium
flame falls on the patch of oxide. As magnesium oxide is a nearly perfect
reflector this gives a source of light bright enough to make all adjust-
. ments. To photograph the resonance spectrum the bulb is turned
slightly till the exciting light falls on clean glass. Care must be taken
that no light is directly reflected into the spectroscope.

Owing to the path difference through the quartz block of rays coming
from different parts of the rectangular aperture, the illumination is not
strictly monochromatic (Dj) over the entire image of the aperture.
Experiments showed that we have pure Dj radiation along slightly
curved and nearly vertical strips two or three millimeters in width, the
distribution of the illumination being somewhat as shown in Fig. 3.

The upper and lower portions of the image of
the patch of resonance radiation thrown on the
slit were excited by both lines when the central
portion was excited by one only. For this reason
any motion of the image on the slit either during
the exposure, or in turning the bulb before the
exposure, had to be guarded against. As in some
cases only a small part of the line was single, it was necessary to com-
pare corresponding parts of the lines of the exciting light and of the
resonance light. This comparison was facilitated by the possibility of
making several exposures on the same plate with the lines side by side.
The usual procedure was to first photograph the exciting light reflected
from the magnesium oxide, then move the plate, turn the bulb and

Fig. 3.

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76 R. W. WOOD AND FRED L. MOHLER. [ISSS

expose to the resonance light, and at the end of the exposure again turn
the bulb and move the plate and expose to the exciting light.

The exposures for the resonance spectrum varied from three to fifteen
hours; usually twelve hours. The exposures for the diffusely reflected
exciting light, to give the same intensity as the resonance light in 12
hours, were from fifteen to thirty minutes when the same type of flame
was used. The brightest resonance is secured when the flame is quite
faint. Wratten and Wainwright panchromatic plates were used.

The method of estimating the intensity ratio of the D lines, when
both appeared, was to match the two lines with sodium lines on a com-
parison plate made by taking a series of exposures of varying length
with a sodium flame of constant intensity. The intensity ratio was
assumed equal to the ratio of exposure times of lines that matched.

Results.

Most of the plates taken were of resonance excited by Dj, for as Dj
is about twice as bright as Di, there are obvious advantages in trying
it first. The efficiency of the polarization method of cutting out Di
was tested and it was estimated that under the best conditions Dt was
at least 50 times as bright as Di, though overlapping due to irradiation
of the Ds line made it impossible to be sure of the ratio.

The results of many exposures to resonance excited by Dj showed
visible traces of Di in nearly every case, but with an intensity ratio of
Dt to Di that varied from about 6 to i, to about 20 to i. This result
led at first to the suspicion that stray sodium light was in some way
thrown on the spectroscope slit. All possible precautions against this
source of error were taken.

When with these precautions both D lines appeared in the resonance
spectrum a further precaution was taken to be sure the effect was not
false. A narrow horizontal strip of magnesium oxide was placed so as
to intercept the rectangle of resonance light in such a way that part of
the resulting spectrum line was formed by resonance,
and part by reflected light. Since the resonance
light is much fainter than the light reflected from a
white surface the comparison strip was made a dark
gray by first coating the bulb with smoke, and then
depositing magnesium oxide until the reflected light
was of about the same intensity as that of the reso- pjg 4

nance. Fig. 4 A shows the form of the oxide patch,
the large rectangular strip being the same as that before mentioned, and
the narrow shaded strip the part that intercepted the patch of resonance.

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Physical Review. Second Series, \'ol. XI,
January, 1918.

Plate I.
To face page 77.

! I

9 10

R. W. WOOD AND FRED L. MOHLER.

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X^ XI.J RESONANCE RADIATION OF SODIUM VAPOR. y/

Fig. 4 B shows the appearance of the resulting spectrum line as it ap-
peared when this method was used. Both D lines appear except at the
place where the exciting light is reflected from the gray strip into the
spectroscope, and there only one line is recorded. If the appearance of
both lines was due to reflection of stray light from the surface of the glass
there would be no break in the line. This effect was found both with
resonance excited by D2 and by Di, and seemed to be conclusive evidence
that D2 light did excite a trace of Di light in the resonance radiation.
Having verified the results by this method the gray strip was dispensed
with in the later work, as it somewhat complicated the adjustment of the
bulb. On all plates, however, three exposures were taken, as is shown in
the accompanying plate. The plates haye been enlarged about ten
times. In each case the middle line, or pair of lines, is the resonance
spectrum, and the two lines on each side are due to the exciting light
diffusely reflected from the patch of magnesium oxide. False effects
due to any change in the exciting light can thus be detected.

Comparison of a number of plates taken under different conditions of
temperature, with bulbs prepared in different ways, did not at first show
clearly under what conditions Di appeared in the resonance spectrum
excited by Dj. This was due to the fact that two causes contributed to
the effect. However all the bulbs from which' the hydrogen was not
carefully removed showed Di distinctly. Now the resonance spectrum
of iodine vapor excited by the green mercury line is changed in the
presence of electro-positive gases such as helium and hydrogen, the effect
of the gases being to transfer energy from the radiation centers directly
excited by the mercury line to other radiation centers. The effect will
be described later. The possibility of a similar effect in the case of
sodium resonance led to the following experiments: The effect of a
change in the density of pure sodium vapor on the resonance excited
by D2 was first investigated. A bulb containing sodium that was as
free as possible from hydrogen was used for three exposures to resonance
excited by Dj at temperatures of 210°, 270® and 340** keeping all other
conditions constant. The exposure at 210** showed no trace of Di in
the resonance spectrum, while at 270*^ a distinct trace of Di was seen.
At 340® the intensity ratio of D2 to Di was about the same as that in a
faint flame, about 2 to i, but the plate was much under-exposed and
the result therefore was subject to error. Figs. 5 and 6 of the accom-
panying plate show the resonance of pure sodium vapor excited by Dt
at 210*^ and 300** respectively.

It may be well to mention here the change in general appearance of
the resonance as the temperature is raised. Resonance light becomes

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78 R, W. WOOD AND FRED L, MOHLER. [ISSS?

visible at about 120°, and appears as a faint glow throughout the bulb.
As the temperature is raised the light becomes brighter at the front
surface and fades out in the interior of the bulb until, finally, the light
is limited to the surface and exhibits a sharp image of the source when
it is focused on the bulb. At 200** the resonance appears only at the
surface though the image of the source is still a little indistinct, but
above 250*^ the image is as sharp as if the light was reflected from a piece
of smooth paper.

The change in the resonance spectrum when hydrogen was put into
the bulb was more marked than the change when the vapor pressure of
the sodium increased. The resonance excited by Dj in a bulb containing
.25 mm. of hydrogen showed Di about a quarter as bright as Da at 210**
and at 300® Di was a third as bright as D2. Figs. 7 and 8 were taken
under these conditions. The faint line in Fig. 7 is of no importance.

A similar series of exposures was taken of the resonance excited by Di.
It is difficult in this case to avoid traces of Dj in the exciting light for
reasons before mentioned, and the intensity of the resonance is reduced
to about half. The effect of increasing the vapor pressure or putting
hydrogen in the bulb is the same in this case as with Dj excitation,
though the intensity ratio of Dj to Di with Di excitation is greater than
that of Di to D2 with Dj excitation when other conditions are the same.
Thus with pure sodium at 210** a trace of Da was visible (Fig. 9) while
with .1 mm. of hydrogen in the bulb Dj is half as bright as Di (Fig. 10).
Some plates, where more hydrogen was in the sodium bulb, showed Da
nearly as bright as Di but the plates were underexposed and there was a
possibility that the effect was false.

All the results mentioned above were verified by repetition of the
experiments. In all about 50 plates were taken in which the resonance
lines were distinct, and the other conditions favorable as far as could
be ascertained.

Estimates of the intensity ratio of the D lines were made in each case.
They agreed roughly under apparently similar conditions of vacuum,
temperature of bulb, etc., but there was quite a range of uncertainty
both in the estimation of the intensity ratio, and in the ability to get
conditions identical in two cases. The observations may be summarized
as follows:

D2 Excitation.

Bulb as free from hydrogen as possible.

At 210° (no trace of Di) intensity ratio of D2 to Di at least 20 to i-
Fig. 5.

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Not'i'!^^'] RESONANCE RADIATION OF SODIUM VAPOR. 79

At 300**, ratio of Dj to Di 5 to i. Fig. 6.
Bulb containing about .25 mm. of hydrogen.
At 220**, ratio of Dj to Di 4 to i. Fig. 7.
At 300**, ratio of Dj to Di 3 to i. Fig. 8.

Di Excitation.
Bulb free from hydrogen.

At 220®, a trace of Dj seen. Fig. 5.

At 300**, ratio of Di to Dj 3 to i.
Bulb containing .1 mm. of hydrogen.

At 220**, ratio of Di to Dj 2 to i. Fig. 6.
Bulb containing .25 mm. of hydrogen.

At 250**, ratio of Di to Dj possibly 3 to 2.

Conclusion.

As it has been shown that the presence of hydrogen causes both D
lines to appear when resonance is excited by one D line only, it is safe
to conclude that the appearance of both D lines at high temperatures is
due to the increase of the pressure of the sodium vapor. From the
measurements of vapor tension made by HackspilP we can estimate the
pressure of sodium vapor at the temperatures used. Extrapolating the
vapor-tension temperature curve given by him gives the following values
of vapor pressure:

At 200®, .003 mm.

At 250®, .01 mm.

At 300°, .025 mm.

Thus at 200° the vacuum is nearly as good as in a cold bulb, but at 300°
the amount of sodium vapor is comparable to the amount of hydrogen
present, in the bulbs made to show the effect of that gas.

There is a striking analogy to this effect of hydrogen and sodium vapor
on the resonance spectrum of sodium, in the case of the resonance spec-
trum of iodine vapor excited by the green mercury line when traces of a
chemically inert gas are present. This effect was described by one of us
in 191 1.* Iodine vapor at room temperature in a high vacuum when
excited by the green line of the Cooper-Hewitt mercury arc emits a
spectrum consisting of a series of doublets spaced at nearly equal fre-
quency intervals. The first member is in coincidence with the exciting
line and the last (or 28th) is at wave-length 7683. If a long exposure is

> Hackspill, Annales de Chemie et de Physique, 28, 680. 1913.
* Wood and J. Franck, Phil. Mag. (6), 21, p. 265.

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8o R. W. WOOD AND FRED L. MOHLER. [^^

given It is found that traces appear of very r^ular bands, similar in
appearance to that of the A line of the solar spectrum. If helium at
3 mm. pressure is introduced into the bulb, the doublets weaken and the
bands increase in intensity. As the helium pressure increases the
doublets become fainter and the bands stronger in proportion; that is,
there is a transfer of energy from the system or systems giving rise to
the doublets, to that responsible for the band spectrum. The same thing
occurs with xenon or krypton, or any other electro-positive gas. An
electro-negative gas, however, merely decreases the intensity of the
resonance, and so far as is now known, does not give rise to the transfer
of energy. It is of course possible or even probable that there is some
transfer in this case, but the intensity is so greatly reduced that its
detection is difficult.

We conclude that the transfer of energy from the Di to the Di emission
centers, or vice versa, is in some way the result of molecular collision,
either of sodium with hydrogen or of sodium with sodium. It has been
shown that hydrogen and sodium vapor, both electropositive, cause this
transfer of energy, and the analogy to the similar transfer in the case of
iodine resonance is of considerable interest.

In a bulb of pure sodium at 220® the surrounding vapor is not dense
enough to have an observable effect on the radiation centers, and only
one line appears in the resonance spectrum. The appearance of the
other line results from an increase in the collision frequency, which
increase can be caused either by the introduction of hydrogen at low
pressure or by increasing the density of the sodium vapor.
Johns Hopkins Univbrsity.
June, 19x7*

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Second Series. February, igi8 Vol. XL, No. 2

THE

PHYSICAL REVIEW.

THE BRIGHTNESS SENSIBILITY OF THE RETINA.^

By Julian Blanchard.

THE eye is able to perceive with ease and comfort a very wide range
of light intensities, a range extending over a billion times. It is
able to do this because the sensibility of the retina automatically adjusts
itself to the stimulus applied, its action being analogous to that of such a
physical instrument as a galvanometer with a continuously variable
shunt. In this analogy the current through the galvanometer corre-
sponds to the light flux, the scale reading to the brightness sensation
produced by the light and the derivative of the scale reading with respect
to the current to the sensibility of the retina. The sensation of course
cannot be measured directly, but it can be relatively determined by
getting a measure of the sensibility at the corresponding stimulus.
Since the sensibility is the derivative of the sensation, or scale reading,
with respect to the stimulus, the sensation is conversely the int^ral
of the sensibility with respect to the stimulus.

When light falls upon the retina the sensation produced depends
upon a number of variables. It is a function of the intensity of the
light flux, the length of time it has been acting (before equilibrium is
reached), the wave-length, the area and part of the retina affected and
the physiological condition of the eye determined by its previous treat-
ment. It would be a difficult matter to determine this general brightness
sensation function, but by holding certain factors constant it is easy to
obtain a number of limited relations.

The principal object of this investigation is to measure the brightness
sensibility of the retina under certain definite conditions. There are
three different ways of doing this, or rather three different sorts of
sensibility, which are as follows: (i) Threshold Sensibility: This is
measured by the least brightness that the eye can see. It is proportional
to the reciprocal of the least perceptible brightness instantaneously

* Communication No. 45 from the Research Laboratory of the Eastman Kodak Company.

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82 JULIAN BLANCHARD, [to»

substituted fqr that at which the sensibility is desired and to which the
eye has been previously adapted. (2) Contrast Sensibility: This is
sensibility to brightness difference, or contrast, and is sometimes called
photometric sensibility. The reciprocal of the least perceptible difference
in brightness between two adjacent fields is taken as proportional to
the sensibility at the brightness being used. Of the same nature as this
IS flicker sensibility, but this will not be considered. (3) Glare SensibiMty:
This is measured by the reciprocal of the brightness that just appears
glaring with the eye previously adapted to any given field brightness.
It gives an indication of the ability of the retina to stand an overload.

In this paper data will be given on each of these different kinds of
sensibility, on the rate of dark adaptation, and on the equilibrium size
of the pupil for different field brightnesses.

The literature on visual sensitometry is extremely varied and is too
extensive to be reviewed here. Some of the best work that has been
done on contrast sensibility is that of Kdnig and Brodhun,^ while Nagel
and his pupils' have made use of the threshold method in various ways,
particularly in measuring the rate of adaptation. In this laboratory
Dr. P. G. Nutting has used the threshold method in an improved manner
and some preliminary results have been published.* In the present
work both the contrast and threshold methods are used with the Nutting
type of sensitometer.

Apparatus. Method of Measurement.

The apparatus used in these experiments is the same as that described
by Nutting* with some alterations. It may be called a visual sensitom-
eter. It consists of a matte
white board B (Fig. i) about
"-C^ 60 cm. square with an opal glass
'^^"" window T in the center, 3 cm.

square, which is illuminated from
behind to any desired inten-
sity. For this purpose there is
/^' *.^ ^ a Nemst filament N focused by

a lens L on a slit 5, and sliding
in metal ways over this slit is an accurately calibrated absorbing wedge W
for controlling the intensity. This small square is termed the test spot.
Means are provided for moving the wedge by the observer sitting in

1 a. Kttnig, Ges. Abh.. pp. 115. 135.

* Cf. Helmholtz. Phys. Optik, 3d Ed.. Vol. 2. p. 264.
» Trans. 111. Eng. Soc.. Vol. 11, p. i.

* Loc. clt.

If-

The visual Sensitometer.

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Na*a^'*] BRIGHTNESS SENSIBILITY OP RETINA, 83

front of the board and for recording its position. The board is illuminated
to any desired intensity by means of a lamp F inclosed in a box to the
rear of the observer, the illumination being altered in steps by means of
neutrally dyed gelatine filters of known transmission placed over the
opening in the box. This is called the sensitizing field, or the pre-,
adaptation field. When using high candle power lamps which glow for
a considerable time after the current is cut off, the field was darkened
by operating a moving curtain camera shutter in the opening of the box.
The wedge W was made by coating a plate of plane glass with a thin
layer of neutrally dyed gelatine uniformly increasing in thickness from
one end towards the other. Two such wedges, separately calibrated,
were placed together with the gelatine faces inside to avoid injury. The
density increased from 0.95 one centimeter from the thin end by about
0.4 per centimeter of length, the calibration being carried to a density
of 7.5. (Optical density is defined as the logarithm of the opacity, or
the logarithm of the reciprocal of the transmission.) The calibration
of the wedge for white light is given in Table I. Although very nearly

Table I.

Calibration of Absorbing Wedge.

Cm 1 2 3 4 5 6 7 8 9

Density 0.95 1.36 1.77 2.16 2.59 3.02 3.46 3.92 4.39

Cm 10 11 12 13 14 15

Density 4.86 5.34 5.85 6.33 6.85 7.43

non-selective it was not exactly so and it was therefore calibrated for
each of the colors used.

In making an observation on threshold sensibility the procedure is
as follows. The eye at £, 35 cm. in front of the test spot, is fully adapted
to the sensitizing field being used, the field is flashed off and by repeated
trials the wedge is set so that the test spot is just visible immediately
after extinguishing the field. Or if the threshold is desired at any
subsequent time the wedge is moved along so that the test spot is just
visible all the while, the position of the wedge being recorded at definite
intervals of time as marked off by a sounder. In order to make the
determination of the instantaneous threshold easier a white card was
held in front of the test spot and at the instant of extinguishing the field
this was quickly moved away and back again, giving an exposure of a
small fraction of a second in which to decide whether or not the spot
was visible. The brightness of the field and of the test spot was measured
by means of a portable brightness photometer (modified Beck ** lume-
ter **), recalibrated to read directly in millilamberts over a range from
0.02 to 2 and provided with decimal filters for reading as high as 2,000

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JULIAN BLANCHARD,

rSBCX>N»

LSsmiBS.

ml. The very small intensities, below the range of the instrument,
were calculated from the known density of absorbing screen used to cut
down a measured higher intensity. In order to obtain the highest field
brightnesses the lamp F was focused on a small r^ion around the test
spot and viewed through a bright tin-lined tube to enlarge the field of
brightness. Since this necessitated using only one eye the other measure-
ments were also made with monocular vision.

In all of this work the unit of brightness used is the " lambert," or
millilambert, which is o.ooi lambert. It has been officially adopted by
the Illuminating Engineering Society and is defined in the 1915 Report
of the Committee on Nomenclature and Standards^ as " the brightness
of a perfectly diffusing surface radiating or reflecting one lumen per
square centimeter," that is, in accordance with Lambert's cosine law.
A perfectly diffusing surface emitting one lumen per square foot will have
a brightness of one foot-candle, which is equal to 1.076 millilamberts.
A brightness of ten meter-candles is equal to one millilambert. The
lambert is to be preferred as a unit of brightness since the foot-candle
and the meter-candle are also generally used as units of illumination.

Threshold Sensibility.
In the manner described above the instantaneous threshold was

Table II.

Instantaneous Threshold for Different Field Brightnesses.
All values are in millilamberts.

White.

Blue.

Qreen.

Yellow.

Red.

Loff B, Loff 7.

Log B, , Log T.

lAigB,

Logy.

Log^.

Log 7;

Logi?.

Logr.

- 6.15 - 5.85

- 7.26 - 6.72

-6.85

-6.40

-5.70

-5.35

-4.83

-4.26

-5.95

-5.80

-6.96 -6.66

-6.60

-6.35

-5.45

-5.33

-4.68

-4.20

-5.80

-5.72

-6.61 -6.61

-6.31

-6.32

-5.28

-5.23

-4.36

-4.08

-5.65

-5.73

-6.26

-6.49

-6.02

-6.22

-4.98

-5.17

-4.06

-4.01

-5.35

-5.60

-5.72

-6.24

-5.12

-5.65

-4.65

-5.00

-3.48

-3.74

-5.05

-5.44

-4.77

-5.69

-4.20

-5.18

-3.70

-4.40

-2.92

-3.42

-4.15

-4.92

-3.87

-5.01

-3.30

-4.56

-2.70

-3.93

-2.26

-3.10

-3.20

-4.35

-2.92

-4.17

-2.40

-3.95

-2.20 -3.50

-1.40

-2.60

-2.30

-3.52

-2.11

-3.56

-1.57

-3.05

-1.75 -3.15

-0.80

-2.40

-1.35

-2.80

-1.71

-3.26

-1.24

-2.72

-1.15 -2.70

-0.18

-2.00

-0.40

-2.28

-1.11

-2.76

-0.67

-2.33

-0.17 -2.12

0.37

-1.70

0.55

-1.75

-0.58

-2.39

0.26

-1.98

0.10 -1.90

1.00

-1.37

1.50

-1.02

-0.18

-2.29

1.03

-1.64

0.80 -1.75

1.30

-1.33

2.00

-0.75

0.42

-2.01

1.32

-1.50

1.10 - 1.52

1.56

-1.12

2.40

-0.37

0.66

-1.86

1.62

-1.20

1.41 1 - 1.25

1.81

-0.97

2.97

0.29

0.97

-1.61

1.91

-0.93

2.12

-0.78

3.30

0.71

1.34

- 1.36

* Trans. 111. Eng. Soc.. Vol. lo. 191 S. P- 642.

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Vol. XI.I
Na2. J

BRIGHTNESS SENSIBILITY OF RETINA.

determined for fields varying in brightness from the highest obtainable
(about 2 lamberts for white) down to the threshold itself, with white light
and with blue, green, yellow and red. The data are given in Table II.
and the curves in Figs. 2 and 6. On account of the great range of values
involved it is necessary to plot logarithms of the variables. It is to be
noted that — log threshold is proportional to log sensibility, since the
reciprocal of the threshold is taken as proportional to sensibility. In
Fig. 2 the individual points determining the curves are omitted to avoid

C/f£l

■^^

U/£

LUM>

-is

^£0

**^

^fc_

-7 -6 "J -4 -3 '£ -/ O / £ J 4

LOe HELD

Fig. 2.

Threshold Sensibility for Different Colors.

confusion. The deviations from the smooth curves are no greater
than for white light shown in Fig. 6.

The data given are the average of results obtained on three different
days, in most cases with several days intervening. In beginning a run
it was customary to remain first in darkness about thirty minutes in
order to bring the eye into about the same initial condition each time.
Observations were made at the threshold first, proceeding to gradually
higher intensities, the eye being adapted to each brightness for several
minutes before threshold observations were made.

In order to express the results consistently in the same unit of bright-
ness it is necessary to take into account the Purldnje phenomenon. If
two fields of different color are illuminated to the same apparent bright-
ness and both cut down by equal amounts the brightness will not decrease
in the same ratio. For example, red will grow darker much faster than
blue. But at very low intensities it is impossible to measure brightness
by any photometric means, and without having a definite measure of
the Purldnje effect for the different colors the only feasible way of
expressing relative intensities is in fractions of a certain measured
intensity above the brightness at which the effect sets in. In these

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JULIAN BLANCHARD.

[Sbcond
Sbribs.

experiments all the colors were measured photometrically at a brightness
of 10 millilamberts, which is safely above the Purkinje effect, and the
lower intensities calculated from a knowledge of the filter densities.

In working with the colors both the test spot and the field were colored.
These colors were obtained by using filters over the corresponding light

sources. The filters were chosen
to give a fairly narrow spectral
band without having too great
a density and their transmission-
wave-length curves are given in
Fig. 3. In the case of yellow the
ordinates have been multiplied
by ten. For this color it was
necessary to combine two filters,
resulting in a rather high density.
The curve for white light is
seen to be practically a straight
line with the exception of the extreme intensities and may be repre-
sented over this portion by the equation,

B \--

\ /

M«4Mr LCffTIt (/Ut)

Fig. 3.
Relative Transmission of Color Filters.

B \Bof '

in which T is the test spot threshold for any field brightness B, Bo the
absolute field threshold and » a constant. From this, when B = Bo
the threshold T is equal to the field itself, although as seen from the
curve the test spot threshold is greater than 5©. The reason for this is
that the area of the test spot was smaller than the field and the peripheral
regions of the retina are more sensitive than the foveal. The angular
size of the fovea is between 2 and 3 degrees and the test spot subtended
an angle of approximately 5 degrees. If the straight line is extended it
will pass through the point where T is equal to the observed 5o.

The lower part of the curve begins to bend at about 100 ml. and in a
region between this point and about 2,000 ml., that is, corresponding
to bright interiors and outdoor daylight, the curve has a slope equal to
unity, which means a constant, and minimum, ratio of T* to 5 over this
region. This is analogous to the well-known Fechner constant in con-
trast sensibility, in that case the least perceptible difference being a
nearly constant fraction of the intensity over a much wider range of
moderate and high intensities. (At the threshold this fraction is equal
to unity and the minimum value is about 0.0175, which is Fechner's
constant.) Beyond this region the ratio rises again and at blinding

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No'a?'*] BRIGHTNESS SENSIBIUTY OP RETINA. 8/

intensities it would approach unity, that is the instantaneous threshold
would be equal to the sensitizing field itself, just as at the other end of
the curve.
The equation may be written, taking logs,

log r = (I - ») log 3 + » log 5o,

so that » can be easily determined from the slope of the line. The
value of n for white light is here equal to 0.33. The other constants are
5o = 0.00000071 ml. (minimum field threshold), T© = 0.0000014 ml.
(minimum test spot threshold), minimum T/B = 0.0017 (about one
tenth the Fechner constant).

This curve shows at a glance the very wide range over which the
eye can operate and the enormous change in its sensibility. The present
experiments cover a range roughly from lO"* to lo* millilamberts, one
billion times, and over this range the sensibility as measured by the
instantaneous threshold changes more than a million times.

The curves for the different colors are very similar to that for white,
the instantaneous thresholds being nearly equal for moderate bright-
nesses and diverging most for the lowest brightnesses. This is appar-
entiy another manifestation of the Purkinje effect, the threshold being
least for red and greatest for blue as measured by fractions of the same
high intensity. All the color curves except red show a decided dip,
indicating a depression of sensibility, in a region roughly between o.oi
and I ml., a region corresponding to about the average range of interior
brightnesses at night.

For convenience of reference the four principal brightness levels that
are encountered are indicated by the crosses in Figs. 5 and 6. These are
exteriors at night, o.ooi ml., interiors at night, o.i ml., interiors in
daylight, 10 ml., and exteriors in daylight, 1,000 ml. These are of
course merely rough averages, each lower level being one per cent, of
the next higher.

Contrast Sensibility.

The least difference in brightness between two fields that the eye can
perceive depends not only upon the brightness of the fields but also
upon such factors as their areas and configuration, the previous adapta-
tion of the eye and the time of adaptation to the fields contrasted. With
the visual sensitometer contrast sensibility is easily measured with these
factors under control. In the experiments as carried out the two fields
were obtained by covering the upper half of the test square previously
described with a strip of neutral gray gelatine of a certain density, thus
affording a fixed contrast between this and the lower half depending
upon the transmission of the film. The method of procedure is to adapt

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JUUAN BLANCHARD.

fSacoNo
LSxRin.

the eye to a certain sensitizing field brightness, flash off the field and
then by moving the wedge adjust the test spot brightness until the
difference between the two halves is just perceptible after any time
desired. In this way time-contrast curves for white light were obtained
for several different contrasts, the results appearing in Table III. and

Table III.

Time and BrigfUness to Detect Fixed Contrasts.

Eye initially adapted to o.i ml.
Values are log brightness of brighter field, in millilamberts.

Contrast.

JO,

•39.

J67.

.87.

0 seconds

-2.80

-2.63

-2.40

-2.10

-1.20

1 "

-3.47

-3.36

-3.00

-2.46

-1.57

2 "

-3.82

-3.58

-3.13

-2.49

-1.67

5 "

-4.30

-3.74

-3.22

-2.48

-1.69

10 "

-4.49

-3.85

-3.21

-2.55

-1.59

20 "

-4.60

-3.97

-3.33

-2.54

-1.63

40 "

-4.89

-4.06

-3.46

-2.67

-1.73

60 "

-5.03

-4.23

-3.48

-2.73

-1.78

Fig. 4. The maximum contrast was secured by using an opaque strip,
in which case the actual threshold was determined, and the minimum

by means of a thin film of
clear celluloid having a trans-
mission of approximately
0.97. The size of the fields
was 3 cm. X 1.5 cm. viewed
at a distance of 35 cm. (5
degrees X 2.5 degrees), and
the brightness of sensitizing
field was o.i ml. One eye
only was used, with natural
pupil. The curves are plotted
with the brighter of the two
contrasted fields as ordinates
and show at what brightness
a given contrast can just be perceived at any time up to one minute
after extinguishing the sensitizing field. It is seen that when the con-
trast is very small the minimum brightness for it to be perceived does
not change much with the time after the first few seconds, but with
large contrasts the time factor is very important.

It is easy to obtain from these results the " Fechner fraction," which
is the ratio of the least perceptible difference to the brightness at which

-J

V7-/2

4sr

"■ —

.S3

' — '

■ '

Jb7

.67

^ ,

.97

30
SECONDS

Fig 4.

Time and Brightness to Detect Fixed Contrasts.

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Vol. XI.l
No. a. J

BRIGHTNESS SENSIBILITY OF RETINA,

to n

0 Si tOAfOS

\ \

\
\

■^v, \

INT mwT

MT o^r

eXT^DJlY

-J -£ -/
LOG F/ELD

Fig. S.
Fechner's Fraction.

It IS measured. According to Fechner's law this is a constant over a
wide range of moderate and high intensities, but it increases for both
extremes. The difference has been generally expressed as a fraction
of the lower intensity but it seems more logical to include the increment
in the denominator of the
fraction, since otherwise the
ratio at the absolute threshold
is meaningless. Theoretically
at the threshold the least per-
ceptible difference is the
threshold itself, thus making
the ratio here equal to unity.
This ratio can be obtained
from the above results by
merely taking a cross-section
of the curves at any given
time. The Fechner fraction,
AB/Bf is equal to one minus the contrast ratio and this is plotted
against the corresponding value of log 5, where B is the higher bright-
ness. A series of such curves is given in Fig. 5 for times of o, 2, 10
and 60 seconds after extinguishing the sensitizing field, which shows very
clearly the effect of time of adaptation and brightness on sensibility to
contrast.

The Work of Konig and Brodhun.

K5nig*s work (in collaboration with Brodhun) has already been
referred to. He determined the least perceptible difference over a very
wide range of intensities for white light and for several different wave-
lengths. His results, however, are deprived of some practical value on
account of the uncertainty of his unit of brightness. This he states was
the brightness of a magnesium oxide surface illuminated normally by
0.1 sq. cm. of freezing platinum at a distance of one meter and parallel
to it. Since this light source is o.i the Violle standard, approximately
23 candle power, and since the reflecting power of magnesium oxide is
85 per cent.,^ this gives as his unit a brightness of 0.20 millilambert.
This value, however, is obviously much too high.

For comparison with the results on contrast given above and for
obtaining another estimate of Konig's unit, a partial repetition of his
sensibility curve for white light was made on a photometer bench. Two
color-matched lamps of about the same candle power were mounted on
the bench and by moving the photometer head back and forth the least
perceptible difference in brightness between the two halves of the field

» Nutting. Jones and Elliott, Trans. 111. Eng. Soc., Vol. 9, p. 593-

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JULIAN BLANCHARD.

[Sbcomd

was determined. The low intensities were secured by screening with
neutral filters of known density. This is not the same form of apparatus
as used by Kdnig, although the principle is the same. In his arrange-
ment the contrasted fields were secured by the use of polarized light
and crossed nicols. In computing the Fechner fraction K5nig used the
ratio of the least difference to the lower intensity and his results have
therefore been recalculated using the higher intensity instead, for the
reason stated above. His data are given in Table IV., along with the

Table IV.

Least Perceptible Difference for Different Field Brightnesses,
All values are in mUlilamberts.

Prom Kbniff's DaU.

Photometer Bench Method.

Loff^.

LBIB.

LoffA^.

Loffi9.

LBIB.

LofAi?.

3.60

0.0346

2.14

-0.01

0.021

-1.69

3.30

.0266

1.72

-0.41

.025

-2.01

2.90

.0260

1.31

-1.11

.032

-2.60

2.60

.0191

0.88

-1.41

.042

-2.79

2.30

.0170

0 53

-1.71

.060

-2,93

1.90

.0172

0.14

-2.41

.131

-3.29

1.60

.0173

-0.16

-3.05

.246

-3.66

1.30

.0176

-0.45

-3.41

.254

-4.01

0.90

.0178

-0.85

-3.71

.302

-4.23

0.60

.0175

-1.16

-4.02

.372

-4.45

0.30

.0188

-1.43

-4.41

.521

-4.69

-0.10

.0217

-1.76

-0.40

.0290

-1.99

-0.70

.0314

-2.20

-1.10

.0380

-2.52

- 1.40

.0455

-2.74

-1.70

.0560

-2.95

-2.10

.0860

-3.17

-2.40

.110

-3.36

-2.70

.159

-3.50

-3.10

.220

-3.76

-3.40

.274

-3.96

-3.70

.326

-4.19

-4.10

.410

-4.49

- 5.54

(1.00)

(-5.54)

results of the writer, in millilamberts. The latter are plotted in Fig. 5
as circles, whereas the full line curve is that of K6nig after his values of B
have been multiplied by a factor which will bring his curve into as close
coincidence as possible with that of the writer. This factor is 0.0040,
so that if the contrast sensibility of each observer is approximately the
same Kdnig's unit of brightness is about 0.0040 millilambert.

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Vol. XL!
Naa. J

BRIGHTNESS SENSIBILITY OF RETINA.

Kdnig's results were obtained with the eye screened from all light
during the test except that of the fields compared, no mention being
made of the previous adaptation or the time involved. His contrasted
fields were two rectangles, each with apparent sides of 3 degrees and 4J
degrees at the eye, viewed through the natural pupil (presumably, not
stated). In the present experiments the fields had apparent sides of 2.5
degrees and 5 degrees, viewed through the natural pupil with the eye
continuously screened from all other light, and in the sensitometer the
fields were also this size and viewed through the natural pupil. If all
conditions are the same the results should be identical with the different
forms of apparatus. In Fig. 5 it appears that the sensitometer curves
are nearly coincident with the Kdnig and photometer bench curves for
all adaptation times at the highest intensities used and approach the
latter for all intensities as the adaptation time increases. The adapta-
tion time for K6nig's low intensities was probably an hour or more.

As stated in the beginning the
reciprocal of the least perceptible
brightness difference may be
taken as a measure of retinal
sensibility (contrast sensibility)
and the logarithm of this quan-
tity is plotted in Fig. 6 against
the logarithm of the field bright-
ness (the brighter of the two
fields) . The circles represent the
data of Konig and the crosses
the check results of the writer
taken on the photometer bench
(Table IV.). It is significant
that this gives a nearly linear relation of the same general character
and range as the threshold method.

Glare Sensibility.

In addition to threshold and contrast sensibility there is a third sort
which is not as precisely defined or measured. This is glare sensibility,
which is of considerable importance in illuminating engineering. When
the eye is adapted to a certain brightness and is then suddenly exposed
to a much greater brightness the latter may be called " glaring *' if it is
uncomfortable and instinctively avoided by the eye. This judgment will
naturally depend largely upon the criterion adopted by the observer and
different observers may be expected to disagree rather widely. Measure-

•t

^u.

<*3

^
S

■^

"--,

**^

—r

r-^

mtr

\ — r

imn

9 i

trv-

• — '

Loe ncLD

Fig. 6.

Threshold, Contrast and Glare Sensibility.

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JULIAN BLANCHARD.

[Sscotm
Sssiis.

ments were made in the following manner with the use of the visual
sensitometer. A small mirror was fastened over the test spot so as to
reflect into the eye at E (Fig. i) an image of the opal glass window in
the field lighting box F, this constituting the glare source. The angle
subtended at the eye by the glare spot was approximately 4.0 degrees.
The sensitizing board B was illuminated by means of other lights placed
to the rear of the observer. With the eye adapted to a given field
brightness the glare lamp F was snapped on and by trial the smallest
brightness that was considered glaring was determined. With this
apparatus measurements were made with fields from the threshold up
to 200 ml. and the highest fields and glare intensities were obtained by
using sunlight on white paper and through diffusing window glass with
the aid of suitable mirror arrangements. The results of three observers,
including the writer, are given in Table V. and the average of all three

Table V.

Log Field.

Log Glare.

P. R.

P. 0. N.

J.B.

Mean.

-6.0

1.45

0.78

1.81

1.35

-2.0

2.64

2.65

2.50

2.60

-1.0

2.74

2.78

3.18

2.90

0.0

3.30

1.0

3.70

3.76

3.62

3.72

2.30

3.87

3.85

4.00

3.91

2.76

4.09

4.11

4.06

4.09

3.91

4.18

4.16

5.02

4.45

plotted in Fig. 6, using the logarithms of the variables. It is seen that
the curve is a straight line, the upper limit of which will naturally be
where the field is equal to the glare itself. The relation may be repre-
sented by the equation

log C; = a log B + log c,
or

G = cB^,

where G represents the glare brightness, B the field brightness, and
a and c are constants. For the conditions here used a = 0.32, c = 1,700,
so that for a given field brightness the brightness of a small area, such
as a lamp globe or reflector, which will be considered glaring in the sense
here defined may be roughly calculated by taking the cube root of the
field brightness and multiplying by 1,700. It is to be expected that
with a larger area a smaller brightness would be considered glaring,
although no measurements were attempted with different areas.

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Vol. XI.l
Na2. J

BRIGHTNESS SENSIBILITY OF RETINA.

The curves for the three different kinds of sensibilities are given for
comparison in Fig. 6, the negative logarithms of the threshold, least
difference and glare being plotted as ordinates since they are proportional
to the logarithm of the respective sensibilities. It is observed that
although the threshold and contrast methods give very similar results
the range of sensibility by the glare method is very much smaller, being
only about one thousand times. The latter is essentially different in
nature from the other two, being based on a maximal reaction, whereas
the former are both based on minimal reactions.

Rate of Adaptation.

The rate at which the eye increases in sensibility on going from light
to darkness (dark adaptation) has been studied by Nagel and others.*
In his experiments the observer entered a dark room from a daylight
exterior and noted the time required to just see a given brightness. With
the apparatus here employed it is possible to make measurements from
the very instant of turning out the field light and it is easier to work
under definite conditions. In these experiments the eye was adapted
to a given sensitizing field and by adjusting the wedge the threshold was
determined at the instant of turning off the field and at intervals of a

Table VI .

Rate of Dark Adaptation,
Values are — log threshold, in millilamberts.

Sensitixinff Field,

White

Blue.

Green.

Yellow.

Red.

Ml.

O.X.

X.O.

xo.

xoo.

o.x.

0 sees

2.79
3.82

2.20
2.99

1.60
2.30

0.90
1.66

2.82
3.92

2.69
4.08

2.61
3.84

2.32

1 "

2.69

2 "

4.13
4.50
4.75
4.96
5.16
5.32
5.52
5.68

3.27
3.79
4.15
4.51
4.82
5.06
5.22
5.52

2.53
3.08
3.54
3.94
4.31
4.61
4.83
5.22

2.00
2.46
2.64
2.88
3.20
3.84
4.12
4.76

4.36
4.91
5.27
5.53
5.68
5.81
6.00
6.23

4.39
4.82
5.11
5.26
5.43
5.56
5.70
5.80

4.17
4.41
4.65
4.78
5.02
5.09
5.24
5.39

2.98

5 "

3.37

10 *'

3.57

20 "

3.65

40 "

3.73

60 "

3.80

2 mins

3.92

5 "

4.02

10 "

5.70

5.68

5.59

5.38

:o "

5.80

5.81

5.76

5.60

30 "

5.91

5.86

5.83

5.77

40 "

6.01

5.97

5.91

5.82

50 "

5.98

6.02

5.94

5.90

60 "

6.06

6.04

6.01

5.97

' Op. cit.

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JULIAN BLANCHARD.

rSBCOND

LSbkxbs.

few seconds or minutes thereafter. Results for white light with sensitiz-
ing fields of o.i, I, 10, and lOO ml., up to one hour's dark adaptation,
are given in Table VI. and the curves in Fig. 7. Observations were made

n£LO

f ^

10 -
to •

;

" /0 £0 JC ^C SO
S£C0MD3

,^.n

riiLD^

f^L

:^=^'^
y

^
^

too

,r^

/ y

U^^

—

0 fO M so 40 JO
SSCOMOS

Fig. 7.
Rate of Dark Adaptation. White Light.

-ZO JO 40

HtNUTES

Fig. 8.
Rate of Dark Adaptation. White Light.

in this case with both eyes, natural pupil, test spot 3 cm. square at 35 cm.

(visual angle 4.9 degrees). The results are the average of a number of

trials made on different days.

In Fig. 7 are plotted the logarithms of the threshold values and these

curves show therefore the geometrical increase in the sensibility. The

way in which the actual change occurs may be seen better in Fig. 8,

where the reciprocal of the threshold, which is proportional to the sensi-
bility, is plotted against the
time, these values being taken
from the smooth curves in Fig.
7. During the first minute of
darkness the sensibility is rather
small compared with the total
rise and this period is shown on
a larger scale in the inserted set
of curves. It is seen that when
the pre-adaptation field bright-
ness is small the initial rise in
sensibility is quite rapid, but

with increasing field brightnesses the rise is more and more delayed.

The sensibility is still increasing at the end of an hour and continues

to rise slightly for several hours. The curves for all brightnesses of

course eventually merge into one another.

BLU£

me€M

Y£LLMtf

*-*

[

fUNUTCZ

Fig. 9.
Rate of Dark Adaptation, DifTerent Colors.

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No%^'*] BRIGHTNESS SENSIBILITY OP RETINA. 95

Similar adaptation curves for a period of five minutes only were taken
for the colors blue, green, yellow and red, using the filters previously
described. The results are shown in Table VI. and Fig. 9. The sensi-
tizing field was the same color as the test spot and the brightness o.i ml.
In each case. It is observed that the rise in sensibility is greatest and
most rapid for blue and green, which are nearly equal, with red con-
siderably lower and yellow intermediate. The threshold brightnesses
in this series were all calculated from the wedge densities necessary to
cut down an initial test spot brightness of o.i ml., as balanced against
white, at which brightness the Purkinje effect is present to some extent.

Size of Pupil.

The amount of light flux falling upon the retina is directly proportiona
to the area of the pupil, which in turn depends upon the brightness to
which the eye is exposed. When in bright sunlight the pupil contracts
as much as possible to protect the retina from the excessive brightness,
and as the brightness diminishes it gradually enlarges and reaches a
maximum in complete darkness. The average range is approximately
from 2 to 8 millimeters. Several pupillometers have been devised for
measuring the diameter but none of them are applicable for all bright-
nesses, especially for very low intensities. In order to determine the
diameter throughout its entire range the method of flashlight photography
was used. A large white cardboard was fastened in front of the camera
with a hole in the center for the lens. The subject sitting in front of
this was adapted to any brightness desired by means of a flood lamp to
the rear, such as that used at F in Fig. i. An extra long bellows camera
was used so that with the subject close up an enlarged picture of the eye
could be obtained, and a chin rest was used to keep the eye in focus.
After adapting to the given brightness for at least five minutes the
shutter was opened by an assistant and immediately the flash set off and
the shutter quickly closed again. A white paper scale stuck on the face
in the plane of and close to the pupil enabled the diameter to be ac-
curately measured with the help of a pair of dividers. For the highest
brightness used the whole apparatus was moved out of doors. With
moderately bright sunlight on white paper a brightness of 2 lamberts
was obtained, which is beyond the brightness which the eye can steadily
view without discomfort.

When measuring the diameter of the pupil for any brightness it is
necessary to take into account whether one or both eyes are open. If
for instance the right pupil is being measured this will expand immediately
upon closing the left eye and contract when it is opened again. When

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JULIAN BLANCHAKD,

rSscoND
LSbribs.

the left eye is closed it becomes dark adapted with a consequent expan-
sion of the pupil and the right pupil sympathetically changes in the
same direction and thus admits more light. This well-known effect can
easily be observed by watching one's eye in a mirror as the other is
suddenly opened and closed, the effect being most marked at moderate
intensities. A series of measurements under both these conditions is

Table VII.

DianuUr of Pupil.

Field Brightnest, Ml.

Diam.,

Mm.

Both Byes Open.

One Bye Closed.

0.0

7.4

7.5

0.00015

7.15

7.25

0.01

6.7

7.2

0.6

5.3

6.5

6.3

4.1

5.7

126.

2.6

Z.Z

355.

2.3

2.9

2,000.

2.0

given in Table VII. and the curves shown in Fig. lo. The two curves
are practically coincident at both extremes and diverge most for bright-
nesses between i and lo ml., the diflFerence in this region being nearly
1.5 mm.
It is to be noted that the pupil thus measured is not the actual pupil

but its image formed by the re-
fracting media in front of it.
The iris lies just in front of the
lens, and since with diflFerent de-
grees of accommodation the re-
fraction is altered on account of
the change of curvature and
displacement of the lens, the size
of the image of the pupil changes
with accommodation. For the
eye accommodated to 25 cm. the
ratio of the diameters of the
image and actual pupil is 1.02,
for the unaccommodated eye it is 1.14.^ In the photographic experi-
ments the white field viewed was about 35 cm. in front of the eye, so

» See Helmholtz, Phys. Optik, 3d Ed., and P. G. Nutting, Outlines of AppUed Optics,
p. 117.

»•

0M£ £

<£CLC

SCO

MdT"

BOTH

£r£S

opifSn

— \

-i

9 -4

' -J

LOG FIELD ML

Fig. 10.

Diameter of Pupil for Different Field Bright-
nesses.

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Na"a?M BRIGHTNESS SENSIBILITY OF RETINA, 97

that the size of the pupil image thus measured may be taken as equal
to that of the pupil itself, this error being less than that of diameter
measurements.

The diameter of the dark adapted pupil varies to some extent with
different individuals. Steavenson^ gives 8.5 mm. as the average of five
subjects measured by him by the flashlight method. The limits of the
writer are approximately 2 and 7.5 mm. The pupil is also constantly
fluctuating over a small range even when the eye is subjected to a fixed
brightness. Arrangements are being made to study these variations as
well as the rate of opening and closing of the pupil when changing from
one brightness level to another by taking a series of pictures with a
motion picture camera.*

Since the range in diameter of the pupil is roughly from 2 to 8 mm.,
the ratio of the areas, and consequently the flux upon the retina, is i to 16.
This means that from the highest endurable brightness to darkness the
threshold sensibility increases about 16 times merely on account of the
enlargement of the pupil. It has been seen that the total rise in sensi-
bility is more than a million times, so that the increase due to pupil
expansion is rather small in comparison with that due to processes going
on in the retina itself.

The Flux Density at the Retina.

It is of interest to know the actual flux density at the retina for any
given brightness viewed and corresponding size of pupil. This may be
approximately calculated as follows.

Consider a small surface of area ao sq. mm. normal to the axis of the
eye at a distance of u mm. and a brightness of / candles per sq. mm.
Treating this surface as a point source of a©/ candlepower, the illumina-
tion at the pupil will be aol/u^ lumens per sq. mm., and the flux through
the pupil, of area S sq. mm., will be aoIS/u^ lumens. Since all of this flux
falls on an area ai on the retina, the image of ao (the small absorption of
the eye is here neglected), the flux density at the retina will be aoIS/aiU^
lumens per sq. mm. But from geometrical optics we have Oo/fli = uht^Jifly
where v is the back focal length of the eye and n is the index of refraction
of the medium between the lens and the retina. Hence we have for the
flux density, £, in lumens per sq. mm.,

E = ISn^lv^.

* Jour. British Astron. Assoc., Vol. 26, p. 303.

* Since this was written measurements of the dark adapted pupil for eight subjects have
been made, the average being about 8 mm., with values ranging from 7 to 8.7 mm. These
results, together with the data on rate of opening and closing, will be published shortly.

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JULIAN BLANCHARD,

rSaooND
LSeabs.

If the brightness of ao is given in millilamberts, B, instead of candles
per sq. mm., then, since by definition i ml. = i/t X io~* candles per sq.
mm., we will have

£ = i/t X io-*J?5«Vt^.
Table VIII. gives a series of values of E for corresponding values of

Table VIII.

tUmiA 111

Diameter, Mm.

Effective Area.

Lamene per 8q. Mm.

Prom Curve.

Effective.

£.

0.00001

7.30

8.17

52.2

7.0 X 10-"

0.001

6.97

7.80

47.8

6.4 X 10-««

0.01

6.65

7.44

43.4

5.8 X 10-»

0.1

6.00

6.72

35.4

4.7 X 10-«

1.0

5.06

5.66

25.1

3.3 X 10-»

10.

3.86

4.32

14.6

1.9 X 10-«

100.

2.72

3.04

7.25

9.7 X 10-«

1,000.

2.08

2.32

4.23

5.6 X 10-«

2.000.

2.00

2.24

3.94

1.1 X 10-*

B and 5, for the case with both eyes open. In the computations n is
taken as 1.34, v is 20.7 mm. (focus for distant vision), and S is the area
of the pupil image, in computing which the pupil diameters are taken
from the smooth curve in Fig. 10 and multiplied by 1.14/1.02, for the
reason previously explained.

For a given brightness of surface the value of E, and hence the apparent
brightness to the eye, will change only slightly with the distance of the
surface from the eye. For in the above expression for the flux density
at the retina, on which the apparent brightness depends, E is directly
proportional to 5/r*, or to the solid angle subtended at the image on the
retina by the pupil image. On changing the accommodation for near
and far objects both 5 and ti* change only slightly and in the same direc-
tion, so that their ratio remains approximately constant. This inde-
pendence of the so-called natural brightness upon the distance of the
object viewed is borne out by experiment.

Summary.

I. Three different kinds of retinal sensibility have been defined and a
new form of apparatus for measuring the sensibility, called the visual
sensitometer, has been described.

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Na"a^^'] BRIGHTNESS SENSIBIUTY OF RETINA. 99

2. Threshold sensibility (the reciprocal of the least brightness per-
ceptible) has been measured over a wide range of field intensities for
white, blue, green, yellow and red light, and a linear relation (with
exceptions over certain regions) found between log sensibility and log
field brightness.

3. Contrast sensibility has been studied with reference to variations
in contrast, brightness and time of adaptation. Kdnig's work on the
least perceptible difference has been repeated over a limited range and
his unit of brightness thereby determined to be approximately 0.0040
millilambert. Recalculating his results, the reciprocal of the least per-
ceptible difference, another measure of retinal sensibility, has been
plotted as a function of the field brightness. The curve closely resembles
that for threshold sensibility.

4. The least brightness that appears glaring has been determined for
all field brightnesses and a linear relation found between log glare and
log field.

5. The rate of dark adaptation, with different initial sensitizing
brightnesses, has been measured from the beginning of adaptation for
white, blue, green, yellow and red light, with the natural pupil.

6. The diameter of the pupil has been measured by means of flash-
light photography for different field brightnesses throughout its range,
both for monocular and binocular vision, the limits for the writer being
approximately 2 mm. and 7.5 mm.

7. From the results of the above measurements the flux density at
the retina for a given field brightness and corresponding size of pupil
has been calculated for the entire range of vision.

The author wishes to express his thanks and appreciation to Dr. P. G.
Nutting, who suggested and largely directed this work, and to Mr.
Prentice Reeves, of this laboratory, for their valuable assistance and
criticism.

Research Laboratory. Eastman Kodak Co.,
Rochester, N. Y..
April, 191 7.

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ICX) JOHN Q. STEWART, [i5S?S

THE MOMENT OF MOMENTUM ACCOMPANYING
MAGNETIC MOMENT IN IRON AND NICKEL.

By John Q. Stewart.

THE importance of ascertaining whether or not mass is associated
with the electric current was recognized by Maxwell, who outlined
the principles of three different experimental methods of attacking the
problem. Phenomena with which Maxwell was unfamiliar have offered
more suitable means of measuring the mass of electricity, and, on account
of experimental difficulties, not until quite recently have his methods
been successfully applied.

In Electricity and Magnetism, § 577, Maxwell suggests that accelera-
tion of a conductor may generate a current; such currents have been
found by R. C. Tolman and T. D. Stewart.^

The converse experiment is described in § 574 — ^varying the current
might set the conductor in motion. This effect will be discussed later
in this article; it probably is too minute to be detected.

The general idea of § 575, namely, that a magnet (or a paramagnetic
molecule) acts like a gyroscope, forms the basis of the work of S. J.
Barnett, who showed that a rotating cylinder of iron becomes mag-
netized ;* and of A. Einstein and W. J. de Haas, who showed that mechani-
cal moment of momentum accompanies magnetic moment.*

This was first specifically pointed out by O. W. Richardson, who
calculated the relation between the two moments according to the
electron theory.* If magnetism is due to the motion of charged particles
in circular orbits within the atom, a magnetized body must possess in-
ternal moment of momentum, the amount of which about any axis is
proportional to the component of the magnetic moment along that axis.
Working in this laboratory, Richardson made an attempt to verify
experimentally his equation,

U'^2^M''—^^. (I)

e A

» Tolman and Stewart, Phys. Rbv., VIII.. p. 97, 1916.
« Barnett, Phys. Rbv.. VI.. p. 239. 1915.

* Einstein and de Haas. Deut. Phys. Gesell.. 17. p. 152, 1915.

* Richardson. Phys. Rev., XXVI.. p. 248, 1908.

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Na*a^^*l MOMENT OF MOMENTUM. lOl

M' is the magnetic moment, and U' is the corresponding moment of
momentum; the multiplying factor (which hereafter we shall call K)
is a constant determined by the nature of the rotating sub-atomic cor-
puscles. These may be positive or negative; for the former M, E,
and A, for the latter w, e, and a, respectively, denote the mass, charge in
electromagnetic units, and average areal velocity, resolved in the plane
perpendicular to the direction of the magnetic intensity. If, as is
generally assumed, only the negative electrons are rotating, then

X = 2- = 113 X I0-^ (2)

Barnett's derivation of equation 2 follows: Suppose only negatively
charged corpuscles are rotating, one in each orbit; then, if r represents
the radius vector, <a the angular velocity, m the magnetic moment, and u
the angular momentum of each system, we have

M = ea, a = ir*«, and ^ u = tnr^w = 2wa.

Thus

u^ m
- = 2 — .

Since for any given electron orbit the vectors u and m are In the same
direction, summation through any volume gives

l^ _ 2tt _ tt _ m

Richardson thought that the operation of the principle of the con-
servation of angular momentum would give a means of experimentally
detecting the existence of this internal momentum, and of measuring K.
If the intensity of magnetization along any axis in a body be changed it
follows from (i) that the internal moment of momentum about that axis
will correspondingly vary, and from Newton's third law it seems probable
that the whole body will tend to rotate in the perpendicular plane. The
tendency to rotate will be greater as the moment of inertia of the body
about the axis of magnetization is less; this suggests the use of a piece
of soft iron wire suspended vertically by a fine quartz fiber within a
vertical solenoid. Any rotation may be indicated by the movement of a
beam of light reflected from a mirror attached to the wire. When the
current through the solenoid is suddenly varied we may expect a tem-
porary vibration of the suspended system.

From time to time, since 1908, unsuccessful efforts to observe this effect
with such an apparatus have been made in this laboratory. The most

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I02 JOHN Q. STEWART, - [^glS

recent attempt was begun in the spring of iQisbyMr. Maurice Pate and
the writer, under the direction of Prof. H. L. Cooke, and has been carried
on by the writer alone. The difficulty was in eliminating the com-
paratively large disturbances due to the direct action of the field upon
the magnetized wire. It was not until after this work was begun that
we learned that Einstein and de Haas had succeeded in observing the
effect predicted by Richardson, and had determined the value of K to
be that which would be due to negative electrons. Bamett, on the other
hand, had found a value only half so large. Since the method of Einstein
and de Haas was somewhat diiFerent from ours (they got rid of disturbing
influences by using for the suspension a comparatively tough glass fiber
and building up the effect by resonance, with an alternating current),
and since, moreover, the numerical data they published seemed in-
adequate, we thought it worth while to continue the experiment, using
our more direct method.

Our results show that Bamett was right in 1915 in estimating the value
of jST to be only one half that given by (2). A detailed discussion of our
work follows.

Description of the Apparatus.

The apparatus included the solenoid, the optical system, various
compensating coils, and the wires to be tested.

Fig! I is a drawing of the solenoid, with the horizontal scale twice the
vertical. The solenoid was built up of three sizes of
brass tubing. The two smallest tubes carrying the
parallel mirrors, M, M, fitted into one of intermediate
diameter, which formed the framework; and over it
fitted the larger tube on which was wound the solen-
oid proper. This consisted of 2126 turns of number
24 double-silk-insulated copper wire, wound in six
layers, which varied in diameter from 3.52 to 4.52
cm.; its length was 22.2 cm. The winding was done
very carefully: a thin strip of celluloid was wrapped
around each layer on its completion, after the wire
had been shellacked, in order that the layer next out-
side might be wound smoothly. The calculated field
at the center due to a current of i amperes was 126 i
gausses ; the calculated self -inductance was 1 3 henrys ;
and the calculated resistance was about 25 ohms,
agreeing well with the observed value. The tempera-
ture rise per minute in the copper wire, neglecting all
Fig. 1. heat losses, was, in Centigrade d^^rees, lOt*.

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Vol. XL!
Naa. J

MOMENT OF MOMENTUM,

103

Sfe

B T^L u^t^

Fig. 2.

To admit of adjustment to the vertical, the solenoid was mounted
as is shown in Fig. 2. The lower end rested on a brass strip which could
be moved back and forth over the wooden block
J?, which in turn could be rotated into any desired
direction. The upper end fitted into a hole in a
brass disc fastened into the brass pipe D; the hole
was half an inch off center. By this arrangement
the horizontal component of the solenoid field could
be brought into the direction of the block J5, and
then reduced to zero. A screw adjustment was
used at the bottom, and one would have been very
convenient at the top. In order to keep the whole
solenoid from rotating, a projecting rod was held
between the prongs of the fork F.

The solenoid was mounted in a solidly built box secured to a table with
brass screws. One side of the box was left open, and faced north toward
another table on which were placed the lamp and scale. Although these
two tables were put together with iron bolts this iron was not very near
the solenoid, and it caused no trouble.

The optical system was arranged as follows. A Nemst glower was
the source of the light, which was reflected by the flat mirrors, JIf , M
(Fig. i), up to the middle of the solenoid, to the small mirror, m, on the
end of the iron wire, and out again to the scale. As the scale distance
never was more than sixty centimeters (allowing, of course, for the
distance the light travelled down the solenoid), it was unnecessary to
make the mirror m concave. A number of small flat mirrors, in size
about 0.8 mm. by 3 mm., were cut out of thin microscope cover glass,
silvered on one face. The band of light reflected on the scale from one
of these mirrors was about 2 mm. broad, and sharply enough defined
along its vertical edges. Its horizontal edges were not well defined;
and in finding the magnetic moment of the wire, when it was necessary
to measure vertical displacements of the spot of light, a convex lens had
to be placed in front of the Nernst lamp.

The brass tubes to which the mirrors M, M were attached by soft
wax were cut off at exactly 45 degrees ; the plane of either mirror could
be changed slightly by using extra wax. (Some sort of screw adjustment
would have been advantageous.) When things were properly fixed the
spot of light had a range of six or seven centimeters on the scale.

Six compensating coils were required to eliminate the earth's magnetic
field. A cubical framework was constructed and wound with wire,
and fastened to the table with the solenoid at the center. The two

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I04 JOHN Q. STEWART. [iS!S

horizontal coils, each of 78 turns, were designed to neutralize the verti-
cal component; they were connected in series to act together. Two
other coils of 30 turns each were made to oppose the S. N. component,
and two coils of 6 turns each took care of any stray E. W. field. All the
coils were approximately square, 60 cm. on a side, and opposite members
of a pair were almost that distance apart. The axes of all six met in a
point at the center of the cube, where the iron wire was hung. A current
of about 0.25 ampere in the proper direction through the vertical and
S. N. coils neutralized the earth's field at the center. (78/30 is 2.60,
which was the tangent of the angle of dip; in practice, however, each
pair of coils was in a separate circuit.)

The field at a point on the axis of a square coil of sides 2a at distance y
from its plane is

~ (a* + 3^)v/2a2+3^' ^

for current i and number of turns «. Since d^H/dy^ = owheny = 0.545a,
a more uniform field at points not very close to the center of the cube
would have been secured had the coils in each pair been 32.7 cm. apart.

Two exploring coils were needed for a variety of purposes, as will be
explained. The coil C was 90 cm. square, and consisted of 180 turns
of number 23 copper wire. It was fastened in a vertical plane on top
of a heavy box, so that it could be moved about with the center of the
coil at the same height above the floor as the center of the solenoid. A
large cardboard scale of degrees was attached, for determining the direc-
tion of the normal to the coil with reference to a fixed line on the floor.
Since it was of importance to know the number of ampere-turns, the coil
was constructed in two divisions, one of 72, the other of 108 turns; the
field strengths produced by these were compared, in order to make sure
that there were no short circuits. Another exploring coil c was made,
similar to C in size and mounting, but of only 10 turns.

The electrical connections were as follows: All the rheostats used
were solenoidal, with sliding contacts. The rheostats were kept ten or
twelve feet away from the solenoid, except the two employed in eliminat-
ing the horizontal component of the earth's field; these were placed
within six feet. E^ch of the earth's field compensating coils was in a
separate circuit. All lead wires were closely twisted in pairs. The
solenoid was connected in series with a commutator, and could be thrown
either into circuit i or circuit 2. The E.M.F. in circuit I could be varied
by a shunt from o to 120 volts, and could be either direct or alternating
(60 cycles). The E.M.F. in circuit 2 was about 20 volts, and the current
was r^ulated by rheostats. This circuit could be closed through a

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Na*a^'*l MOMENT OF MOMENTUM, i05

switch, or, momentarily, through a mercury contact: a drop of mercury
falling through a glass tube made, in passing, instantaneous electrical
contact with the amalgamated ends of two copper wires. One or other of
the coils C and c could be thrown in circuit with a commutator, rheostats,
and a source of direct E.M.F. that could be varied from o to 120 volts.

This completes the discussion of the auxiliary parts of the apparatus,
but the essential feature, the iron wire itself, remains to be described.
The specimen of wire that was being tested was suspended near the
center of the solenoid by a quartz fiber from the brass rod i?, Fig. i,
which slid in the removable brass stopper S. A number of these brass
pieces were constructed in order that several wires could be mounted at
one time.

All the wires were pointed at each end, and rolled out straight, in
order that the direction of the magnetic moment might lie along the
central axis of the wire, and that the mirror, and especially the quartz
fiber, might be attached exactly at that central axis. In spite of these
precautions there always was a small component of the magnetic moment
transverse to the axis of rotation; and this was the cause of the dis-
turbing effects. The quartz fibers were attached to the top, the mirrors
to the bottom ends of the wires; the fibers by shellac, burnt hard when
an electrically heated, non-magnetic wire was brought near, the mirrors
by minute pieces of soft wax. It was found very convenient in mounting
the fiber and mirror to have the wire held vertically between the plane
parallel ends of two brass rods which slid toward each other through
opposite holes in a brass ring; this ring was fastened to a stand im-
mediately below another brass piece that held the stopper S and rod R.
The fiber until attached could be handled by a U-shaped piece of wire.

Before mounting the mirror the torsion constant of the fiber was
determined; a small brass disc of known moment of inertia was attached
centrally to the lower end of the wire, and the period of vibration was
observed with the system free from magnetic control. At different times,
and to check each other, two such discs were used. Each was about an
eighth inch in diameter, and the calculated moments of inertia were 3.61
and 3.53 by lo"^.

The choice of the size of the wire and fiber is of importance, but it
can only be made after a consideration of equation 4, which will now
be derived.

Size of the Effect.

This is given by equation 4. The equation of motion of the suspended
iron wire is

fPd de

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I06 JOHN Q. STEWART, [iSSS

where c is the torsion constant of the quartz fiber, k the damping coef-
ficient, / the moment of inertia of the suspended system, and 0 the
angle through which it is rotated at time L In practice, k^ < ^cl and
writing w* = ^cl — k^, the solution is

e = — € ^ sin-zt,
m 2/

for the special case in which alone we are interested, viz., when the rota-
tion is due to an impulse U units of angular momentum which acted
when / and 6 were zero.

The period of this damped vibration *s

T = —=^

The amplitude of the first swing is

where X is the logarithmic decrement, usually small. The exponential
term can be expanded in a series, and finally we have for 6, the linear
deflection at scale distance L corresponding to $\

^ 2LKM ^ X . xn / X

5 = ~^Y ^^ " ^'^ "^ 0.227X«), (4)

neglecting (X/t)* and higher powers. KM is substituted for U; M is
the change in magnetic moment giving rise, by (i), to the impulse Z7.
Two other equations we shall need are

c =

%'(^

^S)' w

and

/=^(.-^).

To return to the choice of the size of the wire and mirror — it is governed
by four considerations.

First. The effect sought for must be large enough for easy observation.

Second. The magnitude of disturbing effects must be small.

Third. The wire must not be so tiny as to require excessive care in
manipulation.

Fourth. The wire must not be longer than 8 or 9 cm., or the solenoid
field may be non-uniform near the ends ; but it should not be very short,

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}}S"a^'] MOMENT OF MOMENTUM. IO7

or the demagnetizing factor, as well as the probable value of the trans-
verse moment, will be high.

In (4) the factor M/^cI depends uppn the size of the suspended sys-
tem, and should be as large as practicable. For unit intensity of mag-
netization this factor becomes V/^cI, where V isjthe volume of the
wire. If / is the length and a the diameter, V/'^cI is proportional to
la^/^cla^'d^ or to ^l/c, provided the mirror is quite small. The maxi-
mum weight the fiber can sustain varies directly as the square, and its
torsion constant as the fourth power of its diameter. Calling the latter
f, and supposing the fiber loaded to its maximum, or to its maximum
divided by a factor_of safety, c varies as r*, and fa* varies as r*, or as ^c;
which gives V/^cI proportional to i/a*v//. It is, therefore, of great
advantage to use wires of small diameter.

It is disadvantageous to use the_ smallest possible fibers. In (4) the
factor (i — 0.500X + o.227X*)/v^c depends upon the size of the fiber,
and increases as c decreases; on the other hand, the disturbing direct
action of the field, which is not necessarily impulsive, is much less in-
fluenced by the increase in damping, and rises rapidly in importance as c
is lessened.

Of course, considerably larger values of 6 can be obtained if the wire
is suspended in a vacuum, but this was deemed unnecessary.

Disturbing Effects and Their Elimination.

The rotation which Richardson predicted does not depend upon the
magnetic field produced by the solenoid, but upon the change in orienta-
tion of the magnetic molecules which that field causes. The solenoid
field, however, as well as the earth's field, acts directly upon the mag-
netized wire, and the rotation produced by this direct action usually
is of a much higher order of magnitude. Such rotation could not be
produced if there were no transverse component of the magnetic moment
(by symmetry), but that transverse component is never absent. It is
possible to find by mathematical treatment the exact value of the rota-
tion 0 when the wire is magnetized uniformly at a known angle with its
axis of rotation, and is hanging in a uniform field of given strength and
direction. The uniform field can exert only a couple on the uniform
magnet, and equilibrium is attained when this couple (magnetic) is
balanced by the two other couples acting: one due to the twisted quartz
fiber (torsional), and the other to the opposite pulls of the tension of
the fiber and the weight of the wire (gravitational). Since there are no
sidewise forces the fiber remains vertical, and its point of attachment
to the wire remains fixed in position. Perhaps the assumption of uni-

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io8

JOHN Q. STEWART.

fSECOND

LSbrxis.

form magnetization of the wire is not absolutely correct, but it seems
likely that the departures from uniformity are not large enough seriously
to invalidate this analysis.

Einstein and de Haas turned from the ballistic method of detecting
the Richardson effect to the method of resonance because they believed
the elimination of disturbing effects was impossible. It may well have
been impossible in the case they had in mind, viz., when the magnetic
moment of the wire is reversed by reversing a large, continuous current
in the solenoid. Successful elimination of disturbing effects has been
attained only when it was the residual magnetism of the wire that was
varied. It was possible to work with the residual magnetism in this
research, since for the wires used the ratio length to diameter was so
large that the demagnetizing factors were unimportant, and a high
value of M remained after the solenoid field was discontinued if the wire
previously had been magnetized to saturation. To reverse such residual
magnetization required a large, though only instantaneous, current in
the solenoid ; but to reduce it to zero a relatively small field (the coercive
force) sufficed.

When M is thus varied the behavior of m, the small, accidental trans-
verse moment, requires special comment. Suppose the wire is hanging
in the solenoid and the spot of light is reflected on the scale. When the
wire is magnetized with the north end up (hereafter, for convenience,
simply ** magnetized up **) and the fiber is untwisted, suppose that m
is represented by the vector oi, Fig. 3, making an angle j with the mag-
netic meridian. By means of the exploring coil C the position of m at
any time can be determined ; for when C is placed as indicated in Fig. 3,

and only then, will a heavy current
through C cause no deflection. When
the coil c is placed at right angles to C
the magnitude as well as the direction
of the vector m can be determined. If
now the value of M be reduced to zero
and reversed, by a succession of increas-
ing momentary demagnetizing currents
through the solenoid, then the vector m
will be found to rotate successively to
the positions 02, 03, 04, and not until
M has been completely reversed will
m return to its original direction, 05.
When m is at right angles to its original direction (oj, 06), M is zero as
nearly as can be determined — its value then is certainly less than 5 per

Fig. 3.

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JJ^3^^] MOMENT OP MOMENTUM. IO9

cent, of the saturated value. The ratio length 03 to length 01 (much
exaggerated in the diagram) is of the same magnitude as the ratio diam-
eter of the iron wire to its length.

All the wires tested showed this rotation of w, in some cases in the
other direction. The cause of the phenomenon is plain enough; m is
made up of two components, one of which is the horizontal component
of the total moment of the wire, while the other, very much smaller, is
due to an actual transverse magnetization of the wire, and remains un-
changed, except under large fields.

Af, then, is certainly zero when m has rotated through 90 degrees —
that is, when a current through c produces no deflection.

The essential condition that must be satisfied before the Richardson
effect can be observed is this: the suspended system must be free from
magnetic control as regsu-ds changes in the value of B, This result is
attained if there is no horizontal field, for it is the horizontal field alone
that exerts a couple on the unavoidable transverse component of mag-
netic moment. The rotation of this component as M changes makes
necessary, and also possible, an accurate elimination of the horizontal
field. Part of the field is that of the solenoid, and can be reversed or
reduced to zero at will ; the rest of the field is mainly that of the earth.

The currents through the various compensating coils required exactly
to neutralize the earth's field are determined by a method of trial and
error. The vertical component is eliminated most easily: an alternating
current is sent through the solenoid (circuit i), and gradually reduced
to zero; if after this M is not zero the current through the compensating
coil is changed, and the process repeated. This allows of a very delicate
adjustment of the compensating current. The position on the scale
occupied by the reflected band of light when the wire is exactly demag-
netized is taken as the zero position. The period of vibration is deter-
mined; this is the period of the system when free from magnetic control.
A current is passed for an instant through the solenoid sufficient to leave
the wire magnetized quite strongly; now the spot of light, by adjusting
the current in the S. N. and E. W. pairs of compensating coils, is brought
back to its zero position. There the fiber is untwisted, therefore what
horizontal field (say h) is remaining must be in the direction of the
transverse component of magnetic moment. By varying together the
compensating currents in the horizontally acting coils in such a fashion
as to keep the band of light at zero the value of h can be changed. When
the period of the suspended system becomes that which it had when the
wire was demagnetized we can be sure that h is zero.

The elimination of any horizontal component of the solenoid field is

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no JOHN Q. STEWART, [USSni

carried out in the same manner, still working only with the residual
magnetism of the wire. First the block B, Fig. 2, is rotated into the
direction of the transverse magnet, OC, Fig. 3. Then the pipe D is
revolved until a deflection no longer results on the application of a
small solenoid field in the direction of M, Then the wire is demagnetized
by the direct current (circuit 2), so that w is at right angles to its previ-
ous direction, and the brass plate on the block B is moved until there is
no motion of the spot of light on reapplying the demagnetizing field.

The method of taking periods may not completely have got rid of the
horizontal earth's field; in that case the deflection when the wire is
approximately demagnetized will not be zero. It can be made zero by
adjusting the resistances in the compensating circuits; and this is the
final adjustment for the horizontal earth's field.

Even if the earth's field is accurately eliminated, and the solenoid
field accurately vertical, there remains one disturbing effect: on apply-
ing a large solenoid field the wire tends to swing out of its normal posi-
tion, for ordinarily the direction of its magnetic moment is not quite
vertical. Except with a coarse fiber it is impossible to observe the Rich-
ardson effect on reversing the residual magnetism of the wire, for this
requires too large a field, and the wire is greatly agitated. By far the
best method is merely to reduce the residual magnetism to zero; a
relatively small field (the coercive force), applied only for an instant,
suffices for this.

Aside from the magnetic disturbing effects the only other trouble was
caused by shifts in the zero position of the suspended system due to
temperature variations. To guard against this a current was never
allowed to flow in the solenoid for more than a few seconds at a time;
and the zero was redetermined rather frequently. With most of the
wires this effect was absent or negligible, with a few it was annoying,
it was serious with none.

Observations Necessary.

Equation 4 is fundamental, but may be transformed into a more con-
venient working formula. Let Ti be the period of the suspended system
when a known moment of inertia /i, large compared with that of the
wire, has been added. From (5),

for in practice the damping here is negligible. Substituting for c in (6)
gives

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Na*2^^*] MOMENT OF MOMENTUM, III

where T is the period of the wire and mirror. Here X, the logarithmic
decrement, cannot be neglected, since / is small. Substituting in (4)
these values for c and /,

5 = ^ ^* (I - 0.500X + o.278X». . ')ML. (7)

For the two inertia-discs used at different times the values of 7i were,
respectively, 3.61 and 3.53 by io~*. Substituting the value of K given
in (2), and expressing L in meters and h in millimeters, the magnitude of
the constant factor K/irli comes out o.ioo for inertia-disc i, and 0.102
for inertia-disc 2. When / was not negligible in comparison with 7i
correction had to be made.

To calculate, then, what d would be if the value of K were that for
the negative electrons, it is necessary to observe Ti, T, X, L, and M.
M is found from an observation of the angle ^ in the vertical plane be-
tween the normal position of the wire and its position when a horizontal
field H, due to coil C, acts along OC, Fig. 3. If the spot of light reflected
on the scale moves vertically a distance p when H is set up, then

^ = ^cosj,

supposing the direction of the normal to the mirror is that of the mag-
netic meridian. (The angle j is measured from the magnetic meridian —
see Fig. 3.) Equating the magnetic and gravitational couples,

MH^\Wgl4^, (8)

where Wg is the weight of the wire in dynes, and / is its length. Allow-
ance must be made for the weight of the mirror also; in milligrams this
was 0.40 times its area in square millimeters. If cos j is small M cannot
be found, and the mirror must be readjusted.

Manipulation.

The wire to be tested was pointed, weighed, measured, and straight-
ened, the inertia disc was attached by a little soft wax, and the fiber
was mounted. The wire was placed inside the cubical framework of
coils that compensated the earth's field; and the solenoid also was
slipped over the wire, which was then demagnetized by gradually re-
ducing to zero an alternating current through the solenoid. The solenoid
was removed, and Ti observed with the suspended system thus freed
from magnetic control. The inertia disc was removed, the mirror was
attached, and the wire was ready for the test. Usually several suspended
systems were constructed at one time.

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1 I 2 JOHN Q, STEWART, [ImJm.

When the solenoid and compensating coils were back in position, the
wire was lowered into the solenoid until the reflection of its mirror could
be seen. It was demagnetized by the alternating current, and turned
until the spot of light appeared in a central position on the scale. Then
the wire was magnetized with the north end up by a momentary current
of about an ampere (circuit i), and the horizontal component of the
earth's field was eliminated more or less completely. By the exploring
coil C the position of the transverse component m was found, the block B
was brought parallel to it, and the lower mirror was turned to bring the
spot of light back to its original zero. By turning the pipe D the hori-
zontal component of the solenoid field was brought into the direction of m.
The coil c was placed at right angles to the coil C, and the solenoid, with
the commutator reversed, was thrown into circuit 2. By trial the
instantaneous current just sufficient to demagnetize was found. The
criterion for demagnetization was that no deflection be produced by a
current in coil c. Once this demagnetizing current — the coercive force —
had been determined no further adjustment of the rheostats in circuit 2
was made. Before the coercive force could be found the vertical com-
ponent of the earth's field had to be eliminated, but this was practically a
permanent adjustment. The adjustment of the solenoid to the vertical
was next completed, and the final compensation for the horizontal earth's
field was effected.

The solenoid was returned to circuit I, and the wire again strongly
magnetized up. The Richardson effect, a sudden throw to the left,
could be observed on again demagnetizing by circuit 2.

The horizontal earth's field and the current in the compensating coils
would keep varying slightly; and before every observation the deflection
had to be reduced to zero by slight changes in the adjustment of the
rheostats. With most of the wires, however, the band of light remained
nearly steady on the scale, in satisfactory fashion.

After 5 had been determined, T, X, and M were measured. In finding
M several readings were made for two or more values of p, and the
wire was once or twice remagnetized between times. M always was the
same up as down.

The Experimental Results.

Twenty-four wires were tested — seventeen of iron, six of nickel, and
one of silver. The effect sought for was shown by all but the silver wire.
Of its reality there can be no question, for it was shown not only by every
wire but also by every observation, and the observations agree quanti-
tatively as well as qualitatively.

For nearly all the wires the Richardson effect — ^a sudden throw to

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}i^,^^] MOMENT OP MOMENTUM, II3

the left when the wire had been magnetized up, or to the right when the
wire had been magnetized down — ^appeared in company with another
impulsive twist, the direction of which was independent of the sense of
the magnetization. It can hardly be called a disturbing effect, for it
always was of about the same magnitude as the Richardson effect, and
obviously the two could easily be distinguished. It varied irregularly
in direction and magnitude from wire to wire, and also with the same
wire under different conditions; it may have been caused by magneto-
striction.

It was impossible to cause variation in what was believed to be the
Richardson effect, provided things were not thrown far out of adjust-
ment, when observations could not be taken. Every reasonable test
left it unaltered. The same sudden throw was obtained when the
demagnetizing field was applied permanently, as when it was allowed
to act only instantaneously; but it seemed safer to apply it only in-
stantaneously, in order to eliminate all chance of inaccuracy from imper-
fect adjustment of the solenoid to the vertical. Changing the time-
constant of circuit 2 in the ratio 20/1 left 8 unchanged. When one of
the wires was rotated through 180 degrees and the light reflected from
the other side of the mirror, 6 was the same as before.

A very certain disproof of the presence of any effect due to the solenoid
field was this: with a rather coarse fiber it was possible to get the Rich-
ardson effect when the residual magnetism was reversed, instead of being
merely brought to zero; and this admitted of varying the field without
changing the flux through the wire. No change in 5 was found when
the momentary reversing field was increased a hundred per cent, and
more. This proved that the effect reached a maximum when the magnet
was saturated. That it decreased in ratio with M was also shown.
Furthermore one of the wires was so well constructed that it was possible
to get the effect on magnetization', it was of opposite sign to that
obtained on demagnetization, but of exactly the same size.

Table I. shows the results for fifteen of the iron wires and six nickel
wires. (Numerical results were not obtained for the first two iron wires
tried.) In column 11 5 is the observed deflection reduced to scale-
distance 50 cm. ; in no case did the scale-distance differ from this by more
than a few centimeters. The significance of the results is brought out
in column 13, which gives the values of K calculated from the observed
values of 5 by equation 7. For convenience in interpretation these
values of K are expressed as the ratios of the observed K to the value
(1.13 X IO"0 which K would have if only negative electrons were
moving, and if all the reaction were effective in imparting angular momen-

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114

JOHN Q, STEWART.

[Sbcomd
Sbuks.

turn to the wire. The ratio observed K to calculated K is the same as
the ratio observed 5 to 5 calculated by (7).

Table I.

Complete Table of the Experimental Results.

10.

II.

la. 1 13.

£•0

ill

0
I

-<•

•0

•4

Fe:

Ni:

Ag:

0.31.5

0.48
0.20

0.13

0.50
0.31

0.25
0.33

52
52
52
48
35
34
69
75
49

40
39
31
52

61
49
44
52
53
25

28.3

28.6

26.5

24.9

17.9

18.2

84.6

105.9

10.9

12.9

11.8

3.6

3.4

2.7

4.2

100.6
77.6
28.0
33.1
32.6
10.8

32.4

950
870
590
470
700
880
320
340
520
540
620
730
640
460
670

120
100
120
80
160
110

4.7
2.8
3.9
4.3
6.0
6.3
3.8
2.8
5.2
5.0
5.0

8.8
7.4
6.1
6.4

30
30
28
28
28
38

1.3
1.5
1.4
1.3
1.3
1.5
1.1
1.2
1.5
1.7
1.8
2.0
2.2
2.0
2.2

1.1
1.1
2.0
1.8
1.5
1.5

1.5

4.7
5.3
5.1
4.3
2.7
4.2
25.2
36.6
1.7
1.5
1.1
1.2
0.9
1.0
0.9

35.5
27.2
7.5
6.7
6.0
2.4

6.5

21.2
4.1
2.5
4.9
4.8

16.9
4.8

32.7

10.7
5.9
7.8
8.0
6.8
3.7
2.4

14.0
11.2
5.2
5.7
8.5
6.2

2.5

0.22
38
67
43
37
19
46
19
37
46
35
12
28
48
51

18
26
40
41
32
32

6.6
10.5
8.2
5.5
9.0
4.9
5.7
1.8
3.3
7.2
8.4
2.1
4.4
1.9
4.3

1.2
0.8
2.5
2.1
1.0
0.5

3.7

3.4

2.3

1.7

1.8

2.3

4.0

4.6

0.78

0.87

0.93

0.37

0.32

0.18

0.45

1.4

1.0

0.39

0.33

0.6

0.13

Jo eflfec

0.56
.47
.46
.51
.58
.55
.52
.40
.58
.84
.88
.51

1.04
.68
.49

.60
.40
1.30
1.30
.40
.50

In the remainder of this paper K will be expressed as this ratio; abso-
lute values of K will not be employed.

In Table I. the value taken for 8 is in each case an average of six or
eight observations. Naturally it is the least accurately determined of
all the observed quantities. In some instances the figure in the decimal
place was almost guessed at; but the estimate was made before M had
been determined and K calculated, and was never revised after K had
been figured out.

A few examples are given below of the consistency of the individual
observations. ** Up " means the wire had been magnetized up; a
throw of negative sign corresponds to a clockwise rotation, viewed from

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No^a^^*] MOMENT OP MOMENTUM. II5

above, which was the direction of rotation of the negative electrons when
the wire was magnetized up. The Richardson effect was distinguished
from the accompanying irreversible eflfect in this manner: Suppose that
the observed throw when the wire had been magnetized up was 81, and
when the wire had been magnetized down suppose that the observed
throw was 6t. Then 6\ the throw due to the irreversible effect, was
i(^i + ^^)f while the magnitude of 5, the throw due to the Richardson
effect, was i(5i — 6i). The sign of 5, calculated by this formula, always
came out negative — ^which means that the effect always was in the direc-
tion predicted for negative electrons. Examples of the observations
of 5 follow:

Wire 2, L = 50 cm. Up, + 5, 7, 5. 4» 7; Down, + 28, 27, 27, 26,
27 mm. (Average agreement.) Wire 9, L = 49. Up, — 5.5, — 5,
- 5-3» - 47, - 4.5. - 5.7, - 5.0; Down, + 1.5, i, 1.7, 1.5, i, 1.5, 1.4.
(Average agreement.) Wire 12, L = 51. 2d = 3.8, 4, 2.5, 5.0, 5.5, 4.5,
3.2, 2.5, 4.5, 3.2, 4.4, 4.3, 5.5, 5.8, 5. (Worst of all the wires.) For
nickel — ^Wire 20, L = 50. Up, — 5.2, — 5.0, — 5.2, — 4.8, — 4.8;
Down, - 3.3, - 2.8, - 3.3, - 3.3, - 2.8.

No observation was recorded unless the steady deflection was zero
before and after the wire was demagnetized. All the throws were sharp
and distinct.

The numbers in column 7 of the table indicate how well each system
was constructed. The observed value of / was in every case greater
than the calculated value. (Values of / were calculated from the
geometrical dimensions of the systems, taking into account the mirrors.
For no mirror did the moment of inertia about its own central axis exceed
lO""'.) Those systems were best constructed for which the ratios in
column 7 are nearest unity. Some of the smaller wires apparently were
injured in the process of mounting, and a few of these gave wild values
of K. All the wires, however, for which the ratio observed / to calcu-
lated / was less than 1.6 gave consistent values of K, and these only
should be considered in taking the final averages.

The smallest wires were not intended to improve the mean value of K,
but to prove that K does not vary with the diameter and hence that the
internal angular momentum actually is proportional to the volume, as
(i) demands. This constancy of K seems sufficiently established. The
table of results also makes it very evident that the observed K was inde-
pendent of such factors as the intensity of magnetization, the coercive
force, etc.

The value of K seems to be about the same for nickel as for iron. The
numerical accuracy of the results is less for nickel, because nickel is far

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Il6 JOHN Q. STEWART. [sbrie_

less magnetizable; and because its coercive force is much larger, which
makes it harder to eliminate disturbing eflfects. The mean value of
K/i.ii X 10"^ for the nine iron wires for which the ratios of column 7
are less than 1.6 is 0.51 ± 0.04. For four nickel wires the corresponding
mean is 0.47 ±0.11.

The Isu-ge departures from the means all are positive. The cause of
this phenomenon is unknown (unless it be simply that there is more
room for error on that side).

Einstein and de Haas obtained for K a value about twice that found
by the writer.^ They tried only two wires; the first gave K = 0.75,
and they built a new apparatus. The second gave K = 0.98, but they
published only seven numerical observations of the value of the ** double
throw," these all on the same resonance curve — ^and in taking the mean
they discarded the three smallest ones. The ratios observed / to calcu-
lated / for their wires were i .5 and i .2, respectively. Afterwards another
experiment was made by de Haas by a slightiy different method; of
this later work the writer has seen only the brief account published in
Science Abstracts. ** An electromagnet is hung from a unifilar suspen-
sion with its magnetic axis vertical and performs torsional oscillations.
The current is reversed automatically, so that it can be observed whether
the magnet has a moment of momentum depending upon and reversed
with its magnetism. In one case the moment of momentum was detected
and found to be 1.35 X lO"*. By theory this must be 1.13 X lO"^ the
magnetic moment, which gave 1,200 for the magnet instead of 1,400."*
This would make K = 0.86. The resonance method is ingenious, but
one cannot be sure that it really does eliminate all disturbing effects.
Still another resonance method has been developed by Einstein, but this
one is apparently only a lecture-table experiment. The residual mag-
netism of a suspended iron rod is reversed periodically by an instantaneous
current.*

Maxwell's Second Effect.

When one of the iron or nickel wires was demagnetized the change in
magnetic moment was accompanied by a change of flux and a momentary
induced current. It is necessary to show that this current did not pro-
duce the sudden throws that were observed.

If the current in the wire moves the wire either this motion is caused
by ordinary electromagnetic reaction between the current and the
external field, or it is not. Proof has been given in a previous paragraph

* Einstein and de Haas, loc. cit.

*de Haas, Sci. Abs.. XIX.. p. 351. No. 938, Aug. 25. 1916. K. Akad. Amsterdam. Proc.
x8. No. 8. pp. 1281-1299. 1916.

* Einstein. Chem. Abs., //, p. i777. 1917.

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No'a^^*] MOMENT OP MOMENTUM. I I 7

that the throw 8 was independent of the field. (Even the irreversible
throw that usually accompanied 8 was not caused by the induced current,
for it was dependent upon the vertical, not the horizontal, component
of the solenoid field.) If the current moves the wire, then, it must move
it itself. Such a phenomenon would be of interest, but it does not exist.
Since the current is momentary Maxwell's second suggestion does not
apply; his second effect can appear only when the current is changed.

According to any electron theory of metallic conduction transference
of electricity is by the convection of electrons in the direction opposite
to the electric field, and per unit volume there is an exactly equal quantity
of positive charge. So long as the current flows steadily a state of
statical equilibrium exists, and there is no resultant force of the field
upon the body as a whole. When the current is increasing, however,
although the positive charge remains immobile, the state of motion of
the negative electrons is being subjected to change; and to effect this
change a certain amount of the negative field is being used. The result
is an unbalanced force in the direction opposite to the negative current,
which would give rise to Maxwell's second effect.

Assume the free electron theory. Let there be N free electrons per
unit volume; if their average excess velocity over the free path in the
direction of the negative current is v, then the current density, t, is Nev.
The average momentum per electron is mv, or mi/Ne, and the momentum
in volume V is

G = -Vi.
e

This is the fundamental equation for Maxwell's second effect, on the
free electron theory.

Application of this equation to the case of our suspended iron wires
shows that the Maxwell effect could not produce an impulse comparable
to that caused by the Richardson effect, even if the induced current
could be made to keep on flowing (as in a super-conductor), unless demag-
netization took place in lO"' second.

Nevertheless, in order to make perfectly certain that it was not some
effect of the electrons concerned in conduction that was being observed,
a silver wire was tested in the same manner as the magnetic wires.
It showed a trace of magnetization, due probably to clinging particles
of dust, or to the wax or mirror. The usual adjustments were made,
and the steady deflection remained accurately zero when a solenoid field
of a hundred gausses was suddenly applied. Shifting of the zero on ac-
count of temperature changes was annoying; but 8 certainly was less
than 0.2 mm., and it seemed to be zero. Of course there was no mag-

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Il8 JOHN Q, STEWART.

LSbkiss.

netic moment of the silver wire, but, in order to bring the calculation
into the same form as for the other wires, it is convenient to assume that
the flux, B = fiH, was due to a magnetic moment M = BV/^t, instead
of to the solenoid field H. 7 = 3.32 X lO"* cm'., the volume of the
wire, and m is the permeability, which is unity for silver. When H = loi,
M = 0.0266. Accordingly, if K in silver were five times as large as in
iron (which is what one would expect from the ratio of the conductivities),
the observed value of 8 would have been 0.5 mm. Since 8 certainly was
less than 0.2 mm., we may suppose that the effect is absent in silver.

Einstein and de Haas reported that there is no effect in copper. There
probably is no effect in copper, but they did not prove it. Although the
conductivity of copper is a few times greater than that of iron the perme-
ability is so much less that it would have required an alternating field
of 2,000 gausses, instead of the 50 they used, to get a ** double throw "
of a millimeter with their apparatus — even if the effect did exist in
copper.

Summary of the Experimental Results.

A momentum effect such as Richardson predicted for magnetizable'
substances exists in iron and nickel.

The direction of this momentum is that which would be due to the
rotation of negative electrons within the atom; but the magnitude of
the effect is only half that which Richardson supposed would result
from such rotation of negative electrons.

No such effect exists in silver, whence the effect in iron and nickel
cannot be attributed to the conducting electrons.

Conclusions: The Bearing Upon the Structure of the Atom of
THE Value Found for K.

The internal moment of momentum observed in iron and nickel must
be due to the rotation of matter within the atom. It has usually been
assumed that only negative electrons are moving, but this assumption
leads to an internal momentum twice that observed. It is important to
find a reason for the diminished effect.

There are two possible explanations:

1. Negative electrons alone are moving, but cannot react upon the
suspended wire with the full effect predicted.

2. Positive as well as negative charges are rotating, in opposite direc-
tions.

I. To produce the twist of the suspended wire the rotating electrons
must react upon the atom, and the atom, in turn, must react upon the
wire as a whole. There are these two chances for loss of part of the

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Na*a^^'] MOMENT OF MOMENTUM, I I9

original momentum. Richardson suggested when he predicted the effect
that the reaction might take place upon the electromagnetic field, or that
the iron atoms might be loose and unable to transmit the momentum to
the wire as a whole. The known facts of magnetism, however, render
the latter supposition improbable; and if the reaction had taken place
upon the electromagnetic system that produced the exciting field the
observed effect would not have been independent of the intensity of
magnetization.*

Barnett's first experiment on the production of magnetization by
rotation — ^an effect the converse of the Richardson effect — agreed with
this experiment in giving only half the full effect calculated for negative
electrons. The coincidence between the writer's results and those of
Bamett not only is evidence of the correctness of both experiments, but
also seems to make untenable the loose-atom explanation of the dimin-
ished K.

Quite recently* Barnett has obtained somewhat larger values of K
for steel, nickel, and cobalt. He finds that K has about 80 per cent, of
the full predicted value; but the experimental errors are so large that, as
Bamett himself states, his results can be considered as agreeing with
those of Einstein and de Haas. They certainly agree equally well with
those of the writer.

2. We are thus led to the important conclusion that the internal angular
momentum in iron and nickel is only half what it would be if negative
electrons alone were in motion.

By (i), if expressed as a fraction of 2w/e,'

—

e_MA
Em a

A. —

I
I

A
a

m E

It follows that

A T - ;r

(9)

Experimentally, K has been proved constant with respect to changes in
magnetic intensity. Therefore A la is constant; we proceed to calculate
its value.

Assume that the atom is composed of negative electrons and hydrogen
nuclei (positive electrons), and that in the iron atom these electrons are

» Richardson, The Electron Theory of Matter (1914). P- 396.

« Barnett, Proc. Nat. Acad. Sci., j, p. 178. 191 7-

■ A mistake in sign made by Richardson is corrected here. He wrote NE — ne.

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I20 JOHN Q. STEWART, [&SSS

not packed so closely together that their mass is appreciably changed.
Then, if £ = i and Jlf = i, c = — i and m = 1/1850. If the positive
and negative electrons, respectively, are moving with angular velocities
Q and w in circular orbits of radii R apd r, it follows that A = SHR* and
a = Swr*. Substitute these values in (9), and substitute for K the ob-
served value, 0.51. Then

According to Sir Ernest Rutherford's theory of atomic structure, all
the positive charges are concentrated in a very small " nucleus " at
the center of the atom, while about half the negative electrons are rotating
around this nucleus at distances very large compared with its diameter.
Equation 10, if true, signifies that the central positive nucleus itself is
rotating, but in the opposite direction. A rough calculation based on
the assumptions of Rutherford and Bohr, shows that the ratio in (10)
will be of the order of magnitude there indicated if the angular velocity
of the rotating positive nucleus is about equal (but opposite in sign)
to that of the inner ring of electrons.

H. S. AUen^ has imagined an atom with a rotating positive core sur-
rounded by a ring of revolving electrons, but he assumed 2QiP = Zwr*.
Qualitatively, his assumption of the same sign for Q as for w is necessary
for his explanation of the magneton.

Summary.

This paper is devoted chiefly to an account of an experiment which
showed that iron and nickel, when magnetized, possess internal angular
momentum, as was predicted by Richardson in 1908. The magnitude
of this momentum can be accounted for if positive, as well as negative,
charges are moving within the atom, but in opposite directions. The
experimental results of Barnett and of Einstein and de Haas are in
qualitative agreement with those described.

The writer is indebted to Professor H. L. Cooke for initial assistance
and to Professor K. T. Compton for criticism. It should be possible,
with the experimental method described in this paper, to observe the
Richardson effect in cobalt and the Heusler alloys, and perhaps also in
magnetite.

Palmer Physical Laboratory,
Princeton University.
July 14. 1917.

» Allen. PhU. Mag.. XXIX.. p. 714. IPIS-

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No^a^^'] FLUORESCENCE OF URANYL SALTS. 121

A STUDY OF THE FLUORESCENCE OF CERTAIN URANYL
SALTS AT ROOM TEMPERATURE.

By Frances G. Wick.

THE fluorescence spectrum of the uranyl salts consists, as is well
known, of a number of bands, more or less well defined, which,
at low temperatures, are resolved into bands so narrow as to resemble
the lines of a gaseous spectrum. A careful study of the fluorescence
spectra of a number of these salts at room temperature made by
Nichols and Merritt^ shows certain common characteristics with regard
to location, relative intensity, and shape of the bands. Since data
concerning many of the uranyl salts have not been available, a further
study of the luminescence of these salts at ordinary temperatures seemed
desirable and, at the suggestion of Professor E. L. Nichols, the present
work was undertaken. It includes a study of the relative intensities of
the bands, determinations of the shape of a few bands which show partial
resolution at room temperature and conclusions drawn from measure-
ment of the positions of the crests of the bands of a large number of the
salts.

Relative Intensities of Bands in the Fluorescence Spectrum.
The instrument used in this work was a Hilger constant deviation
spectrometer similar to the one designed and used by Nichols and
Merritt.* It is provided with a Lummer-Brodhun cube and two colli-
mators, so that it forms a Lummer-Brodhun spectrophotometer with a
constant deviation prism and a drum which reads directly in wave-
lengths. During the course of this work the calibration of the drum was
frequently checked by comparison with mercury and hydrogen lines.
For the determination of intensity of fluorescence, the apparatus was
set up as follows: The specimen was placed in front of one of the
collimatoft slits of the spectrophotometer and excited to fluorescence by
light from a mercury-quartz lamp passed through deep blue glass and
brought to a focus by means of condensing lenses. The comparison
source was an acetylene flame placed in a carriage in front of the com-
parison slit. The intensity of illumination of the slit was varied by
moving the carriage along a track.

» Nichols and Merritt. Phys. Rev.. Vol. XXXIII., No. 5, p. 354, Nov., igii.

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122

FRANCES G. WICK.

[SKCONb
Sbriks.

A determination of the intensity of the crest of each band of the salt
under observation was made by first locating the position of the crest
by means of the pointer in the eyepiece of the telescope, then removing
the eyepiece and measuring the intensity of fluorescence of this wave-
length spectrophotometrically in comparison with the light from the
acetylene flame. In order to compare the energy of different parts of
the fluorescence spectrum the values obtained for luminous intensity
were reduced by means of the energy curve of the acetylene flame deter-
mined by Coblentz.^ The intensity of each crest was multiplied by the
ordinate of the energy curve for the corresponding wave-length. The
resulting values were reduced to an arbitrary scale in which lo was
taken as the energy of the brightest crest of each salt. Since there was
great variation in the brightness of the corresponding crests of different
salts the results given in this paper show nothing with regard to the

Fig. 1.

Envelopes of fluorescence bands of the double sulphates.

A, uranyl-ammonium sulphate.

B, uranyl-rubidium sulphate.

C, uranyl-potassium sulphate.
Z>, uranyl-sodium sulphate.
E, uranyl-caesium sulphate.

A\ B\ C, Z>', are the crests of -A, B, C and D with the base line of each curve two units
above that of the curve under it.

absolute intensity of fluorescence in different salts but indicate only the
relative intensities of the different bands of the same salt.

The distribution of energy in the bands of the series is shown for a

* Coblentz, Bulletin of Bureau of Standards, Vol. 7, No. 2, p. 260.

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Vol. XI.l
Naa. J

FLUORESCENCE OF URANYL SALTS,

123

number of salts in Figs, i, 3, and 4. The intensities of the crests of the
bands expressed in terms of energy are indicated by the dotted lines as
ordinates of curves of which the wave-lengths are abscissas. The
envelope of these lines shows the distribution of energy among the bands.
This energy curve is practically the same shape for all the salts examined
and, as has been pointed out by Nichols and Merritt,^ a curve of this
same type represents the distribution of energy in a single fluorescence
band of the uranyl salts and also the energy distribution in the broad
fluorescence bands of such substances as resorufin and fluorescein. The
same form of curve represents the energy in the spectrum of a black body
at a temperature of 1259® C. plotted upon a greatly reduced scale.

For the sake of comparison, the envelopes of the diflferent salts were
plotted in groups. Fig. i shows the envelopes of five of the double sul-
phates. The maxima of these curves, with the exception of uranyl-
caesium sulphate, Curve E, all come at approximately the same position,
as may be observed from the superimposed dotted crests A\ B', C\ D\
The maximum of the caesium salt, curve E, is shifted toward the violet
from the position of the others. This shift may be accounted for by
the fact that the bands of this salt are partially resolved at room
temperature and show two crests. The stronger of the two, the one for

Fig. 2.

Envelopes of fluorescence bands of uranyl
sulphate (tri-hydrate).

•ss

Fig. 3.
Envelopes of fluorescence bands of uranyl

acetates.

A, A', uranyl acetate.

B, uranyl-ammonium acetate.

which the intensity was measured, is on the side of the shorter wave-
lengths. The envelope of the whole fluorescence spectrum, including
both components of the bands, would have its maximum in a position
of longer wave-length, which would tend to bring this salt in line with
the others.

> Nichols and Merritt. Phys. Rev.. Vol. XXXIII., No. 5. P- 354. Nov., 191 1.

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124

FRANCES G. WICK.

fSBCONH

LSbribs.

The bands of uranyl sulphate are also partially resolved into two
components, the crests of which are well marked, and the observations
made upon this salt included the intensities of both crests. A separate
envelope was plotted for corresponding components of the bands and
these envelopes are shown in Fig. 2. The envelope of the component
of shorter wave-length, which, in this case, is the weaker of the two
and is indicated by the dotted line, has its maximum in a position of
shorter wave-length than that of the other component. A single envelope
curve for both sets of components would have its maximum at an inter-
mediate position, which is almost in line with the maxima of Fig. I.

The results obtained for two of the acetates are shown in Fig. 3.
The position of the crest of uranyl-ammonium acetate, Curve B, is in a
position of shorter wave-length than that of uranyl acetate. Curve A.

Fig. 4.

Envelopes of fluorescence bands of uranyl nitrates.

A, A\ uranyl-potassium nitrate.

B, B'\ uranyl nitrate (anhydrous).

C, C. uranyl nitrate (tri- hydrate).
I>, D , uranyl-rubidium nitrate.

Uranyl-ammonium acetate showed a slight degree of resolution but the
secondary crest in each band is very weak compared with the one indi-
cated in Curve B.

Observations made upon four different nitrates are plotted in Fig. 4.
The positions of the crests of the envelopes are approximately the same

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Na"a^''] FLUORESCENCE OF URANYL SALTS, 125

With the exception of uranyl-rubidium nitrate, Curve />, as is shown by
the dotted crests. Here, again, the bands of the salt whose maximum is
shifted are partially resolved and settings were made upon the brighter
of the two crests which, in this case, also, was the shorter in wave-length.

It appears, in all three of the groups of salts, that the position of
maximum is approximately uniform for each group except in the case
of salts which are partially resolved. In such cases, the envelope is
shifted toward the shorter wave-lengths. The same cause which pro-
duces resolution in the bands of the salts appears to shift the energy
curves toward the shorter wave-lengths. Upon close inspection of Figs.
I, 3, and 4, it will be observed that the curves of each group which
have approximately the same position of maximum show slight differ-
ences in position. A study of the curves with reference to molecular
weight may be of interest. In Fig. i, the maximum of the caesium
envelope, Curve £, is in the position of shortest wave-length; next in
order come the ammonium, rubidium, potassium and sodium salts,
Curves A\ B\ C, and D', In the first three curves, £, A\ and B\
there appears to be a slight displacement of maxima toward longer
wave-lengths. In Fig. 3, it will be observed that the uranyl-am-
monium acetate, Curve B, has its maximum toward the violet of
that of the uranyl acetate. Curve A. In Fig. 4, the rubidium salt.
Curve />, has the maximum of shortest wave-length, then in order
come uranyl potassium nitrate, uranyl nitrate anhydrous and uranyl
nitrate tri-hydrate. Curves A\ B\ and C\ There appears to be some
evidence that the increase in the molecular weight causes a shift toward
the violet of the energy envelope. This may possibly be due to a
tendency of the heavier salts to show partial resolution which might be
exi>lained upon the basis of molecular weight.

It has been found by Tut ton that for both single and double salts
of the alkali metals, several of the optical properties follow the order of
molecular weights and that, in the ammonium salts, the NH4 radical
often acts as if it were heavier than the combined weights of its com-
ponents would indicate, so that its position is close to that of rubidium
and sometimes on the side toward caesium, which appears to be the case
here if the shift of the energy curves of a given group of salts is to be
connected with the molecular weight. •

In order to study the effect of the acid radical upon the energy en-
velopes, a curve of average position of maximum was taken from each
group and the three are plotted for comparison in Fig. 5. It will be
observed that there is a decided difference in position of maxima and
that the order of position is such that the salts in which the acid radical

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126

FRANCES G. WICK.

IS heaviest have their maxima in the position of longest wave-length,
the maximum of the sulphates is longest, then the nitrates, then the
acetates. The change in the acid radical seems to produce an effect

Fig. 5.
Envelopes of fluorescence bands of salts of different groups.

A, uranyl-ammonium sulphate.

B, uranyl nitrate (anhydrous).

C, uranyl-ammonium acetate.

upon the energy curve. An increase in weight causes a shift toward
the longer wave-lengths.

Shape of Partially Resolved Fluorescence Bands.
In most of the uranyl salts at room temperature the bands show a
single well-marked crest, but, in some cases, as has been mentioned

Fig. 6.
Shape of a single fluorescence band of uranyl sulphate (tri-hydrate).
Vertical lines indicate the position of lines in the resolved spectrum at low temperatures.

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Vol. XI.l
No. 2. J

FLUORESCENCE OF URANYL SALTS.

127

before, the fluorescence spectrum shows partial resolution and the exact
shape of the bands in which resolution has begun is of interest. The
form of the bands in several partially resolved salts was determined by
making spectro-photometric measurements of the intensity of fluores-
cence at intervals of 5 or 10 Angstrom units. Figs. 6, 7, and 8 show the

Fig. 7.

Shape of a single fluorescence band of uranyl-potassium nitrate (add form).

Vertical lines indicate the position of lines in the resolved spectrum at low temperatures.

results of such measurements upon a single band for three different salts.
It will be observed that the curves are very irregular in shape, showing
many places in which the intensity increases abruptly. The possibility

Fig. 8.

Shape of a single fluorescence band of uranyl nitrate (tri-hydrate).

Vertical lines indicate the position of lines in the resolved spectrum at low temperatures.

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128 FRANCES G. WICK. l^SS

that these sudden changes in intensity might show the beginnings of
the narrow line-like bands which appear in the resolved spectra at liquid
air temperatures, was suggested by Professor Nichols. The wave-
lengths of the lines into which these bands are resolved at low tempera-
tures were obtained from him and the positions of some of these lines are
indicated in the figures by short vertical lines. In m'ost cases there is
not exact coincidence between the position of the line and that of the
maxima of the curves, but this is not to be expected, since there is a
shift in the position of the lines of the uranyl salts toward the violet with
a lowering of temperature. There appears, however, to be some indi-
cation that the lines of the resolved spectrum may have some relation to
the irregularities on the curves.

Positions of Fluorescence Bands.

Measurements were made of the positions of the crests of the fluores-
cence bands in about twenty of the uranyl salts in order to determine
whether the characteristics observed by Nichols and Merritt for some
of the salts are common to all. The positions of these crests were deter-
mined in the usual way by means of the Hilger spectrometer. The
crystal, in pulverized form, was strongly illuminated by light from a
carbon arc passed through a water cell then through deep blue or purple
glass and brought to a focus upon the crystal by means of condensers.
The position of the crest was located by means of the pointer in the
focal plane of the eye piece. In most of the salts seven bands were
observed visually. The sharpness of the crests varies greatly with
different salts — in some cases they are narrow and sharp and the results
of different sets of observations checked in such a way as to show that
the positions could be accurately obtained; in other cases, however,
the bands were more than loo units wide with flat tops, so that no
sharp crest was evident and the determinations were not satisfactory.
Absorption bands made visible by illuminating the specimen with white
or pale blue light were observed and approximately located in some of the
salts. Since these bands are broad and poorly defined it was impossible
to locate them with any degree of accuracy, either visually or photo-
graphically by this method.

The data obtained upon the positions of fluorescence and absorption
bands are not published in this paper, but certain conclusions drawn from
a study of the measurements made may be mentioned. The results
are in agreement with those obtained by Nichols and Merritt for the
salts observed by them. The fluorescence bands form a series with a
frequency interval which is practically uniform for a given salt. Ab-

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No!"a^^*] FLUORESCENCE OP URANYL SALTS. 1 29

sorption bands appear to be a continuation of the fluorescence bands,
but with a shorter interval. The two series of bands overlap and
certain bands in the violet reversing region appear as absorption or
fluorescence bands according to the conditions of illumination.

In the extreme red and violet bands of all the salts observed there is
some variation from the uniform interval which may be explained by
the fact that these bands are dim and, in the violet region, the absorption
overlaps the fluorescence and makes the position of the crest less distinct.
The interval is not the same for all the salts, but there appears to be a
uniformity in the interval for a given group of salts. For instance, the
interval which is characteristic of the nitrates is longer than that of
the sulphates.

From the results of the investigation described in this paper it appears
that the, characteristics of some of the salts observed by Nichols and
Merritt, with regard to number of bands, their distribution, and relative
intensity are common to all. The spectra of the salts differ in that the
intervals between the bands vary and the energy curve is shifted in
position for different groups of salts. The degree of resolution at room
temperature also varies and it appears that the double salts of highest
molecular weight show the highest degree of resolution.

The author wishes to express her sincere thanks to Dr. H. L. Howes
for his efficient assistance in making the spectro-photometric measure-
ments described in this paper and to Professor E. L. Nichols whose
interest and suggestions have made this work possible. The specimens
used belonged to him and a part of the work was done in his laboratory
during the summer of 1916.

Vassar College.

poughkbbpsie. nsw york.

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130 THE AMERICAN PHYSICAL SOCIETY. [&SSS

PROCEEDINGS

OF THE

American Physical Society.

Minutes of the Ninetieth Meeting.

THE ninetieth meeting of the American Physical Society was held in
Rochester, N. Y., on October 26 and 27. On this occasion the visiting
members of the Society were the guests of the Bausch & Lomb Optical
Company, the Taylor Instrument Company and the Eastman Kodak Com-
pany. The program and various entertainment features were arranged by a
committee whose chairman was I. Mayer, of the Taylor Instrument Com-
pany, acting in cooperation with Professor F. K. Richtmyer, chairman of
the Technical Committee of the Physical Society. The generous hospitality
extended included lunch on both days, evening banquet and smoker on Friday
evening, automobile transportation to the several companies* works, a theater
party for visiting ladies, etc. There were sessions for reading papers fore-
noon and afternoon of both days. Friday sessions were held at the Hotel
Seneca, which was Society headquarters for the meeting. At the conclusion
of the afternoon sessions, automobiles conveyed those in attendance to the
works of the Bausch & Lomb Optical Company. Demonstrations were there
given of methods used in handling large masses of optical glass in the furnaces
and of transferring them to the annealing ovens, also of lens grinding and
polishing. The Saturday morning session was held at the Taylor Instrument
Company's works. Afterwards the visitors were divided into small groups and
guides provided to. conduct them through the extensive factory. Each visitor
was presented with a beautiful souvenir thermometer. Then all were taken
by automobile to the Eastman Kodak Company's works at Kodak Park.
Here lunch was provided. The afternoon session was held at the Kodak
Research Laboratory, and an opportunity given for inspection of the laboratory
at the conclusion of the session.

On Friday evening the Society were guests at a dinner at the Hotel Seneca,
which included an elaborate musical and patriotic program. At the smoker
following Dr. F. E. Wright, of the Geophysical Laboratory, gave an interesting
talk on "Optical Glass for Military Purposes," and Major C. E. Mendenhall,
of the National Research Council, spoke of the activities of physicists in
United States war work. One hundred and fifty-six attended the dinner.
The attendance was large at all sessions. A cordial vote of thanks and appre-

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No^a^'*] ^^^ AMERICAN PHYSICAL SOCIETY. I3I

ciation for their generous hospitality was extended to the Bausch & Lomb
Optical Company, the Taylor Instrument Company, and the Eastman Kodak
Company, and to the efficient committee whose excellent plans made the
meeting so instructive and interesting.

The program of papers was as follows:

The Production and Measurement of High Vacua. J. E. Shrader and
R. G. Sherwood.

The Nature of the Ultimate Magnetic Particle. Arthur H. Compton
AND Oswald Rognley.

Bohr's Atom, Zeeman's Effect and the Magnetic Properties of the Elements.
Jacob Kunz. (By title.)

Comparative Accuracy of Whirled Psychrometer, Assman Aspiration Psy-
chrometer. Porous Cup Atmometers, Hair Hygrographs, Piche Evaporimeter,
Saturation Deficit Recorder, Open Water Surface Evaporimeter, and Dry
and Wet Bulb Thermometers. Alexander McAdie. (By title.)

Rotation of the Pulley in Melde's Experiment. Arthur Taber Jones.

An Instrument for Continuously Recording the Percentage of Saturation
and the Weight of the Water Vapor per Unit Volume in the Free Air. Alex-
ander McAdie. (By title.)

A Self- Recording Evaporimeter. Alexander McAdie. (By title.)

Complete Achromatization of a Two-Piece Lens. G. W. Moffitt.

A New Hydrate of Uranium Nitrate; Uranium Nitrate Icositetrahydrate.
Frank E. Germann.

A study of the Fluorescence of Certain Uranyl Salts at Room Temperature.
Frances G. Wick.

On Certain Absorption Bands in the Spectra of the Uranyl Salts. H. L.
Howes.

Optical Range Finders for Military Purposes. Hermann Kellner.

Submarine Periscopes. W. B. Rayton.

An Apparatus for Testing Search Light Mirrors. Henry Kurtz.

Methods of Temperature-Control in Glass- Melting Furnaces. Clarence
N. Fenner.

Note on a Comparison of High Temperature Scales. E. P. Hyde and

W. E. FORSYTHE.

A New Formula for the Temperature Variation of the Specific Heat of
Hydrogen. Edwin C. Kemble.

The Influence of Temperature Upon the Crushing Strength of a Dental
Amalgam. Arthur W. Gray and Paris T. Carlisle, 4th.

High Temperature Measurements. R. C. Schwartz.

Aneroid Barometers. P. R. Jameson.

Mercury-Steel Capillary Thermometers. J. W. Ward.

Heat Treatment of Mercurial Thermometers. H. Y. Norwood.

Emulsions, (a) A New Method for Making Emulsions. (6) Properties of
Emulsions. Wheeler P. Davey.

Images on Silver Photo-plate. C. W. Waggoner.

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132 THE AMERICAN PHYSICAL SOCIETY, [^Sm?

The Mathematical Structure of Band Series, II. Raymond T. Birge.

On the Residual Rays of Rock Salt. Herbert P. Hollnagbl.

The Absorption of Near Infra-red Radiation. W. W. Sleator.

Measurement of Heat Conductivities of Metals at High Temperatures.
Robert W. King.

Standard Turbidity. By title. P. V. Wells.

Visual Sensitometry. Prentice Reeves.

Photographic Sensitometry. L. A. Jones.

Resolving Power. F. E. Ross and Kenneth Huse.

General Outline of Work Being Carried on in Eastman Research Laboratory.
C. E. K. Mees.

A. D. Cole,
Secretary,

The Nature of the Ultimate Magnetic Particle.^
By Arthur H. Compton and Oswald Rognlby.

IT appears highly probable that when a substance is magnetically saturated,
all the so-called "molecular magnets" of which it is composed are arranged
parallel to the magnetic field. Thus as a substance becomes magnetized the
direction of the axes of these elementary magnets ceases to be unordered, and
they are turned in a definite direction. If these ultimate magnetic particles
are groups of atoms, magnetization must therefore be accompanied by a trans-
lation of the atoms, an hypothesis which has been disproved by K. T. Compton
and E. A. Trousdale by showing that the Laue diffraction pattern obtained
through a magnetic crystal is not affected by magnetization. If these particles
are the atoms themselves, the orientation due to magnetization will change
the position of the electrons of which the atoms are composed. In virtue ol
the fact that the intensity of a beam of X-rays reflected from a crystal face
depends upon the arrangement of the electrons in the atoms which make up
the crystal, such a shift of the electrons should make itself known by changing
the intensity of this reflected X-ray beam.

Assume, for example, a crystal composed of atoms of the Bohr type, each
atom having all its electrons arranged in the same plane and perpendicular to
the magnetic axis. When the crystal is unmagnetized, the electronic orbits
will be distributed in all possible planes, so that on the average the electrons
will be at an appreciable distance from the mid-planes of their atomic layers.
If, however, the crystal is magnetically saturated perpendicular to the re-
flecting face, the electronic orbits will all lie parallel to this face. The electrons
will therefore now be in the mid-planes of the layers of atoms which are eflfective
in producing the reflected beam. It can be shown that such a shift of the
electrons must produce a very considerable increase in the intensity of the

» Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 1917.

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50*3^^'] ^^^ AMERICAN PHYSICAL SOCIETY, 1 33

reflected beam of X-rays. On the other hand, if the crystal is magnetized
parallel to the reflecting face, the turning oj the orbits will carry the electrons
farther on the average from the middle of their atomic layers, and a decrease
in the intensity of reflection should result.

We have searched in vain for ^ch an eff'ect on the intensity of the reflected
beam of X-rays when the reflecting crystal is magnetized. In our experiment
a null method was employed. The ionization due to the beam of X-rays
reflected from a crystal of magnetite was balanced against that due to a beam
of the same wave-length reflected from a crystal of rock-salt, so that a very
small change in the relative intensity of either beam could be detected, while
variations in the X-ray tube itself had little effect. By means of an electro-
magnet with a laminated core the magnetite crystal was magnetically satu-
rated, and then demagnetized with an alternating current. The effect of mag-
netization perpendicular to the plane of the crystal face was investigated for
the first four orders. On account of mechanical difficulties the test was made
only in the third order spectrum when the crystal was magnetized parallel tu
the reflecting surface. In no case was any change observed in the intensity
of the reflected beam when the crystal was magnetized or demagnetized, though
the method was sufficiently sensitive to detect a variation in the intensity of
less than i per cent.

A direct calculation shows that a displacement of the atoms of 1/200 of the
distance between the atoms would have produced a noticeable change in the
intensity of the reflected X-ray beam. Our negative result therefore con-
firms the conclusion of Compton and Trousdale that since the atoms are not
appreciably displaced the molecular magnets cannot be groups of atoms.

Similar difficulties are encountered on the hypothesis that it is the atoms
which are the ultimate magnetic particles. With an atom of the Bohr type,
in which all the electrons are arranged in the same plane, a change in the
intensity of reflection as great as 500 per cent, should occur in the higher orders
when the crystal is magnetized. Hull has shown that the intensity of X-ray
reflection is satisfactorily accounted for if the iron atom is composed of electrons
arranged at the corners of cubes of different sizes, but even with this more
symmetrical form of atom one would expect a change of some 30 per cent,
if the atom is turned around by the magnetic field. In fact, on account of
the relatively small number (26) of electrons in an iron atom, it is apparently
impossible to assign them any definite arrangement, consistent with what is
otherwise known about their distribution, which is so isotropic that a rotation
of the atom will not produce a change greater than i per cent, in the intensity
of the reflected X-ray beam. It is possible to conceive of a perfectly isotropic
atom if the electrons, instead of having definite positions or orbits, are arranged
as an atmosphere about the nucleus in a wholly unordered manner. An atom
so constructed, however, would have no resultant magnetic moment.

It seems to us necessary to conclude that it is neither a group of atoms,
such as the chemical molecule, nor the atom itself which is the elementary
magnet. We must look rather to the atomic nucleus, as suggested by Merritt,

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134 ^^^ AMERICAN PHYSICAL SOCIETY. [iSSS

or to the electron, as proposed by Parson, for the ultimate magnetic particle.
The experimental work and part of the theoretical work on this paper was
performed at the University of Minnesota.

Wbstinghousb Lamp Co. and

UNivERsrrv of Minnesota.

The Production and Measurement of High Vacua.*
By J. E. Shradbr and R. G. Sherwood.

THE authors, during their work on the diffusion pump, have designed a
pump which they think has points worthy of consideration. Its con-
struction is of the upright form so designed that the condensed mercury returns
to the boiler without passing through the high vacuum side. This obviates
the objectional feature of Langmuir's early pump in which the condensed
mercury came into contact with the hot tube from the boiler, thus producing a
mercury vapor blast against the intake side of the pump. The upright form
is easier for the glass blower to manipulate in blowing, is more convniente
for attaching the water jacket and makes unnecessary the insulation of the
stem connecting the boiler to the other part of the pump. The pump is quite
effective, pressures lower than i X lo"* mm. Hg. having been attained.

In connection with high- vacua work the Knudsen type of absolute manom-
eter has been chosen as best suited for the measurement of low pressures.
A gauge possessing important improvements over those already described in
the literature has been constructed. These improvements are (i) the method
of supporting the platinum heating strip, (2) the kind of suspension, (3) the
manner of suspending and controling the movable vane.

Without heat treatment of a glass system, pressures as measured by this
gauge lower than i X io~' mm. Hg. can not be obtained. With continued
heat treatment at 500** C. of the entire hard glass system, pressures lower
than I X 10"* mm. Hg have been obtained. Many glass vessels have been
exhausted to pressures of the order of 5 X lo"* mm. Hg.

Testing the pump in connection with the gauge brought out the following
relations:

1. With low backing pressure, 3 X 10"* mm. Hg, the pump begins to operate
with 65 watts in the heater and the speed of the pump increases with watts
input up to 300 watts after which the increase is much less up to 350 watts.
From 350 to 600 watts the speed is practically constant, showing a tendency
to decrease at the higher wattage.

2. Critical backing pressure is proportional to watts input over the range
of backing pressures from 3 X lo"^ to .6 mm. Hg.

3. From comparison with vapor pressure-temperature curves for mercury,
critical backing pressure is a linear function of the vapor pressure of mercury.

* Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 191 7.

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nS"^'*) ^^^ AMERICAN PHYSICAL SOCIETY, I35

4. At low backing pressures the speed of exhaustion at wattages above the
wattage corresponding to critical backing pressure gradually increases with
wattage and comes to a limiting value. With higher backing pressures, the
operation of the pump requires higher wattages, but the speed of exhaustion
increases more rapidly but approaches the same limiting value. At .6 mm.
Hg backing pressure the speed of exhaustion assumes its limiting value with a
slight increase in wattage above the wattage corresponding to its critical
backing pressure.

Wbstinghousb Rbsbarch Laboratory,
East Pittsburgh, Pa.,
October 9, 1917.

On the Residual Rays of Rock Salt.*
By Herbert P. Hollnagbl.

IN 1909 Heinrich Rubens, of Berlin, and I published a paper on the deter-
mination of the wave-lengths of certain residual rays as obtained by an
interferometric method. The curves thus obtained resembled in character
the visibility graphs which Michelson had obtained in his study of mono-
chromatic line spectra, that is they showed beat phenomena.

At the time it appeared advisable, from the appearance of the curves, not
to push beyond the second minimum, t. «., the first beat. Since then, however,
a large number of other residual ray determinations have been made in an
entirely similar manner; it seems to have become arbitrarily established that
an interference curve should include only the first beat, a procedure evidently
somewhat unwarranted and conducive to misleading results.

The energy distributions were likewise approximated as obtainable from
the Bjerknes method of calculating the resonance curve. From these il
appeared that the distributions consisted of an intense band and a weaker
satellite of greater or less wave-length. In fact, this character repeated itself
in succeeding investigations so often that Rubens reinvestigated in 191 3 the
earlier measurements. From this work he concluded that all such bands
were due to HaO vapor absorption for various radiations, saddling a broader
band which was of the nature of a resonance curve. In view of what has been
stated above, not only may the energy distributions in the first paper be in-
correct, but in that of 191 3 it is quite possible that they do not show all the
absorption bands due to H2O vapor.

In the light of these possibilities I have deemed it interesting to attempt to
push the curves a considerable amount further in order to decide whether the
assumptions which are implied in the previous investigations are correct.
Such curves extending over four or more beats have been obtained for rock

^ Abstract of a paper presented at the Rochester meeting of the American Physical Society.
October 26 and 37, 191 7.

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136 THE AMERICAN PHYSICAL SOCIETY. [&SSS

salt. They would seem to indicate that the phenomena are not nearly as
simple as previously supposed.*
Physical Laboratory.

Massachusetts Institute of Technology,
Cambridge. Mass.
September 8, 1917.

The Mathematical Structure of Band Series, II.*
By Raymond T. Birge.

IN the first communication on this subject (Washington meeting, April,
191 7) there was proposed a new band series formula, which had been found
to hold with the greatest possible accuracy for the main (Ai) series of the
3883 CN band. This formula was to the effect that, if the first frequency
differences (Aw) of successive lines be plotted against the ordinary variable
**m,** there is obtained a hyperbola, running through the origin, or very close
to it. The actual frequency is then given by r© + 2At; where vo = frequency
of the head of the series.

Although the Ai series, because of its great length and radical deviations
from Deslandres' Law, has been considered standard material for testing new
formulae, the Ci series of the same band was shown by the author to furnish a
far more crucial test. For while the Ai series fades out just beyond the point
of maximum Ar, the Ci series can be followed for 37 out of the 57 lines forming
the portion from the point of maximum Ai; to the (hypothetical) tail.

Uhler has identified the Ci series from m = 47 to m = 164. His data indi-
cate the presence of a large number of irregularities. Some of these, however,
are only apparent, being due to the confusion of relatively weak Ci lines with
the stronger Bi and Ai lines. In order to obtain as consistent data as possible,
the author has remeasured, from his own plates, the entire Ci series, and has
succeeded, in addition to removing some of the pseudo-irregularities, in identi-
fying the series over the full interval m = 6 to m = 169 inclusive. The data
used in the following calculations are based jointly on the author's and Uhler's
values.

The portion from w = 16 down to m = 6, embracing those lines where the
Ci series, in perfect analogy with the Ai series, merges into the corresponding
doublet (Cs) series, is uncertain, and the values used show a definite divergence
from any simple smooth curve. The Ci series, aside from this portion, follows
the hyperbolic formula with an accuracy commensurate in every way with the
Ai series. The validity of the hyperbolic law is therefore established, and
this law seems to furnish one striking evidence of the nature of the fundamental
field of force of the molecule.

1 Grateful acknowledgment is hereby made to the trustees of the Elizabeth Thompson
Science Fund as well as to the members of the Rumford Committee of the American Academy
of Arts and Sciences for the aid obtained under their respective grants.

« Abstract of a paper presented at the Rochester meeting of the Physical Society, October
a6 and 27, 1917.

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No!"a^''] ^^^ AMERICAN PHYSICAL SOCIETY. I37

This fundamental field, at certain distinct points, is noticeably disturbed,
causing the regular "perturbations." These, while in general equal in number
and similarly situated in the five singlet series of this band (as Uhler has pointed
out), increase in magnitude from the Ai to the Ei series, having values as large
as o.i A in the Ci series. Besides the approximately 20 lines forming the
perturbations, all lines of the Ci series between the first regular perturbation
at m = 35 and the seventh at w = 148, show an extremely interesting system-
atic deviation from the hyperbolic law, viz.:

Beginning at the high-frequency side of any perturbation, the lines have a
frequency greater than that expected, by one part in 270,000 to one part in
400,000 (t. e,, 0.015 A to 0.0 1 A). This deviation then decreases linearly, at
the rate of about .001 A per line until, when the next perturbation has been
reached, it has attained a negative value equal to the initial positive value.
In terms of the hyperbola this would mean that the observed frequency
differences, outside of the perturbations, all lie on a hyperbola identical with
that actually used in the computations, but shifted about 0.00 1 A nearer the
m axis. The difference in the area under the two curves (169 X .001 A) is
then exactly compensated by the perturbations which furnish, on the average,
frequency differences considerably greater than those computed.

By strict analogy the Ai series should show similar deviations having a
maximum value of 0.003 A. This would be practically masked by the ordinary
experimental errors, although the data already presented for Ai do show a
slight trace of the expected deviations. It is hoped that these systematic
deviations from the hyperbolic law may furnish additional material for any
theory of molecular structure.

Dbpartmbnt of Physics.
Syracuse UNrvKRSiTY.

Images on Silvered Photo-plate.*
By C. W. Waggoner.

IN silvering some mirrors on glass negatives, from which the gelatine had
been removed, it was discovered that in a number of cases positive images
appeared on the glass. The images developed only when the side of the glass
from which the film had been removed was silvered and they had the appear-
ances of faint daguerreotypes.

It was first thought that these images were due to imperfect cleaning but
the silvered images reappear after treating the glass with cone. HNOj, cone.
H1SO4, Farmer's solution with KjFeCNe, 10 per cent. HP, aqua regia, con.
NaOH, NaF, and potassium dichromate cleaning solution. Some of the plates
were heated in a furnace to the softening temperature of glass without destroy-
ing the phenomenon. The original gelatine film was removed by dipping the
plates in lye and then subjecting them to steam under pressure. In examining

^ Abstract of a paper presented at the Rochester meeting of the American Physical Society.
October 26 and 27, 191 7.

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138 THE AMERICAN PHYSICAL SOCIETY. [^SS

a large number of plates after the film had been removed it was found that
on a few, perhaps 5 per cent., a very faint image could be seen by reflected
light and when the glass was silvered this image became very pronounced.
This faint image could not be removed by the chemical cleaning mentioned
above.

It appears that this phenomenon is due to the action of gelatine on the
surface of the glass. That a film of gelatine will actually tear pieces of glass
from the surface upon which it is placed and allowed to harden is well known
to glass manufacturers and is the process used in making the so-called ''chipped
glass" surfaces.

The images may be accounted for by the presence of the large amount of
metallic silver in the shadows on the negative which may reduce this tearing
action of the gelatine thus leaving a smoother surface for the silver ifiirror.
The above reasoning would account for the fact that the image is always a
positive image.

West Virginia University.

Emulsions: (a) A New Method for Making Emulsions.
(6) Properties of Emulsions.^

By Wheeler P. Davby.

(a) The use of gasolene and similar organic solvents for japan is attended
by a considerable fire and accident risk. It seemed desirable, therefore, to
devise some means of applying japan which did not involve the use of inflam-
mable solvents. With the increased demand for hydrocarbon oils for military
purposes, came increased incentive to avoid the use of gasolene and similar
solvents in industry. As a result, a method has been devised by which the
japan base is emulsified in water and is later deposited from the emulsion upon
the surface to be japanned. In the course of this work a new method of
making emulsions has been found, and some interesting properties of emul-
sions have been noted.

All the methods reported in the literature to date for making emulsions
involve either a violent mechanical agitation or a grinding action, such as is
found in the "homogenizer." It has been found possible, however, to emulsify
the oils used in making japan bases (linseed oil, wood-oil, fish oil, etc., their
compounds and polymers) by merely heating them with an aqueous solution
of an alkali in an inclosed space. The alkali used in the present experiments
was ammonia. Since the emulsification can only take place at the interface
between the oil and the water, the process may be hastened by providing a
large surface. This is easiest accomplished by means of a stirrer with baffles.
This stirring is, however, not to be confused with mechanical agitation, for it
is carried on at very slow speed, 30 to 60 R. P. M. The fineness of the emul-

^ Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 1917.

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Na*a^^'] ^^^ AMERICAN PHYSICAL SOCIETY, 1 39

sions made by this method may be judged from the fact that no difficulty has
been experienced in making emulsions of japan base in water which could be
put through a cream separator without destroying the emulsion.

Emulsions can be made by this method in two ways, either, (i) all the
alkali and a little water may be added to the oil-phase (in this work, the japan
base) at first, later adding water gradually, or (2) the whole amount of water
may be added to the alkali and oil phase in the beginning. At present, the
first way is to be preferred as giving an emulsion of greater fineness.

{h) All the emulsions made in this work have formed a scum on the surface
if left exposed to the air at room temperature. This has been shown to be
due to COj, for if air from the room is carefully freed from COt it may be
bubbled through an emulsion for a whole day without the formation of scum.
If the apparatus for taking out the CO2 is short circuited by a by-pass a visible
scum will form in a few minutes. It has been found, however, that if the
temperature of the emulsion is sufficiently low, no scum will form in the
presence of CO2 laden air. An emulsion having over 15 square feet of surface
exposed to the air did not scum for weeks when kept at 15^-16** C, but scummed
over night at 17** C. At temperatures over the critical temperature, it is as
though the COf unites with the alkali on the surface layer, thus forming an
electrolyte which breaks the emulsion at the surface, causing a scum. This
scum acts as a partial protection for the rest of the emulsion, so that the rate
of formation of the scum is greatest when the scum is first beginning to form.

The droplets of the discontinuous phase of the emulsion are negatively
charged. This offers a method for separating the discontinuous phase from
the continuous phase by the introduction of electrodes into the emulsions.
The deposition of the discontinuous phase upon the anode is an example of
real electroplating, for the amount deposited is strictly proportional to the
product of the current and the time and is independent of the voltage employed
except in so far as the voltage affects the strength of the current.

No attempt has been made to accurately measure the velocity of transport
of the discontinuous phase under an electric field, but rough measurements
indicate that it is not less than lo"* cm. per second per volt per cm. This is
of the same order as the velocity of other colloids and ions at the same tempera-
ture.

Research Laboratory,
General Electric Co.

Note on a Comparison of High-Temperature Scales.*
By E. p. Hyde and W. E. Forsythe.

WHEN comparing the results of high-temperature measurements by
different authors there is much uncertainty concerning the scale used.
High-temperature scales are for the most part based on the temperatures of

* Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 191 7.

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140 THE AMERICAN PHYSICAL SOCIETY, [sSml

the melting points of some chosen metals; gold, copper, and palladium being
generally used. The temperatures of the standard melting points are for the
most part obtained inside a standard black-body furnace. The temperature
scale is extended beyond these points by means of the various radiation laws.
All of the laboratories participating in this intercomparison, excepting the
Physical Laboratory of the University of Wisconsin, base their temperature
scale on the melting point of gold (1336** K.) and extrapolate by means of
Wien*s equation using for C2 14350 m X deg. At the Physical Laboratory of
the University of Wisconsin the scale is based on the melting point of palladium
taken as 1822° K. For Ct they use 14350 m X deg.

There are three different sources of error, (i) in obtaining the temperature
of the melting point, (2) in the blackness of the furnace used, and (3) in extra*
polation by means of the radiation law. These various sources of error might
well lead to very large uncertainties in the final results. An intercomparison
of the temperature scales of the Bureau of Standards, the Physical Laboratory
of the University of Wisconsin, the Research Laboratory of the General Electric
Company, and Nela Research Laboratory was carried out through measure-
ments made on several tungsten filament lamps sent out by this laboratory.
In each of the laboratories the temperature was measured by means of a
Holborn-Kurlbaum optical pyrometer using red glass as the monochromatic
screen. As the different laboratories used a red glass having a slightly different
effective wave-length, a small correction was necessary to reduce the tempera-
tures to the same wave-length. This correction is necessary because the
temperature measurements were not made on a black body.

Of the lamps used in the intercomparison all, except T-30-C, had flat fila-
ments about 3 cm. long and about ij mm. wide. The exact point at which
it was desired to have the temperature measured was indicated either by a
pointer, a notch on the supporting lead or a small notch in the filament itself.
Three of the lamps were gas-filled and the other two were of the vacuum type,
the gas-filled lamps being marked C, while the vacuum lamps are marked
with a B. T-30-C, a gas-filled lamp, had a 20 mil (0.5 mm.) filament in the
shape of a hairpin loop. As the loop was rather sharp, the exact point at
which it was desired to have the temperature measured was easily indicated.
T-25-C and T-17-C had their flat filaments horizontal to avoid unequal
heatings due to the gas currents within the lamps.

The temperatures were measured in this laboratory, both before the lamps
were sent out and after they were returned from each of the other laboratories.

The final results, all reduced to the same value for the melting point of
palladium, are given in the followfng table. As the temperatures obtained
are black-body brightness temperatures, it is necessary to give the wave-
length to which they correspond.

This intercomparison has been made possible through the codperation of
Dr. Stratton, of the Bureau of Standards, Dr. Mendenhall, of the University
of Wisconsin, and Dr. Langmuir, of the Research Laboratory of the General
Electric Company.

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No. 2. J

THE AMERICAN PHYSICAL SOCIETY,

141

Results op Intercob«parison of Temperature Scales.
Ci = 14350 M X deg. X « 0.665 fi. Melting point of Au. - 1336° K.

(pd. = 1828° K.).
T-25-C,

Nelm Reseftrch
Lmbormtory
(10-17-16).

1826^ K.

2214

2518

Research I«aboratory
of General Electric
Co. (Schenectady).

1828
2214
2518

Nelm Research
Lrmboratory

(ii~a8-i6).

1826
2215
2516

Bureau of Stand-
ards.

Nela Research
Laboratory

(4-»-X7).

T-ie-B.

1429

1431

1427

1618

1613

1617

1619

1614

1816

1811

1813

1812

2128

2116

2122

2121

T-3(hC,

1813

1814

1813

2307

2304

2302

2303

2756

2752

2762

2752

T-17-C,

Nela Research Labora-
tory (3-a7-x6).

Physical Laboratory U
CB. M.

Diversity of Wisconsin.
0. R. 0.

Nela Research Labora-
tory (7-X4-17).

1810
2193
2499

1813
2197
2506

1816
2202
2516

1810
2196
2497

T-JS-B.

1599

1602

1605

1597

1806

1816

1819

1807

2105

2119

2123

2107

Nela Research Laboratory,
National Lamp Works of General Electric Co.,
Nela Park, Cleveland. O.,
October, 191 7.

Methods of Temperature-Control in Glass-Melting Furnaces.*
By Clarence N. Fenner.

THE work described in this paper has been carried out by Dr. F. E. Wright
and the writer at the glass-making plant of the Bausch & Lomb Optical
Co., Rochester, N. Y.

> Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 37. 191 7.

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142 THE AMERICAN PHYSICAL SOCIETY, [^£?

A matter of prime importance in the making of optical glass is proper regu-
lation of furnace temperatures, and to this end the first requisite is a means of
determining temperatures by some quick and reliable method. The furnaces
in the Bausch & Lomb plant have long been equipped with thermoelements of
Pt-PtRh introduced through the furnace walls and leading to a direct-reader
conveniently placed for observation by the furnace-men, and the regulation
of temperatures has been based upon these, but the method has been unsatis-
factory. Probably a chief source of trouble lay in the liability of the thermo-
elements to contamination from furnace gases. It seemed that an optical
pyrometer, constructed on the principle used in the Holborn-Kurlbaum or
Morse instruments, would be much better for the purpose, and we obtained
one of this type from the Leeds & Northrup Co.

Before putting it intp regular use it was considered advisable to obtain
information on two points: first, as to whether the calibration-chart supplied
with the instrument was correct; and second, whether the radiation given by
the furnace walls corresponded to black-body radiation; in other words,
whether the apparent temperature was the true temperature.

For the first purpose a long porcelain tube of small diameter, closed at one
end, was introduced into the furnace at different temperatures and the true
temperature of the end was obtained by a Pt-PtRh thermoelement temporarily
inserted. Then the optical pyrometer was sighted through the tube on the
hot end, and the readings compared. The results showed that within the
limits of error (that is, within a very few degrees) the calibration-chart was
correct.

The second matter was investigated as follows: A water-cooled iron tube,
several feet in length, was constructed in such a manner that thermoelement
leads could be carried from outside through a cool inner tube and about two
feet beyond this into a Marquardt porcelain tube, at the end of which the
ther mo- junction lay. This device, when handled with a little care, could be
inserted into the furnace at as high a temperature as 1400 **.C. and the true
temperature of any region determined. By using this simultaneously with the
optical pyrometer it was found that at the temperatures at which the important
operations of glass-making are conducted (i300**-i400® C.) the determinations
of temperature by means of the optical pyrometer agreed almost precisely
with those of the thermoelement. At lower temperatures the readings of the
optical pyrometer were somewhat high because of reflection of the flames by
the glazed walls, but this was of minor importance.

The reliability of the optical pyrometer having been satisfactorily established,
it has since been used daily for the control of furnace temperatures. It has
been found that the furnace-men could be taught without much difficulty
how to use it, so that at night also the temperatures are controlled by it.

Since adopting this method certain troubles in glass-making which were
formerly encountered have practically disappeared. The difficulties referred
to arose from the fact that if the temperature of melting and fining was a little

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No'a?^^'] "^^^ AMERICAN PHYSICAL SOCIETY, 1 43

lower than it was supposed to be the melt did not fine properly and the resultant
glass was' full of bubbles, or, in certain cases, might turn milky. If the tempera-
ture was too high the pot, even if of best quality, was likely to be corroded and
to contribute stones to the glass, or might even be eaten through. In order to
avoid running in to. one or the other of these troubles we are restricted to a
rather narrow temperature-range, but by the use of the optical pyrometer
close control can be exercised and the difficulties avoided.

Gbophysical Laboratory,
Washington, D. C.
October 10, 1917.

On Certain Absorption Bands in the Spectra of the Uranyl Salts.*

By H. L. Howes.

PROBABLY Mr. G. C. Stokes* was the first investigator to notice that the
fluorescence and absorption spectra of the uranyl salts are slightly
overlapped.

Morton and Bolton' also noticed coincidences in the position of several
fluorescence and absorption bands of the uranyl salts.

J. Becquerel and Onnes* working at low temperature found several coin-
cidences in the positions of the narrowed bands.

Nichols and Merritt^ found that the "reversing region** was of considerable
length; in the case of uranyl potassium sulphate they were able to reverse the
brilliant fluorescence band at 5,130 A. u. whereas previously the reversals had
been limited to the region beyond 5,000 A. u.

In our study of the uranyl double chlorides Prof. E. L. Nichols and the
writer found it possible to reverse a complete group of fluorescence bands lying
between 5,080 A. u. and 4,880 A. u. The desire to extend this "reversing
region*' towards the red led the writer to undertake the present investigation.
A theory of luminescent radiation very recently proposed by Dr. E. H. Kennard
also made the investigation of interest.

Since the crystals are of a greenish yellow color they become rapidly trans-
parent as the light admitted is changed from blue to yellow. This necessitates
the use of crystals of increasingly thicker layers to bring out the dimmer
absorption bands. To a certain extent the crystal acts as a screen to absorb
the blue light which would cause fluorescence, nevertheless it was found
necessary to interpose orange or yellow screens of different densities to eliminate
fluorescence in a region where ordinarily it is at a maximum. At first the
colored glasses made by the Corning Glass Company were used as filters;

' Abstract of a paper presented at the Rochester meeting of the American Ph3r8ical Society,
October 26 and 27, 19 17.

* G. C. Stokes, Phil. Trans., 1852, p. 463.

* Morton and Bolton, Chem. News, pp. 47, 113. etc. (1873).

* J. Becquerel and Onnes. Leiden Communications, No. no, 1909.
» Nichols and Merritt, Phys. Rev.. Vol. 33, Nov., 191 1, p. 354.

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144 ^^^ AMERICAN PHYSICAL SOCIETY. [iSSS

later, solutions of potassium bichromate of varying concentration. It is
evident that the screening must be constantly changed when light from the
arc is used as a background for bands of increasingly longer wave-length.
It was thought that a beam of monochromatic light could be used as a back-
ground and thus obviate exciting the crystal to fluorescence, but a preliminary
study by Dr. D. T. Wilber and the writer indicated that such a beam of dis-
persed light could not be made of sufficient intensity to bring out the dimmer
bands.

The r61e played by these new bands in producing fluorescence is a minor
one, because they are excessively dim. No doubt if special crystals of great
size and exceptional clearness were formed the bands would appear stronger,
and more bands could be. discovered. The present study has added the
reversals of two complete groups to the original group mentioned. For some
reason the bands can not be traced as far into the red when the crystal is
cooled to -r 185**. It is evident that Stokes's law does not hold and it may
be that every fluorescence band has an absorption band of the same wave-
length.

Physical Laboratory o¥ Cornell University.
August 31. 191 7.

Complete Achromatization of a Two-Piece Lens.*
By G. W. Moffitt.

THE performance of many optical instruments depends largely upon the
degree of perfection realized in the achromatization of the thin two-
glass lenses which make up the optical system of the instrument. This because
of the condition that any system of lenses cannot be truly achromatic unless
the individual lenses of the system show complete achromatism. The im-
portance of a definite and complete statement of the conditions which must
be fulfilled by the glasses and by the radii of the lens faces is apparent.

Usually this subject is dealt with in terms of partial dispersions, dispersive
powers, etc. These, while depending upon the properties of the glasses for
their values, are not true constants of the glasses themselves. This is not the
case with the Hartmann dispersion constants which are constants of the
glasses only.

The conditions for complete achromatization of a two-glass thin lens may
be concisely and exactly expressed in terms of the Hartmann constants. The
equations show what must be the properties of the glasses if complete achro-
matization is to be possible, and, granting that the glasses fulfil these con-
ditions, what must be the relations existing between the radii of the lens
faces. It is hoped that the following discussion may be of value in the selec-
tion of glasses for the design of achromats and in the calculation of the radii
to be used.

> Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27. 191 7.

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Na*a^^] ^^^ AMERICAN PHYSICAL SOCIETY. 1 45

The formula for the focal length of two thin lenses in contact may be written :

j = (n-i)^ + (n'-i)3, (I)

where A = i/ri — i/r2, B = i/rj — l/r4, and n and n' are the indices of
refraction of the two glasses for the same wave-length. The Hartmann dis-
persion formula is

» = «• + (; J/.).' (2)

in which uq, c, /o, and a, are constants for any particular glass. The value
1.2 for a has been found to hold for practically all optical glasses. Combining
equations (i) and (2) gives

7 = ("'■' +(T^0^ + ("•'- '+(rri7F)^-

(3)

In order that/ be a constant for all values of wave-length the derivative with
respect to / of the right-hand member of the equation must be zero. That is,

- Aca , - Bc'a'

+ n TT^^f+i " o» (4)

which may be written

(/ - /o')*'+* - BcW
(/./o)^i = -A^ " ^ ^"^^'^'^'- ^5)

This is true when the derivative with respect to / is zero, or when

(/ - lo)(a' + !)-(/- V)(a + I) = o. (6)

This condition can be fulfilled only when

h = h't and a = a', (7)

These are the conditions the two glasses must satisfy if they are to be com-
bined to form a completely achromatized lens. We have here a simple,
direct statement to take the place of the clumsy one relating the partial dis-
persions of the two glasses.

In order to determine the conditions relating the radii of curvature sub-
stitute (7) in (5). This gives

Ac + Be' = o (8)

or, in terms of the radii.

\ri ft/ \r» u/

(9)

If the lens is to be cemented fi = rj, and the formula becomes

- + = -. (10)

r\ r? ft

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146

THE AMERICAN PHYSICAL SOCIETY.

Sbcomd

We have, therefore, a simple method of telling at a glance whether it is
possible to completely achromatize a lens of two given glasses. If the re-
spective values of the Hartmann dispersion constants, a and /©, are the same
for the two glasses it is possible to produce a lens showing complete achromat-
ism. The statement that the partial dispersions must be proportional through-
out the spectrum is now replaced by the simpler statement relating the Hart-
mann constants. When the conditions for complete achromatism are ful-
filled the ratio of the partial dispersions becomes the ratio of the constants c for
the two glasses.

An interesting special case is found when the constants c and c' are equal.
That is, when the dispersion curve of one of the glasses is of the same form as
that of the other, but displaced parallel to the axis of indices on the dispersion-
curve diagram. Equation (10) then becomes

fi = u.

(II)

The cemented lens would be of uniform thickness measured parallel to the
principal axis. Its surfaces might be plane parallel.

As a numerical example let it be required to design a cemented lens of focal
length = — 100 cm. One face of the converging element is to be plane.
The diverging element will, therefore, be meniscus in form. In a limited list
of glasses two are found having the following constants:

/o.

Dense flint

1.70583
1.58882

2.3185 X 10-*
2.2906 X 10-*

0.17254 X 10-*

Ordinary flint

0.10113 X 10-*

= , or fi = 2.410 fj,

It is interesting to note that the textbook from which the list of glasses was
taken gives an illustrative example in the design of an achromatic lens. The
glasses are selected according to custom. The ones thus selected could not
possibly form a lens having the excellence of one made from the glasses tabu-
lated above. This is at once apparent from an inspection of the tabulated
Hartmann constants. Substituting the above values of c in Equation (10)
gives

0.17254 ^ 007 141
ri rj

since ta = infinity.

To find the values of the radii, substitute in Equation (i), using the values
of no and no\ as these are apt to be known more accurately than any other pair
of values of the indices. This gives

— o.oifi = 0.70583(1 — 2.416) + 0.58882(2.416),

from which ri = — 42.31 cm., and fj = — 17.51 cm.

Using the listed values of the indices this gives /d = — 100. i cm., fy =
— 99.88 cm., and fo^" 99-79 cm. The slight progressive change in the

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No'a!^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 1 47

focal length is, no doubt, due to the discrepancy in the values of /o, which is a
little more than one per cent, in this case. Unless the values of /© agree very
closely it would be better to compute the radii in the usual way, using the
new conditions to determine which glasses will combine with the best results.
In general two glasses should be used whose values of the Hartmann con-
stant c differ as much as possible, thereby avoiding great differences in the
curvatures of the lens faces.
Saint Louis, Mo.,
October II. 191 7.

A Self-Recording Evaporometer.*
By Alexander McAdie.

THERE is at present no satisfactory instrument for recording evaporation
in the free air. The Weather Bureau after many years of experimenta-
tion now records evaporation at a number of stations, chiefly west of the
Mississippi River, by exposing in a metalic pan of 24 inches radius a water
surface the level of which is read by means of a hook gage working in a still-
well. By means of a micrometer screw head an apparent accuracy of reading
to the thousandth of an inch is obtained; but in reality since but one reading
is made in 24 hours, generally about 7 A.M., the true variation in level which
may be considerable in the interim, is unknown. The method is objectionable
in that gain or loss of the water content due to causes other than evaporation
are not separated from the evaporation proper. The entire outfit becomes
unserviceable when temperatures are near or below freezing; and in fact the
observer is required to store the outfit during the winter months. On the
other hand in the summer months the level of the water may vary because of
sudden showers and also because of mist or heavy dew. Plainly, evaporation
data based upon one observation in 24 hours are of doubtful value in any
serious purpose to correlate the rate of evaporation with temperature, humidity
and wind movement. At Blue Hill we have been using for some months a
weighing device carrying a nearly constant load of water. Evaporation is
thus continuously recorded and can be studied in connection with other con-
tinuous records such as temperature, wind velocity and direction, vapor
pressure, rainfall and air pressure. The instrument is sensitive enough to
show the increase due to a heavy dew or what might be called negative evapora-
tion occurring when the temperature of the water is lower than that of the
lower air and the vapor pressure near saturation. The records are sufficiently
detailed for the needs of plant physiologists, engineers and climatologists.
The time scale is one centimeter per hour. The evaporation is given in milli-
meters and at a temperature of 10° C. the weight of the evaporated water is

> Abstract of a paper presented at the Rochester meeting of the Physical Society, October
26 and 27. 1917.

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148 THE AMERICAN PHYSICAL SOCIETY.

approximately one gram for every 10 square centimeters of water exposed.
The maximum rate thus far recorded is i millimeter per hour, which occurred
on July 30, 1917, 2 to 3 P.M. and 3 to 4 P.M. At this time the temperature
was 309 A. (1130 N. or 96** F.), the percentage of saturation as determined by
an Assmann ventilated psychrometer varied from 37 to 48 per cent., the wind
270** (t. f., from the west) and the velocity 14 meters per second.

It is hardly necessary to add that these continuous records show plainly
the difference in the rate of evaporation between daylight and night hours
and also are of great value in connection with the study of land and sea breezes.
Blub Hill Observatory.

An Instrument for Continuously Recording the Percentage of Satur-
ation AND THE Weight of the Water Vapor Per Unit
Volume in the Free Air.*

By Alexander McAoib.

THE instrument consists of two metallic thermometers, one covered with
the usual clean linen constantly wet, thus making a dry and wet bulb
set. There is also mounted on the axis of rotation of the thermometers a
stretched bundle of hygroscopic hairs, slightly separated and very sensitive.
This records percentage of saturation for the particular temperature. Relative
humidity as ordinarily determined and recorded means nothing unless the
temperature of both air and water surface be given. It is a ratio with the
important terms suppressed. Yet we find nearly all meteorological bureaus
publishing long tables of relative humidity and these data are used by physi-
cians and others in their discussions of climatic influences. It would be better
to give the absolute humidity or weight of the vapor. In the present instru-
ment this is given by means of a record sheet on which is printed the saturation
weights for the various temperatures. One reads for any minute the percentage
of saturation multiplying by the indicated weight for saturation as shown by
the record. The instrument is a modification of an earlier one by the writer
called a saturation deficit recorder, since it is easy to ascertain the difference
between the weight present and the saturation weight.

Such an instrument, it is thought, will be of some service in sick rooms as
well as drying and curing rooms, since it gives a twenty-four-hour record of
temperature, dew-point, percentage of saturation and weight in grams per
cubic meter of the vapor.

Blue Hill Observatory of Harvard University.

* Abstract of a paper presented at the Rochester meeting of the Physical Society, October
26 and 27, 1917.

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No. 2. J

THE AMERICAN PHYSICAL SOCIETY.

149

^ THOTIOeOUPLlBl

ftoRoumrrz tubc

Measurement of Heat Conductivities of Metals at High
Temperatures.*

By Robert W. King.

IN the Physical Review for December, 191 5, the writer described an
attempt to realize experimentally what in theory is a very simple set of
conditions for the measurement of the heat conductivities of metals at high
temperatures. Recently the work has been definitely abandoned because of
other matters, but since the above article was published considerable time
has been devoted to improving the experimental arrangement, and the work
was carried far enough toward completion to seem to warrant a brief statement
regarding the final arrangement.

The chief alteration from the set-up originally used was the enclosing of
the specimen in a vacuum of such a quality as
to appreciably reduce the loss of heat by con-
vection. The accompanying figure shows the
arrangement of parts. The only feature need-
ing any comment is that used to make good
thermal contact between the heating coil and
specimen. This was satisfactorily accomplish-
ed by making the heating coil a helix through
which the specimen would easily slip, and then
sticking the two together with caementium.
This substance proved itself a very firm bond,
and up to 500° C. seems to be practically an
electrical insulator. At somewhat higher tem-
peratures it might t^ found to conduct to a
troublesome extent.

The pressure which the pump was able to
maintain in the space around the specimen was
never actually measured, but was sufficiently
low to reduce the convection loss to not more
than i/io of its value at atmospheric pres-
sure.

Of course', evaporation sets rather definite upper limits to the temperatures
at which various metals may be maintained in vacuo. The temperatures at
which the evaporation would become so rapid as to interfere with the measure-
ments of conductivity was determined in only a few cases. Tin and lead may
be run to their melting points, while copper showed an appreciable but not
serious evaporation at 400** C. Nickel can probably be run to 800® C.

The following table gives sample determinations on lead and copper, the
only metals for which any final measurements in vacuo were made. The
values of the specific heat given were taken from tables and are not to be

> Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 19 17.

TO FORE rmp

HftlCiL.

HcnTiNecuncNT lerds

HC TOCKETS FOR INSERTION
OF -nCRHOCOifPLE LEIIO&

-^H&VRPORPUHP.
Fig. 1.

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ISO

THE AMERICAN PHYSICAL SOCIETY,

rSBCOND

LSbribs.

considered as applying accurately to the samples used. The copper specimen

was a drawn wire 2.5 mm. in diameter, and the lead specimen was a "squirted**

wire 3.1 mm. in diameter. The periods of the temperature variation used

were 104 sec. and 235 sec.

Table.

Metml.

Distance Between
Tbermojunctions.

Tempermture.

Specific He«t.

Conductivity.

Lead

2.42 cm.

90'' C.
920

92^
210**
210^

.0312
.0313
.0313
.0334
.0334

.0826

.0825
.0824
.0806
.0812

Copper

3.23 cm.

76°

84°

362°

.0937
.0938
.0997
.0997

.914
.917
.897
.882

Western Electric Co.,
New York. N. Y.

Rotation of the Pulley in Melde's Experiment.*
By Arthur Tabbr Jones.

Introductory. — Let the string pass horizontally from the tuning fork to the
pulley and then downward to the load, and let the prongs of the fork vibrate
toward the pulley and away from it. Then if the fork vibrated slowly enough
the load would move up and down and the pulley would rotate back and forth —
both of them in phase with the prong to which the string Was attached. With
the frequencies actually used several observers' have noticed what looks like a
continuous rotation of the pulley, but with the exception of a small amount
of work' a few months ago no study of this rotation appears to have been
made. For a particular fork, string, and pulley [fork making 100 double
vib. per sec, string having linear density 2.24 mg./cm. and elastic modulus
50- 10* dynes, pulley having radius 1.35 cm. and moment of inertia 19.8 g.
cm. 'J this rotation is now studied.

The rotation may occur when the string is vibrating transversely or when
it is not so vibrating, and the rotation may carry the top of the pulley toward
the fork or away from it. Sometimes the rotation is as rapid as two or three
turns in a second, but more often is much slower — frequently two or three
turns in a minute. When the rotation carries the top of the pulley toward
the fork call it a "rotation toward the fork.*' Let // and V mean respectively

* Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 1917.

«J. S. Stokes. Physical Review. 30, p. 659, 1910. Raman and Apparao, Physical
Review. 32, p. 307, 1911. A. W. Porter, mentioned in Raman's paper.

•Jones and Phelps, Physical Review, (2). 10, p. 541, 1917.

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NS!"a?^^*] ^^^ AMERICAN PHYSICAL SOCIETY. I5I

either the horizontal and the vertical parts of the string or the lengths of those
parts.

Experimental, — With small loads and sufficiently great amplitudes of the
fork it seemed to be always possible to obtain a very irregular motion of the
string and simultaneously a very irregular rotation toward the fork.

When there was no transverse vibration of the string and when V was 20
cm. a sufficient amplitude of the fork caused rotation away from the fork for
loads ranging from about 50 g. to 250 g. and for all lengths of H which were
examined, viz., 10, 20, 30, 40, 50, 60, 70, 80, 100, 120, 150 cm. When V was
10 cm. or 30 cm. rotation away from the fork was observed when H had a
number of these lengths — in two cases with loads running up to 700 g. — but
when V was 40, 50, or 60 cm. this rotation was almost never observed. With
no transverse vibration of the string a steady rotation toward the fork occurred
for various lengths of V when H was 10, 20, or 30 cm. and the loads used
were small — 5 g. to 40 g.

When the string had a steady transverse vibration a series of observations
in which F = 10 cm. and il = 40 cm. gave rotation away from the fork for
the smaller amplitudes when there were three loops and what Melde called a
"secondary tension," i. e., a tension such that the transverse vibration of the
string had a frequency which was the same as that of the fork. In every one
of these cases and in no others a rotation away from the fork was observed.
In each case an increase in amplitude changed the sense of the rotation. A
similar series in which F » 20 cm. and /f = 40 cm. gave similar results,
except that the rotation away from the fork was observed in a very few other
cases.

Theoretical, — The steady rotation of the pulley is probably in reality dis-
continuous— the string losing its hold on the pulley and allowing it to slip at a
certain phase of the motion. This slipping would be most likely to occur
when the tension of the string was small and the acceleration of the pulley
large. If the minimum tension was reached when the top of the pulley was
approaching one end of its path the successive slips would give rise to a net
rotation toward that end of the path.

If we neglect the friction at the bearings of the pulley and assume that the
string does not slip on the pulley and that there is no transverse vibration of
the string, it is easy to set up the equation of motion for the system and to
find a particular simple harmonic solution. Studies of the amount of the
friction between the string and the pulley and between the pulley and its
bearings made possible a rough correction of this solution. If the maximum
difference which the solution indicates between the tensions in V and H is
greater than the maximum difference which experiment has shown can exist
without slipping, then at some phase of the motion there will be slipping and
probably a net rotation. Now thesolution shows that the ratio of the ampli-
tudes of the tensions in V and H is independent of H — which checks the
above experimental result for rotation away from the pulley. If the amplitude
of the tension in V comes out in any case greater than that of the amplitude in

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152 THE AMERICAN PHYSICAL SOCIETY. ^3S

H the least tension in the string will occur when the tension in V is a minimum.
If this is when the top of the pulley in its vibration is farthest from the fork
any slipping that may occur will probably cause a net rotation away from the
fork. Similar statements hold for other cases.

For ten cases in which rotation was observed the above calculations have
been made. In all but one of them this reasoning indicates that a net rotation
is to be expected, and for a majority of them the sense of rotation checks with
that found experimentally.

A more complete theory must take account of the phase shifts produced by
the friction at the bearings. The theory of the rotation when there is a trans-
verse vibration of the string is not yet treated.
Smith College,
October 9, 1917.

Comparative Accuracy of Whirled Psychrometer, Assmann Aspiration

PSYCHROMETER, POROUS CuP AtMOMETERS, HaIR HyGROGRAPHS, PiCHE

evaporimeter saturation deficit recorder, open water

Surface Evaporimeter, and Dry and Wet Bulb

Thermometers.^

By Alexander McAdie.

ATTENTION is called to the variety of names for instruments all essentially
designed to indicate percentage of saturation of a mixture of atmospheric
air and water vapor. It would be an advantage to group under one name all
instruments used in studying evaporation and condensation in the free air.
Note also that while the thermodynamics of the atmosphere has been more or
less successfully studied, the hydrodynamics has been hurried over perhaps
because of the absence of reliable data. In the various psychro meters (the
word means a measure of the chilling due to evaporation) molecular energy
change is shown as a fall in temperature. Various corrections are necessary
and the method takes no account of nucleation. The sling psychrometer
which is used as a standard of reference is subject to error in manipulation;
and the writer is of the opinion that some other instrument should be used for
this purpose. The whirled psychrometer as used officially is better, but unless
a known volume of air and vapor mixture is used and some correction applied
for the effect of centrifugal force, the readings are vitiated. An improvement
has been made at Blue Hill by introducing a counter giving the number of
revolutions per unit of time. This practically standardizes the velocity of
air passing over the bulbs. All official humidity data thus far published
need correction for personal error. The porous cup atmometer (Dr. Burton
E. Livingston) is a simple device for measuring evaporation in cubic centi-
meters. It needs a recording device (one was added here) and gives records

* Abstract of a paper presented at the Rochester meeting of the Physical Society. October
26 and 27, 1917.

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Na*2^'*] ^^^ AMERICAN PHYSICAL SOCIETY. 1 53

more consistent than the psychrometers. A black porous cup as well as a
white have been used and as might be anticipated the evaporation is much
larger whenever there is free absorption and radiation of heat. We are using
in another atmometer wood alcohol in place of water to obtain a ratio which
will serve in the winter months when water would freeze. The stationary dry
and wet bulb is not satisfactory.

The data now extending over several months are designed for use in various
ways but more particularly in an effort to evaluate a coefficient best repre-
senting the effect of the flow of air. While the temperature of the water, and
of the air, percentage of saturation, atmospheric pressure and nucleation must
be considered in any evaporation formula, at present the most promising line
of investigation is the determination of the rapidity of removal of the water
vapor; and this is effected chiefly by wind velocity and direction. Evidently
pure diffusion effects are rare in nature and convection or mechanical re-
moval is of chief importance. The wind effect is given by the last term in
the equation

E = C(e, -fd.pXi +aV).
Blue Hill Observatory of Harvard University.

Bohr's Atom, Zeeman's Effect and the Magnetic Properties of the

Elements.*

By Jakob Kunz.

ACCORDING to Bohr's theory the hydrogen atom consists of a nucleus
with the elementary positive charge, surrounded by an electron in
rotation. The electron is allowed to rotate in definite stationary orbits in
which it does not radiate. Radiation occurs only, when the electron, moving
from the outside toward the center, jumps from one stationary orbit to the
next one. The strongest evidence in favor of this atom is the extraordinary
coincidence of the calculated with the observed constant in the radiation
formula of Rydberg. The laws of electrostatics are assumed to hold within
the atom, while the laws of Maxwell's electromagnetic radiation are denied.
The atom of hydrogen has a resultant moment of magnetism, and should
therefore be paramagnetic. When 2 atoms combine to form a molecule, the
resultant system must be as stable as possible. Among the three possible con-
figurations the first seems to be more stable and is paramagnetic, the second,
having no resultant moment, is diamagnetic, and the third of Bohr is para-
magnetic. The experimental results seem to be contradictory; Quincke gave
the positive value 0.008 at i atm. per c.c. while Bernstein found the dia-
magnetic value — 0.005 and Bloudlot — 0.034. This constant ought to be de-
termined again. Helium in Bohr's theory possesses a remaining magnetic
moment, giving rise to paramagnetism, but helium is decidedly diamagnetic.

> Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 1917.

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154 ^^^ AMERICAN PHYSICAL SOCIETY. [iSSS

Strange difficulties occur if we try to explain the Zeeman phenomenon on
the basis of Bohr's hypothesis. H. A. Lorentz in his classical explanation of
the simple Zeeman effect assumes a quasi-elastic force as a centripetal force

/•r = 4ir*nVw.

and deduces by means of the ordinary magnetic action of a charge in motion
the longitudinal and the transversal effect with the result:

e (n« — ni)2TC
m " H •

a relation which has at first yielded an accurate value of e/m. In Bohr's
theory, on the contrary, the centripetal force is equal to eei/r* for the non-
radiating orbits. The fact that the magnetic field produces the Zeeman
effect only in the presence of ionization, speaks in favor of Bohr's theory, and
requires that the action only takes place when the electron is moving from one
orbit to another one. For this transition a new assumption has to be intro-
duced in order to account for the simple and for the more complicated effects.
A certain compromise between Bohr's and Lorentz's theories seems to be
necessary. So far the assumptions in both theories regarding the centripetal
force are contradictory; yet Lorentz's theory gives the right value of e/m and
the right kind of polarization, and Bohr's theory gives the right value of
Rydberg's constant and very approximately the law of the series lines.
University of Illinois,
Urbana. III.

The Influence of Temperature Upon the Crushing Strength
OF A Dental Amalgam. *

By Arthur W. Gray and Paris T. Carlisle, 4th.

WHILE dental amalgams are always used at the temperature of the
human mouth, or approximately 37. 5** C, strength tests of these
important filling materials appear to have been made only at room tempera-
tures. The authors have therefore determined the influence of temperatures
between 25® and 95 ** C. upon the crushing strength of an amalgam prepared
under carefully standardized conditions.

The need for such standardization was made evident by a series of pre-
liminary experiments which showed the effect of variations in such factors as
the proportions of mercury and alloy used in mixing the amalgam, the time
devoted to triturating the mix, the temperature of trituration, the pressure
under which the amalgam is molded into test cylinders, the time that this
condensing pressure is maintained, the height of the test cylinder, the time that
elapses between the making and the crushing of the cylinder, the temperature
at which it is stored during this interval, and the rate at which the crushing
load is applied during the testing.

* Abstract of a paper presented at the Rochester meeting of the American Physical Society.
October 26 and 27, 1917.

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Vol. XL!
Naa. J

THE AMERICAN PHYSICAL SOCIETY.

155

^Imo

'Wm

2boq

•\

looo

•I

«MM r

—

»•

tor

ao>

Fig. 1.

In all the tests forming the subject of this communication the amalgam
was prepared from a "balanced" alloy of the highest grade, that is to say,
an alloy in which the proportions of the constituent metals are so adjusted that
the expansion during hardening caused by the silver is almost, but not quite,
neutralized by the contraction caused
by the tin. This alloy contained ap-
proximately 68 per cent, silver, 26 per
cent, tin, 5 per cent, copper, and i per
cent. zinc. It was in the form of fine
filings, just as furnished to the dentist.
A weighed amount was incorporated
with 1.60 times its mass of purified
mercury by thoroughly triturating in a
glass mortar for four minutes. The
resulting smooth, plastic amalgam was
quickly rolled into a ball and dropped
into a thick- walled steel cylinder with
a polished interior and an accurately
fitting piston, upon which a load of
400 kg. was maintained for 8 minutes.
This squeezed out the excess of mer-
cury and condensed the amalgam, pro-
ducing a cylinder 10.04 n^"^« in diameter by 11.5 mm. high, 40 per cent, of its
mass being mercury. Cylinders prepared in this way were immediately placed
in an incubator kept at 37. 5** C, where they remained for several days before
crushing, thus insuring completion of the hardening process.

The crushing tests were made in a 9,000 kg. Olsen testing machine which
was designed for operation by hand. The authors modified this by the addi-
tion of a motor drive which applied the load with regularity, thus permitting
the beam to be kept balanced to a nicety right up to the moment of failure;
and by electric heaters for bringing the specimen under test to the desired
temperature, which was determined by a suitably placed thermoelement.
An additional thermoelement enabled temperature gradients within the
heated region surrounding the cylinder to be adjusted to negligible values.

The chart represents the individual results of crushing specimens at tempera-
tures distributed fairly uniformly over the entire range. All the determinations
made on three separate days are included. The abscissa of a point represents
the temperature of a cylinder at the time it was being crushed; the ordinate
the force in kilograms- weight sustained by the cylinder (which was 10.04 ni"^*
in diameter) at the instant of failure. All of these points lie close to a curve
which shows that with rising temperature the crushing strength of an amalgam
prepared as described decreases somewhat faster than linearly from 5,300
kg. wt./cm.' at 25° to 4,050 at 45° and 2,550 at 65°. Soon after passing 70°
the strength takes a sudden plunge and drops below 350 kg. wt./cm.' before
80** is reached. From this temperature up to 95® there is but little change

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156 THE AMERICAN PHYSICAL SOCIETY. [i

in strength, none of the cylinders having broken under stresses less than 260
kg. wt./cm.'. At 37.5** the crushing strength was found to be 4,550 kg. wt./
cm.', or nearly 65,000 lb. wt./in.'.

The closeness with which all the points plotted (no observations in this
three-day series have been omitted) follow a smooth curve shows the uni-
formity with which a dental amalgam can be prepared, and also the precision
with which crushing tests can be made, provided proper precautions be taken.

The transition indicated by the rapid drop in strength between 70** and 75**
has also been revealed by other methods. A more detailed account of the
phenomena that occur in this temperature region will be presented in a future
communication.

Physical Research Laboratory,
The L. D. Caulk Company,
MiLFORD, Delaware.

A New Formula for the Temperature Variation of the Specific Heat

OF Hydrogen.*

By Edwin C. Kbmble.

NUMEROUS attempts to account for the rapid decrease in the specific
heat of hydrogen at low temperatures on the basis of the quantum
theory have thus far failed to yield a formula which is satisfactory from both
the experimental and theoretical points of view. Several of the more promising
theoretical formulas are open to objection in that they assume that the rota-
tional specific heat of an assemblage of molecules each of which has two rota-
tional degrees of freedom is twice that of a similar assemblage in which each
molecule has but one rotational degree of freedom. The more recent work of

Fig. 1.
The rotational specific heat of hydrogen. The experimental points plotted are the ob-
served values of C, (reduced to the ideal gas condition in the case of the low temperature
observations of Eucken, and Scheel and Heuse) minus 2.98, the value of Cv for monatomic
gas.

Planck' on the application of the quantum theory directly to systems having
more than one degree of freedom avoids this assumption, but the formula

1 Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 191 7.

« M. Planck. Verb. d. D. Phys. Gcs.. 17. PP- 407 and 438, 1915.

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NoTa^^'] r^^ AMERICAN PHYSICAL SOCIETY. 1 57

which he derives is not in agreement with the experimental facts. (See
figure.)

Planck's discussion is based on his later form of the quantum theory in
which the representative points of the various molecules in the state-space of
statistical mechanics are assumed to be uniformly distributed throughout each
individual region element. This form of the quantum theory can hardly be
considered tenable at present in view of the observations of v. Bahr* (recently
confirmed by Brinsmade and Kemble*) concerning the structure of the infra-
red absorption bands of gases.

The writer has therefore adapted the methods used by Planck in the paper
cited above to the older form of the quantum theory in which the representa-
tive points of the molecules are assumed to be confined to the bounding surfaces
of the region elements. In order to bring the theory into complete harmony
with the observed structure of the infra-red absorption bands of HCl and at
the same time to derive a formula for the variation of the specific heat of a
diatomic gas which would reproduce the observed values in the case of hydro-
gen, it was necessary to introduce the zero-point energy hypothesis in the
form in which it occurs in the Bohr theory of atomic structure. This is done
by excluding zero from the list of the possible values of the energy of rotation.
It was also found to be necessary to take into account the increase in the
moment of inertia of the molecules due to expansion under the influence of
centrifugal force at the higher angular velocities. As a first approximation
in correcting for the variation in the moment of inertia, it was assumed that
the restoring force brought into play by a relative displacement of the nuclei
is a linear function of the displacement.

The resulting formula for the rotational specific heat of a diatomic gas in
calories per mol is

Here

Oi - i (2» + Oe—"",

0. = Z (2» + I )«»«-'-"'.

11=1

V is the frequency of vibration of the atoms along their line of centers; yn is
the ratio of the frequency of rotation to the frequency of vibration, which

» E. V. Bahr. Phil. Mag., 28, p. 71. 1914.

« J. B. Brinsmade and E. C. Kemble, Proc. Nat. Acad. Sci., 3. PP- 420-425, June. 1917.

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158 THE AMERICAN PHYSICAL SOCIETY. liSi»

may be found by graphical solution of the equation
(I - yn') nh

Lo is the moment of inertia for zero angular velocity and / is the mechanical
equivalent of heat. The other symbols have their usual meanings.

Giving Lo the value 2.0 X io~*^ gm. cm.' and v the value 1.2 X 10^* sec."^,
we obtain the curve A of the accompanying figure. The curve B shows the
theoretical specific heat for rigid molecules (v = 00 ) with the same value of Lq.

It is perhaps desirable to emphasize the fact that, though the above formula
contains the frequency of vibration, it gives the rotational specific heat only.
At temperatures above 500** or 600® the vibrational specific heat also must
be taken into account.
BiJFFALO, New York.

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nSJ;-,^*] new books. 159

NEW BOOKS.

Practical Pyrometry. The Theory, Calibration and Use of Instruments for

the Measurement of High Temperatures. By Ervin S. Ferry, Glenn A.

Shook, and Jacob R. Collins. New York City, John Wiley & Sons.

Pp. vii + 143, si X 8. Cloth, ?i.50.

The present book was written for three classes of readers — "college students,
technically trained men who deal with processes requiring high temperature
measurements, and less trained observers who may make the measurements."
The book is practically a synopsis of "Measurement of high temperatures"
by Burgess and Le Chatelier, Wiley, 191 2, but is presented in different form
especially suitable for the class room, as minor details are omitted, and in
several places the text is illustrated by practical problems. Also at the end
of each chapter are several experiments, fourteen in all, which are prepared in
sufficient detail for the ordinary student, and which cover the field of pyrometry
very satisfactorily. The chapters are headed as follows: (i) Standard Temper-
ature Scales; (2) Resistance Pyrometry; (3) Thermoelectric Pyrometry;
(4) Radiation Pjrometry; (5) Optical Pyrometry. The text is well illustrated
and several new American instruments are shown. A few comments may be
made on points of minor detail. In the preface it is stated that "the day is
already past when foundrymen and steel workers depend upon the eye to
judge the temperatures of their product in the various stages of its heat treat-
ment, when makers of ceramic products depend upon the indication of fusible
cones," etc. One needs but visit industrial plants to realize this Utopian
condition is far from being fulfilled. Probably nine out of ten ceramic in-
dustries employ fusible cones or similar means of temperature measurement,
and many of the leading ceramic engineers of this country advocate their use
in preference to more scientific instruments. A point in history is brought
out on page 3. Bolton ("Evolution of the thermometer") states that Celsius
assigned the number 100 to the temperature of melting ice and o to the tempera-
ture of steam. The present assignment of numerals was made by Christ in
1743. Also, according to Bolton, Fahrenheit did not assign the number 212
to the boiling point of water as here stated. The method of correcting for
lead resistance of the resistance thermometer, page 21, is crude. Even for
the most elementary students, the bridge should be arranged as in Fig. 7.
A student will be interested in solving the mathematics of the Wheatstone
bridge in order to see why the arrangement in Fig. 7 compensates properly.
Sulphur should not be boiled in an aluminum tube as illustrated in Fig. 15.
With such a tube electrically heated to the top as shown in the figure, the
vapor can be superheated to almost any value. The heating coil should be

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l60 NEW BOOKS.

much shorter, and for accurate work glass tubes are to be preferred. The
geometrical optics of Fig. 44 is incorrect. Prism M, Fig. 62, should be turned
through 180**. Recent work indicates that Ci is more nearly equal to 14,350
than 14,500 as given on page 91. On page 140 it is stated that "a person of
no training can get better results with a radiation pyrometer than with an
optical pyrometer." This is contrary to experience. Published investigation
has shown that persons who are totally unfamiliar with the optical pyrometer
can set to within 5® or 10** C. To obtain such accuracy with a radiation pyrom-
eter requires a great amount of experience and a consideration of many
factors which are not mentioned in any text-book. Table 3, page 143, giving
log tan' f^ is unnecessary. In plotting data for the Wanner pyrometer, it is
more convenient to use log tan 1^ versus ijT, The demand for engineers
having some knowledge of practical pyrometry is becoming greater every year.
Many schools are offering courses in this subject and the day is near when
pyrometry will be a required course for engineers and chembts. The present
book should serve as a suitable text for a junior or senior course covering one
semester.

P. D. F.

Recreations in Mathematics, By H. E. Licks. New York: D. Van Nostrand

Co., 1917. Pp. V + 155. Price, $1.25.

This book is to entertain and to arouse in students and amateurs an interest
in mathematics. In the few pages devoted to mechanics and physics, the
teaching of mechanics by the physicist is criticized and the following statement
made in apparent seriousness: "Surely the subjects of heat, light, sound and
electricity furnish a sufficient field for the physicist, without encroaching on the
topic of mechanics, which properly belongs to the engineer."

F. B.

The Principles of Electric Wave Telegraphy and Telephony. By J. A. Fleming.

New York: Longmans, Green and Co., 1916. Pp. xvi + 911. Price, $10.00.

The original book of 671 pages (first edition, 1906), expanded in a second
edition (i 910), is now further extended, the total expansion of 240 pages being
due in part to the re-writing of portions of the work and to additions in the
several chapters, and in part to added chapters on Transmission of Radiotele-
graphic Waves over the Earth and on Radiotelephony. As in the earlier
editions, it has been the aim of the author to deal chiefly with principles and
not to devote much space to details of apparatus. Between the covers of the
book is an immense amount of valuable material.

F B.

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Second Series. March, igi8 Vol. XI., No, 3

THE

PHYSICAL REVIEW.

THE MAGNETIZATION OF IRON IN THE ABSENCE OF

HYSTERESIS.

By Winthrop R. Wright.

ANY investigation of the magnetic properties of ferro-magnetic sub-
stances is complicated by the presence of hysteresis. Even the
curve, usually known as the magnetization curve, is, as Steinmetz^ points
out, but one side of an unsymmetrical hysteresis loop, and differs from
any other loop only in passing through the origin. The advantages to
be gained in suppressing hysteresis are evident. Without hysteresis,
the magnetization becomes a single-valued function of the magnfetizing
field and it is feasible to attempt an equation connecting them. Again,
the true effect of the temperature upon magnetization may be investi-
gated, for the effect of temperature upon hysteresis is so marked that
its true effect upon magnetization may be entirely masked, especially in
the case of weak fields.

In general, two methods have been proposed for suppressing hysteresis,
mechanical shocks or vibrations and an alternating magnetic field, either
transverse or longitudinal. Ewing^ employed mechanical vibrations
while Finzi,* Ashworth,* and Steinhaus and Gumlich* used alternating
fields superposed upon the magnetizing field. Ashworth alone investi-
gated the change of magnetization with the temperature, but his results,
while free from hysteresis, were distorted by the alternating field which
was present in the specimen. Steinhaus and Gumlich avoided this
distortion by reducing the alternating field to zero before observing the
magnetization produced in the specimen due to the applied magnetizing
field.

» Steinmetz, Theory and Calculation of Electric Circuits, p. 50.
« Ewing, Phil. Trans., p. 564. 1885.
*Finzi, Electrician, 26, 672, 1891.

* Ashworth. Phil. Mag., 27, 357, 1914.

* Steinhaus and Gumlich, Ber. d. Deut. Phys. Ges.. 17, 369, 1915.

161

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l62

WINTHROP R. WRIGHT.

fSECONO

LSbkibs.

The present work is, in a sense, a repetition of Ashworth's work on
iron, using the method of Steinhaus and Gumlich. Five specimens were
prepared from samples furnished through the kindness of Professor E. D.
Campbell. These included three hypo-eutectoid steels, a very pure basic
open-hearth steel, and an ingot iron. Their composition was furnished
with them and appears in Table I. These five form a series of steels
with decreasing carbon content whose last member approximates pure
iron. The specimens were made in the form of ellipsoids of revolution,
20 cm. long and 0.47 cm. in diameter.

Table I.

Composition of Steels in Per Cent,

Steel.

1 ^*

Mn.

Si.

Cu.

H57

0.57

0.11

0.010

0.17

0.020

H41

0.41

0.08

0.012

0.19

0.016

H35

0.35

0.08

0.009

0.18

0.024

\ 0.04

0.10

0.007

0.029

INI

0.015

0.016

0.005

0.045

0.03

Apparai

rus.

A magnetometer was used for observing the magnetization of the
specimen. Two identically wound solenoids were mounted east and
west with the principal needle of the magnetometer on their common
axis and between them. These solenoids were made of brass tubes,
4 cm. in diameter, with a layer, 60 cm. long, of No. 20 enamelled copper
wire wound on them. They made available magnetizing fields up to
100 gauss in strength. The one solenoid, which was used for mag-
netizing the specimen, had a second layer wound on it, hy which the
required alternating field could be produced. Each solenoid was mounted
in a copper tank which was water cooled. The second solenoid was used
to balance the first and could be shifted longitudinally.

The magnetometer was of the astatic type devised by Kohh-ausch
and Holborn.^ The moving system consisted of two sets of two needles
each, 2.0 cm. long and 0.09 cm. in diameter, mounted at the ends of a
glass rod, 70 cm. long and o.i cm. in diameter, and was suspended by
a quartz fiber, 40 cm. long and 30 microns in diameter. Though the
upper needles were slightly stronger, the instrument possessed a steady
zero point and was sufficiently sensitive, a field of 0.00005 gauss causing
a scale deflection of 2 nmi. with a scale distance of 1.5 m. As the mag-
netometer was to be used in a null method, these were the only require-

» Kohlrausch and Holborn, Ann, d. Phys., lo, 287, 1903.

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Na*i^'*] MAGNETIZATION OF IRON. 1 63

ments to be met and it was not necessary to ascertain to what extent the
needle systems differed.

The magnetization produced in the specimen was measured by means
of a coil, mounted on the side of the magnetometer opposite to the speci-
men and at an equal distance. By passing a suitable current through
this coil, the deflection produced by the magnetization of the specimen
was balanced and the needles of the magnetometer were brought back
to their zero position, which was indicated by the familiar lamp, slit,
mirror, and scale device. The magnetization of the specimen could then
be calculated in terms of the current and the constants of the coil and
the ellipsoid. The coil was made by winding No. 20 enamelled copper
wire upon a core of Keene cement, a disc 17.3 cm. in diameter and 3.1
cm. thick. A slot was cut on the rim of the disc and a single layer of
wire wound on it. This layer was covered with more cement and a new
surface was cut after the cement had hardened. On this new surface, a
second layer was wound and the process was repeated until five layers
had been put on, sepa**ated from each other by from two to four milli-
meters of cement. This method of assembling the coil permitted the
accurate measurement of the dimensions of each layer and the field of
the coil could be calculated from the formula for a single layer.

The data taken for a given magnetization curve involved the deter-
mination of the corresponding values of two currents, that through the
magnetizing solenoid and that through the coil. This method for deter-
mining the magnetization seems to have much in its favor. It is inde-
pendent of changes in the sensitivity of the indicating instrument and
in the strength of the earth's field, even if the magnet systems are not
exactly equal and are not accurately placed in the magnetic meridian.
It replaces readings of a telescope and scale with those of a second
ammeter, one having to be read for the magnetizing current, and thus
affords two observations of the same cype. It would seem that there is
no difference in the rapidity with which observations can be taken since
this depends so largely on the period and damping of the magnetometer
in any method.

A 60-cycle alternating current, regulated by means of a water rheostat,
was used in the outer winding of the magnetizing solenoid to produce
the requisite alternating field. This rheostat had two electrodes of
copper whose area was about 150 cm.^ and, by lifting the movable
electrode, the current could be reduced from about ten amperes to a
few hundredths of an ampere before the final break occurred. It may
be questioned whether such a device for reducing the current is legitimate,
since it does involve a break in the current, though not until the latter

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164 WINTHROP R. WRIGHT. [ISwk!

is small. By this means, however, the same magnetization was produced
in the specimen for a given field, though the initial state was varied as
widely as possible, and this should be a conclusive test for the absence of
hysteresis. An objection to the rheostat may also be based upon its
rectifying action due to inequality in the areas of the electrodes as the
movable one is removed from the water. It was found, however, that
the magnetization did not depend upon the direction of the rectified
current through the solenoid. Evidently, when the alternating current
became small enough to be neglected, the rectified portion was also
neglible.

The specimen was heated by means of an electrical heater which fitted
snugly within the brass tube of the magnetizing solenoid. The heating
wires were of 25 per cent, nickel-steel and ran longitudinally, being held
in place by alundum cement at equal spaces around the heating chamber.
The latter was 60 cm. long and i cm. in diameter. A longitudinal wind-
ing produced no magnetic field within the heating space and secured a
more uniform temperature throughout that part in which the specimen
lay. The necessary thermal insulation was secured by two concentric
quartz tubes, separated by asbestos, which slipped over the hollow alun-
dum cylinder in which the wires were set. The heater was slightly
magnetic below 500° C. but separate observations were taken to correct
for this.

The ends of the magnetizing solenoid were provided with brass cover
plates, made oil tight with asbestos gaskets. Through one plate passed a
brass plug in which were mounted the tubes for a platinum resistance
thermometer. The thermometer wire with its leads was stretched in a
quartz tube, i mm. in bore, which was then bent double. The wire was
long enough to traverse the length of the specimen twice, the latter being
supported by the same tube which contained the wire. The com-
pensating leads were mounted in a shorter piece of the same tubing.
With such a thermometer the average temperature throughout the
specimen was indicated.

Experimental Results.

The usual procedure with a specimen began with heating it for about
an hour and a half in the neighborhood of the Curie point in order to
anneal the specimen and to secure thermal equilibrium in the heater,
solenoid, and oil bath. The temperature was then reduced slowly, step
by step, and magnetization curves were taken at suitable intervals.
The greatest change in magnetization occurred within the first one
hundred degrees below the Curie point and from four to five hours were

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Vol. XI 1
NO..J. J

MAGNETIZATION OF IRON.

165

allowed for this interval. About twice this time was taken for the
specimen to cool completely to room temperature. Measurements were
taken during cooling that they might be more free from irregularities
due to previous thermal and mechanical treatment of the steels.

The magnetization curves obtained for specimen H35, the softest of
the hypo-eutectoid steels, appear in Fig. i. These are typical of the

isothermals obtained for all five steels. The abnormally high suscepti-
bility for low magnetizing fields, which seems to be the most pronounced
characteristic of anhysteretic curves, persists up to the immediate
neighborhood of the transformation point. The curves are uniformly
concave to the ff-axis and do not intersect each other except at the
origin,* though the curves are not conclusive on this latter point. The
true magnetizing field is obtained as the difference between the applied
field and the demagnetizing field due to the ellipsoid itself and this
results in relatively great uncertainty in the value of H when the field
is weak. In the case of the softest of the steels, this difference was less
than the error in the observations for applied fields as large as ten gauss
and intensities of magnetization as high as nine hundred.

If, as seems likely, any given isothermal lies wholly beneath any other
which corresponds to a lower temperature than the former, the mag-
netization for a given field decreases with a rise in the temperature. In
the absence of hysteresis we do not find the anomaly common to ordinary
magnetization curves, namely, that the magnetization for a given field

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1 66

WINTHROP R, WRIGHT.

[Sbgono
Sbkibs.

may either increase or decrease with rise of temperature, depending upon
whether the field is weak or strong. In Fig. 2 are found the magnetiza-
tion curves for all five specimens for a constant field of sixty gauss. It
is evident that the curve for specimen INI, which is most nearly free
from carbon, is by far the most regular. The effect of carbon is to pro-
duce two irregularities, the one just above 700** C. and the other in the
neighborhood of 200° C. The former corresponds to the precipitation
of the carbides which occurs at the eutectoid point. The latter is due to
the magnetic transformation of the cementite in the steel. The actual
shape of the curves at this lower transformation point is not definitely
indicated by the data but must be somewhat as shown by the dotted
portions. The transformation point certainly lies between 180** C. and
220° C. which agrees with Honda's^ work on cementite. For the purpose
of the present investigation, a more exact knowledge of the curves in
this region was not necessary.

Equations for Anhysteretic Curves.

Examination of the curves in Fig. i shows them to be smooth and
regular, whether they are for iron or steel. The curves have at least
three distinguishing characteristics, a uniform concavity to the H-axis,
an infinite slope at the origin, and a finite limit to the ordinate as the
abscissa increases indefinitely. The curves, of course, furnish no con-

> Honda and Takagi, Journ. Iron and Steel Inst.. 92, 181, 1915.

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Na^*3^^*] MAGNETIZATION OF IRON. 1 6/

elusive proof of the third characteristic but they indicate nothing con-
trary to this, the ordinarily accepted view. The appearance of the
isothermals suggests the possibility of obtaining an equation for a given
curve. But Fig. 2 shows clearly that to introduce the temperature as a
variable in the equations will be feasible only in the case of carbon-free
iron.

The only equation yet proposed for anhysteretic isothermals is empiri-
cal and due to Frohlich. Finzi and Ashworth (loc. cit.) have both
attempted to apply this equation to their experimental results. Stein-
metz^ has shown that the same equation may be fitted to limited ranges
of the ordinary magnetization curve and expresses his opinion that it
should probably fit an anhysteretic curve throughout its whole extent.
The equation is based upon the assumption that the susceptibility is
proportional to the amount by which the magnetization may yet be
increased. Expressed in symbols, this becomes

^ = K{Io - D,

where Jo is the maximum intensity of magnetization and K a constant.
This may be transformed into the more useful form

"ii-i;)--'

where -4 is a new constant. This equation is hyperbolic in- H and /,
but is linear in H and H/I. In Fig. 3, the data of Fig. i are plotted
with this second pair of variables as coordinates and it may be seen
to what extent the linear relation holds. Where a straight line fails to
fit the points, a continuation, either straight or curved, has been made
which will do so, in order that there may be less confusion as to corre-
sponding lines and points. The continuations have been indicated by
the dotted lines. In none of the isothermals does the equation seem to
hold for fields much less than twenty gauss and, in two, at least, there is
an indication that the relation is not linear through the upper range of
available fields. This failure of the equation to hold may be considered
from another viewpoint. If we form the derivative from the equation,
we obtain

* Steinmetz, Theory and Calculation of Electric Circuits, p. 54.

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1 68

WINTHROP R. WRIGHT.

tSsCOMD

LSbriks.

At the origin, this becomes

1-) =-

\dHfo A

and the condition for infinite slope can be fulfilled only by making A
vanish, which would reduce the hyperbola to two straight lines.

./?

Ofti

^^^^^

.^-'

-"^^

0 M^Nt

mztN0 4

0 nci

.o i

■ io — '

Fig. 3.

The results indicate that Frohlich's equation does not fit the an-
hysteretic isothermal magnetization curves, though it may be made to
fit a limited range of any curve and may be used as an approximation
for the curve. Ashworth^ not only accepts Frdhlich's equation for a
given isothermal but attempts to use it for the whole family by intro-
ducing the temperature as a third variable. He does this from analogy
with Van der Waal's equation and writes Frohlich's equation in the form

<-7J = «-.

where i? is a constant and T the absolute temperature. For H constant,
this equation is hyperbolic in T and /. But the hyperbola of the equa-
tion is convex toward the T-axis whereas the curves of Fig. 3 are concave.
This difficulty might be met by assuming that Jo is a function of the
temperature but, since it is an unknown function, it does not seem that
Ashworth's equation is a step in advance of that of Frohlich.

* Ashworth, loc. cit.; also Phil. Mag., ZZ^ 349, 191 7.

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)j^3'!^^] magnetization of iron. 1 69

Summary.

1. A null method for using the magnetometer has been described.

2. From a series of steels with decreasing carbon content, the an-
hysteretic magnetization curves for iron have been approximated and
certain characteristics of these curves have been pointed out.

3. It has been shown that the equation proposed by Frohlich does not
fit the anhysteretic isothermal magnetization curves and that the equa-
tion, even when modified as Ashworth proposes, does not give the
magnetization properly related to the temperature.

In conclusion, the writer wishes to acknowledge his indebtedness to
the late Professor K. E. Guthe, at whose suggestion the work was under-
taken, and to the members of the department of physics of the University
of Michigan.

University of Michigan.
May, 1917.

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I70 r. c HEBB. [IJS^

THE IONIZATION POTENTIAL OF MERCURY VAPOR AND

THE PRODUCTION OF THE COMPLETE SPECTRUM

OF THIS ELEMENT.

By T. C. Hebb.

THE results of Davis and Goucher^ and of Bishops seem to prove the
correctness of the suggestion of Van der BijP that the apparent
ionization of mercury vapor when bombarded with electrons possessing a
velocity of 4.9 volts, as observed by Franck and Hertz* and by Newman,*
was due to the photo-electric action of the radiation X = 2536.7 acting
on the receiving plate of the ionization chamber. Their results are also
in harmony with those obtained by McLennan and Henderson* and
also by Tate,^ viz., that the ionization potential of mercury vapor is
10.3 volts.

Neither the above suggestion nor the experimental results quoted,
however, explain the results obtained by the writer:* viz., that the
complete spectrum of mercury vapor appeared at 4.9 volts, and that an
arc struck at that voltage. Millikan,^ however, has suggested that the
same radiation X = 2536.7 acts photo-electrically on the mercury vapor
and produces the necessary ionization. If this should prove to be true
then the fact will cast some light on the photo-electric action.

If, however, it should be found that photo-electric action is not suffi-
cient to explain the arc at 4.9 volts, it would seem to be necessary to
assume that under certain conditions mercury vapor can be ionized by
collision with electrons moving with a velocity of 4.9 volts.

The experiments reported in this paper were undertaken in the hope

that the above question might be decided. The results obtained will

be dealt with under the following five heads: (i) Arcing voltages; (2)

Current-potential Relations; (3) Stria tions; (4) Ionization Potential

and (5) Photo-electric Action.

» Davis and Goucher, Phys. Rev., Vol. 10. p. loi, Aug.. 1917.
« Bishop, Phys. Rev.. Vol. 10, p. 244, Sept., 191 7.
•Van der Bijl, Phys. Rev.. Vol. 9. p. i73» Feb.. 1917.

* Franck and Hertz, Deutsch. Phys. Gessell. Verh., Vol. 11, p. 512, 1914.

• Newman, Phil. Mag., Vol. 28, p. 753, Nov., 19 14.

* McLennan and Henderson, Proc. Roy. Soc., A. Vol. 91, 191 5.
» Tate, Phys. Rev., Vol. 7. P- 686, June, 1916.

■ Hebb, Phys. Rev.. Vol. 9. p. 371, May, 191 7.

• Millikan, Phys. Rev.. Vo!. 9, p. 378. May, 191 7-

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No!"3^^*] IONIZATION POTENTIAL OP MERCURY VAPOR. I7I

I. Arcing Voltages.

The apparatus employed was essentially the same as that used in the
previous work on the mercury arc. A horizontal section is shown in
Fig. I. A was a glass tube about 20 cm. long and about 2.5 cm. in diam-
teter. B and C were iron caps which were fastened to the tube with
Khotinsky cement. Through B and C passed the iron electrodes which
carried the anode D and the cathode E. Pump connections were made
at both F and G, so that in case there was a small leak the resultant air
did not have to pass across the arc space DE, All the joints were sealed

■<j

Fig. 1.

with Khotinsky cement. The anode D was of platinum foil usually about
one centimeter square. The Wehnelt cathode was also of platinum
foil .003 cm. thick and about i.o cm. in length. Its width was usually
about .4 cm. The current used to heat the cathode varied between 10
and 20 amperes. Directly under D and E the glass tube was expanded
into a depression in order to hold the mercury and the expansion was
graded from the two ends of the tube, so that as fast as the mercury
condensed at the ends it ran back. This kept a constant supply of
mercury under the arc DE. The two iron caps, B and C, were surrounded
by cooling vessels through which water circulated. The central part
of the tube was surrounded by a gas-heated asbestos furnace with a
sheet-iron bottom. The mercury evaporated at the center of the tube
and passed both ways to the ends where, as stated above, it was con-
densed and returned to the center. As a result there should be produced
in the region DE an atmosphere of the purest mercury vapor. This
should be true even though the vacuum produced by the pump was
not very high. As a matter of fact the pump used gave a minimum
pressure of .25 mm.

With the apparatus as outlined above it was possible for me to sub-
stantiate my previous result, viz., that the arc could be caused to strike
at a potential difference as low as 4.9 volts. But in doing so I found that
it could be caused to strike at any potential difference above 4.9 volts
by varying some or all of the following factors: (i) The temperature of
the cathode, (2) the temperature of the furnace, (3) the distance between
the anode and cathode and (4) the pressure as recorded by a McLeod
gauge.

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172 T, C, HEBB. [g^

Curve Ay Fig. 2, gives the relation between the striking voltage and
the amperes through the cathode for a particular case. The McLeod
gauge reading was 1.9 mm. In considering this curve it should be noted
that the distance between the mercury and the cathode was about one
centimeter and hence a rise in temperature of the cathode caused a more
rapid evaporation of the mercury. That this made a difference was
proved by the observation that the slope of the curve decreased when the
mercury was not directly under the anode and cathode.

In regard to the effect of the second factor mentioned above, it may
be stated that the striking voltage decreases with a rise in the tempera-
ture of the furnace, although I have no exact data to offer.

And in regard to the third factor I found that the striking voltage
increased with the distance between the anode and cathode.

Curve 5, Fig. 2, shows the relation between the striking voltage and
the reading of the McLeod gauge for a particular case. Everjrthing
else was kept as constant as possible. It will be noticed that the striking
voltage decreases with the pressure, reaches a minimum and then rises
again. No significance should be attached to the fact that the curve
starts at about 10 volts and rises again to that value. It could have
been extended and was in some cases. The minimum point of the curve
only reaches the value of 6 volts, but curves could be obtained in which
the minimum potential difference had any value above 5 volts.

As a result of my experiments on arcing voltages I have. come to the
conclusion that the striking of the arc at 4.9 volts depends on (i) the
density of the electron stream, (2) the density of the mercury vapor,
and (3) the purity of the mercury vapor. If the electron discharge is
weak or if the density of the mercury vapor is low, then there will be no
arc formed at these low voltages. Further if there is the slightest trace
of a foreign gas present, then, even though other conditions are favorable,
the arc will not strike as low as 4.9 volts. This last condition is as would
be expected if one considers the path of an electron which leaves the
cathode and moves towards the anode through a dense atmosphere of
mercury vapor. Owing to the elasticity of the collisions between elec-
trons moving with speeds of less than 4.9 volts and molecules of mercury
vapor, the electron probably makes many excursions back and forth
past a certain point before passing on to the anode. If there were a
molecule of an inelastic gas at that point the probability of collision with
this molecule and the consequent loss of the electron's energy would

be great.

2. Current-Potential Relations.
Using the same apparatus with a low resistance galvanometer in
series with the experimental tube I made a study of the current-potential

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Na'a^'] IONIZATION POTENTIAL OF MERCURY VAPOR. 1 73

relations in the arc. With this arrangement I found, as would be
expected from a consideration of the previous results, that I could get
a current-potential curve which took a decided bend at about 5 volts.
I also found that by varying the same conditions previously mentioned
under Arcing Voltages I could get the bend to occur at any potential

Fig. 2. Fig. 3.

difference greater than 5 volts. Fig. 3 shows nine current-potential
curves taken for a certain arrangement of the tube. The same cathode
was used in all cases with the same current of 20 amperes flowing through
it. The distance between the anode and cathode was about 3 mm.
In all cases the rapid rise in current led to the striking of the arc. Most
of these values were too large to represent on the diagram but they were
utilized in getting the shape of the curve. Curves Ay B, C, D and E
were produced at pressures of 10, 6, 4.5, 2.2 and 1.3 mm. respectively,
as recorded by the McLeod gauge. Everything else was kept constant,
but the temperature of the furnace was low. Curves F and G were pro-
duced at the same pressure of .35 mm., but the temperature of the
furnace was higher than in the previous cases. In the case of G the
evaporation of the mercury was more rapid than in the case of F. For
curve H the pressure was 2.7 mm. and the temperature of the furnace
was still higher. Curve / was produced at a pressure of 5 mm. and at a
continued high temperature. I did not determine these curves for the
purpose of representing them together and hence the differences between
the conditions under which they were taken are quite erratic.

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174 T. C. HEBB. [S^";

3. Striations.

The conditions in a vacuum tube with a Wehnelt cathode are favorable
to the study of striations, and as the striations radiate the complete
spectrum of the element they appear to afford a method of studying
the minimum voltage necessary to produce this radiation. In order to
prevent the arc from striking, however, it is necessary to work with a
comparatively cool cathode. I found that a red-hot cathode separated
about 5 mm. from the anode gave very satisfactory results when the
pressure was from i to 3 mm. If, with these conditions and with the
temperature of the furnace low, the potential difference between the
anode and cathode was raised, light appeared on the surface of the anode.
The potential difference at which this occurred was never low, but usually
in the neighborhood of 10 to 12 volts. If then the voltage was still
further raised, the light on the anode grew towards the cathode and a
portion of it separated from the main body of light on the anode. In
all cases I found that the increase in potential difference necessary to
produce this separation was 5 volts. If after the first stria tion was formed
the potential difference was further increased the phenomenon repeated
itself, the first striation in the meantime having moved nearer the
cathode. The formation of this second striation also required the addi-
tion of 5 volts. The production of each new striation required an extra
5 volts. I have had as high as four distinct striations and the light on
the anode with a potential difference of 32 volts. In this case the initial
light was produced at 12 volts. On the other hand, with the furnace
at a high temperature I have had two striations and the light on the
anode for a potential difference of 15 volts.

The difference between the case where the temperature of the furnace
is low and the case where it is high probably lies in the purity of the vapor
between the anode and cathode. If the temperature is low, then the
evaporation of the mercury will not be sufficient to drive away all foreign
gases and as a consequence the electrons will lose energy in passing from
the cathode to the anode. As a consequence a potential difference
greater than 5 volts is required to produce light on the anode. In spite
of this loss, however, the addition of 5 volts will make a second ionization
possible. In the case where the furnace was at a high temperature,
however, the evaporation of the mercury was sufficiently rapid to drive
away all foreign gases and as a consequence the electrons lost no energy,
other than that due to ionization, in passing from the cathode to the
anode.

In connection with striations it may be of interest to state that I have
had them so close together and so close to the cathode that I could only
see the faintest dark line separating them.

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no'i^^'l ionization potential op mercury vapor. 1 75

4. Ionizing Potential.

It was considered both of interest and of value to determine the
ionizing potential of mercury vapor under conditions somewhat similar
to those in the preceding experiments, that is, to determine the ionizing
potential in an absolutely pure atmosphere of mercury vapor having a
pressure of one or more millimeters. In order to make this determina-
tion the anode of Fig. i was replaced by an ionizing chamber. The
chamber consisted of a platinum cylinder about 4 cm. in length and 1.5
cm. in diameter. The end of the cylinder near the catfiode was covered
with platinum foil containing three slits. The central slit was about
I cm. in length and about .3 cm. in width. The others were somewhat
smaller. A small receiving disk was placed about 2 cm. from the cathode
end of the cylinder. The cathode was separated 1-3 mm. from the end
of the cylinder. Mercury stood under both cathode and ionization
chamber and the apparatus was heated as usual. The ionization chamber
was kept charged to a constant positive potential of 24 volts. The
cathode was charged to a positive potential of less than 24 volts and
hence the electrons were accelerated as long as they were between
the cathode and ionization chamber. As soon, however, as they got
inside of the chamber they were retarded.

The gold-leaf electroscope was set to a sensitiveness of about .05 volt
per division. There was a condenser in parallel with it and the tw^o
together — condenser and instrument — had a capacity of about 230 e.s.u.
With it, therefore, it was possible for me to measure currents as large as
10"* amperes, when charging it to 5 volts. I was not able, however, to
measure very small currents accurately, for I found that the passage of
the mercury vapor over the receiving disk charged it positively. This
was reduced to a minimum by arranging the apparatus so that the receiv-
ing disk was near the center of the furnace. But even under these
conditions many observations were vitiated, apparently, by a sudden
rush of vapor.

The results plotted in curve A\ Fig. 4, were taken without the use
of the capacity mentioned above. The McLeod gauge registered 1.2
mm. The distance between the anode and cathode was i.o mm. The
cathode was new and uniformly coated with BaO and was heated by a
current of 19.5 amperes. The current flowing between the anode and
cathode varied from 14 X io~^ amperes at 4.5 volts to 23 X io~* amperes
at 5.3 volts. The minimum potential difference between anode and
cathode has been lised as abscissa. It is quite evident that ionization
must have started at about 4 volts, and as the drop in potential along
the cathode was .8 volt the ionization potential must have been in the
vicinity of 4.8 volts.

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176 r. c. HEBB. [l^H^^

The results obtained with an old cathode are sometimes very marked
due to the fact that the BaO wears down to narrow patches at either end
of the cathode. Curve B\ Fig. 4, was plotted from data taken with
such a cathode. The McLeod gauge reading was .85 mm. It will be
noticed that the curve is very steep. As a matter of fact the ionization
current increased over one hundred times when the potential difference
between the anode and cathode was changed from 3.9 to 4.0 volts. It
was possible to estimate quite closely the potential drop in the cathode
at this point and this value — .9 volt — added to 4.0 volts gives 4.9 volts.

Fig. 4.

The curves shown — A' and B', Fig. 4 — are similar to those obtained
by other experimenters but I do not believe that the results can be
explained on the assumption that the radiation X = 2536.7 has acted
photo-electrically on the receiving plate of the ionization chamber.
Although such an action must have existed, the current produced by such
action in these experiments must have been very small compared with
the currents measured. This was especially true as the receiving plate
had an area of only .25 square centimeter. And even when the receiving
plate consisted of a small platinum wire sealed in glass it was found that
the ionization current was still large.

Although ionization of mercury vapor occurred at 4.9 volts under
favorable conditions, as shown above, it was also possible to get it to
occur at any potential difference above 4.9 volts. This was accomplished

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Na*3i^^*l IONIZATION POTENTIAL OF MERCURY VAPOR, 177

by simply varying the temperature of the furnace. Some results are
shown in Fig. 4 — Curves A-F, The data for these curves were taken
with a constant current of 16.5 amperes through the cathode. The
latter was separated about 1.5 mm. from the anode. The pressure
indicated by the McLeod gauge was constant at .8 mm. The tempera-
ture of the furnace, however, was progressively lower, beginning with
curve A. The gap between B and C could have been filled with similar
curves had it been desired. The data for the curves C-F were taken
as the temperature of the furnace was gradually lowering. This accounts
to a great extent for the tendency of the curves to bend to the left as
they approach the P.D. axis. The abruptness with which the curves
drop into the P.D. axis is very pronounced in some cases. For example,
in one case the ionization current at 10.8 volts was too small to be de-
tected, if it existed at all. When, however, the potential difference
was increased to 11 volts, the ionization current became about io~*
amperes.

These results appear to me to prove that in order to get ionization of
mercury vapor at 4.9 volts under conditions similar to those in my
experiments it is necessary to have the vapor absolutely pure.

5. Photo-Electric Effect.

The previous experiments seem to prove conclusively that there is a
distinct and pronounced ionization at 4.9 volts. But this ionization may
be due to photo-electric action in a manner suggested by Millikan.*
Further than that the results of Davis and Goucher^ and also of Bishops
would appear to prove that such was the explanation. But even if
some such action as Millikan suggests took place, it does not seem
possible that the effect would be large enough to explain the results.
It does not seem possible that radiation which required two or three
hours to effect a photographic plate could produce io~' amperes photo-
electrically as I have measured. Nor does it seem probable that the
same radiation, even by the reciprocal action suggested by Millikan,
could cause such large increases in the arc currents as I have obtained.
For instance, in one case the current flowing between the anode and
cathode changed from lO"^ amperes at 5 volts to 40 X lo"* amperes at
5.5 volts without the production of an arc. And in the following case
where the arc strtick the increase was much greater. In this case the
current changed from 3 X lO"* amperes at 5 volts to 540 X lO"* amperes
at 5.3 volts. Still another objection to the theory, it appears to me,
is the fact that striations can be obtained in mercury vapor and especially
in such close proximity to one another.

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178 r. C HE3B. [^„^^

However, in order to test whether the photo-electric action was the
cause of the ionization I arranged a mercury arc in air directly outside
of the experimental tube and so arranged that its light passed into the
front end of the ionization chamber. The experimental tube had been
exchanged for one of quartz. Conditions were then arranged so that a
large ionization current was produced by the electrons from the cathode.
The voltage between the anode and cathode was then reduced to zero
and the mercury arc in air started. It was found that the photo-electric
current produced by the 4-ampere arc was, in some cases, equal to the
current produced by the electron stream. Thus in one case at a pressure
of 2.9 mm. and with 5 volts between the anode and cathode the electro-
scope charged up to 2.5 volts in 4 seconds. The voltage between the
anode and cathode was then reduced to zero and the mercury arc in
air started. The latter produced exactly the same ionization current.
A carbon arc produced no results. As the effective radiation produced
by a 4-ampere arc must be hundreds of times greater in intensity than
the radiation X = 2536.7 produced in the experimental tube by the
electron discharge due to 5 volts, it does not seem probable from this
result that the ionization produced by the 5 volts could have been due
to the radiation X = 2536.7.

It was further found that changing the pressure in the tube had very
little effect on the ionization produced by the arc whereas the same
changes caused the ionization current produced by 5 volts to vary from
zero to a large value.

I also tried to find what effect the mercury arc in air had upon the
striking voltage of the arc in the vacuum. Conditions were arranged
so that the arc in the vacuum struck at 8 volts. The voltmeter was then

Fig. 5.

set at 7.9 volts and the mercury arc in air started. If it sets up ionization
in the tube of sufficient amount, then one would expect the arc in the
vacuum to strike lower than 8 volts. No such effect was observed.

The ionization chamber was then arranged as in Fig. 5.

Two platinum cylinders A A were separated by a quartz test tube B and
together with C as a receiving plate constituted the ionization chamber,
A and A were joined electrically and a potential difference of 24 volts
was applied. No electrons from the cathode D could get into the ioniza-
tion chamber K. Mercury was kept in the chamber K as well as under

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NoVi!^'*l IONIZATION POTENTIAL OF MERCURY VAPOR. 1 79

the arc DA. The current flowing between the anode and cathode was
measured and hence I could tell when ionization began. Some of the
radiation produced should pass into the chamber K and produce ioniza-
tion. Of course some of the radiation was absorbed by the quartz test
tube which was about i mm. in thickness and some was absorbed by the
mercury vapor which formed an unavoidable layer between two cylinders
AA, This layer was about .5 mm. in thickness. As mentioned before
the passage of mercury vapor over the receiving plate C causes it to
be charged with positive electricity. I could not obviate it in this case
as in the previously mentioned one and hence it was not possible for me
to detect extremely small currents but in no case did I detect any current
due to the radiation X = 2536.7. That the apparatus would have
responded as expected if the radiation X = 2536.7 had produced ioniza-
tion in sufficient quantity was proved by the fact that the slightest arc
between D and A produced a rapid charging of the electroscope. My
experiments along this line, therefore, have not shown, so far, any evi-
dence of*an ionization of mercury vapor by the ratiation X = 2536.7.

Summary.

1. These experiments prove conclusively that mercury vapor may be
ionized when bombarded with electrons moving with a velocity acquired
in falling through 4.9 volts and that the complete spectrum of mercury
is produced as a result.

2. Experimental evidence is given to show that this ionization is not

produced by the radiation X = 2536.7 acting photo-electrically on the

mercury vapor.

University of British Columbia,
Vancouver, B. C.

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l8o p. W. BRIDGMAN, [ilS?2s.

ON EQUILIBRIUM UNDER NON-HYDROSTATIC STRESS.

By p. W. Bridgman.

T N a recent number of the Physical Review^ Williamson has published
-■- a paper on the subject of the above title, which was also the subject
of an earlier paper of my own. Since Williamson's paper is partly in
criticism of mine, and since the subject is growing to be one of important
bearing in geophysics, it is perhaps appropriate that I should attempt to
make clearer the point of view of my original paper. With regard to
my paper Williamson says: '*More recently Bridgman has deduced a
formula of very formidable appearance dealing with the change of
melting point and transition point with stress. He unfortunately also
makes no mention of assumptions, giving as his reason for this: 'The
formulas were derived by ordinary thermodynamic methods; it is hardly
worth while to reproduce the wearisome details.' As regards the mathe-
matical transformations this is true, but we hope to show that several
of his terms rest on very shaky foundations." Later he says: **The
fundamental assumption made is that of reversibility, which is a neces-
sary premise to the equality of the potential (/*). This assumption
needs some explicit criticism and justification." It seems, therefore,
that some comment is necessary on the method of deducing my formula,
and on the question of reversibility.

The formula, as Williamson hints, is of considerable generality; this
generality consists not only in the range of conditions of stress and
crystalline structure covered by it, but also in the variety of assump-
tions with regard to the nature of the contact conditions which it makes
possible to the user of the formula. I supposed that in general the two
phases were separated by a membrane permeable to the phases, but such
as to support a stress difference. The nature of the stress difference
supported by the membrane may vary with conditions, and must be
appropriately specified in each case. In particular, if there is no mem-
brane at all, the forces on the two sides of the surface of separation are
the same, and this case is also covered by the formula on making the
appropriate substitutions. I did not at all intend to touch the question
as to whether such membranes actually exist; my purpose in giving a
formula of such generality was that many writers have supposed that in

» E. D. Williamson, Phys. Rev., io, 275-283. 191 7.

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Na'i^'J EQUILIBRIUM UNDER NON-HYDROSTATIC STRESS. l8l

actual cases the action is of this nature. The assumption, however, as
to the nature of the action must in each case be made by the user of the
formula. It is significant that my own position in the actual cases dis-
cussed was that the conditions are not such as are represented by a
membrane, but that the usual conditions of mechanical equilibrium must
hold at the interface.

Thermodynamics is competent to state whether equilibrium exists
or not under such conditions. I intended to make clear by my statement
that **the formulas were derived by ordinary thermodynamic methods"
what the nature of the assumptions was. Taking the existence of such
membranes as a fact, the only assumption made in deducing the formulas
was that the first and second laws of thermodynamics hold, and that
the solid is always strained within its elastic limit. Here enters the
second point requiring elucidation ; it is objected that the laws of thermo-
dynamics cannot be applied without making the assumption that the
reaction is reversible, and that in special cases experiment is needed to
justify the assumption of reversibility. This does not seem to me an
accurate statement; we are in most cases given a great deal of informa-
tion about the reversibility of an operation by thermodynamics only,
without any further experiment.

Thermodynamic and mechanical reversibility must be clearly dis-
tinguished ; the only condition demanded in such work as above is that
there be thermodynamic reversibility. The simplest statement of
thermodynamic reversibility is that the entropy increment in any change
(at constant temperature) shall be AQ/T^ where A^ is the heat absorbed.
To find the actual difference of entropy between two phases it is necessary
that we pass from one to the other by some path known to be reversible.
It would of course be begging the question to pass directly from one
phase to the other and forcibly write down the entropy condition.
Now the derivation of the formulas of my paper consisted essentially in
passing from one phase to the other by a process incontestably reversible,
and from this obtaining the conditions for a direct thermodynamically
reversible change. The incontestably reversible method of passing
from one phase to the other is by an elastic change of stress on one phase
until the hydrostatic pressure of two-phase equilibrium at that tempera-
ture is reached, reversible change to the other phase under equilibrium
conditions at the determinate hydrostatic pressure, and elastic change of
stress on the second phase, bringing it to the required final conditions.
This process constitutes three of the four parts of the complete cycle
referred to on page 217 of my paper, and it is the information given by
this part of the cycle that ensures that the fourth and closing step, direct

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1 82 p. W. BRIDGMAN. [iSwi?

passage from one phase to the other, is thermodynamically reversible.
The details are wearisome, it is true, but are perfectly straightforward,
and were certainly not worth the expense of publication.

The argument thus far has established thermodynamic reversibility
under the conditions specified in the formula. Physically this may
mean equilibrium (equilibrium is here used in the sense of no spon-
taneous change), for (in general) neither phase can change to the other
under the conditions imposed by the formula without the addition of
energy to the system. More than this, thermodynamics says that if
the system is displaced in a certain direction, a certain change may take
place, and a certain other change cannot take place. As to whether
any change at all takes place when the system is displaced, or whether
equilibrium fails because an entirely different kind of change takes
place, such as the appearance of another different phase, thermodynamics
has absolutely nothing to say. This is a question of mechanical reversi-
bility; thermodynamic equilibrium is a necessary but not a sufficient
• condition for it. The matter of mechanical reversibility can usually be
settled only by direct appeal to experiment. Besides settling the ques-
tion as to mechanical reversibility, experiment may often perform
another useful function. In many cases it may not be physically obvious
that the variables chosen to specify the state of the system are adequate.
Thus in the example of the next paragraph, that of a crystal growing
under stress, it might be feared that other variables, such as the surface
tension and curvature of the surfaces of separation, might be needed to
adequately specify all the physical factors. In such cases, experimental
proof of mechanical reversibility under the conditions demanded by a
thermodynamic discussion raises strong presumptive evidence that the
variables assumed in the thermodynamic discussion afford a physically
adequate description of the phenomena. It would make an interesting
topic to find just how strong the presumptive evidence is in different cases.

In this connection it is pertinent to mention a recent paper by Wright
and Hostetter, also from the Geophysical Laboratory. They have with
great experimental skill examined crystals growing under stress, and
have proved to their own satisfaction that the ** assumption" of reversi-
bility is justified. In view of the above, it seems to me that the point of
their work is not exactly as they represent it. They have established
experimentally the ptechanical reversibility of the growth on the free
face of a strained crystal. This is certainly an important contribution,
most significant for our conception of the nature of the crystal building
forces, and necessarily one obtainable only from experiment. But their
results are entirely superfluous as far as thermodynamic reversibility goes;

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NoTa^^'] EQUILIBRIUM UNDER NON-HYDROSTATIC STRESS, 1 83

if there is no blunder, the formula above is as secure as thermodynamics
itself, and tells us without question that under certain conditions, one
of which is the non-appearance of a new phase, and another of which is
the physical adequacy of our assumed variables, the crystal can neither
dissolve nor grow, and that under certain other conditions the crystal
can only grow or only dissolve. Results such as this are always obtain-
able by thermodynamic reasoning, and the formula in question is no
exception.

The only room left, it seems to me, for difference of opinion is with
regard to applications of the formula; in any special case is the physical
action correctly represented by a particular membrane or not? A case
to be represented by a membrane is case B of Williamson, in which the
pressure on the solid is not the same as that on the liquid in contact with
it. One might possibly gather from his paper that this case plays a
somewhat prominent part in mine; it was actually treated in just five
lines (bottom of page 218) and was prefaced by the remark, **if we sup-
pose the membrane such that, etc.'* I did not intend to argue whether
in any actual case such a membrane exists, and I can, in fact, think of no
case, except possibly an inert gas in contact with a liquid, in which I
believe this adequately represents the facts, although other writers have.
Williamson argues at some length that in any actual case, such as a
weight resting on a solid, this does not adequately represent the state of
affairs ,with which I agree, and deduces an expression which he prefers,
which is the same as my case 5. I agree that this much more closely
represents the state of affairs in any such case as the melting of snow under
the runners of a sleigh. But Williamson finds an irreversible aspect in
the lateral outflow of liquid, which to his mind makes the treatment
uncertain; I am of the opinion that this irreversible aspect has no effect
and that the formula accurately gives the conditions under which melting
will just begin, because the irreversible process takes place only after
melting has occurred, and cannot therefore affect the actual melting.
The formula applies strictly only to equilibrium; any physical progress
of the transition must imply, as always, a small element of irreversibility.

The substance of Williamson's criticism seems to me, therefore, to
boil down to this; the formula should have been made much simpler
by leaving out the membrane, because it is not certain that such mem-
branes exist. This of course is a question of judgment. But that the
formula, when correctly handled, gives correct results without assump-
tions which require further resort to experiment, of this there can be
no doubt.

Thb Jefferson Physical Laboratory.

Harvard University. Cambridge. Mass.

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184 J' ^' BENADE AND K. T. COMPTON. ^Sm,

ELASTICITY OF IMPACT OF ELECTRONS WITH GAS

MOLECULES.

By J. M. Benade and K. T. Compton.

Introduction. — In the theory of ionization by collision, as originally
developed by Townsend, it was assumed that an electron lost practically
all of its kinetic energy at each impact with a gas molecule. Subsequent
discoveries have shown that this view is substantially correct in the case
of most gases.

On the other hand, it was pointed out by Franck and Hertz^ that
the strong ionization in helium, whose molecules are difficult to ionize,
could only be explained by assuming that in this gas the electrons re-
tained a considerable portion of their energy at encounters, so that their
energy at any instant has been accumulated during the entire path since
the preceding ionizing collision. They proved the existence of this
type of collision in helium, and also in the other monatomic gases neon
and mercury vapor, by showing that in these gases the ionization current
increases abruptly whenever the applied difference of potential between
the electrodes is increased to an exact multiple of the minimum ionizing
potential.^ These experiments have been amply verified by Goucher,'
Bazzoni,* Todd and others. We are therefore justified in distinguishing
two general types of impact, inelastic and elastic.

The question immediately suggests itself: **Are these really two dis-
tinct types of impact, or may there be all degrees of elasticity between
the two extremes of perfect elasticity and complete inelasticity?" At
first sight, the case of hydrogen appears to support the latter alternative.
Impacts in hydrogen are known to be less elastic than those in monatomic
gases, but more elastic than in other multiatomic gases.

As far as we know, the only attempts to measure directly the amount
of energy lost by an electron at a collision were made by Franck and
Hertz.* They projected electrons with a known maximum velocity

» Verh. d. D. Phys. Ges., 15, p. 34. 1913.

* Verh. d. D. Phys. Ges., 16, p. 457, 1914. Professor Bergen Davis and Mr. F. S. Goucher
have shown, in the case of mercury vapor, that these successive discontinuities occur also at
multiples of the "minimum radiating potentials."

» Phys. Rev., 8, p. 561, 1916.

< Phil. Mag., 32, p. 566, 1916.

' Verh. d. D. Phys. Ges., 15, p. 373. 1913.

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No^a^**] ELASTICITY OF IMPACT. 1 85

through a gauze into a long chamber filled with gas at low pressure. If
any electrons returned to an electrode in the plane of the gauze, these
must have been reflected from gas molecules. By measuring the retard-
ing field against which these reflected electrons could reach the electrode,
the energy retained after a collision was found and thus the energy lost
at a collision was determined. It is to be noted that, in these experi-
ments, electrons approaching the detecting electrode obliquely were
treated as if approaching directly, with the result that the apparent
average energy loss was much greater than the actual loss. Realizing
this, Franck and Hertz can only conclude that the average loss of energy
at a collision, expressed in equivalent volts, is less than 0.3 volt in helium,
1.6 volts in hydrogen, and that in the common gases practically all the
energy is lost. These considerations, of course, apply only to impacts
with velocities less than the minimum ionizing velocity. When ioniza-
tion occurs, the electron must lose at least the amount of energy neces-
sary to ionize the molecule.

Recently the writers^ have suggested a theory of the loss of energy by
an electron while passing through a gas, according to which the electron
should lose very little energy in a monatomic gas, whereas in multiatomic
gases, the loss of energy should be least in light gases of simple molecular
structure and greatest in heavy complex gases. Qualitatively, at least,
this is in accordance with the facts. The vital point in the theory,
however, is that the loss of energy in the two types of gases is due to dis-
tinctly different processes^ so that we should not expect to find all degrees
of elasticity of impact between the most and the least elastic gases.

In the present investigation we have developed a method for measur-
ing the loss of energy at an impact which has enabled us to measure
accurately losses of the order of magnitude of a thousandth of a volt.
Measurements of the loss in helium indicate that impacts of electrons
with helium atoms are perfectly elastic in their nature, i. e., that the
only energy lost by the electron is due to the motion imparted to the
atom during impact. The method is so sensitive to changes in the
elasticity of impact that the experimental measurements prove the
coefficient of restitution at impacts in helium to be unity with a possible
experimental error of not more than o.oi per cent. In other words, the
coefficient of restitution, if not unity, is at least greater than 0.9999.
In hydrogen and oxygen the loss of energy is much greater and is shown
to be of a more complicated type than in helium. Attempts to measure
the loss in argon have failed, up to the present, owing to the failure to
obtain gas of sufficient purity for these experiments. These points will

> Phys. Rev.. 8. p. 449, 1916.

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1 86 J. M. BENADE AND K. T. COMPTON. [iJSS

be discussed more fully after the experimental evidence has been pre-
sented.

Calculation of the Average Energy lost by an Electron at a Collision with a
Gas Molecule. — Let us consider, for the moment, the case of an electron
of mass m moving with velocity v and colliding in "head on" fashion
with a stationary molecule of mass M. After impact the velocities of
electron and molecule are Vi and Vi respectively. The electron loses a
fraction k' of its original kinetic energy, which we may easily calculate
from the relations

mv = MVi — mvu

ev = Vi + Vu
where e is the coefficient of restitution. We find

v" - vi^ AP(i - e") + 2Mm{i + e)

V =

v" {M + my

Since we may take M = M + tn without appreciable error, this ex-
pression may be written

*' = (! -e^)+2(i+e)^.

In the actual case of electrons traveling through a gas, not all collisions
are of the "head on" type, in which the velocities are in the direction of
the line of centers at impact. Many electrons strike more or less ** glanc-
ing" blows, and we have to average the effect of all. To make calcula-
tion possible we shall assume the molecule to be spherical. We may then
multiply the energy lost by an electron which strikes the surface of the
molecule at a given angle by the probability of striking at that anglci
and integrate over all possible angles (o to 7r/2), thus determining the
average loss of energy at a collision. Even this calculation is difficult
except in the particular case of interest to us, when e is very near to unity.
In this case we find approximately

(I - e^) (I + e)m
k =----+ -^-- (I)

for the average fraction of its energy lost by an electron at a collision.
This approximation becomes more accurate as e approaches unity, and
if collisions are perfectly elastic the relation is exact, taking the form

which is just half the value of ife' for "head on" collisions alone.

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Na*3^^*] ELASTICITY OF IMPACT. 1 87

We have assumed, thus far, that the molecule is at r^t when struck.
The question therefore arises: What is the effect of the thermal motion
of the molecules on the decrease in the kinetic energy of the electron at
impact? We may take this into account by averaging the effects of two
types of collisions: between electrons and molecules moving in opposite
directions and between those moving in the same direction before impact.
Assuming perfect elasticity and denoting the average molecular velocity
before impact by F, we find that, out of N collisions, there are

^ V

collisions of the first type, resulting in an average energy loss equal to

^{(s)'-'+»

and

^ V

collisions of the second type with an average energy loss equal to

"{(M^-l'-}-

We can therefore obtain the total loss of energy by the electrons in all N
collisions and thence find the average loss per collision. When this is
divided by the average energy before collision, we obtain

This expression illustrates the equipartition theorem, for it shows that,
in the absence of external forces, the two types of particles will exchange
energy until their average kinetic energies are equal, when the proportion
k determining the average loss of energy at a collision becomes zero.

In the present case, however, the velocities v with which we have to
deal so far exceed the thermal velocity V that the second term is entirely
negligible in comparison with the first. We are therefore justified in
taking equation (i) to represent the fraction of energy lost by an electron
at a collision, if impacts are very elastic.

In the case of helium, substitution of the relative masses of an electron
and a helium atom leads to the value

k = 0.0002685 (4)

if the collisions are perfectly elastic.

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i88

J. M. BENADE AND K, T. COMPTON.

fSSCOKD

LSbrxbs.

We shall proceed to a description of the experimental method of
determining k. If the experimental value of k should differ somewhat
from 0.0002685, the appropriate value of the ctoefficient of restitution
could be calculated from equation (i).

Method. — ^Since the energy lost at a single collision between an electron
and a monatomic molecule is known (or assumed for the present) to be
small, in order to measure this loss it is necessary to deal with the aggre-
gate effect of a large number of successive collisions. This has been done
by liberating electrons at a negative plate and driving them through the
gas to a second electrode parallel to the first and positively charged.
The number of collisions made by an electron is a function of the gas
pressure p and the distance d between the plates.

Curves representing the increase in the electronic current with in-
creasing potential difference indicate by an upward inflection, or *' break,"
the potential at which ionization begins; and this occurs as soon as an
appreciable number of electrons have a quantity of energy, in the case
of helium, corresponding to a fall through 20 volts, the well-known
ionization potential. The difference between the applied potential and
20 volts represents the energy lost by collisions with molecules, and can
be made as large as we please by increasing the product pd.

fON/ZATioN Chamber

Quartz

[To

-^_. -- PoTE/rriAL

Electrometer. Divioino S£t.

Pump

Fig. 1.

The earlier curves were plotted from data obtained by the use of an
ionization chamber similar to that used by Partzsch in his work on
Stoletow's constant,^ but later a simpler and more satisfactory one was
substituted. The latter is shown in Fig. i. It consists of a glass tube
of about 5 cm. diameter and 14 cm. length, with other parts as shown in
proportion. The brass cap on the end, with a fine wire gauze flush with
its inner surface serves as one of the electrodes. Behind this electrode

» Ann. d. Phys.. 40. p. 157. I9I3'

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Vol. XI.l
No. 3. J

ELASTICITY OF IMPACT.

189

and parallel to it is a brass disk, the second electrode, which is mounted
on a horizontal threaded shaft held in a nut and journal coaxial with the
glass container. On the rear end of the shaft is a cross bar with two
iron lugs which, with the aid of an external electromagnet, serve to adjust
the distance between the electrodes. A wire gauze closely fitting the
inner surface of the chamber surrounds the adjustable electrode and is
electrically connected to it. This prevents the accumulation of a charge
on the surface of the glass when the distance d is large. The surfaces of
both electrodes were heavily coated with platinum, by -sputtering, to
insure constancy of photoelectric effect and to avoid contact difference
of potential.

Ultra-violet light from a quartz mercury vapor lamp enters the chamber
through a quartz window and the gauze and liberates electrons from the
movable electrode, which is connected to a sensitive quadrant electrom-
eter shunted with a resistance of about 100 megohms. The electrom-
eter gave a deflection of about 2,000 mm. per volt, so that the arrange-
ment is equivalent to a galvanometer with a sensitivity of about 5(10)""^'
amperes per division. (The shunt resistance was very satisfactory and
consists of a thin film of platinum deposited on hard rubber or glass,
with globules of mercury for contacts.) The fixed electrode is connected
to a conveniently adjustable potential source, and voltmeter.

flfMTf

Fig. 2.

The ionization chamber is connected to a hand mercury pump, gas
reservoir and McLeod gauge, as shown in Fig. 2. Before introducing
gas for investigation, the apparatus was exhausted by a Gaede pump,
allowed to stand for some time and again pumped down to the lowest

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190 /. M. BENADE AND K. T. COMPTON. [^Sm.

attainable pressure to get rid of adsorbed gases. As far as possible, the
glass parts were heated during part of this process.

The helium was introduced as follows: A U tube, with one arm drawn
out to form a capillary tube with the end open, was inmiersed in mercury
as shown at the left of the figure. The stopcock above the U tube was
opened while the apparatus was being exhausted and mercury allowed to
rise in the tube to a point a little above the stopcock, so that the U tube
was entirely filled with mercury and the open end was beneath the
surface of the^mercury in the cylinder. The tube containing the gas to
be introduced was scratched and the end broken off under mercury.
The end of the capillary was then introduced into this gas container,
which was pressed down allowing the gas to be forced into the apparatus
when the stopcock was opened. In this way not more than a cubic
millimeter of gas was lost in the transfer. The first bit of gas transferred
was pumped out again, in order to carry out traces of other gases re-
maining in the apparatus. Finally, the introducing tube was sealed off.
By means of the hand pump the gas could be pumped from the ionization
chamber into the reservoir, so as to get any desired pressure in the
chamber. The mercury sealed valve between the pump and the reservoir
carried an iron weight on the stem so that the valve could be held open
by an electromagnet when it was desired to let gas flow back into the
ionization chamber.

A spectrum tube connected with the ionization chamber was used
with a direct reading Hilger spectrometer to indicate the presence of
impurities in the gas. When working with helium, a U tube filled with
cocoanut charcoal and surrounded by liquid air was used to remove
impurities. This was very effective except in the removal of hydrogen.
It was found that the hydrogen spectrum was much reduced when an
electrodeless discharge tube was substituted for the original one, which
had aluminium electrodes. This indicates that much of the hydrogen
came from the electrodes, as had been proved by Winchester.^ In order
to remove the remainder of the hydrogen, the following method was
found the most satisfactory of several methods tried. A small bulb
containing a platinum coil which was heavily copper-plated and well
oxidized was attached as shown in Fig. 2. After keeping the copper
oxide at a bright red heat for several days the hydrogen spectrum was
so much reduced as to be almost invisible at low pressure discharges,
though it was quite evident at the higher pressures. In this connection
it should be remembered that the presence of helium in a discharge tube
has the effect of greatly enhancing the spectra of any other gases which

» Phys. Rev., 3. p. 287. 1914.

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Vol. XI.l
Na3. J

ELASTICITY OF IMPACT,

191

may happen to be present in the tube. It is possible, also, that most
of the hydrogen observed was liberated by the discharge in the spectrum
tube, and may not have been present in the ionization chamber during
the tests. At any rate we feel quite safe in assuming that our helium
could be considered pure, for a simple calculation shows that the results
of our experiments would have been impossible had there been present
in the gas as much as one part of hydrogen in one hundred thousand parts
of helium. Several mercury lines were also faintly visible, but with the
liquid air trap the amount of mercury vapor present could not have
been serious, and even this small amount would not be likely to affect
the results because it is fairly well established that collisions in mercury
are elastic.

\( [

(

3«

f "

«t

«*4

IMU

%io

7*mt

/nil

4»

'/»5

r««

X M

</<

u>.

.i^

!T--

\/6

L-n

Fig. 3.

Figs. 3 and 4 give typical examples of a large number of curves ob-
tained by plotting the electronic current in helium as a function of the
applied potential V for various gas pressures p and distances d between
the plates. At extremely low pressures there is no evidence of ionization
of the gas, the currents quickly reaching saturation as the potential drop
is increased. When the product of the pressure and distance pd is
larger, so that an appreciable number of collisions occur, ionization sets
in when the applied potential is 20 volts, as indicated by the *' break"
in the curve. For larger values of pd this *' break" is shifted toward
larger values of the applied potential, proving that energy is being lost

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192

/. M. BENADE AND K. T. COMPTON.

[Second
Sbribs.

by the electrons at collisions. Some of the curves are extended to show
two or three ** breaks/* indicating potentials at which the electrons
liberated by the preceding ionization are themselves ionizing the gas.

Fig. 4.

It isjnteresting to note that the second and third "breaks" do not come
at^exactly two and three times the potential of the first, except when
this is at 20 volts. This is due to the fact that the average number of
collisions made by an electron while acquiring sufficient energy to ionize

M^—i

4 0

i**

>•

0 to 20 SO 4-0 SQ 60 10 80 9fi JOO

FiK. 5.

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Vol. XI.l
No. 3. J

ELASTICITY OF IMPACT.

J 93

is less in the second and third cases than in the first because of the
greater potential gradient in these cases.

The conclusions regarding the energy lost at impact are drawn from
the variation of the shift of the *' break" point (observed ionizing poten-
tial) with the product of the pressure and distance pd. The data from
observations made after the apparatus was working satisfactorily are
given in Table I. and are shown graphically by Curve i, Fig. 5.

Table I.

/ (Mm.).

^(Cm.).

pd.

Shift s.

11.70

0.425

4.97

3.7

11.70

0.2125

2.48

1.8

5.55

0.2125

1.18

0.5

4.35

0.900

3.91

3.7

4.35

1.010

4.39

4.5

4.34

0.476

2.06

1.6

4.34

0.370

1.60

0.8

4.34

0.265

1.15

0.5

46.60

0.846

39.40

59.0

46.60

1.060

49.30

70.0

43.00

0.636

27.30

35.0

43.00

0.848

36.50

60.0

43.00

1.060

45.50

70.0

43.00

1.270

54.60

85.0

43.40

1.270

55.00

85.0

30.00

1.270

38.10

51.0

19.80

1.270

25.06

30.0

13.30

1.270

16.90

19.0

43.70

0.210

9.20

10.0

18.70

0.210

3.93

3.7

10.55

1.800

19.00

20.0

13.30

1.800

23.95

27.5

5.40

1.800

9.72

10.0

In order to use these experimental results to determine the degree of
elasticity of impact, it is necessary to picture to ourselves the phenomena
accompanying the passage of an electron between the electrodes in the
gas, and to express the energy of the electron at any point in its path in
terms of the gain from the field and the loss from collisions.

Change of Kinetic Energy of an Electron passing through a Gas. — The
photoelectric relation between the nature of the emitting cathode and
the eflfective wave-length of the ultra-violet light is such that we may
neglect the initial velocities of the electrons. We have to deal, therefore,
with a group of electrons which start from rest at the cathode and move
toward the anode, bounding and rebounding from the molecules with

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194 ^- ^- BENADE AND K. T, COMPTON. IISim!

which they collide. During each free path the motion of an electron is
determined by the electric field and the velocity retained after its pre-
ceding impact. At each collision, however, a fraction k of its energy is
lost. Our problem is to determine the average energy Ue of an electron
after it has moved a distance d through the gas at pressure p under the
action of a uniform field of intensity X, and thus to calculate the difference
of potential through which the electron must move in o»^er to acquire
the energy necessary to ionize a molecule.

Let us express the average energy of an electron at any point in the
gas by Ue, where U is the energy in equivalent volts. The average
rate at which the electron is acquiring energy at this point of its path
is e{dU/dx). However the electron gains energy from the field at the
rate eX per centimeter. Thus e[X — {dU/dx)] represents the average
amount of energy lost at collisions per centimeter advance toward the
anode.

If iV is the average number of collisions made by an electron in a centi-
meter path through the gas at one millimeter pressure, then pN is the
average number of collisions per centimeter path at the pressure p. The
average number of collisions made while advancing one centimeter
toward the anode we shall denote by v, which is much greater than pN
because of the zig-zag character of the path. The relation between v
and pN is found as follows:

During a free path / the electron experiences an acceleration X{e/m)
in the direction of the field for a time equal to (//»), where v is the average
speed. Therefore

gives the average distance moved in the direction of the electric field
during one free path. The reciprocal of 5 is v and of / is pN, whence

2mv^p^N^

We could put mv^ = 2 Ue, were it not for the fact, discussed later, that
the electrons quickly acquire Maxwell's distribution of speeds about
the mean speed of advance, so that we must distinguish between the
square of the mean speed i^ and the mean square speed v^. Let the
ratio i^/r* equal r*, whence mv^ = 2r^Ue. Then

" = Y • (5)

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No'a'!^^'] ELASTICITY OF IMPACT. I95

We may therefore write the average amount of energy lost per collision
by an electron in the region of the gas specified by x in the form

li-

-(-f)

dx r 4rWp'm

This expression must equal kUe^ where k is the fraction of energy lost
at a collision. Thus we obtain

for the average net rate of gain of energy by an electron whose energy
is Uf expressed in equivalent volts.

If the anode is at a distance d from the cathode, the average energy
of the electrons reaching the anode is given by

whence

Jo X^' - 4r^^N^kU^ Jo X'

^ " ^Ns^kpd 7^''p^~+~i ' ^^^

where V has been written for Xd, the total difference of potential between
the anode and the cathode.

In order to adapt this relation to our experimental results in Table I.,
we note that we were able to ascertain the value of i7 as soon as it became
equal to the minimum ionizing potential Fo, whence we shall consider
equation (7) when U has the value F©. Now F — Fo = ^ is the "shift"
whose experimental values are given as a function of pd in Table I. and
Fig. 5. Solving equation (7) for this quantity, we find

r2rNs/kpd{e'^''''-'+i) -I

In order to understand the application of this equation to the experi-
mental results, attention should be called to the fact that the equation
applies to mean values of the kinetic energy of the electrons, while in
our experiments we detect ionization and thus determine the values
of s when an appreciable number of the fastest electrons attain the
minimum ionizing energy. The following considerations enable us to
take account of the difference between these points of view.

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196 J. M. BENADE AND K. T. COMPTON. [I^S.

When the product pd is small, so that relatively few collisions are
made by each electron, there is small probability that the speed of
any electron will differ appreciably from the mean speed. Consequently
equation (8) may be safely used for small values of pd. When pd is
increased, however, the relation between 5 and pd approaches a linear
form, which indicates that energy is being lost by collisions at almost
the same rate that it is acquired from the field. This state of equi-
librium is most easily expressed by placing (dU/dx) = o in equation (6),
whence

~ 2rpN^k

gives the mean energy of electrons in a steady state of drift in the field X.
Strictly speaking, this state would not be reached until the electrons had
moved an infinite distance through the gas, but it was reached within
the limits of experimental accuracy in a number of our measurements
with large values of pd. In other words, we were able to increase pd
indefinitely, keeping X constant, without appreciably increasing the
mean energy U.

Under these conditions, Langevin^ and Boltzmann^ have shown that
the velocities of the electrons are distributed according to Maxwell's
law about the mean velocity of drift. That this really applies to the
case under discussion may be shown by an argument based on two
equations derived by Pidduck* in a paper on **The Abnormal Kinetic
Energy of an Electron in a Gas.**

He considers electrons of mass m and charge e moving with a steady
mean rate of drift «© in a field X through a gas consisting of perfectly
elastics pherical molecules of mass M, each set having velocities distrib-
uted according to Maxwell's law. His equations, with certain symbols
changed to avoid ambiguity with the present paper, are

ZeX / 6 _\i/2

"^ i6iW\7rmXJkfF2/ '

where N' is the number of molecules per unit volume, a is the molecular
radius, V is the square root of the mean square velocity of molecular
agitation and X is the ratio of the mean kinetic energy of an electron to
that of a gas molecule.

» Ann. Chim. Phys., 105, 5, p. 245, 1905.
• Boltzmann, Gastheorie, Vol. i, p. 114.
» Roy. Soc. Proc.. 88. p. 296, 19 13.

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5o!"3^'] ELASTICITY OF IMPACT. 1 97

If we substitute riVV = pN in the first equation and use the second
equation to eliminate Uo, we obtain

MK^-ffj^

neglecting the factor (X — i)/X which does not differ appreciably from
unity. The first member is, by definition of X, equal to the mean kinetic
energy of an electron, which we have expressed in the form eU. Thus

By equation (2) we may replace ^M/m by ^2/jfe. Equation (10)
thus becomes

^^ 3^12^ X X

U = -^^ - —7-^ = 1. 151

32 pN^k 2pN^k

This is seen to be identical with equation (9) of the present paper, since
the numerical term 1.151 is identical with i/r, which is the ratio of the
square root of the mean square speed to the average speed in a Max-
wellian distribution.

The point of this discussion is that we may apply equation (8) directly
to our experimental results only when dealing with such small values of
pd that the maximum speed of the electrons at any point of the gas does
not differ appreciably from the mean speed. Under these conditions the
ratio r equals unity. As the value of pd increases, the ratio r diminishes,
approaching the value 1.151"* as a limit. For very large values of pd,
equation (8) becomes

5 = V^{2rN^kpd- i). (11)

If we know, from the characteristics of our apparatus, the least pro-
portion of the electrons whose ionization can be detected, we may apply
equation (11) to our experimental results if we give to the average
energy, not the value Fo, but such a smaller value as will give, according
to Maxwell's distribution, the necessary proportion of electrons with
energies equal to or greater than the minimum ionizing energy Fo. In
this case the constant r in equation (11) should be given the value 1.151"^

We have, therefore, two methods of using the experimental results to
determine the value of jfe. Of these methods, the one utilizing very small
values of pd is the more direct and accurate.

Calculation of Elasticity of Impact in Helium. — ^The experimental
determinations of the relation between 5 and pd are shown plotted along

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198

/. M. BENADE AND K. T. COMPTON.

fSSCOND

LSbuss.

Curve I, Fig. 5. For very small values of pd the points are plotted on a
larger scale in Fig. 6, which includes the region marked off by the small
rectangle near the origin in Fig. 5.

In equation (8) Fo has the value 20 volts, and iV will be taken to be 8.5 .
This value is calculated from values of the mean free path of helium
atoms at i mm. pressure by taking the mean free path of an electron
to be 4 V2 times that of an atom, in accordance with Maxwell's conclu-
sions regarding a small particle moving with relatively high speed among
larger particles. Different methods of estimating the mean free path
of a helium atom give somewhat different results, so that a weighted
mean value of these results was used to determine the value iNT = 8.5.
As a matter of fact, N enters into the equation in such a way that the
conclusions arrived at would not be appreciably affected if any of the
individual values rather than their mean had been used. With these
values equations (8) and (11) become

= 20 I

and

s = 2o{ijr^kpd — i).

(12)
(13)

The ratio r = i when pd =^ o in equation (12) and decreases gradually
as pd increases, approaching the value r = 1.151"* for equation (13).

In Fig. 5, Curve 2 represents equation (12) on the assumption that
impacts are perfectly elastic, so that k = 0.0002685 by equation (4).
It is seen to coincide with the experimental Curve i when pd is very

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}j2;-3^^] ELASTICITY OF IMPACT. 1 99

small, and at large values of pd to approach the straight dotted Curve 3,
which represents equation (3).

(a) Use of Small Values of pd to Determine k. — In Fig. 6 are shown
graphs of equation (12) for various arbitrarily chosen values of k. The
correct value of k is the smallest value for which the curve of equation
(12) lies entirely below the experimental results, approaching coincidence
with the experimental curve at the origin. The reason for this choice
is obvious from the discussion in the preceding section. For instance,
k is less than 0.002, since a curve with a smaller value of k can obviously
be drawn without passing above and intersecting the experimental curve.
Similarly k is greater than 0.000134, since this curve, near the origin,
lies above the experimental curve. An examination of the relation of
the curves of Fig. 6 to the plotted experimental values shows that k
cannot be smaller than about 0.00024 and cannot be larger than about
0.00035. Mechanical considerations show that k cannot be less than
0.0002685, which represents perfect elasticity. Thus the value of k is
fixed with considerable certainty between 0.0002685 and 0.00035. These
values of fe, by equation (i), show that the coefficient of restitution
cannot differ from unity by more than o.oi per cent.

This degree of accuracy in the determination of e seems, at first sight,
impossible. It is possible because of the very small proportion of energy
lost per impact, whence a very slight decrease in the degree of elasticity
would greatly increase the proportion k of energy lost.

(b) Use of Large Values of pd to Determine k, — ^A consideration of the
sensitiveness and constancy characteristics of our apparatus leads us to
the conclusion that a consistent increase of 5 per cent, in the electronic
current is about the least increase which we could detect and take as
definitely indicating a ** break** in the experimental curves of Figs. 3 and 4.
We will therefore take 5 per cent, to be approximately the proportion of
the electrons present which must have energies equal to or greater than
20 volts in order that ionization may be detected. In a Maxwellian
distribution it is found that 5 per cent, of the particles have kinetic
energies equal to or greater than 2.6 times the mean energy. Thus, in
the present case, 20 volts represents 2.6 times the mean energy Z7, whence
the mean energy at the "break points** must have been close to Z7 = 7.7
volts.

The slope of the theoretical pd — s curve for large values of pd is
shown by equation (11) to be (2ForiVVife)~S if the average energy were
represented by Fo, or 20 volts for helium. We have just seen, however,
that the average energy appropriate to our experiments must be taken
to be about 7.7 volts. Substituting this value in place of Vo and taking

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2CX)

J. M. BENADE AND K. T. COMPTON,

[Sbcond
SSRIXS.

r = i.i5i~^ and N = 8.5, we should obtain the slope of the experimental
Curve I, Fig. 5, which is very near 0.5. Thus

1. 151

whence

2(7.7)8.5^*
k = 0.00031

T = 0-5.

Obviously there is much greater uncertainty with regard to calcula-
tions by this method than with regard to results determined by the
method previously discussed. However the order of magnitude cannot
be in error, whence this method affords a confirmatory check of the
results of the first method.

An Attempt to Apply the Method to Hydrogen and Oxygen. — Extensive
series of measurements similar to those made with helium were made
with carefully purified hydrogen and oxygen in the apparatus. In deal-
ing with either of these gases it was found very difficult to determine
definitely the point at which ionization begins, the "break points'* in the
experimental curves being much less sharply defined than in the case of
helium. This was particularly true when working at small values of
pressure times distance pd. We never found any indication of a second
''break" in a curve. Furthermore, the upward inflections in the pd — s
curves, shown in Fig. 7, cannot be explained on the assumptions under-
lying equation (8). For this reason it is not deemed important to
present here the original data or curves, although certain conclusions of a
qualitative nature may be drawn from the results.

.(^

-y

Of,

^ri-

--.^

tS-

—

)

♦

)

ipo

Fig 7.

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X°^*3'^^ j ELASTICITY OF IMPACT. 20I

In Fig. 7 are shown the potentials which must be applied to produce
ionization for various values of pd for oxygen and hydrogen. Curve i
of Fig. 5 for helium is also reproduced for comparison. The feet of the
curves correspond to the minimum ionizing potentials 8.5, n.o and
20.0 volts respectively.

If ionization is due only to the impacts of electrons, and if the average
energy losu by an electron at a collision may be represented by a constant
fraction of its energy for all values of energy below that necessary for
ionization, then there is no reason for an upward inflection like that in
the oxygen and hydrogen curves. This inflection probably indicates
either ionization by positive ions or by radiation from the molecules
excited by the impacts, both of which phenomena would be expected to
be more effective at the larger values of pd. If these, or other super-
imposed effects, account for the upward inflection, it appears that the
course of the curves, had these effects been absent, would have been
somewhat as shown by the dotted lines. At any rate, the trend of the
curves for the smaller values of pd indicates that less energy is lost at
impacts in hydrogen than in oxygen, but that both of these gases are
much less elastic than helium.

The difficulty in obtaining sharp "break points" in the curves for
small values of pd and the failure to find a series of ** break points"
indicates that the group of electrons emitted from the cathode loses its
homogeneity more quickly as it travels through oxygen or hydrogen
than if moving through helium. This again implies that energy is lost
in relatively large amounts at individual collisions, and possibly that the
amount lost may depend on the angle at which the molecule is struck.

Summary.

1. A method is developed for measuring the average fraction of its
energy lost by an electron at a collision with a gas molecule for impact
velocities less than the minimum ionizing velocity. This method can
only be applied to a study of those gases in which the amounts of energy
lost are relatively small and in which no appreciable amount of ionization
is produced, within the range of pressures, distances and applied potentials
used, by any agency except the impacts of the electrons.

2. Collisions of electrons with helium atoms appear to be perfectly
elastic for velocities less than the velocity corresponding to 20 volts.
If any energy is lost by an electron in addition to that transferred to
kinetic energy of translation of the atom, such a loss is certainly less
than 0.02 per cent, of the energy before impact. From this it seems
safe to conclude that :

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202 J. M, BENADE AND K. T. COMPTON. [iSSS

{a) The constituents of a helium atom are held so firmly together
that they are not appreciably displaced, relatively to each other, when
the atom is struck by an electron whose velocity is less than the ionizing
velocity. Or, if such displacement does occur, the natural frequency of
the displaced parts must be so high that there is no appreciable lag
between their motion and that of the approaching and receding electron.

(fc) There is no "minimum radiating potential" below the ionizing
potential 20 volts. The only appreciable effect of the passage of the
electrons through the gas is to slightly increase the mean kinetic energy
of the atoms and thus slightly increase the ordinary heat radiation. The
same effect on the radiation from the gas could be produced by warming it.

3. Collisions of electrons with molecules of hydrogen and oxygen are
much less elastic than in the case of helium and the loss of energy is of a
more complicated type, to which the method of this paper cannot be
applied.

It should be of great interest to apply this method to a study of the
other inert gases and to mercury vapor.
Palmer Physical Laboratory,
Princeton, N. J.

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Vol. XI.1
Nas- J

MERCURY DROPLETS IN MILLIKANS EXPERIMENT.

203

THE USE OF MERCURY DROPLETS IN MILLIKAN'S
EXPERIMENT.

By John B. Derieux.

PROFESSOR MILLIKAN, in his preliminary work on e, tried,
among droplets of other liquids, a few of mercury, and obtained,
as he felt, consistent results within the limits of experimental error.^
Other observers who have since used mercury have had difficulty with it,
often getting very erratic results. Ehrenhaft obtained no consistency
whatspever.* Silvey, however, used it with very good success and while
his results show a slight variation, he attributes it to experimental con-
ditions, viz. : (i) evaporation of the droplets; and (2) "distortion of the
electrical field by the piling up of the fallen droplets."*

That the first is a probable source of error may be seen by Tables I.
and II. which observations I made upon two droplets in the preliminary
part of this work. These tables show the extent of the evaporation often
encountered. In each case the time of observation was about 30 minutes.

Tables Showing the Excessive Evaporation of Mercury

Droplets.

Table I. Table II.

Time Under Gravity.

Time Under Field.

1 Time Under Gravity.

Time Under Field.

16.5

13.4

1 17.8

18.0

17.2

12.1

18.2

17.6

17.8

11.6

1 17.8

17.2

11.6

18.4

17.4

21.4

35.8

1 18.6

16.8

30.4

18.8

16.2

24.4

1 22.8

16.2

20.6

23.0

16.2

26.2

18.8

23.4

27.8

13.8

1 26.2

31.4

11.2
10.6
10.4

27.2

12.2

35.6

10.0
9.8
9.4

9.4

1 R. A. Millikan, Phys. Rev., pp. 389, 191 1.
> Ehrenhaft, Ann. der Phys., 44. 1914; 46. 1915.
» O. W. Silvey. Phys. Rev., Jan.. 19 16.

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204 JOHN B. DERIEUX, [iSSS!

The second also seems a probable source, for after a series of observa-
tions the drop formed by the coalescence of the droplets often has a
radius of one millimeter or more.

Liquid droplets, owing to the certainty with which their density and
sphericity can be known, are preferable to solid ones and since mercury
is a conductor, it is desirable to have, if possible, satisfactory results
from its use in this experiment.

Accordingly this work was undertaken with the following objects in
view:

1. To repeat Silvey's work to see if consistent results could be ob-
tained with mercury if the source of error to which he attributes his
variations be eliminated as far as possible.

2. If consistent results can be obtained, to determine for mercury the
correction for Stokes's Law.

3. To see if the value of e obtained for mercury would agree with that
obtained from oil and shellac.^

4. To extend Silvey's work to reduced pressures and, if possible, to
varying pressures on the same droplet, thus determining more accurately
the slope and intercept of the line connecting e*^' with ijpa.

Apparatus.

The apparatus employed was of the same general form as that used
by Millikan and Silvey; in fact, it was the same that the latter used,
except for a few changes. Sections of it are shown in Figs. lA and iB,

The condenser plates P\ and Pt were 22 cm. in diameter and separated
by glass pillars gggy 1.587 cm. high. A thin ebonite strip surrounded
the plates, glass windows being placed in it at bbb. Through the center
of the upper plate were six holes about .5 mm. in diameter through which
the droplets entered These holes were protected by controllable
shutters ai and ai. Surrounding the condenser plates was an airtight
pressure cylinder C, 30.5 cm. in diameter, the heads of which were each
secured with sixteen stud bolts. Surrounding this cylinder was a
constant temperature jacket /, which was of heavy gas-engine oil, except
during the summer, when it was found necessary to substitute water so
that ice could be used to reduce the temperature. This jacket was
contained in a heavy galvanized tank T, Leading into the upper head
of the cylinder was a pipe from the iron mercury boiler H, which con-
ducted the vapor from the boiler to the cylinder. In the boiler, this
pipe terminated just above the mercury surface, so that the vapor that
passed was the hottest and purest. Attached to the boiler was a glass

» J. Y. Lee, Phys. Rev., Nov., 1914.

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Na'i^'l MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT. 205

gauge G and funnel / for filling. The entire attachment, boiler and
gauge, was hermetically sealed into the cylinder. By means of the
gauge and funnel the amount of mercury in the boiler at any time could
be easily noted and when low replenished with the cylinder under reduced
pressure without changing to atmospheric. This was accomplished by

' Horizontal section.

Fig. I A.
Vertical section.

Fig. IB.

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206 JOHN B. DERIEUX. [iS^S

first putting into the funnel the amount of mercury desired and then
slightly opening the stop-cock just below, the mercury was drawn in
and closing the stop-cock just before it all had passed, the admission of
air was prevented. This could be done without disturbing seriously the
pressure in the cylinder. The vapor from the boiler was carried into the
cylinder by a blast of air admitted by the stopcock. Connected to the
pipe leading into the cylinder was a line of pressure tubing to the pump
and monometer M.

For observation, the space between the condenser plates was illuminated
through a glass window W, by a right-angled arc A. The rays of the
arc were focused by a cylindrical lens L on the line joining the centers 0
of the plates which was the line of fall of the droplets. The heat rays
from the arc were absorbed by a water filter /^, 80 cm. long and a cupric
chloride filter 7^2, 4 cm. thick.

A telescope Y having a magnifying power of 24 and a focal length of
about 25 cm., was used in observing the droplets. In the focal plane of
the eyepiece was a scale, the smallest division of which corresponded to
2 mm. of fall. The extreme distance of possible fall was 1.5 cm. In
focusing, the whole telescope was moved backward or forward by means
of a rack and pinion, the eyepiece remaining fixed in the tube. Observa-
tions were made through a window 90 degrees from the one through which
the light entered.

For timing short intervals, five to forty seconds, a Hipp chronoscope X ,
indicating to one thousandth of a second, was used. This was controlled
by a switch Sa at the observer's side, readings from the chronoscope
being noted and recorded by an assistant. Three calibrations of this
instrument were made during the work, the three giving practically the
same errors which were, including personal error, + 0.07 for five seconds
and — o.io for forty seconds with a linear relation between. The longer
times were taken on a stopwatch reading to .2 of a second.

The potential of the plates was furnished by battery B of 2,500 small
storage cells which furnished about 2 volts each, giving a total potential
of about five thousand volts. These potentials were measured by a
Braune static voltmeter F, three calibrations of which were also in
accord. The potential on the condenser was controlled by a double
switch Si by means of which the condenser could be charged, grounded,
and reversed. This switch was made of a large paraffin block with mer-
cury wells for contact. A variation of the potential, when desired, was
secured through a controller E.

For changing the charges on the droplets, an X-ray tube X, was used
to ionize the air between the condenser plates. The rays entered through

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Na'ii^^*] MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT. 207

a window about 30 degrees behind the one through which the illumination
entered, or about 120 degrees from the one through which observations
were made. The X-ray tube was controlled by a switch Sz. In the
latter part of the work an ultra-violet light £7, was used which changed
the charge through photoelectric eflfect on the droplet, the window Q
through which it entered being of quartz.

The temperature of the air in the condenser was taken from a ther-
mometer / placed inside the cylinder besides the plates, readings being
taken through the window Q. This work was done in a constant temper-
ature room and a thermostat controlling an electrical heater kept it in
the winter within .2 of a degree of constancy. In addition, there was a
jacket of oil surrounding the cylinder; therefore, the temperature of
the air in the condenser was kept practically constant. In the sununer,
when it was found necessary to substitute water for the oil so that ice
could be used to keep the temperature down, the ice was applied some
time before a series of observations was begun to insure uniform tempera-
ture and consequent absence of convection currents.

Evaporation.

•

The change in the apparatus proposed by Professor Millikan to
eliminate the source of error in Silvey's work was to cover the lower
plate of the condenser with a pool of mercury. This should diminish
the first mentioned source of error in his work, viz., evaporation, for it
should keep the space surrounding the droplets saturated with mercury
vapor. It should at the same time eliminate his second error, viz., the
piling up of fallen droplets, by simply allowing them to become a part
of the mercury of the pool.

The oil which had been used in the previous work inside the cylinder
surrounding the condenser was carefully removed by several applications
of benzine. To insure all trace of the benzine vapor being removed, the
cylinder was left open for several hours with an electric fan playing into it.

The proposed alterations in the condenser were made and a few pre-
liminary droplets caught to see the effect on the rate of evaporation.
These showed a great reduction in it; in fact, it was almost entirely
stopped. One of the droplets was held for two hours and four readings
of the time required for it to fall i cm. under gravity taken at intervals
of about thirty minutes were 48 sec, 48 sec, 46 sec, and 48 sec. It
seemed as though the plan was successful. Hence regular observations
were begun.

After several days, however, the rate of evaporation was found to
slowly increase. Opening the cylinder to see if a cause might be surmised.

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208 JOHN B. DERIEUX. [ISSS

it was found that the jacketing oil had leaked in. From this it appeared
that the presence of oil vapor increases the evaporation of mercury
droplets and that the reduced evaporation above resulted from the
absence of oil vapor rather than the presence of the mercury vapor.
To verify this supposition, the tank was again thoroughly cleaned and
the pool of mercury removed. Readings again taken showed about as
slow evaporation as in the first instance. Observations on a droplet
just preceding this change and one just following it are recorded in
Tables III. and IV., respectively. In these the time under the field is
omitted because at the close of the observation a broken battery con-
nection was found and the readings, therefore, are not considered trust-
worthy. The entire time of observation was 20 minutes and 55 minutes,
respectively, and must be considered in comparing the rates of evapora-
tion; it is important to know too that the droplet in Table III. was not
in a thoroughly saturated atmosphere of oil vapor for the reason that
the leak was only slight and the oil was only present a short time.

Tables Showing Decreased Evaporation with the Elimination of

Oil Vapor.

Table III.

Table IV.

Presence of Oil Vapor,

Absence of Oil Vapor.

Tim« Under Qravity.

Time Under Qravity.
6.9

Time Under Qravity.

6.6

1 9.6

9.7

6.8

7.0

9.7

9.8

6.9

7.4

9.6

9.7

6.9

7.1

9.6

9.8

6.9

7.4

1 ,9.6

The increased rate of evaporation in the presence of oil vapor is in
accord with Silvey's high rate of evaporation, for his work was done in
an atmosphere saturated with oil vapor. This effect is probably pro-
duced by a coating formed by the condensation of the oil vapor upon the
droplet. This is in accord with McKeehan's work who found that a
coating of other liquids upon the surface of a mercury droplet increased
its rate of evaporation.^

Finding that by eliminating the oil vapor the proposed alterations for
reducing the evaporation were not necessary, the work was carried on
without the mercury pool, the air being kept free from oil vapor.

The second source of error, the piling up of the droplets, was eliminated
by frequent cleaning of the plates.

»L. W. McKeehan, Phys. Rev., Aug., 1916.

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na'i^'] mercury droplets in millikan's experiment. 209

Manipulation.

The droplets were secured by condensing the vapor from boiling
mercury. The vapor was generated in boiler H (Fig. iB) and carried
into cylinder C by a blast of air. During a blast, shutter at was held
open to allow free entrance to the cylinder, shutter ai being closed to
prevent the holes in the upper plate of the condenser from becoming
clogged by large droplets. Following a blast, shutter aj was closed and
after waiting for a few seconds for the large droplets to fall to the bottom
of the cylinder, shutter ai was opened and the small droplets were seen
to enter the condenser. A droplet of desired size, as judged by the
velocity of fall, was selected and the potential was thrown on to "the
condenser. If the droplet carried a charge it responded and by manipu-
lating the reversing section of switch Si it was drawn toward the upper
plate. Shutter ai was then closed to prevent the further entrance of
droplets, and the chosen one held until the field was clear and air currents
had subsided. •

The time required for the droplet to fall i cm. under gravity and that
required to return under the field were observed a number of times. By
means of the X-rays the charge on the droplet was changed and another
series of readings was taken. These operations were repeated as often
as desired. If only constant pressure results were sought, the drop was
then released, another caught and similar observations taken.

In the work at varying pressures the droplet was caught at atmospheric
pressure and a set of readings taken as for constant pressure. It was
then drawn near the upper plate, the pump started, and the stopcock
leading to it gradually opened. As the ebonite strip around the con-
denser fitted snugly, the main exit for the air in the condenser was
through the holes in the center of the upper plate, consequently, a rising
current of air was produced around the droplet. By placing it at a
certain point it would be held just in balance by this current with the
condenser discharged. Slightly nearer the upper plate it would be carried
upward and at another point, still nearer, with the condenser reversed,
it would be held in balance again, if a droplet passed beyond the last
mentioned point it could be returned by closing the stopcock leading to
the pump.

When the desired reduction in pressure had been made the stopcock
was closed and another set of readings taken. While reductions in
pressure in the work on a given droplet could be obtained as often as
desired it was never repeated more than four times because evaporation,
though slight, resulted in the equivalent of a different droplet if a given
droplet was held too long. The values of the radii of the drop and the

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210 JOHN B. DERIEUX. [^m.

values of Ci^'^ were obtained precisely as detailed in Professor Millikan's
paper^ and the relation between ei*'* and i/pa graphed as there described.

Results.

In Tables V. and VI. are recorded typical readings on a droplet at
atmospheric pressure, Tables VIII. and IX. at reduced pressure, and
Tables XL and XII. at varying pressures. The numbers given in the
columns headed tg ^^ the readings taken on the times of descent through
I cm. under gravity, those headed h give the times of ascent under the
field: i/tf the reciprocals of the times of ascent, and i/t^f denotes the
reciprocal of the time of ascent after a change in charge. Columns n'
contain the number of elementary units of change in charge on the
droplets and are the quotients obtained by dividing the numbers in the
column {i/ly — i/trd by their greatest common divisor. Under n are
recorded the total number of units of charge on the droplets, determined,
as in the previous case, by- taking the quotients obtained by dividing the
numbers under {i/tg — i/tji) by their greatest common divisor.

In Tables VII., X., and XVIII. are given the stimmaries of the results
obtained at atmospheric, reduced, and varying pressures, respectively.
In these Tables, under ig are recorded the average times in seconds of
the fall of the droplets, under p, the pressure in cm. of mercury inside
the pressure cylinder surrounding the condenser, under P.D. the potentials
in volts between the condenser plates, and under Tem. the temperature
in degrees (Cen.) of the air in the cylinder. In the columns headed a,
are recorded the radii of the droplets, under i/pa, the reciprocals of the
products of the radii and the pressures, and under //a, the quotients of
the mean free path of the molecules by the radii of the droplets. Under n
are recorded the extreme number of elementary units of charge upon the
droplets during the observations, under Ci*'', the two thirds power of the
values of the elementary unit of charge in electrostatic units, obtained
without the application of the correction to Stokes's law, under c*'* the
two thirds power of the values of the elementary unit after the corrections
to Stokes s law, according to Millikan's method, have been applied.
These last are obtained from the graph and are the intercepts on the e^^^
axis of lines through the points representing the droplets and having the
same slope as the general line for all of the droplets.

iR. A. Millikan, Phys. Rev., ist Sen, 32. 1911; 2d Ser., II. (1913), 117; Phil. Mag.,
July, 1917.

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Vol. XI.1
No. 3. J

MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT.

211

Atmospheric Pressure.

Table V.
Drop No. 10.

I
Tf

tp /y

~n\tF tF*)

- + -

=(f/^)

48.6

16.96

49.4

.0206

.0814

.0271

.0791

.0264

17.01

9.91

16.89

9.88

.1020

.1605

.0268

16.88

9.88
6.58

.0545

.0272

6.55

.1565

.2150

.0269

17.00

6.50
6.26

7.72
7.67

.0279

7.98

.1296

.1881

.0269

7.99

7.63

.1080

.0270

46.4

47.3

47.0

.0216

.0801

.0267

46.2

.0272

20.34

20.69

.0488

.1073

.0268

17.81

20.48
13.24

.0267

13.53

.0755

.1338

.0268

17.95

13.27
13.35

17.40

.0271

.0269

Duration of exp. -« 30 min.
Temp. - 23.0*> C.
Pres. - 74.40 cm. Hg.
P. D. - 4.702 volts.

a ■ 5.616 X 10-» cm.
i\pa - 239.3.
*!«'» - 67.81 X 10-«,
e*/* « 60.65 X 10-«.

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212

JOHN B. DERIEUX,

[Sbcomo
Sbriss.

Table VI.
Drop No. 14.

X I

n'Xtp tp)

i- + -^

K^^i)

tF tp*

tg^tF

26.19

15.79

26.02

15.88

26.02

15.88

.0633

.1016

.0339

26.17

15.81

26.07

15.83

10.29
10.34

.0343

10.29

.0976

.1359

.0339

26.20

10.36
10.24

34.40
34.58

.0685

.0342

33.90

.0291

.0674

.0337

26.05

34.36
34.27

15.87
15.74

.0349

15.91

.0630

.1013

.0338

15.98

16.04

.0338

34.21

34.27

34.16

.0292

.0675

.0337

26.19

34.18
34.29

15.90
16.06

.0333

16.10

.0625

.1008

.0336

16.03

26.11

_ .

.0341

.0337 _

Duration of ezp. « 55 min.
Temp. « 23.0*» C.
Pres. « 74.27 cm. Hg.
P. D. « 4,630 volts.

a = 4.521 X 10-» cm.
ilpa = 297.9.
fi'^» - 69.87 X 10-».
e'^» = 60.71 X 10-».

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Vol. XL!
No. 3. J

MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT.

213

Table VII.
ResuUs at Atmospheric Pressure.

No.

Tem.oc.

(Cm. Hg)
75.10

P.D.

(Volts)

/^(Sec.)

aXxo»
(Cm.)

^i^Xio*

*?Xio«

22.9

4,580

4.56

11.230

118.6

23-40

64.96

61.36

23.0.

75.10

4,475

6.02

9.764

136.4

13-48

65.30

61.16

23.0

74.92

4,645

7.53

8.695

153.5

10-26

65.76

61.10

23.0

74.61

4,690

8.09

8.364

160.2

9-13

66.21

61.34

23.0

73.81

3,375

9.66

7.661

176.9

8-19

66.01

60.65

23.0

74.61

4,650

9.77

7.575

177.4

6-14

66.75

61.36

23.0

74.88

4,930

11.84

6.&82

194.1

4-11

66.79

60.90

23.0

75.33

3,700

12.19

6.778

195.8

10-25

66.99

61.04

23.0

75.64

4,425

17.21

5.660

233.6

4-15

67.87

60.77

23.0

74.40

4,702

17.40

5.616

239.3

3- 8

67.81

60.54

22.8

75.12

4,690

18.73

5.413

246.0

2- 6

68.10

60.63

22.9

75.81

4,845

21.20

5.046

261.5

3- 7

69.50

61.56

23.0

74.44

4,690

22.00

4.953

271.2

4- 7

69.28

61.04

23.0

74.27

4,630

26.11

4.521

297.9

2- 4

69.87

60.83

23.1

74.27

4,500

34.60

3.852

349.5

2- 4

71.78

61.16

23.0

74.45

3,935

39.60

3.604

372.6

1- 3

72.74

61.42 1

23.0

75.98

3,905

40.58

3.563

369.5

1- 4

72.62

61.39 li

22.9

74.83

3.775

48.04

3.244

411.8

1- 2

74.05

61.54

23.0

74.33

4.105

49.80

3.195

421.0

1- 2

73.47

60.68

Mean

61.08

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214

JOHN B. DERIEUX.

iSBCom
LSBun.

Reduced Pressures.

Table VIII.
Drop No. 33.

X X

X / X X

n'\tF tp

tF tr

27.38

1\.13

27.43

24.41

.0410

.0391

12.54

27.64

12.47
12.47

.0801

.0383

.0380

23.74

.0418

28.15

23.46

.0426

.0394

310.

.0032

300.

.0033

.0408

22.61

.0441

28.80

22.21
22.06

.0453

.0403

' .0403

11.70

29.28

11.73

.0856

•

11.61

.0395

21.59

.0461

29.65

21.28
20.92

.0478

.0406

138.

.0072

.0406

20.8

.0478

30.3

20.5
20.0

.0502

.0405

10.92

.0907

31.12

10.76
10.79

.0927

.0412

19.38

30.95

19.55
19.21

.0515

.0414

.0412

31.68

99.0
98.0

.0101

29.50

.0401

Duration of exp. =

Temp. «

Pres. «

P. D. =

35 min.
23.1° C.
56.11 cm. Hg.
4,590 volts.

.0773

a « 4.086 X 10-* cm.
ilpa « 436.2.
fi2/» - 75.37 X 10-«.
e^'* - 62.00 X 10-«.

X /jt_ _x_\
nytg'^tF)

.0386

.1164

.0388

.0778

.0389

.0385

.0793

.0396

.1196

.0399

0807

.0403

.0405

.0820

.0410

.1229

.0410

.0837

.0418

.0401

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Vol. XI
No. 3.

] MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT. 215

Table IX.
Drop No. 35.

/jr 1 iF tF*

n'\tF trJ

^{h^h)

9.72

•

9.74

.0141

.1661

.0277

16.16

9.69
20.50

.0554

.0277

16.20

20.55

.0487

.0546

.0273

.1101

.0275

- 168. (fall)

.0059

.0545

.0272

.0454

.0272

20.55

.0486

16.40

20.43
20.17

13.09

.0498

.0274

.1103
.1370

.0276
.02-4

16.45

12.87
12.96

.0772

16 30

1 .0274

.0275

Duration of exp. =15 min.
Temp. = 23.3° C.
Pres. = 56.86 cm. Hg.
P. D. - 4,645 volts.

a « 5.673 X lO"* cm.
ilpa - 310.0.
«!«/» « 71.00 X 10-«.
«»/» = 61.50 X 10-».

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2l6

JOHN B, DERIEUX.

rSSCOKD

LSbribs.

Table X.
Results at Reduced Pressures,

No.

Tern, o C.

(Cm. Hg)

P. D.

(Volts)

f, (Sec.)

(Cm.)

/iJx»o»

^txioi

22.9

33.85

4,560

16.85

5.295

558.0

2- 5

79.17

61.97

22.9

33.65

4,775

31.75

3.597

826.2

1- 2

91.12

(65.64)

23.0

30.89

4,545

46.25

2.817

1150.0

2-4

102.00

(66.54)

22.7

40.49

4.690

22.45

4.648

531.4

2- 5

77.23

60.85

23.0

57.70

4.560

32.58

3.885

446.2

1- 4

76.25

62.49

23.0

51.44

4,520

10.10

7.396

260.7

5- 9

68.91

60.87

23.1

52.07

4,480

27.75

4.286

445.3

1-4

73.30

59.57

23.0

56.76

4,645

21.62

4.876

361.3

2- 6

72.64

61.50

23.0

55.44

4,610

26.75

4.424

407.8

1- 4

71.32

58.75

23.5

51.73

4,195

11.66

6.875

281.2

5-12

67.86

59.19

23.0

56.24

4,625

16.03

5.685

312.8

3- 8

72.28

62.63

23.4

60.96

4,610

14.00

6.173

265.3

3- 7

69.39

61.21

23.1

50.43

4,600

37.50

3.556

557.7

1- 3

78.74

61.54

23.1

56.11

4;590

29.50

4.086

436.2

1- 3

75.37

61.92

23.0

53.52

4,630

36.10

3.722

502.1

1- 3

76.02

60.54

23.2

56.86

4,645

16.30

5.673

310.0

2- 6

71.00

61.44

23.3

58.00

4,600

23.90

4.588

375.8

1- 5

74.30

62.72

23.7

58.11

4,570

50.20

2.994

574.8

1- 2

80.13

62.41

23.4

46.49

4,570

28.30

4.129

521.0

1- 2

76.81

60.75

24.3

32.04

4,580

8.96

7.570

412.3

5-12

73.31

60.59

24.7

33.36

4,555

14.30

5.782

518.4

3- 7

78.34

62.36

25.3

74.71

4,600

24.01

4.671

286.5

2- 6

71.36

62.53

26.2

74.67

4,565

14.80

6.113

219.1

3- 5

68.00

61.25

26.5

74.67

4,520

35.65

3.767

355.7

1- 3

71.85

60.89

26.5

38.57

4,570

25.50

4.227

613.4

1- 3

82.12

(63.21)

25.7

41.69

4,590

14.94

5.806

413.1

3- 7

74.44

61.70

27.6

45.37

4,515

36.33

3.612

610.3

1- 3

79.52

60.71

28.6

59.23

4,515

10.08

7.404

227.9

5-10

67.92

60.89

28.5

74.89

4,560

15.65

5.965

223.9

3- 7

67.20

60.30

28.0

74.89

4,635

38.16

3.717

358.4

1- 3

71.53

60.38

22.9

74.93

4,560

15.73

5.923

225.3

3- 5

67.74

60.79

Mean

: 61.16

Values of e^^* inclosed in parenthesis are considered as beyond the breaking point of the
curve smd are not used either in the graph or the mean.

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Vol. XL!
Na3. J

MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT.

217

Varying Pressures.

Table XI.
Drop No. 59 A.

tF tjr'

H'XfF tF'}

•■.*h

\{r,-rr)

23.27

52.6

.0190

.0617

.0308

23.30

.0313

23.34

19.66

19.97

.0503

.0930

.0310

20.04

.0313

23.29

12.35
12.44

12.25

.0816

.1243

.0311

12.33

.0623

.0311

51.6

23.40

51.8
20.02

.0193

.0317

.0316

.0620

.0310

19.75

.0511

.0936

.0312

19.78

.0314

.0315

23.60

12.22

23.58

12.28

12.25

.0824

.1251 •

.0313

23.44

12.11

23.36

.0314

.0311

Duration of exp. « 30 min.
Temp. - 23.0** C.
Pres. - 75.09 cm. Hg.
P. D. - 4.625 volts.

a - 4.815 X 10-» cm.
ilpa -276.0.
<?!«/» « 69.00 X 10-«.
e«/» - 60.6 X 10-».

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2l8

JOHN B. DERIEUX.

[Sboond
Sbribs.

Table XII.
Drop No, 59B.

X X

tF tF'

»'

n'\tF tF")

4*i

nXtg^tFl

20.53

39.67

20.76

39.78
16.22

.0251

.0370

.0737

.0368

16.14

.0621

.1107

.0369

16.09

.0379

20.79

10.15
10.09

10.03

.1000

.1482

.0374

10.07

.0744

.0372

20.90

38.97

38.80

.0256

.0736

.0368

38.96

.0369

20.82

16.15

16.13

.0625

.1104

.0368

16.05

.0375

20.84

10.10

20.73

9.97

10.15-

9.98

.1000

.1480

.0373

20.80

.0373

.0370

Duration of exp. « 35 min.
Temp. = 23.0** C.
Pres. « 34.81 cm. Hg.
P. D. « 4,565 volt8.

a - 4.704 X 10-» cm.
if pa - 609.6.
ei^^ - 81.14 X 10-«.
^^ - 62.6 X io-».

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No. 3. J

MERCURY DROPLETS IN MILUKAN'S EXPERIMENT,

219

Table XIII.
Drop No. 59C.

Z X

i.^h

-.(^f.)

16.96

30.84

16.89

31.10
31.03

.0322

.0466

.0897

.0449

17.31

12.78
12.69

12.93

.0788

.1363

.0454

12.65

.0469

17.19

7.98
8.15

7.95

.1257

.1832

.0458

8.07

7.98

.0921

.0460

17.40

29.58

30.15

.0336

.0911

.0455

29.48

.0460

17.41

12.63

12.S8

.0796

.1371

.0457

12.54

12.70

.0463

.0460

17.52

8.00

17.39

8.00

17.37

8.13
8.05
8.13

.1256

.1831

.0458

17.39

.0465

.0455

Duration of exp. * 25 min.
Temp. - 23.0* C.
Pres. - 19.63 cm. Hg.
P. D. - 4,540 volts.

a - 4.641 X 10-» cm.
ilpa = 1097.0.
ei*'* - 99.86 X 10-«.
«»/» - 65.8 X 10-«.

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220

JOHN B. DERIEUX.

rSBCOI«D

LSbries.

Table XIV.
Drop No. 60i4.

tF tF"

n'\tF if^j

i-T,

nXtg^tf)

19.96

37.23

19.77

36.79
37.37

.0269

.0776

.0259

19.96

18.59

18.77

.0538

.1045

.0261

18.48

.0266

19.76

12.54

12.51

.0804

.1311

.0262

12.47

12.51

.0541

.0270

19.73

37.37

37.90

.0263

.0770

.0257

38.41

38.07

.0273

19.90

18.61

18.80

.0536

.1043

.0261

18.57

.0267

19.69

12.47

19.64

12.52

12.59

.0803

.1310

.0262

19.87

12.62

19.80

12.50

19.76

.0269

.0260

Duration of exp. « 30 min.
Temp. - 22.9*» C.
Pres. - 75.10 cm. Hg.
P. D. - 4,612 volts.

a » 5.445 X 10"* cm.
ilpa - 247.7.
«!«/» - 65.80 X 10-«.
f«/» - 58.3 X 10-«.

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Vol. XL!
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MERCURY DROPLETS IN MILLI KAN'S EXPERIMENT.

221

Table XV.
Drop No. 60B.

X X

tp tp.

n'\tp ip)

4*4

.V4)

18.02

33.76

18.13

33.81
34.29

.0293

.0296

.0858

.0286

17.93

17.11

17.08

.0589

.1147

.0287

16.82

.0591

.0295

8.54

8.69

8.35

17.91

8.54
8.69
8.33
8.54
8.45

.1180

.0887

.0296

.1738

.0289

17.88

33.84

33.82

.0293

.0851

.0284

34.54

.0284

17.95

17.48

17.36

.0577

.1135

.0284

17.31

.0299

18.01

11.51

11.62

.0876

.1434

.0287

11.54

11.22

.0304

18.06

8.51

8.62

.1180

.1738

.0289

8.46

.0305

18.02

11.53

18.01

11.56
11.45

.0875

.1433

.0287

17.92

.0297

.0287

Duration of exp. — 45 min.
Temp. = 23.0** C.
Pres. ■» 43.07 cm. Hg.
P. D. - 4.600 volts.

a - 5.377 X 10-» cm.
ilpa -431.8.
ex^^ - 72.23 X 10"

^j/i

> 59.1 X 10-«.

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222

JOHN B. DERIEUX,

[Sbconb
Seribs.

Table XVI.
Drop No. 60C.

z
*F

X I

M^-??)

r/r.

n\tg ty)

16.55

31.77

16.37

32.49
31.75

.0312

.0322

.0926

.0309

- 1000 (falling)

.0010

.0646

.0323

.0622

.0310

16.35

15.72

.0636

.1248

.0312

15.78

.0646

.0323

- 1000 (falling)

.0010

.0324

.0622

.0311

16.43

31.72

32.23

.0314

.0926

.0309

31.46

.0327

.0324

16.39

15.73

15.52

.0641

.1253

.0313

16.44

15.63

16.34

.0323

.0311

Duration of exp. » 30 min.
Temp. = 23.1* C.
Pres. - 29.95 cm. Hg.
P. D. - 4.590 volts.

a - 5.394 X 10-» cm.
ilpa - 619.0.
ei^* - 78.84 X 10-«.
^* - 60.2 X 10-«.

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Vol. XL!
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MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT,

223

Table XVII.
Drop No. 60D.

tp ip ^y

It'

n\tp tpf)

n\tg^ tp)

- 1000 (falling)

.0010

. .0390

.0390

.0730

.0365

13.79

13.93

26.29

26.19

.0383

.1107

.0369

25.86

.0392

13.78

12.91

12.78

.0775

.1499

.0375

13.28

12.94

.0780

.0390

- 1000 (falling)

.0010

.0390

.0730

.0365

14.00

26.23

26.40

.0381

.1105

.0368

26.14

.0386

i)386

13.84

12.96

13.88

13.27
13.11
13.02

.0767

.1491

.0373

13.80

.0389

.0369

Duration of exp. ■> 20 min.
Temp. = 23.1** C.
Pres. - 18.00 cm. Hg.
P. D. = 4.580 volts.

a - 5.363 X lO"* cm.
ilpa - 1036.0.
ei«/» - 94.19 X 10-«.
<?«/» - 61.8 X 10-«.

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224

JOHN B, DERIEUX.

fSBCOND

LSbribs.

Table XVIII.
ResuUs at Varying Pressures.

No.

Tem.oC.

51^

23.0

•• B

23.0

52 A

23.0

•* B

23.0

53 A

22.9

" B

23.0

54A

22.9

*' B

23.0

55 A

22.9

" B

22.9

56 A

22.8

" B

23.0

" C

23.1

57 A

23.0

" B

23.4

5SA

23.0

" B

23.5

59 A

23.0

" B

23.0

" C

23.0

60 A

22.9

" B

23.0

" C

23.1

" D

23.1

61 A

23.7

" B

23.9

(CnuHf)

74.89
29.49

74.64
31.31

74.67
44.30

74.92
40.92

74.74
32.79

75.17
29.84
16.46

75.11
36.16

74.69
33.29

75.09
34.81
19.63

75.10
43.07
29.95
18.00

74.84
41.26

P. D.

(Voltk)

4,560
4,550

4,440
4,420

4,550
4,560

4,580
4,580

4,610
4,600

4,555
4,555
4,550

4,545
4,547

4,597
4,585

4.625
4,565
4,540

4,612
4,600
4,590
4,580

4,607
4,590

^,(Sec.)

10.53
13.80

12.54
18.44

12.70
12.62

22.83
26.51

19.36
18.38

14.26
13.70
11.33

14.61
13.94

24.90
21.75

23.36
20.80
17.39

19.76
17.92
16.34
13.80

14.80
13.50

flXto*

iCm.)

7.328
5.869

6.604
5.163

6.829
6.631

4.939
4.307

5.381
5.184

6.151
5.727
5.641

6.117
5.902

4.763
4.764

4.815
4.704
4.641

5.445
5.377
5.294
5.363

6.074
6.085

rjlxxol

182.3 5-9
577.9 I 5-6

199.5
618.7

196.1
340.4

270.3
567.4

248.6
588.3

216.3

585.2

1076.0

217.6
468.6

280.6
630.5

247.7

431.8

619.0

1036.0

220.0
398.3

4-8
2-5

5-9

5-7

2-5
1-3

2-5
2-5

3-5
3-5
2-4

3-6

3-5

1-3
1-3

276.0 I 2-4

609.6 I 2-4

1097.0 ! 2-4

3-5
3-^
2-4
2-4

3-5
3-5

66.98
79.57

65.65
76.10

63.16
67.30

67.05
76.03

66.68
75.61

69.34

83.30

103.80

68.52
76.91

65,98
76.78

69.00
81.14
99.86.

65.80
72.23
78.84
94.19

68.55
74.89

i Xio»

13.04
41.35

14.24
44.27

14.03
24.35

19.34
40.60

17.79
42.09

15.47
41.87
77.00

75.57
33.53

20.07
45.10

19.74
43.61
79.97

17.72
30.89
44.29
74.11

15.74
28.49

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Na*3^^*] MERCURY DROPLETS IN MILLIKAN'S EXPERIMENT. 2 25

Table XIX.
Slopes at Varying Pressures.

Drop No... 52. ^ sa.

53. 1 54. 55. 56.

57.

58.

59. 1 60.

6x. 1 Mean.

Slope

1 1

X 10«.

44.46] 34.80

40.13

42.25 36.76' 52.88

46.71

43.15

50.86 49.08

49.73 44.63

Value of

1 ! •

1 '
1

_.__

! ! .730

^,5/y/ _ ex^fv ^ Slope

Slope =--- . ^ =61.13 X To- •

Summary.

I. Consistent results are obtainable from the use of mercury droplets
if the necessary precautions are taken. The greater variation in the
results at reduced and varying pressures, are due, I think, partly at least,
to the higher rate of evaporation present during this part of the work.
The extent of it, in some instances, may be seen from Table VIII.

II. As the correction term constant. A, for Stokes's law, the results at
atmospheric pressure give .695, reduced pressures .705, and varying

Graph from results at atmospheric pressure.

^iO

Fig. 2.

pressures .730. The greater value in the last instance is due, I believe,
to a change in the surface of a droplet between the first and last observa-
tions upon it. It is probable that an oxide film forming upon it increases
the coefficient of slip toward that of solid spheres. In taking the mean,
therefore, I would give the above values weights of 3, 2, i, respectively,
thus giving A the value .704.

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226 JOHN B. DERIEUX. [^».

III. The value of ^'' obtained from the mean of the results at atmos-
pheric and reduced pressures is 61.12 X io~® which is practically the
same as that obtained from the use of oil, t. c, 61.13 X ^o~^.

Graph from results at reduced pressures.

Fig. 3.

In conclusion I wish to express my thanks to Professor R. A. Millikan
for suggesting this problem and for his kindly advice during the investi-
gation, and also to Professor H. G. Gale for his timely suggestions. To
my wife, also, I wish to express my appreciation for her assistance in the
experimental part of the work.

Ryerson Laboratory,

University of Chicago.

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Vol. XI.^
No. 3. J

THE OPTICAL PROPERTIES OF RUBIDIUM.

227

THE OPTICAL PROPERTIES OF RUBIDIUM.

By J. B. Nath ANSON.

OOME time ago there appeared in the Astrophysical Journal,^ an ac-
^ count of an investigation, I made, on the reflecting powers of
sodium, potassium and rubidium. A direct method was used, employing
a photo-electric cell as a photometer.

Up to the present, the polarimetric method of investigating the optical
properties of the alkali metals, has been applied only to sodium by Paul
Drude,* and to sodium and potassium by R. W. and R. C. Duncan.' It
therefore seemed desirable to apply the polarimetric method to the
determination of the optical properties of rubidium, at the same time
affording a comparison between the values of the reflecting powers of
rubidium as obtained by the former direct method, and the present
polarimetric method.

The Mirror.

The rubidium mirror used in this investigation was the same as that
used in the former one, the mirror still being in very good
condition. A description of the method of preparation of
the mirror was given in The Astrophysical Journal, but
for the sake of clearness it will be briefly repeated. The
mirror was prepared in a vacuum by the distillation of
the rubidium upon a piece of plane parallel glass P
(Fig. i), 2.5 cm. square, and 1.74 mm. thick. This
glass plate formed part of a glass cell C. A mixture
of rubidium chloride and calcium was placed in the
hard glass tube D. Upon heating to a high tempera-
ture, the rubidium vapor passed to A^ where it was
condensed. The metal was purified by being redistilled
from A to B. A small globule of the molten metal was
then transferred to F, from where on further heating
the metal was vaporized and condensed upon the glass
plate P, the outside of which was kept ice cold. After
the formation of the mirror, the cell was sealed off at E.
Of several mirrors made, the best one was used in this investigation.

* Astrophysical Journal, 44, 137, 1916.
' Annalen der Physik, 64. 159. 1898.
» Phys. Rev., 36, 294. 1913.

Rwkidivm,

fb Pumb

(

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228 7. B. NATHAXSOy. [sSSS.

The Experimental Method.

The optical constants were evaluated from observed values of the
phase difference and azimuth of the reflected elliptically polarized light.
These were determined by means of a simple Babinet compensator and
two nicols mounted on a large spectrometer of the Societe Genevoise.
A 250-watt nitrogen-filled tungsten lamp was used as a source of light.
One filament of this lamp was focused on the slit of a Hilger spectrom-
eter Hf Fig. 2. The eyepiece was removed, allowing a very narrow
beam of monochromatic light to fall upon the slit of the collimator C.

The beam of parallel rays then
»*« ^ ^ passed through the nicol Ni, whose

plane of polarization was at an

angle of 45° with the plane of in-

; J_ cidence.

^ ^sn \ In order to avoid the disturbing

U^ fl J_ reflection from the glass surface of

I T A^ the mirror Jlf , the latter was pressed

A against the hypotenuse side of a

_.. - right angle prism, cedar oil being

placed between the prism and mir-
ror. Light incident on one leg of the right angle prism was reflected from
the mirror at an angle of 45®, passing out normally through the other
leg of the prism. Thus the only changes in azimuth and in phase differ-
ence were those due to reflection at the metal glass boundary.

After reflection from the mirror, the elliptically polarized light was
rendered plane polau-ized by the Babinet compensator B, and extinguished
by the analyzing nicol N2 which was viewed by the eyepiece E.

Method of Observation.

The constant of the Babinet compensator was determined several
times for each wave-length used. Settings were made on the band of
zero phase difference, and then on the bands of — 2ir and + 2t, there
being ten readings taken for each position. The mean value of the con-
stant for any wave-length was calculated from as many as 180 individual
settings. Having obtained the position of the dark band representing
zero phase difference, the telescope carrying the compensator and
analyzing nicol was rotated through 90®, the mirror put in place, and the
new position of the band noted. The amount of displacement of the
dark band represents the phase difference A produced on reflection at
the rubidium surface.

In order to obtain the azimuth ^, the polarizing nicol was set with its

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Vol. XI 1
No. 3. J

THE OPTICAL PROPERTIES OF RUBIDIUM,

229

plane of polarization making successively angles of 45°, 135®, 225®, and
315® with the plane of incidence. For each position of the polarizer, the
two positions of the analyzing nicol were determined by setting for
maximum blackness of the bands. Ten readings were taken for each
position, or a total of 80 settings for the determination of ^. The mean
of all the readings of the analyzer for two positions of the polarizer 180°
apart was subtracted from the corresponding mean of all the readings
for the other two positions of the polarizer. This difference is equal
to 2^.

The following example will illustrate briefly the method of calculating
2^ and A.

Table I.

X « 454.6/1/4.

Position of Polarizer

0° 18'.

180° 18'.

90° 18'.

270° 18'.

Position of analyzer

•I

237° 42'
54° 36'

237° 42'
54° 54'

141° 48'
323° 54'

141° 54'
323° 30'

Mean

146° 9'

146° 18'

232° 51'

232° 42'

Mean of means

146° 14'

232° 47'

Difference = 2^

86°

33'

For Babinet Constant.

20.270 1

-fair.

Position of compensator

27.581

34.839

Differences

7.311

7.258

Mean

7.285

Position of compensator upon reflection from rubidium = 29.613

A =

29.613 ~ 27.581
7.285

X 360 = loo"" 25'.

Attention must be called to the use of the right angle prism in elimi-
nating disturbing reflections from the front of the mirror. Considerable
trouble in the determination of A was experienced with the first prism
used. It was found when studying the reflection from the prism itself,
that the value of A obtained for internal reflection was about 30 per cent,
less than the theoretical value of A as given by Drude's equation,

tan— = - ^n^ — 2,
2 n

(I)

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230 /. B. NATH ANSON. [ISbS

where the angle of incidence is 45^, and n is the index of refraction of
the glass prism. No amount of cleaning of the prism altered the value
of A. It was accordingly assumed that this deficit in A was due to
internal strains, and so another prism was finally obtained which upon
close examination yielded values of A agreeing to within one per cent,
of the theoretical value.

FORMULiE.

Drude's equations in the rigorous form were used. The approximative
equations as used for ordinary metals cannot be employed in this case
due to the low value of the index of refraction, t. e., the square of the
sine of the angle of incidence cannot be neglected in comparison with the
complex dielectric constant.
Let

tan Q = sin A tan 2^,

cos 2P = cos A sin 2^,

5 = sin <^ tan <^ tan P,

where <^ is the angle of incidence = 45*^ throughout this investigation.
The coefficient of absorption k is given by

* = tan - , (2)

where

S^ sin 2Q

X =

52 cos 2Q + sin2 <^ •
The index of refraction n is given by

5^ cos 20 + sin2 <^

»'= - T^r^i • (3)

The principal angles of incidence and of azimuth are evaluated by means
of the following equations:

sin* 0 tan* 0 = n^i + k^y - 2n^ii - k^) sin^ $ + sin* $, (4)
k = tan 2^. (5)

The reflecting power R of the metal for normal incidence is given by

n\i +k^) +2n + i' ^^^

Results.

The values of A and 2^ and of the calculated optical constants are
given in Table II. The values of A and 2^ are the results of an extended

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Vol. XLl
No. 3. J

THE OPTICAL PROPERTIES OF RUBIDIUM.

231

series of observations. The constants refer to the metal in contact with
glass. The values of the reflecting powers as obtained directly by the
use of the photo-electric cell are listed in the last column to afford com-
parison with those obtained by calculation from Drude's formulae.

Table II.

Metal — Glass Boundary.

X in /i/i.

86° 52'

y? (Gale).

1 R (Direct.)

640.9

119*' 30'

0.093

10.51

0.827

1 0.840

589.3

113 23

86 46

0.087

9.28

0.810

i 0.808

539.6

110 41

86 29

0.093

7.97

0.787

1 0.817

488.8

104 34

86 33

0.089

6.49

0.766

1 0.816

454.6

100 36

86 38

0.091

5.28

0.745

0.789

In general the reflecting powers as obtained directly by use of the
photo-electric cell are somewhat lower than those obtained by the
polarimetric method. It is possible that this may have been due to a
slight deterioration of the mirror surface. It is also interesting to note
that with the polarimetric method, the reflecting powers decrease more
rapidly for the smaller wave-lengths than is the case with the photo-
electric cell method . A comparison

)

<£

MO 450

of the curves for the reflecting
power is shown in Fig. 3.

The principal angles of azimuth ?
^ and of incidence 0 can be cal- |
culated from the values of k and
n. In this case the values of

490 500 950

n in Table II. must be multiplied

by the refractive index 1.51 of the p- 3

glass plate of the mirror, in order

to obtain the values of n referring to the metal in contact with the air.

It is assumed that k remains the same. The results of the calculations

are given in Table III., together with the reflecting powers for the

metal-air boundary. There is very little variation in «.

Table III.

Metal — Air Boundary.

A in nfi.

ft.

/? (calc).

640.9

0.140

42° 17'

62° 42'

0.840

589.3

0.131

41 56

60 1

0.811

539.6

0.140

41 26

58 44

0.780

488.8

0.134

40 37

1 55 29

0.739

454.6

0.137

39 39

1 53 22 •

0.700

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232 J, B. NATHAN SON. [sSSs!

From Tables II. and III. it appears that for the larger wave-lengths
the reflecting powers for the air-metal boundary are greater than the
reflecting powers for the metal-glass boundary, as we should expect.
Oddly enough this is however reversed for the smaller wave-lengths.

Examination of R. W. and R. C. Duncan's^ results for potassium,
reveals a parallel case. For X = 665.0 /*/* and 589.3 /*/*, the reflecting
powers of potassium for the glass-metal boundary are less than for the
air-metal boundary, while for X = 472.0 /i/i, the case is just reversed,
i. e., R (air-X) = 86.9 per cent, while R (glass-X) = 87.8 per cent. It
follows that for some value of the wave-length, the reflecting power of
the metal must be the same irrespective of whether there is air or glass
as the medium in contact with the metal. If this is the case, then

n^(i -f jfe^) - 2n + I __ n^(i + fe^)i.5i^ - 2n-i.5i + i
n\\ + Jfe2) + 2n -t- I " n2(i + Jfe2)i.5i' + 2n-i.5i + i '

where 1.51 is the index of refraction of the glass, and n refers to the
glass-metal boundary. Solving this equation for *,

ife = - v/o.66 - n\ (7)

For large values of k and small values of n, i. e., n < 0.81, the right-hand
side of the equation is real, and the equality is possible.

The calculations for the reflecting powers have been made on the
assumption that k of the metal is not affected by the character of the
medium in contact with that metal. Various investigations on this
point do not seem to be in harmony. IngersolP showed experimentally
that the reflecting power of a metal in contact with air can be obtained
from the values of n and k for the metal in contact with a transparent
medium, by multiplying n by the refractive index of that medium, and
assuming k unchanged. On the other hand Tate's^ results for silver in
contact with air and with glass, show that k as well as w is affected by the
medium in contact with the metal, k being about half as large for the
silver-glass boundary as for the silver-air boundary. In fact Tate's
values for the reflecting powers of silver in contact with air cannot be
obtained from the values of n and k for the silver-glass boundary, by
merely multiplying w by 1.51 and keeping k constant.

From all the aforesaid, it therefore appears unreliable to calculate
the reflecting power of an air-metal boundary from the values of n and k

» Phys. Rev., 36, 294, 1913.
« Phys. Rbv.. 39, 392, 1909.
» Phys. Rev., 34. 327. 1912.

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Na'a^^*] ^^^ OPTICAL PROPERTIES OF RUBIDIUM. 233

obtained from the metal-glass boundary, by merely correcting for n.
It IS not safe to assume that k remains the same. Further investigation
of this question is desirable.

Summary.

The optical constants of rubidium were obtained for wave lengths
ranging from 454.6 mm to 640.9 nn. A simple Babinet compensator and
two nicols were employed to measure the phase difference and azimuth.
The constants were calculated by means of Drude's formulae.

The rubidium mirror was formed by distillation of the metal in vacua,
with subsequent condensation upon a piece of plane parallel glass. A
right angle prism served to eliminate troublesome reflections from the
glass front of the mirror.

The reflecting powers of the metal in contact with glass were, with the
exception of that for X = 589.3 mm» somewhat lower than those obtained
directly by means of a photo-electric cell in a previous investigation.

The results do not warrant the assumption that the coefficient of

absorption of rubidium remains constant irrespective of the medium in

contact with the metal.

Carnegie Institute of Technology,
Pittsburgh, Pa.,
October, 191 7.

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234 ^- ^- COMPTON AND J, M. BENADE. [^SS

THE THEORY OF IONIZATION BY COLLISION.
IV. Cases of Elastic and Partially Elastic Impact.

By K. T. Compton and J. M. Benade.

Introduction, — In previous papers by one of the writers^ a theory was
developed by which the rate of ionization of molecules of a gas at pressure
p by electrons moving in a field of intensity X could be calculated in
two particular cases, viz., if the collisions of electrons with molecules are
inelastic and if the collisions other than ionizing collisions result in no
loss of energy. In the latter case, which was called **the case of elastic
impact," it was shown that the average number of ionizing collisions a
made by an electron while advancing one centimeter bears to the pressure
p and the intensity X the relation

in which the form of the function ^ is determined by

a:== Pp =. pN>/P (2)

and

' I + P 1 [vx,{l + P)] "^ [vx,{i + P)]2 "^ fvxo(i + P)Y

^ ^ [vx^{l + P)Y^-^ ^ [j^o(l + P)\^ J ' ^^^

In these equations P is the probability of ionization at a collision; v is
the average number of collisions made by an electron while advancing
one centimeter toward the anode; pN is the average number of collisions
made by an electron while moving one centimeter in its actual zig-zag
path; N is this quantity calculated for i mm. pressure, and is the re-
ciprocal of the mean free path at i mm. pressure; xo = VqJX, where
Fo is the minimum ionizing potential. These equations were found to
agree well with experimental determinations of a in helium^ when the
constants Fo and N were given values differing very little from accepted
experimental values. The small discrepancy between theory and experi-
ment was attributed to impurities in the helium.

» Phys. Rbv., 7, pp. 489, 501, 509. 1916.
« Phil. Mag., 23, p. 837. 1912.

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Na*3^^'] ^^^ THEORY OF IONIZATION BY COLLISION. 235

Two lines of evidence, however, have recently indicated that the
assumptions underlying equations (i), (2) and (3) must be modified if
they are to be applied to helium and similar gases, and have suggested
the nature of this modification. The first of these is the fact that, even
though collisions in helium are perfectly elastic, yet sufficient energy is
transferred from the electron to the molecule at impact to affect ap-
preciably the rate of ionization of the gas. A detailed study of this loss of
energy has recently been published by the writers.^ The second line
of evidence is based on the following study of Stoletow's constant.

Stoletow's Constant, — It has been shown by Townsend^ that, if there
is a functional relation of the type

^/(f)■

it necessarily follows that the ratio of the intensity X to the pressure pm
at which a is a maximum is constant for all values of X. This ratio
X/pm, whose value is characteristic of the gas, is Stoletow's constant
and has been measured and verified in the case of a number of gases of
the inelastic type.

If there were a gas in which electrons lose no energy at imjjacts, except
in the process of ionization, it is obvious that for such a gas pm would be
infinite and Stoletow's constant X/pm would equal zero. The following
experiments were made to test this point in the case of helium.

Carefully purified helium was introduced at various pressures into an
ionization chamber containing two parallel electrodes. From one of
these, electrons were liberated by ultra-violet light and moved under the
influence of the applied field to the second electrode, which was connected
to an electrometer, shunted with a high resistance. The details of the
purification of the helium and the construction of the apparatus have
been described in an earlier paper. The experimental procedure was to
vary the pressure, keeping other conditions constant, until the pressure
was discovered at which the current through the gas was maximum.
A small correction of these results was necessary to take account of the
regular decrease of photoelectric emission from the cathode as the pressure
was increased. This correction was easily determined by a control
experiment. Fig. i shows the result of a number of such tests with
various values of the field X and the distance d between the electrodes.

It is very evident that X/pm, cannot be considered constant. That this

» Phys. Rev., 10, pp. 77, 80, 1917-
* Electricity in Gases, p. 300.

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236 K. T. COMPTON AND J. M. BENADE. [ISwbJ!

lack of constancy is not due to insufficient purity of the helium is proven
by our previously reported measurements of the elasticity of impact in
this same helium. It is necessary to conclude, therefore, that the func-
tional relation of equation (i) is not true in the case of helium, which

Fig. 1.

proves that the energy lost at non-ionizing collisions in helium cannot
be neglected.

The following treatment of the theory takes account of small energy
losses at collisions and should be applicable to all cases of elastic and
nearly elastic impact.

Theory. — Let A«, where e is the charge on an electron, represent the
average amount of energy lost by an electron at a non-ionizing collision.
Then, of the energy Xe acquired from the field while advancing i cm.,
an electron loses on the average an amount v^.e by these collisions.
Thus, if X'e represents the net gain of energy per centimeter, we have

X'e = Xe- vAe. (4)

Obviously, if we insert X' in place of the actual intensity X in equations
(i) and (3), we take account of losses of energy at non-ionizing collisions.
Thus equation (i) in its general form should be written

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VoL.^XI.J p^£ THEORY OF IONIZATION^ BY COLLISION, 237

In case there is no loss of energy except in ionization, A = o and equa-
tion (5) reduces to equation (i). In case collisions are entirely inelastic,
A is proportional to X and equation (5) reduces to Townsend's relation

t-'(j)'

in which form of the function / has been discussed in preceding papers.
For cases in which collisions are nearly or entirely elastic, it is evident
that A depends on the maximum energy Voe acquired and not appreciably
on the field X. We shall proceed to develop equation (5) into a form
applicable to experimental measurements in gases of this latter type.
It was shown in an earlier paper^ that

' = Xe ' '

where v is the average velocity of an electron just before it ionizes.
From equation' (4) ,

I _ X^jt^vAe

But

X'e

hmv^

= a =- Pv

is the average number of times an electron ionizes while advancing one
centimeter, while

where d is the ratio of the average energy lost at a non-ionizing collision
to that lost at an ionizing collision. Thus

V = (^ + ^^' (^^

Eliminating P by the relation Pv = a, and solving for v we obtain

2N^p

(7)

P >'^

If .we substitute this value of v in equation (5) we obtain the relation

2AN^ _ \

P+4N^SJ

(8)

» Phys. Rev., 7, p. 510. 1916.

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238

K. T. COMPTON AND J. M. BENADE.

rSBOOMD

LSbribs.

which is in a form suitable for experimental test. The most convenient
method of handling experimental data is to substitute the observed
values of Xjp in equation (8) and calculate X' jp, Ex[uations (2) and
(3) are then directly applicable if we put xq = Vo/X\

Ex[uation (3) has been solved for P corresponding to the values of
vxo given in Table I. Corresponding values of pNVo/X' are determined
by use of equation (2). Intermediate values may be determined graphi-
cally.

Table I.

I'^O.

VJ-o.

/A^ro

0.2490

0.499

0.0265

3.255

0.1610

0.802

0.0186

4.090

0.1213

1.045

0.01436

4.793

0.0984

1.255

0.00989

5.965

0.0831

1.441

0.00755

6.950

0.0723

1.613

100

0.00613

7.830

0.0574

1.917

150

0.004175

9.695

0.0478

2.186

200

0.003175

11.270

0.0340

2.768

275

0.002332

13.300'

Comparison with Experiment. Helium. — ^The values of X/p and a/p
in Table II. were determined experimentally by Gill and Pidduck,^ and
the values of X^/p were calculated by equation (8). To do this Vo and
N were chosen to give the best agreement between theory and experi-
ment; A was taken to be the energy lost at an impact by an electron
moving with half the ionizing energy, and is known with considerable
accuracy as a result of our recent measurements of energy losses;
8 = A/Fo.

Table II.

Vo = 21 volts.

N = 8.7.

A = 0.00282 volts.

6 = 0.000134.

—

_ . . —

— —

A''

5.0

0.127

3.83

10.0

0.275

9.31

10.0

0.285

9.33

20.0

0.560

19.63

20.0

0.597

19.65

38.1

1.035

37.90

40.0

1.080

39.80

80.0

1.835

79.90

120.0

2.100

120.0

200.0

2.370

200.0

» Phil. Mag., 23, p. 837, 1912.

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No^3^^*] ^^^ THEORY OF IONIZATION BY COLLISION. 239

The last two sets of observations are not plotted, since the experi-
mental conditions under which they were taken have been shown in an
earlier paper to be misleading.

Fig. 2.

The remarkable agreement between theory and experiment is shown
by Fig. 2, in which the solid curve represents equations (2) and (3) and
the dots represent the observations in Table II. The discrepancies are
certainly within the limits of experimental error.

Further support of the theory is afforded by the values of Vo and N,
which are the parameters of the equations. Probably the minimum
ionizing potential is nearer 20 volts than 21 volts, but 21 volts is within
the range of accepted direct measurements. It is not so easy to decide
on the correct value of N, since we estimate N from considerations based
on the kinetic theory of gases, and it is not certain that the effective
molecular cross section which functions in collisions of molecules with
each other is pertinent to the present problem. Assuming that it is,
however, we find values ranging from iV = 8.3 to iV = 13.5, depending
on the method of calculation^ The smaller values result from taking the
electronic free path to be 4^2 times that of a gas molecule and the larger
values from N = Trr^n, where r is the molecular radius and n the number
of molecules per unit volume. The former method of calculation has
been more widely accepted, and there is no reason, therefore, for doubting
the accuracy of the value N = 8.7.

The Case of Hydrogen. — It is supposed that impacts in hydrogen are
more elastic than those in other gases, with the exception of the mona-

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240 K. T. COMPTON AND J. M. BENADE. [iSSS

tomic gases. This view is supported by rough measurements by Franck
and Hertz^ of the average energy lost at a collision and by attempts to
apply equations for inelastic impact to the case of ionization in hydrogen.
For instance, if an attempt is made to fit the equation for inelastic
impact developed by one of the writers* to the experimental data pub-
lished by Townsend' and Townsend and Hurst,* good agreement is
obtained if the minimum ionizing potential is taken to be Fo = 9.56 volts.
In dealing with all other gases the equation leads to values of Vq which
are too large, while in this case it leads to a value which is distinctly too
small. The most probable explanation of this discrepancy is that
electrons retain some energy after non-ionizing impacts. The equations
of this paper, however, are much less successful than those of inelastic
impact. This supports the evidence, which we have advanced in our
former papers, that losses of energy at impacts in hydrogen are due to
processes similar to those which are effective in the so-called inelastic
gases, and which are typically different from those which produce energy
losses in gases like helium. The energy lost in inelastic gases, we believe,
appears as energy of vibration of parts of the molecular complex.

Discussion, — ^The equations developed in this paper should be, and
appear to be, more accurate than any that have been proposed for the
case of elastic impact. The reason for this lies in the fact that all
such equations must be based on some assumption regarding the proba-
bility that an electron, whose energy is greater than the minimum ionizing
energy, will ionize at a collision. Until the mechanism of ionization is
better understood, the expressions suggested for this probability must be
entirely empirical and the best of them is probably only an approximation
to the truth. Any error in the form of this expression, however, affects
the accuracy of equations for elastic impact much less than those for
inelastic impact. For if an electron, possessing at least the minimum
ionizing energy, fails to ionize at an inelastic impact it loses its chance
until it has gathered a new supply of energy; while if it fails to ionize
at an elastic collision it retains its ability to ionize at the next collision.
Since collisions are comparatively numerous in elastic gases, this means
that an electron advances very little beyond the point at which it has
accumulated the ionizing energy until it ionizes. There is reason, there-
fore, for confidence in equations (2), (3) and (8).

Palmer Physical Laboratory,
Princeton. N. J.

* Verh. d. D. Phys. Ges.. 15, p. 373, 1913.

* Log. cit.

» Phil. Mag.. 6. p. 598, 1903.

* Ibid., 8, p. 738, 1904.

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No'a^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 24I

PROCEEDINGS

OF THE

American Physical Society.

Vacuum Gauges of the Radiometer Type.^
By R. G. Sherwood.

A VACUUM gauge, based on the principle of molecular bombardment,
was designed in 1910 by M. Knudsen.* Woodrow* modified the design
to remove some of its limitations. By making further modifications in con-
struction, Mr. J. E. Shrader and myself at the Westinghouse Research Labora-
tory produced a gauge of simple construction capable of measuring pressures
as low as 10"* mm. of Hg., possessing good stability and not expensive to build.

The theory of. the gauge as derived by M. Knudsen makes this gauge
applicable as an absolute instrument only at comparatively low pressures.
It is desirable to extend the range well up into that covered by a mercury
manometer. This may be done by making the proper corrections for molecular
collisions and for unbalanced impacts.

The principle involved in the operation of this type of gauge is that of
molecular bombardment. Molecules of gas leaving a platinum strip, heated
electrically, bombard a suspended vane hung parallel and close to the platinum
strip causing it to turn. If the distance between the movable vane and the
platinum strip is small compared with the mean free path of the gas molecules
and the dimensions of the vane and strip such that the edge effect can be neg-
lected then Knudsen has shown that the following formula holds:

(I) P= ""'''

T^lJ2 __ fjiji •

where T2 = temperature absolute in gas without vanes, Ti = temperature
absolute of heated platinum strip, and F = force of molecular repulsion.
For temperature differences not greater than 250° C. the formula holds well
if written

4FT2

(2) P =

Ti - T2

* Abstract of a paper presented at the Chicago meeting of the American Physical Society,
December i, 191 7.

•Ann. d. Phys., IV., 32, 809, 1910; 44, 525, 1914.
» Phys. Rev., IV., 6, 491, 1914.

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242 THE AMERICAN PHYSICAL SOCIETY.

If Ri = electrical resistance of platinum strip when heated,
Rt « electrical resistance at temperature of gauge,
K = constant of the gduge.
S " scale reading.

Then as a working formula (2) reduces to
(3) P= ^^'

Ri- Rt

For the dimensions of the elements in the gauge designed for laboratory
use, pressure above io~* mm. of the Hg cannot be measured with any degree
of precision from the above formulae without correcting for

(i) Collisions,
(2) Edge eflFect.

The following formula has been found to give the necessary corrections for
one of these gauges up to 0.05 mm. of Hg on air.

where X = mean free path of the air molecules, d = distance between the
movable vane and Pt heating strip, c = constant depending upon the ratio
of the width of the suspended vane to d; the length of the vane being large as
compared to the other dimensions is not considered in deriving the expres-
sion for the above correction, e ■■ base of natural logarithms.

For greater pressures up to i or 2 cm. of Hg the gauge makes an ideal de-
tector for small changes in pressure, but in its present form is not suitable
for absolute measurements.

The sensibility of the gauge increases from nearly zero at about 2 cm. Hg
to a maximum at about 0.05 mm. Hg; then decreases toward zero for very low
pressures.

Westinghouse Research Laboratory,
E. Pittsburgh, Pa.

Further Verification of Knudsen's Equations for Resistance to

Molecular Flow.^

By l. e. Dodd.

KNUDSEN* has developed from the kinetic theory of gases expressions
for the "resistances" of an aperture and of a tube of given dimensions,
to the passage of gas molecules under conditions of sufficiently low pressure
that the molecular collisions occur in relatively small number and the flow is

* Abstract of a paper presented at the Chicago meeting of the American Phsrsical Society,
December i, 1917.

* Knudsen, Annalen der Physik, 28, p. 75, also p. 1009, 1909.

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No'a^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 243

thus purely "molecular." In the case of an aperture the resistance is given
by Wi = 2tI^ Ay where A is area of aperture. For a tube the resistance is

W2 = 3/8 ^ir/2 I o/i4* dly where L is length of tube, o is circumference,

and A cross-sectional area. Knudsen verified these expressions experimentally
with hydrogen, oxygen, and COj. By their practical use he determined the
vapor tension of mercury over the temperature range from 890** down to
- 50" c.

Egerton* in England, working on the vapor tensions of zinc and cadmium,
has further verified the equations with mercury as the standardizing material
for his tubes. He used not only a single aperture but as many as seventeen
apertures in parallel in the same partition, finding that in the case of two or
more apertures of equal area in parallel the total resistance is obtained by
dividing the resistance for one aperture by the number of apertures.

In connection with work on the vapor tension of selenium the writer has
found that Knudsen's expressions for resistance to molecular flow are experi-
mentally valid. Preliminary to the measurements on selenium it was thought
desirable to standardize two tubes with mercury. The tubes were similar
to those employed by Egerton. One of them had two apertures in parallel,
and the other tube six apertures. With the tube having the two apertures
the mean value of sixteen separate determinations of the resistance (due both
to apertures and the portion of the tube lying between apertures. and region of
condensation) agreed well with the value as predicted from the Knudsen
equations. The per cent, of probable error from the mean was less than two,
which was regarded as satisfactory. With the other tube the equations also
hold, at least approximately.

State University of Iowa.
lowA City. Ia.

Rectification of Alternating Current by the Corona.'
By J. W. Davis.

IT has been possible to rectify voltages as high as 42,000 volts effective by
means of the corona discharge in hydrogen. The rectification is prac-
tically perfect, but the efficiency is not very high, as a large amount of energy is
wasted in the discharge itself. For a given gas pressure the maximum voltage
which may be rectified is approximately directly proportional to the radius of
the outer cylinder, when the inner cylinder is small compared with the outer
cylinder. An incandescent wire will give a croona discharge at voltages much
lower than those necessary to start a discharge from a cold wire. The heat

» Capt. A. C. Egerton. Philosophical Magazine, 33, p. 33, Jan., 191 7.
* Abstract of a paper presented at the Chicago meeting of the American Physical Society,
December i, 1917.

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244 ^^^ AMERICAN PHYSICAL SOCIETY, [ISiS

conductivity of a gas is largely increased in regions where ionization by col-
lision takes place.

UNrvERSiTY OP Illinois,
Urbana, Illinois,

November 15, 1917.

A Mono-Wave-Length X-Ray Concentrator.*
By Elmer Dbrshbm.

THE derivation is given of the mathematical equation of a curved surface
which may be used to concentrate X-rays of a single wave-length by
reflection from bent mica crystals placed on this surface. This surface is
shown to be a logarithmic spiral surface of revolution.

Methods of constructing such a surface and experimental results are given
showing that it is possible by this means to concentrate upon a small area
X-rays of a single frequency a thousand times as intense as can be obtained
by reflection from plane crystals.
State UNivERsmr of Iowa.

Wave-Lengths of the Tungsten X-Ray Spectrum.*
By Elmer Dbrshem.

THE factors affecting the resolving power of an X-ray spectrometer are
discussed and it is shown that for precise measurements a thin crystal
must be used and corrections made for the width of the source.

Experimental results are given showing that the L group of the tungsten
X-ray lines contains at least 19 lines and precise values of their wave-lengths
as well as those of the four K lines of tungsten are given. These results are
compared with those of other investigators.

State University of Iowa,
Iowa CrrY, Ia.

A Megaphone with a Rectangular Aperture.*
By F. R. Watson.

THE theory for such a horn has been given by Rayleigh.' When a train
of parallel waves pass through a slit whose width is equal to or smaller
than half the wave-length, they spread out as if they come from the aperture
as a center of disturbance. When the width of the aperture is large compared
with the half wave-length, there is but little spreading out and the waves
proceed almost undisturbed. Using this conception, Rayleigh constructed
a horn with an elliptical aperture, the major axis of the ellipse being large

> Abstract of a paper presented at the Chicago meeting of the American Phydcal Society,
December i, 1917.

s On the Production and Distribution of Sound, Phil. Mag., Vol. VI, pp. 289-305, 1903.

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NoI"3^^*] ^^^ AMERICAN PHYSICAL SOCIETY, 245

compared with the wave-length and the minor axis rather smaller than the
half wave-length. If the major axis is held vertical and the axis of the horn
is horizontal, the sound is spread out in a fan-shaped horizontal layer.

Rayleigh applied this horn experimentally in testing several properties of
sound waves. He also suggested that similar horns of larger dimensions
might be useful in fog signalling, a suggestion that was carried out with
successful results.^

It occurred to the author that the principle might be extended to the im-
portant domain of speech sounds. With this object in view, several horns
with rectangular apertures were constructed, the dimensions being varied in
the different horns. These were tried in an open field and pronounced results
were obtained. When the horn was held horizontally with the rectangular
aperture vertical, the sounds were diffracted more than 90® from the straight-
forward direction, and observers off to the side heard easily. When, however,
the horn was rotated 90^, so that the long edge of the rectangular opening was
horizontal, the sound heard by the observers was indistinct. Several applica-
tions of the horn are suggested. It would be serviceable in making announce*-
ments to a crowd on bleachers, in direccing the sounds from a phonograph, etc.

The results obtained bear on another point of some importance, namely,
the mean wave-length of speech. The fact that speech sounds were diffracted
by the narrow dimension of the aperture, but not by the large dimension
indicates that some effective component of speech has a half wave-length
lying between these two limits. This deduction is of value in estimating the
dimensions of relief work on the walls of auditoriums, where it is desired to
scatter the sound. It is also useful in telephony in adjusting the pitch of
telephone plates to resound to the speech sounds.
UNrvERSiTY OP Illinois.

A New Hydrate of Uranium Nitrate; Uranium Nitrate

I COSITETRAHYDR ATE.'
By Frank E. E. Germann.

WHEN a water solution of uranium nitrate is cooled to — 180® C. it is
possible to get various distinct fluorescent spectra from it, depending
on the rate of cooling of the solution. H. L. Howes described what seemed
to be five distinct spectra, varying from a sharp-lined spectrum in the case of
slow cooling, to a broad-banded spectrum in the event that the solution was
plunged directly into liquid air. The other spectra were the result of other
chance intermediate methods.

It was while trying to find the cause of this unexplained action that the
author discovered a hitherto undescribed hydrate of uranium nitrate, stable
below about — 19** C, forming spontaneously at about — 35® C, at which

» Sound Signals. Soc. Arts Journal, Vol. 50, pp. 315-327. 1902.

* Abstract of a paper presented at the Rochester meeting of the American Physical Society,
October 26 and 27, 191 7.

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246 THE AMERICAN PHYSICAL SOCIETY. [^S?

point there is very rapid liberation of heat, warming up the specimen as much
as 20® in some cases. Due to the phenomenon of supercooling, the tempera-
ture of formation, and the maximum temperature of stability have not yet
been definitely fixed.

The composition of the new hydrate was determined by the method of
thermal analysis, working with thermo-couples, and measuring the heats of
formation from equal volumes of solutions of varying percentages of con-
centration. Neglecting the fact that the specific heats of different concentra-
tion solutions are not equal, and plotting heat liberated against percentage
concentration, two straight lines resulted, cutting each other sharply at a
percentage corresponding to 47.6 parts of anhydrous uranium nitrate, UOt-
(NOa)i, to 100 parts of solution. The uranium nitrate hexahydrate, UOj-
(NOj)j .6H1O, which is the stable nitrate at room temperatures, contains 78.5
per cent, anhydrous salt, whereas a percentage of 47.7 anhydrous salt corre-
sponds to the formula U0j(N0f)t .24HJO, which we may call uranium nitrate
icositetrahydrate. Although a compound containing twenty-four molecules of
water is by far the most probable, still it may be worthy of noting that a mole-
cule containing twenty-three molecules of water would contain 48.8 per cent,
salt, and one with twenty-five molecules would contain 46.7 per ceni.

The transformation can be suppressed by rapid cooling, in which case it
takes place on heating up. The formation is accompanied by a fairly large
increase in volume, so that by cooling a specimen down in a very heavy glass
tube, the transformation may be suspended, even when cooled slowly, but on
warming up, the tube is usually shattered at the transformation point.

The formation of the icositetrahydrate explains in part the various spectra,
but it does not explain the fact that a banded spectrum may be produced.
This may be due to an amorphous condition of the solid mass, or to a possible
solidification in the exact state in which it existed as a solution, in which state
it normally gives a banded spectrum. The author will take up the latter
consideration in a future article.

Physical Laboratory,
Cornell University.
Ithaca, N. Y.,

October 11, 191 7.

A Correction in xitE Theory of Ionization by Collision.*
By Jakob Kunz.

IT has been shown by Bergen Davis, F. S. Goucher, Y. T. Tate, and P. D.
Foote, that for the metallic vapors radiation is emitted without ionization
when electrons collide with the atoms of the vapor, a radiation, which may
give rise to a photoelectric effect on the electrodes and thus resemble an

» Abstract of a paper presented at the Chicago meeting of the American Physical Society,
December i. ipi?.

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No^3^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 247

ionization by collision. These "resonance" voltages are for

Hg : 4.9 volts, Zn : 4.1 volts, Cd : 3.88 volts.

Na : 2.10 volts, K : 1.55 volts,

The ionizing potentials, however, are:

Hg : 10.4, Zn : 9.5, Cd : 8.92,

Na : 5.13, K : 4.1.

Davis and Goucher found, moreover, that an increase in the intensity of radia-
tion takes place at an impact voltage of about 6.7 volts in Hg vapor. The
results obtained for H by these authors are quite different; ionization by impact
and emission of radiation occur at 11 volts. A second type of ionization by
collision without increase of radiation occurs at about 15.8 volts and a second
type of radiation without an increase in ionization is emitted at 13.6 volts.
In these measurements accelerating potential differences of 2 up to 20 volts
have been used. In the experiments on ionization by collision by Townsend
and others potential differences of 100 to 400 volts have been used. Never-
theless it has been assumed that the current only increased by the increase of
the number of positive and negative ions through the process of collision. But
the ultra-violet light, which in many cases will arise under the influence of the
high potential differences, must contribute to the ionization. This may
explain the fact that in many cases the saturation current is not constant but
increases slightly. If we assume that the ultra-violet light is distributed
uniformly through the ionization chamber and that it produces n electrons
per unit volume and per unit time, then we have in a layer of thickness dx
the number itidx^ which when moving through x will produce dn = tiidx e**
new electrons, and the number

me'^dx = -(«•'- I)

has to be added to the number of ions tii = «« c*', which are produced by col-
lision alone. If the light is not uniformly distributed between the two plates
or if the electrodes are of different chemical material, a photoelectric effect of
the plates must be considered in addition.

The existence of the resonance potential raises a very interesting question
with respect to the photoelectric effect. For instance, in sodium vapor a
potential difference of 2.10 volts is sufficient to produce yellow light according
to e7 = hn. If this yellow light were able to ionize the vapor, then we would
have a photoelectric effect, and the resonance potential would not be dis-
tinguished from the ionization potential which is 5.13 volts, corresponding to
ultra- violet light. These potential differences, if correct, indicate therefore
that Bodium vapor will show a photoelectric effect only for ultra-violet light,
while sodium metal of course shows a photoelectric effect for visible light.

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248 THE AMERICAN PHYSICAL SOCIETY. [^S2

It look? therefore as if sodium vapor and sodium metal were very diflerent
with respect to the photoelectric effect. Measurements to decide this question
are in progress in our laboratory.
University of Illinois,
Urbana, III.

Mobility of Ions in Air. Hydrogen, and Nitrogen.*
By Kl\-Lok Yen.

THE primary aim of this experiment was to determine the mobility of
the hydrogen and nitrogen ions by means of the high-frequency high-
potential method employed by L. B. Loeb in his determination of the mobility
of ions in air (see Phys. Review, N. S., Vol. VIII., No. 6, 1916, pp. 633-650).
But, as the Loeb experiment was the only one of its kind that had ever been
performed before, it was thought worth while to repeat it before extending it
to other gases. Consequently, the mobility of ions in air was redetermined
before the determination of the hydrogen and nitrogen ions by the same
method

When working with air, a field strength of as high as 14,160 volt/cm. was
employed and neither the positive nor the negative ions exhibited any tendency
to deviate from the law that the product of the mobility times the pressure is
a constant. A potential of 6,668 volt/cm. was applied in the case of hydrogen
and there was no indication whatsoever of any abnormal increase in either the
positive or the negative mobility. For nitrogen, the potential employed was
as high as 17,670 volt/cm. and yet not even the slightest deviation from the
law, as stated above, was manifested by either the positive or the negative ion?.

Free electrons were found in both hydrogen and nitrogen; more in the former
than in the latter. It might be expected that with high potentials the appear-
ance of electrons would be more favored, but in the experiments made to test
this point, fewer electrons were found in hydrogen and nitrogen with high
potentials than when the mobilities were measured with the ordinary 60 cy.
low alternating potentials. This seems to fit in with the idea suggested by
Wellisch that a certain speed is necessary before the negative electron can
attach itself to a neutral molecule to form a negative ion.

Besides the free electrons and the normal negative ions no trace of any
other kind of negative ions could be found.

Thus, an additional argument is offered by these results in favor of the
small-ion theory as well as against the cluster hypothesis.
Ryerson Laboratory,

UrnvsRSiTy of Chicago,
Chicago, III.

1 Abstract of a paper presented at the Chicago meeting of the American Physical Society,
December i. 1917.

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NoT^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 249

The Determination of Organic Compounds by an Optical Method.*
By Thos. E. Doubt and B. B. Frbud.

THE index of refraction has long been recognized as one of the character-
istics of a body. The index of refraction for a number of wave-lengths
may be determined by a single photograph of Talbot's bands for a known thick-
ness of the body. Gibbs has proved that for a number of common substances
his interferential constant which is obtained by dividing the number of Tal-
bot's bands between two spectrum lines by the density of the substance is inde-
pendent of the temperature. He suggested that this new constant be used in
determining the composition of mixtures. We have found no further applica-
tion of this suggestion. A comparison of this constant with the other so-called
constants; namely, Newton's, Gladstone and Dale, and Lorentz and Lorenz
is made in the paper. The values of these constants for benzol and toluol
are given in tables and it is seen that the values of the interferential constant
differ by the greatest amount. Between the two given lines for a layer of
liquid one centimeter thick there are no bands more in the case of toluol
than in the case of benzol.

Armour Institute op Technology.
Chicago. III.

The Analysis of Polarized Light Reflected from Small Opaque

Crystals.^

By LeRoy D. Weld.

WHEN plane-polarized light falls upon a polished metal, it is in general
elliptically polarized upon reflection, the elements of the elliptic
vibration being often used to calculate the optical constants of the metal.
Artificially polished metal surfaces have, however, given very inconsistent
results, owing perhaps to films left by the polishing material. Metallic crystals,
on the other hand, are usually so small as to render ordinary methods of
polariscopic analysis exceedingly difficult to apply.

The present method is a modification of one used originally by Voigt for
the identification of elliptically polarized light. The light under examination
passes first through an arrangement of quartz wedges acting as a Babinet
compensator, then through a "rotator" consisting of another pair of quartz
wedges cut perpendicular to the axis, one from right-handed, the other from
left-handed quartz; and finally through a large Glan-Nicol prism. The result
is that the field is filled with rows of black spots in regular arrangement; and
from the location of these spots with reference to the cross-hairs, as photo-
graphed, the exact character of the elliptic vibration can be readily calculated.
In this particular application the light being studied comes by reflection

* Abstract of a paper presented at the Chicago meeting of the American Phsmical Society*
December i. 1917.

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250 THE AMERICAN PHYSICAL SOCIETY. [iSSS

from one facet of a small crystal, and the beam available is therefore very
slender, so that only a very small portion of the field is illuminated at once.
In order to produce the spot pattern, the analyzing apparatus is carried back
and forth with a sort of weaving motion^ at right angles to the beam', until the whole
field is covered. The pattern then appears clearly on the plate, and measure-
ments are easily made upon it. The apparatus used for this purpose is em-
bodied in an instrument for which the name suggested is the crysteUiptometer.
Excellent plates have been obtained by this method from very small spike-
lets of selenium and tellurium. The results exhibit beautifully, not only the
double refraction of these crystals, but also the continuous transition from one
set of optical constants to quite a different set as the crystal is gradually turned
with reference to the plane of reflection, the exact nature of which transition
has been carefully investigated. The work is being conducted in both the
visible and ultra-violet regions.

CoE College and UNrvERSiTV op Iowa.

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No'a^^*] NEW BOOKS. 25 1

NEW BOOKS.

The Nature of Solution, By Harry C. Jones. New York: D. Van Nostrand

Co., 1917. Pp. xxiii + 380. Price J3.50.

This book, published after the author's death, is not a text-book or treatise,
but rather, as indicated in the preface, a semi-popular exposition of the present
state of our knowledge of solutions. It is interestingly written, and most of
it could be j-ead without difficulty by a student with only an elementary knowl-
edge of physics and chemistry. On the other hand it contains an array of
facts, many of which are likely to have been overlooked by physicists, and
perhaps chemists also, who have not followed closely the development of
physical chemistry.

It seems to the reviewer that it could have been improved by less elaboration
in the simpler parts of the subject, and more of it in the more difficult chaptnr
on colloidal solutions, which, though long, impresses one as being written
rather hastily. There are evidences that on a very few matters the author's
physical concepts were not entirely clear, as when (p. 195) he remarks on the
great contrast between the numerical values of the speeds of gaseous molecules
and the mobilities of ions in solutions, quantities which are too different in
character to admit of comparison.

H. M. R.

Everyday Physics. A Laboratory Manual, By John C. Packard. New
York; Ginn and Co., 1917. Pp. vi + 136. Price Ji.oo.
This is a manual designed for high-school laboratories. The experiments
are selected from everyday familiar objects and mechanisms, such as gas and
electric stoves, incandescent lamps, heating systems, pressure gauges, water
meter, sewing machines, life preservers, etc. On the whole the experiments
seem well selected and the plan of the book excellent.

O. M. S.

The Electron, By Robert Andrews Millikan. Chicago: The University

of Chicago Press. Pp. xii + 268. Price, J1.50 net.

Occasionally in science as in other fields of human activity a classic appears,
that is to say a work which is practically finished and which has a permanent
value. It does not seem too much to assign this title to that part of this small
volume which describes the author's measurement of the elementary electrical
charge, for it seems highly probable that no better method or much higher
degree of accuracy of measurement of this fundamental constant will ever be
attained. In addition to achieving its principal end, the method has given
some important by-products, such as its indication of the limits of validity
of Stokes's law; the proof that ionization by X-rays and beta and gamma

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252 NEW BOOKS. [to»

rays consists in the detachment of a single electron from a molecule; the
verification of Einstein's calculations of the displacement of particles in the
brownian movement in gases; and it has given strong evidence in opposition
to Thomson's "ether string" theory. In addition to the discussion of the
elementary charge there are chapters on early views regarding electricity;
the extension of electrolytic laws to conduction in gases; the mechanism of the
ionization of gases by X-rays and radium rays; brownian movements in gases;
the evidence disproving the existence of a sub-electron; the structure of the
atom, and the nature of radiant energy. In all the chapters except the last
we have the record of the positive and wonderful achievement of the past
twenty years; and in the last chapter there is a clear statement of the great
outstanding problem and some suggestions which may be helpful in its solution.
The Bohr atom is accepted as giving a correct picture of atomic structure,
in spite of its apparent inconsistency with established electromagnetic laws,
in the belief that these contradictions will disappear when we reach a clearer
conception of the relations between atoms, electrons, and the ether which
determine radiation. The text avoids mathematics, but the most important
mathematical developments and atomic data are given in appendices. The
book is clearly written, and for the most part may be easily followed by any
one who has an elementary knowledge of physics. To this class of readers
it will give a most interesting and convincing demonstration that atoms and
electrons are not the fantasies of visionaries, but realities; and to the pro-
fessional physicist it offers a well-balanced review and thoughtful criticism of
the most important work of recent years.

E. P. L.

The Mystery of Matter and Energy, By Albert C. Cr^hore. New York:
D. Van Nostrand Co., 1917. Pp. xi + 161. Price, Ji.oo.
This little book has for its object the presentation to the general reader of
the problem of the structure of matter, with the hope of arousing interest and
enthusiasm by making clear the nature and importance of the ends to be
attained, and also to give in non-mathematical language the results of the
author's speculations and calculations in this field. There are chapters on
the atomic constitution of matter; the discovery of the electron and measure-
ment of its charge; electromagnetic waves; the ether and relativity theory;
X-rays and atomic numbers. The author describes the results of his calcula-
tions, based on the theories of Thomson and of Lorentz, which indicate that
gravitation may be explained as the result of forces between revolving electrons,
and that the arrangements of atoms in crystals and various crystalline proper-
ties may be explained as results of these forces. It is interesting to note
that this theory predicts the temperature effect on gravitation which Shaw
claims to have discovered. The concluding chapter discusses Planck's quan-
tum theory and suggests an explanation consistent with electromagnetic
theory. Much of the subject matter of the book is admittedly hypothetical,
but it will be found interesting and suggestive.

E. P. L.

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Second Series.

April, igi8

Vol XI., No. 4

THE

PHYSICAL REVIEW.

THE BREAKDOWN EFFECT IN BORON CONDUCTORS.

By F. W. Lylb.

WHEN across a layer of any of the ordinary insulating materials
a voltage greater than a certain critical value is impressed, the
familiar phenomenon of "breakdown" occurs; that is, its insulating
property is lost, usually with the accompaniment of destructive physical
and chemical changes. It is frequently considered that the latter are
the actual causes of the disappearance of insulating power and so really
constitute the "breakdown." There are, however, materials which
exhibit all the electrical characteristics of the action without any such
destructive accompaniment. A consideration of the results of some
experiments with such substances may therefore be of interest, in which
some of the similarities to the "breakdown" or "rupture" of ordinary
insulations will be pointed out.

The materials exhibiting this electrical " breakdown " have, like
the conmion insulating materials, a neg-
ative temperature coefficient of resistance.
As an example of this action we may con-
sider a slab of the element boron placed
between two terminals, across which vari-
ous direct current voltages can be im- «^
pressed. The temperature-resistance curve
of such a piece is shown in figure i. If,
at first, a low voltage is applied, only a
very small current will flow, the material
having at 20** C. a resistivity of 2 X lo*
ohms per centimeter cube. For a few
moments a gradual increase of ciurent occurs by reason of the heating
effect of the current, but a condition of current stability is soon reached
and the material behaves simply as a large ohmic resistance. If now

253

«•

«7

«« 3

M N b-

—

J — ;

r-5

Fig. 1.

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254 P' ^' LYLE. [i

larger and larger voltages are successively applied more current will flow,
but always in amount measured by milliamperes.

Finally, however, a voltage will be reached at which instability
suddenly appears in the circuit. The current increases rapidly and,
unless a separate resistance is in series, a short circuit of the line ensues.
As is evident, the effect in the electric circuit is very much like that
occurring in the breakdown of insulation. By the use of resistance,
however, the current may be held at such a value that, although the
piece may become red hot, further current rise is prevented. If now the
circuit be opened and the boron allowed to cool, it will be found to be in
the same state chemically and physically as before "breakdown."

The "breakdown" action above described can readily be shown to be
due, in a general way, to the cumulative effect of internal heating on
the electrical resistance of the substance. By reason of its negative
temperature coefficient the latter continually decreases as the tempera-
ture of the slab rises. When this has proceeded far enough the heating
becomes very rapid and the current rises quickly to the limiting value
imposed by external resistance. It will be noticed that breakdown does
not occur instantaneously but that time is required for it to set in, just
as in the case of ordinary insulating materials.

Minimum Voltage PRODuaNG Breakdown.

It might at first thought appear that breakdown will eventually take
place in such materials on any voltage, however low, provided it is
applied for a sufficiently long time. This, however, is not the case.
There is found to be a definite value of voltage below which breakdown
will never occur, no matter how long awaited. All voltages above this
value produce breakdown with a rapidity depending on their excess
over it. This really critical voltage may be called the "breakdown at
infinite time"; its parallel in the case of common insulations is familiar.
The conditions determining the value of this dividing line between
voltages at which breakdown will and will not take place will now be
considered.

The rise in temperature which takes place in the specimen when
voltage is impressed has two effects; the increase in electrical conduc-
tivity alluded to above, and, of course, a dissipation of heat to the sur-
roundings. The first tends to produce further temperature rise, the
second to arrest it. If the two can come to a balance, equilibrium of
temperature and current can be attained; if no balance is possible, as
will be seen to be the condition on higher voltages, breakdown will take
place. This question of the relations between heat development and

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Na'4'i^'*] BREAKDOWN EFFECT IN BORON CONDUCTORS. 255

dissipation requires quantitative treatment and this will be taken up in
the following paragraphs.

Heat Development and Dissipation.

The electrical conductivity, C, which is a function of the temperature
6, may be represented by

C = CoF{e),

Co being conductivity when ^ = o.
The heat developed under any impressed voltage E is thus equal to

E^CoF{e).

The heat dissipation is a function of 6 also, and as a first approxima-
tion for small temperature rises, may be taken as proportional to
{6 — Or)t Or being ambient or "room" temperature.

Thus at equilibrium

E^CoFiS) = a{e - Br), (i)

and the value of temperature, if any,
at which equilibrium is possible can
be found by solving this equation for
6. For the present purpose this may
most readily be done graphically.
Equation (i) may be rewritten

F{d) ^^-c^iO-Br). (la)

F(B) is a characteristic for the ma-
terial, and that for boron is plotted T^mp^rafyre *c
in Curve I., Fig. 2. Incidentally,
most insulators show a curve concave
upward of the general type of the curve here shown.

d
^^ {B — Br) may be plotted also (Curve II., Fig. 2) and is a straight

line crossing the B axis at the value of "room temperature," Bt> For
any ordinary breakdown test the coefficient of heat dissipation "o," the
room temperature "^r," and the cold conductivity "Co," are constants
and only the applied voltage "£ " is varied. Thus under the conditions
of experiment. Curve I., Fig. 2, is fixed and the slope of Curve II. is
the only quantity which can vary.

It will be seen that for small voltages this slope a/(£*Co) is la^ge and
Curve II. intersects Curve I. in a point "ft," giving a temperature Bh,
for which there is equilibrium of heat evolution and dissipation. Under

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256 F. W. LYLE,

this impressed voltage* therefore, breakdown does not occur, and Curve
II. corresponds to the condition of stability met with when the applied
voltage is less than the "breakdown" value.

As the value of £, the impressed voltage, is increased the slope of the
Curve II. decreases and ultimately a value is reached for which, by reason
of the form of Curve I., no intersection of II. with I. occurs. Breakdown
therefore takes place under the circuit conditions so represented, as
there is no point at which equilibrium of heat generation and dissipation
exists. Temperature and current rise thus continue until stopped by
the external resistance in the circuit. The reason for the circuit remain-
ing stable indefinitely at lower voltages and becoming unstable after
a time at higher voltages, or, in other words, the cause of the "break-
down effect," is thus seen to lie in the effect of internal heating on the
variable electrical resistance of the material.

The determination of the precise value of voltage at which stability
is changed to instability may, of course, be made from these same curves.
It is evident that the limiting voltage dividing breakdown from non-
breakdown is that corresponding to the tangent II« to the Curve I.
All higher voltages correspond to lines II. of less slope which cannot
intersect Curve I., all lower voltages to lines which do intersect Curve I.
and so denote a stable circuit. The tangent thus represents the smallest
voltage producing instability and so the "breakdown at infinite time"
already referred to.

Temperature at Breakdown.

It is obvious that, as Curve I. is characteristic of the material used,
the point of tangency of the line lie starting from a given room tempera-
ture Br is always the same, for instance, for boron. This temperature,
Oct is that which would eventually just be reached under the minimum
breakdown voltage, ♦. c, the "breakdown at infinite time," and it is
interesting to note that this is always the same for a given material.

It will be seen further that, whenever the specimen has reached a
particular value of the temperature, B, during a test, the heat generated
inside it is proportional to the corresponding ordinate of Curve I., while
the heat dissipated is proportional to that of Curve II. The difference
of these ordinates represents the heat being absorbed by the slab and
raising its temperature. Moreover it will be apparent that for voltages
not greatly exceeding the "breakdown at infinite time" this difference
begins to increase rapidly not long after the temperature 6c alluded to
in the last paragraph is passed. The rapid heat evolution here indicated
is what is usually taken as marking "breakdown." As a rough approxi-

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Vol. XL!
No. 4- J

BREAKDOWN EFFECT IN BORON CONDUCTORS.

257

mation, " breakdown " may be considered as occurring when the specimen
reaches the temperature $e. For this reason therefore $e may be dis-
tinguished as what may be called the "temperature of breakdown,"
which is of considerable importance and which is furthermore a char-
acteristic of the kind of material under test. Its magnitude is evidently
of considerable interest because of its part in determining the occiurence
of breakdown. The curves of Fig. 2 show it to be in the vicinity of 45® C.
for boron under ordinary test conditions.

Time Required to Effect Breakdown.
It has been noted that time is required for any voltage to effect
breakdown. Thus it will be seen from the above that this time is that
required for that particular voltage to
heat the test piece up to the tempera-
ture $e- It will also be apparent that
voltages in excess of the "breakdown
at infinite time" heat the specimen up
to the necessary temperature with a
rapidity determined by such excess and
so that the time of breakdown decreases
as the impressed voltage increases. The
time of breakdown may even be roughly
calculated on this basis. The curve of F»fir- 3.

Fig. 3 shows this action as determined experimentally on boron.

Effect of Room Temperature and Thickness.

It is also found that their ambient or "room" temperature greatly
affects the voltage at which specimens break down, and this may also
be seen from the curves of Fig. 2. Curve I. of course remains unaltered,
as it is the characteristic temperature-conductivity curve of the material
under test. The straight line II. crosses the temperature axis at a point
corresponding to room temperature. Raising the latter from $r to $,
displaces this intersection point to the right as shown. As a result the
tangent to Curve I. from this new intercept 69 has a greater slope than
that starting from 6^ This slope is proportional to the inverse square of
the breakdown voltage, so the latter must be smaller as this slope is
greater. The breakdown voltage thus decreases with rise of room tem-
perature in accordance with experimental results.

It is also found that the breakdown voltage does not increase pro-
portionally with the thickness of the slab tested, the volts per millimeter
being less the thicker the specimen, just as in the breakdown of ordinary

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—

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258 F. W, LYLE, [i

insulations. This can be explained in a general way on the basis of
the energy considerations embodied in equations (i) and (la). As
explained above, breakdown occurs when the specimen has reached the
temperature B^ which is a fixed quantity for a given material. Now at
that temperature the total heat dissipated from the specimen to its sur-
roundings is proportional to the heat dissipation constant "a" of equa-
tion (i). But the heat evolved in the slab is certainly not dissipated
more readily where part of it has to pass from inside to outside of a
thick slab; therefore "a" will surely not be greater for thick than for
thin slabs. Then the total heat developed in a thick slab cannot be
greater than in a thin one, and so the heat evolved per cubic centimeter
must be less the thicker the specimen. Now at a given temperature the
heat per cubic centimeter is proportional to the square of the voltage
gradient; therefore this must decrease as the thickness of the slab in-
creases. The above treatment deals only with rough approximations,
but is sufficient to indicate that the voltage gradient at breakdown
should be less for thick specimens than for thin ones, as is the case.

Current-Time Curves.

In the case of materials so far examined by the writer this temperature
Be at which breakdown sets in is far below that causing any chemical
decomposition in the material. It is possible, therefore, by placing a
proper current meter in series with the specimen, to watch the rise of
current flowing through the material under any applied voltage during
test. As the conductivity is a known function of the temperature, the
moment when the breakdown temperature is reached can be determined
from the measurement thus given of conductivity. It is possible thus
to tell whether break down will take place under any impressed voltage
by watching the rate of current rise with time. As an instance of this
Fig. 4 gives a curve of current and time during the test of a boron slab
at a voltage less than the minimum breakdown. The rate at which
current increases with time continually grows less and soon becomes
virtually zero. Stability of temperature is attained and breakdown
does not take place.

In Fig. 5 is a similar curve on the same specimen at a higher voltage.
The slope of the curve first decreases; then after reaching the point
marked "/*' it begins to increase, continuing to grow greater and greater
until it becomes practically vertical. Breakdown is taking place; at
'7" the piece has reached the "breakdown temperature'* and breakdown
is then inevitable under that voltage of test. The circuit can be inter-
rupted at this point without allowing the action to proceed to destruc-

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Vol. XL!
No. 4. J

BREAKDOWN EFFECT IN BORON CONDUCTORS,

259

tively high temperatures. In this way the breakdown voltage may be
determined in advance without ever allowing breakdown to occur at all,
or the material to be injured by destructively high heating.

Breakdown with Alternating Voltages.
The above considerations apply, of course, only to breakdown on
tests carried out, as above stated, with direct current. The same general
ideas could however be applied to breakdown under alternating voltages
except that for the simple "ohmic" resistance losses, the total losses
including, for instance, the dielectric hysteresis loss, must be substituted.

sto
tm

fOO

00
to

ki.-

0^^^

•W

' — a

• /I

to A

iJ— Z

s-x

i-3

B-?

!• -^

' J

5-1

B-3

0 0,

> 4

L. J

Fig. 4.

Fig. 5.

It has been found that for a given temperature of the material, in the
case of most substances, the losses on A.C. are, just like the D.C. losses,
proportional to the square of the applied voltage. Therefore in the equa-
tions (i) and (la) given above there may be substituted for the electrical
conductivity CoF($) an analogous quantity, Co^P{d), characteristic of
the material under test, and which when multiplied by the square of
the applied voltage gives the heat loss. This is the exact parallel of the
electrical conductivity on D.C. and, as measurements show it in many
cases to be a curve concave upward of the same general type as Curve I.,
Fig. 2, all the arguments given above as applying to D.C. breakdown
should apply equally well to A.C. tests. It is interesting to observe
in this connection that the A.C. losses at a given temperature and
voltage are in many cases of ordinary insulating materials considerably
greater than the D.C. and correspondingly the A.C. breakdown voltage
is smaller than the D.C.

It may also be pointed out that in the case of insulations generally
an increase of the frequency of the applied voltage increases the dielectric
losses, and also the breakdown voltage at higher frequency is less than
at low as a rule.

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260 F. W. LYLE. [^^

Conclusion.
The material boron is thus seen to show under certain voltage stresses
many of the characteristic phenomena exhibited by insulators at "break-
down." The existence of a breakdown action, the time needed to effect it,
the existence of a critical voltage of "breakdown at infinite time,"
and the influence thereon of room temperature and thickness of the test
specimen are all paralleled by similar characteristics of ordinary insula-
tions. These phenomena in the case of boron are all readily explained by
consideration of the variation of its resistance with temperature, as has
been shown above. The fact that the same or similar treatment applies
to the ordinary insulations points strongly to the possibility that thermal
effects are controlling factors in the breakdown of these also.
Lynn. Mas

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Na*iJ^'i ^ GENERAL THEORY OF ENERGY PARTITION. 26 1

A GENERAL THEORY OF ENERGY PARTITION WITH
APPLICATIONS TO QUANTUM THEORY.

By Richard C. Tolman.

Introduction. — ^The principle of the equipartition of energy was one
of the most definite and important results of the older statistical mechan-
ics, and the contradiction between this principle and actual experimental
findings, in particular in the case of the distribution of energy in the
hohlraum, has led many physicists to believe that the imderlying struc-
ture of statistical mechanics must itself be false. More specifically, since
statistical mechanics is most conveniently based on the equations of
motion in the Hamiltonian form, many critics of the older statistical
mechanics have come to the conclusion that Hamilton's equations are
themselves incorrect, and indeed some extremists have gone so far as to
believe that any set of equations would be incorrect which, like those of
Hamilton, take time as a continuous variable, since they think that time
has in reality an atomic nature and that all changes in configuration
take place by jumps.

It is well known, however, as shown by the work of Helmholtz,
Maxwell, J. J. Thomson, Planck and others^ that for all macroscopic
systems whose behavior is completely known it has been found possible
to throw the equations of motion into the Hamiltonian form, provided
we make suitable choices for the functional relationships between the
generalized coordinates ^^s'-'^n* the generalized velocities ^1^2- "^nf

> The appended references may be consulted as an evidence of the genexal applicability
of the principle of least action in all known fields of d3mamic8. The methods of transposing
the equations of motion from the form demanded by the principle of least action to the
Hamiltonian form are well known. In canying out this transformation it should be re-
membered that the system must be taken inclusive enough so as not to be acted on by
external forces.

See Helmholtz, (Vorlesungen fiber theoretische Phjmik) ; note the development of electro-
magnetic theory from a djmamical basis by Maxwell (Treatise on Electricity and Magnetism)
and by Larmor (Phil. Trans., i4-7i9 (1884), p. 694 (1895)); the treatment of various fields
by Sir J. J. Thomson (Applications of Dsmamics to Phsrsics and Chemistry, Macmlllan,
z888); the presentation of optical theory on a djmamical basis by Maclaurin (The Theory
of Light, Cambridge, 1908); and considerable work in newer fields based on the principle
of least action by Planck (Ann. d. Physik, 26, z (1908)), Herglotz (Ann. d. Physik, 36, 493
(19ZZ)), de Wisniewski (Ann. d. Physik, 40, 668 (19x3)), Tolman (Phil. Mag., 28, 583 (1914),
and The Theory of the Relativity of Motion, University of California Press, 1917)*

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262 RICHARD C. TOLMAN.

the generalized momenta ^i^f-^», and the Hamiltonian function H.
For this reason the writer is inclined to believe that in the case of the
ensembles of microscopic systems considered by statistical mechanics it
is very unwise to abandon the Hamiltonian equations of motion unless
we are absolutely forced to it. It should also be noted that the variables
involved in an equation of motion can always be considered as having
ultimately a continuous nature, since apparent jumps in configuration
can always be accounted for by the assumption of immeasurably high
velocities. Such considerations make it necessary to investigate the
whole structure of statistical mechanics and determine if the Hamiltonian
equations of motion actually do necessitate the principle of the equi-
partition of energy.

We shall find that the principle of the equipartition of energy is not
in the least to be regarded as a necessary consequence of Hamilton's
equations, but has been derived from those equations merely because
energy has, quite unnecessarily, always been taken as a homogeneous
quadratic function of the generalized codrdinates. We shall be able,
furthermore, to derive a new and very general equipartition law for the
equipartition of a function, which reduces to energy for the special case
that energy does happen to be a quadratic function of the coordinates.
Our methods will further permit us to study the actual partition of
energy with various functional relations between energy and the codrdi-
nates, and we shall consider a number of interesting systems where
energy is not equiparted which have hitherto been neglected. Finally,
in the case of the hohlraum, we shall consider a functional relation be-
tween energy and the codrdinates which does lead to the partition
of energy actually found experimentally, and also leads to the absorption
and evolution of radiant energy in a relatively discontinuous manner in
amounts Av, thus agreeing with the photoelectric and inverse photoelectric
effects.

This treatment of the hohlraum which we shall present leads to the
expression

e*^- I

for the average energy associated with a mode of vibration of frequency v,
in a hohlraum which has come to thermodynamic equilibrium at tempera-
ture T. This expression is known to agree at least substantially with the
experimental facts and is the expression proposed by most forms of the
so-called quantum theory of radiation. Our treatment of the hohlraum
differs, however, from previous forms of quantum theory in not disturbing

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No^i^^'l ^ GENERAL THEORY OP ENERGY PARTITION. 263

in the least the fundamental structure of the familiar classical statistical
mechanics. In essence, our development adopts the essentials of the
older statistical mechanics, and merely grafts on to it the new idea,
that energy is not necessarily a quadratic function of the generalized
co6rdinates and momenta which appear in the equations of motion in the
Hamiltonian form.^ The methods of attack, which are here considered,
are moreover much more general than any hitherto employed by the
quantum theory, since they permit a study of the partition of energy
for an infinite variety of forms of relation between energy and the co-
ordinates. Thus in the present article, we shall consider the energy
partition in a number of systems besides those which can be treated
by the quantum theory, including for example the partition of energy
in a gas subjected to the action of gravity. Indeed it is to be specially
emphasized that we shall find the structure of statistical mechanics quite
big enough to account for any desired number of different modes of energy
distribution besides the particular one proposed by the quantum theory.*

Part I. Statistical Mechanics.
The Equations of Motion. — Consider an isolated system whose state is
defined by the n generalized coordinates {<t>i<h" ' <t>n) and the corre-
sponding momenta (^1^2* • '^n). Then in accordance with Hamilton's
equations we may write the equations of motion for this system in the
form

dH dH

dH . dH .

where H is the Hamiltonian function, and ^ = (d^l^/dt), etc.

Geometrical Representation. — Employing the methods so successfully
used by Jeans,* we may now think of the state of the system at any
instant as determined by the position of a point plotted in a 2»-dimen-
sional space. Suppose now we have a large number of systems of the
same structure but differing in state, then for each system we should
have at each instant a corresponding point in our 2n-dimensional space,
and as the systems change in state, in accordance with equations (i),
the points will describe stream lines in the generalized space.

'The investigations already referred to show the possibility of a variety of functional
relationships between energy and the generalized coordinates and momenta.

* This fact might assume unexpected importance if more accurate measurements of the
distribution of energy in the hohlraum should lead us to discard Planck's formula as experi-
mentally correct.

* The Dynamical Theory of Gases* 3d edition, Cambridge, 1916.

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264 RICHARD C. TOLMAN.

.ffOTlWff.

The Maintenance of Uniform Density. — ^Suppose now that the points
were originally distributed uniformly throughout the space, then it is
a necessary consequence of our equations of motion that the distribution
will remain uniform. To show this, we note that we may write for the
rave at which the density at any point is increasing:

^__ /^4.^4.^4. 4. £^4. ^4. ^4. \

dt ' ^ \a«i "^ d<h d<h "^ a^i a^i a^8 "^ / '

and since our equations of motion (i) evidently lead to the relations

we see that the original uniform density will not change.

This important result means that there is no tendency for the repre-
sentative points to crowd into any particular part of the generalized
space, and hence if we start some one system going and plot its state in
our generalized space, we may assume,^ that, after an indefinite lapse
of time, its representative point is equally likely to be in any one of the
infinitesimal elements of equal volume {dif>id4>^4>i' * *^^i^^at/^s* • •} into
which we can divide our generalized space, provided of course the co-
ordinates for the location of this element correspond to the actual
energy content of our system.

Microscopic State, — ^As a convenient nomenclature, we shall say that a
statement of the particular element of volume {d<t>id4>^4>z' • -(f^i^f^af/^s
• • •) in which the representative point for our given system is found is
a specification of the microscopic state of the system. And the principle,
which we have just obtained, states that all the different microscopic states
possible have the same probability.

Statistical State. — ^Let us suppose now that our system is a thermo-
dynamic one composed of a large number of identical elements, such
as atoms, molecules, oscillators, modes of vibration, etc. We may
let Nai Nb, Ncf etc., be the number of elements of each of the different
kinds A, B, C, etc., which go to make up the complete system, and
may consider our original 2n coordinates and momenta as divided up
among these different elements.

For such a thermodynamic system we shall be particularly interested
in the number of elements of any particular kind A which have co-
ordinates and momenta falling in a given infinitesimal range (dA<t>i dA<h

^ It is not within the scope of our present undertaking to enter into the vexed discussions
as to the validity of this assumption.

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No*^^! ^ GENERAL THEORY OP ENERGY PARTITION. 265

- ' - dA^^i dA^ * * *) and this determines what we shall call the statistical
state of the system.

The microscopic state of the system and the statistical state differ
in that the former determines the codrdinates and momenta for each
individual element, while the latter only states the number of elements
of the different kinds which have coordinates and momenta of a given
magnitude, without making any distinction as to which particular ele-
ments are taken to supply a quota. Thus we see that, corresponding
to a given statistical state of the system, there will be a large number
of microscopic states, and, since we have already seen that all micro-
scopic states are equally probable, we obtain the important conclusion
that the probability of occurrence for a given statistical state is pro-
portional to the number of microscopic states to which it corresponds.

Probability of a Given Statistical State. — ^Let us now specify a given
statistical state by stating that iNa iNa zNa • • • iNb zNb iNb • • •
iNc tNc iNc ' • • , etc., are the number of elements of each of the kinds,
which have values of coordinates and momenta which fall in the particular
infinitesimal ranges Nos. 1-4, 2-4, 3-4, •••, i S, 2 S, 3B, •••, etc.
Then it is evident from the principles of permutation that the number
of microscopic states corresponding to this statistical state will be:

W \N^\N,JN^^

'' _ AT. L \7. L\7. . . . L A7_ I. A7_ - - . LA7_ I_ A7_ . A7- -A7_ . . . V.'^/

iNa IiNa \zNa ' ' ' \iNb IiNb --{iNb \iNc \tNc \tNc

and we shall call this the probability of the given statistical state, without
bothering to introduce any proportionality factor.

Let us assume now that each of the numbers iNa iNb, etc., are large
enough so that we may apply the Stirling Formula,

\N^^^2rN('j) . (3)

Introducing into (2), taking the logarithm of W for greater convenience,
and omitting negligible terms we obtain :

., IiNb, iNb , tNa, tNa , tNa, iNB , \ , n

-^c(^

Nc, iNc , tNc, tNc , zNc. zNc , \

— etc.
The ratios iNa/Na, 2Na/Na9 etc., evidently give the probability that

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266 RICHARD C. TOLMAN,

any particular element of the kind in question shall have values of
the coordinates and momenta falling within particular infinitesimal
ranges {dA4>i dA<h • • • ^.i^i dA^h '") Nos. i A, 2 A, etc., provided the
system is in the given statistical state. Let us denote these ratios by
the symbols iWa, jWa, etc.,

iNA iNB iNc ^ , .

'^^^Nl-'^'^Nl^ .tc;c=j^, etc. (5)

Then we may rewrite equation (4) in the form

logW == — Na 2 tWA log (Wa -- Nb 23 iWB log tWB

<=irM.«. <=xi,2.8,...

^ Nc 2 jW'c log iWc — • • •. (6)
<«i, a. t, ...

State of Maximum Probability, — Having obtained this expression for
the probability of a given statistical state, let us determine what par-
ticular state is the most probable with a given energy content. The
condition of maximum probability will evidently be:

5 log TT = — Na 2(log iWA + 1)5 iWA — Nb S(log avb + i)5 w^ • • •

= 0. (7)

The variation 5, however, cannot be carried out entirely arbitrarily
since the number of elements of any particular kind cannot be varied
and the total amount of energy is to be a constant.

In accordance with equations (5) we may write

Na-- Na:^ {Wa, Nb=^ Nb:s: cwb, etc.,

and since the total number of elements Na^ Nb^ etc., of each kind cannot
be varied we have

Na ^^,Wa = o, Nb S ^iWs = O, etc. (8)

Furthermore, let us write the total energy of the system equal to the
sum of the energies of the individual elements,

E^ NaI^ iWa ^Ea + Nb^ <u)BiEB+ '",

where iE^i, etc., is the energy of an element of kind A with values of
coordinates and momenta falling in the infinitesimal region No. iA, etc.
Since E is to remain constant during the variation we may write

5£ = iV^ S iEa^wa + Nb^ iEB^WB + • • • = o. (9)

The simultaneous equations (7) (8) and (9) may now be solved by the
familiar method of undertermined multipliers giving us

log iWa + I + X <-E^ + Ma = o, t = I 2 3 • • •,

(10)
log iWs + I + X i£s + MB " o, 1 = I 2 3 • •',

etc.

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Na*i^^'*l ^ GENERAL THEORY OP ENERGY PARTITION. 267

The quantities X, m-Ai Mb, etc., are undetermined multipliers, where it
should be specially noticed that X is the same quantity for all the equa-
tions, while fiA, MB, etc., depend on the particular kind of element in
question.

For our purposes these equations can be more conveniently written
in the form

etc.,

where e is the base of the natural system of logarithms and the constants
aAf (XBf etc., correspond to the earlier fiA, mb, etc., and P corresponds to m-
These are the desired equations which describe the state of maximum
probability. Thus, in accordance with fhe equations of definition (5),
flUA is the probability that any particular element kind A will have values
of codrdinates and momenta falling in the particular infinitesimal region,
(dA<l>if dA<hf • • ', dA^u dA^h, • • Ot No. iA, when the system has attained
the state of maximum probability.

Introduction of a Continuous Variable. — ^The quantity tWA determines
the number of elements that fall in the specific region No. iA. We
have seen, however, in equations (11) that hva is determined by the
energy corresponding to this region, and this in turn is a function of the
coordinates and momenta. This makes it possible to introduce a new
and convenient quantity, a variable, wa^ which is a function of these
coordinates and momenta, and which gives the probability, per unit
generalized volume, that a given element of kind A will have coordinates
and momenta corresponding to the energy £a, we may then write

WAdA4fidA<h' • 'dAi^idA^* • • = aAe'~^^'^dA<lndA<h' • 'dA^^idA^* • •,

(12)
WBdB<l>idB<h' ' 'dB^idB^^* ' ' = a Be ^dB^idB<h' ' '^b^i^b^* • •,

as expressions for the chance that a particular element of kind A, B,
etc., will have values for co5rdinates and momenta falling in the infini-
tesimal ranges indicated.

Final Expression for the Distribution of Elements in State of Maximum
Probability. — It will be noticed that the constants a^, as, etc., which
occur in equations (12) correspond to the yLAt fiBi etc., in equations (10)
and hence these values will be determined by the particular kind of
element A, B, etc., involved. j8, on the other hand, corresponds to the
earlier X and hence its value is independent of the particular kind of
element involved. In case the elements involved are the molecules of a
perfect monatomic gas, it is well known that P has the value of i/kT,

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268 RICHARD C. TOLMAN. [^SS

where k is the ordinary gas constant divided by Avagadro's number,
and T is the absolute temperature. Hence we may now write as our
final expression for the probability that a given element of any particular
kind will have values of codrdinates and momenta falling within a given
infinitesimal range, .

ae-'^''^d4ndW • -di^idyh^ • • . (13)

where the value of a depends on the particular kind of element -4, S,
C, etc., in which we are interested, and E is the energy of one of the
elements, expressed as a function of its generalized coordinates and
momenta (^i^* • '^lyh' ' ')•

Two Fundamental Equations of Staiistical Mechanics. — ^Since any ele-
ment must have some value for its coordinates and momenta we may
write the important equation, •

ff'"ff" -ae-'^f'^d^idih' • 'dhdh' • • = I, (14)

CO w

where the limits of the integration are such as to include all possible
values of the ^'s and ^'s.

Furthermore, it is evident that we may write for the average value
of any property P of an element, the equation

Pav ^ff -ff" -ae'^'^^Pdilnd^h' • -d^id^- • •, (15)

CO CO

where P is to be taken as a function of the co5rdinates and momenta,
and the limit of integration is as above.

The General Eguipartition Law. — ^We may now derive a very general
equipartition law. Let us integrate the left-hand side of equation (14)
by parts with respect to 0i, we obtain

[/•••//••-'-'^^*-^w*.-]t:rru:™:

(16)
- j j ' • • JJ" 'ae-^^''% (1^)66^^*^^*^' ' 'd^id^h' • • =1.

Let us confine ourselves now to cases in which ^ becomes either zero
or infinity at the two limits, and in which E becomes infinite if ^ does.
Then the first term of (16) vanishes and we may write

// ' " // ' ' •^^''''^''^i^f ^*i^*»- • 'dhdh' • • = *r. (17)

In accordance with (15), however, this gives us the average value of
[<lnidE/d^i)] and hence, applying similar consideration to the other co-
ordinates and momenta, we may now write as our general equipartition
law:

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Na*4^^'] ^ GENERAL THEORY OF ENERGY PARTITION. 269

hllL-hllL--hil-ha---'<-'>

and this law will apply in all cases in which th^ above condition as to
the limits of integration is fulfilled.

The General Equation for the Partition of Energy. — In the particular
case that the energy is a homogeneous quadratic function of the co-
ordinates and momenta the above equation (18) will evidently reduce
to the value ikT for the energy associated with each co5rdinate or
momentum, which is the familiar principle of the equipartition of energy.

Whatever may be the relation, however, between energy and the
coordinates and momenta, we may obtain its average value for a given
kind of element with the help of equation (15), which permits us to write

^•» = //• • •//• • -ae'^'^Edilndfh' • -dW^- • •• (19)

In order to eliminate the constant a we may divide (19) by (14) and
obtain,

^ SJ-'SJ-'e-''^'^Ed4>,d4n'-di^idh'- , ^

JJ'JJ" -e-^^'^diPidih' • 'd^id^' . .

We may now apply equations (18) and (19a) to. obtain information
as to the partition of energy in a number of interesting cases.^

Part IL Miscellaneous Applications.
Gas Subjected to Gravity. — For the first application of our equations
let us consider a monatomic gas subjected to the action at gravity, in a
tube of infinite length. Considering the Z axis as vertical we can write
for the energy of any given molecule,

6 ' 2 '2 2 '

where z is the height of the molecule above the surface of the earth. In
terms of the components of momentum, our expression for energy may
be rewritten :

2f?t 2f?t 2in

> In applying these equations it is to be noticed that we do not need to make the elements
into which we divide our statistical system agree with what are ordinarily thought of as the
physical elements of the system. Thus if our S3rstem is a quantity of a monatomic gas, instead
of taking each atom with its three positional coordinates and its three momenta as an element
we may take these variables as belonging to six different elements. Indeed it is obvious,
from our methods of deduction, that we shall need to class coordinates and momenta together
as belonging to the same element only in groups large enough so that any given coordinate
momentum will not appear in the expression for the energy of more than one of our elements.

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270 RICHARD C. TOLMAN. ^SS

where the components of momentum are given by the equations

^, - mi, ^y = my, ^, = mz.
Applying our equipartition equation (18) we obtain

Lff» Jav l^tn Jav Lm Jav

or, introducing the equations defining momenta, we obtain

And we see that according to our equipartition law, the average potential
energy per molecule is twice as great as the average kinetic energy in
any direction.

This is a particularly simple case of a deviation from the principle
of the equipartition of energy, and of course it could have been shown
by methods which have long been familiar, that the average potential
energy per molecule is twice as great as the average component of kinetic
energy. It should be specially noticed that this is a deviation from the
principle of the equipartition of energy which bears no relation to those
which have more recently been discovered and studied by the quantum
theory.

The Energy Any Simple Power of the Codrdinates, — ^The above devia-
tion from the equipartition of energy was due to the fact that the poten-
tial energy of these molecules was proportional to the first power instead
of to the square of the coordinate involved. We may point out with
the help of equation (18) what the general relation will be. If the energy
for a given elementary coordinate or momentum is proportional to the
nth power of that invariable,

E = Cit>\ (20)

then by (18) we shall have

Thus, for example, if we had in our system oscillating elements in which
the restoring force, instead of following Hook*s law, was proportional
to the square of the displacement, then the average potential energy
of these oscillators would be ^kT instead of the familiar ikT.

These considerations will be of value in case we find it convenient to
express the energy of an element by an empirical formula of the form

E ^ a + b4f + c4^ + dit>^ + • • • .

Relativity Mechanics. — ^As another example of a deviation from the

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Vol. XL!
No. 4* J

A GENERAL THEORY OF ENERGY PARTITION,

271

principle of the equipartition of energy, we may consider a monatomic
gas whose molecules are considered as particles, obeying the new "rela-
tivity" laws of motion instead of Newton's laws of motion, which we
now know are only the approximate form assumed by the correct laws
of motion at low velocities.

According to these new laws of motion we must write for the com-
ponents of momentum of a particle:

^. =

^.=

fftoX

W^ ? —

moy

+ / + Z'

(21)

fitoZ

+ 3^ + 2^

where mo is the mass of the particle at rest and c is the velocity of light
For the kinetic energy of the particle we may write

E =

4r-^-

+ ii' + ^'

(22)

a quantity which except for a constant reduces to itWoCx* + >^ + 2*) at
low velocities. In terms of the momenta we may rewrite this expression
for the kinetic energy in the form

Applying equation (18) we obtain

(23)

I ^* ^c*tn^* + ^.* + W + 1^.* -I" L ^'

''v/c*f«o* + i^.* + W + f

= etc. = kT,

and introducing our previous equations, this may be written

I r y»oX^ "I _ £ r Woj^

_ I r mps*

(24)

= i*r.

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272 RICHARD C. TOLMAN. l^S

We thus see that in relativity mechanics we have the equipartition of a
function which reduces to the kinetic energy §f«oi*, etc., at low velocities,
but at high velocities is not even the same as the relativity expression
for energy.^

These few examples are sufiicient to illustrate the application of our
methods, in fields other than those treated by the quantum theory.
Let us now turn our attention to the partition of energy between the
different modes of vibration of a hohlraum.

Part III. Application to the Hohlraum.

The Idea of Quanta. — In developing a theory of the hohlraum, we may
base our considerations on the fact that radiant energy is known to be
absorbed and evolved substantially in quanta of the amount Av, where
h is Planck's new constant and v is the frequency of the radiation in-
volved. This is an experimental fact, illustrated most simply by the
photo-electric effect and the inverse photo-electric effect, and is cer-
tainly the expression of a fundamental characteristic of radiant energy.

This important fact can be incorporated in our new system of statistical
mechanics by assuming that the energy associated with a given mode of
vibration in the hohlraum increases with the amplitude of the vibrations
in a relatively discontinuous fashion by amounts of the magnitude hv.
If ^ is a generalized co5rdinate which determines the displacement for
a given mode of vibration and ^ is the corresponding generalized momen-
tum, then in the older dynamics the energy associated with the mode
would have been given by the formula

£ = *«» + /^, (25)

where k and / are constants. According to this formula the potential
energy fe^* increases continuously with the square of the displacement
and the kinetic energy /^ with the square of the momentum.

In our new dynamics let us assume that the energy is practically
zero until k4^ + /^ reaches the value hv and that it then increases
with great suddenness to the value hv, remaining again practically con-
stant until it increases to the amount 2hvj when fe^ + /^ itself reaches
the value 2hv, and so on, for following intervals, the energy attaining
successively the values sAv, 4A1', etc.

Expression for Energy. — Such a relation between energy and the co-
ordinates can be expressed algebraically by the equation

* This new equipartition law for tlie special case of relativity mechanics was first derived
by the author, Phil. Mag.. 28, 583 (1914). The same article or an earlier one by Jtittner,
Ann. d. Physik, 34, 856 (191 1), may be consulted for an investigation of the actual energy
partition in this case.

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No^i^'I ^ GENERAL THEORY OP ENERGY PARTITION. 273

where n is some number large enough so that the exponents of e change
suddenly from minus infinity to zero when jfe0* + l^ assumes the suc-
cessive values hv, 2hv, ^hv^ etc, If n were itself given the value infinity,
the energy would increase in absolutely abrupt steps of the magnitude hv.
It is not our belief, however, that the energy changes absolutely abruptly
at the points in question, since if this were the case the whole application
of our statistical mechanics would be fallacious, since it is based on the
Hamiltonian equations which presuppose a motion which is at least con-
tinuous when regarded from a fine-grained enough point of view. Fur-
thermore it is not to be supposed that the precise relation between
energy and the coordinates is necessarily given by equation (26). The
expression presented or any other which makes the energy increase in
the way described, substantially in quanta, is quite suitable for the
purposes of integration which we have in view, but might not be suitable,
if we should desire to differentiate (26) for the purpose of determining
the equations of motion in the Hamiltonian form.

Before leaving the discussion of equation (26), we should point
out that V is the frequency of the particular mode of vibration in-
volved and h is Planck's new universal constant which has the magnitude
12.83 X 10"^ erg X seconds, so that even with a frequency of many
billions per second, the energy would apparently increase with the
amplitude of vibration in a perfectly continuous fashion in accordance
with the simple equation E = k<t^ + /^, which has been made familiar
by experimentation with those everyday vibrating systems whose fre-
quencies are low.

Partition of Energy in the Hohlraum. — Having described the relation
between energy and the coordinates which we believe to exist, let us
proceed to determine the partition of energy in the hohlraum, by the
methods which we have developed in the earlier part of the article.
In accordance with equation (19a) we may write for the average energy
associated with a given mode of vibration,

fJe-^f^^'Editd^p

In order to evaluate these integrals for our particular case, we may note
in accordance with equation (26), that the energy E will have the value
zero for all values of 4> and ^ which He inside the ellipse k<t? + /^ = hv,
the value hv for all values of ^ and ^ falling in the space between this
ellipse and the concentric one k(t^ + /^ = 2hv, and so on for successive
concentric ellipses. This permits us to rewrite the above equation in
the form

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274 RICHARD C. TOLMAN.

Since the area enclosed byjthe successive ellipses increases by equal
steps of the amount (rhv/^kl), the above expression can be reduced to

which upon division is seen to be

£o» — jk^/ir^^j t (27)

which is the well-known expression, assumed by the quantum theory
upon empirical grounds, as the average energy for a mode of vibration
of frequency v. The result is of significance in showing that our general-
ized dynamics, in which the energy can be any function of the codrdinates
and momenta, leads to a statistical mechanics broad enough to account
for the actual partition of energy found in the hohlraum.

Emission of Energy by Quanta, — Before leaving this discussion we
should point out that the relation (26) between energy and the generalized
codrdinates which we have chosen, not only accounts, as we have just
seen, for the partition of energ>' in the hohlraum, but also explains the
photo-electric and the inverse photo-electric effects. This arises from
the fact that in accordance with the fundamental structure of our system
of statistical mechanics all microscopic states for a given mode of vibra-
tion are equally probable, and since the vast majority of these microscopic
states correspond to an energy content, which is an exact multiple of hv,
we shall expect generally to find radiant energy absorbed and emitted
in amounts hv or some multiple thereof.

Nature of the Electromagnetic Field. — It is, further, to be pointed out,
if we are permitted to trespass for a moment in a field of uncertain
speculation, that our relation (26) between energy and the coordinates
indicates a somewhat fibrous structure for the electromagnetic field
when viewed from a fine-grained enough, and not too fine-grained, point
of view. It seems to the writer, that this conclusion might furnish
support to those theories of the atom^ which assign very definite positions,

* See, for example, Lewis, J. Amer. Chem. Soc., 38, 762 (1916).

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Na*4'^^'] ^ GENERAL THEORY OF ENERGY PARTITION. 275

with reference to the positive nucleus, to those electrons which determine
the chemical properties of the atom, since the fibrous structure of the
electromagnetic field surrounding the positive nucleus might easily pro-
vide rather definite pockets where these electrons would find their
positions of equilibrium.

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276 JOHN B, DERIEUX. [ISSS

PHOTOELECTRIC EFFECTS ON MERCURY DROPLETS.

By John B. Dbrieux.

Simultaneous Discharges.
TT has been shown by Professor R. A. Millikan and Mr. Harvey
■■■ Fletcher that never more than one elementary charge at a time is
detached from a neutral air molecule by primary or secondary X-rays.^

The question naturally arises as to whether in photoelectric effect
more than one electron at a time is detached from a molecule of the
metal by the ultra-violet light. Particles suspended in a Millikan
condenser furnish a convenient manner of making this determination.

A. Joffe in work in the photoelectric effect on small particles by the
above-mentioned method notes variations in the time of liberation with
the size of the particle, intensity of illumination, and wave-length of the
light.* He made no study, however, of whether more than one electron
at a time was liberated, but his tables show doubles in a few instances.
Edgar Myer and Walther Gerlach, by the same method, determined
the variation in the time of liberation with pressure of the surrounding
air, but neither do they take note as to simultaneous liberations.'

Method.
Mercury droplets were secured as in the work on the elementary
charge and by the method used there the number of units of charge on
them was determined. Ultra-violet light was allowed to fall upon them
until a change in their charge was noticed. The new number of units of
charge was then determined and the difference between the two taken
as the number of units of the change in charge.

Apparatus.

The electric condenser for the apparatus was comix)sed of two circular

plates about 15 cm. in diameter separated about 1.8 cm. and supported in

a horizontal position. The potentials of the condenser were obtained

from a 5, 000- volt battery of storage cells. A variation in the potential

> Phil. Mag., June, 191 1.

' Sitzungsberichte d. Bayer Akad.. 191 3.

* Arch, des Sd. and Nat., March. 1914.

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No*^^*] PHOTOELECTRIC EFFECTS ON MERCURY DROPLETS. 277

was secured by means of a controller consisting of a revolving handle and
contact points connected to different points in the battery. A quartz
mercury-vapor lamp was used as a source for the ultra-violet light, an
X-ray tube for the ionization of the air, and a right carbon arc for the
illumination of the droplets. A cathetometer telescope with a scale
in the eyepiece was used in observing.^

Manipulation.

The mercury lamp was placed in the plane passing midway between
the condenser plates and at an average distance of about 50 cm. from their
centers. The light from it entered through a diaphragm which was so
adjusted that the beam in the condenser had a height of about i cm.
and passed through without striking the plates. Admission was con-
trolled by a shutter just in front of the diaphragm.

With the shutter closed, a droplet was secured and a small negative
charge given it, through ionization by the X-rays. The times required
for it to fall i millimeter under gravity and to rise i millimeter under the
full potential of the battery were noted. The assistant then connected
the first point of the controller to the battery at such a place that the
potential obtained from it was sufficient to hold the drop suspended or
cause it to slowly rise. The droplet was then placed about midway
between the plates so that it would be in the path of the ultra-violet
beam and the shutter was opened until an electron had been liberated.
With the droplet balanced, as indicated, the instant of liberation was
very marked, for the droplet which had previously been stationary, or
gradually rising, suddenly began to descend. The rising speed under
the full potential of the battery was then taken, a balance secured from
the second point of the controller and another exposure made. This
process was continued until the droplet was discharged or the full
potential of the batteries was required to produce a balance. The droplet
was then recharged through ionization by the X-rays and another series
taken. With the points of the controller connected as in the first series,
a balance of the droplet in any case could be secured by simply moving
the controller handle to the proper point. It was of course necessary
to reconnect the controller for the initial series on each droplet.

Assuming .electricity to be atomic in structure and the unit of charge
to be 4.77 X lO"^® e.s.u. it was sufficiently accurate to take readings
over a distance of only i millimeter with a stop watch in order to deter-

1 The apparatus and arrangement was the same as that used in work by the author on
"Use of Mercury Droplets in Millikan's Experiment," a detailed drawing and description
of which was published in The Physical Review for March, 191 8.

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278 JOHN B. DERIEUX, [iSSE?

mine, without a doubt, the number of changes on a droplet. The com-
putations were made as in the work on the elementary charge.

Results.
In Tables I., II., III., and IV. are shown sets of typical observations.
The numbers in the columns headed tg indicate the time in seconds
required for the droplet to fall i millimeter under gravity, those under /jr,

Fig. 1.

the time in seconds under field. Table V. gives the results for all the
droplets observed. In the column headed a are recorded the radii of
the droplets.

Discussion of Results on Simultaneous Discharges.

As is shown in Table V., simultaneous discharges occurred in several
instances, but it may be noticed that the percentage of them decreased
with an increase in the mean time of liberation, becoming zero, as is
strikingly shown by the graph, at a value of about 50 seconds.

A plausible explanation of this is found in the wide extremes of the
times of liberation. It is possible, and even probable, that if a minimum
of .5 of a second occurred on a droplet having a maximum of 159 seconds
that a minimum of .1 of a second, or less, might have accompanied a
maximum of only 30 seconds. In fact, such was observed in a few
instances, the results, of course, being discarded, as the intervening
charge could not be determined. Liberation within such a short interval
was probably not always distinguished and hence appeared as doubles.

Suspecting this, an effort was made to increase the minimum time
of discharge by decreasing the intensity of the ultra-violet light. This
was done gradually until observations on droplet number 6 had been
made. The decrease in the percentage of doubles seemed to verify the

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Vol. XI.1
Na4. J

PHOTOELECTRIC EFFECTS ON MERCURY DROPLETS.

Table I.

Drop No. 6,

279

-J

III

-i

^11
*o8

l|li

1^1

3.6

1.4
2.2
8.2

3
2

1
0

20.4

10.8

7.5

2
3

4.2

1.2
2.0
5.4

3
2

1
0

64.4

21.0

5.6

15
16
17

3.7

1.2
6.0

3
2
0

47.5
23.0

4
5

4.4

1.2
5.4

1
0

36.2
48.2

18
19

3.8

1.2
2.0
5.7

3
2

1
0

13.0
5.0
2.0

7
8

4.2

1.1
1.9
5.3

3
2

1
0

1.8
24.2
13.8

20
21
22

4.4

1.1
1.8
5.5

3
2
1
0

10.2
14.8
17.4

9
10
11

4.4

1.1
1.8
5.3

3
2

1
0

59.0

3.0

29.4

23
24
25

4.3

1.0
2.0
5.3

3
2

1
0

3.0
10.5
63.8

12
13
14

4.1

1.1
1.9
5.2

1.1
2.0

5.3

3
2

0
3

1
0

2.0
25.2
23.6

10.2
4.2

26
27
28

29
30
31

Time of Observation « 1 hr. 10 min.

P. D. - 4,850 volts.
Number of Changes - 31
Number of Simultaneous " - 2 doubles

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28o

JOHN B, DERIEUX.

rSscoMo
LSbkiss.

Table II.

Drop No. 13,

-i

Ill

No. of
Chargea
Liber-
ated.

1^1

^5S

•ii

No. of

Chargee

Liber.

ated.

3.1

1.6

1.2

78.4

14.4

3.1

1.5

19.5

bal.

3.2

19.4

bal.

1
0

61.0

3.0

1.1
1.7

4
3

113.0

3.0

9.5

14.5

3.0

1.2

17.4

50.4

bal.

1.5

35.4

51.4

3.2

2
0

62.0

3.1

1.1
1.7

4
3

12.2

26.8

80.6

3.1

1.2

112.0

73.5

bal.

•

1.7

43.0

44.4

3.0
bal.

2
1

5.4

1.2

9.8

100.6

1.6

60.5

3.2

56.8

60.0

bal.

1.2

9.0

111.4

1.7
3.1

3
2

4.4

Time of Observation * 1 hr. 20 min.

P. D. - 4.760 volts.
Number of Changes — 31
Number of Simultaneous *' * 1

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}5JJ-^^] photoelectric effects on mercury droplets.

281

Table III.

Drop No. 8.

-^j

6\tQ

1^1

-i

iih

^ll

*S8

^5S

a 9
^Z

*8§

Zg2«

4.6

1.0
1.5
4.5

3
2

1
0

9.2

27.0
37.0

1
2
3

1.0
1.5
4.5

3
2
1
0

1
1

43.8
20.5

5.4

16
17
18

4.8

i.o

1.5
4.5

1.1
1.4
4.6

3
2

1
0
3
2

1
0

26.0

• 5.0

61.6

131.2
13.0
35.0

4
5
6

7
8
9

0.9
1.7
4.7

3
2

1
0

1
1

6.2
76.0
10.0

19
20
21

5.0

.9
1.4
4.6

3
2
1
0

167.0

155.0

44.0

10
11
12

4.9

1.0
1.5
4.5

3
2
1
0

23.0

179.0

5.0

13
14
15

Time of Observation — 1 hr. 40 min.

P. D. - 4.730 volts
Number of Changes - 21
Number of Simultaneous ** * 0

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282

JOHN B, DERIEUX,

ISmmsmm,

Table IV.

Drop No. 14,

»j

o'«Q

nil
P5S

-'i

*8g

III

4.4

1.0

1.4

14.6

35.4

1.4

2.4

4.5

50.0

2.2

9.0

31.0

6.0

8.5

24.4

—

4.6

1.0

113.4

1.0

1.5

113.0

32.0

1.4

2.4

83.0

64.6

2.2

8.6

36.2

29.8

8.3

15.0

—

Time of Observation — 1. hr.

P. D. - 4.000 volts.
Number of Changes » 15
Number of Simultaneous ** — 0

Table V.

Results on Simultaneous Discharges,

Die.

Slmul.

Per

Chargea

Time of Diacharge (Seconda).

Drop

t,(8ec.
onda).

(Cm.).

chargea

Ob.
aenred.

taneoua

Die.
chargaa

Cent.

Simul.

Itaneoua.

on
Droplet.

No.*^

Ifaximum.

Ifinimum.

Mean.

2.9

4.23

0-3

K?)

2.6

4.52

1-4

3(?)

3.2

4.05

1-3

2(?)

4.1

3.53

0-3

K?)

2.1

5.08

1-6

3(?)

4.0

4.06

6.5

0-3

2(?)

2.3

4.86

2-6

252

110

4.8

3.22

0-3

167

1.9

5.32

1-5

182

4.1

3.54

0-4

143

3.7

3.75

0-3

2.3

4.80

3.5

1-5

159

0.5(?)

2.9

4.20

3.2

0-5

113

4(?)

4.4

3.89

0-4

113

4.5

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Vol. XL!
Na4. J

PHOTOELECTRIC EFFECTS ON MERCURY DROPLETS,

Table VI.

Results on the Long Wave-Length Limit of Mercury,

283

Drop

t,(8ec
onde).

aXio*

(A.).

Wave-
length

(MM).

Die-
chargee

Ob.
aenred.

Simul-
taneone

Die-
chargea.

Chargee

on
Droplet.

Time of Diecharge (Seconde).

No.

Ifaximum.

Ifinimum.

Mean.

17
II

2.5
II

3.8

2.2

4.60
II

3.68
II

4.91
II

253.5
II

312.6
253.5
253.5
312.6

4
2
0

1
3
0

0
0
0
0
0
0

1-5
1-3

3-4
2-4

57
559

454

24
223

240

391»
(27inin.)
lOmin.

347
(ISmin.)

> Taken after 10 min. pause.

supposition ; a very decided decrease was then given it and droplet num-
ber 7 gave no doubles. Thinking perhaps that this was a farther decrease
in the intensity than was necessary, it was gradually increased until
droplet number 12 had been observed, when doubles again appeared.
Decreasing it again, they disappeared on droplet dumber 14.

The conclusion was drawn from this that a decrease in the illumination
increased not only the maximum time of discharge but the minimum as
well, and when it had reached a value of .5 of a second or more every
change was distinguished and no doubles were recorded.

Hence it seems probable that in the photoelectric effect on mercury
droplets two electrons are never liberated at the same time and that
when two liberations appear to be simultaneous it is in reality two
distinct liberations, the interval between them being too short for the
observer to separate them. Since each droplet contains an enormous
number of molecules, the results lend strong support to the point of
view that in the photoelectric effect on mercury, simultaneous liberations
from a given molecule do not occur.

The Long Wave-Length Limit of Mercury.

In this work a prism spectrometer was used to separate the spectral
lines. Owing to the minuteness of the surface furnished by the droplets
the lines were found too faint to give a rapid discharge even with the
collimator slit open wide and the lamp operating on high energy. As
may be seen from Table VL, no doubles appeared, but this was attributed
more to the long times of discharge rather than to the single wave-length.

As to the long wave-length limit, liberations were obtained after long
exposures from the strong line 253.5 fifi. The next line tried was the
strong one, 312.6 ^/i, and it gave no discharge. It was tried upon two

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284 JOHN B, DERIEUX. [iSS

droplets each of which was tested by the line 253.5 MM to make sure that
the droplet was in the proper condition for discharging.

The lines between these were too faint to give results in a reasonable
time, but it is evident that the long wave-length limit lies between
253-5 MM and 312.6 /»/*•

I wish to thank Professor Millikan for suggesting and supervising these

experiments and also my wife for her assistance in the experimental part.

Rybrson Laboratory,

unrvbrsity of chicago.

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No*^^] POUR DOUBLE CHLORIDES OF URANYL, 285

ON THE UNPOLARIZED FLUORESCENCE AND ABSORPTION
OF FOUR DOUBLE CHLORIDES OF URANYL.

By Edward L. Nichols and H. L. Howes.

IN a recent paper^ an account was given of the fluorescence spectrum
of ammonium uranyl chloride and more recently the polarized
fluorescenC:e and absorption of the four double chlorides, UOjCU, 2NH4CI
+ 2H2O; U02CU-2KC1 + 2H20; UOjCU^RbCl + 2H,0 and UOjCl,
•2CsCl have been described and discussed.^ Complete measurements of
the fluorescence spectra and absorption spectra of this remarkable group
of fluorescent compounds have since been completed and it is our purpose
in the present paper to put these data on record and to consider their
bearing upon the structure of fluorescence spectra and the relations be-
tween fluorescence and absorption.

As was shown in the paper on the polarized fluorescence, just cited,
these four double chlorides have spectra which are partially resolved at
+ 20** and which exhibit an extraordinary similarity of structure. The
departures from complete identity, moreover, are of such a nature as to
reveal the relation of the more fully resolved bands obtained by excitation
at low temperatures to those of the spectrum as observed at + 20®.

Fluorescence Bands at + 20®.

The methods of locating the fluorescence bands were in the main
those described in previous communications on the spectra of the uranyl
compounds. Both photographic and visual measurements were made,
thus checking the estimates of wave-length. Averages of the results of
the two methods, which were in good agreement, have been used in the
compilation of Table L in which the wave-lengths and frequencies of
all the fluorescence bands observed in the spectra of the four double
chlorides at + 20** are given.

It is necessary to recognize the existence of eight groups of bands in
these spectra although the terminal groups i and 8 are only visible under
the most favorable conditions. Powerful excitation and freedom from
stray light are necessary to bring out even the stronger bands in group i ,

» Nichols and Merritt, Phys. Rev. (2), VI.. p. 358 (191 S).

« Nichols and Howes, Proc. Nat. Acad. Sc., I., p. 444, and more fully in Phys. Rev. (2),
VIII., p. 364 (1916).

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286

EDWARD L. NICHOLS AND H. L. HOWES.

[SacoMD
S

Table I.

General List of the Fluorescence Bands in Spectra of the Double Uranyl Chlorides at + 20** C.

8«riM.

Potasaium Uranyl
Chloride.

Ammonium
Uranyl Chloride.

Rubidium Uranyl
Chloride.

Csainm Uranyl
Chloride.

Qroap.

ixic.

IX-.

.6809

1469.7

.6716

1489.9

.6635
.6571
.6501

1507.1
1521.8
1538.2

.6436

1553.7

.6430

1555.3

.6420

1557.6

.6401

1562.3

.6375

1568.6

.6358

1572.9

.6354

1573.8

.6336

1578.3

.6303

1586.6

.6291

1589.6

.6281

1592.2

.6289

1590.1

.6225

1606.4

.6231

1604.9

.6206

1611.3

.6219

1608.0

.6171

1620.5

.6172

1620.2

.6162

1622.8»

.6156

1624.4

.6111

1636.5

.6103

1638.6

.6098

1640.0

.6090

1642.0

.6051

1652.5

.6041

1655.3

.6030

1658.3

.6015

1662.5

.5983

1671.5

.5978

1672.7

.5967

1675.9

.5970

1675.0

.5919

1689.5

.5923

1688.2

.5903

1694.1

.5911

1691.9

.5869

1704.0

.5866

1704.8

.5860

1706.4

.5854

1708.2

.5816

1719.4

.5813

1720.3

.5800

1724.0

.5789

1727.4

.5759

1736.4

.5752

1738.6

.5742

1741.6

.5729

1745.4

.5698

1754.9

.5696

1755.7

.5686

1758.7

.5689

1757.9

.5642

1772.3

.5642

1772.3

.5625

1777.8

.5631

1775.9

.5595

1787.2

.5593

1787.9

.5588

1789.4

.5587

1789.7

.5551

1801.4

.5546

1803.1

.5537

1806.1

.5529

1808.6

.5497

1819.3

.5492

1820.7

.5486

1822.8

.5472

1827.5

.5442

1837.6

.5436

1839.7

.5430

1841.5

.5433

1840.5

.5390

1855.3

.5385

1856.9

.5377

1859.8

.5379

1859.1

.5349

1869.6

.5342

1871.8

.5339

1873.1

.5339

1873.1

.5306

1884.7

.5300

1886.8

.5291

1890.0

.5288

1891.1

.5259

1901.5

.5250

1904.6

.5248

1905.5

.5234

1910.4

.5208

1920.1

.5200

1923.2

.5195

1925.0

.5198

1923.6

.5159

1938.3

.5153

1940.5

.5145

1943.5

.5147

1942.7

.5119

1953.5

.5112

1956.3

.5110

1957.1

.5113

1955.7

.5078

1969.4

.5072

1971.5

.5066

1973.8

.5067

1973.5

.5039

1984.4

.5031

1987.6

.5027

1989.1

.5024

1990.3

.4990

2004.0

.4986

2005.7

.4979

2008.4

.4989

2004.4

.4946

2021.7

.4940

2024.1

.4935

2026.2

.4937

2025.6

.4909

2036.9

.4904

2039.2

.4899

2041.4

.4904

2039.2

.4869

2053.8

.4867

2054.6

.4857

2059.0

.4863

2056.3

C
D
E
A

.4836

2068.0

.4829

2071.0

.4824

2072.8

.4819

2075.0

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Na'4^^*] FOUR DOUBLE CHLORIDES OP URANYL 2%J

which lies in the full red of the spectrum. The weaker terminal bands of
the group which have an intensity of less than i per cent, of that of the
crest are almost or quite invisible. Long exposures of photographic
plates specially sensitized for red afford the best method for this part of
the spectrum.

In group 8 the difficulties are scarcely less serious on account of the
overlapping of fluorescence and absorption. Fortunately the frequency
intervals for the various series having been established, one may supple-
ment, with considerable assurance, the missing values by computation
and this has been done, where necessary. Computed values are indicated
as such wherever they appear in the tables.

Fluorescence series are designated as 5, C, 2>, £, ^4, instead of the
6, c, d, e and a used in the papers on the polarized spectra, already cited.

The small letters are reserved for the indication of the related absorp-
tion series, which were formerly denoted by Greek characters.^

By means of the data in Table I. the conclusions reached in the previous
study of the ammonium uranyl chloride may be extended to all four of
the double chlorides now under consideration.

These conclusions are as follows:

1. In all four salts the fluorescence series, 5, C, D, £, A have constant
frequency intervals; i. «., there is no indication in passing from group i
to group 8 of a change in the interval of sufficient size to be detected.

2. The interval is essentially the same for the potassium, ammonium
and rubidium chlorides but appears to be somewhat smaller in the case
of the caesium chloride. It will be shown in a later paragraph that the
discrepancy is only an apparent one.

3. The interval is nearly the same for different series but the evidence
from these measurements while not in itself conclusive seems to indicate
small but real variations. The strongest indication is found in the C
series which has the lowest average interval.

The Distances between Groups.

Since it is at least approximately true that all the fluorescence series
are series of constant interval and that in each salt the groups are identical
as to the arrangement of the bands, it is of interest to treat the groups
as units*

To determine the distances between groups, what may be termed the
center of each group was found by averaging the frequencies of the five
bands. The location of these centers and the intervals, for groups 2, 3,

1 Two series, however, which come into coincidence with members of the B and C fluores-
cence series respectively in group 8 instead of in group 7 have been designated as fi and 7.

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288

EDWARD L. NICHOLS AND H. L. HOWES.

[Sbcomd
Sbribs.

4, 5, 6 and 7 are given in Table II. Groups i and 8 for which insufficient
data are available are omitted, except in the case of the ammonium
chloride.

Table II.

Distances between Fluorescence Croups.

Potftssium
Uranyl Chloride.

Ammonium
Uranyl Chloride.

Rubidium
Urenyl Chloride

Csoium
Urenyl Chloride.

Group.

Center of
Group.

Inter-
val.

Center of Inter-
Group. vaU

Center of
Group.

Inter-
val.

Center of
Group.

Inter-
vaU

1587.2
1670.8
1754.0
1836.6
1919.6
2003.3

83.6
83.2
82.6
83.0
83.7

1505.3
1588.6
1671.9
1755.0
1838.4
1922.3
2005.6

83.3
83.3
83.1
83.4
83.9
83.3

1591.5
1674.9
1758.3
1840.7
1924.2
2007.8

83.4
83.4
82.4
83.5
83.6

1592.6
1675.9
1759.3
1841.8
1924.7
2006.6

83.3
83.4

82.5

82.9

81.9

Average distances

83.22

83.38

83.26

82.80

The results bring out clearly the uniformity of interval throughout the
spectrum for each substance and the essential identity of structure in the
spectra of the first three salts. The only departure from uniformity is in
the caesium chloride, where the average interval is unmistakably lower
and where there is a suggestion of a diminishing interval from red towards
violet. It will be seen later that this apparent departure from the law of
constant intervals, a law which characterizes the fluorescence of all the
uranyl compounds, is due to the effects of absorption and to the fact
that we are dealing with complex bands.

The Arrangement of Bands within the Groups.
To the eye the fluorescence spectra under consideration appear to
consist of an assemblage of evenly spaced bands which vary periodically
in intensity so as to form a succession of similar groups. This is not
strictly the case, however, as may be shown by comparing the frequencies
of the bands in a given group. The average distances between neighbor-
ing bands, thus obtained from the data in Table I. are presented in
Table III.

Table III.

Average Distances between Neighboring Bands in the Fluorescence Spectrum at + 20** C.

Plnoreednf Subetence.

U0,C1,.2KC1...
U0,C1,.2NH4C1.
U0,CI,.2RbCl..
U0,C1,.2C8C1...

General Averages .

Average Dietancee.

C—B,

15.97
17.56
16.20
18.25

16.99

D^C,

18.66
17.74
18.43
12.85

16.92

E^D.

17.96
17.86
18.50
18.63

18.24

A--E.

B-A,

14.70
15.67
12.75
14.52

14.41

15.58
15.67
17.12
18.10

16.62

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Vol. XI.1
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FOUR DOUBLE CHLORIDES OF URANYL,

289

In the rubidium spectrum bands A and E are crowded together and
in the caesium spectrum D and C are similarly much nearer to one
another than are the other pairs of bands. It will be noticed further
that the average distance between A and E is less for all four chlorides
than the other average distances.

The arrangement of bands within the group, in the four spectra, is
conveniently compared by means of the diagram in Fig. i, in which the

B i

D 1

1 i

""♦

C«

1
1

1
•

«P 9 ap 4^ 1

Fig. 1.

centers of the groups are in the same vertical (dotted) line. It will be
seen from the diagram:

1. That the group center is in all cases almost coincident with the
crest of the D band.

2. That the arrangement of the bands within the group is essentially
the same in all, except for the marked displacement of A in the spectrum
of rubidium chloride and of B and C in that of the caesium chloride, as
mentioned above.

The explanation of these discrepancies involves a consideration of the
effect of cooling upon the spectra and will be found in a later paragraph
of this paper.

Intervals of the Individual Series.

The average interval for each series has been computed by obtaining
the differences between the observed frequency of each band and the
frequencies of all the other bands of the series and dividing the sum by
the total number of intervals in question (see Table IV.).

Here as in averaging by groups we must leave the question of the
reality of the apparent but smaU differences in the intervals of the various
series and of the various salts to be determined from the study of the
more completely resolved bands at the temperature of liquid air.

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290

EDWARD L, NICHOLS AND H. L. HOWES,

Table IV.

Average Intervals by Series at + 20® C.

LSbribs.

Series.

NH4.

Rb.

C«.

Avermres by

Series.

83.42
83.11
83.30
83.00
83.23

83.34
82.99
83.21
83.81
83.65

83.49
82.97
83.17
82.97
83.77

82.32
82.50
82.85
83.45
82.85

83.14

82.89

83.13

83.31

83.37

Averages

83.21

83.40

83.27

82.80

83.17

Influence of Molecular Weight upon the Position of Fluores-
cence Bands.

While the determinations thus far described may be deemed indecisive
as to small differences of interval, the influence of molecular weight
upon the position of bands in the spectrum is unmistakable. In Table I.
the fairly regular increase in frequency of each band as we pass from
potassium to caesium is sufficiently evident. In Fig. 2 this general shift,
which is present in all the groups and affects all series, can be seen at a
glance.

Almost the only reversed shifts occur in the case of those bands of the
spectrum of the caesium chloride which show anomolous placing in the
spectral groups. In Table II., where the accidental errors pertaining to
individual bands are submerged in the process of averaging, the shift is
still more systematic.

Ignoring group 7, in which the bands are more or less displaced by
absorption, we find the following values for the shift.

Shift of the Croups {K to Cs),

Group 2 3 4 5 6

Shift 5.4 5.1 5.3 5.2 5.2

Average shift from K to Cs 5.2.

The shift is therefore approximately uniform throughout the spectrum.
If all of the series were of the same constant frequency interval these
shifts would be the same.

The shift is much greater between NH4 and Rb than between K and
NH4 or between Rb and Cs, the averages being as follows:

Average Shift of Gtoups.

K to NH4 1.3

NH4 to Rb 2.9

Rbto Cs 1.6

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Vol. XL!
Na4. J

FOUR DOUBLE CHLORIDES OP URANYL,

291

In this discussion, as in the consideration of the same effect in the case
of the polarized spectra of these chlorides^ the order of the molecular
weights used is K, NH4, Rb, Cs. This is in accordance with the results

!•

— r
21

NNm

J I I I I L_L

""*! I I III!

J I I I I I L

J I L

J l__L

J I I I I L-i

J I I I I L_l

J I I i I I

!!!!i_l I I I I I

Ri^

J l_J I I L

J I I I L_L

J I L

NNf

J I L

J L

UH^

J I L

Ri^

J I L

J L

^yU,

J L

•se/^

_^/H

Fig. 2.

of Tutton^ who has shown that whenever the optical constants of crystals
vary with the molecular weights, NH4 lies between K and Rb; as though
its effective molecular weight were larger instead of being smaller than
that of K.

The Effects of Temperature.

Although the results obtained by exciting ammonium uranyl chloride
at the temperature of liquid air have already been published, as have the

> Nichols and Howes. 1. c.

* Tutton, A. E., Crystalline Structure and Chemical Constitution (London, 1916).

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292

EDWARD L. NICHOLS AND H, L, HOWES.

Table V.

General List of the Fluorescence Bands in Spectra of the Double Uranyl Chlorides at — 185® C.

SeriM.

PoUiMium
Uranyl Chloride.

AmmoBium
Urmnyl Chloride.

Rubidium
Uranyl Chloride.

Caeaium
Uranyl Chloride.

Oroup.

ixic.

^Xic.

-^Xic.

ixio..

.6398

1563.0

.6330

1579.8

.6283

1591.5

Et"

.6207

1611.0

.6110

1636.7

.6079

1645.0

.6056

1651.3

.6035

1657.0

.6016

1662.1

.6018

1661.7

.5991

1669.2

.6006

1665.0

.5990

1669.4

.5964

1676.7

.5968

1675.6

Et"

.5899

1695.0

.5803

1723.2

.5791

1726.9

.5764

1734.9

.5721

1747.9

.5752

1738.4

.5733

1744.4

.5731

1745.0

.5705

1752.7

.5724

1747.0

.5704

1753.1

.5703

1753.4

.5684

1759.4

Dt
Et'
Et"

.5641

1772.7

.5677
.5624

1761.4
1778.1

•

.5652

1769.3

.5603

1784.6

.5595

1787.3

.5573

1794.5

.5564

1797.2

.5569

1795.8

.5546

1803.1

.5526

1809.5

.5542

1804.4

.5524

1810.4

.5520

1811.5

.5500

1818.1

.5508

1815.5

.5493

1820.5

.5489

1821.9

.5464

1830.2

.5489

1821.7

.5471

1827.7

.5471

1827.8

.5452

1834.1

Dt'

.5440

1838.2

.5461

1831.0

.5445

1836.7

.5444

1836.9

.5427

1842.5

Dt'

.5412

1847.7

.5437

1839.4

.5420

1845.1

.5419

1845.2

.5395

1853.7

Et'

.5389

1855.7

.5379

1859.0

Et"

.5370

1862.0

.5358

1866.4

.5354

1867.6

.5345

1870.8

.5326

1877.7

.5318

1880.4

.5321

1879.5

.5300

1886.8

.5286

1891.8

.5297

1888.0

.5279

1894.4

.5277

1895.0

.5260

1901.1

.5279

1894.3

.5262

1900.4

.5250

1904.8

.5247

1905.9

.5223

1914.6

.5250

1904.6

.5234

1910.6

.5231

1911.7

.5214

1918.0

Dt'

.5201

1922.7

.5226

1913.5

.5206

1921.0

.5207

1920.3

.5191

1926.3

Dt'

.5179

1930.9

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Vou XI.l
Na4. J

FOUR DOUBLE CHLORIDES OF URANYL.

293

PoUMiom

Ammonium

Rubidium

Caesium

Urmnyl

Chloride.

Urmnyl Chloride.

Uranyl Chloride.

Unnyl Chloride.

Qroop.

8«riM.

Jxxo».

XX--

^Xic.

-Ixio..

.5200

1922.9

.5184

1929.2

.5182

1929.9

.5163

1937.0

£,'

.5155

1939.9

.5149

1941.9

.5137

1946.8

Et"

.5141

1945.0

.5127

1950.4

Cont.

.5124

1951.6

.5118

1953.7

.5107

1957.9

.5098

1961.6

.5092

1963.9

.5092

1963.9

.5080

1968.7

.5073

1971.4

.5059

1976.5

.5070

1972.3

.5056

1977.9

.5054

1978.6

.5038

1984.9

.5056

1977.8

.5028

1988.7

.5006

1997.6

.5031

1987.6

.5018

1992.7

.5018

1993.0

.5007

1997.2

.4989

2004.5

.4991

2003.7

.4979

2008.5

.4963

2014.9

.4982

2007.4

.4967

2013.4

.4967

2013.2

.4950

2020.2

.4956

2017.8

.4938

2025.1

Et'

.4940

2024.1

.4926

2030.0

£,"

.4918

2033.3

.4930

2028.4

.4917

2033.8

.4916

2034.2

.4902

2040.0

.4904

2039.2

.4857

2058.9

effects of cooling upon the polarized spectra of the four double chlorides,
it has seemed desirable to record here the measurements subsequently
made upon the unpolarized spectra at low temperatures. Future students
of this subject are perhaps more likely to deal with the unpolarized
spectra on account of the difficulty in procuring crystals that yield the
polarized bands satisfactorily. It is moreover of interest to compare
the mode of resolution for the different chlorides.

The positions of the bands in Table V. are from observations upon the
spectra when excitation occurs at — 185**. The nomenclature is intended
to indicate as far as possible the relation of the bands at — 185** to those
at + 20**; Bu B2, etc., denoting components of 5, etc., which have
been rendered visible by the resolution effected by cooling.

The explanation offered in the paper on the ammonium uranyl chloride
(pp. 366 and 369) to account for the very large temperature shifts applies
equally well to the potassium and rubidium salts. It was based on the
observation, at intermediate temperatures, that each band at + 20^ is
an unresolved doublet the components of which are in general of unequal
intensity. The effect of cooling is to resolve these doublets and at the
same time to weaken one component and strengthen the other. The

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294

EDWARD L, NICHOLS AND H. L, HOWES,

[SSOOMD
S

«•• i 1 "r f I

ie^b

+ao'

-tnr

♦ao* }

»L

i c.fc

weakened component sometimes disappears altogether or more frequently
remains visible only in the strongest groups. In the case of caesium
uranyl chloride the relations are complicated by the further resolution
of these components so that the connection with the original complexes
is less easily traced.

To indicate the general character of these resolutions and the apparent
temperature shift which results therefrom the positions of the bands of
group 6 at — 185** are plotted for all four chlorides (see Fig. 3). Intensi-
ties of the — 185** bands are indicated
roughly by the height of the lines. The
corresponding crests of the bands at
+ 20** are represented by dotted lines.
Group 6 was selected because it offers
better examples of the further breaking
up of the components and of other
phases of the process of resolution than
do groups towards the red in which reso-
lution is progressively less complete.

Two questions which were left unde-
termined in the study of the spectra at
+ 20** may be regarded as settled by
these measurements of the bands at
- 185^

I. That the intervals are not the same
for all series in a given spectrum is clear-
ly established. For example the compo-
nents Ci, Ci which take the place of the C bands in all four spectra
have distinctly different intervals, i. e., 84.00 for Ci and 82.75 for Cj.
It is noteworthy that Ci, which becomes the crest of the group in place
of C, also has the small interval.

It might be questioned whether these so-called components are not
merely accidental neighbors rather than products of the same vibrating
system, but for the fact that they are present in all the spectra and have
very nearly if not precisely the same relative positions to each other in all.
2. The average interval of all series in the spectrum of the caesium
chloride (82.80) at + 20** which causes the notable displacement of the
bands of that substance, becomes 83.44 when we take the average of the
intervals of the bands at — 185®. That is to say it is, within the errors
of observation, the same as the general average for the other salts. On
the basis of the measurements at low temperatures (see Table VI.), we
must conclude that the four double chlorides have approximately the
same average frequency interval.

' nS9 IfBd

Fig. 3.

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Vol. XI.1
Na4. J

POUR DOUBLE CHLORIDES OF URANYL.

295

Table VI.

Average Intervals of the Fluorescence Series at - 185® C.

8«riM.

NH4,

Rb.

Cs.

Avermfs.

83.9
83.1
83.5
84.9
82.7

83.1

84.1

83.6

83.3

83.0
83.2

84.1
82.7

83.8

84.2

82.5
83.3

83.1

84.2
83.6

84.0
82.9

83.6

84.0

82.1
83.6

83.0
83.4

83.7
82.8

83.1
84.5
83.6
83.6

83.2
83.5

83.4

83.53

83.33

84.18

82.78

83.40

2>i'

83.98

!>.'

£.'

£,"

83.10
83.40

82.83

83.50

83.58

83.32

83.50

83.44

The Absorption Spectra.

A glance at the absorption spectra of the double chlorides, obtained
by viewing through a spectroscope the light transmitted by the crystals
at room temperature, shows the same higher degree of resolution that
characterizes the fluorescence spectra of these salts. The salient feature
is a series of strong, rather narrow bands, equally spaced, as to frequency,
like the broader bands of the other uranyl compounds. Thf interval,
as in all uranyl absorption spectra, is distinctly smaller than the fluores-
cence interval. Between these are several series of weaker bands.

The complete mapping of the absorption spectra is difficult. It can-
not be done visually since the bands extend out into the darkness of the
ultra-violet. Photography adds considerable detail but does not greatly
extend the range towards the shorter wave-lengths on account of the
rapidly increasing opacity. In the brighter regions of the spectrum, on
the other hand, more can be seen with the eye than can be found on the
photographic plate.

The data which we have obtained and which are presented in the
following tables have been procured by using both methods.

A great variety of light filters and combinations of light filters have
been employed in different parts of the spectrum, with widely different
exposures for the strong and weak bands. The thickness of the trans-
mitting layer has likewise been varied as far as the available material

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296

EDWARD L. NICHOLS AND H, L. HOWES,

rSBCOVD
LSSBIBt.

Table VII.

General List of Bands in the Absorption SpeUra of the Double Uranyl Chlorides ol + 20^ C.

Poussium Uranyl Chloride.

Ammonium Uranyl Chloiide.

Group.

Series.

-Jx«-.

Group.

Series.

ixio..

.5549

1802.1

.5548

1802.5

.5494

1820.2

.5492

1820.8

.5445

1836.5

.5438

1838.9

.5417

1846.0

.5409

1848.8

.5390

1855.3

.5383

1857.8

.5362

1865.0

.5350

1869.2

.5351

1869.0

.5342

1871.8

.5322

1879.0

.5301

1886.5

.5305

1885.1

.5246

1906.2

.5257

1902.2

.5197

1924.2

.5206

' 1920.9

.5149

1942.3

.5161

1937.6

.5109

1957.4

.5116

1954.7

b
c

.5076
.5029

1970.1
1988.5

.5076

1970.1

.4996

2001.6

.5037

1985.2

.4978

2008.9

.5008

1997.0

.4942

2023.3

.4989

2004.3

.4899

2041.2

.4947

2021.4

.4906

2038.5

.4860

2057.5

.4829

2070.6

.4869

2053.8

.4808

2080.1

.4837

2067.4

.4776

2094.0

.4819

2075.1

'.4733

2113.0

.4783

2090.9

.4704

2126.0

.4667

2142.6

.4742

2108.8

.4652

2149.5

.4705

2125.4

.4618

2165.5

y
d

.4679
.4659

2137.0
2146.4

.4601

2173.5

.4627

2161.0

.4577

• 2185.0

.4507

2218.9

.4588

2179.6

€"

.4455

2244.5

.4501

2221.8

.4432

2256.2

.4449

2247.8

.4370

2288.5

.4363

2291.9

.4331

2309.0

.4323

2313.0

.432
.4293

2314.6
2329.5

.4293

2329.4

.4237

2359.9

.4235

2361.3

.4202

2379.9

.4199

2381.6

.4194

2384.6

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Vol. XI.1
No. 4. J

FOUR DOUBLE CHLORIDES OF URANYL,

297

Table VII. — Continued.

PotftMium Uraayl Chloride.

Ammonium Uranyl Chloride.

Group.

Series.

XX--

Group.

Series.

IX-.

.4169

2398.7

.4113
.4095

2431.5
2442.0

h
d

.4166
.4112

2400.3
2432.0

tf"

.4077

2452.8

tf"

.4073

2455.2

.3995
.3962

2503.1
2524.0

.3997
.3957

2501.8
2527.4

.3938

2539.4

.3899

2565.1

.3906

2560.2

.3885

2573.7

.3884

2574.8

.3863

2588.7

.3842

2603.0

.3815

2620.9

.3811

2623.8

.3792

2637.1

.3789

2638.9

.3757

2661.7

.3738

2675.0

.3714

2692.8

c
d'

.3713
.3687

2693.3
2712.2

y
d'

.3692
.3685
.3648

2708.6
2713.7
2741.2

.3627

2756.8

Rubidlom Uraayl Chloride.

Caesium Uranyl Chloride.

Group.

Scries.

XX-.

Group.

Series.

ixio..

.5747

1740.0

.5582

1791.5

E
A

.5622
.5588

1778.7
1789.5

B
C

.5531
.5467

1808.0
1829.2

B
C

.5537
.5485
.5450
.5430

1806.1
1823.2 •
1834.9
1841.6

.5426
.5416
.5373
.5339

1843.0
1846.4
1861.2
1873.0

E
A

.5377
.5342

1859.8
1872.0

B
C

.5289
.5233

1890.7
1911.1

.5294
.5243
.5190
.5150
.5144
.5123
.5105

1889.0

1907.2

1926.7

1941.7?

1944.0

1952.0?

1958.7

6
7

D
E
A

b
c
d
e
a
b

.5198
.5143
.5108

.5065
.5017
.4999
.4937
.4909
.4894

1923.8
1944.4
1957.8

1974.2
1993.1
2004.9
2025.6
2037.1
2043.3

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298

EDWARD L. NICHOLS AND H, L. HOWES.

rSacoii

ISSUB

Rabidium Urmnyl Chloride.

CKsium Uranyl Chloride.

Qronp.

Series.

ixic.

Qroup.

Seties.

.Jxic.

.5066

1974.0

.4864

2056.0

.5028

1989.1

.4844

2064.4

.4996

2001.6

.4828

2071.3

.4982

2007.1

.4816

2076.3

df'

.4966

2013.7

.4774

2094.7

.4938

2025.3

.4892

2044.0

.4731

2113.9

.4860

2057.6

.4701

2127.1

.4830

2070.5

.4661

2145.5

d
e

.4808
.4776

2080.1
2094.0

.4618
.4578

2165.6
2184.3

.4729

2114.4

.4547

2199.3

.4694

2130.4

.4520

2212.2

y
d

.4670
.4653

2141.3
2149.2

.4497

2237.0

.4616

2166.4

.4434

2255.3

.4578

2184.6

.4406

2269.6

.4547

2199.3

.4378

2284.0

.4527

2209.0

.4329

2310.0

.4492

2226.0

.4473

2235.6

.4297

2327.0

.4447

2248.5

d'
e

.4247
.4205

2354.6
2378.2

.4434

2253.1

.4361

2293.1

.4169

2398.4

.4314

2318.0

.4147

2411.4

.4285

2333.7

.4121

2426.6

.4229

2364.8

.4085

2448.0

.4160

2403.9

y
d

.4126
.4106

2423.7
2435.4

b
d'

.4047
.4006

2471.0
2496.6

.4065

2460.0

.3968

2520.2

.4046

2471.6

.3940

. 2539.7

14.

.4011

2493.1

.3893

2568.7

1**

.3994

2503.9

.3843

2602.2

.3956

2527.8

.3934

2542.1

.3816

2620.5

.3879

2577.7

.3793

2636.8

.3858

2592.0

.3739

2674.2

.3837

2606.5

.3715

2691.8

c
d'

.3810
.3785

2624.5
2642.0

.3732

2679.5

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Vol. XL!
No. 4. J

FOUR DOUBLE CHLORIDES OF URANYL,

299

Table VIII.

General List of Bands in the Absorption Spectra of the Double Uranyl Chlorides at — 185® C.

PotftMium Uranyl Chloride.

Ammonium Urmnyl Chloride.

Qroup.

8«riM.

Jxic.

Group.

Series.

ixic.

£1'

.5150

1941.7

Et"

.5139

1945.9

€1

.5134

1947.6

.5119

1953.5

€t'

.5116

1954.7

.5111

1956.6

.5101

1960.4

et"

.5093

1963.5

.5087

1965.8

.5082

1967.7

.5070

1972.4

bt'

.5067

1973.6

.5057

1977.5

.5058

1977.1

.5038

1984.9

bt"

.5048

1981.0

c,"

.5027

1989.3

.5038

1984.9

.5005

1998.0

.5020

1992.0

.4978

2008.8

1996.8

.4965

2014.0

d,'

.5008

2002.8

et'

.4942

2023.4

di"

.4983

20P6.8

bi'

.4928

2029.1

dt"

.4965

2014.1

.4907

2038.1

et"

.4924

2031.0

.4893

2043.6

.4906

2038.5

.4860

2057.6

bt'

.4889

2045.5

.4834

2068.8

bt"

.4875

2051.1

.4810

2079.0

.4863

2056.5

et'

.4774

2094.5

.4843

2064.7

bi'
at
bt

.4760
.4743
.4731
.4701

2100.8
2108.5
2113.7
2127.4

di"
dt"
ei
et"

.4813
.4792
.4778
.4756

2077.9
2086.8
2092.7
2102.4

.4674

2139.5

.4742

2109.0

.4654

2148.9

bt'

.4724

2116.9

.4640

2155.2

bt"

.4711

2122.7

et'

.4619

2165.0

di"

.4681
.4653

2136.5
2148.9

bi'

.4606

2170.9

dt"

.4639

2155.5

.4589

2178.9

.4625

2162.1

.4579

2184.0

et"

.4599

2174.4

di
dt
ei

.4551
.4528
.4510
.4485

2197.3
2208.5
2217.1
2229.4

bi
bt'
bt"
bt

.4587
.4571
.4560
.4551

2180.2
2187.7
2193.1
2197.3

.4436

2254.3

.4530

2207.3

Ct'

.4417

2264.2

di"

.4508

2218.2

.4389

2278.5

dt"

.4490

2227.0

.4371

2287.6

.4478

2233.0

e,'

.4337

2305.5

et"

.4460

2242.2

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300

EDWARD L. NICHOLS AND H. L. HOWES,

Table VIU.— Continued.

PotftMium Uranyl Chloride.

Ammonium Urmnyl Chloride.

Group.

Soriea.

Jxic.

Group.

Seriee.

jXio*.

.4311

2319.6

.4443

2250.9

.4300

2325.6

bt"

.4413

2265.9

.4287

2332.7

.4389

2278.3

.4277

2337.8

d,"

.4370

2288.5

Ct"

.4262

2346.1

dt"

.4352

2298.0

.4244

2356.1

.4341

2303.4

.4232

2362.7

.4221

2369.1

.4305

2322.8

et'

.4211

2374.9

bt"

.4277
.4259

2338.2
2348.1

.4194

2384.4

dx"

.4239

2359.1

a,"

.4181

2391.9

dt"

.4222

2368.3

Ct'

.4160

2404.0

«i

.4209

2376.0

.dt

.4141
.4116

2414.9
2429.2

et"

.4188

2387.5

.4105

2436.3

.4177

2394.0

.4097

2441.0

bt"
bt

.4152
.4146

2408.7
2411.9

.4071

2456.4

.4134

2419.0

.3983

2510.6

di"

.4114

2430.9

ft'

.3971

2518.3

dt"

.4102
.4090

2437.9
2445.0

.3959

2525.6

et"

.4066

2459.7

a,"

.3947

2533.3

Ct'

.3933

2542.3

.4054

2466.8

.3893

2568.7

bt"

.4034

2479.0

.3873

2582.0

.4028

2482.5

.4016

2489.9

.3854

2594.7

dx"

.3997

2502.0

a,"

.3835

2607.5

.3975

2515.8

et"

.3951

2530.7

.3941

2537.3

bt"

.3921

2550.1

.3904

2561.6

dx"

.3886

2573.2

.3833

2609.0

bt"

.3813

2622.7

.3808

2626.3

dx"
dt"

.3798
.3780
.3774
.3763

2633.0
2645.5
2650.0
2657.5

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Vol. XL!
No. 4. J

FOUR DOUBLE CHLORIDES OF URANYL.

301

Rubidium Urmnyl Chloride.

Caesium Uranyl Chloride.

Group.

Series.

^Xio*.

Group.

Series.

^-Xic..

dt"

.5143

1944.4

Cf,"

.5118

1953.9

e,'

.5122

1952.4

.5111

1956.6

.5116

1954.7

«i'

.5105

1958.9

i4i

.5107

1958.1

.5084

1967.0

ai'

.5092

1963.9

.5074

1970.8

&l"

.5066

1973.9

.5048

1981.0

.5065

1974.3

.5036

1985.7

.5055

1978.2

.5011

1995.6

ht'

.5043

1982.9

.4987

2005.2

.5031

1987.7

.4975

2010.1

.5022

1991.3

(it"

.4960

2016.1

.5006

1997.6

tx'

.4947

2021.6

.4986

2005.6

€%

.4924

2030.7

.4976

2009.6

.4909

2036.9

Dt'

dt''

.4960
.4945

2016.1
2022.2

61"

.4892

2044.2

et'

.4927

2029.6

.4877

2050.4

et"

.4916

2034.1

.4856

2059.3

a,'

.4907

2038.1

.4843

2064.7

(ii

.4818

2075.4

.4889

2045.3

(/»"

.4792

2086.8

ht'

.4874

2051.6

fi'

,4776

2093.6

.4850

2061.9

.4760

2101.0

Ci'

.4844

2064.3

,4745

2107.5

.4836

2067.8

di'^

.4804

2081.6

61"

.4728

2114.9

dt'

.4793

2086.2

.4714

2121.4

dt"

.4778

2092.7

.4692

2131.3

et'

.4761

2100.4

.4685

2134.5

et"

.4749

2105.5

.4660

2145.7

ax'

.4743

2108.4

dt"

.4633

2158.2

.4725

2116.4

.4615

2166.8

bt'

.4710

2122.9

.4603

2172.5

.4684

2134.9

ai'

.4591

2178.2

Ct'

di"

.4670
.4646

2141.3
2152.4

.4577

2184.9

dt'

.4637

2156.4

.4563

2191.6

dt"

.4621

2163.8

.4545

2200.0

et'

.4607

2170.6

.4534

2205.4

et"

.4595

2176.1

di
dj

.4515
.4502

2214.9
2221.4

.4589

2179.1

ei'

.4478

2233.1

bi'

.4574

2186.5

.4471

2236.7

bt'

.4559

2193.5

.4460

2242.2

Ci'

.4535

2204.9

Ct'

.4520

2212.4

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302

EDWARD L. NICHOLS AND H, L, HOWES,

LSSBIBt.

Rubidium Uranyl Chloride.

C««inm Uranyl Chlorido.

Group.

SariM.

XX-

Oroup.

SoriM.

lx.0..

.4419

2262.7

dx"

.4506

2219.1

.4401

2272.0

dt'

.4497

2223.7

dt'

.4362

2292.6

.4486

2229.2

«i'

.4340

2304.2

dt"

.4478

2233.1

.4331

2309.0

et'

.4467

2238.6

««

.4323

2313.2

et"

.4454
.4445

2245.0
2249.7

bi"

.4294

2328.8

.4270

2341.9

.4419

2263.0

Ct"

.4251

2352.4

.4412

2266.3

.4237

2360.2

.4408

2268.6

dt'

.4231

2363.3

.4398

2273.8

tx'

.4211

2374.7

.4388

2278.7

«i

.4204

2378.7

.4380

2283.1

.4197

2382.7

di"

.4364

2291.3

ax'

.4181

2391.5

dt'

.4355

2296.2

.4346

2300.8

bx"

.4164

2401.3

dt"

.4339

2304.9

.4147

2411.4

et'

.4328

2310.3

ex'

.4088

2446.2

.4322

2314.0

.4081

2450.4

et"

.4314

2317.8

ax'

.4059

2463.4

ax'

.4306

2322.3

ex'

.3972

2517.3

bt'

.4284

2334.0

ax'

.3947

2533.6

.4256

2349.7

.4243

2356.0

bx"

.3935

2541.0

dt'

.4229

2364.4

bt"

.3922

2549.4

.4220

2369.4

Cx"

.3904

2561.5

dt"

.4205

2378.0

.3889

2571.4

.4196

2383.0

dt'

.3880

2577.3

et"

.4187

2388.6

ex'

.3865

2587.5

ai'

.4178

2393.5

«t

.3849

2597.8

bt'

.4159

2404.7

bx"

.3826

2613.4

.4149

2410.5

c,"

.3796

2634.4

.4140

2415.5

.4130

2421.3

bx"

.3722

2686.4

.4119

2427.8

.3707

2697.6

di"

.4104

2436.4

cx"

.3695

2706.4

dt
dt"

bt'

.4097
.4090

.4038

2440.8
2444.7

2476.3

.4031

2480.6

.4013

2491.6

.4003

2498.1

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Vol. XL!
Na4. J

POUR DOUBLE CHLORIDES OP URANYL,

303

Rubidium Uranyl Chloride.

C«eium Uranyl Chloride.

Qroup*

Series.

Jxio«.

Group.

Series.

Jxic.

d,''

.3997

2501.9

dt'

.3986

2508.5

.3979

2513.2

.3960

2525.3

et"

.3953

2529.7

ai'

.3946

2534.3

.3928

2545.5

.3921

2550.4

.3905

2560.5

dt'
dt
et

.3895
.3877
.3869
.3854

2567.4
2579.3
2584.6
2594.7

would permit. We are convinced, however, that the extreme limits of
the absorption, in both directions, have not as yet been reached.

While this study was in progress one of the authors* undertook to
find more absorption bands in the reversing region. As a result of this
investigation several new bands were located, sufficient to extend the
reversals two complete groups toward the red beginning at 5050 A. U.
These bands are excessively dim and were located only after considerable
study. Where, as in many cases, they are reversals of fluorescences
they are designated by capital letters.

The absorption spectra of the double chlorides do not exhibit the same
remarkable approach to identity of structure and regularity of arrange-
ment manifested in the fluorescence spectra. Upon analysis however
they are all found to consist of series having intervals of approximately
70 frequency units. As may be seen from Table IX. this interval for a
given series is very nearly the same for all four salts. The average
interval for all the series of a given salt is constant within the errors of
observation.

The absorption bands, unlike those of the fluorescence spectrum do
not appear to fall into a succession of strictly homologous groups, but
this is because some series disappear, while others increase in strength
towards the violet. A group near the fluorescence region therefore differs
notably in aspect from one in the extreme violet. It is therefore difficult
to base conclusions on the location of the centers of the groups as was
done in the study of the fluorescence spectra.

> Howes, H. L., Phys. Rbv. (2), XI, p. 66. 1918.

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304

EDWARD L. NICHOLS AND H, L, HOWES.

[Sboond
Sbrixs

Table IX.

Average Intervals of Absorption Series at + 20** C.

SeriM.

NH4.

Rb.

c«.

Average.

70.5

71.6

70.4

70.9
70.6

70.9

70.8
70;4

68.8
70.7

70.3
70.4

70.0

70.5

71.1
70.6

71.0
70.3

71.2

70.9
70.3

70.9

70.5

70.0
70.4

69.7
70.8

70.8
69.6

70.6

70.3

70.0

69.3

70.8

69.7

Average ....

70.5

70,4

70.3

70.6

ilMS ■ SIM

K ill
. ll 1 III.

""" 1 1 1 III 1

Ri. 1 « • ' 1

r 1 II 1 1 1 1 1

1 1 II 1 1 1 ll

Fig. 4.

As may be observed in Fig. 4, where
the ninth group for the four spectra at
+ 20° is plotted the distances between the
consecutive bands are of the same order as
the distances between fluorescence bands,
as shown in Fig. i, but are less nearly
equal. It is also evident from this figure
that with increasing molecular weight there
is a general shift toward the violet. The
shift is apparently less systematic than
with the fluorescence bands and several
reverse shifts seem to occur.

In the case of such bands as show a
regular shift, however, the total displace-
ment is approximately the same as that
observed for fluorescence, i. «., five fre-
quency units from potassium to caesium.

The Effect of Temperature on Absorption.

A complete list of the absorption bands which have been observed at
- 185° is given in Table VIII.

In Fig. 4 the absorption bands of the ninth group at
be compared with those of the + 20° spectrum.

185"* may

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VOL. XL!
No. 4. I

FOUR DOUBLE CHLORIDES OF URANYL.

305

Two results of cooling appear: there is a general shift toward the
violet and more bands are present. By the spectroscopist a third and
more striking change would be noticed during the cooling process, viz.,
the very decided narrowing and sharpening of the bands.

These changes are readily accounted for by means of the assumption
already made, in this and previous papers, that the bands at + 20** C.
are concealed doublets and that the effect of cooling is to resolve them
while simultaneously reducing the strength of the stronger and increasing
the strength of the weaker component. The apparent shift thus pro-
duced will vary from zero to five or more units according to the distance
between the components.

A few bands at — 185° are so located with regard to the + 20** bands
that to explain them by this theory we must suppose them to be too
feeble at + 20** for detection and greatly increased in intensity by
cooling.

There is also evidence in places of further resolution into closer narrow
doublets and as the degree of resolution is not always the same with
fluorescence and the corresponding absorption this is a source of trouble
if one attempts to find the fluorescence series which belongs to each series
in the absorption spectrum. Every low temperature band, however,
falls into a series of constant frequency whatever its
position or degree of resolution.

The effect of temperature on the average intervals
can be studied by comparing Tables IX. and X. Al-
though the intervals range from 69 to 71 there is little
that can be termed systematic in the variations.

At liquid air where two or more components are pres-
ent we have used subscripts: such as d^ which corre-
sponds to Z>i, di to D2, etc. Where the reversal is doubled in the man-
ner shown in Fig. 5 we have designated this doublet as di and di", etc.

The average interval of each salt is approximately the same at both
temperatures. It will be noticed in Table IX. that 70.28, the average
of the **c" components is smaller than the*' 6," **d,** **e," or ** a "averages.
This is of interest because the strong ** C" series, which join these series,
have the shortest intervals of the fluorescence series. Since the — 185°
bands are very sharp and easy to locate no doubt the differences found
in Table X. are indicative of real variations in the constant frequency
intervals. It does not follow that the smaller intervals are confined to
one salt or one set of bands, however, since, as has been noted in the case
of series Ci and d of the fluorescence series, the maximum difference in
interval may be associated with two series which are nearly coincident.

1
<

Fig. 5.

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3o6

EDWARD L. NICHOLS AND H. L. HOWES.

The comparison of Table IX. with Table X. shows that the eflFect of
changing temperature on the average interval of a salt is almost n^^ligible
but that the two components of one series of the + 20® spectrum may
vary by 1.9 units in frequency interval.

Table X.

Averagfi InUrvals of Absorption Series at — 185* C.

K. I NH«. ! Rb.

Cs.

70.6
70.5

71.4

71.0

71.4
71.2

71.3
70.7

70.4

70.6
70.2

70.7

70.50

71.40

hi"

bt'

71.30
70.80

70.47

bt"

71.40

6,.

70.95

b average . . .

t
t
1

70.83

Ci'

69.3
70.0
69.0

70.9

70.7

70.4
70.9

70.3
70.5
70.9

70.30

70.60

Ct'

70.10

70.43

Ct"

69.95

c average . . .

70.28

69.8

70.0
70.2

70.8
70.5

70.9
71.2
71.1

70.2
70.5
71.0
70.7

70.35

rfi"

rf.'

70.50
70.85

70.50

dt"

70.68
70.20

d average . . .

70.51

ei'

70.6
70.5

70.7
71.4

70.7
70.9

70.8

70.0
70.3
70.8

70.70

70.73

et'

70.25

70.55

et"

71.10

e average . . .

70.67

ax'

70.0
70.4
71.9

71.3

71.0
70.4

71.0
70.6

71.00

70.65

70.47

71.90

a average . . .

71.00

Average ....

70.22

71.06 1 70.84

70.54

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Vol. XI.l
No;4. J

FOUR DOUBLE CHLORIDES OF URANYL

307

PL.

Reversals and the Reversing Region.

The early observers of uranyl spectra were of the opinion that some
connection or relation must exist between the system of bands of fluores-
cence and absorption. Becquerel and Onnes who first studied these
spectra at low temperatures, were able to confirm the impression of
Stokes that the two systems overlapped and that there was actual
coincidence of position between certain fluorescence bands and absorption
bands.

In the case of the double chlorides at + 20** each series of bands of
the fluorescence system comes into coincidence, or near coincidence with
an absorption band in what we have termed the reversing region, which
is approximately that region occupied by group 7 of the fluorescence
spectrum.

The fact that the reversal sometimes appears to be exact, within the
errors of observation, while sometimes there is a dis-
placement of several units of frequency might seem to
render such a general relation doubtful, but the discrep-
ancy can be shown to be a necessary consequence of
the fact that both fluorescence and absorption bands at
this temperature are unresolved complexes. The true
nature of the case may be seen from Fig. 6 which is
from a sketch of such a reversal at — 185® where the
resolution is more nearly complete. Here the fluores-
cence and absorption are complementary, the strong [
component of fluorescence coinciding with the weak ab-
sorption component and vice versa. When the resolution
is less complete the weaker components will disappear and although the
reversal for each component is exact there will be an apparent failure to
reverse, or in other words we see the strong components displaced.

In the reversing region fluorescence and absorption are mutually
destructive. Consequently one or both are sometimes invisible; but
knowing the intervals we can locate the reversal. By proper screening
the fluorescence may be prevented and the absorption band brought out;
and by taking extra precautions to secure a dark back ground and to
increase the excitation the fluorescence may be seen. Thus the com-
putation may be confirmed.

In the study of the double chlorides the matter is further confused
because the difference between the fluorescence interval (83.+) and that
of the absorption interval (70+) is approximately equal to the distance
between neighboring bands in the fluorescence groups. An absorption
series which comes into coincidence with band C, group 7 will therefore

Fig. 6.

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308 EDWARD L. NICHOLS AND H. L. HOWES, ^SbS?

nearly coincide with band 5, group 8, etc. Furthermore the degree of
resolution in the absorption spectrum as has already been mentioned is
often greater than in the fluorescence spectrum and certain series are
observable of which the corresponding fluorescence bands cannot be
identified.
So far as the spectra at + 20° are concerned, we find that:

1. All absorption bands towards the violet from the reversing region
occur in series with constant frequency intervals.

2. For every fluorescence series there is a corresponding absorption
series.

Whether the relation between absorption and fluorescence outlined
above is significant can best be determined by the study of the spectra
for - 185°.

If for example the explanation of the numerous instances of inexact
coincidence is valid we should expect exact reversals of the components;
also that the components of the resolved absorption spectra form series
definitely related to the components of the- fluorescence spectra in a
manner consistent with the system indicated for the spectra at + 20°.
From a study of the exactness of the reversals in the resolved spectra at
low temperatures it appears that twenty-five out of thirty-eight fluores-
cence series are certainly reversed and that thirty-six fluorescence series
join absorption series in the seventh group. The experimental error in
this group does not exceed 1.5 units. The difference in position between
fluorescence, and absorption is sometimes greater than 1.5 but this may
be ascribed to the dissymetry in the form of the bands.

Fluorescence bands have their crest towards the violet, absorption
bands towards the red. In the case of reversals, these regions tend to
annul each other, leaving a remnant of fluorescence on the red side and a
remnant of absorption on the violet. The result is that in regions where
fluorescence and absorption exist together, fluorescence bands are apt
to be given too great a wave-length and vice versa. In the C2 series of
the rubidium chloride, for example, there is a displacement of 2i6 units
between the observed positions of fluorescence and absorption.

If however we compute the proper positions of these bands using the
average intervals for the C2 and C2 series respectively, thus eliminating
the displacements in the reversal region, the fluorescence band and
absorption thus established agree in position within 0.3 unit. The
impossibility of excluding all absorption when fluorescence is present,
and vice versa, the impossibility of preventing a tendency towards
fluorescence when absorption alone is sought for may well account for
the resulting displacement. The case of the d series is not an isolated

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Vot. XL!
Na4. J

FOUR DOUBLE CHLORIDES OF URANYL,

309

one — probably every reversal is affected somewhat and the stronger
bands the most; there being always an apparent shift of the absorption
band towards the violet and of the fluorescence band toward the red.
This phenomenon has long been recognized by the authors in connection
with the broad fluorescence bands and it must now be recognized in the
reversing of the narrow, line-like bands at the temperature of liquid air.
In the above, the reversals which connect fluorescence to absorption
series have been sought for in the seventh group. There are however
other possible connections, for coincidences occur in the sixth and eighth
groups as well. Since, as has already been pointed out, the difference in

•nun —

POTUSIUM

URANYL CNLORIDC

— 1

"■"

•l '

■t 1

i^ 1

\ '

AMMONIUM

URANYL CHLORIOC

II II

' , '

< 1

• 1

iWl

^MIWOIUM

URANYL CNLORIDC
1

it 1

It 1

'^.l

. '^ .

C.I

CAOIUM URANYL CNLOMDE

•ll

', •

i^l

Fig. 7.

spacing between a fluorescence and absorption interval is nearly l4ie
same as the spacing between fluorescence bands it is often possible to
join equally well two fluorescence series to one absorption series; a fact
which makes it difficult to determine the true relation in the case of this
class of salts.

The actual manner in which the reversals between fluorescence and
absorption occur is shown in Fig. 7, which is a diagram of the reversing
region. Here the plotting is quite accurate, the fluorescence bands above

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3IO EDWARD L, NICHOLS AND H, L, HOWES. [^S

and the absorption bands below the horizontal. Dotted lines indicate
computed positions. This cut is approximately ten times as large as
the original negatives. To avoid confusion the various series occurring
in each salt are vertically displaced instead of being drawn on a single
line, as they appear in the actual spectra. An inspection of this diagram
will suffice to indicate the approach to complete coincidence in the re-
versals and the type of departure from coincidence.
With regard to the reversing region at — 185** it can be stated that

1. The majority of the fluorescence series reverse in the seventh
group.

2. Thirty-six out of thirty-eight fluorescence series are joined in the
seventh group to absorption series.

3. The exactness of reversal depends not only on the structure of the
band but on the simultaneous presence of fluorescence and absorption in
this region.

4. Other reversals and connections are present in the groups adjacent

to group seven.

Physical Laboratory op Cornrll Univbrsity,
October 10, 191 7.

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No^^^'l YOUNGS MODULUS OP DRAWN TUNGSTEN, 3II

YOUNG'S MODULUS OF DRAWN TUNGSTEN AND ITS

VARIATION WITH CHANGE OF TEMPERATURE,

INCLUDING A DETERMINATION OF THE

COEFFICIENT OF EXPANSION.

By H. L. Dodge.

THIS paper is the fourth of a series upon the effect of temperature
upon the elasticity of wires and deals with tungsten. The method
is the same, in general, as that employed in previous work with copper,*
mild steel,' and aluminum' wires, but the apparatus has been entirely
rebuilt and embodies a number of improvements. In the present form
it permits of the measurement of Young's modulus up to a temperature
of about 800^ C. with external heating and with internal heating to still
higher temperatures.

Open Tubular Furnace Approximating a Black Body.

The most important improvement has been in the new furnace, which
is entirely different in construction and principle from the one formerly
used. The old furnace consisted of a long rectangular box of asbestos
board with a glass top. The heating element lay on the bottom. Thus
there was a large temperature gradient in the space around the wire and,
although every precaution was taken to insure that the thermo-couples
should give the temperature of the wire, there was always some error,
the possible magnitude of which could be estimated only roughly.

The new furnace is constructed of a series of three coaxial tubes, each
thirty inches long. The inner tube is of copper and has an inside diameter
of five eighths of an inch and a one eighth-inch wall. Next comes an
alundum tube wound with a heating element of nichrome ribbon. Sur-
roimding this is an outside covering of vitribestos. In the top and in
the side, 10 cm. from each end, are holes extending through all the tubes.
Above the vertical holes are placed two stereopticon lamps for illumina-
tion; the wire is viewed through the horizontal holes. All the holes
have mica windows.

As the loss of heat from the furnace is very much greater at the ends

» Phys. Rbv.. 2, 2. 431. 1913.
» Phys. Rev.. 2. 5. 373. 1915.
• Phys. Rev., 2, 6, 312, 1915.

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312 a, L. DODGE, [ISS?

than at the center it is necessary to find by trial the best distribution of
the heater winding to secure the most uniform temperature throughout
the length of the inner tube. The latter, being of heavy copper, smoothes
out all local irregularities in temperature.

In a furnace of this kind advantage can be taken of the fact that,
except at the ends, the interior of a long tube which is at a uniform
temperature is equivalent to a black body.* Even though there is an
appreciable temperature gradient along the tube it is safe to assume that
the temperature over any given cross-section is uniform and the same
as that of the wall of the tube at that point. It is also true that every
pqint on a wire suspended in the tube will take up a temperature almost
exactly that of the cross-section in which it happens to fall. Therefore,
in order to determine the temperature of a certain point on the wire, it is
not necessary to place the thermo-couple in contact with the wire but
merely to determine the temperature at any point situated in the same
cross-section.

However, when the heating is by an electric current in the wire itself
this method cannot be followed nor can thermo-couples be applied directly
to the wire. It has been found that the most satisfactory method is
one depending upon thermal expansion. The coefficient of expansion of
the wire having been determined once for all, the same observations of
length necessary for the measurement of the modulus also determine
the temperature. The expansion coefficient is found by the following
method.

Measurement of the Coefficient of Thermal Expansion.

A certain current is passed through the heating element and allowed
to flow for a definite time, let us say one hour. During the last few
minutes the current is kept very steady by means of a potentiometer.
At exactly the end of the hour the electromotive force of a thermo-
couple, inserted to the middle of the furnace, is read. A larger current
is then passed for a definite time, known to be sufficiently long for the
furnace to reach a condition of equilibrium. Readings of the heating
current and of the thermo-couple E.M.F. are again taken. This process
is repeated until the highest temperature permitted by both furnace and
wire is reached.

After the furnace has cooled the thermo-couple is removed and the
wire suspended in the furnace. Then exactly the same procedure as
before is followed, except that the thermo-couple readings are replaced
by measurements of the change of length of the wire. Thus for every

1 Analogous to the uniform field of a long solenoid.

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Vol. XIl
Na4. J

YOUNG'S MODULUS OF DRAWN TUNGSTEN.

313

thermo-couple reading there is a corresponding measurement of the
increase of length of the wire, made under identically the same conditions
of temperature. From these observations the coefficient of thermal
expansion can be readily computed.

The variation of temperature along the tube was investigated in order
that the average temperature of the wire over the portion imder observa-
tion could be found from the temperature measured. When the center
of the furnace was at 673** C. at no point between the centers of the
windows did the temperature differ from this value by as much as five

degrees.

The Tests.

The tests were made upon a piece of drawn tungsten wire secured
through the kindness of Dr. A. G. Worthing, of the Nela Research
Laboratory. The wire was obtained in December, 1914, and was said
to contain approximately 99 per cent, tungsten and one per cent, thorium.
It has a diameter of 0.65 mm.; the length under observation was 593.6
mm. The thermal expansion was found to be practically imiform over
the temperature range covered, namely 20° C. to 675** C, the coefficient
of expansion being .00000456 per degree Centigrade. This value checks
exactly, for the temperature range covered, with that of Worthing* but

Youngs Modulus - Tungsten 1

per cm.*'*
33

• Ltmjtk S93.6 mm.

Jftmm^lhr .Sfmm.

32 Umi ^lf9fk, 3SSO3.

ZOQ'C

7-B

6C(q'c

aofi'c

mit

Fig. 1.
Effect of temperature upon the Young's modulus of drawn tungsten.

does not verify that of Langmuir,^ from which it differs by as much as
fifty per cent. Worthing's formula was used in determining tempera-
tures above 675® C.

In measuring the modulus of elasticity the permanent load was 2,109
g., the added load, 3,550 g. The Young's modulus of drawn tungsten
was found to be 35.5 X 10" dynes* per cm.' at 20® C. This value is

» Jour. Frank. Inst., 181. 857, 1916; Phys. Rbv., 2, 10, 638. 1917.
» Phys. Rev., 2. 7, 329, 1916.

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314

H. L, DODGE,

undoubtedly accurate to within two or perhaps three per cent. This is
somewhat lower than the value given by Fink^ of 42,200 kg. per sq. mm.,
but it is entirely possible that there is that much difference in the modulus
of wires prepared at different places and at different times, for the art
of drawing tungsten wires has had a recent and rapid development.

The change of the modulus with increase of temperature was observed
up to 1,000® C. at which temperature the oxidation of the wire became
very rapid. However it was possible to check back after readings at
about 900® C, as shown in Fig. i. The dots represent observations
taken with increasing temperature, the last at 880*^ C. The cross is the
value found immediately after the wire had cooled. The dotted circles
represent the next series of readings.

Only two series of readings are shown in the figure. These were pre-
ceded by a great deal of preliminary work, necessary to determine the
magnitude and general nature of the effect of temperature and to learn
what loading should be used. On account of the extremely high value

Variation of
Youngi Modulus

wiU Tempenitun

-L

J-

san M^ «M^ M*

Fig. 2.

Comparative effects of temperature upon the Young's modulus of aluminum, copper,
mild steel and tungsten wires.

of the modulus much heavier weights than usual were necessary. Even
with a load of over 3.5 kg. the variation in the stretch aver the whole tern-
perature range amounted to but eighteen thousandths of a millimeter. The
actual stretch in thousandths of a millimeter corresponding to the
different values of the modulus is indicated at the left edge of Fig. i.
All of the observations were taken when the heating was by a ciurent

» Trans. Am. Electrochem. Soc.. 22. 503, 1912.

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Na*i^'*l YOUNGS MODULUS OF DRAWN TUNGSTEN. 315

in the wire itself as it was found that the manner of heating did not
affect the results and this method was the more convenient.

A temperature of 1,000** C. is so low in comparison with the melting
point of timgsten that one could hardly expect it to show the character-
istics of the other metals with lower melting points. However there is
nothing in the behavior of timgsten which is not in harmony with the
general conclusions already reached regarding the effect of increase of
temperature upon elasticity.* In Fig. 2 the effects with tungsten and
with the three other metals are compared.

Summary.
The Yoimg's modulus of drawn timgsten is 35.5 X 10" dynes per cm.'
at 20^ C. The modulus decreases uniformly with increase of tempera-
ture up to 1,000® C. at which temperature it is 32.3 X 10" dynes per cm.*

Physical Laboratory.

State Uniyershy of Iowa.

> Dodge. Phys. Rbv.. 2, 6, 316. 1915.

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31 6 A, J. DEMPSTER.

gyfflKf,

A NEW METHOD OF POSITIVE RAY ANALYSIS.

By a. J. Dbbcpstbr.

THE analysis of positive rays is based on the determination of the
ratio of the charge to the mass of various constituents. The corre-
sponding measurement for the negative corpuscle has however been
carried to a much greater degree of accuracy by means of methods in-
volving the magnetic deflection of the rays through large angles, and
the refocusing of rays which make slightly varying angles with each
other. Apart from the accuracy of the measurement, there is also in
these methods a great resolution between slightly different speeds;
thus Rutherford and Robinson* have separated distinct groups of /8
rays from RaC which differ by 2 per cent, in energy; also the photo-
graphs given by Classen* for electrons show such sharpness that if elec-
trons had masses differing by as little as i in loo, the various groups
would be separated. With positive rays the slit method used by Richard-
son' is suitable for weak sources and allows a fairly exact measurement
of a mean molecular weight, but the curves given in the above paper
show that the power of separating different elements is very small.
The method used by J. J. Thomson is capable of comparatively great
resolving power, elements being sharply separated which differ in molec-
ular weight by i in i6,* but this is obtained only with a great loss in
intensity. The method developed in the present experiments was ex-
pected to give great intensity with moderate resolution. It was found
that the method could also be developed to give a very great resolving
power among the elements.

The method is essentially identical with that used by Classen in his
determination of e/m for electrons. The charged particles from some
source fall through a definite potential difference. A narrow bundle is
separated out by a slit and is bent into a semicircle by a strong magnetic
field ; the rays then pass through a second slit and fall on a plate connected
to an electrometer. The potential difference (P.D.), magnetic field

» Phil.. May 26. p. 725, 1913.

' Jahrb. d. Hamburg Wiss. Anst., Beiheft. 1907.

* Phil., May 16. p. 757, 1908; The Emission of Electricity from Hot Bodies, p. 196.

* Nature, 86, p. 468, 191 1.

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Na*^''] POSITIVE RAY ANALYSIS. 317

(Ho), and radius of curvature (r) determine the ratio of the charge to
the mass of the particles by the usual formula

The apparatus consisted of the glass tube G, where the positive par-
ticles fell through a definite potential difference, and the analyzing
chamber A, in which a strong magnetic field was produced between two
semicircular iron plates 2.8 cm. thick and 13 cm. in diameter. The iron
plates were soldered into half of a heavy brass tube £ so as to leave a
passage or slot 4 mm. wide between the plates. A plate of brass on top
C closed this slot except for three openings into which short brass tubes
were soldered. The glass tube G fitted into the first opening and a tube
for exhausting into the second. The electrometer connection passed
to a receiving plate through an ebonite plug E which formed a ground
conical joint with the third brass tube. The two openings for the rays
had adjustable slits Su 5j, and a screen D was introduced into the
analyzing chamber to prevent reflected rays getting into the second slit.
The whole was placed between the poles of a powerful electromagnet.
The strength of the magnetic field and the
manner in which it fell off above the entrance
was determined with a test coil. The throws
obtained on removing the coil rapidly were
compared with the throws obtained from two ;
coils whose mutual inductance was known,
when the current through one was broken.
In this way a curve was drawn connecting the
field strength and the ciurent through the
electromagnet. The current was always re-
versed slowly several times before taking a
reading. The field strength was the same *^'

over the whole area of the plates to within one per cent. The rays were
obtained either by heating salts on platinum strips, as in Richardson's
experiments, or by bombarding salts with electrons; in the latter case
the salts were either heated by the bombardment or were heated inde-
pendently while being bombarded.

It might be thought from the elaborate precautions taken in the
experiments by Wien and Thompson to prevent the discharge tube
being influenced by the magnetic field used for deflecting the rays, that
great difficulty would be experienced in introducing the rays properly
into a sufficiently strong magnetic field, and in drawing conclusions from

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3i8

A. /. DEMPSTER.

the deflection observed. But such is not the case. The equations for
the motion of a charged particle in a longitudinal electric field (PD/a)
parallel to the 2-axis,* and a transverse magnetic field H{z) parallel to the
X-axis are

dt* " m' a ' dt^ ^ m di '

The integration of the first gives

dz _ \2elPD

dt ~W

;!/».

fn«a

and using this in the second we get on integrating

' r H{z)d.

2PD

(I)

If we put

^ = I-
dz Sm

s-^i* (' H{z)dz = Kiz)

(i) also applies to the case of particles moving in a magnetic field alone.
The magnetic field was reduced to zero at the place of origin of the rays
by the use of a secondary electromagnet, and the values of the above
integrals were observed and calculated by means of a coil wound on a
long rectangular frame. If the first slit were placed directly at the
entrance to the 4 mm. slot, it was found that the rays would be

deflected a distance ya = .96 mm. and
through an angle whose tangent {dy/dz)a
= 1/9.3. This might be sufficient to de-
stroy the refocusing and to make uncertain
the value of r in the equation

m _ goV«
e " 2'PD'

These difficulties may however be com-
pletely avoided by the simple device of
moving the entrance slit out in front of the
iron plates. Let the shaded portion in Fig.
2 represent the iron plates, and 8x8% the
two slits where the distance 81B is much exaggerated. The geometrical

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nS4^^1 positive ray analysis. 319

condition for refocusing is that SiOSt should lie on a straight line. We

therefore wish that the figure as drawn should apply to the rays. For

this we must have 7 = a + j8, Where a = angle of deflection in A Si
and j8 = angle of deflection in SiB. That is, if SiC = 6,

b I r^ I r^

^J^H{z)dz.

This value was calculated to be .93 cm. and the slit Si was placed at that
distance in front of the iron plates. The distance BC was calculated
to be .25 mm. The correct radius of curvature is very closely
{SiSi — BC)l2 to which (5i5j)/2 is a sufficient approximation. A high
vacuum was obtained by a mercury vapor pump, which acted in connec-
tion with a Gaede rotary mercury pump. Mercury vapor must be kept
away from the apparatus at all times by the use of liquid air, for in a very
short time sufficient will diffuse over and condense on the brass to
prevent a high vacuum being obtained.

If the charged particles all fall through the same potential difference,
the most reliable method for analyzing the rays is to keep the ms^netic
field constant, and vary the potential difference so as to bring successive
elements onto the slit, for in the fundamental equation and in (i), m
and PD occur only in the product in^PD, and the rays will therefore
follow identical paths for in^PD = const. This would allow the com-
parison of molecular weights with the accuracy of a potential measiue-
ment; and if a molecular weight is known the original m^^netic field
determinations can be corrected. If, however, charged surface layers
are formed on the salts from which the ions start, the above method
would not be reliable. It was found that in practically all cases the
calculated molecular weights came out very close to the chemical mo-
lecular weights, so that no assumptions of surface layers comparable to
the potentials used, and only small corrections to the magnetic field
determinations were necessary. An exception occurred with very weak
magnetic fields, but this is at present ascribed to the difficulty in repro-
ducing the magnetic fields with very weak currents.

Resolving Power.

If the rays were uniformly distributed over the entrance slit and the

refocusing perfect, the curve obtained for the charge as the potential or

field strength is varied to bring various parts of the bundle on the exit

slit, would be of the form given in Fig. 3. Let 5 be the width of the slits

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320

A, J, DEMPSTER.

[Sbcomd
LSbkixs.

and AiAf represent the abscissae where the curve is half its maximum
value. S s= hihi if the abscissae represent distances. In order to see
what change in m is necessary to produce a dis-
placement AiAf, we have from the formula

7n —

2PD

Am
m

2Ar

where d f= 2r. This may be called the limit of
resolution, and if two molecular weights diflFer
by this amount, the point Ai of the one coincides
*^" * with the point At of the other. In the apparatus

d = iocm.,so that for slits § mm. wide we should have

Am _ I
m "" loo*

Preliminary Experiments.

The first experiments were made with ions obtained by heating a
mixture of sodium phosphate and calcium oxide on a platinum strip.
Several widely separated groups of rays were observed with slits about
2 mm. wide. The molecular weights agreed approximately with Na and
K for the strongest positive, and with Of and CaO for the strongest nega-
tive lines. The positive emission changed gradually with heating, from
being entirely potassium to being mostly sodium.

In another experiment manganous chloride (MnClj) was heated and
the negative emission was observed. Three distinct molecular weights
were observed which agreed approximately with negatively charged
oxygen molecules, manganese with a double negative charge, and man-
ganous oxide with a single charge.

Positive Ions from Aluminium Phosphate.
The positive ions obtained from heated aluminium phosphate have
been used by many experimenters. These ions were analyzed and found
to consist usually of sodium and potassium, although on one occasion
after standing overnight, the emission was at first entirely hydrogen
atoms. This wore off in a few minutes and the emission became sodium
and potassium. At first the potassium was very much stronger than
the sodium, but after heating some time it died off and became much
weaker. The emission was examined only at low temperatures as with
increasing temperature the currents soon became inconveniently large.

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Vot. XI-l
Na4. J

POSITIVE RAY ANALYSIS.

Table I.

321

P.D.

Current.

P.D.

Current.

679

22.79

3.8

705

21.93

117.

685

22.57

17.8

711

21.74

80.

689

22.44

43.5

715

21.62

58.8

693

22.31

90.9

719

21.50

20.8

699

22.12

133

723

21.39

3.3

As an example the figures in Table I. give the actual readings in one
measurement of the sodium line. The entrance slit was 1.9 mm. wide,
the exit slit 1.65 mm, wide and a screen 3.3 mm. wide was placed half way
around the semicircle. The current through the electromagnet was
kept constant at .8 ampere giving a magnetic field of 3,580 gausses
according to the curve drawn from the original determinations. The
potential difference {PD) which was obtained from banks of small
storage cells is given in volts, and . the molecular
weight M = w/mi, is calculated from

eH\r^
2V
and

wi = ^— ; r = 5 cm., e = 1,591

X 10

>-20

Fig. 4.

The current given was observed with the electro-
meter for the different potentials between the heated
salt and the slit. The maximum comes at 22.1,
but, ^ there can be no doubt that this line really is
sodium, we can explain the difference as due to the
value of the magnetic field being 2 per cent, too low. The difference is
probably not due to the ions falling through less potential difference than
the total applied, since, with other values of the magnetic field, values
of M very close to 23 were obtained. The curve, Fig. 4, is drawn with
the magnetic field corrected to bring the maximum at 23, and shows an
approximation to the theoretical form of Fig. 3. The limit of resolution
should be between

Am _ 2 X 1.65

m
and

100

= .033

2 X 1.9
100

= .038,

whereas that observed is .7/23 = .028. The form of the qurve shows
that the influence of the small amount of gas remaining is very slight.

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322

A. J. DEMPSTER.

R^f^,

^^%' 5 gives the curves for sodium and potassium under slightly poorer
vacuum conditions, both taken while the magnetic field was held constant
at 5,200 gauss. The maximum for sodium was obtained with 1,433
volts and for potassium with 845 volts. The ratio is almost exactly 39
to 23. The curve is drawn with a slightly corrected magnetic field so as
to bring the sodium maximum from 22.8 to 23.00. The potassium
ordinates are multiplied by 50 so that the sodium in this case was about
90 times as strong as the potassium. These curves indicate that the
charged particles actually fall through the total potential difference.

Fig. S.

The emission starts rather suddenly as the temperature of the strip
is raised, in the manner discussed by Richardson; but it was observed
that the potassium emission conmiences at a lower temperature than the
sodiimi. As the temperature was lowered the sodium disappeared while
the potassium was still strong. The Table II . gives the currents observed

Table II.

Na.

1.9

38.4

1.4

62.S

71.4

208

52.6

2000

for each as the temperature was raised by increasing the heating current.
The potassium is much stronger than the sodium at first but at higher
temperatiu-es the sodium becomes the stronger.

No great difficulty is expected in extending the investigation to all
the substances found by Richardson and others to emit positive or nega-
tive ions on being heated. With weak sources it will be necessary to
widen the slits and be content with less resolution.

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Vol. XLI
Na4. J

POSITIVE RAY ANALYSIS.

323

Positive Ions from Electron Bombarpment.

It was thought that the bombardment of salts by electrons might
break up the chemical compounds and give rise to many positive ions.
At first a Wehnelt cathode was used; the ions formed passed beside the
cathode (Fig. i) and were then accelerated by a large potential difference.
Aluminium phosphate on a piece of platinum foil was first bombarded.
The intensity of the rays increased very rapidly with a slight increase in
the amount or energy of the bombarding electrons, indicating that the
salt needs to be heated to a certain degree before the ions are separated.
Although the aluminium phosphate was chemically pure, the rays ob-
tained under the bombardment of 128 volt elec-
trons were very complex; the following ions were
observed besides a couple of unresolved groups;
Hi, Hj, Li (weak), Oi (strong), Na (strong), Os
(?) (weak), Af = 62 (weak, possibly NajO), M =
67 (strong, possibly H8PO2 = 66), Af =76 (strong),
Af = 86 (weak, possibly Rb = 85.5), Af = 112
(strong, possibly P^Os « no).

The experiments indicated the convenience of the
method of obtaining* positive rays and opened up
an interesting field for investigation.

The experiments were however first directed
towards testing out the possibility of obtaining
still greater resolving power. The curve in Fig. 6
for oxygen from the bombardment of aluminium phosphate was obtained
with J mm. slits and two screens with 2 mm. openings placed in the
path of the rays. Table III. gives the actual observations. The mag-

Fig. 6.

Table III.

P.D.

Current.

P.D.

Current.

1,758

15.76

7.3

1,728

16.03

1,752

15.81

7.3

1,722

16.09

1,746

15.87

15.6

1,716

16.14

1,740

15.92

38.6

1,710

16.20

1,734

15.98

netic field has been corrected so as to bring the maximum from 16.73 to
16. The theoretical resolution is

Am 2 X .5

100

= .01;

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324

A, /. DEMPSTER.

[ Second
Sbribs.

the observed is .2/16 = .012. From the bombardment of aluminium
phosphate to which a Httle lithium chloride and sodium chloride had
been added strong bundles of hydrogen atoms and hydrogen molecules
were obtained. With slits i mm. in width and a screen with an opening
4 mm. in width placed in the path of the rays, the curves in Fig. 7 were

Fig. 7.

obtained. The magnetic field has been corrected to shift the maximum
from .92 to 1. 00 and from 1.77 to 2.00. The actual observations for the
first curve are given in Table 4. The limits of resolution observed are
.015 and .017.

It is generally assumed that the hydrogen and oxygen atoms are
perfectly homogeneous so that the object in developing the above re-
solving power was to apply it to elements whose homogeneity has recently
been considered a questionable matter. In a recent lecture Professor
Soddy says^:

Table IV.

Voltt.

Af.

Current.

Volu.

Current.

1,470

1.018

2.8

1,496

1.000

1,478

1.013

11.1

1,502

.9961

71.4

1,480

1.011

22.2

1,508

.9922

62.5

1,482

1.009

35.7

1,514

.9883

33.4

1,486

1.006

62.5

1,520

.9845

16.7

1,490

1.004

71.4

1,530

.9780

6.7

'* When, among the light elements, we come across a clear case of large
departure from an integral value, such as magnesium 24.32 and chlorine
35.46, we may reasonably suspect the elements to be a mixture of iso-
topes." With the resolving power in 'the above examples this question
can obviously be definitely decided, for, if the element is really homo-
» Nature. 1917 also Scientific Monthly, p. 516. Dec. 191 7. See also Fajans. Phjrs. Zeit.. 1916.

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No"^^*] POSITIVE RAY ANALYSIS. 325

geneous, the curve will lie entirely between two integral values, and if it
is a mixture of elements differing by integers, the molecules will be com-
pletely separated. The only experimental difficulty is to get the rays,
and this is the matter now under investigation. Magnesium has been
tried by bombarding it with electrons from a tungsten filament while
it was being heated by a platinum strip around which it was wrapped.
With slits 1.9 mm. and 1.65 mm. in width intense rays of oxygen mole-
cules (calculated 32.01) were obtained and after heating for some time
rays of nitrogen or carbon monoxide (28.00) appeared. Rays that are
probably chlorine have been obtained from the bombardment of a heated
anode of aluminium phosphate, potassium chloride and potassium iodide
with electrons from a tungsten filament. The apparatus was however
at the time slightly contaminated with mercury, and the curves were so
broadened that no conclusion could be drawn. A crystal of KI was
bombarded and found to give strong Hi and Ht rays; no Hj or helium
was observed.

The experiments described above are concerned chiefly with the
development of the method, and they are published now only because
the writer expects to be engaged in other duties for some time.

The writer wishes to express his appreciation of the kindness of Pro-
fessor Michelson and Professor Millikan in placing the equipment of the
laboratory at his disposal and in rendering every possible assistance.

Summary.
An apparatus for analyzing positively or negatively charged particles
is described. Examples are given of the analysis of the ions from heated
salts and of the positive rays obtained by bombarding various substances
with electrons. The high resolving power obtainable with the method
is also illustrated.

Rybrson Physical Laboratory,
Chicago,

October ao, 191 7.

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326 THE AMERICAN PHYSICAL SOCIETY, KS?

PROCEEDINGS

OF THE

American Physical Society.

Minutes of the Ninety-First Meeting.

THE ninety-first meeting of the American Physical Society was held in the
Ryerson Laboratory of the University of Chicago on Saturday, De-
cember I. Morning and afternoon sessions were held.
The following papers were presented:

Vacuum Gauges of the Radiometer type. R. G. Sherwood.
Further Verification of Knudsen*s Equations for Resistance to Molecular
Flow. L. E. DoDD. (By title.)
A Megaphone with a Rectangular Aperture. F. R. Watson.
The Forces Which Hold Liquids and Solids Together. William D. Har-

KINS.

Rectification of Alternating Current by the Corona. J. W. Davis.

The Determination of Organic Compounds by an Optical Method. Thos.
E. Doubt, and B. B. Freud.

The Analysis of Polarized Light Reflected from Small Opaque Crystals.
Lerot D. Weld.

Resonance and Ionization Potentials for Electrons in Cadmium, Zinc, and
Potassium Vapors. John T. Tate and Paul D. Foote.

A New Method of Positive Ray Analysis. A. J. Dempster. (By title.)

Mobility of Ions in Air, Hydrogen, and Nitrogen. Kia-Lok Yen.

A Correction in the Theory of Ionization by Collision. Jacob Kun7.

Wave Lengths of the Tungsten X-Ray Spectrum. Elmer Dershem.

A Mono-Wave-length X-Ray Concentrator. Elmer Dershem.

The Crystal Structure of Ice. Angel St. John.

Characteristic Curves of Various Types of Audions. A. D. Cole.

The Angle of Contact between Liquids and Glass, and the Determination of
Surface Tension. William D. Harkins.

The Absorption and Solubility of Long-Chain Molecules. William D.
Harkins.*

A. D. Cole, Sec,

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Noir^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 327

Note on a Phosphorbscent Calcite.*
By E. L. Nichols and H. L. Howbs.

ASPECIMEN of calcite from Franklin Furnace, N. J., showing the usual
red-yellow phosphorescence of short duration was studied. The after
glow falls to 1/660 of its initial brightness within 0.5 second. The decay is
remarkably slow at first following the usual law J"*"*: /.

After about .16 sec, for the excitation employed, a second "linear ' ' process
begins of more rapid decay and at .30 sec. from the close of excitation this is
followed by a third "linear" process of still more rapid decay. The law of
decay therefore is that recently described by the authors' and supposed to be
peculiar to the uranyl salts. Detailed spectrophotometric observations show
that what appears to be a single broad band extending from .66 /x to .54/x/is a
complex of narrow overlapping bands as in the case of the spectra of the
phosphorescent sulphides.* A second very feeble band lies between .52 /x and
.50 /x with its crest at about .514 m-

CORNBLL UnTVBRSITY,

December. 191 7.

The Visibility of Radiation in the Blue End of the Visible Spectrum.*

By L. W. Hartman.

IN investigations of this type, two general methods have been utilized: (i)
the direct comparison method in which the luminosity of light of succes-
sive wave-lengths emitted by the source is compared directly with that of light
emitted by a second source considered as a standard, and (2) the flicker method
in which the criterion of equality is the disappearance of flicker.

The first method was utilized in this paper and had been used previously in
another investigation^ in this laboratory. It consisted primarily of an adap-
tation of the arrangement of the parts of the Holborn-Kurlbaum optical pyrom-
eter. One advantage of this method is that it permits the use of greater
brightness so that measurements in the extreme regions of the spectrum can be
made. In order to secure sufficient brightness in the extreme blue end of the
spectrum, a bright, high temperature source was selected, viz., a tungsten
lamp with broad vertical flat filament maintained at a color temperature* of
2695^ K. A magnified image of this fiat filament was projected on the colli-
mator slit of a Hilger constant deviation spectrometer. Upon passing through
the prism, the light from this source formed a spectrum in the focal plane of the
telescope of the spectrometer where the horizontal filament of a small tungsten

* Abstract of a paper presented at the meeting of the American Physical Society held in
Pittsburgh, December 27-29. ipi?-

* Nichols and Howes. Physical Rbvibw (2). IX., p. 292.

* Nichols. Am. Philos. Soc. Proc.. LVL. p. 258.

* Hyde and Forsythe, Astrophys. Jour., 42. p. 285. ipiS*

» Hyde, Cady and Forsythe. Phys. Rev. (2), 10. p. 395. 19 17.

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328

THE AMERICAN PHYSICAL SOCIETY.

fSBOOND

LSBKin.

pyrometer lamp served as a comparison source. A lens, in turn, placed be-
tween this comparison source and the eyepiece of the instrument, focused an
image of the incandescent filament of this small lamp together with the spec-
trum of the source on a narrow adjustable slit placed in the focal plane of the
eyepiece. In front of the eyepiece was mounted a blue glass screen. The
visual measurements consisted of brightness comparisons of the pyrometer
filament with various portions of the spectrum of the broad filament.

The spectral energy curve for the broad filament source was computed from
its color temperature with the aid of Wien's equation in which Ct was taken
equal to 14,350 micron degrees. Correction for slit widths, for scattered light,
for the absorption ol the blue glass screen, and for the dispersion and selective
absorption of the optical system of the apparatus were then made.

In Table I. the determinations have been reduced to a value of 100 at
X = 450 MM* In this table are also included the visibility values of Nutting,^
and Coblentz and Emerson' for the same range of wave-lengths, similarly re-
duced to a common value of 100 for X = 450 mm* It will be noted that the re-
sults here presented are lower in the extreme blue than those obtained from the
data of Nutting, and Coblentz and Emerson.

With the data at hand one can compute for some definite temperature inter-
val the effective wave-length of the blue glass screen mounted in the eyepiece.
This was done for the temperature interval 1781® to 2475® K., and the value
found by computation was 466.8 mMi while the experimental value found by
Dr. ForsytKe was ^d^jxii,

TABLE I.

Wava-lcDgtha.

Mean Vieibility of
Twenty SubjecU.

Mean Valuee Given by
Nutting. <

Mean Values Given by
Coblents and Bmereon.

410 mm

1.7

9.5

420

11.4

17.1

430

32.6

30.3

440

. 61.6

58.0

450

100

460

153

168

137

470

240

266

202

480

376

392

305

490

620

566

474

500

905

828

770

Nbla Research Laboratory,

National Lamp Works of General Electric Co..
Nela Park, Cleveland, O.

* Phil. Mag. (6), 29, p. 301, 19x5 (corrected values).
« Bull. Bur. Stds., 14. p. 167, 1917.

* These values, kindly furnished by Dr. Nutting, differ slightly from his published data
owing to a redetermination of the distribution of energy in the spectrum of the acetylene
flame used.

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NoI"^^*l ^^^ AMERICAN PHYSICAL SOCIETY. 329

Theory op Thermal Conductivity in Metals.*
By Edwin H. Hall.

IT is generally admitted that there are "free" electrons in the interatomic
spaces of a metal and that their number per unit volume increases with
rise of temperature. Hence there must be, in a detached metal bar hot at one
end and cold at the other, a mechanical pressure tending to drive the free elec-
trons down the temperature gradient. If this tendency prevails, even to a
very slight extent, it makes the hot end of the bar electrically positive and the
cold end negative.

If, now, some of the associated electrons are capable of progressive motion,
from one atomic union to another during contacts, they will yield to the in-
fluence of the electric-potential gradient, whereas they will not be subject to
the direct influence of the mechanical-pressure gradient. The result of the
conditions described will be a constant procession of free electrons from the
hot to the cold end of the detached bar and an equal procession of associated
electrons from the cold to the hot end. These movements must be attended by
a constant process of ionization, absorbing heat, at the hot end and a constant
reassociation, releasing heat, at the cold end. That is, the free electrons will
function like a vapor, and the metal bar will be somewhat analogous to the
familiar Regnault apparatus for testing the boiling point ot liquids, the hot end
corresponding to the boiler and the cold end to the condenser, from which the
liquid trickles back under the influence of gravity.

Doubtleiss a complete theory of the action in question must take account of
ionization and reassociation at other points than the very ends of the bar; but,
ignoring this complication for the present, we can get some notion of the pos-
sible heat-carrying power of the operations described by the following course of
reasoning, partly conjectural:

The E.M.F. of a copper-iron thermoelectric couple for i degree temperature
difference is about i X io~* volts at 20® C. Let us suppose that the contri-
bution of the copper to this total is something between one quarter and one
tenth of the whole, that is, something between 2.5 X io"*and i X lo"* volts.
Let us suppose, further, that the electric conductivity 01 copper is one half due
to the associated electrons, so that the specific resistance, the associated elec-
trons only being considered, would be about 3 X 10-6 ohns. These estimates
give, as the magnitude of the constant electric current, in each direction, in
a detached copper bar with unit temperature gradient, something between
0.83 and 0.33 ampere per sq. cm. of cross section.

If, now, we suppose that the ionizing heat corresponds to a potential dif-
ference of 5 volts, which seems a not unreasonable estimate from such data as
we possess, we find that our apparatus should carry heat at a rate between
4.15 and 1.65 joules per second per sq. cm. of cross section. The known ther-
mal conductivity of copper is about i calorie, that is, about 4 joules. No great

> Abstract of a paper presented at the meeting of the American Phjrsical Society held in
Pittsburgh, December 27-29. I9i7-

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330 THE AMERICAN PHYSICAL SOCIETY. f

importance should be attached to the closeness of the agreement here; but the
calculation, uncertain though it be, is enough to show that the theory under
consideration is worthy of further development.
Cambiudgb, December a6, 191 7.

The Size and Shape of the Electron.*
By Arthur H. Compton.

IF the electron is sensibly a point charge of electricity, the mass absorption
coefficient for X-rays and gamma rays should, according to classical
theory, never fall below 0.188 in the case of aluminium. The experiments of
Barkla with hard X-rays and of Ishino and others with hard gamma rays, show
a value considerably less than this, falling as low as 0.045 when the penetrating
radiation from radium C is used. Moreover, the scattered radiation from very
hard rays should by classical theory be equally intense on the incident and the
emergent sides of a plate through which the rays pass — a prediction contrary to
the experimental observation that the intensity of the scattered radiation on
the emergent side is much the greater.

These difficulties may be explained if the electron, instead of being a point
charge, is considered to have a radius comparable with the wave-length of the
incident beam. The scattering of gamma rays by electrons of appreciable
diameter has been calculated, both on the assumption that the electricity is
distributed in a spherical shell and on the ring electron hypothesis. Both
types of electrons are found to be capable of explaining quantitatively the low
absorption observed, with very short rays if the electron has a radius of about
2.5 X 10"*" cm. Such a large electron accounts also for the difference in
intensity of the incident and the emergent scattered radiation, though the ring
electron appears to give the better quantitative agreement in this case. The
ring electron has the further advantage that it is capable of explaining A. H.
Forman's observation that iron has a slightly greater absorption coefficient
when magnetized parallel to the transmitted X-ray beam than when unmag-
netized. This is due to the fact that when the axis of the ring is parallel with
the incident X-rays, the energy scattered by the electron is a maximum. It
appears probable, therefore, that the electron consists of a ring of electricity
whose radius is about 2.5 X lo~*" cm.

Rbsbarch Laboratory,

Wbstinghousb Lamp Co.,
December 15, 19 17.

Characteristic Curves of Various Types of Audions.*
By a. D. Colb.

THIS paper presented the general results of a study of the change in the
value of the plate current and the grid current of an audion tube as the

> Abstract of a paper presented at the meeting of the American Physical Society held in
Chicago. December i, 191 7.

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Na*4^'*] THE AMERICAN PHYSICAL SOCIETY, 33 1

following factors were varied: viz., the P.D. between filament and grid, the
P.D. between filament and plate, the magnitude of filament current, magnitude
of received signal, type of signal source, kind of audion used and closeness of
coupling in the sending signal circuit.

Seven different types of audions were used and three kinds of signals. In
each experiment, with other conditions fixed, the P.D. between the negative
end of the filament and the grid was varied step-by-step by a potentiometer
arrangement and the value of both plate-current and grid-current noted for
each step. These current values were plotted. At each step it was noted how
much the value of each of the currents was changed when an incoming signal
superposed an alternating P.D. upon the D.C. voltage corresponding to that
step. These current changes were plotted as " plate-signal *' and " grid^signal **
curves.

Diagrams were shown for the set-ups used for different types of signals.
The kinds of signals used were waves from a neighboring high-frequency oscil-
lating audion circuit, waves of same frequency from a buzzer circuit and low
frequency from a 6o-cycle A.C. source.

About a dozen lantern slides and charts were shown, each giving a typical
group of the four characteristic curves, plate-current, grid-current, plate-signal
and grid-signal.

Ohio State UNrvERsriY,
December, 191 7.

The Effect Produced upon Audion Characteristic Curves by Various
Kinds of Signals (Buzzer, Electron Relay and 6o-Cycle A.C.).*

By a. d. Colb.

THE present study is a continuation of the work reported upon at the
Chicago meeting of the American Physical Society under the title
"Characteristic Curves of Various Types of Audions." Three of the seven
types of audions included in the earlier study were particularly examined to
find how much the magnitude of the plate signal and the grid signal depend
upon the kind of excitation used. The terms plate signal and grid signal are
used in the sense defined by Dr. L. W. Austin in a recent paper;' viz., the
changes in the magnitude of the plate current and grid current produced by
the momentarily applied alternating E.M.F. It was found that the magnitude
of the effect, its law of change with variation of the D.C. voltage applied to
grid and even its sign were different, according to whether the signal E.M.F.
was produced by a buzzer, an oscillating audion or 60-cycle A.C. source. But
the kind of variation was different in different types of audions. For example
in an "oxidized-filament" De Forest bulb, excited by high frequency signals

^ Abstract of a paper presented at the meeting of the American Physical Society held in
Pittsburgh, December 27-29, 191 7.

* Radiotelegraphy — Notes on the Audion; L. W. Austin, Jour. Wash. Acad., Vol. 7, No.
IS. Sept.. 1917-

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332 THE AMERICAN PHYSICAL SOCIETY, [&SSS

of about 2,000 meters wave-length from another audion, the plate-current
curve, grid-current curve and grid -signal curve were normal and similar to
those shown in the figure of Dr. Austin's paper above referred to; the ordinate
of the plate-signal curve changed sign at the usual place, but positive values
were unusually small and negative values unusually large. With buzzer
excitation, however, positive values were relatively larger, the change of sign
occurred later, and negative values never exceeded the positive; the form of
the grid-signal curve was peculiar, with large positive values throughout the
entire range of D.C. voltage used. The 6o-cycle excitation gave a form of plate-
signal curve different from either, the ordinates never becoming negative; its
grid-signal curve was much like that obtained with the buzzer.

With a Western Electric audion of cylindrical pattern, both high-frequency
audion and 6o-cycle sources gave plate-signal and grid-signal curves slightly
abnormal but much alike. The buzzer curves, however, were quite different;
the ordinates of the plate-signal curve changed sign at the usual place, but
positive values gave a curve with remarkably flat top, while the negative were
larger with the usual well-marked maximum. The grid signal showed large
positive values throughout the entire voltage range used.

Similar curves were shown and comparison made between the same three
kinds of excitation for De Forest Hudson-filament bulbs. High-frequency
audion and 6o-cycle excitation gave similar signal curves, all quite normal.
But here also the buzzer excitation gave signal curves that were both quite
far from normal, and also different from those obtained from the other types
of tube.

This work was done at the U. S. Naval Radio laboratory at the suggestion
of its Director, Dr. L. W. Austin, and the resources of his laboratory generously
placed at the author's disposal. The work is being continued at the Ohio
State University. A full description accompanied by many curves will soon
be published, probably in the Proceedings of the Institute of Radio Engineers.
Omo State Untversity,
December. 19 17.

Report on the Construction of Certain Mathematical Tables.*
By C. E. Van Orstrand.
The following tables are ready for publication.

2 r*

Table I. — Values of y = -p f e~^dx ranging from 5 to 8 places of decimals
at intervals of 0.000 1 from 0.0000 to 3.0000.

2 r*

Table II.^ — Inverse values of y = -p f e'^dx to 5 places of decimals at in-

VttJo
tervals of o.oooi from 0.0000 to 0.9000 and at intervals of 0.0000 1 from 0.90000
to 1. 00000.

^ Abstract of a paper presented at the meeting of the American Physical Society held in
Pittsburgh, December 27-29. 1917.

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Na"^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 333

Tablb III. — Values of the reciprocal of n! to 108 places of decimals at inter-
val? of unity from i to 74.
Table IV. — ^Values of «• to 42 significant figures at intervals of unity from

0 to 100.

Tablb V. — Values of e* to 33 significant figures at intervals of o.i from 0.0
to 50.0.
Table VI. — Values of «* to 62 places of decimals at decimal intervals from

1 X 10-" to 9 X 10-^

Table VII. — Values of f~* ranging from 52 to 62 places of decimals at inter-
vals of unity from o to 100.

Table VIII. — Values of «"* ranging from 33 to 48 places of decimals at inter-
vals of o. I from 0.0 to 50.0.

Table IX. — Values of «"* to 63 places of decimals at decimal intervals from
I X 10-" to 9 X 10-*.

Table X. — Values of e *(»»/'*^) to 23 places of decimals or significant figures
at intervals of unity from n = o to n ■* 360.

Table XI. — Values of «**' to 25 places of decimals or significant figures
for various values of n.

Table XII. — Values of sin x and cos x to 23 places of decimals at intervals
of unity from o to 100.

Table XIII. — Values of sin x and cos x to 23 places of decimals at intervals
of 0.1 from 0.0 to lo.o.

Table XIV. — Values of sin x and cos x to 23 places of decimals at intervals
of 0.00 1 from 0.000 to 1.600.

Table XV. — Values of sin x and cos x to 25 places of decimals at decimal
intervals from i X lO"" to 9 X lO"*.

Table XVI. — Miscellaneous values of e*. «"■, sin x and cos a? to a great num-
ber of decimals including Doorman's value of e.

Table XVII. — Values of sin d and cos d to 28 places of decimals for various
values of d expressed in seconds,

U. S. Gbological Survby,
Washington, D. C.

The Optical Properties of Rubidium.^
By J. B. Nathanson.

HE optical constants of rubidium were obtained for wave lengths ranging
from 454.6 fAfi to 640.9 /i/i. A simple Babinet compensator and two
nicols were employed to measure the phase difference and azimuth. The con-
stants were calculated by means of Drude*s formulae.

The rubidium mirror was formed by distillation of the metal in an atmos-
phere of rarified nitrogen, with subsequent condensation upon a piece of plane
parallel glass. A right angle prism served to eliminate the troublesome reflec-
tions from the glass front of the mirror.

^ Abstract of a paper presented at the meeting of the American Physical Society held in
Pittsburgh, December 27-29, 19 17.

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334 ^^^ AMERICAN PHYSICAL SOCIETY. [to»

The coefficient of absorption was found to vary from 5.28 for X « 454.6/1/4
to 10.51 for X = 640.9/1/1. There was only a very slight variation in the value
of the index of refraction which was equal to about 0.14.

The reflecting powers of the rubidium in contact with glass varied from 74.5
per cent, for X « 454.6 /i/i to 82.7 per cent, for X =« 640.9 /i/i. These values are
(with the exception of that for X » 589.3 /i/i) somewhat lower than those ob-
tained directly by means of a photoelectric cell in a previous investigation.*
Carnbgib Institutb of Technology,
PrrrsBURGH, Pa.

* Agtrophjrsical Journal, 44, 137, 1916.

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uSr^^'] ^^w BOOKS. 335

NEW BOOKS.

Table of Logw Sec^ d. By P. S. Helmick. i6 pp. Published as University

of Iowa Monograph No. 4. 191 7.

This table is intended for use with photographic density apparatus employ-
ing nicol prisms in their construction, and gives the photographic density of

the plate, t. e,, Logw ( ^ ; : t .T" I» directly in terms of the angle of

\ Transmitted Light /

rotation of the nicols. The value of the function is given every o**.05 from

0° to 89**, and every o^'.oi from 89** to 90**, together with the tabular difference

for each o**.oi for the whole range. The table may be obtained on request

from The Librarian of the State University of Iowa, Iowa City, Iowa.

A College Text- Book of Physics. By Arthur L. Kimball. New York:
Henry Holt and Company, 191 7. Second edition, revised. Pp. x + 694.
In the six years since the publication of the first edition this book has enjoyed
a well-merited success, due especially to its emphasis on the physical rather
than the mathematical side of the subject. In clarity and exactness it com-
pares favorably with most existing texts. The reviewer is -among those friends
of the book who had hoped that its favorable reception would have encouraged
the author to make more radical departures from convention when revising
for the new edition, in order to make the treatment still more aggressively
physical. In this respect we are disappointed, as the new edition shows only
minor changes. A few paragraphs rewritten to bring them up to date, ampli-
fication of the treatment of wireless telegraphy and telephony — these are
changes that could have been predicted. The new section on the flicker
photometer does not seem to fill any crying need and could have been omitted
without detriment. There are two appendices, one on Carnot*s cycle and the
other a proof of Newton's wave formula. The first of these should have been
incorporated in the text. A very genuine and substantial improvement is
effected in the arrangement of the chapters on mechanics by placing the sec-
tions on statics earlier. The substitution of the elements of electron theory
for those of displacement theory is also to be commended, as well as the
improvement in the definitions of the electrical units.

The weakest part of the book is its collection of problems. The great merit
of the text treatment is its emphasis on physical rather than mathematical
reasoning; but when we turn to the problems we find for the most part a rather
conventional collection of numerical examples of the formula-substituting
kind. The evil is exaggerated in some cases by giving unproved formulas in
the text, and then problems requiring the use of such formulas. As an instance.

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336 NEW BOOKS. [ISSS

we may cite the formula for the speed of water waves, or the formula for the
force with which a magnet holds its armature. It is of small advantage to
avoid the use of mathematics as an instrument of reason if the student is to be
thus encouraged to use it as an instrument for avoiding thought. A larger
number of problems of a kind incapable of numerical solution would be much
more to the author's purpose.

One or two errors of fact may be noted. The meter is defined in terms of
the mHre des archives instead of the International Prototype Meter, and the
metric equivalents of the English foot and yard are given where the American
standards would be better. In Article 146 it is stated that the spin of a shell
causes it to keep pointing in a nearly constant direction in spite of air resistance.
The facts appear to be that because of air resistance the axis of the shell keeps
parallel to the trajectory. A spinning shell mounted on gimbals has been
found to turn its nose into a blast of air. The Leyden jar with removable
coatings reappears and seems hard to get out of our texts, in spite of the fact
that the whole phenomenon depends on the heterogeneity of the dielectric.

The comparative triviality of these blemishes serves only to emphasize the

accuracy of the text as a whole.

C. M. S.

Organic Evolution. By Richard S. Lull. New York: Macmillan Company,

1 91 7. Pp. xviii + 729. Price, J3.00.

This textbook (designed for use in college courses) gives an account of the
principal theories advanced to explain the existence of the various species of
plants and animals. It contains many interesting facts relating to the physical
and chemical properties of protoplasm, and to the extraordinary mechanisms
by which organisms nourish themselves and reproduce their kind.

In the last two thirds of the book the evidences of organic evolution are
presented, especially those derived from paleontology. This section closes
with interesting statements concerning the evolution of man.

A physicist cannot help being struck by the number of far-reaching general-
izations that have been deduced in this branch of science from what appears
to him to be very meager non-quantitative evidences.

Students of physical science who are interested in the development of bio-
physics will find the book very useful and suggestive.

W. D.

Building Human Intelligence. By Dr. Arnold Lor and. Philadelphia:
F. A. Davis Co., 1917. Pp. xii + 451. (Received.)

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Second Series. May, igiS Vol. XL, No. $

THE

PHYSICAL REVIEW.

THE MOBILITIES OF GASEOUS IONS.*

By Kia-Lok Yen.

Part I. Method and Procedure.

I. Introductory Statement.

IN spite of the great number of investigations devoted to gases
during recent years the question whether an ion is a molecule or
an atom carrying an elementary charge, or whether it is a number of
neutral molecules clustering about a charge is not as yet definitely
settled." ^ So wrote Franck eight years ago. Even now in spite of all
the researches carried on along the same line since then the question is
by no means settled, for its various solutions are far from being imiversally
accepted.*

When the phenomenon was revealed that the mobilities and the
diffusion coefficients of the ions in gases were relatively small in com-
parison with those of the uncharged molecules, the first hypothesis
formulated for its explanation was that each individual ion, instead of
being a single charged molecule, was a cluster of neutral molecules around
an elementary charge.* Thus the ion, being a cluster of molecules had
a mass greater than that of a single uncharged molecule, and conse-
quently would move more slowly than the latter imder similar conditions.
Later, in 1909, Wellisch* and Sutherland* offered another hypothesis

* Presented at the Chicago meeting of the Physical Society, December i, 1917*

1 Franck, Verh. der Deut. Phys. Ges., 11, 397, 1909. t)ber die lonenbeweglichkeit der
radioaktiven Restatione und die Masse des Gasions.

* An idea of the extent of the work on this subject may be had by adding to the list of
references given by J. Franck in his article "Bericht Qber lonenbeweglichkeit," Jahrbuch
der Radioaktivit£lt, 9, 335, 1912, the following: Townsend and Tizard, Proc. Roy. Soc., A,
87, 1912; A, 88, *I3; Moore, Phys. Rbv., 1912; Todd, Phil. Mag., 1913; Wellisch, Am. Jour.
Sd., May, 1915; Phil. Mag., March, 1916; Haines, Phil. Mag., 30, 19x5; 31. I916; Loeb,
Phys. Rbv.. N. S.. VIII., No. 6, 1916.

* Rutherford, Radioactive Substances and their Radiation, p. 56.

* E. M. Wellisch, Trans. Roy. Soc, A, 309, 1909.

* W. Sutherland, Phil. Mag., 18, 341, 1909.

337

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338 KIA-LOK YEN. [g^S

for the explanation of the same phenomenon. In opposition to the
older assumption of the "cluster" they claimed the ion to be a single
charged molecule and its low mobility to be a consequence of the retarda-
tions along its path through the gas by virtue of the charge it carried.
The charge of the ion would attract the uncharged gas molecules and
thus would cause it to collide more often with the latter than would an
uncharged molecule in traversing the same distance. Thus the relatively
slower mobility of an ion was ascribed by one hypothesis to the increase
in its mass and by the other to the increase in the number of collisions
with the gas molecules; and both explanations were equally plausible.

The contradictory and rival hypotheses once having been adopted,
their verification was in order. Their possible consequences were made
the best possible criteria of their verification. It was reasoned that if
the ion was a cluster of neutral molecules about an elementary charge,
either an electron or a positive corpuscle, it would break up as soon as
it had acquired a kinetic energy sufficiently high to cause such an effect.
This disintegration of the ion would result in a decrease of its mass;
in accordance with the hypotheses this decrease would manifest itself
in an abnormal increase of its mobility. On the other hand, if the ion
was a single charged molecule — a "small ion " — ^it would not disintegrate,
and consequently its mobility would remain constant.

Thus, the measurements of the mobilities of ions were considered the
best methods for the verification of both the "cluster" and the "small
ion " hypothesis. For if the mobilities were found to increase abnormally
when a high kinetic energy was imparted to the ions, and if this increase
could not be attributed to an3rthing other than the increase in the kinetic
energy, then the "cluster" nature of the ions would be positively estab-
lished. But if the mobilities did not increase even after the ions had
gained a high kinetic energy, the "small ion" hypothesis would be
verified. Hence the ions were caused to travel under electric field and
at pressures designed to impart to them enormous velocities. If the ions
remained intact — if no disintegration occurred — their velocities would
be proportional directly to the field strength and inversely to the pressure.
But if the "cluster" dissociated, the proportionality would not hold.

Early experiments along the general direction described led to varied
and conflicting results. Latty,^ Kovarick,* Todd,* Townsend* and
Franck* obtained abnormally high mobilities whereas Chattock* and

> R. F. Latty, Proc. Roy. Soc., A, 84. 1910.

* A. P. Kovarick, Phys. Rbv., 30, 415, 1910.

* Todd, Phil. Mag., S. 6, Vol. 22, p. 791, 191 1; Phil. Mag., June, 1913.

* J. S. Townsend, Proc. Roy. Soc.. A, 85. 191 1.

* J. Franck, Ann. der Phsrsik., 22, 972, 1906.

* Chattock, Phil. Mag., 48, 401. 1899*

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XS"5^''] MOBILITIES OF CASEOUS IONS. 339

WelHsch* found the mobilities to remain normal through a wide range of
pressures and field strengths. The latest additions to the collections of
data in support of the cluster hypothesis was the work of Moore,* and
that of Haines;* while the most recent additional proof for the small ion
theory was embodied in the works of Wellisch* and Loeb.* The latest of
the ** cluster" exponents, namely Haines, even went a step further and
maintained that the results of his experiments indicated not only that
the ions were formed by clusters of molecules but also that the ions of
the same gas — Hydrogen being the case under consideration — ^were made
up of the combination of molecules varying in numbers. Contrary to
this Loeb's work with air at potentials of as high as 12,450 volt/cm.
gave absolutely normal results.

Thus the facts as they stood apparently pointed in contrary directions.
But it is only in keeping with modem experimental methodology that
reasonable explanations be discovered for the apparently contradictory
facts. It was for this reason that further work along this line was con-
sidered desirable; and hence the work herein described was undertaken.

All the observations, excepting those of Franck, Moore, and Loeb,
employed only ordinary low potentials; and even the field strength
employed by Franck and Moore, though higher, was merely roughly
approximated. The method employed by Loeb in his work in air ap-
peared to be the most definite and most direct method ever designed.
And for this reason and for reasons that will become apparent later on,
this method was adopted.

An attempt was first made to repeat Loeb's experiment with air under
different conditions by increasing the frequency of the alternating field
to nearly twice as high and the field strength by about fifteen per cent.

Then the mobilities of hydrogen ions were measured in fields varying
from 9 to 6,669 volts per cm., and those of nitrogen ions in fields varying
from II to 17,670 volts per cm.

The results, be it anticipated, indicated no tendency on the part of
the ions to disintegrate; that is, the mobilities were found to be abso-
lutely normal within the limits of experimental errors, and the law
Up = constant, where U is the mobilities and p the pressure, was found
to hold over the whole range of fields and pressures employed.

> E. M. Wellisch, Am. Jour. Sci.. May, 1915; Phil. Mag.. Mar., '16.
•Moore, Phys. Rbv., 191 2.

* Haines, Phil. Mag., S. 6, Vol. 30. 1915; Vol. 31, 1916.

* Wellisch. PhU. Mag., July. 1917.

* Loeb, Phys. Rbv., Vol. VIII., 633, Dec., 1916.

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340 KIA'LOK YEN, [sSSSi

2. The Method.
The method here employed was the Rutherford*-Franck* alternating
potential method as employed by Loeb. It consists in the determination
of the distance traversed by an ion (or rather by a number of ions)
parallel to the direction of a known electric field during a half period of
the alternation. From this distance d, the known potential E, and the
frequency n, the mobility J7 was calculated from the formula:

Tfid*

^2E'

3. The Apparatus.
The apparatus here employed was essentially the same as that used by
Loeb.' In fact it was Loeb's apparatus modified in a few details to meet
some mechanical criticisms which had made their way into the mind
of the present writer. However, the general structure of the apparatus
remained the same.

4. Establishment of Potential.*^
The low-frequency alternating field employed was obtained from the
ordinary city supply. The high-frequency field was established by an
oscillating circuit in which the oscillations were generated by a Chaffee
Arc' By way of supplementing Loeb's account, it may be pointed out
here that the desired high-frequency oscillation potential was obtained
by the application of the following formula for syntonic coupled circuits^

Vi y/ci'

where Ci and Vi represent the capacity and potential across the con-
denser plates — of one circuit, and Ct and V% the capacity and potential
of the secondary circuit. From the above formula and from the familiar
formula CiLi = CtLt it can be seen that with a given primary circuit
CiLi and a variable circuit CjLi it will be necessary to increase Lj and
decrease Ct in order to increase the potential across Ct and at the same
time to keep the circuits syntonic, or, to be exact, almost so.
The most important condition to be satisfied here was that the potential

» Rutherford: Pro. Camb. Phil. Soc., IX., 410, 1898.

• J. Franck: Ann. d. Phys., 21. 985, 1906.
» See Loeb, loc. cit., for description.

< See Loeb, loc. dt., for description.

• £. L. Chaffee. Proc Am. Acad. Arts and Sci., Nov.. 191 1.

• See J. A. Fleming, The Principles of Electric Wave Telegraphy and Telephony, 3d ed.,
p. 302, 1916.

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No*^^'] MOBILITIES OP GASEOUS IONS, 34 1

might be as high as could be obtained provided the frequency was neither
too high to render the critical distance d equal to or smaller than the
sparking distance between the gauze and the collecting plate, nor too
low to render the critical distance greater than that up to which the uni-
formity of the field between the gauze and the place could be maintained.
Since

^ = ^^

UE^/2

.'. d* = ;

Tit

-J^/-

UE^^2 Z^-

Thus, for a given potential £, assuming the mobility C/ to be constant,
the critical distance d is inversely proportional to the square root of the
frequency n.

But the sparking distance d is directly proportional to the potential
£, say d = KB.

Comparing this equation with that just derived above, namely,

<f = J^^^

Tit

it can be easily seen that if

tK^E

sparking would occur across the gauze and the plate before they were
brought sufficiently close to each other in order to enable the ions stream-
ing from the gauze towards the plate to reach the latter before the sign
of the potential was reversed.

On the other hand if n was so small as to render d too large, the gauze
and the plate would have to be very far from each other in order to reach
the critical distance. This would destroy the uniformity of the field
between the plate and the gauze. Besides, the critical distance might
be beyond the range of the apparatus.

There was also a practical limitation in this connection. If the poten-
tial was too high there would be brush dischai^es from the edges and
comers inside the chamber, and this would give rise to serious dis-
turbances.

The arrangement found to be satisfactory in this work was that which
gave a potential of 5,000 volts at 14,758 cycles per second. This rendered
the critical distance, especially that for nitrogen, very near to the
sparking distance.

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342

KIA'LOK YEN.

[Sbcond
LSbkibs.

5. The Determination of Frequency.

The frequency of the alternating field employed was determined by
photographing from a revolving mirror the sparks jumping across r
when the balls were brought sufficiently close to each other. As it was
necessary to keep the capacity of the circuit as nearly constant as possible,
so that the frequency measured from the spark might be the same as
that at which the mobility measurements were made, the spark gap r
was kept in the circuit all the time. During the mobility measurements
the gap was adjusted slightly wider in order to prevent sparking from
occurring across it.

A camera with a Cooke anastigmatic lens, / = 3.5, was used. The
photography was done in three different ways; first by clamping the
camera on the table before the revolving mirror, then by sliding the
camera up a vertical stand, and then by sliding the negative holder up,
with a known speed, behind a lens fixed before the mirror.

The last method was developed under the impression that the first
two were not accurate enough, but the results proved the inaccuracy of
the two methods to be negligible in comparison with the other sources of
error. However, the mechanical superiority of this method justifies a
brief description.

Fig. I represents the essentials of the arrangement. Before the re-

Fig. 1.

volving mirror M was a light-proof box B with a lens L in the front,
and a plate holder P sliding up and down at the back. When in opera-
tion P was pulled upward by a cord c passing over the pulleys />, p, and
attached to the wheel W. The arrow in the figure indicates the direction
in which the beam of light from the spark reached the photographic plate.
Both the revolving mirror M and the wheel W were geared to a small

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No's^''] MOBILITIES OP GASEOUS IONS. 343

electric motor. When in operation the plate registered a horizontal
series of sparks at each revolution of the mirror. Thus the time taken
for P to traverse a distance equal to that between two successive series
of images was the same as the time for M to make one revolution. And
by measuring the speed of the mirror and that of the plate independently
by direct measurements, the results served to check each other, and the
time t taken for one revolution of the mirror could be obtained with
great accuracy.

In view of the fact that the maximum potential was only 5,000 X ^2
volts, the sparks were not very intense when the mirror M was placed
from two to three meters away from the gap. Thus a powerful lens was
necessary to render the images noticeable.

The distance between two successive sparks was determined by photo-
graphing on the same plate, when both M and P were at rest right after
the photographs of the sparks were taken, a horizontal scale inserted
between the gap with its length at right angles to the straight line joining
the gap and the center of the mirror. Thus the image of this scale on
the same plate with those of the sparks enabled the actual — ^and at the
same time the apparent — distances between the latter to be determined
directly.

From the time /, of one revolution of the mirror, the distance 5 between
two successive sparks, and the distance D between the gap and the
mirror, the frequency N of the sparks was computed by using the formula

As the frequency of the sparks was doubled the frequency of the
alternating field we have

^N^2tD

" 2 " ts *

The average of twelve plates taken by the various methods previously
described, and on several different occasions, with different I^s and fs,
gave the frequency mentioned elsewhere in this report.

6. Measurement of Potential and Distance.

The high-frequency oscillating potential was measured, while the deter-
minations were being made, by a calibrated Braim electrostatic volt-
meter having a range of ten thousand volts. The low-alternating poten-
tials were measured at times by an ordinary General Electric voltmeter
and at times by a calibrated Kelvin unicellular voltmeter.

The distance between the gauze G and the collecting plate P were
measured by a cathetometer which gave them an accuracy of o.i mm.

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344 KIA-LOK YEN. [^JS

7. MobiUly Determinations.

In the determinations with high potentials the frequency and the
potential were kept constant, and the distance between the gauze and
the collecting plate was varied. The accumulated charges on the
collecting plate for a chosen interval were communicated to the elec-
trometer quadrants through platinum contact switches, and the deflec-
tions corresponding to the various distances between the gauze and the
plate were recorded. A number of deflections were taken for each
variation of distance.

The determinations with low potentials were made in two ways; by
varying the distance keeping the potential constant, and by varying the
potential keeping the distance constant. In both cases the electrometer
readings were taken as above.

The electrometer deflections were plotted against either the corre-
sponding distances or the corresponding potentials, and the critical
distances or the critical potentials, as the case might be, were determined
by finding the points of inflection on the curves.

The determinations of the positive and negative mobilities were made
simultaneously by reversing the sign of the retarding field.

8. Production and Purification of Gases.

When the determinations were made in air the c6ntent of the chamber
was first pumped out with a Pearson pump and fresh air was let in through
a number of bottles containing concentrated sulphuric acid and a series
of tubes containing calcium chloride and phosphorus pentoxide.

The hydrogen used was generated by a Kipp generator from HCl and
zinc. It was passed successively through bottles containing KOH and
concentrated H2S04f and tubes containing PjOs and CaClj, and then
through two bulbs containing charcoal of cocoanut shell and immersed
in liquid air, before its admission into the chamber. The chamber was
revacuated and refilled three or four times before each set of readings
were taken. This method, in all probability, produced, as far as the
results have shown, very pure hydrogen.

The nitrogen employed in this work was produced by warming a
mixture of sodium nitrite and ammonium sulphate. It was purified,
before its introduction into the chamber, by its passage through solutions
of KOH, FeS04, and concentrated H2SO4, and through tubes containing
PaOs, CaClj, and heated copper. The content of the chamber was, as
it was in the case of hydrogen, vacuated from three to four times before
each set of readings were made.

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Na*s^''] MOBILITIES OP GASEOUS IONS. 345

Part II. Results.

I. Air.

Fig. 2 shows a characteristic set of curves plotted from the measure-
ments with air at atmospheric pressure (749 mm. of mercury). I. and

a
§

Fig. 2.

Air. I. and II. With N - 14.758 cycles; E - 5,000 volta; P - 748 mm.
III. and IV. With iNT - 60 cycles; £ = 118 volts; P - 748 mm.

II. were respectively positive and negative curves obtained with the high
frequency oscillating potential of 5 ,000 volts. The critical distances were,
as it may be seen on the curves, 0.5 cm. for the positive and 0.55 cm. for
the negative ions.

Curves III. and IV. were obtained with the ordinary 6o-cy. iio-volt
alternating potential, i.io cm. and 1.25 cm. were taken as the critical
distances for the positive and negative ions.

The results obtained for air are summarized in Table I. The first and
second columns contain respectively the positive and negative mobilities
computed from the formula,

deduced elsewhere in this report. The third and fourth columns contain
the potential gradients calculated from the formula

A' = — ^•

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346

KIA-LOK YEN,

Table I.

Table of Results Obtained for Ionic Mobilities in Air, February-March, IQ17.
1. 60cy. 119 volts.

£^+.

U^.

^+.

A--.

1.10

A-.

1.12

1.75

168

134

746

1.72

1.56

1.12

1.75

168

134

746

1.10

1.72

1.56

1.12

1.75

168

134

752

1.10

1.73

1.56

1.25

1.73

168

134

742

1.22

1.70

1.38

Mean

1.14

1.72

1.51

2. 14,758 cy. 5.000 volte.

1.64

1.98

14,160

12,870

752

1.62

1.92

1.57

1.84

14.160

12,870

750

1.56

1.82

1.64

1.98

14.160

12.870

749

1.61

1.95

1.57

1.84

14.160

12,870

746

1.55

1.81

1.82

2.10

13.810

12,650

692

1.66

1.92

2.26

2.61

12,300

11,550

558

1.66
1.61'

1.91

1.16

Mean

1.90

1.18

Mean of both sets .

1.37

1.81

1.34

17* + * Mobility of positive ions.

17" — — Mobility of negative ions.

X » Field strength in volt/cm.

P - Pressure in mm. -R - X — /IC +.

K " Mobility at 760 mm. pres.

X -IP Max. - 20.70. Min. - 0.18.

X +/P Max. - 22.04. Min. - 0.22.

In the fifth column are the various pressures under which the determina-
tions were made. Ki represents the positive, and Kt the negative
mobility reduced to the pressure of 760 mm. of mercury. In the last
column 2?, is found the ratio between the positive and the negative
mobilities.

The potential used was as high as 14,160 volt/cm. for the positive and
12,870 volt/cm. for the negative ions. The maximum value of x/p was
20.70 for the negative ions and 22.04 for the positive.

The above results, as it may be seen, show that both the positive and
the negative mobilities remained, within the limits of experimental error,
absolutely normal, and thus no indication whatsoever could be foimd of
there being any tendency of the ions of either sign to disintegrate under
the potentials of the magnitude employed.

These results more than amply substantiated those obtained by Loeb
in his work and it is therefore quite safe to conclude that the evidences
obtained so far point in the direction of the "small ion" theory.

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No's^^'] MOBILITIES OP GASEOUS IONS. 347

2. Hydrogen.

Fig. 3 shows a characteristic set of curves plotted from the measure-
ments on hydrogen with the high-potential high-frequency oscillating
field.

The peculiarity that distinguishes these curves from those previously
obtained for air is the extension of the negative curves II., and IV. —
one obtained under a pressure of 748 mm., while the other under 290 mm.
— beyond the workable range of the apparatus. That this extension
could not be the result of mechanical error is clear from the fact that the
curves obtained for air under similar conditions showed no such extension,
and even in the case of hydrogen the extension made its appearance only
when the chamber was newly filled with gas directly from the generator

X -PMirwr •-N«fiLtl«f« Plat«. di«Un«« mmm.

Fig. 3.

Hydrogen. I. and II. With N - 14.758 cycles; E - 4.OOO volts; P « 748 mm.
III. and IV. With N « 14.758 cycles; E « 4,000 volts; P = 290 mm.

V. taken 7 hrs. after IV. was taken.

VI. with iV - 60; £ = 118 volts; P « 748 mm.

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348 KIA-LOK YEN. [^SS!

and through the purifying agents. When the gas was left in the chamber
for some time this peculiar characteristic disappeared altogether. Curve
V. (Fig. 3) was plotted from measurements on the same content, and
under similar conditions, of course, as that from the measurements of
which Curve IV. was plotted, except that the gas had been left in the
chamber for about seven hours.

Again, this extension could not be attributed to the possibility that
the gas had been charged when it was freshly prepared. In the first
place, in the process of purification, the gas had to pass through twelve
layers of glass-wool located in different parts of the purifying and drying
agents. In the next place if the gas had carried any charge with it on
entering the chamber the presence of this charge would have been
indicated by the electrometer when the gas came in contact with the
collecting plate. As the electrometer did not show any indication, it is
only reasonable to conclude that the gas did not carry any charge at all
when it entered the chamber.

3. Existence of Free Electrons.
The most plausible explanation for this extension, therefore, must be
sought in the existence of free electrons as was suggested by Wellisch.^
On the basis of that hypothesis the deflections constituting the upper
part of the curves II. and IV. may be interpreted to consist of the effects
of both the normal negative ions and the free negative electrons, whereas
those constituting the lower part of the curves may be conceived as
due entirely to the free negative electrons. And such curves as those
represented by V. may be said to be due entirely to normal negative ions.
The ephemeral existence of these free electrons as proved by this latter
case may conceivably be the result either of their fast dissipation into
the walls of the chamber or of their ready formation of negative ions with
the neutral molecules of either hydrogen or the impurities that found their
way into the chamber in the meantime. Whichever way it might be,
it is clear that these results indicate the existence of free negative electrons
in hydrogen — at least in freshly prepared hydrogen.

4. Existence of Other Species of Negative Ions?

As mentioned previously, Haines^ reported that he found two kinds

of negative ions in hydrogen other than the normal negative ions. The

existence of these ions was inferred from the fact that from the curves

he obtained three different negative mobilities could be deduced. These

> Am. Jour. Sd., May. 1915; Phil. Mag., March, 1916.
* Haines, loc. cit.

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Nol"^'*] MOBILITIES OF GASEOUS IONS. 349

mobilities were 40.6, 15.9 and 7.9 respectively. Thus from these mobili-
ties he inferred that the number of hydrogen molecules constituting the
positive and the three species of negative ions were respectively 9, 6, 3,
and I, at 76 cm. pressure and 15° C.

An effort was made to search among the results of the present experi-
ment for premises from which the above mobilities could be inferred.
And since, by virtue of the method employed, the inflections of the curves
were the only ground on which computation of mobilities was based, the
various curves were closely scrutinized to see if more inflections could not
reasonably be found. Take Curve II. (Fig. 3) for example: if Haines's
ions existed in the present experiment, there would be besides the inflec-
tion at the plate distance of 10 mm., two other inflections, one at about
14 mm. and the other at a distance of between 23 and 25 nmi. As all

Fig. 4.
Hydrogen. With P — 752 mm.; d — 2.0 cm.; AT — 60 cycles per sec.

efforts toward this end proved of no avail, it was concluded that either
there were no such ions at all as Haines's B and C, or that they were
actually present, only that the disposition of the apparatus employed
was not sufficiently adequate for their detection. Furthermore, if it
could be proved that these ions were not present the question still
remained as to whether they were non-existent in general, or whether
they did actually exist in Haines's but not in the present experiment.

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350 KIA-LOK YEN. [^2S

On account of the above considerations the experiment was diverted
to a slightly different direction. It was for the sake of the ratification of
the method and apparatus thus far employed that an attempt was made
to repeat Haines's experiment. Haines's experimental conditions were
reproduced as exactly as possible according to his descriptions* with the
expectations of obtaining similar results.

The results of this attempt were typified by the curves in Figs. 4 and 5.
As it may be seen, there were striking similarities between these curves

Fig. 5.
Hydrogen. P — 498 mm.; d — 2.0 cm.; ^ — 60 cycles.

and those obtained by Haines from whose report Fig. 9 was copied;
excepting the absence from the former of the inflections from which
the mobilities 40.6 and 15.9 might be computed. The abundance of
free electrons at the start manifested itself very markedly in all the
curves obtained; and this would seem to vitiate all possible questions
regarding the purity of the gas. The normal negative ions — namely those
having the mobility 8.45 according to this experiment, or 7.9 according
to Haines's — ^were distinguished by the definite inflections and intercepts
of the curves.

Thus, these results agree with those of the employment of the high-
frequency high-potential oscillating field in pointing to the conclusion
that there were, in all probability, no other species of negative ions in
hydrogen besides the one kind that were ordinarily found.

» Haines, Phil. Mag., S. 6, Vol. 30. 1915-

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Na's!^^'] MOBILITIES OF GASEOUS IONS. 35 I

Perhaps it will be proper to mention here the fact that no sooner had
the above conclusion been arrived at than it received corroboration from
Wellisch's latest paper^ in which it was reported that no trace could be
found of Haines's ions B and C

But how did Haines come to get these different mobilities? Such a
question is not at all superfluous, since the spirit of experimental method
demands a reasonable explanation for each and every apparent fact, and
a mere denial or a conclusion to the contrary effect can no more explain
away what had been considered fact than it can cause the earth to revolve
in the opposite direction. A careful study of Haines's figures seemed to
point to the possible ground on which some explanations may be based.
The part of the curves below the point ^4, as it may be seen from Fig. 6,

Fig. 6.

Haines's curve for hydrogen, reproduced from Phil. Mag., S. 6., Vol. 31,
p. 340, Fig. I, April, 1916.

which is a reproduction of his Fig. i, shows irregularities which might
very well be due to the fluctuation in the electrometer deflections caused
by residual charges on the insulating material near the collecting plate.
This source of disturbance was found in the present experiment to be the
most troublesome, particularly when the high frequency oscillating field
was employed. Besides, even without any promiscuous charges, fluctua-
tions of some sort in the electrometer deflections were unavoidable, though
they would not be so high, in most cases, to confuse the legitimate results
provided proper precautions were taken; and no attempt was made to
draw the curve to pass all the points. For instance, the portions of the
curves in Figs. 4 and 8 corresponding to the parts of those in Fig. 7, in

> Wellisch, Phil. Mag., S. 6, No. 199. p. 32, July, 1917. This number of the Phil. Mag.
reached Ryerson Lab. just after the work was completed.

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352 KIA-LOK YEN.

which the inflections B and C occurred, might be drawn in such a way as
to have as many inflections as there were points; and with some imagina-
tion equally as many different mobilities might be deduced and hence as
many kinds of ions might be inferred therefrom. But would these inflec-
tions be definite enough to justify the might-have-been conclusions? The
answer seemed to be decidedly n^ative. A comparison of the inflections
B and C with those designated by A in Haines's curves would conduce at
once to the conclusion that the former were not sufficiently definite to
justify the inference of any sort of n^^ative ions other than the normal.
The lower parts of Haines's curves could be interpreted to indicate noth-
ing other than the gradual decay of the ephemeral free electrons. Even
Haines himself was not quite definite, as he said, about the existence of
that class of ions he designated by C.

Thus while it would not be in keeping with the spirit of modem experi-
mental methodology to make any dogmatic statement regarding the
existence or non-existence of these other kinds of negative ions in hydro-
gen, there seems to be in Haines's experiment no evidence of the existence
of these other ions which he claimed to have discovered.

Aside from the fact that no indication of these ions could be found in
the present experiment, and that there was no evidence inherent in
Haines's results of their existence, there were positive experimental
evidences against them. Franck^ had found the mobility of the rest-
atoms, namely the positively charged atoms of thorium D, in hydrogen,
the same as that of the positive hydrogen ions. Now, as the molecular
weight of hydrogen is 2 and that of thorium D is 208, it would follow,
so reasoned Franck on the basis of the theory which led Haines to infer
these other ions, that the positive hydrogen ion must consist of at least
20 hydrogen molecules in order to have the same mobility as the restatom.
That being the case, the normal negative ion, according to the ratio
given by Haines, must be a cluster of at least 14 molecules, and the
supposed ions B and C must be constituted respectively by at least 7 and
2 molecules. Whether the number of molecules constituting the various
species of ions be deduced from the results of Franck or from those of
Haines, it would be expected that the ions would disintegrate when a
high electric field was applied; only the disintegration would occur
much sooner if the former were the case. Furthermore if disintegration
did appear it would appear with the positive ions first, then with the
normal negative ions, and then with the other; and if there were ions
that were likely to remain intact it would be the ions designated by

» J. Franck. Ver. d. Deut. Phys. Ges.. 11. 397. 1909. Also Franck u. J. Weitner. Ibid.
13, 671, 1911.

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No's^'l MOBILITIES OF GASEOUS IONS. 353

Haines as C. In other words, the positive and the normal negative ions
would be the first to dissociate, and their dissociation would manifest
itself in the disappearance of the inflections of the curves from which
their normal mobilities were computed, and there would remain only the
inflections indicating the mobilities of C — ^and possibly B. But as the
results of the present experiment showed the positive and the negative
mobilities to remain absolutely normal imder the high field employed,
whereas no indication of the higher mobilities could be found, it is
evident that no combinations such as claimed by Haines ever existed and
that each ion was a single charged molecule. If, on the other hand,
Franck's conclusion that the mobilities of ions were independent of their
masses^ was accepted, then it would at once shatter the foundation upon
which these various congregations of molecules called ions were built.

Thus it can be asserted with reasonable certainty that there existed
in hydrogen no species of negative ions other than the one kind which
was constituted by a single negatively charged molecule.

5. Relative Amount of Free Electrons under High and Low Potential.

As to the amount of free electrons found at high potential as com-
pared with that found at low potential no absolute comparison could
be made. Such comparison was rendered impossible by the difference
between the time necessary for one and the other set of measurements.
A set of measurements with the high-frequency high-potential oscillating
field took from two and a half to three hours, whereas a set of measure-
ments with the low-potential took only from forty-five minutes to an
hour. Thus in the former case the rate of dissipation of the free electrons
was great in comparison with the rate at which the measurements were
made, and undoubtedly a large proportion of the free electrons had
decayed before the measurements were completed. That this was the
case may be seen from Figs. 4 and 5 where the slope of the lower part of
the curves dropped considerably when the measurements were made a
few hours later.

However, an approximate comparison may be made between the
critical distances and potentials in the two cases by making proper
allowance for the aging effect. Thus a comparison may be made between
curve II., Fig. 3, and curve II., Fig. 4. In the case of the former the
chamber was freshly filled just before the measurements were started;
and the measurements represented by the point A were made about an
hour and a half afterwards — that is, at the middle of the set. Curve II.,
Fig. 4, was taken three hours after the chamber was filled. Thus the

» J. Franck, loc. cit.

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354

KIA-LOK YEN,

measurements represented by A in Fig. 3, and those represented by A'
in Fig. 4, may be considered as taken when the gases in the two cases
were approximately of the same state in so far as aging effect is concerned
— A of course was reached an hour earlier. Now, at the point A the plate
distance was 10 mm., the potential was 4,000 volts, and the pressure
was 748 nun., while at the point A' the plate distance was 20 mm., the
potential 56 volts, and the pressure 752 mm. If the amount of free
electrons was the same in both cases A should have a much greater
ordinate than A'. But just the reverse is shown by the curves. Thus
it would be reasonable to conclude that at these points the amount of
free electrons was less in one than in the other case. And since the
aging effect, the only factor found thus far to have any influence upon
the amount of free electrons present in the gas, was approximately the
same in both cases, and since the only difference between the conditions
under which the measurements were made was that of potential, it
follows that the amoimt of free electrons present in the gas was smaller
imder high than under low potential.

This would seem to suggest that the electrons — some of them at least —
did actually attach themselves to neutral molecules and thus form, when
a high potential was applied, negative ions. This would not be at all
impossible since the tremendous velocity imparted to them by the high
electric field would enable them to produce ions from neutral molecules
by attaching themselves to the latter at collision. It would be interesting
to find out where, that is, at what potential — other conditions remaining
the same — this sort of ionization actually would begin.

6. Summary of Results for Hydrogen.
The results of the mobility measurements for hydrogen are given in
Table II. The annotations of the various columns are similar to those
of Table I.

Table II.

Results Obtained from the MeasuremeiUs on Hydrogen, May-June, IQ17,
1. 14,758 cy. 4,000 volts.

i/4-.

I/—.

-v+.

X—,

/r+.

A'—.

Jf.

5.51

8.20

6,669

5,668

748

5.43

8.10

1.49

5.92

8.20

6,669

5,668

748

5.81

8.10

1.38

5.51

8.20

6,669

5,668

746

5.40

8.10

1.49

8.20

12.21

5,668

4,723

518

5.58

8.35

1.49

14.94

20.99

4,192

3,524

290

5.70

8.15

1.41

14.94

20.99

4,192

3,524

300

5.84

8.35

1.41

Mean

5.56

8.19

1.45

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Vol. XI.1
Nas. J

2. 60 cy.

MOBILITIES OP GASEOUS IONS,

355

5.28

77.8

748

5.21

5.50

8.80

25.0

16.5

746

5.41

8.65

1.52

6.60

11.19

20.0

13.0

600

5.22

8.80

1.62

8.95

13.28

29.5

24.0

498

5.85

8.70

1.48

13.90

22.00

19.8

11.5

300

5.49

8.69

1.58

22.91

31.06

16.5

9.0

198

5.95

8.15

1.34

9.26

28.0

746

9.26

....

Mean

5.52

8.71

1.57

Mean of both fre-

5.54

8.45

1.51

quencies

X -IP

Max. - 12.15.

Min. - 0.38.

X +IP

Max. - 14.45.

Min. - 0.66.

It may be seen that with a potential gradient of 6,669 volt/cm.,
or x/p = 14.45, the positive mobility remained absolutely constant.
The negative mobility remained constant with 5,668 volt/cm., and

Nitr»,,n J,^^^^ i>.-.t«^ce m mm.

Fig. 7.
Nitrogen. P « 750 mm.; N - 14,758 cycles; E « 5,000 volts.

x/p = 12.15. Thus it can be concluded that the law Up = constant
was verified for hydrogen up to these limits.

7. Nitrogen,
Fig. 7 shows the kind of curves obtained for nitrogen under the high-
potential oscillating field. The negative curve here exhibited no exten-

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356 KIA-LOK YEN. [^^

sion and thus indicated the absence of free electrons during the measure-
ments. As there were in the low-potential measurements indications of
the presence of free electrons it seems highly probable that the complete
disappearance of them under the high field was due to their forming
negative ions with the neutral molecules.

The presence of an abundance of free electrons is indicated by the
curves in Fig. 9, plotted from the measurements under 140 mm. pressure.

However, as it may be seen from Fig. 8, the amount of free electrons

Fig. 8.
Nitrogen. P - 360 mm.; d — 1.0 cm.; iV « 60 cycles.

present in nitrogen was much smaller than that in hydrogen at the same
pressure.

The aging effect here, as it was in the case of hydrogen, was to reduce
the amount of free electrons. This might be due to the dissipation of the
electrons into the wall of the chamber or to the presence of impurities
which had crept in in the meantime.

Table III. shows a summary of results obtained for nitrogen. The
maximum potential gradient employed was 17,670 volt/cm., for the
positive, and 14,880 volt/cm., for the negative ions. The mobilities
remained absolutely normal up to these limits and the law Up = constant
is applicable here as it was in the case of air and hydrogen.

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Vol. XL!
No. 5. J

MOBILITIES OP CASEOUS IONS.

357

1. 60 cy.

Nitrogen Viyfts

Fig. 9.
Nitrogen. P - 140 mm.; d = 2.0 cm.; iV - 60 cycles.

Table III.

Results Obtained for Nitrogen, July, 1917.

i/+.

U".

XAr.

X-,

A-^-.

A--.

17.60

llSid

15.0

11.5

1.39

1.81

1.30

....

10.15

• • . .

26.0

140

1.87

....

2.81

3.88

47.0

33.5

360

1.33

1.84

1.38

1.27

1.65

51.0

40.0

750

1.26

1.62

1.30

1.36

1.84

50.0

38.0

745

1.33

1.80

1.35

1.34

1.82

49.8

38.0

745

1.31

1.78

1.36

Mean

1 1.32

1.79

1.34

2. 14.758 cy. 5.000 volts.

1.31

1.84

17,670

14,880

750

1.29

1.82

1.40

1.31

1.84

17.670

14.880

745

1.28

1.80

1.40

1.31

1.84

17.670

14.880

742

1.28

1.80

1.40

2.76

3.93

13.910

10.110

360

1.31

1.86

1.42

2.76

3.93

13,910

10.110

345

1.26

1.78

1.42

Mean

1.28

1.81

1.41

Mean of both Ire-

1.30

1.80

1.38

quencies

A--/P

Max. - 29.0.

Min. - 0.05.

X+IP

Max. - 40.0.

Min. - 0.07.

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358 KIA-LOK YEN. [^^

Conclusion and Discussion.

As no indication was exhibited by the results of the present experi-
ment of the breaking down of the law Up = constant, it must be con-
cluded therefrom that both the positive and the negative ions did not
disintegrate at the potentials employed.

It has been indicated elsewhere in this paper that the cluster hypothesis
demands the disintegration of the ions when the potential gradient X,
or the ratio Xjp (where p is the pressure in mm. mercury) is sufficiently
high. According to Townsend* the disintegration should commence
when Xjp is about o. i . In the present experiment the potential gradients
applied were 14,160, 6,669, ^^d 17,670 volt/cm., respectively, for air,
hydrogen, and nitrogen, when the positive mobilities were measured.
The values of Xjp here ranged from 0.22 to 22.04 for ^r, 0.66 to 14.45
for hydrogen, and 0.07 to 40.0 for nitrogen. The negative mobilities
were measured at potential gradients as high as 12,870, 5,668, and 14,880
volt/cm., for the gases in the order named. The values of Xjp here
ranged from 0.18 to 20.70 for air, 0.38 to 12.15 for hydrogen, and 0.05 to
29.0 for nitrogen. As the results show no tendency on the part of either
the positive or the negative ions to disintegrate under these conditions
they must be interpreted as contradictory to the hypothesis.

On the contrary, these results are in perfect agreement with the atom-
ion hypothesis. Taking this in conjunction with the results of other
experiments, especially those of Wellisch and Loeb, there does not seem
to be any doubt at all regarding the validity of this hypothesis; and the
cluster hypothesis must resort to other than the usual arguments for
its support.

There is left an experimental fact which the cluster hypothesis may
conceivably rely upon for support, and that is the difference between the
positive and negative mobilities found by actual measurements. On the
basis of the cluster hypothesis the relatively smaller mobility of the
positive ion is attributed to its greater size as compared with the negative
ion. It is argued that if both the positive and the negative ions are
single-charged molecules why should they have different mobilities when
their charges and sizes are the same? The difference between the posi-
tive and the negative mobilities therefore must be conceived as due to
the difference between the sizes of the two kinds of ions. The positive
mobility being smaller, the positive ion must therefore be heavier. This
appears quite plausible at first sight; and it does seem, indeed, as though
no such reasonable explanation could be offered by the exponents of the
small ion.

■* Townsend. Electricity in Gases. Oxford, 1915.

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No's^^'] MOBILITIES OF CASEOUS IONS. 359

This difficulty of the small-ion hypothesis, however, is more apparent
than real. For, in view of recent theories as to the electronic constitu-
tion of matter it would not be reasonable for the exponents of the small
ion to expect equality between the two kinds of mobilities. The ordinary
theoretical derivation of the formulae for mobilities, it should be re-
membered, involved a fundamental presupposition that the mean free
path is the same for the positive as for the negative ions. That this
assumption is unjustifiable will be seen from the following considemtions.

If an atom is formed by a positive nucleus surrounded by a system of
negative electrons held together by attractive force from the nucleus,*
the phenomenon of ordinary molecular collision must be attributed to
the repulsion between the two systems of negative electrons on the
colliding molecules. "The reason that two molecules thus rebound
from one another when in their motion of thermal agitation their centers
of gravity approach to a distance of about 2 X lO"^ cm., is presumably
that the atom is a system with negative electrons in its outer regions.
When these negative electrons in two different systems which are coming into
collision approach to about this distance, the repulsions between these simi-
larly charged bodies begin to be felt, although at a distance the atoms are
forceless. With decreasing distance this repulsion increases very rapidly
until it becomes so great as to overcome the inertias of the system and drive
them asunder.** *

There does not seem to be any reason why the above conception may
not be extended to the case of a collision between an ion, which is a
charged molecule, and a neutral molecule. When the ions approach
the neutral molecules the negative electrons in the two systems are
brought close to each other and the force of repulsion between these
peripheral electrons will begin to manifest itself.

Thus between an ion and a neutral molecule there exists, besides the
attraction due to the charge in the ion, a repulsion due to the peripheral
negative electrons. These two forces would effect the mean free path
of the ions in opposite direction — the former causing it to decrease while
the latter cause it to increase — ^and the effective mean free path would
depend on their algebraic sum.

Furthermore, if the process of positive ionization consists in the detach-
ment of a single negative electron from a neutral molecule, and that of
negative ionization consists in the attachment of a negative electron to
a neutral molecule, it should be expected that the repulsive forces would
be different when the two kinds of ions collide with a molecule which is

» Rutherford. Phil. Mag.. XXI.. 669. 191 1.

* Millikan. The Electron, 181, 1917. Italics mine.

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360 KIA-LOK YEN.

not charged. The repulsion between a negative ion and a neutral
molecule would be greater than that between a positive ion and a neutral
molecule, since there are more negative electrons in the n^ative ions
than in the positive.

Thus, assuming that the attraction between the positive ion and the
neutral molecule is the same as that between the n^^ative ion and the
neutral molecule — and there is every reason to suppose this to be the
case — ^we should expect the effective mean free path to be greater for the
negative ion than for the positive. And since the mobility is proportional
to the effective mean free path the negative mobility would be greater than
the positive.

An illuminating example of this may be derived from the Bohr atom*
which is an embodiment of the nucleus atom. As we are here primarily
interested in the molecule we may take as example the Bohr hydrogen
molecule,* which is the simplest treated. A hydrogen molecule here is
conceived of as a system of two positive nuclei situated at a distance 26
apart with two negative electrons travelling in a circle of radius a in the
plane perpendicular to and bisecting the axis joining the nuclei. Ex-
tending this conception to the hydrogen ions, we have the positive ion
consisting of a single negative electron, and a negative ion of three
negative electrons, all circling about an axis joining two positive nuclei.
Thus the number of negative electrons in the colliding systems would be
5 in the case of a collision between a negative ion and a neutral molecule,
and 3 in that of a collision between a positive ion and a neutral molecule.
The ratio of the negative to the positive mobilities must somehow vary
with the ratio of 5 to 3 — although the writer is not prepared at present
to say what sort of proportionality there exists between the two quan-
tities.

From this point of view we may expect the ratio of the negative to the
positive mobility to approach unity as the total number of negative elec-
trons in both the ions and the neutral molecules increases. For, as the
difference between the total number of negative electrons in a positive
ion colliding with a molecule and that in a negative ion colliding with a
molecule is always two, it can easily be seen that this difference would
not result in an appreciable difference in the ratio between the two
numbers when they are sufficiently large. This is what has actually
been found in the cases of gases the molecules of which are of a more
complex structure. The positive mobility is found in these gases to
approach the negative.

» Bohr. Phil. Mag.. XXVI.. 1913. PP- i. 476 and 857; XXIX.. 191S. p. 332; XXX..
191S. p. 394.

« Phil. Mag.. XXVI., 1913. p. 863.

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Na*^^*] MOBILITIES OF CASEOUS IONS. 36 1

Furthermore, as the repulsive force varies inversely with the distance
between the colliding systems it follows that the more peripheral the
negative electrons are the smaller this force would be. And hence with
charged and uncharged molecules of gases of more complex structure the
repulsive forces would be very nearly the same whether the ion contains
one more or one less negative electron than the imcharged molecule.
Thus we should expect the two kinds of mobilities to approach each other
in the cases where the gases are of a more comlpex nature.

But the above explanation for the differences between positive and
negative mobilities would not be applicable to the cases where the ratio
of the negative to the positive is less than unity. This would be a real
stumbling block indeed if the mobilities in such cases had been accurately
determined and the differences found between them had been sufficiently
great. As far as evidences are available the differences between the
positive and negative mobilities are, when the former are greater, never
more than a few per cent., which may very well be due to experimental
fluctuations.

However, an experiment is now in progress to redetermine the mobilities
of some of the gases in which the positive had been found to be greater
than the negative, and until conclusive evidence resulted in the actual
establishment of real differences which cannot be attributed to experi-
mental fluctuations, the above explanation seems to be the most reason-
able one so far advanced.

Summary.

To reiterate then :

1. The previous experiment of Loeb on the ionic mobilities in air has
been repeated and confirmed.

2. The law Up = constant was found to hold for the negative ions
from 134 to 12,870 volt/cm. or from X/p = 0.18 to 20.70; and, for
positive ions from 186 to 14,160 volt/cm., or from X/p = 0.22 to 22.04.

3. The experiment was extended to hydrogen and nitrogen, and the
law Up = constant was found to hold in both cases.

4. The law Up = const, was verified in hydrogen for negative ions
from 9 to 5,668 volt/cm. or from X/p = 0.38 to 12.15; and for positive
from 16 to 6,669 volt/cm. or from X/p = 0.66 to 14.45.

5. In nitrogen, negative mobility was found to remain constant from
II to 14,880 volt/cm. or from X/p = 0.05 to 29.0; and the positive
mobility constant from 15 to 17,670 volt/cm., or from X/p = 0.07 to 40.0.

6. Free electrons were found to exist in both hydrogen and nitrogen
even at atmospheric pressure; more in hydrogen than in nitrogen.

7. More free electrons were found with low potentials than with high
potentials.

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362 KJA'LOK YEN. ^SSSl

8. The aging effect upon the gases at constant pressure was to reduce
the relative amount of the free electrons.

9. No indication was found oC Haines's n^ative ions B and C and in
general no indication was found so far which would prove to be favorable
to the cluster theory.

10. The difference between positive and negative mobilities are ex-
plained by the nucleus-atom theory, and an experiment is now in progress
with the gases where the proposed explanation does not seem to be
applicable.

In conclusion the writer wishes to register his appreciation and grati-
tude to Professor R. A. Millikan for the kind encouragement and direction
he received during thfe present experiment. He also wishes to thank Dr.
A. J. Dempster, to whose enthusiasm and experience he resorted during
Professor Millikan 's temporary absence from Ryerson Laboratory. And
finally he wishes to express his appreciation for his initiation into the
technique of the experiment by Dr. Leonard B. Loeb, his friend and
former colleague.

Rybrson Laboratory,

The University of Chicago.

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Vol. XL!
Nas. J

ELECTRICAL RESISTIVITY OF CARBON.

363

EFFECT OF HYDROGEN ON THE ELECTRICAL
RESISTIVITY OF CARBON.

By T. Pbczalski.

/^"^ERTAIN measurements made on the change in the resistance of a
^^-^ carbon filament, first when heated in vacuum and then in a gas
to the same temperature, showed changes which were opposite in direction
from what might be expected due to the changes in temperature inside of
the filament. This was especially noticeable in hydrogen and a further
study has led to the results here described.

Effect of Hydrogen on Resistivity of Carbon at Room

Temperatures.
Description of Apparatus. — ^The apparatus is shown diagrammatically
in Fig. I, in which there is represented a small chamber capable of with-

BtZ=Z Br

Fig. 1.
Diagram of apparatus.

standing pressures of several atmospheres. It contained a window W
and a screw S which was electrically insulated from the wall. To this
screw and to a projecting copper wire I on the opposite wall, a carbon
filament F was fastened by means of paste P such as is commonly used
in carbon lamps. The filaments used, which were kindly furnished by
Dr. Moore, of the National Carbon Company, were about 1.6 mm. in
diameter, 10 cm. long and composed of coke carbon. By means of small

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364

T, PECZALSKI.

tubing, connections were made through the necessary valves with a
pressure gauge G, a hydrogen tank H and a vacuum pump V. The ends
of the filament were connected with a battery Bt and a Wheatstone bridge
Br, as is indicated in the diagram.

Measurements. — ^The method of procedure for the most part has been
as follows: The chamber was first evacuated and the resistance of the
filament (F) measured. Then the filament was electrically heated and,
after cooling, the resistance was measured again. Several repetitions of
the resistance measurements were made until steady state values had
been obtained. Following this hydrogen was passed into the chamber.
The resistance was again measured after a steady condition had been
reached; then the filament while thus immersed in the gas was reheated
to the high temperature for a short time. Again after cooling the

Table I.

The Resistance of a Carbon Filament in Hydrogen Maintained at Room Temperature under

Various Pressures.

Resistance.

Pressure in Atmospheres.

Time.

2.740 ohms

l(air)
24 (hydrogen)
24
33
24

In
10 n

4 hours 30

5 " 45

21 " 30

22 " 10

2.740 "

linute

2.760 "

linutes

2.750 "

2.740 "

2.755 "

2.735 "

Fig. 2.

Cold resistance changes of a carbon filament following several consecutive heatings in
hydrogen (cross-hatched) at 33 atmospheres and in vacuum (not cross-hatched). The dura-
tions of the intervals of heating in seconds are indicated by the numbers just below the plat.

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Vol. XI.I
Nas. J

ELECTRICAL RESISTIVITY OP CARBON.

365

resistance was measured. The temperatures (approximately 2,000° K.)
were roughly determined by comparing the color of the luminous flux
from the filament with that from a standard source by means of an
ordinary photometer arrangement.

As a preliminary test the resistance of a filament was measured, first
in a vacuum and then in hydrogen under a high pressure. These meas-
urements were continued for about twenty-four hours to see whether
the effects observed could be accounted for without heating the filament
to high temperatures. The results of such a test are indicated in Table I.
These results are not sufficiently accurate to prove the existence of a
variation in the resistance of the filament in hydrogen under pressures
varying from very nearly o to 33 atmospheres.

Following this a new filament was placed in the chamber and its

Fig. 3.

Cold resistance changes of a carbon filament following several consecutive heatings in
hydrogen (cross-hatched) at 3 atmospheres and in vacuum (not cross-hatched). The duration
of the intervals of heating in seconds are indicated by the numbers just below the plat.

resistance was measured at various times in conformity with the general
plan outlined above. The accompanying resistance changes (always at
room temperature) throughout the experiment are recorded in Table II,
and shown graphically in Fig. 2.

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366

r. PECZALSKI.

I Second
Sbbibs.

Similar measurements made on another filament but with the hydrogen
pressures of the order of 3 atmospheres, gave results which are platted in
Fig. 3. It is to be noted that the results are exactly similar in character
to what were obtained at the higher pressures but that the effects are
less in magnitude.

Table II.

The Resistance of a Carbon Filament in Hydrogen and in Vacuo after Having Cooled to Room
Temperatures^ FoUowing Heatings for Short Intervals at about 2^000^ K,

Time.

Prestura.

Resistance.

Duration of Heatinf Just

Following Previous
Resistance Measurement.

0 hr. 0 min.

Oatm.

2.780 ohms

1 0

2.257

5 sec.

1 30

1.800

1 33

1.805

fl 36
ll 39

1.910

1.905

—

fl 44
11 48

1.995

1.992

—

1 50

2.000

f 1 56
ll 59

1.858

—

f2 4
12 7

1.768

1.767

—

2 10

1.768

(2 14
12 17

1.820

1.815

—

2 24

1.890

19 0

1.915

—

19 5

1.913

f 19 8
119 12

1.850

1.843

—

19 19

1.853

19 24

1.845

—

(19 28

1.940

• 19 30

1.930

—

1 19 35

1.927

—

fl9 40

1.990

19 43

1.988

—

1 19 45

1.988

—

119 50
119 56

2.033

—

In this work the precision of measurements was of the order of i per
cent. This uncertainty was due largely to the change in the temperature
of the room and of the chamber containing the filament. Careful meas-
urements of the resistance of a similar filament at room temperature
and at 1,590*^ K. indicate an average temperature coefficient of — 0.00027

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Vou XI.l
Nas. J

ELECTRICAL RESISTIVITY OP CARBON,

367

per degree. The room temperature changes together with the slight
heating of the tank can account for 50° variation as a maximum in the
low temperatures at which resistance measurements were made. This
would account for a change of 1.3 per cent, in resistance. It is probable
that the variation was never as great as this, however.

The experiments already described were carried out under conditions
which resulted in a rapid disintegration of the filament. Equilibrium
conditions were not obtained in any instance. In order to further verify
the apparent effects and to determine roughly some further character-
istics, six regular lamp filaments of untreated carbon were mounted in
lamp bulbs, exhausted, burned in vacuo for some time until the initial
well-known resistance variations had been eliminated, and then carried
through a set of measurements similar to those already described. There
were these differences, however. The incandescent temperatures ob-
tained were considerably lower in this set, and the filaments were operated
in vacuo or in hydrogen until equilibrium states had been approximately
reached. Of the six lamps only two survived a complete cycle. The
cold resistance for one of these as a function of the time the filament
had been heated to incandescence is shown in Fig. 4. The results for the

yr-»-

= =-

—

Fig. 4.

Cold resistance changes of a regular untreated carbon lamp filament following successive
heatings to incandescence in vacuo (00) and in hydrogen (xx). The filament had been pre-
viously aged and therefore had reached a steady state previous to these observations.

Other lamp surviving the cycle as well as the results as far as they were
obtained on the other four lamps fit in with this plat. In nearly all cases
there were a few erratic measurements such as the one corresponding to
a time of heating of 128 minutes in Fig. 4. No explanation other than
accidental errors is offered for these. Also no significance is to be
attached to the apparent discontinuities at the points of change from
hydrogen to vacuum and vice versa, since at these points the lamps were
rebased and small accidental changes in resistance may have occurred.
R^ardless of these, the gradual asymptotic changes from one equilibrium
state to another suggestive of an exponential law, seem definitely demon-
strated.

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368 r. PECZALSKi. [gj^

It is to be noted (i) that the filament apparently maintains its resis-
tance unchanged in vacuum or in hydrogen up to pressures of 33 atmo-
spheres for an indefinite length of time provided that it is not heated
appreciably above room temperatures; (2) that a new filament decreases
considerably in resistance (approximately 35 per cent.) due to a short
heating in a vacuum; (3) that after every heating in the hydrogen the
resistivity of the carbon increases asymptotically with time; and (4)
that after every heating in the vacuum the resistivity of the carbon
filament (already previously heated in hydrogen) decreases asymp-
totically with time and quantitatively by about the amount of the
preceding increase, in case the filaments are not seriously disintegrated
by the process.

The Effect of Hydrogen on the Resistivity of Carbon at
Incandescent Temperatures.

Description of Apparatus. — In order to determine the resistance varia-
tions at incandescent temperatures the above method, modified some-
what, was made use of. For this test filaments similar to those already
described were mounted in* large glass lamp-bulbs. In order to eliminate
any errors due to the cooled portions of a filament near the lead-in
wires and of the changes in resistance of these lead-in wires, potential
leads of timgsten were inserted, which were attached to the filament at
points sufficiently remote from the pasted junctions to insure measure-
ments on a fairly uniformly heated portion. In order to insure that the
temperature of the incandescent filament was the same when heated in
vacuum and in hydrogen to within a negligible error, the lamp containing
the filament and a standard lamp were moimted at the opposite ends of a
photometer bench, and a nearly constant temperature throughout the
experiment was maintained by keeping the luminous intensity of the
filament constant. The uncertainty in this temperature was not greater
than 10°, which corresponds to a variation in resistance less than 0.3
per cent., an effect which is negligible.

Measurements. — ^The lamp was first evacuated by means of a molecular
pump and brought to the desired temperature, a brightness temperature*
of 1,590® K., as directly determined by Dr. Forsythe. By means of a
potentiometer the resistance of the lamp as a whole and also of that
portion of the filament between the potential terminals were then
measured. After a fairly steady state was reached, as indicated by suc-
cessive readings, the filament was allowed to cool to room temperature
and the resistances were measured again. Then with hydrogen intro-

> Hyde, Cady and Forsythe, Phys. Rev., II., 4, p. 396, 191 7.

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Vol. XL!
Nas. J

ELECTRICAL RESISTIVITY OF CARBON.

369

duced, resistance measurements at the previous high temperature were
made; then again at room temperature, and again on heating up to the
previous high temperatiu^ in vacuum, and finally at room temperature
as before. The exact values of current, potential, resistance and tim^
occurring in a special case are indicated in Table III. The resistance
variations are shown graphically in Fig. 5.

Table III.

Resistance of a Carbon Filament at Incandescent and Room Temperatures when in Hydrogen at
J Atmosphere and in a Vacuum,

Portion Between Potential Leads.

Lamp

at a

Whole.

7^/C.

f Am-
peres.

t Volts.

Ohms.

r' Volts.

Ohms.

1 1 1
Heating in the vacuum

1590

11.170
11.189

17.961
17.981

1.608
1.607

23.736
23.780

2.125
2.125

101
10

lours 20 minutes

" 30 "

Heating current turned off

u 31 u

300 (approx.)

1 3.050

" 53

1 3.050

" 43 "

Hydrogen passed into the lamp

" 55 "

1590

13.486
13.459

21.967
21.995

1.629
1.634

29.234
29.303

2.168
2.178

1
1

" 20

u 31 1.

13.412

22.020

1.642

29.351

2.188

" 40 "

13.388

22.022

1.645

29.363

2.193

" 55 "

13.354

22.002

1.647

29.353

2.198

Heating current turned off

II 5 II

300

1 1 1

1 3.250

3
3

" 20

1 1 1 • •

The lamp was evacuated

" 30 "

1590

11.374
11.305

18.494
18.353

1.626
1.623

24.608
24.429

2.164
2.161

3
3

•• 40 "

M 49 U

11.268

18.237

1.618

24.263

2.153

" 00 "

11.271

18.179

1.613

24.196

2.147

II 12

11.308

18.104

1.601

24.097

2.131

II 27 •*

11.410

18.092

1.586

24.110

2.112

II 37 II

11.384

17.949

1.576

23.931

2.102

II 47 u

11.372

17.861

1.571

23.810

2.094

" 56 "

Heating current turned off

II 57 u

300

3.090

1. 39 II

(next day)

In general the table and plat show a progressive increase in resistance
of ^he filament when heated in hydrogen at a brightness temperature of
1,590° K., which amounted to about 3.5 per cent, at this temperature
and a similar change of approximately 6.5 per cent, in the value at room
temperature. The effect is reversible. There are superposed upon these
changes some secondary effects, such as the sublimation of the filament,
the allotropic transformation of the carbon, etc. These secondary effects,

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370

r. PECZALSKI.

however, do not mask the prindpal effects of increasing the resistance by
heating the filament in hydrogen and of decreasing by heating in vacuum.

Repeated measurements on various
filaments showed same general results.
Tests made on a lamp which was
evacuated and sealed off after the
filament was heated in hydrogen
showed evidence of the evolution of
gas from the filament which was de-
tected by means of the ordinary high
frequency discharge method.

Fig. 5.
Resistance of a carbon filament lamp
under various conditions in hydrogen
(cross hatched) and in vacuo (not cross-
hatched), as a function of time that the
filament is incandescent (a brightness
temperature of i,590** K.).

A. Resistance of lamp as a whole at
incandescence.

B. Resistance of filament between po-
tential leads while at incandescence.

C. Resistance of filament as a whole
at room temperature following successive
changes from hydrogen to vacuum, etc.

given temperature and pressure.

Possible Explanation of
Phenomena.
The changes in resistance, together
with the giving up of gas on the
heating in vacuum show that absorp-
tion of hydrogen by the carbon fila-
ment takes place. The ordinary ab-
sorption of gas by porous substances
in which there is a purely mechanical
entrance of the molecules of gas into
the pores cannot explain the observed
phenomenon. Gas thus mechanically
absorbed disappears when the absorb-
ing substances is placed in a vacuum
or when heated to moderate tempera-
tures such as 300° C. According to
the measurements here recorded it is
evident that only a portion, if any, of
the gas is held thus mechanically. It
may be reasonably supposed that at
the high temperature the gas enters
the carbon and that a solid solution of
carbon with hydrogen or of carbon
with some hydro-carbon is formed.
This solid solution will be stable at the

This means that at the high tempera-
ture the molecules possess velocities which under a given pressure are
consistent with maintaining a solution of some specified concentration.
When the temperature is suddenly greatly decreased the same solution

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Na*s^^'] ELECTRICAL RESISTIVITY OF CARBON, 37 1

may well still exist. When the filament is heated to the same high tem-
perature under a pressure somewhat lower, a less concentrated solution
might be expected. This is consistent with what was found in going
from a pressure of 33 atmospheres to a pressure of 3 atmospheres. When
still at the same high temperatiu^ the pressure is decreased to low values
such as are obtained with vacuum pumps, the concentration which
may be expected to be stable will be naturally considerably fiuther
reduced, as was foimd to be the case. It may well be noted in this
connection that observations with metals show that the formation of a
solid solution by the introduction of a small amount of some other
substance, increases considerably the electrical resistivity of the metal.
It is possible that some similar phenomena occur here.

Summary.

The effect of hydrogen on the electrical resistivity of carbon has been
studied at different temperatures and pressure. It has been found

(i) That hydrogen apparently produces no effect on the resistivity
at ordinary temperatures for pressures up to 33 atmospheres;

(2) That the resistance of carbon increases considerably when the
filament is heated to a high temperature (1,590° K. brightness tempera-
ture) in hydrogen ;

(3) That the resistance at room temperatures following such a heating
in hydrogen shows a similar and more marked increase ;

(4) That subsequent heating of the filameitt in vacuum to the same
temperature produces the opposite effects;

(5) That the effect is greater for the higher pressures tha 1 for the
lower pressures; and

(6) That these changes are suggestive of an exponential law (see
Fig. 4, in which case only has a sufficient number of measurements bee 1
recorded to show the character of the changes) and are about equal in
magnitude in cases where the filaments are not injured appreciably by
the processes involved.

The thanks of the author are due to Dr. Hyde and Mr. Cady for all
their courtesies during his stay at the laboratory, and to Dr. Worthing
for his many valuable discussions and for final corrections as to English.
The author is particularly obliged to Mr. George Hathaway for complet-
ing certain measurements which his departure from the laboratory before
the completion of the work necessitated.

Nbla Research Laboratory,

National Lamp Works of General Electric Co.,
Nela Park, Cleveland, O.
November, 191 7.

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372 p. S. HELMICK. [^2S

THE VARIATION IN THE BLACKENING OF A PHOTO-
GRAPHIC PLATE WITH TIME OF EXPOSURE, TOTAL
ENERGY REMAINING CONSTANT.^

By p. ^. Hblmick.

FOR many years following the discovery of photo-chemical action,
it was believed that if the product of the intensity of light producing
the exposure and the time of exposure were constant, the resulting photo-
chemical effect would be constant. R. Bunsen and H. Roscoe* expressed
this idea as early as 1862. Subsequently Abney,' Miethe,* Eder,*
Michalke and Schiener, Schwarzschild,* Lemon,^ Kron,® and others
showed variations from this so-called "Reciprocity Law," but directed
their attention to the determination of relations between intensity and
time which would give constant blackening, rather than finding the
variation in the blackening with time, with total energy remaining
constant. Abney' and Kron^^ seem to have made the only progress in
this last-named problem. « Both claim that when blackening is plotted
against time of exposure, with total energy remaining constant, that the
resulting curve will show a maximum; but neither investigator directly
obtains this curve.

It has been the purpose of the writer to investigate Abney's and Kron's
conclusion, and actually obtain the curve showing the maximum, if it
existed. By exposing the plate to different rates of flow of constant light
energies, it was believed that some additional knowledge of the physical
mechanism in a light-sensitive plate might be gained.

^ A paper read before the American. Physical Society, December, 1916.
'Ami. der Phys.. 117, 538; 1862.

* "Chemical Action and Exposure," Phot. Joum., Oct.. 1893; "The Failure of a Photo-
graphic Law with Intense Light," J. C. C, 8, 46.

* Inaug. Diss. Gottingen., 1899.

* Handbuch, Band a. Jahrbuch, 1899, 457.

• Phot. Corr., 1899, 171; Beitrage zur Phot. Photem. d. Gestime; Astrophys. Joum., 11.
89. 1900.

^ Astrophys. Joum., 39, 204, 19 14.

• Ann. der Phys., 41, 755, 1913.

• Treatise on Photography, 395, 190 1.
^0 Loc. dt.

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NoIr/^'*l BLACKENING OP PHOTOGRAPHIC PLATE. 373

Apparatus and Method.

The plates used were coated on special plate glass, and the variations
of density due to unevenness of coating were of the order of i per cent.
The following emulsions were used: Seed 23; Seed 27 G. E.; and Seed
Graflex. The sensitiveness of these plates in the camera was roughly
I, 3, and 9.

Two sources of light were used: the integral light from a 4 volt carbon
lamp, and green light of wave-length 545 mm transmitted through a
Hilger monochromatic illuminator from a 32 C.P. coil filament tungsten
lamp. The plates were exposed in a light-tight box 350 cm. long. The
intensity of the light was varied by altering the distance between the
plate and the light, and the value of the intensity for any distance was
computed by the "inverse square law," as modified by Hyde^^ for finite
sources.

Exposures greater than one second were made by a sliding shutter
operated by hand, with the aid of a telephone receiver clicking seconds.
Shorter exposures were made by a modification of an apparatus used by
Wood.^* Electric contacts attached to a large sector disk rotating at a
constant predetermined speed operate an auxiliary sliding shutter, per-
mitting the shutter to be opened just before the revolving sector disk
reaches the point where it allows the plate to be exposed, and permanently
closing the shutter immediately after the sector disk exposes the plate.
The minimum exposure, uniform to 91 per cent.," which this particular
apparatus could give with a sector speed of lo r.p.s. was 1/37,600 second.

Plates were developed for constant time and practically constant
temperature in a developer compounded after Brush's formula.^* Densi-
ties were measured in a modification of Lemon's spectrophotometer" in
which the prism is replaced by two mirrors inclined to one another so
as to reflect two beams of light into the observing telescope. One beam
of light, reduced in intensity by the interposed plate whose density it
was desired to measure, was matched with another beam whose intensity
was regulated by the rotation of a nicol prism. The density of the plate
in terms of the angle of rotation of the nicol is given by the expression
Logio Sec« ^."

" Bull. Bur. Stands., 3. 81, 1907.

" Phil. Mag.. 6. 577, 1903.

" Traite Encyc. de Phot., i. 436.

" Phys. Rbv.. 31. 243, 1910.

» Loc. cit.

>* A table of Logio Sec* 9. with differences to 0*^.01 has been prepared by the writer, and
may be obtained on request from the librarian of the State University of Iowa, lowar City,
Iowa.

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374

p. S. HELMICK,

Sbcomb

Results.
The three different brands of plates were exposed to the integral, or
"white" light of the carbon filament lamp, and to the monochromatic
green light of wave-length 545 mMi and plotting density and time, a definite

i.i

1.9

:^-

oiLnM

'Ni

•

x«t -

ooaat

:.i.

<>,

Ibl

• ' Lifl

It.

6 16 Sa 64

8«cooda Ixposur* .

Fig. 1.

maximum density as time varied but with intensity times time constant,
was obtained in each case. A few of the curves obtained are shown in
the two figures, and are characteristic of all the ciu^es obtained. The

Fig. 2.

curves show that the blackening of a plate is dependent upon the rate
of flow of energy, with total energy constant; and that for each brand
of plate and quantity of total energy there is a maximum blackening
given by a certain rate of flow of energy.

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No's^^'] BLACKENING OF PHOTOGRAPHIC PLATE, 375

The relative heights of the curves in Fig. i are not important, for no
fog strip was taken, and the temperature varied a trifle, but the relation
between the time of exposure to produce maximum blackening and the
speed of the plate seems significant, for with the same value of total
energy upon each plate, the positions of the maxima vary as the speeds
of the plates. By using this rule, the writer was able to shift the maxima
of the curves at will.

Summary.

1. An accurate electric shutter has been designed for photographic
exposures.

2. A simple density-determining apparatus has been described.

3. Plates of three different speeds have been exposed to white and to
green light. The rate of flow of energy was varied, but the tot^l energy
the plate received was kept constant. In every case there was a maxi-
mum blackening, and the time of exposure to produce maximum blacken-
ing varied as the speed of the plate.

In conclusion, it is a pleasure to acknowledge the encouragement re-
ceived from the staff of the department of physics of the State University,
and particularly from Professor H. L. Dodge.

Physical Laboratory.

The State University of Iowa.

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376 LEIGH PAGE,

IS A MOVING MASS RETARDED BY THE REACTION OF ITS

OWN RADIATION?

By Lbigh Pagb.

OINCE the promulgation of the principle of relativity by Einstein in
*^ 1905, a number of alleged inconsistencies with the classical theory
of electrodynamics have been pointed out. That these apparent incon-
sistencies must be due to failure to analyze correctly the problem under
consideration, and that the electrodynamic equations can in no way
come into contradiction with the principle of relativity — ^reference here is
to the relativity of constant velocity systems, not to the broader concep-
tion of general relativity recently developed by Einstein — ^might have
been surmised from the very first, for Lorentz^ had already shown that
the electrodynamics of moving systems could be reduced to that of
fixed systems by a group of transformations substantially the same as
those deduced by Einstein from the principle of relativity. Moreover,
looking at the question from the other side, the author* of this paper
has shown that the electrodynamic equations may be obtained in their
entirety and exactly, from nothing more than the Idnematical trans-
formations of relativity and the assumption that each and every element
of charge is a center of uniformly diverging tubes of strain. Hence,
although the electrodynamic equations may not cover as broad a ground
as the principle of relativity, they can contain nothing that is in contra-
diction with this principle.

One of the most important supposed inconsistencies of the principle
of relativity with classical electrodynamics has been connected with the
phenomenon of anomalous dispersion. Here we have an index of refrac-
tion less than imity, leading, apparently, to the conclusion that the
velocity of light in the dispersing medium is greater than the velocity of
light in vacuo. Since the essence of the kinematics of relativity lies in
the fact that the velocity of light in vacuo shall be an absolute maximum,
it seemed at first sight that here we had an experimental disproof of the
conception of relativity. Not imtil the masterly papers of Sonunerfeld
and Brillouin* were published in 1914 was the matter finally cleared up.

* Theory of Electrons, p. 197.

* "Relativity and the Ether." Am. Jour, of Sci.. 38, p. 169. 1914.

* Ann. d. Physik, 44, p. 177, 1914.

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XS*^'] A MOVING MASS. 377

These authors showed that the velocity with which the index of refrac-
tion IS concerned is a "phase" velocity, and not a "signal" velocity.
By a very ingenious mathematical method they were able to investigate
the propagation of a wave train of limited length through a material
medium, whether in the region of anomalous dispersion or not, and to
show that the velocity of the front of the disturbance, i. e., the "fore-
runners," would be always exactly the same as the velocity of light in
vacuo — never greater, never less.

Another criticism of the principle of relativity of the same nature
as the above, although not concerned with electrodynamics, is based on
the alleged possibility of transmitting a signal with a velocity greater
than the velocity of light by means of a gravitational disturbance. More
than one author refers to the "inunense . . . speed of propagation of
gravitation," * although it has repeatedly been pointed out that none
of the facts revealed by astronomical investigation requires for its
explanation a velocity of propagation for gravitation greater than the
velocity of light.* .

The object of the present paper is to clear up what is, so far as the
author is aware, the only supposed inconsistency of the principle of
relativity with classical electrodynamics which remains a subject of
serious consideration on the part of contemporaneous physicists. This
is the radiation reaction experienced by a moving mass on account of
its own emission of radiant energy. The problem is treated in some
detail by Professor Sir Joseph Larmor in the Proceedings of the Fifth
International Congress of Mathematicians* held at Cambridge in 1912,
and in a recent number of Nature' he emphasizes the contradiction to
the principle of relativity involved in his solution of this problem.

Consider a radiating mass, such as a star, which is moving in a straight
line with velocity V. The reaction of its radiation is found by Larmor
to constitute a resistance to the velocity equal to

F=-i22V, (I)

where c is the velocity of light in vacuo, and R the total energy emitted
per imit time.

Now consider an observer A at rest, and a star at rest. The star will
remain at rest indefinitely in so far as the reaction of its own radiation
is concerned. However the case is quite different if we consider an

' Proc. of Fifth International Congress of Math., I., p. 207. 191 2.

*0. Heaviside. Electromagnetic Theory. I.. Appendix B; H. A. Lorentz, Amsterdam
Proceedings, 2. p. 573, 1900.
* Nature. 99. p. 404, 191 7.

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378 LEIGH PAGE.

Sbbibs.

observer B who is moving in the Z direction with a constant velocity F.
A star initially at rest relative to him ^11 gradually acquire a velocity
(relative to observer 5, of course) in the — Z direction on account of
the reaction of its own radiation. This velocity will increase asymp-
totically until it reaches the final constant value V. Hence the systems
of observers A and B cannot be equivalent, and the principle of relativity
comes into contradiction with classical electrodynamics when applied
to this particular problem.

Such would be the only possible conclusion if the deduction of equation
(i) from the electrodynamic equations were correct. In order to point
out the tacit assumption which invalidates Larmor's derivation of (i),
we shall reproduce in somewhat more rigorous form what is substantially
the analytical reasoning pursued by him. Then we shall investigate
the problem quite rigorously by a somewhat different method, and show
that the electrodynamic equations do not lead to a radiation reaction
which depends upon the velocity, but to a reaction which is exactiy in
accord with the principle of relativity. IncidentaUy we shall develop
the complete dynamical equation of an electron to the fifth order.

If we use the units of electric charge and magnetic pole advocated by
Heaviside and Lorentz — ^a unit i/^4t smaller than the electrostatic or
electromagnetic units respectively — classical electrodynamic theory is
contained in the five vector equations^

V-E = p. (2)

VXE=-;H. (3)

V-H = o, (4)

V X H = ; (E + pT), (5)

F= p|^E+ jvXHJ,

(6)

where equations (2) to (5) inclusive describe the effect of the distribution
of matter upon ether, and (6) gives the effect of ether on matter. From
(3)? (5)1 and (6) we obtain at once the familiar energy equation for the
region inside the closed surface Z, namely

J^ [hS{E^+ IP)dT] + c / (E X H) .dcr + /F-vdr = 0, (7)

where dr is an element of volume and do* a vector element of surface

> Gibbe's vector notation is used.

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No*^^] ^ MOVING MASS. 379

having the direction of the outward drawn normal, the volume integrals
being taken throughout the volume enclosed by the surface 2 and the
surface integral over this surface. The first term represents the rate
of increase of electromagnetic energy, the second the rate of escape of
energy through the enclosing surface, and the third the rate at which
work is done by the field on the matter contained in this region.

Now we are interested in the reaction of the ether on the material
oscillators which constitute the radiating body under consideration. To
find this reaction we may proceed by either of two equivalent methods,
which we shall designate as methods A and B.

Method A.
We may eliminate p and pv from (6) by means of the field equations
(2) to (5). This yields for the resultant force on the matter within the
closed surface Z the familiar expression

K = JFdr = /(EE +HH).d<r - i/(£« + H«)d<r - i ^/(E X H^r,
• c dt

where the surface integrals are taken over the surface 2 and the volume
integral throughout the region enclosed by this surface.
Let us write

Ki = / (EE + HH) -da - J / (£« + H^)dir. (8)

K,= --'|^/(EXH)dr. (9)

Then Ki is the stress which Maxwell considered to be exerted by the
ether without the surface 2 on the ether within this surface, and Kj
has been interpreted as the rate of decrease of electromagnetic momentum
within the enclosing envelope,

; (EX H)

being the momentum of the ether per unit volume.

If, now, we imagine a closed surface to surround the matter on which
we wish to find the force K, our problem reduces to the evaluation of the
integral expressions for Ki and Ki. To determine the values of the
integrands, however, it is necessary to know the distribution of p and pv
in space and time, so as to solve the field equations (2) to (5) for E and H.

Method B.
We may solve (2) to (5) for E and H in terms of p and pv, substitute in
(6), and evaluate the integral

K = /F(/r, (10)

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38o

LEIGB PAGE.

where the volume integral need be taken only over those regions where
p is not zero, i. «., over the matter on which we wish to find the force K.
The second method is somewhat the more direct, and has the great
advantage that in most cases the integration covers a very small r^on,
so that if it is necessary to expand E and H in terms of the distance
between the elements of charge considered, there is no difficulty in
developing convergent series. Nevertheless in certain problems, par-
ticularly those in which

/(ExH)dr

does not change as time goes on, the first method is very convenient
and less laborious than the second. Obviously the two methods are
equivalent, and must lead to exactly the same result.

Whichever method is used, it is necessary to solve the field equations
(2) to (5) for E and H. Lorentz's* solution is as follows:

where

E = - V« - - A,
c

H = V X A,

0 s — I — (/r,
4^J r

^TTCj r

the quantities in brackets being retarded, i. e., values of p and pv respec-
tively at a time r/c earlier.

For a point charge these reduce to the familiar Lienard* potentials

«[V]

K-t)]

47rc

Differentiating these retarded potentials, we obtain the usual expres-
sions for E and H due to a point charge' at a time r/c later,

E =

^(i - ^0

4x1^

(-T-y

('-H

{'x('-^)|x

(II)

* Theory of Electrons, p. 17 rf stq.

* Eclairage Electrique. 16, p. 5, 1898.

' M. Abraham, Theorie der Electrizitftt. 2. p. 97.

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Xf^j^'l A MOVING MASS. 38 1

({.x(.-:,)}xO

H- '<■-«

4Tr»

(-tT

(12)

where fi s v/c and f is the acceleration.
From these it appears that

H = i(rXE). (13)

Consider now a radiating body, such as a star, which is moving with a
velocity V relative to the reference frame to which we apply the electro-
dynamic equations. The total force due to the emitted radiation will
consist of two parts, (a) the reaction on each oscillator of the radiation
which it, itself, emits, (6) the force exerted on each oscillator by the radia-
tion proceeding from the neighboring oscillators. Now to compute the
reaction on the aggregate of material oscillators by the rigorous method
we are going to pursue would be exceedingly involved. Fortunately
we can simplify the problem to the extent of dealing with a single oscil-
lator, i. e., a single vibrating electron, and yet obtain a result that will
be a perfectly general test of Larmor's expression for the radiation
retardation. For this expression gives the retarding force as a function
of the rate of total radiation and the velocity of the radiating body, and
of these quantities alone. Hence if the ether exerts a reaction on a
group of moving oscillators, it will exert a similar reaction on a single
oscillator; and conversely, if there is no reaction on a single vibrating
electron due to its drift velocity, there can be none on a group of such
vibrators.

Reaction of the Radiation.

Method A.

To find the reaction of the radiation, Larmor uses method A. The
following reasoning is somewhat more rigorous than his, but is substan-
tially the same and leads to the same result, provided the same approxi-
mations are made.

Draw a fixed sphere of radius r (Fig. i) with center at the point occupied
by the vibrating electron at a time r/c earlier. Take the X axis in the
direction of the velocity which the electron had at this earlier time.
Let r be very great compared to the linear dimensions of the electron.
Then terms involving r""' will be negligible compared to those in f"^
and E and H at the surface of this sphere will be at right angles to the
radius vector. Hence

where u is the energy density of the radiation.

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382

LEIGH PAGE.

gy»|^f,

Hence, in the X direction

Ki^ ^ ^ J u cos B d<r.
Now consider the part Ki' of Ks due to the fact that the electron's

Fig. 1.

field is moving with it. Since the flow of energy at the surface of the
sphere is along the radius vector

|EXH| = tt

and, as is obvious from the figure,

-r/(EXH)^r = - fuvcos^edtr

KiJ = fup cos* 6 dff,
hence

Kz = — / tt(i — iS cos e) cos 6 sin 6 dS d4> (14)

is the force due to the stresses over the surface of the sphere plus that
due to the rate of decrease of electromagnetic momentum occasioned by
the translation of its field with the electron. That part of Ks due to the
rate of decrease of electromagnetic momentum inside a sphere of radius
r moving with the electron is zero when averaged over a whole number
of periods, provided the electron's field at the end of this time is the same
as it was initially.
From (13)

E X H = - I £«r - E-rE i

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No"^^'] ^ MOVING MASS. 383

Hence, from (11), (14) becomes

e* J Tcos 6 sin dd6d(l> Cf^f^ ^^^ ^ ^^^ BdBd4>

KJ ^ -

{ rcos Bsm BdBd4> Cfrfv cos B sin BdBd

^ J (I -iScos"^)» "^ ^^ j (I - /3 cos ^)*

^\ fA* cos g sin dddd<^ 1
""^'"^^J (i-/3cosd)* f*

where, without loss of generality, we can assume f to lie in the XY
plane, so that

/» = / cos ^,

Jr = /(cos ^ cos ^ + sin ^ sin ^ sin 4>).

Performing the integration over the surface of the sphere

Similarly

««_ f rsin'gsin »dg(f0 r/r/> sin« B sin »d^d0

^^ -'^-^'^ t j (I - /3 cos ^)» ■*■ ^^ j (I - iS cos <?)*

""^'"^U (i-/3cos^)* [•

l6irV

which gives on integration
From symmetry

k: = o.

Hence, to the first degree of approximation

K' = - ^y. (X5)

Now, to the same degree of approximation, the rate of radiation from
the electron is given by

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384 LEIGH PAGE. TSwxwd

ISbbus.

where R is the mean rate of radiation. But

Jvi^t = Vt.

Hence, on the average

Ki' = --^RV.

This is the expression found by Larmor for the resistance due to the
reaction of the radiation. But are we justified in neglecting the part of
Kl^ which depends upon the decrease in the integral

/(EXH),dr

taken over the region enclosed by a sphere of radius r moving with the
electron? The average impulse due to this part of the total force during
a time / is

JKrdt = -7, j [/(E X H)^r]^ -[/(EX H)^r]J .

Now the integrals within the brackets are equals and hence annul each
other, if, and only if, the field within the moving sphere of radius r is the
same at the end of the whole number of periods over which we are averaging
as it was at the beginning, that is to say, if the periodic motion of the electron
is undamped. But the energy of a radiating electron is continually
decreasing, and consequently its motion cannot be truly periodic unless
energy is supplied to it from some outside source. But if energy is to be
supplied it must be shown that no impulse on the electronic vibrator
accompanies the transfer. The author has not succeeded in devising a
method by which a transfer of electromagnetic energy might be effected
in such a way that the impulse imparted could be easily calculated.
Energy from non-electromagnetic sources — such, for example, as the
energy imparted to the radiating electrons on the sun's surface from its
gravitational potential energy as the whole mass shrinks — must be
excluded from consideration on account of insufficient knowledge of the
laws governing the intricate phenomena concerned. In fact, our problem
is essentially one in electrodynamics, and the connection between gravita-
tion and electrodynamics is unknown. Consequently in our further
treatment of the problem we shall assume that the electron is left to itself
and that its radiation is at the expense of the energy of its vibration.

Moreover, from the standpoint of the electron theory, Lorentz* has
shown that the dynamical equation of an electron contains a damping
force which depends upon the rate of change of acceleration, and which is
independent of any assumptions as to the distribution of the charge.

* Theory of Electrons, p. 49.

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Vol. XL!
Nas. J

A MOVING MASS,

385

In fact it is easily shown that the energy radiated is accounted for by
the work done against this resisting force. From this point of view as
well, then, an undamped periodic vibration is impossible unless energy is
supplied from some outside source.

It may be urged that by making the mass of the electronic vibrator
sufficiently large, the din^inution in energy due to its radiation and
consequently the value of the part of Ks which we have neglected may
be made as small as desired. But it must be remembered that increase
in mass involves decrease in the radius of the electron, and hence the
volume integral whose decrease we have neglected has to be extended to
regions where E and H are very large, and where any proportionately
small change in these quantities will account for a relatively large change
in the integral.

Although we are not going to complete the solution of our problem by
the method we are here pursuing — for the analytical difficulties in
evaluating

/(EXH)rfr

are far more formidable than those encountered in the equivalent method
B — it may not be superfluous to show the existence of a force which
exactly compensates the resistance found by Larmor. [We are dealing

Fig. 2.

here with a single vibrating electron which is receiving no energy from
outside sources.] Equation (14) gives K' for the time o in terms of f
and V at a time — (r/c), where r is the radius of the sphere over whose
surface the integration is to be performed, r being very large compared
to the linear dimensions of the electron. Let Pi (Fig. 2) be the position
of the electron at the time — (r/c), Pj the position at the time — (r/c) +d/.

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386 LEIGH PAGE, ^SS.

Pt that at the time — (r/c) + 2dt, etc. Let the outer full-line circle be
the trace of a sphere of radius r with center Pi, and the outer dotted
circle that of a sphere of the same radius but center Pt. Let the next
full-line circle have center Pj and radius r — cdt^ and the innermost
center Ps and radius r — 2cdt^ the dotted circles having respectively the
same radii but centers at Pa and Pi. For the time o then, E and H
over the outer full-line sphere will depend upon the velocity and accelera-
tion which the electron had when at Pi, while for the second full-line
sphere the velocity and acceleration of the electron when at Pi are the
ones that must be taken into consideration. At a time dt later, the full-
line spheres must be replaced by the dotted spheres, and the effective
positions Pa, Pa, and Pa made use of instead of Pi, Pj, and P«. Now as
the regions between these spheres are far from the electron, the parts of
E and H having f~* as a factor are negligible compared to those involving
only the inverse first power. Hence the flow of energy is along the radius
vector, and the value of

/(ExH)^r

for the region between the first and second dotted spheres at the time
dt will be the same as the value of this integral for the region between
the second and third full line spheres at the time o, and so on. Hence
at least part of the decrease in the total integral will be the value of the
integral for the region between the two outer full-line spheres. Since
the distance between these spheres is

cdt{i — fi cos e)

we find for this part of Kt^

KiJ" = / w(i - /3 cos e) cos e sin eded4f

which exactly annuls the expression (14) previously obtained. This is as
would be expected, since it is not to be supposed that the reaction on the
electron would depend upon the velocity and acceleration which it had
at a time r/c previous, where r may be made indefinitely great, but at
most upon the state of motion at a time ale earlier, where a is its greatest
linear dimension. The portion of the integral which is conditioned by
the state of motion at this comparatively more recent time is that in the
vicinity of the electron. On account of the difficulty of developing a
convergent series for E and H we will not evaluate this integral directly,
but resort to the equivalent method B.^

» On the dynamical theory of the ether as developed in particular by the English school of
physicists, the force exerted by radiant energy on matter is conceived to be due to a transfer
of momentum from the ether to the body affected. Let us consider the problem under dis-
cussion from this point of view. The ether inside the large £a>here of radius r (this sphere

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Na"^^*l , ^ MOVING MASS. 387

Method B,

This method consists in obtaining E and H from the equations of the
electrodynamic field, substituting in the expression for the force exerted,
and integrating over the region occupied by the electron. In order to
carry out the solution we are obliged to make certain assumptions
regarding the shape and distribution of charge of the electron. However,
we are at liberty to make any such assumptions we choose, for the
expression found by Larmor for the radiation reaction is independent
of the shape or distribution of charge. As a matter of fact we shall
see that terms of the form of Larmor's expression are independent of any
such assumptions.

Larmor speaks of the radiation reaction found by him as a first order
effect. As a term in the equation of motion of the electron it must be
considered of the fifth order. For if A is the amplitude of the electron's
vibration, it is obvious that

--r IS of the order /S*,
—-7- P is of the order /3*, and

where a is the radius of the electron. It is this last quantity which is
involved in his result. Consequently we shall retain in our analysis
all terms of the firs^ five orders. Fortunately a great many complica-
tions, such as variations in the distribution of charge on the electron
due to its state of motion, do not enter until the sixth order is reached.*
Our first step is to expand the retarded expressions (11) and (12) for
E and H due to a point charge in terms of the actual velocity and its
derivatives. Suppose we have a charge e at a point whose co5rdinates
are x, y, and 2 at a time o, and let v, f , f , etc., be its velocity, acceleration,

must be large compared to the diameter of the electron if terms involving r"* are to be
neglected as compared to those in r"^ but may be very small compared to a millimeter) to-
gether with the electron at its center is losing momentum to the ether outside, and since the
momentum passing out in the direction of motion is greater than that passing out in the
opposite direction, there is a force of exactly the amount found by Larmor. But the ether
inside this sphere is also losing momentum in the direction of motion due to the damping of
the vibration. Now. by the law of conservation of momentum.
Momentum lost by electron * Momentum gained by ether outside sphere — Momentum

lost by ether inside sphere.
Method B will show that the terms on the right-hand side of this equation (the second of which
is overlooked by Larmor) must be equal and hence annul each other.
» Relativity and the Ether, p. 185.

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388 LEIGH PAGE, . [toS

rate of change of acceleration, etc., at this instant. Now expressing (n)
in scalar form, we have for the x component of the electric intensity at
the origin at the time o

--j^.(-+'i?r{('-^^')(-?-"f)

-'^•(■+^-)i- <■«

where the quantities with subscript e refer to the effective position of
the charge, i. e., its position at a time rjc earlier. Hence

r- I ^ r.« I : f / I •; r / i 7 r /

».. =

6-^V +24-^'

A =

and similar expressions for the y

and z components.

Put

^'^ c' ^'^ c*

8 -^-^

«. s

••

Then

+ ^(«.m + 48P + 37*)^* - ^Ot"" + 5«P + io8y)^* • • } .

Put

* a (I - ^)-».

b = •ym**,

caCS-m + sYP)**.
rfs(€.m + 48.p + 3y)jfe*,

es(5.m + 5€.p + io8.Y)*»,

where a is of the first order, h of the second, and so on. Then

3 12 60 ^ *'

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Vol. XI,
No.

^^'] A MOVING MASS. 389

After some reduction we find that

+ 0

- - yJi'^i - H-o+o + |cT»- —dr* + — CT»- • . )

2 ' \ 6 12 ' 40 /

+ - 8Ji*7* ( - 2 + ar + o +lci* - —dr* + —67* • • ']

3 \ 6 12 ^ 40 /

- g«^T* f-3+20T + 0 + 0- j^dr* + ^<T»- • • j

+ ^^**'^(~* + 3«r + 0-gCr» + 0+^«r»-. •)•..} (19)

Hence

£.= -^*r/-»J. (20)

Returning to (17) and solving for t by successive approximations,
we find

T = i-a(i --o+o + gC» + oj

+ ij(i_2a+|a* + o)+|6*(i-?a)
- ^c (i - 30 + 4a*) - - Jc
+ ^d(i-4a)

120

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390 LEIGH PAGE. [^^

Substituting this value of r in (20), we obtain after a laborious reduction

-^«^{i-fa + 2*...) + |«.*^(i-?a...)-^r^...}. (21)

We need H to the fourth order only, as it is multiplied by v/c in the
force equation (6). It is obtained most easily from (13), the x component
of which is

which gives, after considerable reduction

- Wiyyfis - 7^.) + fi'C^.^. - i^y) • • • } . (22)

If now, we wish the electric and magnetic intensities at a point x, y,
z due to a charge at the origin, we must change the signs of the co5rdinates
in (21) and (22), and have

+ ^f^"-). (23)
H. = ^ J (/S,m. - /9.m,) ^ I - ^fflj* - ^6r • • j

+ myyfi» - y^,) - ii'CM. - «.i8») • • • } , (24)

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nS"^'] ^ MOVING MASS. 39 1

where

ai 5 p-mJfe,

bi s y-mk^

cx^ (S-m-aY-P)*",
dis (€.m-48.p-3y)*^,
«is (5.m-5€.p - io8.Y)ft«.

Before we can find the reaction of its field on the electron from these
expressions for E and H we must make some assumption as to the dis-
tribution of charge on the electron, just as we should have had to do in
method -4, if we had attempted to evaluate

/(ExHMr

in the vicinity of the electron. As already noted, the radiation reaction
obtained by Larmor is independent of this distribution, and hence, if
existent, must hold irrespective of the assiunption we make here.

We might assume the electron to be a rigid conducting sphere —
Abraham's electron. The determination of the dynamical equation for
such an electron is comparatively simple, and the actual carrying through
of the analysis shows the existence of no such resistance as that found
by Larmor. However, such an electron is of little interest today, so we
shall not burden our readers with the algebra involved. Instead we
shall confine ourselves to the deformable electron first proposed by
Lorentz, the formula for the mass of which has been abundantly verified
experimentally by Bucherer,* Neumann,* and others. This electron, it
will be remembered, contracts when moving, so that its dimensions in
the direction of motion are diminished in the ratio of ^i — /3* : i.
Parenthetically it may be remarked that the Lorentz electron is the only
one whose field outside the surface is exactly that of a point charge.
We shall take the distribution of charge to be such that the electron,
when at rest, is a uniformly charged spherical shell.

At first we shall restrict ourselves to motion in a straight line. Take
the X axis as the direction of the velocity. Then since the electron
contracts as its velocity increases, the velocity and its derivatives at a
time o will be less for a point P than for a point O, if P is a distance x
farther along the X axis than O. In fact we easily see that after a time
dt has elapsed

\ dx 2 dx ' 6 dx )

« Phys. Zeitschr., 9, p. 755. 1908.
> Ann. d. Physik, 45, p. 529. 1914.

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392 LEIGH PAGE.

But

Xtkt = xkf
where

Equating coefficients of like powers of dl in these equivalent expressions
for X|, we find

dv f

|=-**S-**^f (.6)

and by carrying out the analysis to the second order of x,

g=2fe»/S^(i+^) + **/3»^. (28)

Now let x' be the X codrdinate of a point Q on the electron relative to
O when the electron is at rest, and x this distance when it is in motion.
Then

But
Substituting and integrating

Equations (25) and (28) show that the coefficient of x* is of the sixth
order and hence negligible. So we have

x' =

fcc-

-l^^^^

•i**aiV.

-/.

-«'.

f. . 3..

. 3_

A O _ •»

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SS"^^] A MOVING MASS. 393

and we find from (23) for the electric intensity at a point x, y, z due to
an element of charge de at the origin

-|«.'*»(n-^a,.-.)+^f.'*»---}, (30)

where

«'o*' -v'--^ 8'=^' «'oJ^* t'J^

To obtain the force exerted on an element of charge de' by the charge
de at the origin, in so far as it is due to the electric intensity, we must
multiply (30) by de'. Then integrating with respect to de' we find the
force exerted on the rest of the electron by de. Finally, integrating with
respect to de we obtain the total force in the X direction due to the re-
action on the electron of its own field. The magnetic intensity does not
come into the problem in the case of linear motion which we are here
discussing, since the force due to the magnetic field is always at right
angles to the direction of motion.

Hence neglecting terms which must give rise on integration to equal
and opposite pairs of forces, (30) reduces to

8 c*

and the total reaction

where we do not take into account the variation of f and f from point to
point on the electron, since reference to (26) and (27) shows that the only
term of less than sixth order vanishes upon int^jation.

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394 ^^Cfl PAGE. [^St

Since

we get on integration

J. ^ . <^P/. , gy.

9TC*(i - /S*)* ■•■ i8tc»(i - ^)» "

(32)

for the X component of the reaction exerted on the electron by its own
field, all terms to and including the fifth order having been retained.
The coefficient of /« is the usual expression for the longitudinal mass,
and the third term is the damping effect of the radiation. It is obvious
from synunetry that the y and z components of the reaction are zero.

Let us now treat the general case of any type of motion. Consider
the axes so oriented that the velocity of the point 0 on the electron is in
the X direction and its acceleration in the XY plane at the instant
considered. Let P be another point whose codrdinates relative to 0
are x, y, o. Designate by a the angle which the velocity of 0 makes with
the X axis at the end of the time di. Then

Moreover

sm a = -T- cos a = I. (33)

But

(x« cos Of + yi sin a)'^k? + (xi sin a — yt cos a)* = o?k^ + 3^*, (35)
where

»if. = v^+fydt.
Substituting in (35) the values of sin a and cos a from (33) and those
of X| and yt from (34), we get on equating to zero the coefficients of x*
xy^ and y*

dx ' ^^ c'
^-^'■

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ISS:^^'] ^ MOVING MASS. 395

Now, if there is to be no rotation of the electron as a whole

dVx

Hence

Now consider a point Q near P. Let dx', dj'', o be the coordinates of
Q relative to P when the electron is at rest, and dx, dy, o these coordinates
when it is in motion. Let dr' and dr respectively denote the distance
PQ under the same conditions, let a be the angle which r makes with the
X axis, and let 6 be the angle which the instantaneous velocity of P
makes with this axis. Then

dr'* = k^dr^ cos^ 6 + dr^ sin* B.
But

tan (a- (?) = -^ = - k'^x.

Hence

dr' = kdr v^i - /8* sin* 6 - k^dx^^^x cos 6 - k^dx0^^^x sin 6.

If ^ = 0

If (? = 90^

dx' = kdx - k^P'^xdx,
x' = kx--k'0'^o(^.

dy' ^dy- k^P'-^xdx,

Hence

y = y + -ai*yy,
'^ ~ '^ I + ai* •

ntyk rn^kf 3 3 3 \ , i koi^yy

(37)

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396 LEIGH PAGE. [j

Therefore we obtain from (23) for the x component of the electric
intensity exactly the same expression (30) as in the case of linear motion.
So far as the part of the x component of the force which depends upon
the magnetic field is concerned, the first term which does not vanish on
integration is of the sixth order and hence negligible. Remembering that

x' V
r r

and integrating, we get for the x component of the reaction exerted on
the electron by its field the same expression (32) as in the case of linear
motion.
For the Y direction we obtain from (23) and (37)

Neglecting terms which give rise to equal and opposite pairs of forces,
this reduces to

Also, from (24) and (37)

;(vXiH), = -/WH.
c

Me
= — -^ { - /8*m,,(i - J6i • • •) + aii3*(7,w„ - 7„fn,)

+ J/8** (5*w„ - 5yW,) - Ji8*»(€,W„ - €„W.)
which reduces, when we neglect terms which give rise to equal and oppo-

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No!"s^M ^ MOVING MASS. 397

site pairs of forces, to

-if^^k'-}. (39)
Hence

(40)

and the total reaction

Integrating we find

where the coefficient of fy is the usual transverse mass. We obtain a

similar expression for K,. It is to be noted that the coefficient of f -ff

as well as that of f is independent of the assumption as to the distribution

of the charge.^

It may be of interest to give, in passing, the equation of motion of

the deformable electron to all orders — n^lecting products of derivatives

of the velocity — for the instant when the electron is at rest relative to

the observer. The analysis is omitted. We find for the reaction of the

electron's field

* It is to be noted that in (3a) and (41) are obtained for the first time general expressions
for the longitudinal and transverse masses respectively which are not limited to a quasi-
stationary state of motion.

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398 LEIGH PAGE,

LSBun.

j[ -- j_ I J ,

6icac^ 6tc' Qirc* iSirc^ 45^^* 135^^^

i2Ta2£;

^ 2a <f

l2iraH

- 5 % 2a. (42)

TAe /orc« exerted on an electron by its own field is equal to a constant
multiplied by the velocity which it had at a time earlier equal to the time
taken by light to travel across the electron's diameter. Now, if we choose
the proper point inside the electron to take as the one to which the
derivatives of v in the equation above apply, we can make the product
terms which we have neglected vanish exactly. So there is a point inside
the electron for which (42) is the exact equation of motion.

To return to our problem. Inspection of expressions (32) and (41)
shows that the reaction on the electron due to its own field contains
terms having the directions (except for the aberration due to the differing
powers of I — /P in the denominators of the components) of f , f and
higher derivatives of the acceleration. There is no term representing a
force opposed to the velocity^ as Larmor's result would imply. Hence
the reaction constitutes a resistance to the acceleration, etc., and not
to the velocity of the vibrating electron. In fact we shall now show that
in every term — mass reaction as well as radiation reaction — the form of
equations (32) and (41) is precisely that demanded by the principle of
relativity.

Let symbols without primes refer to a system K (o), which we may
for convenience call the rest system, and let symbols with primes refer
to a system K (v) which has a velocity v in the X direction relative to
K (o). Consider a moving point. Its velocity, acceleration, and higher
derivatives relative to an observer in K (v) are found in terms of these
quantities relative to an observer in K (o) by differentiating the Lorentz-
Einstein transformations. Suppose now that the point is, at the instant
considered, at rest in K (v). Then the transformations obtained reduce to

/.' = k%.

// = *»/» + 3*^- P7.

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No'*^''] •* MOVING MASS. 399

fi = **/, + terms of sixth and higher orders,

/i.' = *•/.+ •••,
// = *»/»+••••

If now, our point represents an electron, its equation of motion relative
to an observer in K {v) is obtained by putting /8 = o in (32) and (41),

tEz = 2 i ~" Z~:i H H ^""Tir + nigner orders,

"^ erac^ ere' "^ girC" iSirc* "^ " "'
But the relativity theory gives the familiar relations
£/ = Eg,

Hence we have

cEg =

^jf^ gy>

e|£, + ^ (V X H), j - ^ ^ , - ^

which agree exactly with (32) and (41), showing that fi enters into the
equation of motion of a moving electron in exactly the same way whether
we obtain that equation directly from electrodynamics, or obtain it by
applying the electrodynamic equations to an electron at rest and then
using the kinematical transformations of relativity to find it relative
to an observer with respect to whom the electron is in motion. So we
conclude that the equation of motion of an electron as determined from
the electrodynamic equations is completely in accord with the principle
of relativity, at least 05 far as the fifth order. Hence a moving vibrator
experiences no retardation on account of its radiation. And since the
retardation in question depends only upon the drift velocity and rate of
radiation, this conclusion is equally true of any moving body, however
complex.

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400 LEIGH PAGE. [i

Summary.

(a) Professor Larmor's deduction from the electrodynamic equations
of a radiation reaction on a moving mass has been shown to rest upon a
tadt assumption which utterly invalidates his conclusion.

{b) It has been shown rigorously that classical electrodynamics leads
to no retardation on a moving and radiating mass, but is completely in
accord with the principle of relativity.

{c) The equation of motion of the Lorentz deformable electron has been

computed from the electrodynamic equations as far as and including terms

of the fifth order, and found to be in exact agreement with the principle

of relativity. The result obtained is more general than any previously

published in that it is limited to no particular type of motion, such as

quasi-stationary motion in a straight line.

Sloanb Physics Laboratory,
Yalb Univbrsity,

December 19, 191 7.

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Na"^'] X-RAY SPECTRA OP CERTAIN ELEMENTS. 4OI

AN EXPERIMENTAL INVESTIGATION OF THE ENERGY IN
THE CONTINUOUS X-RAY SPECTRA OF CERTAIN

ELEMENTS.

By Clayton T. Ulrby.

IN the classical research of W. H. and W. L. Bragg* on the reflection
of X-rays from crystals it was shown that besides the characteristic
lines emitted by the target of the X-ray bulb there was always present a
considerable amount of radiation in the neighborhood of the lines which
could not be resolved into separate lines by the X-ray spectrometer.
In photographs of X-ray spectra this continuous part of the spectrum
manifests itself by the "fogged " background upon which the character-
istic lines are superimposed.

The purpose of this investigation was :

(i) To obtain the energy-wave length distribution curves for the
continuous spectra of various elements with the special object in view of
determining the relation between the amount of energy radiated and the
atomic number (or atomic weight) of the element, and

(2) To investigate the effect of a variation of voltage applied to the
tube on the amount and distribution of energy in the spectrum.

Professor William Duane and F. L. Hunt* investigated the energy
distribution in the continuous X-ray spectrum of tungsten and found
that the short wave-length end of the spectrum has a very definite
boundary whose wave-length is given by the relation

where Xo = minimum wave-length excited, V = constant voltage applied
to the tube, e = electron charge, h = Planck's radiation constant, and
c = velocity of light. They showed that the energy, as measured by its
ionizing effect, increases rapidly with increasing wave-length and soon
reached a maximum value and then decreases less rapidly with a further
increase of wave-length.
Similar radiation curves of tungsten have been obtained by Dr. A. W.

1 Royal Society. Proc., A, 88, July. 1913; and X-Rays and Crystal Structure, Chapter 6.
« Phys. Rev., VI., Aug., 1915.

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402 CLAYTON T, ULREY. [toSS

HulP and by Dr. Hull and Miss Rice,* which show in a general way
how the maximum is shifted toward the shorter wave-lengths as the
voltage applied to the tube is increased. Dr. Hull' has also compared
the radiation curves of tungsten and molybdenum obtained under iden-
tical conditions (at 45,000 volts). Inspection of these last curves shows
that the intensities of the maxima are in the same ratio as the atomic
numbers of the elements tungsten and molybdenum.

The problem of the dependence of the intensity of X-radiation upon
the atomic weight of the element emitting the radiation has been investi-
gated in a number of researches, among which may be mentioned those
of G. W. C. Kaye,* of R. Whiddington,^ of R. T. Beatty,« and of C. S.
Brainin.^ They all agree that there is no definite relation existing
between the total emission and the atomic weight. Kaye, however,
obtained an approximate proportionality between intensity and atomic
weight when he interposed a sheet of aluminum of several millimeters'
thickness between the X-ray tube and ionization chamber. The explana-
tion given for this effect of the aluminum is that it absorbed most of the
characteristic radiation from the elements of low atomic weight where
the characteristic constitutes a large percentage of the total radiation.
If this be the correct explanation we may expect to find the true relation
only when the characteristic radiation is entirely eliminated. Analysis
of the spectrum by the X-ray spectrometer is a suitable method for
making this elimination. It is not improbable that a comparison of the
intensities of corresponding characteristic radiations of different elements
may also reveal valuable information in regard to this same problem.

Description of Apparatus and Method.
For these experiments a special X-ray tube was constructed, with a
steel anticathode in the form of a hexagonal prism upon each face of which
was mounted a sheet of one of the metals, chromium, nickel, molybdenum,
palladium, tungsten and platinum. To the base of the prism and in line
with its axis was attached a steel tube whose inside diameter was just
sufficient to allow it to slip down over a steel rod mounted vertically in
the bulb and acting as one electrode. Thus the anticathode was free
to rotate about a vertical axis so that each of its faces could be brought

^ American Journal of Roentgenology, II.. Dec., 1915.

« Proceedings National Academy of Science, II., May, 1916.

» Curves published by Bergen Davis. Phys. Rbv.. IX.. Jan., 191 7.

* Phil. Trans. Roy. Soc., A, 209, 1908-9.
' Proc. Roy. Soc.. A, 85, 191 1.

• Proc. Roy. Soc., A, 89, 1913-14.
' Phys. Rev., X., Nov., 191 7.

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No's'!^^*] X-RAY SPECTRA OF CERTAIN ELEMENTS. 403

into position to be bombarded by the cathode stream. The rotation was
accomplished by use of an electromagnet outside the bulb acting upon a
bar of soft iron fastened at right angles to the steel tube and as far below
the prism as possible.

A Coolidge cathode obtained from the General Electric Co. was sealed
into one side of the X-ray bulb in a horizontal position. The bulb was
exhaustecf by means of a mercury diffusion pump in connection with a
Gaede rotary pump for producing the fore-vacuum. In order to prevent
mercury vapor from reaching the X-ray tube a condensation chamber was
sealed between the bulb and pump. During the operation of the pumps
this chamber was surrounded by a Dewar flask containing slush of carbon
dioxide snow and ether. By this means a vacuum was attained which
was high enough to prevent any trace of a gas discharge at 50,000 volts.

A step-up transformer was used to obtain high voltages. Energy was
supplied to the transformer by a 5-kilowatt, 500-cycle generator whose
speed was maintained constant by use of an auxiliary synchronous motor.
The voltage was regulated by adjustment of a variable resistance in the
generator field circuit which was separately excited by a storage battery
of 120 volts. The current from the transformer was rectified by the use
of two kenotrons, one connected to each terminal of the secondary of the
transformer. In order to reduce the voltage fluctuations in the high-
voltage circuit to a minimum, a resistance and a specially designed
high-voltage condenser of .016 microfarad capacity were inserted after
the manner suggested by Dr. A. W. HuU,^ of the General Electric Co.

The voltage applied to the X-ray tube was measured by an electro-
static voltmeter designed by Professor Davis. It was essentially a
Coulomb's balance in which a pair of movable spheres were repelled by a
pair of stationary ones. A mirror attached to the suspension of the
movable spheres reflected a beam of light upon a scale at a distance of
approximately one meter. The instrument was calibrated by means of
a spark gap between spheres of 12.5 centimeters' diameter.

The filament of the cathode was heated by a current from a storage
battery. The electron current through the X-ray bulb was read by
means of a milliammeter placed next to the bulb, so that it would indicate
only the current through the bulb and not the leaks along the line.

The X-ray bulb was completely surrounded by a lead shield of .6
centimeter thickness with a narrow aperture on the side facing th6
spectrometer. The beam of X-rays after passing through this aperture
and the first slit of the spectrometer was reflected from the (100) face
of a crystal of calcite for which the distance between reflecting planes is

» Phys. Rbv., VIL, March, 1916.

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404 CLAYTON r. ULREY, [^SSl

3.030 X 10"* cm. The reflected beam passed through the second spectrom-
eter slit and a thin mica window into the ionization chamber. The
crystal used in these experiments was finally selected as being the most
nearly perfect out of a large number which were tested by examination
of the photographs obtained when the crystal was used as a reflector for
a narrow band of general X-radiation.

The ionization chamber consisted of a hollow steel cylinder 75 cm.
long and 7.5 cm. diameter, in which was supported a small steel rod
insulated from the chamber and parallel to the axis of the chamber, but
decentered far enough to prevent any X-rays from impinging upon it.
The chamber itself was earthed and the insulated electrode was charged
to a potential of 400 volts. A gold leaf attached to the end of this
insulated electrode was viewed by means of a low power microscope with
a scale in the eyepiece. The rate of leak was determined by observing
the time required for the image of the leaf to move over a certain part of
the scale (10 divisions). The sensitivity was about 5 divisions per volt

In order to increase both the absorption and the ionization, ethyl
bromide (CsHsBr) vapor was used in the ionization chamber. At a
temperature of 20^ C. the absorption in a mixture of air and saturated
ethyl-bromide vapor is approximately 2.4 times that in air, since the
pressure of the vapor is 387 mm. and its density relative to air is 3.78.
Hence the absorption in this mixture was equivalent to that in a chamber
180 cm. long if filled with air alone.

Discussion of Results.
I. Comparison of the Energy Distribution Curves at Constant Voltage,
In Figs. I and 2 are shown the radiation curves of the six metals
investigated. The data for these curves were obtained under identical
conditions with a potential difference of 35,000 volts applied to the X-ray
tube, a current of i milliampere, and a slit width of .4 millimeter. The
ordinates represent intensities, as measured by ionization, and the
abscissas wave-lengths calculated from Bragg's formula, X = 2d sin B.
After the maximum of the tungsten curve had been located and its
intensity measured, this was chosen as a standard and readings were
taken for this setting of the spectrometer during the observations for
each of the other metals. This procedure was necessary in order to make
corrections for variations in the sensitivity of the electrometer from day
to day. The only other correction was made for the natural leak and
scattered radiation from the crystal and other sources. These two
errors were corrected at the same time observing the rate of leak whenby
the X-ray tube was in operation but the crystal and ionization chamber

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No's'^^] X-RAY SPECTRA OF CERTAIN ELEMENTS, 405

slightly out of step. The curves are extended only to .9 A.U. since
beyond this limit the broad characteristic bands of the L series of platinum
and tunsgten appear and also the absorption of ethyl bromide undergoes
a sharp change in this region which corresponds to the edge of the K
series absorpNiion band of bromine. These curves have practically the
same form except where they are modified by the presence of the char-
acteristic radiation and the accompanying absorption in that region.

Fig. 1. Fig. 2.

X-radiation curves of different metals.

There is a shift of the position of the maximum toward shorter wave-
lengths with increasing atomic weight. The shift is small and there
does not appear to be any simple relation between the position of the
maximum and the atomic weight.

The total energy which an element can emit in the form of radiation
is given by:

/»00

Energy = I €^d\

and the area under the radiation curve is proportional to this integral.
The curves shown above do not represent the true radiation curves since
they have not been corrected for the reflecting power of the crystal or
the absorption in the glass of the X-ray bulb, both of which vary with the

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4o6

CLAYTON T. ULREY.

Sbcomd

wave-length. However, since the curves extend over the same range of
wave-lengths, their areas will still give the relative values of the energy
emitted by the various elements. The areas were obtained by means
of a planimeter and are given in Table I. The areas due to the char-

Table I.

Blement.

Atomic Weight.

Atomic Number.

Area of Radia-
tion Curve.

Intensity of
Maximum.

Platinum

195.2

184.0

106.7

96.0

58.7

52.0

78
74
46
42
28
24

100.0
90.0
60.3
54.3
45.7
34.6

100.0

Tungsten

89.9

Palladium

58.6

Molybdenum

Nickel

50.1
43.7

Chromium

33.9

acteristic radiation were not included in the integration. When these
areas are plotted against atomic weights or atomic numbers of the
radiating elements the relation appears to vary in a periodic manner,
the periodicity coinciding with that of the chemical periodic system.
For convenience of reference the arrangement of these elements in the
periodic table is shown in Table II. The numbers are the atomic

Table II.

Series.

Group VI.

Group VIII.

24
Cr. 52

28
Ni. 58.7

42
Mo. 96

46
Pd. 106.7

74
W. 184

78
Pt. 195.2

Fig. 3.

numbers and atomic weights. The
same phenomenon is shown in a more
striking manner when the intensities
of the maxima are plotted against
atomic numbers, as in Fig. 3.

The values of the intensities shown
here are averages of a number of ob-
servations (4-6) taken on the differ-
ent elements in succession, except in
the case of palladium where the char-
acteristic radiation falls on the maxi-
mum. The value in this case was
determined indirectly by finding its

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No's^^'l X-RAY SPECTRA OP CERTAIN ELEMENTS, 407

relative intensity for a wave-length slightly shorter than that of the
maximum. The straight lines drawn through the points correspond-
ing to the members of the same series are nearly parallel. The same
periodicity was found when different voltages were used and also when
the intensities of a wave-length greater than that of the maximum were
compared.

It would be desirable to have similar data for a large number of
elements before any definite conclusions in regard to this phenomenon
be drawn, but it seems probable from these results that the number of
radiating electrons which are active in producing the continuous X-ray
spectrum, or the amplitude of their vibrations (or both) is a periodic
function of the atomic number, i. «., of the nuclear charge of the radiating
element.

II. Effect of Voltage Upon the Energy Distribution Curves.
Fig. 4 shows the radiation curves of tungsten for voltages of 20, 25, 30,
35i 40, and 50 kilovolts. A Coolidge X-ray tube was used in this case

Fig. 4.

Tungsten X-radiation curves.

as it could be operated more easily and at higher voltages than the one
previously used. The power supplied to the tube was maintained con-

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4o8

CLAYTON T. ULREY,

rSBCX>ND

Lssun.

stant at 35 watts and the results reduced to intensity per milliampere.
This was necessary in order to prevent shifting of the focal spot due to
expansion of the metal rod supporting the target. The same corrections
were made as in Part I.

The similarity between these curves and those of the radiation from
a '* black body " suggests comparison. Temperature in the " black body *'
radiation curves corresponds to voltage in the X-radiation curves. To
test the apparent similarity quantitatively we must determine how the.
frequency of the maximum varies with voltage, i. e., we must determine
the displacement law for the X-ray ciuT'es. In order for the similarity
to be complete we should have Xmax F = const, corresponding to Wien's
displacement law, Xmax^T = const, or what amounts to the same thing,
we should have the ratio, Xm«xAo ^ const, since XqF = const, as has been
proved experimentally by Hull* for voltages up to 100 kilovolts.

In Table III. are given the experimental values of the minimum

Table III.

Volts.

Area of Radia-
tion Curve.

Amax*

Amax

K>K

Amax^i.

XW-»

20,000

0.46

.615 A.U.

.710 A.U.

1.15

1,230

100.4

25,000

1.85

.490

.620

1.26

1,225

98.0

30,000

3.96

.405

.555

1.37

1,215

96.1

35,000

6.78

.355

.520

1.47

1,243

97.3

40,000

10.06

.310

.500

1.61

1,240

100.0

50,000

16.34

.250

.470

1.88

1,250

105.1

wave-length, Xo, the wave-length of the maximum energy, Xm«, and the
ratio, Xm«/Xo for the various voltages used.

From these results it is clear that the ratio Xmax/Xo increases with the
voltage and shows no tendency toward a maximum value within this
range of voltage. When the values of this ratio are plotted against the
square root of the voltage, the relation is found to be nearly linear.

Hence

-°^ = *7* + const.

Ao
XmaxF* = const.

The last column in the table shows how nearly this relation holds. It is
probable that if corrections for absorption in the walls of the X-ray
tube and in the crystal could be made, the variation in the ratio Xm«/Xo
would be less. This latter correction would involve a knowledge of the

» Phys. Rev.. VII., Jan., 1916.

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No's^'*] X-RAY SPECTRA OP CERTAIN ELEMENTS. 409

variation of reflecting power of the crystal with wave-length, which, un-
fortunately, has not yet been determined.

The sixth column in the table shows XoF to be constant which is in
agreement with the results of other observers who used the spectrometer
method to measure X©. The value of h calculated from the average
value of this constant is 6.54 X io~".

The fact that Xm^/Xo increases with voltage means that the maximum
frequencyy v©, increases at a greater rate than the frequency of the maximum^
VmtiX' This would account for the deviation from a straight line which
was obtained by R. Ledoux-Lebard and A. Dauvillier* when they plotted
maximum frequency against voltage, since they determined the frequency
by observing the position of the short wave-length limit of the continuous
spectrum from photographs. Since the intensity falls rapidly from Xmax
to zero at Xo, they probably chose as the
limit of the spectrum, a point nearer to
Xmax than Xq.

An estimate of the relative energy rad-
iated at the different voltages may be
obtained in two ways:

1. Since the radiation curves in Fig.
4 are similar and vary continuously with
the voltage, the equation of such a curve
may be deduced and when integrated
this will give a measure of the energy*
The equation of such a curve has been
deduced froin theoretical considerations
by Professor Davis.^

2. The integration of the experimental

curves may be performed directly by ob- p- 5

taining their areas with the planimeter.

The latter method was used here and the areas were plotted against

the square of the voltage in Fig. 5.

Assuming that the areas are proportional to the energy radiated, this
method shows a linear relation between the energy in this part of the X-
ray spectrum and the square of the voltage, between 25 and 40 kilovolts.
For both higher and lower voltages there are deviations from the straight
line relation. The errors previously cited may be even more serious
here, since the radiation curves extend over different ranges of wave-
length.

The curvature in the lower part of the graph is partially due to the

^ Comptes Rendu. Dec., 1916.
* Phys. Rev., IX., Jan.. 1917.

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4IO CLAYTON T, ULREY. [i

fact that a greater percentage of the total radiation is absorbed in the
walls of the tube and in the crystal for the lower voltages than the higher,
since the absorption coefficient is greater for the longer wave-lengths.
The low value of the energy for 50 kilovolts may be due to the fact
that at this voltage radiation is present which is too penetrating to be
completely absorbed in the ionization chamber. The graph does not
pass through the origin since the integration extended only to a wave-
length of .975 A.U. which is excited at a voltage of 12.66 kilovolts. For
lower voltages than this the only radiation excited would have wave-
lengths greater than .975 A.U. and therefore would not be included
in the above measurements. This also contributes to the curvature in the
lower part of the graph since, obviously, a greater percentage of the total
. energy is neglected at the lower voltages.

For the sake of comparison of methods, the data for the total X-ray
energy emitted by a Coolidge tube and measured by means of a bolometer
by P. T. Weeks* are shown in Fig. 5 by the dots. The fact that his
measurements included the effect of the characteristic L radiation would
account for the greater rate of increase of energy with voltage which

he found.

Summary.

The continuous X-ray spectra of platinum, tungsten, palladium,
molybdenum, nickel and chromium have been investigated by the X-ray
spectrometer method.

By comparison of the areas and maximum ordinates of the radiation
curves of the different elements, it appears that the energy emitted in
the form of X-radiation in this part of the spectrum is not directly pro-
portional to the atomic weight or the atomic number, but is a periodic
function of either, the periodicity coinciding with that of the chemical
periodic system.

The continuous spectrum of tungsten has been investigated over a
range of voltage from 20 to 50 kilovolts. Within this range the following
relation between the wave-length of maximum energy, Xm«x, and the
voltage is found to hold

XnuaV'* = const.

The areas under the tungsten radiation curves are proportional to the
square of the voltage between 25 and 40 kilovolts.

In conclusion I wish to acknowledge my indebtedness to Professor
Bergen Davis who suggested this work and whose development of the
X-ray laboratory made it possible.

Phoenix Physical Laboratories.
Columbia University.
» Phys. Rev., X.. Nov., 191 7.

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No's^^*] SECOND POSTULATE OP THEORY OP RELATIVITY. 4 1 I

ON THE SECOND POSTULATE OF THE THEORY OF REL-
ATIVITY: AN EXPERIMENTAL DEMONSTRATION OF
THE CONSTANCY OF THE VELOCITY OF LIGHT
REFLECTED BY A MOVING MIRROR.^

By Q. Majorana.

THE theory of relativity is based upon two well-known fundamental
postulates. The first postulate asserts the impossibility of de-
tecting the; movement of a system without referring it to other systems;
that is, it denies the physical reality of absolute movement. The second
declares that c, the velocity of light in free space, is a universal constant.
Both of these postulates are generalizations from facts or principles
heretofore accepted by physicists.

In fact, the first postulate may be considered as the extension of a
principle of classical mechanics to the optical or electrical phenomena;
an extension justified by the negative results of the experiments (Michel-
son & Morley, Crouton & Noble) designed to discover the absolute
movement of the earth or the ether which permeates all terrestrial
objects. The second postulate is the generalization of the elementary
principle of the electromagnetic or the undulatory theory of ether.

But, if these principles were taken from quite different chapters of
physics, and were severally accepted by modem physicists — ^ignoring
their origin, there would result from their union an ingenious construc-
tion ; the theory of relativity. This theory, even though contested by
Einstein and others, is a theoretical conception which led to the formula-
tion of the second postulate (the ether), and serves to explain the failure
of the experiments cited.

Now our thought, accustomed, as W. Ritz had said, to "substan-
tialize" the optical phenomena, may easily grasp the essence of the first
postulate, but it cannot do so with the second; especially since, as
mentioned before, the relativistic theories do not depend necessarily
upon the existence of a transmitting medium to explain the constancy
of c. On the other hand, the conclusions which seem artificial and
strange to all the relativistic theories* are due to the second postulate,

1 Manuscript rendered from French by Kia-Lok Yen, Ryerson Laboratory, University of
Chicago.

« Carmichael. Phys. Rev.. 191 2. XXXV., p. 168.

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412 Q. MAJORANA. [^JS

or, more precisely, to certain parts of it. This second p)Ostulate should
be understood in the sense that an observer who measures the velocity
of light, finds its value the same whether both he and the source are
relatively or absolutely (provided he admits the possibility) at rest, or
whether either the source or the observer or both of them are in uniform
motion. That is, the second postulate affirms the absolute independence
of c of whatever contingent unaccelerated velocity of either the source or
the observer.

It is known that an hypothesis of a mechanical character (emissive or
ballistic), according to which the velocity of the source should be added
to the ordinary velocity of light, could, as the theory of relativity, explain
the failure of the experiments cited before. But such an hypothesis
would be in radical contrast with the electromagnetic theory and con-
sequently would not find much favor.^ But in any case laboratory
experiments which could decide between said hypothesis, or mechanical
theory, and the relativistic theory, are imaginable. Indeed, it is p)Os-
sible to see that some method, even already known, adopted for the
verification of Doppler's principle in optics, may be able to furnish a
solution to this problem.

In order to see this, let us consider a source of light 5, which emits
waves the length of which is X and the frequence n, and which moves
with a velocity v toward the observer remaining at rest at O (Fig. i).

Fig. 1.

If we suppose that the waves are transmitted through a fixed ether,
the n waves emitted from 5 in one second will be distributed over the
segment S^A =» c — v. In the same interval there will pass by 0 all
the waves n distributed over the segment, OB = c. Consequently we
have:

c — v c . c

^— = -7 . or

n" c — v

livjc = /9, we have n' = n(i + /9)f neglecting the terms containing fi of
higher than the first order. And since c = nX = n'X. Therefore
X' = X(i — /9), which is the length of the new waves.

If instead of the hypothesis of the fixed medium we employ the previ-
ously mentioned ballistic or emissive hypothesis, we will find that in one
second the n waves emitted from 5 will be distributed over the segment

> In this connection attention should be called to the important critical work of W. Rits
(Ouvres, p. 317). which, perhaps, has not received sufficient consideration from physicists.

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No!"s^^'] SECOND POSTULATE OF THEORY OF RELATIVITY. 4I3

S'A' = c. In an equal interval there will pass by O, n' waves which
will distribute over the segment OB' = c + v. Thus we will have:

- = —7-, or n' = w(i+i8).
ft ft

And since in this case c = wX and c + v = n'\\ therefore X' = X.

As far as frequency is concerned the same result — excepting the terms
in p^ — ^is reached by both the ether and the ballistic hypotheses. But,
the values for the wave-length resulting from the two hypotheses are
different, and these values differ for the first order of /9. Thus, if Dopp-
ler's effect is measured by the observation of the wave-length, different
results will be obtained according to whether one or the other of the
hypotheses is accepted.^ Now the observations of Doppler effect have
been made up to the present by measuring the displacement of the
spectral lines by means of either prisms or diffraction gratings. In the
case of prisms, it may be observed that the theories of dispersion hereto-
fore accepted conduce to the supposition that this phenomenon may
depend only upon the frequency of the incident light. Consequently
the displacement of the spectral lines may be caused by the simple
variation of frequency due to the Doppler effect, and so the ether and
the ballistic hypotheses are equally acceptable. From this point of
view, therefore, the question whether the velocity of the propagation of
light emitted from a source does or does not change with the velocity of
the latter cannot be settled.

But besides prisms, Doppler effect has been verified by diffraction
gratings for the astronomical as well as the terrestrial sources.* If the
function of the grating is considered, from the geometric point of view,
as dependent entirely upon the incident wave-lengths, the positions of
the successive spectral lines will remain exactly definite. But since,
according to the ballistic hypothesis, the value of X does not vary with
the velocity of the source, it can be easily seen that gratings will not
give appreciable results in the examination of the Doppler effect, and so,
as has been said, will not confirm the experiment. Therefore it may be
concluded from the observations of the Doppler phenomenon in the
stars and the sun, with moving mirrors (Galitzin and Wilip), or again
in the canal rays (Stark, Paschen), that the velocity of light is constant
and entirely independent of the movement of the source; which is
equivalent to the rejection of the ballistic or emissive theory. Tolman*

> These conclusions are the same as those already published by others; see, for instance,
Tolman, Phys. Rev., 1910, XXL, p. 26.

* Galitzin et Wilip, Communications Ace. Russe, 1907, p. 213; Stark, Ann. d. Phys.,
1909. 38, p. 974.

* Phys. Rev., 1912, XXXV., p. 136.

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414 Q' MAJORANA. [15^

IS of this opinion as contrary to that of Stewart.^ As a matter of fact,
it should be remarked that the common theory of grating* would no
longer be exact in the case of the mechanical (ballistic or emissive) theory
of light. In any case it is necessary to note that the astronomical
observations of the Doppler effect are not always made with the a priori
knowledge of the relative velocity between the source and the observer.
In the case of the sun, on the contrary, it is necessary to establish a rela-
tion between the displacement of the lines and the velocity of the borders
by the observation of the sun spots; in fact, the light of the borders
may be entirely refracted by the peripheral incandescent gas, and con-
sequently the value of Doppler effect may change considerably.* In so
far as the terrestrial observations and those of the canal rays (Stark,
Paschen) are concerned, they do not give very precise measurement of
the phenomenon, and it is not possible to determine the exact velocity of
the luminous particles by another method. Finally, the observations
made with moving mirrors are not correlative to the moving sources and
so may give different and misleading results.*

Hence it may be concluded that we have not so far possessed an
altogether sure proof of the immutability of c by the variable velocity
of the source — ^if , of course, we do not wish to admit as definitely accepted,
either the simple electromagnetic theory, or Lorentz's theory of moving
bodies, or Einstein's theory of relativity. The confirmation of this
conclusion may be found in the works of those who strongly support the
last theory, and implicitly the second postulate. In these works there
is frequently found expressed the desire to discover further facts in order
to confirm definitely the said theory; this desire is found in the recent
discussions of this theory.

But, on the other hand, as Levi-Civita observed, after Einstein's last
investigations which gathered into an admirably comprehensive synthesis
all the physical phenomena (gravitation included), it is difficult to avoid
the impression that in so far as the theory of relativity is concerned there
is present something which is definitely unquestionable. But even if
this is taken into accoimt it does not mean that an attempt to obtain a
final confirmation, from an experimental point of view, of a theory which
has upset even our most simple physical ideas may be neglected. This
confirmation may arise from the accurate study of the velocity of propa-
gation of light emitted from a rtioving source, or, what amounts to the
same thing, of the value of the wave-length X of this light.

» Phys. Rev., 1911, XXXII., p. 418.

* La Rosa, Nuovo Cimento, 191 2, III., p. 356.

* Michelson, Astroch. Jour., 1901, 13, p. 192. Harnack, Ann. d. Phya., 1915, 46, p. 558.

* See theory proposed by Ritz, Oeuvres, p. 321, 371, 444.

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No's^^*] SECOND POSTULATE OP THEORY OP RELATIVITY, 415

In order to realize such study it will be necessary to imagine a disposi-
tion which, free of all external disturbance, would facilitate the examina-
tion of the structure of the light wave in its propagation, — or transmis-
sion— ^when the velocity of the source is varied at will. Now even leaving
aside the fact that the execution of the experiment under the eventual
action of the earth will be inevitable,^ there will remain still two serious
and almost insurmountable difficulties in the way of the realization of
such a programme. In the first place, it is difficult to produce arti-
ficially a rapid movement in a luminous source,* more so if the latter is
to remain rigorously monochromatic; however I shall give an account,
in a future publication, of a disposition of this nature on which I am
experimenting. Secondly, in order to examine the structure of the light-
wave emitted from a moving source, no matter with what disposition,
it is necessary to subject the same light to reflections, refractions, etc.,
which are sometimes quite numerous; that is, the light pencil has to
encounter ponderable material after leaving the source. Thus, even if c
in free space does vary with the proper velocity of the source, the in-
tensity would not return to the same fixed value after said phenomena
of reflection, refraction, etc. It would be better, therefore in an experi-
ment of this kind, to try to eliminate the greatest possible number of
cases of complications from the phenomenon, and, in any case, to dis-
cuss carefully its result.

However, in order to begin a relatively simpler experiment, the study
of the wave-length of a light pencil reflected from a moving mirror may
be undertaken. This is like the experiment already performed, several
years ago, by Belopolski, and repeated afterwards by Galitzin and Wilip.
But if the first of these authors employed prisms in the observation of
Doppler effect — ^and, consequently did not solve the question of the
eventual variation of X — the two others employed diffraction gratings
which gave rise to the controversy mentioned before. It will be better,
therefore, to examine the pencil reflected from a moving mirror by an
interferential method which is simpler than those dependent upon the
function of the diffraction grating.

Before stating this method it may be well to point out that considerable
theoretical work has been done upon the influence of the motion of the
mirror upon the wave of the reflected light. Among these treatments are
those of Abraham, Brown, Edser, Harnack, Larmore, and Plank. These

^ I am not imagining an interferential experiment of the sort proposed jocularly by Rose-
Innes. See PhU. Mag., 1914. XXVIL, p. 150.

' I mean by that a velocity greater than several hundred meters per sec. Such value may
perhaps be reached but it is difficult to conceive of a practical disposition for a greater velocity.
Naturally I set aside the employment of canal rays which do not give pure and also known
velocities.

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41 6 Q. MAJORANA. [sbriw.

works have been simply concerned either with geometrical study or with
the application of the electromagnetic theory of light. But without
discussing the results of these studies we may accept the conclusions of
Hamack^ regarding the frequency of the vibrations reflected from a
uniformly moving mirror. If v be the velocity of the mirror measured
normally to its plane, and evaluated positively when towards the source,
c the velocity of the light pencil in free space which makes an angle of
incidence / with the mirror, n, n' the frequencies of the pencil before
and after reflection, and if both the source and the observer are at rest,
we will have, putting p = v/c, the following formula:

, I + 2/g cos J H- ^

1 - ^ '

which may be reduced, by neglecting the terms containing /3*, to:

n' = fi(i + 2j8 cos /),

which is the same as that of Ketteler,* which was employed by Belopolski*
in his study of Doppler effect, and which was deduced similarly from the
consideration that the image of the source moves with a velocity 2v
along the normal to the mirror and consequently the component of this
velocity along the reflected pencil is 2v cos 7.

Now if, by suitable devices, the pencil is reflected k times, with the
incidence /, upon several mirrors moving with a velocity v, we will have

n' = n(i + 2kfi cos I).

Consequently, according to hypothesis of the constancy of the velocity
of light, we will have (neglecting the terms containing /3*) :

X' = X(i - 2*i8cos/).

If, on the other hand, the velocity of the reflected light is variable, and
is equal to c = 3'io^® cm. plus the component of the velocity of the
image along the pencil, we will have (/ = c + 2kv cos /. And since
c' = fi'X' and c = wX, we will have X' = X. The question then is to
see experimentally whether or not, besides the Doppler effect, any vari-
ation in the value of X could be detected, and hence whether c remains
constant upon the reflection by the moving mirror. I have not observed
the Doppler effect in this investigation since its existence has without
doubt been verified experimentally by the authors cited; I have rather
investigated whether and how X does vary with the velocity of the
mirror.

» Ann. d. Phsrs., 1912. 39, p. 1053; and 1915. 46. p. 547.

* Astronomische Undulationtheorie.

• Communications Ace. Russe, 1900, 13, p. 461.

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No!"5^''] SECOND POSTULATE OF THEORY OP RELATIVITY, 417

Belopolski's device for the study of Doppler effect had a disadvantage
due to the minuteness of the light pencils necessary for obtaining multiple
reflections upon the same mirror. For this reason he could not observe
the displacement of lines on the photographs. Consequently an airange-
ment as represented by Fig. 2 is adopted. On the periphery of the
horizontal brass wheel i?, 35 cm. in diameter and 6 mm. in thickness,
which can be turned with a maximum speed of 80 revolutions per sec.,
are mounted 10 glass mirrors M with their planes vertical and their back
surfaces silvered. Thus the velocity of the centers of the mirrors at
the maximum speed of revolution is more than 100 meters per second.
The number of revolutions of the wheel is determined accurately in each
experiment. The mirrors, equally spaced on the circumference of the
wheel, make an angle a of 29^ with the radius of R passing through each

Fig. 2.

of their centers. They are fastened securely to the wheel by screws
capable of rigorous adjustment. The support of the axle of R carries
the fixed mirrors F with their planes vertical as M. They are three in
number but may be decreased or increased at will up to nine. The
positions of M and F are such that when i? is at a determined angular
position a parallel beam of light L may, after a number of reflections —
7 in the figure — travel in the direction L'. Naturally the intensity of V
is considerably smaller than that of L; and the diminution is much
greater when R is in motion, since in this case the light travels in L'
only in very short instances — 10 times per revolution. It was observed
that practically the four moving and the three fixed reflections resulted
in L't a light still sufficiently intense even when R is in motion. Thus it
will be possible to make direct observations — ^without photographs — in
order to verify the light phenomenon.

In order to study the value of X, the light L' is examined by the well-
known Michelson interferometer indicated schematically in the figure.

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41 8 0. MAJORANA. [ISSS?

It IS known that if the distances SiS^ and StSz are exactly equal fringes
can be seen in the telescope c even if the light is not monochromatic:
these fringes will have the appearance of the Newton rings. But as
soon as there is a difference of path — even of only several microns — ^the
fringes can no longer be produced by white light. It is necessary to
employ monochromatic light, and the order of the interference fringes
increases with (the path) this difference. Their visibility is greater when
the vibrations are simpler. Michelson's* studies showed that from this
point of view the line which gives the greatest visibility to the fringes
with the largest path difference is the green mercury line (X = 546 /ift).
In this case, the circular fringes at infinity are visible even with a path
difference of / = 2{siSt — StSt) = 40 cm. Consequently, the mercury
arc in vacuimi is here chosen as the source L; the light from the arc is
filtered through solutions of potassium chromate and nickel chloride in
order to absorb the violet and the yellow radiations. Thus the circular
fringes at infinity can be observed with sufficient clearness by means of
the telescope c even when / = 32 cm. But in this investigation the
path difference is limited to 13 cm. or even less.

The disposition described is especially suitable for detecting the very
small variations in the wave-length of the incident light. In fact, as
the path difference is large, there are contained in this distance a very
large number of X — 200,000 if X = 0.5 n and / = 10 cm. — ^and conse-
quently very sensible displacements in the position of one fringe, cor-
responding to the variations, can be observed.

The apparatus thus arranged, the observation is made by first setting
the cross hair of the telescope micrometer in a position identical with
that of a certain fringe — for instance the first central bright one — when R
is at rest, or, better still, when it is moving with a negligible speed — say
I revolution per sec. Now if the speed of R is increased to about 60
revolutions per sec. a displacement of the fringe referred to will be seen
clearly. This displacement will indicate the diminution of X if the mirrors
move in the direction opposite to that of the incident ray; and will
indicate the augmentation if the movement of the wheel is reversed. To
determine the sense of the displacement it may be said that in examining
the system of circular fringes with the telescope focused for parallel
rays, the diameter of each of them inci eases when the mirrors are moving
against the incident light, and :*s those of greater diameter displace very
little, these fringes crowd together; and at the same time some new
fringes come into being out of the center of the system. On the other
hand, when the mirrors are moving in the direction of propagation of

* Travaux et Memoires, Bur. Int. de poids and m^sures, 1895, XI., p. 146.

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No's^''] SECOND POSTULATE OF THEORY OF RELATIVITY. 4I9

the incident light, the diameter of each of the fringes decreases, ajnd the
fringes become widely separated and some of them remain as if swallowed
up by the center.

Before saying what would be the extent of the displacement observed,
it may be anticipated by way of a hypothesis that the velocity of the
light reflected from a mirror would be the same as that of the incident
light. Let g be the number of revolutions of R per second, and d — the
distance between the centers of two opposite mirrors — be the diameter
of R, then irdg will be the instantaneous linear velocity of the mirrors.
Since these mirrors make angle a with the radius of the wheel passing
through each of their centers the component of this velocity in the direc-
tion normal to the plane of each of these mirrors will be:

V = irdg cos a.
Therefore we have:

r . 2kTrdg cos a cos /I
«' = «[!+ J;

and from the hypothesis of the immutability of c\
__ r 2kTrdg cos g cos /I

A — A I I ~" I •

L c }

Therefore when X changes into X' — that is when the velocity of the
wheel varies from zero to g revolutions per second — the number of
fringes which will pass the cross hair of the telescope micrometer will be

/ 2kTrdg cos a cos I
^ "l ~c '

where / is the difference of path of the two interfering pencils in the
Michelson interferomete»*.

If the observation is made by locating first the position of the fringes
when the wheel is turning in one direction with a speed g and then that
corresponding to an equal and opposite speed, the number of fringes
which will pass the crosshair of the micrometer will be 2/.

Now in the present apparatus, d = 38 cm., a = 2<f, I = 27**, fc = 4
(as in the figure). If X = 0.546 m (green Hg line), / = 13 cm., c = 3-10^®
cm., and g = 60 rev./sec. we will have by reversing the speed of i?,
according to the preceding formula, a displacement of 2/ = 0.71 fringe.

Actual experiment gives, for the case cited, a displacement of from
0.7 to 0.8 fringe; and it is not possible, on account of the visibility, to
push the accuracy of observer any further. But, as it may be seen,
the agreement between the predicted and observed results is sufficient.
This agreement is confirmed by observations made by choosing other

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420 Q. MAJORANA.

convenient values for / and g\ but the discussion of these may for the
sake of brevity be dispensed with here.

In view of this result we are justified in concluding that the reflection
of light by a moving metallic mirror does not modify the velocity of propaga-
tion of that light in air, and consequently — with great probability — also in
free space; this is at least so under the experimental conditions herein
described. This experimental result, about which there can be no
question, is contrary to the hypothesis of some authors, such as Stewart,^
who, on the ground of Thomson's electromagnetic theory of emission,
asserts the possibility that the light, after reflection, may travel with
a velodty c + v; where v is the component of the velocity of the image
in the direction of the reflected ray.

In order to complete these investigations I intend, as I said before,
to study further, with the same interferential disposition, the velocity
of propagation of the light from a source set in motion artificially. But
this study, as well as the general conclusions which may be drawn from
these investigations, I reserve for future publication.
Turin, Italy.

* Phys. Rev., 1911, XXXII., p. 418.

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Second Series. June, 1918. Vol. XI., No. 6

THE

PHYSICAL REVIEW.

A PRELIMINARY STUDY OF THE LUMINESCENCE OF THE
URANYL SALTS UNDER CATHODE RAY EXCITATION.

By Frances G. Wick and Loihse S. McDowell.

THE luminescence of the uranyl salts, including the fluorescence and a
short-time phosphorescence, has been extensively investigated.
The fluorescence spectrum consists of a number of more or less sharply
defined bands forming a series in which the frequency interval is prac-
tically constant. The bands of the absorption spectrum form a similar
series with a slightly shorter interval, and in the violet region of the
spectrum the two sets of bands overlap.

The fluorescence bands in the violet region are less sharp and the
measured frequency interval is slightly less than the usual interval for
the series. As the position of the absorption bands is very nearly coin-
cident with that of the fluorescence bands it seemed probable that the
change in the interval was due to the fact that a portion of each fluores-
cence band under light excitation was cut off by absorption so that the
observed position of the crest differed slightly from the true position.
To determine whether any such effect occurs the writers undertook, at
the suggestion of Professor E. L. Nichols, a comparative study of the
fluorescence of the uranyl salts under excitation by light and by cathode
rays, since in the latter case the effect is only upon the surface and there
is no absorption to shift the apparent position of the maximum.

In the course of the investigation there was discovered a long-time
phosphorescence of the uranyl salts under cathode-ray excitation, at
liquid-air temperature. Since the phosphorescence of these salts hitherto
observed had been of much shorter duration, it seemed important to
investigate further this long-time phosphorescence.

Fluorescence.
Since the variation from the uniform interval in the violet region of
the spectrum is small it was necessary that any comparison of the posi-

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422

FRANCES G, WICK AND LOUISE S. McDOWELL,

Sbcomd

tion of bands under excitation by light and by cathode rays should be
made by observations upon spectra in which the bands are narrow and
sharply defined. At low temperatures the fluorescence bands of all the
uranyl salts are resolved into groups of bands comparable in width with
the lines of a gaseous spectrum. In the chlorides, however, the bands
are resolved at room temperature and it was hoped that these salts might

be used, to avoid the experimental
difliculties involved in the use of
liquid air. Tests of rubidium, potas-
sium, c^um, and ammonium chlor-
ides showed in no case sufficient
fluorescence under cathode-ray exci-
tation to be observable in the spec-
troscope. It was necessary, therefore,
to use other crystals in which the flu-
orescence was brighter, but the bands
Fig. 1. of which were resolved only at liquid-

air temperatures.
The arrangement of apparatus is shown in Fig. i. The crystal was
placed in a cathode-ray tube, T, in such a position that the direction of
bombardment made an angle of about 45** with the surface of the crystal.
To cut off stray light, the tube was siurounded with black paper, save
for an opening about fifteen millimeters square in front of the crystal, C.
To facilitate the removal of the crystal, made necessary by the large
number of salts to be examined and by their instability, the specimen
was fastened by fine wires to a cylindrical aluminum holder, H. The
tube was then immersed in liquid air, in an unsilvered Dewar cylinder,
Df and exhausted by a Gaede rotary pump. An arc light, A^ was so
placed that the crystal could be excited alternately by cathode rays and
by light from the arc passed through violet glass, V. As a result of
observations upon a large number of crystals the salts tested were grouped
under three heads:

(a) Salts showing practically no fluorescence under cathode-ray excita-
tion.

The chlorides.
(6) Salts too wet to allow the attainment of a sufficiently high vacuum
or giving a deposit which coated the glass and prevented
observation.

1. Uranyl nitrate (hexahydrate).

2. Uranyl nitrate (oystal plates).

3. Uranyl-anunonium sulphate (with two molecules of water).

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Vofc. XI.1
Na6. J

LUMINESCENCE OP URANYL SALTS.

423

4. Uranyl -sodium sulphate (with two molecules of water).

5. Uranyl -rubidium sulphate (with two molecules of water),
(c) Salts of bright fluorescence and relative stability.

1. Uranyl-potassium nitrate, KsU02(N08)4 (crystallized from

10-30 per cent, nitric acid).

2. Uranyl-potassium nitrate, K8UOi(N08)4 (long crystals from

2-3 per cent, nitric acid).

3. Uranyl-potassium nitrate, KUOi(N03)8 (water form).

4. Uranyl-potassium nitrate, KU02(N08)s (anhydrous).

5. Uranyl-potassium sulphate.

6. Uranyl-potassium sulphate (with two molecules of water).
Of the salts in the last group the uranyl-potassium sulphate. No. 5,

was the most brilliantly fluorescent and was therefore selected for further
study. The fluorescence spectrum of the crystal was first observed under
alternate excitation from the two sources following in immediate suc-
cession. The pointer in the focal plane of the eye-piece was set upon a
given band under light excitation and, without change in the position of
the pointer, the crystal was excited by cathode rays. Observations of
the green bands showed no shift in the position of the lines with a change
in the excitation, but the first violet band, the only one observable, pre-
sented a markedly different appearance. Under light excitation it
looked like a somewhat broad, faint band, imperfectly resolved. Under
cathode-ray excitation, it showed a group of lines exactly similar to the
other groups of the series, and the brightest line in the group was found
to be of somewhat shorter wave-length than the crest of the arc-excited
band.

First Determination.

Under Arc Excitation.

Under Cathode-Ray. Excitation.

1/AXI0>.

Interval.

I/AXXO.

Interval.

.5870
.5600
.5340
.5110
.4920

1703.6
1785.7
1872.7
1956.9
2032.5

82.1
87.0
84.2
75.6

.5870
.5605
.5345
.5113
.4898

1703.6
1784.1
1870.9
1955.8
2041.6

80.5
86.8
84.9
85.8

Second Determination.

.5600
.5345
.5117
.4925

1785.7
1871.6
1954.2
2030.5

85.9
82.6
76.3

.5890
.5605
.5345
.5117
.4912

1697.1
1784.1
1870.9
1954.3
2035.8

86.4
86.8
83.4
81.5

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424 FRANCES G, WICK AND LOUIJSE 5. McDOWELL. [^SK

An independent determination of the wave-length of the brightest line
in each group which was sufficiently bright for accurate settings was
made with each source of excitation. The results obtained are shown
in Table I. The intervals calculated from the observations are in terms
of frequency, in the unit ifK X lo*.

Under cathode-ray excitation the interval in the violet end of the
spectrum is practically equal to the other intervals of the series. Under
light excitation, as has previously been observed, this interval is less.
It appears therefore that the inequality in the interval and the change
in the appearance of this violet band under light excitation are due to
absorption.

Phosphorescence.

The short-time phosphorescence produced in the uranyl salts imder
the action of violet light at liquid-air temperatures has been investigated
by Nichols and Howes.^ All the uranyl salts examined possess the same
type of phosphorescence under light excitation. The intensity falls to
one thousandth of its initial value in .0035 second. Under X-ray
excitation, some of the salts exhibit a phosphorescence of greater intensity
and longer duration permitting observation for 20 or 30 seconds.* The
discovery of a phosphorescence under cathode rays of much longer
duration than either of these opened a new field for investigation. Only
a preliminary study of the phenomenon is included in this paper. The
original observation of this phosphorescence was made during the study
of the fluorescence, in which the crystal had been alternately excited by
light from a carbon arc and by cathode rays. At the time it was not
apparent whether one or both of these sources of excitation produced the
phosphorescence. Further observations showed that the long-time
phosphorescence was produced only by cathode rajrs, after prolonged
excitation, at liquid-air temperature.

An examination was made of all the uranyl salts in group C, large,
well-formed crystals of which had been made by D. T. Wilber. They
were found to exhibit phosphorescence in varying degrees. Some showed
no phosphorescence at all. The following salts were the brightest.

1. KU02(N08)8f crystallized from acid without water of crystalliza-
tion.

2. K2U02(N08)4, discovered by D. T. Wilber and crystallizing in two
different forms. The first, form -4, was crystallized from a 10-30 per
cent, solution of nitric acid and the second, form B, from a 2-3 per cent,
solution. Although the crystallographic sj^tem is identical, form A

* Nichols and Howes, Phys. Rev. (2). IX.. p. 292.
« Frances G. Wick, Phys. Rkv. (2). V., p. 418.

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Na*6f' 1 LUMINESCENCE OP URANYL SALTS, 425

crystallizes in short, thick crystals and form B in long, slender crystals.
There appeared to be a slight difference in the phosphorescence of the
two forms. It is possible, however, that the difference observed might
have been due to some variation in the conditions under which the
phosphorescence was produced.

3. K,U02(S04)i • 2H.O.

4. K,U0,(S04),.

5. Uranyl nitrate, plate crystals.

The specimens finally selected for further study were No. 2, forms
A and 5, and No. 4, hereafter referred to as Specimens i, 2, and 3.

The work of Nichols^ had shown the spectrum of the short-time phos-
phorescence of the uranyl salts to be identical with the fluorescence
spectrum. Observations were made to determine whether the same rela-
tion holds for the long-time phosphorescence. The pointer of the eye-
piece was set upon the brightest line of each of a number of bands in the
fluorescence spectrum. After a short interval to rest the eye of the ob-
server the crystal was again excited and the phbsphorescence spectrum
observed. In every instance the |X)inter was found to be exactly upon
the corres|X)nding line of the phosphorescence spectrum. Independent
determinations of the wave-lengths of lines of the fluorescence and phos-
phorescence spectra were also made and the two found to be identical.
The latter measurements were made possible by the brilliance and long
duration of the phosphorescence which allowed ample time to make
settings uix)n the brighter lines of the spectrum.

The decay curves for the short-time phosphorescence had been found
by Nichols and Howes* to differ from the usual type in that, of the two
processes of decay, the second was more rapid than the first. Observa-
tions were made of the decay of the long-time phosphorescence of Speci-
mens I, 2, and 3. • The arrangement of apparatus is shown in Fig. 2.

Fig. 2.

A Lummer-Brodhun cube, A^ was placed at one end of a track, -YF,
about three and one half meters long. The crystal, 5, was placed
opposite one face of the cube. The comparison source, L, was a 5-volt
tungsten lamp placed in parallel with a suitable rheostat u|X)n a 55-volt

> Nichols, Proceedings of National Academy of Sciences. Vol. II.. p. 328.
* Nichols and Howes, Phys. Rev., 1. c.

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426

FRANCES G, WICK AND LOUISE 5. McDOWELL.

Smrnxma.

circuit. The lamp was mounted in a carriage, C, running on the track,
XYf on which at intervals of about twenty-five centimeters stops were
placed. Green, blue, and groimd glass absorption plates, P and P',
were inserted to obtain a comparison source of the proper color and
intensity. A chronograph was used to record the time. The zero of
time was in every instance recorded when the primary circuit of the
induction coil was broken. When the intensity of phosphorescence
matched that of the source in the first possible position the time was
again recorded and the carriage moved to the next stop and allowed to
remain imtil a match was obtained as before. This procedure was
continued imtil the phosphorescence was too faint to observe or until the
end of the track was reached.

The interpretation of the results was difficult since the instability of
the crystals rendered imcertain both the control of the vacuum and the
maintenance of the crystal surface unchanged during prolonged bom-
bardment. The general shape of the decay curve after long excitation
is shown in Fig. 3. The ciuves are plotted in the customary way with

r»

rM.1

rw^

rM.B

-^.

fr*

•

— 1

■ s

\s — ^

' — ■»

SB '

— J

^ —

--W

io — '

k — '

Fig. 5.
Time of excitation 20

Fig. 3. Fig. 4.

Fig. 3. Curves showing long-time decay. Specimen No. i.
seconds, Interval between excitations 600 seconds.

Fig. 4. Curves showing decay 'after different lengths of excitation. Specimen No. i.
Curve I. long excitation; Curve 2. medium excitation; Curve 3. short excitation.

Fig. 5. Curves showing change in time of beginning of second process. Specimen No.
2. Time of excitation unknown.

the reciprocal of the square root of the intensity as a function of the time.
This decay curve is of the usual type, consisting of two linear processes
of which the first is the more rapid. Under different conditions phos-
phorescence was observed to last froni less than a minute to ten or fifteen
minutes. The exact form of the curve varied with the time of excitation,

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Vot. XL!
Na6. J

LUMINESCENCE OP URANYL SALTS,

427

the voltage applied, and the vacuum. The time of decay was found to
increase with the time of excitation as shown in Fig. 4, but the initial
brightness changed relatively little. There was some evidence to indi-
cate that under similar conditions of vacuum the rate of the first process

•

SUA

_^?^

•

•w

^ir

■AA

-/3

^^^*

siceiios

Fig.- 6.
Curves showing efifect of varying length of excitation. Specimen No. 3. Curves i and
a. time of excitation ao seconds; Curve 3, time of excitation 40 seconds; Curve 4, time of
excitation 80 seconds.

remained practically unchanged for varying times of excitation but that
the second process began sooner for the longer excitation as shown in
Figs. 5 and 6. In Fig. 6, Curves i and 2, obtained by a short-time
excitation, show only the first
process, whereas Curves 3 and •"'
4, obtained by excitations of 40 aoo
and 80 seconds respectively,
indicate that a state of satura-
tion had been reached such
that added excitation produced
no change in the phosphores-
cence.

As has been stated the in-
itial brightness and rate of de-
cay were found to depend also
upon the strength of the bom-

^40.

■CONDI

Fig. 7.
Curves showing repetition after short excitation.

bardment. as varied by the fP^cimen No. ,. Time of «citation ao seconds.

Intervals between exatations 63 seconds, 67 seconds.

pressure in the tube and by the

voltage applied to the induction coil. The curves of Fig. 3, for example,

were obtained with a relatively high vacuum whereas those of Fig. 7

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428

FRANCES G. WICK AND LOUISE 5. McDOWELL,

fSlCOMD

LSbeus.

SICONOS

■TOT

Fig. 8.
Curves showing repetition after
long excitation. Specimen No. i.

were obtained with a very low vacuum, so that the decay was com-
paratively rapid and there was only a suggestion of the beginning
of the second process in the position of the last point observed. Slight
changes in temperature, such as were produced when the liquid air fell
below the line of the crystal were fotmd also to produce changes in the
initial brightness and rate of decay.

To determine whether the excitation produced any secondary change
in the crystal which persisted after the phosphorescence had disappeared,

so that there would be a progressive
building up of the phosphorescence, ex-
citations were made of equal length,
repeated at as nearly equal intervals as
decay observations permitted. Fig. 7
y shows that at a fairly low cathode vac-

/^ uum an excitation of 20 seconds repeated

at approximately one-minute intervals
produced identical decay curves. The
same effect is shown in Fig. 8 for a
much longer period of decay. When the
time between excitations was short as
compared to the time and strength of
excitation there appeared to be a progressive change as indicated in
Fig. 9-

As a result of this investigation three
definite conclusions may be drawn :

1. The irregulaiities in the fluorescence
spectrum of the uranyl salts under light ex-
citation are due to absorption.

2. The spectrum of the long-time phos-
phorescence produced by cathode-ray exci-
tation at liquid-air temperatures is identical
with the fluorescence spectrum.

3. The decay curve is of the type usual
to phosphorescence of long duration in
which the second process is less rapid than
the first.

No satisfactory conclusions as to the
effect of variations in time of exposure and
strength of cathode-ray bombardment, or
the influence of previous excitation can be drawn imtil conditions can

SUA

A-

AAA

•

iv-

\ — '

— 11

SICONOS

Fig. 9.
Curves showing effect of pre-
vious excitation. Specimen No.
a. Time of excitation, ao seconds.

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No'd'^''] LUMINESCENCE OP URANYL SALTS. 429

be more exactly controlled. It is hoped with further study to obtain

results capable of more exact interpretation.

The investigation was carried on at Cornell University during the

summer of 1917, and the writers wish to express their sincere thanks to

Professor E. L. Nichols for his kindness in making the work possible.

Vassar Collbgb,
Wellbsley College.

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430 ARTHUR H. COMPTON.

NOTE ON THE GRATING SPACE OF CALCITE AND THE
X-RAY SPECTRUM OF GALLIUM,

By Arthur H. Compton.

TN a recent number of this journal^ Uhler and Cooksey have described a
-■• method of measuring the angle of reflection of X-ray spectrum lines
which seems to be remarkably free from systematic errors, and capable
of high precision. They applied their method to the determination of
the angle of reflection of the characteristic K lines of gallium from a
crystal of calcite. In calculating the wave-length of these rays they
obtained the grating space of calcite by comparing it experimentally
with the grating space of rock-salt, which can be determined in terms of
the known crystal structure. In making this comparison, however, they
determined the angles of reflection from rock-salt by an "old" method
which, as they point out, is liable to introduce appreciable errors. Their
determination of the grating space of calcite and hence also of the wave-
length of the characteristic X-rays from gallium, is therefore no more
accurate than the measurements made by the "old" method which they
criticize.

The reason assigned by Uhler and Cooksey for making this experi-
mental determination of the grating space is "because a sufficiently
satisfactory reduction factor [the ratio of the grating space of calcite to
that of rock-salt] if present in the literature of the subject, has escaped
our notice." It should be noted that the grating space in the case of
calcite may be calculated from the known crystal structure as well as
in the case of rock-salt. The formula to be used is given by W. H.
Bragg* and the writer* as,

where Mi is the molecular weight of CaCOa, pi is the density of the calcite
crystal, N is the number of molecules per gram molecule, aind <l>(fii) is
the volume of a rhombohedron the distance between whose opposite
faces is unity, and the angle between whose edges is Pi. This function is*

» Phys. Rbv.. 10, 64s, 1917.

«W. H. Bragg. Proc. Roy. Soc. A., 89. 468 (1914). "X-rays and Crystal Structure.'*

p. 1 12.

» A. H. Compton. Phys. Rbv., 7. 655 (1916).

* A. H. Compton. loc. cU, Professor Bragg uses the value ^(fi) » 1.08, which makes his
value of d for calcite differ appreciably from that here obtained.

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No'ef^'l GRATING SPACE OF CALCITE, 43 1

_ (l+COS|gi)^

^^'^ " sin /3i(i + 2 cos iSi) •

For calcite j9i = loi** 55'^ which makes ^(iSi) = 1.0963.
The corres|X)nding expression for the grating space of rock-salt is

(2)

"^m''

the subscripts 2 indicating that the molecular weight and density are
those corresponding to rock-salt. The reduction factor sought by
Uhler and Cooksey is, therefore,

(3) R =

di _ / Mips

,)'

which gives the ratio of the grating space of calcite to that of rock-salt.

Bragg's expression* is not dependent upon the details of the arrange-
ment of the atoms in the calcite crystal. It expresses only the fact
that each elementary rhombohedron contains half a molecule of CaCOj.
The imcertainty of the applicability of this formula is thus no greater
than in the corresponding case of rock-salt. In fact the calculated value
of the grating space of calcite is probably the more accurate, since this
crystal is more perfect and is less apt to contain inclusions than is rock-
salt.

Substituting in formula (i) the values:

Ml = 100.075,'

Pi = 2.71 16 g. cm.-V

N = 6.062 X 10^ per gram molecule,*

«05i) = 1.0963,

we find for the grating space of calcite,

d = 3.0281 X io-« cm.

The greatest uncertainty in this value is due to iV, whose probable error
is d: 0.1 per cent. Since N occurs in the 1/3 power, the probable error
in d is about .033 per cent. Thus the grating space of calcite is

di = 3.0281 ± .0010 X 10-® cm.
The value determined by Uhler and Cooksey by comparison with rock-

» Calculated from Dana's value of 74*55' for the dihedral angle.

« W. H. Bragg and W. L. Bragg, "X-rays and Crystal Structure." p. no.

'International Atomic Weights 191 7.

* A. H. Compton, loc. dt.

» R. A. MUlikan, PhU. Mag.. 34. 13 (1917).

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432 ARTHUR H, COMPTON,

salt, using dt = 2.814 X io-« cm. is di = 3.0307 X io~* cm. Gorton*
has determined the grating space of calcite by a similar comparison
method, using the same value of dj, and obtains di ■= 3.028 X lO"* cm.,
which agrees absolutely with the theoretical value. Millikan* gives for
the grating space of calcite the value (3.030 ± .001) X io~® cm., calcu-
lated by D. L. Webster* using Millikan's value of e. In this calculation
Webster has made use of Bragg's value of 4>(fi^ = 1.08 instead of
the true value 1.0963, which accounts for the difference between his value
and that here given.

The wave-lengths of the characteristic X-rays from gallium given by
Uhler and Cooksey require revision because of this error in their deter-
mination of the grating space of calcite. Their determinations of the
angles of reflection from calcite were verified by their "new** method, and
hence are not subject to the errors introduced when they determined the
angles from rock-salt by their "old ** method. Their values for the angles
of reflection from calcite may thus be accepted without discount. Their
values for the wave-length are given in the following table together with
the corrected values using the value of di = 3.0281 ± .0010 X lo*^ cm.

Line.

on.

Rtfltction Angle from Calcite.

12° 47' 15" ± 2"
12** 45' 5" ±2"
11" 28' 30" ±2"

AX 10* cm. Uhler ft Cookeey.

1.34161 ± .00004
1.33785 ±, .00004
1.25691 ± .00000

Axio* cm. Corrected.

1.34046 ± .00045
1.33673 ±, .00044
1.20482 ^ .00041

The probable error in the wave-length is estimated by Uhler and
Cooksey on the basis of their probable error in measuring the angle.
It should be noted that a much larger error in the wave-length is intro-
duced by the uncertainty of the grating space.

Rbsbarch Laboratory,

Wbstinghousb Lamp Company,
January 2a, 1918.

» W. S. Gorton, Phys. Rbv.. 7, 209 (1916).

* R. A. MilUkan, loc. cit., p. 16

» D. L. Webeter, Phy§.'Rbv., 7, 607 (1916).

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S2-6^^] X-RAY EMISSION. 433

CHARACTERISTIC X-RAY EMISSION AS A FUNCTION OF
THE APPLIED VOLTAGE.

By Bergen Davis.

RECENT experiments of D. L. Webster^ show that the energy of
emission of characteristic (line) radiation from a rhodium target
increases rapidly as the voltage applied to the Coolidge X-ray tube is
increased. The radiation is not produced at all unless the voltage is
greater than a minimum Fo. This minimum voltage is slightly greater
than that corresponding by the quantum relation to the frequency of
the P line (X-radiation). This law is undoubtedly true also for the
characteristic X-ray emission from other elements.

It may be of some interest and value to investigate how this emission
should depend on the voltage from a consideration of well-established
physical facts. The following facts relating to the problem may be
regarded as established by experiment.

(a) The characteristic line emission is zero for all voltages less than a
critical voltage Fo.

(ft) The voltage Fo at which the characteristic radiation is produced
is that corresponding by the quantum relation, V^e = A«, to a frequency
slightly greater than that of the K^ radiation of the element.

(c) At voltages equal to and greater than F© both the a and P lines of
the K radiation are emitted. These two lines increase rapidly in intensity
with the voltage, their ratios remaining approximately constant.

((/) X-radiation is not only emitted from the surface atoms of the
target, but also from the atoms beneath the surface when they are im-
pacted by the electrons of the cathode stream.*

(e) The electrons penetrate a short distance into the surface of the
target, but their velocity diminishes rapidly with depth of penetration.

(/ ) The emitted X-rays are absorbed on their passage through matter.
This absorption depends on the thickness and nature of the material
traversed.

The only hypotheses adopted will be directly in keeping with the
Bohr theory of the atom. The Bohr picture of the atomic mechanism,
which is so successful in the case of the ordinary radiation from hydrogen,

> Phys. Rev., June, 1916.
* Kaye, X-rays, p. 40.

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434 BERGEN DAVIS. [^^

is almost equally successful in the case of characteristic X-radiation,
since the frequencies of the K^ radiation from many elements may be
readily calculated by the Bohr equation for the hydrogen atom.

According to this theory the frequency of the radiation emitted by an
atom depends on the change of the potential energy of one or more elec-
trons of the atom with respect to a central nuclear charge. This change
of potential energy is radial with respect to the central nucleus.

It will be considered that radiation can only be excited by the transfer
of energy from the impacting electron along a radius with respect to the
center of the atom.

The mechanism of the atomic nucleus will be considered to emit a
quantum of energy whenever an impacting eleckon possesses such velocity
that the energy due to the radial component of this velocity shaU be equal to
or exceed the minimum energy (Voe) required for the excitation of the
particular radiation. The work done along the radius must be equal
to or exceed the quantity (Fo«) where Fo is the least voltage that will
excite the characteristic radiation.

Let N represent the number of electrons striking the surface of the
target per second. Let B represent the probability of any one electron
making impact with or coming within the spheres of influence of the
atomic nuclei in unit distance. The number of such impacts in a distance
dx will be

BNdx.

The X-radiation appears to have its origin in the nucleus of the atom.
It is considered that the impacting electron in order to excite the radiating
mechanism of this nucleus must come within an undefined region about
the nucleus which will be referred to as the sphere of influence of the
nucleus. The probability Bdx of an electron striking one of these
nuclear spheres in a path dx is quite small.

Not all of these BNdx impacts with the nuclei will excite radiation,
but a fraction of them will do so. The capacity to excite radiation
depends on the nature of the impact. Only those impacts will be effective
in which the energy due to the radial component of the velocity is equal to
or exceeds a minimum (Voe), This assumption which has previously
been applied to ionization by impact^ is, as has just been pointed out, in
agreement with the Bohr theory of the atom.

The fraction of the BN electrons that are effective may be readily
found by consideration of Fig. i.

For the purpose of presenting a picture to the mind one may tentatively
regard an atomic nucleus to be represented at C, and the bounding sphere

» Phys. Rev., Jan.. 1907. An. d. Physik.. Band 42. 1913.

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Vol. XI.I
Na6. J

X-RAY EMISSION.

435

of influence within which the electrons must penetrate in order to excite
radiation to be represented by abed.

If the velocity of the electrons on approaching this bounding sphere is
that corresponding to Fo, only those that make impact along the line h
will be capable of producing the
radiation. All other electrons
will have a radial component
too small to be effective. As
the voltage is increased, elec-
trons approaching the nucleus
further from the atomic pole
a, as along fg, may have a ra-
dial component at least equal
to Vq. As the voltage is fur-
ther increased electrons ap-
proaching along a line as far
from the pole as m n may be
effective. The fraction of the

Figl.

impacts that will be effective is the ratio of the cross-section of the zonal
area nn to the area of cross-section of the nuclear sphere bd. This ratio
may be expressed in terms of the voltage V and is

V-Vo

V '

Of BNdx impacts in a region dx at a depth x within the target the
fraction

will be effective in producing radiation where Vg is the voltage corre-
sponding to the velocity that an electron may have at a depth x beneath
the surface of the target.

Each of these effective impacts will emit a quantum of energy of some
frequency. All of the X-radiation does not appear at one frequency,
but there are other frequencies emitted in addition to the stronger a
and P radiations. The electrons in general do not possess sufficient
energy to excite both the a and P lines, since the energy required would
be (An. + htip).

Of all the effective impacts, a fraction will produce a disturbance
that results in the emission of radiation of one frequency, the* Ka radia-
tion for example. The fractional part of the total effective impacts that
result in the production of radiation of frequency «« will be designated

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436 BERGEN DAVIS. [I

by £.. This constant £. will be more fully discussed in the last para-
graph of this section of the paper. Each of these

EJBN^'Z^'dx

y *

impacts will produce a quantum of energy A«.. The energy radiated
will be

dh = E,{hn:)BN^' 71 ^Ux. (i)

y m

The law of decrease of the velocity of electrons penetrating a metallic
surface has been derived by Sir J. J. Thomson* and experimentally
confirmed by Whiddington.* This law is expressed by the equation

i?,4 = i;< — ax, (2)

where r, is the velocity at a depth x and a is a constant depending on the
nature of the material. This equation may be expressed in terms of the
corresponding kilo- volts F and becomes

F,« = V« - bx, (3)

where b is the corresponding value of the constant a.
Equation (i) may then be written

7. = £.(A„.)Biv[/dx - j^Jfl^y^} . (4)

The X-rays when emitted from a region djc at a depth x below the
surface will be subject to absorption in passing up through the material
of the target. The quantity emitted from any depth x will be

where fi is the coefficient of absorption of the material for the radiation
of the given frequency, and ex is the thickness traversed by the rays in
emerging from the target. The radiation actually emitted becomes:

/ = E,{hn:)BNl r e'^^'dx - Vo T {V* - 6jc)-i/««-^"^1 .

(5)

The limit R is the range of the electrons before their velocity is reduced
to that corresponding to the voltage F©. From equation (3)

Fo» = F« - bR,
and

I^'^^. (6)

^ Conduction Through Gases, p. 378.
« Proc Roy. Soc.. Vol. 86, 1912.

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No'^'*! X-RAY EMISSION, 437

The indefinite integral of (5) is not obtainable, but a close approxima-
tion may be obtained by expanding the exponential term. Since this
expanded term is rapidly convergent for the values iicx here required it
IS necessary to retain only a few terms of the series. The resulting
integral is

J = £.(AnJ ^ r A (I _ e-c«M/»xn- W)

-2Fo(F- Fo)+^yFo{2F»- Fo(l^+Fo*)}

-iV,{V^'-Vmi (7)
The variable part of this equation contains no arbitrary constants. The
constants b and cii may be obtained by independent experiment.

In order to compare this equation with experiment, I have taken some
results just obtained by Mr. B. A. Wooten (not yet published) for the
emission of the K characteristic (a line) radiation from molybdenum.
The difficulty of making this comparison arises from the fact that no
experimental results are at hand either for the decrease of velocity of
electrons (constant b) or for the absorption of rays of this particular
frequency (constant /*) for molybdenum.

The constant a has been determined by Whiddington^ for gold and
aliuninium.

(Al.) a = 7.32 X io*«.

(Au.) a = 2.54 X io«.

If the density of the material be represented by p

(Al.) - = 2.83 X io«

(Au.) - = 1.33 X io«

The stopping power of a metal does not appear to be directly related
to its density. One can only estimate its value for molybdenum. la
the absence of experimental data I shall tentatively assume a value
between that found for gold and aluminium.

Taking alp = 2.2 X 10**, the value of a is 1.9 X io*». The corre-
sponding value of this constant when the velocity is expressed in terms
of kilovolts is

6 = 1.5 X io«.

^ Loc. cit.

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438

BERGEN DAVIS.

ISboona
Sbubs.

The absorption coefficient m of molybdenum for its own K character-
istic radiation has not been determined, but the coefficient of absorption
of these rays in silver is given by Kaye^ as

p = 24.4.

Since molybdenum does not differ much from silver in atomic weight
and density, this will be provisionally taken as the absorption coefficient

of molybdenum for its own
characteristic radiation.

fjL = 200.

In the particular experi-
ments of Wooten the X-rays
were taken from the target
at such an angle that the
path of the rays emerging
from the target was about
1.5 times the path (x) of the
penetrating electrons that
produced them. The con-
stant c is 1.5. The group
constant bfcfi of equation (7)
has the approximate numer-
ical value 5,000.

The theoretical equation

as derived is calculated and

plotted in Fig. 2. The

*^' * curves are plotted with the

square of the applied voltage (kilovolts) as abscissae, since this makes

the greater part of the curve nearly a straight line. The circled points

represent the observed results obtained by Wooten.

The form of the calculated curve is similar to that obtained by experi-
ment. Since the variable part of the equation contains no arbitrary
constants, the assumptions underlying its derivation appear to be
justified.

The energy of emission of different elements may be expected to in-
crease rapidly with the atomic number. The energy emitted is propor-
tional to A«, where n is a frequency slightly greater than that of the Kp
characteristic of the element, and this frequency is nearly proportional

» X-rays, Kaye, p. 138.

►

IJl

A'i

(

r c

>■

—

"^n

QTi

r-^

—

"To

55^

"«

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JKi"^'-] X-RAY EMISSION. 439

to the square of the atomic number. If the constant £. were of the
same value for all elements, this increase in emissivity would be approxi-
mately proportional to the quantum hn.

The factor B, which is a constant for any one element, may depend
on the atomic number. The introduction of this constant is required,
since it is assumed that every effective electron at impact will give rise
to a quantum of radiant energy. The fraction of the total electrons
of the cathode stream that are effective must be very small. The greater
part of them dissipate their energy directly in the production of heat, or
indirectly by the excitation of other types of radiation by disturbance
of the electrons in the outer regions of the atom. It is possible that the
greater part of the transfer of kinetic energy of the impacting electrons
to the atoms does not take place directly through the interchange of
momentum, but they may excite radiation in the ultra-violet, visible
and infra-red regions by disturbance of the more loosely bound electrons
of the atom. This radiation is absorbed by the atoms and finally appears
as heat.

Equation (7) without the constant E^(hnJ would represent the number
of impacts of the electrons that have a radial component of velocity
equal to or greater than that corresponding to the critical voltage Vq.
All the energy of these effective impacts cannot appear as radiation of
any one frequency, tie for example (where n© is the frequency correspond-
ing to the critical voltage Fo). There are at least two strong lines (a
and p) and a number of weaker lines in the JST-radiation, also there are
a number of lines in the L characteristic radiation. In addition there is
the general radiation of the " continuous*' X-ray spectrum. Each effec-
tive electron at impact gives rise to only one quantum of energy, so that
the same electron cannot excite the characteristic lines as well as the
general radiation. There must be some statistical partition between
the number that give rise to each type of radiation.

The constant £. expresses the fraction of the effective impacts that
excite radiation of one frequency and the combined constant £. (An.)
expresses the fraction of the radiated energy produced by the effective
BN electrons that appear as radiation of one frequency, the K^ radiation
in the present discussion.

This partition or distribution of energy between the characteristic
and the general radiation appears to be nearly constant and independent
of the voltage. The experiments of Brainin^ show that the total radia-
tion (characteristic plus general) from molybdenum increases as the
square of the applied voltage. The experiments of Wooten show that

» Phys. Rev.. Nov.. 191 7.

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440 BERGEN DAVIS.

the characteristic radiation increases approximately according to the
same law. It follows that the partition of energy between the two types
is constant independent of the voltage.

X-Radiation from Thin Films.

D. L. Webster^ has proposed experiments with thin films for the
purpose of studying the nature of the general or "white" X-radiation.
An investigation of the emission of characteristic (line) radiation from
thin films would also be of interest and value.

The rapid increase of the emitted energy with increase of voltage may
be regarded as due to two causes:

(a) The increase in the emission from each atomic nucleus due to the
increased energy of the impacting electrons.

{b) The penetration of the electrons into deeper layers of the target
with sufficient energy to excite the radiation.

In the case of thin films, if the velocity of the electrons at entrance
to the film is sufficiently great they may pass completely through the
film and emerge on the far side with sufficient energy still to produce
radiation. The part of the radiation that would have been produced by
these electrons after passing through the film will be absent and the
curve representing the emitted energy will have a break at this point.

A convenient method of investigating this by experiment would be to
deposit a thin film of the metal of known thickness upon another metal
as a support. If the frequency of the characteristic radiation of the solid
supporting target differs from that of the film, the line radiation of the
supporting element will not enter the slit of the spectrometer. The
radiation from films much thinner than could be independently supported
may thus be readily investigated.

From such a film as the voltage is increased the radiated energy will
at first increase rapidly in intensity. When the voltage becomes such
that the electrons emerge from the far side with an energy greater
than (Fo«), the increase in radiation will not be so rapid. That part
of the emission due to deeper penetration at this voltage will be absent.
There will be a change in the slope of the radiation curve as indicated at
ft» Fig. 3. This will be true independently of any special theory of X-ray
emission other than that a portion of the increased emission is due to
deeper penetration of the electrons into the target. This phenomenon
furnishes a convenient method for measuring the decrease of velocity
of electrons on passing through matter. Thus the point b in Fig. 3 corre-
sponds to a voltage across the X-ray tube of about 33.5 kilovolts. The

' Phys. Rev.. March, 191 7.

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Na"6^^'] X-RAY EMISSION. 44 1

electrons entered the film with a velocity corresponding to 33.5 kilovolts,
and emerged from the far side with a velocity corresponding to
Vo = 19.2 kilovolts. These results are calculated for a film of molyb-
denum 5 X io~* cm. thick using the value of the constant b previously
deduced from Whiddington's experiments.

The form of the radiation curve for a thin film may be readily derived
in a similar manner to that for a solid target.

Consider a film of thickness d deposited on a solid support. The radia-
tion will be that from a solid target of the same material as the film less
that emitted by the portion of the solid target lying at a depth greater
than d.

If^E^ihnJBNlJ'' ^^^^^e-'^^dx-e-'^^ £^^y ^'e^^dxi^ .

The depth of the electron within the surface of the solid portion of the
target is designated by xi. All of the radiation produced in the xi
region passes through the film of constant thickness d, hence the absorp-
tion due to the film d may be placed outside the integral sign.

The first term of the right-hand member is the same as equation (5).
Let / represent this term. Let /, represent the second term.

// = / - /., (8)

I.^E^ihnJBNj -''-y^e-'^^dxi.
Introducing the law of decrease of electron velocity

(9)

V^* = F/ - bx,
and expanding the exponential, the equation is integrated as in the case
of (7).

The voltage corresponding to the velocity with which the electrons
emerge from under side of film and enters the Xi region is designated by
F«i. The range R of the electrons in the Xi region is

Fo» = Fd* - bR.
The R limit is

^= b •
The integral of (9) for the specified limit is

Cfl

- 27o(Fd - Vo) + 2/3^ F,{2F<i» - Fo(F/ + Vo*)]

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442

BERGEN DAVIS,

- 7^'(yy{8^-'(^- - ^o) - 4V<fVo{v^ - Vo

-3n(F^- Fo«)m]. (io)
The value of Vd is given by the relation

Fd« = F» - W,

where V is the voltage applied to the X-ray tube.

The above equation is zero for Vd — Vo as it should be. It is to be
calculated only for values of Vd greater than F©. A plot of this equation
is shown at ntn p in Fig. 3. The constants b and m are given the same

111

\ri

»iS

■*c

U
t

./^

. 1.

f A

^jf

^ \

/—

-R

•0

£_

Fig. 3.

values as in the plot of Fig. 2. The thickness of the film is taken to
be d = 5 X 10-* cm.

This curve is subtracted from the curve abed as indicated by (8).
The resultant curve ab ef represents the radiation from a thin film.

The equation and its plot indicate that the radiation could not in-
definitely increase, but at a high voltage it would approach a maximum
independent of the voltage. Consideration of the physical processes
involved would also lead one to anticipate this result.

An inspection of equation (7) for large values of m (that is very soft

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Na*6f^*] X-RAY EMISSION, 443

rays) shows that the radiation from a solid target (Fig. 2) would not in-
definitely increase with the voltage. The energy emitted will tend
toward a maximum independent of the voltage. This result is also to
be expected from a consideration of the physical processes involved.
In the case of elements such as copper, chromium, etc., which have a
characteristic radiation of long wave-lengths, the radiation emitted from
atoms at considerable depths below the surface would be largely absorbed
in the target. The resultant emission would be similar to that from thin
films. The above remarks are true in a degree for the characteristic
emission from all elements. The energy radiated cannot increase in-
definitely with the voltage. This is necessarily true, otherwise at ex-
tremely high voltages the radiated energy might become greater than
that of the bombarding electron stream — a result that is manifestly
impossible.

Emission from Thin Films. (Far Side.)

Another matter of interest is the emission of the characteristic radia-
tion from the far side of a thin film. The expression for the radiation
for this case is readily derived by the methods pursued in the previous
developments.

Let the thickness of the film be designated by d. The thickness of
material traversed by the X-rays emitted from any depth x and emerging
from the far side will be (d — jc).

The radiation may be represented by

I ^ EMna)BN P—^^e-^^^-'^dx. (11)

Since

/ = E.ikn.)BNe-^\j\^^dx - ^of ^V^,]. (12)

The constants and the limit R have the same significance as in the
equation for a solid target.
The integral equation is

/ = E.(A»J5iV^ T-(«-('*'»X'^^«« - 1)

2 M

- 2V,{V - 7o) -- J F,{2 7» - Vo{V* + Fo»)}

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444

BERGEff DAVIS.

A plot of this equation is shown in Fig. 4. It is to be noticed that the
curve is much more concave upward than the curve for the emission from
a solid target (Fig. 2). The variable part of the equation does not con-

r—

-•)

"lo

«0

—

Fig. 4.

tain the term involving the thickness of the film. The form of the

radiation curve is independent of the thickness of the film provided this

thickness is greater than the range R of the electrons producing the

radiations.

PHotNix Physical Laboratory,

Columbia University,

January, 1918.

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Na*6f ^'1 NEGATIVELY ELECTRIFIED RAIN DROPS. 445

ON THE FORMATION OF NEGATIVELY ELECTRIFIED RAIN

DROPS.

By Fernando Sanford.

IT IS known that in fair weather the electrical condition of the atmos-
phere is usually positive everywhere over the earth's surface. This
is regarded as the normal condition of the atmosphere, and it is subject
to periodical changes which for a given place are fairly constant, day after
day and year after year. It is also well known that on account of its
high specific inductive capacity water will take a positive electrical
charge by contact with nearly all known substances. Lord Kelvin,
Lenard and especially Coehn and Mozer* have shown that gases bubbled
through pure water carry off charges and leave the water positively
electrified. This makes it practically certain that the positive elec-
trification of the air is located upon the minute drops or the molecules
of water in the air.

It has also been known for a long time that the air in the vicinity of
waterfalls becomes negatively electrified, and Elster an4 Geitel showed
that this condition may be appreciable to heights of at least 500 meters
above the waterfall. Lenard* showed that the negative electrification
arises near the foot of the waterfall where the water is dashed or blown
into spray, and that it seems to occur wherever in rapids or falls spray is
produced, while it is imperceptible over a smoothly flowing stream.

Dr. Simpson' showed that when drops of distilled water fall through a
vertical air blast strong enough to produce spray the small drops of water
formed have negative charges much more often than positive charges.
Since the small drops are carried upward much faster by a rising current
and since they fall more slowly through still air than the large drops, they
may become separated by air currents or by gravitation from the larger
electropositive drops. Since drops of water cannot fall through still air
faster than about 8 meters per second without being torn to pieces by
atmospheric resistance, it would seem that an electric separation must
be produced whenever large raindrops fall from a considerable elevation.

> Ann. d. Phya., 43, X048 (1914).

* Ann. d. Phys.. 46, 584 (1892).

* Quoted from Humphreys's article on '* The Thunderstorm and Its Phenomena " in Monthly
Weather Review, June, 1914.

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446 FERNANDO SANPORD, [^SS

Given the small negatively electrified drops that are thus blown off
from the positive drops, it seems possible to account for all the phenomena
of thunderstorms, and Humphreys has done this very successfully in
the paper to which reference has been made. The question which
seems thus far to have been impossible of explanation is how negatively
electrified drops may be blown from positively electrified drops by a wind
which regularly gives off positive charges to water. In order to find an
answer to this question it is important to know how exretmely small
drops, such as take negative charges, may be formed from larger drops.

It has frequently been observed that when a drop of liquid breaks
away from a larger mass the liquid which joins the drop to the larger
mass is drawn out into a narrow cylindrical neck before it is pinched off
at one end by the contraction of its surface film. Plateau^ has shown that
a liquid cylinder is in a condition of unstable equilibrium when its length
exceeds about three (t) times its diameter. Such a cylinder will break
up into segments whose distances apart are approximately equal to the
circumference of the cylinder, and these segments spontaneously take
the spherical form. Accordingly, when such a liquid cylinder has been
drawn out between two separating drops and is pinched off at one end
by its surface film it immediately forms one or more small drops which
break away from the larger drop.

The formation of these little drops between larger ones has frequently
been shown photographically, but it may be observed directly without
any artificial aids. Thus if ink be dropped from a pen filler which is
held before an illuminated white surface, as a sheet of white paper against
a windowpane, a small drop may almost invariably be seen following the
larger drop. If a low power magnifying glass be placed in front of the
falling drop so that it will come into the field of view just after breaking
away from the dropper, the little drop may be seen to form from the
liquid neck which clings to the falling drop instead of to the dropper.
That is, the liquid which forms the little drop breaks away from the
dropper and then later from the falling drop. The little drops may be
collected and their size compared with that of the larger drop by catching
them on a moving piece of paper. Since the little drop falls more slowly
than the large drop it may easily be caught to one side of it. The same
thing may be done by giving the dropper a horizontal motion just as the
drop separates from it. When the drops are collected in this way, the
large drop is seen to have several thousand times the volume of the
little droplet.

If a drop of ink or of colored glycerine be dropped through a hori-

* Statique Des Liquides, Vol. i, p. 75.

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Noe"!^^'] NEGATIVELY ELECTRIFIED RAIN DROPS, 447

zontal air blast, such as is used with a laboratory blow pipe, the drop
will be blown to pieces if the velocity of the air is sufficiently high.- By
spreading sheets of paper below the falling drop the separate drops may
be collected. It will then be seen that there are a few larger drops and
a great many little droplets. If the blast is not too strong, the original
drop still remains larger than any of the
others, and the drops of intermediate size
are apparently blown off from this one at a
time. This conclusion may be verified by
dropping a liquid from a sufficient height to
cause the drops to be separated by air fric-
tion, when it will be seen that the first divi-
sion is into two drops of very unequal size.
Figure i shows a photograph of the splashes
made on a sheet of absorbent paper by a
drop of ink falling from a height of about 20

feet. An observer noticed that the drop struck the paper as two sep-
arate drops, and the splashes show that one was much larger than the
other.

It is plain that when the drops of intermediate size are blown off from
the larger drop there are always one or more of the little droplets formed
from the liquid neck which is drawn out between the two, and these tiny
droplets are those which receive the negative charges. The conditions
for forming the negative droplets are then pretty definitely known.
First, a drop smaller than the original positively electrified drop is
blown off from it. This drop is also positively electrified. Before it
breaks away from the original drop, a narrow neck of water is drawn out
between them. This breaks away from the original drop, then from the
' secondary drop, and becomes a negatively electrified droplet.

This phenomenon of charging a small body by induction between
two similarly electrified bodies may easily be reproduced in the laboratory.
If two insulated metal spheres or cylinders of unequal radius be placed
in contact and charged positively and then be separated to a small dis-
tance while still remaining charged, a very small insulated sphere when
introduced between them may take a positive charge by contact with
the surface of the larger sphere or cylinder or a negative charge by contact
with the smaller. Thus the inductive effect of the larger sphere upon the
smaller is sufficiently great to cause it to give off a negative charge to a
small conductor touched to the point nearest to the larger sphere; or to
put it another way, the charge which the little conductor may take by
induction between the two spheres is greater than the opposite charge
which it may take from the smaller sphere while in the same position.

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448 FERNANDO SANPORD. [ISS?

The conditions under which the negatively electrified water droplets
are formed seem to be exactly reproduced in this laboratory experiment.
The little droplets are formed between two positively electrified drops of
unequal size. They break away first from the larger drop, and then
while still very close to it, from the smaller drop, taking a negative
charge by induction of the larger drop.

The only reference to the above induction experiment which the

present writer has been able to find in the literature of electricity is in

Dr. Thomas Thomson's Heat and Electricity, which was published in

1830. Dr. Thomson attributes the discovery of the phenomenon to

Coulomb. He says that by using two globes, one 1 1 inches in diameter

and the other 8 inches in diameter, which were positively charged while

in contact. Coulomb was able to take a negative charge from the smaller

globe when their surfaces were separated by one inch, and that when a

globe 4 inches in diameter was used with the 11 -inch globe. Coulomb was

able to take a negative charge from the smaller globe when they were

two inches apart.

Stanford Untvbrsity,
January 22, 1918.

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Vol. XI-l
Na6. J

AIR-DAMPED VIBRATING SYSTEM.

449

THE AIR-DAMPED VIBRATING SYSTEM :» THEORETICAL
CALIBRATION OF THE CONDENSER TRANSMITTER.

By I. B. Crandall.

IN a recent paper* Mr. E. C. Wente has given an account of the con-
denser transmitter which he developed for the purpose of measuring
sound intensities in absolute terms. This instrument has a sensibility
which is nearly uniform over a wide range of frequencies — s, property
which results from the high stiffness atnd dissipaticy^^ brought into play
by the air film between plate and diaphragm. ..r

In further work with the condenser transmitter, I have made a study
of the air-damping and elasticity as they occur in this instrument and
a treatment of these matters may be of interest as an extension of the
mechanics of the system. To anticipate the results, it has been found
that both damping and stiffness can be calculated according to a simple
theory, and that there are important frequency variations in these
quantities. For example, Wente found that the damping coefficient
of his system at resonance was of the order of 6,000, while theory and
experiment show that the damping at 100 p.p.s. is more than 100 times
as great. The theory enables an absolute calibration curve to be readily
computed which is sufficiently accurate for practical purposes,' and in
addition shows how various combinations of resistance and stiffness
can be given to a vibrating system, by a suitable application of the
air-damping film.

Fig. 1.

Fig. 2.

The condenser transmitter is shown diagranunatically in Fig. i . When

the diaphragm vibrates it causes two kinds of motion in the air film:

» Paper presented at meeting of the American Phsrsical Society, December 28. 191 7.
» Phys. Rev., N. S.. Vol. X., 1917. P. 39-

* This paper deals with the calibration at various frequencies in terms of the calibration
at zero frequency. The calibration at zero frequency has been given by Wente.

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450 /. B. CRANDALL. [^SS?

simple compression, and a lateral escape of air towards the edge of the
disc. At very low frequencies the air has ample time to escape, conse-
quently there is a maximum amount of dissipative reaction (due to
viscous flow) and a minimum of elasticity due to accumulated pressure
in the film. At high frequencies the situation is reversed, and very little
air escapes from the edge of the disc, thus giving rise almost wholly to
a compressive reaction.

For the sake of simplicity we shall first consider a system in which
the diaphragm is replaced by a plane piston of equivalent mass, the
radius of the piston being equal to the radius of the disc (Fig. 2). The
piston is given an oscillating motion { = {0 cos nt. As the air film is
thin, and both bounding surfaces are of metal, the expansion and con-
traction of the airtake place isothermally, and the excess pressure at
any point in the film due to simple compression is B{^/d) in which B is
the atmospheric pressure.^

From this must be subtracted the decrease in pressure due to lateral
air flow which takes place symmetrically toward or from the center of
the disc; this is

^'-^-^|--Ki'+7).

(I)

in which p is the total excess pressure and ri the radial air displacement.
There is no pressure gradient normal to the radius. The radial pressure
gradient is

dp dp' nf^'fj.^^'f 'f\ M

In the theory of fluid motion in narrow crevices it is shown that the
velocity of motion* is proportional to the pressure gradient:

1 The following considerations justify the use of the isothermal hypothesis. The velocity
of propagation of heat waves in a gas is '>l4irfk in which / is the frequency and k the "dif-
fusivity" of the gas (.17 cm'/sec at o^ for air). Assuming that compression at first raises
the temperature of the interior of the film, a large part of the film should cool to the same tem-
perature as the metallic boundary within a time comparable to that taken by a temperature
wave, originating in the center of the film, to reach the boundary. For example, in a film
whose half thickness is i.i x io~* cm. this propagation time at 20,000 frequency is approxi-
mately 5 X io~^ sec. or about one tenth of the period of vibration. Thus even in extreme
Cases the temperature adjustment in the film is practically instantaneous.

As there is little compression at low frequencies, it is to be expected that the low-frequency
resistance formula (equation iia) would be independent of any assumption as to the nature
of the compression. Consequently from low-frequency measurements on resistance no
evidence could be obtained as to which hypothesis is the proper one to use. At higher fre-
quencies, however, where compression is an important factor, the evidence is in favor of the
isothermal hypothesis: the good agreement between the calculated and observed values of
the damping of Wente's system at 17,000 cycles being upset if the adiabatic hypothesis is used*

» This theory frankly neglects the inertia of the moving air; the results of experiment
justify this in the case considered.

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Na'6'!'''] AIR-DAMPED VIBRATING SYSTEM. 45 1

dr, I dp

'*='dt^--K-dr' ^3)

in which ic is a resistance coefficient appropriate to the shape of the
crevice. For a fluid of viscosity m flowing between parallel walls sepa-
rated by a distance d,

.-f.- (4)

From (i) and (3) we have the equation for the excess pressure

dr* '^r dr B dt ' ^^'

the solution of which is, for the state of steadily maintained vibrations,

/>' = [C/o(ar <i) + DK^{ccr Vi)€*»«], (6)

and C, D, are adjusted to the boundary conditions.

On account of symmetry about the center of the disc the velocity
u = o when r = o, which specifies that the pressure gradient shall
vanish when r = o, thus disposing of the term in Ko(ar^fi). Writing
for C, CV* and using /o(ar V7) = ber ar + i bei ar, we have, retaining
only the real terms,

/>' = />- B^ = C'[ber ar cos (nt + ^) - bei or sin (n/ + $)]. (7)

To determine C and ^ we note that the pressure p vanishes at the edge
of the disc because of the free communication with the atmosphere.*
Evaluating these constants we have finally

B^o ( ber ar ber aR + bei ar bei aR \

-f(

ber ar bei oJ? — bei ar ber ctR \ .

ber«a/e + bei^a^ -jsmn/. (8)

The coefficient of cos n/, being in phase with the amplitude ({© cos nt)
of the piston represents pure compression, while the coefficient of sin nt
.is in phase with the velocity (— Ji^n sin nt) and represents pressure

1 Lamb, Hydrodjrnamics. 4th ed. (1916), p. 576.

* The volume of air in the channel around the disc in Wente's instrument was about 100
times that of the air in the film between plate and diaphragib.

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45 2 ^' ^' CRANDALL.

gm*t

dissipated in producing air flow. These two coefficients must be inte-
grated over the area of the piston in order to obtain the elastic constant
(5) and the resistance constant (p) of the system. That is

and

whence

P jj = - p{o« sin nt = 2t J /^^.-r-dr (9)

5{ = 5{o cos w/ = 2t I p^r dr, (10)

2tBR /bei oi? bei^ oi? + ber oi? ber^ aR\

''^ nda \ ber* oJ? + bei» oJ? /

and

TBR*f 2 beraRheVaR'-her' oRbeioR'

^" d V ctR her^oR + hei^aR

(II)

(12)

To s must be added whatever stiffness the system possesses inde-
pendently of the air film; t. e., the inherent stiffness in the diaphragm.

The Air-Damped System at Low Frequencies.

For frequencies near zero, 5 vanishes and we have to consider only
the resistance constant, which may rise to enormous values if the air
film is thin. For values of ctR < i.oo (11) becomes*

2irBo^R^ 3 t/lR* , ,

using the value of k from (4).

Formula (iia) has been subjected to experimental test by Mr. F. W.
Kranz, of this laboratory, using a very heavy vibrating system, and
measuring the damping for three values of air gap. The condenser
transmitter was arranged as in Fig. 3, a heavy disc M being fastened to

Fig. 3.

the diaphragm to insure piston-motion at the center, and also to bring
the natural frequency of the system down to a few hundred cycles.
The transmitter was polarized in the usual way and connected through a

>See Russell, Phil. Mag., April, 1909, p. 524 on ''Methods of Computing ber and bei
Functions, etc."

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Vol. XL!
Na6. J

AIR-DAMPED VIBRATING SYSTEM.

453

distortionless two-stage amplifier to an oscillograph. Impulses were
given to the system by tapping M lightly with a pencil, and oscillograms
of the natural oscillations taken from which the damping was easily
determined. The data are given in the following table:

Total moving mass M » 42.9 g. (including diaphragm).

Radius of discs 1^ » 1.63 cm.

Viscosity of Air, m "* i-8 X lo*^ gram/cm. sec.

Stparatien

Namber of
DtttrmiaatioBS.

Mean Damp-
ing, A.

RMittanc*
p^sifA.

Rtsittance

Preqaency of
OscillatiOBs
(Approx.).

0.0029 cm.
0.0069 "
0.0124 "

3,400

196

292.000

16,800

2,900

246,000

18,600

3,100

501
500
500

Considering the difficulty of measuring the separation accurately,
and the fact that the resistance is very sensitive to changes in separation,
the theory can be taken as practically verified at low frequencies.

Still dealing with the low frequency case, it is worth while inquiring
how great will be the departure from (iia) when the moving piston is
replaced by a flexible membrane, as in the condenser transmitter. As-
suming that the membrane takes the shape of a paraboloid when dis-
tended, and that pressure reactions from the film do not change this shape
appreciably, let us consider the simplest case, in which membrane and
disc have the same radius, R.

The form of the membrane at any instant is given by

f(r)

•4-5)

COS nt.

(13)

the static and dynamic deflections being taken as small compared with
the thickness of the air film. Instead of (2) the pressure must satisfy
the equation :

l[,-.f(.-^H.f(0+if), (.,

the solution of which is

/> = ^°( I - ;^) «•- + CJ,(ar Vi)«'C-'+») - I

(60

The /o function being chosen as before in order that the pressure gradient
shall vanish when r = o. Determining C and * for the pressure to
vanish at the boundary, we have

* Nearly aperiodis.

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454 ^- ^' CRANDALL, [I

Sboomd
.Skubs.

^ r/ f« \ 45» (ber arheioR- bei ar her oR) 1
/> = 5to[(^i-^j-;;;^ be^c^ + bii^^^^ J"^'^'

45*{o r ber ar ber aU + bei ar bei ai? "1 . ,

Now as oR is small, we may use approximations for the ber and bei
functions and neglect all terms higher than a^R^.^ Making the proper
substitutions, we have

Considering only the resistance factor, the rate of dissipation of energy
in the system is

/* IT ttilR^

m-p.,.-rdr^--~-n^k<?. (15)

In a condenser transmitter, a paraboloidal membrane with disc of equal
size can be replaced (from the standpoint of electromotive force gen-
erated) by a plane piston of equal area, whose amplitude of motion is
one half that of the membrane at its center. In terms of this average
amplitude f' the rate of dissipation of energy is \p'n^li!^ = ip'n'fo*.
Equating this to (15) we have for the average resistance constant of the
membrane system

, II TTtiR^ . , .

P' = --^. (n'a)

The membrane transmitter thus experiences at low frequencies a re-
sistance to motion nearly twice as great as the piston instrument which
would generate the same electromotive force, both membrane and piston
being damped with an air layer extending to the edge.

In Wente's instrument the radius of the disc was three quarters of the
radius of the diaphragm. The average deflection of the diaphragm over
the surface of the disc was 0.69 of the maximum. It is clear that the
resistance constant of this device at low frequencies should have a value
intermediate between that given by (iia) and that given by (11 'a).

In practice, we may wish to damp a membrane with a disc of smaller
size placed close to its center. In this case the piston formula is probably
sufficiently exact.

In other cases, as for example using annular damping plates, or discs
perforated with a number of holes, the damping can be calculated by
an obvious extension of this theory. The formulae for annular damping
are somewhat complicated and need not be given here. The perforated

> Russell, loc. cit.

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Nad!^^*] AIR-DAMPED VIBRATING SYSTEM. 455

disc (with large holes and close adjustment to diaphragm) can be con-
sidered from the standpoint of damping as equivalent to a number of
small discs of a certain size, and the determination of the diameter of
the equivalent small discs is not a difficult matter.

As an inunediate application of the 'Mow-frequency" theory, consider
the problem of applying a maximum of damping to a piston system of
arbitrary area, without adding to the stiffness of the system. It is clear
that the separation d of the damping disc should be small, while at the
same time the quantity

R /247rM/
-d\-

aR-.^, ^

should be less than unity for the frequency at which the natural oscilla-
tions take place. The conclusion is that a number of separate damping
''discs" should be used of such a size that the ratio R/d has the proper
value: or, if a one-piece damping plate is applied, it must be furnished
with suitably spaced holes or grooves to allow the escape of the im-
prisoned air.

The Air-Damped System at High Frequencies.

The painstaking and accurate calibration data given by Wente for the
condenser transmitter from zero to 18,000 frequency offer the best
possible check on the calculated values of the resistance and elasticity
of this system over an extended range of frequencies. The following
data were taken by Wente :

(i) Static calibration (zero frequency).

(2) Calibration at 20 p.p.s. using piston apparatus.

(3) Calibration from 20 to 120 p.p.s. using platinum thermophone in

(large) air enclosure.

(4) Calibration from 160 to 18,000 p.p.s. using gold-leaf thermophone

in a smaller volume of hydrogen.
In looking over these data we find that the calibration from 20 to 80
p.p.s. agreed with the static calibration to within 4 per cent. From 80
to 120 cycles, the calibration showed a 20 per cent, decrease in sensitive-
ness as compared with that at zero frequency. (This fact was not men-
tioned by Wente as it was believed to be due to experimental error;
but the theory here given shows that this decrease was a real effect.)
According to the gold-leaf calibration, the sensitiveness fell by 74 per
cent, from 120 to 160 p.p.s., so that the sensitiveness at 160 p.p.s. was
only 1/16.6 that at zero frequency. It seemed improbable to us that
there could be such a marked change in the sensitiveness of the instru-

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45<>

/. B. CRASDALL.

ment o\-er the range from 120 to 160 p.p.s. and ooosequently the departure
of the gold-leaf observations was attributed to an increase in the heat
capacity of the gold-leaf in hydrogen whidi would reduce its sensitiveness
as a thermophone element.^ It is undoubtedly true that the precision
of the results obtained with the gold-leaf thermophone below 1,000 p.p^
is less than for higher frequencies, and also less than the precision of the
calibration from 20 to 120 p.p^., using the heavy platinum thermophone
in a large enclosure of air.

The calibration data of Wente, and a computed (theoretical) curve
of sensitiveness vs. frequency are shown in Fig. 4. In computing the

Fig. 4.
Ezperimental and theoretical caUbratkm ci the condenaer

d » o.ooaa cm.

transmitter. R - 1.63 cm.

theoretical curve, the sensitiveness is taken as proportional to the
amplitude of an equivalent system of one degree of freedom, that is,

{' =

constant

Vp%« + {mn^ - sY •

in which fw, 5 and p are respectively the mass, stiffness and resistance

1 When this question arose Dr. Arnold and I tried, by simple experiments, to measure
any gas that might be absorbed by the gold-leaf element when it was placed in hjrdrogen.
No quantity measurable with our apparatus was obtained. On the other hand. Mr. Wente.
experimenting with platinum and gold thermophone elements side by side in the same endo-
sure, found varying discrepancies between the actual and computed values oi sound intensity
when the gold thermophone was used. The thermal capacity of the gold-leaf element is at
present indeterminate.

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Vol Xl.l
Na6. J

AIR-DAMPED VIBRATING SYSTEM.

457

coefficients, n is 2ir times the frequency. The mass coefficient is of no
consequence at low frequencies, but the stiffness and resistance constants
should be known.

The stiffness constant at zero frequency (5o) is the force required to
produce unit average deflection ({') over the surface of the disc. The
tension in the diaphragm was T = 6.57 X 10^ dynes/cm., and as the
average amplitude over the disc was 0.69 times the maximum, we have

5o = ^ = 1.2 X lo* C.G.S.
.69

The added stiffness due to the air film was computed from (12) for
frequencies up to 20,000, assuming that the transmitter behaved like a
piston system. The total stiffness (5) is plotted in Fig. 5.

Fig. 5.
Resistance and stiflfness factors of condenser transmitter as used by E. C. Wente. U - i .63 cm..

d - o.ooaa cm.

The resistance constant (p) was computed from (11) for frequencies
from 1,000 to 20,000. For frequencies from zero to 500 the plotted
values are 40 per cent, greater than those calculated from (11). This
allowance is made as previously explained, because the membrane main
tains its paraboloidal shape in vibrating at low frequencies.

From the stiffness constant at resonance {s = 4.5 X lo* at 17,000

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458

/. B. CRANDALL.

rSBCOND

LSbuks.

p.p.s.) the mass coefliicent at high frequencies is found to be w = 0.395
gram. This is practically the same as if the portion of the membrane
directly opposite the disc moved parallel to itself, back and forth, and is a
justification of the piston assumption.

Referring again to Fig. 4, the damping coefficient as computed from
the shape of the experimental calibration curve near resonance is
A = 5,400. The computed resistance coefficient at resonance is
p = 4400, and this would give a damping coefficient A = p/2w = 5,600.
The agreement between theoretical and experimental values of damping
shows that the calculated value of resistance is correct, and hence that
the scale of sensitiveness on which the theoretical curve is plotted is
correct. The theoretical calibration is therefore well established as the
true calibration of Wente's condenser transmitter, and the sensitiveness
as determined with the gold-leaf thermophone in hydrogen is to be
multiplied by a factor of approximately 3 (see the dotted curve in Fig. 4)
if it is to agree with the theoretical calibration.

Application of the Theory to Design of the Condenser

Transmitter.

For the sake of further insight into the mechanics of the air-damped
system, amplitude-frequency curves have been computed for four piston
systems having the same mass and low-frequency stiffness, but with
variable separation between moving and stationary discs. The constants
are

tr to

trttto^

Fig. 6.
p and J for four ssrstema of var3dng separation.

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Vol XL

No. 6.

AIR-DAMPED VIBRATING SYSTEM.

459

Mass m = 0.40 gram,
Low frequency stiffness, 5o = 1.2 X 10* C.G.S.,
Radius of discs 22 = 1.63 cm.,

System II, separation d = .005 cm.,

" III = .0075,

IV = .0100,

"V = .0150,

(Wente's transmitter may be considered as system I of this series.)
The resistance and stiffness factors are given in Fig. 6. The amplitude-

Fig. 7.
Relative sensitiveness at different frequencies for four systems of varying separation.

frequency characteristics are shown in Fig. 7. None of these systems
are aperiodic, but they show what can be done with air damping if equal
response over different ranges of frequency is desired.

In the condenser transmitter it is not desirable from the standpoint of
sensitiveness, to increase the separation between disc and diaphragm

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460 /. B. CRANDALL. [i

although this would give the system more uniform resistance-frequency
and stiffness-frequency characteristics, which prc^erties might be desir-
able for some work. It seems preferable to make the most of the close
adjustment but to facilitate the escape of air from the film by perforating
the disc or cutting deep grooves in it, so that the proper combinations
of pure resistance and added stiffness is obtained.

In particular, let it be required to design a
condenser transmitter whose mass coefficient is
0.40 gram, whose back plate is a disc of radius
2? = 1.63 cm. separated from the diaphragm by
a distance d = .002 cm., and whose sensitive-
ness is to be almost rigorously uniform over
the frequency range from zero to 8,000 cycles.
Pig g If the low frequency stiffness is the same as in

the several systems considered above, the added
resistance and stiffness due to the air-damping should have frequency
characteristics somewhere in between those given for systems II and III.
For a system having properties intermediate between II and III the ratio
of radius of disc to separation should be approximately

R 1.63

and this condition can only be met with the given separation of .002 cm.,
by cutting grooves in the disc in such a way that all points in the film are
distant less than R' = 270 X .002 = .54 cm. from a low impedance
pathway to the open air. Fig. 8 shows one way in which the disc may
be grooved to bring this about — the different sections A^ B, C of the disc
being very closely equivalent to small discs of radius .54 cm. This
example should sufficiently illustrate the principle to be followed in
designing this type of air-damped vibrating system.

The object of this paper has been to complete as far as necessary the
mechanical theory of the condenser transmitter. The mechanism of
air-damping has been determined, and formulae have been obtained from
which practical calculations can be made. A complete theoretical
calibration of a condenser transmitter has been given which is consistent
with the experimental calibration, and which does not disturb the uniform
frequency-sensitiveness characteristic of the instrument except at fre-
quencies very near zero. The principles have been given for the design
of air-damped systems of maximum damping, and condenser transmitters
having rigorously uniform sensitiveness over an extended range of
frequencies including zero.

Rbsbarch Laboratory of thb American Tblbphonb and Tblbgraph Co.
AND Western Electric Co.. Inc.

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Vol. XI.

Na6V J TUNGSTEN X-RAY SPECTRUM, 46 1

WAVE-LENGTHS OF THE TUNGSTEN X-RAY SPECTRUM.

By Elmbr Dbrshsbc

Introduction.
OINCE the X-ray spectra of practically all the available elements
*^ had been studied by one investigator or another with results which
did not very closely agree and which in general comprised only a few of
the principal or most prominent lines, it seemed wise to begin the present
investigation with a view to determining more completely and accurately
than heretofore the number of lines and their wave-lengths in the spec-
trum of at least one element. The element most easily tested and the
one whose spectrum would be of the greatest value in the X-ray analysis
of crystals was tungsten on account of its use as the anticathode of the
Coolidge tube, the only type of tube which could be used during the long
intervals of time necessary to secure spectral photographs, if the condi-
tions required for the greatest resolving power and the greatest accuracy
of measurement were complied with.

The photographic method was chosen for this work in preference to an
ionization chamber and electrometer because in the latter method the
intensity of the reflected beam must be great enough to give a continuous
effect on the electrometer while the photographic plate gives a summation
of the intensity of the reflected beam over a time that may be made so
very much longer that weak lines have an opportunity to appear.

We shall now consider the factors affecting the accuracy of measure-
ment and resolving power of an instrument using a crystal as a diffraction
grating for X-rays. Resolving power is, as usual, defined as the ratio
of a wave-length to the smallest difference which may exist between this
and a neighboring wave-length and yet have the instrument show that
the two waves are separate and not identical. A consideration of these
factors will then show that the conditions for the best resolving power
are those which lead to a decrease in intensity and would make impossible
the securing of sufficient intensity to affect an electrometer under the
necessary conditions of a narrow source, great distance from the crystal
to the detector and a thin crystal which means less intensity because
there are fewer reflecting planes. The theory will also show that the
position of the central maximum of the reflected beam is not the true
criterion by which the wave-length must be determined but it is instead

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462 ELMER DERSHEM. [ISSS

the outer edge, which when corrections are made for the width of the
source, gives the true measurement. The impossibility of measuring
anything other than the central maximum with an ionization chamber
eliminates this as a possible accurate method and leaves the photographic
plate as the only recourse.

Resolving Power of a Crystal Used as a Diffraction Grating

FOR X-Rays.

In this discussion the assumption will be made that the slit, or source,
is the same distance from the crystal as is the photographic plate. In
this case, as shown by Bragg,^ the amount of surface of the crystal
exposed to the X-rays makes no difference in the sharpness of the lines
since the same wave-length is always reflected to the same point on the
plate. This will not be true if the atomic planes are not parallel. In
reality the cleavage surfaces of crystals are quite noticeably warped
and it is desirable to limit the surface of the crystal exposed to the rays
by means of a narrow slit between lead blocks placed close to the crystal
even though it does cause a decrease in intensity. It will also be assumed
that the crystal is thin enough that the rays may penetrate entirely
through the crystal and be reflected from the planes on the back side
and again traversing the crystal to reach the photographic plate.

With these assumptions as to con-
ditions which may be easily obtained
in practice, the question to be deter-
mined is, What difference of wave-
length is necessary that it may be
possible to separate two waves of
nearly the same length?
Let the source be a slit of width 5 at a distance r from the crystal.
Fig. I. Assume that the crystal is in a position to reflect some particular
wave-length where nX = 2d sin d, in which n is the order of the spectrum*
X the wave-length, d the grating constant or distance between the
atomic planes and d the angle between the incident rays and the crystal
surface. Then a ray coming from the side M of the slit may be reflected
at A to yl' on the photographic plate and a ray from the side N must
strike the crystal at the same angle and consequently be reflected at the
point B to the point B\ It is easily seen that the reflected rays AA'
and BE' are at the same distance apart as the incident rays MA and
NB, Hence due to the slit alone a single wave-length would cause a
line on the photographic plate the same width as the slit.

1 Bragg and Bragg, X-Rays and Crystal Structure, G. Bell and Sons, London. 191 5*

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Na^6*^'l TUNGSTEN X-RAY SPECTRUM. 463

Considering next the question of the variation of the width of image

with the thickness of the crystal, let DE be drawn perpendicular to AA\

Then DE is the width of the reflected beam due to the penetration into

the crystal. Let DF = i be the thickness of the crystal. Then

/ = AD sin ^and

.r. DE
AD ^ --,
sm 26

Then by substitution

DE sin e DE sin 6 DE

t =

sin 20 2 sin 6 cos 6 2 cos B *

Whence DE = 2/ cos 6. *

Since DE is the width of beam due to penetration into the crystal the
total width of beam is 5 + 2/ cos 6, in which s is the width of the slit,
or source, / the thickness of the crystal and B the angle which the incident
ray makes with the crystal.

Then 5 + 2/ cos 6 is the width of the line on the photographic plate.
In order to resolve two lines of nearly the same wave-length it is necessary
that their images on the plate should not overlap or, in other words,
that the centers of their images must be further apart than the width
of beam, 5 + 2/ cos 6,

Assume two wave-lengths, X and X + AX. To find how small AX
may be and these wave-lengths still be clearly resolved on the plate.
Using the formula n\ = 2d sin B let X take on a small increment AX
and 6 the corresponding increment A^. v

Then by differentiation we have nAX /^^

= 2d cos B^B. This is justified in */X^\

practice by the fact that A^ is small /y^ \

in comparison to B, ^ ^\ \

According to the above if the crys- %J^ ^^^

tal is in a position to reflect a wave ^. ^

Fig. 2.

of length X it must rotate through an

angle A^ in order to reflect a wave of length X + AX and since the re-
flected ray rotates twice as fast as the crystal the reflected ray must
rotate through the angle 2A^. (See Fig. 2.)

If the distance of the crystal from the plate is r then the displacement of
the beam along the plate when the reflecting angle is changed from B to
^ + A^ is 2rA^. In order that rays reflected at these angles be separated
it is necessary that this distance, 2rA^ be greater than the width of beam
5 + 2/ cos B,

2rAB > s + 2t cos B,

But

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464 ELMER DERSHEM. [SSSJ?

nAX

2d COS 9

and by substitution

2nrA\
2d cos d

dcosO , ,

AX > (5 + 2/ cos 0).

nr •

AX is then the smallest difference between the lengths of two waves
that is permissible if the images due to these waves are to be separated
on the plate. However the images must be separated by a slightly
greater distance in order to leave a clear space between them. Just how
much space is necessary for this is not a mathematical problem but a
question which must be answered by experience. Probably but little
need be added to AX on this account. Neglecting for the time being the
question of the necessary space between lines it may be of interest to
determine the resolving power under the best conditions that were
obtained with the apparatus used in the present work. For example,
taking the line in the central part of the L spectrum having a wave-
length of 1. 241 X IO-* cm. the experimental values of the quantities
contained in the above formula were:

5 = 0.032 cm.,

t = 0.019 cm.,

d = 2.814 X io~*cm.,

f = 62 cm.,

cos ^ = 0.977,

n = I.

Substituting in the inequality

(5 + 2/ cos e)

the above values of the quantities gives

AX > 0.00375 X io-« cm.

Since resolving power is defined as X/AX and for this case X is
1. 241 X 10"® cm. we have

X 1. 241

AX .00375 '

^<33i.

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Na*6f^l TUNGSTEN X-RAY SPECTRUM, 465

The resolving power in this case was less than 331, although the experi-
mental values of the width of slit, thickness of crystal and distance to
the plate were so chosen as to give the greatest possible resolving power
consistent with the necessary requirement of retaining sufficient intensity
in the reflected beam to affect the photographic plate in an exposure of
a reasonable duration.

It is apparent that the ways in which the resolving power may be
increased are to use a higher order than the first, to narrow the source,
to decrease the thickness of the crystal and to increase the distance
between the crystal and the plate. To do any one of these things tends
to decrease the intensity and make necessary a longer exposure and this
is not altogether desirable, as it gives the latent image an opportunity to
spread and blurr the image and also increases the liability to fogging of
the plate due to stray radiation. An increase of distance from crystal
to plate decreases the intensity by absorption in the air and this may be
a factor of considerable importance in working with the longer wave-
lengths. Therefore at present it would not seem possible to so greatly
increase the resolving power of a crystal used as a diffraction grating for
X-rays as to make it at all comparable to the resolving powers of the
grating or echelon used for ordinary light.

From this theory it may be seen, by reference to Fig. i, that the true
angle of reflection must be determined by measuring the position of the
outer edge or most deviated portion of the spectral line and subtracting
one half of the width of the source from this. This will eliminate any
error of measurement due to penetration into the crystal but the crystal
must be thin if two nearly equal wave-lengths are to be separated.

Methods of Applying the Theories Concerning Resolving Power.

Since it was the object in this work to make as accurate measurements
of the wave-lengths as possible the apparatus and methods of using it
will be described somewhat in detail.

The previous theory requiring the use of a thin crystal, the following
method of securing and mounting one was adopted. A crystal of rock
salt having a perfect cleavage face of about one square centimeter area
was chosen and this was fastened face down onto a glass surface by the
use of a wax especially prepared for the purpose by mixing Canada
balsam and hard sealing wax in such proportions as would give a wax
that was hard and tough at ordinary temperatures but which became a
thin liquid when slightly heated. After the crystal was firmly cemented
to the glass by pressing the two together while warm with a small quantity
of wax between and allowing them to cool, the crystal was ground away

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466 ELMER DERSHEM, [llSS

until a thickness of not more than 0.019 cm. remained. It was found by
experience that attempts to make the crystal thinner than this resulted
in causing the crystal to crack and become useless.

The measurements of the position of the lines on the photographic
plates were made with a Societa Genevoise dividing engine which was
guaranteed by the makers to be accurate to o.oi mm. in a total length
of 40 cm.

To check against possible variations in the pitch of the screw the plates
were measured a number of times and each time the setting was changed
so that the measurement would be made by a different part of the screw.
However the principal object of repeating the measurements was to
compensate for the errors of setting by securing a number of readings
and averaging the results.

A number of different methods of securing accurate settings of the
dividing engine were tried and the one giving the most consistent results
was the following. An achromatic combination lens of ij inches diameter
was placed in a tube 22 inches long. Two parallel hairs were placed at
one end of the tube and brought very close to the photographic plate
so that the parallel hairs and the spectral line on the plate should be
practically in one conjugate focal plane of the instrument at the same
time. The spectral line and the parallel hairs were then viewed through
a peep hole at the other end of the tube which was near the other con-
jugate focus of the lens. Owing to the great length of the tube as com-
pared to the distance between the parallel hairs and the photographic
plate there was very little parallax and owing to the large diameter of the
lens the field of view was large enough to avoid to a considerable extent
the loss of contrast that comes from magnifying a small section of surface
which shades gradually from one portion to another. It is this difficulty
that makes it impossible to use the ordinary microscope having a small
objective. To secure proper illumination the apparatus was placed so
that the observer looked through the plate toward a clear sky.

Whenever two objects are very close together they appear to blend
into one, especially if the edges are not sharp and clearly defined. Owing
to this effect as the photographic line approaches the parallel hairs of the
microscope it blends with them while not really coinciding with them.
To avoid as far as possible, the inaccuracies due to this effect, small dots
were made with the point of a needle as nearly as possible along the
outer edge of the line and it was then possible while the line was in the
field of view of the microscope and yet not too close to the parallel hairs
to choose the particular dot which most nearly denoted the position
of the edge of the line and then take the measurement when this dot
came exactly between the parallel hairs.

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Vol. XI
Na6

] TUNGSTEN X-RAY SPECTRUM. 467

Description of Apparatus Used in Securing the X-Ray Spectrum.

The apparatus used in this work can perhaps best be described by
referring to the isometric drawing of the framework, Fig. 3.

The mechanism was enclosed in a box lined with sheet lead J inch
thick in order to cut out stray radiation, but for simplicity this is not
shown in the drawing. The crys-
tal was mounted on the rotating
axis A which was fitted with ad-
justable bearings such that this ^rf(^
axis could be made truly vertical
with respect to the horizontal
plane of the instrument. Between
the source and the crystal, as
close as possible to the latter, a ^^ p- 3
vertical lead plate J inch thick

was placed. This is not shown in the drawing. The area of crystal
surface upon which the X-rays might strike was limited by a slot 3
mm. wide cut through the center of this plate.

One end of the framework of cast iron and steel carried the block of
lead L which was about 2 inches thick and of sufficient area to subtend
a solid angle at the anticathode of the X-ray tube greater than that
subtended by the photographic plate and in this way served to protect
the plate from the direct radiation of the tube. The previously men-
tioned lead-lined box enclosing the apparatus served to protect the plate
from the radiation reflected from the walls of the room. A slot about
3/16 inches wide was cut through the center of this block of lead and this
slot was covered by the two lead plates or jaws P and P' which had their
inner surfaces plane polished and which could be set at any distance
apart by means of gauges placed between their upper and lower edges.
The slot or space between these two surfaces could then be considered
as the source of the X-rays, since it was sufficiently close to the focal
spot of the target that this spot subtended a larger angle at the slit than
did the crystal, the latter being comparatively far away.

The other end of the framework carried a bar of angle steel, the vertical
surface 5 of which was planed true and then set accurately at right angles
to the line joining the center of the source and the center of the rotating
axis on which the crystal was mounted. The photographic* plate was
placed in a light-proof envelope and clamped tightly to this surface and
since the distance of the surface from the center of rotation of the
crystal could be accurately determined by means of a bar of adjustable
length which could later be measured on the dividing engine, it was

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468 ELMER DERSHEM, [j

possible to determine the distance of the fihn from the center of rotation

by subtracting the thickness of the plate and the paper back of the plate

from the measured length of the bar.

The mechanism for holding the crystal is shown in Fig. 4. One side

of the shaft A was plane surfaced as was also the block of brass F and

these could be firmly clamped together by the two screws H and K,

These surfaces could then be separated and placed together at will,

always fitting together in the same position. The

block F carried the block E attached to it by three

screws in such a way that the surface BC could be

adjusted to the desired plane and then locked

there by the pressure of the screw /. With the

shaft set in its bearings the upper and lower parts

of the surface BC were adjusted until when viewed

through a microscope both the upper and lower

edges remained in the axis of rotation as the shaft

p. . was rotated. Then this surface BC would contain

Fig. 4.

the axis of rotation and by pressing a crystal
surface against this face plate and waxing firmly from behind, the crys-
tal surface would also contain the axis of rotation. The face plate
could then be removed by taking out the screws H and K and the
crystal would be left properly mounted.

The axis A was made perpendicular to the framework by first placing
a piece of silvered glass in the position of the crystal and adjusting the
bearings until the image of a straight horizontal line drawn along the
middle of the surface 5 was projected back onto the line at all points
as the axis was rotated. When these adjustments were made it was
assured that the axis of the shaft bearing the crystal was perpendicular
to the horizontal plane of the instrument and that whenever a crystal
face was placed against the removable face plate its surface would also
contain the axis of rotation. The only other adjustment was to set the
apparatus as a whole so that the slot between the jaws P and P' was on
the straight line joining the focal spot and the axis of rotation of the
crystal.

It was necessary to have a precise reference line marked on the photo-
graphic plate near the point where the undeviated portion of the X-ray
beam would strike in order that a photograph might be taken with the
crystal set to reflect toward one side of the apparatus and later one taken
on another plate with the crystal turned to reflect to the other side of the
center line. From these two plates the mean distance of any particular
spectral line from this reference line could be found and having once

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5a"6^^'] TUNGSTEN X-RAY SPECTRUM, 469

determined the position of this reference line with respect to the true
center it was possible to determine the true deviation of any wave-length
from a photograph taken on one side of the instrument. To check
against changes of position the instrument was frequently calibrated by
taking photographs on both sides of the center. The reference line was
made by allowing part of the portion of the X-ray beam which passed
undeviated through the crystal to pass through the narrow slot between
the two plane surfaced lead bars N and N' which were soldered to the
brass bars M and JIf ' for the purpose of strength and stiffness. These
lead surfaces were separated by thin strips of paper between their upper
and lower edges and the narrow beam of X-rays that passed through
marked a very fine line on the plate.

While the photographs were being taken the crystal was slowly
rotated by means of a fine wire which extended from the pulley R,
Fig. 3, to a lever which was connected to a float in a tank of water.
Water was siphoned into this tank from another tank in which the level
was maintained constant and by regulating the rate of flow, the rate of
rising of the float, and the rotation of the crystal could be regulated to
any value desired.

While taking the photographs of the L radiation the current for the
Coolidge tube was supplied by a transformer excited directly from the
1 10- volt alternating current mains. The transformer stepped the voltage
up to a maximum potential of 58,000 volts and the tube rectified its own
current, a well-known property of the Coolidge tube provided, as in this
case, that the temperature does not become too high.

In order to avoid the necessity of remaining in the room during the
long time required for taking the spectral photographs a motor-operated
rheostat was placed in the heating circuit of the Coolidge tube and the
motor controls were placed in another room. A wattmeter in this room
indicated the power input to the transformer and it was possible by
regulating the heating current of the tube to secure any power input
desired. It was found that when the heating current was such that
the power input of the transformer was 240 watts the target remained
at a cherry red heat but did not get hot enough to cause damage to the
tube. Of this power about 100 watts went to supply the losses in the
transformer and the remaining 140 watts represented the power actually
used in the tube.

For the K radiations the same method was followed except that the
applied maximum potential was raised to 80,000 volts and the current
through the heating circuit was set at such a value as to cause the tube
to take 140 watts from the transformer as before.

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470 ELMER DERSHEM. [^S?

It was found that the power input would remain constant for an hour
to within five or ten watts, hence it was possible to work at other things
during the long time of exposure required and thus the labor was very
much reduced.

Experimental Results for the L Radiations.

Some writers on this subject have used the first letters of the alphabet
to designate the shorter wave-lengths and others have used these same
letters to indicate the longer wave-lengths, while others have used Greek
letters. Owing to these confusing methods of nomenclature it has been
thought wise to submit the following means of identifying each particular
wave-length. The first three significant figures denoting the wave-
length in Angstrom units are used as subscripts to the Greek letter X
which is usually used to denote a wave-length. If the knowledge of
X-ray spectra shall increase to that point where three figures no longer
distinguish two neighboring wave-lengths it will be possible to use four
or more figures.

In the experimental work a number of photographs were taken using
different distances from the crystal to the plate, always keeping the
distance from the source to the crystal as nearly as possible equal to this
distance. The method of procedure is shown by the following example.
Plate No. 104 was placed so as to register the center line and the spectrum
on the left side. Later Plate No. 105 was similarly placed on the right
side, each being given an exposure of more than twenty-four hours.
When measured on the dividing engine the distance of the most deviated
side of the spectral line X1.27 from the central reference line was found to
be 29.99' cm. to the left on Plate No. 104 and 30.03* cm. to the right on
Plate No. 105. The reference line was therefore one half of the difference
or 0.023 cm. to the left of the true center. This correction could then
readily be applied to photographs taken later on only one side of the
apparatus. The deviation of the outer edge of this spectral line was
therefore 30.01® cm. and since the slit width was 0.032 cm. subtracting
one half of this according to the previous theory gives the true deviation
of the line to be 30.00° cm. The distance from the axis of rotation of the
crystal to the plateholder was 61.10® cm., from which must be subtracted
the thickness of the plate 0.260 cm., also the thickness of the paper
envelope enclosing it, which was 0.013 cm., giving 60.82^ cm. as the
distance from the film side of the plate to the axis of rotation. The
quotient of the distance from the center to the spectral line divided by
the distance from crystal to film gives the tangent of twice the glancing
angle of reflection and denoting this angle by B we have

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Vol. XL!
Na6. J

TUNGSTEN X-RAY SPECTRUM.

471

^ ^ 30.00^

Tan 2d = f-o-= .
60.82^

Whence 6=1^^ f 35", from which by the use of the formula
nX = 2d sin B, in which n is unity and d has the value 2.814 X lO""* cm.
We find X to be 1.278* X lO"* cm.

Table I.

Summary of ResuUs for The L Radiations Wave-Lengths X 10"« Cm.

Line.

Plates 104
and 105.

Plates X15
and 117.

Plate lax.

Plate zaa.

Plate laa.

Xi.«

1.4820

1.4836

X1.47

1.4719

1.4725

1.4723

Xi.«

1.4163

Xi.if

1.2979

1.2968

1.2976

1.2983

Xl.M

1.2868

Xl.t7

1.2781

1.2780

1.2784

1.2793

Xi.»

1.2589

1.2580

1.2588

1.2593

1.2598

Xl.S4

1.2418

1.2412

1.2413

1.2414

1.2421

Xi.a

1.2205

1.2199

X1.J0

1.2102

1.2094

Xl.17

1.1773

Xi.ii

1.1297

1.1286

Xi.ot

1.0948

1.0951

1.0948

1.0955

1.0963

Xl.07

1.0705

Xi.«

1.0645

1.0649

1.0643

1.0645

1.0656

X1.06

1.0587

1.0586

1.0581

1.0587

1.0593

Xl.04

1.0427

X1.02

1.0250

1.0246

1.0258

1.0250

1.0262

»x..,

.9153

.9158

.9165

.9171

X ,70

.7058

.7079 ]

'X .«

.4835 [

.4838

.4828

.4838 !

Average.

1.482«
1.472«
1.416»
1.297'
1.286»
1.278*
1.258«
1.241"
1.220«
1.209«
1.177*
1.129«
1.095*
1.070»
1.0648
1.058'
1.042'
1.025*
.915»
.706*
.483*

1 Wave-lengths shorter than X .91 are selectively absorbed by the bromine in the plate
causing a dark band at the position of this wave-length.

* The silver of the plate selectively absorbs wave-lengths shorter than X .48 thus causing
dark band at the position of this wave-length.

In a similar way the angles of reflection and the wave-lengths were
determined for the other characteristic L rays and the results of five
separate tests are recorded in Table I. These results were computed
from an average of eight separate measurements of each plate. The
agreement between the different tests is a fair test of the accuracy of
the work since the distances to be measured were different in each case.
Table II. gives a summary of the results of different investigators each
of whom had either used rock salt crystals directly or had compared the
gtating constant of some other crystal with that of rock salt so that in
every case the results are based on the value of 2.814 X lO"^ cm. for the

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Physical Review, Vol. XI.. Second Series. Plate I.

June. 19 18. Face page 472.

Fig. 5.

Showing the position of the 19 lines of the L group and also the boundaries of regions of
greater blackening of the plate corresponding to wave-lengths of .9159 and .4833 Angstrom
units which are due to selective absorption by tie bromine and silver of the plate of waves
just shorter than their own K radiations, (de Broglie. Comptes Rendus. Vol. 158, p. 1493.
and Vol. 163. p. 87; Wagner, Annalen der Physik, Vol. 46. p. 868.)

Lines X .48 are Ag absorption lines, the upper one being first order, the lower one second
order. Line X .91 is Br absorption line.

Fig. 6.

ELMER DERSHEM.

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VOL.XI.1

Na6. J

TUNGSTEN X-RAY SPECTRUM.

473

distance between the atomic planes in halite. Fig. 5 is a photograph
showing the position of the L lines of the tungsten spectrum.

Before doing the preceding work it was thought possible that the
distance between planes of atoms in a crystal might not be identical for
all crystals of the same substance but might vary with the conditions of
growth of the crystal. To test this some preliminary measurements
were made using crystals of halite obtained from different parts of the
earth. The results showed that to within the limits of error of measure-
ment there was no variation of the grating constant.

Experimental Results for the K Radiations.

In securing the photographs of the K radiations the same methods
were followed as in the case of the L radiations except that a higher
potential was required. On account of the great penetrability of these
rays the use of a thin crystal was much more imperative. Fig. 6 shows
a photograph of the four K lines of tungsten. Owing to the use of a
thin crystal these lines are all clearly separated in the first order. Other
observers using a thick crystal have found difficulty in separating the
two lines of shortest wave-length in the first order. Table III. gives the
results of four tests for the wave-lengths of the K lines of tungsten and

X.JO
X.ii

X.17

Table III.

The K Radiations of Tungstbn.
Wave-Lengths in Angstrdm Units.

Plftte 58.

Plate IC9. 1 Plate 1x4.

Plate 119.

1 Weighted
1 Average.

.2121
.2075
.1833
.1784

.2126 .2118
.2075 .2069
.1818 .1831
.1786 .1778

.2126
.2078
.1837

.1785

i .212*
.207«
.183*

1 .178*

Table IV.

a Comparison of trb Results obtained by Different Investigators of the K

Radiations of Tungsten.

Wave-Lengths in Angstrom Units.

de Broglie,

Comptes Rendus,

April, 1916.

a, .2032
/J, .1768

Hull,

O. B. Review,

July, 1916.

r.212
''1.208
fi .185

Ledoux-Lebard

and Dauvillier,

Comptes Rendus,

December, 1916.

ai .2128
at .2053
fix .1826
/9t.l768

—

Dershem.

x„

.212*

X.so

.207«

X.ii

.183*

X.IT

.178*

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474 ELMER DERSHEM, [^SS

Table IV. gives a comparison with the results of other observers. In
Table III. in finding the weighted average the last plate is assigned a
weight of three and the others a weight of unity since they were not so
perfect as the last. In these tests the distance from crystal to plate
varied slightly for the different plates, but was always between 60 and
61 centimeters.

Accuracy of the Measurements.

Since the extreme variation from the mean value is not greater than
0.1 per cent, for any characteristic line of the L group the probable error
is less than this amount. In the same way the probable error for the K
lines is less than 0.8 per cent. On account of the smaller angles these
cannot be so easily measured as the L lines.

There is very little possibility that the lines observed may in part be
due to impurities in the tungsten target. I have no direct information
in regard to the purity of the latter but understand that no impurities
can be shown by chemical analysis.

These results agree well with such results as are reported by Siegbahn
and Friman and also with those computed from the values of the reflec-
tion angles as given by de Broglie but disagree with most of the others.
This is to be expected in some cases. Gorton used a film wrapped onto
a cylindrical surface. It would seem possible that the film might either
shrink or stretch in the process of development. Compton recorded the
deflections of an electrometer photographically on a moving film. This
gives a graphical representation of the relative intensities of the different
lines but it would be difficult to get a precise measurement of wave-length
in this way since the angular position of the crystal is not accurately
known at the moment when the electrometer deflection is being recorded
by the photographic film.

Theoretical Considerations.

Considerable work has already been done, notably the work of
Moseley,^ in correlating the X-ray spectra of the different elements but
little progress has been made toward determining whether, or not, the
lines of a single element might be group)ed into series such as some of
the spectral lines in ordinary light are grouped to form the well-known
Balmer's series. The theoretical work of Bohr* shows that these series
in the case of some of the lighter elements may be derived from a theory
of atomic structure and it is the belief of many that X-rays are to the

* Phil. Mag., Vol. 26. pp. 1024-34, and Vol. 27, p. 703.

* Phil. Mag., Vol. 26, pp. 1-25, pp. 476-505, and pp. 857-75.

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Na*6!^^'] TUNGSTEN X-RAY SPECTRUM. 475

heavier elements what light rays are to those of lesser atomic weight.
If X-rays are produced by the change of motion of electrons near the
central nucleus it might be possible to work back from an empirically
derived series to the mechanism by which these rays are excited. So far
such a series has not been found, but this may easily be due to the fact
that so far only a comparatively small number of lines has been found.
The failure to find them is more probably due to a lack of resolving power
rather than to the existence of but few lines. In the case of the plate
giving 19 lines in the L group the resolving power was less than 170 and
we know that with such low resolving powers we would have learned
but little of that which we now know of light spectra.

By the use of Bohr's theory KosseU has attempted to explain the origin
of the K and L radiations by assuming several stable orbits of different
radii near the nucleus and that the hardest of the K lines is due to the
falling of an electron from the outer to the inner orbit. These theories
led to the conclusion that the difference in frequency of the two K lines
(at the time he wrote the K lines were treated as only two but these
are now known to be double lines) should be the frequency of the L
line of longest wave-length. This has been said to hold true for a number
of .elements, but if we take the average wave-length of the K doublets
as found in this work we should have

III

.1809 .2100 XL*

Whence XL = 1.30 instead of 1.48 Angstrom units as it should if the
theory were correct. This is a greater variation than is permissible,
even granting the greatest possible errors in these measurements.

Summary.

1. This work shows that accurate wave-length measurements and the
separation of close doublets can only be achieved by limiting the thick-
ness of the crystal and the width of source and making the distance
between crystal and photographic plate as great as is practicable with
regard to the necessary intensity.

2. The L group of the tungsten X-ray lines by these means is shown
to contain at least 19 lines and measurements correct to o.i per cent,
are given of their wave-lengths. From considerations of the resolving
power of the apparatus it seems possible that the true number may be
as great as the number of lines in the light spectra of an element.

3. It is shown that the K lines of tungsten may be clearly separated

» Ber. d. Physik. Gesel., Vol. 12, p. 953, 1914.

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476 ELMER DERSHEM, [SSS2!

in the first order if the conditions required for the highest practicable

resolving power are complied with.

In conclusion I wish to thank the staff of the physics department and

especially Professor G. W. Stewart, who directed the work, for many

helpful suggestions and encouragement in the carrying out of this task

and also to Mr. A. M. McMahon, who gave much assistance in the

performance of the work.

Physics Laboratory,
University of Iowa,
December, 191 7.

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Na6^') ^^^ AMERICAN PHYSICAL SOCIETY. 477

PROCEEDINGS

OF THE

American Physical Society.

Minutes of the Ninety-third Meeting.

A REGULAR meeting of the American Physical Society was held in South
Hall, University of California, Berkeley, on March 30, 1918, at 3 p. m.

Papers were presented as follows:

The Formation of Negatively Electrified Rain Drops. Fernando Sanford.

The Specific Inductive Capacity of Metals. Fernando Sanford.

The Relation of Nuclear Atomic Charges to Serial Numbers. Fernando
Sanford.

Note on a Reverse Concentration Cell. Fernando Sanford.

Law of Motion of a Droplet Moving with Variable Velocity in Air. R. B.
Abbott.

Conditions Affecting the Distribution of Deposit from Cathode Disinte-
gration. L L. Jones.

Velocity of Waves as Depending on Velocity of Source. Dinsmore Alter.

The Effects of the Chimes on the Mechanical Vibrations of the Sather
Tower. Elmer E. Hall.

An Harmonic Synthesizer Having Components of Incommensurable Period
and any Required Decrement. W. J. Raymond.

The Experimental Illustration of Harmonic Motion. John C. Shedd.

Ther mo-Couples for Student Use in Calorimetric Work. Ralph S. Minor.

Demonstration of a Laboratory Wave Model. Joseph G. Brown.

Some Peculiarities of Line Structure in Arc and Furnace Spectra. Arthur
S. King.

Equivalent Resistance of an Iron Core and Absorption Resistance of a Con-
denser. F. J. Rogers.

About 30 members and visitors were in attendance.

In the evening 22 members dined together at the Faculty Club.

E. P. Lewis,
Local Secretary for the Pacific Coast,

Minutes of the Ninety-Fourth Meeting, April 27, 1918.

THE ninety-fourth meeting of the American Physical Society was held in
Fayerweather Hall, Columbia University, New York, on Saturday,
April 27, 1918. Vice-President Ames presided in the absence of the president.
Professor H. A. Bumstead, who is serving as Military Attache at the American
Embassy in London. About seventy members and visitors were present.

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478 THE AMERICAN PHYSICAL SOCIETY, [I

At the meeting of the Council the following elections took place: elected to
regular membership: E. D. Williamson; elected to associate membership: Thomas
F. Ball, R. F. Bichowsky, Martha C. Bolton, L. B. Clark, Charles A. Corcoran,
N. VV. Cummings, Hugh L. Dryden, Alex F. Feild, Erick Hausmann, Kang-
Fuh Hu, G. R. Greenslade, Wm. H. Hoover, C. Moreau Jansky, Jr., Adolph
Lomb, Max H. Petersen, Toyoji Shinomiya, Leonard T. Troland, Cletus C.
Van Voorhis, Mabel Weil; transferred from associate to regular membership:
O. E. Buckley, K. T. Compton, Irving B. Crandall, H. L. Dodge. Saul Dush-
man, A. W. Hull, W. H. Kadesch, J. R. Roebuck, Otto Stuhlmann, L. D. Weld,
Frances Wick.

Twenty papers were presented as follows, three being read by title:

The Spectral Photoelectric Sensitivity of Molybdenite. (Read by title.)
W. W. CoBLENTZ, M. B. Long, and H. Kahler.

Electronic Frequency and Atomic Number. Paul D. Foote.

The Resonance and Ionization Potentials for Electrons in Thallium Vapor.
Paul D. Foote and Fred L. Mohler.

On the Relation Between the X-Ray Series and the Atomic Numbers of the
Chemical Elements. William Duane and Kang-Fuh Hu.

The Relation Between the General X-Radiation and the Atomic Number of
the Target. William Duane and Takeo Shimizu.

On the Critical Absorption and Characteristic Emission X-Ray Frequencies.
William Duane and Kang-Fuh Hu.

Photoelectric Effect at X-Ray Frequencies. Kang-Fuh Hu.

The Spectra of Hot Sparks in High Vacua. R. A. Millikan and R. A.
Sawyer.

The Law of Symmetry of the Visibility Function. Irwin G. Priest.

A Precision Method for Producing Artificial Daylight. (Read by title.)
Irwin G. Priest.

The Photo-Luminescence and Katho-Luminescence of Calcite. (Read by
title.) E. L. Nichols, H. L. Howes and D. T. Wilbur.

Thermionic Amplifier. H. J. van der Bijl.

Increase in Length of Life of Tribolium Confusum, Due to X-Rays. Whee-
ler P. Davey.

A Method for the Quantitative Study of Gases in Metals. H. M. Ryder.

On the Observation of the Apparent Focus of Auroral Streamers. C. C.
Trowbridge.

Photograph of an Aurora Model. C. C. Trowbridge.

Meteor-Train Spectra and Probable Erroneous Conclusions of the Observers*
C. C. Trowbridge.

The Influence of Amalgamation Variables Upon the Mercury Content and
the Crushing Strength of a Dental Amalgam. Arthur W. Gray and Paris
T. Carlisle, 4TH.

The Influence of Amplitude and of Electromagnetic Driving on the Fre-
quency of Tuning Forks. Dayton C. Miller.

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NoTd!^'*) ^^^ AMERICAN PHYSICAL SOCIETY, 479

Some Optical Constants of Certain Organic Compounds. H. P. Holl-
NAGEL. • Dayton C. Millef

Secretary

Thermo-couples for Student Use in Calorimetric Work^
By Ralph S. Minor.^

ON account of the difficulty in securing sensitive thermometers for general
laboratory use, a variety of thermocouples have been designed for use
with a galvanometer and an adjustable resistance so that the galvanometer read-
ing in centimeters equals the temperature difference in degrees C. Both copper-
constantan and nickel-iron couples have been used, the choice depending upon
the sensitiveness of the galvanometer. Calibration is accomplished by placing
one junction in ice and the other in a bath at the temperature of boiling ether,
35® C, and adjusting the resistance until the scale deflection is i cm. per
degree C.

An Harmonic Synthesizer Having Components of Incommensurable
Period and any Desired .Decrement.^

By William J. Raymond.

IT is known that when two oscillating electric circuits containing inductance
and capacity are connected, either by electromagnetic or by electrostatic
coupling, under certain conditions the current in each circuit is complex,
damped harmonic, each of the two constituents of the resultant oscillation
having its own period and decreasing according to the logarithmic law. The
oscillation shows recurrent maxima, similar to beats in sound, gradually de-
creasing as the currents die away. If the first circuit is subjected to some form
of impulse excitation, by the "quenched gap** for example, the oscillation of
current in the second circuit will quickly reach a single maximum of amplitude
and then die away more slowly with its own natural period and logarithmic
decrement. Coupled pendulums have been constructed which show the same
complexity of oscillation, neither of the constituent periods agreeing with the
period of either pendulum, oscillating by itself, and each of the constituent
oscillations having its own damping factor. When three pendulums are con-
nected there are in general three diminishing components in the resultant oscil-
lation, although one or two of them may be suppressed by appropriate choice
of initial conditions. The three constituent periods differ from the natural,
uninfluenced periods of the pendulums and they are in general incommensur-
able.

> Abetract of paper presented at the Berkeley meeting of the American Physical Society,
March 30, 1918.

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480 THE AMERICAN PHYSICAL SOCIETY. [toS!

Curves exhibiting these complex oscillations as functions of time may be
obtained by means of photography. It has been usual to measure the con-
stants of the coupled systems, such as the inductance, capacity and resistance
in each of the electric circuits, and then to construct curves, point by point,
computing the ordinates from theoretical equations for comparison with the
photographic curves. If there is agreement in all respects it affords confir-
mation both of the correctness of the measurement of the constants, and of the
validity of the equations from which the curves were constructed. One of the
purposes of the synthesizer named in the title of this abstract is to draw con-
tinuous curves which will show graphically the characteristics of complex
harmonic motions. It is hoped that the curves may be drawn with sufficient
precision and predetermination of form to serve as a check upon the measure-
ment of the constants of connected circuits or pendulums, as well as to test
the applicability of the equations employed. After setting the machine and
drawing a curve, any number of ordinates may be obtained without the labor
of repeated computations.

In 1906 J. R. Milne^ described **A New Form of Harmonic Synthetiser"
which provided for an incommensurable ratio of the speeds of two components
by means of parallel cones connected by a shifting leather belt. The amplitude
of one component could be altered while the machine was in motion by a
manually operated device, but apparently not according to any predetermined
or numerical value of the decrement. A synthesizer, with essential parts to
be described briefly, is now being constructed by the mechanician of the de-
partment of physics of the University of California. Three parallel shafts
carry truncated cones of the same vertical angle, the larger end of one cone
opposite the smaller end of the next. Friction wheels transmit the motion
from cone to cone, and by setting a wheel at any desired place along the slope
of the cones any required ratio of speeds may be obtained, commensurable or
incommensurable. Each shaft carries also a shallow, circular box on the
cover of which is a projecting, eccentric pin which actuates a slotted cross-head
of the usual type. If the pin is at a fixed distance from the center of the box
and if the shaft turns uniformly, the motion of the cross-head is simple har-
monic. But if the pin is made to move toward the center while the shaft is
turning, the motion of the cross-head is damped harmonic, the kind and amount
of the damping depending upon the rate at which the pin is moved toward the
center. The decrement of the motion may be logarithmic or rectilinear or of
any other desired type. To secure the centripetal motion of the pin a cam is
placed inside of the box, the cam being actuated by an independent shaft which
passes centrally through the hollow shaft which carries the box. The pin is
carried by a slide on the cover of the box and projects inwardly through a slot
in order to engage with the cam. The curve of the cam and the relative angular
velocity of the cam and the box will determine the rate at which the pin is
drawn toward the center of the box and consequently the nature of the motion

» Proc. Roy. Soc. Edinburgh, Vol. 26, pages 207-233, with plate.

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Na*6^^'] ^^^ AMERICAN PHYSICAL SOCIETY, 48 1

of the cross-head. By the use of a cord passing over pulleys attached to the
cross-heads the motions of two or more of them may be compounded and shown
graphically by a pen fastened to the cord. The pen draws a transverse trace
on a band of paper which is rolled uniformly from one drum to another.

The synthesizer may be used in any one of the following ways: (i) It will
draw a simple harmonic curve of any required amplitude and wave-length
within the limitations of the construction of the machine. (2) It will draw a
damped harmonic curve: (a) with a logarithmic decrement; (6) with a rectilinear
decrement; (c) with a decrement corresponding to the motion of an oscillating
system damped by resistance proportional to the square of the velocity; (d)
with a decrement of any other specified type. (3) It will compound two or
three simple harmonic curves of the same or different periods, commensurable
or incommensurable. (4) It will compound two or three damped harmonic
curves of any type and magnitude of decrement, within the limitations of the
construction. (5) It will compound simple harmonic and damped harmonic
curves. While the present synthesizer is designed to have three components,
others may be added if the need arises.

University op California.
March 30, 1918.

Variation of Velocity of Waves Due to Motion* of the Source.^
By Dinsmorb Alter, Captain C.A.N.A.

IN Lick Observatory Bulletin 305 was published a hypothesis concerning
variable velocity of light and of gravitation. According to this hypoth-
esis the velocity for comparatively short distances is the vector sum of the
normal velocity of light or gravitation and the velocity of the source. Certain
results of the hypothesis were considered. It was shown that the Michelson-
Morley experiment is satisfied; that binary stars are pushed continually farther
apart and that their orbits become more excentric. This last is an astronomical
phenomenon for which an explanation has been much needed. Beyond out*
lining the hypothesis and a few of its results, no proof was offered.

Two entirely different sets of experimental data, as well as a theoretical
consideration, prove that, contrary to the commonly accepted belief, the ve-
locity of sound is affected by the velocity of the source and does not depend
only on the medium as hitherto supposed. The theoretical consideration is
based on Poynting's equations as given in the Encyclopaedia Britannica, Vol.
25f page 440. All that it has been necessary to add to these is to show that
the external pressure mentioned in his equations does exist for a moving source.
The experimental proof consisted first of showing that the data collected by
Wolf, .and quoted in Winklemann's Handbuch der Physik, Band II., seite
523-526, are perfectly satisfied by the theory, and secondly in the fact that the
whistling of shells, coming toward the observer at twice the normal velocity of

^ Abetract of a paper presented at the Berkeley meeting of the American Physical Society,
March 30, 1918.

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482 THE AMERICAN PHYSICAL SOCIETY. [toSn?

wound was observed by the author, by Private George H. Bardsley, formerly
Whiting Fellow in physics in the University of California and by Lieutenant
George McFarland, C.A.C., and by numerous other observers at other times.

We have, therefore, two sets of experimental data entirely different from
each other, as well as our mathematical theory to assert that the velocity of
sound depends upon the velocity of the source as well as upon the kind of
medium.

Since our equations have been built from energy relations it can be seen at
once that the same reasoning will apply to all waves in any similar medium.
If, therefore, we assu-me a medium similar to air for light, the same reasoning
as for sound must apply and the velocity of light will depend upon the velocity
of the source. It is interesting to say, in this connection, that the Michelson-
Morley experiment, which has been assumed by many to prove that the ether
does not exist, becomes, in the light of this theory, one of the strongest proofs
of its existence.

The argument against an emission hypothesis for light as obtained from
observations of binary stars and quoted by Tolman, Comstock and others do
not apply to the variable velocity of light demanded by this work because at a
distance of a few light hours from the source the velocity of light will have
become sensibly normal.

At short distances, observed results, according to the emission hypothesis,
or to this, would be nearly the same in this regard. At the very great astro-
nomical distances, varying all the way from four to thousands of light years,
at which binaries are observed, there is a great divergence. The primary
postulate of relativity seems to be that it is impossible from observations made
in any system to tell which bodies of the system are moving. At astronomical
distances this can be done under our hypothesis, and, therefore, it is not rela-
tivity.

By analogy we have strengthened the hypothesis for gravitation stated in
the earlier paper. The astronomical arguments advanced there seemed fairly
strong, even before there was this proof of what seems an analogous case.
The perturbations due to this hypothesis should be computed for every pos-
sible binary in order to get a certain test as soon as possible.

Photograph of an Aurora Model.^
By C. C. Trowbridge.

IN order to study the optical effects of perspective produced by the auroral
rays, a model of the aurora was constructed covering the larger portion
of a room. A large number of strips of paper an inch broad and three feet
long were fixed to wires near the ceiling of the room so that they gave an in-
clination of s^bout 73** with the horizontal. This value was taken as approxi-
mate to the supposed dip at a certain station at Lat. 46® N. Photographs of

^ Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27. 191 8.

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No'e!^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 483

this model show a beautiful apparent focus of the artificial rays in the position
corresponding to 17® south of the zenith in the model. When one looks towards
the "north" there is another focus below the "northern horizon." When the
observer looks towards the "south" the rays do not focus below the horizon.
It was explained how the direction of the auroral rays could be determined by
means of a surveyor's transit; by examining the slant of the rays in the northern
sky.

The most recent and carefully made observations of StSrmer and others
indicate that the auroral discharge takes place between 55 and 90 miles with a
maximum between 60 and 64 miles. The altitudes of 29 meteor trains, the
records of which have been collected and classified by the writer, give a maxi-
mum at about 60 miles altitude, showing an approximate coincidence between
these two zones of the atmosphere of the earth. Both zones depend on the
existing gas pressure. The dimensions of the model were therefore based on
the latest information as to the height of the auroral streamers.

Professor Elihu Thompson in a recent number of the Transactions of the
National Academy of Science argues in favor of a vertical direction of the
auroral rays. All data seems to point to the fact that they are not vertical,
but are approximately parallel to the magnetic lines of force. The observations
in general seem to indicate an anomalous behavior relative to the declination,
but the records seem to be fairly consistent with respect to the dip.

On the Observation of the Apparent Focus of Auroral Streamers.*

By C. C. Trowbridge.

THE great aurora of August 26, 1916, which was seen both in England and
all over the northern portion of the United States, was observed in
Prince Edward Island, Canada, by the writer. The aurora appeared there
both in the south and in the north of the heavens, the general appearance being
that of a luminous umbrella, showing a clearly defined focus about 2° south of
the star Gamma Lyra at the time of observation. From the position of the
apparent focus, or radiant point, and the hour, 8:20 p. m. (Atlantic time), and
also the latitude and longitude of the place, the altitude and azimuth of the
point in the heavens from which the streamers seemed to radiate was com-
puted. The results show the streamers to be within 2® of the magnetic ele-
ments of the place. The "inclination" (dip) of the rays was computed to be
about 73® 00' and the "declination" about 22® 40'. There are conflicting
theories in regard to the question whether the rays are parallel to the magnetic
lines of force or not. Birkeland in his recent treatise points out that the matter
is an undecided question.

The only other accurate observation of the focus of the aurora of August 26,
19 1 6, was made by Professor Joel Stebbins, near Frankfort, Michigan. The
observation was published in the Journal of the Royal Astronomical Society of

* Abstract of a paper presented at the New York meeting of the American Physical Society.
April 27, 191 8.

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484 THE AMERICAN PHYSICAL SOCIETY. [ilS?S

Canada for April, and shows that the magnetic dip and the direction of the
streamers were almost identical, but that the focus point was 2 1/2** due east
of the magnetic zenith.

In the Monthly Weather Review of August, 1916, published in October,
seventy-odd descriptions of the aurora of August 26 were given as reported to
the Weather Bureau from different stations throughout the United States.
About twenty of the observers refer to a focusing of the rays, or a tendency of
the rays to focus. In several of the reports the statements are indefinite.
In the paper referred to there are quotations from ten of these descriptions
in which it is definitely stated that the radiant point or apparent focus of the
streamers was anywhere from a few degrees to 15® south or southeast of the
zenith. It is a noteworthy fact that the observations with one exception on
the Atlantic seaboard mention the radiant point as being east or south, while
all those in the central portion of the country give the radiant point as south of
the zenith, which is to be expected if the declination of the rays is nearly that
of the magnetic needle.

During the summer of 1917, the writer made observations on four evenings,
of the apparent focus or radiant point of the aurora overhead. The altitude
and azimuth of the focus have been computed in the case of each of the four-
teen observations made, and a very close coincidence has been found between
the altitude and the magnetic dip or inclination. In the case of the azimuth,
considerable variation has been found among observations made at short inter-
vals, these changes in all probability corresponding to sudden changes in the
earth's magnetic field due to the violent magnetic storm reported at that time.

Meteor Train Spectra and Probable Erroneous Conclusions of the

Observers.^

By C. C. Trowbrwge.

METEOR trains seen at night, or the so-called persistent phosphorescent
streaks which are deposited by large rapid meteors are self-luminous.
This fact is evident because they occur in the heavens where reflected sunlight
is impossible and since the spectra of these trains consist of a few bright lines
or bands.

Observations have been made of meteor-train spectra by A. S. Herschel,
J. Browning, A. Secchi and N. von Konkoly. Herschel's observations showed
a bright yellow line or band and indications also of a faint continuous spectrum
in certain cases.

Browning's observations were not very conclusive, but indicate in some
trains a "lavenders-colored band.

Secchi observed a train spectrum for ten minutes which was composed of a
red, a yellow and a green line (or bands).

Von Konkoly observed a train spectrum for eleven minutes which showed
one yellow and one green line (or narrow bands), and also some red and other

» Abstract of a paper presented at the New York meeting of the American Physical Society.
April 27, 1918.

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Na*6!^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 485

colors which he thought were caused by coal gas. The most prominent lines
or bands were attributed to the yellow of sodium and the green of magnesium
and the others to lithium, thallium, coal gas, etc. Apparently no direct com-
parisons were made, by any of the observers as seems to be shown by a study
of all the original papers.

It seems impossible with the present knowledge of physics and the evident
cold gaseous nature of meteor trains that metallic spectra were observed.
A meteor train after ten minutes may readily occupy five or ten cubic miles.

The only possible solution of the questions is that the spectrum was a gaseous
one, either a brush-like discharge or more likely a phosphorescent condition of
the gas, which the writer considers highly probable.

The visual spectrum of nitrogen in the phosphorescent, or "active" state,
consists of very bright yellow and green bands and also several others, chiefly
one in the red and one in the blue green more faint.

While at present there is no positive evidence that meteor trains show the
spectrum of a gas in the phosphorescent state, there seems to be very great
doubt of the possibility that Herschel, Secchi and Von Konkoly saw metallic
spectra in the meteor trains they observed.

The Photo-luminescence and Katho-luminescence of Calcite.^
By E. L. Nichols. H. L. Howbs and D. T. Wilbbr.

IN addition to the brief phosphorescence of calcites of the Franklin Furnace
variety described in a recent paper* these calcites, when subjected to
kathodo bombardment, have been found to exhibit phosphorescence which
persists for several minutes. The curve of decay of this kathodo luminescence
is of the form characteristic of persistent phosphorescence in general, consisting
of three successive processes each less rapid than the preceding. The photo-
luminescence, on the other hand, as shown in the paper just cited, is of the
opposite type, hitherto supposed to be peculiar to the uranyl salts, with three
successive processes each more rapid than the foregoing one. We have there-
fore, as in the case of the uraiiyl salts' two distinct types of phosphorescence
according to the mode of excitation. Having followed the kathodo phos-
phorescence for 300 seconds by the usual well-known method of a single excita-
tion and determined the form of the curve of decay, the relation of this curve
to that obtained by photo-excitation is of importance. In the method of single
excitation the earliest observation practicable is about .5 sec. after the close of
excitation, whereas the entire visible duration of photo-excitation is less than
.4 sec.

To obtain observations of the earlier portions of the decay curve for kathodo
phosphorescence we devised a special form of disk phosphoroscope workable

* Abstract of a paper presented at the New York meeting of the American Physical Society.
April 27. 1918.

* Nichols and Howes, Am. Physical Soc.. Pittsburgh meeting. 1917. Phys. Rbv.. April.
1918.

•Wick and McDowell. Phys. Rev.. Vol.. XI.. No. 6. p. 421. 1918.

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486 THE AMERICAN PHYSICAL SOCIETY. [toSS

in vacuo with which apparatus it was possible to make measurements for the
entire range between .06 seconds and 90 seconds.

In this manner it has been established that the curve for kathodo lumines-
cence is independent throughout in character from that for photo luminescence
and is not to be regarded as in any sense a continuation of the latter. The
two modes of excitation clearly produce quite different conditions within the
phosphorescent material. It has further been shown that kathodo- bombard-
ment does not produce a change in the surface layers such that subsequent
photo excitation will cause persistent phosphorescence. The two effects'
indeed may be superimposed without mutual interference.

A Method for the Quantitative Study of Gases in Metals.^
By H. M. Ryder.

THE metal studied, in the form of a long strip of small cross section, is
mounted on tungsten supports in a bulb surrounded by a water jacket,
and is heated by the passage of an electric current, its temperature being de-
termined by the resistance change, or by the use of very small thermocouples.
The gases are pumped into a second bulb by a diffusion pump immediately
upon being released and then analyzed for O2, N2, Hi, CO, COj, HjO, and CH4,
in a glass system at low pressure, separations being made by liquid air and solid
CO2, with provision for the addition of O2 or CO which reacts with the Hi, CO,
CHj, or Oj in a small combustion bulb, a platinum filament being used for
ignition. Quantities of gas as small as i mm.' equivalent at atmospheric con-
ditions can be analyzed quantitatively with a probable error of not more than
5 per cent. The amounts of CO2, CO, H2O, O2, H2, and Ni given off from a
specimen of silicon steel in each 50 degree step from 20® C. to 1000® C. are
given.

Westinghousb Research Laboratory,
East Pittsburgh, Pa..
April, 19 1 8.

The Resonance and Ionization Potentials for Electrons in Thallium

Vapor.^

By Paul D. Foote and Fred L. Mohler.

THE resonance and ionization potentials for electrons in thallium vapor
have been measured by the method described in earlier papers, with
the modification of the use of a hot equal-potential surface instead of a hot
wire as a cathode. The cathode was similar in principle to that used by
Goucher and consisted of a platinum (or better, a nickel cylinder) insulated
from a helix of tungsten wire, inside, which was used as the heater. The entire
apparatus was mounted inside a glazed porcelain tube and heated to about
900** C. At this temperature all parts of the ionization chamber show ther-

* Abstract of a paper presented at the New York meeting of the American Physical Society,
April 37, 1918.

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Na'6^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 487

mionic emission, so that the measurements are attended by leakage difficulties
which were not present in the work with other metals and hence the accuracy
obtained in earlier work is not to be expected. The pressure as measured by a
McLeod gauge was less than 0.002 mm. Hg. Ionization could be detected at
temperatures as low as 700** C, but resonance did not appear until the vapor
density was considerably higher, corresponding to about 900** C. Ionization
was accompanied by a strong emission of green light, undoubtedly the com-
plete line spectrum in which the line 5351 stands out most prominently,
Inelastic collision of the resonance type occurred at multiples for the applied
accelerating potential of 1.08 volts. Ionization occurred at an applied poten-
tial of 6.6 volts, which when corrected for the initial velocity, observed as 0.7
volt, gives the final value for the ionization potential of 7.3 volts. The
thallium spectrum is characterized by a set of doublet series. The resonance
potential of 1.08 volts is given within experimental errors by the quantum
relation hv ^ eV^ where v is the frequency of the stronger line (X = 11 51 3)
of the first doublet of the principal series, sometimes denoted by v = 2.5 5 — 3^.
The theoretical value of the resonance potential computed on this basis is
1.07 volts. We believe this is good evidence that the single-line spectrum of
thallium is X = 11513.

We were unable to detect any signs of ionization accompanying resonance
or any resonance due to the line X = 13014. If thallium acted in a manner
similar to sodium or potassium, one would expect from the analogous relations
in the series of these elements to find ionization determined by the quantum
relation hv = eV, where v is the limit of the principal series v = 22786. This
requires a value of F = 2.81 volts which cannot be considered in the light of
the experimental data. We believe that our work enables the prediction of a
new series in thallium. It is very possibly of the form p = 1.55 — mP, a
single-line series converging at 1.55 lying between 57000 and 60000. The
highest convergence frequency of any series so far known for thallium is 49263.
The present work again brings up the question of the separate excitation of
lines constituting a doublet. Thallium appears to offer a fruitful field for work
in this regard.

Bureau of Standards,
Washington, D. C,
April 10, 191 8.

Electronic Frequency and Atomic number.^
By Paul D. Foote.

EXCEPTION is taken to the theory proposed by Dr. Allen relating
electronic frequency and atomic number, described in three recent
papers appearing in Phil. Mag. and Proc. Roy. Soc. London. The present
article is given in the Phys. Rev., 1918.

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488 THE AMERICAN PHYSICAL SOCIETY. [^SS

On the Relation Between the K X-ray Series and the Atomic Numbers
OF THE Chemical Elements.^

By William Duanb and Kang-Fuh Hu.

MANY attempts have been made to find some characteristic of the chemical
elements that would increase by equal amounts in passing from one
element to the next.

Moseley's classical experiments show that the square roots of the frequencies
V of corresponding lines in characteristic X-radiation are almost, but not quite,
linear functions of the atomic numbers.

Recent researches confirm this, and indicate that the jump in the value of
the square root of the frequency in passing from one element to the next in-
creases with the atomic number, the curves representing Vi' as functions of
N bending slightly upward.

It might be expected that the critical absorption frequency in the K X-ray
series would bear the simplest relation to the atomic number, for it appears to
be the most important frequency characteristic of an element. Its importance
rests upon the following facts. The frequency is (o) the critical aljsorption
frequency; {h) the critical ionization frequency (this probably means critical
frequency for the emission of electrons with definite energy) ; (c) the frequency
for which the equation Ve — 1/2 mt^ = hp holds (1/2 mi^ being the energy of
the electron required to produce the K series) ; {d) the highest frequency known
to be characteristic of the element [It lies very close to the highest emission
frequency, if any thing slightly (1/5 per cent.) above it].

Mr. F. C. Blake and one of us last year measured the critical absorption
frequencies for most of the elements from bromine ( iV = 35) to cerium ( iV =
58) and found that they approximately obey the law, p = pq (N — 3.5)*, in
which Po is the Rydberg fundamental frequency. There appears to be a small
systematic variation from this law, however.

We have extended these critical absorption measurements recently, so that
we now have most of the critical absorption frequencies from manganese
(iV = 25) to cerium (N — 58), all measured with the same apparatus. In
order to measure the lower frequencies we used a specially designed X-ray
bulb with a long glass side tube carrying a thin glass window at its end and
extending out toward the X-ray spectrometer. This markedly reduced the
absorption of the X-rays by the glass and the air.

The results confirm those obtained last year. The Vv is not quite a linear
function of N,

It is interesting to inquire whether some other characteristic of the X-radia-
tion might not be a linear function of the atomic number.

Calculating the velocity v of the electron required to produce the K radiation
from equation (i) we find that it is accurately represented by the equation

r = vo (iV - 1.5), (2)

1 Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27. 1918.

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No'd^'l ^^^ AMERICAN PHYSICAL SOCIETY, 489

in which ro = .006780 X c (c - velocity of light). None of our measure-
ments differs from the value given by this equation by as much as 1/5 per cent.,
and there does not appear to be any systematic variation from the linear re-
lation.

This equation (2) also represents the velocity required to produce the K
X-radiation of the elements calculated from the highest frequencies recorded
in Siegbahn's tables as far as, and including magnesium {N = 12). Further
it gives the velocity required to produce the K radiation of tungsten calculated
from Hull's data.

That this critical velocity should be a linear function of N — i. e., should
increase by equal amounts from one element to the next, appears extraordinary.
It would seem to indicate that some of the fundamental laws connecting X-
radiation with other characteristics of the chemical elements represent velocity
relations and not momentum or energy relations.

On the Critical Absorption and Characteristic Emission X-Ray

Frequencies.^

By Wojliam Duanb and Kang-Fuh Hu.

IT is well known that a marked change in the absorption of X-rays by one
of the chemical elements occurs in the neighborhood of the emission lines
of the iiT-series of that element.

Last year Professor F. C. Blake and one of us* measured the critical abosorp-
tion wave-lengths (Xa) for most of the elements from bromine to cerium, both
inclusive, estimating the error of measurement at about o.i per cent. These
wave-lengths differ from the shortest emission wave-lengths in the iiT-series of
the elements that have been measured by considerably more than o.i per cent.

To determine, if possible, whether there is a real difference between the
critical absorption wave-length (Xa) and the wave-length (X-y) of the 7 line in
the emission spectrum, we have undertaken to remeasure both of these quanti-
ties, using as nearly as possible the same experimental conditions in the two
cases.

For this purpose we have employed a Coolidge X-ray tube with a rhodium
target, the current through it coming from a high potential storage battery.
In most of the experiments we held the voltage applied to the tube constant at
37750 volts by means of a variable resistance in series with the tube, and cor-
rected for unavoidable variations from this value. A current of 2 milli-
amp^res passed through the tube. The X-rays were analyzed by means of an
X-rays spectrometer, the 100 planes of a crystal of calcite reflecting the rays.
The formula

X = 6.056 X 10""* sin 0

gives the wave-length in terms of the grazing angle 6.

> Abstract of a paper presented at the New York meeting of the American Physical Society,
April 37, 1918.

* The Critical Absorption of Some of the Elements for High Frequency X-rays, F. C.
Blake and William Duane, Phys. Rev., Dec., 1917.

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490 ^^^ AMERICAN PHYSICAL SOCIETY, [sSa^

The X-rays passed through two narrow slits between the tube and the
spectrometer, and the slit in front of the ionization chamber was broad enough
to include the entire beam reflected from the crystal. Thus we eliminated
errors coming from the penetration of the X-rays into the crystal, etc.*

In order to avoid actually determining the zero of the instrument we either
measured the lines on each side of it, or else determined their ix)sitions in the
spectra of both the first and second orders. The fact that the two sets of
measurements agree shows that the planes of the crystal were not appreciably
curved. The following table contains the data.

K'Series of Rhodium (45) X X 10« cm.

as.

.6164 I .6122
.6163 1 .6121
.6161 I .6120

.5451 1 .5342

.5453 I .5343

.5454 ! .5342

In determining curves representing the ionization currents as a function of
the angle 0, we took readings 15" of arc apart. The slits were so narrow that
the peaks corresponding to the two a-lines were completely separated from
each other, although the difference between their wave-lengths is only 2/3 per
cent. Under these conditions the ionization method furnishes an indicator
so sensitive that the errors made are only those incurred in measuring an angle
of 10** by means of two verniers. The verniers were supposed to read to 5" of
arc. The readings may be in error, however, by almost 10", which means an
accuracy of about 1/20 per cent., just about the variation in the table.

The critical absorption wave-length of rhodium. determined last year was
Xo = .5324 X 10"*, i. e., about 1/3 per cent, shorter than the wave-length of
the 7-line in the above table. We have redetermined Xa, using a tungsten
target and an absorber consisting of a layer of rhodium salt, and find that, if we
measure from the mid-points in the sharp drops on the two sides of the zero
line, we get Xa = -5330 X io~®, and this differs from \y by almost 1/4 per cent.

In order to obtain further evidence on the point we have made a series of
experiments with the rhodium target tube with and without the rhodium salt
absorber.

The curves obtained indicate that the rhodium has no appreciable selective
absorption for its own ai, aj and /3 lines and that the marked increase in ab-
sorption occurs in the peak corresponding to the y line. Further the wave-
length corresponding to the center of the peak is about 1/3 per cent, longer than
that corresponding to the center of the absorption drop. This agrees with the
above experiments.

It appears, therefore, that either the critical absorption wave-length is about
1/3 per cent, shorter than that of the 7-line, or else the wave-lengths do not

« See Phys. Rbv., Dec.. 1917, pp. 624-637.

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Na'6'!^M ^^^ AMERICAN PHYSICAL SOCIETY, 49 T

correspond to the centers of the peak in the emission spectrum and of the drop
in the absorption curve.

We have also made some experiments designed to detect any possible dif-
ference between the critical absorption wave-length of iodine and the wave-
length corresponding to the sharp increase in ionization, when iodine is one of
the elements in the gas in the ionization chamber. For this purpose we filled
the ionization chamber with methyl-iodide, and used potassium iodide as an
absorber. According to our measurements the critical absorption wave-
length and the critical ionization wave-length are the same, namely X = .3737
X lo""' cm.

(This value agrees better with the data for neighboring elements than the
value obtained last year for the critical ionization wave-length of iodine.)

The Relation Between the General X-Radiation and the Atomic
Number of the Target.^

By William Duane and Takeo Shimizu.

IT is known that in general the intensity of the X-rays from a tube, other
conditions being the same, increases with the atomic weight of the ele-
ment used as a target. The literature, however, does not indicate conclusively
whether the increase in intensity depends upon the atomic weight or the atomic
number of the element. We know that the frequencies of the characteristic
X-rays increase with the atomic numbers (not the atomic weights) of the
elements, and it might be supposed from analogy that the intensity of the
general X-radiation would also increase with the atomic number.

To decide this point we have investigated the general X-radiation from the
four elements iron (26), cobalt (27), nickel (28) and copper (29). The atomic
numbers of these elements appear in the brackets, and they are arranged in
order of ascending atomic numbers. If they were arranged in order of as-
cending atomic weights the position of cobalt and nickel would be reversed,
the atomic weight of cobalt being greater than that of nickel.

Sheets of these four elements each in the form of a quadrant of a circle were
attached to the face of a circular copper disk, which was suspended in an X-
ray tube so that it could be rotated about its axis. By means of a magnet
outside of the tube acting on a piece of soft iron attached to the axle we could
place any desired element in front of the cathode.

The current in an ionization chamber containing methyl iodide was taken as
a measure of the intensity of radiation.

The table on following page contains the rates of increase in the potential
of the ionization chamber's electrode in volts per second, when the different ele-
ments were used as targets. The first column contains the voltage V applied
to the tube. A high potential storage battery produced the current which was
maintained at I milliampere throughout the experiment.

1 Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27, 1918.

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492 THE AMERICAN PHYSICAL SOCIETY, [serwu

Volts.

Ion.>Current (Volts p«r Sec.)*

19,140
21,430
24,120
27,300
30,110
32,400

Cu (39).

Nl (a8).

Co (17).

P« (16).

.0124

.0120

.0114

.0110

.0386

.0375

.0344

.0336

.0544

.0532

.0502

.0492

.0812

.0790

.0762

.0732

.1088

.1061

.1021

.0981

.1327

.1295

.1251

.1210

The characteristic X-rays from these elements do not pass through the glass
walls of the tube in perceptible quantities, unless the walls are very thin; so
that in this experiment the radiation contained only general radiation up to
frequencies given by the equation Ve = hv.

It appears that without exception the intensity of the X-radiation increases
as the atomic number (not the atomic weight) of the target increases

The intensity of radiation is approximately proportional to the atomic
number, but the range of atomic numbers is too small to test the point ac-
curately.

The Influence of Amalgamation Variables upon the Mercury Con-
tent AND the Crushing Strength of a Dental Amalgam.^

By Arthur W. Gray and Paris T. Carlisle, fourth.

THIS communication presents the results of some experiments undertaken
for the purpose of determining how the mercury content and the crush-
ing strength of a dental amalgam are affected by varying the mercury : alloy
ratio and the trituration time.'

Cylinders of amalgam 10.04 mm. in diameter were prepared and tested as
described by the authors at the Rochester meeting of the Physical Society.'

In one series of tests the mercury : alloy ratio was varied from 0.5 to 2.5,
while the trituration time was maintained uniformly at 1.5 minutes. This
varied the mix from a very stiff one to a very pasty one. When the cylinders
were molded under a packing pressure of 141 kg. wt. per circular cm., both
mercury content and crushing strength increased rapidly in the same general
way to maximum values which remained constant as the mercury : alloy ratio
was still further increased. Cylinders packed under 400 kg. showed the same
general characteristics, but to a lesser degree; and the maxima were reached
sooner. Increasing the packing pressure to 1,131 kg. produced cylinders of
uniform mercury content and almost uniform strength.

^ Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27, 1918.

* The mercury: alloy ratio refers to the masses of mercury and alloy that are triturated to-
gether to form an amalgam. In the process of molding this amalgam into cylinders for crush-
ing tests some of the mercury, along with a small amount of alloy, is squeezed out by the
packing pressure exerted through the piston of the mold. The per cent, of mercury in the
finished cylinder is here designated as the mercury content,

•A. W. Gray and P. T. Carlisle. Phys. Rev.. II., 154-156. 1918.

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No!"6^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 493

In a second series of tests the trituration time was varied from i to 8 minutes,
while a constant mercury : alloy ratio of 140 was used. The curves represent-
ing the results show that, in general, more mercury is retained in a test cylinder
by prolonging the trituration; but it is interesting to note that when the packing
pressure is low, less mercury seems to be left in the cylinder by increasing the
trituration time from one to two minutes. Apparently this is because the
shorter trituration leaves many of the alloy granules so large that a low packing
pressure is insufficient to squeeze out the free mercury from the spaces among
the solid particles. The curves also show that for a given trituration time the
mercury content changes almost inversely as the logarithm of the packing
pressure.

Increasing the trituration time while the packing pressure is kept constant is
accompanied by a progressive increase in strength until the latter reaches a
maximum when the trituration is maintained for about six minutes. Pro-
longing the time beyond this brings about a very gradual falling off in strength
on account of the partial setting of the amalgam during the mixing. The
results also indicate that the logarithmic law connecting crushing strength and
packing pressure, which the authors announced at the Pittsburgh meeting, is
applicable for any given trituration time within the range investigated.

The experiments outlined above are of considerable practical importance in
demonstrating that, contrary to the views now generally held both by dentists
and by manufacturers of dental alloys, the strength of a tooth filling made from
a high-grade dental amalgam is not lessened either by excess of mercury in
making the mix or by long trituration within practicable limits; while on the
other hand, a deficiency in mercury or too short a trituration time does result
in a marked deficiency in strength. Moreover, the evidence undeniably con-
tradicts the prevalent belief that the strength necessarily decreases with in-
crease in the amount of mercury retained, and because of the mercury. Tests
in addition to those reported here are all in harmony with the view that any
procedure which makes for more intimate union between the mercury and the
particles of alloy also makes for stronger tooth fillings. Thorough trituration
with mortar and pestle, and sufficient mercury to make sure of saturating
every granule of alloy, help in producing the desired intimate union.

Physical Research Laboratory,
The L. D. Caulk Company,
MiLFORD. Delaware,
February 20, 191 8.

Increase in Length of Life of Tribolium Confusum, due to X-Rays.*

By Wheeler P. Davey.

THE effects of X-rays upon living organisms, as reported by various
investigators, fall into three distinct classes.

1. A stimulation.

2. A destructive effect which takes place only after a certain latent interval.

* Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27, 1918.

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494 ^^^ AMERICAN PHYSICAL SOCIETY. [^SS

3. An instant destructive effect.

I. By analogy with the action of various drugs, it would be expected that
the rays could be made to act in any one of these three ways at will by merely
varying the size of the dose. In a previous paper,^ the writer has shown that
this is true for the last two of the three effects mentioned above. It is the
purpose of the present paper to present evidence that this is true for the first
effect also.

The organism used was the grain pest Triholium confusum. The apparatus
and technique were the same as in previous work. The present experiment is
in two parts: (i) to find the effect of doses smaller than the minimum lethal
dose, and (2) to find the effect of very small doses repeated daily. It has been
shown possible to duplicate results, time after time, subject only to those
general limitations which are inseparable from biological work.

I. The doses employed were 100, 200, 300 and 400 milliampere minutes at
25 centimeters distance and 50 kilovolts. In every case a group of beetles as
large as the groups to be X-rayed, was kept as a control. In the experiment
particularly described here there were approximately 850 individuals for each
dose. The beetles were rather old, so that the controls were all dead on the
fortieth day of the experiment. There were so few beetles still alive after the
thirty-fifth day that the results of the last five days are not of the same order
of accuracy as those of the first 35 days.

(a) The group which was given 100 MAM/25* at 50 kv. For the first 10
days this group had the same death rate as the controls. After the tenth day,
the death rate was considerably less than that of the controls. This group and
the control group were divided into two equal subgroups, and although it was
found that the idiosyncrasy was such that the subgroups were not exactly
alike, still after the tenth day the highest death rate of the X-rayed groups
was lower than the lowest death rate of the controls. Out of each 100 indi-
viduals in the group, there were on the fiftieth day after raying,

3 more beetles alive than in the control group,

7 " " " *' " " " on the twentieth day

13 " " " " " " " " '' twenty.fifth "

10 " " " '* " " " " *' thirtieth

5 " " " " " " " " " thirty-fifth "

(6) The group which was given 200 MAM/25' at 50 kv. During the first 17
days of the experiment, this group had a higher death rate than the controls.
After the twentieth day the death rate wa^ identical with that described under
(a). When divided into two equal subgroups as described above, it was found
that after the 22d day the highest death rate of the X-rayed group was lower
than the lowest death rate of the control group.

(c) The group which was given 300 MAM/25' at 50 kv. During the first 29
days of the experiment, the death rate of this group was greater than that of

» Phys. Rev.. June, 1917.

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495

the controls. After the twenty-ninth day the death rate was less than that
of the controls.

(d) The death rate of the group which was given 400 MAM/25* at 50 kv.
was at all times greater than that of the controls.

2. Six' groups were taken, of approximately 950 individuals each. These
were known as groups IV, IW, IX, I F, IZ and J A,

Group IV was the "control"

IW was given 6} MAM/25* at 50 Itv.— 25 MA daily

IX was given 12^ **

/ Y was given 25 "

IZ was given 50 "

J A was given 100 "

a 4( <4

l< <4 <<

<< <l l(

After 159 days the beetles were practically all dead. Death rates are shown
in the following table:

Group IV
(Control).

Per cent. Dead.

Group IV.

Group IZ.

Number

of Days

After Raying.

Group /^.

Group IX.

Group J A.

1
10

40 !

60 ;

70 1

100

90 1

100 i

By dividing each group into two equal subgroups, as described in (i) it was
shown that, although the idiosyncrasy was great enough so that the curves of
the subgroups could not be exactly superimposed, yet the lowest death rate
among the controls (group IV) was higher than the highest death rate among
the beetles of groups IW, IX and I ^ , It is interesting to note in this con-
nection that the total dose received by these beetles was greatly in excess of
that minimum dose which, when given all at once, would have caused prema-
ture death.

By plotting the data on probability paper, it was found that the curve for
each group was composed of portions of three accurate probability curves,
joined end to end. It is as though there were three causes of deaths, each
represented by its own probability function. These three portions of the
death rate curve will be termed A, B, and C. Portion C represents those
beetles which lived the longest in their group. The following table gives the
death rate per 100 in each group for ^4, B and C.

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496

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[Sbcond

Group.

IV.
IW.
IX.
lY..
IZ..
JA.

Daily Dose.

i which Died of

control

. 25

100

«i which Died of
"B."

26
36
26
35
61
17

)( which Died of

30
32
48
44
16
19

It is evident that the smallest daily dose (group IW) decreases the death rate
of " A '* and that those beetles which are kept from dying of " A " die of " B."
Deaths from cause ** C" are practically unaltered. A larger daily dose (group
IX) causes almost half of those which would normally die of "i4" to die of
" C." A still larger daily dose (group lY) causes half of those which would
have died of "-4** todie of *'-B" and " C." A still larger daily dose (group
/Z) acts much like the previous dose in causing about half of those which
would have died of 'M" to die of '* B,'* but it differs from it in that some of
those which would normally have died of ** C" are prematurely killed. The
largest daily dose employed (group J A) caused about a third of those which
would have died of " J5'* and ** C" to die of '' Ar

The following is an effort at an interpretation which does not involve too
deeply questions of .histology. Group J A shows that the lethal action of
X-rays is tied up in some way with cause of death ** i4." It is well known that
the lethal action of X-rays is more marked on cells in the process of division
than on those in the resting state. Therefore, small daily doses (larger than a
certain minimal value) can kill off those few cells which happen to be in a state
of division at the time of raying. The deaths of these few cells stimulate the
production of more to take their places. Therefore, small daily doses, instead
of increasing the death rate from cause ** ^4," actually decrease it by stimulating
the processes of repair. The whole individual beetle, therefore, has a smaller
chance of dying from *'yl'* and is compelled to die of either "B'* or ** C*
When the daily dose is increased to such a value that the daily destruction of
cells is equal to or greater than the production of new cells, premature death
results from causes '*B'* or *M" (see groups IZ and J A, above). At any
rate, irrespective of what the cause of death of the Triholium confusum may
be, and irrespective of what may be the method by which X-rays produce
their effect, we may regard it as well established that it is possible for X-rays
to cause in these beetles an increase in length of life.

Summary.
Using the same kind of organism throughout the whole experiment, it has
been shown that by merely varying the size of the dose, a purely physical
agent (X-ray) may be made to produce at will, (i) a stimulation, (2) a de-
structive effect which occurs only after a latent interval, or (3) an instant
destructive effect.

Research Laboratory.

General Electric Co., Schenectady.

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497

The Spectral Photoelectric Sensitivity of Molybdenite.
By W. W. Coblentz. M. B. Long and H. Karlbr.

CONTINUING this investigation,^ we have found that (i) samples of
molybdenite, obtained from various localities, differ greatly in sensitivity;
(2) there are maxima of sensitivity at 0.6/1, o.75m» 1.02/1, and 1.8/1; (3) there
is no simple law governing the variation in the photoelectric response with
variation in intensity of the radiation stimulus; (4) the increase in photoelectric
current with increase in intensity of the incident radiation is greatest in the
infra-red. It is greatest for low intensities and it is greatest on the long wave-
length side of the maximum; (5) the photoelectric sensitivity increases with
decrease in temperature. At 70** C. the bands at 1.02/1 and 1.8/1 have prac-
tically disappeared.
Washington, D. C,
April 6. 191 8.

The Influence of Amplitude and of Electomagnetic Driving on the
Frequency of Tuning Forks.'

By Dayton C. Moxbr.

TUNING forks are commonly considered as having a frequency of one
standard value. Only in rare instances is attention given to the in-
fluence of conditions of operation and usually notice is taken of the temperature
effect only. Three other causes produce variations which may be as great as
that due to temperature: (a) the resonance box, its presence or absence, and
its tuning, whether sharp or flat of the fork; (b) the amplitude of the motion of
the prong of the fork; (c) the effect of electromagnetic maintenance of vibration.
The Koenig Clock-Fork has been used in an extended investigation of the

-#3«04fl

rw|H^^

^sff.oaa

Fig. 1.

Fig. 2.

frequency of tuning forks, and a report is made of the effects of amplitude and
of electromagnetic driving. Figs, i and 2 show results for two forks of a kind

* Reported upon at the Pittsburgh meeting, Dec. 28, 191 7.

* Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27. 1918.

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498 THE AMERICAN PHYSICAL SOCIETY. [toiS

in common use; the first, having a frequency of loo, is such as would be used
in chronographic work, and the other, having a frequency of 435, is in common
use in connection with musical scales.

Fig. I shows that the fork, at 20° C, and electromagnetically driven, when
vibrating through 0.75 mm. double amplitude, has a frequency of 100.000.
When the fork is struck with a felt hammer and allowed to vibrate freely and
when the amplitude has naturally decreased from a greater initial value to
that previously mentioned, 0.75 mm., the frequency is 99.975. Thus the
electromagnetic driving increases the frequency in this instance about one part
in 4,000. When being driven electromagnetically, if .the width of swing
(double amplitude) is increased from 0.75 mm. to 2.0 mm. the frequency falls
to 99.990, that is, it is decreased by one part in 10,000.

Fig. 2 shows the effect of the amplitude on the frequency of a fork of 435
vibrations per second; for a double amplitude of 0.05 mm., the frequency is
435055; for double amplitude of 0.20 mm. the frequency is 435.030.

The diagrams show that change in pitch is a linear function of the amplitude
for each fork, and a further study indicates that for various forks, it is a func-
tion of the square of the frequency. The following equation expresses the
results in a convenient form for calculating the change in frequency. An, in
terms of the arbitrary coefficient k, the frequency n, and the double amplitude
(width of swing of end of prong) 2a:

An = k.n^.2a.

The numerical value of the coefficient which satisfies the measures so far
made is it = 8.4 X io"«.

The fact that the variation in the frequency with a change in the amplitude
is a function of the square of the frequency suggests that variation in amplitude
causes a change in the elasticity of the material of the fork, but further con-
sideration shows that the probable change in elasticity would affect the fre-
quency in a direction contrary to that observed. Therefore it seems more
probable that the variation in amplitude changes the eflfective length of the
prong. If this is true the numerical value of k would be dependent upon the
shape of the yoke of the fork. All the forks so far tested are of the shape
commonly known as that of Koenig. Further investigation will be made for
discussion in the full report.

The Law of Symmetry of the Visibility Function.*
By Irwin G. Pribst.

IF the relative visibility of radiant power is plotted as ordinate against wave-
length as abscissa, a striking characteristic of the resulting curve is its rough
approximation to symmetry about the maximum ordinate.* Troland indeed

> Abstract of a paper presented at the New York meeting of the American Physical Society,
April 27, 1918.

* See determinations of visibility by Ives. Nutting, Coblentz and Emerson. Phil. Mag.,
Dec., 1912, p. 853. Trans. I. E. S., q, 633 (1914). B. S. Sci. Paper joj.

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499

has particularly drawn attention to this fact and used it as a basis for deduc-
tions in regard to the nature of the response of the retina.^ He has, moreover,

— " - . " ^ ^_ — — ^_

_"_ " — — _ _ _ ^_.

— : "_ _ '_ — _

_ — — — _

Wave Lengths,
Millimicrons.

Frequency""'"""'.
^ ' lec. X 10"

Relative Retinal Visi-

bility from Original

Fig. X4 B. 8. 8ci. Pap.

303.

^-O.O0OIM4{/-6«)".

420

714

0.028

430

698

033

440

682

041

450

667

055

460

652

073

469

640

104

0.074

470

638

107

476

630

138

121

480

625

161

484

620

192

190

490

612

248

492

610

270

281

500

600

385

508

590

545

527

510

588

585

520

577

762

526

570

849

799

530

566

892

' 540

556

962

545

550

985

979

550

546

996

560

536

998

566

530

979

968

570

526

959

577

520

915

889

580

517

890

590

508

785

600

500

669

639

610

492

538

612

490

510

500

620

484

409

625

480

350

371

630

476

290

638

470

203

261

640

468

184

650

462

115

652

460

102

174

660

454

067

670

448

037

680

441

020

682

440

018

066

690

435

010

700

428

005

710

422

003

720

417

001

' Trana. I. E. S. //, 956 (1916), and Jour. Op. Soc. of Am.. /. 14 (1917).

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500 THE AMERICAN PHYSICAL SOCIETY. [^Sk

pointed out that, for this purpose, the experimentally determined visibility
should be corrected for the selective absorption of the ocular media so as to
obtain the visibility to the retina; and has stated that Nutting's data reduced in
this way gives a very symmetrical curve. Coblentz and Emerson have re-
duced their own data in the same way, applying the same correction as used
by Troland* and state that the resulting curve has a very symmetrical form.*
The degree of symmetry is not easily inferred from their published figure.
Dr. Coblentz has kindly given me the original from which this figure (Fig. 14,
B. S. Sci. Paper 303) was reproduced. Values read from this original figure
are shown in table on page 499.

It appears that while this curve is more nearly symmetrical than the uncor-
rected curve, the symmetry is still far from perfect, as is shown in the accom-
panying figure where these same data have been replotted in a way to exhibit
the departure of the curve from perfect symmetry.

It would seem a priori more likely that a simple relation should exist between
frequency and visibility than between wave-length and visibility. That this
assumption is justified will be shown below. It will be shown that for all
values of visibility greater than 15 per cent, of the maximum, the retinal
visibility curve with respect to frequency is much more symmetrical than the
one with respect to wave-length.

The corrected data of Coblentz and Emerson mentioned above have been
plotted against frequency in the accompanying figure. From this plot the
following conclusions are drawn:

1. For all values of visibility greater than 20 per cent, of the maximum, the
curve of average retinal photo pic visibility plotted against frequency is symmetrical
about the ordinate of maximum visibility at 541 vibrations per trillionth of one
second.

2. In more general terms, we may say: The average photopic visibility-
frequency curve of the retina is perfectly symmetrical throughout the spectral region
in which it is accurately known and not affected by extraneous phenomena. (Wave-
length = 490 to 690 millimicrons. Frequency = 612 to 435 vibrations per
trillionth of one second.) There may be some ground for questioning this
latter conclusion, but it is supported by the following considerations:

(a) The correction to be applied for the selective absorption of the eye
depends upon the age of the subject and is doubtless very uncertain for fre-
quencies greater than six hundred trillions per second. (Wave-length = 500
millimicrons.)

(6) The symmetry of the curve is literally perfect throughout the region in
which Coblentz and Emerson claim high accuracy for their data based on a
large number of observers.*

(c) The rise of the experimental curve above the symmetrical eurve in the
blue and violet may be due in part at least to the fluorescence of the retina or
ocular media which logically should be considered apart from true visibility.

» Trans. I. E. S., //, p. 956. Fig. 2.

« B. S. Sci., 303, p. 222, and Fig. 14, p. 216.

* B. S. Sci., 303, p. 221.

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(d) The determinations of visibility at the ends of the visible spectrum are
probably affected by unavoidable scotopic conditions.

3. To an approximation which is quite close relative to the diflferences
between individuals, the average retinal visibility shown by the solid line in

nftfciiwrn*'

Fig. 1.

RELATIVE VISIBILITY OF RADIANT POWER.

Data of Coblentz and Emerson corrected for selective absorption of ocular media (Fig. 14,
B. S. Sci. Paper 303).

Visibility plotted against frequency scale at bottom of figure.

Visibility plotted against wave-length scale at top of figure.

00000 Points S3rmmetrical with right-hand

part of visibility-frequency curve.

xzxzz Points symmetrical with right-hand

part of visibility-wave-length curve.

AAAA Points determined by equation

y „ ^-0.00(tt6M(/-Ml)«

About ordinate axis at frequency — S4i.-
000,000,000,000 per second.
(Wave-length. '^SSS millimicrons.)

Note: The wave-length scale at top and the frequency scale at bottom have been placed to
make the maximum ordinates of the visibility curves coincide, but there is no other assigned
relation between these two scales. The wave-length scale at the bottom gives merely wave-
length equivalents of frequencies on the frequency scale.

the accompanying figure is represented by the one term exponential formula
( ' * probability curve * *)

y _ ^-O.000a6«4(/-Ml)2

where / is frequency in vibrations per trillionth of one second and V is the
ratio of visibility at frequency/ to the maximum visibility at frequency = 541.

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502 THE AMERICAN PHYSICAL SOCIETY. [^S!

Computations by this formula are compared with the above data in the ac-
companying table and figure.

It may be noted that through the brighter part of the spectrum the sym-
metry of the curve is slightly more accurate than is the representation of the
curve by the probability function.

A different value of the exponential constant might be chosen which would
give a smaller average departure for a greater wave-length range; and a more
complex equation could of course be formulated which would better represent
the whole curve including the ends of the spectrum; but in the present state
of experimental knowledge,^ it is hardly worth while to make these more
precise adjustments for the retinal curve. Such equations representing
effective visibility, are already available for practical purposes.*

The essential purpose of the present paper has been accomplished in exhibit-
ing and quantitatively formulating the striking symmetry of the retinal visi-
bility-frequency curve for the higher luminosities, on the basis of the best data
now available. It is hoped that the simple relations herein established may
be useful in the development of the theory of the physico-physiological process
of light perception.

National Bureau of Standards.
April 5, 1918.

A Precision Method for Producing Artificial Daylight.'
By Irwin G. Priest.

LIGHT having a spectral distribution of energy closely approximating
that of daylight (black body at 5,000® abs., sun at the earth's surface or
sun outside the earth's atmosphere) may be produced by passing the light from
an artificial source (acetylene flame, vacuum tungsten lamp or gas-filled
tungsten lamp) through two nicol prisms with a crystalline quartz plate be-
tween them, the path of the light being parallel to the optic axis of the quartz,
and the thickness of the quartz as well as the angle between the principal
planes of the nicols being properly chosen. If three nicols are placed in series
in the beam, one quartz plate being placed between the first and second nicols
and another quartz plate between the second and third nicols, the approxima-
tion to a desired spectral energy distribution may be made still closer.

Nicols are designated i, 2, 3, in order from the source of light.

0 = angle of rotation of nicol No. 2, measured from its position for extinc-
tion with nicol No. i (quartz removed), the rotation being in the same direction
as the rotation of the plane of polarization by the quartz plate.

0' = angle of rotation of nicol No. 3, measured from its position for extinc-
tion with nicol No. 2 (same convention as above).

L = thickness of first quartz plate (near source).

> Coblentz and Emerson. B. S. Sci. Paper joj. p. 221.

* Kingsbury, Phys. Rbv.. 7, p. 161 (1916). Cobtentz and Emerson. B. S. Sci. Papa*
joj, p. 223.

» Abstract of a paper presented (by title) at the New York meeting of the American
Phywcal Society, April 27, 1918. (Submitted for March 2 meeting which was cancelled.)

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THE AMERICAN PHYSICAL SOCIETY.

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V = thickness of second quartz plate.

.^ . e /degrees\

a = specinc rotation of quartz ( ) .

\ mm. /

Functions

wave-length.

£1 = relative energy of actual source used.
£j = relative energy after light has passed through
quartz-nicol system.

Relative energy for any wave-length is computed by:
£2 = £1 Sin* (La — 0),
if a simple system of two nicols and one plate is used,
or £2 = £1 Sin» {La - <t>) Sin* {Va - 4>')

if a compound system of three nicols and two plates is used.

The rotatory dispersion of quartz has been previously used by others in
"chromoscopes," etc. The novelty of the present communication consists
solely in showing how it may be used in producing "artificial daylight"; and
in presenting precise specifications for producing the results.

Constants of apparatus to produce certain particular spectral energy dis-
tributions have been computed as follows:

I. Black Body at 5000® ahs, {Planck Equation),

(a) Simple system of two nicols and one quartz plate.

Relative Energy.

—

Wave Length.

Black Body.

Above System.

410 MM

480

590

100

680

720

Source: Acetylene flame or vacuum tungsten lamp at 1.22 w. p. m. h. c.

L = i.oo mm. 4> = 5-5 degrees.

The resultant spectral energy curve is smooth through the visible with a flat
maximum at X = 570MM-

(6) Compound system of three nicols and two quartz plates.

Source: Acetylene flame or vacuum tungsten lamp at 1.22 w. p. m. h. c.

L = I.oo nun. 0 = 2.0 degrees. V = 0.5 mm. 0' = 145 degrees.

The resultant energy distribution through the visible (420/1/1 to 720/1/1)
matches the theoretical black body distribution closely, the maximum de-
parture being about 4 per cent.

2. Sun at the Earth's Surface,
Simple system of two nicols and one quartz plate.
Source: Gas-filled tungsten lamp at 15.6 I. p. w.
L = 0.50 mm. 0 = Zero (crossed nicols).

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504

THE AMERICAN PHYSICAL SOCIETY,

rSBCOND

LSbribs.

See accompanying figure.

RELATIVe CNCRGY Of SUNUCHT^TTHC
CARTH^ SURFACE AT NOON IN WASH-
INGTON. J O^TA rROI1AB80TlS LETTER
or N0Vt7T9l7 TO BUROT STANDI AND
FROM ANN. A9TR0p. 065 OF SMITH.
IN5r. VDL3 P. 175)

. . WAVELCNClTH.

FDR MEAN(»dwi) ATMOSPHERIC hctw$»i<P|

TRANSMISSION.

-FOR UOW ATMOSPHERIC TRANSMISSION.

— FOR HI6H ATMOSPHERIC TRANSMISSION.

OO O l^tE^LATlVE ENCRCY, CAS-riUCD TUNCSTEN LAMP ATlSf (aJL^ c,M*a.Spc
^ UCKTA FffOH COBLENTZ. APa \1. /9I7 FOR aSUHPl7l7^liaVj* ^ ^^

Fig. 1.

Showing the reproduction of sunlight by passing the light from a gas-filled tungsten lamp
through a quartz plate 0.500 thick between crossed nico!s. the path of the light being par*
allel to the optic ax's of the quartz.

3. Sun Outside Atmosphere,

Simple system of two nicols and one quartz plate.

Source: Gas-filled tungsten lamp at 22 1. p. w.

L = 0.50 mm. 0 = i.o degree.

The spectral energy of the light by this system agrees with the spectral
energy of the sun outside the earth's atmosphere (Abbot) to within about 2
per cent, between wave-lengths 520/1 fi and 690/1/1. The maximum diflference
in the visible occurs at 470/i/i and is about 13 per cent.

This method, of course, is not adapted to illuminating large surfaces and so
is not a commercial competitor with the blue glass method or other "artificial
daylights." It is, however, very well adapted to use with instruments (pho-
tometers microscopes, etc.) where the quartz-nicol system may be inserted
between the eyepiece of the instrument and the observer's eye.

The chief advantages of this method over the blue glass method are:

1. A much more accurate reproduction of the desired spectral energy dis-
tribution. The distributions obtained by the use of blue glass {e. g., Luckiesh's,
''Trutint" or Corning, "Daylite") are always distorted from the desired dis-
tribution by a sharp maximum at X = 570/i/i as well as by a rise in the red for
X greater than 660.

2. Certain reproducibility and definiteness of specifications.

3. Adjustability. By varying 0 the distribution may be slowly changed by
known amounts.

A more detailed treatment of this subject will probably appear later in the
Bulletin of the Bureau of Standards.

The author expresses his appreciation of the assistance of Messrs. H. J.
McNicholas, J. T. Filgate and H. E. Cole in carrying through the very ex-
tensive computations by which the above results were obtained and checked.

National Bureau of Standards.
February 15, 1918.

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Na*6f''] ^^^ AMERICAN PHYSICAL SOCIETY. 505

Transparency of Certain Carbon Compounds to Waves of Great

Length.^

By H. P. HOLLNAGEL.

THE high transparency of quartz to residual rays of rock salt (X = 52 /i)
is well known. A search has been made for other substances of high
transmission of energy. It has been found that benzene is two and one half
times more transparent, carbon tetrachloride eight times and carbon bisulphide
ten times more transparent to radiation of this length (X = 52 /i) than is
quartz. It seems evident that studies of transmission may throw some light
on molecular structure. A number of substances, among which are ethyl
alcohol, ethyl ether, methyl alcohol, glacial acetic acid, acetyl chloride,
glycerine, show practically total absorption of energy of this wave-length in a
thickness of i mm.

Massachusetts Institute of Technology,
Cambridge. Mass.

Some Preliminary Results in a Determination of the Maximum Emis-
sion Velocity of the Photoelectrons from Metals at
X-Ray Frequencies.^

By Kang-Fuh Hu.

IT has been known for some time that when X-rays are allowed to fall on a
metallic plate, a stream of electrons of great velocities is emitted. Early
experiments brought out the existence of a close relationship between their
maximum velocity and the frequency of the incident rays, together with the
independence of this velocity on the intensity. The known approximate
equality of this maximum velocity to the critical minimum velocity of electrons
in the tube generating the parent X-rays, when coupled with the known
quantum production of X-ray, suggests strongly, that the same law might
apply also to this inverse process of photoemission in agreement with other
evidences in this field. But quantitative results are lacking. Whiddington's
results (and others using the same method) do not show numerical agreement
with the quantum values. Robinson and Rawlinson, using a different method,
obtained some interesting results. But they are hard to interpret beyond
establishing the fact that in some way both the nature of the source and that
of the radiator are involved. The present work is a preliminary account of an
attempt to get some qualitative and quantitative data regarding this important
question.

The method used in obtaining the main results was similar to that employed
by several other experimenters. Briefly it is this. A plate (radiator) is placed
in a uniform magnetic field and exposed to X-rays. The paths of electrons,
deflected into circles by the field, are intercepted by a photographic plate.

» Abstract of a paper presented at the New York meeting of the American Physical
Society, April 27. 1918.

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506 THE AMERICAN PHYSICAL SOCIETY. [^S

The image, the source and a slit across the path of the electron together deter-
mine the radii involved in the calculation of velocities.

With a constant applied potential on a tungsten Coolidge tube and a con-
stant magnetic field, silver and lead plates, and a silver foil backed or not
backed by a lead plate were successively tried as radiators. A continuous
spectrum was obtained, the limiting edge of which was identical in every case.
With the silver radiators, two strong lines were found in addition. Their
external edges were taken as the true maximum velocities of the electrons in-
volved in the emission, and the measurements were compared with the values
calculated from the known characteristic X-ray wave-lengths (from Siegbahn).
They are readily shown to correspond to the K^ and K. doublets of silver.
The faint limiting edge of the continuous spectrum was found on measurement
to have the same relative agreement with that calculated from the applied
voltage on the tube by \ rm^ ^ hv = Ve, The numerical agreement or disa-
greement with the quantum value is about 5 or 6% (calculated on velocity),
the experimental being always the smaller of the two, but the exact figure may
need further revision. A lead plate gave no L lines under the above conditions.

The same relative agreement among the K lines and the limit of the con-
tinuous spectrum is interesting, as the line and continuous spectra have dis-
tinct origins. In order to further confirm this point, a tin foil was placed in
front of the silver plate. Its thickness was about .025 mm., enough to stop the
electrons of maximum velocity twice over. There was consequently no chance
for electrons starting from the Ag plate to get through. The spectrum ob-
tained showed four lines, two of which nearly coincided. Two of the lines of
small velocities were identical with the Ag lines previously obtained, while
the other two new ones were found to be Sn K^ and K«, the latter coinciding
with the K^ of Ag, as is evident from the X-ray data. But here again, all
four sets of electrons started from the tin, though two of these were directly
excited by the primary X-rays in the body of Sn itself and the other two only
indirectly excited by the secondary Ag X-radiations produced. Thus the
two apparently distinct processes involved (which we may call ** characteristic "
and " independent " emission respectively, in analogy with the X-rays) gave the
same result, a point not to be expected, if we consider the reverse process of
X-ray emission. This is evidently due to the important part that the secon-
dary electrons must be playing in the emission of the characteristic X-radia-
tions.

Experiments are still in progress to see whether there is a characteristic L
electronic emission in connection with the K and to see if there is a real dif-
ference from the simple equation J ini^ = hv^ such as would be suggested by
the term *' — p" in Einstein's form of the equation.

In order to define v still more accurately, attempts were made to use a rho-
dium tube. The point was to obtain the line spectrum of rhodium, the source
on the same plate as that due to the radiator. Not only this would be the
most direct evidence for the point, but this would enable us to study the ques-

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Na"6^'*] ^^^ AMERICAN PHYSICAL SOCIETY. 507

tion whether the characteristic electrons are separately excitable or whether
they must be excited together under certain critical conditions, as suggested
by research in X-rays. They are unsuccessful chiefly on account of the in-
sufficient intensity.

Qualitative results have also been obtained with the method of retarding
potential, so universally used in the regions of lower frequencies, but never
yet tried with the high frequencies, evidently owing to the extreme difficulties
in operation. Unfortunately the work had to be abandoned, while fairly on
way to quantitative measurements, owing to an accident to the bulb which
the writer has not yet been able to replace satisfactorily. A simple electroscope,
containing the radiator as a part, was mounted inside a vacuum bulb and
carefully insulated. X-rays were allowed to fall on the plate. Of the quali-
tative results, it is perhaps interesting to note that an accumulation of -\- charge
amounting to about 300 volts (capacity = 3 to 4 cm.) was observable in the
course of the first 30 minutes, with a Ag plate and a silvered bulb, both initially
uncharged, indicating a current of some magnitude. No accumulation time
was observable. The electroscope would go up or down according as it was
previously charged to a -)- or — potential but ultimately charged up positively
in all cases. The true effect was however only observable with the highest
attainable vacuum and after the electrons from the ends of the glass tube had
been removed by a magnetic field, else the leakage due to these electrons and
the attending ionization from all sources would be at least twice as great as the
effect sought, showing however still the proper polarity in emission, within
certain limits of the conditions. The vacuum was pumped by the charcoal
method, it was so high that the absorption power of charcoal at ordinary
temperature was not distinguishable from that with the liquid air. In one
case, even under a vacuum somewhat inferior to the present one, a Pt wire
electroscope was charged to 15,000 volts and left standing for over a week
without being perceptibly discharged.

The effect was however always in the reverse direction, when the plate was
made of Al instead of Ag. It seems that there is a tremendous difference in
the emitting power among the various chemical elements, so that the scattered
X-rays are able to excite more electrons from the Ag wall than the primary
ray can from the Al plate itself. This might have had a bearing on many
previous observations, where the conditions were not so definitely known.

With a retarding potential of slightly under 20,000 volts, the proper effect
was observed with Ag and W plates, though not measured. The potential
on the X-ray tube was about 40,000 volts. The quantitative investigation
bf the maximum velocity and the velocity distribution were interrupted
prematurely.

Perhaps a combination of these two methods would be desirable, as the
photographic method is very insensitive (at least 25 hrs. with an input of 200
watts into a tungstun tube) and the method of retarding potential, though
feasible, is at best, a risky proposition.
Jefferson Physical Laboratory,
Harvard University.

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5o8

ERRATUM.

SlKUl.

ERRATUM.

Vol. XL, May, 1918, page 363, article by T. Peczalski, entitled " Effect
of Hydrogen on the Electrical Resistivity of Carbon **; in Figs. 2, 4 and
5, the scale values and meaning of coordinates were omitted. These
figures are here reproduced with the co5rdinates and scale values cor-
rectly indicated.

«« JLO

Time in *tconl^

Fig. 2.

Fig. 5.

t-ILI

k-^

-A

•0 P

^ •- US.L

ft: ^•'•*

—

O JO /OO ISO zoo ISO dOO 3SQ 'fOO vso soo

Ovfo^tion oi h^atin^ of lii^ifient in minvtc^.
Fig. 4.

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Vol. XI.l
No. 6. J

INDEX TO VOLUME XL

509

Index to Volume XL, Series II.

Abaorption, On the Unpolarized Fluores-
cence and, of Four Double Chlorides
of Uranyl, Edward L, Nichols and
H, L. Howes, 285.

Absorption Bands, on Certain, in the
Spectra of the Uranyl Salts, H. L.
Howes, 66.

Absorption Bands, On Certain, in the Spec-
tra of the Uranyl Salts, H. L. Howes,
143.

Achromatization, Complete, of a Two- Piece
Lens, G. W. MojffUt, 144.

Air, Mobility of Ions in. Hydrogen, and
Nitrogen, Kia-Lok Yen, 248.

Air-Damped Vibrating System, The, Theo-
retical Calibration of the Condenser
Transmitter, /. B. CrandaU, 449.

Alter. Dinsmore, Variation of Velocity of
Waves due to Motion of the Source,
481.

Alternating Current, Rectification of, by the
Corona, J. W. Davis, 243.

Amalgamation Variables, The Influence of,
upon the Mercury Content and the
Crushing Strength of a Dental
Amalgam, Arthur W. Gray and Paris
T. Carlisle, Fourth, 492.

American Physical Society:

Abstracts, 132, 241, 326, 479.
Minutes, 130, 477.

Artificial Daylight, A Precision Method for
Producing. Irwin G. Priest, 502.

Assmann Aspiration Psychrometer, Com-
parative Accuracy of Whirled Psy-
chrometer, Porous Cup Atmometers,
Hair Hygrographs, Piche Evapori-
meter Saturation Deficit Recorder.
Open Water Surface Evaporimeter,
and Dry and Wet Bulb Thermometers,
Alexander McAdie, 152.

Atomic Number, Electronic Frequency, and,
Paul D. Foote, 487.

Audion Characteristic Curves, The Effect
Produced upon, by Various Kinds of
Signals (Buzzer, Electron Relay and
60-Cycle A. C), A. D. CoU, 331.

Audions, Characteristic Curves of Various
Types of, A. D. Cole, 330.

Aurora Model, Photograph of an, C. C.
Trowbridge, 482.

Auroral Streamers, On the Observation of
the Apparent Focus of. C. C. Trow-
bridge, 483.

Benade, J. M., Elasticity of Impact of
Electrons with Gas Molecules, 184.

Benade, J. M., The Theory of Ionization by
Collision. IV. Cases of Elastic and
Partially Elastic Impact, 234.

Bichowsky, F. Russell v.. The Necessary
Physical Assumptions Underlying a
Proof of the Planck Radiation Law,
58.

Birge, Raymond T., The Mathematical
Structure of Band Series, II., 136.

Blanchard, Julian, The Brightness Sensi-
bility of the Retina, 81.

Bohr's Atom, Zeeman's Effect and the
Magnetic Properties of the Elements,
Jakob Kunz, 153.

Boron Conductors, The Breakdown Effort
in, F. W. Lyle, 253.

Breakdown Effort, The. in Boron Conduc-
tors, F. W. Lyle, 253.

Bridgman, P. W., On Equilibrium under
Non-Hydrostatic Stress, 180.

Brown, Thomas B., Kathodo-Fluorescence
of Crystals, 39.

Buzzer, The Effect Produced upon Audion
Characteristic Curves by Various
Kinds of Signals (Electron Relay and
60-Cycle A. C), A. D, Cole, 331.

Calcite, Note on a Phosporescent, H. L.
Howes, 327.

Calcite, Note on the Grating Space of, and
the X-Ray Spectrum of Gallium,
Arthur H. Compton, 430.

Calcite, The Photo-Luminescence and Katho-
Luminescence of, E. L. Nichols, H, L.
Howes and D, T. Wilber, 485.

Calorimetric Work. Thermo-couples for
Student Use in, Ralph S. Minor, 479.

Carbon, Effect of Hydrogen on the Elec-
trical Resistivity of, T. Peczalski, 363.

Carbon Compounds, Transparency of Cer-
tain, to Waves of Great Length,
H. P. HoUnagel, 505.

Carlisle, 4th, Paris T., The Influence of
Temperature Upon the Crushing
Strength of a Dental Amalgam, 154.

Carlisle, Fourth, Paris T.. The Influence of
Amalgamation Variables upon the
Mercury Content and the Crushing
Strength of a Dental Amalgam, 492.

Cathode Ray Excitation, A Preliminary

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INDEX TO VOLUME XI.

[Sbcoho
Sbbiss.

Study of the Luminescence of the
Uranyl Salts under, Frances G. Wick
and Louise S. McDowell, 421.

Coblentz. W. W., The Spectral Photoelectric
Sensibility of Molybdenite, 497.

Coefficient of Expansion, Young's Modulus
of Drawn Tungsten and its Variation
with Change of Temperature, in-
cluding a Determination of the.
H. L. Dodge, 311.

Cole, A. D., Characteristic Curves of Various
Types of Audions, 330.

Cole, A. D., The EflFect Produced upon
Audion Characteristic Curves by
Various Kinds of Signals (Buzzer.
Electron Relay and 6o-CycIe A. C),
331.

Collision, The Theory of Ionization by, IV.
Cases of Elastic and Partially Elastic
Impact, K. r. Compton and J. M,
Benade, 234.

Collision, A Correction in the Theory of
Ionization by. Jakob Kunt, 246.

Compton, Arthur H., The Nature of the
Ultimate Magnetic Particle, 132.

Compton, Arthur H., The Size and Shape of
the Electron. 330.

Compton, Arthur H. Compton, Note on the
Grating Space of Calcite and the
X-Ray Spectrum of Gallium, 430.

Compton, K. T., Elasticity of Impact of
Electrons with Gas Molecules, 184.

Compton, K. T.. The Theory of Ionization
by Collision. IV. Cases of Elastic
and Partially Elastic Impact, 234.

Condenser Transniitter, The Air-Damped
Vibrating System, Theoretical Cali-
bration of the, I. B. Crandall, 449.

Crandall, I. B.. The Air-Damped Vibrating
System, Theoretical Calibration of
the Condenser Transmitter, 449.

Crystals, Kathodo-Fluorescence of, Thomas
B. Brown, 39.

D Lines, The Ratio of the Intensities of the.
of Sodium, Vivian Voss, 21.

Davey, Wheeler P., Emulsions: (a) A New
Method for Making Emulsions, (b)
Properties of Emulsions, 138.

Davey, Wheeler P., Increase in Length of
Life of Tribolium Confusum, 493. |

Davis, Bergen, Characteristic X-Ray Emis- -
sion as a Function of the Applied
Voltage, 433.

Davis, J. W., Rectification of Alternating 1
Current by the Corona. 243. '

Dempster, A. J.. A New Method of Positive j
Ray Analysis, 316.

Dental Amalgam, The Influence of Tem-
perature upon the Crushing Strength
of a, Arthur W. Cray and Paris T,
Carlisle, Fourth, 154.

Dental Amalgam. The Influence of Amal-
gamation Variables upon the Mer-
cury Content and the Crushing

Strength of a, Arthur W, Cray and

Paris T. Carlisle, 492.
Derieux. John B., Photoelectric Effects on

Mercury Droplets, 276.
Dershem, Elmer. A Mono-Wave-Length

X-Ray Concentrator, 244.
Dershem, Elmer, Wave-Lengths of the

Tungsten X-Ray Spectrum. 244.
Dershem, Elmer, Wave-Lengths of the

Tungsten X-Ray Spectmm, 461.
Derieux, John B., The Use of Mercury Drop-
lets in Millikan's Experiment. 203.
Dodd, L. E., Further Verification of Knud-

sen's Equations for Resistance to

Molecular Flow. 242.
Dodge, H. L., Young's Modulus of Drawn

Tungsten and its Variation with

Change of Temperature, including a

Determination of the Coefficient of

Expansion, 311.
Doubt, Thomas E., The Determination of

Organic Compounds by an Optical

Method, 249.
Duane, William, On the Critical Absorption

and Characteristic Emission X-Ray

Frequencies, 489.
Duane, William, On the Relation between

the K X-Ray Series and the Atomic

Numbers of the Chemical Elements.

488.
Duane, William, The Relation between the

General X-Radiation and the Atomic

Number of the Target, 491.

Elasticity of Impact of Electrons with Gas
Molecules, J. M. Benade and K. T,
Compton, 184.

Electrical Resistivity, Effect of Hydrogen
on the, of Carbon, T. Pectalski, 363,
508.

Electromagnetic Driving, The Influence of
Amplitude of, on the Frequency of
Tuning Forks, Dayton C. Miller, 497.

Electron. The Size and Shape of the, Arthur
H. Compton, 330.

Electrons. Elasticity of Impact of, with Gas
Molecules, J. M. Benade and K. T,
Compton, 184.

Electrons, The Resonance and Ionization
Potentials for. in Thallium Vapor.
Paul D. FooU and Fred L. Mohler, 486.

Electron Relay. The Effect Produced upon
Audion Characteristic Curves by
Various Kinds of Signals (Buzzer.
6o-Cycle A. C). A. D. CoU, 331.

Electronic Frequency and Atomic Number.
Paul D. PooU, 487.

Emission Velocity, Some Preliminary Re-
sults in a Determination of the
Maximum, of the Photoelectrons from
Metals at X-Ray Frequencies, Kang-
Fuh Hu, 505.

Emulsions: (a) A New Method for Making
Emulsions. (6) Properties of Emul-
sions, Wheeler P, Davey, 138.

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Vol. XL!
No. 6. J

INDEX TO VOLUME XI.

511

Energy Partition, A General Theory of, with

Applications to Quantum Theory,

Richard C. Tolman, 261.
Equilibrium. On, under Non-Hydrostatic

Stress, P. W. Bridgman, 180.
Erratum, 508.
Evaporimeter, A Self-Recording, Alexander

McAdie, 147.

Fenner, Clarence N., Methods of Tempera-
ture-Control in Glass-Melting Fur-
naces, 141.

Fluorescence, On the Thermodynamics of,
E. H. Kennard, 39.

Fluorescence, A Study of the, of Certain
Uranyl Salts at Room Temperature,
Frances G. Wick, 100.

Fluorescence, On the Unpolarized, and
Absorption of Four Double Chlorides
of Uranyl, Edward L. Nichols and
H. L. Howes, 285.

Foote, Paul D., The Resonance and Ioniza-
tion Potentials for Electrons in.
Thallium Vapor, 486.

Foote, Paul D.. Electronic Frequency and
Atomic Number. 487.

Forsythe, W. E., Note on a Comparison of
High-Temperature Scales, 139.

Freud, B. B., The Determination of Organic
Compounds by an Optical Method,
249.

Gallium, Note on the Grating Space of
Calcite and the X-Ray Spectrum of,
Arthur H. Compton, 430.

Gas Molecules. Elasticity of Impact of
Electrons with, y. M. Benade and
K, T. Compton, 184.

Gaseous Ions, The Mobilities of, Kia-Lok
Yen, 337.

Germann, Frank E. E., A New Hydrate of
Uranium Nitrate; Uranium Nitrate
i-cositetrahydrate, 245.

Gray. Arthur W., The Influence of Tem-
perature Upon the Crushing Strength
of a Dental Amalgam, 154.

Gray, Arthur W., The Influence of Amal-
gamation Variables upon the Mercury
Content and the Crushing Strength
of a Dental Amalgam, 492.

Hair Hygrographs, Comparative Accuracy
of Whirled Psychrometer, Assmann
Aspiration Psychrometer, Porous Cup
Atmometers, Piche Evaporimeter Sat-
uration Deficit Recorder, Open Water
Surface Evaporimeter, and Dry and
Wet Bulb Thermometers, Alexander
McAdie, 152.

Hall, Edwin H.. Theory of Thermal Con-
ductivity in Metals, 329.

Harmonic Synthesizer, An, having Com-
ponents of Incommensurable Period

and any Desired Decrement, William
J. Raymond, 479.

Hartman, L. W.. The Visibility of Radiation
in the Blue End of the Visible Spec-
trum. 327.

Heat Conductivities, Measurement of, of
Metals at High Temperatures, Robert
W. King, 149.

Hebb, T. C, The Ionization Potential of
Mercury Vapor, 170.

Helmick. P. S.. The Variation in the Black-
ening of a Photographic Plate with
Time of Exposure, Total Energy
Remaining Constant. 372.

High-Temperature Scales. Note on a Com-
parison of, E. P. Hyde and W. E.
Forsythe, 139.

High Vacua. The Production and Measure-
ment of, J. E. Shrader and R. G.
Sherwood, 134.

Hollnagel, Herbert P., On the Residual Rays
of Rock Salt, 135.

Hollnagel, H. P., Transparency of Certain
Carbon Compounds to Waves of
Great Length. 505.

Howes. H. L., On Certain Absorption Bands
in the Spectra of the Uranyl Salts, 66.

Howes, H. L., On Certain Absorption Bands
in the Spectra of the Uranyl Salts, 143.

Howes, H. L., On the Unpolarized Fluores-
cence and Absorption of Four Double
Chlorides of Uranyl, 285.

Howes, H. L., Note on a Phosphorescent
Calcite, 327

Howes, H. L., The Photo-Luminescence and
Katho-Luminescence, of Calcite 485.

Hu, Kang-Fuh. Some Preliminary. Results
in a Determination of the Maximum
Emission Velocity of the Photo-
electrons from Metals at X-Ray Fre-
quencies. 505.

Hu, Kang-Fuh, On the Critical Absorption
and Characteristic Emission X-Ray
Frequencies, 489.

Hu, Kang-Fuh, On the Relation between the
K X-Ray Series and the Atomic Num-
bers of the Chemical Elements. 488.

Hyde, E. P., Note on a Comparison of High-
Temperature Scales, 13Q.

Hydrogen. A New Formula for the Tem-
perature Variation of the Specific
Heat of, Edvnn C. Kemble, 156.

Hydrogen, Mobility of Ions in Air, and
Nitrogen, Kia-Lok Yen, 248.

Hydrogen, Effect of, on the Electrical Re-
sistivity of Carbon, T. Peczalski, 363,
508.

Ionization, A Correction in the Theory of,

by Collision. Jakob Kunz, 246.
Ionization Potential, The, of Mercury Vapor,

r. C. Hebb, 170.
Ionization Potentials, The Resonance and,

for Electrons in Thallium Vapor.

Paul D. FooU and Fred L. Mohler,

486.

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512

INDEX TO VOLUME XI,

Ionization, The Theory of, by Collision.
IV. Cases of Elastic and Partially
Elastic Impact. K. T, Compton and
J. M. Bcnade, 234.

Ions, Mobility of. in Air, Hydrogen, and
Nitrogen. Kia-Lok Yen, 248.

Impact. The Theory of Ionization by Col-
lision. IV. Cases of Elastic and
Partially Elastic. K. T. Compton and
J, M, Benade, 234.

Image Formation, The Geometry of, in
X-Ray Analysis, Horace Scudder
UhUr, I.

Intensities, The Ratio of the, of the D Lines
of Sodium, Vivian Voss, 21.

Iron, The Magnetization of, in the Absence
of Hysteresis, Winthrop R. Wright,
161.

Jones, Arthur Taber, Rotation of the Pulley
in Melde's Experiment, 150.

K X-Ray Series, On the Relation between

the, and the Atomic Numbers of the

Chemical Elements, 488.
Kahler. H.. The Spectral Photoelectric

Sensibility of Molybdenite. 497.
Katho-Luminescence, The Photo-Lumines-
cence and. of Calcite. E. L. Nichols,

H. L. Howes and D, T. Wilber, 485.
Kathodo-Fluorescence of Crystals. Thomas

B. Brown, 39.
Kemble. Edwin C. A New Formula for the

Temperature Variation of the Specific

Heat of Hydrogen, 156.
Kennard. E. H., On the Thermodynamics

of Fluorescence, 29.
King, Robert W.. Measurement of Heat

Conductivities of Metals at High

Temperatures, I49«
Knudsen's Equations. Further Verification

of, for Resistance to Molecular Flow,

L. £. Dodd, 242.
Kunz, Jakob. Bohr's Atom, Zeeman's Effect

and the Magnetic Properties of the

Elements, 153.
Kunz. Jakob. A Correction in the Theory of

Ionization by Collision, 246.

Light, An Experimental Demonstration of
the Constancy of the Velocity of.
Reflected by a Moving Mirror.
Q. Major ana, 411.

Ix>ng. M. B.. The Spectral Photoelectric
Sensibility of Molybdenite, 497.

Luminescence, A Preliminary Study of the,
of the Uranyl Salts under Cathode
Ray Excitation, Frances G. Wick and
Louise S, McDowell, 421.

Lyle. F. W., The Breakdown Effort in Boron
Conductors. 253.

McAdie. Alexander. A Self-Recording Evap-
orometer, 147.

McAdie, Alexander, An Instrument for
Continuously Recording the Per-
centage of Saturation and the Weight
of the Water Vapor per Unit Volume
in the Free Air, 148.

McAdie, Alexander, Comparative Accuracy
of Whirled Psychrometer, Assmann
Aspiration Psychrometer, Porous Cup
Atmometers, Hair Hygrographs, Piche
Evaporimeter Saturation Deficit Re-
corder, Open Water Surface Evaporim-
eter. and Dry and Wet Bulb Ther-
mometers. 152.

McDowell, Louise S.. A Preliminary Study
of the Luminescence of the Uranyl
Salts under Cathode Ray Elxdtation,
421.

Magnetic Moment, The Moment of Momen-
tum Accompanying, in Iron and
Nickel. John Q. Stewart, 100.

Magnetic Particle, The Nature of the Ulti-
mate, Arthur H, Compton and Oswald
Rognley, 132.

Magnetic Properties, Bohr's Atom, Zeeman's
Effect and the, of the Elements,
Jakob Kuns, 153.

Magnetization, The, of Iron in the Absence
of Hysteresis, Winthrop R. Wright,
161.

Majorana, Q., On the Second Postulate of
the Theory of Relativity: An Ex-
perimental Demonstration of the
Constancy of the Velocity of Light
Reflected by a Moving Mirror, 411.

Mathematical Tables. Report on the Con-
struction of Certain, C. E. Van
Orstrand, 332.

Megaphone, A, with a Rectangular Aperture,
F. R. Watson, 244.

Melde's Experiment. Rotation of the Pulley
in, Arthur Taber Jones, 150.

Mercury Content, The Influence of Amal-
gamation Variables upon the, and
the Crushing Strength of a Dental
Amalgam. Arthur W. Gray and
Paris T. Carlisle. Fourth, 492.

Mercury Droplets, The Use of, in Milikan's
Experiment, John B. Derieux, 203.

Mercury Droplets, Photoelectric Effects on,
John B. Derieux, 276.

Mercury Vapor. The Ionization Potential
of, r. C. Hebb, 170.

Meteor Train Spectra and Probable Erron-
eous Conclusions of the Observers,
C. C. Trowbridge, 484.

Miller, Dayton C, The Influence of Ampli-
tude of Electromagnetic Driving on
the Frequency of Tuning Forks,
497.

Millikan's Experiment, The Use of Mercury
Droplets in, John B. Derieux, 203.

Minor. Ralph S., Thermo-couples for Stu-
dent Use in Calorimetric Work, 479.

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Vol. XI.l
Na6. J

INDEX TO VOLUME XI.

513

Mobilities. The. of Gaseous Ions, Kia-Lok
Yen, 337.

Moffitt, G. W.. Complete Achromatization
of a Two-Piece Lens. 144.

Mohler, Fred L., Resonance Radiation of
Ssodium Vapor Excited by One of the
D Lines. 70.

Mohler, Fred L., The Resonance and Ioni-
zation Potentials for Electrons in
Thallium Vapor, 486.

Molybdenite. The Spectral Photoelectric
Sensibility of, W. W. CobUtUt, M. B.
Long and H. Kahler, 497.

Momentum, The Moment of. Accompanying
Magnetic Moment in Iron and
Nickel, John Q. Stewart, 100.

Moving Mass. Is a, Retarded by the Reac-
tion of its Own Radiation?, Leigh
Page, 376.

Nathanson, J. B., The Optical Properties of

Rubidium. 227.
Nathanson. J. B.. The Optical Properties of

Rubidium, 333.
New Books, 159, 251, 335.
Nichols, E. L., On the Unpolarized Fluores-
cence and Absorption of Fpur Double

Chlorides of Uranyl, 285.
Nichols. E. L., Note on a Phosphorescent

Calcite. 327.
Nichols, E. L., The Photo-Luminescence

and Katho-Luminescence of Calcite,

485.
Nitrogen, Mobility of Ions in Air, Hydrogen

and, Kia-Lok Yen, 248.

Opaque Crystals. The Analysis of Polarized
Light from Small, LeRoy D, Weld,
249.

Optical Method, The Determination of
Organic Compounds by an, Thomas
E. Doubt and B. B. Freud, 249.

Optical Properties, The, of Rubidium,' J. B.
Nathanson, 227.

Optical Properties, The, of Rubidium, J. B,
Nathanson, 333.

Organic Compounds, The Determination
of, by an Organic Method, Thomas
E. Doubt and B, B. Freud, 249.

Page. Leigh, Is a Moving Mass Retarded by

the Reaction of its Own Radiation?,

376.
Peczalski, T.. Effect of Hydrogen on the

Electrical Resistivity of Carbon, 363,

508.
Phosphorescent Calcite, Note on a, E. L.

Nichols and H. L. Howes, 327.
Photoelectric Effects on Mercury Droplets,

John B, Derieux, 276.
PhotOi'lectrons, Some Preliminary Results

in a Determination of the Maximum

Emission Velocity of the, from Metals
at X-Ray Frequencies, Kang-Fuh Hu,
S05.

Photographic Plate. The Variation in the
Blackening of a. with Time of Ex-
posure. Total Energy Remaining
Constant, P. S. Helmick, 372,

Photo-Luminescence. The, and Katho-Lumi-
nescence of Calcite. E. L. Nichols,
H. L. Howes and D, T. Wilber, 485.

Photo-Plate. Images on Silvered, C. W.
Waggoner, 137.

Piche Evaporimeter, Comparative Accuracy
of Whirled Psychrometer, Assmann
Aspiration Psychrometer, Porous Cup
Atmometers. Hair Hygrographs. Open
Water Surface Evaporimeter. and
Dry and Wet Bulb Thermometers,
Alexander McAdie, 152.

Planck Radiation Law, The Necessary
Physical Assumptions Underlying a
Proof of the, F. Russell v. Bichowsky,
58.

Polarized Light. The Analysis of. Reflected
from Small Opaque Crystals, LeRoy
D. Weld, 249.

Porous Cup Atmometers, Comparative
Accuracy of Whirled Psychrometer,
Assmann Aspiration Psychrometer,
Hair Hygrographs, Piche Evapori-
meter, Saturation Deficit Recorder,
Open Water Surface Evaporimeter,
and Dry and Wet Bulb Thermometers,
Alexander McAdie, 152.

Precision Method. A, for Producing Artifi-
cial Daylight. Irwin G. Priest, 502.

Priest, Irwin G.. A Precision Method for
Producing Artificial Daylight, 502.

Priest, Irwin G., The Law of Symmetry of
the Visibility Function, 498.

Quantitative Study of Gases, A Method for
the, in Metals, H. M. Ryder, 486.

Quantum Theory, A General Theory of
Energy Partition with Applications
to. Richard C. Tolman, 261.

Radiation. The Visibility of, in the Blue End
of the Visible Spectrum, L. W. Hart-
man, 327.

Rain Drops, On the Formation of Negatively
Electrified, Fernando Sanford, 445.

Ray Analysis, A New Method of Positive,
A, J. Dempster, 316.

Raymond, William J., An Harmonic Syn-
thesizer having Components of In-
commensurable Period and any De-
sired Decrement, 479.

Rectification of Alternating Current by the
Corona, J. W, Davis, 243.

Relativity, Theory of. On the Second Pos-
tulate of the. An Experimental
Demonstration of the Constancy of

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5>4

INDEX TO VOLUME XI.

Sbrbs.

the Velocity of Light Reflected by a
Moving Mirror, Q. Majorana, 411.

Residual Rays. On the, of Rock Salt, Herbert
P. HoUnagel 135.

Resonance Radiation of Sodium Vapor Ex-
cited by One of the D Lines. R. W.
Wood and Fred L. Mohler, 70.

Resonance, The, and Ionization Potentials
for Electrons in Thallium Vapor,
Paul D. FooU and Fred L. Mohler,
486.

Retina. The Brightness Sensibility of the,
Julian Blauchard, 81.

Rock Salt. On the Residual Rays of. Herbert
P, HoUnagel, 135.

Rog^ey, Oswald, The Nature of the Ulti-
mate Magnetic Particle, 13a.

Rotation of the Pulley in Melde's Experi-
ment, Arthur Taber Jones, 150.

Rubidium. The Optical Properties of, J. B.
Natkanson, 333.

Rubidium. The Optical Properties of, J. B.
Nathanson, 227.

Ryder, H. M., A Method for the Quantita-
tive Study of Gases in Metals. 486.

Sanford, Fernando. On the Formation of
Negatively Electrified Rain Drops,
445.

Saturation, An Instrument for Continuously
Recording the Percentage of, and the
Weight of the Water Vapor per Unit
Volume in the Free Air. Alexander
McAdie, 148.

Second Postulate, On the, of the Theory of
Relativity: An Experimental Demon-
stration of the Constancy of the Ve-
locity of Light Reflected by a Moving
Mirror, O. Majorana, 411.

Sensibility, The Brightness, of the Retina,
Julian Blanchard, 81.

Sherwood, R. G., The Production and
Measurement of High Vacua, 134.

Sherwood, R. G., Vacuum Gauges of the
Radiometer Type. 241.

Shimizu. Takeo. The Relation between the
General X-Radiation and the Atomic
Number of the Target. 491.

Shrader. J. E., The Production and Measure-
ment of High Vacua. 134.

Sodium Vapor, Resonance Radiation of,
Excited by One of the D Lines, R.
W. Wood and Fred L. Mohler. 70.

Specific Heat, A New Formula for the Tem-
perature Variation of the, of Hydro-
gen, Edwin C. Kemble, 156.

Spectra. On Certain Absorption Bands in
the. of the Uranyl Salts, H. L. Howes,
66.

Spectral Photoelectric Sensibility of Molyb-
denite, The. W. W. CobUntz, M. B,
Long and H. Kahler, 497.

Stewart. John Q., The Moment of Momen-
tum Accompanying Magnetic Mo-
ment in Iron and Nickel. 100.

Stress, On Equilibrium under Non-Hydro-
static. P. W. Bridgman, 180.

Structure, The Mathematical, of Band
Series II.. Raymond T. Birge, 136.

Surface Evaporimeter. Comparative Ac-
curacy of Whirled Psychrometer,
Assmann Aspiration Psychrometer.
Porous Cup Atmometers. Hair Hy-
grographs. Piche Evaporimeter Satur-
ation Deficit Recorder. Open Water,
and Dry and Wet Bulb Thermometers,
Alexander McAdie, 152.

Temperature, The Influence of, Upon the
Crushing Strength of a Dental Amal-
gam. Arthur W. Gray and Paris T,
Carlisle, 4th, 154.

Temperature-Control. Methods of. in Glass-
Melting Furances. Clarence N. Fen-
ner, 141.

Thallium Vapor, The Resonance and Ioniza-
tion Potentials for Electrons in, Paul

D. FooU and Fred L. Mohler, 486.
Thermal Conductivity, Theory of, in Metals,

Edwin H. Hall, 329.
Thermo-couples for Student Use in Calori-

metfic Work, Ralph S. Mincer, 479.
Thermodynamics, On the, of Fluorescence.

E, H. Kennard, 29.
Thermometers, Comparative Accuracy of

Whirled Psychrometer, Assmann As-
piration Psychrometer, Porous Cup
Atmometers, Hair Hygrographs, Piche
Evaporimeter Saturation Deficit Re-
corder, Open Water Surface Evaporim-
eter, and Dry and Wet Bulb, Alex-
ander McAdie, 152.

Tolman, Richard C. A General Theory of
Energy Partition with Applications
to Quantum Theory, 261.

Transparency of Certain Carbon Com-
pounds to Waves of Great Length,
H. P. HoUnagel, 505.

TriboUum Confusum. Increase in Length of
Life of. Wheeler P. Davey, 493.

Trowbridge, C. C, Photograph of an Aurora
Model, 482.

Trowbridge, C. C, On the Observation of the
Apparent Focus of Auroral Streamers,
483.

Trowbridge, C. C, Meteor Train Spectra
and Probable Erroneous Conclusions
of the Observers, 484.

Tungsten. Young's Modulus of Drawn, and
its Variation with Change of Tem-
perature, including a Determination
of the Coeflicient of Expansion, H, L,
Dodge, 311.

Tungsten X-Ray Spectrum, Wave-Lengths
of the, Elmer Dershem, 461.

Uhler, Horace Scudder, The Geometry of Im-
age Formation in X-Ray Analysis, i.

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Vol XI.1
No. 6. J

INDEX TO VOLUME XI,

515

Ulrey. Clayton T., An Experimental Inves-
tigation of the Energy in the Con-
tinuous X-Ray Spectra of Certain
Elements. 401.

Uranium Nitrate; A New Hydrate of.
Uranium Nitrate Icositetrahydrate,
Frank E. E. Gennann, 245.

Uranium Nitrate Icositetrahydrate, A New
Hydrate of Uranium Nitrate, Frank
E. E. Germann, 245.

Uranyl, On the Unpolarized Fluorescence
and Absorption of Four Double
Chlorides of, Edward L. Nichols and
H. L. Howes, 285.

Uranyl Salts, On Certain Absorption Bands
in the Spectra of the, H. L. Howes, 66.

Uranyl Salts, A Study of the Fluorescence
of Certain, at Room Temperature.
Frances G. Wick, 100.

Uranyl Salts. On Certain Absorption Bands
in the Spectra of the, H. L, Howes,
143.

Uranyl Salts, A Preliminary Study of the
Luminescence of the. under Cathode
Ray Excitation. Frances G. Wick and
Louise S. McDowell, 421.

Van Orstrand. C. E., Report on the Construc-
tion of Certain Mathematical Tables,
332.

Vacuum Gages of the Radiometer Type,
R. C. Sherwood, 241.

Velocity, Variation of, of Waves, due to
Motion of the Source. Dinsmore Alter,
481.

Visible Spectrum, The Visibility of Radiation
in the Blue End of the, L. W, Hartman,
327.

Visibility Function, The Law of Symmetry
of the, Irwin G, Priest, 498.

Voss, Vivian, The Ratio of the Intensities of
the D Lines of Sodium, 21.

Waggoner, C. W., Images on Silvered Photo-
Plate, 137.

Water Vapor, An Instrument for Con-
tinuously Recording the Percentage
of Saturation and the Weight of the.
per Unit Volume in the Free Air,
Alexander McAdie, 148.

Watson, F. R., A Megaphone with a Rec-
tangular Aperture, 244.

Weld, Leroy D., The Analysis of Polarized
Light Reflected from Small Opaque
Crystals, 249.

Whirled Psychrometer, Comftarative Ac-
curacy of, Assmann Aspiration Psy-
chrometer, Porous Cup Atmometers,
Hair Hygrographs, Piche Evaporim-
eter Saturation Deficit Recorder,
Open Water Surface Evapori meter,

and Dry and Wet Bulb Thermometers,

Alexander McAdie, 152.
Wick, Frances G.. A Study of the Fluores-
cence of Certain Uranyl Salts at

Room Temperature, 100.
Wick, Frances G., A Preliminary Study of

the Luminescence of the Uranyl Salts

under Cathode Ray Excitation, 421.
Wilber, D. T., The Photo-Luminescence and

Katho-Luminescence of Calcite, 485.
Wood, R. W., Resonance Radiation of

Sodium Vapor Excited by One of the

D Lines, 70.
Wright, Winthrop R., The Magnetization

of Iron in the Absence of Hysteresis,

161.

X-Ray Concentrator, A Mono- Wave-Length,
Elmer Dershem, 244.

X-Ray Emission, Characteristic, as a Func-
tion of the Applied Voltage, Bergen
Davis, 433.

X-Ray Frequencies, On the Critical Absorp-
tion and Characteristic Emission.
William Duane and Kang-Fuh Hu,
489.

X-Ray Frequencies, Some Preliminary Re-
sults in a Determination of the
Maximum Emission Velocity of the
Photoelectrons from Metals at, Kang-
Fuh Hu, 505.

X-Radiation, The Relation between the
General, and the Atomic Number of
the Target, William Duane and
Takeo Shimizu, 491.

X-Ray Spectra, An Experimental Investi-
gation of the Energy in the Con-
tinuous, of Certain Elements, Clayton
r. Ulrey, 401.

X-Ray Spectrum, Wave-Lengths of the
Tungsten, Elmer Dershem, 244.

X-Ray Spectrum, Note on the Grating
Space of Calcite and the. of Gallium,
Arthur H. Compion, 430.

X-Ray Spectrum, Wave-Lengths of the
Tungsten, Elmer Dershem, 461.

Yen, Kia-Lok, Mobility of Ions in Air,
Hydrogen, and Nitrogen, 248.

Yen, Kia-Lok, The Mobilities of Gaseous
Ions, 337.

Young's Modulus of Drawn Tungsten and
its Variation with Change of Tem-
perature, including a Determination
of the Coefficient of Expansion, H. L,
Dodge, 311.

Zeeman's Effect, Bohr's Atom, and the
Magnetic Properties of the Elements,
Jakob Kunz, 153.

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