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1 



I 



THE 



PHYSICAL REVIEW 



A Journal of Experimental and 
Theoretical Physics 



CONDUCTED BY 

EDWARD L. NICHOLS, ERNEST MERRITT 
AND FREDERICK BEDELL 



Vol. Ill 



RUBLISHED FOR CORNELL UNIVERSITY 
MACMILLAN AND COMPANY 

NEW YORK LONDON 
BERLIN: MAYER AND MUELLER 

1896 






* • 






• ♦, • • ••• « • , 

• • * * • m 0* 



• ••• ••* • • ••• •• 



THE Nl 



■ ."•!K 



1231 02 

ASTviR, LFNdX ANO 
TILDLN f-OUNOAriONS. 

R 1b99 L 



Copyright, 1895 and 1896, 
By MACMILLAN AND CO. 



J. 8. Cothing It Co. - Berwick k Smith 
Norwood Mmi. US. A. 



• • ••• 

• • • 
•• • •• 



• • • 



• ••»••;•/ • 



CONTENTS OF VOLUME III. 

XIII. JULY-AUGUST, 1895. 

PACB 

ThMmAl CondoctiTity of Copper, n. R, W, Quick, C, D, Child, and B, S, Lanpkear i 

On Ternary Mixtures. I. Wilder D, Bancrofi 21 

On tlie Secnlar Motion of a Free Magnetic Needle, n. L, A, Bauer . . '34 

A GalTanometer for Photographing Alternating Current Cnnres. H, J, Hotchkiss and 

P,E,MiUis 49 

Minor Contribotiont : (i) Experiments with a New Polarizing Photo-chronograph as 
applied to the Measurement of the Velocity of Projectiles, A, C, Crehore and 
G. O. Squitr; (a) Experimental Demonstration of a Law of Fluid Pressure, 

W, J, Humphreys 63 

Vtw Books : Hertz : Die Principien der Mechanik. S, P, Thompson : Elementary Les- 
sons in Electricity and Magnetism. Yeo: Steam and the Marine Steam Engine . 73 



XIV. SEPTEMBER-OCTOBER, 1895. 

A Study of the Holarixation of the Light emitted by Incandescent Solid and Liquid 
Surfaces. R. A, Millikan 81 

Alternating Currents when the ElectzomotiTe Force is of a Zigsag WaTo Tjrpe. 

E. C. Rimmington 100 

On Ternary Mixtures. U. W, D. Bancroft 114 

Minor Contributions: (i) On a Simple Method of Photographically Registering the 
Infra-red Energy Spectrum, A>««/ /4«^j/r<J/«/ (2) On the Electrolytic Conductivity 
of Concentrated Sulphuric Acid, Dr, K. E, Guthe and L, J. Briggs .... 137 

Hew Books : Helm : Grundziige der Mathematischen Chemie. Ostwald's Klassiker 
der Exacten Wissenschaften. Mach: Popular Science Lectures. Proceedings 
of the Electrical Society of Cornell University. Naber : Standard Methods in 
Physics and Electricity Criticised 152 



XV. NOVEMBER-DECEMBER, 1895. 

Variation in Electrif ConductiTity of Metallic Wires in Different Dielectrics. Fer- 
nando San/ord 161 

A Study of the Polarisation of the Light emitted by Incandescent Solid and Liquid 

Surfaces, n. R, A. Millikan 177 

On Ternary Mixtures, m. W. D, Bancroft 193 

On the Changes in Length produced in Iron Wires by Magnetization. L, T. More . 210 
Hotes : Eli W. Blake ; The American Association for the Advancement of Science . 226 
Minor Contributions: (i) The Limits of Pitch for the Human Voice, W, LeConte 

Stevens ; (2) The New Physics Laboratory at Lille, E, L, Nichols .... 230 

Hew Books : Hertt : EUectric Waves. Glazebrook : Mechanics 234 

iii 



iv CONTENTS. 

XVI. JANUARY-FEBRUARY, 1896. 

PAGE 

On the Photometry of Differently Colored Lights and the "Flicker" Photometer. 

Frank P, Whitman 241 

The Chemical Potential of the Metals. Wilder D, Bancroft 250 

On the Freexing-points of Dilute Aqueous Solutions. E, H, Loomis .... 370 
Minor Contributions : (i) Some Questions in Regard to the Author's Method of Meas- 
uring Freezing-points of Dilute Solutions. E. H. Loomis; (2) A Comparison of Two 
Concave Rowland Gratings, Alice H. Bruire; (3) A New Apparatus for the Study 
of Color Phenomena, Ernest A*, von Nardroff; (4) On a New Form of Water Bat- 
tery, L. W. Austin and C. B, Thwing 293 

New Books: Daniell: Principles of Physics. Whetkam: Solution and Electrolysis. 
.S. P, Thompson: Polyphase Motors. Palax: Industrial Photometry. Walter: 
Oberflachenfarbcn. Gierke : The Herschels and Modem Astronomy . -3" 



XVII. MARCH-APRIL, 1896. 

On the Viscosity of Certain Salt Solutions. B,E, Moore 321 

Notes on the Theory of Oscillating Currents. Charles Proteus Steinmetx ... 335 
An Experimental Study of Induction Phenomena in Alternating Current Circuits. 

F,E,Millis 351 

Demagnetization Factors for Cylindrical Rods. C Riborg Mann 359 

A Photographic Study of Arc Spectra. I. Caroline Willard Baldwin .... 370 
Minor Contributions: (i) The Surface Tension of Liquids, Arthur L, Foley ; (2) The 

Resistance of Tin-foil as changed by Electric Waves, C D, Child . . . .381 
Hew Books : Lamb: Hydrodynamics ; J, J, Thomson : EUements of the Mathematical 
Theory of Electricity and Magnetism ; Story-Maskelyne : Crystallography, a Treat- 
ise on the Morphology of Crystals ; Nipher : Electricity and Magnetism ; Stanley : 
Notes on the Nebular Theory; Glazebrook: Mechanics and Hydrostatics; Men- 
schutkin : Analytical Chemistry ; Stevens : Ellementary Mensuration ; Nichols and 
Franklin : Elements of Physics, I 390 



XVIII. MAY-JUNE, 1896. 

Solids and Vapors. Wilder D, Bancroft 401 

On the Heat Effect of Mixing Liquids. C. E. Unebarger 418 

The Influence of Heat, of the Electric Current, and of Magnetization upon Young's 

Modulus. Mary Chilton Noyes 432 

A Photographic Study of Arc Spectra. U. Caroline W, Baldwin 448 

Minor Contributions: (i) A Method for the Use of Standard Candles, C //. Sharp; 
(2) The Graphical Representation of Magnetic Theories, //. A^ Allen ; (3) On the 

Alternating Current Dynamo, W. E. Goldsborough 458 

New Books : Roscoe and Harden : A New View of Dalton's Atomic Theory ; Loudott 
and McLennan : A Laboratory Course in Elxperimental Physics ; Ball : A Primer 
of the History of Mathematics ; Bedell and Cr chore : Etude Analytique et Graphique 
des Courants Altemati£s ; Theorie der WcchsclstrOme in Analytischer und Graphi- 
scher Darstellung; Holman : Computation Rules and Logarithms, with Tables of 
Other Useful Functions ; Hornby : A Text-book of Gas Manufacture . . . 483 



{ 



Volume III. July-August, i8g^. Number /. 



THE 

PHYSICAL REVIEW. 



THERMAL CONDUCTIVITY OF COPPER. 
By R. W. Quick, C D. Child, and B. S. Lanphear. 

Part II. 

CONDUCTIVITY AT LOW TEMPERATURES. 
By R, W, Quick and B, S, Lanphear, 

IN Part I. appeared an account of an investigation on conductivity 
of copper between the range of temperature 70** to I7o^ As 
was there stated, many investigations have been made rela- 
tive to the subject at ordinary and high temperatures, but, to the 
knowledge of the writers, no experiments had hitherto been made 
with the object of determining the absolute value of the thermal 
conductivity K and its dependence on temperature at tempera- 
tures below the freezing point. This fact induced the writers to 
extend their observations on the copper bar already described, 
to temperatures as low as— 60** C. 



The Measurement of Temperature, 

In dealing with low temperatures, the method employed for 
measuring the temperature of the bar has to be considerably modi- 



2 R. W. QUICK AND B. S, LANPHEAR. [Vol. III. 

fied ; for the Wheatstone slide wire bridge cannot, in this case, be 
calibrated directly for temperatures of the bar by means of a 
mercury thermometer, as was done in the first part of this investi- 
gation. Therefore, in addition to the requirement of a means of 
detection of small changes of resistance, the measurement of the 
low temperatures of the bar involves : (i) a knowledge of the tem- 
perature coefficient of resistance of the wire on the collar through 
the range o** to — 6o^ and (2) a knowledge of the temperature 
difference between the wire on the collar and the bar beneath it, 
if such difference exists. 

(fl) Determination of the temperature coefficient of the wire. 

Now if the curve of resistances and temperatures of the wire be 
a straight line, the determination of the coefficient a would involve 
only a measurement of resistance of the wire corresponding to two 
known temperatures. Dewar and Fleming,^ who investigated 
resistances of various metals from high temperatures to nearly 
— 200"* C, found that the curve of resistance and temperature of 
electrolytic copper wire was almost exactly a straight line, with a 
coefficient 0.00410. In consequence of this fact, together with the 
fact that experiments on the wire, conducted by the writers, at 
temperatures above the freezing point, seemed to give a fairly 
straight line, it was decided to obtain the resistance of a portion 
of the wire at the temperatures of melting ice and melting 
mercury (the latter temperature being well established), to cal- 
culate a from these observations, and by observing the tempera- 
ture corresponding to a certain resistance of .the wire on the 
collar, draw a straight line at proper pitch through the point 
thus located, and to use this curve in reading temperatures 
corresponding to any resistance. The slide wire bridge was of 
course easily calibrated for resistances by aid of a standard Wheat- 
stone plug bridge. 

To obtain the temperature of the wire at the freezing point of 
mercury, the following arrangement was used, which proved in 
every way successful : Referring to Fig. 6, / is a tube about i cm. 
long and 7 mm. in diameter, open at one end, and constructed 
from very thin sheet copper. On the outside of this cylindrical 

^ London Electrician, v. 29. 




No. I.] THERMAL CONDUCTIVITY OF COPPER. 3 

tube, and separated from it only by tissue paper to secure good 

insulation, a portion of the fine insulated copper wire was wound 

in a single layer, having its terminals joined to very heavy wires 

which passed through holes in the 

cork of a glass tube /' about 5 cm. 

long and 2 cm. in diameter, into 

which the small copper tube / was 

placed, as shown in the figure. The 

glass tube was then enclosed in a 

glass bottle 7", with an air space of 

about I cm. between the two. In the copper tube was placed a 

small globule of pure mercury. 

Since both the mercury and the wire were in close contact with 
the same good thermal conductor, and since no sudden change 
could afifect the copper tube by virtue of the double air space, the 
wire was very nearly at the temperature of the mercury. The 
precise moment of solidification of the mercury was told by the 
cessation, under slight jars, of the gliding motion peculiar to 
the globule so long as a surface film existed. Likewise, in pass- 
ing from the solid into the liquid, at the moment a surface film 
was formed, the globule which in its solid state remained motion- 
less when subjected to slight jars, would glide off on the bottom 
of the tube. In order to prevent the formation of white frost on 
the inside of the glass, which would obscure the observations, 
perfectly dry air was passed for a considerable length of time into 
the tubes, after which the bottle was sealed with paraffin around 
the cork. The terminals a and b were joined to the slide-wire 
bridge, and the bottle was cooled by surrounding it with a cotton 
jacket containing carbon dioxide snow. A small aperture in the 
jacket directly above the top of the copper tube permitted obser- 
vations on the condition of the mercury globule. An artificial 
light could not be used, owing to low radiant efficiency and conse- 
quent emission of sufficient heat to affect the temperature of the 
wire. To eliminate any error that might have arisen by simply 
taking the resistance when the globule solidified, the latter was 
alternately frozen and melted many times in succession by simply 
pressing tightly or loosening the cotton jacket filled with COj 



R, W, QUICK AND B. S, LANPHEAR. 



[Vol. III. 



snow ; and, moreover, these changes were brought about so gradu- 
ally that the readings on the slide bridge corresponding respec- 
tively to the freezing and the melting of the mercury were brought 
within one division of each other, — where one division is equiva- 
lent to 0.2** C. 

To obtain the resistance near o^ the bottle T (Fig. 6) was sur- 
rounded by melting snow, and after the mercury of the thermom- 
eter wWch was inserted through the two corks, so that its bulb 
was inside tube /', came to a stationary point, resistance and 
temperature were recorded. The temperature of the copper tube 
did not fall quite to o^ on account of the heat conducted in by 
the leading-in wires. The temperature of freezing mercury was 
taken as — 38.6^ 

Table V. gives the data from which the coefficient a was 
computed. 

Table V. 



Temperature. 


Bridge reading. 


Resistance of wire. 


"38.6 
+ 1.5 


402.5 
667.6 
o = 0.004147 


7.142 
8.556 



The coefficient thus obtained lies between the determination 
by Dewar and Fleming, 0.00410, and that of Cailletet and Bouty, 
0.00423, both being over ranges of low temperatures. From the 
above value of a, and from the fact that the resistance of the coil 
on the collar at a temperature of 19.5** was 9.461, we have 

^• = 8.753(1+0.004147/), 

which gives temperature in terms of resistance of the collar. 
(p) Dctermifiation of difference of temperature of collar and bar. 
It was found by experiment that at great temperature excesses 
of the bar over the air, the temperature of the wire of the collar 
was less than the temperature of the bar directly beneath the 
middle turn of the coil ; and as the latter temperature is that 



\ 



\ 



No. I.] THERMAL CONDUCTIVITY OF COPPER. 5 

which is required in both the statical and the absorption experi- 
ment, it was necessary to determine the correction to be applied 
to the temperatures obtained for the coil. This correction was 
arrived at under the following apparently justifiable assumption : 
If the collar be placed upon the bar, and the latter be heated to 
a certain temperature, giving a certain excess, the difference of 
temperature between the coil and the bar will be the same as 
when the bar is cooled to a temperature that gives the same 
excess (but of opposite sign). Three sets of observations were 
taken: First, when the end of the short bar containing a ther- 
mometer bulb was inserted through a board screen (viz. the end 
E of the box afterwards described, and shown in Fig. 7) and 
heated by an electric current to different stationary temperatures, 
with the collar placed upon the bar between the heated end and 
the thermometer ; second, when the thermometer was between 
the heated end and the collar ; and third, when the bar was heated 
to a uniform temperature by means of a solenoid conveying an 
electric current, and then allowed to cool, — in each case simul- 
taneous readings being taken on the slide bridge to which the 
collar was attached, on the thermometer whose bulb was inside 
the metal bar, and on the thermometer which registered the tem- 
perature of the surrounding medium. From the data thus ob- 
tained, two curves were plotted with abscissae as temperature 
excess of collar over air, and ordinates as temperature difference 
of bar and collar. The first curve was drawn from the first two 
sets of observations, and was used in correcting temperatures 
obtained from the resistance of the collar in the statical experi- 
ment ; the second curve was drawn from the last set of observa- 
tions, and gave the correction in case of the curve of absorption. 
Although the points located were quite irregularly disposed, they 
indicated the direction of the curve, and showed that the correc- 
tion is by no means inappreciable, being at a temperature excess 
of 8o^ between 4** and 5^ 



J- 



/ 



R, W. QUICK AND B. S, LANPHEAR. 



[Vol. III. 



11. 
Determination of Data for the Statical Curve, 

We now come to the determination of the final distribution of 
temperature along the bar when one end is maintained at the 
constant temperature of about — 70** C. When high temperatures 
are used, this experiment offers no special difficulties ; but as soon 
as the bar becomes very cold, frost will be deposited upon it, 
which not only vitiates the surface, but prevents the movement 
of the collar. The bar must therefore be placed in an air-tight 
box with everything so arranged that the dew-point of the air 
within it may be reduced to a very low temperature, that the 
collar may be moved along the bar without introducing air into 
the box, and lastly, that a constant low temperature may be main- 
tained at one end of the bar. 

The box was constructed of dry wood with glass sides, and to 
insure imperviousness to moisture, the wood was painted on the 
inside with shellac and twice with asphalt varnish. The complete 
box is shown in Fig. 7. The front and back sides are each formed 



N Ij^ ^. ^.:- " ^-^ 




Fig. 7. 

of three panes of glass. P and /" are two movable glass plates 
that were sealed during the experiment. B is the copper bar, one 
of whose ends projects about i cm. through the wooden end E of 
the box, while the other end rests on the wooden support 5. 
rand r' are two iron rods about 8 mm. in diameter, which pass 
through the end E of the box on a level with the bar, and which 
admit of longitudinal movement in the grooves of two wooden 



No. I.] THERMAL CONDUCTIVITY OF COPPER. 7 

supports, m and n. The inside ends of these rods are so bent 
that a small torsional force applied at their protruding extremities 
will bring these ends in contact with the projections c or c^ (Fig. i, 
Part I.) of the collar. A longitudinal movement of the rods will 
then move the collar to any desired division on the bar, without 
the introduction of air, inasmuch as they pass through tightly 
fitting rubber tubes at d and / The terminals of the collar were 
joined to a cable, and the latter was brought out of the box at q, 
A copper test tube T, extending into the box about 5 cm., pro- 
vided means of testing the dew-point of the air within by showing 
whether frost was deposited on its surface when it was filled with 
a cooling mixture of COg snow and ether. / and /' are thermom- 
eters used to determine the temperature of the air in the box. 
For about 24 hours immediately preceding the time of observa- 
tions, air which had previously traversed a series of Y-shaped tubes 
filled with pumice-stone saturated with concentrated HjSO^, was 
forced into the box through A, and after diffusing itself through 
the air in the box, found its exit at //'. In this way the dew-point 
was sufficiently reduced to prevent deposition of frost on the tube 
7" when filled with COj snow and ether. 

The end of the bar that extended through the wooden box was 
neatly soldered into the side of a copper box which had a capacity 
of about a liter. Fig. 8 is a horizontal cross- 
section of the cooled end of the bar and its 
surroundings. Around the copper box By into 
which the cooling mixture was placed, were three 
wooden boxes d, b\ b^\ having only one common 
side, and separated from each other by the three 
air spaces a^ a\ a!\ loosely filled with cotton to F»8r- 8- 

prevent convection currents. These boxes were provided with 
small slide covers for the purpose of renewing the liquid in the 
copper receptacle. 

When the test for the dew-point showed that the air was suf- 
ficiently dry to begin cooling the bar, the box at the end of the 
bar was filled with ether, and COj snow added until the liquid 
became saturated with the snow. The temperature of this mixture, 
according to Cailletet and Colardeau, is —75°; but since its exact 




8 



R. W. QUICK AND B. S. LANPHEAR. 



[Vol. III. 



temperature was not required in the experiment, no determination 
of it was made. According to the authority above quoted, this 
mixture of a saturated solution of carbon dioxide snow in ether 
undergoes scarcely any changes of temperature. The dioxide was 
obtained in this solid state by drawing off the liquid kept in iron 
cylinders under high pressure. About two quarts of snow were 
drawn off at each time, and this was maintained ready for use 
with small loss from evaporation, in a box surrounded with other 
boxes, much in the manner as the liquid at the end of the bar was 
guarded from heat. 

To test the constancy of the temperature at the end of the bar, 
two devices were employed. A therm o-j unction was placed in the 

Table VI. 

DATA FOR CURVE OF HNAL DISTRIBUTION OF TEMPERATURE ALONG 
THE BAR WHEN ONE END IS MAINTAINED AT A CONSTANT LOW 
TEMPERATURE. 



Dist. in 
cm. from 
cold end. 


Temp, of 
airia 
box. 


Bridge 
readings. 


Resist- 
ance from 
curve. 


Resist- 
ance of 
collar. 


Temp. 

of 
collar 


Excess 

collar 

over air. 


Excess 

bar over 

collar. 


Excess 

bar over 

air. 





14.7 


378.6 


7.550 


6.900 


-5L1 


-65.7 


-3.3 


-69.0 


5 


14.6 


417.5 


7.751 


7.900 


-45.6 


-60.2 


-2.8 


-63.0 


10 


14.8 


453.4 


7.936 


7.286 


-40.4 


-55.2 


-2.4 


-57.6 


15 


14.9 


477.6 


8.061 


7.411 


-37.0 


-51.9 


-2.0 


-53.9 


20 


15.0 


498.2 


8.167 


7.117 


-34.1 


-49.1 


-1.9 


-51.0 


25 


15.1 


518.4 


8.272 


7.662 


-31.2 


-46.3 


-1.7 


-48.0 


30 


15.2 


543.0 


8.400 


7.750 


-27.6 


-42.9 


-1.4 


-44.3 


35 


15.4 


555.1 


8.466 


7.816 


-25.8 


-41.2 


-1.3 


-42.5 


40 


15.6 


570.8 


8.556 


7.906 


-23.3 


-38.9 


-1.2 


-40.1 


45 


15.7 


582.7 


8.627 


7.977 


-21.4 


-37.1 


-1.0 


-38.1 


50 


15.8 


594.7 


8.701 


8.051 


-19.3 


-35.1 


-0.9 


-36.0 


55 


15.9 


6(H.l 


8.753 


8.103 


-17.9 


-33.8 


-0.9 


-34.7 


60 


15.9 


611.7 


8.793 


8.143 


-16.8 


-32.7 


-0.8 


-33.5 


65 


15.9 


620.5 


8.833 


8183 


-15.7 


-31.6 


-0.8 


-32.4 


70 


15.7 


627.7 


8.S66 


8.216 


-14.8 


-30.5 


-0.7 


-3L2 


75 


15.7 


632.3 


8.8S8 


8.238 


-14.2 


-29.9 


-0.7 


-30.6 


80 


15.6 


637.6 


8.915 


8.265 


-13.4 


-29.0 


-0.6 


-29.6 


85 


15.9 


643.7 


8.948 


8.298 


-12.5 


-28.4 


-0.6 


-29.0 


90 


15.2 


639.8 


8.928 


8.278 


-13.1 


-28.3 


-0.6 


-28.9 


95 


H.9 


643.3 


8.947 


8.297 


-12.6 


-27.5 


-0.6 


-28.1 


100 


153 


646.0 


8.962 


8.312 


-12.2 


-27.5 


-0.6 


-28.1 



No. I.] 



THERMAL CONDUCTIVITY OF COPPER, 



cooling mixture very close to the end of- the bar, and the terminals 
joined through keys to the slide bridge galvanometer. Also, just 
inside the end E of the wooden box, a few turns of the 0.002 in. 
insulated wire were wound directly on the bar, and its terminals 
joined to a Wheatstone plug bridge. 

About three hours after the cooling mixture was placed in the 
receptacle B (Fig. 8), the bar came to a statical temperature con- 
dition, as was indicated by the slide bridge to which the collar was 
connected. By frequent observations of the thermo-element, and 
of the resistance of the fine wire directly on the bar, it was ascer- 



5 10 15 20 25 30 35 40 45 50 56 60 65 70 75 80 85 90 95 100 


-10 
-20 


1 


1 


1 


DIST 


VNCES \Y 


C.M.FRC 


M COLD 


END 


1 


1 




CO 






















I 

Mi 
O 
X 
UJ 






















-30 
-40 






UJ 








^ 


^ 












UJ 




y 










































-wi 


/ 


r 








CUF 
TEP 


VEOFF 
UPERATl 


NAL OIS' 
BE ALO 


RIBUTIO 
4Q THE 


NOF 
BAR 




-70 

























Fig. 9. 



tained that the fluctuations of temperature at the end of the bar 
were not large enough to appreciably affect the distribution of 
temperature along the bar. In Table VI. are the observed and 
calculated data for the construction of the statical curve shown in 
Fig. 9. The second column is the average of the readings of the 
two thermometers that registered the temperature inside the box. 
Column 4 is obtained from the * calibration curve of the slide 
bridge. Column $, which is made up from the preceding column 



lO R. W. QUICK AND B. S. LANPHEAR. [Vol. III. 

by subtracting the resistance 0.65 of the line in the room, and not 
subjected to temperature changes, is converted into temperatures 
of column 6 by the formula already obtained, 

^1 = ^753 (i +0.004147 /). 

Subtracting (algebraically) the temperature of the air from num- 
bers in column 6, gives column 7, and adding to these the temper- 
ature difference of collar and bar as obtained by curve already 
described, gives the last column, which, together with the corre- 
sponding distances in centimeters of column i, gives the coordinates 
of the curve in Fig. 9. 

III. 

Cooling and Absorption Experiments, 

In investigations on conductivity, it seems to have been custo- 
mary to obtain the curve of cooling of a short bar of the same 
material and cross-section, and to use this curve in connection 
with the statical curVe of the long bar. In the present case, 
experiments of cooling on the two bars, whose lengths it will be 
remembered were respectively about 100 cm. and 20 cm., showed 
that their rates of cooling at the same temperature excess were 
noticeably different, the surface being as nearly the same as 
possible. And since it is probable that the emissivity is a function 
of the temperature, it was necessary to obtain the rates of heat 
absorption of the long bar at different negative excesses. Although 
the method devised for obtaining the requisite observations for the 
absorption curve of the short bar was applicable to the long one, it 
was not feasible on account of the limited supply of liquid COj at 
our disposal, and hence the rates of absorption of the long bar 
were obtained in an indirect manner. Now it must be nearly, if 
not rigorously, true that the ratio of the rates of cooling of the 
short and long bars at any positive excess is the same as the ratio 
of their rates of heat absorption at an equal negative excess, — 
other conditions being the same. Hence if at a certain excess, 
B and b are the tangents to the curve of cooling of the long and 



No. I.] 



THERMAL CONDUCTIVITY OF COPPER, 



II 



short bars respectively, and A and a are the respective tangents to 
the curves of absorption at an equal negative excess, we have 



^ = 



aB 



(2) 



which gives the rates of heat absorption of the long bar in terms 
of obtainable quantities. Observations must hence be taken for 
three curves, viz., absorption curve of short bar and the cooling 
curves of both bars. 

(a) Absorption curve of short bar. 

In order to obtain observations for this curve, the bar must be 
cooled in a perfectly dry atmosphere, to a uniform temperature as 
low as the lowest temperature observed in the statical experiment ; 
it must be removed from the cooling apparatus and placed in the 
dry atmosphere of the wooden box, so as to be under conditions 
similar to those of the long bar in the statical experiment ; and, 
moreover, this must be done with the collar on the bar, not only 
to afford a means of ascertaining its temperature condition before 
being removed from the cooling chamber, but to be ready to begin 
observations soon after thus removed. 

The above requirements were met in the following way : The 
collar was placed on the short bar and the latter placed in a 
specially constructed, 
tightly fitting, tin box, 
which is shown in Fig. 
10. This box, -ff', which 
contained the bar, was 
soldered into another 
tin box, By such that 
there was an air space 
of about 2 cm. sur- 
rounding the box B^ 
on five sides. In the 
figure a portion of the outside box is broken away, showing this 
air chamber, with which there was no communication except 
through the two glass tubes t and t\ each about \ inch in diam- 
eter, that extended through the end E of the wooden box of 




12 



/?. IV. QUICK AND B, S. LANPHEAR. 



[Vol. III. 



Fig. 7, from which the long bar had teen removed, a^ b are the 
terminals of the collar, and w^ w^ are wires passing through very 



Table VII. 

DATA FOR TIME CURVE OF ABSORPTION OF SHORT BAR. 



Time. 


Temp, 
of 
air. 


Bridge 
readings. 


Resist- 
ance from 
curve. 


Resist- 
ance of 
collar. 


Temp. 

of 
collar. 


Excess 

collar 

over air. 


Excess 
bar over 
collar. 


Excess 

bar over 

air. 


min. sec 

IS 


16.1 


371.6 


7.515 


6.865 


-52.0 


-68.1 


-4.0 


-72.1 


1 5 


16.1 


383.3 


7.574 


6.924 


-50.4 


-66.5 


-3.8 


-70.3 


2 24 


16.1 


400.9 


7.665 


7.015 


-47.9 


-64.0 


-3.5 


-67.5 


4 12 


16.0 


422.7 


7.778 


7.128 


-44.8 


-60.8 


-33 


-64.1 


5 16 


16.0 


435.7 


7.845 


7.195 


-42.9 


-58.9 


-3.1 


-62.0 


6 52 


16.0 


452.7 


7.933 


7.283 


-40.5 


-56.5 


-2.8 


-59.3 


8 30 


16.0 


470.2 


8.023 


7373 


-38.0 


-54.0 


-2.6 


-56.6 


9 55 


16.0 


484.8 


8.099 


7.449 


-35.9 


-51.9 


-2.4 


-54.3 


10 58 


15.9 


494.9 


8.150 


7.500 


-34.5 


-50.4 


-23 


-52.7 


12 47 


15.9 


512.0 


8.240 


7.590 


-32.0 


-47.9 


-2.1 


-50.0 


13 46 


15.9 


520.5 


8.284 


7.634 


-30.8 


-46.7 


-2.0 


-48.7 


14 59 


15.9 


530.4 


8.334 


7.684 


-29.5 


-45.4 


-1.8 


-47.2 


16 19 


15.9 


542.0 


8.3% 


7.746 


-27.8 


-43.7 


-1.7 


-45.4 


18 13 


15.9 


556.5 


8.474 


7.824 


-25.6 


-41.5 


-1.5 


-43.0 


21 2 


15.8 


576.0 


8.587 


7.937 


-22.5 


-38.3 


-1.4 


-39.7 


23 19 


15.8 


590.2 


8.675 


8.025 


-20.0 


-35.8 


-1.2 


-37.0 


25 33 


15.9 


603.1 


8.748 


8.098 


-18.0 


-33.9 


-1.1 


-35.0 


28 16 


15.9 


6173 


8.817 


8.167 


-16.1 


-32.0 


-1.0 


-33.0 


30 38 


15.9 


628.1 


8.867 


8.217 


-14.7 


-30.6 


- .9 


-31.5 


32 18 


15.9 


635.3 


8.903 


8.253 


-13.7 


-29.6 


- .9 


-30.5 


35 


15.9 


616.1 


8.963 


8313 


-12.1 


-28.0 


- .7 


-28.7 


37 13 


15.9 


654.7 


9.010 


8.360 


-10.8 


-26.7 


- .7 


^27.4 


39 8 


15.9 


661.4 


9.051 


8.401 


- 9.7 


-25.6 


- .7 


-263 


40 54 


15.9 


667.5 


9.088 


8.438 


- 8.7 


-24.6 


- .6 


-25.2 


42 34 


16.0 


673.2 


9.123 


8.473 


- 7.7 


-23.7 


- .5 


-24.2 



small holes in the top of the wooden box and fastened respectively 
to two loops of small wire that passed around each end of the bar. 



No. I.] 



THERMAL CONDUCTIVITY OF COPPER, 



13 



In order to cool the bar, a viscous mixture of CO^ snow and 
ether was poured into one of the glass tubes till the liquid began 
to rise in the tubes, which easily carried off the vapor arising from 




Rg. 11. 



14 



R, W. QUICK AND B, S. LANPHEAR. 



[Vol. III. 



the violent ebullition of the liquid. To maintain the liquid at a 
low temperature, carbon dioxide snow was constantly pushed 
down the glass tubes (alternately) by means of a closely fitting 



Table VIII. 

DATA FOR CURVES OF COOLING. 



Short \ims. 


Long bar. 


Time. 


Excess of bsf over 
air. 


Time. 


Excess of bar over 
• air. 


min. sec. 




min. sec. 




40 


73.2 


36 


74.2 


1 53 


70.7 


1 57 


71.7 


3 12 


68.2 


3 27 


69.4 


4 27 


65.7 


4 51 


67.2 


5 49 


63.3 


6 15 


65.0 


7 11 


60.9 


7 56 


62.7 


8 40 


58.3 


9 35 


60.4 


10 10 


55.9 


11 18 


58.3 


11 50 


53.5 


13 


56.1 


13 25 


51.2 


14 53 


54.0 


15 8 


48.9 


16 45 


51.9 


17 8 


46.8 


18 45 


49.8 


19 12 


44.5 


20 50 


47.7 


21 14 


42.2 


23 15 


45.7 


23 21 


40.0 


25 26 


43.7 


25 40 


37.6 


27 57 


41.8 


28 11 


35.3 


30 21 


39.9 


31 15 


33.1 


33 15 


38.1 


35 25 


29.6 


36 8 


36.0 


37 18 


28.6 


40 40 


33.1 


40 55 


26.6 


42 27 


32.3 


44 45 


24.3 


45 48 


30.4 






47 43 


29.3 






49 38 


28.5 






53 31 


26.8 






55 41 


25.8 






57 53 


24.8 



wooden piston. When the slide bridge to which the collar was 
attached showed that the temperature was sufficiently low and 
constant, the bar was lifted out of the receptacle by means of 
wires w^ w' (Fig. lo), and swung off out of the influence of the 



No. I.] THERMAL CONDUCTIVITY OF COPPER. 1 5 

cooling chamber by aid of the wire W which passed through 
each end of the large wooden box. Soon after, observations were 
begun. The air of the large wooden box had, of course, been 
previously thoroughly dried in the manner already described. 

In Table VII. are the data, both observed and calculated, for 
the absorption curve of short bar. As the columns are arranged 
in the same manner as in Table VI., no explanation is necessary. 
From the first and last columns of this table, curve ^, Fig. 11, 
was constructed. 

ip) Cooling curves of both bars. 

These observations were made according to the method which 
has already been described in IV, Part I., except that in this 
case each bar was allowed to cool within the wooden box, in order 
to preserve the conditions for radiation as nearly the same as 
possible as those for absorption. The bridge was calibrated 
directly for temperatures, as was described in Part I. The reason 
for calibrating the bridge for these observations directly for 
temperatures of the bar is twofold : first, in order to obtain read- 
ings on the slide bridge over the range of 20** to ic»°, the resist- 
ances r and t' (Fig. 2, Part I.) had to be changed, thus, in any 
case, necessitating a re-calibration of the bridge; second, the 
temperature coefficient of the coil on the collar might be slightly 
dififerent for high temperatures, and this difference would have 
to be determined. 

In Table VIII. are given the data for the curves of cooling of 
both bars, from which curves a and b (Fig. 1 1) were constructed. 
The diflference in the rates of cooling of the long and short bars is 
plainly evident, and also a slight difference in the direction of the 
curves of cooling and absorption of the short bar. 



IV. 

Deduction of Results. 

It now remains to construct the curve whose area, multiplied by 
the product of specific heat and density, is equal to the quantity of 
heat absorbed per second by the bar when one of its ends was main- 




i6 



R, IV. QUICK AND B, S, LANPHEAR. 



[Vol. III. 



tained at a low temperature. Table IX. contains the calculated 
data for this curve. Columns 2, 3, and 4 are the respective tan- 
gents to the cooling curve of short bar, absorption curve of short 
bar, and cooling curve of long bar. These were taken from the 



Table IX. 

DATA FOR CURVE OF RATES OF ABSORPTION CORRESPONDING TO 
DIFFERENT POINTS ALONG THE BAR WHEN UNDER THE CON- 
DITIONS OF THE STATICAL EXPERIMENT— INTEGRATION CURVE. 



Distance in cm. 
from cold end 


Tangent to curve 
of cooling of 

.hortbar.(-^.) 


Tangent to curve 
of fliDBorption of 

abort bar. (-^^.) 


Tangent to curve 
of cooling of 


Tangent to curve 

of absorption of 

long bar (cal- 

culated). (^-l) 





0.03355 


0.03500 


0.02721 


0.02840 


5 


0.02950 


0.03100 


0.02400 


0.02522 


10 


0.02773 


0.02872 


0.02166 


0.02240 


15 


0.02375 


0.02545 


0.01914 


0.02C50 


20 


0.02180 


0.02330 


0.01720 


0.01838 


25 


0.02010 


0.02240 


0.01548 


0.01724 


30 


0.01890 


0.02125 


0.01400 


0.01574 


35 


0.01810 


0.02030 


0.01300 


0.01460 


40 


0.01700 


0.01880 


0.01214 


0.01343 


45 


0.01594 


0.01695 


0.01146 


0.01220 


50 


0.01533 


0.01592 


0.01080 


0.01123 


55 


0.01421 


0.01392 


0.01030 


0.01010 


60 


0.01328 


0.01236 


0.01000 


0.00931 


65 


0.01267 


0.01160 


0.00944 


0.00865 


70 


0.01200 


0.01097 


0.00900 


0.00823 


75 


0.01160 


0.01067 


0.00853 


0.00785 


80 


0.01110 


0.01037 


0.00827 


0.00772 


85 


0.01076 


0.01033 


0.00796 


0.00764 


90 


0.01053 


0.01024 


0.00783 


0.00762 


95 


0.01046 


0.01010 


0.00780 


0.00753 


100 


0.01024 


0.00977 


0.00773 


0.00752 



curves of Fig. ii at temperature excesses of the bar, which were 
read from the statical curve of Fig. 9 at the different distances of 
column I. The numbers of the last column are tangents to the 
hypothetical absorption curve of long bar, and are obtained accord- 
ing to formula (2) ; />., by dividing the product of columns 3 and 



No. I.] 



THERMAL CONDUCTIVITY OF COPPER. 



17 



4 by column 2. From the first and last columns the curve in 
Fig. 12 was plotted, and its area was obtained by integration in 



.028 
.026 
.024 
.022 
.020 
.018 
.016 
.014 
.012 
.010 
























\ 






th«a 
toi 


rM b«twM 
knrtount of 


INTEG 

n any two 
hMt abtor 


RATION 

ordinatM 
bedbyth« 


CURVE. 

of which 
t portion < 


It propof 
a bar p«r 


tional 

MC. 




N 


N 




















- 


s 


N 
























H 


V 














z 
lli 

1- 








^^ 


'^ 












.008 


•t 






















.006 
.004 
.002 








.J 






DI8TAN 


:e in c.^ 

— 1 — 


I.FROM C 


OLCJ EN 


) OFjBAH 


1 


1 




1. .. 


1^ 



6 10 16 20 26 80 35 40 46 60 55 60 65 70 76 80 86 90 95 100 

Fig. 12. 

Table X. 

DERIVED DATA FOR THE CURVE OF CONDUCTIVITY (A'). 



Distance (x) in 

cm. from cooled 

end of bmr. 


area. 


Tangent to stati- 
cal curve. 
dv 
dx 


Temperature of 
copper. 


Conductivity, ' 


80 


0.1692 


0.125 


-13.6 


1.059 


65 


0.2917 


0.217 


-16.3 


1.050 


55 


03855 


0.289 


-19.0 


1.040 


45 


0.4952 


0372 


-22.4 


1.035 


40 


0.5575 


0.422 


-24.5 


1.025 


35 


0.6255 


0.475 


-26.9 


1.020 


30 


0.6999 


0.542 


-29.6 


0.999 


25 


0.7812 


0.605 


-32.6 


0.9% 


20 


0.8701 


0.690 


-36.0 


0.971 


15 


0.9676 


0.785 


-39.8 


0.946 


10 


1.0748 


0.873 


-44.0 


0.942 


5 


1.1939 


0.986 


-48.7 


0.923 





1.3273 


1.095 


-53.9 


0.921 



i8 



R. W. QUICK AND B. S, LAJSTPHEAR. 



[Vol. III. 



parts as is indicated in column 2 of Table X. In this column, to 
each number is added the area corresponding to the heat absorbed 
per second by the free end of the bar. This table is made up in 
the same way as the corresponding table of Part I. For the want 
of experimental data on the relation between specific heat and 
temperature over the range o° to —60°, the same formula was used 
here as in the case of high temperatures, viz. : — 

5, =.0892(1 -f 0.00073 t). 

Also the same variation in density was made use of, viz.: — 

A =8.862(1 -0.000056/).^ 

In Fig. 13 is the curve of conductivity plotted from the last two 
columns of Table X. and Table IV. (Part I.), and shows graphically 
the results of the complete investigation. 

1.20 
1.10 
1.00 

.90 
.80 
.70 
.60 
.50 
.40 
.30 
.20 
.10 



- 


a 


oo* 


1.10 

..1 Oft, 












h 






■-^ 


r^ 




0.90 






•WW 


■■ 


"^ ^ 


° 






- 
























- 






> 


















- 






3 

























l_„ 


« 




TEMP 


■RATUf 


tES 









Fig. 13. 



Discussion of Results, 

It is to be observed that the average value obtained for K over 
the range —54° to —13** is slightly higher than the average value 
over the range 74® to 166°, — being in the former case 0.994, and 
in the latter, 0.954. A curious fact is the much greater slope of 

1 Sec v., Part I. 



No. I.] THERMAL CONDUCTIVITY OF COPPER. 19 

the curve over low temperatures. From these results one of two 
inferences may be drawn : first, that a maximum value of K exists 
at a temperature near o**, since, if the curves a and b were joined, 
a point of inflexion must exist between —10° and +70°; second, 
that owing to some error, the values of AT in a are too great, or 
that the values of AT in ^ are too small, thus producing the irregu- 
larity in the curve. As regards the latter inference, the authors 
state that the observations were not only taken with the greatest 
of care, but were also reduced with the utmost precaution to 
eliminate error. Of course, if values of K were obtained for 
temperatures between —10** and +70% a more definite conclusion 
could be reached. The reason those points were not obtained, 
thus filling in between the curves a and b (Fig. 13), may be briefly 
stated thus : when the excess of the temperature of the bar over 
air, or air over bar, is 30** or less, the slope of the curve of final 
distribution of temperature along the bar is so small in the case 
of copper, that great inaccuracies arise in the calculation of the 
tangents. A method for overcoming this difficulty, but which 
would impose conditions hard to realize, is to place the bar in 
an atmosphere whose temperature is maintained constant at o®, 
and a temperature of about 80** kept at one end ; or to maintain 
a temperature of about — 15** at one end of the bar which is placed 
in an atmosphere kept constant near 80**. In either case a good 
gradient would be obtained. 

Over both ranges of temperature the results show an increase 
of K with increase of temperature. This is in accordance with 
the results of Tait, Lorenz, and Kirchoff and Hansemann, but is 
contrary to those of R. W. Stewart, who found a decrease of K 
in electrolytic copper, with increase of temperature over a range 
of high temperatures. His values of K were considerably greater 
than those hitherto obtained, a fact indicating that conductivity 
increases with the purity of the metal. Stewart's value of K at 
o*' obtained by extrapolation, coincides almost exactly with the K^ 
obtained from curve a. It is to be hoped that further investi- 
gation will be made on electrolytic copper at temperatures near o®, 
also at low temperatures, by using, perhaps, a cooling mixture 



20 R. W. QUICK AND B, 5. LANPHEAR, [Vol. III. 

whose boiling point is even lower than that of carbon dioxide 
snow and ether. 

The authors desire to acknowledge their obligations to Dr. E. 
L. Nichols, who not only suggested the line of work, but who 
made many valuable suggestions as to details throughout the 
investigation. 

Physical Laboratory of Cornell UNrvKRsiTY, 
December, 1894. 



No. I.] TKRNARY MIXTURES. 21 



ON TERNARY MIXTURES. 

FIRST PAPER.I 
By Wilder D. Bancroft. 

FOLLOWING out the analogy between dissolved substances 
and gases, Nernst deduces the law that, when two dissolved 
substances have no common ion and do not react chemically, the 
influence of each on the solubility of the other is zero, within 
certain undefined limits. He says:^ "Die Analogie zwischen der 
Auflosung und Sublimation bezw. Dissociation fester Stoflfe zeigt 
sich nun auch deutlich ausgesprochen, was den Einfluss fremden 
Zusatzes betriflft. Ebenso wenig wie die Sublimationsspannung 
bei Gegenwart fremder indiflferenter Case sich andert, wird die 
Loslichkeit eines festen Stoflfes durch Zusatz eines zweiten (in 
nicht zu grosser Menge) beeinflusst, wofem der hinzugefiigte 
fremde Stoff nicht chemisch auf jenen einwirkt ; und ebenso wie 
die Dissociationsspannung im hochsten Maasse durch Zusatz 
eines der gasformigen Zersetzungsproducte beeinflusst wird, so 
\'ariirt entsprechend auch die Loslichkeit derjenigen Stoflfe. bei 
welchen die Auflosung mit einem mehr oder weniger vollstandi- 
gen Zerfall verbunden ist, die also bei ihrer Auflosung mehrere 
Molekiilgattungen liefern, wenn eine dieser letzteren der Losung 
hinzugefiigt wird." There are several things in this statement 
which are open to criticism. If taken literally, the author implies 
a fundamental difference between solutions of liquids in liquids, 
and solids in liquids, a distinction which is not in accordance with 
the view that in dilute solutions the solute,' whether liquid or 
solid in the pure state, behaves like a gas at that temperature. 

1 A paper presented to the American Academy of Arts and Sciences, May 9, 1894. 

* Theor. Chemie, p. 383. 

• There seems to me a need for a word denoting the dissolved substance. In future 
I shall use the word " solute/* meai^ing the substance dissolved in the solvent. Instead 
of the phrase " infinitely miscible liquids,'* I propose " consolute '* liquids. 




22 DR, IV, D, BANCROFT. [Vol. III. 

If applied to any dissolved substance, the statement just quoted 
is too inaccurate to need any comment. The precipitation of salts 
by alcohol is a well known instance where it does not apply, and, 
in general, adding to a solution a substance in which the solute is 
practically insoluble diminishes the solubility of the latter. This 
is recognized by Nemst, for he has based a method for determin- 
ing reacting weights upon it.^ Even if limited to solids, the propo- 
sition cannot be admitted. We have the precipitation of lactones 
by potassium carbonate as an intermediate step, and the precipita- 
tion of salts by phenol as a definite case of diminished solubility 
without the presence of a common ion. Other cases could be 
cited, if necessary, and there are also examples where an increase 
of solubility takes place when a solid substance is added to a 
solution containing another solid as solute. The explanation 
usually offered under these circumstances is, that "double mole- 
cules " are formed, a mode of getting round the facts which is not 
always entirely satisfactory. 

Since in the application of the gas laws to solutions there has 
been observed no difference between a solid and a liquid when 
dissolved, I am inclined to think that the general statement should 
be, that in all cases where a third substance. By is added to a 
solution of A in 5, the solubility of A undergoes a change. This 
variation may be large or small, positive or negative, depending 
on the nature of the three substances, A^ B, and S. When both 
A and B are liquids, or even when only one of them is, the effect 
is so marked as to be familiar to all ; when both are solids, the 
effect is not yet recognized by so competent an authority as 
Nernst. 

The work of the last few years on solutions has been devoted to 
bringing out the analogy between the dissolved substance and 
gases. In the cases of changed solubility, no common ion being 
present, the analogy is no longer with gases, but with liquids. 
The added substance acts as a liquid, precipitating the solute more 
or less in proportion as the dissolved substance happens to be 
more or less soluble in it. The laws governing these displace- 
ments are entirely unknown, with the exception of Nernst*s Dis- 

1 Zcitschr. f. ph. Chem., VI. i6. 189a 



No. I.] TERNARY MIXTURES. 23 

tribution Law,^ which is only a first approximation, in that it takes 
no account of the changing mutual solubilities of the hypothetically 
non-miscible liquids. Under these circumstances it seemed to me 
desirable to investigate the laws governing systems composed of 
three substances, and the experiments which I communicate in 
this paper have been made on the simplest form of ternary mix- 
tures, — that where all three substances are liquids. The subject 
has been very little studied, the only researches known to me 
being by Tuchschmidt and Follenius,^ Berthelot and Jungfleisch,* 
Duclaux,* Nemst,* and Pfeiffer.® Of these, all except the first 
and last deal with the equilibrium between two liquid phases ; the 
paper of Tuchschmidt and Follenius contains but one series of 
measurements, while Pfeiflfer remarks, apropos of his own extended 
investigations, that " there is very little to be made out of them." 
In this he does himself an injustice, for, as I shall show, his results 
are very satisfactory and astonishingly accurate when one remem- 
bers how they were made. 

The simplest case of three-liquid systems is when one has two 
practically non-miscible liquids, and a third with which each of the 
others is miscible in all proportions ; for then any complication 
due to the mutual solubility of the two dissolved liquids is avoided. 
It is possible to say something a priori about the law which 
governs these saturated solutions. Let A and B be two non- 
miscible liquids, 5 the common solvent with which A and B are 
miscible in all proportions when taken singly, and let the quantity 
of 5 remain constant, so that we are considering the amounts of 
A and B, namely x and yy which will dissolve simultaneously in a 
fixed amount of 5. It is known, experimentally, that the presence 
of A decreases the solubility of B^ and vice versa ; it is required 
to find the law governing this change of solubility. This, being a 
case of equilibrium, must come under the general equation of 
equilibrium. 

<■> ^■^+^*-°. 

* Teilangssatz. * Ibid., [5.], p. 264. 1876. 

« B. B.. IV. 583. 1871. 6 Zeitschr. f. ph. Chem., VI. 16. 1890. 

» Ann. chira. phys., [4.], XXVI. 396. 1872. • Ibid., IX. 469. 1892. 




24 DR. W. D, BANCROFT. [Vol. III. 

where dx and dy denote the changes in the concentrations of A 
and By respectively. 

This equation, though absolutely accurate, is of no value prac- 
tically so long as the differential coefficients are unknown functions. 
In regard to them we may make two assumptions. The decrease 
in the solubility of A may be proportional to the amount of B 
added, and independent of the amounts of A and B already present 
in the solution. The differential equation expressing this is : — 

(2) adx+bdy=o, 

where a and b are proportionality factors and constants. This equa- 
tion may be rejected on a priori grounds, because it does not show 
that when B is absent, the miscibility of A with 5 is infinite, and 
also because it has no similarity with the other equations repre- 
senting chemical equilibrium. The second assumption is that the 
change in solubility may be a function of the amounts of A and B 
already present. This is the usual condition of chemical equilib- 
rium, and is known as the Mass Law. Its mathematical expres- 
sion is : — 

5^+^=0, or 

X y 

(3) <wflog;r+/8^/logj/=o, 

where x and y denote the amounts of A and 5 in a constant 
quantity of 5, « and fi are proportionality factors, and the loga- 
rithms are natural logarithms. 

If a and fi are constants, this equation is integrable, and gives, 
when cleared of logarithms : — 

(4) ;ry^ = Constant. 
If we make ^=s«, we shall have: — 

(s) ^y^c, 

where C is of course different in value from the constant in equa- 
tion (4). 

Before we proceed to test equation (5) experimentally, it remains 
to be seen in what unit x and y should be expressed. It is obvious 



No. I.] TERNARY MIXTURES, 2$ 

that the nature of the unit has no effect on the general form of 
the equation, nor upon the exponential factor «. The only change 
will be in the value of the integration constant log C, so that the 
measurements may be expressed in any form that is convenient, 
as chemical units,^ for example, grams per liter, volumes, reacting 
volumes, or anything else. It is not even necessary that x and y 
be expressed in the same unit, though it would probably always be 
more practical. In my own experiments, x and y are expressed in 
cubic centimeters because they were measured directly as such, 
and in this way it was not necessary to make determinations of 
the densities of the liquids used, nor any assumptions in regard to 
their reacting weights. Equation (5) will not remain unchanged 
if the reacting weight of -^ or -ff varies, that is, if the ratio of the 
active mass to the actual mass changes as ;r or j/ changes. The 
converse of this is also true, that if the system follows the law 
r*^ = C the common solvent remaining constant, the reacting 
weights of the substances A and B cannot have varied with the 
concentration. 

I have found that the equation, ;r*^= Constant, is the expression 
representing the saturated solutions of two non-miscible liquids in 
a constant quantity of a consolute liquid. I find, however, that 
in most cases the concentrations cannot be given by one curve, 
but involve two, so that for one set of concentrations I have the 
relation x^^y^C^y for the other set x'^y'=^C^, This cannot be true 
unless the two sets of saturated solutions correspond to different 
conditions. This is the case. Duclaux^ found that a saturated 
solution of amylalcohol and water in ethylalcohol became turbid 
on adding a drop either of amylalcohol or of water. In other words, 
the solution was sensitive to an excess of either liquid.^ I have 
confirmed this result, and it is perfectly general. It is not proper, 

* I have adopted the following nomenclature for molecular and atomic weights, viz. 
reacting and combining weights. As the reacting weight is proportional to the chemical 
unit experimentally, I propose that the gram molecule in the unit of volume (reacting 
weight in grams per liter) be called the chemical unit, or simply the unit. The object 
of these arbitrary changes in our chemical terms is to do away with everything involving 
or implying the assumption of the existence of molecules and atoms. 

« Ann. chim. phys, [5.], VII. 264. 1876. 

* Ostwald, Lehrbuch, I. 819. 




26 DR, W. D. BANCROFT. [Vol. III. 

however, to draw the conclusion that the solution is saturated in 
respect to both liquids. If to a given saturated solution of chloro- 
form, water, and alcohol, for instance, one adds a drop of water or 
of chloroform, the solution becomes turbid; but what separates 
out is the same in both cases. It is analogous to a saturated solu- 
tion of salt in a mixture of alcohol and water. It is indifferent 
whether one adds alcohol or salt to the solution. In either case, 
there is a precipitate ; but in both cases the precipitate is salt, and 
the solution is saturated in respect to salt, not in respect to alcohol. 
It is not so easy to see what takes place in a system composed of 
liquids because the precipitate, being itself a liquid, dissolves part 
of the solution, and the new phase is not composed. of pure sub- 
stance. This need not trouble us, for, theoretically at any rate, 
the precipitate may be treated as pure liquid, and the final equi- 
librium looked upon as due to a subsequent reaction. One of the 
two curves represents, then, the set of solutions which is saturated 
in respect to chloroform, and not in respect to water. Whether 
one adds water or chloroform to these solutions, the precipitate is 
chloroform. The other curve represents the mixtures which are 
saturated in respect to water, and not in respect to chloroform. 
Either water or chloroform, when added to these solutions, pro- 
duces a precipitate of water. These two sets of solutions are 
easily distinguishable qualitatively, because in the first case the 
new phase, containing a large percentage of chloroform, is denser 
than the mixture from which it separates, while in the second case 
the new phase, containing chiefly water, is lighter than the original 
solution. The point where the new phase changes from being 
denser to being lighter than the first phase is the point of inter- 
section of the two curves. At this point only is the nature of the 
precipitate determined by the nature of the infinitely small excess 
added. The intersecting point represents the concentration at 
which, were chloroform and water solids at that temperature, both 
could be in equilibrium with the solution and its saturated vapor. 
It corresponds to the concentration of a solution containing two 
salts with a common ion which is in equilibrium with the two solid 
salts, formation of a double salt being excluded. In one respect 
the analogy between a system having three liquid components and 



No. I.] TERNARY MIXTURES, 2 7 

one composed of two solids and a liquid does not hold. If to a 
saturated solution of silver bromate silver acetate is added, the 
precipitate is silver bromate, and, conversely, the precipitate is 
silver acetate if silver bromate be added to a saturated solution of 
silver acetate. The salt with the less concentration precipitates 
the one with the greater, up to a certain point. In a ch]ort)form- 
water-alcohol mixture in which chloroform is present in large quan- 
tities, the precipitate is water, or the substance with the greater 
precipitates the one with the lesser concentration. This differ- 
ence of behavior is due to the new phase being a solid in the one 
case and a liquid in the other. By a suitable choice of the three 
components, and by varying the temperature, the substance in 
respect to which the solution was saturated could be made to sepa- 
rate either as a liquid or a solid phase, and this difference could be 
made zero. The transition point would come when the equilibrium 
was between four phases, one solid, two liquid, and one gaseous. 

There is no apparent theoretical reason why the two curves 
should not be prolonged beyond their intersection ; but there is a 
very good practical one. Beyond the point of intersection the 
curves denote saturated but labile solutions, and a supersaturated 
system composed of liquids is almost impossible to realize. When 
I come to the study of ternary mixtures having one or more solid 
components, I hope to be able to follow one of the curves at least 
beyond the intersecting point ; but in the present work I have 
made no such attempt. 

I will now describe the method used in my work, and then take 
up the experimental data obtained. As pairs of non-miscible 
liquids, I have taken chloroform and water, benzol and water; 
and as consolute liquids, ethylalcohol, methylalcohol, and acetone. 
The next point was how to determine the composition of the 
saturated solutions. The methods of quantitative analysis are 
useless in this case ; but the problem is solved without difficulty 
by quantitative synthesis. Instead of making a saturated solution 
and analyzing it, I measured the quantities required to make a 
saturated solution at the required temperature. Definite amounts 
of the consolute liquids were put in test tubes by means of a 
carefully graduated pipette; varying quantities of one of the 



28 DR, IV, D. BANCROFT, [Vol. III. 

non-miscible liquids were run in from a burette, and the second 
non-miscible liquid added from another burette to saturation. 
The test tubes were corked, warmed just above the temperature 
at which the final readings were made, so that there should be 
a single homogeneous liquid layer, and placed in a constant 
temperature bath. If the tube clouds, it is beyond the saturation 
point ; if it remains clear, it is not up to it, the required value 
lying between the two. By making a series of experiments one 
can bring the limiting values very close together, and thus deter- 
mine the saturation point with great accuracy. The constant 
temperature bath was at 20** C. No correction was made for the 
amounts of the three liquids evaporating off into the vapor space 
in the upper part of the test tubes ; but by using different sized 
test tubes this space did not vary much, being about five cubic 
centimeters, so that the error due to this may be neglected. 

The chloroform used (Squibb*s) was treated with sodium bi- 
sulphite solution to free it from acetone, washed thoroughly with 
water, dried over calcium chloride and fractionated, twelve hundred 
grams going over within one quarter of a degree. Kahlbaum*s 
crystallized benzol was recrystallized twice and fractionated to 
constant boiling point. The ethylalcohol was dried over lime and 
copper sulphate and fractionated. The lot used distilled within 
half a degree. Part of the acetone (from Eimer and Amend) was 
converted into the bisulphite compound, back again, dried over 
potassium carbonate and calcium chloride, and fractionated. An- 
other portion was treated direct with calcium chloride and frac- 
tionated. I could detect no difference between the two lots. I 
tried to purify a sample of acetoiie from Cutler Brothers, purport- 
ing to be manufactured by Merck in Darmstadt ; but it was so bad 
that I used none of it in my experiments. The methylalcohol 
(from Kahlbaum) was dried over anhydrous copper sulphate and 
fractionated. 

The measurements in the tables are the mean of at least four 
determinations, and the error is probably not more than 5 per cent, 
except in the cases where the quantity of one component is less 
than 0.20 cc, when it may easily rise to 10 per cent. The values 
for n are accurate to within 2 per cent without much question. 



No. I.] 



TERNARY MIXTURES. 



29 



The values for log C are more untrustworthy, being much affected 
by a slight variation in «, while the term C is liable to even greater 
fluctuations, and is not given, as being too uncertain. Under the 
headings "Calc.** are the. values required by the formula to corre- 
spond with the experimental data for the other component. The 
figures in the column marked log C are Briggsian logarithms. As 
will be noticed, I have not always taken the mathematical mean 
of this column as the value of log Cin the formula. It seemed 
better to take the value which best satisfied the experimental data, 
and to ignore numbers which were obviously faulty. 



Table I. 

X c.c. HjO; y c.c. CHCls; 5 c.c. Alcohol. Temp. 20°. 
Formula y»>'=Ci; «i=1.90; log Ci= 1.190. 



Water. 


CHOI,. 




Calc. 


Found. 


Calc. 


Found. 


log Ci. 


9.94 


10.00 


0.195 


0.20- 


1.195 


8.99 


9.00 


0.24 


0.24 


1.192 


7.98 


8.00 


0.30 


0.30 


1.193 


7.14 


7.00 


0.385 


0.37 


1.174 


6.00 


6.00 


0.515 


0.515 


1.190 


5.97 


5.00 


0.73 


0.73 


1.191 


3.97 


4.00 


1.12 


1.13 


1.197 



Average, 



1.190 





Formula jcy«= 


= Ca; «a = l.lll; 


log Cs=0.742. 












log C,. 


3.00 


3.00 


1.73 


1.73 


0.741 


1.99 


. 2.00 


2.49 


2.51 


0.745 


1.01 


1.00 


4.66 


4.60 


0.737 


0.92 


0.91 


5.07 


5.00 


0.736 


0.755 


0.76 


5.96 


6.00 


0.745 


0.635 


0.63 


7.06 


7.00 


0.738 


0-55 


0.55 


8.00 


8.00 


0.743 


0.48 


0.49 


8.86 


9.00 


0.750 


0.43- 


0.425 


10.06 


10.00 


0.739 


0.20 


0.20- 


20.00 


20.00 


0.742 


0.127 


0.125 


30.24 


30.00 


0.738 



Average, 



0.741 



30 



DR. W, D, BANCROFT. 



[Vol. III. 



Table II. 

X c.c. Water; y c.c. CHCls; 5 c.c. Methyl Alcohol. Temp. 2(P. 
Formula x*»>'=Ci; «i=2.30; log Ci = 1.291. 



Water. 


CHCl,. 




Calc. 


Found. 


Calc. 


Found. 


log C,. 


9.91 
5.01 
4.03 
1.99 


10.00 
5.00 
4.00 
2.00 


0.10 
0.48 
0.81 
3.97 


0.10 
0.48 
0.80 
4.00 


1.300 
1.288 
1.283 
1.294 



Average, 



1.291 



Formula jr'^>'=C2; n%-\2S\ log Ca= 1.061. 



1.49 
134 
1.12 



1.49 
1.35 
1.12 
Average, 



7.00 

7.93 

10.00 



7.00 

8.00 

10.00 



_logC^ 

1.061 
1.065 
r061 
1.062 



Table III. 

X c.c. Water; y c.c. Chloroform; 5 c.c. Acetone. Temp. 20°. 
Formula x*»>'=Ci; «i = 1.415; log Ci= 0.194. 



Water. 


Chloroform. 




Calc. 


Pound. 


Calc. 


Found. 


logC. 


5.01 


5.00 


0.16 


0.16 


0.193 


4.00 


4.00 


0.22 


0.22 


0.194 


3.47 


3.50 


0.266 


0.27 


0.201 


3.00 


3.00 


033 


0.33 


0.193 


2.49 


2.50 


0.43 


0.43 


0.196 


2.01 


2.00 


0.586 


0.58 


0.189 



Average, 
1.50 
1.20 
1.00 
0.93 
0.79 
0.71 
0.58 
0.53 
0.505 
0.38 
030- 
0.25 
0.21 
0.19 
0.16 
0.12 




No. I.] 



TERNARY MIXTURES, 



31 



Table IV. 

X c.c. Water; y c.c. Benzol; 5 c.c. Alcohol. Temp. 20°. 
Formula jr>=C; «=1.60; log C= 0.554. 



Water. 


Benzol. 




C&lc. 


Pound. 


Calc. 


Pound. 


logC. 


19.87 


20.00 


0.03 


0.03 


0.557 


10.65 


10.00 


0.09 


0.08 


0.503 


7.^ 


8.00 


0.13 


. 0.13 


0.559 


4.97 


5.00 


0.273 


0.275 


0.557 


4.00 


4.00 


039 


0.39 


0.554 


3.02 


3.00 


0.61 


0.61 


0.558 


2.01 


2.00 


1.18 


1.17 


0.550 


1.72 


1.72 


1.50 


1.50 


0.553 


1.50 


1.50 


1.87 


1.87 


0.554 


1.44 


1.45 


1.98 


2.00 


0.559 


1.00 


1.00 


3.58 


3.57 


0.553 


0.605 


0.605 


8.00 


800 


0.554 


0.526 


0.525 


10.04 


10.00 


0.552 


034 


0.34 


20.14 


20.00 


a551 



Average, 



0.551 



Table V. 

X C.C. Water; y c.c. Benzol; 5 c.c. Methyl Alcohol. Temp. 20^. 
Formula yy=Ci; «i = 1.48; logCi=0.216. 



Water. 


Bensol. 


• 


Calc. 


Pound. 


Calc. 


Pound. 


»okQ. 


5.05 


5.00 


0.15 


0.15 


0.211 


3.95 


4.00 


0.21 


0.215 


0.223 


3.01 


3.00 


0.32 


0.32 


0.211 


2.00 


2.00 


0.59 


0.59 


0.216 


1.40 


1.40 


1.00 


1.00 


0.216 



Average, 



0.215 



Formula x*«>'=Ca; «2=2.00; log Ca= 0.281. 











logC^ 


1.13 


1.13 


1.50 


1.50 


0.282 


1.00 


1.00 


1.91 


1.90 


0.279 


0.80 


0.80 


299 


3.00 


0.283 


0.69 


0.69 


4.01 


4.00 


0280 


0.49 


0.49 


7.% 


8.00 


0.283 



Average. 0.281 



32 



DR, W, D, BANCROFT. 



[Vol. III. 



Table VL 

X C.C. Water; y c.c. Benzol; 5 c.c. Acetone. Temp. 20^. 
Formula y»j'=Ci; wi=1.40; log Ci= 0.262. 



Water. 


Benxol. 




Calc. 


Pound. 


Calc. 


Found. 


loK Cj. 


7.97 


8.00 


0.10 


0.10 


0.264 


7.00 


7.00 


0.12 


0.12 


0.262 


5.04 


5.00 


0.19 


0.19 


0.258 


4.03 


4.00 


0.26 


0.26 


0.258 


2.99 


3.00 


0.393 


0.395 


0.264 


2.49 


2.50 


0.51 


0.51 


0.265 


2.18 


2.20 


0.61 


0.615 


0.269 


2.01 


2.00 


0.69 


0.69 


0.260 



Average, 



0.2625 



Formula xy*»= Ca ; ifs=1.35; log Ca=0.114. 











loK C,. 




1.67 


1.67 


0.833 


0.833 


0.114 




1.50 


1.50 


0.90 


0.90 


0.114 




1.30 


L30 


1.00 


1.00 


0.114 




1005 


1.00 


1.215 


1.21 


0.112 


^ 


0.65 


0.65 


1.67 


1.67 


0.114 




0.51 


0.51 


2.00 


2.00 


0.114 




0.38 


0.38 


2.49 


2.50 


0.116 




0.295 


0.295 


3.00 


3.00 


0.114 




0.20 


0.20 


4.00 


4.00 


0.114 




0.15 


0.15 


4.96 


5.00 


0.119 



Average 0.1145 



There is but one exception, in the chloroform-water-acetone 
series. As chloroform and water behave normally with alcohol 
(Table I.), water and acetone with benzol (Table VI.), the dis- 
turbing effect must be due to chloroform and acetone in presence 
of each other. I have not yet had time to investigate mixtures 
of chloroform and acetone in the absence of water, to determine 
whether they are abnormal in respect to any other physical proper- 
ties. In the other five cases the agreement between observed 



No. I.] TERNARY MIXTURES, 33 

and calculated values is a remarkable one, well within the limits 
of experimental error, and this in spite of the wide range that the 
measurements cover. In the benzol-water-alcohol series the ratio 
of benzol to water varies as one to forty thousand ; in the chloro- 
form-water-alcohol series the ratio chloroform-water varies as one 
to twelve thousand. In the last measurement of Table I., the 
chloroform forms over 85 per cent by volume synthetically of 
the solution, so that in this instance we are well beyond the 
realms of the •* dilute solutions," without noticing any disturbing 
effect due to "variations from the gas laws." The series benzol- 
water-alcohol is represented by a single curve; but it must not 
be thought that in this it forms a real exception to the other 
mixtures. Theoretically, there are two curves for this series ; but 
the two happen to have the same direction, and therefore appear 
as one. The point where the precipitate ceases to be less dense 
than the original solution lies between the mixtures benzol 2,00 c.c, 
water 1.45 cc, and benzol 3.57 cc, water i.oo c.c. 

( To be continued,) 




34 ^R' ^' ^' BAUER. [Vol. III. 



ON THE SECULAR MOTION OF A FREE 
MAGNETIC NEEDLE. lU 

By L. A. Bauer. 

ACCORDING to the principle explained in the first part of this 
article^ all the curves on the two plates given have been con- 
structed In this paper no attempt at a detailed account of 
maierial employed, or of construction formulae, can be given. 
it will suffice to present in tabular form the final construction 
datn. 

With the aid of Tables 1, and II, appended, the curves on 
Wale L were drawn. Only a part of the material collected by the 
writer has been utilised thus far. The object was to gi\'e only so 
much as was absolutely necessary to establish the conclusions here 
gi\Tii, To be able to do this to the best advantage, it was the aim 
to select such stations as would exhibit most clearly the various 
phases ol the secular variation. To further facilitate the study, 
mo^t of the stations were selected approximately in latitude 
40* Nm and encircling the earth. The idea was to make a first 
attempt with the aid of such stations to follow a secular wave 
Hiimml the globe, It will be seen by turning to the plate, that the 
[wuiUh (Ua* inlcrsectiona of the broken lines) which represent the 
mc4« r^Uucs {D^ and /^) for each station have been placed in 
the latitude of that station. Owing to the difference in the si^e 
itf the curves, the mti difference in longitude between the various 
itiitlinu rouhl not be preserved ; the points {D^, I^ have, however, 
iilw4y<i betm placed relative to each other in the proper longitude. 
Till* plitc diK^s not exhibit everjahing as clearly as the author 
wiuiht hi^ve \vi,Sihed ; a larger scale could have been employed to 
guild advantage. It should be remembered, however, that these 
twrVf?* \\AVt been drawn for the first time, and that in the nature 

1 A \s^\\¥% \%'hA \w{\>\c Uie NitiMdAl Acikdciny vfEdencc»»Wfuhttigtun, April 16, 1895; 
MH4ikiJl«i4 (t»*wi \^H^ 4*'5* 



No. I.] SECULAR MAGNETIC VARIATION^. 35 

of the case this preliminary chart had to be more or less a trial 
one. The author hopes to be able to present, in the near future, 
a more complete and more comprehensive picture of the secular 
variation of geomagnetism. 

But one more point with regard to the construction of the 
curves remains to be referred to. By turning to the Paris curve, 
it will be seen that the curve has been drawn from 1540 to 1890. 
For this station we possess declinations 1 541-1895, but inclina- 
tions only from 1671 to 1895. How was it possible then to 
construct the curve from 1540 to 1671, since for this interval we 
possess the knowledge of but one ordinate, viz., declination ? In 
this way. From the declination interpolation formula, it is found 
that the minimum value, —9^6, or maximum easterly digression, 
was reached in about 1580. The secular variation curve must 
then have run in 1580 tangent to the declination ordinate corre- 
sponding to the value of 9^6 E. With the aid of this fact the 
curve can be extended backward from 1671 to 1580. Having 
done this, we can scale off an approximate value of the inclination 
for 1580, i.e. for a date for which we possess no such observations. 
This method of deriving inclinations for periods for which no data 
are at hand is here given for the first time. That the values 
thus derived can be relied upon to within i"* to 3^ is shown from 
the following. The scaled value of the inclination for Paris in 
1580 lies between 70** and 72°; Norman observed at London in 
1576, 7i**.8. This would imply a value for Paris lying between 
70** and 71**. Hence the value 7I^o±l^o cannot be far from the 
truth. With this value we can now extend the use of our inter- 
polation formula, which had been established for the epoch 1671- 
1890. The formula gives for 1580, 71^0; we can consequently 
use it without great error back to 1580. The drawing of the curve 
can thus be undertaken without difficulty. Between the years 
1541 and 1580 we know that the easterly declination was increas- 
ing; hence the secular variation curve, 1541-1580, must have 
approached the tangent point (1580) from the left. This part of 
the curve (1541-1580) is of course determined but very roughly, 
as no other values of the inclination were at hand than the extra- 
polated ones from the formula; but the direction of the motion 



DR. L. A. BACER, [Vol. III. 

and that is the chief object of these investi- 
T.at from 154 1 to 1 890, i.e. for over 350 years, 

:.iockwise. In precisely the same way, the 
.\.^ended from 1576 to 1540; the Rome curve 

,1 the latter case the direction has therefore 
vv.l -r.ich 400 years. For the epoch of maxi- 
.♦ )r., viz,, 11^6 E. in about 1570, we scale off 

- / ^. As the earliest reliable inclination 
^'.-^^a.^ at London in 1576, 7I^8±I^ the 

- -r:.n boast of being one of the oldest that 

- 'tr^n^ed is that for all the stations (24) on 
' -.'.x-^^r'eis throughout in the direction of the 

- ^ ,:.T has now been tested for more than 
.♦ .r <iines scattered over the earth. Where 
■ ^ : u:v»Ti, or the series covered a sufficient 
. \ .> round to hold in every case. As the 
,^ j^-^ not simple geometrical ones, but are 

-^ ,*c smaller waves, the writer does not mean 

. - s: jl:^ drawn on a very large scale and, say, 

^ i-^Kkwise motion will obtain through- 

ps«)f which Ihe curve may be composed, 

\m every case for the larger part of the 

^socitUr variation broadly considered^ the law 

tfar which the curves have been drawn. The 

tested with the aid of the published 

rt« itogofli*^ ^"^ ^^^^ isoclinic charts for the 

'Z fi^m these charts the data were scaled for the 

->c paniH^ls of latitude 60° N., 40^ N., 20" K, o\ 

^. c ^ith the meridians 20'' apart. The secular 

Ttur paralWs of latitude 40' N., o' and 40^ S.. ta 

have been drawn. For about a do^en there 

S ^ to the direction of the curve ; in the rest, the 

iln revealed itself. The doubtful curves were 

■ the earth's surface where the data are very 

i^' (or the interval drawn the curve is in reality 

fly a straight line, i.t\ the greater part of the 





No. I.] SECULAR MAGArET/C VAR/ATIOIV. 37 

variation occurs in the inclination, the declination suffering very 
little change (see, for example, Manila curve). We believe then, 
that we can safely draw our first conclusion, — 

In consequence of the secular variation of geo^nagnetism^ the north 
end of a freely suspended magnetic needle viewed from the center 
of suspension of the needle ^ moves on the whole earth in the direction 
of the tiands of a watch. 

So much care has been given the establishment of this law for 
two reasons : — 

a. Because, knowing now that it is a law that the secular 
variation observes, the means are given herewith to judge some- 
what as to the value of doubtful data.^ 

b. Because it , is recognized that in the above law we have 
already-one criterion, with which to decide between some of the 
causes of the secular variation that have been suggested. This 
law will doubtless play an important rdle in the next step of these 
investigations, — the mathematical examination and critical dis- 
cussion of the possible causes.^ 

Very little can as yet be said as to the true geometric nature 

* This can be elucidated by the following example. In 1885, Mr. Schott, the well- 
known geomagnetician, drew the secular variation curve for a mean station of New England, 
and for the interval 1820-1885. He knew approximately when the needle had reached 
its maximum easterly point, and also the value of the declination for this period. He 
could determine then the line to which the curve would have to run tangent, prior to 
1820. Although he had had an experience of over forty years in terrestrial magnetic 
matters in the United States, he nevertheless did not dare to extend the curve back to 
this tangent line for the reason that he could not tell whether the extension would have 
its convex side turned downwards or upwards. Inclinations had been observed at 
Boston in 1 780, but as they appeared doubtful to him no use was made of them. When 
the writer laid his preliminary investigations before the A. A. A. S. in 1892, he could then 
say how Mr. Schott 's curve ought to be extended prior to 1820, viz., the convex side must 
be turned downwards in order to make the direction of the motion correspond to that 
obtaining at the European stations. Or, if the observed inclinations for 1780 were 
utilized, the curve would proceed in the direction as prescribed by the law. The curve 
fir Boston was then exhibited for the period 1 780-1 885, and the direction prior to 1780 
also indicated with the aid of the observed declinations. In the latter part of 1894, the 
uriter's attention was called by Professor Geveland Abbe to a work in which he obtained 
an observed inclination at Boston for the year 1722, this being probably the earliest 
observed inclination in the United States. With these data the Boston curve has now been 
laid down from 1722 to 1885. ^^ ^s seen that the law of the motion obtains throughout, 
and that consequently the observed inclinations for 1780 cannot be far from the truth. 

' See Americao Journal of Science for August, 1895, ^^^ following numbers. 




38 DR, L, A, BAUER. [Vol. III. 

of the secular curve. To the great question, however, whether 
it consists of a single branch or of several, an answer can be 
attempted. It may be remarked that it would be far more aston- 
ishing if the curve were a single closed one, than if it were shown 
to consist of branches or loops, since the daily and annual variation 
curves are known to be very complex indeed. Indications of loops 
are shown at two stations, Rome and the Azores. At the first 
station, by means of the so-called compass-charts of the 14th and 
15th centuries, we are able to gain some knowledge of the mag- 
netic bearing of the needle for that epoch. On these charts the 
directions from port to port are laid down magnetically. By com- 
parison with charts on which astronomical directions are given, 
some knowledge of the magnetic declination for the period of the 
compass-charts can be obtained. Thus it was found that accord- 
ing to the compass-charts of 1436, by Andrea Bianco, the magnetic 
declination at Rome ought to be about 5"* E. If we now assume 
that the law governing the secular variation of the declination 
from 1508 to 1890 holds good also from 1400 to 1508, we find 
that in 1400 the declination ought to be 12^ W., and for 1436, 
7® W. Prior to 1400 the westerly declination would be increasing. 
The material with which Bianco's charts were constructed is doubt- 
less older than 1436. If we make the most favorable assumption, 
however, that the value S** E. refers to 1436, we find a difference 
of 12'' between compass-charts and formula. For 1400 the differ- 
ence would be even 17^ and prior to that still greater. The best 
plausible explanation we can give of such large discrepancies, is 
that a different law of the secular variation came into play, or, in 
other words, a loop was described prior to 1500. A similar con- 
clusion is reached at the Azores station, by considering the 
observed compass-bearing of Columbus in 1492, in the vicinity of 
these islands. Even if we assume that the value is erroneous so 
far as 6^ there still remains an outstanding difference between 
observation and formula of 8°. The writer does not mean to say 
that the foregoing considerations should be regarded as sufficient 
proofs, but simply as indications of loops. The singular points 
exhibited at some of the stations drawn, e,g. Acapulco and station, 
40** N., 40** W., are doubtless due chiefly to inaccurate data. If 



No. I.] SECULAR MAGNETIC VARIATION', 39 

we compare the two curves 40** N., 60** W., and 40** N., 40** W., we 
find that they both observe the law of motion, and yet there is a 
striking difference between them. The former follows the United 
States type, the latter the European. Some remarkable change 
in the curve must have occurred between these two stations. The 
European type cannot change suddenly into that of the United 
States. The change must be a progressive one, and be made by 
means of loops or singular points. It is probable that the curves 
in this region will contain such singularities. 

As to the period, nothing definite can be said as yet, and it 
moreover appears questionable whether there really exists a secular 
variation period, at the close of which the needle describes the 
same orbit it did before. The time interval between the epochs 
of maximum westerly and easterly digression of the needle can be 
determined for a number of stations to within about ten per cent. 
Thus this interval for London is, 1812 — 1580=232 ± 10 years ; for 
Paris, 1809— 1580=229 ±10; for Rome, 1810—1570=240 ±15. 
Accordingly, we might say that this interval for western Europe 
is about 235 years. For the eastern part of the United States the 
interval appears to be on an average about 1 50 years. We have a 
proof here at once that if the secular variation period has the same 
length all over the earth, we cannot then regard the interval 
between the extreme digressions as covering half the period ; for, 
if this were so, then the period for Europe would be about 470 
years, that for the eastern United States only about 300. We are 
then forced to conclude that either the period is different for various 
portions of the earthy or that the secular curve is not a single closed 
curve^ but consists of loops. This is our second conclusion. 

Now let us follow a secular wave around the earth. We will 
begin with London, and proceed in an easterly direction. The 
London curve seems to be approaching the upper extreme point, 
i,e. the inclination is diminishing with a speed that has become 
less and less ever since about 18 10, or, in other words, it is nearing 
a minimum value which may be reached about the middle of the 
next century. Paris appears somewhat nearer this phase ; Rome 
and Berlin still nearer, where it will probably take place shortly. 
At Tiflis this phase has already been passed, in about 1875. At 



40 DR, L. A. BAUER. [Vol. III. 

Bombay the minimum inclination phase has long ago occurred, 
and in about 1880 the curve had already reached its maximum 
easterly digression. Irkutsk, Peking, Manila, Petropawlowsk, 
station 40** N., 180** E., are either nearing the maximum incli- 
nation phase or have already passed through it. It is extremely 
difficult to say through what phase the San Francisco curve has 
passed, for the reason that in the Pacific Ocean and on the western 
coast of the United States, secular waves of opposite phase, but of 
different amplitudes, seem to make their appearance, and conse- 
quently partially annihilate each other. St. Louis, Boston, Ber- 
mudas, 40® N., 60** W., have passed through their extreme lower 
points, and are approaching now the maximum westerly digression. 
The latter will take place in time in the reversed order of the 
stations. At station 40° N., 40® W., the maximum westerly elon- 
gation has just occurred, or will occur soon. At the Azores it 
took place about 1852, and the needle, as at London, is bent now 
upon reaching its upper extreme position. We have now followed 
a wave around the earth. 

Our next conclusion is that the secular variation curves appear to 
develop themselves more and more as we go around the earth east- 
ivardly ; or, in other zvords, the secular wave appears to travel in 
the main, roughly speaking, westward. We might then conclude 
that by obtaining a composite of the various parts of the suc- 
cessive secular variation curves for stations, somewhere near a 
parallel of latitude, we could get the total curve. If we do this 
mentally, we shall find at once that the curve constructed thus is 
not a single looped one, as there are two regions where the needle 
is passing through a maximum inclination phase, and likewise 
two where the maximum easterly (or minimum westerly) phase 
is taking place. 

But what does this unfolding of the secular variation curve, with 
eastward progression, imply ? If this continuous development has 
been caused by a wave traveling from east to west around the 
earth, would it not follow that if we made an instantaneous circuit 
of the earth in an easterly direction with a free magnetic needle, 
the same phenomenon would unfold itself from station to station, 
as occurs at any fixed station in the lapse of time } Let us see if 



No. I.] SECULAR MAGNETIC VARIATION'. 41 

this be true. In 1885 we will start from a point, the latitude of 
which is 40** N., and longitude o^ We will take with us a free 
magnetic needle, and travel with it eastwardly around the earth 
along the parallel, 40'' N. At points distant 20'' in longitude, we 
will observe the direction of the needle ; measuring the declination 
and the inclination. Throughout the circuit the needle is con- 
stantly changing its direction. If we now suppose that the center 
of suspension of the needle is fixed, but the needle itself subject 
to the changes encountered during the circuit, we can construct 
the curve described by the north end, in a manner analogous to 
that which was followed in drawing the secular variation curves. 
We thus obtain the striking curve exhibited on Plate II., — the 
heavy curve on the left. The only difference from the secular 
variation curves is, that instead of time we now have longitude 
marking the various points of the curve. Instead of actually 
making the circuit, we can obtain the necessary data from the 
excellent isogonic and isoclinic charts for 1885, constructed by 
Professor Neumayer, director of the German Naval Observatory. 
The broken places correspond to the data for the points 20** distant 
in longitude, and lying in latitude 40° N. It will be observed that 
this curve also proceeds throughout in the direction of the hands 
of a watch ; even the small loop follows this law. Furthermore, 
the part without the loop exhibits a great similarity to the secular 
variation curves for London, Paris, and Rome. Is this mere 
accident > Suppose we make our circuit along other latitudes, or 
for other epochs, — will a similar condition of things obtain } To 
answer this the writer has drawn first the instantaneous curves for 
latitudes 75^ N., 70^ N., 60° N., 50** N., 40* N., 20** N., o^ 20^ S.. 
40** S., 60** S., from data of 1885, and secondly the curves for 
40** N., o^ and 40'' S., for the additional years 1780 and 1829. In 
every case the direction of motion was clockwise. On Plate II., 
these latter curves are drawn for the three years; the necessary 
data are given in Table III. It will be observed that although the 
nine curves present many irregularities and singularities, they never- 
theless all unite to exhibit a hitherto unsuspected law. Before we 
formulate the new conclusion to be drawn, let us see what we 
shall get if we make the circuit in some other way than along a 



42 DR. L, A. BAUER. [Vol. III. 

parallel of latitude. Of course the circuit must always be made 
eastwardly as the waves come, generally speaking, from the east. 
Likewise is it apparent that for every circuit we shall get a closed 
curve. At first sight it might appear more natural to make the 
circuit along a magnetic parallel. If we define the latter as an 
isoclinic, then the curve will reduce to a straight line, since along 
an isoclinic the inclination is constant, the declination alone vary- 
ing. If we regard an equipotential line as a magnetic parallel, 
and make the circuit e.g. along the zero equipotential line or along 
the magnetic equator, we get the peculiar curve given on Plate II., 
middle figure. This curve has a large loop proceeding clockwise, 
and two small loops, one going anti-clockwise and the other clock- 
wise. It will at once be seen that this curve does not present 
such a striking similarity to the secular variation curve. It seems 
then that the circuit must be made somewhere near a parallel of 
latitude. Is this not an indication that the secular variation is 
in some manner connected with the rotation of our mighty geo- 
magnet ? This matter is at present being investigated. Our next 
conclusion is then : — 

The north end of a free magnetic needle^ viewed from the center 
of suspension of the needle ^ moves clockwise in making an instanta- 
neous easterly circuit of the earth along a parallel of latitude ; or. 

The north end of a free magnetic needle^ whose center of sus- 
pension is fixed in space close to the earth's surface^ will describe a 
curve as the earth rotates under it, which as viewed from the center 
of suspension of the needle^ moves anti-clockwise}- 

In the foregoing we have already hinted at a connection between 
the secular variation and the distribution of geomagnetism, in that 
they both observe similar laws. This connection is also revealed 
in another way. By turning to Plate I., it will be seen that the 
largest secular curves seem to occur at stations somewhere near 
the equator, — see Ascension and St. Helena islands. Likewise 
the curve for Rome is smaller than the one for Cape Town, lying in 

1 The original formulation of this law was given in the first form. The curves are 
indicated then on Plate II., as proceeding clockwise. For the second form the arrows 
would have to be reversed. The motion is now reversed since the earth rotating from 
west to east is equivalent to making a wtsterly circuit of the earth with the needle. 



No. I.] SECULAR MAGNETIC VARlATlOAr. 43 

about the same latitude south. Turning now to Plate IL, it will 
be seen that a precisely similar condition of things prevails. Thus 
the largest instantaneous curve is described at the equator ; like- 
wise the curves for 40'' S. are larger than those for 40° N. A 
connection seems to prevail also with regard to the loop in the 
northern hemisphere. This cannot be exhibited here, however. 

Our final conclusion is then : — 

The secular variation and tlie prevailing distribution of geo- 
ntagneiisnt appear to be closely related. 



46 



DR. L. A. BAUER. 



[Vol. III. 






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Berlin . . . . 
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St. Louis . . 
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Rio de Janeiro 
Cape Town . . 
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No. I.] 



SECULAR MAGNETIC VARIATION. 



47 



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48 



DR. L. A, BAUER. 



[Vol. III. 



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BAUER. PLATE 1. 






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To face pa^^e 4 



BAUER. PLATE II. 




No. I.] GALVANOMETER FOR PHOTOGRAPHING CURVES. 49 



A GALVANOMETER FOR PHOTOGRAPHING ALTER- 
NATING CURRENT CURVES. 

By H. J. HoTCHKiss and F. K Millis. 

IN the latter part of 1893 one of the writers undertook an 
experimental study of the extra currents corresponding to 
the exponential term in the common expression for the current 
curve produced upon closing a circuit containing an harmonic 
electromotive force, resistance, and self-induction ; and the other, 
an investigation of the variations of current and armature lag in 
synchronous motors when the load is suddenly changed. For the 
experimental study of these subjects we wished an instrument 
which would readily and accurately record the alternating current 
curve from the instant of changing the conditions until the perma- 
nent form was reached. Photographing on a moving plate the 
spot of light reflected from a modified form of M. BlondeVs oscil- 
lograph ^ seemed to lend itself best to our purpose. The modified 
form is essentially a galvanometer having a very small needle of 
soft iron, a very strong field for the directing force, and a single 
small coil carrying the alternating current which deflects the 
needle. 

That the curve thus obtained might not be distorted by the 
inertia of the vibrating needle and mirror, both were as small as 
they could be conveniently made, and were mounted with their 
greatest dimensions in the axis of vibration. That the natural 
period of the needle may not affect the shape of the curve, it 
should be much less than that of the current. 

We experimented with many forms of mounting for the needle, 
and finally succeeded in getting one sufficiently sensitive which 
made a little more than 3500 double vibrations per second. The 
frequency of the current experimented upon in the study of extra 

1 Electrician, Lond., Vol. XXXI., March 17, 1893; P*gc 57 *• 



50 



H. J. HOTCHKISS AND F. E. MILLIS. [Vol. III. 





^^^ 





CO 






"T>- 




h 



iffli 




No. I.] GALVANOMETER FOR PHOTOGRAPHING CURVES. 5 1 

currents was 120 complete alternations per second, and it was not 
possible to detect the slightest distortion of the curve due to the 
combination of the period of the needle with that of the current. 

Figures i and 2 show the manner of mounting the needle and 
its position between the poles N^ S, of the electromagnet. Figure 
I is a horizontal projection, and Fig. 2 a vertical section through 
Fig. I along the line ad} The needle n, and the small coil c around 
it, were supported upon a vulcanite block d, having a rectangular 
hole 6x15 mm. cut into one end. The latter was cut down until the 
walls were quite thin, in order to bring the coil close to the needle 
and not to separate the pole pieces too far. Within, shoulders were 
left, on which to mount the coarse quartz fiber /, to the middle of 
which the needle and mirror were fastened, on opposite sides, with 
shellac. The needle was made from a piece of soft iron such as is 
used for armature cores. The mirror was cut from a microscope 
cover-glass silvered. The dimensions of the parts are given in 
column I. of the table. 

The small coil c, around the needle, contained about 480 turns 
of copper wire heavy enough to carry 3 or 4 amperes. With this 
apparatus an alternating current of 2.35 amperes gave an amplitude 
of about 18 mm. on the photographic plate. 

A top view of the electromagnet and photographing apparatus, 
drawn to a scale of about one-fifteenth, is given in Fig. 3. The 
wrought iron cores, about 2 inches in diameter, were connected 
at the bottom by a large yoke piece, while the magnetizing coils, 
each of which contained about 970 turns of heavy wire, were 
excited by a current of about 10 amperes. The light from an arc 
lamp, Z, passed through a vertical slit a few inches from the lamp 
and fell upon the mirror, from which it was reflected to a narrow 
horizontal slit in the slide carrier 5. The photographic plate was 
allowed to drop vertically in front of the slit. No lenses were used. 

The natural period of the needle was determined by mounting a 
very small mirror on the end of a heavy tuning-fork which was 
known to make 5 1 2 double vibrations per second, and then placing 
this fork in such position that its mirror would reflect a spot of 
light from the lamp to the horizontal slit in the slide carrier beside 
^ Figures i, 2, 4, 5, and 6 are drawn about one-half natural size. 



52 H. J, HOTCHKISS AND F. E. MILL/S. [Vol. III. 

the spot of light from the mirror on the needle. The needle was 
deflected by a current from a storage battery, the fork bowed, and 
the sensitive platfe dropped. A trip was so arranged that as the 
plate passed the slit it broke the battery circuit. By comparing 
the curve from the fork with that made by the needle as it came 
to rest, it was found that the needle made seven times as many 
vibrations as the fork, or about 3580 complete vibrations per 
second. 

Curves were taken from different sources of alternating electro- 
motive force giving different forms, which, when compared with 
those taken by other methods, showed that the photographed 
curves could be depended upon, and were probably much more 
accurate than the others. 

In the study of extra currents, some preliminary experiments 
were made, in which curves were taken showing the dying out of 
current in a closed circuit containing resistance and self-induction 
when the impressed electromotive force was suddenly removed by 
short-circuiting the leads from the source. The curves in Figs. 7 
and 8 (see Plate) are portions of two thus taken, one for direct 
current and the other for alternating, the resistance being 5.1 
ohms, and the self-induction 0.032 henries. When superimposed 
they coincide quite exactly. The small sinusoidal curve in Fig. 7 
is that of the tuning-fork before mentioned. 

Others, not shown, were taken for increase of current when the 
electromotive force was suddenly impressed. Their form was the 
same as Fig. 7 would appear if turned over, except that the straight 
line ended abruptly where the curve began at the instant the elec- 
tromotive force was impressed. 

When taking these curves, the arc lamp was always operated so 
as to give as bright a spot of light as it was capable of producing. 
The varying brightness of the curves is probably due to the hiss- 
ing of the arc. 

The final results of the investigation obtained with the galva- 
nometer described were quite satisfactory. These, however, will not 
be discussed here, since this article relates more especially to the 
galvanometer itself, using as illustrations a few of the various 
kinds of curves that have been photographed with it. 




to 








No. I.] GALVANOMETER FOR PHOTOGRAPHING CURVES. 53 

The galvanometer may be modified to adapt it to the particular 
use to be made of it. For the study of synchronous motors, new 
apparatus was made, with modifications, some of which were made 
necessary by the new conditions, and others tried with a view to 
improvement and to extending the range of usefulness of the 
galvanometer. The same electro-magnet was used, but it was 
necessary to use other coils having only about 1050 turns instead 
of 1940. Slide 5, Fig. 3, was made a little longer in order to give 
the plate a higher speed as it passed the slit. The latter was two 
feet below the top. The average speed of the plate while passing 
the slit was about ten feet per second. In place of the arc lamp 
enclosed in a box, a light wooden box about 8Jx lox 12 inches, 
lined with asbestos paper, was used to enclose the light and support 
hand-fed carbons at an angle of about 30° or 35® from vertical, so 
as to have the maximum intensity directed horizontally toward the 
narrow slit in the side toward the galvanometer. When fed by 
hand, curves could be obtained without the variations of brightness 
seen in Figs. 7 and 8. A space was left between the wood and the 
asbestos lining, so that atr could circulate. 

The mode of supporting the needle was somewhat modified, as 
shown in Figs. 4, 5, 6 ; Fig. 4 being a plan, 5 an elevation, front 
view, and 6 a vertical section. For convenience in making, and to 
get the coil c nearer the needle laterally, the coil was supported 
on two \ inch rods f^. Figs. 5 and 6, set in holes | inch between 
centers in a piece of wood cP, Portions of the rods were cut away 
as shown. On one a shoulder was left, to which one end of the 
fiber / was fastened, the other end being attached to a spring w, 
which should give as much tension as the fiber will safely bear. 

For supporting the coil in position between the pole pieces, ^V 
5, a standard, ^, was fastened to a base that was clamped to the yoke 
piece of the magnet by a screw. The block d! is held against the 
ends of two screws through the standard by tightening the screws 
in the bent end of the metal strips ^, which draw upon the rod //, 
through the block. These form a sort of universal joint, convenient 
for adjusting the needle so as to bring the spot of light from the 
mirror on the slit of the slide ; also, one needle and coil could be 
readily removed and replaced by another in the experiments made 



54 



H, J, HOTCHKfSS AND F, E, MILLIS. 



[Vol. IIL 



for the purpose of comparing the behavior of needles of different 
dimensions and suspensions. The block d^ served also to hold the 
binding screws for the small coil. 

Several needles were made and tried. Dimensions and data for 
five of them are given in Table I. The mirrors for the last four 
were obtained by selecting from a large number of microscope 
cover-glasses one that had a plane surface, as shown by the 
interference bands that appeared when the glass was placed 
on a standard plane surface. The glass was .08 mm. thick. 



Table I. 

MEASUREMENTS OF GALVANOMETERS. 

METERS. 



DIMENSIONS IN MILLI- 



Numbers. 


I. 


II. 


III. 


IV. 


V. 


Fiber 


Material . . . 

Length .... 

. Diameter . . . 


Quartz. 
14. 
0.14 


Quartz. 


Quartz. 
12. 
0.015 


Quartz. 
12. 
0.057 


Silk. 
12.5 
0.035 (?) 


Needle ^ 


Length .... 

Width .... 

.Thickness . . . 


2.4 
1.25 
33 


> 
a; 

>> 

"5 


l.SO 
0.56 
0.065 


2.50 
L23 
0.07 


2.81 
2.56 
0.07 


r Length .... 

Mirror ] Width .... 

L Thickness . . . 


2.00 
1.25 
0.30 




O.SO 
0.45 
0.10- 


1.72 
0.65 
0.10 


1.44 
0.49 
0.10 


Approximate vibration fre- t 
quency with about 10 ,• 
amperes in field coils . J 


3580 


3950 


3450 


3900 


2850 



After silvering by Draper's method,^ and varnishing, the thickness 
was between .09 and .1 mm. It was then cut to the desired size 
with a small marking diamond. 

In mounting the iron and mirror on the fiber, a metal plate was 
supported a few inches above the table, upon which was fastened 
one end of the fiber ; the other was allowed to hang over the edge, 
with a lump of wax attached to keep it straight and in place. The 
iron was placed on the plate under the fiber. Two minute particles 
1 Smithsonian Contributions to Knowledge, Vol. 14, Article IV., p. 3, 1S65. 



No. I.] GALVANOMETER FOR PHOTOGRAPHING CURVES. 55 

of dry shellac were then placed on the fiber, or close against each 
side, above the iron, and heat was applied by a bunsen burner beneath 
the plate until the shellac melted and spread as much as desired. It 
was then allowed to cool before putting the mirror in position upon 
the shellac. When the mirror was carefully adjusted, heat was 
again applied beneath. The mirror was lightly pressed down 
upon the melted shellac with a plane surface so as not to spring 
it, and left to cool slowly. The fiber was cut off to the required 
length and mounted on the supports with melted shellac. The 
small pieces of iron and mirror may be conveniently handled with 
two fine pointed glass rods by slightly wetting the end of one and 
touching it to the corner of the piece to be lifted ; then use the 
dry one to remove the piece from the other, and to place it. 

Figures 7-1 1 inclusive are full size copies of portions of a few 
curves photographed, the whole plate being 2|^ x 8 inches. Figure 
9 shows the natural vibration frequency of needle II. for com- 
parison with Fig. 10, which is a current curve for an eight-pole 
alternator in the Dynamo Laboratory taken with the same needle 
and 7.8 amperes in the small coil (2) of 34 turns of number 18 
copper wire. The plate passed the slit with the same mean speed 
of about 120 inches per second for both. The frequency of the 
alternating current was about 98, and that of the needle about 
3950 per second. The straight line in Fig. 9 shows the width of 
spot of light that may be obtained, and that the needle remains 
perfectly steady while the plate falls if not deflected by current ; 
also that the plate falls without being disturbed by friction or jar. 
At the end of the short, straight line the circuit from a storage 
battery was closed by a trip operated by the falling plate holder. 
When the vibrations due to inertia had nearly died out, the circuit 
was broken by another trip. In Fig. 10, the parts of a second 
curve are due to the plate being dropped twice for the same current 
a few minutes apart. The speed of the dynamo had changed a 
little. 

For part of our work a much slower motion of the plate was 
desired. This was accomplished by an arrangement on the prin- 
ciple of the Atwood machine. A string hooked to the top of the 
plate holder passed over a pulley mounted on the top of the slide. 



56 



H, J, HOTCHKISS AND F. E. MILLIS, 



[Vol. III. 



and supported on the other side a weight which nearly counter- 
balanced the plate holder. A stretched rubber band started the 
holder and weight, which maintained quite nearly the same speed 
after the band ceased to act. Figure 1 1 shows a curve thus taken 
for electromotive force between two terminals of a three-ph^e 
generator on open circuit ; the frequency being about 22 cycles 
per second. Needle IV. was used with the 300 turn coil (3) of 






Fig. 12. 

number 28 copper wire. A tracing of a current curve for the 
same dynamo with the plate dropping at full speed is shown a 
little more than one-half size by IV., Fig. 12. The other three 
curves are similarly reduced. 

In Fig. 12, I. is a curve for current through a synchronous 
motor run by one of the large transformers in the laboratory. 



No. I.] GALVANOMETER FOR PHOTOGRAPHIISTG CURVES, 57 

Curve II. is for current from a small 50-volt, loampere West- 
inghouse alternator having a smooth cored armature, it being the 
same one used in the experiments on extra currents. 

Curve III. is for current from another alternator of the same 
typ*^ except that the armature coils are laid in grooves cut in the 
core. The small variations, plainly noticeable by the shading of 
the line in the plate, cannot be represented by the tracing. The 
irregularities of the curve, indicated not only by change of direction 



40 
30 
20 
10 

10 
20 
SO 
40 




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Fig. 13. 

of line, but by the shading, recur regularly in each cycle, being of 
the same number, shape, and position in the cycle ; and were evi- 
dently not due to the natural period of the needle. Figure 13 is a 
curve for the same dynamo taken by the instantaneous contact 
and telephone method. 

A photograph was taken the same way as Fig. 9 to try the effect 
on the frequency of the needle when the field was weakened ; and 
also to show the promptness with which the needle obeyed the 
deflecting force. With about 12 amperes in the field coils the first 
throw of the spot of light was 0.55 inch ; while with 1.7 amperes 
in field coils it was 1.3 inches. Under these same conditions the 
frequency was reduced from about 3900 to 2700. When a square 
was applied to the angle between the first throw and the axis 
for zero current, its variation from a right angle could not be 
detected near the axis. The spot of light in the first throw and 
return travelled about 2.6 inches, while the plate travelled ^ inch 
in about ^^^ second. For taking curves the slide was usually 
between 12 and 18 inches from the needle. 



58 



H, y. HOTCHKISS AND F. E. MILLIS. 



[Vol. III. 



To determine whether the deflection of the needle is propor- 
tional to current in the small coil, for constant field excitation, a 
calibration curve for needle III. was taken, with the result shown 
by line D, Fig. 14, which is a straight line; showing that the 
galvanometer may be depended upon to give ordinates propor- 
tional to current when properly adjusted. The needle should be 
adjusted relative to the pole-pieces until the spot of light remains 
at rest when the field current is suddenly made or broken. 

When using different needles it was noticed that with one there 
was very little deflection when there was no current in the field 






f : 


4 .^ ____ 


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,____i___,^^: 


\ \.-' . 


\ y%^. 




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I 



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10 20 /Sca/« /or 30 Ce/rre5^;Z}: 40 50 60 

5 10 i» " 15 »»-4,^,(7,Z>.'20 25 80 

D^/UcUotii in twtnlUtht of an Inchi.JSccUe Uittanee U incAet, 



Fig. 14. 

coils, while for another the deflection, under the same conditions, 
was very large. This led to taking the curves shown in Fig. 14, 
and further explained in Table II. 

The three curves, A, B, C, were taken for the same current and 
with the same conditions, except the use of different needles. 
Before beginning the readings, the residual magnetism was that 
left after breaking the circuit when 9 or 10 amperes were flowing 
in the coils. The cores and pole-pieces being of wrought iron, 



No. I.] GALVANOMETER FOR PHOTOGRAPHING CURVES. 59 

it was quite small. The magnetizing current was then gradually 
increased, giving the curves as plotted. 

In order to get the complete curves like A and B, so as to show 
the magnitude of the deflections for zero field-current relative to 

Table 1 1. 

EXPLANATION OF CURVES IN FIGURE 14. 



Carve. 


Needle used. 


Constant current in small coil of 300 turns. 




A 
A' 


IIL 
III. 


0.5 ampere 
0.06 " 




B 


V. 


0.5 «' 




B' 


V. 


0.034 " 


- - 


C 


IV. 


0.5 " 




D 


III. 


(Constant current in magnet coils=9.4 
( amperes. 



those for higher magnetization, the curves A\B^ were taken for 
smaller currents in the small coil. 

From the curves A^ B, A\ B\ it seems that for constant current 
the action and sensitiveness of the smallest needle with the fine 
quartz fiber is about the same as that of the comparatively large 
needle with the silk fiber ; and that, for both, the maximum deflection 
corresponds to a magnetization equal to or less than the residual 
value. Curve Vindicates that the coarse fiber is so stifif that a much 
smaller deflection in a stronger field is the maximum. Other things 
not yet experimented upon may have a part in determining the form 
of curve C. A study of the behavior of different needles under 
different conditions with comparatively low magnetic fields is in 
progress. If sufficient steadiness and freedom from vibration can 
be obtained by the use of a permanent magnet, or a small electro- 
magnet, it would be much more convenient for a portable apparatus 
and would be very much more sensitive for experiments in which 
only small currents can be used. 

For one part of the synchronous motor experiment a galva- 
nometer giving a large deflection for small currents of comparatively 
slow variations was desired. For this purpose a U-shaped perma- 



6o 



H. J. HOTCHKfSS AND F. E. MILLIS. 



[Vol. III. 




nent magnet of about \ square inch cross-section was mounted 
in such a way that any one of the five needles could be readily ad- 
justed ; needle V., however, was made especially for use with this 
magnet. There were four small coils on the permanent magnet 
which could be used to increase the field if found necessary. The 
pole pieces were loose and rested on a block to which the needle 
block was fastened. Either the pointed ends or the square ends 
could be placed against the coil around the needle, or drawn away 
from it if a weaker field were desired. 

In the spring of 1895 Messrs. A. Barnes and H. Zimmerman 
undertook^ an experimental determination of the variations of 
temperature at the inner surface of the walls of an engine cylinder 
during a double stroke of the piston ; also the variations at different 

depths below the sur- 
face. The use of a 
quick-acting galvanom- 
eter was suggested to 
them by one of the 
writers. After a pre- 
liminary trial with the 
large electro -magnet 
and needle II., they 
decided to adopt the 
method ; so the one 
described above with 
needle V. and coil 3 
was constructed and used for the purpose. The general method 
was to have the changes of temperature produce a corresponding 
change in the resistance of a fine wire, and thus to vary the 
amount of current flowing through the galvanometer. The 
latter was placed in shunt with the resistance. The plate was 
moved up $ind down in front of the slit by a cord connected to 
a reducing motion operated by the movement of the piston, so 
that the spot of light from the galvanometer traced out a closed 
curve for the complete cycle, quite like an indicator diagram. 

* Thesis in Cornell University Library; Abstract in Sibley Journal of Engineering, 
June, 1895. 




Fig. 15. 



No. 1.] GALVANOMETER FOR PHOTOGRAPH IXG CCRVES, 6 1 

A tracing from one of them, and a slightly reduced copy of 
the indicator card taken at the same time, are shown in Fig. 1 5. 
The abscissae for both are the same, representing parts of the 
stroke. The ordinates of the upper loop represent temperatures, 
while those of the lower are pressures. The gauge pressure was 
40 pounds, and the speed 84 r.p.m. 

The vertical width of the upper loop shows the range of varia- 
tion of deflection, while the total deflection due to the current of 
0.4 or 0.5 ampere flowing was about 5 or 6 inches; the plate was 
perhaps 18 inches from the galvanometer. Each o.i inch of 
change of deflection was found to represent a change of tempera- 
ture of 12.5"* C. The needle trembled slightly, making the finely 
toothed line about -^ inch wide, the line itself being perhaps yj^ 
inch wide. The width of loop decreased as the speed increased, 
the results being quite uniform, and apparently in accord with 
theory. The galvanometer seemed to be quite reliable without 
any field excitation. For part of the work the pole pieces were 
turned with the square ends toward the coil, and were also drawn 
apart to a width of | inch instead of W inch, as before. The de- 
flections were increased, but the trembling was also increased, so 
that there was not much gained. 

The vibration due to inertia does not take place to any great 
extent, even with a rather weak field, if the current is continually 
varying without very large or sudden changes in the rate of varia- 
tion ; for then the condition for simple harmonic motion — that 
the displacement be proportional to the acceleration — does not 
exist, if the period of the needle differs from that of the current or 
its harmonics. It was found that the needles with quartz fibers 
were more reliable than those having silk fibers, especially for 
high frequencies and strong fields. For these conditions it is 
better to have the fiber as large as can be used without too much 
decrease of deflection or increase of size of the small coil. 

It was found that with needles II. and IV. the spot of light was 
improved by placing a small lens of 10 or 12 inches focal length 
immediately in front of the small coil, so that the light passed 
through it both to and from the mirror. The lens was supported 
on an arm from the standard ^, shown in Fig. 3. With the other 



62 H. J. HOTCHKISS AND F. E. MILLIS. [Vol. III. 

needles no lens was used. If the mirror is plane, a real inverted 
image of the arc is obtained at all distances, the principle being 
the same as in the case of a pin-hole camera. This fact may be used 
to test the mirrors after they are cut and before and after mount- 
ing, to determine whether they have been sprung in mounting 
and whether they are suitable for use. 

In the construction of the apparatus described prominent con- 
siderations were that it be inexpensive and easily made from 
materials, and with means, most readily obtained. Other considera- 
tions would doubtless have led to a quite dififerent construction. It 
was deemed best, however, to investigate the working of the cheap 
and simple apparatus for special uses, before undertaking a more 
expensive and elaborate design for more general use. 

The original plan for the synchronous motor experiment was to 
photograph on the same plate simultaneous records of current 
and lag variations by having the spots of light from two galva- 
nometer needles thrown upon the slit in the slide. The work 
along this line is not yet completed ; however, there does not seem 
to be anything to prevent the use of two or more galvanometers, 
or needles for obtaining simultaneous curves for current, electro* 
motive force, etc., on the same plate. 

The results thus far obtained seem to warrant a more careful 
study, and such modifications in design as will adapt the instru- 
ment to the many uses to which it may be applied. 

Physical Laboratory of Cornell Universffy, 
May, 1895. 



No. I.] A NEW PHOTO-CHRONOGRAPH. 63 



MINOR CONTRIBUTIONS. 

Experiments with a New Polarizing Photo-Chronograph 
AS Applied to the Measurement of the Velocity of 
Projectiles.^ - 

By Albert Gushing Crehore and George Owen Squier. 

IN May, 1894, a paper' was read at the general meeting of the American 
Institute of Electrical Engineers in Philadelphia describing a novel 
method of measuring the variations in an electric current. The point of 
novelty consisted in the fact that the indicator or the vibrator, which 
actually describes the curve representing the current, possesses no mass, 
and is therefore not subject to the laws of inertia. It is the application of 
a modification of this instrument to the measurement of the velocity of 
projectiles which forms the subject of this paper. 

The instrument, as used for measuring current, made use of a dark band 
in the spectrum to indicate by its movement along the spectrum the vary- 
ing values of the current. This band is obtained as follows : Instead of 
taking sunlight direct and analyzing it into the colors of the spectrum, it is 
first passed through a polarizer and then through a quartz plate to rotate 
the planes of polarization of the component colors in different amounts 
depending upon the color, and finally through an analyzer, whose office it 
is to extinguish only that color which is rotated to the same extent as its 
plane. The resulting light emerging from the analyzer is colored, due to 
the absence of the color which the analyzer abstracted from the white light. 
Upon analyzing the emergent light into the pure colors of the spectrum, 
the color which the analyzer abstracted is absent, and in its place is a dark 
band in an otherwise continuous spectrum. The motion of this band is 
effected by placing between the polarizer and analyzer a transparent sub- 
stance surrounded by a coil of insulated wire ; that substance to have the 
property of rotating the plane of polarization when in a magnetic field. 
This field is produced by the current to be measured flowing in the coil of 

1 For a detailed account of these experiments, see the Journal of the United States 
Artillery, July, 1895, published at Fort Monroe, Va. 

«*«A Reliable Method of Recording Variable Gurrent Gurves," by A. G. Grehore; 
Transactions of the American Institute of Electrical Engineers, Vol XL, No. la 
October, 1894; also The Physical Review, Vol 11., No. 2. 1894. 



64 ALBERT C. CREHORE AND GEORGE O. SQUIER, [Vol. III. 

wire, and its strength is consequently proportional to this current, since no 
magnetic material, such as. iron, is present. 

It may not be evident at a glance what the relation is between an instru- 
ment which will accurately measure a variable electric current, and the 
measurement of the velocity of projectiles. In regard to this it may be 
said that any good instrument for measuring a variable current possesses the 
essentials of a chronograph, and a chronograph is the essential instrument 
for measuring the velocity of projectiles. A good current measurer must 
give sufficient data to construct a curve, the horizontal axis representing 
time, and the vertical axis current. The time interval between any two 
phenomena can therefore be measured by such an instrument if the phenom- 
ena referred to are capable of either interrupting the current or changing its 
strength in any way. The instrument referred to is therefore adapted to the 
measurement of the velocity of projectiles ; for screens may be placed at any 
desired intervals along the trajectory, and the current mechanically inter- 
rupted. The instrument measures the time between these screens by 
indicating when the current is changed ; the distance is measured on the 
field. The average velocity of the projectile is this distance divided by the 
time interval. 

In the present application to the measurement of the velocity of pro- 
jectiles, since it is only necessary to indicate the presence or absence of a 
current, the instrument may be simplified by omitting not only the quartz 
plate, but also the arrangement for resolving the light into a spectrum. The 
operation of the instrument is now as follows : White light is passed through 
the polarizer, and then through the transparent substance possessing the 
property of rotating the plane of polarization when in a magnetic field, and 
then through the analyzer. A lens is used to intensify the light emerging 
from the analyzer by bringing it to a focus on the photographic plate. 
The analyzer is then *' crossed " and set for total extinction, so that nor- 
mally no light is admitted to the plate. When a current is sent through 
the coil, all the planes are rotated, the blue more than the red. The effect 
is that light immediately emerges from the analyzer, and is recorded on 
the plate. The light persists as long as the current flows, but is cut off 
completely upon its interruption, — much more suddenly than it could be 
interrupted by any mechanical shutter. In fact, the office of the whole 
combination of polarizer, analyzer, and medium for rotating the planes of 
polarization is to play the part of a shutter. 

The experiments with this instrument were made at the United States 
Artillery School, Fort Monroe, Va., between the dates of Dec. 27, 1894, and 
Jan. 12, 1895. The instruments used were homemade and quite hastily 
assembled. Many things adopted for the sake of expediency were a disad- 
vantage in experimenting, and these things, if instruments were now manu- 



No. I.] A NEW PHOTO-CHROIsrOGRAPH. 65 

factured for the purpose, might be avoided. The camera was made at 
Dartmouth College and the instrument shipped to Fort Monroe during the 
latter part of December, where it was installed after the 27th inst. Besides 
this, many things remained to be done after this time, such as running 
wires to the temporary proving grounds, arranging suitable supports for the 
novel kind of ballistic screens used, etc., etc. 

The camera is shown in the views Figs, i and 2. [See Plate.] It consists 
of a rectangular box A^ 10 x 10 x 2.^^ inches inside measurement. The 
cover B is removed, showing a small auxiliary dark chamber C, which con- 
tains the electromagnetic device D with armature E attached to the spring 
Fiox releasing the camera slide G, This slide is shown withdrawn from the 
grooves in which it normally slides by passing it through the opening at 
the top after removing the cover H, The narrow horizontal slit through 
which the light is admitted to the plate is shown at /. The slit is made 
of sheet brass, the upper jaw being stationary and parallel to a radius of 
the plate. The lower jaw y is a sector of sheet brass which slides between 
two guides so as to make the slit always a sector of the plate, the object 
being to secure a uniform exposure for every point of the plate. When 
the camera slide is in position, the nail at K rests on the top of the brass 
spring Fy and the upper edge L of the lower part of the slide covers the 
slit. When the current passes through the magnet by the binding posts 
M, the slide is released. The slit is only exposed while the opening in the 
camera slide is passing by. The upper part of the slide G is capable of 
adjustment along the rods of the slide, and the time of exposure of the slit 
thus under control. When the cover B is in position, the space contain- 
ing the release mechanism is a complete dark chamber in itself. A cap N 
in this cover B is removed just before the camera is to be used. The 
wires at O are for the purpose of producing on the plate reference circles 
by casting their shadows. The entire back of the camera is removable, 
and its outside face is shown at P, Through the back a horizontal shaft 
Q passes which revolves in the bearing R, 

The inside of the camera is seen in Fig. 2. The slide is shown with the 
upper part G removed. The plate is mounted on the shaft at S, 

The object of the camera slide is to prevent the exposure of the plate 
frpra extending over more than one revolution and thus spoiling the record 
by a second exposure. 

The polarizer used was a Nicol prism the dimensions of which are 104 by 
39 mm. on the side, while the diagonals of the ends measure 60 by 49 mm. 
The analyzer was similar to the polarizer. Between polarizer and analyzer 
was placed a tube 45 cm. long and 3 cm. internal diameter, made of glass 
and fitted with plane glass ends. This tube was filled with liquid carbon bisul- 
phide, which has the property of rotating the plane of polarization when in 




66 ALBERT C. CREHORE AND GEORGE O, SQUIER. [Vol. III. 

a magnetic field, and only then. The tube was wound with No. i8 single 
cotton magnet wire from end to end in four sections. Each section had 

725 turns, which made in all 2900 turns when the 
^ c-g-j I I T r I ' four coils were connected m series. 
Li fi. ^^^ diagram of the circuit which contained 

mJ this tube is seen in Fig. 3. Current is supplied 

["h fcjtt^ T at a constant electromotive force of no volts 

^QP T by the dynamo D. The amount of current is 

Pig, 3, regulated by a bank of resistance lamps. The 

tube is at T and a switch at S. Line wires 
ZjZa lead to the proving ground, where the screens X^X^X^X^ are erected 
in the path of the projectile. At YiY^Y-i are placed devices for establishing 
the current immediately after it is broken by 
the preceding screen. The device to re-estab- 
lish the current is a simple arrangement 
represented in Fig. 4. The springs CC are 
separated by a small insulating plug D^ which 
is attached to a wire running across the path 
of the projectile. This is mechanically pulled out by the projectile, which 
therefore establishes the current by connecting the binding posts BB^ 
together. 

The camera shaft was coupled directly to a small electric motor oper- 
ated by four cells of storage battery. A fly wheel was placed on this shaft, 
which served a double purpose. It was a gear wheel havhig fifty-six teeth. 
My holding the edge of a card against it, a tone is given out whose pitch 
depends u|)on the speed. It was thus that the speed was adjusted before 
each shot. The speed was not obtained in this way, but it is desirable to 
have a speed sueh that the plate will revolve nearly once around while the 
hlide is passing by the slit. The note thus obtained was compared with a 
tuning fork in the otlier hand of the observer just before each shot, and the 
negatives show that this method gave pretty uniform results. 

The record of the time is recorded on the plate itself at the time the 
•»h»)! iH filed. A tuning fork mounted to run electrically is placed so that 
the ^hiulow of one prong is brought to a distinct outline on the plate. This 
MliadiJW gives a sinusoiilal wave on the negative. On the average about 35 
wave-* ol the lork used can be counted on the negative. The convenience 
nl \\\\\ inethoti pr\>ved to be very great, not only because the record of 
time \% on the plate itself, but because it was not necessary to time the 
levMhnmnn l»efi»re and alU'r tiring. 

The tuning tv»ik \\^v\\ niaile 512 complete vibrations per second, and was 
ill nni4on with another similar fork before it was mounted electrically. 
Allei it wa** nuMtntcil, it was observed to beat with the other fork, so that 



[A 



No. I.] 



A NEW PHOTO-CHRONOGRAPH, 



67 



its vibrations afterward were calculated to be 509.46. This makes the 
average time of exposure of the negatives about .066 of a second. A 
speed which will make the plate revolve once during the exposure is thus 
about 12.25 revolutions per second, or about 735 per minute. 

The complete arrangement of the instruments showing the electrical 
circuits used with the different pieces of apparatus is shown in diagram, 
Fig. 5, in which D is the dynamo, T the transmitter tube, S a switch to 
complete the transmitter circuit a moment before firing to prevent heating 
the coils, LxLi the line wires leading to the proving ground, XxXoX^, etc., 
the screens, YiY.^Y^^ etc., the devices for restoring the current successively 




Fig. 5. 

between the screens, and L and V two arc lamps in series, which for con- 
venience w5re lighted by the same dynamo D, F is the electrical tuning 
fork controlled by the cells E^ and M is the motor for running the camera ; 
and at O are the four storage cells for energizing the same. G is the 
gravity switch for exposing the camera and firing the gun, and C is the 
camera whose slide is operated by the cells / through the gravity switch at 
VV. The firing circuit contains the electric primer P at the gun, the line 
wires /'i/j, the dry cells S\ and the gravity switch terminals UU, 

The shortness of the time of exposure was the cause of the greatest 
experimental difficulty ; for to obtain a record of the projectile, it must be 
made during the particular .066 of a second when the camera is exposed. 
Of course a camera made in the future for this purpose can be so arranged 
as to avoid this difficulty. There is a certain unknown inter\-al of time 
between the closing of the primer circuit, which fires the gun, and the 



68 ALBERT C. CREHORE AND GEORGE O, SQUIER. [Vol. III. 

arrival of the projectile at the muzzle, which is known as the " firing interval." 
There is also an unknown interval between the closing of the camera circuit 
and the exposure of the plate. The relation between these intervals must 
be determined before the camera can be used to obtain a record. It 
turned out that the camera circuit should be closed a short time before the 
primer circuit, to bring the muzzle record at the beginning of the exposure. 
A gravity switch was constructed with the object of keeping this position 
when once found constant. It consisted of a brass rod standing vertically 
between two uprights, and a cylindrical brass weight four inches long with 
a hole through its axis to permit it to fall down the rod. Near the bottom 
of the rod are two pairs of contacts, connected to the two uprights having 
projecting springs so that the falling weight will first " make " the camera 
circuit and then the primer circuit. The time interval between is adjust- 
able by dropping the weight from different heights. When the proper 
height was found, this switch gave satisfaction. 

The gun used was a 3.2-inch B. L. field rifle. No. 56, model of 1892, and 
the service charge of 3J lb. of I. K. H. powder was uniformly employed. 
The projectiles were common shell, so selected that each weighed 13 lb. 
6 oz. 

Length of bore of gun 25.2 calibers. 

Travel of projectile in bore 21.81 " 

Powder chamber capacity 108.9 cu. ^^• 

Density of loading 0-953 15« 

For the gun two siege platforms were laid in prolongation and leveled, 
giving a suitable direction of fire out to sea. The firing was conducted 
without applying the wheel breaks, and the recoil was approximately con- 
stant at 48 ft. total, or 28 ft. on the platform and 20 ft. on the ground. 

The arrangement of screens for this work possesses some interesting 
features. A skid 12" x 12" x 15' long was placed in approximate pro- 
longation of the axis of the bore of the gun elevated at 3 degrees, being 
supported by two solid upright posts. Beyond this, shifting planks were 
placed end to end, spiked together, and supported by scantlings set into 
the ground at intervals. The first shots with the gun showed that the blast 
was not to be feared so much as anticipated. The screens were made of 
two strong, upright pieces, spiked to the sides of the skid. Along the 
straight edge of these pieces on the side towards the gun, wire nails were 
driven in at close intervals, and wire wound around the nails and stretched 
back and forth, three times being usually sufficient. These screens were 
placed at various intervals, always beginning at the muzzle of the gim itself. 
Care was taken to place the muzzle screen at a distance in front of the 
muzzle equal to the length of the projectile, so that the first screen is not 
broken until the projectile is out of the bore of the gun. 



No. I.J 



A NEW PHOTO-CHRONOGRAPH. 



69 



Figure 6 is a reproduction of the first negative obtained when the circuits 
were arranged as in Fig. 5, the first screen being at the muzzle and the 
second 40.13 ft. from the first. The record of the muzzle screen appears 
at Xx on the negative, the make at Ki, and the second break at Xj- The 
angle between the breaks can be read with considerable accuracy. It was 
measured with a large spectrometer, the circle of which is graduated 
directly to ten minutes, and with the verniers' the reading is to ten seconds. 
The plate is mounted horizontally on the turning table, and centered by 
means of the reference circles at A and B put on the plate for the purpose 
by the wires in the camera at O, Fig. i. On this plate an average of nine 
readings of the angle makes it 108° 5 '.815 ± .'444 or 108^.0969 ± .°oo74. 
The probable error shows that this angle is measured with an accuracy of 
.0068% of the whole, or of one part in 14,630. Of course the percentage 
of error depends upon the whole angle measured, but 40 ft. is a smaller 
distance than it is customary to use with other chronographs. The tuning- 
fork record shows that an angle of 294''.54 subtends just 34 waves of tuning- 
fork, seen at the CD, Fig. 6. The time of one wave being so9.4~6 ^^ ^ 
second, the angular velocity of the plate is 44i3°.42 per second. The 
velocity of the projectile is 

where s is the distance between screens, 6 the angle between breaks meas- 
ured on the plate, and <o the angular velocity. Upon substituting the 
values found, the velocity is found to be 1638.5 ft. per second. 

It was next attempted to obtain observations at several points along the 
trajectory, at regular intervals, at first fifteen-foot, then ten-foot, and 
lastly five-foot intervals were tried, to a distance of 45 ft. in each case. 
Records with all of the intervals above mentioned were successfully ob- 
tained, and in Fig. 7 is reproduced a negative taken, showing five-foot 
intervals beginning at the muzzle and extending to a distance of 45 ft. 

It is interesting to note that when the interval between the screens is so 
small as 5 ft., it is necessary to place the device to establish the current 
before the previous screen, as the projectile moves four or five feet while 
the jaws of the springs are coming together. Measurements on this plate 
give the following angles : — 



s 


B 


s 


9 


5 


13° 49. 29 


30 


82*^ 28'. 25 


10 


27" 19'.29 


35 


— — 


15 


40^ 53'. 79 


40 


110^^ 10'. 46 


20 


54^ 3r)'.00 


45 


123^ 50'.8S 


25 


6S° 24'. S3 







70 ALBERT C CREHORE AISTD GEORGE O, SQC/IER, [Vol. III. 

The relative velocities calculated from these angles considering the 
muzzle screen as the first one in each instance, are 



s 


V 


s 


V 


2.5 


1599^4 


15.0 


1608.3 


5.0 


1610.8 


17.5 


— 


7.5 


1621.7 


20.0 


1605.3 


10.0 


1619.5 


22.5 


1606.5 


12.5 


1615.7 







If the five- foot screen is taken as the first, the same angles give the 
following velocities : — 



s 


V 


s 


V 




2.5 


1599.4 


17.5 


1610.5 




7.5 


1637.5 


20.0 


— 




10.0 


1633.0 


22.r 


1606.0 




12.5 


1626.8 


25.0 


1607.3 




15.0 


1619.7 







These tables are exhibited graphically in Fig. 8, which shows that the 
velocity increases outside of the bore of the gun up to a certain maximum 
point at a distance of six or seven feet from the 
muzzle. This same effect is exhibited on all the 
negatives obtained with five-foot intervals, and 
they all compare well together. The increase 
is so great, about 2.\% of the whole, that one 
cannot attribute the increase to errors. 

The reason why the points do not lie on a 
smooth curve is of course because of errors, but 
it is more probable that the error arises from the 
fact that the projectile does not strike consecu- 
tive screens exactly alike, and thus the intervals 
are not precisely five feet, than that they are due 
to the measurement of the angles on the nega- 
tives. So it appears that there is now greater 
accuracy in measuring the time interval than in 
Fig. 8. finding the exact distance. 



19i0 










1 


r' 








1630 




v\ 






^ 


ih 








1620 

V 


F 


V 


\ 






/r 

9 


V\ 


\ 




-f 








^ 


J- 


Mutt 

6 8 I 


'2 u 


rtft4t. 

16 ^e : 


I22?4 




No. I.] 



LAIV OF FLUID PRESSC/RE, 



71 



Experimental Demonstration of a Law of Fluid Pressure. 

By W. J. Humphreys. 

IT is well known that the pressure at any point of a perfect fluid is equal 
in all directions, whether the fluid be at rest or in motion, and that this 
equality of pressure is also true of viscous fluids, provided they are at rest. 
Of course it can be rigidly demonstrated mathematically that this is a con- 
sequence of the inability of fluids to sustain a tangential stress, but such a 
demonstration is beyond the grasp of the average student when he first 
begins the study of physics ; consequently 
an experimental demonstration becomes use- 
ful. The piece of apparatus here described 
for demonstrating this principle is easily 
manipulated and is well adapted to class- 
room work. 

It would be easy to criticise several experi- 
ments suggested by elementary text-books 
for the demonstration of this law of fluid 
pressure, but I will simply say that one of 
the best I have seen is that of exhausting 
a pair of Magdeburg hemispheres, and then 
showing that they are held together in what- 
ever direction they be turned. This shows 
that there is pressure in every direction, but 
does not show how much in any direction. 

The piece of apparatus which I constructed 
for this purpose consists of a single Magde- 
burg hemisphere A (see figure), to which 
is connected a stopcock C for exhausting air, 
and a spring dynamometer F for measuring 
the pressure exerted. As shown in the 

illustration, a thin but strong rubber diaphragm D is made fast, by means 
of a metallic rim E^ to the top of the hemisphere. To the center of 
this diaphragm is fastened a metallic button B to which is hoSked the 
rod that communicates with the spring dynamometer. The dynamometer 
can be placed at any desired distance from the diaphragm and held in 
that position by means of the rack and catch K, The apparatus was so 
constructed that it was easy to remove an old and put on a new diaphragm, 
though occasion for this seldom occurred. 

The experiment is performed as follows : Place the dynamometer as near 
the diaphragm as it will go, exhaust the air from the hemisphere by means 




i 



72 ^. y. HUMPHREYS, [Vol. in. 

of the stopcock to any degree desired (this can be done sufficiently well 
by the mouth) , and then by means of the handle H raise the dynamometer 
to a suitable position and fasten it with the rack and catch. The index P 
will now show a certain pressure which will remain constant, no matter in 
what direction the rubber diaphragm be turned, up, down, or sidewise at 
any angle ; thus experimentally demonstrating that within the limits of 
delicacy of the apparatus the pressure of the atmosphere — and presumably 
of other fluids — is at any place equal in all directions. Evidently appa- 
ratus of the same general plan could be used to demonstrate this law in the 
case of liquids. 

I used this device in the physical lecture room of the Miller Manual 
Labor School, Crozet, Va., for several classes, and it always gave entire 
satisfaction. 

Johns Hopkins UNrvERsrry, April, 1895. 



^ 



No. I.] NEIV BOOKS. 73 



NEW BOOKS. 

Die Principien der Mechanik in neuem Ziisatnmenhange dargestellt. 
Von Heinrich Hertz. 8vo, pp. xxvii, 307. Leipzig, Johann Ambro- 
sius Barth, 1894. 

The work before us possesses a melancholy interest, not only as being 
the crowning labor of the short life of its gifted author, but as being pre- 
ceded by a most sympathetic and appreciative preface by his great master 
Helmholtz, who was so soon to follow his favorite pupil. To have been 
the favorite pupil of Helmholtz was in itself no small honor, but to have 
justified the expectations of the master with such completeness as was the 
case with Hertz, was indeed extraordinary. Helmholtz, great and clear- 
sighted as he was in all the domains of knowledge that he touched, can 
hardly be said to have founded a school, for although he had many clever 
and appreciative pupils, few seem to have been so imbued and penetrated 
with the ideas of Helmholtz as to have followed in the creative work char- 
acteristic of him. The single exception is Hertz. The whole work of 
Hertz shows the influence of Helmholtz. The philosophical consideration 
of fundamental principles, the frequent introduction of metaphysical con- 
siderations, the logical and systematic deductions from the premises, and 
the exceedingly general nature of the principles enunciated, all bear the 
stamp of the master. This is true in a large degree of the present work, 
although the manner and matter are highly original. 

In a preface of fifteen pages Helmholtz gives an account of the life of 
Hertz, and a review of the development of the science to which he made 
the greatest contributions. What Helmholtz thought of Hertz may be 
gathered from the following quotation : " Favored with the rarest gifts of 
mind and character, in his too short life he gathered a full harvest of almost 
unhoped-for fruits, for which during the preceding century many of the 
most talented of his fellow-scientists had striven in vain. In ancient 
classical times it would have been said that he had fallen a sacrifice to the 
envy of the gods. Here Nature and fate seemed to have favored in a 
quite uncommon manner the development of a mind which united in itself 
all the faculties necessary to the solution of the most difficult problems of 
Science. ... I myself felt this grief deeply, for among all the pupils that 
I have had I might consider Hertz the one who had penetrated most 



74 NEW BOOKS. [Vol. III. 

deeply into my own circle of scientific thoughts, and upon whom I might 
place the surest hopes for their further development and enrichment." 

When Hertz finished school at the age of eighteen, he chose the profes- 
sion of an engineer, being, with characteristic modesty, somewhat doubtful 
of his success should he take up theoretical science. This doubt lasted two 
years, after which he began the study of physics under Helmholtz at Berlin. 
The latter immediately recognized his talent, and at the end of the second 
semester, having to propose the subject for a prize in physics, chose a sub- 
ject in electrodynamics, in the hope that Hertz would interest himself in 
the subject and attack it with success. This subject was no less than a 
research intended to throw light on the critical question of action at a dis- 
tance, as opposed to action from particle to particle. The various theories 
of Weber, Ampere, Neumann, Riemann, Grossman, and Clausius are char- 
acterized by Helmholtz as a " brilliant bouquet of hypotheses, very little 
* Ubersichtlich ' in their consequences, so that the domain of electrodynamics 
had at that time become a pathless desert." Weber had undertaken to 
remove certain difficulties in his theory by the hypothesis that electricity 
had a certain amount of inertia. To find out whether this was true was the 
problem attacked by Hertz. By means of experiments on extra-currents 
in double coils he showed conclusively that not more than one-twentieth of 
the extra-current could be due to inertia of electricity. But Hertz was not 
satisfied with this result. Recognizing that the induction in straight wires 
could be calculated with much greater accuracy than in coils with many 
turns, he experimented with wires forming two rectangles, and thus reduced 
the effect that might possibly be attributed to inertia to less than one two- 
hundred-and-fiftieth of the whole. Further experiments were still more 
convincing as to the untenability of Weber's hypotheses. It is easy to see 
how these experiments were the beginning of Hertz's study of electrical 
theory. Helmholtz, the first convert and aposde in Germany of the 
Faraday-Maxwell theory opposing action at a distance, considering the 
experimental demonstration of the existence of a magnetic effect due to 
the changes of dielectric polarization in an insulator (Maxwell's displace- 
ment currents), to be a crucial point in the decision between the rival 
theories, made it the subject of one of the great prize contests of the 
Berlin Academy of Sciences. The result was his now famous research on 
High Frequency Electrical Oscillations, and the experimental proof of the 
correctness of Maxwell's theory, making it highly probable that luminous 
vibrations are of an electromagnetic character. 

After the preface by Helmholtz comes the author's preface, in which he 
states the object of physics to be the explanation of all natural phenomena 
by means of the simple laws of Mechanics. What these laws are is, how- 
ever, not a matter of common agreement. It is the aim of the author to 



No. I.] NEIV BOOKS. 75 

embrace all the laws of mechanics, including Newton's fundamental laws 
of motion, in some principle that shall be so simple as to be intrinsically 
probable, the truth of which shall be justified by its agreement with experi- 
ence. Helmholtz had proceeded in such a manner in his work on the 
Principle of Least Action, starting with the assumption of Newton*s laws 
and Hamilton's principle. The same ideas appear in the work of J. J. 
Thomson on the applications of Dynamics to physical phenomena. Hertz, 
however, proceeds in a different manner, the reason for which he explains 
in a long philosophical introduction. In this he discusses with great logical 
acumen the necessary and sufficient properties that must be possessed by 
any " image " that shall represent to us the true essence of the phenomena 
of motion, and of such images he considers in detail three, in historical 
order. In the first system the conceptions supposed given a priori are the 
ideas of space, time, mass, and force. Force is introduced as the cause of 
motion, existing before and independently of the motion. Kinematics con- 
nects the ideas of time and space, and Galileo's conception of inertia gives 
a relation between space, time, and mass. In Newton's laws appear all 
four fundamental conceptions, and the principle of d'Alembert gives the 
general statement of all that is predicated of them. The rest is simply 
deduced by logical processes. While the system here treated is perfectly 
logical, and is therefore a satisfactory " image," the conception of force has 
given rise to a number of difficulties, chiefly of a metaphysical nature, and 
has in recent times been the subject of vigorous attacks. 

The second image treated is the far more modern one in which the 
notion of energy appears as a fundamental concept instead of that of force. 
Although this system has been frequently advocated, there exists no text- 
book of* mechanics which follows it out completely, introducing the idea of 
energy before that of force. In this system the two conceptions of space 
and time have a simple mathematical character, while the other two, mass 
and energy, are introduced as given indestructible physical entities. In 
order to connect all four, there is needed besides the principle of conserva- 
tion of energy a further principle, which may be taken as that of Hamilton. 
This would give as the sole result of experience needed the principle that 
every system of natural masses moves as if it had the task set of reaching 
given positions in a given time in such a manner that the mean difference 
between kinetic and potential energy throughout the motion should be as 
small as possible. This second image avoids the difficulty of the first of 
speaking of things of whose nature we know little or nothing, and which 
have also little influence on the result. For in speaking of forces we must 
ultimately come to speak of forces between individual molecules and atoms, 
of which our notions are by no means directly derived from experience. 
The following quotation may possibly impress others as agreeably as it did 
the reviewer. 



76 ^E^' BOOKS, [Vol. III. 

"It affected almost painfully so rigorously thinking an investigator as 
Gustav Kirchhoff, to see atoms and their vibrations thrust into the midst 
of a theoretical deduction without dire necessity." Such a statement is 
refreshing in these days when every student, nay, almost every dynamo- 
tender, talks so glibly of molecules and of the ether. " The arbitrarily 
assumed properties of the atoms may be without influence on the final 
result, the latter may still be correct. Nevertheless, if the details of the 
deduction itself are in a large degree presumably false, the deduction is 
illusory. The older conception of physics leaves us here hardly any 
choice or mode of escaping the difficulty. On the contrary, the theory of 
energy and our second image of mechanics possess the advantage that 
there appear in the statement of the problem only things directly appre- 
ciable by experience, parameters, or arbitrary co-ordinates of the bodies 
considered ; that the discussions proceed with the help of these quantities 
in finite and complete form, and that the final result can be immediately 
translated back into terms comprehensible by experience." 

Hertz does not, however, adopt this second, or energy-image, partly 
because, like any other, the principle of Hamilton is not of perfect univer- 
sality, partly because the principle does not possess the simplicity of enun- 
ciation requisite for a fundamental principle, as well as for more or less 
metaphysical reasons. The third image, to which the present work is 
devoted, differs from the others in that it contains but three fundamental 
conceptions instead of four. These are space, time, and mass. The fact 
that these three were sufficient was made prominent by Kirchhoff in his 
philosophical treatment of mechanics in his celebrated text-book. In order 
to fill the apparent gap without introducing a new conception, Hertz sup- 
poses that in addition to the masses that are perceived by our senses, there 
act certain " concealed " masses, which are recognizable only by the effect 
that they produce on ordinary bodies. Such bodies are the ether. Lord 
Kelvin's and Maxwell's vortical fluid, and the matter treated by Helmholtz 
in his work on " Cyclic Systems." This hypothesis has the advantage not 
only of eliminating all mysterious forces from mechanics, but also of pre- 
venting their entrance at all. In carrying out this principle, Hertz makes 
the further supposition that the connections between parts that act upon 
each other are rigid, thus returning to the idea that preceded that of action 
at a distance. Unfortunately, as Helmholtz remarks. Hertz does not give 
examples to explain how he conceived such intermediate members between 
bodies not in contact, and it will probably require a large expenditure of 
physical imagination in order to explain even the simplest cases of physical 
forces. Physicists of such extraordinary intuitional powers as Maxwell and 
Kelvin would probably have no difficulty in so doing. It is comforting to 
know that Helmholtz himself obtained more satisfaction by the ordinary 



No. I.] NEW BOOKS, 77 

methods of considering the facts as represented by the differential equations 
of physics. 

The first half of the body of the book, treating of kinematics, concerns 
itself merely with definitions and terminology. This is very carefully worked 
out, and although appearing very abstruse, is found, when the idea of the 
author is once seized, to be of considerable simplicity. Ideas generally 
considered as applicable to the motion of a point are generalized in such a 
manner as to apply to systems composed of any number of material points. 
The length of a displacement of a system is defined as the quadratic mean 
(square root of mean square) of the displacements of all its mass-points, 
every particle of mass m being supposed in taking the mean to consist of 
m separate mass-points. It is easily shown that the distance or displace- 
ment between two positions of a system is always less than the sum of the 
distances of the two from a third, and that consequently it is possible to 
represent three such distances by the sides of a triangle. Any displacement 
may thus be considered as the resultant of two others, and may be represented 
by a single vector. This vector does not, of course, give us the position of 
each point of the system, but it has a definite relation to the configuration 
of the system. We may, by means of the triangle, define the difference in 
direction between two displacements. In particular we may define the 
amount and direction of infinitesimal displacements, and proceeding from 
one configuration to another we may consider the path of a system. The 
path is defined as straight if its direction is constant, which will be easily 
seen to involve the condition that the paths of every particle of the system 
are straight in the ordinary sense. If the path is not straight, we may 
define its curvature as the rate of change of direction per unit length of 
p;^th traversed. An element of a path is straighter than another if its curva- 
ture is less. A straightest element of path is one that is straighter than all 
other possible elements having the same position and the same direction. 
A path all of whose elements are straightest elements is called a straightest 
path. 

These definitions being premised, we may state the fundamental princi- 
ple enunciated by Hertz, the consequences of which are elucidated in the 
second half of the book treating of dynamics. 

Every free system persists in its state of rest or of uniform motion in a 
straightest path, 

Systema omne libentm persevarare in statu suo quiescendi vel movendi 
uniformiter in directissimam. 

This law, which is merely a generalization of Newton's first law by the 
changes necessary in substituting the word "system" for " material point,** 
contains in itself all three laws. From these are immediately deduced the 
integral of energy, and Hamilton's principle. As all the definitions have 



78 ^EW BOOKS. [Vol. III. 

been free from reference to any particular system of co-ordinates, the equa- 
tions of motion are obtained in generalized co-ordinates in the form given 
by Lagrange. The motion of systems under geometrical constraint is then 
treated, and finally the motion of systems under the action of forces. Force 
does not here appear as a fundamental notion, but simply as a sort of 
analytic expression for the amount of deviation of a system from the 
straightest path, accompanied by an equal and opposite deviation of an- 
other system. This conception is after all not different from that of Kirch- 
hoff, but the enunciation of it is here extremely precise and lucid. 

The aim and general method of the work before us have now been 
described. There follows a treatment of the important case of cyclic 
systems, following Helmholtz, concealed cyclic motions, illustrating the 
fundamental supposition, and finally treatment of discontinuous motions. 
Whether the method of deducing the fundamental equations employed by 
our author is preferable to the usual methods may be considered doubtftil 
— it seems to be merely a question whether we shall take a little more or 
less for granted. The present reviewer must confess that he feels rather 
content to be satisfied with the representation of the physical facts by the 
equations than with an attempt to reconcile them with va simple principle, 
and to confine his flight far below the upper air of metaphysics ; and he is 
glad to be supported by the opinion of Helmholtz already quoted. How- 
ever this may appear to others, the work of Hertz shows that it is not 
without reason that in German universities natural science finds its place in 
the philosophical faculty, and we can but admire the clear insight and the 
logical exposition of a system, which evince the treatment of a most 
difficult subject by a master mind. 

Arthur G. Webster. 



Elementary Lessons in Electricity and Magnetism (New Edition). 
By SiLVANUS P. Thompson, F.R.S. 8vo, pp. XV4-628. Macmillan & 
Co., 1895: 

An elementary text-book in science which has lived fourteen years, and 
which has had a sale of a number of thousand copies each year, must be a 
remarkable book, deserving the attention of all teachers. The book before 
us is no less than this, and in a completely revised edition will be welcomed 
by all who are interested in technical education. This book has no doubt 
been used as the first step in the electrical instruction of a majority of 
American technical graduates who are now employed in the electrical 
industries, and numberless men holding responsible offices will remember 
with interest their study of " Thompson's Lessons " during one of the terms 
of their sophomore year at college. 



No. I.] NEW BOOKS. 79 

The new edition of this book bids fair to be as useful as the old. It has 
been brought fairly up to date, and on the whole has been made to conform 
very well to our present methods of scientific thought. The book has 
more and possibly better competitors for the attention of students and 
teachers than formerly, but none are so clear and satisfactory for the 
reader. There are one or two text-books that probably make a better 
foundation for the sophomore lectures and laboratory practice in electricity 
and magnetism which are presented to the students of our technical schools 
(Chapter XVI. of the revised Daniell's Physics, for instance) ; but, while 
these give a better preparation for the advanced work of the technical 
student, they are, as a general rule, too heavy for the less strongly prepared 
general student or the undirected reader. The reviewer is not a teacher 
of physics, but he feels safe in saying that Thompson's Lessons has no real 
rival as a text-book in the general course in college, or for a place in the 
hands of the general reader who wishes to obtain a knowledge of electricity 
and magnetism. 

For elementary course instruction, the additions which have been incor- 
porated in the new edition relating to dynamo calculations, working of 
alternators, theory of transformers, etc., are of questionable utility, but for 
the general reader these articles must be of considerable interest, and may 
possibly be useful. It is always possible for a reviewer to find defects in a 
book, especially if he is inclined to resort to special pleading, but the 
defects in the book before us are amply compensated by virtues. It is 
unfortunate that the author's proof reading was not more carefully done, 
especially with a view to bringing the phraseology of the old portions of 
the book into harmony with the more modern forms of the new. Many 
slips in spelling might also have been corrected ; but the most prominent 
fault of the book is to be found in its definitions, which may sometimes be 
misleading to an inexperienced student. This is particularly unfortunate 
in a beginner's book, as a young student is readily led into error or thrown 
into perplexity by statements which are perfectly plain to a more experi- 
enced reader. The use of the erroneous term "virtual" instead of the 
formally adopted term " effective," when referring to alternating volts and 
amperes, must be strongly criticised. Alternating current phenomena are 
such a stumbling-block to the average student throughout his studies, that 
it is especially desirable to avoid any artificial addition, however small, to 
the difficulties which may be caused by a double use of terms, and it is to 
be hoped that the word "virtual" will be replaced in the plates by 
" effective " for the benefit of future reprints. 

The mechanical execution of the book is carried out in the excellent 
style for which the publishers are justly noted. 

DuGALD C. Jackson. 



8o NEIV BOOKS. [Vol. III. 

Steam and the Marine Steam Engine, By John Yeo. 8vo, pp. 
xiv-l-196. Macraillan & Co., 1894. 

This work is professedly intended for naval officers and for students of 
engineering in the earlier part of their training. 

With this end in view, the size of the book has been kept within small 
limits, and the evident purpose has been to give, in plain, readable style, 
the salient features of modern marine engineering practice. 

Judged from this standpoint, the work seems to have been conscientiously 
done, and the selections from the broad field of engineering practice have 
generally been made with care and judgment The treatment of propulsion 
and resistance is, however, exceptionally brief, the latter being dismissed 
with less than one page, presumably on account of its less vital connection 
with the main subject in hand. 

The illustrations are numerous and excellent, and the make-up of the 
book is in the usual good style of the publishers. 

On the whole, there seems to be little to criticise adversely, and much to 
commenfl, when viewed from the standpoint of the author's avowed pur- 
pose. Viewed more broadly, however, the extent of the field of usefulness 
for such works may be fairly called in question. No book of 200 octavo 
pages can satisfactorily present even the leading features of so broad a 
subject as that here dealt with ; and, while such works may serve as an 
introduction to more extended study, or for those who only wish a general 
outline of the subject, they must be laid aside early in the student* s course 
to give place to sources of more extended and exact information. 

W. F. DURAND. 



Volume III. September-October., r8g§. Number 2. 



THE 

PHYSICAL REVIEW. 



A STUDY OF THE POLARIZATION OF THE LIGHT 
EMITTED BY INCANDESCENT SOLID AND LIQUID 
SURFACES.! 

By R. a. Millikan. 



Introductory, 

IN spite of the prodigious activity of physicists during the first 
three quarters of this century in attacking the problems of 
reflection, refraction, and polarization in all their different phases, 
both from the side of experiment and that of mathematical theory, 
the problem of polarization of light by emission seems to have 
received comparatively little attention. Although the fact that 
incandescent solids and liquids emit, at oblique angles of emer- 
gence, partially polarized light, was discovered more than seventy 
years ago, it does not appear even to-day to be very generally 
known. Few, even of the more complete text-books on physics, 
make any mention of the fact. Verdet, in his Optigjie, published 
in 1870, devotes a short paragraph to ** Polarization by Emission," 
in which he says that "there exists upon the subject but a small 
number of experiments, due mainly to Arago." The summary 
of these experiments, which he subjoins, reveals none whatever 
that are quantitative. Since the time of Verdet, no one, so 

^ A paper presented to the New York Academy of Sciences, April, 1895. 

81 



$2 DR. R. A, MILUKAX, [\'OL. IIL 

far as I am able to discover, has made any careful or elaborate 
study of the phenomenon with a view to ascertaining its gener- 
ality, verifying or disproving Arago's assumption as to its cause, 
or classifying different substances with reference to their power 
of prwiucing the phenomenon in greater or less degree. 

Since even a hasty examination reveals the fact that different 
substances emit light of widely different percentages of polariza- 
tion, it appears that a study of the relations of different bodies 
in this respect ought either to add something to our knowledge 
of the optical properties of the substances considered, or else, if 
this particular property is deducible from the already known 
properties, as Arago assumed it to be, its relation to these prop- 
erties ought to be definitely proved. This investigation has 
therefore been undertaken for the purpose, first, of making a 
somewhat wide range of qualitative experiments upon the nature 
and generality of the phenomenon ; and, secondly, of subjecting 
Arago's explanation of the cause to the test of comparison with 
carefully determined experimental quantities. 



II. 

Historical Review. 

The simple facts of polarization of light by emission can best 
be observed, and in fact were first noticed, upon platinum. If 
a sheet of that metal be heated to incandescence in the flame of 
a Bunscn burner, and the emitted light examined by means of a 
Nicol prism, or any other instrument adapted to the detection 
of partially polarized light, it will be observed that when the ex- 
perimenter is viewing the surface normally the emitted light 
exhibits no trace whatever of polarization, but as the instrument 
is inclined so as to receive rays emerging obliquely from the 
surface, the light begins to show evidences of polarization in 
a plane perpendicular to the plane defined by the normal and 
the emerging ray. If this plane be called the plane of emission, 
and the angle included between these two directions the angle of 
emission^ the complete phenomenon may be roughly described by 



No. 2.] POLARIZATION BY EMISSION". 83 

saying that the polarization increases as the angle of emission 
increases, and becomes, in the case of platinum, exceedingly 
strong as the emission angle approaches ninety degrees. 

The announcement of this fact, and the consequent overthrow 
of the common belief that light coming immediately from self- 
luminous bodies is always natural, was made first in 1824 by 
Arago. In a report made in that year to the Royal Academy 
of Sciences (see Annates de Chemie et de Physique (i) 2j^ p. 
89) he announced that he had some time before made a series 
of experiments upon the light which emanates from incandescent 
bodies. "He found that if the bodies are solid or liquid this 
light is partially polarized by refraction when the rays observed 
form with the emitting surface an angle of a small number of 
degrees. As for the light of an ignited gas it presented under 
no inclination traces of sensible polarization." From these ex- 
periments he drew the conclusion " that a considerable portion of 
the light which enables us to see incandescent bodies is produced 
in the interior and at depths which are not yet completely deter- 
mined." " Even when the surface of a solid or liquid was not well 
polished," Arago still found that he " was able to detect evident 
traces of polarization." The substances upon which he experi- 
mented and from the observation of which he drew his conclusion 
were only four in number, viz. — solids, wrought iron and platinum ; 
liquids, molten iron and glass (see Astronomie Populairc^ II., p. 
103). He made no quantitative measurements, nor even used an 
instrument which was capable of indicating roughly amounts of 
polarization. His polariscope consisted of a single quartz crystal 
cut perpendicularly to the optical axis, and a crystal of Iceland 
spar. The latter produced a double image of an opening in a 
diaphragm placed just beyond the crystal of quartz. The two 
images were of course colored when the light was polarized and 
uncolored when it was natural. 

Arago applied the results of his experiment to the determina- 
tion of the character of the sun's surface. Being unable to detect 
any trace of polarization in the light emitted by the outer edge of 
the sun's disk, he drew the well-known conclusion that the surface 
of the sun can be neither liquid nor solid, but must be gaseous. 



84 DR, /?. A, MILLIKAN'. [Vol. III. 

After the discovery of the polarization of heat, and the con- 
struction of an instrument by Melloni for its detection and 
measurement, Provostaye and Desain examined the heat rays 
emitted by luminous platinum and found that they, like the light 
rays, were polarized in the plane perpendicular to the plane of 
emergence. Their experiments were few in number and confined 
entirely to platinum. In 1866 Magnus extended this method of 
experiment to obscure heat rays, making quantitative measure- 
ments upon the heat emitted at the temperature of 100° C, and at 
an angle of 35°. His experiments embraced the following list of 
substances : Paraffine, glycerine, white wax, melted calophony, 
rubol, black glass, transparent glass, quicksilver, aluminium, 
copper, and tin. For these substances he found a polarization 
at 35° ranging from 5 per cent to 27 per cent. He drew the 
conclusion that obscure heat, like light, must undergo refraction 
in emerging from the surface of the radiating body. 

Verdet, in the paragraph upon polarization by emission pre- 
viously referred to, while stating that little has been done in the 
investigation of the subject, gives the same explanation of the 
phenomenon as that first offered by Arago. He says that " it is 
due to the fact that it is not alone the surface molecules which 
radiate light ; those of the interior layers also radiate, at least 
to a certain depth; and the rays emitted by the interior mole* 
cules undergo refraction at the surface." Since the time of 
Verdet, I believe no one has made any experiments upon the 
subject except Violle, who has a brief note in the Comptcs Rcndus 
of 1887, Vol. 105, p. Ill, in which he states that, while making 
some other experiments upon molten silver, he took occasion to 
measure the percentages of polarization in the light emitted by 
that substance at various incidences. He plotted the curve of 
these percentages and found that it was very well represented by 

the empirical formula p^ — (\ —cos /') ( i -|-cos 75° -f - ], where/, rep- 
resents the ratio of a polarized light to the whole light in the 
emitted beam, and i the angle of incidence. 

Assuming, then, the phenomenon to be due to refraction, he 
argues that the equality of the amounts of polarization in the 



\ 



k. 



No. 2.] POLARIZATION BY EMISSION, 85 

reflected and refracted beams would require that ep^—fr^ where e 
is the proportion of the whole light emitted, r the proportion 
reflected, /, the proportion of polarized light in the emitted beam, 
and /, the proportion of polarized light in the reflected beam. 
Then, since the whole light is either emitted or reflected, ^-fr= i, 

and the formula r— —^ — immediately follows. Taking the experi- 
A+A 

mental values which have been determined for /^ by reflection at 
ordinary temperatures, he finds that his own results for /„ when 
substituted' in this formula, give a uniformly high reflecting power 
for molten silver ; a result which agrees with the known properties 
of ordinary polished silver. This forms the nearest approach to a 
verification of Arago's assumption which has yet been given. 

Such is the extent of the work which has thus far been done 
upon polarization by emission. 



III. 

Discussion of Aragos Explanation, 

The explanation of Arago and Verdet is as yet the only one 
which has been offered to account for the phenomenon. This 
explanation does not rest upon careful experimental proof, and, 
furthermore, there seems to be considerable reason for doubting 
its correctness. According to that explanation the light which 
comes to the eye from the surface particles is natural light ; but 
mixed with this unpolarized light is a quantity of light which 
has worked its way up from uncertain depths, has undergone 
reflection and refraction at the surface, and is consequently polar- 
ized upon emergence. Aside from the intrinsic difficulty of this 
conception, the first experiments which were made in this research 
upon platinum seemed to be inconsistent with such an explana- 
tion ; for, when a well polished platinum strip was heated to 
incandescence by means of an electric current and the glowing 
surface examined by means of a double WoUaston prism, the 
polarization was found to be so nearly complete for angles in 
the neighborhood of grazing emergence that one of the images 



86 DR. R. A. M/LLIKAN'. [Vol. III. 

almost disappeared. But, since platinum is known to be altogether 
opaque, except in the case of exceedingly thin laminae, it would 
seem as though the surface molecules must play a considerable 
part in the luminosity of the glowing metal ; so that, even if the 
assumption were made that the laws of reflection and refraction 
would require complete extinction of the ray polarized parallel 
to the plane of emergence, there still ought to be a considerable 
amount of light emitted in this plane from the surface molecules ; 
at least, a sufficient quantity to prevent so nearly complete extinc- 
tion as experiment showed to exist for angles of 88 or 89 degrees. 

The only apparent method of reconciling the facts with Arago*s 
explanation was to assume that the opacity of the platinum was 
greatly diminished by an increase in its temperature. And yet, 
such experiments as were made to determine whether or not 
this was the case, gave only negative results. The thinnest 
sheet of platinum which was capable of being heated to incan- 
descence without melting, was placed in the focus of a powerful 
beam of light from an arc lantern, the beam having been first 
polarized by transmission through a Nicol. The plane of the 
glowing platinum being perpendicular to the beam, the light 
emerging normally on the other side of the platinum was exam- 
ined by means of a delicate polariscope. No trace of polarization 
was detected. Neither could the outlines of the focus be dis- 
tinguished on the side of the platinum away from the lantern. 
The sheet of platinum employed was evidently just as opaque 
as at a lower temperature. 

This difficulty of accounting for the extreme polarization no- 
ticed at large angles of emergence appeared to be considerably 
diminished if another cause for the phenomenon were assumed 
than that given by Arago. 

According to the conclusions of Fresnel, Cauchy, Stokes, Mas- 
cart and most of the advocates of the elastic solid theory of 
light, the direction of vibration of the ether particles in plane 
polarized light is perpendicular to the plane of polarization. It 
would follow that the light emitted at large angles by platinum 
vibrates mainly in the direction of the normal to the surface. 
It is not unnatural to suppose that at the boundary between 




No. 2.] POLARIZATION BY EMISSION. 87 

very dense and very rare media, like platinum and air, there 
may be less resistance to vibration in a direction away from the 
surface than in a direction parallel to the surface, and therefore 
that the light emitted is composed mainly of vibrations in a 
direction normal to the surface. If this were the case, the light 
emitted normally would be unpolarized, while that emitted at 
oblique angles would be polarized in the plane perpendicular to 
the plane of emission. Furthermore, the polarization would in- 
crease with the angle and might be very great at large angles, in 
case the difference in density between the two media were very 
great — conclusions all of which are in accordance with the facts. 
In view, then, of the inability to account, by Arago's assumption, 
for the extreme polarization at large angles of emergence, and in 
view of the plausibility of the other explanation, the following 
qualitative experiments were made in order to determine with 
more certainty the nature of the phenomenon. 

IV. 
Qualitative Experiments, 

The object of this part of the research was : — 

(i) To make certain that the property of polarization is due to 
the incandescent body itself, and is not caused by the refraction 
of the light as it passes through the layers of air of varying 
density which rest upon the luminous surface ; and, 

(2) To make observations upon as wide a range of substances 
as could be made to emit light without combustion, in order to 
ascertain whether any substance could be found which does not 
possess the characteristic, and also in order to determine in a 
general way the relations of different bodies with reference to 
this property. 

For these purposes two instruments were employed ; the first, 
a polariscope similar to that of Arago, save that the simple quartz 
crystal was replaced by a bi-quartz plate, and the crystal of calc- 
spar by a double Wollaston prism. This is the same instrument 
which was afterwards used by Arago in his polarimeter, and it 
has an advantage over the first form in that the two colors to 



88 DR. R, A, MILUKAAT. [Vol. III. 

be compared are brought into immediate juxtaposition. It is 
delicate to the extent of detecting a polarization of about 3 per 
cent (as was shown by succeeding experiments), when white light 
is under examination. When the light to be tested is mono- 
chromatic, as was the case in some of the following experiments, 
the second form of polariscope was found to be preferable. 

In this instrument the bi-quartz is replaced by a cube of glass 
which has been subjected to strain in cooling. A Nicol also 
takes the place of the Wollaston prism of the first polariscope. 
The glass being in the state of strain, is doubly refracting and 
exhibits with polarized light the familiar dark or light cross which 
is characteristic of doubly refracting crystals, when cut perpen- 
dicularly to the optic axis and viewed by convergent light. With 
this instrument a polarization of two or three per cent could be 
easily detected, and it had the further advantage of indicating 
immediately the azimuth of the plane of polarization. Also, by 
careful observation of the distinctness of different parts of the 
figure it was possible, after a small amount of practice, to esti- 
mate with considerable correctness the degree of polarization. 

I. In all experiments which have been previously performed 
upon this subject, 'the white-hot body has been in immediate 
contact with the air. The emitted light was therefore obliged 
to pass through layers of air of varying density before it reached 
the eye of the observer. That the light might thus suffer 
a large number of refractions between the incandescent body 
and the eye, and so be endowed with the property in question, 
seemed entirely possible. It was therefore necessary to make 
some experiment in order to determine whether or not this was 
the entire or partial cause of the phenomenon. For this purpose 
the contrivance shown in Fig. i was employed. A strip of 
platinum foil A about 4 cm. in length and 5 mm. in width was 
attached to the platinum and copper wires B and C. The former 
was sealed into the glass tube Gy and the latter was passed 
through the cork F which closed the other end of the tube. 

The instrument was first sealed with wax and then connected 
with the air pump by means of the small tube Z>, and with a 
strong electric current by means of the wires B and C Care 



No. 2.] POLARIZATION BY EMISSION", 89 

was taken to place the platinum strip as near the axis of the 
tube as possible, in order that light emitted by it might pass 
normally through the sides of the tube. Otherwise polarization 
would have been caused by the passage of the beam through the 
glass itself. The tube being exhausted until the gauge showed 
a pressure of only four millimeters, the current was turned on 
and the glowing strip examined by means of the bi-quartz polari- 

G 




Fig. 1. 

scope. The emitted light was still found to be polarized for 
oblique angles of emergence and did not appear to have under- 
gone any change in intensity. In order, however, to ascertain 
whether or not the effect of the air was altogether negligible, 
more delicate experiments were necessary. These will be here- 
after described. 

2. Having thus proved, that the phenomenon is inherent in 
the body itself, experiments were made upon the following sub- 
stances with results as indicated : — 

SouDS. — Metallic, 

Platinum (polished). — Polarization very strong near grazing emergence, 

but falling off rapidly as the angle diminishes. Scarcely perceptible 

at ten degrees. 
Silver. — Polarization strong, larger for small incidences than in the case 

of platinum. 
Gold. — Polarization strong; similar to platinum, but apparently less 

for large angles. 
Copper. — Polarization weak, probably due to roughening of surface 

through oxidization. 
Brass. — Polarization weak — (oxidization). 
Iron. — Polarization weak — (oxidization) . 
SouDS. — Non-metallic — transparent. 

Glass. — Polarization weak; imperceptible except at large angles of 

emergence. 
Mica. — Polarization weaker than in glass. Surface roughened by heat. 



90 DR. R. A, MILUKAN, [Vol. III. 

Solids. — Non-metallic — opaque. 

Porcelain. — Polarization similar to that produced by glass. 

Black Glass. — Polarization similar to that produced by transparent 
glass. 
Liquids. 

Molten Silver | polarization similar to that in solid state. 
" Gold J 

" Iron. — Polarization strong ; almost as strong as in molten gold. 

" Bronze. — Polarization strong; almost as strong as in molten 

gold. 

Lead. — Polarization weaker than for preceding metals. (Difficult to 

get a clear surface.) 

Zinc. — Polarization weaker than for preceding metals. 

From these experiments it will be seen, (i) that the metals 
show uniformly high percentages of polarization so long as the 
surface is non-diffusing ; (2) that none of the non-metallic sub- 
stances used produce strong polarization at any angle; (3) that 
the transparency or opacity of a substance has apparently little 
effect upon its power of producing polarization in the emitted 
light; and (4) that any cause which interferes with the perfect 
smoothness and regularity of the surface destroys in large meas- 
ure the polarization. 

V. 

Imtrument employed for Quantitative Experiments. 

In order to accomplish the second and main object of the re- 
search, it became necessary to devise some means of making 
accurate determinations of the relations of the constants of the 
partially polarized beam. The instrument which has been most 
employed for such work by previous investigators is the polar- 
imeter of Arago. This is an instrument simple enough in prin- 
ciple, but difficult in construction. Moreover, it does not possess 
a very high degree of accuracy, owing to the fact that its use 
depends upon the detection, by means of a bi-quartz polariscope, 
of the exact point at which all polarization disappears from a 
beam of light. 

Both because of this difficulty of construction and because my 
own experiments with the bi-quartz polariscope made me distrustful 



No. 2.] 



POLARIZATION BY EMISSION. 



91 




of the accuracy with which the point of no polarization could be 
determined, another form of instrument was devised for these 
experiments which is greatly superior to the Arago polarimeter in 
simplicity, and is probably more than equal to it in accuracy. The 
credit of the first conception and use of this method of measuring 
the constants of partially polarized light is due to Cornu. VioUe 
also used a similar instrument in his determinations upon silver. 

In view of the exceeding naturalness and simplicity, as well as 
the accuracy of the method, it is surprising that it was not earlier 
discovered and has not been more generally employed. Cornu's 
description of his instrument was 
published in *82 in the Assn Fran- 
qaise pour r Avancement des Sciences , 
Comptes Rendus ; but so far as I can 
discover, no reference was made to 
it at the time in any of the scientific 
journals, nor has it taken its place 
among other polarimeters in any of 
the text-books on optics. The in- 
strument as constructed and used 
for the purposes of these experi- 
ments was as follows. A rectangu- 
lar opening (?, i mm. in width and 
2.5 mm. in length, was made in a 
diaphragm H which stood a short 
distance in front of the double 
WoUaston prism A, The prism 

was rotated until the extraordinary image of the opening was 
to the left of the ordinary ; the distance of the screen from 
the prism was then adjusted until the opposite edges of the two 
images exactly coincided. A Nicol prism B, capable of rotating 
about its axis and furnished with a graduated circle and vernier 
for reading azimuth to a tenth of a degree, constituted the only 
other essential part of the instrument. A small telescope C was 
used for viewing the images of the rectangular opening O, The 
instrument was mounted upon a support (7, furnished with a 
horizontal axis at F^ about which the upper portion of the appa- 




92 DR, R. A, MILUKAN, [Vol. III. 

ratus could be revolved. The axis of the tube bearing the double 
prism and Nicol could thus be inclined so as to make any desired 
angle with the vertical. Since the two images furnished by the 
double prism consist of light polarized in planes at right angles to 
each other, the rotation of the Nicol will evidently extinguish each 
of them in turn. There will be four extinctions in the course of a 
complete revolution of the Nicol, and between any two extinctions 
there is a point for which the images, as seen through the Nicol, 
have exactly equal intensities. If now a partially polarized beam 
is under examination, and if, the plane of polarization of this beam 
being known, the principal sections of the prism are set parallel 
and perpendicular to this plane, that position of the Nicol which 
equalizes the two images, evidently defines the relation between 
their original intensities, which is also the relation between the 
constants of the partially polarized beam. 

If we let a and b represent the original amplitudes of vibration 
in the two images, then the intensities of these images are repre- 
sented by c? and H^ respectively. The proportion of polarization is 
evidently the difference between these intensities divided by their 
sum. If w is the angle which the transmitting plane of the Nicol 
makes with the direction of vibration of the more intense of the 
two beams, say cfi, then the intensities of the two images as seen 
through the Nicol will be by the law of Malus, 

c? cos^ w and ^ sin^ w. (i ) 

Hence for the position of equality we have, 

(? cos^ w = b^ sin^ w (2) 



or 



7 OIH LV / f*\ 



If we call the degree of polarization in the original beam /, 
we have 



No. 2.] POLARIZATION BY EMISSION. 93 

or, from (3), 

^ sin^w — cos^zf/ cos^^ — sin^zc; ^ ,^. 

/= -^o — ■ 2~ = = "^^s 2 ^- (S) 

Sin^Z£/ + COS^Z£/ I 

Hence, when the position of the Nicol which produces equality 
in the images has been found, the amount of polarization is imme- 
diately given by (5). 

Cornu, in discussing the instrument, shows in addition, that, 
when the principal sections of the partially polarized beam are 
not known, the degree of polarization may still be found by tak- 
ing one set of readings in any position whatever of the axes of 
the double prism, and then rotating the whole instrument through 
an angle of 90° and taking a second set of readings. The degree 
of polarization can then easily be shown to be given by the 

formula 

/=sin i^v^—w^. 

In this work, however, we are not concerned with this last 
formula, since the principal sections were always known. 

VI. 
Adjustment of the Instrument. 

Since the series of experiments here considered were all made 
upon horizontal surfaces, and since the polarization of the emitted 
light is always in a plane normal to the surface, but one adjust- 
ment of the instrument was necessary, viz. that of bringing the 
principal sections of the double prism into coincidence with the 
horizontal and vertical directions. 

This adjustment was effected in the following way. The axis 
of the tube bearing the prism and Nicol was first set, by meas- 
urement, parallel to the cross-piece DM of the supporting frame. 
The base G was then carefully leveled by means of a common 
level. The leveling of DM then brought the axis of the tube 
into coincidence with the horizontal line. The telescope was 
then focussed upon a very fine line of light reflected from the 
edge of a carefully leveled sheet of white paper placed just in 



94 DR, R. A, MILLIKAN'. [Vol. III. 

front of the rectangular opening O, Since the line joining the 
two images produced by a crystal of calc-spar is always parallel 
to the optical axis of the crystal, it follows, that, when the two 
images of the horizontal line of light form with each other an 
unbroken line, the principal sections of the crystal have the 
desired directions, and the adjustment is perfect. The line of 
light used in this case was so narrow that the adjustment could 
be made with great accuracy. This done, the crystal was per- 
manently fastened in position. Thereafter, it was only necessary, 
before each observation, to level the base of the instrument G^ 
in order to bring the principal sections of the crystal into the 
desired positions. 

In order to set the axis of the tube at any desired angle with the 
vertical, the cross-piece DM, parallel to this axis, was leveled, and 
the angle DEG, between the movable arm and the vertical support, 
was measured by means of a protractor. The zero position being 
thus determined, any desired inclination could be secured by giving 
to the angle DEG the proper value. 

VII. 

Degree of Accuracy of the Instrttmcnt, 

The great sensitiveness of the eye in detecting slight differences 
in the intensities of images of the same color when brought into 
close proximity has often been the subject of remark. Cornu 
claims that the position of equality can be determined with a 
precision that reaches -^ of a degree. My own observations would 
not lead me to attribute to the instrument so high a degree of 
accuracy. Furthermore, these observations are subject to the 
objection which attaches to all photometric experiments, that the 
sensitiveness of the eye varies greatly with the physical and mental 
condition of the observer. At times the extreme difference in 
my readings for a given set of conditions would be as high as 2\ 
degrees. Usually, however, the extreme difference was not more 
than \\ degrees. For the sake of testing the probable accuracy 
of the results which are to be given later, several sets of observa- 
tions were made upon the unpolarized light of a gas flame. The 



No. 2.] POLARIZATION' BY EMISSION'. 95 

following illustrate about the average course of the readings. The 
zero of the instrument not being known, the positions of equality 
on each side of the positions of extinction were determined : — 



Left. 


Right. 


50.5 


39.2 


50.0 


« 39.1 


50.0 


38.7 


50.4 


38.8 


51.3 


40.0 


50.0 


40.0 


51.0 


40.0 


51.1 


39.9 


50.2 


39.2 


49.5 


39.0 


50.4 


3937 




2«^ = 89.77 




w = 44.88 



Since the light from a gas flame is unpolarized, the value of w 
should have been 45°. The difference is not large, but is slightly 
greater than the maximum error ascribed to the instrument by 
Comu. The above is about an average set of readings. The 
extreme difference is 1^.8, a diflference perhaps slightly greater 
than that usually found. 

A second slight error may sometimes arise in the use of this 
instrument from the fact that the two images produced by the 
double prism do not correspond to exactly the same points on the 
luminous surface. Hence, in order that the results may be correct, 
it is necessary that the adjoining portions of the incandescent sur- 
face be exactly alike. In none of the experiments here recorded 
were the portions of the luminous surface producing the two 
images more than 3 mm. apart. Care was always taken to direct 
the instrument toward a portion of the surface which appeared to 
be entirely uniform. This error may, I think, be safely disregarded 
in all of the following cases except one, which will be mentioned 
later. 

A third remark which should be made upon the accuracy of the 
instrument is that observations for large amounts of polarization 
are less subject to error than those made upon small amounts. 
For, since the intensities of the two images compared are propor- 



96 DR, R. A. M/LUKAN'. [Vol. III. 

tional to sixflw and cos^w, the change in intensity of one of 
them will be very rapid when w is in the neighborhood either of 
zero or of 90*^. When, however, w is near 45°, the change in 
intensity corresponding to a small change of angle is comparatively 
small. Hence, when the polarization is large, and zv consequently 
either large or small, the position of equality can be determined 
with considerably greater accuracy than when the polarization is 
weak and w in the vicinity of 45°. 

The results obtained for large angles may therefore be considered 
more trustworthy than the results for small angles. 

VIII. 
Measurement of the Air Effect, 

In the qualitative experiments previously described it was ascer- 
tained that the amount of polarization was at least not greatly 
afifected by the contact of the air with the heated surface. Before 
proceeding to careful quantitative measurements it was necessary 
to determine whether or not its effect upon the phenomenon is 
altogether negligible. This could be easily done by means of the 
polarimeter. 

The sealed glass tube containing the platinum strip was again 
connected with the air-pump, and the air exhausted until the press- 
ure was about 4 mm. The current was turned on, the polarimeter 
arranged so as to receive the light emitted from the glowing surface 
at an angle of about 80°, and the Nicol turned until the images 
were brought into equality. The stop-cock was then suddenly 
turned and the air admitted. No change whatever could be per- 
ceived in the equality of the images. The experiment was repeated 
a number of times and in a variety of ways, but always with the 
same result. The conclusion was, that, if the air has any effect 
whatever upon the proportion of polarization in the beam, that 
effect is so slight as to be altogether negligible ; a result exceed- 
ingly fortunate for the purposes of this investigation, since, had 
it been necessary to work upon substances in a vacuum, the fol- 
lowing experiments would have been much more difficult, if not 
altogether impossible. 



No. 2.] POLARIZATION- BY EMISSION. 97 

IX. 
Experiments upon Uranium Glass, 

The chief difficulties which beset the investigation of polariza- 
tion by emission are, ist, the difficulty of obtaining a perfectly 
definite and regular incandescent surface with which to work, and 
2d, the difficulty of ascertaining with certainty the optical con- 
stants of any bodies at the temperature of incandescence. 

The similarity between a body emitting light by incandescence 
and a body emitting light by fluorescence was first suggested to 
me by Professor Rood. According to Tait, the phenomenon 
of fluorescence is confined mainly to the surface layers. What- 
ever the cause, then, of polarization by emission, the light coming 
from a fluorescent surface ought to be polarized in the same 
way as the light coming from glowing platinum. 

Experiment showed this conclusion to be entirely correct. 
The polarization seen in uranium glass was similar in every 
respect to that observed in incandescent porcelain, being scarcely 
discernible at any angle less than 50®, but becoming quite marked 
between 85^ and 90^, and evidently reaching a maximum at graz- 
ing emergence. 

That this polarization was not due to diffusing particles on the 
surface was certain for three reasons: i. The surface was not a 
dififusing surface except to an exceedingly small extent. 2. The 
light which exhibited the phenomenon of polarization was the 
characteristic yellowish-green light which uranium emits, and 
not the blue light which fell upon the surface. 3. The reflecting 
particles on the surface would have produced a polarization in 
the dififusing plane, i,e, in the plane defined by the direction of 
the beam which entered the instrument and the direction of the 
incident beam, which was in this case normal to the surface. 
As a matter of fact, the polarization was perpendicular to this 
plane. 

Here, then, was an instance of polarization by emission in 
which the surface was perfectly definite and at the same time 
the optical constants of the substance could be easily and accu- 
rately determined. 



98 



DR. R, A. M/LLlKAI\r, 



[Vol. III. 



Accordingly, a careful series of observations was made with 
the polarimeter. The experiments were all conducted in a well- 
darkened room, and care was taken not to allow any light to 
enter the instrument except that emitted by the uranium glass. 
In order to make the determination of the angles of emission 
convenient, the light from the lantern was thrown vertically down 




Fig. 3. 

upon the surface of the uranium glass by means of total reflection 
in a right-angled prism. The cube of glass was carefully leveled 
so that the emitting surface was always horizontal. The arrange- 
ment of apparatus is shown in Fig. 3. 

Ten readings were taken for every angle of emergence. The 
results are given in full. 



87°.5 


85^ 


9fP 


75° 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


40.5 
39.5 
39.8 
40.0 
39.0 


29.8 
29.9 
28.5 
29.0 
28.9 


42.3 
43.0 
42.5 
41.7 
40.9 


30.7 
31.2 
30.5 
30.9 
31.0 


43.0 
433 
43.8 
44.0 
43.3 


32.0 
32.5 
32.3 
32.6 
32.3 


44.5 
45.0 
44.3 
44.5 
44.5 


34.5 
35.0 
35.0 
33.5 
34.4 


39.76 


29.22 

68^.98 
J58 


42.1 
/ = 


30.86 

72^.86 
.293 


43.48 
2w = 


32.34 

75^.82 
.245 


44.56 


34.5 

79<^.06 
.191 



No. 2.] 



POLARIZATION BY EMISSION. 



99 



rP 


65^ 


50° 




i-«ft. 


Right. 


Left. 


Right. 


Left. 


Right. 






45.5 
46.4 
46.5 
47.0 
463 


35.0 
36.4 
36.5 
35.0 
36.2 


47.0 
47.2 
47.5 
48.0 
47.4 


37.0 
363 
37.5 
37.0 
36.0 


49.1 
48.9 
49.0 
50.0 
493 


38.2 
38.2 
38.9 
393 
39.0 






4634 

2w = 
/ = 


35.8 

= 82^.1 
= .139 


47.62 

2«/ = 

/ = 


36.8 

840.4 
.098 


49.26 
2«; = 


38.52 

87°.78 
.039 







The chief difficulty encountered in making these determina- 
tions was the lack of perfect uniformity in the emitting surface. 
The uranium glass, being rendered self-luminous by the beam 
from the lantern, could not have entire uniformity over its sur- 
face unless the illuminating beam was uniform in intensity, which 
was not the case. The images corresponded to points on the 
surface not more than 2 mm. apart, and yet it was found that 
the equality of the images could be sometimes disturbed by direct- 
ing the instrument toward a new portion of the field. As great 
care as possible was taken to direct the polarimeter toward such 
portions of the field as appeared to have a uniform illumination, 
and it is not thought that the error due to this cause could have 
been gfreat. 

Phosphorescent bodies were also examined for polarization, 
but the light emitted by such bodies is so weak that no definite 
results were obtained. 



\Tohe continued^ 



1235 02 



lOO E, C, RIMINGTON. [Vol. III. 



ALTERNATING CURRENTS WHEN THE ELECTRO- 
MOTIVE FORCE IS OF A ZIGZAG WAVE TYPE. 

By E. C Rimington. 

ALTHOUGH no alternate-current dynamo will give an electro- 
motive force of a zigzag form, still with some commercial 
machines, the electromotive force may be nearer to this type than 
to a sine curve, so that it is useful to investigate the current in 
the limiting case of a pure zigzag electromotive force. 

Figure i represents 

a wave of this type. 

It is composed of the 

broken straight lines 

DE, EF, FG, all of 

^' ' equal length and 

equally inclined to the horizontal axis. OB will represent the 

periodic time 7^, and OD the maximum value of the electromotive 

force or E, 

The equation to these lines will be 




r=±^(i-|./) 



the plus sign being employed when they slope downwards, as DE 

and FG^ and the minus sign when they slope upwards, as EF. 

The time / must always be reckoned from a point of maximum 

or minimum electromotive force, such as (7, A^ By or C, and must 

T 
be between the limits O and — 

2 

Of course an electromotive force of this form could be expressed 
as a function of time continuously reckoned onwards from some 
zero point by means of a Fourier sine series, and the current 
equation obtained as a sum of terms, of which one is contributed 
by each of the terms in the Fourier series. This method does 



No. 2.] ZIGZAG ELECTROMOTIVE FORCES, lOI 

not lead to satisfactory results, and the better one to follow in 
this case is what may be called the ** piecemeal " method. The 
manner in which it is to be carried out may be sketched shortly 
thus. We must presuppose some initial condition. The one here 
taken is that the electromotive force has been acting steadily, and 
the current has attained a steady value. Obtain now the current 
equation for the portion of the electromotive force zigzag DE^ and 

£ 

assuming the initial current at D to be — , find the final current 

T 
at E, i.e, the current when time equals — . This will be the initial 

2 

current for the second half period or the portion EF\ we can thus 
find the final current or current corresponding to point F, By 
a similar way of procedure, the current at the end of each half 
period can be found, and it will be seen that a single law is fol- 
lowed so that the current at the end of any half-period {i.e, when 
the electromotive force is a maximum or a minimum), after an 
indefinitely long time has elapsed, can be found, and this will be 
independent of the assumed initial condition. Remembering that 
the current at the end of a half period is obviously the same as 
the initial current of the next half period, we can now obtain the 
current equation for any time /, during a half period, / being 
reckoned from its commencement. This is the method of treat- 
ment that will be employed in the following. Many of the steps 
in the mathematical working are omitted on account of length, 
but enough have been put in to make clear the method employed. 
Suppose that the electromotive force 4- -£" has been acting 
before the time denoted by the point O in the diagram, and that 

the current has the steady value ~ Let R be the resistance and 

R 

L the self-inductance of the circuit. Then the current equation is 

at 
and consequently for the portion such as DE on the diagram, 

dC 



4-f)-^^+^f 



102 E. C. RIMIN'GTON'. [Vol. III. 

This is an equation of the well-known type 

where P and Q are functions of x only. Its solution is 

y^e'l'^ j fel^Qdx+k j, 

where ^ is a constant and ^=2.718 •••. 
Hence 

=fl-f('-i)l-^'-^'- <■> 

when the electromotive force is diminishing. 
And similarly 

^=-ft-f('-i)!-^'-^'' <^) 

when the electromotive force is increasing. 

Now consider the portion of electromotive force wave repre- 
sented by DE, 

When /=o, C=^— by assumption. Hence, substituting these 
values in (i), 

u^ A EL 

Call, for shortness, — r- = «, or «=the half -period f—j divided 

by the time constant of the circuit ( -^ J' 
Then we may write 



^-i(-f-;-^"'} 



T 
Again, when /=— , 
2 



c,.|j|,.-o-.!.-f|.-^<.-oi 



No. 2.] ZIGZAG ELECTROMOTIVE FORCES, 1 03 

Now the current at the end of the first half-period is obviously 
the same thing as the current at the beginning of the second half- 
period. Hence, making /=o in equation (2), we have 

it !<-'-)- 1 -!(-;)-*'• 

*'=|.2(.-0. 

T 
Substituting this value in (2), and making /= — , gives the cur- 

2 
rent at the end of the second half-period ; or 

^rl!-l<-'~''l=fl-^<-'"^<'-'"^!- 

Proceeding in a similar manner for the third half-period, it will 
be found that 

k — |f|x+(x-0'}; 

/v ft 

and Q=-||^i-^j(i-^-){i-^-(i-01l] 

In the same way the current at the end of the fourth half- 
period is 

Q=|ri-^[(i-OM-^-"(i -^-•5^=^)1]] 

and so on. Hence the current at the end of a half-period after 
the zigzag electromotive force has been acting for a considerable 
period of time will be 

Cj=±| j i-^(i-0(i-^"*+^"*'-^"'"+^'^-. etc.) j. 



r/.r. 



[VOL. III. 



'-- etc. is a geometrical pro- 
— 1~*, and this is fractional ; 






tanh - 



n 

2 



(3) 



rtt^l from the fact that 



i •\iif«u^ thi: half*pcnaJ under consideration 
mk- bcca increasing, and the — sign if 



,^^^«»r» 4ii*l 'linking /=o, we have, by the aid of (3), 



Ky-Mitc 



-»r 






S.'vl ri-'i 






(4) 



r 






w^k-^A^^ •^•^ "<• 



No. 2.] ZIGZAG ELECTROMOTIVE FORCES, I05 

The -f sign is to be taken when t is reckoned from the time of 
a + maximum of electromotive force, and the — sign when reck- 
oned from a — maximum. 

To find the time at which the current is a maximum or mini- 
munt^ and its value. 

Dififerentiating (4) with respect to time, and equating to zero, 
gives _^ 

T Ln i+c-'' 

or, . Z t 2 /^v 

» t=^ — log, . (5) 

If / be reckoned from a maximum of electromotive force, the 
current will be a maximum ; if from a minimum of electromotive 

L 2 

force, a minimum. The term — log, — evidently represents 

the time lag of the maximum and minimum values of the current, 
behind those of the electromotive force, respectively. 

Substituting the above value for / in equation (4), we obtain 

^ _E { |2_2, __2 4 I * 

c«x.-^ I I +^ ^ log, ^ ^^^^ ^^_^^ . 

R 



i-?log,. 



may be called the impedance of the circuit, and 



n ° 1+^"- 

is a function of R^ L, and T, Thus we have the maximum cur- 
rent equal to the maximum electromotive force divided by the 
imp)edance, in an analogous manner to the case of a sine function 

I -f ^ -> and 

is a function of R^ Z, and T. 
Again, from equation (4), 



dC^EUR _£_ 



dt R\Ln \-\-e 






_». 



and dK^ ^ER e •- 



106 E,C. RIMINGTON. [Vol. III. 

Now these values apply to a half-period, during which the 

electromotive force is diminishing, since the -f sign has been 
taken in (4). The current increases until 



R °'i+^-" 

dC 
and then decreases. Hence — is first positive and then becomes 

Air 
negative; — ;^ is always negative. This means that the rate of 

T 

change of current is greatest when /=o and /:= — ; that is, at the 

2 

times when the electromotive force has its maxima and minima. 
From equation (4) it is seen that the current is zero when 

T n i-\-e^ ft 

but unfortunately this equation does not admit of a general 
solution. 

To find the virtual current. 

By the virtual current is meant the square root of the mean 

square value. It is found by squaring equation (4), multiplying 

T 
by dty integrating between the limits — and o, then dividing by 

T ^ ^ 

— , and taking the square root. 

Squaring (4) gives 

n\ nji-j-e'' nT i-f^ J 

T 
Multiplying by dt and integrating between limits — and o, we 

have 



^ 
K' 



l\ n) 2 7^ 24 T\ n) 8 ti^ 2R (i +0^ 
A »/ 14-^''^ nT R i-\-e-U2 R\ J) J 



No. 2.] 



ZIGZAG ELECTROMOTIVE FORCES. 



107 



Dividing by — and simplifying, this becomes 



^( I 






tanh- 
2 



2 



Hence the virtual current is 



^•4VFfFH^>lJ^ 



tanh - 
2 

n 

2 



. (7) 



As an example, take a circuit whose resistance /? = i ohm, self- 
inductance Z = .oi henry, in which the maximum electromotive 
force, or E=20 volts, and the frequency = 100, or periodic time 

T=^.oi second. Then «=^=1. 

2L 2 



Equation (4) then becomes 

C= ± icx)(i -. 8 j^-. 995936 • A 



where j^=y/= 100/; or 

C=±ioo{i— .87— .995936 (cosh^— sinh^')}. 

The latter is the more convenient form for the purposes of 
calculation, as a very good set of tables of values of cosh B and 
sinh B for values of B from .01 to 4 at intervals of .01 has been 
published by the Physical Society of London, the working out 
being due to Mr. Blakesley. 

From equation (5) it is found that the value of y for maximum 
current is .2191, and the maximum current from (6) is 2.474 
amperes. 

The following table has been worked out for values of y differ- 
ing by .05, for a half-period, during which the electromotive force 
diminishes from +20 to —20. Obviously for the next half- 
period, during which the electromotive force will increase from 



io8 



E. C. RIMINGTON-. 



[Vol. III. 



— 20 to -f 20, the values of the current will be the same with their 
signs changed, as will be seen from equation (4). 



/ 


y 


Current in 
amperes. 


Remarks. 


0.0 


0.0 


+0.406- 


Rate of increase a maximum. 


0.0005 


0.05 


+ 1.264 




0.001 


0.1 


+ 1.884 




0.0015 


0.15 


+ 2.279 




0.002 


0.2 


+ 2.460 




0.002191 


0.2191 


+ 2.474 


Maximum current 


0.0025 


0.25 


+ 2.436 




0.003 


0.3 


+ 2.219 




0.0035 


0.35 


+ 1.818 




0.004 


0.4 


+ 1.240 




0.0045 


0.45 


+0.496 




0.005 


0.5 


-0.406 


Rate of decrease a maximum. 



The maximum current = 2.474. The virtual current = 1.798 
from equation (7). 

With a sine function electromotive force having a maximum 
value of 20 volts, 

the maximum current = 3. 145, 
the virtual current =2.223. 





r 










2& 




,,^^ 


-*V. 






2. 


Y- 


\ 


\ 




X Seconds > 


.001 


SfA 


\fc .0*1 Us 


.006 .Ui 


jy dn -^ M 


1. 


• 






\y 


/ - 


15 

2. 


. 




\^ 


\^ 


/ 


3.5 








\* 


Hf-^ 



s 



Fig. 2. 

E. M. F. and current curves for one complete period. E- 
r^.Ol sec; frequency = 100; max. current = 



= 20 volts; /?=l ohm; L-.Ol heavy; 
2.478 ; virtual current » 1 .8. 



Figure 2 shows these results plotted as a curve, the scale of 
volts being one-tenth that of amperes. The points of maximum 
and minimum current are marked with crosses. It will be noticed 
that in this particular circuit the current curve is not very unlike 



No. 2.] 



ZIGZAG ELECTROMOTIVE FORCES. 



109 



a sine curve in appearance. With less self -inductance, however, 
it will become more pointed, as evidently in the limiting case of 
no self-inductance, it must coincide in shape with the curve of 
electromotive force. 

To find the mean power. 

The electromotive force at any instant when decreasing is 

and the corresponding current 

R\ n T n i-^e'V 
Hence the power at any instant is 

^\ TA n T n 1+^ / 

T 
Multiplying by dt^ and integrating between limits — and o gives 

J" R\ 2 I n R 1+^-" 



n RTl 2 R^ M 5 



Now mean power or 



f^Pdt 



£*Mi_^ 8^ i-^- 



2 



-f r©' 



tanh- 



I— - 



2 



(8)- 



This result is, of course, equal to the virtual current squared 
and multiplied by R, 



no 



E. C. RIMmGTON'. 



[Vol. III. 



We may also write P^ in the form 



P^^EC^ 



r(;A-;-'"" 



S 






Again, since ^=£'f i— -^/j, the virtual electromotive force, 



or 



^.= 



X'^^^ 



=— — ; and C,=^\ — (-) ( i — tanh-Y 



Hence P^ may be written 

/'.=^.C-.V.-3(H)"(.-f.a„hD 



It is interesting to consider the other limit of wave-type of an 
alternating dynamo, viz. the rectangular wave-type as shown in 

Fig. 3. This is the case 
of a constant electromo- 
tive force periodically 
reversed, and its investi- 
gation is considerably 
simpler than the fore- 



+E 



-E 



+E 



8T 



•fE 



Fig. 3. 



going one. It can, however, be treated in a precisely similar 
manner, and the results obtained are that the current at the 
end of a half-period reckoned from the instant of reversal of elec- 
tromotive force is 



a=±f.i^=±|tanh«. 
5 R i+e^ R 2 



(9) 



Here n has the same meaning as before, viz. — ; the -t- sign is 

'R 
to be taken when the reversal has been from a negative value of 

the electromotive force to a positive one, and vice versd. 




No. 2.] ZIGZAG ELECTROMOTIVE FORCES. 

We also obtain 



III 



_ -£" I 2(coshj/— sinhj/) ) 
R \ I +cosh «— sinh n S 



(lO) 



where y^ as before, equals •— /. 



The current is zero when 



2 -f« 



or when 



1+^"" 
/=^log^r— ^— , 



the same value of / that made the current a maximum or minimum 
in the case of the zigzag electromotive force. There is no macthe- 

matical maximum or minimum for the current, but obviously from 

T 
(lo) it is greatest or least when /=— , that is, at the moments of 

2 

reversal, or. 



The virtual current, or 



V 



tanh^ 

2 

n 

2 



(") 



The formula given in (ii) has been published by Mr. Kennelly in 
the Electrical World, Nov. ii, 1893, page 397, where, however, it 



is misprinted as -— 




The mean power or P^ will obviously be 

E^ 



P^^OR^ 



R 



tanh?^ 



I — 



n 

2 




112 



E. C. RIMINGTON. 



[Vol. III. 



The following table has been calculated from equation (lo) for 
the same circuit as considered previously. With numerical values 
substituted, (lo) becomes 



and 



^r= ±2o| I — 1. 24492 (cosh J/— sinh J/)}, 



R 



y=—t=ioot. 



/ 


y 


Current in 
amperes. 


Remarks. 


0.0 


0.0 


-4.898 


Current a minimum. 


0.0005 


0.05 


-3.684 




O.OOl 


0.1 


-2.528 




0.0015 


0.15 


-1.430 




0.002 


0.2 


-0.3850 




oroo2i9i 


0.2191 


0.0 


Current zero. 


0.0025 


0.25 


+0.6082 




0.003 


0.3 


+ 1.555 




0.0035 


0.35 


+ 2.454 




0.004 


0.4 


+3.310 




0.0045 


0.45 


+4.124 




0.005 


0.5 


+4.898 


Current a maximum. 




Fi?. 4. 

E. M. F. and current curves for one complete period. £ = 20 volts: R=\ ohm: I ■» .01 heavy; 
F" 1 sec. ; frequency =100; naax. current » 4.898 ; virtual current = 2.85 1 . 



No. 2.3 ZIGZAG ELECTROMOTIVE FORCES. 1 13 

The maximum current =4. 898, 

the virtual current =2.851 from (11). 

For the zigzag electromotive force the values were 

maximum current = 2.474, 
virtual current = 1.798. 

For a sine electromotive force 

maximum current = 3. 145, 
virtual current =2.223. 

Figure 4 gives the above results plotted on the same scale as in 
Fig. 2, the scale of volts being one-tenth those of the amperes. 

It will be seen that with a sinusoidal electromotive force, the 
maximum and virtual currents have values which lie between those 
of the two extreme cases of rectangular and zigzag electromotive 
forces. 



1 14 DR. W. D. BANCROFT. [Vol. III. 



ON TERNARY MIXTURES. 11. 
By Wilder D. Bancroft. 

THE formula ;r*^= Constant, which was found to express the 
condition for equilibrium in a saturated ternary solution,^ is 
not wholly satisfactory, since it contains no term expressing the 
variation of the consolute liquid in case one of the non-miscible 
liquids is kept constant, and also because a change in the units in 
which X and y are expressed or a change in the amount of the 
consolute liquid taken affects the constant of the formula. This 
can be remedied by the following reasoning. According to Gibbs 
and to experiment, the absolute mass of a phase has no effect on 
the equilibrium. Therefore increasing the quantities of x and y 
w-fold involves increasing the quantity of the consolute liquid 
w-fold if the solutions are to remain at the saturation point. This 
would increase the value of the constant w*"^^ times. If then x 
and y denote the values in cubic centimeters of the non-miscible 
liquids A and B, z the corresponding value for the consolute liquid 
5, we have as equation of equilibrium for saturated solutions the 
expression : — 

If, as was done, z is kept constant, this simplifies to formula (4), 
which I will renumber \a, : — 

\iy is constant, x and z varying, we have : — 

» Physical Review, VoL III., No. i. 



No. 2.] 



TERNARY MIXTURES. 



115 



And if X is constant, y and z varying, we have : — 
\c. 






In Equation I., the value of C is a function of the nature of the 
units in which jr, j/, and z are expressed ; but independent of the 
size. Thus grams and kilograms give the same result, cubic 
centimeters and liters ; but the weight constant is different from 
the volume constant, and the constants for reacting weights or 
reacting volumes would have still other values. C is also depen- 
dent on the absolute value of the exponential factors a and /8. 
We can, however, eliminate this effect by writing 

(6) c=/:-+^ 

in which case K remains entirely unchanged, when we substitute 
^=«. In Table VII. I give in the first two columns the values for 

log C according to the general formula ~^=C when x,y^ and « 

are expressed in volumes. Since r=s in all these measurements. 
Table VII. gives the constants of the preceding tables less the 
corresponding values of («-f i) log 5. It would have been better 
to calculate the integration constant using the rational exponents 
a and /8; but only their ratio can be determined by a study of 
equilibrium in one liquid layer, and the case of two liquid layers 
will form the subject of a separate communication. In columns 
three and four are the corresponding values of K^ and K^ accord- 
ing to Equation (6). They are the constants of the preceding two 
columns divided by the appropriate values of /i-f i. 

Table VII. 



Mixtures. 


logC,. 


log C,. 


log AT,. 


log AT,. 


HA CHOt, QHsOH . 


T.163 


T.266 


1.711 


1.652 


H,0, CHCU. CHsOH . 


2.984 


T.489 


1.692 


T.773 


H,0, CHCU, CHsCOCHa 


2.506 


• • « • 


T.381 


.... 


H,0, C«H6, CjHjOH . 


2.737 


2.737 


T.514 


T.514 


H,0, C«H«, CHsOH 


2.482 


2.184 


I.3S8 


1.395 


HA C«H«, CHjCOCHs . 


2.584 


2.471 


1.410 


T.349 



Il6 DR, W. D. BANCROFT. [Vol. III. 

The values given under x and y in Tables I.-VI. are amounts 
of the liquids A and j5 in a given quantity of 5, — in this case 
5 c.c. A glance at the tables will show that these figures are 
very far from expressing volume concentrations, i.e. quantity of 
substance in a given volume of the solution. As most theoretical 
generalizations in chemistry are expressed in volume concentra- 
tions, it will be necessary to see what effect such a change would 
have on general Formula I. If there is no contraction or expan- 
sion on mixing, the volume of the solution will be the sum of the 
component volumes, or F=;r-f j'-f -sr, and the volume concentrations 

will be , — '^ , , respectively. This simple 

x-\-y'\-z x-\-y'\'S x-\-y-\-2 

case may be said never to occur, and the volume of the solution 
is an at present unknown function of the component volumes 
represented by the expression V=F{x, y, s). While the knowl- 
edge of the form of this function is necessary to enable us to 
calculate the volume concentrations of a given solution from our 
experimental data, it is superfluous in the present discussion. 
We have (from Formula I.) : — 

alog;r+/81og^ — (a-h/8)log^=log C. 
Now a log r+/81og F-(a-h/3)log V=0) 

.-. alog^+/31og-^-(a4-y8)log-^=logC; 

or -^ = C, if ;r, y, and z denote volume concentrations instead of 

having their previous significance. Since a, yS, and C remain 
unchanged, we find that Equation I. represents the series of satu- 
rated solutions obtained at constant temperature with any two 
non-miscible liquids, and a third liquid miscible in all proportions 
with each of the other two, provided no chemical reaction takes 
place, and provided the reacting weights of the liquids remain 
unchanged. It is immaterial whether ;r, ^, and s denote volume 
concentrations, or concentrations of two of the substances in a 
constant quantity of the third. 

As has been said, volume concentrations are generally looked 
upon as the only scientific way of expressing data. This is per- 



No. 2.] TERNARY MIXTURES, \ \ 7 

fectly natural when we remember that our theoretical ideas have 
been formed almost entirely upon a study of the gaseous state. 
It is not a necessary method, and in tliis particular case it is 
decidedly disadvantageous, practically to use volume concentra- 
tions. It involves a determination of the density of each solution, 
increasing the work and bringing in a new source of error. When 
expressed in volume concentrations, all three components vary, 
and while it is a simple matter to plot three variables in a plane,^ 
I know of no way in which this can be done for the logarithms 
of these variables. By the method which I have followed, one 
constituent can be kept constant, no density determinations are 
necessary, and there are only two variables. The formula being 
hyperbolic, by plotting the data on logarithmic coordinates one 
gets a straight line, any variation from which is easily seen, while 
the constants of the curve can be determined from the diagram with 
more speed and accuracy than by substituting the experimental 
values in an equation and solving for two unknown quantities. 

The next case to be considered is when we have two partially 
miscible liquids, and a third miscible in all proportions with each 
of the others. Formula I. cannot apply here, because it was 
deduced for two non-miscible liquids, and this condition is no 
longer fulfilled. There are two ways of treating a problem like 
this. One is to change the conditions of the experiment until 
they agree with the formula ; the other is to change the formula 
till it conforms to the conditions of the experiment. I have done 
both. I will suppose, for the sake of clearness, that the two 
partially miscible liquids are ether and water. Saturated solutions 
of water in ether are absolutely non-miscible at the temperature 
for which they are saturated, being thus an improvement over 
benzol and water, which are slightly miscible theoretically. If x 
and y in Equation \a mean quantities of saturated water and 
saturated ether solutions, instead of pure water and pure ether, 
the conditions are satisfied for which this formula was deduced, 
and the equation must apply. I have found that it did, and the 
experimental proof is given in Tables IX. and XI. 

* Gibbs, Thermodynamiscbe Studien, p. 141; Roozeboom, Zeitschr. f. pb. Cbem., 
XII. 369. 1893. 



1 18 DR, W, D, BANCROFT. [Vol. III. 

This being settled, we can attack the second part of the prob- 
lem. Let X denote cubic centimeters of saturated solution of 
ether in water, Y cubic centimeters of saturated solution of water 
in ether which saturate a given quantity of a consolute liquid. It 
is found experimentally that 

(7) ^•K^= Constant, 
or, if we set 3 =«> we shall have 

(8) X^Y^C 

If $1 is the solubility of ether in water, s^ the solubility of water 
in ether, both expressed in volumes per cubic centimeter of the 
solvent synthetically, we shall have, if no contraction or expansion 
takes place in forming the saturated solutions of water in ether 
and ether in water: — 

(9) X=A'\'S^A\ Y=B+s^B; 

(10) {A-\-s^Ay{B'\-s^B) = C; 

where /i=c.c. water in X, B=cx. ether in K As we must 
assume some contraction or expansion, let the ratio of the actual 
volume to the sum of the component volumes be o-j in the satu- 
rated solution of ether in water, and a^ in the saturated solution of 
water in ether. We have then : — 

(i I) X=^(r^{A -\-s^A) ; Y=a^{B+s^B) ; 

(12) Wi(A^s,A)\-\<T^{B^s^B)\=^C^; 
which can be rewritten : — 

(13) {A^s,A)-(B-^s^B)=.-^ 

If X and y denote cubic centimeters of pure water and pure 
ether dissolved in a given quantity of the consolute liquid, we 
have : — 

(14) x=A+s^B; y=^B+s^A, 
Solving for A and B : — 

(15) ^ = £:z£aJ:; ^=Z:i£i£. 



No. 2.] TERNARY MIXTURES. 1 19 

Substituting these values in (13) : — 

Since o-j, o-j, ^i, ^2* ^^ constants for constant temperature, we 
can simplify equation (16) into : — 

(17) {x-s^yY{^y-s^x)^C^ 

where the relation between C\ and C, is 

^ ^ C2 (1-V2)-"' 

Eliminating the effect due to the arbitrary quantity of consolute 
liquid used, we have : — 

(19) (^-wj;y-^.^) =.c-3; 

r 

where ^3= — ^ Reverting to the most general form, so as to 
2 

make the equation correspond in form to Equation I., 

Equation II. is more general than Equation I., the latter being 
merely a special case of the former, where the terms representing 
the mutual solubilities are so small that they can be neglected. 

In testing these equations I took, as pairs of partially miscible 
liquids, ether and water, ethylacetate and water. The ether was 
distilled over sodium, the ethylacetate dried with calcium chloride 
and fractionated, the boiling point rising a full degree for a liter 
distilled off. I think, however, that no essential error was intro- 
duced in this way, and that, for my purposes, it was sufficiently 
pure. The solubilities were determined volumetrically. In all 
cases I took 10 c.c. of the solvent in a test tube and ran in the 
solute from a burette till the solution clouded. One can deter- 
mine this point to o.oi c.c without difficulty. In Table VIII. I 
give the solubilities at 20** expressed in cubic centimeters of solute 
in 10 c.c. of solvent. The solubilities of ether and ethylacetate 



I20 



DR, W. D, BANCROFT. 



[Vol. III. 



in water decrease with increasing temperature ; the solubilities of 
water in ether and ethylacetate increase with increasing tempera- 
ture. This behavior is well known for ether; but I have not 
found it stated anywhere for ethylacetate. 



Table VIII. 



Solute. 


Solvent. 


SoIubiUty. 


Ether 
Water 
Ethylacetate 
Water 


Water 

Ether 
Water 
Ethylacetate 


1.03-41 
0.08 
0.926 
0.2^ 



It will be remembered that, when two liquids were practically 
non-miscible, the series of saturated solutions formed by these 
with a consolute liquid were expressed by two curves of the same 
general form, but having different constants; and it was found 
that these two curves represented, the one the series of solutions 
out of which liquid B is precipitated on addition of either A or B; 
the other, the converse series, when the solution was saturated in 
respect to A but sensitive to an excess of either A or B. When 
the liquids A and B are partially miscible, the case becomes appar- 
ently more complicated, for we have four curves instead of two. 
These refer to four distinct sets of equilibrium, there being the 
following four series of saturated solutions. 

1. The solution is saturated in respect to B. Excess of A pro- 
duces no precipitate. 

2. The solution is saturated in respect to B, Excess of ^ or -5 
produces a precipitate of B. 

3. The solution is saturated in respect to A. Excess oi A or B 
produces a precipitate of A. 

4. The solution is saturated in respect to A, Excess of B pro- 
duces no precipitate. 

Series 2 and 3 correspond to the two series observed with two 
non-miscible liquids. In these two series the consolute liquid is 
the solvent, whereas in series i and 4 we have, in addition, A and 

^ Schuncke finds 1.04-5, '^eitschr. f. ph. Chem., XIV. 334. 1894. 



No. 2.] TERNARY MIXTURES. 1 2 1 

B respectively as solvents. In Tables IX.-XIII. I give the meas- 
urements made with ether and water, ethylacetate and water with 
the consolute liquids alcohol, methylalcohol, and acetone. In 
Tables IX. and XI. the experiments were made with saturated 
solutions; in Tables X., XII., and XIII., with pure liquids. The 
first method has the advantage that the readings obtained are final, 
involving no correction and no knowledge of the mutual solubil- 
ities. On the other hand, it is necessary to keep the solutions in 
the burettes at the same temperature as that at which one makes 
the determinations, a very difficult thing to do usually, so that the 
second method is to be preferred. The exponential factors are 
the same according to both methods, as I have already shown. 
The integration constants are different, standing to each other in 
the relation given in Equation (i8). It would have been well if 
I had determined the densities of the saturated solutions so that 
they could be recalculated into cubic centimeters of the pure 
liquids ; but I shall have to make an extended series of density 
determinations in connection with the equilibrium between two 
liquid phases, and I have postponed these others till then. The 
measurements in Tables IX.-XIII. are about as accurate as those 
in Tables I.-VL, with the exception of the solutions when water is 
part solvent. The precipitate in these cases is lighter than the 
solution, consists of a few drops only, and is very difficult to dis- 
tinguish from air bubbles, especially in the ether solutions, where 
the clouding at best is very slight. For this reason the first series 
in each table must be considered as very doubtful as the absolute 
measurements go. The determination of the saturation point for 
these cases depended on the light, the state of my eyes, and the 
mood which I happened to be in on the days when the measure- 
ments were made. So difficult are the determinations sometimes, 
that I give no results for ether-water-acetone because I obtained 
dififerent measurements every day. The agreement between the 
observed and the theoretical values is no test of the absolute 
accuracy of either ; but merely shows that the solutions follow the 
same general law, the constants, exponential, and integration, vary- 
ing with the degree of cloudiness which the observer takes as 
denoting the point of saturation. The values of n are not so accu- 



122 



DR, W, D, BANCROFT. 



[Vol. III. 



rate as in the first set of tables, because the curves cover a more 
limited extent, and therefore the variations are smaller, and be- 
cause when the value of n is large, say over 2, a very slight change 
in the direction of the logarithmic curve produces a very large 
corresponding change in n. The amounts of ethylacetate and 
water which dissolve in 5 c.c. of alcohol, methylalcohol, or acetone 
were so large that I was forced to work with one cubic centimeter 
of these liquids as solvent. 



Table IX. 

A'c.c. Sat. Water; K c.c. Sat. Ether; 5 c.c. Alcohol. Temp. 20°. 
Formula JTK** = Ci; if i = 2.60; log Cx = 1.994. 



Sat. Water. 


Sat. Ether. 


log Cx. 


Gale. 


Pound. 


Gale. 


Pound. 


49.89 
24.89 
10.02 


50.00 
25.00 
10.00 


1.30 
1.70 
2.41 


1.30 
1.70 
2.41 


1.995 
1.996 
1.993 



Average, 



1.995 



Formula X'^Y - C%\ n^- 1.49; log Cj = 1.867. 











logC,. 


9.04 


9.00 


2.79 


2.77 


1.864 


7.% 


8.00 


3.33 


3.35 


1.870 


7.72 


7.70 


3.52 


3.50 


1.865 


6.00 


6.00 


5.10 


5.10 


1.867 



Average, 



1.867 





Formula XY - Cz\ log d 


^ = 1.493. 












logC,. 


5.19 


5.21 


5.97 


6.00 


1.495 


4.45 


4.45 


7.00 


7.00 


1.493 


3.99 


4.00 


7.78 


7.80 


1.494 


3.89 


3.87 


8.03 


8.00 


1.491 


3.11 


3.10 


10.05 


10.00 


1.491 


2.08 


2.08 


14.95 


15.00 


1.495 


1.78 


1.77 


17.58 


17.50 


1.491 



Average, 



1.493 




No. 2.] TERNARY MIXTURES. 

Table IX. {continued), 

Fonnula A^**K= Ci; n^ = 1.73; log C4 = 1.665. 



Average, 



123 



Sat. Water. 


Sat. Ether. 


log C4. 


Calc. 


Found. 


Calc. 


Found. 


1.62 
1.43 
1.09 
0.% 


1.61 
1.43 
1.10 
0.95 


20.28 
24.95 
39.27 
50.47 


20.00 
25.00 
40.00 
50.00 


1.661 
1.673 
1.666 
1.659 



1.665 



Table X. 

X c.c. Water; y c.c. Ether; 1 c.c. Methyl Alcohol. Temp. 20°. 
Formula {x - 0.008^)0^ - 0.103 x)"* = Ci; «i = 1.50; log Ci = T.502 



Water. 


Ether. 


log C,. 










Calc. 


Found. 


Calc. 


Found. 




10.05 


10.00 


L13 


1.13 


T.500 


9.00 


9.00 


1.04 


1.04 


T.502 


7.03 


7.00 


0.85 


0.85 


T.500 


4.97 


5.00 


0.68 


0.68 


T.505 


4.00 


4.00 


0.60 


0.60 


T.502 
T.502 



Formula (x - O.OOSy)"* (y - 0.103 x) = G; «j = 1.13; log Cj = T.928. 











logC^ 


2.95 


3.00 


0.555 


0.56 


T.936 


2.50 


2.50 


0.56 


0.56 


T.928 


2.03 


2.00 


0.60 . 


0.59 


T.920 


1.80 


1.80 


0.63 


0.63 


T.929 


1.50 


1.50 


0.70 


0.70 


T.929 
T.928 



124 



DR. W. D, BANCROFT. 



[Vol. III. 



Table X. {continued). 
Formula {x - 0.008>')''» {y - 0.103 4:) = C,; «8 = 2.04; log Cs = 0.045. 



Water. 


Ether. 


log C^. 










Calc. 


Pound. 


Calc. 


Found. 




1.20 


1.20 


0.90 


0.90 


0.047 


1.00 


1.00 


1.23 


1.23 


0.045 


0.90 


0.89 


1.53 


1.50 


0.035 


0.83 


0.83 


1.79 


1.80 


0.047 


0.78 


0.78 


2.00 


2.00 


0.046 


0.64 


0.64 


3.01 


3.00 


0.043 


0.57 


0.57 


3.99 


4.00 


0.047 


0.52 


0.52 


5.00 


5.00 


0.045 


0.47 


0.47 


6.89 


7.00 


0.053 
0.045 



Formula (x - 0.008 >')''* {y - 0.103 x) = C*; «* = 4.4; log C^ = T.057. 











log C4. 


0.44 
0.45 
0.45 


0.44 
0.45 
0.45 


10.30 
11.62 
15.04 


10.00 
12.00 
15.00 


T.044 
T.071 
T.056 

T.057 



Table XI. 

A'c.c. Sat. Water; Kcc. Sat. Ethylacetate ; 1 c.c. Alcohol. Temp. 20°. 
Formula XY"*^ = Ci; «i = 2.S6; log Q = T.280. 



Sat. Water. 


Sat. Ethylacetate. 


log C,. 


Calc. 


Pound. 


Calc. 


Pound. 


10.05 
8.07 
7.11 
5.97 
4.97 
3.94 


10.00 
8.00 
7.00 
6.00 
5.00 
4.00 


0.25 
0.27 
0.28 
0.30 
0.32 
0.34 


0.25 
0.27 
0.28 
0.30 
0.32 
0J5- 


T.278 
T.276 
T.263 
T.282 
T.2S3 
I.2S6 



Average, 



T.278 



No. 2.3 



TERNARY MIXTURES. 



125 



Table XL {continued). 

Formula X*^Y ^ G; m = 1.80; log Cj = 0.549. 



Sat. Water. 


Sat. Etbylacetate. 


loff C,. 


Calc. 


Found. 


Calc. 


Found. 


3.00 
2.50 
2.00 

Ave 


3.00 
2.50 
2.00 

raf e. . • 


0.49 
0.68 
1.02 


0.49 
0.68 
1.02 


0.549 
0.548 
0.550 

0.549 


'••6*'> • • 







Formula A'*»K= Cg; ifs = 1.36; log Cz = 0.433. 











loff C,. 


1.45 


1.50 


1.56 


1.59 


0.445 


1.25 


1.25 


2.00 


2.00 


0.433 


1.06 


1.06 


2.51 


2.50 


0.432 


1.00 


1.00 


2.71 


272 


0.434 


0.93 


0.92 


3.04 


3.00 


0.428 


0.75 


0.75 


4.00 


4.00 


0.432 



Average, 



0.434 



Formula A'**K= C*; «4 = 1.765; log d = 0.372. 











lOff C4. 


0.65 


0.65 


5.02 


5.00 


0.369 


0.59 


0.59 


5.98 


6.00 


0.373 


0.54 


0.54 


7.00 


7.00 


0.372 


0.50 


0.50 


8.00 


8.00 


0.372 


0.44 


0.44 


9.% 


10.00 


0.370 



Average, 



0.371 



126 



DR, W. D. BANCROFT. 



[Vol. III. 



Table XII. 

X C.C. Water; y c.c. Ethylacetate; 1 c.c. Methyl Alcohol. Temp. 2(P. 
Formula {x - 0.029^) (y - 0.093 x)"^ = Ci; «i = 1.20; log Ci = 0.002. 



Water. 


Ethylacetate. 




Calc. 


Found. 


Calc. 


Found. 


loff C,. 


9.92 


10.00 


1.08 


1.08 


0.006 


6.% 


7.00 


0.85 


0.85 


0.005 


5.08 


5.00 


0.72 


0.72 


T.995 


3.96 


4.00 


0.69 


0.69 


0.006 


3.01 


3.00 


0.68 


0.68 


0.000 


2.51 


2.50 


0.70 


0.70 


0.001 



Average, 



0.002 



Formula (x - 0.029^)*« (y - 0.093 x) = G; «2 = 2.78; log C% = 0.631. 











log C,. 


2.03 


2.00 


0.83 


0.82 


0.637 


1.80 


1.80 


1.04 


1.04 


0.630 


1.72 


1.70 


1.19 


1.15 


0.617 


1.49 


1.50 


1.63 


1.69 


0.644 


1.41 


1.41 


1.99 


2.00 


0.633 



Average, 



0.632 



Formula {x - 0.029^)*« {y - 0.093 jt) = Cs; «« = 2.00; log Cs = 0.550. 











log C,. 


1.29 


1.29 


2.51 


2.50 


0.549 


1.20 


1.20 


2.99 


3.00 


0.551 


1.07 


1.07 


4.03 


4.00 


0.547 


1.00 


1.00 


4.88 


4.90 


0.552 



Average, 



0.550 



Formula (x - 0.029>')''* {y - 0.093 x) = C*; «4 = 7.00; log C4 = 0.078. 











log C,, 


0.97 


0.97 


6.00 


6.00 


0.078 


0.98 


0.98 


7.02 


7.00 


0.076 


1.00 


1.00 


7.61 


8.00 


0.100 


1.03 


1.03 


9.98 


10.00 


0.079 



Average, 



0.083 



No. 2.] 



TERNARY MIXTURES. 



127 



Table XIII. 

X c.c. Water; y c.c. Ethylacetate; 1 c.c. Acetone. Temp. 2(P. 
Fonnula {x - 0.029^) {y - 0.093 jp)** = Ci; «i = 1.54; log Ci = T.364. 



Water. 


Ethylacetate. 




Calc. 


Found. 


Calc. 


Found. 


loff C,. 


10.12 


10.00 


1.02 


1.01 


T.359 


6.99 


7.00 


0.76 


0.76 


T.365 


5.01 


5.00 


0.60 


0.60 


1.363 


3.00 


3.00 


0.47 


0.47 


T.364 


2.00 


2.00 


0.43 


0.43 


T.365 



Average, 



T.363 



Formula (. 


r - 0.029^)''« (^ 


-0.093jr) = C2; 


m = 1.16; log Ca = 1.721. 










loff C,. 


1.50 
1.00 


1.50 
1.00 


0.47 
0.63 


0.47 
0.63 


T.721 
T.721 



Average, 



T.721 



Formula (jr - 0.029^) {^y - 0.093 x)*» = Cj; nz = 1.26; log Cj = T.653. 











loff Ca. 


0.79 


0.80 


0.74 


0.74 


T.656 


0.69 


0.69 


0.80 


0.80 


T.652 


0.51 


0.51 


1.00 


1.00 


T.652 


031 


OJl 


1 1.50 


1.50 


T.653 



Average, 



T.653 



Formula {x - 0.029 y)"* (y - 0.093 x) = d; «4 = 3.00; log Ca = Z.135. 











loff C,. 


0.25 


0.25 


2.01 


2.00 


2.134 


0.25- 


0.25 


2.48 


2.50 


2.138 


0.286 


0.285 


3.01 


3.00 


2.134 


0.29 


0.29 


5.00 


5.00 


2.135 



Average, 



2.135 



In this set of tables, as in the first set, the amount of one non- 
miscible liquid which will dissolve in the consolute liquid decreases 



128 VR. W, D. BANCROFT. [Vol. III. 

as the quantity of the other non-miscible liquid increases. In this 
case, however, the non-miscible liquids are saturated solutions, and 
it does not follow that the quantity of one pure liquid decreases 
as the other increases. There comes a point where the rate of 
increase of one component in the solution in which it is solute 
is greater than its rate of decrease in the solution in which it 
is solvent. If we take the general equation (17), 

{x-s^)\y-s^x) = C2, 

it is obvious that as x increases y will first decrease, pass through 
a minimum, and then increase. If the same equation expressed 
the two equilibria, the point where y was a minimum would be the 
point where the solution is no longer sensitive to an excess of x. 
In general, the equilibrium for this second stage is given by a 
second equation, and all we can say in our present knowledge is 
that at the intersection of these two curves y should have a mini- 
mum value. This does not seem to hold in Table XII., where the 
amount of ethylacetate soluble in i c.c. methylalcohol in presence 
of 2.50 c.c. water is more than will dissolve when either three or 
four cubic centimeters of water are added. I am inclined to attrib- 
ute this to experimental error, as I do not see how there can be 
two saturated solutions of the same substance in the same solvent. 
Such a case would be entirely new, and would involve such conse- 
quences that it is not to be assumed on the strength of a variation 
of two one-hundredths of a cubic centimeter in measurements 
where the probable error is known to be very large. I propose to 
repeat these measurements on a larger scale, so as to determine 
what the facts really are. There are also one or two things in 
respect to the ether-water-methylalcohol curve which need to be 
gone into more closely. In Table XIV. I give the values for log C 
when cleared of the term for -sr, and the values for log K when 
the effect of the exponential factor has been eliminated. Both 
log C and log K are calculated for ;r, j/, and z, being expressed in 
cubic centimeters. A discussion of these values is not possible at 
present, and in any case they should be reduced to reacting vol- 
umes or reacting weights before a rational treatment could be 
thought of. 



No. 2.] 



TERNARY MIXTURES. 



129 



Table XIV. 



Mixtures. 


loff C,. 


loff C,. 


logCa. 


logC^. 


log^,. 


log/r,. 


loff/r,. 


logJ^r,. 


S. HjO, S. Ether, Alcohol 


T.478i 0.126 


0.095 


T.757 


T.855 


0.051 


0.047 


T.911 


H,0, Ether, Methylalcohol 


T.502 


T.928 


0.045 


T.057 


T.801 


T.966 


0.015 


T.825 


S. H2O, S. Et. Ac, Alcohol 


T.280 


0.549 


0.433 


0.372 


T.814 


0.1% 


0.182 


0.134 


HjO, Et. Ac, CH3OH 


0.002 


0.631 


0.550 


0.078 


0.001 


0.167 


0.183 


0.001 


HjO, Et. Ac, Acetone 


T.364 


T.721 


T.653 


2.135 


T.749 


T.871 


T.894 


T.534 



The measurements already communicated would be sufficient 
by themselves to establish the general law governing this class of 
equilibria; but I have in addition experiments by other investi- 
gators which give the same result. In 1871 Tuchschmidt and 
Follenius^ noticed that carbon bisulphide was not infinitely misci- 
ble with aqueous alcohol, and they made a series of experiments to 
determine the saturation points when carbon bisulphide was added 
to alcohol of known strengths. They expressed their results by 
means of a complex empirical formula. This is not necessary, as 
the general equation for two non-miscible liquids cover the case 
entirely. In Table XV. the first column gives the number of 
cubic centimeters of carbon bisulphide which will dissolve in ten 
cubic centimeters of aqueous alcohol of the percentage composition 
by weight given in column two. In column three is the strength 
of alcohol as required by the formula. 

Table XV. 

X = g. HaO; y = cc CS,. Temp. 17°. 
Formula xy* = C; « = | ; log C = 1.345. 





Per cent Alcohol. 




y- 


Cmlc. 


Found. 


k«C. 


18.20 


98.8 


98.5 


1.457 


13.20 


98.0 


98.15 


1.318 


10.00 


97.0 


%.95 


1.345 


7.00 


95.0 


93.54 


1.456 


5.00 


91.5 


91.37 


1.350 


3.00 


84.3 


84.12 


1.324 


2.00 


74.0 


76.02 


1.310 


0.20 


— 


48.4 


— 



Average, 



1.366 



1 B. B., IV. 583. 1871. 



1 30 DR. W, D, BANCROFT. [Vol, III. 

When one considers that the carbon bisulphide was evidently 
determined very roughly, the agreement is an excellent one. 
Here, too, we find the existence of two curves. The last measure- 
ment lies on the second curve when water is the precipitate, and 
not carbon bisulphide. As only one point on this curve was 
measured, it is impossible to determine the constants even ap- 
proximately. The object of this investigation by Tuchschmidt 
and Follenius was to obtain a method for determining the strength 
of aqueous alcohol quickly and easily. Owing to the unpleasant 
properties of darbon bisulphide, their choice of liquids was bad, 
though the method seems to me a good one. If one were to make 
a complete table for benzol or chloroform and aqueous alcohol at 
zero degrees, the rest would be simplicity itself. One would take 
ten cubic centimeters of the alcohol to be tested and run in chloro- 
form from a burette till saturated, when a glance at the table 
would give the percentage composition of the alcohol. The 
method would be quicker than any except with a hydrometer, 
and more accurate than that. An idea of the accuracy is given 
by the fact that at 20^ 5 c.c. of 96 per cent alcohol require about 
20 C.C. chloroform, while the same amount of 97.5 per cent alcohol 
requires about 30 c.c. for saturation. For a weaker alcohol the 
change for each per cent is much less ; but the measurements can 
be made more accurately. 

I will now take up the measurements of Pfeififer^ on the misci- 
bility of various esters with alcohol and water. The measure- 
ments were not made under the most favorable circumstances. 
A known amount of the ester was poured into a beaker, a definite 
quantity of alcohol added, and water run in till the saturation 
point was reached. Nothing was done to prevent evaporation, 
nothing, so far as is mentioned, to keep a constant temperature, 
and there was no means of warming the solution above the final 
temperature in order to insure that equilibrium had been reached. 
The necessity of this last had already been pointed out by Du- 
claux,^ who found that, on cooling a solution below its saturation 
point, it clouded at once; but on warming, the equilibrium was 

* Zeitschr. f. ph. Chem., IX. 469. 1892. 
2 Ann. chim. phys., [5.], VII. 264. 1876. 



No. 2.] 



TERNARY MIXTURES, 



131 



reached much more slowly. Given these untoward conditions, 
the comparative accuracy of the measurements is remarkable. 
While Pfeiffer has given us series upon series of valuable measure- 
ments, showing the increase of miscibility of esters and water in 
presence of alcohol, he has curiously enough omitted all deter- 
minations of the miscibility of water and esters when no alcohol 
is present. This is still more remarkable if one considers the 
uselessness of comparing the effect of equal quantities of alcohol 
on ethylacetate and water, amylacetate and water, without allow- 
ing for the fact that ethylacetate is roughly forty times as soluble 
in water as amylacetate. As these solubilities had to be known 
at any rate approximately, in order to apply Equation II. to 
PfeifFer's experimental data, I have determined several myself. 
Through the courtesy of Mr. Dunlap of the organic laboratory, I 
received small quantities of ethylbutyrate, ethylisovalerate, and 
isoamylacetate. I dried them over calcium chloride and fraction- 
ated. The change of boiling point of the portions used was four 
degrees for the ethylisovalerate and two degrees for each of the 
others. The amounts at my disposal made it not worth while to 
attempt further purification. In Table XVI. I give the solubilities 
in cubic centimeters of the solute in ten cubic centimeters of the 
solvent at 20"*. For purposes of comparison I have also inserted 
in this table the values for ethylacetate from Table VIII. 

Table XVI. 



Solute. 


Solvent. 


Solubility. 


Ethylacetate 


Water 


0.926 


Water 


Ethylacetate 


0.294 


Isoamylacetate 


Water 


0.02 


Water 


Isoamylacetate 


0.12 


Ethylbutyrate 


Water 


0.08 


Water 


Ethylbutyrate 


O.Of-5 


Ethylisovalerate 


Water 


0.02- 


Water 


Ethylisovalerate 


0.0f+ 



For these four esters I have found that the solubility in water 
decreases with increasing temperature, while the solubility of 



132 



DR, W. D, BANCROFT. 



[Vol. III. 



water in the ester increases with increasing temperature, both 
observations being made at 20^ As there is no obvious reason 
why these four esters should all be abnormal, it is more than 
likely that this behavior is characteristic of all esters at ordinary 
temperatures. As it is improbable that the solubility of the esters 
in water can continue to decrease indefinitely with increasing 
temperature, there must be some point where it reaches a mini- 
mum, and it is quite possible that a determination of this tem- 
perature for different esters might give interesting results. The 
experiments could be made with great ease, as the amount of 
saponification during the time necessary for a measurement would 
be very small. 

Quite recently, de Hemptinne ^ has determined the solubilities 
of several esters in water at 25^ His measurements are given in 
grams of the solute per liter of solution. I have reduced his 
measurements to cubic centimeters of solute in ten cubic centi- 
meters of solvent by dividing by the densities as far as I could 
get them out of Landolt and Bornstein's tables and Roscoe and 
Schorlemmer's text-book, disregarding the -difference between a 
liter of solution and a liter of solvent. The results which I give 
in Table XVII. are only rough approximations, but quite sufficient 
for my purpose. The figures in the second column are the densi- 
ties used in recalculating de Hemptinne's figures. 

Table XVII. 



Solute. 


Solubility. 


Density. 


Isobutylacetate 


0.07 


0.88 


Amylacetate 


0.02- 


0.88 


Methylbutyrate 


0.115 


0.94 


Ethylbutyrate 


0.08- 


0.898 


Amylbutyrate 


0.006 


0.85 


Propylpropionate 


0.06+ 


O.SS 


Amylpropionate 


0.01 + 


0.88 


Ethylvalerate 


0.03 


0.86 



De Hemptinne did not measure the solubility of water in the 
esters, and I have not been able to find any data on the subject 

1 Zeitschr. f. ph. Cbem., XIII. 561. 1894. 



No. 2.] 



TERNARY MIXTURES. 



133 



beyond the few measurements which I have made myself. In 
considering Pfeiflfer's results, this is not very serious, because he 
worked always with three cubic centimeters of esters, adding 
alcohol in varying quantities, and water to saturation. As the 
solubility of water in the different esters can be rarely more than 
one per cent, the error in calculating the amount of water required 
to saturate will in no case be more than a tenth of a cubic centi- 
meter, and will rarely exceed two or three hundredths. The solu- 
bilities of esters in water, which have not been determined by 
de Hemptinne or myself, have been filled in as best I could by 
analogy, remembering that increase of carbon means decrease of 
solubility, and that among isomeric esters the one with the smaller 
acid radical was rather the less soluble. In deciding where 
between two limits an unknown solubility should be put, I have 
taken the figure which satisfied the experimental data best. The 
solubilities thus obtained lay no claim to being accurate ; but they 
are not very far out, probably in no case more than 100 per cent, 
and this rough approximation is better than treating the esters 
and water as absolutely non-miscible. In Table XVIII. I give 
the solubilities which I have used in calculating Pfeiffer's results, 
expressed in cubic centimeters of the ester in ten cubic centi- 
meters of water. 

Table XVIII. 



Solute. 


Solubility. 


Solute. 


Solubility. 


Methylvalcrate 


0.20 


Propylacetate 


0.30 


Ethylvalerate 


0.03 


Butylacetate 


0.07 


Methylbutyrate 


0.12 


Amylacetate 


0.02 


Ethylbutyrate 


0.08 


Propylformiate 


0.40 


Propylbutyrate 


0.02 


Butylformiate 


0.10 


Ethylpropionate 


0.30 


Amylformiate 


0.05 


Propylpropionate 


0.065 







Starting, as Pfeiffer did, with a constant quantity of ester, his 
results necessarily lie almost entirely along the curve representing 
the equilibrium when addition of water or ester produces a pre- 



134 -^^- ^- D^ BANCROFT. [Vol. III. 

cipitate of ester. In a few cases there are a few measurements, 
never more than two, on the curve where water or ester produces 
a precipitate of water. There are not enough of these measure- 
ments to enable me to determine the direction of this second 
curve, and in the tables I have therefore given no calculated values 
in these cases. The point where, according to Pfeiffer, infinite 
miscibility occurs is the beginning of the curve where the solution 
is saturated in regard to ester ; but water produces no precipitate. 
The corresponding curve where the solution is saturated in respect 
to water, while addition of ester produces no precipitate, did not 
come within the scope of PfeifFer's investigations at all. It will 
be noticed that in the last measurements of each series the 
amount of water required to saturate is very generally greater 
than the theoretical quantity. I attribute this variation entirely 
to experimental error. When one is working with one hundred 
cubic centimeters of solution or more, it becomes almost impos- 
sible to determine the first appearance of clouding with great 
accuracy. In Tables XIX. to XXXI. I give Pfeiffer's results, 
with the values for the water calculated according to the formula 
at the top of each table. It is only fair to Herr Pfeiffer to say 
that, if I had arranged the exponential factors so that z should 
have been raised to the first power only, the differences between 
the observed and the calculated values would have been less than 
they now are. I felt, however, that, as the water was the thing I 
was calculating, I would make its exponential factor unity instead 
of that of the alcohol. 

\To be continued^ 



No. 2.] 



TERNARY MIXTURES. 



135 



Table XIX. 

>» = 3 c.c. Methylvalerate; x = c.c. Water; z = c.c. AlcohoL 
Formula x{y - 0.02 xf^/t'^ - C; log C = T.807. 



s. 


Calc. 


Pound. 


logC. 


3 





1.66 


__ 


6 


5.04 


5.06 


T.809 


9 


8.88 


9.03 


T.815 


12 


13.28 


13.40 


T.809 


.15 


18.34 


18.41 


T.809 


18 


23.90 


24.00 


T.809 


21 


30.09 


30.09 


T.807 


24 


36.80 


36.72 


T.806 


27 


44.35 


44.15 


T.805 


30 


52.80 


52.37 


T.803 


33 


62.60 


62.25 


T.804 


36 


74.25 


74.15 


T.806 


39 


91.45 


91.45 


T.807 


42 


^~ 


00 


T.807 



Table XX. 

^ = 3 c.c. Ethylvalerate; x = c.c. Water; « = c.c Alcohol. 
Formula x (j^ - O.Q03f^/z^-^ = C; log C= T.682. 



s. 


Calc. 


Pound. 


logC, 


3 


__ 


1.42 


__ 


6 


3.81 


4.14 


T.718 


9 


6.73 


7.18 


T.710 


12 


10.07 


10.51 


T.701 


15 


13.81 


14.13 


T-692 


18 


17.80 


18.09 


T.688 


21 


22.15 


22.40 


T.687 


24 


26.80 


26.83 


T.683 


27 


31.65 


31.70 


T.683 


30 


36.70 


36.62 


T.681 


33 


42.15 


41.81 


T.678 



136 



DR. W. D. BANCROFT. 



[Vol. III. 



Table XX {continued). 



M. 


Calc. 


Pound. 


logC. 


36 


47.65 


48.00 


T.685 


39 


53.40 


53.13 


T.679 


42 


59.40 


58.35 


T.674 


45 


65.55 


63.60 


T.668 


48 


71.90 


69.97 


T.670 


51 


78.50 


76.90 


T.672 


54 


83.25 


84.25 


T.688 


57 


92.40 


90.53 


T.673 


60 


99.50 


98.60 


T.678 


63 


106.80 


105.20 


T.675 


66 


114.70 


112.80 


T.674 


69 


122.40 


121.90 


T.680 


72 


130.40 


131.00 


T.684 


75 


138.90 


140.20 


T.687 


78 


148.00 


158.70 


T.712 


81 


157.50 


180.00 


T.740 
T.687 



Table XXI. 

^ = 3 c.c. Methylbutjnrate; x = cc. Water; t = c.c. Alcohol. 
Formula x Ck - OMZf^/z^^ = C; log C = T.888. 



s. 


Calc. 


Pound. 


logC. 


3 


2.33 


2.34 


T.8S9 


6 


6.75 


6.% 


T.902 


9 


12.67 


12.62 


T.886 


12 


19.90 


19.45 


T.878 


15 


28.38 


28.13 


T.884 


18 


38.76 


38.80 


T.8S9 


21 


50.85 


55.64 


T.927 


24 


— 


00 


T.892 



No. 2.] INFRA-RED ENERGY SPECTRUM, 1 37 



MINOR CONTRIBUTIONS. 

On a Simple Method of Photographically Registering 
THE Infra-Red Energy Spectrum.^ 

By Knut Angstrom. 

UP to the present time it has been possible to photograph directly only 
an extremely small part of the infra-red spectrum, and the spectro- 
bolometric method is still the only one which affords us a means of obtain- 
ing a more intimate knowledge of the distribution and intensity of the 
longer wave-lengths. It is also to be noted that this method gives a 
means of comparing the different parts of the spectrum quantitatively y 
which is scarcely possible by photography. The investigation of the infra- 
red spectrum with the aid of the spectro-bolometer is nevertheless so 
tedious, and, with the apparatus which has heretofore been commonly used, 
occupies so much time, that we might safely predict that unless the method 
is further developed, it will be possible to continue investigation in this 
field only very slowly. 

In a communication to the British Association on August 11, 1894, 
Professor Langley, who was the first to develop the spectro-bolometric 
method, has so perfected this method that the work can now be carried 
out in the infra-red almost as easily, and with almost as great accuracy, as 
in other regions of the spectrum. This is made possible partly by such 
refinement in the construction of the optical parts of the instrument as has 
heretofore never been reached ; partly, also, by substituting for the observer 
a photographic plate. As the result of the optical improvements, such 
sharpness and dispersive powers were gained that the instrument not only 
shows both of the D lines, but also the nickel line in the solar spectrum 
lying between the two. Through the possibility of recording the indica- 
tions of the spectro-bolometer by photographic methods the labor of the 
observer is of course lightened in the highest degree. 
The principle of the new method is briefly the following : — 
The telescope and scale of the galvanometer are replaced by the photo- 
graphic plate, upon which falls a beam of light reflected from the mirror of 
the galvanometer. The telescope of the spectro-bolometer is driven by 

^ A paper presented to the Royal Society of Sciences of Upsala, April 10, 1895. 



138 



KNUT ANGSTROM, 



[Vol. III. 



accurate clock-work, which also gives to the photographic plate a vertical 
movement. The motor is constructed with such accuracy that the two 
movements, viz. that of the telescope and that of the plate, are as nearly 
as possible synchronous. For each minute of arc through which the 
bolometer wire is moved, the photographic plate moves one centimeter. 







"H — h 



Fig. I. 




Fig.Z 



With the instrument constructed by Langley it appears that the extreme 
limits of sensitiveness and sharpness which are possible with the methods 
and apparatus at our disposal, have been reached. Such an instrument, 
however, can only be obtained by a richly endowed laboratory. For that 
reason I have undertaken the problem of simplifying the photographic 
method of registration, and shall describe below an apparatus which seems 
to offer a satisfactory solution. 



No. 2.] INFRA-RED ENERGY SPECTRUM, 139 

The essential difference between this instrument and that of Langley 
consists in the fact that the photographic plate is rigidly fastened to the 
bolometer tube, so that both can be moved at the same time. The beam 
of light reflected from the mirror of the galvanometer is then thrown upon 
the moving plate. The movement of the spot of light resulting from a 
rotation of the galvanometer mirror, must, however, take place in a direc- 
tion at right angles to the motion of the plate. In order to accomplish 
this, the apparatus is arranged as shown in Figs, i and 2. 

The light horizontal arm DE is fastened to the rather solidly built support 
A of the telescope, so that the former may be rotated with the tube C of 
the bolometer. The photographic plate with its holder is placed in a 
horizontal position at the end of this arm. Almost vertically above the 
plate stands the galvanometer G which is used with the bolometer. The 
light from the source L passes through a slit O and falls upon the mirror 
of the galvanometer at an angle of 45 degrees. After reflection the beam 
is brought into a vertical direction by means of the mirror S, and the image 
of the slit falls upon the photographic plate P. When the galvanometer 
mirror is rotated, this image moves in the direction of the bolometer arm 
(in the plane of the drawing in Fig. 2) . If the arm is rotated, however, 
the beam of light describes a line perpendicular to the first direction. If 
the tube, and with it the arm DE, is rotated, the bolometer wire passes 
through the different portions of the spectrum, and the galvanometer gives 
for each position the corresponding intensity of the radiation. The posi- 
tion of the spot of light upon the plate is thus determined at each instant 
by the position of the arm and the position of the galvanometer mirror. 
In the curve which the spot of light describes under these circumstances, 
distances perpendicular to the arm are therefore proportional to the angu- 
lar position in the spectrum, while distances in the direction of the arm 
are proportional to the intensity corresponding to this position. Since the 
photographic plate and the bolometer wire are rigidly connected, the 
movements are here of necessity absolutely synchronous. 

Between the galvanometer mirror and the mirror S a lens is placed 
which throws a sharp image of the slit O upon the plate. The latter is sur- 
rounded by a small box KKx in order to cut out stray light, and for the 
same reason a conical pasteboard tube HHi is placed upon the box. One 
side of the box is formed of two parts, which can be taken off" in order to 
make it easier to remove the plate. Between them is a horizontal opening 
four centimeters wide to allow a free movement of the arm. The upper 
cover has a very narrow slit extending in the direction of the bolometer 
arm, by means of which the image (whose length is perpendicular to the 
opening of this slit) is limited practically to a point 

With this arrangement, a means of moving the telescope with extreme 




I40 KNUT ANGSTROM. [Vol. III. 

accuracy is entirely unnecessary. The only requirement is that the move- 
ment of the bolometer tube should take place rather uniformly, and with- 
out jerks. I have used with good results a very simple clock-work for this 
purpose, the movement being damped by an air cushion. By varying the 
adjustment of the latter the rapidity of the motion could be regulated. The 
most rapid rotation which I have used was ten minutes of arc per minute. 
In this case the length of the arm, and therefore the distance from the axis 
of the spectrometer, was two meters. A rotation of the bolometer tube 
through an angle of one degree thus caused the image to describe an arc 
on the photographic plate 3.48 cm. long ; or, in other words, each minute 
of arc corresponded to the movement of the plate of 0.58 mm. If it is 
desired to have the movement of the plate greater, this can of course be 
accomplished by lengthening the arm. In connection with the apparatus 
at my disposal the motion of the plate mentioned above was, however, 
sufficiently great. For the preliminary investigation of many questions, 
also, a greater dispersion of the spectrum is hardly necessary. 

I shall take this occasion to mention also another solution of the problem 
of photographically registering the indications of a bolometer, although I 
have not yet tested the method. Figure 3 indicates the arrangement. The 
ray of light proceeds from the galvanometer mirror G to the mirror 5, 
making an angle of 45° with the latter. It is here reflected in a vertical 
direction, and then by means of mirror S^^ whose plane is perpendicular to 
the plane of the first mirror 5i, again reflected in a horizontal direction 
and projected upon the photographic plate. The last mirror is fastened 
upon the bolometer tube T above the axis of the spectrometer. On rotat- 
ing the tube, the spot of light 
moves upon the plate in a horizontal 
direction, while if the galvanometer 
mirror rotates, the motion of the 
spot of light is in a vertical direc- 
tion. This arrangement has the 

Pj 2 ^' advantage that the movement can 

more easily be made much greater. 
For example, if the distance between 5, and P is ^st meters, the spot of 
light will move 2.9 mm. in a horizontal direction for a rotation of the 
theodolite of one minute. 

Up to the present time I have had an opportunity of testing the first 
method only in the case of the radiation from gas flames. I have, how- 
ever, been able to convince myself of the practicability of the method. 
In addition to the two large maxima first discovered by Julius, and whose 
origin was more carefully investigated by myself, the photographic record 
of the spectrum of the Bunsen flame shows very clearly the two small 




No. 2.] CONCENTRATED SULPHURIC ACID. 141 

maxima lying nearer to the visible portion of the spectrum. The latter 
maxima have been given by Paschen in the radiation of the oxyhydrogen 
flame and the Bunsen flame. For the case of a rock salt prism with a 
refracting angle of 60°, the positions of these four maxima as indicated by 
their angular deviation from the D line are as follows : — 

10 25' 12" corresponding to X = 1.48/i; 

1° 34' 32" corresponding to X = 1.96 /* ; 

1° 45' 35" corresponding to X = 2.80 /* ; 

2° 6' 0" corresponding to X = 4.34/1. 

In this brief preliminary note I have merely wished to show the possi- 
bility of obtaining a photographic registration of bolometer indications with 
comparatively simple apparatus; and that it is possible to construct an 
instrument which shall at least bear the same relation to that of Langley as 
does the direct-vision spectroscope to the larger instruments of its class. 



On the Electrolytic Conductivity of Concentrated 
Sulphuric Acid. 

By Dr. K. E. Guthe and L. J. Briggs. 

IT is a well-known fact that the specific conductivity as well as the 
molecular conductivity of sulphuric acid is a minimum for a concentra- 
tion corresponding closely to the hydrate H2SO4 -f- H.O. The investiga- 
tions of F. Kohlrausch, Bouty, and Ostwald have shown, moreover, that 
this minimum becomes less pronounced, the higher the temperature is. 
Seemingly this acid forms an exception to the rule that the water of 
crystallization has no influence upon the conductivity of electrolytes. Our 
experiments were undertaken in order to provide more data for solutions 
of this acid at a concentration near 84.5 per cent (corresponding to the 
hydrate), with reference to the changes produced by temperature. 

Similar work has been done by Miss Klaassen *, but since her work may 
include errors of even more than 2 per cent we have repeated part of it. 
The conclusions drawn from our experiments are new. 

Experiments as to the conductivity of the hydrate in the solid state have 
to our knowledge not been published before. 

Our arrangement differs in some points from the usual one. As the 
source of electricity we used an alternating current, produced by a two- 
phase dynamo designed by Professor Carhart and represented in the accom- 
panying cut. The field is formed by a revolving electromagnet excited by 

1 Proc. of Cambr. Phil. Soc, Vol. VII., p. 137. 



142 



DR, K. E. GUTHE AND L, /. BR/GGS. 



[Vol. III. 



an independent current from the storage battery which can be varied at 
will. In our experiments we used, of course, the sinusoidal current from 
only one pair of terminals. The bridge was formed by an ordinary slide 
wire bridge of manganin wire, lengthened by additional strictly non-induc- 
tive resistances of the same metal (each of 26 ohms' resistance = 6360 cm. 
of the bridge). Instead of a telephone we took a very sensitive electrody- 
namometer, the stationary coils of which were connected in parallel with 
the bridge. 

Since we used for the determination of temperature a calibrated ordinary 
thermometer, which could not be read more accurately than to one- twentieth 




Fig. I. 

of a degree, we arranged the conditions so that the errors of observation 
would not exceed o.i per cent. For this purpose we sent only 0.8 ampere 
through the field of the generator. Since this current can easily be increased 
to 16 or more amperes, one can apply this arrangement for the measurement 
of conductivity of bad conductors just as well. The objection to the use 
of alternating currents for such a purpose raised by M. Wildermann ^ cannot 
be applied here. The time spent for one observation is very short, and 
not longer than that necessary for the determination by telephone. 

The specific gravity in each case was determined by a delicate Mohr's 
balance, and from this value the concentration obtained. All calculations 
necessary were based upon the data given iu Landolt and Boemstein's 
Tabellen (2d ed.). 

^ Zeitschr. f. phyi. Chemie, 14, p. 247, 1894. 



No. 2.] 



CONCENTRATED SULPHURIC ACID. 



143 



Tne vessel was of the common U form, and its capacity repeatedly deter- 
mined from its resistance when filled with a concentrated NaCl solution. 
The acid, which we obtained through tlie kindness of Mr. F. W. Edwards 
of the Chemical Laboratory, was Baker & Adamson*s strictly chemically 
pure H2SO4 of 1.84 spec. grav. 

We give in the following tables the data of a number of our solutions 
sufficient to show the results obtained. In the first column the temperature 
is given ; in the second, the actual resistance of the liquid ; in the third, 
the specific conductivity. These values have to be multiplied by io~^^ 
In the fourth column we find the molecular volume or molecular domain, 
i^. the volume occupied by \ gram-equivalent of H2SO4 expressed in 
cubic centimeters ; finally, in the fifth column the molecular conductivity, 
the product of molecular volume into specific conductivity. 



Table I. 

97%H2S04. Sp.Gr. = 1.841 at 150 c. 



Temp. 


Res. 


Sp. coDd. 


Mol. vol. 


Mol. CODd. 


2^.8 C. 


433.0 ohms 


67.45 xlO-w 


27.29 


1.83X10-W 


8<^.0 


370.0 


78.93 


27.36 


2.16 


12°.9 


321.0 


90.98 


27.43 


2.50 


22^.5 


248.0 


117.80 


27.56 


3.25 


29°.0 


212.5 


137.41 


27.65 


3.80 


17^.5 


282.0 


103.61 


27.50 


2.85 



Table II. 

93.05 %HsS04. Sp. Gr. = L834atl50C 



Temp. 


Res. 


8p. cond. 


Mol. vol. 


Mol. cond. 


2^.5 C. 


426.0 ohms 


68.56x10-12 


28.56 


1.96x13-13 


(PA 


377.0 


76.47 


28.61 


2.22 


\7PA 


317.0 


92.13 


28.69 


2.64 


16^.7 


278.0 


105.06 


28.76 


3.02 


2P.4 


243.0 


120.20 


28.83 


3.46 


28°.3 


202.8 


144.00 


28.94 


4.17 



144 



DR, K. E. GUTHE AND L, J. BRIGGS. 



[Vol. III. 



Table III. 

91 % HsS04. Sp. Gr. = 1.825 at 15° C 



Temp. 


Res. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


0°.6 C. 


470.0 ohms 


62.14x10-" 


29.31 


1.82x10-" 


6°4 


385.0 


75.85 


29.40 


2.23 


12°.3 


320.0 


91.27 


29.48 


2.69 


17^.0 


279.0 


104.7 


29.55 


3.09 


22^.9 


237.0 


123.2 


29.64 


3.65 


28^\8 


202.0 


144.6 


29.73 


4.30 


23^.2 


233.0 


125.4 


29.65 


3.72 



Table IV. 

8.6% HaSO*. Sp. Gr. = 1.812 at 15° C. 



Temp. 


Rei. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


P.OC 


505.0 ohms. 


57.83 X 10-" 


30.33 


1.75 X 10-" 


6°.0 


422.0 


69.21 


30.41 


2.10 


IP.O 


352.0 


82.97 


30.49 


2.53 


17^.0 


293.0 


99.67 


30.58 


3.05 


2P.8 


253.0 


115.4 


30.66 


3.54 


29°. 2 


204.6 


142.6 


30.77 


439 



Table V. 

86.55 % HaSO*. Sp. Gr. = 1.798 at 15° C 



Temp. 


Rei. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


0°.0C. 


552.0 ohms. 


51.51 X 10-" 


31.26 


1.61 X 10-" 


3°.8 


480.0 


59.24 


31.32 


1.85 


8°.9 


390.5 


72.82 


31.41 


2.29 


14°. 6 


319.7 


88.95 


31.53 


2.80 


19°. 1 


277.0 


102.66 


31.59 


3.24 


23°.3 


242.0 


117.51 


3L65 


3.72 


29°.3 


205.0 


138.72 


31.75 


4.40 



No. 2.] 



CON'CENTRATED SULPHURIC ACID. 



H5 



Table VI. 

85.7 % HaSO*. Sp. Gr. = 1.790 at 15° C 



Temp. 


Res. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


0^.0 C. 

8^.0 
15^^.5 
23^.0 


572.0 ohms. 
421.0 
319.0 
249.0 


49.72 X 10-12 
67.55 
89.11 
114.21 


31.71 
31.85 
31.98 
32.10 


1.58 X 10-12 
2.15 
2.85 
3.67 



Table VII. 

9AS % HjSO«. Sp. Gr. = 1.780 at 15° C 



Temp. 


Ret. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


0^.0 C 


591.0 ohms. 


48.12 X 10-12 


32.34 


1.56 X 10-12 


5^.9 


468.0 


60.76 


32.44 


1.97 


11^.8 


367.0 


77.49 


32.54 


2.52 


17^.4 


301.5 


94.32 


32.64 


3.08 


24°.0 


242.5 


117.27 


32.75 


3.84 


30^.5 


199.0 


142.90 


32.86 


4.70 



Table VIII. 

80.75 % H,S04. Sp. Gr. = 1.741 at 15° C 



Temp. 


Res. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


0°.OC 


487.0 ohms. 


58.39 X 10-12 


34.60 


2.02 X 10-12 


6^.0 


404.0 


7039 


34.71 


2.44 


10°.0 


345.0 


82.43 


34.78 


2 87 


15°.5 


286.0 


99.43 


34.88 


3.47 


20^.0 


248.0 


114.70 


34.97 


4.01 


24^.9 


214.0 


132.89 


35.06 


4.66 


yp3 


184.0 


154.55 


35.16 


5.43 




146 



DR. K. E. GUTHE AND L. /. BR/GGS. 



[Vol. III. 



Table IX. 

78.6% H,S04. Sp. Gr. = 1.717 at 15° C. 



Temp. 


Res. 


Sp. cond. 


Mol. vol. 


Mol. coBd. 


O^.O C. 


417.0 ohmi. 


68.20 X 10-" 


36.02 


2.45 X 10-" 


5°.8 


342.3 


83.05 


36.13 


3.00 


10^.7 


289.0 


98.39 


36.22 


3.56 


14^.8 


253.0 


112.40 


36.30 


4.08 


20°.l 


216.0 


131.66 


36.40 


4.79 


240.4 


193.0 


147.34 


36.48 


537 


29°.8 


167.0 


170.28 


36.53 


6.23 



Table X. 

76.2 % HjSO*. Sp. Gr. = 1.689 at 15° C 



Temp. 


Res. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


0^.0 C. 


349.0 ohms 


81.48x10-" 


37.80 


3.08x10-" 


5^.7 


297.0 


95.75 


37.92 


3.63 


10°.0 


256.5 


110.87 


38.00 


4.21 


14-\9 


221.0 


128.67 


38.10 


4.90 


19^.7 


193.0 


147.34 


38.20 


5.63 


24^.3 


170.0 


167.28 


38.29 


6.41 


290.0 


151.0 


188.33 


38.39 


7.23 



Table XI. 

73.88 % HjSO*. Sp. Gr. = 1.663 at 15° C 



Temp. 


Res. 


Sp. cond. 


Mol. vol. 


Mol. cond. 


00.0 C. 


295.0 ohms 


%.40xl0-" 


39.57 


3.81x10-" 


50.3 


252.0 


112.84 


39.69 


4.48 


100.8 


214.8 


132.39 


39.80 


5.27 


150.3 


189.0 


150.46 


39.90 


6.00 


190.3 


168.5 


168.77 


39.99 


6.75 


240.1 


150.0 


189.58 


40.09 


7.60 


300. 5 


129.0 


220.45 


40.22 


8.87 



No. 2.] 



CONCENTRATED SULPHURIC ACID. 



147 



From the tables we platted for each solution the temperatures and the 
molecular conductivity, and determined from the curves the molecular 
conductivity of each at the temperatures 0°, lo^ 18°, 25°. By calculation 
we found, moreover, the molecular volume for each solution at those tem- 
peratures. The following table gives the results. 







fp 




vp 


No. 










Mol. vol. 


Mol. cond. 


Mol. vol. 


Mol. cond. 


1 


27.25 


1.66x10-" 


27.39 


2.29x10-" 


2 


28.52 


1.80 


28.67 


2.48 


3 


29.30 


1.78 


29.46 


2.50 


4 


30.31 


1.69 


3a48 


2.44 


5 


31.26 


1.61 


31.43 


2.39 


6 


31.71 


1.58 


31.89 


2.33 


7 


32,34 


1.56 


32.50 


2.35 


8 


34.60 


2.02 


34.78 


2.87 


9 


36.02 


2.46 


36.21 


3.49 


10 


37.80 


3.08 


38.00 


4.21 


11 


39.57 


3.82 


39.79 


5.14 







18° 




«5° 


No. 










Mol. vol. 


Mol. coad. 


Mol. vol. 


Mol. cond. 


1 


27.50 


2.88x10" 


27.59 


3.46x10" 


2 


28.78 


3.14 


28.88 


3.83 


3 


29.57 


3.19 


29.67 


3.88 


4 


30.60 


3.15 


30.72 


3.90 


5 


31.58 


3.14 


31.67 


3.92 


6 


32.03 


3.12 


32.14 


3.90 


7 


32.65 


3.14 


32.77 


3.97 


8 


34.93 


3.77 


35.06 


4.68 


9 


36.36 


4.51 


36.49 


5.47 


10 


38.16 


5.37 


38.31 


6.51 


11 


39.97 


6.47 


40.11 


7.77 



Platting four curves, for o^ io% 18**, and 25"* respectively, taking the 
percentages of the solution as abscissae and the molecular conductivities as 
ordinates, we find that the minimum does not correspond to the same con- 
centration, as was given by Bouty.^ But in platting the molecular vohime« 

^ Comptes Rendus, 108, p. 394, 1889. 



148 



DR. K. E, GUTHE AND L, J, BRIGGS. 



[Vol. III. 



instead of the percentage, we find that all four curves show a minimum of 
conductivity for the same molecular volume, i,e, 32.1. Thus ii is not the 
concentration but the molecular volume which determines the conductivity of 
the acid. 

The latter four curves are shown in Fig. 2. There is a very slight dis- 
crepancy between the fourth and fifth solutions, owing to the fact that the 



























y 


^25 




7 > 
























/ 






> 






















/ 




























/ 


/ 


A 






3 


















/ 


r 


/ 


/ 






a 
5^ 
















/ 


V 


/ 


/ 


/ 


lO* 




t 














y 


/ 


y 


/ 


/ 


/ 






4 












^ 


/ 


y 


/ 


/ 


/ 




0* 




>* 


^ 








"^ 




y" 


/ 


y 


/ 


y 


V 






3 


^ 




-^ 




^ 






y 


/ 


y 


y 








y 












^ 


\y 




y 


y 










2 


""^ 








— ' 


^ 


_^ 


M 














^ 


— 




^=^ 




_^^^ 




\ 
















1 






























2 


i 2 


9 


3 


) s 


I t 


i 


3 


3 I 


4 I 


5 % 


u 


3 


MC 
7 3 


LECU 
8 3 


.AR VpLUMI 
40 4 


1 



Fig 2. 

first four solutions were taken from a different bottle from that for the rest. 
But it is so small, in fact, as not to influence the result in the least. 



Temperature coefficient. 

In the following we give the first temperature coefficient for the different 
solutions worked out for the formula : — 



No. 2 ] 



CONCENTRATED SULPHURIC ACID, 



149 



It is apparent that the temperature coefficient is the larger, the smaller 
the conductivity, a result already found by F. Kohlrausch and others. As 
to the second coefficient, we could not obtain regular values, due to the 
degree of accuracy in our method. It surely becomes smaller with increas- 
ing dilution, and varies from 0.00039 to 0.00016, and is always positive. 



No. 


I 


s 


3 


4 


5 


6 


a 


0.0271 


0.0291 


0.0294 


0.0315 


0.0326 


0.0338 



No. 


7 


8 


9 


10 


XI 




a 


0.0346 


0.0321 


0.0295 


0.0290 


0.0273 







Electrolytic Properties of the Crystallized Hydrate of Sulphuric Acid, 

Since we obtained from one of the solutions crystals of Hj{S04 + HgO, we 
thought it worth while to determine its conductivity, since that has to our 
knowledge not been done before. From the experiments of W. Kohl- 
rausch, Bouty, Poincar^ and Graetz we know that the electrolytes con- 
duct electricity when in a solid state and that the conductivity of some 
increases very rapidly near the melting-point. In some cases it becomes 
at this temperature equal to the conductivity of the liquid, while in other 
cases there seems to be a sudden change with liquefaction. Though these 
experiments are of the greatest importance for our knowledge of the molec- 
ular structure of the salts, they do not agree satisfactorily for the salts 
investigated, which all melt at a high temperature.^ 

Our measurements were taken without difficulty, the crystals melting at 
7^.5 C, and the electrolytic properties are very characteristic. W. Kohl- 
rausch * found that the conductivity of the crystallized acid SOj 4- H2SO4 
was extremely small, and varied according to the way in which they crys- 
tallized. He attributed the remaining conductivity to enclosed liquid 
particles. 

The salt H^O 4- H2SO4 shows entirely different properties. We crystal- 
lized the same repeatedly, and obtained in some cases microscopical 
crystals (after having undercooled the liquid), in other cases crystals 2 to 4 
cm. long. The resistance was always the same at the same temperature, 
showing clearly that the conductivity is not due to enclosed liquid particles, 
but is characteristic for the solid acid. 

» Graetz, Wied. Ann., Vol. 40, p. 18, 1890. « Wied. Ann., Vol. 17, p. 80, 1882. 



ISO 



DR, K, E, GUTHE AND L, /. BRIGGS. 



[Vol. III. 



In the following table is given one series of observations, in which we 
calculated only the specific conductivity. The second taWe gives the 
measurements of the same solution in the liquid state. 



CRYSTALS. 



Temp. 


Res. 


8p. coDd. 


-20^.0 C. 


34000 ohms 


0.846x10-^ 


-15^.0 


25000 


1.147 


- 8^.0 


16200 


1.755 


:F 0^.0 


8200 


3.47 


5^.0 


3530 


8.06 


7^.2 


1514 


18.78 


7°.5 


1000 


28.44 



LIQUID. 



Temp. 


Res. 


8p. cond. 


0°.0C. 
4<^.8 
9°.5 
11^.0 


585 ohms 
481 
402 
376 


48.61x10-1* 
59.12 
70.74 
75.63 



































80 
















70 










f. 


/* 




«l 








d 


V 






1- 








/ 








-i 








r 


i 
















• 

1 

t 






20 










1 






10 










) 








C 


rysta 


l8^_ 


^ 









.15 



•10 5 5 

TEMPERATURES 



Platting the temperature and the 
specific conductivity, we see that 
the latter increases first slowly, but 
more rapidly the higher the tem- 
perature. Between o** and 7**.5 this 
increase is enormous, but the con- 
ductivity of the crystallized acid 
does not reach that of the liquid. 
It reaches only the value 28.44 ^^ 
7**.5 while that conductivity of the 
liquid is 65.4. The last point for 
the crystals has been computed 
from the curve drawn with the 
resistances and the temperature as 
coordinates. 

This increase of the conductivity, 
while the change from the solid to 
the liquid state takes place, seems 
to stand in a certain relation to the 



Fig. 3. 



No. 2.] CONCENTRATED SULPHURIC ACID. 151 

energy taken up by the acid during liquefaction. In the curves the dotted 
line represents this increase. 

This result does not agree with Fonssereau's,^ who found the conduc- 
tivity of the solid salts at the melting-point a thousand times smaller than 
that of the liquid. It agrees much better with Graetz's observations, though 
there is a slight sudden increase at the melting-point, while he finds no 
such step. In fact, a difference of only i** C. would be sufficient to make 
one curve reach the other. 

The sudden change of the temperature coefficient is very characteristic, 
and we see also that such a change does not take place when we undercool 
the solution. 

1 Comptes Rendu*, 98, p. 1325, 1889. 
Physical Laboratory of the University of Michigan. 



152 NEIV BOOKS. [Vol. III. 



NEW BOOKS. 

Grundzuge der Mathematischen Chemie^ Energetik der Chemise hen 
Ersckeinungen, Von G. Helm. Leipzig, W. Engelmann, 1894. 

At a time like the present, when both physics and chemistry are obscured 
by so many unnecessary hypotheses, every attempt to show the power and 
simplicity of general methods is very welcome. Although the general 
methods may themselves rest on certain assumptions, the fact that these 
assumptions, are few, simple, and easily kept in mind is a great advantage. 
For one of the greatest difficulties the student has to encounter is that of 
remembering, often, indeed, of discovering, the hypotheses upon which the 
correctness of a theoretical result depends. The usefulness of thermo- 
dynamic, or energetic, methods has nowhere been greater than in the 
borderland between physics and chemistry. We are, however, inclined to 
think that pure physics may profit quite as much as physical chemistry 
from greater attention to the part which energy and its transformations 
play in natural phenomena, and that the greater advances in this direction 
made by physical chemistry are due rather to freedom from a long history 
of special hypotheses than to any intrinsic difference between the two fields. 

The work before us is an attempt to give a concise and consistent treat- 
ment, based, as far as possible, only on the two laws of thermodynamics, of 
some of the recent advances in theoretical chemistry. It is divided into 
four parts, which treat Energy^ Entropy^ Chemical Intensityy and The 
Degree of Freedom of Chemical Phenomena, 

Part I. contains a very good treatment of the law of the conservation of 
energy as applied to thermo-chemistry ; in other words, of the proposition 
that the variation of the internal energy of a system depends only on the 
initial and final states of the system. We have two faults to find with Part 
I. The first is the failure to define temperature carefully. A satisfactory 
treatment of temperature must of course be left till the second law has 
been introduced, but we feel, especially at p. 14, that the meaning of 
"Celsius temperature" needs a precise definition. The second fault is 
a lack of clearness in the definition of molecular weight. It is, in our 
opinion, altogether a mistake to say (p. 15) that by the "law" of 
Avogadro the gas constant R in the equation/?^ = RT \% the same for one- 
gram molecule for all gases. This so-called law is simply our only defini- 



No. 2.] NEIV BOOKS. 1 5 3 

tion of the molecular weights of gases, and our chemical molecular symbols 
are not independent of it, but deduced from it. The mere fact that our 
molecular weights so obtained are in general very simply related to the 
compositions of the gases in question, does not make us the less dependent 
on the fundamental definition in originally finding them. 

Part II., headed Entropy, treats the second law of thermodynamics, and 
applies it to several problems, especially such as come under the head of 
Clapeynon*s equation. This part seems to us the least satisfactory in the 
book, and we doubt whether the student who is not already familiar with 
the equation 

will make much out of what is here given on that subject. The greatest 
care and precision are necessary if the meaning of entropy and of the ex- 
pression I —^ is to be understood, and this precision of statement is often 

lacking. One wishes that the meaning of reversibility might be as well 
set forth as in that delightful book of M. Duhem, the Introduction d la 
Mecaniqu€ Chimique, It is perhaps carping to object to the statement 
that the eflciency of an irreversible engine is always less than that of a re- 
versible one, but we have never seen a satisfying proof of that proposition. 
M. Bertrand*s remark seems just when he says in Chapter XII. of his 
Thermodynamiquey "Je serai tr^s bref sur les cycles irr^versibles ; les 
demonstrations et les ^nonc^s memes de leurs propri^t^s me paraissent 
jusqu'ici manquer de rigeur et de precision." There is, to be sure, an air 
of originality about the whole treatment, and this in itself is attractive, but 
the result seems to us less clear and simple than more ordinary methods. 
Alter this unsatisfactory section on entropy comes a short but very good 
introduction to free energy, the thermodynamic potential, and Gibbs's 
potentials, here called " chemical intensities." Most of the rest of Part II. 
is given up to applications of the foregoing principles to cases of equilibrium 
between two phases, — evaporation, allotropic changes, etc., — and to the 
theory of the reversible galvanic cell. In this last the author again fails to 
discuss reversibility, the question of the irreversible Joule heat not being 
mentioned. There follows an interesting paragraph on the relation of 
chemical intensity and electromotive force, and Part II. closes with a few 
pages on the conductivity of electrolytes. 

Part III. begins with a section on the general properties of the chemical 
intensity, in which Gibbs is followed. The remainder of this most interest- 
ing division of the book considers a number of subjects by means of the 
chemical intensity. Among them are chemical equilibrium, osmotic pres- 



154 NEW BOOKS. [Vol. III. 

sure, and diffusion, which may serve to indicate the wide range covered by 
Gibbs's theory. 

Part IV. deals with the phase rule, of course from Gibbs's standpoint. 

Throughout the work numerical examples are introduced very judiciously 
to illustrate the theoretical results obtained. 

To the student who is not already familiar with the elements of thermo- 
dynamics, and to some degree with free energy or the thermodynamic 
potential, the book will be hard reading. But the more advanced student 
will find it very useful as a short statement of a theory which he would 
otherwise have to dig out of many scattered and often obscure papers. 
The general impression left in the reader's mind is that so good a book 
ought to have been better written ; but the faults are faults of detail, while 
the merits are those of unity and generality. We cordially recommend 
this work to all who are interested in physical chemistry, and we hope that 
this first example may find imitators in America, as it is sure to do in 
Europe. 

Edgar Buckingham. 

Brvn Mawr, May 7th, 1895. 

OstwalcTs Klassiker der Exacten Wissenschaften} 8vo. In Leinen 
Gebunden. Leipzig, Wilhelm Engelmann, 1894. 

It is often difficult to realize that knowledge regarding many of the 
familiar facts of to-day has in many cases had a slow and laborious growth. 
Conceptions which we at the present time accept without a thought as to 
their origin have startled the scientific world at their announcement, and 
have set at work many a patient observer who, by his labors, has contrib- 
uted no unimportant share to the world's present store of knowledge. 

In a most charming series of little volumes, entitled OstiuahVs Klassiker 
der Exacten Wissenschaften^ Professor Ostwald of Leipzig has republished 
the original papers of early investigators along different scientific lines, and 
has thus brought these truly classic pieces of scientific literature within the 
reach of all. The interest felt in these papers is increased when one 
realizes that from these as a germ much of the present science has 
grown. Throughout this series of works the groping of the investigator 

^ No. 52. Uber die Krafte der ElectricitSt bci der Muskclbcwegung. Alobius 
Galvani, 1791. 

No. 56. Die Gesetze der Ueberkaltung und Gefrierpunktserniedrigung. Sir Charles 
Blagden, 1788. 

No. 57. Abhandlungen fiber Therraometrie, von Fahrenheit, Reaumur, and Celsius. 
1724-1730-1733-1742. 

No. 59. Otto von Guericke*s neue Magdeburgische Versache fiber den leeren 
Raum. 1672. 



No. 2.] NEIV BOOKS. 1 55 

is always apparent. If the reader occasionally marvels that a wrong con- 
clusion was drawn from facts observed, or that phenomena apparently 
so patent escaped detection, he is quite as frequently delighted at the 
originality of the ideas, and the brilliancy of the conceptions, which seem 
now almost to have come by intuition. In all, there have been up to the 
present time about sixty of these little volumes published. The four men- 
tioned below may serve to give some idea of the value of the series. 

In No. 52 is contained the account by Galvani of his experiments with 
electricity in producing the muscular contractions in a frog's legs. At 
first statical electricity alone was employed, and the effects of insulators 
and conductors, of positive and negative electricity, were carefully investi- 
gated. Galvani's next step was to examine the effects produced by atmos- 
pheric electricity. A pointed rod, carefully insulated from the roof, was 
placed upon the house, and securely grounded by being connected with the 
water in a well. The prepared frog's legs were placed across a break in 
this rod, and violent contractions were observed whenever a flash of light- 
ning was seen. That Galvani was aware of the danger attending this 
experiment, and of the fatal result to Richmann of a precisely similar 
experiment in 1753, is evident from his remark that "a careful and intelli- 
gent arrangement in this experiment must be observed." Galvani's later 
and more important experiments consisted in effecting the muscular con- 
tractions by the difference of potential produced by the contact of two 
different metals. These contractions occurred whenever the metal hook, 
which passed through the spinal column of the frog, touched the metal 
plate upon which the frog's legs rested. These phenomena Galvani 
attributed to the electricity resident in the frog. " It is easy, however," 
he says, " to be deceived by experiment, and to imagine that to be seen 
and found, which one wishes to see and find." Reil of Halle, and later 
Volta, argued that " the seat of the irritation is in the metals, that of the 
irritability is in the organism." Thus early began the discussion as to the 
seat of the electromotive force, which even to-day is not settled. 

No. 56 of the Klassiker contains an account of two important 
researches carried on by Sir Charles Blagden, about the year 1 788. The 
first is on the supercooling of water ; the second is the more famous one 
on the depression of the freezing-point of liquids due to dissolved sub- 
stances. Both researches are models of logical experimentation, and are, 
for their time, very accurate. In the first, the author repeated earlier 
experiments on supercooling, and studied the effects of various substances 
— salts and gases in solution, substances in suspension, etc. — in increas- 
ing or decreasing the amount of possible supercooling. The second paper 
contains the record of experiments which established the law that the 
depression of the freezing-point is proportional to the amount of the dis- 



156 NEW BOOKS, [Vol. III. 

solved substance. Blagden's work remained unnoticed, and the same law 
was rediscovered by RUdorff after a lapse of nearly eighty years. The 
history of these investigations, carried out first by Blagden, later by 
RUdorff, Coppet, and Raoult, forms one of the most interesting chapters 
of modern chemistry, and leads up to the important generalizations of 
van*t Hoff, regarding the nature of dissolved substances. 

No. 5 7 of this series contains the original papers in which Fahrenheit, 
Reaumur, and Celsius published their discoveries regarding the proper 
construction and calibration of thermometers. Fahrenheit, according to his 
own statement, was led to construct a thermometer through the announce- 
ment by Amontons that water always boils at the same temperature. 
Wishing himself to observe this " beautiful phenomenon," Fahrenheit con- 
structed the first mercury thermometer, and fixed thereto the arbitrary 
scale which now bears his name, and which contained three fixed points. 
For the zero of this scale he chose the point of " most intense cold," which 
was the temperature obtained by mixing water, ice, and sal ammoniac or 
common salt. The second fixed point was determined as the temperature 
of melting ice, which was 32 on Fahrenheit's arbitrary scale, and the third 
as the temperature of a healthy person, which temperature fell at 96. That 
the temperature of boiling water fell at 212, was purely accidental. It is 
strange indeed that Fahrenheit nowhere speaks of the proportions of his 
freezing mixture, whereby his zero was determined, and also equally strange 
that he should not have chosen the boiling-point of water as one fixed 
point, inasmuch as his attention had been especially directed to the con- 
stancy of this temperature. 

Reaumur, who appears to have been ignorant of Fahrenheit's work, 
thought mercury to have a coefficient of expansion too small to permit of 
its use in a thermometer, and so chose alcohol as his thermometric sub- 
stance. To obtain a sufficiently high sensibility he was obliged to use a 
bulb four and one-half inches in diameter, although, as he himself foresaw, 
so large a bulb could not indicate rapid changes of temperature. The 
principle employed by R^aumuf in graduating his scale was radically differ- 
ent from that used by Fahrenheit. Reaumur assumed that only one fixed 
point was necessary, and chose for this the temperature of melting ice. 
He then determined the volume of the bulb, and so graduated his tube 
that each division or degree represented one one- thousandth of the entire 
volume of the alcohol in the bulb, when at the temperature of melting ice. 
As the alcohol expanded when heated, the actual increase in volume was 
then read off on the stem. Under these circumstances, the temperature 
of boiling water was indicated by the point 80 on his thermometer, although 
it is clearly evident that the temperature of the thermometer was not that 
of the boiling water in which it was placed. 



No. 2.] NEW BOOKS. 1 5 7 

Celsius, whose work followed closely upon that of Reaumur, chose the 
two fixed points now used — the melting-point of ice, and the boiling-point 
of water — and divides this interval into one hundred equal parts. He, 
however, mentions the fact, also referred to by Fahrenheit, that the 
temperature of boiling water varies with the pressure of the air, and sug- 
gests a constant barometric height at which this temperature should be 
taken. An important feature of Celsius* work was the introduction of the 
loo-degree scale, although such a scale had in all probability been sug- 
gested by du Crest in France. It is worthy of notice that Celsius, in his 
original paper, called the temperature of boiling water o, and that of melt- 
ing ice 100. Not until this paper appeared in the eleventh volume of the 
Proceedings of the Swedish Academy, do we find these figures reversed, 
and the scale given in the familiar form in which it is universally used. 

Otto von Guericke, in the fifty-ninth volume of this series, writes of the 
properties and pressure of the atmosphere, and later describes the air 
pump devised by him, and gives the details of his many experiments with 
this remarkable piece of apparatus. After demonstrating the impossibility 
of exhausting the air from a barrel, owing to the porosity of the wood, von 
Guericke substituted a thin copper sphere for the barrel, only to find the 
sphere crushed by the pressure of the air. Later followed the construction 
of the large hemispheres, which, when exhausted, twenty-four horses were 
not able to pull apart. That the air has weight, he proved by weighing a 
receiver filled with air, and then empty, and noticing the diminished weight 
in the latter case. The pressure of the air due to its own weight, he argued, 
must diminish as one ascends a mountain, and he proved this to be so. 
The abhorrence which nature was supposed to possess toward a vacuum he 
showed to be identical with the atmospheric pressure. Furthermore, he 
argued, this pressure of the air could be balanced by an equal pressure, and 
proved his statement by exhausting the air from the upper end of a long 
closed tube, the lower end of which was open, and under the surface of 
water. The water rose in the tube, until, as he explained, the pressures at 
the surface of the water in the reservoir, outside and inside the tube, were 
equal. In his study of this column of water, von Guericke noticed its rise 
and fall with the varying pressure of the air, and placed within the tube a 
little floating figure, whose finger pointed to a scale on the outside of the 
tube, indicating the atmospheric pressure. On one occasion, as the figure 
sank far below his usual position, indeed, even below the scale on the 
tube, von Guericke announced to his friends that a storm was approaching. 
In less than two hours the storm broke, and thus was fulfilled probably 
the first weather prediction based upon meteorological instruments. Von 
Guericke's original air pump, as well as the colossal Magdeburg hemi- 
spheres, are now guarded as among the most valued treasures in the Berlin 
Physical laboratory. ^^^ ^ 3^^^^ 



158 NEW BOOKS. [Vol. III. 

Popular Scientific Lectures. By Ernst Mach, translated by 
Thomas J. McCormack. 8vo, pp. 313. Chicago, The Open Court 
Publishing Co., 1895. 

This work is a translation of a series of lectures delivered by Professor 
Mach of Prague at various times between 1864 and 1894. The name 
Popular Scientific Lecture often conveys to the scientist the idea of dilet- 
tanteism, and the practice is condemned, and rightly, too, if the kctarer 
only brings before his audienc e a mass of details, interesting in themselves, 
but leaving in the minds of the hearers no one central idea. When done 
well, however, as in the present case, nothing but praise is the lecturer's 
due, and scientific inquiry is distinctly advanced. The book easily divides 
itself into two parts, the first seven lectures dealing with explanations of 
simple phenomena, and the last five lectures dealing with questions of a 
more philosophical and educational nature. 

The first group of seven lectures belongs to the earlier period of Professor 
Mach's career. The first requisite of a lecture is that it shall impart infor- 
mation, but more important is it that the information so imparted shall 
cause the listener to think. The lecturer must choose from the mass of 
illustrations at hand those most explanatory, and must confine himself to a 
single line of thought. Judged in this way, these lectures are admirable. 
Professor Mach takes a few common, every- day phenomena, and in simple 
language leads his audience from the fact itself to the larger concepts that 
lie behind it, without their ever feeling that they are beyond their depth. 
Perhaps the best of all the group is the first one of this volume on " The 
Forms of Liquids." To the unthinking, he says, the most noticeable 
property of liquids is their want of form ; but a discussion of the raindrop 
and the soap-film, in a simple and elementary but masterly way, leads to a 
very different conclusion. Then follow two lectures on Acoustics: viz. 
" The Fibers of Corti " and the " Causes of Harmony." Three lectures on 
Optics, under the headings "The Velocity of Light," "Why has Man Two 
Eyes?" and "On Symmetry," treat in a very elementary manner of some 
of our commonest observations, the simple explanation of which is not 
always easy even to one who has studied them. Mach shows that the 
pleasing effects of symmetry are due to the repetition of sensations ; where 
symmetry does not produce such repetition, as in the passage from a major 
to a minor scale in music, this agreeableness is not experienced. The 
lecture on "The Fundamental Concepts of Electrostatics" is a good 
example of the possibility of putting in simple, untechnical language such 
difficult ideas as those contained in the measurement of current, electro- 
motive force, capacity, etc., and in a manner, too, suited to the most non- 
mathematical person. 



No. 2.] NEW BOOKS. 1 59 

Perhaps the chief interest to a reader of this volume will lie in the last 
half of it The lecture on ** The Conservation of Energy " deals historically 
with the part which the principle of the impossibility of perpetual motion 
has played in the subject of mechanics, and the proof of the principle of 
the conservation of energy as derived from that subject His statement 
of the results to be deduced from the fact that heat has a mechanical 
equivalent will repay careful reading. It does not follow that heat is not a 
substance, he says, and the idea that heat is a quantity is due entirely to 
historical connection. There is no doubt that much of the subject matter 
of dynamics has yet to be recast ; the laws of Newton are not yet in their 
best possible form. The chapters on "The Economical Nature of Physical 
Inquiry," ** Transformation and Adaptation in Scientific Thought," and ** On 
the Principle of Comparison in Physics," treat in a clear and thoughtful 
way of those broader aspects and methods common to all scientific inquiry. 
The last address, " On Instruction in the Classics and the Sciences," is a 
forcible plea for the study of mathematics and the sciences ; but it is a pity 
to see a man of the stamp of Professor Mach put forward some of the argu- 
ments which he does against the study of the classics. That much is to be 
said for a more general study of the sciences is true, but that this end should 
be gained by crying down the value and power of a classical education is 
to be deplored. His plea for less work in the preparatory schools, and a 
restriction of the number of subjects studied, is one that appeals strongly to 
us in this country also. " A single philological, a single historical, a single 
mathematical, a single scientific branch, pursued as common subjects of 
instruction for all pupils, are sufficient to accomplish all that is necessary 
for the intellectual development" (p. 290). 

The translator deserves praise for the general excellence of his rendering 
in spite of a few evident traces of its being a translation. The publisher's 
work is aU that could be desired. ^ ^^^^^ Mackenzie. 

Proceedings of the Electrical Society of Cornell University, Vol. 
II., 1894-5. 8vo, pp. 122, Ithaca, Andrus & Church, 1895. 

The second volume of the Proceedings of the Electrical Society of Cor- 
nell University includes the following papers: Difference of Electrical 
Potential between Substances in Contact ; Metals for Magnet Cores ; Fuse 
Wire; Lightning Arresters; Mechanical Equipment of Power Stations; 
Some Points in Connection with the Modem Theory of Primary Batteries ; 
A Method of Reducing Hysteresis Losses in Armature and C*R Losses in 
the Field ; Electricity and Mining ; Electrical Resonance and Some Allied 
Phenomena; Alternating Current Motors; Metallic Conduction and the 
Influences which affect it 



l6o NEW BOOKS. [Vol. III. 

Standard Methods in Physics and Electricity criticised^ and a Test 
for Electric Meters proposed. By H. A. Naber. 8vo, pp. 114. London, 
George Tucker, 1894. 

The volume before us is principally devoted to presenting 4he advantages 
of the Naber gas voltameter, for which the author makes the most extrava- 
gant claims. The useful applications claimed for the instrument extend to 
almost all branches of scientific and technical electricity, from the accurate 
measurement of current and electromotive force, both direct and alter- 
nating, to the determination of the form of an alternating current curve. 
Frequent references throughout the book to authorities show on the part of 
the author an extensive acquaintance with the literature of electricity. It 
is to be regretted that so little appreciation is shown of the value, in fact 
the necessity, of experiment. In spite of the claims made for the voltam- 
eter in question, no quantitative tests of its action are cited. Most 
readers will I think join with the reviewer in postponing af serious considera- 
tion of the contents of the book until the author's claims have received 
some experimental verification. t» vr 



Volume III. November-December, i8g^. Number j. 



THE 

PHYSICAL REVIEW. 



VARIATION IN ELECTRICAL CONDUCTIVITY OF 
METALLIC WIRES IN DIFFERENT DIELECTRICS. 

By Fernando Sanford. 

IN a paper published in 1892, entitled "Some Observations 
upon the Conductivity of a Copper Wire in Various Dielec- 
trics," ^ I called attention to the fact that, with the copper wire 
used by me in the experiments referred to, the conductivity varied 
in different liquid and gaseous dielectrics by an amount approxi- 
mating in some cases to 0.2 of one per cent of its air resistance at 
the same temperature. 

In a later paper, entitled " A Necessary Modification of Ohm's 
Law,"^ I referred to a similar observation made upon the conduc- 
tivity of a silver wire. 

The apparatus used in the experiments referred to in the above- 
mentioned articles consisted of a copper tube 120 cm. in length 
and 2.5 cm. in internal diameter, closed at the ends with copper 
plugs provided with stopcocks. To the inside end of one end 
plug was connected a copper wire i mm. in diameter, which was 
stretched lengthwise through the center of the tube, and passed 
out through an insulating plug in the center of the other end plug. 
The resistance of the wire and tube was measured at various tem- 

* Leland Stanford Jr. University Publications. Studies in Electricity, No. I. 

* Phil. Mag., January, 1893, Vol. 35, p. 65. 

161 



1 62 PROFESSOR FERNANDO SANFORD. [Vol. III. 

peratures when the tube contained air, and again when the tube 
contained other liquid and gaseous dielectrics. A side tube mid- 
way between the ends of the long tube served to admit a ther- 
mometer, by means of which the temperature of the dielectric 
inside the tube and near the wire was measured. 

Some fifteen different liquid and gaseous dielectrics were used, 
and, in general, the conductivity of the wire was found to vary 
from its air conductivity at the same temperature by an amount 
which was different for each dielectric used, and which was con- 
stant for any particular dielectric. 

The accuracy of the observation was attacked upon both theo- 
retical and experimental grounds (see especially The Electrician^ 
London, of January 13, 1893, and Professor Henry S. Carhart in the 
Physical Review, Vol I., p. 321), and though it had been verified 
by me with several different wires, and though I had collected con- 
siderable material bearing upon the nature of the phenomenon, I 
have thought best to publish nothing further upon the subject 
until the observation had been verified by some one outside of 
my own laboratory. 

I have recently received a memoir by Professor Grimaldi and Dr. 
Platania, of the University of Catania,* giving the results of a long 
and very careful series of experiments upon the resistance of a 
copper wire in air and petroleum. These researches have been 
conducted with greater refinement and more delicate apparatus 
than have any previous experiments upon the same subject with 
which I am acquainted. The results show a degree of concordance 
quite remarkable, when the difficulties of the determinations are 
taken into account. In every case the resistance of the wire in 
petroleum was found to be less than in air. This difference in 
resistance was, however, when reckoned as a percentage of the 
whole resistance of the wire, only about one-twelfth as great as in 
the case of the wire with which the phenomenon was first dis- 

1 Sulla Resistenza Elettrica dei Metalli nei diversi Dielettrici. Memoria del Dott 
Giovan Pietro Grimaldi, Profcssore di Fisica nella Regia University di Catania, e Dott 
Giovanni Platania, Assistente al Gabinetto di Fisica della stessa University Parte I. 
Ricerche sulla variazione di resistenza del rame nel petrolio. See also, Dal Bollettino 
mensile dell* Accademia Gioenia di Scienze Naturali in Catania Fascicolo XXXVIIL, 
seduta del mese Dicembre 1894. Also Nuovo Cimento July 1895. 



No. 3.] CONDUCTIVITY IN DIFFERENT DIELECTRICS, 163 

covered by me ; but the total variation in resistance amounted, 
taking the mean of all the determinations, to 0.00002 ohm, while 
in the same dielectric with the wire originally used by mc it 
amounted to 0.00006 ohm. The wire .used by Signors Grimaldi 
and Platania was 304 mm. in length, and 0.22 mm. in diameter. 
Its variation in resistance per unit length was accordingly greater 
than in the wire used by me, while the corresponding surface 
exposed was less than one-fourth as great. 

The intelligence and care shown in the published work of 
Signors Grimaldi and Platania, and the remarkable uniformity of 
their results, make it improbable that the existence of the phe- 
nomenon will again be questioned. 

The method and apparatus used in the following experiments 
were practically the same which I described in my former papers. 
The wires whose conductivities were to be measured were stretched 
lengthwise through the tube used in the earlier experiments, and 
were sometimes soldered and sometimes connected by means of 
a binding screw to the inner end of one plug, and were carried 
through the insulating plug at the other end of the tube. The 
resistance of the wire and tube was at first measured by means of 
a Hartmann & Braun resistance box and bridge, with bridge arms 
of 1 : 1000, the comparison coils being divided to tenths of an ohm. 
Later, a Nalder Brothers resistance box and bridge, with arms of 
I : loooo was used, the comparison coils being divided to tenths 
of an ohm. The galvanometer used gave a noticeable deflection 
for a change in resistance of 0.00002 ohm, and later for o.ooooi 
ohm. 

The temperature of the interior of the tube was measured by 
a standard thermometer graduated to o.i^ inserted into the side 
tube with its bulb in contact with the wire, and read through a 
telescope which enabled the observer to estimate to 0.01° with a 
fair degree of accuracy. 

The wire first used had with the tube a resistance of 0.0335 ^^m 
at 18° C, and a temperature variation of 0.000014 ohm for one- 
tenth of a degree centigrade. By reversing the current it was 
possible, even with the least sensitive galvanometer used, to esti- 
mate the resistance accurately to 2 in the fifth decimal place ; and 



1 64 PROFESSOR FERNANDO SANFORD, [Vol. Hi. 

with the galvanometer used later, an error of i in the fifth decimal 
place would not be made, even without reversing the current. 
This, while not the highest attainable accuracy in resistance meas- 
urement, is sufficiently accurate for the work, since the tempera- 
ture of the wire could not be known with certainty to a greater 
accuracy than o.i°. Had the measurements been made at a tem- 
perature differing greatly from the room temperature, or had the 
wire been perceptibly heated by the current, even this degree of 
accuracy would be improbable, since what was really observed was 
the temperature of the thermometer in the tube near the wire, 
and the small wires used would almost certainly change in tem- 
perature more rapidly than the thermometer. To guard against a 
possible error of this kind, the measurements were all made at the 
room temperature, which very rarely varied so much as io° in 
twenty-four hours. The measurements were also made at all 
hours of the day, and sometimes late at night, in order that 
approximately the same number might be made with rising as 
with falling temperature. 

To guard against the error due to heating of the wire by the 
current, the resistance of the wire at the same apparent tempera- 
ture was observed for a wide range of current strength, and the 
current strength was kept far below the point where the resistance 
of the wire seemed to increase. The zero method of measurement 
was used throughout, and the current was passed through the wire 
only long enough to enable the galvanometer deflection to be read. 
In the first work, in order to secure a constant current strength, 
a battery of thirty-two silver chloride cells with high internal 
resistance was used with loo ohms additional resistance in the 
battery circuit. Later, one Edison-Lalande cell was used with a 
resistance of from 50 to 100 ohms in the battery circuit. 

That temperature fluctuations did not cause serious error may 
be seen from the data published with the first mentioned paper. 
The curve shown in Fig. 3 of that paper is reproduced here as 
Fig. I. It represents the resistance of the wire in air, and in the 
gasoline burning gas used in the laboratory. There are twenty-six 
measurements made with the tube filled with air. These were 
made at irregular intervals for six days, the tube having been in the 



No. 3.] CONDUCTIVITY IN DIFFERENT DIELECTRICS, 165 

meantime filled with burning gas, and seventeen measurements 
made on three successive days with the wire in this dielectric. 
The tube and wire were neither disconnected nor moved in chang- 
ing the dielectric. The gas was admitted through one of the end 
stopcocks, which was attached by a rubber tube to a gas cock in 



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11 12 13 14 U 16 17 18 19 20 21 
TEMPERATURE C 

Fio. 1. 



22 23 24 



the laboratory, and was removed by blowing air through the tube 
with a bellows. 

Of the twenty-six points platted for the air measurements, nine- 
teen were made before the tube was filled with the gas, and seven 
were made after the gas had been removed. The greatest distance 
of any single air point from the curve corresponds to a resistance 
of o.oocx)2 ohm, or a temperature variation of o. 14®. In the seven- 
teen measurements made with the tube filled with the burning gas, 
the greatest distance of any point from the curve corresponds to a 



1 66 PROFESSOR FERNANDO SANFORD. [Vol. III. 

difference in resistance of 0.000025 ohm, or a temperature varia- 
tion of o.I5^ while only one point in the seventeen is more than 
0.0000 1 ohm from the curve. 

The average difference in the resistance of the wire and tube 
with the dielectrics named was 0.000058 ohm, corresponding to a 
temperature difference of 0.41°, while the nearest approach of any 
gas point to the air curve represents a difference in resistance of 
0.00005 ohm, corresponding to a temperature difference of 0.36^. 

That the temperature of the wire can be known with sufficient 
accuracy when the above precautions are taken is shown by the 
data published in the article by Professor Carhart, of which mention 
has already been made. In the investigation reported by Professor 
Carhart, a tube and wire combination similar to the one above 
described was heated up to 30° C. by warm water, and a series of 
resistance measurements was made while the temperature was 
falling to 20® C. Even with this arrangement, and with a ther- 
mometer reading only to half degrees, and a wire whose resistance 
varied by 0.000018 ohm for one-tenth of a degree, the different 
measurements show a very uniform decrease of resistance for the 
estimated decrease of temperature. 

I lay special stress upon this point, because in the editorial 
article in The Electrician^ previously referred to, the writer charges 
that it is " a great assumption to suppose that the temperature of 
the wire is the same as that of the dielectric," and says: "The 
wire is, of course, being heated by the current, and a slight change 
of temperature would necessarily result from change of emissivity, 
owing to the different thermal properties of the various dielectrics 
used." This explanation would hardly have been offered had the 
author read with any care the article which he was criticising, 
since it would make it necessary to assume from the data there 
given that the temperature of the wire in petroleum was 0.43 of a 
degree less than in air, while in petroleum containing a little wood 
alcohol its temperature with the same current through it as before 
was 0.5 of a degree greater than in air. As a matter of fact, 
increasing the current strength fourfold did not alter the apparent 
resistance of the wire at the same temperature. In the very care- 
ful provisions made for maintaining the wire at constant tempera- 



No. 3] CONDUCTIVITY IN DIFFERErrr DIELECTRICS, 167 

ture by Signers GrimaJdi and Platania, this possibility of error was 
still further eliminated, so that it is certain that, whatever else may 
be the cause of the phenomenon, it is not due to a temperature 
variation of the wire. 

The following table gives the change in resistance observed in 
the above-mentioned wire in eight different dielectrics, and the 
temperature change necessary to account for such variation in 
resistance upon the hypothesis advanced by The Electrician. 



Dielectric. 


Resistance change. 


Equivalent temperature change. 


Petroleum 


-0.00006 ohm 


—0.43 degree 


CSj and turpentine .... 


-0.00003 ohm 


—0.2 degree 


Wood alcohol and benzine . . 


+0.00005 ohm 


+0.36 degree 


Absolute alcohol 


+0.00006 ohm 


+0.43 degree 


Wood alcohol and petroleum . 


+0.000075 ohm 


+0.53 degree 


Laboratory burning gas . . . 


+0.000058 ohm 


+0.4 degree 


Chloroform vapor 


+0.00005 ohm 


+036 degree 


Ether vapor 


+0.000083 ohm 


+0.6 degree 



Following the publication of my first paper upon this subject, a 
number of measurements were made with a silver wire i.i mm. in 
diameter, using as dielectrics air, petroleum, wood alcohol, absolute 
alcohol, ether vapor, chloroform vapor, laboratory burning gas, and 
a mixture of wood alcohol and petroleum. While the same phe- 
nomenon was observed as with the copper wire previously used, 
the variation in resistance was not so great. The most important 
difference, however, was in the different order of arrangement of 
the dielectrics with reference to their influence upon the conduc- 
tivity of the wire. While the copper wire had shown a lower 
resistance in petroleum than in air, the resistance of the silver wire 
was very slightly increased in petroleum ; and whereas the resist- 
ance of the copper wire had been greater in sulphuric ether vapor 
than in any other dielectric used, the resistance of the silver wire 
was less in the ether vapor than in any of the other dielectrics. 
The following table will show the results of the measurements 
made upon the silver wire : — 



1 68 



PROFESSOR FERIVANDO SANFORD. 



[Vol. III. 



DIAMETER OF WIRE, 1.1 mm.; RESISTANCE OF WIRE AND TUBE AT 
IS'^ C, 0.02705 ohm; TEMPERATURE VARIATION FOR 0.1 degree, 
0.000009 OHM. 



Dielectric. 



Resistance change. 



Equivalent temperature change. 



Petroleum 

Absolute alcohol .... 

Wood alcohol 

Wood alcohol and petroleum 

Ether vapor 

Chloroform vapor .... 
Laboratory burning gas . . 



H- 0.00002 ohm 
H- 0.00003 ohm 
-f 0.000045 ohm 
+0.000046 ohm 
-0.000025 ohm 
H- 0.000025 ohm 



+0.2 degree 
+0.3 degree 
+0.5 degree 
+ 0.5 degree 
—0.3 degree 
+ 0.3 degree 



Uncertain. Resistance slightly greater than in air 



The results hitherto mentioned have been referred to in previ- 
ous publications. Those which follow were oiade under practi- 
cally the same conditions, except that the temperature of the room 
was more constant, and rarely varied so much as five degrees in 
twenty-four hours. The time used in making a single set of com- 
parison measurements varied from one to two weeks, during which 
time several measurements were usually made each day. Care 
was taken, as before, that approximately the same number of meas- 
urements should be made with rising as with falling temperatures. 

The copper wire already mentioned will hereafter be referred 
to as Cy Its diameter, as before stated, was approximately i mm. 
In order to observe any possible effect of an increase of surface 
of the wire, the same tube was provided with a copper wire, 
of 1.27 mm. in diameter, hereafter designated as C. The resist- 
ance of this wire and tube when the tube was filled with air at 
20° C, was 0.02618 ohm. The resistance when the tube was filled 
with the mixture of air and gasoline vapor used as burning gas 
in the laboratory was 0.02626 ohm, showing an increase in resist- 
ance of 0.00008 ohm. 

With the wire C\, which was of the same length in the tube, 
the resistances in these two media at the same temperature was 
respectively 0.03375 ohm, and 0.03381 ohm, showing a change in 
resistance in the burning gas of 0.00006 ohm. This showed that 
while the surface of the wire had been increased about 60 per cent. 




No. 3.] CONDUCTIVITY IJST DIFFERENT DIELECTRICS, 1 69 

the difference in resistance had been increased about 30 per cent. 
As this is the greatest variation observed in any wire with the 
change in dielectric, I give in Fig. 2 the curves representing the 
resistance of the wire in the two media. The data upon which 
the figure is based are given below. The only change made in 
the apparatus when the gas was introduced was the opening and 
closing of the stopcocks in the end plugs, as the tube was already 
attached to the gas cock in the laboratory. 



5 

4 
u 

V 

1 
0.280 

oj»e 














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17 



18 



19 20 21 

TEMPERATURE C. 

Fig. 2. 



In order to determine whether all the dielectric in the tube was 
concerned in the resistance change, or only a thin layer of it in 
contact with the wire, the wire was withdrawn from the tube, and 
its surface was very thinly coated with paraffine oil, after which 
it was replaced in the tube, and a second set of measurements 
was made with the same dielectrics as before. These measure- 
ments gave exactly the same resistance in the two dielectrics. 
This, together with the fact, mentioned in my first paper, that 
after the tube had contained a liquid dielectric the wire frequently 
required a considerable time before it returned to its air resistance, 



170 



PROFESSOR FERN'AN'DO SANFORD. 



[VOL. 111. 



has led me to believe that the phenomenon is due to a very thin 
film of the dielectric adhering to the surface of the wire, and pos- 
sibly absorbed to some extent by the wire. It was especially 
noticed that after the tube had contained ether vapor it required 
a long time, frequently several days, to return to its previous air 
resistance. In one case, the wire continued to show an augmented 

COPPER WIRE Cj, 1.27 mm. IN DIAMETER. 



Date. 


Hour. 


Dielectric. 


Temperature. 


Retittance. 


Nov. 4 


12.30 


Air 


21.1- 


002629 


Nov. 4 


3.30 


Air 


22.6 


0.02642 


Nov. 4 


5.45 


Air 


22.0 


0.02638- 


Nov. 5 


10.30 


Air 


18.5 


002604- 


Nov. 5 


11.45 


Air 


19.25 


0.02612 


Nov. 5 


5.10 


Air 


20.5 


0.02623 


Nov. 7 


10.00 


Air 


17.0 


0.02590 


Nov. 7 


11.15 


Air 


17.8 


002597 


Nov. 7 


2.00 


Air 


19.7 


002616- 


Nov. 7 


5.00 


Air 


21.1 


002628+ 


Nov. 7 


5.10 


Burning gas 


21.1 


002639 


Nov. 8 


8.45 


Burning gas 


18.2 


002609 


Nov. 8 


11.00 


Burning gas 


19.8- 


0.02624 


Nov. 8 


1.45 


Burning gas 


21.6 


0.02642- 


Nov. 8 


3.20 


Burning gas 


22.3 


002647 


Nov. 8 


5.00 


Burning gas 


22.7 


0.02650 


Nov. 9 


9.10 


Burning gas 


19.3 


002619+ 



resistance, apparently due to ether vapor, after air had been drawn 
through the tube by a filter pump for more than twenty-four hours, 
and it returned to its air resistance only after the tube had been 
filled with alcohol for some time and was then emptied and dried. 
It was also noticed that during all this time the odor of the ether 
could be detected in the tube. 

In order to observe whether any effect would be produced by 
increasing the surface of a given wire, another wire, C3, 1.27 mm. 
in diameter, was cut from the same spool as C^, and was ham- 
mered flat to increase its surface. This wire was placed in the 
tube, and its resistance was measured in the two dielectrics which 



No. 3.] CON'DUCTIVITY IN DIFFERENT DIELECTRICS, 171 

had been used with Q, but no increased resistance could be 
observed in the gas. The wire had been much hardened by ham- 
mering, but what change had been produced in its surface is not 
known. 

The next wire used was 1.66 mm. in diameter, and is designated 
C4. Instead of giving an increased difference of resistance cor- 
responding to its increase of surface, its resistance change in burn- 
ing gas was less than that of either C\ or Q. Its resistance in air at 
18° was 0.01915 ohm, and in burning gas at the same temperature 
it was 0.01917 ohm, showing a difiference of only o.cxxx)2 ohm. 
The same wire was tested in absolute alcohol and in petroleum 
poured in after the alcohol had been drawn off, in both of which 
dielectrics it gave a smaller difiference of resistance than did C^ 
In alcohol this difiference amounted to about 0.00004 ohm, and in 
petroleum with trace of alcohol to about 0.00005 ohm. 

Another copper wire, Q, 1.27 mm. in diameter, was cut from the 
same spool as Cj, and was amalgamated upon the surface by immers- 
ing it a short time in a solution of mercuric chloride. Its resistance 
at 20** was 0.02640 ohm in air, and 0.02646 ohm in ether vapor. 
In freeing the tube from ether vapor, one of the contacts was 
loosened, and the apparatus was disconnected and remained 
standing unused from Feb. 9 to March 6. It was then recon- 
nected, and measurements were made with air, burning gas, petro- 
leum, and a mixture of wood alcohol and petroleum. By the time 
these measurements were undertaken the surface of the wire had 
become blackened, instead of showing the bright mercury surface, 
and the resistance of the wire had appreciably increased. All of 
the following measurements made with this wire showed much 
more than the usual irregularity, but in the case of air and petro- 
leum this irregularity was not great enough to bring any point 
made with the wire in one dielectric upon the curve made with 
the wire in the other dielectric. The resistances at 20^ were as 
follows: In air, 0.02660; in petroleum, 0.02656. In the case of 
burning gas and the mixture of wood alcohol and petroleum, the 
irregularity was so great that some of the points fell upon one 
side of the air line, and some upon the other, and the measure- 
ments were accordingly rejected. 



172 



PROFESSOR FERNANDO SANFORD, 



[Vol. III. 



The apparatus was next fitted with a copper wire, C^, about 
0.35 mm. in diameter, and its resistance was measured in air, 
burning gas, and petroleum. In this wire, a change of temperature 
of o. i^ corresponded to a change in resistance of 0.00008 ohm, 
so that any resistance change in the different media was masked 
by possible temperature differences. The mean of fifteen meas- 
urements in air, and five in burning gas, seemed to indicate an 
increase in resistance in the gas of about o.ooooi ohm, but this 
was probably purely accidental. In petroleum, no difference 
could bo^ observed. Evidently, the detection of the resistance 
v'hangos in such fine wires requires a more delicate means of 
uuMsuring temperature than was afforded by my apparatus. That 
this ditfcrence in resistance may still be considerable in much finer 
vviivs than any used by me is shown in the work of Signors Grimaldi 
and IMatania, where a wire only 0.22 mm. in diameter gave a differ- 
ence in resistance per unit length as great as my wire C\. 

Silver Wires, 

The measurements made with the silver wire referred to in my 
pa|H'r in the Philosophical Magazine have already been mentioned, 
l ho actual resistances observed at the same temperature in the 
v<nious dielectrics used are given below. These numbers are 
l[\c mean of three series of measurements, but not all the dielec- 
liicji were used in each series. 

SILVER WIRE, 5i, 1.1 mm. IN DIAMETER. 



An , , , , 



Retittance. 


Dielectric. 


Resistance. 


0.02722 ohm 
0.02724- ohm 
0.02727- ohm 
0.0^725 ohm 


Ether vapor . . . 

Chloroform vapor . 

Wood alcohol and 

petroleum . . . 


0.02719- ohm 
0.02725- ohm 

0.02727- ohm 



\\w\ I ho above measurements were made, the wire was removed 
\\.n\\ \\w UdH\ and was coated electrolytically with copper from 
4 l*aU vU vv>iipcr sulphate. The copper coating, while adherent 
u. cUv ^tlwu was very rough and porous, and it was very difficult 



No. 3.] CONDUCTIVITY IN DIFFERENT DIELECTRICS, 1 73 

to remove any adhering liquid from it. The measurements made 
with it were more irregular than those which had been made with 
the wire before coating it with copper, but there was no possibility 
of confounding the air curve with the curve made when either 
of the other dielectrics was used. The resistances at 20° in the 
dielectrics used were as follows : — 

SILVER WIRE, S2, Si, COATED ELECTROLYTICALLY WITH COPPER. 



Dielectric. 


Retittance. 


Dielectric. 


Resistance. 


Air 

Petroleum ■ 


0.02561 
0.02562+ 


Petroleum and wood alcohol 
Ether vapor 


0.02564 
0.02559 









It will be seen that not only the arrangement of the dielectrics 
with regard to their influence upon the conductivity of the wire is 
the same as before the wire was copper-plated, but that the abso- 
lute difference in resistance is almost the same as before. This 
result was entirely unlooked for on my part. 

The following table is intended to show the resistances at corre- 
sponding temperatures in the dielectrics used of all the wires 
above mentioned : — 

RESISTANCES. 



Dielectrics. 


Ci 


Ct 


c» 


C4 


c. 


Air 


0.03375 


0.02618 


0.02842 


0.01915 


0.02640+ 


Petroleum .... 


0.03369 


— 


— 


? 


— 


Wood alcohol . . . 


0.03376 


— 


— 


— 


— 


Benzine 


0.03377 


— 


— 


— 


— 


Wood alcohol and 












benzine .... 


0.03380 


— 


— 


— 


— 


Absolute alcohol . . 


0.03381 


— 


— 


0.01919 


— 


Wood alcohol and 












petroleum . . . 


0.03382 


— 


— 


— 


— 


Alcohol vapor . . . 


0.03377(?) 


— 


— 


— 


— 


Chloroform vapor . . 


0.03380+ 


— 


— 


— 


— 


Burning gas . . . 


0.03381 


0.02626 


0.02842 


0.01917 


— 


Ether vapor . . . 


0.03383 


— 


— 


— 


0.02646 



174 



PROFESSOR FERNANDO SANFORD. 



[Vol. III. 



RESISTANCES {continued^ 





Q 










Dielectric. 


second 
series. 


c^ 


Sy. 


St 




Air 


0.02660 


0.17715 


0.02722 


0.02561 




Petroleum .... 


0.02656 


0.17715 


0.02724- 


0.02562+ 




Wood alcohol . . . 


— 


— 


0.02727- 


— 




Absolute alcohol . . 


— 


— 


0.02725 


— 




Wood alcohol and 












petroleum . . . 


? 


— 


0.02727 


0.02564 




Alcohol vapor . . . 


— 


— 


— 


— 




Chloroform vapor. . 


— 


— 


0.02725- 


— 




Burning gas . . . 


? 


0.17716 


— 


— 




Ether vapor . . . 


— 


— 


0.02719- 


0.02559 





Thus far I have offered no explanation of the above-mentioned 
phenomenon. The only hypothesis which I am able to advance, 
while it would suggest the probability of a difiference in resistance 
in different dielectrics, would hardly account for the irregularity 
observed in different wires. It will be noticed, however, that 
while the irregularity in quantitative results is very great, the 
variations in resistance with wires of the same material are always 
in the same direction. This is true of the copper wire before and 
after having its surface amalgamated, and of the silver wire before 
and after being copper-plated. In the results already referred to, 
which have been published by Signors Grimaldi and Platania, the 
variation observed between the air and petroleum resistances of 
the copper wires used, while less than some of the variations 
observed by me, were in the same direction. Since the hammer- 
ing of a wire or the oiling of its surface may produce such a 
marked change in the degree to which its conductivity is afifected 
by different dielectrics, it is not strange that dififerent observers, 
working with different samples of wire, should get very different 
results ; and there is, accordingly, nothing contradictory in Pro- 
fessor Carhart's results and my own. 

The only explanation which I am able to offer is based upon 
the assumption that the passage of a current through a metallic 
conductor is accomplished by means of disruptive discharges from 



No. 3.] CONDUCTIVITY IN DIFFERENT DIELECTRICS. 1 75 

molecule to molecule through the intervening ether. These dis- 
charges would, like the discharge of a Leyden jar, be of an oscil- 
latory character, although the discharge in one direction would be 
of much greater intensity than in the opposite ; and their rate of 
oscillation would be affected by the elasticity and density of the 
intervening ether. While I am not aware that the rate of oscilla- 
tion of a condenser discharge has been observed to vary in differ- 
ent dielectrics, it is known that the capacity of a condenser does 
so vary, and this would necessitate a variation in the rate of 
oscillation of its discharge. In the case of the outer layer of 
molecules of a wire, the surrounding dielectric would influence 
the rate of oscillatory discharge between contiguous molecules. 
If the dielectric should penetrate for some distance into the wire, 
the rate of discharge of a correspondingly great number of layers 
of molecules would be affected. That gases, at least, frequently 
do penetrate for some distance into metals is well known. In the 
case of some of the dielectrics used by me, something of this 
character seemed to take place. This was especially noticeable 
in the case already referred to of the sulphuric ether vapor and 
the copper wire. If, however, the dielectric should penetrate to a 
definite depth into the wire, the difiference in resistance should be 
more marked in fine wires than in coarse ones, since a larger pro- 
portion of the molecules would have their rate of discharge influ- 
enced by the surrounding dielectric. My own results are too 
irregular to enable me to decide whether this is the case or not, 
but the variation in resistance observed in the fine wire used by 
Signors Grimaldi and Platania was much greater in proportion to 
the cross-section of the wire than in any of the wires used by me. 

It seems probable that after a current has been once established 
in a wire, all the molecules in a given cross-section will receive 
their charges at the same time, and part with them at the same 
time. This would necessitate the same rate of discharge for both 
external and internal molecules. It might, nevertheless, occur 
that the hastening or retarding of the rate of discharge of the 
external molecules would affect the rate of all the molecules of 
the wire. 

One conclusion which seems necessarily to follow from this 



176 PROFESSOR FERNANDO SANFORD. [Vol. III. 

hypothesis concerning conductivity is that the variation in resist- 
ance in different dielectrics should be greater for alternating than 
for direct currents. I have not, however, been able to verify this 
conclusion, owing to the difficulty experienced in measuring resist- 
ance accurately by means of alternating currents. 

In my first paper, I published the results of some attempts to 
find a relation between the effect of the different dielectrics upon 
the conductivity of the copper wire surrounded by them and their 
refractive index for light. In this attempt I was unsuccessful, 
but scarcely more so than have been the other attempts to estab- 
lish a relation between the refractive index and the specific induc- 
tive capacity. Aside from the general discrepancy observed 
between the values of these two properties of dielectrics, it seems 
probable that neither Fresnel's nor MacCuUagh's theory of the 
propagation of light in material bodies will give a complete expla- 
nation of the phenomenon, and that the refractive index of a sub- 
stance will not alone enable one to judge of the elasticity or the 
density of the ether in that substance. 

In a similar manner, if some dielectrics are absorbed more than 
others by the surface of a conductor, a mere knowledge of the 
specific inductive capacity of a dielectric will not enable one to 
foretell its effect upon the conductivity of a wire immersed in it. 

I am aware that this hypothesis as to the nature of metallic 
conductivity leads to certain conclusions not experimentally estab- 
lished as to the nature of the field of force surrounding the cur- 
rent. If such oscillatory discharges as are here presumed take 
place between the molecules of a conductor, the entire field about 
the conductor would be filled with Hertzian waves of very short 
period. Whether the magnetic field about a current can be ac- 
counted for on the assumption of the existence of these waves, I 
do not know. The velocity of electro-magnetic induction could 
be satisfactorily explained in this way, and it is certain that very 
rapid ether vibrations of this kind can produce magnetic effects, 
but whether the magnetic polarity of the field may be accounted 
for by the greater intensity of the discharges in one direction than 
in the opposite, I do not know. 

Stanford University, June 28, 1895. 



No. 3] POLARIZATION BY EMISSION. 1 77 



A STUDY OF THE POLARIZATION OF THE LIGHT 
EMITTED BY INCANDESCENT SOLID AND LIQUID 
SURFACES, n. 

By R. a. Millikan. 

X. 

Application of FresneVs Formula for Vitreous Reflection, 

THE main object of this research being to determine whether or 
not polarization by emission could be experimentally proven 
to be a phenomenon of refraction, Fresnel's laws for reflection 
and refraction, which have been shown by many experiments to 
accurately represent the facts, were now applied to the determi- 
nation of the amounts of polarization which should be produced 
by single refraction of light passing through the boundary sur- 
face between uranium glass and air. In order to apply these 
laws it is necessary to assume that all of the light emitted by the 
uranium glass, whether coming /r^;« the surface molecules or from 
the interior layers^ has undergone the process of refraction — an 
assumption not contained in Arago's explanation of the cause 
of the phenomenon. 

Taking the intensity of the incident ray as unity, Fresnel's 
formulae give for the intensities of the reflected and refracted 
rays when the incident beam is plane polarized in the plane of 
incidence, 

reflected ray =r^ =5iBii^:z^ 

f .. J (4 cos' a sin' B 

refracted ray=r/= ^ . „ " ^ -. 

a being the angle of incidence and /9 the angle of refraction. 



178 



DR, R. A, M/LL/KAN. 



[Vol. III. 



For a ray plane polarized in a plane perpendicular to the plane 

of incidence _ 

reflected ray =r,= ^^"^-^>. 
^ ^ tan^(a-f/8) 

r -. J / 4C0s^asin^i8 
refracted ray = rJ = . ^7 — ' ^ ^ 

^ ^ sin2(a-f/8)cos2(a-/8) 

Since ordinary light may be considered as composed of two 
equal plane polarized beams, polarized in planes at right angles 
to each other, the amount of polarization in a beam of natural 
light which has undergone single refraction is 

I 
l^hri _ ^^^^Ja^) ^ _ I -cos^ (a-)8) _^ 



iV + iV' 



-H-i 



IH- cos^ (a H-y8)" 




Fig. 4. 



COs2(a-f/3) 

The only unknown quantity in this formula is 
the angle /8. In order to determine / for any 
given angle it was only necessary to determine 
the index of refraction of the uranium glass. 

The glass being of considerable thickness, the 
microscope method was the one best adapted to 
this determination, d being the thickness of the 
glass, and a the change in focus due to the intro- 
duction of the glass between the object O and 
the objective, the index u is given by the formula 
(see Kohlrausch, Praktische Physik, p. 151), 



326 mm. 



1.51 = 



sm a 



d—a 326 mm. — 1 10 mm. sin/8 

The substitution of the various values of /8, thus found, in the 
formula for/ gave the following values : — 



a 


^ 


/ 


/ (observed) 


87° 30' 


41° 25' 


0.351 


0.358 


85° 


41° 17' 


0.315 


0.293 


80° 


40° 42' 


0.251 


0.245 


75° 


39° 46' 


0.206 


0.191 


70° 


38- 29' 


0.153 


0.139 


65° 


36° 53' 


0.125 


0.098 


50° 


30^ 29' 


0.058 


0.039 



No. 3.] POLARIZATION BY EMISSION. 1 79 

The correspondence between the results given by experiment 
and those given by this calculation from Fresnel's formulae was 
unexpected. The experiments were completed more than a month 
before any calculations were made, so that I had no idea at the 
time of making the experiments what would be the nature of the 
results given by calculation. 

The differences between the two sets of values are hardly 
greater than the possible errors of observation. The differences 
at 65° and 50° are quite large, but might have been due to the 
lack of perfect uniformity in the luminous surfaces. On the 
whole, the agreement between the two sets of results indicates 
strongly that in the case of uranium glass, at least, the phenome- 
non is one of simple refraction at the surface ; but that the 
WHOLE of the emitted light undergoes the refraction process, 

XI. 
Experiments upon Platinum. 

It is evident that no such comparisons as those just made for 
uranium glass could be made for the case of incandescent metals, 
unless, in the first place, the surface experimented upon could 
be assumed to be a perfectly definite, non-diffusing surface. The 
chief source of difficulty in the work upon platinum was to ful- 
fil this condition. 

It was found, after considerable work had been done upon 
platinum, that continual heating roughened the surface to a 
slight degree, and changed the amount of polarization. The 
results of several sets of laborious observations upon platinum 
were discarded altogether, because they were found to be erro- 
neous from this cause. However, the change is so gradual that a 
well-polished platinum surface may be heated to incandescence 
for several minutes without showing any perceptible change in 
character. The rapidity of the change could be delicately observed 
by viewing the surface at a large angle of incidence by means of 
the polarimeter. For a period of two or three minutes no change 
was perceptible in the equality of the images, but for much 
longer periods of heating the slow blistering of the surface began 



i8o 



DR. R, A, MILUKAN. 



[Vol. III. 



to be manifest in the disturbance of the equality of the images. 
Hence, in order to avoid this error, the surface of the platinum 
was carefully polished with rouge after every set of readings for a 
given angle. 

A second slight source of error in the observations upon plati- 
num was the lack of exact horizontality in the surface examined. 
The attempt was made to avoid this error by rotating the instru- 
ment through 90° according to the suggestion of Cornu. This 
brought the extraordinary image either above or below the ordi- 
nary; hence, when the angle of emergence was very large, the 
two images corresponded to points on the surface at a considerable 

distance from each other, 
as shown in the figure. 
This introduced the 
likelihood of a much greater error than that due to a slight error 
in horizontality. The incandescent platinum was therefore ren- 
dered as nearly horizontal as possible by comparison with carefully 
leveled reference planes placed in the immediate vicinity. The 
adjustment could thus be easily made to within one degree. 

In all of the following experiments sheets of rolled platinum 
0.06 mm. in thickness were heated to a white heat by means of 
a Bunsen burner, care being taken to prevent light from any 
other sources from vitiating the results. The observations are 
here given in full. 



Fio. 5. 



8o» 


70° 


60^ 


Left. 


Right. 


Left. 


Right. 


Left. Right. 


23.1 


12.0 


30.2 


20.7 


36.9 


24.5 


21.4 


11.5 


32.2 


21.0 


36.8 


26.1 


22.5 


11.3 


32.1 


21.2 


35.0 


25.0 


22.3 


10.9 


31.0 


20.5 


37.0 


25.4 


23.2 


11.4 


32.1 


21.3 


35.6 


25.5 










35.5 


25.4 


22.5 i 11.42 


31.52 1 20.94 


36.05 1 25.2 


2 w = 340.0 


2 w= 520.4 


2 Wrr 61^.25 


/= 0.829 


/ = 0.610 


/ = 0.481 



No. 3.] 



POLARIZATION BY EMISSION. 



181 



50^ 


40° 


30' 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


40.0 
39.1 
41.2 
39.4 
41.0 


29.7 
29.0 
293 
28.5 
29.6 


45.6 
45.5 
44.4 
43.8 
44.4 


35.0 
333 
34.2 
34.6 
34.5 


47.6 
47.5 
47.2 
47.8 
48.0 


38.0 
36.3 
36.2 
37.1 
36.0 


40.14 

2w = 
/ = 


29.2 

69034 
0349 


44.74 

2w = 
/ = 


343 

79°.0 
0.191 


47.62 

2w; = 
/ = 


36.72 

84°.34 
0.099 





XII. 

Application of Cauchy's Formula for Metallic Reflection to the 

Case of Platinum, 

Fresnel's formulae for reflection rest upon the hypothesis that 
the time required in the process of reflection is infinitesimal in 
comparison with a wave period, and hence that the phase of 
vibration of the reflected ray is either the same as that of the 
incident ray, or else differs from it by the quantity tt. It follows 
from this assumption that the reflected ray is plane polarized, if 
the incident ray is plane polarized. 

When the reflection takes place at the boundary surface be- 
tween air and a metal, experiment shows this assumption to be 
incorrect, and hence FresneFs formulae become inapplicable. 

If the phenomenon here considered be due to reflection, the 
laws for reflection which apply to the boundary surface between 
platinum and air are, of course, the laws to apply to the deter- 
mination of the amounts of polarization which ought to be caused 
by a single refraction at this boundary. 

The application of Fresnel's laws of vitreous reflection re- 
quires, as has been seen, the determination of but one constant, 
the index of refraction, or the ratio of the velocities of propaga- 
tion of light in the two media. Cauchy extended these laws so 
as to cover the case of metallic reflection by introducing another 
constant which he calls the coefficient of extinction. The con- 



l82 DR. R. A. JdlLUKAN, [Vol. III. 

stant corresponding to the index of refraction is, as in the case 
of transparent bodies, the tangent of the angle of maximum 
polarization. The coefficient of extinction is a constant depend- 
ing upon the opacity of the body, and is found from the ratio 
between the amplitudes, after reflection, of two equal beams 
polarized respectively perpendicular and parallel to the plane of 
incidence, and reflected at the angle of maximum polarization. 
This ratio is evidently the tangent of the azimuth of re-established 
plane polarization, when the incident beam is polarized in a plane 
making an angle of 45^ with the plane of incidence, plane polari- 
zation being re-established after reflection by means of a quarter- 
wave plate or a Babinet compensator. 

This angle may be determined by experiment. Thus the two 
constants of metallic reflection are, (i) the angle of maximum 
polarization, and (2) the azimuth of re-established plane polariza- 
tion at this angle. According to the theory of Cauchy, these 
two consonants being known, the intensity of a beam reflected 
at any angle may be calculated. 

The complete explanation of Cauchy's theory and the deduc- 
tion of Cauchy*s formulae were given by Eisenlohr in 1858. (See 
Pogg, Ann, 104, p. 368.) 

The final forms of the formulae given by Eisenlohr are 

;ir2=tan (/-4S"), /i:'2=tan (^-45"), (i) 

in which K^ is the intensity of the reflected beam when the in- 
cident beam is polarized in the plane of incidence, AT'^ the 
intensity when the incident beam is polarized in the plane per- 
pendicular to the plane of incidence, and / and g are variables 
given by the equations 

cot /= cos (e'\-ii) sin (2 arctan — — ) 
V cos a) 



cot ^= cos (e—u) sin [2 arctan ^^^ ) 
in which u and c are variables determined by the relations 
cot (2 « + ^) = cot e cos { 2 arctan ^^^ ) 



(2) 



o2=. 



sm 2e 



sin (2 ;/-f 2 e) 



(3) 



No. 3.] POLARIZATION BY EMISSION, 183 

in which a is the angle of incidence and e and 6 are given by the 
final formulae 



sin 2 ^= tan^ A sin (4 H— 2 e) 



^ sin (4 // — 2 e) 



(4) 



A is the angle of maximum polarization, called the "principal 
angle of incidence," and H is the azimuth of re-established plane 
polarization when the incident beam is polarized in the azimuth 
45°. If is called the "prime azimuth." The forms here given 
for e and are due to Jochman (see Pog^, Ann, CXXXVI., p. 
856). These formulae, first published by Cauchy in 1839, were 
shown by Jamin, by an elaborate series of measurements, to very 
closely represent the facts of reflection from metallic surfaces. 
The prime angles of incidence and the prime azimuths for all 
the common metals and for the different Fraunhofer lines were 
determined by Quincke in 1874 (see Phil. Mag. XLVIL, p. 221). 

Now, in order to apply these formulae to calculations similar to 
those which have already been made with Fresners formulae upon 
uranium glass, it was necessary to assume, as before, that the 
whole of the light emitted had undergone refraction, and it was 
also necessary to know the two optical constants for platinum at 
the temperature of incandescence. These constants could not be 
determined. However, in a number of experiments made by 
W. R. Grove (see Phil. Mag. (4) 17, p. 177) upon the reflection of 
light from incandescent platinum, he was unable to detect any 
change in the reflecting properties of the platinum due to the fact 
of incandescence. Plane polarized light being reflected from the 
cold surface, the plane of polarization of the reflected beam was 
not affected by heating the platinum to the incandescent temper- 
ature. These experiments were not performed with delicate appa- 
ratus, yet they give reason to assume that the optical constants of 
platinum are not greatly altered by temperature. 

Assuming, then, the values of A and H given by Quincke for 
the sodium line, the calculations of the amount of polarization 
in the emitted beam were made for all the angles of emergence 



1 84 



DR. R. A. M/LL/KAN 



[Vol. III. 



for which experiments had been made. These calculations were 
made as follows : — 

Quincke's values for the D line are 

^ = 77° 8', /^=32^46'. 
Formulae (4) give 

^=64'' 22\ log ^=0.62276. 
Then for ^=80° formulae (3), (2), and (i), give 

A:2=o.9348, A^'2=o.40I3. 

Assuming now the incident beam to have had an intensity 
unity, the emitted beam polarized in the plane of emergence 
would have an intensity 

i-A^=o.o6S2 

and the beam polarized in the plane perpendicular to the plane of 
emergence an intensity 

I -Ar'2= 0.5987. 

Therefore the degree of polarization =/= '^^J~ J^ =0.834. 
^ ^ ^ 0.5987+0.0652 ^^ 

The complete results of the calculations for the platinum are as 

follows : — 



a 


K* 


K'* 


x-AT* 


x-A"» 


P 


80^ 


9348 


4013 


0652 


5987 


0.834 


70^ 


8757 


4044 


1243 


5957 


0.655 


60° 


8234 


4813 


1766 


5187 


0.492 


50° 


7782 


5483 


2218 


4517 


0.341 


40° 


7409 


5981 


2591 


4019 


0.216 


30° 


7115 


6330 


2885 


3670 


0.117 



Considering the number of assumptions which have been made, 
the correspondence between these quantities and those given by 
experiment is altogether remarkable, and points with as much cer- 
tainty as the work upon uranium glass to the conclusion that the 
phenomenon is simply one of refraction. 



No. 30 POLARIZATION BY EMISSION. 185 

XIII. 
Differe^e in Color of Images, 

In the course of these observations upon platinum, another at 
first unaccountable phenomenon was noticed. At large angles 
of emergence the color in the two images was notably different. 
The image corresponding to the component polarized perpendicular 
to the plane of emergence was markedly redder than the other. 

If we assume the phenomenon to be due to reflection and 
refraction, this appearance is readily explained by a reference to 
Quincke's values for the angles of maximum polarization for the 
different Fraunhofer lines. This angle for the line C, Quincke 
g^ves as 78° 28', and for the line G his value is 73° 39'. Now if a 
is the amplitude of vibration in the reflected ray when the inci- 
dent beam is polarized in the plane of incidence, and a' the ampli- 
tude when the plane of polarization of the incident beam is 
perpendicular to the plane of incidence, the angle of maximum 

polarization will be reached when -r is a maximum, i.e, when 

a' 

— is a minimum. The experiments of Jaiiiin show that this angle 

coincides, at least very nearly, with the angle for which a^ is a 
minimum ; a conclusion which one would expect without the aid 
of experiment. Hence the angle 78° 28' is that angle for which 
the component of the reflected vibration parallel to the plane of 
incidence is a minimum for the case of red light, and the compo- 
nent of the ^w/V/^^/ vibration in the same plane is a maximum. On 
the other hand, the angle of maximum emission of violet light in 
this plane occurred at 73"^ 39'. Accordingly, it is evident that 
red light predominates in the beam emitted at the angle 78° 28', 
and violet in the beam emitted at 73° 39'. The approximate 
ratio between the two colors for any angle is shown in Fig. 6. 
It is evident that light emitted at any angle larger than 75° will 
be predominantly red. At the same time, the shape of the curves 
accounts for the lack of any noticeable predominance of violet in 
the neighborhood of 73° 39'. 
The figure shows the curves of intensities of the reflected com- 



1 86 



DR, R. A, MILUKAN. 



[Vol. III. 



ponents of vibration parallel to the plane of incidence as roughly 
plotted from the values given above. The lines mo, miDj, etc., 
represent the intensities of the emitted red vibrations in this plane 
for various angles; while the lines no, njOj, etc., represent the 
intensities of the emitted violet vibrations for the same incidences. 
The lines nM, n^Mj, etc., are the measure of predominance of red 
over violet, or vice versa. The steepness of the curves at points 
corresponding to angles greater than the angle of maximum polar- 




Fio. 6. 

ization, and the lack of steepness at points corresponding to angles 
less than the angle of maximum polarization are evidently the 
causes of the predominance of red at large angles, and the lack of 
marked predominance of violet at any angles. This characteristic 
of the curves follows from the fact that the points of maximum 
polarization correspond to very large angles. 



XIV. 

Experiments upon Silver. 

Owing to the great kindness of Mr. Herbert G. Torrey, Assayer 
of the U. S. Assay Office, I was next able to make a series of 
observations upon molten silver. These experiments were the 



No. 3.] 



POLARIZATION BY EMISSION. 



187 



most satisfactory of any which were made in the course of the 
research. All of the sources of error which had existed in preced- 
ing cases were here eliminated. The surface was perfectly defined, 
it was accurately horizontal, and there were no variations in inten- 
sity from point to point. The results of the experiments are given 
in full. 



30^ 


35^ 


40^ 


45^ 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


46 


1 36.0 


44.5 


33.4 


43.3 


31.7 


42.0 


30.5 


47.2 


36.0 


45.0 


33.7 


42.8 


32.5 


42.0 


31.0 


46.5 


35.0 


44.5 


34.0 


43.3 


32.0 


41.1 


31.3 


46.3 


35.0 


45.0 


34.0 


43.5 


32.0 


42.5 


30.5 


46.5 


, 35.5 














46.5 


1 35.5 


44.75 


33.8 


43.72 


32.05 


41.9 


30.8 


Iw 


= 0°.82 


2w= ' 


78<^.55 


2«/ = ' 


r5°.27 


2w=72°7 


P 


= 0.139 


/ = 


0.189 


/ = 


0.254 


/ = 0.297 



50^ 


55- 


60° 


65^ 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


Left. 


Right. 


40.6 
40.0 
40.0 
40.5 
40.0 


28.5 
29.0 
29.8 
29.1 
28.8 


38.0 
38.3 
37.5 
37.5 
38.0 


27.0 
27.5 
27.1 
26.3 
26.5 


34.7 
35.0 
34.0 
35.4 
35.7 
34.5 


24.1 
24.0 
24.1 
23.8 
24.0 
24.0 


32.0 
32.5 
32.6 
32.5 
32.5 


21.0 
21.5 
21.0 
20.5 
21.5 


40.2 


29.04 

69^.24 
0.354 


37.8 

2«/ = 
/ = 


26.8 

64^.6 
0.429 


34.9 
2«/ = 


24.0 

58°.9 
0.517 


32.4 
2w = 


21.3 

53°.7 
0.592 



1 88 



DR, R. A, MILLIKAN, 



[Vol. III. 



70° 


75° 


800 




Left. 


Right. 


Left. 


Right. 


Left. 


Right. 






30.0 


20.0 


27.0 


16.5 


24.1 


13.5 






30.0 


19.5 


27.0 


16.5 


24.1 


13.5 






29.6 


19.9 


27.0 


16.5 


24.2 


14.0 






30.0 


20.4 


26.5 


16.1 


23.9 


13.7 






30.5 


19.5 


27.0 
26.5 


16.4 
15.5 


24.0 


13.9 






30.0 


19.9 


26.8 


16.25 


24.1 


13.7 






2w = 490.9 


2w; = 43°.05 


2^ = 370.8 




/= 0.644 


/ = 


0.731 


/ = 


0.789 





All of the previous observations had been subject to errors of 
unknown magnitude, aside from the errors of observation ; and 
the results, while agreeing very closely with the calculated values 
for some angles, differed from them by considerable amounts at 
others. For example, the agreement for platinum at 80° was very 
close, while at 70° the difference was as large as .045. Similarly 
for uranium glass, the difference at 50° and 65° was quite large. 
Hence I did not consider the results given by the experiments 
upon uranium glass and platinum altogether trustworthy as accu- 
rate quantitative measurements. The experiments upon silver, 
however, were free from all possible error so far as I was able to 
discover, except the observational error. Mention has already 
been made of the fact that Violle had previously made a number 
of determinations of the same general nature upon silver. His 
results do not agree very closely with those given above, being uni- 
formly larger. I am altogether unable to account for the uniformity 
in the excess of his values over those given by these experiments. 
His results are here inserted for the sake of comparison. 



Angle. 


Violle. 


Millikan. 


30 


0.168 


0.139 


50 


0.383 


0.354 


60 


0.546 


0.517 


65 


0.630 


0.592 


70 


0.708 


0.644 


75 


0.770 


0.731 


80 


0.826 


0.789 



No. 30 



POLARIZATION BY EMISSION. 



189 



The application of Cauchy*s formulae to silver was made in 
the same way as in the case of platinum. For polished silver 
Quincke gives for the D line, 

Prime angle of incidence, A = 72° 10', 
Prime azimuth, I/=4i^ 40'. 

Formulae (4) give ^=82"^ 34'-3i log ^=0.4480. 

Formulae (3), (2), and (i) then give 



a 


fC* 


K'* 


x-AT* 


t-K"* 


P 


80 


0.9735 


0.8037 


0.0265 


0.1963 


0.762 


75 


0.9606 


0.7628 


0.0394 


0.2372 


0.716 


70 


0.9482 


0.7510 


0.0518 


0.2489 


0.655 


65 


0.9361 


0.7540 


0.0639 


0.2460 


0.588 


60 


0.9250 


0.7632 


0.0750 


0.2368 


0.519 


55 


0.9136 


0.7740 


0.0864 


0.2260 


0.446 


50 


0.9033 


0.7869 


0.0967 


0.2131 


0.376 


45 


0.8937 


0.7985 


0.1063 


0.2015 


0.309 


40 


0.8847 


0.8093 


0.1153 


0.1907 


0.246 


35 


0.8767 


0.8187 


0.1233 


0.1813 


0.190 


30 


0.8695 


0.8268 


0.1305 


0.1732 


0.140 



It will be noticed that the agreement between these quantities 
/ and those given by my experiments is closer than for either 
the platinum or the uranium glass ; the largest difference being 
at 8o^ where it amounts to 0.027. 



XV. 

Experiments tipon Gold and Iron. 

Through the kindness again of Mr. Torrey and the Superin- 
tendent of the Subtreasury, I was permitted to make observa- 
tions upon a pot of molten gold ; but accuracy of work was 
impossible on account of (i) the rapidity with which I was obliged 
to work ; (2) the lack of quiescence of the liquid surface ; (3) the 
impossibility of excluding other light from the surface; and (4) 
the rapidity of oxidization of the molten gold. The results were 
therefore altogether untrustworthy as quantitative measurements. 
Hence no attempt was made to compare them with results given 



I90 



DR, R. A. MILLIKAN. 



[Vol. III. 



by Cauchy's formulae. Molten iron was also made the subject of 
similar observations with equally unsatisfactory results. 



XVI. 

Discussion of Results. 

The comparisons made between experimental determinations 
and calculated values are condensed in the following tables : — 



Uranium glMt. 


Platinum. 


Silver. 


< 


i 


i 


«> 


5 


1 
d 


i 

d 


5 


t 


1 

d 


6 

2 

d 




S7i 0.358 


0.351 


0.007 


80 


0.829 


0.834 


-0.005 


80 


0.789 


0.762 


+0.027 


85 


0.293 


0.315 


-0.022 


70 


0.610 


0.655 


-0.045 


75 


0.731 


0.716 


+0.015 


80 


0.245 


0.251 


-0.006 


60 


0.481 


0.492 


-0.011 


70 


0.644 


0.655 


-0.011 


75 


0.191 


0.206 


-0.015 


50 


0.349 


0.341 


+0.008 


65 


0.592 


0.588 


+0.004 


70 


0.139 


0.153 


-0.014 


40 


0.191 


0.216 


-0.025 


60 


0.517 


0.519 


-0.002 


65 


0.098 


0.125 


-0.027 


30 


0.099 


0.117 


-0.018 


55 


0.429 


0.446 


-0.017 


50 


0.039 


0.058 


-0.019 










50 
45 
40 
35 
30 


0.354 
0.297 
0.254 
9.189 
0.139 


0.376 
0.309 
0.246 
0.190 
0.140 


-0.022 
-0.012 
+0.008 
-0.001 
-0.001 



In view of the general agreement between the observed and 
calculated values, and in view of the further fact of the colora- 
tion of the images at large angles, so beautifully accounted for 
by the reflection theory, it may be considered that the phenom- 
enon of polarization of light by emission has thus been quanti- 
tatively proven to be a phenomenon of reflection and refraction. 

It will be remembered that the apparently insuperable objec- 
tion to the explanation which Arago offered was that that explana- 
tion attributed to all of the surface molecules the property of 
emitting natural light, and gave as the entire cause of the polar- 
ization, the refraction of light which works its way up from a 
certain depth beneath the surface. 

The above calculations were all made upon the assumption 
that all of the light emitted by the glowing body had under- 



No. 3] POLARIZATION BY EMISSION'. I91 

gone a refraction. Considering the closeness of agreement be 
tween the calculated and observed values, it is difficult to escape 
the conclusion that this assumption is correct, and that no parti- 
cles whatever of the incandescent solid send out into the air 
natural light, save in the case in which the angle of emergence 
is zero. This simply means that all of the particles of the light- 
emitting body, including the so-called surface layers, lie within 
the denser medium, and beneath the plane at which reflection 
and refraction take place. This relieves the refraction theory 
of the causes of the phenomenon of its greatest difficulty: viz., 
the difficulty of conceiving that, in the case of an exceedingly 
opaque body like platinum, the uppermost molecules send out 
but a very small proportion of the whole light emitted. If we 
follow the explanation of Arago and Verdet, we are obliged by 
the results of this research to conclude that the emitted light 
originates almost entirely in molecules other than those of the 
uppermost layer. On the contrary, it seems much more reason- 
able to assume that in the case of such a body as platinum the 
light emitted is due mainly to this topmost layer, but that the 
reflection process takes place entirely above the platinum. 

Quincke has shown that when light from an external source is 
reflected at the surface of a metal, the reflection does not take 
place in the geometrical plane between the two media, but rather 
takes place in the metal itself, the vibration penetrating for a cer- 
tain depth into the denser medium. The converse is also doubt- 
less true that the vibration originating in the metal is not reflected 
instantaneously at the surface of the rarer medium, but is reflected 
in the layer of air of finite thickness which borders upon the metal. 
Thus all light originating in the platinum, whether in the surface 
layer or the sub-surface layers, must undergo the process of reflec- 
tion and refraction before it can emerge into the air. 

Lastly, the calculated values were all obtained under the assump- 
tion that the optical constants of the metals are the same for high 
temperatures as for low ; that is, that the reflecting properties 
of an incandescent metallic surface are precisely the same as the 
reflecting properties of a cold metallic surface. The closeness of 
agreement between the results given by this assumption and the 



192 DR. R, A. MILLIKAN, [Vol. III. 

facts as determined by experiment seems to warrant the conclusion, 
that the change in the optical properties of metals due to incan- 
descence is exceedingly slight ; a conclusion to which the some- 
what inexact experiments of Grove upon the reflecting properties 
of incandescent platinum would also lead. 

The results of the investigation may therefore be summarized 
as follows : — 

(i) Experiments upon polarization by emission have been ex- 
tended to a wider range of substances than had previously been 
investigated, and these substances have been classified with refer- 
ence to their power of producing the phenomenon. 

(2) The polarization of the light emitted by flourescent bodies 
has been, I believe for the first time, observed and measured. 

(3) The difference in the color of the principal components of 
the light emanating at large angles from white-hot metals has 
been observed and explained. So far as I am able to discover, 
this fact had not been before known. 

(4) Some experimental ground has been given for the conclusion 
that all light originating in an incandescent body, whether in the 
surface molecules or in the interior molecules, must suffer a reflec- 
tion and refraction before actual emergence. 

(5) The reflecting properties of metals have been shown to be 
but little, if at all, affected by the fact of incandescence. 

(6) The phenomenon of polarization of light by emission has 
been shown conclusively to be a phenomenon of refraction, first, 
by the closeness of agreement between a large number of experi- 
mental and calculated quantities, and second, by the fact of the 
difference in the color of the images at large angles of emergence 
which finds complete explanation in the refraction theory. 

In conclusion, I will add that this investigation was suggested 
to me by Professor Rood, and I wish here to express my thanks 
to him, and to Professor Hallock, and also to Professor A. A. 
Michelson, of Chicago University, for aid furnished during its 
progress. I am also under obligations to Herbert G. Torrey, 
Assayer of the U. S. Assay Office, who most kindly placed at my 
disposal large masses of molten gold and silver. 

Physical Laboratory of Columbia College. 



No. 3.] 



TERNARY MIXTURES, 



193 



ON TERNARY MIXTURES. III. 

By Wilder D. Bancroft. 

IN addition to the results given in Tables XIX.-XXXI.^ Pfeiffer 
made a few measurements on amylalcohol, monochlor-, dichlor-, 
and trichloracetic ester in the presence of alcohol and water. The 
solubility of amylalcohol in water is given by Roscoe and Schorlem- 
mer as two parts in a hundred, and I have used this value. I could 
find no data whatsoever in regard to the chloracetic esters, so I have 
calculated the values on the false assumption that they are non- 
roiscible with water. The effect of this error is seen very markedly 
in the case of the monochloraceticester, which is undoubtedly the 
roost soluble of the three. I give these tables in spite of the known 
inaccuracy, because the absolute values of the constants are, for the 
time being, of little value, whereas it is essential to show that the 
same general law covers all substances and that the substitution of 
chlorine for hydrogen does not affect the action of the Mass Law. 
The coincidence of the three chloraceticesters having the same ex- 
ponential factor is probably only superficial, as the correction for 
the solubilities would alter the exponential factor somewhat. 

Table XXXII. 

^^ = 3 c.c. Amylalcohol ; x = cc. Water ; z = c.c. Alcohol. 
Formula x{^y = 0.02 xf'*/%-^ = C ; log C = 0.100. Temp. 9.1°. 



s. 


Calc. 


Pound. 


logC. 


3 


3.81 


3.21 


__ 


6 


10.26 


10.35 


0.104 


9 


18.53 


18.34 


0.095 


12 


28.45 


27.47 


0.085 


15 


40.85 


41.25 


0.104 
0.097 



* Tables XXIIl.-XXXl. are given at the close of this article. 



194 



DR. W. D. BANCROFT. 



[Vol. III. 



Table XXXIII. 

^ = 3 C.C. Amylalcohol ; x = c.c. Water ; s = c.c. AlcohoL 
FormuU x O - 0.02 x)®*/**'* = ^ ; log C = 0.112. Temp. \9.2P. 



X, 


C«lc 


Found. 


logC. 


3 


3.93 


3.50 


.^ 


6 


10.55 


10.80 


0.122 


9 


19.10 


19.10 


0.112 


12 


30.05 


29.15 


0.099 


15 


42.30 


43.15 


0.121 
0.114 



Table XXXIV. 

^ = 3 C.C. Monochloraceticester ; x = c.c. Water ; z = c.c. Alcohol. 



Formula jc/ *'/«*'= C; log C = T.700. 



s. 


Calc. 


Found. 


logC. 


3 


1.54 


1.32 


T.644 


6 


4.05 


4.01 


T.695 


9 


7.23 


7.30 


T.705 


12 


10.91 


10.78 


T.695 


15 


15.04 


16.16 


T.731 


18 


19.50 


22.16 


T.756 


21 


24.33 


28.74 


T.772 
T.714 



Table XXXV. 

^ = 3 c.c. Dichloraceticester ; x = c.c. Water ; s = c.c. Alcohol. 
Formula xy^^/z^ = C ; logV = T.479. 



u. 


Calc. 


Found. 


\ogC. 


3 


0.90 


0.90 


T.477 


6 


2.44 


2.45 


T.481 


9 


4.35 


4.33 


T.477 


12 


6.54 


6.60 


T.482 


15 


9.04 


9.20 


T.4S7 
T.4S1 



No. 3] 



TERNARY MIXTURES. 



195 



Table XXXVI. 

^ = 3 cc. TricbloTMeticester; x = c.c. Water; t = c.c. AlcohoL 
Formula xy'^^/t^ = C; log C= IJ36. 



z. 


Calc. 


Pound. 


logC. 


3 


0.65 


0.65 


T.336 


6 


1.76 


1.80 


T.347 


9 


3.13 


3.02 


1.321 


12 


4.72 


4.50 


T.315 


15 


6.50 


6.50 


T.336 
T.331 



Tables XIX.-XXXI. furnish a striking confirmation of the way 
in which the Mass Law applies to this class of phenomena ; while 
some of the results are not as satisfactory, perhaps, as I should 
like, there are some, notably those with propylbutyrate, where the 
agreement between the observed and the calculated values is 
something marvelous, though it is unfortunate that the solubility 
of propylbutyrate in water has never been determined experi- 
mentally. 

As it might be thought a mere assumption that the first meas- 
urements in several series were determinations of another equi- 
librium, namely, of a saturated solution from which water or ester 
precipitated water, I have made a few measurements with the few 
esters I had on hand. The object of these measurements was to 
show that the change from one equilibrium to another did come at 
the point shown by Pfeiffer's results, and to make sure that the 
variations in Pfeiffer's data were due to experimental error. On 
this account I have made no measurements on the end curves, 
where water and where ester are part solvents, and in the case of 
ethylisovalerate I have measured only one series. The results are 
given in Tables XXXVII.-XXXIX. 




196 



DR, W. D. BANCROFT. 



[Vol. III. 



Table XXXVII. 

X = C.C. HjO; y = c.c. Ethylisovalerate; 5 c.c. Alcohol. Temp. 20°. 
Formula (x - 0.004;^)* (j^ - 0.002 x)/^^^ = C; n = 2.45; log C = 1.149. 



Water. 


Bt. 


Val. 




Calc. 


Pound. 


Calc. 


Pound. 


lofC. 


9.98 


10.00 


0.15 


0.15 


T.152 


8.05 


8.00 


0.24 


0.23 


T.142 


6.01 


6.00 


0.46 


0.46 


T.147 


4.99 


5.00 


0.72 


0.72 


T.152 


4.00 


4.00 


1.23 


1.23 


T.149 
T.148 



Table XXXVIII. 

x = C.C. HjO ; y = c.c. Ethylbutyratc ; 5 c.c. Alcohol. Temp. 20°. 
Formula (x - 0.005 ;^)''» (^ - O.QOSx)/$^^'^^= Ci; m = 2.44; log Ci = T.449. 



X. 


y- 




Calc. 


Pound. 


Calc. 


Pound. 


log C». 


9.99 


10.00 


0.34 


0.34 


T.450 


8.01 


8.00 


0.51 


0.51 


1.447 


5.97 


6.00 


0.95 


0.% 


1.453 


5.01 


5.00 


1.45 


1.44 


T.447 


3.99 


4.00 


2.46 


2.47 


r.451 
T.449 



Formula (x - O^O^Sy)"* {y - 0.008 x) /«*«-^' = Ca; «j = 1.20; log Cj = T.623. 











log C,. 


2.% 
2.46 
2.12 


2.96 
2.48 
2.10 


3.99 
4.94 
6.07 


4.00 
5.00 
6.00 


T.624 
T.628 
T.618 

T.6?3 



No. 3.] 



TERNARY MIXTURES. 



197 



Table XXXIX. 

X = C.C. Water; y = c.c. IsoamylaceUte; 5 c.c. Alcohol. Temp. 20°. 
Formula (x - 0.012^)"' (^ - 0.002 x)/.'^+* = Cy, «i = 3.50; log Cj = 1.414. 



X. 


f- 




Calc. 


Pound. 


Calc. 


Potind. 


logC,. 


7.00 


7.00 


0.41 


0.41 


T.414 


6.00 


6.00 


0.70 


0.70 


T.414 


5.01 


5.00 


1.32 


1.31 


T.411 
T.413 



Formula (x - 0.012 ;^)''« (^ - 0.002 x)/«««^* = G; wj = 1.50; log Cj = T.559. 











log C,. 


3.62 
3.00 
2.60 


3.61 
3.01 
2.60 


3.00 
3.99 
5.00 


3.00 
4.00 
5.00 


T.558 
T.560 
T.559 

1.559 



Although Pfeiffer does not say so, his amylacetate and ethyl- 
valerate are unquestionably iso- and not the normal compounds. 
We can now take up the results given in Tables XXXVII.- 
XXXIX. and see how satisfactorily they fulfil their object. 
Ethylbutyrate and amylacetate show the change from one equi- 
librium to the other at the same point that Pfeiffer found. The 
ethylbutyrate and ethylisovalerate mixtures are perfectly regu- 
lar at concentrations beyond those used by Pfeiffer, and the 
isoamylacetate is normal throughout both in Pfeiffer's work and 
in mine, so that the variations in Tables XXIX.-XXXI. are due 
to experimental error. The agreement in results between the two 
sets is shown in Table XL., where I give in the first column the 
value of the exponential factor n-\-\ from the formula 

and in the second column the values for the simplified integration 
constant log K. 



r 



198 



DR. W. D, BANCROFT. 



[Vol. ill 



Table XL. 



Btter. 




»I + X. 


log AT. 


Ethylisovaleratc 


PfeiflFer 


1.40 


T.773 


Ethylisovalerate 


W. D. B. 


1.41 


r.754 


Ethylbulyrate 


PfeiflFer 


1.41 


T.847 


Ethylbutyrate 


W. D. B. 


1.41 


T.840 


Isoamylacetate 


PfeiflFer 


1.294 


T.893 


Isoamylacetate 


W. D. B. 


1.286 


T.870 



As will be seen, the values of «+ 1 are identical, the values for 
log Ky though very close, are not quite the same. This may be 
due to inaccuracies in the work, but I am more inclined to attribute 
it to differences in temperature. It is not known at what tempera- 
ture Pfeififer worked, and it would take only a slight difference to 
account for the variation. In Table XLI. I have tabulated the 
«+ 1 values from Pfeififer's results, together with log C and log K. 

Table XLI. 



Ester. 


n-¥\. 


logC. 


log/r. 


Methylisovalerate 


1.37 


T.807 


T.859 


Ethylisovalerate 


1.40 


T.682 


T.773 


Ethylisovalerate * 


1.41 


T.653 


T.754 


Methylbutyrate 


1.52 


T.888 


T.926 


Ethylbutyrate 


1.41 


T.785 


T.847 


Ethylbutyrate ^ 


1.41 


T.774 


T.840 


Propylbutyrate 


1.378 


T.651 


T.747 


Ethylpropionate 


1.39 


T.931 


T.878 


Propylpropionate 


1.45 


T.733 


T.816 


Ethylacetate 1 


1.555 


— 


— 


Propylacetate 


1.23 


0.166 


0.135 


Butylacetate 


1.30 


T.912 


T.932 


Isoamylacetate 


1.294 


T.861 


T.893 


Isoamylacetate ^ 


1.286 


T.832 


T.870 


Propylformiate 


1.38 


T.%7 


T.976 


Butylformiate 


1.333 


0.057 


0.043 


Isoamylformiate 


1.35 


T.808 


T.858 



* My own measurements. 



No. 3.3 TERNARY MIXTURES. 199 

The first thing that strikes one about this table is the way in 
which so many of the »+ 1 values approximate to 1.40. Why this 
should be so is entirely unknown. In the log K values we notice 
that, for the same acid, increasing the carbon atoms in the alcohol 
radical diminishes the constant. There is only one exception to 
this, butylformiate, and here the possible error is very large. It 
looks also as if the constants might be additive, being made up of 
one factor for the alcohol and another for the acid radical; but 
the experimental data are too insufficient to justify this hypothesis. 
It is very much to be hoped that some one will make a careful 
series of experiments to settle this point. 

Formula 11. was deduced for the case when the reacting weights 
of the substances in equilibrium are not functions of the concen- 
tration. The measurements of Pfeiffer and myself show that, with 
the possible exception of the chloroform-water-acetone series, this 
condition has been satisfied in all the cases studied, though the 
experiments extended over a wide range of concentrations. This 
is in flat contradiction with the determinations of the reacting 
weights by the boiling-point and freezing-point methods. These 
methods give accurate results only for very dilute solutions, and 
even then only for certain solutes in certain solvents. To explain 
the variations, we are forced to assume "double molecules" in 
some cases, polymerization with increasing concentration in prac- 
tically all cases, and "variations from the gas laws." I have 
brought together a large series of measurements in which there 
is no sign of any of these things. I see only two possible hypoth- 
eses to account for this discrepancy : first, to enunciate a new and 
most interesting law, to wit, presence of a third substance prevents 
"polymerization" and "variations from the gas laws"; second, 
the formula for the change of vapor pressure with the concentra- 
tion is incorrect. The first hypothesis seems to me out of the 
question, and there remains only the second. It is a bold thing to 
question so universally accepted a formula, but I feel convinced 
that it is not right, and that equal reacting weights of different 
substances do not produce the same change of vapor pressure. I 
think that the mistake in the past lay in assuming that the work 
done in compressing a dissolved substance ftom the volume V^ to 



200 DR. IV. D, BANCROFT. [Vol. III. 

the volume V^ by means of a semipermeable piston is equal to 
fpdv between those limits, irrespective of the nature of solute 
and solvent. I have already collected some experimental evidence 
in favor of this view, and I hope before lopg to be able to establish 
my point. 

The facts brought out in this paper throw light on a research by 
Abegg 1 carried out under the direction of Arrhenius. Abegg let 
alcohol diffuse into a salt solution and found, to his surprise, that 
the salt, instead of remaining equally divided throughout the liquid, 
diffused somewhat into the part not yet reached by the alcohol. 
He concludes that this extraordinary behavior can only be ac- 
counted for on the assumption that alcohol increases the osmotic 
pressure of a dissolved salt. What happens is very simple. When 
the alcohol has diffused only a little way, one may consider the 
solution as composed of two parts, one containing a large amount 
of alcohol, the other very little. The dissolved substance, being 
in this case less soluble in the first layer than in the second, dif- 
fuses into the second only to go back again as the alcohol becomes 
more evenly divided throughout the liquid. Except that the part 
containing much alcohol and little water merges insensibly into 
the part containing much water and little alcohol, and is not in 
equilibrium with it, the case does not differ from two layers formed 
by ether and water, where it is well known that the concentration 
of a third substance is not the same in the two layers. The effect 
of the alcohol is not, as Abegg assumes, to increase the osmotic 
pressure of the solute, but to diminish its solubility in that portion 
of the liquid. If, instead of taking salts which were only slightly 
soluble in alcohol, Abegg had let water diffuse into water contain- 
ing in solution some substance very soluble in alcohol, slightly 
soluble in water, he would have observed the opposite effect, and 
the dissolved substance would have diffused partially into the layer 
rich in alcohol. 

Another line of reasoning which is not quite defensible is that 
taken by Wildermann,^ in his paper, " Ueber cyclische Gleichge- 
wichte.*' His train of thought is something as follows : Suppose 
he has a system of three phases, bromine, a solution of bromine 

1 Zeitschr. f. ph. Chem., XI. 248. 1893. ^ Ibid., XI. 407. 



No. 3.] TERNARY MIXTURES. 201 

in water, and the vapor of bromine and water, it being assumed 
that the amount of water which dissolves in the bromine can be 
neglected. He adds to the aqueous solution some substance 
which does not dissolve in bromine perceptibly, such as potassium 
bromide or sulphuric acid. The three phases, when in equilibrium, 
have still the same concentration of liquid bromine and of bromine 
vapor. Therefore the solubility of the bromine in the liquid can- 
not have changed. It does change experimentally ; therefore, in 
order to reconcile the reasoning with the facts, he concludes that 
the apparent change, decrease or increase, is due to chemical 
action, and that the amount of bromine dissolved as such remains 
unchanged. This may be true in the special examples studied by 
Wildermann.i That I cannot say ; but it is not true that it is a 
necessary theoretical conclusion, and there is no proof that it is 
correct in any case. If, instead of adding potassium bromide, we 
add to the water some liquid in which bromine is readily soluble, 
the amount of bromine dissolved will increase without there being 
any reason to assume chemical action in order to account for it. 
Bromine is not a good substance to consider, because there are so 
few liquids soluble in water in which it dissolves without decom- 
position, and also because we cannot ignore the solubility of the 
added substance in it. Let us rather treat the case when we have 
iodine instead of bromine. Suppose we have the system, solid 
iodine, a solution of iodine in water, and vapor of iodine and 
water ; we add alcohol to the solution. The concentrations of the 
solid iodine and the iodine vapor will remain practically unchanged ; 
therefore the solubility of iodine in the water and alcohol should 
remain unchanged according to Wildermann. As a matter of fact 
it does change, and I do not see how this variation can be attrib- 
uted to chemical action unless all solution is defined as chemi- 
cal action, which begs the question, though very possibly true. 
There may be a radical difference between the action of the alco- 
hol and the action of potassium iodide ; but that difference has 
not been shown. As far as I can see, Wildermann's conclusions 
require that adding alcohol to a saturated salt solution should 
have no effect on the concentration of the salt, because the equi- 

1 See Jakovkin, Zeitschr. f. ph. Chem., XIII. 539. 1894. 



202 DR. W. D. BANCROFT. [Vol. III. 

librium between the solid salt and its own vapor would remain 
unchanged. 

Early in this paper I proposed the word "solute" as something 
distinct from "solvent," and it is necessary for me to justify that 
distinction. The usual way of looking at binary solutions is to 
consider them as mixtures, and that it is purely arbitrary which of 
the two substances we consider as solvent and which as dissolved 
substance. The following citations will show what the prevailing 
opinion at the present moment is. 

Lothar Meyer, after pointing out that in alcohol-water mixtures 
it depends on the nature of the semipermeable membrane which 
substance exerts the osmotic pressure, says:^ " Mit der Beschaffen- 
heit der Membran tauschen beide Stoffe die RoUen ; es ist daher 
eine Willkiir wenn wir den einen als gelost, den anderen als das 
Losungsmittel bezeichnen." Ostwald is consistent to the bitter 
end, paying: 2 "Losungsmittel ist derjenige Stoflf des Gemenges, 
welcher bei dem betrachteten Vorgange ausgeschieden wird." 
This view is heroically logical, for it means that when a salt crys- 
tallizes from a saturated solution, the mother liquor consists of 
water dissolved in the salt. 

Nernst's position on the subject is doubtful. He puts solutions 
under the head of physical mixtures and remarks : ^ " Die ver- 
diinnten Losungeu sind Gemische welche eine Komponente in 
grossem Ueberschuss zu den iibrigen enthalten ; erstere bezeichnen 
wir in diesem Falle als das Losungsmittel, letztere als geloste 
Stofife." On the other hand, he draws a distinction between freez- 
ing out the solvent and crystallizing out the solute.* He does not 
accept the view that the salt is the solvent in a saturated solution ; 
but he does not suggest in any way that there may be diflferent 
laws for the solute and the solvent. Planck is very clear and 
precise ; he defines dilute solutions in almost the same words as 
Nernst, and goes on:^ "Bei einer beliebigen Losung kann jeder 
Bestandtheil derselben als Losungsmittel oder als geloster Stofif 
aufgefasst werden." This means that in a mixture of two liquids 

1 Zeitschr. f. ph. Chem., V. 24. 1890. • Thcoretische Chcmie, p. 115. 

2 Ibid., XII. 394. 1893. * l^it^M p. 393- 

* Grundriss der Thcrmochemic, p. 131. 



No. 3.] TERNARY MIXTURES. 203 

either may be considered as the dissolved substance, and will 
therefore decrease the partial vapor pressure of the other, and this 
decrea3e of the vapor pressure will be greater the greater the con- 
centration of the dissolved substance. This is not in agreement 
with the facts. A saturated solution of elher in water has the 
same partial vapor pressures as a solution of water in ether satu- 
rated at the same temperature.^ For the moment we will consider 
ether as the dissolved substance. In the first solution, the volume 
concentration is roughly 10 per cent ; in the second, about 99 per 
cent at 20** ; and yet this enormous change of concentration has 
no effect on the partial vapor pressures. The figures are still 
more remarkable if we consider solutions of chloroform in water 
and water in chloroform, when one of the components is present 
in infinitesimal quantities. We must assume one of two things : 
either that our present formula for the change of the vapor pres- 
sure with the concentration is all wrong, since it does not admit 
of the vapor pressure of one of the components passing through a 
minimum; or that there is a difference between solvent and solute, 
and that each has its own law expressing the change of its vapor 
pressure with the concentration. This time I prefer the second 
assumption, with all that it implies. The equations of van *t HoflF 
and Raoult are the rough statements of the laws for the solvent. 
The corresponding expressions for the solute have not yet been 
worked out. The distinction between solvent and solute is very 
clear in solid solutions of metals in metals. Starting from either of 
two pure metals a depression of the freezing point is noted when 
the other is added, the two curves thus formed meeting at the 
melting* point of the eutectic alloy. Here there can be no ques- 
tion that along one curve the first metal is solvent, while on the 
other it plays the role of solute. In the case of two partially 
miscible liquids there is also no difficulty in determining which is 
solvent and which solute. When ether and water are shaken 
together, the upper layer contains water as dissolved substance, 
the lower ether. With completely miscible liquids having a maxi- 
mum (or minimum) vapor pressure at some concentration, such as 
propylalcohol and water (formic acid and water), it is probable 

1 Wied. Ann., XIV. 219, 1881; Ostwald, Lehrbuch, I. 644. 



204 DR. W. D, BANCROFT. [Vol. III. 

that the change of solvent occurs at the concentration correspond- 
ing to the maximum (or minimum) vapor pressure. With such 
things as ethylalcohol and water, which are infinitely miscible and 
which show no maximum or minimum vapor pressure, it is impos- 
sible at present to say -at what concentration alcohol ceases to be 
the solvent and water assumes that duty. As soon as we have 
worked out the relation between the concentrations in the solution 
and in the vapor, I feel certain that we shall find that it requires 
two curves to express the relation, and not one. The intersection 
of these curves will be the point where the solvent changes. I 
look upon my own results with ternary mixtures as very significant 
in this respect, the change from one curve to another coming at 
the point where the precipitate or the solvent changed. It is 
interesting to note that at the point, for instance, where an excess 
of one of the partially miscible liquids first has no effect, the 
solubility curve of the dissolved substance has a "break." The 
possibility of such a case has always been denied except by the 
upholders of the "hydrate theory.'* 

The effect of temperature on the various equilibria will form 
the subject of a special paper, and I shall reserve for it the discus- 
sion of changes of temperature coefficient at the intersections of 
two curves, one or two very striking instances of which I have 
come upon incidentally in my work so far. I hope also to be able 
to present a paper on equilibrium in two liquid layers, a subject 
which is of especial interest because the theoretical treatment 
based on the experimental work in this paper gives results which 
are not in accordance with the assumptions on which Nernst 
bases his Distribution Law. Besides, there is the application of 
the Mass Law to the case where one or more of the components 
is solid, and to the instances where there is an increase instead of 
a decrease of solubility. 

The results of this paper may be summarized briefly as follows : 

1. The equilibria between two partially miscible liquids and a 
consolute liquid follow the Mass Law. 

2. There are four sets of equilibria corresponding to four differ- 
ent series of solutions. 



No. 3.] 



TERNARY MIXTURES. 



205 



3. If the two liquids are practically non-miscible, there are only 
two sets of equilibria. 

4. The reacting weights of the liquids studied were not functions 
of the concentration, — possibly with one exception. 

5. There is a fundamental difference between the solute and the 
solvent. 

6. The solubility curve of a substance in a varying mixture of 
two liquids at constant temperature has a break. 



Table XXIII. 

^ = 3 c.c. Propylbutyrate; x = c.c. Water; t = c.c. AlcohoL 
Formula x {^y - 0.002 xf^^/z^^^ = C; log C =; T.6S1. 



*. 


Calc. 


Pound. 


logC. 


3 


_ 


1.19 




6 


3.49 


3.55 


T.658 


9 


6.11 


6.13 


T.652 


12 


9.05 


9.05 


T.651 


15 


12.31 


12.31 


T.651 


18 


15.92 


15.90 


T.650 


21 


19.68 


19.68 


T.651 


24 


23.72 


23.72 


T.651 


27 


27.92 


27.84 


T.650 


30 


32.20 


32.10 


T.649 


33 


36.71 


36.71 


T.651 


36 


41.66 


41.55 


T.650 


39 


46.64 


46.49 


T.649 


42 


51.56 


51.60 


T.652 


45 


56.80 


56.90 


T.652 


48 


62.64 


62.40 


T.649 


51 


67.84 


68.00 


T.652 


54 


73.93 


73.85 


T.650 
T.651 



r 



206 



DR. W. D. BANCROFT 



[Vol. III. 



Table XXIV. 

y = Z c.c. Ethylpropionate; x = c.c. Water; z = c.c. Alcohol. 
Formula x {y - 0.03 xf^/z^ = C; log C = T.931. 



M. 


Calc. 


Pound. 


Ids C. 


3 


2.36 


2.32 


T.924 


6 


6.89 


6.87 


T.930 


9 


12.38 


12.35 


T.930 


12 


19.10 


19.17 


T.933 


15 


27.12 


27.12 


T.931 


18 


36.84 


36.84 


T.931 


21 


50.35 


50.42 


T.932 


24 


— 


00 


T.930 



Table XXV. 

j^ = 3 C.C. Propylpropionate ; x = c.c. Water; f = c.c. Alcohol. 
Formula x(y- 0.0065 xf^/^^'^ = C; log C = T.733. 



M. 


Calc. 


Found. 


\ogC. 


3 


^__ 


1.58 


__ 


6 


4.45 


4.70 


T.757 


9 


8.27 


8.35 


T.738 


12 


12.25 


12.54 


T.743 


15 


17.04 


17.15 


T.736 


18 


22.27 


22.27 


T.733 


21 


28.00 


27.83 


T.731 


24 


34.20 


33.75 


T.727 


27 


40.80 


40.24 


T-727 


30 


47.95 


47.15 


T.725 


33 


55.70 


54.65 


T.725 


36 


63.50 


63.18 


T.731 


39 


72.25 


71.59 


T.729 


42 


81.15 


83.05 


T.743 


45 


91.30 


93.91 


T.746 


48 


102.00 


107.46 


T.756 
T.737 



NO.-3-] 



TERNARY MIXTURES. 



207 



Table XXVI. 

^ s= 3 c.c. Propylfltcetate; x = c.c. Water; « = c.c. Alcohol. 
Formula x (^y - 0.03 xf'^/z^^ C; log C= 0.166. 



♦ 


s. 


Calc. 


Found. 


logC. 




3 


4.44 


4.50 


0.170 




6 


10.57 


10.48 


0.163 




9 


17.75 


17.80 


0.167 




12 


25.95 


26.00 


0.167 




15 


35.72 


35.63 


0.165 




18 


46.50 


47.50 


0.178 




21 


59.00 


58.71 


0.164 




24 


— 


00 


0.168 



Table XXVII. 

^ = 3 C.C. Butylacetate; x = c.c. Water; z = c.c. Alcohol. 
Formula x(y- 0.007 xf^/z^ = C ; log C = T.912. 



M, 


Calc. 


Pound. 


logC. 


3 


^_ 


2.08 





6 


6.06 


6.08 


T.914 


9 


10.29 


10.46 


T.920 


12 


15.04 


15.37 


. T.922 


15 


20.10 


20.42 


T.918 


18 


25.64 


25.60 


r.9ii 


21 


31.49 


31.49 


1.912 


24 


37.60 


37.48 


T.911 


27 


44.05 


43.75 


T.909 


30 


50.74 


50.74 


T.912 


33 


58.00 


59.97 


T.927 
T.916 



i 



208 



DR. IV. D. BANCROFT. 



[Vol. III. 



Table XXVIII. 

j^ = 3 c.c Amylacetate ; x = c.c. Water ; i = c.c. Alcohol. 
Formula x(,y- (^.02x)^^/%^^ = C; log C = T.861. 



*. 


C«le 


Found. 


loe c. 


3 


,^^ 


L76 





6 


— 


4.24 


— 


9 


9,03 


9.03 


rs6i 


IZ 


13.11 


13.24 


T.S66 


IS 


17.43 


17-52 


L864 


18 


22.22 


22.22 


T.S61 


21 


26.W 


26,99 


L861 


» 


32.24 


32.14 ; 


T.S60 


«? 


37.59 


37.23 


T.S56 


3d 


42. 7S 


42.66 


T.S59 


33^ 


48-41 


48.41 


X.861 
L861 



Table XXIX. 

^ = 3 ex. Propyl formi ate ; x = c.c* Water ; z = c.z. Alcohol, 
ForniuU 4r(7 - 0,(H xf^/%^^ = C; log £7= T.967- 



s. 


CaJc 


Pound. 


lofC 


3' 


2.82 


2.E3 


T,969 


4 


7.52 


T.50 


T.966 


^ 


13.65 


1X50 


T.962 


n 


21.30 


2L60 


T.973 


u 


30.95 


30,60 


T.%2 


IS 


52.40 


53.00 


1.972 


n 


— 


cc 


T.%7 



No. 3] 



TERNARY MIXTURES. 



209 



Table XXX. 

y = 3c.c. Butylformiate ; x = c.c. Water ; « = c.c. Alcohol 
Formula x i^y - 0.01 j-) 5 /zt = C ; log C - 0.057. 



%. 


Calc. 


Found. 


logC. 


3 


3.43 


3.45 


0.060 


6 


8.71 


8.83 


0.063 


9 


15.02 


14.75 


0.049 


12 


22.32 


21.45 


0.W1 


15 


30.25 


29.65 


0.W8 


18 


39.00 


39.00 


0.057 


21 


48.80 


51.80 


0.083 


24 


— 


00 


0.057 



Table XXXI. 

^ = 3 c.c. Amylformiate ; x = c.c. Water ; « = c.c. Alcohol. 
Formula x(^y - 0.005 xf^/z^ = C ; log C = T.808. 



%. 


Calc. 


Found. 


logC. 


3 


__ 


1.80 





6 


4.92 


5.17 


T.829 


9 


8.54 


8.77 


T.820 


12 


12.63 


12.64 


T.809 


15 


17.10 


17.01 


T.806 


18 


21.90 


21.86 


T.807 


21 


27.06 


27.06 


T.808 


24 


32.50 


32.31 


T.805 


27 


38.31 


38.31 


T.808 


30 


44.40 


44.50 


T.809 


33 


50.71 


50.71 


T.808 


36 


57.20 


57.82 


T.813 


39 


62.70 


65.21 


(T.830) 


42 


71.35 


77.05 


(T.842) 


45 


78.75 


85.10 


(T.842) 


48 


86.55 


^.20 


(T.845) 
T.811 




2IO DR. L. T, MORE, [Vol. III. 



ON THE CHANGES IN LENGTH PRODUCED IN 
IRON WIRES BY MAGNETIZATION. 

By Louis Trenchard More. 

THIS investigation was undertaken at the suggestion of Pro- 
fessor Rowland, and has for its object the finding of a 
relation between the change of length produced in iron wires by 
magnetization, and the intensity of magnetization existing in the 
wire. It was hoped thus to obtain results that would be com- 
parable, and to avoid certain errors common to all previous work. 

Historical. 

That magnetizing an iron rod causes it to alter in length was 
first discussed by Joule ^ in 1847. His attention was called to the 
phenomenon by a machinist of Manchester, who imagined that 
the volume of a mass of iron was increased by magnetizing it. 
Joule, to test the opinion of the machinist, immersed a mass of 
iron in a closed vessel full of water in which stood a fine capillary 
tube. When the iron was strongly magnetized, the height of the 
column of water in the tube remained unaltered, showing that 
within the limits of accuracy of his apparatus, for the intensity 
employed, the volume of the iron was unchanged. BidwelP has 
also investigated this subject and found, on the contrary, that the 
volume was altered by magnetization. The volume diminishes at 
first and attains a minimum ; it then increases until with suffi- 
ciently intense fields the original size is regained ; after reaching 
this point the volume continues to increase. As a consequence of 
this relation, if Joule had used an intensity either greater or less, 
he probably would have noticed a change in the volume. Joule 
afterwards, by means of a system of levers, found that the length 

1 Joule, Phil. Mag. (3), Vol. XXX., pp. 76, 225. 

2 Bidwell, Proc. Roy. Soc, Vol. LVL, p. 94. 



No. 3] CHANGES DUE TO MAGNETJZATIOPl. 211 

of a rod was increased by the magnetizing force, and gave as a 
result of his observations the following laws : — 

1. When soft iron rods are magnetized, their length is increased 
and the elongation is approximately proportional to the square of 
the magnetizing force. 

2. Tension applied to the rod diminishes the elongating efifect, 
and — " In the case of a bar one foot long and one-quarter inch 
in diameter, a tensile force of about 6oo pounds caused all the 
phenomena of changes of length to disappear." 

3. "That the elongation is greater, for the same intensity of 
magnetism, in proportion to the softness of the metal. It is greatest 
of all in the well annealed iron bars, and least in hardened steel. 
This circumstance appears to me to favor the hypothesis that the 
phenomena are produced by the attractions taking place between 
the magnetized particles of the bar, an hypothesis in perfect accord- 
ance with the law which I have pointed out," — that the elongation 
was proportional to the square of the intensity of magnetization. 

The first two laws pointed out by Joule have been often con- 
firmed, but the third seems to rest on a single experiment, and 
until very recently there have been no published records, that I 
have seen, bearing on the result found by Joule. ' Shelf ord Bidwell^ 
while investigating the subject obtained results the converse of 
Joule's, — that not only hardening, but also annealing, the iron 
diminished the elongating efifect. He mentions one specimen 
that when annealed contracted in length instead of elongating 
upon the application of the feeblest magnetizing force. 

Barrett 2 in 1870 discovered that nickel when magnetized con- 
tracts instead of elongating. Three years later A. M. Mayer* 
published an account of his experiments on this subject. His 
results in the main verified Joule's observations, with the excep- 
tion of the action of hard steel. This discrepancy was shown 
some years later by Bidwell to follow from their different methods 
of experimenting. Joule applied a current of the same intensity 
but once, and both on making and on breaking the circuit observed 
an elongation ; while Mayer used specimens already perma- 

1 Bidwell, Proc. Roy. Soc. Vol. LV., p. 228. ^ Barrett, Nature, 1882, 

« Mayer, PhU. Mag. Vol. XLVL, p. 179. 



r 



2 1 2 DR. L. T. MORE. [Vol. III. 

nently magnetized, and on observing the temporary magnetiza- 
tion, found a contraction on making circuit and an elongation on 
breaking it. 

Mayer also observed hysteretic effects ; that is, the elongation 
due to a magnetizing force was less if the force had been reached 
by successively increasing values, than it was if the current had 
been decreased from a maximum, the rod remaining slightly 
elongated after the magnetizing force had been removed, an effect 
analogous to the lagging of the induction behind the magnetizing 
force. Nagaoka^ has discussed this phenomenon in the article 
cited, and has obtained complicated curves showing the complete 
cycle of the hysteretic phenomena for both iron and nickel. 

The experiments mentioned were limited to comparatively weak 
fields ; the work of finding the effects due to intense fields has 
been most thoroughly done by Shelford Bidwell,* who has found 
that rods do not continue to elongate indefinitely with increasing 
strengths of field, as the other investigators supposed, but that a 
maximum value is after a time reached. The rod then begins to 
shorten, and very intense fields produce an absolute contraction 
which approaches a limiting value asymptotically. He also experi- 
mented with rings of iron, and with rods of steel, nickel, manga- 
nese steel, cobalt, and bismuth. 

Investigations upon this subject have also been made by Ber- 
get,8 Nagaoka,* Lochner,^ Jones,^ and Bock.^ 

For convenience, I have collected in a summary the results 
obtained by the different observers. 

Soft Iron. — Soft iron elongates when magnetized. The elon- 
gation attains a maximum and then diminishes with increasing 
strength of field until a state is reached when the rod returns to 
its original length. Further increase of field causes the rod to 
contract. 

1 Nagaoka, Phil. Mag., Vol. XXXVII., p. 131. 

2 Bidwell, Proc. Roy. Soc, Vol. XXXVIII., p. 265; Vol. XL., pp. 109, 237; Vol. 
XLVII., p. 469; Vol. LV., p. 228; Trans. Roy. Soc, Vol. CLXXIX. (A), p. 205. 

8 Berget, Comp. Rend., torn. CXV., p. 722. 

* Nagaoka, Wied. Ann., LIII., pp. 481, 487; 1894. 

* Lochner, Phil. Mag., Vol. XXXVI., p. 504; 1893. 

6 Jones, Phil. Mag., Vol. XXXIX., p. 254; 1895. ' Bock, Wied. Ann.; 1895. 



No. 3.] 



CHANGES DUE TO MAGNETIZATION, 



213 



There is no minimum length, the rod approaching asymptotically 
a limiting value. 

With a given strength of field, both hardening and annealing 
diminish the elongation and increase the contraction shown by 
the rod before it was subjected to these operations. (Bidwell.) 

Tension also diminishes the elongation and increases the con- 
traction of the rod. 

For a sufficiently great tension no elongation occurs, the rod con- 
tracting upon the application of the smallest magnetizing forces. 

For a given length, the effects both of elongation and of con- 
traction are greater for thin than for thick rods. (Bidwell.) 

S. J. Lochner^ comes to the conclusion from his own experi- 
ments that the converse is true, — that thick bars show greater 
elongation than thin ones. 

Very little reliance can be put in these last experiments, and 
the dependence of the change of length upon the ratio of the 
length to the diameter cannot be inferred from them. Bidwell 
used three rods 10 cm. long and 2.65, 3.65, and 6.25 mm. in 
diameter, and assumed them to be of iron of similar composition. 
It is well known that different specimens of iron, apparently 
similar in structure, give results that vary 25 per cent and more, 
so that the small variations in the change of length noted by him 
cannot safely be said to be due to the differences in their diameters, 
especially as he made no determination of the permeability. Loch- 
ner avoided this error by testing an iron rod, and then after having 
cut off a portion, testing it again. He, however, took no precau- 
tion to have the field uniform. His solenoid was nearly four times 
as long as the shortest rod used, and the ratio of the diameter to 
the length of the rod was only i to 32. Besides the uncertainties 
introduced by such a poor arrangement for a uniform field, great 
errors would be produced by the strong poles created at the ends 
of the rod. 

Object of Experiment, 

A careful study of the results obtained for iron by the different 
observers will show that although the general appearance of their 

^ Lochner, loc, ciL 



214 ^^' ^' ^' ^^JORE, [Vol. III. 

curves is very similar, yet their absolute values vary widely, two 
specimens often having maximum elongations that dififer 20 or 
30 per cent. There is, unfortunately, no way of comparing these 
results, for it has been the custom to use as co-ordinates the change 
of length and the intensity of the external field. For a given 
apparatus this intensity depends only on the current used, and not 
at all on the specimen to be examined. The elongation is depend- 
ent upon the intensity of magnetization in the wire, and this is 
the quantity that varies with the specimen employed. For that 
reason the relation should be found between these two quantities. 

It is, of course, essential to have the rod uniformly magnetized 
throughout its length ; that is, the field should be uniform and 
there should be no free poles. These conditions may be best 
obtained in one of two ways, either by having the metal in the 
shape of a ring, and observing the change in diameter of the ring 
when magnetized by a solenoid wound upon it, or by using long 
wires of the metal. In the second case only the middle part of 
the wire should be observed, and the solenoid used to magnetize 
it should be considerably longer than the portion of the wire 
experimented upon. In this investigation the latter method was 
chosen, as rings are less convenient, and also because it was 
desirable to observe the effects of tension in the metal. 

When a rod of iron is magnetized, the change in length observed 
is due to several causes, — three at least, — and to obtain a correct 
idea of the phenomena these causes and their effects should be 
separated. There is first the direct action of the magnetism, and 
this may possibly be due to the orienting of the magnetized par- 
ticles of the rod. Secondly, there are indirect actions of the 
magnetism which tend to change the length of the rod. These 
indirect actions are the mechanical stresses created in the rod by 
the magnetism. The first of these mechanical stresses is the 

tractive force of the magnet and is measured by That this 

7r 

force exists, tending always to contract the rod, is seen from the 

fact that if the magnet is cut in two, the ends are held together 

by a force -— per square centimeter, showing that this force 
7r 



NO. 3.] 



CHANGES DUE TO MAGNETIZATION 



215 



must always be present when a rod is magnetized. The agree- 
ment between the theoretical value - — and the experimental law 

for the lifting power has been recently shown by E. Taylor Jones.^ 

This effect for high intensities of magnetization is a large one, 

and becomes one of the most important factors in the observed 

changes in length. The second of these mechanical stresses is 

the effect due to the change in Young's modulus when the rod 

is magnetized. That the elasticity is influenced by magnetization 

was shown theoretically by J. J. Thomson,^ and the phenomenon 

was observed last year in some experiments made by the writer ; 

but no quantitative results could be obtained beyond the fact that 

the elasticity for soft iron was slightly diminished. A. Bock^ 

concludes from his work that the decrease in elasticity must be 

less than one-half per cent. If the wire is not stretched by 

weights, this decrease in the elasticity will afifect only the contrac- 

m 
tion due to the — force. On the other hand, if the wire is loaded 
87r 

with weights, this effect becomes very marked, since a large quan- 
tity, the stretch of the wire by the great weight, is altered. This 
question will be more fully discussed later in the paper. 

If these two indirect actions were allowed for, there would 
remain only the direct action of the magnetism upon the metal 
under a constant tension. This latter relation would evidently 
furnish comparable results, and may in the future throw some 
light upon the action of magnetism on matter. 

Apparatus, 

Since it was necessary to obtain the modulus of elasticity for 
the specimen experimented on, in order to make a proper correc- 
tion for the electro-magnetic stress, and as I wished to observe 
the effects of mechanical stress, it was convenient to experiment 
on thin, long wires of the metal placed in a vertical position. To 
magnify the phenomena a system of levers was used, involving the 

1 Jones, he, cU, 

• J. J. Thomson, Application of Dynamics to Physics and Chemistry, p. 58. 

« Bock, lot. Hi. 



2l6 DR, L, T. MORE. [Vol. IIL 

tilting of a mirror mounted on three legs very close together, — a 
method first invented by Professor Rowland. The general plan 
of using levers and a jacket cylinder was suggested to me by 
Dr. Ames. 

The wire to be tested was suspended from a tall tripod standing 
on a stone slab that rested on two brick piers. A hole was cut in 
the slab so that the wire could be passed through it and the free 
end permitted to almost reach the floor of the room. A hollow 
brass cylinder 1.6 cm. in diameter and about 68.0 cm. long (Fig. i) 
was screwed to the wire at a point a, a short distance above the 
stone slab ; a loosely fitting cork plug in its open upper end served 
to keep the wire in the axis of this cylinder. To the cylinder was 
screwed the brass arm deb. At e was screwed a hard steel support 
for the fulcrum of the lever. The side view of the support was 

of this shape, | |, the two projections supporting the knife 

edge, and the body of the lever passing between them. To keep 
the lever horizontal and to register changes of length, another 
knife edge with its blade upwards was embedded in the lever. 
This knife edge pressed against the piece w«, which was screwed 
to the wire at m. Now if the points nt and a were separated or 
brought close together, the knife edges would no longer remain in 
a horizontal line, and the lever would tilt. The end / of the lever, 
and the surface d of the arm bed^ were made planes to support a 
small brass table having on its upper face a vertical plane mirror, 
and for legs three short bits of needles, two of which stood on p 
and one on d. By this arrangement the change in the length of 
may already magnified by the lever, was much more apparent when 
the tilting of the mirror table was read by means of a telescope 
and scale. The most important dimensions are : — 

Length of wire stretched, ma . , . . 69.9 cm. 

Ratio of lever arms i-i2 

4.65 

Distance between needle points ... 2.3 mm. 

Distance to telescope and scale . . . 1660.0 mm. 

The multiplying power of the apparatus was, therefore, — 

iiQ 1660 ^ 

—f-y^ X 2 = 36941. 

46s 2.3 ''"^ 



No. 3] CHANGES DUE TO MAGNETIZATION 21 7 

And as the scale was graduated to millimeters, one scale division 
represented an actual change of length of 2.7 x io~^ mm. 

The coil to magnetize the wire stood on the stone slab and was 
long enough to reach just below the arm ce^ so that the part of the 
wire ma experimented on was in a practically uniform field. 

The principal dimensions of this coil were as follows : — 

Length of coil 83.7 cm. 

External diameter 6.3 cm. 

Internal diameter 3.6 cm. 

Number of wire 18. 

Number of turns 3045. 

Number of layers 7. 

Number of turns per cm 36.4 

Resistance of coil 10.53 ohms 

Strength of field per ampfere . . . 4575 C.G.S. 

Maximum field 260.00 C.G.S. 

The core of this coil was made of two co-axal brass cylinders 
fastened together by the end plates of the coil. The space 
between these two cylinders was filled with water, which proved 
to be an excellent way of retarding the heat effects produced by 
the current. 

Method, 

I at first intended to measure the elongation and the corre- 
sponding induction simultaneously, but found this difficult, and so 
adopted a more convenient and apparently as accurate a method. 
This was to first measure the current used to produce a given 
intensity of magnetism and the consequent changes in length, and 
afterwards to get the relation between the strength of field and 
the intensity of magnetization in the iron, the apparatus in the 
meanwhile remaining untouched. As the laboratory is situated 
in the city, the work had to be done late at night after traffic had 
stopped ; for, in spite of all the precautions that could be thought 
of, the shaking of the apparatus could not be prevented. For this 
reason the induction was not determined immediately after obtain- 
ing the elongation curve, but was done the next morning. The 




2l8 DR. L. T, MORE. [Vol. III. 

induction was measured by the method of reversals.^ The induc- 
tion coil used for this purpose consisted of 2CX) turns of No. 36 
wire wound in one layer on a paper cylinder slightly greater in 
diameter than the specimen. This little cylinder was slipped over 
the wire and fixed half-way between am. The galvanometer was 
calibrated by means of a standard coil having a wooden core. 
The secondary of the standard coil also consisted of 200 turns of 
wire, which plan saved much computation. The intensity was 
then calculated by the formula -5= H-\-^irL Knowing the change 
in length and the intensity of magnetization for any current, of 
course the relation between these two quantities could be easily 
platted. The current was supplied by a battery of storage cells, 
and the resistance was regulated by a slide resistance of copper 
sulphate. 

Results. 

My first results were obtained from a specimen of moderately 
soft commercial iron wire, one millimeter in diameter. This wire 
was free from stress, except that due to the jacket cylinder screwed 
to it, which weighed 350 grams. The elongations given (Table I.) 
are those due to temporary magnetism, and each value is the mean 
of two or three readings which did not vary by more than one per 
cent. The current was applied suddenly, and as soon as a reading 
was taken the contact was broken. This operation was then re- 
peated, the current being increased each time, and readings taken 
until the maximum current was reached. By this means tempera- 
ture effects, which are relatively slow to act, were avoided. 

Figure 3, C shows the relation between the elongation per unit 

hi 
length, y X 10^ and the intensity of the field, H. This curve is 

seen to closely resemble in form those given by Shelford Bidwell. 
When the relation is expressed between change of length and in- 
tensity of magnetization, the curve takes the very different form 
given by Fig. 3, B, The wire slowly increases in length until an 
intensity of about 800 is reached. From that point, until a maxi- 
mum length is attained, at an intensity of 1 2cx^, the elongation is 

^ Ewing, Lond. Electrician, April, 1894. 



No. 3] CHANGES DUE TO MAGNETIZATION 219 

more marked. After reaching this maximum it rapidly contracts, 
the last portion of the curve being approximately a nearly vertical 
straight line. The figure also shows that the point of maximum 
length does not correspond to the point of greatest permeability of 
iron, as is seen by comparing this curve with the curve for per-* 
meability plotted on the same figure. 

It is now necessary to make corrections for the contraction due 

to the — - force. This contraction is obtained from the formula 

/ M 

where M is the modulus of elasticity. My apparatus was well 

fitted for measuring the latter quantity. A weight of about five 

kilograms was hung on the wire, and the elongations due to the 

additions of weights of 20, 50, and 100 grams were read. From 

these Young's modulus was calculated in the usual manner. It 

was found to be 2.2 x 10^ for the specimen used. The contrac- 

m 
tions due to the — - force were then calculated, and are given in 

column 6 of Table I. 
The last column of this table was found by taking the difiference 

between the observed elongation and the -— contraction. The 

oTr 

relation between this corrected elongation, due to what has been 
called the direct action of the magnetism, and the intensity of 
magnetization, is graphically shown by Fig. 3, A, The effect of 
this correction is to make the elongation much greater for a given 
intensity. The maximum value of the elongation is more than 
twice as great as the observed maximum. And the greatest in- 
tensity employed, i^oo C.G.S. units, produces an elongation and 
not a contraction as observed. 

No correction for the change in elasticity was made. For the 
present case it would be insignificant. See discussion of errors at 
end of this paper. 




220 



DR, L, T, MORE, 



[Vol. III. 



Table I. 



H 


M 


/ 


B 


^^obs) 




fcco..) 


4.6 


384.8 


141 


1770 


+0.10 


-0.7 


+0.80 


7.3 


507.0 


294 


3700 


— 


— 


— 


10.5 


752.4 


623 


7900 


1.16 


11.3 


12.46 


11.8 


733.0 


700 


8800 


— 


— 


— 


12.8 


726.7 


739 


9300 


2.71 


15.65 


18.36 


15.5 


695.0 


856 


10770 


5.71 


20.98 


26.69 


19.7 


627.0 


981 


12350 


14.71 


27.60 


42.31 


24.2 


541.4 


1041 


13100 


18.78 


31.05 


49.83 


28.8 


482.7 


1104 


13900 


22.92 


34.95 


57.87 


37.6 


389.1 


1163 


14630 


25.55 


38.53 


64.13 


53.0 


286.3 


1203 


15170 


24.78 


41.69 


66.47 


60.4 


253.7 


1214 


15320 


23.23 


42.47 


65.70 


67.7 


227.7 


1222 


15410 


2130 


42.96 


64.26 


80.0 


193.8 


1228 


15500 


18.74 


43.46 


62.20 


93.3 


167.2 


1235 


15600 


15.49 


44.02 


59.51 


103.8 


150.8 


1238 


15650 


12.81 


44.30 


57.11 


111.6 


140.7 


1241 


15700 


11.03 


44.59 


55.62 


121.2 


130.0 


1244 


15750 


9.20 


44.88 


54.08 


145.4 


109.6 


1257 


15930 


5.42 


45.90 


51.32 


159.1 


100.6 


1261 


16010 


+ 1.94 


46.37 


48.31 


186.5 


86.9 


1274 


16200 


-2.94 


47.47 


44.53 


210.3 


77.8 


1281 


16360 


6.97 


48.42 


41.45 


246.9 


67.1 


1299 


16570 


12.97 


49.67 


36.70 


260.6 


63.9 


1304 


16650 


16.65 


50.15 


3330 



The effect of hardening the wire was next considered. A piece 
of the same quality of iron was heated to a bright red by passing a 
current through it, and then suddenly cooled. After the operation 
the wire was much harder, and only slightly burnt on the surface. 

The observed changes in length, those due to — - and the corrected 

O TT 

values are given in Table II. Hardening the iron makes the 
elongation smaller, and for the present specimen the least intensity 
of magnetization caused the iron to contract (Fig. 4, B), The 
corrected relation between the change of length and the inten- 
sity is shown by B\ On this plate is also plotted curve A, 
the same relation, taken from Fig. 3, for the wire when not hard- 
ened; and curve A^ shows the corrected relations for the same. 



No. 3.] 



CHANGES DUE TO MAGNETIZATION', 



221 



Although the observed change for the hardened wire was a con- 
traction, the contraction due to the -— force was sufficient to bring 

OTT 

the values above the zero axis. So, again, the direct action of the 
magnetization is to elongate the wire, and the corrected curve is 
very similar to the curve for the iron in its original state. The 
absolute values are, however, much diminished, and the maximum 
occurs, for this specimen, with a less intensity. The correction 
for the change of elasticity can be neglected as in the first case. 

Table II. 



H 


/ 


B 


f(obs.) 




11 

7 (corr.) 


5.0 


8 


100 


-0.00 


-0.00 


+0.00 


8.7 


53 


670 


0.05 


0.08 


0.03 


12.8 


272 


3420 


0.10 


2.12 


2.02 


18J 


709 


8920 


0.20 


14.41 


14.21 


27.4 


923 


11620 


0.50 


24.44 


23.94 


36.6 


947 


11940 


0.70 


25.77 


25.07 


45.7 


1012 


12770 


1.85 


29.48 


IIX^ 


57.2 


1044 


13180 


3.10 


31.42 


28.32 


68.5 


1060 


13390 


4.10 


32.42 


28.32 


96.5 


1074 


13600 


7.40 


33.43 


26.03 


118.8 


1064 


13490 


5.44 


32.93 


27.53 


138.5 


1100 


13560(?) 


15.00 


34.24 


20.24 


180.1 


1126 


14320 


24.20 


37.11 


12.91 



To find the effect of strain the wire was loaded with a weight 
of 750 kg. per square centimeter, and the relation between the 
elongation and the intensity of magnetization obtained as in the 
previous cases. The wire was then loaded with a weight of 1750 
kg. per square centimeter, and the same relations found. The 
values are given in Tables III. and IV. The effects of strains 
are also shown graphically by Fig. 5, for the observed and cor- 
rected values. By consulting the figure it is seen that straining 
the wire produces the same change that hardening it does. The 
values » are reduced, and the maximum points occur with less 
intense magnetization. The curves in this figure, as well as in the 
two former figures, marked no load, have an inaccuracy due to the 




222 



DR, L, T, MORE. 



[Vol. III. 



Strain caused by the weight of the jacket cylinder, and should 
have ordinates a trifle greater. 

Although the change in elasticity has hitherto produced little 
effect, as soon as the wire is much strained this correction becomes 
very important, and will modify the curves materially. This 
alteration in the curves it has not been possible to make, as the 
relation between the change in elasticity and the intensity of 
magnetization is unknown. However, from Bock's results some 
approximations may be arrived at ; and these will be considered 
when the errors likely to occur in this investigation are discussed. 

Table III. 



H 


/ 


B 


^(ob..) 




11 

7 (corr.) 


6.9 


636 


8000 


+0.12 


-11.58 


+ 11.70 


11.4 


918 


11550 


0.62 


24.14 


24.76 


18.5 


1080 


13600 


2.63 


33.46 


36.09 


24.2 


1109 


13960 


3.73 


35.27 


39.00 


30.2 


1139 


14340 


3.87 


37.19 


41.06 


347 


1150 


14480 


3.48 


37.94 


41.42 


43.9 


1167 


14700 


2.42 


39.09 


41.51 


55.8 


1184 


14930 


+ 1.20 


40.33 


41.53 


73.2 


1204 


15200 


-0.39 


41.79 


41.40 


81.8 


1212 


15300 


1.16 


42.35 


41.19 


100.6 


1223 


15470 


4.41 


4330 


38.89 


122.5 


1235 


15640 


9.10 


44.24 


35.14 


148.1 


1247 


15820 


14.13 


45.27 


31.14 


157.7 


1253 


15910 


15.80 


45.80 


30.00 


175.1 


1265 


16070 


18.58 


46.71 


28.13 


192.1 


1276 


16230 


25.05 


47.65 


22.60 


228.6 


1287 


16400 


29.03 


48.65 


19.62 


251.4 


1293 


16500 


32.13 


49.26 


17.13 



Possible Errors, 

It has been shown that the change in elasticity occurring when 
an iron wire is magnetized modifies the relation between the 
intensity of magnetization and the elongation ; and it has been 
assumed that, except for heavily loaded wires, this effect will be 



No. 30 



CHANGES DUE TO MAGNETIZATION, 



223 



very small. Bock^ found as a result of his experiments that 
magnetizing soft iron made it more incompressible, and that the 
change in elasticity was less than one-half per cent. He could not 
find any relation between the intensity of magnetization and change 

Table IV. 



H 


/ 


B 


7 (obs.) 




fccorr.) 


5.5 


581 


7300 


-0.19 


-9.64 


+9.54 


9.1 


922 


11600 


0.58 


24.35 


23.77 


13.7 


1011 


12720 


1.26 


29.27 


28.01 


21.5 


1070 


13470 


2.90 


32.83 


29.93 


27.4 


1100 


13860 


4.06 


34.76 


30.70 


36.6 


1134 


14280 


5.90 


36.89 


30.99 


45.7 


1155 


14560 


7.36 


38.36 


31.00 


54.9 


1167 


14710 


9.68 


39.14 


29.46 


73.2 


1178 


14880 


13.84 


40.05 


26.21 


86.9 


1186 


14990 


16.64 


40.65 


24.01 


96.0 


1190 


15050 


19.74 


40.97 


21.23 


111.1 


1198 


15160 


23.63 


41.58 


17.95 


128.0 


1207 


15290 


27.87 


42.29 


14.42 


139.4 


1212 


15370 


32.51 


42.74 


10.23 


150.9 


1217 


15440 


33.97 


43.12 


9.15 



in elasticity, so that it is impossible to give more than a probable 
maximum to the correction it is necessary to make in the curves 
given in this investigation. 
If we take B = 20,000, 



-— = — X 10® dynes per square centimeter, 



and 



27r 



hi , 



— XIC? 

27r 



M 



= -73. 



Zl 



A change of one-half per cent in — would give a correction of 

0.005 X 73 = .4 of a unit. This correction may therefore be neg- 
lected, as errors greater than this would occur in measuring the 
induction. 

^ Bockf he. cit. 



224 ^^- ^- ^- MORE, [Vol. III. 

It was also assumed that when the wire was not stretched, 
except by the jacket, the correction might be neglected. 

The weight of this jacket was 350 grams, or 42000 dynes per 
square centimeter; then 

«'XI07=42^XI0'=200. 

A change of one-half per cent in 200 is i.o. Consequently the 
curves marked no load are not significantly changed by making 
this correction. 

But when we consider the case of the wire loaded with 750 kg. 
per square centimeter, we get, by a similar calculation, a correc- 
tion of 15 units; and for the wire under the greatest tension, 
1750 kg. per square centimeter, a correction of 40 units. Since 
the magnetism makes the metal more incompressible, this correc- 
tion enters as a contraction, and must be added to the ordinates 
of the curves plotted on Fig. 5. It is impossible to say how 
these curves would be affected by the correction, but probably the 
correction increases with the intensity of magnetization. 

Changes in the length of the wire due to variations in tempera- 
ture are another possible source of error. These changes take 
place more slowly than the elongation produced by the magneti- 
zation, so that the two effects may be separated. To retard them 
still more, the core of the solenoid was made of two co-axal cylin- 
ders, and the space between them filled with water. With this 
arrangement the current could be applied, the reading taken, and 
the current shut off, before the gradual change of the zero point 
due to the heating of the wire by the current could be observed. 
Changes in the temperature of the room when they did occur were 
too slow to noticeably affect the results. 

Summary, 

The following is a summary of the results obtained by this 
investigation : — 

I. A relation has been obtained between the elongation due 
lo magnetization and the intensity of magnetization for soft iron. 
When the elongation has been corrected for the contraction caused 



1 







Cf ^FULCRA 



^ 



«— - — • -t.7 I 



^ 
-^- 



DETAIL OF IXVER 




■Ml,—. ,,. ^ 



MORE: CI 



i^ 



No. 3.] 



CHANGES DUE TO MAGNETIZATION. 



225 



by the - — force, the relation may be expressed thus : A rod of 

O TT 

iron elongates slowly until an intensity of about 800 is reached. 
After that point the rod elongates more rapidly and attains a 
maximum value of about 60 x lO""^ part of its length at an inten- 
sity of 1200. With greater intensities the elongation diminishes, 
the curve being approximately a nearly vertical straight line. 

2. Hardening the wire diminishes the corrected elongation, and 
the wire attains its maximum length in a less intense field. 

3. It has been shown that when the wire is stretched, the 
change in elasticity due to the magnetization produces an impor- 
tant effect. Neglecting this correction, the efifects of stretching 
are similar to those caused by hardening the wire. 

Before concluding I would acknowledge my indebtedness to 
Professor Rowland, not only for suggesting the investigation to 
me, but also for his assistance and kind consideration afterwards. 

I also owe many thanks to Dr. Ames and to Dr. Duncan for 
advice and help. 




226 NOTES, [Vol. III. 



NOTES. 

Eli W. Blake. — Professor Blake was born in New Haven, Conn., April 
20, 1836 ; he died at Hampton, Conn., October i, 1895. 

He was graduated at Yale in the class of 1857. After graduation he 
devoted a year to teaching in a private school at Unionville, Conn., and 
subsequently another year to study in the Sheffield Scientific School. 
Next he studied in Germany for three years and a half, — at Heidelberg 
under Bunsen and Kirchhoff, at Marburg under Kolbe, at Berlin under 
Dove and Magnus. He devoted his attention to both chemistry and 
physics ; for although he became ultimately a physicist, it was his origi- 
nal intention to be a chemist. Upon his return, he was for a year 
(1866-67) professor of chemistry and physics in the University of Ver- 
mont and State Agricultural College ; for the year 1868-69, acting-profes- 
sor of physics in Columbia College, New York ; and later, professor of 
physics and mechanic arts at Cornell University, then just opened. From 
1870 to 1895, he was Hazard professor of physics in Brown University. 
Owing to the ill health of a member of his family, he resigned this chair to 
take effect June, 1895; ^^^ before that date he was taken slightly ill himself, 
and he did not recover. His constitution was weakened by the continuous 
and confining labors incidental to his profession, and he died after an 
illness of about five months. He was twice married, his second wife sur- 
viving him. By his first wife, who was a sister of Professor Ogden N. Rood, 
he leaves two children, — a son, Eli Whitney Blake, and a daughter, Mrs. 
Barclay Hazard, of California. 

Professor Blake received the honorary degree of A.M. from the Univer- 
sity of Vermont and State Agricultural School, and the degree of LL.D. 
from Brown University. 

While he was at Brown University, that institution received from the late 
George F. Wilson, a bequest of above J 100,000, to be devoted to a physi- 
cal laboratory. Wilson Hall, immediately erected, will long stand, a monu- 
ment to the generous donor; 45ut it is also a monument to Professor 
Blake, to whose able, unwearied, and conscientious labors are largely due 
its appropriate and convenient arrangements. 

Professor Blake had mental and spiritual qualities of a very high order. 
His sincere devotion to truth led to a conscientiousness, a high sense of 
honor, and great moral courage, — beautiful elements of character which he 



No. 3.] 



NOTES. 



227 



wore like parts of himsdf, and in no sense as garments, to be put on and 
off. His interest in his students was intense and genuine. He was one of 
the most unselfish of men. He was the warmest and truest of friends. 
While he devoted little time to society he was welcomed as a brilliant 
writer and talker, and as an affectionate and delightful companion. 

By nature, Professor Blake had very strong mechanical and scientific 
tendencies. Indeed, they were in the blood ; for he was grand-nephew of 
Eli Whitney, whose cotton-gin was an epoch-making machine. He was 
son of Eli Whitney Blake, of New Haven, himself a scientific man, manu- 
facturer, and an inventor. 

Professor Blake was an indefatigable worker in the laboratory. He was 
there from morning to night. He pursued experimental study in every 
department of physics, oftenest with apparatus of his own designing and 
the product of his own hands. Of his published work, the best known is 
the Method of recording Articulate Vibrations by Means of Photography 
(.American Journal of Science, vol. 16, 1878). 

John Howard Appleton. 

The American Association for the Advancement of Science. — The forty- 
fourth meeting of the association was held at Springfield, Massachusetts, 
beginning on August 28, 1895. The hall for the general sessions, and the 
rooms for the various sections and affiliated societies, were conveniently 
located in the Christian Association Building and the Springfield High 
School, while a hall in the immediate neighborhood was put at the disposal 
of the association for the presentation of such papers as required the use 
of the lantern. Among the many pleasant features of the meeting were the 
receptions offered by the citizens of Springfield to the members of the 
association, and the Saturday excursion to Amherst and Northampton. 

Although the attendance of physicists was not above the average, the 
sustained interest shown in the sessions of Section B, as well as the number 
and character of the papers presented, justify the remark made by several 
members that the meeting of this section at Springfield was one of the 
most satisfactory in recent years. In addition to the address of the vice- 
president. Professor W. Le Conte Stevens, on "Recent Progress in Optics," 
twenty-five papers were read as follows : — 

" Expansion of Jessop*s Steel, measured by Interferential Method," by 
E. W. Morley and William A. Rogers ; " Flow of Alternating Current in an 
Electrical Cable," by M. I. Pupin ; "The Most General Relation between 
Electric and Magnetic Force and their Displacements," by M. I. Pupin ; 
" Relations of the Weather Bureau to the Science and Industry of the 
Country," by Willis L. Moore ; " Solar Magnetic Radiation and Weather 
Forecasts," by Frank H. Bigelow ; " Clouds and their Nomenclature," by 




2 28 NOTES, [Vol. III. 

Cleveland Abbe; "Cloud Photography," by Alfred J. Henry; "A New 
Apparatus for Studying Color Phenomena," by E. R. von Nardroff ; " Voice 
Production, with Photographs of the Vocal Cords in Action," by F. S. 
Muckey and William Hallock; "Note on the Limits of Range of the 
Human Voice," by W. Le Conte Stevens ; " Voice Analysis, with Photo- 
graphic Record," by F. S. Muckey and William Hallock ; " Observations 
on the Relations of Certain Properties of Line Spectra to the Physical 
Conditions under which they are produced," by J. F. Mohler and W. J. 
Humphreys; "The Reproduction of Colors by Photography," by F. E. 
Ives ; " Color Definitions for the Standard Dictionary," by William Hallock ; 
" The Significance of Color Terms," by J. H. Pillsbury ; " On Standard 
Colors," by J. H. Pillsbury; "The Analysis of Floral Colors," by J. H. 
Pillsbury; "On the Comparison in Brightness of Differently Colored 
Lights, and the ' Flicker ' Photometer," by Frank P. Whitman ; " Electro- 
lytic Reproduction of Resonators," by William Hallock ; " A Photographic 
Method of Comparing the Pitch of Tuning Forks," by William Hallock ; 
" Illustration of Gems, Seals," etc., by William Hallock; "An Experimental 
Investigation of the Rotary Field," by H. S. Carhart ; " Phenomena with 
Electric Waves analogous to those of Light with a Diffraction Grating," by 
C. D. Child ; "The Effect of Age upon the Molecular Structure of Bronze, 
Glass, and Steel," by William A. Rogers ; " A New Determination of the 
Relative Lengths of the Yard and Meter," by William A. Rogers ; " An 
Examination of the Statement of Maxwell that all Heat is of the Same 
Kind," by William A. Rogers. 

A noticeable feature of the meetings of Section B was the extensive use 
made of the lantern, not only for ordinary projection, but also for purposes 
of demonstration, as in the case of several of the papers dealing with color. 
The conditions under which papers are presented to the association render 
it, in fact, especially desirable that facilities for illustration and demonstra- 
tion should be at hand. The plan of printing abstracts in advance, which 
has been adopted with such excellent results by many societies, does not 
yet appear feasible in the case of the American Association. Few mem- 
bers know even the tides of the papers presented until the day on which 
they are read. In order, therefore, that the points brought out may be 
fully appreciated, and that the discussion of a paper may be of value, the 
greatest possible clearness in presentation is essential. It is for this reason 
that the use of the lantern deserves to be encouraged ; for there is nothing 
that contributes so much to clearness and concreteness as a well chosen illus- 
tration or experiment. In view of the rapid improvement in the provision 
made for scientific and technical education throughout the country, we may 
perhaps hope that in the near future Section B will always be able to find a 
place of meeting that offers all the facilities of a modem physical lecture- 



No. 3.] 



NOTES. 



229 



room. In the meantime the committee in whose hands is placed the 
arrangements for the coming meeting should realize that for the physics 
section the projecting lantern has become a necessity, and should make 
provision accordingly. 

The next meeting of the association will be held in Buffalo, beginning on 
Monday, August 24, 1896. The officers of Section B are : Vice-President^ 
Professor C. L. Mees, of Terre Haute, Ind. ; Secretary^ Professor F. P. 
Whitman, of Cleveland, O. 

The change in the time of the first general session from Thursday to 
Monday is an innovation which it is hoped will lead to good results. Here- 
tofore the Saturday and Sunday excursions have fallen at such a time as to 
divide the meeting practically into two ; and in spite of the fact that the 
excursions are always enjoyable, and often possess a scientific interest, it 
has been the opinion of many that the interruption of the regular business 
meetings was undesirable. Under the new arrangement, four consecutive 
days will be available for the regular meetings of the sections. 

The change mentioned above in the time. of meeting is only one of the 
changes that were proposed and discussed in the council meetings. Several 
plans for strengthening the association were suggested and earnestly dis- 
cussed ; but it appeared best to postpone final action until these plans could 
be more thoroughly considered in committee. If we may judge by the 
earnestness and enthusiasm which marked the meetings of the council, an 
increased interest in the work of the association, and in consequence an 
increase in its usefulness, are to be confidently expected. 




230 IV, LE CONTE STEVENS. [Vol. III. 



MINOR CONTRIBUTIONS. 

The Limits of Pitch for the Human Voice. 
By W. Le Conte Stevens. 

IN connection with the interesting experiments on voice production and 
voice analysis, as communicated by Dr. Muckey and Dr. Hallock 
at the recent Springfield meeting of the American Association for the 
Advancement of Science, it may be advisable to record some observations 
on the limits of range actually reached. 

The determination of pitch in vocalization depends usually upon the 
musical training of the observer. With moderate practice it is quite pos- 
sible to estimate the vibration frequency with such accuracy that the error 
is much less than a semitone. Assume that the observer has a tuning-fork 
of known pitch, such as C4 (512 double vibrations per second). If the 
frequency of the tone to be investigated is between 256 and 1024, differing 
thus less than an octave from the standard, and if it makes a recognizable 
interval, such as a major third or minor sixth, with the standard taken as 
keynote, the application of the corresponding numerical ratio gives the 
pitch at once. If the interval be not exact, its departure from exactness 
has to be estimated ; and here the training of the physicist has to be con- 
joined with that of the musician. If the observed pitch differ from the 
standard by an interval much wider than an octave, a tone in unison with 
it can be instantly sounded with the voice or by whistling. The succession 
of octaves above or below are then sounded until a pitch is attained that 
is easily comparable with the standard ; or this process may be reversed, 
the standard being taken as starting-point, and a succession of octaves 
above or below it quickly furnishes the means for comparison. During 
my college days I acquired the habit of carrying a tuning-fork (512 v5.) ; 
and this habit has been retained to the present day, though the fork is 
utilized much less frequently than during the earlier period of musical 
activity. The estimation of pitch by its aid was so much practised as to 
become very easy, and the extremes of pitch noticed in concert or at the 
opera were often estimated. When the printed music is at hand, the 
correctness of such an estimate is readily verified. 

The lowest vocal pitch hitherto recorded is Fq, about 43 vs., which is 
credited to a German basso, Fischer, who lived during the sixteenth century. 



No. 3.] LIMITS OF PITCH FOR THE HUMAN VOICE. 23 1 

In modern opera the basso is rarely ever required to sound lower than C^ 
(64 vs.) . This limit may be passed by an ordinary masculine voice under 
abnormal conditions. With the vocal cords thickened by an attack of 
influenza, I have sounded as low as A© (53 vs.), but the sound was faint 
and of the poorest musical quality. 

An ordinary soprano voice may reach C5 (1024 vs.) ; and it may be 
safely stated, in round numbers, that the limits of range of the average 
adult human voice are from 100 for basso to 1000 for soprano. Adelina 
Patti is said to sing as high as G5 (1536 vs.) without sacrifice of good 
quality. At Parma in 1770 Mozart tested the voice of Lucrezia Ajugari, 
who trilled on D5 (1152 vs.), and sang several passages of higher pitch, 
one of which included Q (2048 vs.). An American soprano, Miss Ellen 
B. Yaw, has lately surpassed this limit, attaining a pitch which is stated to 
be E« (2560 vs.). This statement is made in the advertisement of a 
concert manager. For the exceptional adult human voice the limits may, 
therefore, be given as about 50 for basso and 2500 for soprano. 

In early childhood all the tissues of the human body are softer and more 
elastic than after maturity is reached, and it is well known that the conver- 
sational pitch in childhood is higher than it is afterward in youth. But I 
have seen thus far no published record of the highest observed pitch of a 
child's voice. A few years ago my attention was casually attracted to the 
squeal of a child at play. The tuning-fork standard at once enabled me 

to estimate the pitch as Gc (3072 vs.). 

This result was so remarkable that,^ in 

the absence of any immediate oppor- 

Q — tunity for verification, I rejected it as 

aT ^g ^^ .... C4 .... 5xa possibly the outcome of faulty obser- 

\y -^ir~ .... Cb .... 956 vation. A few months afterward, while 

lingering near a group of children at 
play, I estimated the pitch of quite a 
succession of squeals, with results vary- 
ing from 2500 to 3000 double vibra- 
tions per second. The observation has since been repeated many times, 
so that there is no reasonable doubt of the correctness of the first estimate. 
Under the excitement due to either terror or enthusiasm, the voice may, 
without conscious strain, reach a limit quite unattainable in song. 

These results are conveniently expressed in musical notation. The 
extreme range is seen to be a trifle in excess of six octaves. For a single 
voice the range after maturity is rarely greater than three octaves. Ajugari 
sang as low as Gj (192 vs.), reaching the phenomenal range of four and a 
half octaves. Two octaves is the range commonly assigned for the average 
adult voice. 



G. . 
Ce . 


. . 307a 
. . 9048 


c. . 


. . xo«4 


Q . 


. . 5" 


c. . 


. . a56 


c, . 


. . xa8 


c, . 


. . 64 
. . 43 




232 



E. L. NICHOLS. 



[Vol. III. 



The New Physics Laboratory at Lille. 
By E. L. Nichols. 

ON June I and 2, 1895, the University of Lille,^ celebrated by a series 
of magnificent fites the opening of seven new buildings devoted to 
learning. The cost of these, which amounted to 3,500,000 francs, was 
shared equally by the state and by the city of Lille. 

One of the new buildings, the exterior of which is shown in Fig. i, is an 
institute of physics. It is not large, compared with many modem Euro- 
pean laboratories, but it is well arranged ; and it shows in its interior fit- 
tings a sumptuousness such as nature, until very recently at any rate, has 




OAUTHIER DE 



Fig. 3. 



been unaccustomed to find in the temples devoted to her service. Some 
of these decorative features appear in the view of a comer of the large 
lecture-room. Fig. 2. 

The characteristic feature of this laboratory is the subdivision of its 
interior into many small rooms, each of which is well lighted and easily 
accessible. These are arranged around a central court 

1 Officially known as the " Academic de Lille," an institution which, like all the 
French provincial universities, is affiliated with the University of France. 




Fig. 2. — Large Lecture-room. 




Fig. 1.— The Physical Laboratory at Lille. 




No. 3.] THE NEW PHYSICS LABORATORY AT LILLE. 233 

Thus, on the first floor, Fig. 4, there is a suite of nineteen small labora- 
tory rooms, devoted to elementary practice work. In these the apparatus 
for such work is permanently mounted, there being only one or two experi- 
ments in a room. These rooms are not thrown together, but all may be 
entered from a corridor which serves as means of communication. 

On the lower floor, the plan of which is shown in Fig. 3, the correspond- 
ing set of rooms is used for research laboratories, offices, etc. There is 
no corridor, but the adjoining rooms are connected throughout by doors. 

This arrangement of many small rooms, within which the multitude of 




Fig. 4. 



special operations of which experimental physics consists may be per- 
formed, each in an apartment assigned td it and planned for it, will meet 
the approval of nearly all physicists. 

The Lille laboratory has its own installation of electric lighting. This, 
like that of nearly all the newer European laboratories, consists of a gas 
engine, two small dynamos, and a set of accumulators of considerable 
capacity. The voltage of these batteries is sufficient to serve for arc and 
glow lighting, as well as for general laboratory purposes. 

The low price of gas, and the high stage of development to which both 
the gas engine and the storage battery have been brought in Europe, 
render this an economical and a very convenient arrangement. 



234 ^^^ BOOKS. [Vol. III. 



NEW BOOKS. 

Electric Waves, being Researches on the Propagation of Electric 
Action with Finite Velocity through Space. By Dr. Heinrich Heftz, 
Professor of Physics in the University of Bonn. Authorized English 
Translation by D. E. Jones. 8vo, pp. xv, 278. London, Macmillan & 
Co., 1894. 

At this time of writing, there is small need to describe Hertz's experi- 
ments. The term Electric Waves has become a household word, and the 
demonstration of electromagnetic radiations has become a matter for the 
popular lecture as well as the class-room. A host of investigators has 
followed in the steps of Hertz, and this region of research is at present in 
the heyday of popularity. The ether is a favorite subject of conversation 
and of publication by authors whose knowledge of mathematics is of the 
most rudimentary character. This is one of the unfortunate results of the 
existence of fashions in science, and of the attempt at popularization of 
difficult subjects by such men as Kelvin and Lodge. Not that the reviewer 
wishes to discourage popularization, but that it has its disadvantages. One 
has only to pick up a newspaper or magazine article with the heading 
" Tesla " to see an example. The present work does not deal with " wag- 
gling the charge of the earth," although it contains the account of the 
original experiments on oscillations of the charges of conductors disturbed 
from equilibrium, and measurements of the action of these oscillations. It 
is a matter for congratulation that the different researches of Hertz on this 
subject were collected by him into a volume, and it is a matter for satisfac- 
tion to the non-German-reading scientific world (alas that there is one !) 
to have them translated into English. The title of the work has been 
changed in the translation, which is also furnished with a preface by Lord 
Kelvin on the history of the controversy between the adherents of Action 
at a Distance and the contrary, from the times of Newton and Descartes 
to that of Hertz. Hertz is indeed fortunate in his preface-writers. To 
have one's principal works prefaced by the greatest physicists of two of the 
greatest nations in science does not fall to the lot of many authors, and is 
not to be lightly valued. In the preface it is stated that Faraday himself, 
when last seen by I^ord Kelvin, was attempting to discover whether mag- 
netic force was propagated with a finite velocity. Nothing came of these 
experiments, however. 



No. 3.] NEIV BOOKS 235 

The author is also fortunate in his translator. Mr. Jones has given us an 
excellent rendition of the sense of the original without considering it neces- 
sary to preserve the German spirit by the use of such misshapen English 
as we often get from enthusiastic pupils of distinguished German professors. 
Whether it was this fact, or the insight displayed in wishing to present 
Hertz*s work in an English dress, or the experimental work done by the 
translator under the direction of Hertz, that the Royal Society considered 
worthy to be honored by a medal, we can only guess. 

In the introduction Hertz gives an account of the manner in which he 
came to make these researches. An account of his first introduction to the 
subject has been given in a previous number of this journal.^ The prize 
question set by the Berlin academy for a relation between electromagnetic 
force and dielectric polarization of insulators, set him to thinking of what 
results could be obtained by the use of Leyden jars or the open circuits of 
induction coils. Consideration seemed to show that the effects desired 
would be too small to measure. Not discouraged, however, but continually 
ruminating on the properties of electrical oscillations, a chance observation 
of a side spark from one of a pair of coils, when a Leyden jar was discharged 
through the other, set him at work on methodical observations of the phe- 
nomenon which contained the germ of his whole subsequent discoveries. 
His subsequent course of procedure is described with charming frankness, 
his mistaken conclusions being related with the same readiness as his suc- 
cessful ones, and full acknowledgment being made of the work of other 
savants with whom he at times found himself in controversy. It is interest- 
ing to see how very nearly Professor Lodge came to making the same dis- 
coveries as Hertz, who declares that Lodge was on the way to the observation 
of waves in air, and would probably thus have discovered the finite velocity. 
The last part of the introduction is devoted to a comparison of the old 
theories with Maxwell's theory, and to answering the question, " What is 
MaxwelPs theory?" After admitting his inability to understand just what 
Maxwell intended as the physical representation of his mathematical con- 
ceptions, — a state of mind that will be sympathized with by every careful 
student of Maxwell, — he gives the very sensible answer : " Maxwell's the- 
ory is Maxwell's System of equations. Every theory which leads to the 
same system of equations, and therefore comprises the same possible 
phenomena, I would consider as being a form or special case of Maxwell's 
theory." This will be seen to be in line with the views of Helmholtz on 
mechanics mentioned above. This is a point that cannot be too strongly 
impressed on amateur theorizers, that the test of a theory is that it leads to 
the equations which are known to express the facts. If it does not, it 
is good for the waste-basket. The writer, and, as he supposes, all teachers 

1 Physical Review, Vol. III. p. 73. 



236 NEW BOOKS. [Vol. III. 

of physics, is in frequent receipt of visits from people with favorite 
elaborate theories, destined to overthrow Newton, Maxwell, or somebody 
else, the inventor having invariably no knowledge whatever of mathematics. 
If these people could be put at some mild employment that would keep 
them from inventing theories it would be a great gain to the world. 

The whole of these fourteen papers, with the exception of the second, 
on the influence of . ultra-violet light in reducing the potential at which dis- 
charge takes place, possess a remarkable degree of continuity. Few are more 
admirable than the first, in which is shown the means of disturbing the 
charge in a wire conductor so as to cause oscillations, and in which the 
function of the spark of the induction coil in giving the necessary impulse 
and lowering the resistance of the air gap enough for the oscillations to 
occur is clearly described. The existence of wave propagation in the wires 
is recognized, and the position of the nodes of vibration determined. The 
existence of resonance was first predicted from theoretical considerations, 
and then observed and found to increase and decrease precisely as theory 
demanded. 

After admiring the close thinking shown in the performance of these 
experiments, it comes somewhat as a shock to the reader to find in the 
next paper quotations from a paper by von Bezold, published seventeen 
years before, in which many of the same phenomena were observed, the 
methods of exciting the vibrations being identical. Of the existence of 
this paper Hertz was at the time of his work of course unaware. It is 
curious to look over the work of Lodge done at about this time, and to see 
how similar were the methods used, also with a perfect comprehension of 
the issues involved. The one thing lacking in Lodge's work was quantita- 
tive results of the same order of precision as Hertz's. The present writer 
remembers that soon after the time of these researches, while he was 
engaged in demonstrating some of Lodge's experimental results in the 
laboratory in Berlin, on the occasion of the visit of a number of distinguished 
physicists connected with the newly established Reichsanstalt, Professor 
von Bezold seemed quite interested in the experiments, and quietly remarked 
that he had noticed something similar several years before, giving the 
reference to his paper. The question naturally arises, how could von 
Bezold's paper have attracted so little attention, while Hertz produced 
such a stir years after. Probably because Hertz followed up his researches 
with others in a logically conducted series resulting in a new discovery. 
In the next of the series, the effect of the oscillator at various points in 
space is calculated, and the effects of the magnetic force separated from 
the electric force by experiments devised with extreme penetration. Next 
the effect of the electromagnetic action upon insulators is demonstrated, 
and thus one of the original objects of the investigation fulfilled. Next 




No. 3-] NEW BOOKS, 237 

by the interference of waves in air with waves propagated in a wire, the 
existence of a finite velocity is proved, and an attempt made to estimate it 
by the determination of the wave-length in the wire, the period of the vibra- 
tion being calculated by the old theory. It is to be noticed that this is the 
case in the whole series of researches, the calculation of the period depends 
upon a theory, and hence no direct verification of the velocity demanded 
by Maxwell's theory would thus be possible. It is wprthy of note that 
neither Hertz nor any of his immediate successors, though they measured 
wave-lengths without number, ever made a direct determination of the 
velocity by observing the other needed element, the time. The present 
writer described such a direct method to Professor Kundt five years ago, 
and was advised to carry it out, but the facilities not being available, it was 
put by till a more convenient season. Before this occasion arrived, the 
experiment had been carried out by Blondlot in the same manner, de- 
scribed in his paper on the determination of the Velocity of Propagation 
by a method independent of any theory. This was the first and only direct 
determination until the recent publication of the work of Professor Trow- 
bridge and Mr. Duane, which again anticipated the completion of a pre- 
cisely similar piece of work done under the direction of the writer. It 
is, however, desirable to have this velocity determined as often as 
possible, until it can take its place with other well-authenticated physical 
constants. 

It is in this last research that Hertz had his only disappointment. He 
thought he had shown that the velocity was different in air and in wires, a 
mistake that was soon corrected by others. Hertz says that although he 
may have been lucky elsewhere, certainly here he was unlucky. This is 
certainly too much modesty. Never could a man with less justice have 
had his success attributed to luck. With Hertz everything was deliberately 
planned. After proving the velocity of propagation to be finite, knowing 
that the waves should be capable of reflection and refraction, he makes 
them reflect and refract. Knowing that oscillatory currents should not 
penetrate into the interior of conductors, he demonstrates that they do 
not. Having calculated what mechanical forces they should exercise, he 
straightway observes them. These researches are a notable example of 
how experimental work should be prosecuted, and convey a lesson that 
should be taken to heart by the student. The proper order of procedure 
may be stated: "Think, calculate, plan, experiment, think, — and first, 
last, and all the time, think.'' The method often pursued is : " Wonder, 
guess, putter, guess again, theorize, and above all avoid calculation." 
Throughout Hertz's work we are constantly reminded of Faraday by the 
remarkable acuteness of interpretation of results as well as in the skilful 
devising of the experiments. Hertz adds to Faraday's experimental skill a 



238 ^ElV BOOKS, [Vol. III. 

mathematical ability that Faraday did not possess, although he had an 
intuition which nearly replaced it. 

Finally, and, in the opinion of the writer, of most importance. Hertz 
concludes with two mathematical papers on the fundamental equations, 
that is, with an exposition of Maxwell's theory. In these he brings out 
with the greatest vividness the complete duality of all electrical and magnetic 
phenomena, with the exception of conduction. It is no discredit to Hertz 
that Heaviside had previously done the same thing with equal clear-sighted- 
ness. Heaviside suffers under the disadvantage of having written so much 
and so diffusely that ten students will read Hertz's papers for one that reads 
Heaviside's. Maxwell's great work is full of obscurities, incongruities, and 
contradictions. These he would doubtless have removed in rewriting the 
work if he had lived. None of his commentators have done it for him, 
with the exception of these two. Both have adopted unconsciously the 
same method, namely, that of considering the two vectors, electric and 
magnetic force, as the essential quantities that are propagated, avoiding 
introduction of the potentials and vector-potentials, and eliminating alto- 
gether the magnetizations. The notation of Hertz commends itself by its 
perfect symmetry and simplicity. A pair of equations saying that the time 
derivative of the indue Hon y electric or magnetic, is proportional to the curl 
of the other forccy another pair saying that either induction is a linear 
vector function of its own force, — that is all. The real electricity or 
magnetism is defined by the corresponding induction, the free, or apparent, 
by the force in the same manner. The treatment of the equations for mov- 
ing bodies is the most logical that has been given, and by proceeding in a 
straightforward manner terms are introduced which are lacking in Max- 
well's equations. The effect of static charges carried by moving conduct- 
ors, demonstrated by Rowland's famous experiment, is one of these. 
There are other effects of a dual nature that are still left to verify, of which 
more may be said later. 

The only fault that can be found with Hertz's notation is that it involves 
the use of German letters for the components of the inductions. These are 
inconvenient for writing by Anglo-Saxons, and the writer ventures to suggest 
a substitution, which he has been accustomed to make use of in his lectures, 
of the French round letters frequently used by architects in lettering, which 
are easy to write, not impossible for printers, and easy to name in reading, 
distinguishing " round X " and ** square X" He hopes that this mild sug- 
gestion will not be run afoul of by some member of the American Institute 
of Electrical Engineers, stating that M. Hospitalier has already proposed 
these for something entirely different. 

In conclusion, let us advise the student to place this volume on his 
shelves with its first, experimental side next to Faraday's Experimental 



No. 3] NEW BOOKS. 239 

Researches, and with its second, or mathematical part, next to Maxwell's 
Treatise, " for on these three hang all the law and the prophets " of 
electricity. 

Arthur G. Webster. 



Mechanics, an Elementary Text-Book, Theoretical and Practical, 
for Colleges and Schools: Dynamics, By R. T. Glazebrook, M.A., F.R.S. 
8vo, pp. xii+256. Cambridge, the University Press, 1895. 

The past year has been prolific of works on Physical Science. Having 
come to realize that existing text-books are of doubtful utility, because of 
their ancient character, the scientific world has aroused itself to the task of 
producing new ones that are at once the result and the harbinger of a 
more practical method. The text-books by R. T. Glazebrook are espe- 
cially deserving of notice. The one mentioned above is one of a series by 
this writer which bear the same general character as to method, and which 
give promise of covering quite thoroughly and efficiently that portion of 
physics usually taught as a Sophomore or Junior course in college. 

The conviction is at once forced upon the reader that the book in ques- 
tion is the outgrowth of the author's method of teaching, and he is there- 
fore the more gratified on turning to the preface to read : " The portions 
of the following book designated Experiments have, for the most part, 
been in use for some time as a Practical Course for Medical Students at 
the Cavendish Laboratory." . . . "The rest of the book contains the 
explanation of the theory of those experiments, and an account of the 
deductions therefrom." In fact, it would seem that the author's method 
of presenting physics to a class is the best calculated to secure results, and 
is at the same time within the reach of any teacher, and of any institution 
— even one of limited resources. The author develops the theory, and 
immediately proceeds to give definite instructions for its verification and 
practical application, describing in connection therewith apparatus suitable 
for the purpose, of so simple a character that it can be easily set up and 
adjusted in any laboratory. The same apparatus, moreover, is suitable for 
lecture-room purposes ; for in the preface we find the statement : " most of 
the lecture-room experiments are performed with the apparatus which is 
afterwards used by the class, and wherever it can be done, the theoretical 
consequences are deduced from the results of these experiments." This 
plan seems an ideal one for teaching physics, giving, as it does, to the lec- 
ture, recitation, and laboratory a unity of character that can scarcely be 
obtained otherwise ; and it is no small advantage in a book that makes this 
method possible. The style of the book is best described as tangible. 



240 N-EIV BOOKS. [Vol. III. 

A first book in Mechanics should appeal to the experience of the student, 
for the science itself is built upon the everyday experiences of life. In 
expounding Newton*s Third Law, he makes clear what is meant by 
"Action" and "Reaction," nor does he consider it undignified to appeal 
to the case of horse drawing the canal boat, and even the tyro in mechani- 
cal science cannot fail to see clearly the application. 

The classification of the subject is a happy one. The first chapter is 
devoted to measurements of length, area, and volume. Two chapters are 
then taken up by Kinematics — Velocity and Acceleration, respectively. 
Momentum is then presented in an inductive manner, while the fourth 
chapter deals with rate of change of momentum, — Force. The sixth, 
seventh, and eighth chapters are devoted to Newton's Laws of Motion, the 
last one including, naturally enough, the treatment of energy. In the ninth 
chapter curvilinear motion is presented, which subject includes quite a full 
treatment of Projectiles. The tenth chapter is devoted to Collisions, while 
the eleventh, entitled " Motion in a Circle," deals with a variety of sub- 
jects, including the Hodograph, Circular Motion, Simple Harmonic Motion, 
and The Pendulum. 

The chapters on force and energy are especially clear and fiill. The 
treatment of Newton's Laws is no less good, as is also that on Collisions. 
It would seem, however, from the small amount of space devoted to the 
subject, that the author underrates the importance of simple harmonic 
motion. The same criticism might well be passed upon his treatment of 
the pendulum ; and an even more glaring defect is the entire absence of 
any mention of the moment of inertia and the whole subject of moments. 
In fact, it would seem that after a most excellent treatment of the subjects 
included in the first ten chapters, the publication of the book was hurried 
to the extent of grouping all that was left of mechanics — not a small por- 
tion — in the last, the eleventh, chapter. 

The book is remarkable for its accuracy, both of principle and detail. 
Seldom does it happen that a first edition does not present errors to be 
corrected in a second. The absence of even typographic errors makes the 
book conspicuous in this particular. The excellent historical treatment of 
the subject is also to be noted. Nor should a review of the book omit 
mention of the excellent collection of problems included at the close of 
each chapter. 

Text- books on this subject are generally too simple or too elaborate for 
a conception of elementary mechanical principles. This book cannot fail 
to recommend itself, therefore, for a first course, preliminary to the study 
of physical science. No other book presents in the same space, with the 
same clearness and exactness, so large a range of mechanical principles. 

Henry E. Lawrence, 



Volume III. January-February y i8g6. Number 4. 



THE 

PHYSICAL REVIEW. 



ON THE PHOTOMETRY OF DIFFERENTLY COLORED 
LIGHTS AND THE "FLICKER" PHOTOMETER.^ 

By Frank P. Whitman. 

IN November, 1893, during measurements on some colored disks, 
it became necessary to know the relative luminosities of the 
colored papers employed. An attempt was first made to estimate 
the luminosity directly by comparison with Maxwell disks of black 
and white, smaller in diameter, and mounted on the same axis. 
The relative proportions of black and white were changed until, on 
rotation, they formed a gray, which was estimated to be about 
equal in brightness to the colored disk under examination. This 
method, practiced by certain experienced observers, doubtless has 
afforded good results, but in my hands proved difficult and un- 
certain. 

Trials were then made by four other observers, all somewhat 
skilled in physical measurement, whose general color-sense was 
found to be similar, but their estimates of luminosity were found 
to vary in such an irregular fashion as to make any comparison 
impossible. 

Later experiments, carried out with the help of some thirty 
undergraduate students, led to similar results. Differences of 
50 per cent between two different observers frequently arose, 

^ Read at the Springfield meeting of the A. A. A. S., Aug. 30, 1895. 

241 



242 FRANK P. WHITMAN. [Vol. III. 

when the light to be compared differed no more than an ordinary 
from a Welsbach gas-burner ; while the same observers, working 
with light of the same color, would agree at least within 2 or 3 per 
cent. 

By practice the margins of difference may be rendered smaller, 
yet experts often differ in their estimates of the brightness of arc 
lights when compared with standards of different color ; and it is 
questionable whether one can always be sure that by practice in 
such measurements he gains greatly in accuracy. His measure- 
ments agree with each other better than at first, but if his method 
of comparison have in it something of an arbitrary or personal 
quality, as it must from the very nature of the case, it remains 
uncertain whether he may not be fixing himself in an erroneous 
practice rather than approaching a correct one. 

The character of these results, and the need of some more exact 
method of comparing color-luminosities, led to the consideration 
of Professor Rood*s "flicker" experiments.^ 

Rood prepared about fifty gray disks differing successively, as 
equally as possible, in depth of tint from black to white. If a dark 
shade was combined with a light shade in the usual way, and 
rotated rather slowly, the familiar unpleasant sensation known as 
a flicker was produced ; but if successive pairs, more and more 
nearly alike, were chosen, the flicker became less, until it almost or 
quite disappeared. Nearly the same effect was produced if, instead 
of a gray, some other color was substituted on one of the disks. 
It was always possible to combine with it a gray disk of such a 
shade that the flicker nearly ceased, showing that this sensation is 
apparently independent of the wave-lengths of the lights compared, 
and dependent only on their relative luminosities. Professor Rood 
suggests that the principle may be easily applied to ordinary 
photometric work, but indicates no method. The special arrange- 
ment described in his paper serves admirably to compare pigments, 
when in such form that they can be spread upon disks and 
mounted in the whirling machine. 

For ordinary photometric purposes, however, there is necessary 
some arrangement by which luminosity can be varied continuously 

^ American Journal of Science, Vol. XLVI., September, 1893. 



No. 4] COLORED LIGHTS AND FUCKER PHOTOMETER, 243 



instead of step by step, as with a set of gray disks, which can be 
mounted on a photometer bar so as to- compare colored lights as 
well as colored pigments, and which is reasonably quick and con- 
venient in use. No doubt there are many ways of applying Pro- 
fessor Rood's flicker principle ; the one which I, after some trial, 
found most successful was as follows : — 

A card was cut in the shape AHBG, in the figure, so as to 
form two semicircles of about 5 and 8 cm. radius respectively, 
joined along a common diameter. This could be rotated at any 
desired speed about the axis K, in earlier experiments by clock- 





Fig. 1. 



work, but afterward, and more conveniently, by hand. A dia- 
grammatic plan of the apparatus as used is shown in the figure. 
DE represents the photometer bar, AB is the revolving disk, C is 
a card, which may be white or colored with any pigment which it is 
desired to study, -F is a tube through which the observer looks. 
It is evident that when the apparatus is in the position shown 
in the figure, the outer portion of the revolving disk only will be 
visible through the tube, but when the disk is rotated half a turn, 
the small semicircle will not come into view at all, and the observer 
will see only the card C. As the disk revolves, the two pieces will 



244 



FRANK P, WHITMAN. 



[Vol. III. 



be presented to the eye in rapid succession, and, if they diflfer in 
luminosity, will produce the sensation of "flicker." If equal lights 
are placed at the ends of the photometer bar, the relative illumi- 
nation of the card and disk can be varied by sliding the photometer 
along the bar. The flickering sensation can thus be entirely 
destroyed, whatever the colors are upon the card and disk. 
(Various colors were tried upon the disk, — red, white, and diflfer- 
ent grays, — but white was finally adopted as in all cases the most 
convenient.) When the proper position of the photometer was 
reached, not only did the flicker vanish, but the sense of color in 
the field of vision became much weaker or entirely disappeared, so 



0.9 

as 

0.7 
0.6 
0.5 
0.4 
0.3 

a2 
ai 




5 ^ 

o o 

* i 

III 



\ \ 



a CD 



9 -I 
5 aa 



Fig. 2. 



that it was frequently difficult or impossible to tell what color was 
upon the card. A slight movement of the photometer in either 
direction revived the sense of color and reestablished the flicker. 
The results obtained with this instrument were surprisingly good 
in ease, rapidity, and precision. 

Work was interrupted at this point until May, 1895, when the 
measurements were taken up again, and the instrument itself 
somewhat carefully studied. 

The colors used for experiments on pigments were chosen from 
the well-known series of colored papers made by the Milton Brad- 




No. 4.] COLORED UGHTS AND FLICKER PHOTOMETER. 245 

ley Company of Springfield, Mass., and included the whole range 
of the specjrum. These papers were pasted upon perfectly flat 
cards, and placed successively in the position marked C in the 
figure. Three curves are shown to illustrate the capacity of the 
instrument, exhibiting the relative luminosities of these nineteen 
colors, when illuminated by the light of a kerosene lamp, of a dull 
gray sky, and of a bright blue sky. 

The predominance of the lamp-curve toward the red end of the 
spectrum and of the clear sky at the other end is manifest, while 
the similarity of the curves shows that the measurements are of 
like character and definiteness, whatever the source of illumination. 
In all these cases the revolving disk was white, lighted by a 
lamp, while the colors on the card were exposed to the light under 
investigation. Since the flicker eflfect is independent of the wave- 
length, any source of light which is constant may be used to illu- 
minate the disk without changing the results dependent on the 
luminosity of the colored card. The curves from sky light and 
cloud light, though the mean of several trials, were not entirely 
satisfactory on account of the comparatively inconstant brightness 
of these sources of light. The observations on lamplight, how- 
ever, were made twice, at an interval of over two months, with 
practically identical results. 

A greater interest, perhaps, lies in the instrument itself. An 
apparatus so new, and depending on a physiological principle which 
has been so little studied, presents many points for investigation, 
before its utility as a practical photometric apparatus is assured. 
The remainder of this paper is occupied with a study of some 
of these points. 

I. The precision of setting, as compared with other types of 
photometer, was tested in over one hundred settings on nineteen 
dififerent colors. The difference between two successive readings 
was seldom more than one per cent, though a few readings differed 
as much as two or three per cent. As these readings were made 
over the whole range of the spectrum, it seems fair to say that the 
instrument can be used upon lights presenting the widest differ- 
ences of wave-length, with a precision approaching that of ordinary 
types of photometer when comparing lights of the same color. 



246 FRANK p. WHITMAN. [Vol. III. 

2. Since the photometer depends, not on the actual comparison 
of like quantities, but on the distinctness of a peculiar physi- 
ological sensation, — the flicker, — it is worth while to see whether 
different observers will agree. To test this question, and inciden- 
tally to try the instrument with colored lights instead of colored 
papers, both disk and card were made white, and equal lamps, the 
colors of which could be changed at pleasure by the interposition 
of colored glass, were placed at the ends of the photometer bar. 
Two observers, whose eyes were known to be similar, compared 
successively the brightness of the two naked lamps, first by an 
ordinary photometric method, then by the flicker. A red glass 
was then placed in front of one lamp, a green glass in front of the 
other, and the same observations were made again. One of the 
two observers had never seen the instrument before. The results 
follow, each being the mean of four or five concordant observations. 
The actual readings are given in feet and hundredths, not reduced 
to comparative luminosities. One lamp stood at 3.CX), the other at 
9.00 on the photometer bar. 

Observer F. Observer W. 

Ordinary. Flicker. Ordinary. Flicker. 

BoUi lights naked. 
5.98 5.% 5.98 5.98 

Left lamp red, right green. 
5.59 6.79 6.08 6.88 

Thus, in the last case, the setting of F by direct estimation 
differed from that by flicker by 1.20 feet, that of W by 0.80 foot. 

The setting of F by estimation differed from that of W by 0.49 
foot ; while F's flicker setting differed from W's by only 0.09 foot. 
The last disagreement is comparable with the errors of observa- 
tion. 

At a later time, three other observers, making comparisons for 
technical purposes between coal-oil lamps and a standard candle 
which differed from them somewhat in color, were able with the 
flicker photometer to obtain accordant results among themselves 
much more easily and surely than by ordinary methods. 



No. 4.] COLORED LIGHTS AND FUCKER PHOTOMETER, 247 

3. Two " disks " like those in the cut were mounted on the same 
axis in the photometer. By sliding one upon the other, the frac- 
tion of a revolution during which the card was visible could be 
varied between 180° and o®. The relative length of exposure of 
the eye to the two lights could thus be varied within wide limits. 
Several comparisons were made of lights differing widely in color, 
and with openings from 22 J® to 180®, but no differences in reading 
were observed that could be traced to this cause. While it is true 
that the sensitiveness of the retina differs for lights of different 
wave-lengths, and probable that differently colored lights require 
different periods of time to produce equal sensations in the eye, 
it appears from these experiments that there is time, at the com- 
paratively slow rate of rotation of the disk, for every color to 
produce its full effect, so that errors which might be produced 
by irregularity in rate of rotation or in shape of the disk are 
negligible. 

4. In much of the work, the photometer and the standard lamp 
were kept at fixed points, and the balance obtained by moving the 
other light, thus making all comparisons at the same actual degree 
of illumination. This method of using any photometer has some 
obvious advantages, though the sensitiveness is not quite so 
great as when the photometer itself is moved. To determine 
whether the absolute brightness has any effect on the settings, 
measurements were made of six colors — red, orange, yellow, 
green, blue, violet — under widely differing illuminations. When 
the light \vas faint the measurement became much more difficult, 
but the results obtained with bright and faint light did not appre- 
ciably differ, showing that the well-known greater sensitiveness of 
the eye to blue light is not important in measurements made 
under conditions proper to this photometer. When the illumina- 
tion is small the flicker is very faint and may be invisible while 
the photometer is moved over as much as 6 or 8 cm., but by 
reading the points each side of this space where the flicker again 
becomes visible, and taking the mean of the two readings, results 
may be obtained almost as trustworthy as with brighter light. It 
should be remarked that this method in general depends for its 
value somewhat on the state of the eye. It appears certain that 



248 FRANK P. WHITMAN. [Vol. III. 

two normal eyes, in a reasonably fresh condition, would obtain like 
results, but if the eye is wearied from long-continued observation 
or loss of sleep, the perception of the flicker becomes more diffi- 
cult, and the difficulty appears to vary with different colors in a 
way that has not yet been studied. 

5. The question still remains, whether the flicker method gives 
in all cases a true measure of luminosity comparable to that which 
would be obtained by any more direct photometric method. To 
test this, the luminosity measures afforded by Maxwell's disks 
were used. 

Suppose, for example, three colors — say red, green, blue — com- 
bined on the whirling machine into a neutral gray, which is 
matched by the combination of a black and a white disk. The 
amount of white in the latter combination, corrected for the white 
light reflected by the black portion, is of course the measure of 
the luminosity of the colored disk in terms of white, which quan- 
tity, again, is dependent upon the luminosities of the three colors 
of which it is composed. 

If now the fraction of the whole circle occupied by any color 
is multiplied by its luminosity as measured with the flicker pho- 
tometer, the result will be the amount of white equivalent to that 
colored sector, and the sum of. the results obtained by treating 
each of the colored sectors in this way should equal the amount 
of white in the black and white disk. Two examples are given 
below. The circumference of the disk was divided into one hun- 
dred equal parts, so that the numbers given are direct percentages 
of the whole circle. 

The upper row of figures in each case is the ordinary color-disk 
equation. The second is the luminosity of the given colors 
referred to white, as measured by the flicker, the lower line gives 
the product in each case. The sum of these products given under 
white should be the same as the white in the upper row, which is 
the corrected reading from the black and white Maxwell disks. 

Red. Green. Blue. White. Red. Green-Yellow. Blue. White. 

Color-equation 40.5 49.2 10.3 22.6 18.5 34.0 47.5 30.4 

Luminosity 0.238 0.295 0.106 — 0.238 0.617 0.106 — 



9.64 14.50 1.09 25.23 4.41 20.96 5.03 30.40 



No. 4] COLORED UGHTS AND FUCKER PHOTOMETER, 249 

Fourteen such trials were made with different colors, the results 
differing by one to three per cent from exact equality. 

Summary. 

The flicker photometer used to compare lights of any color 
approximates in convenience and accuracy any of the ordinary 
photometric appliances used with lights of the same color. Dif- 
ferent observers whose vision is normal obtain like results. 

Irregularities in the division of the disk or the rate of rotation 
are without appreciable effect on the precision of the measure- 
ments. 

Differences in the absolute brightness of the lights compared 
present no greater difficulties than in any photometric method. 

The instrument gives a true measure of luminosity comparable 
with that obtained in other trustworthy ways. 

Adelbert College, Nov. i, 1895. 



250 WILDER D. BANCROFT. [Vol. III. 



THE CHEMICAL POTENTIAL OF THE METALS. 

By Wilder D. Bancroft. 

IN a previous paper ^ I have communicated the numerical values 
of the electromotive force of certain cells, consisting of two 
metals and a single solution. It is now desirable to consider the 
relation between these single-liquid polarizable cells and the cor- 
responding constant reversible cells of the Daniell type. Accord- 
ing to the theory of Nernst, the potential difference between a 
metal and a solution of a salt of that metal is given by the 
expression ^ 

RT P 

ir=: log - X lO"* volts, 

ne p 

where ir is the potential difference, n the valency of the kation, / 
its partial osmotic pressure, e the quantity of electricity transported 
by a gram-equivalent, and P the solution pressure of the electrode 
metal. The electromotive force of a cell of the Daniell type M^ 
pyMyX\p^M^X\M^ will be the algebraic sum of the two potential 
differences between the metals and the solutions, plus the differ- 
ence of potential between the solutions. I leave out of account a 
possible potential difiference between the metals, as this term is 
negligible so far as our present knowledge goes. The electro- 
motive force of this type of cell will be 

7r=^log ^H-log ^A X 10-*+^ volts, 
ne \ PM^ "^ pj 

where 2 represents the difference of potential between the solu- 
tions, and the valency of the metals M^ and M^ is the same. If 
the wandering velocities of the ions M^ and M^ are nearly equal, 

^ Zeitscbr. f. ph. Chem., 12, 289, 1893. Through a misprint on p. 290, the cor- 
rection for Pb|Hg in Nal, and BijHg in NaQ, reads 0.25 and 0.75 volts, instead of 
0.025 and 0.075 volts respectively. * Ibid., 4, 148, 1889. 



No. 4] CHEMICAL POTENTIAL OF THE METALS. 25 1 

and p^ and p^ be made so, the value of z approaches zero, while the 

term log-^ drops out entirely. The electromotive force of the 

P\ 
cell, M^pM^X\pM^\M^y is given very nearly by the expression 

and is independent of the absolute concentration of the salts M^X 
and M2X. Let us take as a concrete case the cell ZnlZnSO^I 
CuSO^jCu, and let the concentrations of the zinc and copper 
sulfates always be equal. It has been found experimentally that 
the electromotive force of this cell is independent of the absolute 
concentration.^ Suppose that instead of diluting the two solutions 
with pure water, we add a solution of K2SO4. According to 
Nernst's theory, this will have no influence on the electromotive 
force, except in so far as it affects the dissociation of the two 
sulfates, and thereby the concentrations of the Zn and Cu ions. 
If the dilution be carried far enough, we shall come at last, with- 
out change of electromotive force, to the cell with neither zinc 
nor copper sulfate, to the cell Zn|o ZnS04+;irK2S04loCuS04 + 
jtKjSO^ICu, which is the same as the cell Zn|;irK2S04|Cu. In 
other words, the one-liquid, non-reversible cells are the limiting 
cases of the two-liquid, reversible cells in which the concentrations 
and wandering velocities of the reversible ions are equal, the 
dissociation being assumed to be complete. This last clause is 
necessary ; for if the percentage dissociations of the zinc sulfate 
and copper sulfate were different, equal concentrations of the 
two sulfates would not correspond to equal concentrations of zinc 
and copper ions, and this would afifcct the potential difference 
between the solutions. The concentration of the KjSO^ should 
have no efifect, and it was shown in my previous paper ^ that 
this was the case. It is clear that in measurements made with 
two-liquid, reversible cells, there are two sources of error besides 
those due to the surface conditions of the electrodes. These are 
dififerences of concentration and dififerences of wandering velocities. 

1 Wright. Phil. Mag. (5), 13, 265, 1882. 

« Zcitschr. f. ph. Chem., 12, 294, 1893, Tables II., V. 



mi 



252 



WILDER D. BANCROFT. 



[Vol: III. 



The eflfects of these two errors are that the terms log^ and s do 

A 
not disappear. The determinations made with single-liquid cells 

are free from these sources of error; but the difficulties due to 

polarization are so great that the variations are apt to be much 

larger than in measurements made with two-liquid, reversible cells. 

In Table I. are some of the results obtained with the two styles of 

cells. In the first four columns are the measurements of Paschen,^ 

myself, Overbeck and Edler,* Ostwald,^ all made with single-liquid 

cells. In the next three are the figures of Wright and Thompson,* 

Neumann,^ Braun,^ with reversible cells. In the eighth are the 

data of Magnanini,^ and in the ninth those of Regnauld,® the 

former being for polarizable, the latter for non-polarizable cells. 

Table V 



1 


1 

s 


1 

1 


A 
Q 

i 


d 


1 

O 


i 


d 


1 


-a 

« 

m 


ii 


ZnCd 


Chlorides 


0.2% 


0.333 


0368 


0.360 


0330 


0329 


0334 


032 


0.235 


ZnCd 


Bromides 


0.293 


0.333 


0.364 


0340 


0315 


— 


0.256 


0.30 


0.235 


ZnCd 


Iodides 


0.298 


0331 


0365 


0.304 


0322 


— 


0.262 


0.20 


0.235 


ZnCd 


Sulfates 


0.35 


0334 


0.430 


0.401 


0360 


0.362 


0.33-37 


0.36 


0.307 


ZnCd 


Nitrates 


— 


0.332 


0.446 


0.411 


0352 


0352 


0.27-37 


038 


0.235 


ZnCd 


Acetates 


— 


0.332 


— 


0373 


— 


— 


0336 


— 


— 


ZnPb 


Chlorides 


0.512 


0.526 


0.561 


0.610 


♦0.591 


♦0.598 


— 


0.51 


— 


ZnPb 


Bromides 


0.525 


0.528 


0.541 


0.599 


0.571 


— 


— 


0.45 


— 


ZnPb 


Iodides 


0.545 


10.527 


0.558 


0.587 


0.455 


— 


— 


038 


^__ 


ZnPb 


Sulfates 


0.525 


0.527 


0.502 


0.592 


* 0.50-55 


— 


— 


0.51 


— 


ZnPb 


Nitrates 


— 


0.526 


0.589 


0.598 


0.585 


0.589 


0.44 


0.51 


— 


ZnPb 


Acetates 


— 


> 0.527 


— 


0.638 


0.607 


0.601 


0.54-58 


— 


— 


CdPb 


Chlorides 


0.216 


0.195 


0.192 


0.249 


* 0.260 


♦0.269 


— 


— 


— 


CdPb 


Bromides 


0.232 


0.194 


0.181 


0.259 


0.256 


— 


— 


— 


— 


CdPb 


Iodides 


0.247 


10.194 


0.188 


0.256 


0.24 


— 


— 


— 




CdPb 


Sulfates 


0.18 


0.194 


0.17 


0.191 


* 0.13-17 


— 


0.18-22 


— 


— 


CdPb 


Nitrates 


— 


0.193 


0.243 


0.187 


0.233 


0.237 


0.240 


— 


— 


CdPb 


Acetates 


— 


10.194 


— 


0.265 


— 


— 


— 


— 


— 



* Wied. Ann., 43, 590, 189 1. 

* Ibid., 42, 209, 1891. 

» Zeitschr. f. ph. Chem., i, 583, 1887. 

* Phil. Mag. (5), 19. I, 1885. 



* Zeitschr. f. ph. Chem., 14, 193, 1894. 
« Wied. Ann., 16, 575, 1882. 
^ Rend. Ace. Line, 6, 182, 1890. 

• Wiedemann ElectrizitSt (2. Aufl.), I, 792. 



^ Values marked ^ are calculated from the other experiments and are not direct 
observations. 



No. 4] CHEMICAL POTENTIAL OF THE METALS. 253 

The agreement is not so striking as one might wish ; but it is 
sufficient. The values marked with a star are not properly com- 
parable, because the two solutions were not of the same concentra- 
tioa Nemst's formula for the cells we have been discussing is 

,r= :^ log ^ X 10-* volts. 

It is, therefore, necessary to consider the nature of log P. Nernst 
has not made any direct statement, so far as I know, about a pos- 
sible connection between log P and the negative ion of the salt 
solution. Ostwald ^ and his pupils look upon log Z' as a function 
of the electrode metal and the temperature only, and hold that it 
is independent of the nature of the negative ion. If this be so, 
we ought to find that all cells of the type M^pM^ X\pM^ X\M^, 
should have the same value so long as M^ and M^ remained the 
same and that a change in X should have no effect, barring 
secondary disturbances such as dififerences of wandering veloci- 
ties, of dissociation, etc. In the non-reversible cells M^RX\M^, 
where these disturbing influences are eliminated, this should be 
even more noticeably true. That this is the case for certain 
metals, I have already shown.^ The results of other investiga- 
tors, as given in Table L, show this same thing, though not quite so 
clearly. The values for Zn|Cd in solutions of chlorides, bromides, 
and iodides are found to be identical by Paschen, by Overbeck and 
Edler, and by Regnauld, though the three sets differ hopelessly in 
absolute value. Braun makes the bromides and iodides the same, 
and puts the chlorides, sulfates, and nitrates in a group together. 

There is not the same agreement among the reversible cells in 
which Pb forms one of the electrodes ; but this is due in part to 
the insolubility of the lead salts. With the polarizable cells 
things are much clearer, though the discrepancies between the 
values found by different observers complicates matters very much. 
Ostwald finds practically the same value for Zn|Pb in all solutions 
except acetates. Paschen makes the bromides and sulfates the 
same, while Overbeck and Edler find the chlorides and iodides 

1 Lehrbuch, II., 855. 

« Zeitschr. f. ph. Chem., 12, 294, 1893, Table III. 



254 



WILDER D. BANCROFT. 



[Vol. III. 



identical. On the whole we may say that the theory of Nernst 
has predicted the facts with great accuracy thus far. If, however, 
the single-liquid cells are the limiting cases of the two-solution 
reversible cells, and if log -P is a function of the electrodes and 
temperature only, the electromotive force should always be inde- 
pendent of the nature of the negative ion of the salt solution. 
That this is not so will be seen from Table II. 

Table II. 



Electrodes. 


Electrolytes. 


Paschen. 


W. D. B. 


O. ft E. 


Ostwald. 


W. ft T. 


ZnHg 


Chlorides 


1.112 


1.151 


1.121 


1.173 


1.12-26 


ZnHg 


Bromides 


0.983 


0.991 


0.9% 


1.036 


0.972 


ZnHg 


Iodides 


0.846 


0.847 


0.830 


0.841 


0.801 


ZnHg 


Sulfates 


1.300 


1.302 


1.302 


1.484 


1.46-51 


ZnHg 


Nitrates 


— 


1.200 


1.330 


1.422 


1.499 


ZnHg 


Acetates 


— 


1.228 


— 


1.451 


— 


CdHg 


Chlorides 


0.816 


0.818 


0.755 


0.813 


0.812 


CdHg 


Bromides 


0.690 


0.659 


0.632 


0.696 


— 


CdHg 


Iodides 


0.548 


0.515 


0.465 


0.535 


— 


CdHg 


Sulfates 


0.968 


0.969 


0.%2 


1.083 


— 


CdHg 


Nitrates 


— 


0.867 


0.884 


1.011 


— 


CdHg 


Acetates 


— 


0.898 


— 


1.078 


— 



The variation in passing from a chloride to an iodide solution is 
about 0.3 volts, far more than can be accounted for by any experi- 
mental error. This necessitates a reconsideration of the Nernst 
hypothesis to see wTiere the flaw in the reasoning occurs. The 
assumption made is that, if a metal be dipped into a solution of 
one of its salts, the metal will go into solution, and the electrode 
become charged negatively towards the electrolyte, if the "solu- 
tion pressure ** of the metal is greater than the osmotic pressure 
of the corresponding ion in the solution. If the latter is greater 
than the "solution pressure," ions will be precipitated upon the 
metal which would become positive to the solution. This reasoning 
is applicable to zinc in a solution of potassium chloride, for instance. 
The initial concentration of the zinc ions in the solution is zero, and 
the metal will therefore send ofif ions until the potential difiference 



No. 4] CHEMICAL POTENTIAL OF THE METALS. 255 

corresponding to equilibrium is reached. This will not be the 
case when we consider mercury in a solution of potassium chloride. 
There are no mercury ions in solution to precipitate on the metal, 
and it remains an unanswered problem how the mercury is to 
become charged positively in respect to the solution. Yet this 
takes place and the value of the potential difference, as deter- 
mined by the dropping-mercury electrode method, is a perfectly 
well defined one. This value should be independent of the nature 
of the salt solution if Ostwald*s assumption about log P is correct. 
This is not the case. In this connection I may say that the ques- 
tion as to the value of the dropping-mercury electrode as a means 
of measuring single potential dififerences does not affect this dis- 
cussion at all. It is an experimental fact that the sum of the 
potential dififerences M^RX and RX\M^, as determined by this 
method is equal to the electromotive force of the cell M^RX\M^ 
and it is immaterial for the present purposes whether the single 
determinations are wrong by a constant amount, as I am only 
considering variations in the values. I will now try to show what 
conclusions may be drawn from the measurements of Paschen^ 
on the potential dififerences between metals and salt solutions not 
containing the metal of the electrode as ion. He points out him- 
self that the potential difiference is not a function of the positive 
ion of the salt solution. It is not a function of the concentration. 
Paschen inclines to the opposite view ; but I think he is wrong 
and that his own results as tabulated in Table III. will bear me 
out. The first column gives the nature and concentration of 
the solution ; the second, third, and fourth the potential dififerences 
between the metals, mercury, zinc, and cadmium, and the solu- 
tion. Mercury is positive towards the solution, zinc and cadmium 
negative. 

* Wied. Ann., 43, 590, 1891. 



256 



WILDER D, BANCROFT. 



[Vol. III. 



Table III. 



SolutiOB. 


SollHg 


ZnlSol 


CdlSol 


Solution. 


SoliHg 


ZnlSol 


CdSol 


HQ = 11. 


0.560 


0.560 


0.248 


H,S04= 200 L 


0.825 


0.668 


0.261 


= 10 


0.551 


0.610 


0.272 


HBr 


= 0.272 


0.503 


0393 


0.175 


= 100 


0.584 


0.643 


0.242 




= 0.983 


0.490 


0.423 


0.202 


KQ = 0.28 


0.524 


0.525 


0.260 




= 10 


0.493 


0.567 


0.238 


= 1 


0.539 


0.547 


0.249 




= 100 


0.4% 


0.610 


0.246 


= 10 


0.553 


0.575 


0.251 


KBr 


= 0.402 


0.474 


0399 


0.203 


= 100 


0.584 


0.523 


0.240 




1 


0.483 


0.441 


0.186 


NaQ =0.239 


0.562 


0.521 


0.262 




= 10 


0.493 


0.422 


0.167 


1 


0.556 


0.512 


0.266 




= 100 


0.505 


0.496 


0.183 


= 10 


0.557 


0.541 


0.268 


HI 


= 10 


0.411 


0.427 


0.U7 


= 100 


0.590 


0.557 


0.268 




= 100 


0.417 


0.515 


0.159 


MgQa = 0.971 


0.546 


0.525 


0.252 




= 1000 


0.386 


0.584 


0.214 


2 


0.547 


0.531 


0.277 


KI 


= 0.795 


0.400 


0.250 


0.113 


= 20 


0.548 


0.598 


0.258 




1 


0.400 


0.233 


0.113 


= 200 


0.580 


0.516 


0.245 




= 10 


0.412 


0.308 


0.110 


BaQa =0.809 


0.562 


0.512 


0.259 




= 100 


0.412 


0.369 


0.120 


2 


0.555 


0.554 


0.249 




= 1000 


0.386 


0.454 


0.199 


= 20 


0.553 


0.583 


0.281 


K,SO< 


I = 2.152 


0.700 


0.618 


0.287 


= 200 


0.586 


0.566 


0.240 




= 20 


0.720 


0.573 


0.274 


H8S04= 2 


0.835 


0.653 


0.319 




= 200 


0.730 


0.592 


0.252 


= 20 


0.817 


0.668 


0.284 













The values for SoljHg are identical for dilutions of i 1. and 
10 1. with the exception of KCl, KBr, KjSO^, and HjSO^ ; the 
variations for KjSO^ and HjSO^ are in opposite directions and 
certainly due to experimental error. There is no reason to assume 
that KCl is different in behavior, theoretically, from NaCl or BaCl^, 
and we must conclude that this discrepancy is also accidental. 
In passing from dilutions of 10 1. to those of 100 1. there is a 
distinct increase in potential difference between mercury and 
chloride solutions. With the other solutions the change is either 
non-existent or much less marked. On the other hand, cadmium 
shows this behavior only with HI and KI solutions, zinc with HCl, 
NaCl, HBr, KBr, HI, and KI solutions. The solutions of HBr, 
KBr, HI, and KI are not the ones where mercury shows a marked 
change of value with increasing dilution, so that there is no 
qualitative regularity in the phenomena. As there is also no 



No. 4] CHEMICAL POTENTIAL OF THE METALS. 257 

quantitative connection to be detected between the change of 
concentration and the change of potential difference, and as the 
experimental error is very large in the case of determinations 
with dilute solutions, I see no reason to assume that there is any 
change of potential difference, at any rate within wide ranges of 
concentration.^ I am led to this conclusion the more strongly 
because, if we admit with Paschen that the potential difference 
increases with increasing dilution, we must admit that the electro- 
motive force of the cell Cd|KCl|Hg is a function of the concen- 
tration, and I have already shown that this is not the case.* 

Paschen has pointed out that these potential differences are 
functions of the metal forming the electrode and of the anion. 
This can hardly be accounted for on the Ostwald-Nernst hypoth- 
esis. If the potential difference between Hg and KCl or KBr 
solutions are due to the amount of mercury as ion which has gone 
into solution, we must say that the amount varies as we change 
from KCl to KBr, or, in other words, that the negative ion has an 
effect. This is quite apart from the difficulty of accounting for 
the sign of the potential difference. I do not see that the relative 
solubilities of mercurous chloride and bromide can be used to 
help out matters, because we do not have a saturated solution at 
all, and the difference in the electromotive forces is more likely 
to be connected with the difference of solubility as cause than 
as effect. 

There are no experimental data, so far as I know, on potential 
differences at the contact surface of reversible electrodes except 
some measurements by Neumann,^ and these do not establish 
the point they were intended to prove owing to an unfortunate 
choice of solutions. He measured the potential difference between 
thallium and solutions of thallium salts. Most of the salts were 
salts of organic acids, and Ostwald * had already found that when 

' This will not hold true till the concentration of the salt becomes zero; else we 
should get in all cases the same potential difference, that of the metal against pure water, 
which is not true. There will certainly be a minimum concentration beyond, which the 
dissolved substance will not have the properties of matter in mass, and the potential 
difference will then be a function of the concentration. 

' Zeitschr f. ph. Chem., 12, 295, 1893, Table V. 

*lbid., 14, 225, 1894. ^ Ibid., I, 605, 1887, 



258 



WILDER D. BANCROFT. 



[Vol. III. 



the negative ion was an organic radical its nature was immaterial 
To settle this question one should take negative ions which show 
marked differences with non-reversible electrodes, such as chlo- 
rides, bromides, and iodides. As the negative ion has a very 
marked influence in these last-named cases, and as there is no 
reason to suppose that the haloid salts form a class by themselves, 
the simplest assumption is that the negative ion always has an 
effect, and that in the cases in which this does not appear, such 
as the organic radicals, we are measuring something else which 
is the same in all the cases. Le Blanc ^ found something similar 
in his studies on polarization, where, beyond a certain point, he 
obtained the value for the primary decomposition of water. 

There are certain quantitative relations connected with the 
change of the negative ion which deserve to be brought out, and 
in Table IV. are given the most probable values for the potential 

Table IV. 



Solution. 


ZolSoI 


CdlSol 


SollHg 


Chlorides 


0.589 


0.255 


0.562 


Bromides 


0.507 


0.174 


0.483 


Iodides 


0.436 


0.104 


0.410 



dififerences of the metals Hg, Zn, and Cd in solutions of chlorides, 
bromides, and iodides ; while in Table V. are the corresponding 



Table V. 



Solution. 


ZnlSollHg 


CdlSollHg 


Chlorides 


1.151 
0.990 
0.846 
1.302 


0.817 


Bromides *..*•••..•.••.. 


0.657 


Iodides ••••*•• 


0.514 


Sulfates 


0.969 







^ Zeitschr. f. j)h. Chem., 8, 315, 1891. 



No. 4.] 



CHEMICAL POTENTIAL OF THE METALS, 



259 



values for the single-liquid non-reversible cells with Zn and Hg, 
Cd and Hg as electrodes.^ 

We notice that the numerical change in passing from a chloride 
to a bromide or iodide solution is the same for these three metals 
and that the sign is the same for zinc and cadmium as is shown 
in Table VI. This enables us to formulate matters a little more 



Table VI. 



Solution. 



Zn 



Cd 



Hg 



KQ-KBr 

KBr-KI 

KQ-KI. 



0.082 
0.071 
0.153 



0.081 
0.070 
0.150 



-0.079 
-0.073 • 
-0.152 



clearly. The potential difference between a metal and a salt 
solution is the sum of two terms, one due to the metal and the 
solvent, the other to the negative ion. For certain metals in 
certain solutions, the term due to the negative ion is independent, 
numerically, of the nature of the metal considered. For instance, 
the potential difiference Zn|KCl, Zn|KBr, Cd|KCl, Cd|KBr, Hg|KCl, 
and Hg|KBr will be A-^ta, A-hi, B-Va, B-\-b, C-a, and C-b, 
The electromotive forces of the cells Zn|KCl|Cd and Zn|KBr|Cd 
will be Ei=A'ha—B^a and E2=A'{'b—B—b, whence we see 
that Ei^E^ which had already been found experimentally. For 
Zn|KCl|Hg and Zn|KBr|Hg we shall hsLVC E^^A-ha-C-ha and 
E^=A-hb—C'hb, and E^ will not be equal to E^. By means of 
the data in my first paper on this subject,^ we can now extend our 
generalization and make it more precise. With the metals, Mg, 
Zn, Cd, Sn, Pb, and Bi in solutions of chlorides, bromides, iodides, 
sulfates, nitrates, acetates, carbonates, and oxalates, the term due 
to the negative ion is not a function of the electrode. There is 
not much doubt but that the alkaline metals, the metals of the 
alkaline earths, and the metals of the iron group belong in this 

1 There is certainly an error in the relative positions of Sn and Pb as shown by my 
determinations, and 1 do not therefore give any data for them in Table V. 
* Zeitschr. f. ph. Chem., 12, 294, 1893, Table 111. 



26o WILDER D. BANCROFT. [Vol. III. 

series. Oswald's measurements show that most organic acids may 
be added to the above list of solutions. With mercury the numer- 
ical value of the term due to the negative ion is the same as with 
the previous metals, but the sign is opposite. With platinum the 
numerical value is no longer the same. In which of these three 
groups copper, silver, gold, and the other metals belong I cannot 
say, though silver is probably like mercury. The results in Tables 
IV. -VI. open up a whole series of problems to be settled by future 
investigators. The values for the differences of the terms for any 
two negative ions have to be determined with accuracy; the 
behavior of the metals Cu, Ag, etc., must be examined. The 
work of Magnanini^ shows that other relations hold when the 
dissolved salt is an oxidizing or reducing agent, and that the value 
Zn|RX|Cd, for instance, is independent of the metals only when 
RX is not an oxidizing agent. It is also well known that in cases 
where the electrode metal cannot exist in the solution as ion, 
the general relations already pointed out do not hold. From the 
results of Negbaur* and of Jones ^ we must conclude that the term 
which I have represented by Ay B, C, etc., varies with the nature 
of the solvent. The amount of this variation is entirely unknown 
as yet, and it is equally impossible to say beforehand how a change 
in the solvent will afifect the term due to the negative ion. 

If we consider the cell ZnlZnCljIZnBrjIZn, the two solutions 
being assumed to be of the same concentration and dissocia- 
tion and the wandering velocity of the bromine ion being further 
assumed to be identical with that of the chlorine ion, we should 
expect an electromotive force of 0.080 volts. This has not been 
taken into account by Goodwin* in his determinations of the 
solubilities of silver chloride, bromide, and iodide. Goodwin 
determined the electromotive force of the cells 

AglAgNOglAgCl -hKCllAg, AglAgNOal 

AgBrH-KBr|Ag, Ag|AgN08|AgI+KI|Ag. 

1 Rend. Ace. Line., 6, 182, 1890. ^ Wied. Ann., 47, 27, 1892. 

» Zeitschr. f. ph. Chem., 14, 346, 1894- 

* Ibid., 13, 645, 1894. It is only fair to Mr. Goodwin and to myself to say that I have 
pointed out to him privately the objections I made to his results in order that he might 
correct them himself if he felt so inclined. He thinks, however, that it would be better 
for me to make my comments in print, and I have accordingly done so. 



No. 4] CHEMICAL POTENTIAL OF THE METALS, 26 1 

From the observed electromotive forces the solubilities were 



calculated by the formula 5 = \/ v^^ where log <^ = 7;. In 

this equation s is the solubility, p^ the concentration of the Ag 
ions in the nitrate solutions, p<^ the concentration of the CI, Br, 
or I ions in the corresponding solutions, E is the electromotive 
force of the cells, and C the integration constant which is equal 
at 25*^ to 0.0256. It is more than probable that a correction 
should be applied for a possible difference of log P in nitrate 
and chloride solutions, but as this value is not accurately deter- 
mined, I will first calculate the solubilities on the assumption that 
log /^No. = log PGi> We find from Table VI. log Pqx - log P^r 
= 0.080 and log /*a — log /'i = 0.152 volts. These values are 
to be subtracted from the electromotive forces observed in the 
cells with AgBr and Agl, in order to get the term E called for 
by the formula. In Tables VII.-IX. I give the results of these 
calculations. In the first column are the values for p^ ; in the 
second those for p^\ in the third the observed electromotive 
forces ; in the fourth the solubilities as calculated by Goodwin ; 
in the fifth the solubilities as calculated by myself under the 
assumption that log P^o^ = log Pq\ ; and in the sixth the values 
if one assumes further that log PnOs — log Pa = 0.03 volts. I 
also give the solubilities found by Kohlrausch and Rose,^ and 
by HoUeman^ with the conductivity method. 

It will be seen that the second column of solubilities agrees 
much better with the results obtained by other investigators 
than the solubilities calculated by Goodwin. The solubilities in 
the last column do not show so good an agreement ; but I do 
not feel sure that this proves that the formula by which they 
are calculated is wrong. It seems to me quite as probable that 
these figures represent the actual solubilities in the cells examined 
by Goodwin, but not the real solubilities of AgCl, AgBr, Agl. 
The solubilities of AgCl and AgBr are much changed by contin- 

* I use the term log Pci to denote the value of log P for a given metal when in a 
chloride solution, log Pa denotes log P for the metal M without reference to any par- 
ticular solution, and is a purely abstract conception having no numerical value as yet 

> Zeitschr. f. ph. Chem., 12, 324, 1893. * Ibid., 12, 125, 1893. 



262 



WILDER D. BANCROFT. 



[Vol. III. 



Table VII.i 



Cone. As 
ions = /i. 



Cone. CI 
ions = P%, 



E.M.P. 



Cale. Sx 



Calc. St 



Calc. 5^1 



0.0861 0.451 

0.0861 0.449 

0.04455 0.418 

0.04455 0.419 

Solubility. AgCl at 25° Average . , 

Kohlrausch & Rose 

HoUeman 



0.0813 
0.0813 
0.04295 
0.04295 



1.24 X 10-6 
1.28 X 10-5 

1.25 X 10-6 
1.23 X 10-* 
1.25 X 10-6 
1.44 X 10-6 
1.81 X 10-6 



1.25 X 10-6 
130 X 10-6 
1.25 X 10-6 
1.22 X 10-6 
1.25 X 10-6 

at 250 

at 250 



2.25 X 10-» 
234 X 10-« 
2.24 X 10-« 
2.20 X 10-« 

2.26 X 10-« 



Table VIII. 



Cone. Ag 
ions = A. 


Cone. Br 
ions = /,. 


B.M.P. 


Cale. 5i 


Cale. St 


Cale. S^ 


0.0813 


0.0861 


0.598 


7.1 X 10-7 


33.8 X 10-7 


60.7 X 10-7 


0.0813 


0.0861 


0.603 


6.4 X 10-7 


30.1 X 10-7 


55.0 X 10-7 


0.0813 


0.0861 


0.597 


7.2 X 10-7 


34.4 X 10-7 


61.9 X 10-7 


0.04295 


0.04455 


0.570 


6.4 X 10-7 


30.5 X 10-7 


54.9 X 10-7 


0.04295 


0.04455 


0.571 


6.3 X 10-7 


29.9 X 10-7 


53.8 X 10-7 


0.04295 


0.04455 


0.570 


6.4 X 10-7 


30.5 X 10-7 


54.9 X 10-7 


Solubility. A 


gBr at 25° Average . . 


6.6 X 10-7 


31.5 X 10-7 


56.9 X 10-7 


Kohlrausch & 


Rose 


20.9 X 10-7 


at 250 




Holleman . 




30.2 X 10-7 


at 250 





Table IX. 



Cone. As 
ions = /i. 


Cone. I 
ions = /,. 


E.M.P. 


Cale. 5i 


Cale. St 


Cale. 5, 


0.0813 


0.0861 


0.815 


1.02 X 10-« 


19.9 X 10-8 


35.7 X 10-8 


0.0813 


0.0861 


0.813 


1.06 X 10-8 


20.7 X 10-8 


37.2 X 10-8 


0.0813 


0.0861 


0.815 


1.02 X 10-8 


19.9 X 10-8 


35.7 X 10-8 


0.04295 


0.04455 


0.787 


0.94 X 10-8 


18.0 X 10-8 


32.3 X 10-8 


0.04295 


0.04455 


0.786 


0.% X 10-8 


183 X 10-8 


32.9 X 10-8 


0.04295 


0.04455 


0.790 


0.88 X 10-8 


17.0 X 10-8 


30.5 X 10-8 


Solubility. Agl at 25° Average . . 


0.98 X 10-8 


19.0 X 10-8 


34.0 X 10-8 


Kohlrausch & 
Holleman . 


Rose 


60.00 X 10-8 
395.00 X 10-8 


at 18<^.0 
at 28°.4 









^ S\ and S^ in this table should be identical, as they are calculated from the same data 
by the same formula; the variations are due to errors in calculation. 



No. 4] CHEMICAL POTENTIAL OF THE METALS. 263 

ued shaking,^ and I cannot find that Goodwin has taken this into 
account at all. I conclude, therefore, that if he had shaken his 
AgCl and AgBr, he would have found much smaller electromotive 
forces than those recorded in his paper. He has tried to prove 
the accuracy of his formula in two ways. Having calculated the 
solubilities by substituting the experimental data for the electro- 
motive forces in the formula, he reverses the operation, and sub- 
stituting the solubilities he calculates the electromotive forces. 
It is true that there is an intervening step, but the principle is 
the same, also the result. If he had taken the cells 

AglAgNOjIAgCl + KCl|Ag and AglAgNOglAgBr + KBr|Ag 
and substituted directly in these the fallacy of such a test would 
have been patent. Instead of this he has combined the two cells 

AglAgCH-KCllAgNOslAglAgNOslAgBr+KBrlAg 

= Ag| AgCl + KC1| AgBr + KBr| Ag, 

calculated the electromotive force of the resultant cell, and com- 
pared this with the experimental value and with the difference 
of the mean of the two component cells. Any other formula, 
which had given fairly constant values for the solubilities, would 
have stood the test equally satisfactorily. If, instead of taking 
Goodwin's formula and his value for AgBr, 6.6 x io~' reacting 
weights per liter, one takes, for instance, my first modification of 
his formula and the corresponding value for AgBr, 31.5 x lO""' 
units, one will reproduce his table exactly. One cannot agree 
with him when he says in regard to this table : ^ " Die Ueberein- 
stimmung der beobachteten mit der berechneten Werten ist eine 
sehr gute, wie sie ja nicht anders sein konnte, wenn die friihere 
Formel (25), nach der die Loslichkeiten berechnet wurden, iiber- 
haupt richtig war. Sie bestatigt also diese Formel." The 
other proof is not satisfactory in the light of my experiments. 
Goodwin determined the solubility of thallium bromide by the 
electrical and by the analytical methods, the difiference between 
the two being about 10 per cent of the total solubility. This result 
cannot be compared with the experiments on the solubilities of 
the silver haloids, because the conditions were not the same. 

^ Proc. of Am. Acad, 50, 325, 1894. ' Zeitscbr. f. ph. Chem., 13, 651, 1894. 



264 



WILDER D. BANCROFT. 



[Vol. III. 



In the thallium determinations the cell used was of the form 
TllTlBr-fKNOglTlBr+KBrlTl. There were bromine ions in con- 
tact with both electrodes, while with the silver salts the bromine 
ions came in contact with one electrode. 

One other point remains to be considered, whether the potential 
difference at the surface of a reversible electrode is a function of 
the concentration at all. The only direct measurements are those 
of Neumann,^ which confirm the Nernst theory in every detail. 
In addition, there are many determinations on two-liquid cells, 
made chiefly by Ostwald's pupils, and in all these cases there is a 
most satisfactory agreement between the theory and the facts. 
On the other hand, there are a few observations by other people 
which are not so easily reconciled with the theory. In Table X. I 
give some measurements of Paschen*s^ on cells having zinc and 
mercury electrodes, and solutions of ZnS04 and MgSO^ of varying 
concentrations as electrolyte. The first column gives the nature 
of the cell ; the second, the specific gravity of the electrolyte ; the 
third, the concentration in grams per hundred grams of the solu- 
tion ; the fourth, the electromotive force observed. The values 
for the concentrations are only approximate because they were not 
determined by Paschen directly, and I have taken them from 
Landolt and Bornstein's tables. 

Tabi<e X. 



Blectrodent. 


Electrolyte. 


Density. 


Per cent in 
gTAms. 


E.M.P. 


ZnHg 


MgS04 


1.042 


4.0 


1.194 


ZnHg 


MgS04 


1.040 


4.0 


1.236 


ZnHg 


MgS04 


1.040 


4.0 


1.186 


ZnHg 


ZnS04 


1.433 


32.9 


1.249 


ZnHg 


ZnS04 


1.409 


31.5 


1.252 


ZnHg 


ZnS04 


1.403 


31.1 


1.309 


ZnHg 


ZnS04 


1.402 


31.1 


1.327 


ZnHg 


ZnS04 


1.400 


31.0 


1.236 


ZnHg 


ZnS04 


1315 


25.5 


1310 


ZnHg 


ZnS04 


1305 


25.0 


1.238 



^ Zeitschr. f. ph. Chem., 14, 225, 1894. 



^ Wied. Ann., 43, 570, 189 1. 



No. 40 



CHEMICAL POTENTIAL OF THE METALS, 



265 



These figures lose a good deal of their value owing to the con- 
siderable variation in the determinations for the same solutions, 
and because the range of concentrations is too limited ; but two 
things are very noticeable in spite of this. In the cells ZnlZnSO^I 
Hg, the electromotive force does not decrease with increasing 
concentration of zinc sulfate, as it should according to the theory. 
The cells ZnlMgSO^IHg, have the same value as the cells Zn| 
ZnS04|Hg, or a smaller one, while the theory demands a larger 
one. The same thing is seen, though in a less satisfactory manner, 
in the experiments of Damien.^ He used zinc and copper as 
electrodes, and his results are given in Table XI. The first 

Table XL 



ZnCu Electrodes. 



Electrolyte. 


Density at 15°. 


Per cent in 
grams. 


E.M.P. 


Amalg. Zn 
E.tyr.P. 


KjS04 .... 


1.036 


4.5 


1.035 


1.067 


NajSO*. . 






1.038 


*10.0 


1.012 


1.037 


(H4N),S04 . 






1.075 


13.1 


1.012 


1.019 


MgS04 . . , 






1.035 


*5.8 


1.047 


1.059 


Al2(S04)s . 






1.135 


5.8 


1.050 


1.062 


ZnSO* . . 






1.064 


♦9.2 


1.004 


1.047 


KQ . . . 






1.077 


12.0 


0.788 


0.802 


NaQ . . 






1.061 


8.5 


0.805 


0.810 


NH4a . . 






1.039 


13.0 


0.845 


0.850 


BaQz . . 






1.110 


12.0 


0.782 


0.820 


CaOa . . 






1.212 


23.0 


0.743 


0.751 


ZnCla . . 






1.384 


37.5 


0.746 


0.752. 



Values with a * refer to hydrated salt. 

column shows the electrolyte ; the second, the specific gravity of 
the solution ; the third, the percentage composition ; the fourth, 
the electromotive force when ordinary zinc was used ; the fifth, the 
corresponding values when the electrode was amalgamated. 

As will be noticed, there are marked variations even in cases 
where no one claims that there should be any, such as between 

1 Ann. chim. phys. (6), 6, 289, 1885. Th« reference to Vol. V. in Wied. ElektririUU 
I, 734, also in Beibl. 10, 185, is a misprint 



266 



WILDER D. BANCROFT. 



[Vol. III. 



ammonium sulfate and potassium sulfate solutions, between cal- 
cium chloride and ammonium chloride. This weakens the con- 
clusions which one would like to draw from these experiments; 
but, making allowance for a large experimental error, it is still very 
curious that Zn|ZnS04|Hg should give so nearly the same value 
as the cells with indifferent sulfates, and that zinc chloride should 
be indistinguishable electrically from calcium chloride. The ex- 
periments of Hockin and Taylor ^ may be interpreted either way. 
They found that the combination of zinc and another metal in 
sulfuric acid gave a higher electromotive force than the same two 
metals in a saturated solution of zinc sulfate. This is not so con- 
vincing as if they had used potassium sulfate instead of sulfuric 
acid, because in all except dilute solutions free acids do give a 
higher value than the corresponding salts. The reason for this 
variation is unknown. When it comes to the absolute values in 
the zinc sulfate solution, matters are no better. In some of the 
metals, notably cadmium and mercury, the zinc sulfate appears 
to give the same value as any other sulfate ; with others there is 
a qualitative agreement with Nemst's theory. The same remarks 
hold true of the work of Lindeck.^ I have not access to the origi- 
nal paper of Wolff, and the review of it ^ is two meager to be of 
much assistance. He investigated, among other things, the effect 
of changing the concentration of the zinc sulfate in a one-liquid 
cell. His results are given in Table XII. The first column 

• 

Table XII. 



Density. 



B.M.P. 



Zn|ZnS04Cu . 
Zn|ZnS04!CuO . 
ZnlZnSOilFe . 
Zn|ZnS04|Pb . 
ZnlZnQalCu . . 
^njZnaalFe . . 
Zn|Zn(N08)2|Cu 



1.438-1.001 
1.427-1.003 
1.427-1.003 
1.427-1.003 
1.637-1.003 
1.917-1.003 
1.496-1.004 



0.%5-1.066 
1.008-1.015 
0.378-0.385 
0.456-0.587 
0.734-0.930 
0.385-0.390 
0.669-0.698 



1 J. Tel. Eng., 8, 282, 1879. « Wied. Ann., 35, 311, 1888. 
« Bcibl., 12, 700, 1888. 



No. 40 



CHEMICAL POTENTIAL OF THE METALS. 



267 



shows the electrodes and the electrolyte ; the second, the concen- 
trations of the latter in specific gravities; the third, the corre- 
sponding electromotive forces. 

In all cases there is a qualitative agreement with the theory; 
that is, the electromotive force increases with decreasing concen- 
tration of zinc sulfate. The quantitative agreement is not so 
satisfactory. In the second, third, sixth and last cells given in 
the table the variations are much too small ; while, in the other 
cases, they are too large. The ratio of the strongest solutions to 
the weakest in the experiments of Wolff lies between lOO and looo 
to I, which corresponds to a change of electromotive force of 0,05-9 
volts owing to the bivalence of zinc. Some experiments which I 
made with the cell CdlCdCl^'Hg, the strength of the solution being 
unknown, gave me 0.S15, 0.S21, 0.814, average 0.S17 volts» the 
same value which I had already found for the KCl solution. 

The simplest way to decide what effect the concentration of the 
reversible ion, if I may use such a phrase, has on the electromotive 
force would be to make a series of measurements on reversible 
electrodes by the dropping-mcrcury method I have not been in 
a position to do this, and I have had to find an easier, though less 
satisfactory manner of settling the question. Suppose we have 
electrodes of zinc and copper in a mixture of zinc and copper 
sulfates, one solution. Increasing the concentration of the zinc 
sulfate or decreasing the concentration of the copper sulfate must 
diminish the electromotive force of the cell, and vice versa if the 
reverse operations be performed. Through the courtesy of Pro- 
fessors Trowbridge and Pcirce of the Physical Laboratory, I have 
been able to make the few experiments necessary. As it was 
only required to find out whether there was any change at all, 
there was no need of determining the absolute value of the electro- 
motive force. This made the experimental part very easy, I 
connected the cell with a large external resistance and a galva- 
nometer. I changed the ratio of the two components in the solu- 
tion and noted the position of the galvanometer needle, I made 
measurements with the electrodes in pure zinc sulfate solutions, in 
pure copper sulfate solutions, and in mixtures of these in varj'ing 
proportions. Under all these different conditions I obtained the 



268 WILDER D. BANCROFT. [Vol. III. 

same electromotive force, showing that it is a function neither 
of the relative nor of the absolute concentrations.^ Although 
* one obtains the same value from the different solutions, they do 
not behave exactly alike. With solutions of pure copper sulfate 
or with mixtures containing copper sulfate in any quantity, the 
maximum value is obtained at once and is very constant. With 
solutions of pure zinc sulfate or mixtures containing only traces 
of copper sulfate, the maximum value can be obtained only by 
vigorous stirring and is very inconstant. There is, of course, 
nothing surprising about this, as it is what one would have pre- 
dicted. It is a very curious fact that the Nemst formula, though 
deduced from apparently erroneous assumptions, should yet give 
the effect of changes of concentration in a two-liquid cell with 
such surprising accuracy. 

It will be noticed that the electromotive forces of the non- 
reversible cells have nothing to do with the heats of reaction. 
This has always been known ; but it acquires a new significance, 
since it has been shown that the non-reversible cells are to be 
considered, as far as the electromotive forces are concerned, as 
limiting cases of the reversible two-liquid cells. In the cell 
Zn|H2S04|Ag there is not much doubt what reaction takes place; 
but it has nothing to do with determining the electromotive force. 
An interesting example of this, which also brings up another 
point, is the cell CulCuSOJPt. Here the reaction consists in the 
replacement of copper by copper. What happens experimentally, 
on closing the circuit, is that copper is dissolved from the copper 
electrode and precipitated on the platinum until the latter becomes, 
electrically considered, an electrode of pure copper, when further 
action becomes impossible.^ Overbeck ^ made some experiments 
a few years ago to determine what thickness of copper made a 
platinum electrode behave like a piece of pure copper. His 

1 This applies only to electrodes reversible in respect to the kation. I hope to treat 
the case of electrodes reversible in respect to the anion in another paper. 

Since this paper was written I have seen the article of J. Meyer, Wied. Ann., 53, 898, 
1894, which confirms my views, though with certain exceptions. 

^ When I performed this experiment I was not aware that a similar one had been 
described by Gladstone and Tribe, Proc. Roy. Soc., 1876. 

« Wied. Ann., 31, 337, 1887. 



No. 4.] 



CHEMICAL POTENTIAL OF THE METALS 



269 



method was to deposit copper on platinum electrolytically, and was 
open to the objection that it was almost impossible to be certain 
that the copper was deposited uniformly over the surface of the 
platinum. By using the cell Cu|CuS04|Pt, it would seem that 
this difficulty might be avoided, as the plating is stopped automati- 
cally as soon as the minimum thickness is reached. Suppose we 
balance this cell to some extent by an electromotive force less than 
its own. There will still be a tendency for copper to be deposited 
on the platinum ; but it cannot be deposited to the thickness corre- 
sponding to pure copper, as it must then dissolve up again under 
the influence of the external electromotive force. It can precipi- 
tate only till equilibrium is reached, and we shall have the condi- 
tion referred to by Gibbs,^ of a substance present in too small 
quantities to have the properties of "matter in mass." By mak- 
ing the external electromotive force differ infinitely little from the 
electromotive force of the cell, it would be possible, theoretically 
at any rate, to obtain an infinitely thin film of copper. It is to the 
separation of the ion on the electrode in such small quantities as 
not to have the properties of matter in mass that is due the 
gradual change of the polarization instead of having a sudden 
jump from the initial to the final value. 
The main results of this research may be summed up as follows : 

1. The potential difference between a metal and an electrolyte 
is not a function of the concentration of the salt solution nor of 
the nature of the positive ion except in certain special cases. 

2. It is a function of the electrode, of the negative ion, and of 
the solvent. 

3. In aqueous solutions, the potential difference is the sum of 
the terrti due to the electrode and the term due to the negative 
ion in the normal cases. 

4. For most metals in most electrolytes the term due to the 
negative ion has the same numerical value and the same sign. 

5. For mercury it has the same numerical value, but the oppo- 
site sign ; for platinum, neither the same numerical value nor the 
same sign. 

Cambridge, December, 1895. 

^ Thermodynamische Studien, p. 393. • 



> 



270 E. H. LOOMIS. [Vol. III. 



ON THE FREEZING-POINTS OF DILUTE AQUEOUS 

SOLUTIONS. 

By E. H. Loobus. 

TWO years ago I submitted a series of freezing-points of dilute 
aqueous solutions.^ After a year of unavoidable interruption 
the work was resumed, and the new results form the material of 
the present paper. 

The method has remained entirely unchanged and is fully de- 
scribed in the former papers. 

The only change in the apparatus was the enlargement of the 
" freezing-tube," so that it now receives 2CX) cc. of the solution 
instead of 70 cc. as before. It was thought .that this change 
would eliminate a possible source of error which might have come 
from the "sensitiveness" of the smaller quantity of the solution 
to external temperatures, No reduction, however, of the experi- 
mental error has resulted from this change. 

The thermometer was the same instrument used in the former 
observations. The work was done in a basement room of the 
John C. Green School of Science Building. Here it was possible 
to avoid serious temperature changes during the entire day. The 
temperature was kept as near 0° C. as possible, and maintained 
fairly constant by means of the strong draught of a ventilation 
shaft opening into the room. By regulating the admission of cold 
air at the window, the temperature changes were kept within the 
limits of 1-2 degrees. It is much to be regretted that this work 
could not be done at the constant temperature of 0° C. A degree 
of accuracy could thus be reached, I think, which is otherwise 
unattainable. 

The thermometer was kept throughout the entire period of the 
observations within about i°C. of the freezing-point. 

Attention may be called to four points in regard to the method. 
^ Physical Review, Vol. I., 1893, PP- ^99 *^^ ^74- 



No. 40 



FREEZING-POINTS OF SOLUTIONS. 



271 



1. The freezing-point is determined with so slight traces of ice 
present that no correction for change of concentration in the solu- 
tion is necessary. (The overcooling is but o°.i5 C.) I am not 
aware that the value of this correction so generally applied in 
other methods has been experimentally determined, and since it 
not infrequently amounts to 10 per cent of the entire observed 
depression it may perhaps be dangerous to apply it without some 
experimental justification. 

2. The method eliminates all possibility that the observer's bias 
may affect the results. 

3. The reading of the thermometer is made with the mercury 
column absolutely stationary during 1-2 minutes. 

4. The solution to be examined, as well as the water in which 
the zero point of the thermometer is determined, is surrounded 
by a medium which is but o°.3 C. below its own freezing- 
point, and is further carefully insulated from this by two glass 
walls aftd the air layer between them. Thus the solution and its 
"ice" are able to come to their equilibrium temperature in as 
nearly an adiabatic condition as possible. 

It may be said that as soon as this last feature of the method 
suggested itself I employed, as was natural, a bath whose tem- 
perature was exactly that of the freezing-point to be determined, 
but it was soon found that the observed freezing-points were too 
high (Nemst's convergence temperature), and the temperature 
difference of o°.3 C. was finally chosen, since it was found that 
this reduced the *' convergence temperature " to the actual freezing- 
point sought. The method by which this was ascertained was by 
observing at what temperature of the bath the freezing-points of 
water, obtained with only slight traces of ice in the water, agreed 
with those obtained with large quantities of ice present.^ 

The vast theoretical importance of these freezing-points has 
occasioned much very careful work in this field during the past few 
years, and many questions have arisen in regard to the various 
methods thus developed. Some of the more important of these 
questions will be considered in a subsequent paper.^ 

The present series of observations comprises the following com- 
pounds, all of which are electrolytes : — 

1 Physical Review, Vol. I., p. 213. * p. 293. 



i 



272 



E. H. LOOMIS, 



[Vol. III. 



. 1 







-1 



1% 

8"* 



1 




I 



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No. 4.] 



FREEZING-POINTS OF SOLUTIONS, 



273 



In the foregoing table, and elsewhere throughout the present 
paper, tn denotes the gram-molecular concentration of the solution ; 
that is, »^=i, for example, indicates that a liter of the solution 
contains as many grams of the compound as there are units in its 
molecular weight. Columns 4 and 5 give respectively the specific 

gravity f — 3- J, and electrical conductivity of the standard solutions 

whose respective concentrations are found in column (2). In addi- 
tion, for the sake of ready reference, the table gives the specific 
gravity of the solutions for the molecular concentration, /«=o.20, 
and further the name of the makers from whom the compound was 
obtained. In the last column is given the manner in which the 
solution was prepared. 

Solutions, 

The solutions which were prepared by direct weighing were 
made from carefully recrystallized salts. The drying was accom- 
plished as thoroughly as the nature of the salt would permit in 
accordance with the prescribed methods. 

The solution, H8PO4, w«=J, was prepared for me by Mr. Hullet 
of the Princeton Chemical Laboratory, and I wish here to thank 
him for the careful manner in which the titration and subsequent 
analysis were performed by him. 

In every case the specific gravity and electrical conductivity of 
the standard solutions were determined in order to control their 
accuracy. I cannot agree with Mr. Jones,^ who appears to be of 
the opinion that the specific gravity and conductivity of a sup- 
posedly standard solution can furnish no conclusion in regard to 
its accuracy. 

In fact, there seems to be no reason to believe that a normal 
solution made from carefully prepared salts, in accordance with 
accepted tables of specific gravity, and found to have the exact 
specific gravity and electric conductivity corresponding to such a 
solution should not be " pure," at least within the limits of accu- 
racy yet reached in the present methods of making freezing-point 
observations. I think it cannot be too strongly urged that in all 

» Wcide. Ann., Bd. 53, 1894, p. 394. 



i 



274 ^' ^' LOOMIS, [Vol. III. 

such work both these constants be determined, not more for the 
sake of the easy control which they furnish, than for the con- 
venient comparison with others* results, which these data in regard 
to a solution permit. 

By comparing the results in Table I. with those of Kohlrausch ^ 
it is found that sufficient agreement exists except in the case of 
HCl. This solution was titrated by Mr. HuUet from acid found to 
be free from the impurities likely to be present in it. The stand- 
ard solution against which it was balanced, was a normal Na^COg. 
The Na^COg was made from Trommsdorff's c. p. NaHCOg by 
glowing to constant weight. The specific gravity of this solution 
is given in the foregoing table. 

The electrical conductivity was measured according to the 
familiar method of Kohlrausch. The " Resistance Capacity " of 
the electrolytic cell employed was found in the usual manner 
by assuming Kohlrausch's values for the conductivity of NaCl and 
Na^COg. 

Determination of Specific Gravity, 

The specific gravity was determined by using a modified form 
of Sprengel picnometer, whose volume at i8^C. was 51.3232 c.c 

(jt p At (a) the glass tube is constricted to a bore of 

I mm., and at this point a fine mark is etched 
around the tube. At (p) the tube is reduced 
to a point, whose opening is less than i mm., 
so that the greater capillary attraction at this 
point over that at (a) may hold the liquid always 
at (*), and thus permit changes of volume in the 
liquid contents to be observed at (d). The body 



\y 



Fig. 1. 

of the picnometer is further provided with a 

small glass ball. This provides for the easy displacement of air 
bubbles, which sometimes form on the inside walls. It is found, 
however, that these bubbles do not form, if one takes the precau- 
tion to keep the picnometer when not in use always supplied 
with water, so that its walls may not become dry. This seems to 
indicate that the source of these troublesome air bubbles is not 

^ Leitfaden d. Pbysik, Leipzig, 1892, p. 404. 



No. 4.] 



FREEZING-POINTS OF SOLUTIONS, 



275 



the air dissolved in the solutions, but the air "condensed" on 
the dry walls of the glass itself. 

The picnometer is filled and placed in a water bath whose tem- 
perature is kept at 18° C. ±o°.05. The solutions were usually 
about 20° C. when introduced into the picnometer, and thus when 
placed in the colder bath the liquid in the arm (a) would shrink 
back toward the body of the picnometer, rapidly at first, and slowly 
at last, as its temperature became more nearly equal to that of the 
bath. Liquid is added at the point (b) as may be needed from 
time to time, by touching it with a glass rod or stopper moistened 
with the solution. When the liquid column remains stationary 
at (a), 1-2 minutes, it is known that the solution in the picnometer 
has the same temperature as the bath, 18° C. 

Experiment showed tliat whether the solution was initially at 
temperatures below or above 18^ C, the same result was obtained^ so 
far at least as would affect the fifth place of decimals. 

It is to be noted that three entire series of freezing-point obser- 
vations, KHO, NaHO, and HNOg, had to be rejected, since their 
specific gravity and electrical conductivity were found to be at 
such variance with the Kohlrausch values as to indicate some 
marked impurity. At the earliest opportunity I hope to deter- 
mine the specific gravity and electrical conductivity of normal 
solutions of these compounds, together with HCl, using the 
utmost care in preparation of the material, and shall then meas- 
ure their respective freezing-points. 

The distilled water used throughout the present work had an 
electrical conductivity 8.10"*®. 

Res7ilts, 

The following tables present the experimental results. — In 
column (2) is given the molecular concentration (w) of the solu- 
tion, in (3) the observed depression of the freezing-point (A), 

and in (4) is found the molecular depression f — J. This is the 

value of the molecular depression as reckoned by Arrhenius. 
Raoult and others reckon with gram-molecules per 1000 grams 
of water ^ instead of i liter of solution. In order to compute this 



i 



£. H, LOOMIS. 



[Vol. III. 



5.:} ^ 













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No. 4-] 



FREEZING-POINTS OF SOLUTIONS. 



277 



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278 



E. H. LOOMIS. 



[Vol. III. 









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(0.3780) 
(0.710) 


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0.1750 
0.3409 
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»o 


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3.409 

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♦ 


Molecular 
depression of 
freezing-point, 

m 


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3.46 
3.52 
3.46 


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3.314 

3.194 


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0.8770 


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0.8339 


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0.3314 
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i 






No. 4] 



FREEZING-POINTS OF SOLUTIONS. 



279 



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'CJ O O B U 



28o E. H. LOOMIS. [Vol. III. 

value of the molecular depression, one needs in addition the spe- 
cific gravity of the solution. This is found in Table I., column 

(6), from which the value of — in accordance with Raoult's defini- 

m 

tion is easily reckoned. The difference, however, is so slight, even 
in the most concentrated solution used, that there seems to be 
no advantage in publishing both values as was done in the former 
papers. Thus this difference amounts to only i % in the case 
of NH4NO3, w=o.20 where it is the greatest, while in Na^COg it 
vanishes altogether. 

The value of the depression in column (3) is the mean of 5-9 
entirely independent determinations, which show on the average 
a variation of o°.ooi C. The largest average variation shown in 
any complete series was o°.ooi3 C. in the case of BaCl^ (43 sepa- 
rate observations). The smallest average variation was o°.ooo6 C. 
in the case of Na2C0g (36 distinct observations). This is almost 
exactly the variation observed in the former work, and shows that 
the enlargement of the freezing-tube has not affected the sources 
of error. 

Graphic Representation of Results. 

The values of — - as a function of m are presented graphically 
m 

in Plate I., Fig. i. Ordinates represent values of — •, abscissas 

m 

those of (w). To avoid confusion, the nitrates are represented 
by themselves in Fig. 2. The scale is the same as that before 
employed. Together with the new series are represented the 
values of NaCl and H2SO4 from the observations of 1893. To 
the NaCl results another has been added at ^=0.40, and thus the 
course of the curve beyond /«=o.20 is determined. The present 
method of representing molecular depressions rather than actual 
depressions commends itself, since it alone is able to show at a 
glance the general nature of the results and throw much light on 
the accuracy of the method. Neither of these appear when the de- 
pressions themselves are graphically represented, since on the one 
hand the departures from Blagden's law of strict proportionality 
between depression and concentration are so very slight compared 



No. 4-] FREEZING-POINTS OF SOLUTIONS, 28 1 

with the total depressions that they do not appear in the graphic 
representation of depressions. Thus even where these departures 
are the most marked, as, for example, in case of Na^COg, the 
"curve** of total depressions differs so little from a straight line 
that it may be distinguished from a straight line only with the 
closest scrutiny. On the other hand, probable errors of many 
thousandths of a degree are scarcely noticeable in the curve of 
depressions. 

The curves for the most part are determined by five observations, 
whose points are connected with straight lines. In the greater 
number of cases the experimental errors appear to be so compara- 
tively small, that it would perhaps have been justifiable to assume 
a perfect regularity of results, and connect the points accordingly 
with the most probable airve, as was done in the former papers. 

In case of MgClj, these five observations, at i«=o.oi, w=o.02, 
0.05, o. 10, and 0.20, were so surprising that three additional ones 
were made, at i«=o.i5, i«=o.25, and /«=o.30. So too with KCl 
and NH4CI an additional observation was made at w/=o.40, to 
determine whether the converging curves actually crossed some- 
where near /«=o.20. It should be added that these two observa- 
tions, together with that on NaCl at the same point, were made 
immediately after a special determination of the zero-point of the 
thermometer. Thus an error in the zero-point could not affect the 
relative depressions of the three salts. The same precaution was 
observed for the two observations on Na2S04 and KaS04 at 
i«=o.30, so that there is no possible doubt that the members of 
these pairs of curves intersect in the region of w=o.20. 

Discussion of Results. 

Apart from any theory it appears here as in the case of the 
electrolytes formerly studied : — 

(i) That the molecular depression increases continuously with 
increase of dilution. The only exceptions are MgClj and HCl in 
the region of greater concentration, each of which thus presents 
a minimum value of the molecular depression at w=o.io. In 
MgClg this minimum is pronounced. In case of HCl it is perhaps 
less striking, but no less well established. It was to remove pos- 




282 E. H, LOOMIS. [Vol. III. 

sible doubt about this minimum in HCl that the value at f»=o.30 
was determined. The position of this new point makes the exist- 
ence of the minimum certain at about m^o.io, 

I find that this same minimum in case of MgCl, appears in the 
results of Arrhenius,^ although he must have looked upon it as due 
to exceptionally large errors, since he makes no reference to it 
in his discussion of results. I find also that in the case of HCl, 
Jones's ^ observations suggest unmistakably the presence of such 
a minimum, although his failure to call attention to it, particularly 
since he calls special attention to the regularity of the results,^ 
would indicate that he believed it due to an error of some 

0'*.002 C. 

(2) The curves are all more or less concave on their upper 
side. 

(3) It now appears that the electrolytes thus far studied are 
sharply divided into two marked groups, the first made up of com- 
pounds containing univalent acid and basic radicals, NaCl, KCl, 
HCl, NH4CI, KNOg. NaNOg, NH^NOg; the second made up of 
those . containing bivalent radicals, MgClj, BaCl^, MgSO^, H2SO4, 
Na2S04, K2SO4, Na^COg, KjCOg. These groups are distinct in 
two particulars, (i) in the amount of the molecular depression 
of the freezing-point, and (2) in the rate at which this increases 
with the increase of dilution. Thus in Plate I., Figs, i and 2, 
the two groups lie wide apart, and while the first (HCl, etc.), 
show slight curvature, those of the second show rapid change in 
curvature in the region of great dilution. 

(4) It appears from the regular course of the results, especially 
when exhibited in the various curves, that there is nowhere in the 
region studied any sudden change in the nature of the solution, 
so far, at least, as its freezing-point is concerned. The irregulari- 
ties which appear (KCl, KNOg) indicate that the experimental 
error at these points is very large, at least o°.ooo6C., and 
though this is much larger than seems to be admissible from the 
other results, still I think the course of the curves in the other 
regions indicates that the irregularities in extreme dilution are due 
to errors. 

* Zeit. Phys. Chcm., Bd. II., p. 496. « Ibid,^ Bd. XII., p. 623. » Ibid,, p. 628. 



No. 4.] 



FREEZING-POINTS OF SOLUTIONS, 



283 



(5) In view of the wide diflference in the freezing-points of the 
more concentrated solutions belonging to the same group, it is a 
remarkable fact that the curves representing their molecular de- 
pressions converge rapidly as the dilution increases, and in such 
a manner as to suggest that in extreme dilution they have perhaps 
sensibly the same freezing-points. This convergence is the more 
striking when it is observed how widely the two extremes in the 
second group, MgClj and Na2S04, differ in their freezing-points at 
the concentration i«=o.30. (See Plate I.) Here the freezing- 
points of the two solutions differ by 0°. 395 C, while at i«=o.oi 
they differ by only 0^0004. So also in the first group, the two 
extremes, HCl and KCl, differ at ^1=0.30 by o°.07 C, while at 
i«=o.oi the difference is inappreciable. 

The exceptions to be noted are NH^Cl and KNO3 in the first 
group, and BaClj, H2SO4, and MgSO^ in the second group. (For 
MgS04 see former paper.) The last two are vital exceptions. The 
others show such confusion in the curves in the region of great 
dilution as to indicate, as stated above, experimental errors. 

It is to be observed that HjPO^ stands by itself, and in spite of 
the fact that it contains a trivalent radical, it depresses the 
freezing-point less than the group containing the univalent radical. 
I hope to be able to study other analogous compounds to compare 
their freezing-points with those of HgPO^.^ 

^ In regard to the present values for phosphoric acid, it needs only to be remarked 
that the former series were known to have no significance, except so far as the regularity 
of the observed depressions might throw light upon the accuracy of the method. 

It was distinctly stated that the '< phosphoric acid " showed abnormal values, both in 
its specific gravity and electrical conductivity,* amounting in the latter to 7 %. The par- 
ticular specimen was the only phosphoric acid at hand, and since it had been known to 
be pure some years before, I used it for my work. Upon testing it, the fact of its great 
impurity was found, as stated in the note to which reference has been made. The present 
acid is from Trommsdorff. The normal solution was titrated by Mr. HuUet, and was 
then analyzed by him and found to contain 70.92 g. PjOs per liter. This corresponds to 
9l gram-molecular strength of 0.3329 instead of J, as required by the titration. The differ- 
ence is altogether negligible. Its specific gravity is now in exact accord with that found 
by Kohlrauscb, though the electrical conductivity is 209, instead of 200, as given by him. 

♦ See Note, Physical Review, Vol. I., p. 282. 



r 



284 ^- -^- LOOMIS. [Vol. III. 

Relation of Results to Dissociation Theory, 

The relation of the present results to the " Dissociation Theory" 
may be seen by comparing the observed depressions A in column 
(3) with those in column (6), which express the values of the 
depression computed on the basis of this theory.^ 

The theoretical values of the molecular depression are also 
found in column (5). 

The theory assumes that the degree of dissociation in any 

given solution is represented by the ratio — , in which /Lt, is the 

Moo 

molecular conductivity of the solution for the given concentration 
X, expressed in gram-equivalent molecules per liter, and /i^ is the 
limiting value of this conductivity as x approaches zero as its 
limit, or, as more generally expressed, the value of the molecular 
conductivity in infinite dilution. For /i, the values as found by 
Kohlrausch are chosen, and for /i-^, I have taken the most probable 
values as assigned by him.^ Van*t Hoflf's constant is taken as he 
gives it, 1.89. 

In the cases of NH4NO3 and MgClg, data for computing the 

theoretical values of A and — are not at hand. In case of H3PO4 

tn 

no theoretical values are given, since at present there seems to be 

insufficient knowledge in regard to the manner of its dissociation. 

It must be remembered that the concentration of the solution 
is represented by Kohlrausch by /i, which expresses the concen- 
tration in grdLVCi-eqinvalent molecules, while in the present paper m 
represents concentration in gram-molecules. Thus the solution, 
BaClj, w= I, is represented by Kohlrausch as BaClg, /a=2, and the 
solution which would be represented by Kohlrausch as H3PO4, 
/i= I, would be represented here by H3PO4, m=\. 

The values in columns (5) and (6) which are inclosed in paren- 
theses are found by graphic interpolations, and are subject to con- 
siderable error in the region of greatest concentration. 

In addition, column (7) contains the difference between the 

1 See notes in former paper Physical Review, Vol. I., p. 286, (i), (2), and (3). 

2 Wiede. Ann., No. 26, pp. 198 and 204 



No. 4.] FREEZING-POINTS OF SOLUTIONS, 285 

observed and computed values of the depression A, and for the 
sake of readier comparison column (8) expresses this difference in 
per cents of the observed values. 



Remarks on the Bearing of the Results on the Dissociation Theory, 

It cannot be denied that in the cases of KCl and K^SO^ 
the agreement is practically complete. And in the cases of 
NH4CI, HCl, BaClg, NajSO^, KNOg, NaNOg, the agreement is 
still surprising, and could hardly be set aside as "accidental." 
The differences, however, in these latter cases at least cannot 
be explained on the ground of some constant experimental error, 
since this would require that all the observed values should be 
uniformly either " too high ** or " too low." While in general the 
present results are found to be lower than the theoretical values, 
it must be observed that in the cases of BaClj and NajSO^ they 
are higher. 

It is further a matter of surprise that the two cases which show 
marked differences between observed and theoretical values are 
K2CO3 and NajCOg, exactly the two where the uncertainty in 
regard to the value of /i^ makes any computation of the theoreti- 
cal values little better than a guess. No doubt the most probable 
value of /i^, taking into account the general course of all the other 
curves in Kohlrausch's graphic representation of his results,^ is 
that selected by him, 140 in case of KjCOg, and 122 in case of 
Na^COg. If one, however, chooses the highest observed value 
of /i for the limiting value /i-^, Le, 122 for K^COg, and 104 for 
Na^COg (plainly an arbitrary choice so far as present knowledge 
goes), then the theoretical values of the depressions become almost 
identical with those observed for the dilute solutions of K^COj, 
and even in the case of Na^COg the agreement is perhaps all that 
the advocates of the theory require. (See Tables, column (8), for 
the two sets of percentage difference for KjCOg and Na^COg.) 

As has been before remarked, the course of the curves for the 
molecular depression of BaClj, NH4CI, and KNOg indicates that in 
the region of greatest dilution the values are apparently affected 

1 Wiede. Ann., 26, No. 10, Figs, i and 2 



286 E, H. LOOMIS. [Vol.111. 

by exceptionally large experimental errors, and it now appears that 
these apparent errors occur at the points where the difference 
between observed and theoretical values are found to be the 
greatest. 

In regard to the differences, in general it may be said that they 
amount to 2.5%, which represents, in the case of extreme dilution, 
a difference, say, of o°.ooisC. As the concentration increases, 
the percentage difference generally increases, reaching 6 % in the 
case of BaClj for »i=o.20. In general, in the greater concentra- 
tions the percentage difference may be put down roughly as 3 %, 
where it represents an actual difference extending into the 
hundredtfis of a degree. These differences, both in the dilute 
and in the concentrated solutions, are many times greater than 
any experimental error which the method and its results would 
seem to make admissible. 

Further, it must be said that the dissociation theory requires 
uniformly that the potassium salts should depress the freezing- 
point more than the corresponding sodium salts. This follows 
directly from the fact that the degree of dissociation is uniformly 
greater in the case of the potassium salts. The present results, 
however, show the reverse, except in the case of the carbonates. 

In case of the nitrates, the confusion of the curves in extreme 
dilution makes any comparison of the depressions difficult. 

The KCl depressions are less than the NaCl, but it is to be 
remembered that the NaCl series was the one series made at a 
room-temperature of 18*^ C, and I now know that trustworthy 
results are to be had only at temperatures not far from 0° C. I 
think it necessary to repeat the NaCl observations before any 
final comparison between the KCl and NaCl depressions should 
be made, though in regard to the observations at ^=0.40 there 
is no doubt ; the NaCl depresses the freezing-point much more 
than the KCl. 

Accuracy of the Method, 

It will be remembered that in the former paper, the experi- 
mental data were presented from which the reader was able him- 
self to estimate the method's accuracy. No attempt was made 



I 



No. 4.] FREEZING-POINTS OF SOLUTIONS. 287 

to fix its numerical value. The same course will be followed here, 
and the greater amount of experimental material now at hand 
throws much light upon this important matter. 

Now, as then, these two questions are fundamental : — 

(i) How far can one rely upon the constancy of these fine 
mercury thermometers } 

(2) What sort of agreement exists between the individual obser- 
vations of a series whose mean value is taken as the required 
freezing-point } 

The answer to the second question given in the former paper 
is entirely unaffected by the new material. Now, as then, a series 
of five entirely distinct observations show on the average a varia- 
tion of o°.ooi C. 

This variation may be attributed to three causes : first, assuming 
the temperature of the solution in each of the dififerent observa- 
tions to be the same^ then the variation could be referred to the 
inconstancy of the thermometer itself ; second, assuming that the 
thermometer actually records the temperature of its " bulb," then 
the variation could be referred to the failure of the method to 
bring the solution to its "freezing-point" in each of the separate 
determinations; third, the variations in the temperature of the 
mercury projecting into the air is able to account for the varia- 
tion. The variation cannot be referred to reading errors, Reading 
errors play absolutely no part in the experimental errors of the 
present method. There is no doubt that a yJ^° thermometer may 
be read accurately to the o°.oooo5 C. The question is, would 
these readings indicate anything in regard to the temperature 
of the solution. 

Since the reading error in comparison with the errors referred 
to above is insignificant, I have directed my attention entirely to 
the elimination of the latter rather than to the entirely super- 
ficial refinement of reducing reading errors either by using larger 
powers in the reading microscope or finer graduation of the 
thermometer. 

In regard to the first question stated above, the same method 
of answer will be observed as in the former paper. 

For this purpose the following table is given of all the observed 



288 



E. H, LOOAf/S. 



[Vol. III. 



zero-points of the thermometer during the three months of the 
observations. 

Table III. 



X 

Date, 
xSgs. 


Barometer. 


3 
Room- 
temperature. 


4 

Observed sero- 

poiat. 


5 

Zero-point corrected 
to 0^ C. and 760 mm. 


Jan. 2 


762.0 


+ 5.0 C. 


o 
0.0416 


0.0397 


7 


759.7 


10.0 


0.0435 


0.0404 


14 


756.7 


0.0 


0.0407 


0.0412 


21 


756.0 


2.0 


0.0416 


0.0416 


25 


765.3 


2.0 


0.0413 


0.0397 


28 


764.3 


0.0 


0.0404 


0.0397 


29 


754.1 


2.0 


0.0393 


0.0397 


30 


757.4 


0.0-4.0 


0.0391 


0.0389 


Feb. 4 


754.4 


3.0 


0.0402 


0.0402 


5 


760.1 


3.0 


0.0402 


0.0392 


11 


760.6 


4.0 


0.0407 


0.0394 


13 


746.9 


2.0 


0.0402 


0.0418 


18 


754.6 


5.0 


0.0420 


0.0414 


20 


754.1 


6.0 


0.0422 


0.0414 


25 


759.8 


4.0 


0.0420 


0.0408 


27 


761.6 


5.0 


0.0426 


0.0407 


Mar. 4 


754.5 


8.0 


0.0439 


0.0423 


5 


764.0 


9.0 


0.0457 


0.0422 


6 


769.4 


7.5 


0.0455 


0.0416 


13 


761.1 


10.0 


0.0460 


0.0427 


14 


758.4 


10.0 


0.0450 


0.0421 


18 


754.0 


7.0 


0.0432 


0.0420 


19 


757.6 


6.5 


0.0420 


0.0404 


20 


759.2 


5.0 


0.0416 


0.0402 


25 


757.7 


7.5 


0.0437 


0.0417 



The table needs no explanation further than to say that the 
correction for pressure was determined in the Reichsanstalt, 
Berlin, and given in the certificate accompanying the thermom- 
eter as 0*^.001 C. for a change of 6 mm. in barometric pressure. 
The correction for room-temperature is the usual one, in which 
it is assumed that the entire mercury column in the air is at 
room-temperature. The apparent coefficient of expansion for 
mercury in glass is taken as 0.000156. 

The results are graphically represented in Plate II., Fig. 6, 
where the dotted zigzag line shows the observed zero-point and 



No. 4.] 



FREEZING-POINTS OF SOLUTIONS. 



2S9 



the full zigzag line represents the corrected zero. The scale is 
S ram. to the y^^ ^- ^^ ^^"^ ^^ ^^^ same sensibility as the 
curves of molecular depression possess in the region of extreme 
dilution. Since the length of a yj^® division in the thermometer 
is 0.4 mm., the actual observed variations in the thermometer are 
raagnified i2S-fold in the "curve.** 
It is to be observed : — 

(i) The zero of the instrument has risen during the period of 
its rest at ordinary temperatures (March, 1893-January, 1895) 
from 0^.029 to o°.040, or roughly at the rate of 0.0035 C* per 
month. This would produce a rise of o°.ooi5 C. during the 
period of the observations. In Fig. 6 the straight line repre- 
sents such a uniform rise of 0*^.0015 C. during the three months. 
The actual observed rise is 0°.0020 C, an agreement which most 
likely is altogether accidental, since, of course, the assumption 
of a uniform rise of the zero-point of a thermometer is not war- 
ranted, even though the instrument, as in this case, has been 
long "seasoned.** 

(2) It is no less remarkable that the zigzag course of the zero- 
point seems to be governed by two laws; first, when the ther- 
mometer rested for more than a single night the zero remained 
either constant, as during the period Jan. 25-28 and Feb. 5-1 1, 
or else rapidly rose, as during the periods Feb. 11-13, Feb. 27- 
Mar. 4, etc. The only exception is the period Jan. 21-25. 
Second, when the thermometer was used two days in succession 
the zero-point is found on the second day to be sharply depressed, 
thus Jan. 29-30, Feb. 4-5, etc. The only exception here is Mar. 
4-5. Could it be that the long-continued jarring of the ther- 
mometer during a day's observations should depress its zero \ 
and that it recovered itself during the longer intervals of rest ! 
The results seem to indicate these conclusions. These two sin- 
gular regularities which appear to characterize the zigzag course 
of the observed zero-point were not known to me until the 
results were plotted in Fig. 6, long after the work was done, and 
I have thus had no opportunity to test the foregoing conclusions* 

This series of freezing-points shows us that the observed zero- 
point of the thermometer was by no means constant 




290 E. H. LOOMIS, [Vol. III. 

This must be carefully considered. 

On the one hand we may assume that the lack of constancy is 
only apparent, and to be explained on the ground of experimental 
errors. Accordingly the zero for Jan. 21 would be assumed to be 
o**.ooi C. too high, and on Jan. 25 as much too low. Similarly at 
Jan. 30 and Feb. 4, and at Feb. 11 and 13, in which latter case 
opposite errors, amounting to 0^.0015 C, would be assumed. (See 
Fig. 6.) These errors would then appear as errors in the depres- 
sions which were measured from the faulty zero-points, and since 
they would have to be assumed to be very great, we should find 
great irregularities in the curves of molecular depressions. For 
the most part such irregularities are entirely wanting. A closer 
analysis of the results in this respect is not without value. To 
this end let us examine the individual depressions measured on 
the days when these assumed erroneous zero-points were taken. 

Jan. 21. — Zero-point apparently too high. 
The depressions measured on that day were 

BaCl2, tn = 0.01, 0.02, 0.05, o.io, 0.20. 
Our assumption that the zero-point was too high would make the 
observed depressions too great in the dilute solutions. The curve 
seems to indicate that they are too small. 

Jan. 25. — Zero-point apparently too low. 

NH4CI, m = 0.0 1, was repeated and a result was obtained which was 
0^.0005 C. higher than the mean value of the table. Thus here the 
assumption that the zero-point was too low on this day does not 
accord with the observed depression. 

Jan. 36. — Zero-point apparently two low. 
The solutions observed were 

KNO3, m = 0.61, 0.02, 0.05, 0.10, and 0.20. 
In this case the assumption that the zero-point was erroneous agrees 
with the apparent error in the curve. 

Feb. 4. — Zero-point apparently too high. 

The entire series, NajCOa, was observed. 

The curve is entirely regular. This, however, would not decide whether 
the zero-point was too high or too low, since a perfectly regular curve 
would result even with a faulty zero-point, providing all the freezing- 
points of the solutions were themselves without error, or affected only 
by constant errors. 



No. 4] FREEZING-POINTS OF SOLUTIONS. 29 1 

Feb. II. — Zero-point apparently too low. 

MgClj, »i = 0.15 and 0.25, observed. 
The curve at these points is slightly depressed and a possible error may 
be assumed which would^ be in accord with the assumption that the 
observed zero-point was too low, 

Feb. 13. — Zero-point apparently too high. 

MgCl,, m = 0.30, was observed. The curve at this point is not " sensi- 
tive " enough to allow any judgment of possible error. 

Feb. 27. — Zero-point apparently too low. 

KCl, m = 0.035 ^^^ NH4CI, m = 0.035, observed. 
The irregularity in the KCl curve would suggest, however, an opposite 
error in the zero-point. 

Mar. 4. — Zero-point apparently too high. 

KjCOs complete series. 
Here, as in the case of NajCOs, the curve presents no irregularities. 
(See remark under Feb. 4.) 

Mar. 6. — r Zero-point apparently too low. 

The rejected series, KHO and NaHO, m = o.oi and 0.02, were made. 
The curves were without irregularities, and were rejected, as has been 
stated already, because their specific gravity and electrical conduc- 
tivity were found to be abnormal. 

Mar. 13. — Zero-point apparently too high. 

NaNOa and NH4NO8, »i = o.oi, 0.02, and 0.03, were observed. 
The curves suggest no errors in this region. 

Mar. 20. — Zero-point apparently too low. 
KNO3, ^ = 0.025, NaNOs, m = 0.20, and NH4NO8, m = 0.20, were 

observed. 
The observed points in the three curves are perfectly regular and point 
to no error. 

Mar. 25. — Zero-point apparently too high. 

HjP04 entire series observed. 
The curve is perfectly regular and suggests no error. (See remark under 
Feb. 4.) 

It thus appears that the assumption that the zero-points were 
erroneously observed on the days when the marked zigzags occur 
in the "curve" of zero-points is insufficient to explain the observed 
changes in the zero-point of the thermometer, since, if this were 
the case, the corresponding errors would, in general, appear in 
the measured depressions. We are thus obliged to admit that 



\ 



294 



E. H. LOOMIS. 



[Vol. III. 



and Wildermann/ are almost identical with mine in the region of middle 
concentration. This agreement becomes more striking from a glance at 
the following table, which I here reproduce from the former paper.' It 
contains the freezing-points of a -j^ normal sugar solution as found by the 
various observers named, together with the year of publication and the 
estimated error of the observers. 

To. this table I now add my own value and the values of the more recent 
observers. 



Observer. 



Year of 
Publication. 



Freezing-point. 



Estimated error. 



Raoult I. . . . 

Arrhenius I. . . 
Traubc .... 

Eykmann . . . 

Arrhenius II. . . 

Tammann . . . 

Pickering . . . 

Raoult II. . . . 

Loomis .... 
Jones .... 
Nernst and Abegg 
Wildermann . . 



1886 
1888 
1891 
1891 
1891 
1891 
1891 
1892 

1893 
1893 
1894 
1894 



0°.24 

0°.210 

00.235 

0^.216 

(F.204 

00.206 

00.202 

00.205 

00.190 
« 00.197 
* 00.187 
•00.190 



0O.01-2 
0O.0-05 
00.005 



00.0005 
00.002 



0O.0001-2 
0O.0001-2 



3. It has been suggested by Mr. Wildermann in regard to the three 
organic compounds examined by me that the observed increase in the molec- 
ular depression with the increase of concentration may be due to some 
experimental error which he thinks may have rendered the observed zero 
point too low. The results hardly admit of this assumption, since the 
assumption would be justified only by a succession of constant differences 
between the freezing-points of the successive solutions, w = o.oi, »i = 0.02, 
m = 0.03, etc., to »i = 0.20. These differences^ however, show an unmis- 
takable increase, which in the case of sugar is from 0^0184 to 0.02o6. 
That is, the addition of each yj^ gram-molecule to the solution lowers the 
freezing-point by an ever-increasing amount. We conclude then that the 
observed increase of molecular depression cannot be due to any error 

1 Zeit. Phys. Chem., 1894, 3, p. 337. ^ Phys. Review, Vol. I., 1893, ?• 200. 

' Graphic interpolation. Mean of two series which differ in this region about 0O.002. 
^ Extrapolation. Mean of three series which differ so widely in their essential nature 
that the extrapolation is very uncertain. 
^ Very slight extrapolation. 




No. 4.] FREEZING-POINTS OF SOLUTIONS. 295 

in the determination of the zero point of the thermometer. The same 
remarks apply to the results for alcohol and urea. 

Further, such an error would necessarily be a constant error, as these 
three compounds were studied in precisely the same manner as all the 
other compounds, now numbering some twenty. That these other results 
seem to be free from such a constant error makes the given assumption at 
least improbable. That the supposed error could have been an acci- 
dental error peculiar to two or three determinations of the zero point from 
which the depressions were obtained, is impossible, since these particular 
depressions for sugar and alcohol were measured from no less i}iX2Xi fourteen 
separately determined zero points, each of which was the mean of 7-9 
entirely independent observations. 

It seems well to compare my results in this particular with those of other 
observers. Among the previous observers, Arrhenius and Tammann each 
had observed this increase of molecular depression with increasing con- 
centration. Of the more recent observers all except Mr. Jones find the 
same increase which I have observed. Thus the results of Nemst and 
Abegg ^ for sugar, although their three separate series of observations differ 
very widely among themselves, — one series showing an increase of molec- 
ular depression with the increase of concentration, a second, a decrease, 
and the third presenting such irregularity that no conclusion may be drawn 
from it in this regard, — still the mean values of the three series show a pro- 
nounced increase. Jones' results show the same increase from the point 
w = o.io ; Raoult's results from the point « = 0.16, while those of Wilder- 
mann show this increase throughout the entire region. See Fig. 4, Plate II., 
where Wildermann's results for sugar are represented by the dotted lines. 
Curve I. was made with an " ice cap " about the bulb of his thermometer, 
II. without this " ice cap," while III. was made under still " more favorable 
conditions." ' Mr. Wildermann regards II. as correct to within o°.oooi-2 C. 
The three facts, then, which appear in this remarkable series must be looked 
upon as final. 

1. There is a marked increase in the molecular depression from the 
value 1.76 in the most dilute solutions, to 1.89 in the most concentrated. 

2. The molecular depression reaches the value 1.89 only in the most 
concentrated solutions, where Mr. Wildermann tells us, later, the value can 
have no significance. 

3. The series shows no tendency to become constant at this highest 
observed value, since a glance at the curve in Fig. 4 makes it plain that 
the results merely cross the horizontal line of constant molecular depres- 
sion, 1.89. 

* Zeit. Phys. Chcm. 189, p. 681. 
« Phil. Mag. 1895, No. 242, p. 126. 



296 BU H, LOOMIS [Vol. III. 

Having reached this value 1.89, Mr. Wildermann stopped his investiga- 
tion. 

Mr. Wildermann says of this interesting series, " der constanU Werth 
(1.89) kommt sehr gut zum Vorschein." 

As Mr. Wildermann explains a similar increase of the molecular depres- 
sion in series I. as due to the " ice cap " about the thermometer bulb, it 
would be desirable to know on what grounds he sets it aside in Series II., 
where no " ice cap " was at hand. 

Although this Series 11. is regarded by Mr. Wildermann as correct to 
within o°.oooi-2, still it does not seem to have been so conclusive to 
Mr. Wildermann as his discussion of it would seem to indicate, since he 
repeated the work " under more favorable conditions." * As a result we 
have Series III. This new series differs irregularly from Series II. by about 
0^.001 y — or about five- fold the possible error of the former series. If this 
Series III. is now to be taken as having reached the utmost limits of experi- 
mental accuracy, we must, I suppose, conclude that Mr. Wildermann under- 
estimated the experimental error of his former work. 

The unprecedented accuracy of this final series makes it worthy of atten- 
tion (see Fig. 4, Curve III.). 

1. It shows a variation from 1.84 to 1.89. 

2. The value 1.89 is reached very abruptly by one only of the five 
observations. This value is preceded by two observations whose values 
are 1.84, and followed by two whose mean value is also about 1.84. 

Still Mr. Wildermann says of this series of observations : " Thus I have 
shown that the constant (1.87-9) holds good in dilute solutions."^ 

This divergence between Mr. Wildermann's results and his interpretation 
of them should be kept constantly in mind in studying his work. 

Thus in the case of alcohol (see Fig. 5, Plate II.) his results obtained 
" without ice caps " (Curve II.) show a steady increase of molecular depres- 
sion from 1. 8 1 to 1.85. The only exception is at m — 0,006521 , Now 
Mr. Wildermann says * of these results : " We obtain the constant value 
1.84 in all concentrations'' 

The third series, "repeated under more favorable conditions," shows 
even more strikingly the same unmistakable increase of the molecular 
depression with the concentration. I do not think it profitable to extend 
this examination to the remaining case of urea where the same facts appear. 

It may be well here to call attention to the remarkable agreement between 
Mr. Wildermann's results, obtained with " ice caps," and my own results for 
sugar and alcohol. This agreement in the case of alcohol (see Fig. 5, 
Plate II., Curve I.) is so close that the two series must be looked upon 
as identical except in the small region of greatest dilution. He explains 

1 Phil. Mag. No. 242, 1895, P- ^26. 2 Zcit. Phys. Chem. No. 3, 1894, p. 342. 



No. 4-] FREEZING-POINTS OF SOLUTIONS. 297 

this agreement by saying that there was undoubtedly a similar " ice cap " 
about the bulb of my thermometer. If Mr. Wildermann will take the 
trouble to refer to my former publication, he will find that the formation 
of these ice layers was carefully discussed there, and will learn that one 
reason for confining the " overcooling " to the narrow limits, 0^.15 to 0^.25, 
was to make the building of these troublesome ice layers impossible. In 
fact, no trace of ice ever forms on either the bulb of the thermometer or 
wall of the freezing vessel. • 

This remarkable agreement is the more difficult to explain since Mr. 
Wildermann regards my results as " merely qualitative," and further s^ys 
the concentrations of the various solutions were incorrectly determined. 

4. May not some such constant error as that discussed in (3) account 
for the fact that in the three non-electrolytes examined by me the " curves " 
of molecular depression^ which differ so little from straight Unes in the 
great part of their course, should all alike show a downward curvature in 
the region of extreme dilution ? 

The results, I think, do not permit a final answer to this question. To 
render the "curve" a straight line throughout its entire course would 
require the admission of experimental errors by no means large, and it is 
perhaps well to regard this matter as still in doubt. 

That such an error is not altogether improbable appears from the fact 
that in the case of those electrolytes which seem to be affected with errors 
in the region of extreme dilution a similar downward tendency of the curves 
appears (BaClj, HCl, NH4CI). 

The fact that Wildermann^ s results show this same peculiarity should not 
be regarded in the light of a confirmation of my results. 

5. A most important question still remains: What are the respective 
advantages to be had by using a thermometer graduated in \^^^ and one 
graduated in -^^ ? 

I am able to discuss this question only on the basis of my own work 
with a j^® thermometer and the published results of other workers who 
have employed the ttJW** instruments. 

First, it must be emphasized that the y^** thermometers are easily read 
to the ten- thousandth of a degree with a possible reading error of half 
that amount. The sufficient proof of this is the fact that I have frequently 
interrupted a series of observations to allow some student who might 
happen to be present to make the reading for me. In no case have such 
readings differed from my own by more than |(^^qq °. This is not at all 
surprising since it is to be remembered that the micrometer scale in the 
microscope enables the observer to read the thousandths directly, and the 
ten-thousandths are as accurately estimated as the tenths of millimeters on 
an ordinary millimeter scale. 



298 E. H. LOOMIS, [Vol. III. 

How, then, is the fact to be explained that a series of five independent 
determinations of a given freezing-point vary on the average about o**.ooi ? 
First, it must be due to the inconstancy of the thermometer itself, or 
second, to the failure of the method to bring the solution to its actual 
freezing-point by amounts within these limits. The first cause of variation 
has been discussed already.^ While it undoubtedly plays some small part 
in this respect, still, I think it may be easily shown that the second cause 
•is the all-important one, and represents the fundamental difficulty in all 
freezing-point determinations. 

Thus, to cite the results of Mr. Jones,* it appears that the great accu- 
racy with which he could read his y^jW** thermometer, together with a 
few preliminary observations lead him to fix his experimental error at 
o°.oooi-2. Certainly the receding error is even less than that. The fact, 
however, appears throughout Mr. Jones' results that his method failed to 
bring the solutions to their freezing-points with this estimated accuracy, 
since in every instance where Mr. Jones furnishes us with two series 
of observations, the corresponding observations on the same solution 
frequently differ by ttjW ^"^^ ^^^ rarely by two or three times this large 
amount. These surprising differences appear quite generally throughout 
his two K2SO4 series and BaCIs series. See Plate II., Fig. i. 

It would seem that a method which thus fails in the fundamental matter 
of bringing a solution to its freezing-point to within o°.ooi-3 has little to 
gain by the use of a thermometer which may be read to o-oooi** C. That 
Mr. Jones seems to have become himself aware of this failure of his 
method to bring the solution to its freezing-point with any great degree of 
accuracy appears certain, since he explicitly refers to the regularity in the 
decrease of molecular depression shown by his HCl results.* See Plate II., 
Fig. I, for the graphic reproduction of his results. That such a " curve " is 
regarded by Mr. Jones as regular indicates his belief that the method 
easily permits experimental errors amounting to several thousandths of a 
degree. 

But we are not left to infer this knowledge on the part of Mr. Jones, 
since he says * of his results for NajCOs : " Their apparent irregularity 
is due without doubt to a slight experimental error." See the graphic 
representation of his NaaCOa results in Fig. i, Plate II. It here appears 
that the " apparent irregularity " amounts to only a little less than a hun- 
dredth of a degree. That Mr. Jones should refer to this as a slight error 
shows how clearly he understood the complete failure of his method in the 
particular under discussion. 

What is true of his NajCOs series appears also in all his later results, 

1 p. 287-91. « Ibid,, 1893, »i., p. 628. 

a Zeit. Phys. Chcm., 1893-1894. * IHd,, p. 638, 



No. 4.] FREEZING-POINTS OF SOLUTIONS. 299 

noticeably in HjS04, sugar, BaCl2, KjCOa, etc. The curves for the two 
latter are given in Fig. i and Fig. 2, Plate II. 

It is hard to see what particular advantage resulted from the use of a 
YtjVtt** thermometer, or on what grounds Mr. Jones justifies his attempts to 
measure the molecular depressions of solutions in the extreme dilution, 
r4ir t^ 10^00 normal, where an experimental error of 0^.0001-2 is absolutely 
fatal. 

The only other observer who has made use of a y^jW thermometer, so 
far as is known to me, is Mr. Wildermann in the application of a method 
devised by Mr. Lewis. That this method likewise fails in this fundamental 
matter of bringing the solutions to their actual freezing-points appears 
from a similar examination of the two series of results which he has fur- 
nished for both sugar and alcohol. 

Series II. in each case is affected according to Mr. Wildermann with a 
possible error 1-3 ten-thousandths of a degree, and Series III. is regarded 
by him as made under " more favorable circumstances." 

Among the differences which these two series for sugar present may be 
mentioned the following : 

At w = o.oi, o'^.oooS 
w = 0.02 0^.0004 
M = 0.03 o**.ooo6 

while in the case of the alcohol series we meet the following : 

At w = 0.01, o^ooo4 

M = 0.02 o®.ooo8 

m = 0.05 o°.ooio 

w = 0.09 0^.0027^ 

Unfortunately he does not publish a " repeated " series for urea, though 
we are left to infer that he made such a series, since he writes : " This 
year I repeated the investigations of cane sugar, alcohol, ^/^."* 

However, we are able to conclude from the data already at hand that his 
estimated experimental error, o**.oooi-2, is in fact about fivefold too small 
to explain his results. 

I know of no way to explain these great differences except by supposing 
that the method failed to bring the various solutions to their real freezing- 
points by 1-2 thousandths of a degree. The great irregularity of his 
results would be explained by Mr. Wildermann, I suppose, in the same way. 
And yet Mr. Wildermann reads his thermometer to the ten-thousandth of a 

^ In order to obtain the actual difference of the two observed freezing-points one has 
to multiply the difference as given in the curves by the corresponding abscissa, or value 
of w. « Phil. Mag., 1895, 242, p. 126. 



300 E. H. LOOMIS. [Vol. III. 

degree, and to avoid reading errors makes from 5 to lo observations of his 
thermometer. This is the more surprising when it is remembered that it 
is now quite generally understood that the mercury in one of these fine 
thermometers, when once it comes to rest in the capillary, remains fixed so 
long as the bulb experiences only slight changes of temperature (such as 
thousandths of a degree) and the thermometer is not vigorously jarred. 
Still Mr. Wildermann assumes that having brought his thermometer to a 
constant reading he has likewise brought his solution to a constant tem- 
perature. 

How, then, does Mr. Wildermann accoimt for the fact that his -j-^** ther- 
mometer placed side by side with his y^^ instrument shows variations of 
some thousandths (1-3)? He tells us that these are reading errors! Is 
it not perhaps possible that these variations may not be wholly due to 
carelessness in reading the instrument, but may arise from actual changes 
of the mercury ! The j^'' thermometer with its small bulb is perhaps 
able to thus indicate the temperature-changes in his solutions which would 
be wholly lost to his j^^ instrument with about joo grams of mercury 
in its bulb. 

I think a careful analysis of the results obtained with a -y^^ thermome- 
ter obliges one to conclude that its use as yet has added nothing to the 
accuracy of the various methods, and indicates that further accuracy is to 
be sought in the direction of greater control of the temperature of the solu- 
tion itself. 

In conclusion it may be well to point out a few matters which lorig 
practice seems to make worthy of attention. 

1. It cannot be emphasized too strongly that the reading of the ther- 
mometer, whatever the method, should never be made until all manipu- 
lation of the solution is done with. 

2. The experimental error of a given method may be safely estimated 
by making a series of entirely independent determinations of the freezing- 
point of water. These should be made on a day when the barometer is 
fairly constant, and special attention should be given to the matter men- 
tioned in (i). 

3. It seems to be important to preserve a record of all the observed 
zero points of the thermometer, together with the dates of observations. 
Thus the very great variation of o°.oo8 * in the apparent zero of Wilder- 
mann's -x^^^ thermometer, during the short period of his observations 
would perhaps lead to some valuable conclusions if systematically studied. 

J The maximum is found on p. 339 (Zeit. Phys. Chem. 1894, III.), where the third 
observed zero point is 0.4873, which becomes, when reduced to 760 mm, 0.4884. The 
minimum is found on p. 362, when the observed zero is 0.4781, or reduced to 760 mm., 
a48o4. 




No. 4.] CONCAVE GRATINGS. 30I 

It remains to be added that there seems to be little profit in correcting 
the misstatements of Mr. Wildermanri in regard to the work of the present 
writer. 

Princeton, N. J., Aug. 15, 1895. 



A Comparison of Two Concave Rowland Gratings. 
By Alice H. Bru&re. 

'T'K) any one who has worked with the spectra produced by diffraction 

X gratings, the irregularities which occur in them are only too well 
known. Even when the grating has been constructed with the utmost care 
in every detail of the work, as is the case with Professor Rowland's concave 
gratings, variations of intensity in the spectra of different orders, or in the 
different parts of a single spectrum, are peculiarities which it seems impos- 
sible to avoid, and the appearance of ghosts, or the lack of symmetry with 
respect to the focal distance of the various spectra, are matters of frequent 
observation. 

Professor Rowland * notes and discusses many of these peculiarities in a 
paper published in 1893. 

Kayser and Runge,* in their article upon the spectra of the elements, men- 
tion a sudden diminution of intensity for the shorter wave-lengths obtained 
from what, in other respects, was an exceedingly fine grating. This seemed 
extraordinary because the phenomenon was repeated at the same wave- 
length in the spectra of all orders, and could therefore not be attributed to 
the shape of the groove. 

The asymmetry of gratings is discussed at length in an article upon his 
observations by Dr. Rydberg,' of the University of Lund, Sweden, in 1893. 

F. Paschen,* in the same year, published some results of bolometric 
determinations of the spectra of glowing solids. Previous to the investiga- 
tion, he believed that the conditions of his experiment were exceptional, 
because in obtaining the spectra by means of a concave grating he would 
avoid the difficulties which arise through the use of a rock-salt prism and 
lenses. The energy curves which he obtained were, however, irregular and 
discontinuous to such an extent, that it was evident the spectrum he was 

* H. A. Rowland, Gratings in Theory and Practice, Astronomy and Astrophysics, 12, 
1893. Phil. Mag. S. 5, 35. 

* Kayser and Runge, Ueber die Spectren der Elemente; Abh. der Berl. Ak. der Wiss. 
18S8. Theill. 

* Dr. J. R. Rydbcrg, On a certain Asymmetry in Professor Rowland's Concave Grat* 
ings. PhiL Mag. S. 5, 35. Astron. and Astroph., May, 1893. 

* F. Paschen, Bolom. Untersuchongen im Gitterspectrum. Wied. Ann. 48 [1893]. 



302 M/SS A. H. BRUkRE. [Vol. III. 

using was not fit for the purpose. Further investigation showed that all 
spectra thus obtained gave different curves for the same substance under 
exactly similar conditions of arrangement and temperature, and that all 
were equally irregular. 

These and similar observations suggested a comparative study of two 
concave Rowland gratings belonging to the Physical Department of Cor- 
nell University, with a view to obtaining additional data upon the irregulari- 
ties of gratings by a method not previously tried. 

One grating is marked " 14438 lines to the inch " ; on the second, there 
is no statement with respect to the ruling, but all observations indicate that 
it is ruled with the same or nearly the same number of lines to the inch 
as the one marked. The length of radius marked upon each is six feet. 
Although not of the best Professor Rowland has ruled, the gratings are 
considered good. 

The first experiment was a photometric comparison of the spectra 
obtained from the two gratings. For this purpose, the grating whose 
spectra appeared more nearly uniform was chosen as a standard. This 
one, for convenience, will be designated as grating " A," and the other 
as grating " B." The two gratings were mounted, one above the other, on 
a vertical support. The arrangement of the apparatus was similar to that 
of Professor Rowland in his spectroscopic work. By means of three 
screws back of each grating, they were adjusted until perpendicular, and 
then inclined toward each other enough to bring the two spectra on the 
screen sufficiently close for accurate observations. 

The intensity of the spectrum obtained from a grating varies with the 
amount of light admitted to it. A comparison of the intensities of the 
spectra obtained from two gratings, receiving light from the same source, 
may therefore be made by comparing the widths of the slits through which 
light is admitted to them. All other conditions being the same, the ratio 
of these widths, when the spectra are of equal intensities, will be the inverse 
ratio of the intensities of the two spectra obtained with equal illumination 
on the gratings. 

This was the method employed. The two gratings were illuminated by 
light from independent slits. A double slit was used, each part of which 
was operated by a micrometer screw. It was carefully mounted, with a 
screen horizontally before it. The latter was adjusted until the beams 
emerging from the two parts were completely separated. This occurred 
when the light on the gratings was divided by a sharp black line, the 
shadow of the screen, midway between them. When the two slits were 
adjusted so that the spectra obtained were of equal intensities, the measure- 
ment was taken in terms of the widths of the slits. For this reason these 
were carefully calibrated to thousandths millimeters. 



No. 4.] CONCAVE GRATINGS. 303 

The spectra were received upon a screen of oiled paper bent into an 
arc of the circle. The diameter of this circle was equal to the radius of 
the grating. Before the screen could be slid an opaque screen, in which 
a rectangular aperture about one centimeter in width had been cut. In 
this way the entire spectrum, except the part in which observations were 
to be made, could be cut off. During the observations upon one spec- 
trum, the position of the translucent screen was fixed. For the best condi- 
tions, its position should have been at the focal distance of the spectra. 
It was impossible to place it so, however, for these distances differed for 
the two gratings by about six inches, and an intermediate position had 
therefore to be chosen. This introduced an error into the measurements, 
but as the entire distance was great as compared with the discrepancy, 
the error is small. 

The light used was that from a zircon disk heated to incandescence by 
the oxyhydrogen flame. The time for one set of observations could not 
exceed one hour, for the sensitiveness of the eye diminished greatly if it 
was extended beyond this. For this length of time, the light from the 
zircon disk was found to be most brilliant and constant. 

The screen was calibrated to wave-lengths by means of bright-line spectra. 
These were obtained by using an arc-lamp whose carbons were cored and 
filled with substances having distinct lines in well-known positions. 

In the measurements, the slit which illuminated grating A was set at a 
fixed width. Comparisons were then made for a number of positions 
throughout the spectra of the first and second orders on both sides. The 
slit which illuminated grating B was adjusted until the spaces in the spectra 
were of equal intensities, and the width of the slit was then read in divis- 
ions of its micrometer screw-head. This could be reduced to thousandths 
millimeters from a calibration curve drawn for this purpose. 

The intensity of a spectrum is dependent on three factors ; the intensity 
of the light on the slit, the width of the slit, and the mtensity due to the 
grating itself for unit width of slit and unit intensity on the slit. The prod- 
uct of the quantities expressing the values of these factors for grating A 
then expresses the true intensity for a given space in the spectrum obtained 
from this grating. Using[ corresponding quantities, the true intensity for 
the corresponding space in the spectrum from grating B may be expressed 
as a product. In the observations these intensities were made equal ; we 
therefore have an equation between them. 

Before and after each observation in a given part of the spectrum an 
observation was taken in that part of the spectrum to which the eye had 
been found to be most sensitive. This served as a check upon the ratio of 
the intensities of the light which fell upon the slits, since for any one posi- 
tion this was the only factor which could vary. A second equation was 



304 



MISS A. H. BRUkRE. 



rVOL. III. 



obtained from the intensities at this position of reference. From the two 
equations, a value for the intensity factor due to grating ^ at a given posi- 
tion was obtained, involving only the ratios of the widths of the slits, and the 
ratio of the intensity factors due to the gratings at the position of reference. 
The former were directly obtained by the experiment; the latter, being 
always in the same part of the spectrum, was a constant. 

Since only a ratio of the intensity due to grating B to that due to grating 
A^ which was assumed as unity, was desired, this constant could be given 
any convenient value. With the product of the ratios of the widths of the 
slits by this value for ordinates, and wave-lengths for abscissae, curves were 
drawn. 

From the values for the ratios of the widths of the slits indicating the 
relation of the intensities of the two spectra, an average ratio for each of the 





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four pairs of spectra was obtained. On the left, that of spectrum I. to 
the standard was 0.5 15; that of spectrum II., 4.5 : 5. On the right, that of 
spectrum I. to the standard was 13 : 5 ; that of spectrum II., 3 : 5. If now 
the constant mentioned above be given the values, 0.5, 4.5, 13 and 3 in the 
respective spectra, and the oroduct of the ratios of the widths of the slits 
by this quantity be platted as ordinates, and wave-lengths as abscissae, 
curves are obtained showing the relation of the four spectra to each other. 
Each curve also indicates the variation throughout a single spectrum. 

The adjoining curves have been obtained in this manner. The first 
spectrum to the left was an exceedingly weak one. The spectrum of the 
same order to the right, which was obtained by reversing the grating, has 
the greatest intensity of those measured. From this it would appear that 
the shape of the groove is such that most of the light for this angle of 




No. 4] CONCAVE GRATINGS. 305 

incidence is thrown in one direction. In both spectra there is a marked 
diminution of intensity in passing from the shorter to the longer wave- 
lengths. In the spectra of the second order, the intensities are more nearly 
equal. The variation of intensity is, however, in the opposite direction 
from that in the first spectra. In both cases the general character of the 
curves for the two spectra of the same order is the same. 

The grating from which these curves were obtained has a change in its 
ruling which is discernible with the eye. It was thought that there might 
be a connection between this defect and the peculiar character of the 
spectra of the first order. A second experiment was therefore performed 
in which the spectra from the two gratings were compared by photography. 
The bright-line spectrum of the carbons of an arc-light was photographed 
when obtained by each entire grating, also when obtained by using parts of 
each grating. 

The only peculiarity found in the spectra obtained from the standard 
grating was a slight shifting of the spectrum in several cases. From the 
grating with the irregular ruling, the spectrum of the first order to the left 
was double, the two spectra being separated 0.0 1 inch. That of the second 
order was distinct and single. Both spectra to the right were double. 
The lines of the two spectra in the spectrum of the first order were so 
close as to appear like a broadening of the lines of one spectrum ; in the 
second spectrum the two were distinct. In the case of each double spec- 
trum, one of the spectra corresponded to the single spectrum obtained by 
using the irregular part of the grating alone. 

From this fact, and the appearance of the grating, the double spectrum 
was thought to be due to a change in the number of lines ruled to the inch. 
The position of the spectrum indicated an increase of dispersion ; the num- 
ber of lines is therefore greater than the marked number, 14438. It was 
calculated to be 14446. 

The results found in these experiments bear in the same directions with 
those mentioned in articles referred to at the beginning of this paper. 
There is nothing fix)m which a definite conclusion may be drawn, and they 
therefore only serve as fiirther evidence of a few facts with regard to grat- 
ings in general, and as a statement of some of the peculiarities of the grat- 
ings compared. 

Physical Laboratory of Cornell XJNivERsrry. 



306 E. R. VOI\r NARDROFF. [Vol. III. 

A New Apparatus for the Study of Color Phenomena. 
By Ernest R, von Nardroff. 

THIS apparatus is virtually an attachment that converts an ordinary 
projection lantern into a triple lantern in which the three beams are 
independent as to intensity and direction. 

The beam from the lantern is first rendered " parallel," either by push- 
ing forward the illuminant, or, better, by removing the forward lens of the 
condenser. In the latter case, if a physical lantern be employed having a 
triple condenser, no adjustment of illuminant is necessary, but with a double 
condenser such as is found in ordinary picture lanterns, besides the removal 
of the forward lens, the illuminant must be drawn back a short distance. 
Next, the regular focusing lens of the lantern is to be removed, and in the 
path of the parallel beam is to be placed the apparatus, preferably as near 
to the condenser as possible. 

The apparatus (Figs. A and B) consists of a mahogany base supporting 
two uprights, to which are attached lenses, slide-holders, and diaphragms. 
The lenses, a, are auxiliary condensers, which produce images of the 
illuininant in the plane of the adjustable diaphragms at d. It is the property 
of such an image that each part of it receives light equally from all parts of 
the lens producing it, and hence the circles of light on the screen, which 
aic images of the apertures,/, formed by the focusing lenses, y^ will be uni- 
Ivvnuly dulled by partially closing the diaphragms, d. The focusing lenses, 
/, arc mounted in sliders. By shifting these, the circles on the screen are 
:ihu ted. The experimenter may thus obtain any desirable amount of over- 
Ki|> or seixiration. The range of this shifting was doubled by having the 
coulcrs of the apertures,/, somewhat nearer together than the optic centers 
ol tho condensing lenses, a. These lenses, therefore, were chosen of a 
yX\ iiucicr considerably greater than the diameter of the apertures,/. The 
avviualc focusing of the apertures,/, is accomplished by sliding in or 
v» a iho broad telescopic tube, /, in which they are mounted. Slide-holders 
vu \\\KK\\ at k for the reception of colored glasses, collodion or gelatin 
\\\\\\^, Ol glass cells containing colored liquids. Of the many colored liquids 
\x OIK \ vlispos^il, I have found solutions of the sulphate, the niGate, the 
t irnoiuo sulphate of copper, and the permanganate of potash particularly 

U V Ul. 

I uv vU-icription of a few experiments will make clear the general method 

luv luu^ in the slide-holders red, green, and blue media, and adjusting 
.N (ivuii ^hdcm for a perfect overlap on the screen, there is obtained a 
... * u\ \iUuuiuated disk, probably tinted with some hue. Any attempt 




Fig. A.— Rear View. 




Fig. B. — Front View 
E. R. VON NARDROFF: COLOR PHENOMENA 



No. 4] 



COLOR PHENOMENA, 



307 



to remove this residual hue by a more careful selection of color media is 
discouraging, because the result is so strongly affected by the iUuminant, 
the color of which is uncertain when either the lime-light or the electric arc 
is employed. However, the whole difficulty is avoided by means of the 
adjustable diaphragms. By manipulating these, the residual hue may easily 
be aboMshed, and an absolutely pure white always obtained. This white 





Fig. 1. 

is also very intense, because its intensity is equal to the sum of the 
intensities of its components, instead of to their average, as with rotating 
colored paper disks. 

If, now, the disks forming the compound white be separated in tri- 
angular fashion, the resulting figure (Fig. i) will display the result of 
mixing the primaries in pairs. This mixing may be further developed by 
cutting off, say, the red and the blue by closing their diaphragms, leaving 
only the green. Then, by turning on the red gradually, and when full, by 
turning off the green, the overlap will pass through all gradations of hue 





Fig. 4. 



from green, through yellow, to red. The same kind of thing can, of course, 
be done with the other pairs of primaries. 

When, instead of with red, green, and blue, we start with purple, yellow, 
and blue-green, we may still by proper use of the diaphragms obtain all 
possible hues as well as white (Fig. 2). Because the purple is a sensation 
that cannot be induced by light of a single wave-length, but requires a com- 



'X X,4JRDR0FF. 



[Vol. III. 



. •u'tjttu. nat the sensadon itself is complex, and 
:ri*'u^ iocs not represent the primary color 
ut> .joiined by compounding these false 
V* uTtf iidn with red, green, and blue. 

. 1 Y vaes may be illustrated by using carefully 

. .* > - '" ^' 3> or else by simply referring to the 
, . Vre it is evident that each initial hue is 
>vic: -jnnpound hue. 
-•, ,ux?^ no explanation. A simple reference to 



x.»*i», veQow-ochre, and olive-green, require a 
1 aw screen, aiotUy dull red still appears red, 
— not a suggestion of brown, — just 
as dull white alone never appears 
gray. Sombre effects require the as- 
sistance of contrast with some stand- 
ard intensity. With color disks this is 
^ present in the general illumination of 

^\ the room, but with screen apparatus it 

must be especially supplied. The front 
sliders being arranged for perfect over- 
lap, two of the slide-holders are left 
dear for white light, and the third is 
provided with some color, as red for 
example. A glass disk. Fig. 5, hav- 
ing attached to it a brass ring, r, and 
» tV ^flescope tube, and in contact with the 

^ H*MvH^'^ to come in front of the aperture corre- 
, fNi ^.Aphragm corresponding to the disk, d^ 

.^.^ * white circle having a black center. Ifl 




^ ^^^n^i A little, a small quantity of red light 

^ ^.Hs'h. ^Anding in contrast to the surrounding 

^^>(1<*A brown (Fig. 6). The effect may be 



No. 4.] ON A NEW FORM OF WATER BATTERY. 309 

varied by turning on a little white by opening the third diaphragm ; and 
then by using a variety of hues instead of the red, a set of tinted grays may 
be obtained. 

Contrast effects are strikingly presented when some saturated color, as 
green for example, is projected and then a white disk previously arranged 
to partially overlap is turned on. The overlap, which is really a tint, 
appears nearly white, while the remaining white appears strongly colored 
of the complementary hue. (See Fig. 7.) If the order of projection be 
reversed, — the white first and then the color, — the sudden change in the 
appearance of the white is very impressive. 

This apparatus, essentially as described, has been in use in my classes for 
several years, but the details have recently been much improved by Mr. 
F. W. Huntmgton, of Montclair, N. J. 



On a New Form of Water Battery. 

By Louis W. Austin and Charles B. TnwiNa 

THE ordinary old form of water battery, consisting of zinc-copper 
couples dipping in short test tubes set in paraffine, while perfectly 
satisfactory in its working, is extremely inconvenient to fill as soon as a 
large number of cells are used, since each cell must be filled separately 
and with great care lest the insulating medium should be wetted. Some 
years ago Professor Rowland* proposed a battery, very convenient for 
many purposes, which consisted of a series of zinc-copper pairs cemented 
to the lower side of a glass plate, each pair being so near to the next that 
when the tips of the metal strips have been dipped in water a drop is held 
between each strip and the adjacent one of the opposite metal in the next 
pair by capillary action. This drop will evaporate in about half an hour, 
when of <^ourse the battery must be dipped again. If for any reason it is 
desired to keep up the potential undisturbed for a longer time than this, 
some other battery must be used. 

The battery about to be described is one designed by the authors for 
use in some electrometer work on which they were engaged. It has 
proved so satisfactory and convenient in its working that we have decided 
to describe it for the benefit of other physicists. It is constructed as fol- 
lows: The required number of zincs and coppers are cut and bent by 
means of a form made by driving small nails into a block of wood in the 
shape shown m Fig. i. The zinc strips differ from the copper ones only 
in having the short bent portion at the top (/, Fig i) omitted. Cuts 4 mm. 

1 Phil. Mag., March, 1887, p. 303. 



3IO 



Z. IV. AUSTIN AND C. B. THWING. 



[Vol. III. 



deep and 28 mm. apart are then sawed in strips of dry pine wood 34 cm. 
loQgy 31 mm. wide, and about 7 mm. thick. The zinc and copper paiis 
are then soldered together and slipped into the cuts, after which ten strips 
are mounted together, with the addition of a blank strip to hold the last 
line of metal pairs in place in the grooved end pieces, and fastened firmly 
with nails. To secure perfect insulation, the wooden portions are next 
dipped for a few moments in a pan containing shellac varnish. The bat- 
tery is completed by springing a i -drachm homeopathic vial over eadi 



10 mm* 



E 
E 




trJTP 



n 



Fig. 1. 



Fig. 2. 



pair, the metal strips being so placed that they hold the bottles in position 
without any other support The battery is filled by setting it over a pan 
(30 cm. by 30 cm. and 9 cm. deep) filled with water. The general 
appearance of one of the frames is shown in Fig. 2. In our battery ten 
such frames of 100 cells each are placed four deep in a portable rack of 
wood. A battery of this sort, while it can be filled almost as easily as 
Rowland's, can be used without refilling for several weeks. 



The Physical Laboratory of the UNiVERsny of Wisconsin, 
August, 1895. 



BOOKS. 311 



.i:W BOOKS. 

iplcs of Physics. By Alfred Daniell. 
i enlarged. 8vo, pp. xxiii-f-ySa. Macmillan 

riiysics is adapted to the wants of students who 

.cnsive knowledge of general physics rather than 

1 accurate details of any branch of it. Numerous 

i ted branches have issued from the press of Great 

larter of a century, and these, to some extent, have 

text- book. But the study of general physics, in 

A branches, has obvious advantages, and the text- 

e in general education. Nevertheless the literature 

. no less remarkable for its poverty of English text- 

\ealth of special treatises. The works of Amott and 

! especially of Olmsted and Silliman in America, which 

iiysics in the middle decades of this century, had no 

Mirs down to the beginning of the last decade. English 

I)Iace of English authorship. Ganot and Deschanel, in 

.;lish dresses given them respectively by Atkinson and 

'St universal sway until 1884, when Daniell's Physics first 

r Stewart, I think, who first broke away from the traditional 

ting physics in disconnected fragments, and courageously 

science of matter and energy. But Balfour Stewart's work 

, lume adapted to younger students. Daniell, viewing physics 

'f the same great truth, but from a standpoint fourteen years 

that of Stewart, redrew the science in bolder outlines, on a 

, more elaborate and adapted to maturer readers. A third edi- 

standard text-book, carefully revised and considerably enlarged, 

re us. A glance along its pages reveals the fact that the spirit 

<1 of the. book have not been changed. But the work of revision 

"en everywhere. Sometimes it is detected in the change of a 

me times in the remodelling of a sentence ; and sometimes in the 

f a paragraph. In some cases it is found in the extension of a 

.on to a more general conclusion ; in others, in the incorporation 



3 1 2 I^W BOOKS. [Vol. III. 

of subject matter iHiich is entirely new. The motive of it all is easily dis- 
covered. Greater accuracy and precision have been secured, important 
gaps have been filled, and the later results of research have been embodied. 
The limits of this review forbid more than a brief record, with scant illus- 
trations of a few selected features of this revision. 

A very welcome modification of the notation has been made. To each 
physical quantity a symbol is assigned which, as fau: as possible, it retains 
throughout the book. Quantities in general are represented by capital 
letters, while quantities per unit area are designated by the corresponding 
small letters. Mr. Heaviside's suggestion that blackfaced type be used 
for directed quantities has been adopted, and other devices in type fiimish 
other distinctive characters. A two-page " index of symbols,** in which 
every character in this system is explained, is thoughtfiilly supplied. Why 
may not this effort be extended to the literature of physics in general? 
The adoption of a uniform and carefiilly adjusted system of notation is next 
in importance to the adoption of a uniform system of units. 

We notice next the incorporation of recently suggested terms, such for 
example as inductance, conductance, and impedance ; permittance and 
permittivity for electrostatic and specific electrostatic capacity. Magneto- 
motive force, magnetic flux, and reluctance appear with their units, and 
their relation, analogous to Ohm*s law, is pointed out The work of the 
international congress, Chicago, is referred to in the appendix as recom- 
mendations only, but the henry is placed among the practical units without 
reserve. Among the properties of matter we find shearability as the recip- 
rocal of rigidity, cubical compressibility as the reciprocal of elasticity of 
volume, and in another connection we find dilatancy to designate the 
change in volume which accompanies change in shape of granular masses. 

Another motive appears throughout the work which, I think, cannot be 
too highly commended. I refer to the author's anxiety to impart clear-cut 
conceptions of physical quantities and to protect the student firom the per- 
nicious influence of ambiguous terras. Think of the difficulties fostered 
by the long-time vague use of the word force. The author tries to avoid 
them by rejecting absolutely the notion of force as a physical entity, and 
using the word as a convenient term to designate a measurable quantity — 
the mutual action of bodies. Think of the inaccuracies involved in the 
ordinary use of the word weight. The author would forestall them by 
defining weight as a measurable action, assigning to it a symbol G, repre- 
senting its value in a formula G = ma^ and recording its value in dynes. 
Think of the confusion incidental to the use of one term in many senses — 
a most common and distracting feature of physical nomenclature. The 
author would preclude it, if possible, by setting the several uses of each 
ambiguous term precisely before the student. " We shall, except where 



No 4 ] I^E^ BOOKS. 3 1 3 

the context makes it plain, avoid the use of the unqualified word s&ess^ 
and endeavor to make it clear whether in any particular instance we refer 
(i) to a condition of stress, (2) to a stress of so many dynes, or (3) to a 
stress of so many dynes per square centimeter" (p. 24). The several 
meanings of an overloaded term are sometimes compiled, with a refer- 
ence number given to each. In the list for pressure no less than five are 
formulated (p. 25). 

There is a gratifying extension of the text to cover the later researches. 
This feature of the revision is especially marked in the chapter on electric- 
ity. Thus we find new paragraphs on the ether as the universal medium 
involved in the phenomena of electricity, magnetism, electro-magnetism, 
light, radiant heat and actinic radiations. New pages are devoted to 
electric waves, Maxwell's theory, and the inferential properties of the 
ether, oscillating currents, dynamo machines, and the transmission of 
energy to a distance. This last-named subject is too briefly treated, and 
Tesla's motives and successes receive scant recognition. 

To those who have yet to make acquaintance with this treatise a brief 
resume of its contents may be usefiil. An introduction supplies the axio- 
matic truths and fundamental laws on which physical investigation is based. 
The work then opens with a discussion of measurement as the foundation 
of all accurate knowledge of phenomena. One short chapter is devoted 
to the fiindamental units of time, space, and mass / another to the derived 
ideas of motion, velocity, acceleration, momentum, and force as measurable 
quantities; a third describes in general terms some practical methods 
adopted in the measurement of those quantities; while a fourth dis- 
cusses work and energy, giving definitions of their units and the law of 
conservation. 

A second group of four chapters follows, based on the doctrine of energy, 
and devoted to the principles of kinematics, kinetics, potential, and gravi- 
tation. Harmonic motion and the propagation of waves, potential and 
the conception of space as a field of force, are here discussed with suffi- 
cient fullness and great care. The older problems also, — acceleration 
and rotation, impact and friction, moments and mechanical powers, gravi- 
tation and the pendulum, — are examined in the light of the all-pervading 
principle of energy. 

These two groups of chapters, I. to VI 11. inclusive, may be regarded as a 
preparatory course. While they keep the problems of the material world 
constantly in view, they withhold the student from an immediate attempt 
to grapple them. Filled with fundamental principles, definitions, and 
physical conceptions, they are the armory and drill-ground where the stu- 
dent may get an adequate equipment and training. In Chapter IX., for 
the first time, the study of physics as a science of phenomena comes to 
the front 



314 ^^^ BOOKS. [Vol. IIL 

A third group of four chapters here begins, which is devoted to the study 
of matter. They comprise^ in general, a discussion of its properties, states, 
and constitution ; and then, in particular, the special features of solids^ 
liquids, and gases. These chapters fairly brisde with modem views. Ether 
takes its place among the states of matter. Molecular structure, viscosity, 
the critical state, and the kinetic theory are prominent The conception 
of matter as substantially one thing, and of its different forms and states as 
incidental variations determined by the energy which each body is, for the 
time being, the reservoir, cannot escape the thoughtful reader. 

Following these is a fourth group of four chapters, discussing the phe- 
nomena of energy under the titles of heat, sound, ether waves, and elec- 
tricity and magnetism. The discussion of heat is brief. One is somewhat 
surprised to find so much of so large a subject in so small a space. But as 
heat is a form of energy, the principles relating to heat may, to a great 
extent, be extracted from the general principle. This is the secret of the 
author's successful brevity. The propositions relating to heat are set in 
the doctrine of energy, like crystals of metal in their native vein-stone. 
The student will sometimes find his strength and skill severely taxed to 
think them out. The chapter is not an easy one. The next, on sound, 
is fairly well written, discloses the essential features of the subject, and is 
quite full on pitch and temperament. It permits close thinking, but does 
not seem to compel it. Not so with the chapter on ether waves. One 
must in the outset learn to think of ether as he thinks of air, — a medium 
whose reality is to be admitted as an inference from the phenomena to 
which it gives rise. The reader must firmly grasp the difficult conception 
of ether motions and ether stresses, and as he has already learned to look 
upon bodies of matter as reservoirs of energy, so must he now behold 
ether as the vehicle for its transfer. 

Beginning with the nature of radiations, the path leads on through color, 
Prevost's law, Stoke*s law to spectrum analyses. Starting again with 
molecular vibrations, we follow the propagation of waves through ether, 
taking, on our way, the phenomena of plane polarization, reflection, refrac- 
tion, interference, double refraction, to elliptical and rotary polarization, 
where we halt to discuss optical instruments and visual perceptions. 
Finally, in the last and longest chapter, the principles of electricity and 
magnetism are discussed with considerable detail, the omnipresent ether 
being invoked to unitize the whole. The time will come, no doubt, when 
this can be done with more complete success than seems to be possible at 
the present time. 

The specialist need not consult Daniell's Physics for technical details. 
The mathematician need not go to it expecting to find a mathematical 
gymnasium. The historian will miss the descriptions of classical experi- 



No. 4.] ^^^ BOOKS. 3 1 5 

ments and the narrations of personal achievements. But the student of 
science will find it to be a cabinet of well-selected facts, mathematical 
reasonings, and experimental results, skillfully arranged to exhibit the sys- 
tem of principles that underlie physical phenomena. 

LeRoy C. Cooley. 



Solution and Electrolysis. By William Cecil Dampier Whetham, 
M.A. pp. viii-f- 296. 19 illustrations. Cambridge, The University Press ; 
New York, Macmillan & Co. 

During the last few years the scientific advances made in physical 
chemistry have been raarvelously rapid, and especially has this been the 
case in those lines which relate to solutions and electrolysis. Questions 
present themselves to the investigator from all sides of the subject, and 
their solutions are often within the reach of limited apparatus and limited 
time on the part of the investigator. As a result, the periodical literature 
is rich in memoirs on the subject. It is therefore not surprising that there 
are many general scientific readers who are incapable of following some of 
the later memoirs. To such persons the present volume will be welcome. 
It will also be of great value to the specialist in this line, because of its 
suggestiveness, and especially because of the tables at the end. 

The book, as its title indicates, has two distinct parts. The first part 
covers six chapters. In them the kinetic theory of solutions is presented 
in very much the same manner as in Muir*s translation of OstwaUTs Solu- 
tions. The numerical results of experiment are omitted except occasionally, 
where their presence makes the presentation of the subject clearer. The 
five remaining chapters are devoted to electrolysis. In the first of 
these the early work of Davy, Faraday, and Grotthus is described, and the 
theory of primary and secondary batteries is presented. In connection 
with the latter, a paragraph on polarization appears, which makes no refer- 
ence to the work done during the last fifteen years. Chapter VIII. is 
devoted to the ions — their nature, their migration, and their velocities of 
migration. Chapter IX. is concerned with the conductivity of electrolytes. 
At this place the dissociation theory of Arrhenius is introduced. Through- 
out the second paragraph of the chapter potential differences are wrongly 
called electromotive forces. Bouty's method of determining the resistances 
of electrolytes is described and illustrated. The prominence given to it 
constitutes a recommendation. Yet Bouty was led into false conclusions 
from its employment ; and, as Kohlrausch stated {Annalen der Physik und 
Chemie, Band XXVI., p. 219), it is surprising that his results were as good 
as they were, considering the liability to temperature errors. The convenient 



JVEH^ BOOKS. [Vol. III. 

. a of eiectrol>tic lesistaa ce Tcssel represented in Fig. i8 will hardly be 
..c^v*>rred SO by American wor k er s . The following chapter is devoted to 
c . ai;>.Jeration of the connections existing between electrical con- 
.v...>*i\, oheinical activity, and osmotic pressure. The last chapter is 

. . .... :o the theories of electroljrsis. 

\ . . i.ai troiu the report to the British Association for the Advancement 

\^.t^c, ot a table of electro-chemical properties of aqneons solutions, 

. .ju I>y the Rev. T. C. Fitzpatrick, occupies the last sixty-nine pages 

.^ >v>ok. I his will prove of great value to investigators. All ordinary 

.V v .\ LC5 arc considered in it, and a mere inspection serves to determine 

.,a coacerning equivalent composition, specific gravity, electrical 

.. .^ i\itv, migration ratios, and fluidity constants. The ^)ecific molec- 

. >.v aical conductivities are given in terms of the true ohm as well as 

.. ncicury unit. g^^^^^ Sheldon. 



. i.^c F.ltctric Currents and Alternate-Current Motors, By 
V N. ^ \\ Thompson. 8vo, pp. vi, 261. New York, Spon & Chamber- 

..aoi assumes that the reader is familiar with the general principles 
..c cuircQts, and begins the book with a chapter on polyphase 
. ,. lu this treatment engineering requirements, details, and data 
.\ o ill it led, and the students attention is directed to the physical 
. Uvl ^ haracteristics of this class of machinery. Brief references 
. . .i.ons are made to the productions of various manufacturing 

.XV i.ipLor deals with the combination of polyphase currents, and 

,. ..aicut in the latter part of the chapter is apphed to com- 

V.. uia_;actic fields. The first part of this chapter is usefiil 

. '\ MU. I regard the latter part as unfortunate, since at this 

, u» loader necessary to use the rotating field hypothesis when 

V, a Ik iiuluction motor. The author's evident purpose is to pre- 

.1 u> accept, in lieu of the polyphase alternating field, a simple 

* v'lie or more pairs of poles. 

.\.uciKe of the practical identity of polyphase alternating 

e Keating fields, the reader witnesses in Chapter III. 

V. a U>ih forms of field. Much attention is paid to their 

K'lu to their differences, — differences of importance in 

.., a >;^a and construction. 

V . v'lcJ to the early development of the polyphase motor is 
\ vwU3 the early experiments that led men to investigate 



No. 4.] r^ElV BOOKS. 3 1 7 

the properties of pol)rphase alternating fields similar to those of simple 
rotating fields. This chapter, however, unfortunately leaves the reader 
with the impression that symmetrical polyphase alternating fields and 
simple rotating fields are practically identical, and that the modem induc- 
tion motor results from a recognition of these facts. 

Chapter V. is probably a good description of European induction motor 
practice. Excepting a reference to Tesla*s early experiments, nothing is 
said about American practice. Yet this country has produced at least three 
of the best forms, based rather on improvements that result from a trans- 
former or rational study of the induction motor, than on the teachings of 
the rotating field hypothesis. 

Chapters VI. and VII. are largely of historical value, as they present the 
hypothetical considerations which led to the ultimate development of the 
modem induction motor, and are not the working theories of the engineers 
who are producing the practice of the present day. The theories of this 
chapter would never lead to the production of an efficient monocyclic 
motor, nor show the important part that is played by the mechanical motion 
of the secondary conductors in the production of the back electromotive 
force. 

The reference to monophase motors is quite complete and well done. 
The last chapters, after a brief and sufficient discussion of polyphase trans- 
formers, illustrate the application of the rotating field hypothesis for pur- 
poses of practical design, and close with some examples of European 
polyphase practice, including details of modem Oerlikon polyphase motors. 

A highly valuable feature of this work is the complete bibliography given 
in Appendix I. 

This book has in it much of value, as the high standing of the author 
warrants ; nevertheless, we do not see why so much of importance belong- 
ing to American practice is absent. Doubtless distance, and the rapid 
rate at which the practice is developing, may in part account for this. 

Harris J. Ryan. 



Industrial Photometry with Special Application of Electric Light- 
ing. Translated from the French of Palaz, by George W. Patterson, Jr., 
and Merib Rowley Patterson. I4.00. pp. 322 -f- vii. New York, 
Van Nostrand, 1894. 

This is a translation of the well-known work of Palaz, a notice of which 
has akeady appeared in the pages of the Review.^ 
It is, in the main, an excellent translation. The original has been closely 
1 Physical Review, Vol. I. p. 238. 



JVEPr BOOKS. [Vol. III. 



.s.^%wvl uucie by artide, and a work, which in the French was : 

^^.>.ou and deamess of statement, has been placed at the disposal of 

-^. ^u :cavicn> in such a form that these vahiable characteristics are not 

. ccd:>ioudily, however, the author lapses from complete lucidity, and 

.■^.*>^uors ^o with him. On pages 8 and 9, for example, we find a 

^ 1 > tiich the approximate Umits of the ultra-violet, and visible. regions, 

. . j.rtain regions in the infra-red of the spectrum are gathered under 
^.. ..:i^ * Character of the vibratory movement." 

..V. . . .:cquently the translators record their disagreement with the author 
.^.^.> 01 brief notes in an appendix. This, on the whole, is a plan to be 

...:;cii^evi, since the form and arrangement of the original is nowise dis- 

V. .. \V here, however, it is a question of an obvious correction, as in 

v..;.^- in which the absorption by a mirror is given at 1.8 per cent 

. ., ; oi iS per cent, a better place to note the error would have been in 

v vl or in a footnote upon the same page. 

; ^iv aid be noted that Professor Ayrton's paper on the arc light, to 

.^ i ;cicicuce is made in section D of the appendix, is unfortunately not 
V loaud in the Proceedings of the Chicago Congress ^ nor elsewhere. 

; iuuia^cript was accidentally destroyed before it reached the hands of 
.v.;uag committee.* 

I K uo^t itui>ortant portion of the appendix is the set of regulations for 
., iiK Hefner lamp. These have been translated from Schillings 

\ tew addenda from the personal experiences of the translators 

. \ V a made in the body of the text, as, for example, where the method 

> .. ^ :i^ _;'iow- lamps pursued in the University of Michigan is described. 

. v u\.iuons are not such, however, as to modify the character of the 

x, ;.; to the conservative treatment, the strong points of the original 

, ,.v. uuacly, the description of photometers and of photometric stand- 

.. v^ a the dau concerning the latter, remain the most important points 

V ui..Atcd work. Those portions of the subject which were weak or 

. . ..\v u ihe original, as, for example, questions of spectrum photometry 

', ^.ud> of ditferences of quality of light, have not been reinforced. 

. \.Hwvcr, the normal function of the translator to remodel the 

. \ . v>,nes under his hands, and doubdess it is to be preferred that 

,.K vild be closely followed even to the point of perpetuating 

... ,;eaKuts. New matter, excepting such as may be casually 

_ . u the form of an appendix, had better form the material for a 

s - i^e» 

E. L. Nichols. 

,. « .1 iSc most important points will be found in a paper by Mrs. Ayrton. 



No. 4] NEW BOOKS. 319 

Die Oberfldchetir oder Schillerfarben, Von B. Walter. 8vo, pp. vi 
-4-122. Braunschweig, Vieweg & Sohn, 1895. 

This monograph upon the nature of surface color is intended primarily 
for zoologists, mineralogists, and chemists, one of the purposes of the 
author being to point out that many of the colors which are usually 
ascribed to structure of the surface layer, and which are classified either as 
colors of thin plates, of grating-diffraction, or of prismatic dispersion, are 
really true surface colors. 

To this end, the laws of the formation of surface color by reflection are 
taken up in a clear and simple manner, and it is shown that bodies, other- 
wise colorless, possess a surface color due to the fact that the intensity of 
each reflected wave length depends upon the refractive index of the reflect- 
ing body for that particular ray. Since the index varies with the wave 
length, the composition of the reflected differs from that of the incident 
light. This is a perfectly obvious matter, but rarely considered in the 
discussion of color formation. Dr. Walter computes the differences in 
intensity between red and violet of the reflected light, and shows that in 
the case of bodies producing high dispersion it is considerable. By normal 
reflection from carbon disulphide, for example, the violet ray gains 16 per 
cent over the red of the spectrum. 

At the interface between certain substances which differ greatly in dis- 
persive power, as, for example, between crown glass and oil of cassia, this 
color, due to reflection, becomes very marked. The violet may become 
three times as intense as the red in the reflected ray. 

The succeeding portions of the monograph deal with the surface colors 
of metals and of the real " Schillerstoffe." These last are substances 
which absorb a single region of the visible spectrum strongly, other parts 
scarcely at all. Fuchsin is one of the best known of this class. The colors 
of these also are shown by the author to be colors of reflection ; and, 
finally, in his concluding chapter, he shows that many of the colors of 
animals and minerals, which are ordinarily ascribed to interference, are 
really surface coloring, and ascribable to reflection. The work is a valu- 
able contribution to the science of color. 

E. L. Nichols. 

The Herschels and Modem Astronomy, By Agnes M. Clerke. 
I1.25. i2mo, pp. vi-h224. London, The Century Science Series, 
Cassell & Co. ; New York, Macmillan & Co. 

Miss Agnes Clerke, whose work upon the history of astronomy has 
rendered her an authority, is admirably equipped for writing the biography 
of the Herschels. A more attractive theme to the lover of biography than 



::c ^TEIV BOOKS. [Vol. III. 

i< -^iauoiis of this remarkable family to the development of modem 
x^ v.ioaiv, it would be difficult to find. The story of the rise of the elder 
•oi^.Ki from the position of an oboe player in a Hanoverian military 
\w*vi :o ttiat of court astronomer to King George, is one to excite the 
%..*.i.i.>t sympathy and interest on the part of the reader. The sketch 
i V .^loonc Herschel is scarcely less interesting than that of her brother. 
X :'c>.Lioa which she has held in the minds of many is simply that of an 
.*.....!;; .u>;>istant in the computing room of the astronomer; Miss Qerke's 
V. i,:u.it reveals to us a woman of great versatility and of great strength of 

V uaAcicr, a woman to whom the reader feels strongly drawn. 

I nc interest of the book centers in the history of William and Caroline. 
W.Ku we come to Sir John Herschel there is a distinct idling ofil The 
^...ci Herschel won scientific feme as other poor men sometimes win 
loiLuuc. John Herschel inherited his position in the scientific world as 
UK a uihent money, and with it definite work in astronomy which he 
;cc.ucJ it his duty to undertake and carry to completion. The magnifi- 

V cat uaaner in which he fiilfilled the scientific obligations which he inher- 
.Uv. irom his father is well described in the pages of this brief memoir, but 
It '3 in possible to imbue such a career, however brilliant, with the romantic 

iuvic^c which one feels for the heroic upward struggle of the founder of 
ttic K>a:>e. 

£. L, Nichols. 



Volume III, March-April^ l8g6. Number 5. 



THE 

PHYSICAL REVIEW. 



ON THE VISCOSITY OF CERTAIN SALT SOLUTIONS. 

By B. E. Moore. 

THE subject of Viscosity was first taken up by Poiseuille,^ 
who used a method depending upon the transpiration of the 
liquid through capillary tubes. Coulomb, in studying the same 
subject, observed the damping of a magnetic needle or bar when 
vibrating in the liquid investigated. This method was also exten- 
sively used by O. E. Meyer,^ Grotian,^ and others. Still a third 
method has been developed by Helmholtz, who placed the solution 
to be studied in a hollow sphere, and observed the behavior of the 
sphere when oscillated. 

These methods have led to very diflferent results. Konig* 
modified the method of Coulomb and used in the place of the 
swinging rod, a sphere, the equation of motion of which KirchhoflF 
had solved, and for which the theory can be completely developed. 
For calculation Konig made use of the expression by Kirchhoff as 
extended and completed by Boltzman, and reached the conclusion 
that the values obtained for viscosity by Coulomb's method were 
in complete agreement with the results obtained by allowing the 
liquid to flow through a capillary tube. Though the agreement 

^ Memoirs des Savants fetrangers, T. IX. Pogg. Ann., Vol. LVIII., p. 434. 

apogg. Ann., Vol. CXIIL, pp. 55, 193. 383. »Pogg. Ann., Vol. CLVII., p. 130. 

* Wicd. Ann., Vol. XXXII., p. 193. 

321 



322 B. E. MOORE. [Vol. III. 

of results by the different methods is of great interest and 
importance, yet observers have generally preferred the original 
method due to Poiseuille, and that because of its simplicity. 
The method requires also a considerably smaller amount of the 
solution, and admits of a much easier and more accurate tempera- 
ture regulation. 

Among the earlier investigations on the subject of viscosity 
may be mentioned those of Graham,^ whose results suggest the 
presence of hydrates in solution. He states further that "slow 
transpiration and low volatility go together." Later investi- 
gations by Rellstab^ dealt with several organic liquids, while 
numerous experiments were made by Hiibner^ on the salts of the 
chloride family. Sprung* investigated a great many cases of 
varying concentration and temperature, the latter ranging from 
0° to 60° C. 

Hagenbach* developed the mathematical formula for transpira- 
tion. His expression for viscosity (17) reduces, when correction 
for the velocity of flow is omitted, to the form known as Poi- 

seuille's formula: 17=— — ; — Herein r denotes the radius of the 
8 Iv 

capillary ; A, the height of pressure column ; Sy specific gravity, and 
therefore the product of h and s the pressure; v represents the 
volume that transpires in time, /; and / is used to designate 
the length of the capillary tube. 

Pribam and Handl^ have made extensive observations on the 
viscosity of organic solution and stochiometrical relations of the 
same. The careful work of Gartenmeister ^ in this field should 
not be omitted. Grotian® was the first to make extended com- 
parisons of viscosity and conductivity of salt solutions. Slotte's ^ 
investigations cover a number of chromates and he shows that the 
temperature variation in viscosity, 17, can be expressed by a for- 
mula, 17=^(1 -{-bty^f where c, b, and n are constants of the liquid, 

1 Royal Society Proceedings, XI., p. 381. i860. 

^Inaugural Dissertation, Bonn, 1868. •Pogg. Ann., VoL CIX., p. 385. 
» Pogg. Ann. Vol. CL., p. 248. • Wien Ber., Vols. 78, 80. 

♦ Pogg. Ann., Vol. CLIX., p. I. ^ S^eitschrift die Ph. Chem., Vol. VI., p. 524. 

8 Pogg. Ann., Vol. CLVII. p. 130; Vol. CLX., p. 238. Wied. Ann., VoL VIII., 
p. 530. » Wied. Ann., VoL XIV., p. 13. 



1 



No. 5.] VISCOSITY OF SALT SOLUTIONS. 323 

Since the announcement of the dissociation theory by Arrhenius, 
the subject of viscosity of solutions has had a much deeper interest, 
and experiments have been carried on, both trying to establish 
some stochiometrical relation, and to establish a relation between 
viscosity and conductivity. With this idea in view, Arrhenius has 
made many investigations. In his first experiments^ he shows 
that the viscosity is a function of x and y, or H{x, y), where x 
and y express either percentage of substance in solution, or gram- 
equivalent per liter. We may say r}=H{x, y)=A'B', where A and 
B are constants of the solution. For a single salt in solution this 
reduces to i; = /l*. Wagner ^ and Reyher^ validified this law for a 
great many solutions. In Gartenmeister*s* experiments the Arrhe-* 
nius exponential formula is not so well satisfied. Reyher found 
a characteristic relation between the friction or viscosity of free 
acids and those of the sodium salts, according as a strong or weak 
acid was present. This variation he made to depend upon the 
unequal dissociation of the strong and weak acids. The dissociation 
theory has given great confidence to the belief in a relation of 
viscosity to conductivity. However, G. Wiedemann,^ previous to 
this theory, noticed that the friction which the ions undergo 
varies in the same way as inner friction; i.e. viscosity. The 
mobility of the ions must then be a function of their fluidity. 
Arrhenius showed that conductivity did not depend upon fluidity 
alone. This investigator made a strong point when he showed 
that the introduction of a non-conducting substance into an elec- 
trolyte affected both its conductivity and its viscosity in the same 
way.^ Other experimenters, by a direct comparison of conductiv- 
ities and viscosities, have come to the conclusion that while the 
conductivities of a series of salts increased, the viscosities in gen- 
eral decreased. However, the increasing and decreasing series 
stand in no definite ratio to each other. 

The following experiments have followed much in the same line. 

iZeitschrifk die Ph. Chcm., Vol. I., p. 285. 
« S^eitschrift die Ph. Chem., Vol. V., p. 31. 
» Zeitschrift die Ph. Chem., Vol. II., p. 744. 

♦ Zeitschrift die Ph. Chem., Vol. VI., p. 524. 
» Pogg. Ann., Vol. XCIX.. p. 177. 

• Zeitschrift die Ph. Chem., Vol. IX., p. 487. 



324 ^- ^- MOORE. [Vol. III. 

The viscosities of a series of salts have been determined, and, in 
so far as was possible, the conductivities of the same compared 
with their viscosities. 

The method employed was the one due to Poiseuille, the 
apparatus being similar to that used by Arrhenius. A glass vessel 
A (Fig. i), of about 24 ccm. capacity, is connected with two tubes, 
a and b, above and below respectively. Each tube has a diameter 
of about 4 mm. A stopcock closes a about 4 cm. from A, b was 
joined to a capillary tube d^ some 40 cm. long. The lower end of 
the capillary dips into the solution to be studied, contained in a 
glass vessel, By of about 200 c.cm. capacity. B is kept water- 
tight by means of a rubber cork ^, and is encased 
in a brass support A. Exactly 50 c.cm. of the solu- 
tion was always brought into the vessel B^ and the 
extremity c of the capillary brought into the plane of 
the upper edge of the brass casing A. This was done 
to secure a constant average height of pressure in all 
cases. But this was later proven to be an unneces- 
sary precaution, as a change in the length of the capil- 
lary, amounting to 18 cm., only made a diflference of 
2.5 seconds in the transpiration of water at 18° C. 
The liquid is brought into the vessel A to some 
point al by exhausting the air through a rubber tube 
/. The time of flow was taken between two marks 
on tubes a and b. As the mean height of the pressure 
column is constant, it is evident that the pressure 
of the diflferent liquids subjected to transpiration varies directly 
as their specific gravities. So that to obtain the transpiration at 
constant pressure, it was only necessary to multiply the observed 
time of flow by the specific gravity of the solution. The time of 
flow of water at 18° C. was taken as standard. The ratio of the 
corrected time of flow of a solution to that of water gives the 
relative viscosity in terms of water as unity. Should the absolute 
viscosity be desired, it is only necessary to multiply this result by 
the absolute value of water. Relative values only have been 
calculated, as the object was to make a comparison of solutions. 
The temperature was regulated by a water-bath, and two ther- 





No. 5.] VISCOSITY OF SALT SOLUTIONS. 325 

mometers enabled one to note the temperature to tenths of 
a degree. Hagenbach's correction for velocity of transpiration 
was sufficiently small to neglect in all cases. 

The specific gravities of the solutions were determined by 
means of a calibrated Mohr's balance, which enabled one to take 
readings to the fourth decimal place. It was part of the original 
intention to make the solutions from weighed portions of the 
salts and of fixed molecular {e.g. double normal, normal, half 
normal, etc.) contents, but the discovery of a mistake in the 
weight of a crucible made it necessary to interpret in many cases 
the per cent of salt in solution from tables of percentages and 
specific gravities. Solutions of KjCOg, KOH, NaOH, and K3SO4 
were made from Kohlrausch's tables.^ Solutions of NajCOj, 
KHCOg. NaHCOg, KHSO4 Na3HP04, NaH^PO^, K3C3O4 and 
NaHC4H40g were made from carefully weighed quantities of the 
salts. Solutions of K8PO4, K3HPO4, KH3PO4 were kindly loaned 
by Herr Forch. All other solutions were made from Landolt and 
Bernstein's Tabellen {zte Anflage). The specific gravities of solu- 
tions of Na^COg check well with Kohlrausch's tables, but not so 
well with those of Landolt and Bernstein. The specific gravities 
of Na3HP04 diflfer also slightly from the latter tables and in solu- 
tions of K3C3O4 the diflference is quite large. However, specific 
gravities of K2C2O4 interpolated from Landolt and Bernstein's 
Tabellen give a viscosity curve of doubtful character. 

The time of flow was noted over considerable range of tempera- 
ture from which the time transpiration at 18° was graphically inter- 
polated. By repeated observation the error in time is reduced to 
about 0.3 seconds. In the following table of observations and 
results, tn denotes the gram-molecular contents ; s, the specific 
gravity; T^ the time; and % the calculated viscosities. In the 
rows containing neither T nor j, the values of m and 17 have 
been graphically interpolated. 

^ Kohlrausch : Leitfaden der practical Phyiik, 7^ Auflage. 



326 



B. E, MOORE. 



[Vol. III. 



Table I. 



Na,CO, 


NaHCO, 


m 


* 


T 


^ 


m 


* 


T 


1 


0.00 


0.9987 


197.0 


1.000 


0.00 


^smi 


194.5 


1.000 


0.25 


1.0250 


220.6 


1.120 


0.25 


1.0139 


205.5 


1.057 


0.5 


1.0517 


251.0 


1.274 


0.5 


1.0286 


218.0 


1.121 


1.0 


1.0980 


328.5 


1.667 


1.0 


1.0575 


245.0 


1.260 


2.0 


1.1880 


616.2 


3.128 






• 




K,CO, 


KHCOa 


0.00 


0.9987 


197.0 


1.000 


0.00 


0.9987 


194.5 


1.000 


0.25 


— 


— 


1.059 


0.25 


1.0146 


200.5 


1.031 


0.273 


1.0340 


210.0 


1.066 


0.495 


1.0298 


206.5 


1.062 


0.4788 


1.0577 


223.0 


1.132 


0.5 


— 


— 


1.065 


0.5 


— 


— 


1.138 


1.0 


1.0581 


218.0 


1.121 


0.9456 


1.1100 


258.0 


1.310 


1.98 


1.1149 


250.0 


1.285 


1.0 


— 


— 


1.341 


2.0 


— 


— 


1.290 


1.974 


1.2183 


381.0 


1.934 










2.0 


— 


— 


1950 











Table II. 



NaHS04 


NaOH 


m 


* 


T 


'J 


m 


s 


T 


1 


0.00 


0.9987 


194.5 


1.0000 


0.00 


0.9987 


194.5 


1.0000 


0.25 


1.0186 


206.0 


1.059 


0.25 


1.0099 


206.0 


1.059 


0.5 


1.0386 


214.0 


1.100 


0.5 


1.0212 


215.5 


1.108 


1.0 


1.0753 


245.0 


1.260 


1.0 


1.0425 


240.0 


1.234 


2.0 


1.1475 


315.5 


1.622 


2.0 


1.0843 


299.0 


1.537 


4.0 


1.2810 


559.0 


2.874 


4.0 


1.1551 


552.0 


2.837 


K,S04 


8.0 


1.2786 


1470.0 


7.557 


0.00 


0.9987 
1.0165 


194.5 
198.1 


1.000 
1.019 


KOH 


0.1195 


0.00 


0.9987 


194.5 


1.0000 


0.125 


— 


— 


— 


0.25 


— 


— 


1.025 


0.243 


1.0328 


20*.5 


1.051 


0456 


1.0212 


203.0 


1.044 


0.25 


— 


— 


1.052 


0.5 


— 


— 


1.051 


0.49 


1.0650 


214.0 


1.100 


0.92 


1.0433 


213.5 


1.098 


0.50 


— 


-^ 


1.106 


1.00 
1.82 


1.0864 


235.5 


1.110 




KH 


SO4 




1.211 










20 






1.237 


0.00 


0.9987 


194.5 


1.0000 


4.0 


1.1793 


307.0 


1.578 


0.5 


1.0439 


209.5 


1.075 


6.8 


1.2900 


452.0 


2.324 


1.0 


1.0866 


223.5 


1.149 










2.0 


1.1712 


263.0 


1.352 











No. SO 



VISCOSITY OF SALT SOLUTIONS. 



327 



Table III. 



0.00 

0.125 

0.25 

0.5 



0.00 

0.25 

0.5 

1.0 

2.0 



Na,HP04 



0.9987 
1.0190 
1.0366 
1.0741 



194.5 
211.3 
231.4 
277.5 



NaH,P04 



KH,P04 



0.00 


0.9987 


0.25 


1.0220 


0.5 


1.0442 


1.0 


1.0885 



194.5 
205.5 
223.0 
254.0 



H,P04 



0.9987 
1.0120 
1.0251 
1.0508 
1.1022 



194.5 
207.0 
222.3 
255.0 
338.3 



1.000 
1.086 
1.189 
1.427 



0.00 


0.9987 


194.5 


1.000 


0.25 


1.0184 


209.3 


1.076 


0.5005 


1.0391 


230.0 


1.182 


1.001 


1.0776 


274.0 


1.409 


2.002 


1.1677 


450.0 


2.313 



1.000 
1.057 
1.146 
1.306 



1.000 
1.064 
1.143 
1.311 
1.739 



0.00 

0.125 

0.14 

0.25 

0.276 

0.50 

0.54 



0.00 

0.125 

0.25 

0.5 

1.0 



0.00 

0.125 

0.25 

0.5 

1.0 

2.0 



N«tP04 



0.9987 
1.0222 
1.0440 
1.0860 



194.5 
214.9 
242.3 
307.2 



K,PO« 



0.9987 
1.0227 
l.(M71 
1.0933 
1.1805 



194.5 
208.5 
219.0 
252.5 
342.2 



K,HP04 



0.9987 
1.0167 
1.0343 
1.0700 
1.1383 
1.2633 



194.5 
202.0 
213.0 
234.0 
300.0 
449.0 



1.000 
1.098 
1.105 
1.220 
1.246 
1.504 
1.579 



1.000 
1.070 
1.126 
1.298 
1.759 



1.000 
1.039 
1.095 
1.206 
1.542 
2.309 



328 



B. E. MOORE, 
Table IV. 



[Vol. III. 





Na^C^H^O. 




NaKC4H«0« 


m 


s 


T 


I? 


m 


s 


T 


n 


0.00 


0.9987 


194.5 


1.000 


0.00 


0.9987 


1^.5 


1.000 


0.141 


1.0185 


209.0 


1.075 


0.20 


1.0273 


212.5 


1.092 


0.25 


— 


— 


1.148 


0.25 


— 


— 


1.112 


0.281 


1.0368 


226.0 


1.162 


0.40 


1.0547 


231.0 


1.188 


0.5 


— 


— 


U35 


0.50 


— 


— 


1.252 


0.562 


1.0730 


269.0 


1383 


0.789 


1.1087 


287.0 


1.476 


1.0 


— 


— 


1.823 


1.0 


— 


— 


1.679 


1.121 


1.1427 


395.0 


2.031 


1.656 


1.2112 


484.0 


2.488 


H,C4H40, 


K,C4H40, 


0.00 


0.9987 


194.5 


1.000 


0.00 


0.9987 


194.5 


1.000 


0.233 


1.013 


207.5 


1.067 


0.1815 


1.0267 


205.5 


1.057 


0.25 


— 


— 


— 


0.25 


— 


— 


1.080 


0.467 


1.0269 


221.5 


1.139 


0.363 


1.0525 


220.0 


1.131 


0.5 


— 


— 


1.160 


0.5 


— 


— 


1.195 


0.833 


1.0542 


256.0 


1316 


0.7345 


1.1036 


255.0 


1.342 


1.0 


— 


— 


1.412 


1.0 


— 


— 


1.489 


1.478 


— 


330.0 


1.6% 


1.48 


1.2072 


363.0 


1.866 


1.666 


1.1092 


365.0 


1.853 


1.5 


— 


— 


(1.883) 


C4H«04 


K,C,04 


0.00 


0.9987 


194.5 


1.000 


0.00 


0.9987 


194.5 


1.000 


0.242 


1.0076 


204.2 


1.050 


0.25 


1.0283 


204.0 


1.049 


0.25 


— 


— 


1.052 


0.5 


1.0571 


214.5 


1.103 


0.483 


1.0166 


215.0 


1.105 


1.0 


1.1121 


239.5 


1.232 


0.5 


— 


— 


(1.110) 


1.5 


1.1663 


270.2 


1.389 


H,C,04 


NaHC4H40, 


0.00 


0.9987 


194.5 


1.000 


0.00 


0.9987 


194.5 


1.000 


0.25 


— 


— 


1.045 


0.147 


1.0121 


205.5 


1.056 


0326 


1.0146 


206.0 


1.059 


0.25 


— 


— 


1.094 


0.5 


— 


— 


1.072 


0.294 


1.0256 


217.0 


1.116 


0.665 


1.0300 


217.5 


1.118 


0.441 


1.0386 


228.5 


1.175 


0.848 


1.0370 


224.5 


1.154 


0.5 


— 


— 


(1.198) 


1.0 




— 


(1.199) 











No. 5.] 



l^ISCOSITY OF SALT SOLUTIONS. 



329 



Curves, 



The curves (Figs. 2, 3, 4, and 5) correspond to Tables I., II., 
III., and IV. of data respectively. The curve for H2SO4 (Fig. 3) 
IS drawn from data by Grotian and is given in order to show 




0J25 0^ 



2.m. 



Fig. 2. 



the effect of displacing an atom of hydrogen in sulphuric acid. 
Curves for KjSO^ and KH2PO4 are not shown, as they nearly 
coincide with 2 KOH and H3PO4 respectively. 



Discussion of Results, 

The viscosity of sodium salts is invariably greater than that of 
the potassium salts, and both are greater than that of the corre- 
sponding acids. The effect of the hypothetical displacement of the 
first atom of hydrogen by a given base is generally not so marked 
as the second displacement by the same base. NaHC4H40g is 
an exception. The effect of the second atom of Na and K in the 
phosphoric acid group (see Fig. 4) is very marked. Whether 



B. E. MOORE. 



[>'ot- l:. 



- zK positioo of the hydrogen atom in tisc 
i^ -y m^'ps easier to raise than to answer 




^ *^ the entrance of the second atom 
^, TJd marked acid to basic character, 

— ■ which also suggests that the first 

j change in HgPO^ (=H-PO^ 
— OH -OH) took place in the 
hydroxide radical, the second in 
the acid radical, and the third 
, again in the hydroxide radical 
The ciir\'e for KH^^PO^ lies too 
near H^PO^ to be credited exten- 
sively, More confidence is to be 
placed in the results for H^PO^ 
than KHpjl^O^, as Slotte's obsen'a- 
tipns for H3FO1 fall practically 
upon the curve here given for 
that acid. Again the neutral phos- 
phate Na^PO^ breaks up \%iry 
easily in the presence of H,^0 into 
V^HP^i and NaOH* which would make 
, . Hi'^ N'vt^PO^ with some hesitation. So 
jif rather diilieult to draw conclusions 



' ^ 



No. sO 



VISCOSITY OF SALT SOLUTIONS, 



331 



concerning changes in the radicals from the viscosities. So much 
difficulty does not present itself with the organic compounds. 
The addition of (CHj)j to CjHjO^ (=COOH-COOH) (see Fig. 
5, curves), giving COOH — CHj— CH3-COOH, increases the vis- 



2.4 

2^ 
2J2 
2J 

2i) 

1 8 














1 


















/ 
















•? 


















/ 


f 


1 












/ 


/ 




07 












/, 


/ 


c 














f/ 


/ 


/ 






1.7 
1.6 










/, 


V) 


/ 














/ 


/ 








1,5 






/ 


y. 


// 


/ 








1 9 






/ 


r/ 


V 












/ 


^ 


/ 


r,.^ 














^ 




^ 














^ 


X ^ 
^ 


^^ 
















g^ 


.^ 















OJ25 



OJO 



0.75 



Uf. 



LOO 



1.75 



2.m. 



Fig. 5. 



cosity over three times as much as the substitution of potassium for 
hydrogen in (COOH)^. The farther substitution of two hydroxyl 
radicals for two atoms of H in (CHj)^ gives also a marked 
increase, and also greater than the effect of potassium substi- 



332 B. E. MOORE. [Vol. III. 

tuted in HJZfi^. Again, a comparison of curves for HjZ^O^ 
and K2C2O4 with the curves for C^fi^ and ¥^C^fi^ shows 
a marked difference in the effects of potassium on the two salts. 
In the first pair of solutions potassium entered the carboxyl, 
giving COOK — COOK, while in the second group the element 
potassium has worked upon the hydroxide, yielding COOH — 
CHOK-CHOK-COOH. 

Arrhenius Exponential Formula, 

When Arrhenius announced the exponential formula, 1; = A', 
he only tested it to 1.5 gram-molecule solutions. Wagner, who 
validified the law for so many solutions, did not go above the 
normal solution. So that it was thought well to see if such a 
formula would hold for more concentrated solutions. To test 
the validity of the law for very dilute solutions, where the law is 
most serviceable, it would be necessary to limit oneself to very 
narrow range of and small changes in temperature. It would 
be imperative to use a bulb A (Fig. i) of smaller volume and a 
capillary d (Fig. i) of very small bore. The latter invariably 
clogs and prevents accurate results. Even such precautions 
would, at the best, only give very small differences, and failure 
to observe these precautions could not account for the variations 
from the logarithmic law observed in these experiments. The 
logarithmic curve, which would represent the viscosities of the 
more dilute solutions of NaOH, e.g. would, if extended to 4 
and 8 molecule solutions, give values 36 per cent and 75 per 
cent too small respectively. No other solutions show so great 
a divergence. Yet in the double normal solutions the agreement 
is rarely better than 3 per cent to 5 per cent. 

Conductivities and Viscosities. 

The values for A in the following table have been taken direct 
from the tables of observations on % except in the phosphoric 
acid group, where A is reckoned from the equation 1; = y4' and 
;r = w = J. The conductivities K are those of the normal solu- 
tions except when otherwise noted. Only those salts are given 



No. 5.] 



VISCOSITY OF SALT SOLUTIONS, 



333 



for which the conductivities could be learaed. They are divided 
in four groups corresponding to Tables I., II., III., and IV. of 
Viscosities respectively. 

Table V. 



Substances. 



xo>. AT 



iNaaCOa . 
i NallCOs 
iKjCOs . 
iKHCOs . 

NaOH . 

KOH . 
iNa2S04 . 
iNaHS04 
JK2SO4 . 
iKHS04 . 

iNa8P04 . 
}NaaHP04 
JNaH2P04 
iHaPO* . 

iQHeOe . 

iQHA • 
iCjHjO* . 
iKjCjO* . 



1.274 


42.7 


1.121 


37.9 


1.138 


66.2 


1.065 


61.3 


1.234 


149.0 


1.11 


171.8 


— 


47.5 


1.10 


— 


1.106 


67.2 


1.075 


173.6 


1.305 


97.5] 


1.260 


79.6 


1.105 


69.8 J 


1.08 


20.0 


1.160 


46.04 


1.110 


16.03 


1.070 


26.7 


1.100 


68.8 



^2 nonnal solution. 



i^^normaL 



That, while the viscosities in general decrease, the conductivities 
of a series of salts increase, as noted in the early part of this article, 
cannot be concluded at all from these salts. This action is notice- 
able, however, in passing from the sodium salt to the potassium in 
the first and second group, but when one passes either from sodium 
carbonate or from potassium carbonate to the acid salts, viscosities 
and conductivities increase and decrease together. The sulphates 
behave in the same manner. In the third or phosphate group, in 
passing from Na3P04 to H3PO4, both viscosities and conductivities 
decrease. In the fourth or organic group, there is an irregularity 
in the conductivity column. This list, though small, is enough to 
show that there is little hope for a successful comparison of vis- 
cosity and conductivity, without an extended series of observations. 



B. E, MOORE. 



[Vol. ii 



jtc solutions in which the mcrease in the 
1,1 will be largely due to the ions, as it is 
^ca- aione with which we have to deal in 




Sjnclusions, 

decreases quite TBpidly with rise in 
of this decrease is very different 
and for different salt solutions,^ 
«os» though doubtless existing, are 
iswivincing. 
Mcottal formula or law, though affording 
^smporison of viscosities of dilute^ even 
tf hold good for the more concentrated 




itions must be made upon the relation 

, perhaps even some new method of 

the two subjects are placed in their 




55, p* I4S, have pointed out that tempera- 
«tf^^#d for cc^mparison of i-iscosity. Ttesc experi- 
^?ti the ajticle by Tlnjrpe and Roiiger^ appeared, 
-^mm ££A3^h tu make such a comparison. 



No. 5.] THEORY OF OSCILLATING CURRENTS. 335 



NOTES ON THE THEORY OF OSCILLATING 
CURRENTS. 

By Charles Proteus Steinmetz. 
§ I. Introduction, 

THE object of the following article is to present a short out- 
line sketch of a modification of the method of complex 
imaginary quantities, applied to oscillating currents. Such oscil- 
lating currents have frequently been considered as ordinary alter- 
nating currents of very high frequency, and treated as such, 
while the essential differences between alternating and oscillating 
currents have been overlooked. An electric current varying 
periodically between constant maximum and minimum values, 
that is, in equal time intervals repeating the same values, is called 
an alternating current if the arithmetic mean value equals zero ; 
and is called a pulsating current if the arithmetic mean value 
differs from zero. Alternating currents have found very exten- 
sive application for light and power. Pulsating currents are the 
currents given by open coil arc-light machines, or by the super- 
position of alternating and continuous currents, etc. 

Assuming the wave as a sine curve, or replacing it by the 
equivalent sine wave, the alternating current is characterized by 
the period or the time of one complete cyclic change, and the 
amplitude or the maximum value of the current. Period and 
amplitude are constant in the alternating current. 

A very important class are the currents of constant period, but 
geometrically varying amplitude, that is, currents in which the 
amplitude of each following wave bears to that of the preceding 
wave a constant ratio. Such currents consist of a series of waves 
of constant length, decreasing in amplitude, that is in strength, 
in constant proportion. They are called oscillating currents in 



r 



336 



C P, STEINMETZ. 



[Vol. III. 



analogy with mechanical oscillations, for instance of the pendulum, 
in which the amplitude of the vibration decreases in constant 
proportion. 

Since the amplitude of the oscillating current varies, constantly 
decreasing, the oscillating current differs from the alternating 
current in so far that it starts at a definite time, and gradually 
dies out, reaching zero value theoretically at infinite time, practi- 
cally in a very short time, short even in comparison with the time 
of one alternating half-wave. Characteristic constants of the 

oscillating current are the period T or frequency N^=^ the 

first amplitude and the ratio of any two successive amplitudes, 
the latter being called the decrement of the wave. The oscillat- 
ing current will thus be represented by the product of a periodic 





^ 


■«»,, 












































> 




'-■ 


.^ 










































\ 






■^'" 


•-.. 


•^, 




































\ 










/ 


*s 


c* 


— 


.^_ 



























( 


, \ 




180 




/ 




960 


N 




540 




y 


;> 


iss 


s 


— 


— 


900 


.-. 


S** 


m 














/ 








\ 




.^ 


/ 








^ 




— 


■^ 




— 








V 




i 


i 






^, 




^ 






























\ 




/ 


.-- 








































^^' 


^ 
















O 


toll 


atlrJ 


(E 


M.I 


• 














x' 


.■^ 




















e 


.5 




o< 











































= 


\± 


c8 


2* 















Fig. 1. 

function, and a function decreasing in geometric proportion with 
the time. The latter is the exponential function A^'^. 
Thus, the general expression of the oscillating current is 



smce 



C=A^-^ cos (2 wNt-A), 
A^'''=A^A-^=c€'*'. 



Where €= basis of natural logarithms, the current may be 
expressed 

C= c€'^ cos (2 IT N't — w) = r€"** cos (<^ — «) , 

where <^ = 27rA7; that is, the period is represented by a complete 
revolution. 



No. SO 



THEORY OF OSULLATmG CURREATTS, 



337 



In the same way, an oscillating electromotive force will be 

represented by 

j?=^€ •♦cos(<^— w). 

Such an oscillating electromotive force for the values 
^=5, a=.i435 or c-*'*^^, w=o, 
is represented in rectangular co-ordinates in Fig. i, and in polar 
co-ordinates in Fig. 2. As seen from Fig. i, the oscillating wave 
in rectangular co-ordinates 
osculates the two expo- 
nential curves 

In polar co-ordinates, the 
oscillating wave is repre- 
sented in Fig. 2 by a spiral 
curve passing the zero 
point twice per period, 
and osculating the expo- 
nential spiral 

The latter is called the envelope of the oscillating wave, and is 
shown separately, with the same constants as Figs, i and 2, in 








Rg. 3. Fig. 4. 

Fig, 3. Its characteristic feature is : The angle, which any con- 
centric circle makes with the curve ^=^e-^, is 

tan a=-^= ^a, 




338 C. p. STEINMETZ. [Vol. lU. 

which is, therefore, constant, or in other words : " The envelope of 
the oscillating current is the loxodromic spiral, which is charac- 
terized by a constant angle of intersection with all concentric 
circles, or all radii vectores." The oscillating current wave is the 
product of the sine wave and the loxodromic spiral 
In Fig. 4 let^=^€-^ represent the loxodromic spiral ; 

let z-=e cos (^— ^j) represent the sine wave ; 

and let E^ee-^ cos (^— «) represent the oscillating wave. 

dE 



We have then tan fi= 



Ed^ 

— sin (^— «)— tf cos (^—A) 



cos(^— «) 
= — }tan(^— w)+a} ; 
that is, while the slope of the sine wave, z^e cos (^— A), is repre- 
sented by tan7= - tan (<^-«), 

the slope of the loxodromic spiral yz=zf€-^ is 

tan a = — tf = constant 
That of the oscillating wave E^ee-^ cos (^— «) is 

tan)8= — {tan (<^— i)+tf{ 

Hence, it is increased over that of the alternating sine wave by 
the constant a. The ratio of the amplitudes of two consequent 

perioils is /7 . 

Eo 

A is called the numerical decrement of the oscillating wave, a 
the exponential decrement of the oscillating wave, a the angular 
decrement of the oscillating wave. The oscillating wave can be 
represented by the equation 

^=^€-4t"* cos (<^- w). 

In the instance represented by Figs, i and 2, we have, -4 =.4, 

.^ = .1435, « = 8.2^ 



No. 5.3 THEORY OF OSCILLAT/N'G CC/RRENTS. 339 

§ 2. Impedance and Admittance, 

In complex imaginary quantities, the alternating wave 

z—ezo^i^—Si) 

is represented by the symbol 

F= e (cos A +y sin 6) = ^j ^/Vj. 

By an extension of the meaning of this symbolic expression, 

the oscillating wave -£'=^e-"*cos(^— fi) can be expressed by the 

symbol 

E^e (cos A+y sin Si) deca= (c^:^je^ dec a, 

where ^=tan a is the exponential decrement, a the angular decre- 
ment, c"*** the numerical decrement. 

Inductance. 

Let r=3 resistance, Z= inductance, and s^2'irNL^ reactance. 
In a circuit excited by the oscillating current, 

C= C€-^ cos (^ — w) = ^ (cos £ +y sin &) dec a = (^j +y<^2) dec a, 
where c-^^c cos S, ^2=^ sin oi, a^ tan a. 

We have then. 
The electromotive force consumed by the resistance r of the 

circuit 

J5',=rCdec«. 

The electromotive force consumed by the inductance L of the 

circuit, 

z? T dC ^ jkTr dC dC 
at aq> a<f> 

Hence J?,= — ^^€-**[sin(^— 5)4-«cos(^— &){ 

'^'^^"** sin (<^ -«+«). 



cos a 
Thus, in symbolic expression, 



E^ss ££-.{^sin («—«)+/ cos («—«){ dec« 

cos a 



= — sc(a 47) (cos & +j sin &) dec a ; 
that is, ^,= —sC{a +j) dec a. 



340 C. p. STEINMETZ, [Vol. III. 

Hence the apparent reactance of the oscillating current circuit 
is, in symbolic expression, 

5"=x(tf+/)dcc«. 

Hence it contains an energy component ox, and the impedance 

is 

(7= (r— S) dec a= {r— ^(^ +y){dec a= (r—as^js) dec a. 

Capacity. 

Let r= resistance, Ar= capacity, and k^ — ^-- = cacpaiCiXy react- 

ance. In a circuit excited by the oscillating current C, the 
electromotive force consumed by the capacity K is 

or, by substitution, 

Ej, = k\ ce^ cos (^ — &)^/<^ 






fc^^Jsin (^-- «) — a cos (^— «) } 
sin (^— «— a) ; 



(i +^ cos a 
hence, in symbolic expression, 

-^4= ST 1 — sin (£+«)+/ cos (w-f-a) [dec a 

(i+^^cosa( ) 

s= ( — rt +7 )(cos £ +y sin 6) dec a ; 

I +^ 

hence, -£"»=— —i(-^+y)Cdec a, 

I -ra^ 

that is, the apparent capacity reactance of the oscillating circuit 
is, in symbolic expression, 

Ar=-^(-^+y)dec«. 

I 'tOT 

We have then : 

In an oscillating current circuit of resistance r, inductive react- 



No. sO THEORY OF OSCILLATING CURRENTS. 341 

ance s, and capacity reactance k, with an exponential decrement a, 
the apparent impedance, in symbolic expression, is : 

U= {r-j(«+y)+-p:^(-«+y)}dec«, 
and, absolute, 



Let C= ^c-^ cos (^ — 5) = current. 

Then, from the preceding discussion, the electromotive force con- 
sumed by resistance r, inductive reactance Sy and capacity react- 
ance ky is 

^=^.r^ jcos(^-fi)[r-^-^>&]-sin (^-5)[^^--i-5j} 
^cujr'^ cos(^— 5+S), 

where tan h = 



r^as ^k 



i-f^-s 



substituting fi+8 for 5, and e^cu^ we have 

E^ee^ cos (^—5), 

C=3— c-^ cos (^ — 5 — S) 

.(cos 8 ,. ^. sin 8 . ,. ^.) 

«^€-^j-^co8(<^-a>)+-^sm(<^-<»)J; 



342 



C p. STEINMETZ, 



[Vol. III. 



hence in complex quantities, 

E^e (cos 5 +y sin 5) dec a, 

C=£J£2i«+y5in«jdec«; 
or, substituting, 



C=£. 



r^as- 



i+cfi 



{'-Th)'<—7T-.*)' 



i+^a 



.dec «. 



Thus in complex quantities, for oscillating currents, we have: 
conductance, 

r—as ^k 



/>= 



i+a^ 



i'-ThH—Thr 



susceptance, 



s — 



Jt 



<r=- 



1+^2 



\ i+aV ^\ i+a2 J 

admittance, in absolute values, 



v—-v^+a^= 



<'-Ty)'<--^J 



in s)niibolic expression. 

Since the impedance is 
we have 



^« 



6/ «• «. *' ^ 






No. 5.] THEORY OF OSCILLATING CURRENTS. 343 

that is, the same relations as in the complex quantities in alter- 
nating current circuits, except that in the present case all the 
constants r^ s^ u^ p, <r, v, depend upon the decrement a. 

§ 3. Circuits of Zero Impedance. 

In an oscillating current circuit of decrement a^ of resistance r, 
inductive resistance j, and capacity reactance k, the impedance 
was represented in symbolic expression by 

U=r.-js,={r-as-^k)-j{s- ^, 
or numerically by 



Thus the inductive reactance s, as well as the capacity react- 
ance >fc, do not represent wattless electromotive forces as in an 
alternating current circuit, but introduce energy components of 
negative sign 

that means, 

"In an oscillating current circuit, the counter electromotive 
force of self-induction is not in quadrature behind the current, but 
lags less than 90** or a quarter period, and the charging current of 
a condenser is less than 90®, or a quarter period ahead of the 
impressed electromotive force." 

In consequence of the existence of negative energy comix)nents 
of reactance in an oscillating current circuit, a phenomenon can 
exist which has no analogy in an alternating current circuit, that 
is, under certain conditions, the total impedance of the oscillating 
current circuit can equal zero : 

In this case we have 

a , k 
r—as r— 5*=o; s 7-11=0, 




342 



C P, STEINMETZ, 



[Vol. III. 



hence in complex quantities, 

E^e (cos 5 +y sin 5) dec a, 

•- cicosS , .sin 8) , 
C^EX Vj >dec a : 



or, substituting, 






[('-i^JH— ifp^J 



S — ' 



1+0:2 



1'-T^;H-«-7f^*)l 



.dec a. 



Thus in complex quantities, for oscillating currents, we have: 
conductance, 



r—as- 



1+^2 



k 



susceptance, 



\-ThH—T^.*r 



s — 



<r=- 



1+^2 



admittance, in absolute values. 



in s)niibolic expression. 
Since the impedance is 



we have 



^ I I r. X. 

6/ «. w/ «/ 



Nos] THEORY OF OSCILLATING CURRENTS, 343 

that is, the same relations as in the complex quantities in alter- 
nating current circuits, except that in the present case all the 
constants r^ s^ u^ p, <r, v, depend upon the decrement a. 

% 3. Circuits of Zero Impedance. 

In an oscillating current circuit of decrement a^ of resistance r, 
inductive resistance s^ and capacity reactance k^ the impedance 
was represented in symbolic expression by 

U=r.-js,^{r-as-^k)-j{s- -±^, 
or numerically by 



Thus the inductive reactance 5, as well as the capacity react- 
ance k, do not represent wattless electromotive forces as in an 
alternating current circuit, but introduce energy components of 

native sign 

a , 

that means, 

"In an oscillating current circuit, the counter electromotive 
*orce of self-induction is not in quadrature behind the current, but 
*^^ 'ess than 90** or a quarter period, and the charging current of 
^ condenser is less than 90°, or a quarter period ahead of the 
^n^Pressed electromotive force." 

*n consequence of the existence of negative energ)- c<*n;pc,r:*r,t% 

^^ reactance in an oscillating current ciroiit, a phenorr^es'^a Ci:i 

^'^'^^ which has no analogy in an alternating current dri -X thil 

^» under certain conditions, the total impedance of th : *^K;rtarizg 

current circuit can equal zero : 

In this case we faame 

m . k 



344 ^- ^- STEIXMETZ. [Vol. III. 

substituting in this equation 



2irNK' 
and expanding, we have 



tf = 



J4X 






2L^f^K 2al 

That is, 

'' If in an oscillating current circuit, the decrement a- 



J4AZ 



and the frequency N= — ^, the total impedance of the circuit 
4iraL 

is zero ; that is, the oscillating current, when started once, will con- 
tinue without external energy being impressed upon the circuit." 

The physical meaning of this is : " If upon an electric circuit a 
certain amount of energy is impressed and then the circuit left to 
itself, the current in the circuit will become oscillating, and the 

oscillations assume the frequency N^ -, and the decrement 

4'rraL 



That is, the oscillating currents are the phenomena by which 
an electric circuit of disturbed equilibrium returns to equilibrium. 

This feature shows the origin of the oscillating currents, and 
the means to produce such currents by distiu*bing the equilibrium 
of the electric circuit, for instance by the discharge of a condenser, 
by make and break of the circuit, by sudden electrostatic charge, 
as lightning, etc. Obviously, the most important oscillating cur- 
rents are those flowing in a circuit of zero impedance, representing 
oscillating discharges of the circuit. Lightning strokes usually 
belong to this class. 

§ 4. Oscillating Discharges, 
The condition of an oscillating discharge is U^o\ that is : 



Ul 2aL 2L^i^K 

Vfe-' 



ass 



No. 5.] THEORY OF OSCILLATING CURRENTS, 345 

If r=o, that is, in a circuit without resistance, we have as*o, 

N^ ^ ; that is, the currents are alternating with no decre- 

2iryjLK 

ment, and the frequency is that of resonance. 

If 4t?— i<o» that is, ^>2\^, a and N become imaginary; 
that is, the discharge ceases to be oscillatory. An electrical dis- 

charge^sumes an oscillating nature only, if ^<2\/— . In the case 

VL 
— we have tf=oc, iV=o; that is, the current dies out with- 
K 

out oscillation. 

From the foregoing we have seen that oscillating discharges, — 
as (or instance the phenomena taking place if a condenser charged 
to a given potential is discharged through a given circuit, or if 
lightning strikes the line circuit, — is defined by the equation : 
£/=odec^. 

Since C = (f^ +jc^ dec a, Er = Cr dec a, 

h 

E^='-'sC{a+j) dec a, ^j= ^C(— ^1+/) deco, 

I -{-or 

^^have ^ ^^ a a— ^ 

hence, by substitution, 

E^=:sC{—a+j) dec«. 

The two constants, c^ and c^ of the discharge, are determined by 
the initial conditions, that is, the electromotive force and the 
current at the time /=o. 

Let a condenser of capacity K be discharged through a circuit 
of resistance r and inductance L. Let ^= electromotive force at 
the condenser in the moment of closing the circuit, that is, at the 
time /sQ or ^»o. At this moment the current is zero, that is. 

Since £lk=jC(--tf+7')dec«=^ at ^=0, 

we have sc^i+al^^e or c^^ — " 



i 



346 C. P. STE/NMETZ. [Vol. III. 

Substituting this, we have, 

C =/ — dec a, Er=^je — ^ dec a, 

E.^—J= (i -» dec «, ^,= — -4= (I +» dec «, 

the equations of the oscillating discharge of a condenser of initial 
voltage e. 

Since s=2irNLy 

I 



«= 






we have s= — =-\%-d-— i : 

hence, by substitution, 



C=jeyjydeca, E'=jerySdeca, 

the final equations of the oscillating discharge, in symbolic 
expression. 

§ 5. Numerical Examples. 

To get an estimate of the numerical values of the constants of osdUating 
discharges, some cases may be investigated. 

A. Very High Frequency. 

A short, straight conductor may be terminated by two balls. The balls repre- 
sent the capacity, while the conductor represents the resistance and inductance. 
Without entering into the exact calculation, let the resistance of the conductor 




No. 5.] THEORY OF OSCILLATING CURRENTS. 347 

r = .0001 ohms ; the inductance of the conductor L = .00025 millihenry ; the 
capacity of the two balls A'sr lO"' microfarads. We have then 

ass 10-^; angle a = 5.7 x lo-*; N=: 32 x 10*; 

that is, 320,000,000 cycles per second. 

The amplitude is reduced to j^ after the time f^p or angle ^q, where 

c--*o=.oi; ^j, = 27rA7o; 
hence, ^0 = 4.6 x lo' ; /<, = -023 ; 

that is, after .023 second the oscillation has practically died out; that is, de- 
creased to y^ of its amplitude, after making 7400,000 complete oscillations. 

The equations of the oscillating discharge are in this case, at ^ = 10,000 volts 
initial charge, 

C = 2oy dec a; Er=^ .002 j dec eu 
Eg =(10,000 — .001/) dec a; Ek = — (10,000 + .00 1/) decou 

As seen, for a moment 20 amperes flow at a potential of 10,000 volts, repre- 
senting an instantaneous flow of about 100 K.W. 

To make the discharge non-oscillatory, the resistance would have to be 

r>2A/=->iooo ohms ; that is, more than 10,000,000 times as much as assumed. 

That b, a wet string, or similar conductor, will not allow electrical oscillation. 

B, Underground Circuit of four Miles in Length, of two Lead- 
covered Cables consisting of Wire No. 00, B. & S. 

r = 3.3 ohms ; Z, = 7.5 microhenrys ; A'= 1.2 microfarads ; 
hence, a = .021 ; N= 1670 ; t^KJ^ = .021 ; 

that is, in .021 seconds, or after 35 cycles, the oscillation has died out to 1^ of 

its initial value. At ^ = 2000 volts initial charge, the equations of phenomenon 

will be 

C= 25.37 deca; Er = 83.5/deca; 

Et = (2000 - 427) dec a £"» = — (2000 + 42/) dec a. 

The phenomenon will become non-oscillatory ; that is, 

A^=o; tf = oo; for r= 158 ohms. 

that is, in such cables electric oscillations can take place at comparatively 
moderate frequency, and of considerable duration. 

C Transatlantic Cable. 

Assuming approximately, r=:4o,ooo ohms, £=30 h., A'=i30o microfarads; 
we then have r<300, the condition under which electrical oscillations can take 
place. 



348 C. p. STEINMETZ, [Vol. III. 

If the resbtance were ^ the value it is in reality, that is, if we had 
r = 200 ohms, we could have a = 0.88, N = 0.6, and in this case, at ^ = 100 volts 
initial charge, the equations of the phenomenon would be, C= 0.658/ dec a, 
Er= I3i.6y deca, E, = (75 - 66/) deca, £"» = - (75 + 66/) deca ; that is, in a 
transatlantic cable electrical oscillations cannot take place, due to its high resist- 
ance. If, however, the resistance were low enough to permit electrical oscilla- 
tions, that is, less than yjj of what it is in reality, the oscillations would take 
place extremely slowly, each complete oscillation occupying more than one 
second. 

In reality, due to the capacity not being centralized in a condenser, but dis- 
tributed over the whole circuit, the phenomenon is more complex, and has to be 
investigated on the lines of circuits containing distributed capacity. 

We see, however, from these instances the enormous range of frequencies, at 
which electrical oscillations take place, from frequencies of hundred millions of 
cycles per second to a frequency of more than a second per cycle. 

§ 6. Oscillating Current Transformer 

As an instance of the sq^plication of the symbolic method of 
analyzing the phenomena caused by oscillating currents, the trans- 
formation of such currents may be investigated If an oscillating 
current is produced in a circuit including the primary of a trans- 
former, oscillating currents will also flow in the secondary of this 
transformer. In a transformer let the ratio of secondary to pri- 
mary turns be /. Let the secondary be closed by a circuit of total 
resistance, ri=ri'+r/', where r/= external, r/'= internal, resist- 
ance. The total inductance Ly^L{-\'L{\ where Zi'= external, 
Zi"= internal inductance, total capacity, K^, Then the total 
admittance of the secondary circuit is 

Ti= (Pi+>i) dec«= -J a ^\ I F^' 

where Sx^2irNL^= inductive reactance: >fe,= — ^7777= capacity 

2irNK 

reactance. Let r^^ effective hysteretic resistance, L^^ induct- 
ance; hence, ^0= 2 9ryVZQ= reactance ; hence, 

To=Po+>o= . Jv V, = admittance 

of the primary exciting circuit of the transformer; that is, the 
admittance of the primary circuit at open secondary circuit. 



No. 5.] THEORY OF OSCILLATING CURRENTS. 349 

As discussed elsewhere, a transformer can be considered as con- 
sisting of the secondary circuit supplied by the impressed electro- 
motive force over leads, whose impedance is equal to the sum of 
primary and secondary transformer impedance, and which are 
shunted by the exciting circuit, outside of the secondary, but inside 
of the primary impedance. 

Let r=: resistance ; L = inductance ; A'= capacity ; hence, 

s^2irNL= inductive reactance, 

>t= — TF7?= capacity reactance of the total primary circuit, in- 
2'n'NK 

eluding the primary coil of the transformer, li E^^E^ Atza 
denotes the electromotive force induced in the secondary of the 
transformer by the mutual magnetic flux ; that is, by the oscillat- 
ing magnetism interlinked with the primary and secondary coil 
we have Ci=i?iTideca= secondary current. 

Hence, C/ =/, C^ dec «=/, ET^ dec a^ primary load current, or 
component of primary current corresponding to secondary current. 

Also, Cq=— ^/Tq dec a =s primary exciting current; hence, the 
total primary current is 

C=C/ + Co=^{To+/*ri} dec«. 

E ' 
E = — ^dec «= induced primary electromotive force. Hence the 

total primary electromotive force is 

^= (£' + ceo dec «= ^ { I + i/To+/«i/Ti}dec a. 

In an oscillating discharge the total primary electromotive force 
E^o ; that is, 

or, the substitution 



(— rf^*)-4-i^) 



1+ , > . 

(^)-<Wo)-^-fo 



('•■-'"■-Tf^*')-^"-!^) 



350 C. p. STEINMETZ. [Vol. III. 

Substituting in this equation, s=2irNKy ^= — -— , etc., we get 

a complex imaginary equation with the two constants a and N. 
Separating this equation in the real and the imaginary parts, we 
derive two equations, from which the two constants a and N of 
the discharge are calculated. 

If the exciting current of the transformer is negligible ; that is, 
if Tq=o, the equation becomes essentially simplified : 

1 ■I.J.' V !+»* ) \ l+W „ . 

(^.-«.-jf^*.)+/'('-— rf^*)=o; 

or, combined : 

(rj - 2 tf ^i) +/2 (f - 2 tfj) = o, 

ri+/»r=2tf(ji+/j), 

k^+fk^{i+c?){s^+fs). 

Substituting for ^i, s^ k^, ky we have 

I 



that is. 






^fL) 



+fK) 



£=:^{i-f./2j/Ti}deca, 

C^pE^t^ dec a, 
Ci=^i'Tideca, 

the equations of the oscillating current transformer, with E^ as 
parameter. 

December, 1895. 



No, s] ALTERNATING CURRENT PHENOMENA. 35 1 



AN EXPERIMENTAL STUDY OF INDUCTION PHE- 
NOMENA IN ALTERNATING CURRENT CIRCUITS. 

By F. E. Milus. 
I. Circuits containing Resistance and Self-induction. 

A DISCUSSION of the current curve produced upon closing a 
circuit containing an harmonic electromotive force, resist- 



ance, and self-induction leads to the well-known equation : 

r^Z-tan-^^Vr^r-f, (i) 



E 
g= sin ( 



in which 

i is the value of the current at any instant, 

E is the maximum value of the electromotive force, 

R is the Ohmic resistance of the circuit, 

L is the self-induction of the circuit, 

CD is the angular velocity, 

/ is the time measured from the instant of closing the circuit, 

r is a constant of integration, 

e is the Napierian base. 

Writers have generally neglected the exponential term in this 
equation, since as / increases, the effect of that term upon the 
current rapidly diminishes, and usually becomes inappreciable 
after the small part of one second. Neglecting this term is 
equivalent to assuming that the current at once reaches its 
permanent condition. It is with the curves as modified by this 
term that the present work deals. If an open circuit be suddenly 
closed, i and / both being zero at the instant of closing, c in the 
above equation is determined by Bedell and Crehore to be 

r= ^ sinffi>/,-tan-^^\ (2) 



35^ ^' ^' MILUS, [Vol- III. 

U being time at which the circuit is closed. For — 

they write /, which represents the maximum periodic value of / ; 



for 



and for 



in f «/— tan"*— ^ j they write ^ sin -^ ; 
in ( «/|— tan"*--^ J they write sin -^j. 



At the instant of closing the circuit V^ss^^i, whence, by substi- 
tution, 

iss/sin-^— /sin-^isso; (3) 

that is, the initial value of the exponential term is equal and oppo- 
site to the value which the current ultimately has when in the 
same phase as that in which the circuit was closed. The greatest 
value of this induced or exponential current will occur when 
sin '^= I, or when the phase angle at closing the circuit is 90®. 
The exponential term would alone give a current curve of the 
form shown in Fig. i, the values being measured from the hori- 




Fig. 1. 



zontal axis downward to the curve. This curve compounded with 
the uniform harmonic current curve represented by the first term 
of the second member of equation (i), gives a resultant current 
curve of the general form of c in Fig. 2. 

As this short-lived induced current is always to a greater or less 
extent present whenever the electromotive force in a circuit is 
suddenly changed or the load varied, it seemed a matter of impor- 
tance as well as of interest to verify experimentally the above con- 
clusions. This induced current becomes an important factor in 

1 Alternating Currents, Bedell and Crchore, p. 55 (ist cd.). 



No. 50 



ALTERNATING CURRENT PHENOMENA, 



353 



alternate current working on circuits of large self-induction where 
the load is subject to great and sudden variation. 

The study of small vibrating needles described in the Physical 
Review, Vol. III., p. 49, indicated that they may be relied upon to 
record the current from the instant of closing the circuit. 

The experiments here described were made with the needle 
making 3580 double vibrations per second, mounted as shown in 
Figs. I and 2 of the above article. The coil surrounding the 
needle had 480 turns, carrying 2.35 amperes; and the magnetic 
field was produced by an electromagnet with two coils, each having 
970 turns and carrying about 10 amperes. The alternating current 




Fig. 2. 



experimented upon was produced by a small 50-volt lo-ampere 
Westinghouse alternator having a smooth armature. Curve II, 
Fig. 12, in Physical Review, Vol. III., p. 56, is taken from this 
alternator when there is no self-induction in the circuit. The 
resistance of the armature of the alternator was about 0.17 ohms. 
The entire resistance in the circuit for the curves which follow 
was 5. 1 ohms and the self-induction was 0.0322 henrys. 

We have seen that if the current phase is zero when the circuit 
is closed there will be no induced current, and that the maximum 
induction is obtained if the circuit is closed when the phase angle 
is 90°. It was consequently desirable to close the circuit in the 



354 



F, E, MILUS. 



[Vol. III. 



latter phase. To accomplish this, a plank 2\ inches thick was 
fitted to the top of the alternator, as indicated in Fig. 3. Through 
this plank holes are bored to admit the electromagnet SN, the 




Fig. 3. 

ends of the magnet being flush with the front surface of the 
plank. To the center of the magnet-armature A is rigidly 
fastened the brass upright BC, pivoted at B. The board D 



No. 5.] ALTERNATING CURRENT PHENOMENA. 355 

is fastened to the back of the plank and a coiled wire spring 
attached to D and C (not shown) draws C back so that the arma- 
ture is h^ld away from 5iVwhen the magnet is not excited. The 
trip-lever L is pivoted to the center of the armature A, A board 
AT is fastened to the front side of the plank, and in this the mer- 
cury cups E^ Gf and F, and the support for the stout wire W are 
placed that they may be in the same plane as the top of the lever 
Z. i? is a hard-wood board secured by three set screws to the end 
of the armature of the generator. P is an iron pin projecting about 
I of an inch from the front surface of this board. 

Now suppose the lever L to hang vertically, its top hooked over 
the end of W^ lifting the contact wire out of the mercury cup F 
and making contact in the cup E, One pole of the alternator is 
connected directly to the galvanometer; the other pole is con- 
nected to the mercury cup G, and the circuit is completed through 
the cup Ey the self-induction coil, and the galvanometer. The 
spring attached to C holds A away from the electromagnet so far 
that the end of the lever L is not struck by the pin P revolving 
with the armature of the machine. But as the photographic plate 
in falling passes the horizontal slit in its slide it closes a battery 
circuit (from 10 storage cells) through the electromagnet pulling 
A in so that P strikes Z, and the dynamo circuit is suddenly 
broken at -£*, the spring H exerting a considerable pull. 

To close the circuit which we are studying we have only to con- 
nect F instead of E into the circuit. As the armature of the 
alternator advances, an appreciable distance between the tripping 
of L and the actual break or make of the circuit at E and F 
respectively, the phase in which the break or make actually took 
place was determined by developing a few trial plates. E and F 
each had a thumb screw projecting into its side by which the 
surface of the mercury could be accurately adjusted through a 
small range in height. These with the set screws in R brought 
the phase of break and make under easy control. 

To get a curve showing the dying away of a current when the 
electromotive force is suddenly reduced to zero, under the con- 
ditions discussed below, it is necessary to cut out the electromo- 
tive force and at the same time leave the remaining portion of 



356 



F, E. MILUS, 



[Vol. III. 



the circuit closed through the same resistance and self-induction 
as before. That is, the circuit must be closed through the self- 
induction and the galvanometer so as to include a new resistance 
equal to that cut out with the electromotive force, and this must 
be done at the same instant that the electromotive force is cut out. 

To accomplish this, E is connected to one pole of the alternator 
(or to whatever source of current one wishes to study), G is con- 
nected to one circuit terminal, and the other circuit terminal is 
connected both to the dynamo and to F, The connection with 
F is through a resistance equal to that cut out with the electro- 
motive force and of the same character. 

The point now requiring care is to make the adjustments such 
that one wire shall leave the mercury at E at the same instant that 
the other touches the mercury at F. Adjustments must be made 
so that only a very small spark, and preferably none at all, shall 
be made at Ey and yet connections at F must not be made soon 
enough to cause a short circuit. This is not difficult to accom- 
plish, provided the mercury cups are large enough so that the 
wires shall not materially change the shape or the height of the 
surface of the mercury upon entering or leaving it. Figures 4, 5, 
and 6 show these different connections. A few make and break 






Fig. 6. 

Cut Out. 



curves from continuous currents were taken as a simple means of 
getting a satisfactory relation between the resistance and the self- 
induction in the circuit, and of making the necessary adjustments. 




No. 5.] ALTERNATING CURRENT PHENOMENA. 357 

Let a continuous cuuent flow in a circuit until it has reached 
its steady state. If the electromotive force be then suddenly cut 
out and the circuit at the same time closed in such a manner that 
the self-induction and the resistance remain the same, the general 
equation 

e^Ri-^rL^^ (4) 

becomes o—Ri-\-L-j. (5) 

which integrates into j=r^-T. (6) 

Substituting for c its value determined by the condition that at 
the instant of cutting out the electromotive force i equals its 
steady value /, we get 

j=/^-x.i (7) 

From the same fundamental equation we get 

/=/(i-^-T) 
or /— /=/^-f, (8) 

as the equation according to which the current attains its steady 
value upon closing the circuit. Hence the curve along which the 
current picks up to its final value upon closing the circuit is of 
the same form as that along which the current dies down upon 
removing the electromotive force, except it is turned upside down 
and displaced vertically the height of its maximum ordinate. Fig- 
ures 7 and 8 show one of each of these curves. When superposed, 
these curves coincide perfectly, except a slight difiference at the 
very beginning due to a lack of perfect adjustment of the mercury 
in the cups E and F. 

If the alternating electromotive force be removed when the 
phase angle is 90®, that is, when i has its maximum value /, we 
have 

i=^Ie-L, (9) 

the same as when removing a constant electromotive force. Such 
a curve is shown fn Fig. 8 of the article above referred to. By 

^ Alternating Currents, Bedell and Crehore, p. 45. 




358 F. E. MILUS. [Vol. HI. 

substituting for c in (i) its value given in (2), that term alone 
gives a curve of the form 

1=-/^"^, (^=90^), (10) 

which is identical with the curve given by equation (8) except it 
is below the axis of reference. This curve cannot be obtained by 
itself on the photographic plate, as can all the others, because as 
soon as the circuit is closed the alternating current interferes with 
it, and the curve actually obtained is the combination of this 
logarithmic curve and the alternating current curve. 

The combination of an alternating curve with another curve of 
any form whatever is in efifect the same as making the alternating 
curve symmetrical about the second curve as an axis. Hence the 
curve obtained upon closing an alternating current circuit having 
self-induction and resistance is symmetrical about the logarithmic 
component of the curve. But this logarithmic component is the 
same as the curve of dying out, inverted and properly displaced. 
Hence if we obtain this curve of dying out on one plate, and 
on another plate obtain the combination curve produced by closing 
the circuit, and then invert the first and superpose them so that 
the same ordinate shall pass through the point of breaking the 
one and the closing of the other, the combination curve should 
be symmetrical about the logarithmic curve as its axis. Figures 
9 and 10 show the two curves obtained separately, and Fig. 11 
shows them superposed as above indicated. The straight line 
in Fig. 9 was made by dropping the plate when the needle was 
not deflected, and is merely to indicate the axis of the curve. 
The plate was dropped a second time to obtain the curve. In 
superposing the curves it was made to coincide with the straight 
line part of Fig. 10, which being the trace of the spot of light 
before the circuit was closed, is in the line of the axis of the curve 
after the distorting efifect of the exponential term has become 
negligible. Careful measurements with the dividers do not show 
any lack of symmetry. 

In a further communication the writer expects to discuss 
experiments made upon circuits containing capacity. 




Fig. 7. 




Fig. 8. 




Fig. 9. 




Fig. 10. 




Fig. 11. 
F. E. MILLIS: ALTERNATING CURRENT PHENOMENA. 



\' 



No. 5.] DEMAGNETIZATION FACTORS. 359 



DEMAGNETIZATION FACTORS FOR CYLINDRICAL 

RODS. 

By C. Riborg Mann. 

THE effect of the form of a substance on the intensity of 
magnetization which it assumes when brought into a mag- 
netic field has been a much-discussed question. F. Neumann^ 
attacked the problem from the analytical side, and showed that 
the intensity of magnetization can be calculated when the mag- 
netization is uniform. He further demonstrated that the magneti- 
zation induced in any substance, when brought into a uniform 
field, will itself be uniform only ^hen the substance is bounded 
by a surface of the second degree.* As the ellipsoid is the only 
surface of second degree whose dimensions are finite, it is the 
only form which is of practical interest to us here. 

For the special case of a prolate spheroid brought into a uni- 
form magnetic field whose lines of force run parallel to the axis of 
revolution of the spheroid, Neumann gives the following formula 
for calculating the intensity of magnetization :* 



i-VNic' 
Or in the modem notation, 

in which |= intensity of magnetization, 
J = strength of field, 
iv = susceptibility, 

iV=a constant depending on the ratio of the axes of the 
ellipsoid. 

1 Neumann, CrcUe's Journal, Vol. XXXVII., p. 44. 

* Maxwell, Electricity and Magnetism, § 437. 

* Maxwell, Electricity and Magnetism, § 438. 



360 C. R. AfANN. [\'oL. III. 

For our special case, the one of greatest practical use, this 
factor N is given by the following formula : 

.v.+4-(j-.)(^,i«g|±-:-.), (., 

in which €=\/i — -, when b stands for the smaller, a for the 

greater semi-axis of the ellipsoid. 

We note that N depends only on a and b, ue, on the form of the 
ellipsoid in question. 

If we clear the equation (i) of fractions, we get 

|=* (3-Nti. ' (3) 

When K is very small, as in all substances except nickel, cobalt, 
and iron, the coefficient of iV, i.e, k% is very small in comparison 
to K% and is, therefore, generally neglected, thus making the 
determination of k practically independent of the form of the 
material investigated, i,e, independent of N, Hence in what fol- 
lows, as we are to discuss iV, we will speak only of the paramag- 
netic substances where k is large. 

When in formula (2) ^ = 00, or e—i, i.e. when the ellipsoid 
considered is endless, iV=o, and formula (3) becomes |=^J, the 
fundamental equation for the intensity of magnetization. As a 
grows smaller, b remaining constant, N increases. Hence this 
N in formula (3) characterizes the effect of the free ends of the 
ellipsoid on its own magnetization, and is called, since the action 
of the free ends in paramagnetic substances is to diminish the 
effective magnetic field, the demagnetization factor. 

If now iVis known, | and ^ being measurable, formula (3) may 
be used to calculate /c, the magnetic susceptibility of any sub- 
stance. Hence we may determine k either on rings, where 
iV=o, as Rowland did, or on ellipsoids, where N can be calcu- 
lated from formula (2). Both of these methods are open to the 
practical objection that it is difficult to obtain either a suitable 
ring or an ellipsoid made of the material whose susceptibility we 
wish to know. Could we but make our observations on cylinders, 
which are easily procured, the task of determining k would in most 



No. sO DEMAGNETIZATION FACTORS, 36 1 

cases be much facilitated. The following investigation was there- 
fore undertaken to determine whether N is independent of ^ and 
I for cylinders as for ellipsoids, and whether or not its value 
is the same for a cylinder as for the corresponding ellipsoid, />. 
one whose greater axis is equal to the length, and whose smaller 
axis is equal to the diameter of the cylinder. The magnetization 
in the case of a cylinder is not uniform, as it is in ellipsoids ; there- 
fore, by the intensity of magnetization of a cylinder is understood 
a mean value obtained by dividing the total magnetic moment by 
the volume. Hence the magnetometric method was preferred for 
this work. 

It was formerly assumed that a cylinder could be used for its 
corresponding ellipsoid of revolution in observations on magnetiza- 
tion by induction.^ Du Bois,^ on the other hand, has shown from 
observations of Ewing* and Tanakadat^,* that this is not the case. 
From these observations he deduces a table giving N for various 

values of the ratio -p — ^-z — of the cylinder, this ratio being de- 
diameter -^ . ^ 

noted m. These values for N may be used to reduce observations 

made on cylinders to those made on corresponding ellipsoids or on 

rings. 

The observations on which this table is based, though the best 

that then existed, are not entirely satisfactory for computing these 

factors, and this for several reasons.^ Firsts those of Ewing were 

made with too short a magnetizing coil, so that his magnetizing 

fields were not uniform throughout the whole space occupied by 

his core. Secondly^ the two sets do not join, as Ewing s shortest 

cylinder had /« = 50, while for Tanakadat^'s longest cylinder m 

was only 39, thus necessitating an extrapolation over the interval 

39—50. Thirdly, the two sets of measurements were made in 

dififerent ways, Ewing having used the ballistic, Tanakadat^ the 

magnetometric method. In my opinion the results from these 



^ W. Weber, Electrodynamische Maasbestimmungen, III., p. 573, 1867; Kirchhoff, 
Get. Abh., p. 221 ; Oberbeck, Poggendorifi Annilen, CXXXV., p. 84* 1868. 

* Magnetische Kreifte, Berlin, 1895. 

* Philosophical Transactions, 176, II., p. 535, 1885. 

4 Philosophical Magazine, 5 Series, Vol. XXVI., p. 450, 1888. * loc. di. p. 535. 



„. .?. MAaVAT, [Vol.111. 

^:^ L measurmg induction cannot be used 
: .; case like this. 

*:> . trcently published a table of these factors 
. ^..'.lis on cylindrical bundles of iron wire, 

>^y \vith that of Du Bois. Nevertheless it 

v. .. these numbers of Ascoli's could be used 
^ ..c magnetization factors of solid cylinders, 

•v.ic, as has been noted already by several 
a^. cowards magnetization as do solid cylinders 
.w, 'engtb, and cross-section, which we may 

...c the problem satisfactorily, I proceeded as 
. ong series of magnetization curves, using 
..c material but of different form, using also 
^ exceedingly careful that the results should 
. c Nvith each other, and from these deduced 
.. jclow. To give a detailed list of the obser- 
. .At too much space. The method used was 

. a wire was taken, for which #« = 300 (length 

.^ o»> ;o cm). After determining the curve of 

^ . ic valuation between | and % equal lengths 

.,. xv> that the wire assumed the form m = 200. 

. ^ c was again determined and the wire again 

. \ .wc » until m became equal to 50. These 

. vttcr the usual magnetometric method, 

s ^ ot 1.5 cm. inner diameter, thus assuring 

..ca^hoyt the entire space occupied by the 

^ .icasurcd by a carefully calibrated ammeter 

,... c uculated in the usual way by multiply- 

^ . V. .V hy the constant of the coil obtained by 

..acvizing coil on the magnetometer was 

.<**.A a^i Uncei, 3, p. 190, 1894. 
^^. V Kc. 01, II., p. 771, 1870; Warburg and Honig, 

, ^.<ub<^ as a dissertation in Berlin, 1895, ^luc^ ob^T 



No. SO 



DEMAGNETIZATION FACTORS. 



363 



balanced by another smaller coil through which the magnetizing 
current flowed in the opposite direction to that which it took in 
the main coil. This small coil was so placed that it just balanced 
the efiFect of the magnetizing coil on the magnetometer when the 
needle was at the zero point. Slight corrections had to be applied 
in many cases to the readings of the magnetometer when the 
needle was deflected, because this compensation was not perfect 
except at the zero point Having adjusted this smaller coil so 
that the reading of the magnetometer remained the same when 
the current through both coils was flowing in either direction or 



1400 




c*"^*' 


'^ 


^ 


^ 


Ttw, 


aJ2*- 




1- 


m 


60 


yiAONETIZATION , 




^ 


>^^ 




,^ 


■-^ 












J 


V/' 


/ 


^' 
















1 


' / 


/ 




















f 






















s 




ly 


/ 




















'^ 























10 ao ao 40 so eo to so m 100 no 

MAQNETIZINQ FORCE JC 
Fig. 1. 
Magnetization Curves for Cylinders for Values ol m between 300 and 50. 

not flowing at all, the iron to be investigated was brought into 
the center of the magnetizing coil and subjected to a small field. 
The readings of both ammeter and magnetometer were taken and 
the polarity of the field was reversed, its strength remaining as 
nearly constant as possible, and then a second reading was taken. 
The means of these two opposite readings were used to calculate, 
by the usual formula,^ the corresponding values of P and |. The 
field was then strengthened and the same operation repeated, — 
in short, the method of ascending reversals was used. From these 
cylinders made of iron wire, the magnetization curves in Fig. i 
for values of m between 300 and 50 were made. 

1 Wiedemann, ElectriciULt, 3, § 438. 



362 C. /p. AfAAW. [Vol.111. 

two dififerent methods of measuring induction cannot be used 
together with certainty in a case like this. 

Ascoli,^ however, has recently published a table of these factors 
obtained from observations on cylindrical bundles of iron wire, 
which agreed very closely with that of Du Bois. Nevertheless it 
seemed doubtful to me if these numbers of Ascoli's could be used 
with certainty for the demagnetization factors of solid cylinders, 
because bundles of wire, as has been noted already by several 
physicists,* do not react towards magnetization as do solid cylinders 
of the same material, length, and cross-section, which we may 
term corresponding cylinders. 

In order now to solve the problem satisfactorily, I proceeded as 
follows : I made a long series of magnetization curves, using 
cylinders of the same material but of different form, using also 
bundles of wire, being exceedingly careful that the results should 
be strictly comparable with each other, and from these deduced 
the conclusions given below. To give a detailed list of the obser- 
vations were to take far too much space. The method used was 
briefly this :* 

A long thin soft-iron wire was taken, for which #« = 3oo (length 
25.08 cm., diameter 0.0836 cm.). After determining the curve of 
magnetization, giving the valuation between | and J, equal lengths 
were cut from each end, so that the wire assumed the form m = 200. 
The magnetization curve was again determined and the wire again 
shortened to m = iso, etc., until m became equal to 50. These 
observations were made after the usual magnetometric method, 
using a coil 38.5 cm. long of 1.5 cm. inner diameter, thus assuring 
me of a uniform field throughout the entire space occupied by the 
iron. The current was measured by a carefully calibrated ammeter 
and the strength of field calculated in the usual way by multiply- 
ing the number of amperes by the constant of the coil obtained by 
the well-known formula. 

The effect of the magnetizing coil on the magnetometer was 

^ Rendiconti della royale Academia del Lincei, 3, p. 190, 1894. 

2 V. Waltcnhofen, Wiener Berichtc, 6i, II., p. 771, 1870; Warburg and H6nig, 
Wiedemann's Annalen, p. 828, 1883. 

' The details of this work were published as a dissertation in Berlin, 1895, which may 
be obtained from the author. 




No. 5-] 



DEJU^SJET. 



r :& T :i??v rr-^ 



balanced by anodier s 

current flowed in the :c 

the main coil. This sbelI n£ 

the effect of the nagryTTXTj: r:£ x rzr. 3: 

needle was at the zero pccaL SLrir r--T-r 

in many cases to the m^^3 a: r^i :i:i 

needle was deflected, beci?y -irs r":r-::r=a 

except at the zero poml Hr^-mr ii 

that the reading of the Kirrjsi.jmas: 

the current through both cxs 



'^..z: m "HI, 



*: :r « 



. IT" * 



ir siir.j- 



ME 




^ 


^:5^::===^-^_— — 


i 


u 


v^^ 


'T^- — '^ 


< 

■ m 




^ 


z 

3 

< 










m / 




1 

1 


1 

* 
















1 



40 m 

MAGNETIZIMGf 



3C 



Fig. 1. 



^^«f^ for Cylinders for Values rf k betweo: 3D: and 

=«^ii^ m C the iron to be investigated was brou,;;ht into 



-'<- -^arer if ne :::agnetizing coil and subjected to a sn-i 



;U1 tiol^l 



^ t -Esffii^s if :i:di ammeter and magnetometer were 
-^ -inr: t "iie 5eld was reversed, its strength rcm^i^^*^^^ j^^ 
^v^icajri5>:^-bie, and then a second reading wn^ ^^'^^'^^ 
'[^^ •: ^es t¥^o opposite readings were used to "'^ '*\j.j,^ 
^- '^ ^ nnii,: the corresponding values of 3 »"^ *' . 
^ ^ ^ '- ^c^inaened and the same operation tm ^ ^^^^^ 
- •• -I. "^ ^^"^'^^ '^ ascending reversals was used. ^^ y^^, i 
■~'-^> lacc ir riQ wire, the magnetization curves 
^ * ler^ran 300 and 50 were made. 

- V^dEMnn, Electricitat, 3> § ^' 



364 



C. /?. MANN. 



[Vol. III. 



For shorter cylinders a different method was used. A short, 
thick rod for which tn was only 5 (length, 11.850 cm.; diameter, 
2.370 cm.), was gradually turned down, the length remaining con- 
stant, till in reached the value 50 ; i.e. till its form was the same 
as that of the shortest of the former set. Thus the two sets 
joined together, and in each the same iron was used throughout. 
This second set (w = 5 to /« = So) was made twice, using different 
qualities of iron and a different length.* 

The first set was executed three times and the mean taken. 
Each curve of the other set was run at least three times and the 



1400 

oiaoo 

z 


P 1000 


.vi^J 


fA 


^ 


P^ 


^ 


._^ 


^' 




'^^ 




^600_ 


If/ 


/? 


V\ 


k1 


,^ 


_^ 


.^ 


.-^ 

^-^ 


^^ 








/// 


/ 


/ 


A 


y 


y 


^ 


y^ 








// 


'A 


/ 


'/ 




y' 












C iflD 


// 


/ 


Z 


r 


y^ 














\M 


^ 


y 





















VW/y 


y 





















100 



auo 300 



800 900 



1000 1100 



400 BOO 600 700 

MAQNETIZINQ FORCE 3C 

Fig. 2. 

Magnetization Curves for the First Cylinder. 

mean taken. The curves given in Fig. 2 are these mean curves. 
To get the demagnetization factors N from the curves, we proceed 
as follows : Let ^^ and J2 be values of ^ which belong to the same 
I on any two curves, and N^ and N^ the corresponding values of 
N. Then from (3) 

|=^(i,-iV,|)=^(S3-^;j), 



or 



iV^,=^i+' 



(4) 



i.e, we must measure the difference in ^ of the two curves under 
consideration along the same |-line, and divide this difference 

* 1 For the second cylinder the length was 9.620 cm. 



No. 5.] 



DEMAGNETIZATION FACTORS. 



365 



by the | which belongs to that line, and add the quotient thus 
obtained to the demagnetization factor corresponding to the first 
curve. 

This method presupposes the knowledge of Ny There are 
several methods by which this factor can be determined. In my 
table below I assumed the curve for which w = 300 as the curve i. 
The value of the corresponding N, which I will designate N^^, I 
unfortunately did not have time to determine by an independent 
method before the work was of necessity broken off. I assumed 
A30(^= 0.00075, the value belonging to the corresponding ellipsoid, 
and for the following reason : Du Bois has shown theoretically 
that, for cylinders whose length is very much greater than their 
diameters, the quantity Ntrfi should be constant. From Ewing's 
observations he deduces the value of this constant as 45. If I 
assume this theoretical law of du Bois, I have the condition nec- 
essary to determine A^^o from my observations as du Bois did.^ 
The work is as follows, using the data from my observations: 



300 
200 
150 
100 



N 



0.00079 + X 
0.00172 + X 
0.00438 + X 



Mean 



0.00041 
0.00041 
0.00041 
0.00041 



A^w* 



48.0 (200 and 150) 
48.0 (200 and 100) 
47.9 (150 and 100) 
48.0 



It is quite evident that my observations do not satisfy the theo- 
retical conclusions of du Bois. A similar calculation for ellipsoids 
gives : 



300 
200 
150 
100 



N 



0.00085 + X 
0.00185 + X 
0.00465 +x 



0.00044 
0.00042 
0.00040 



Mean 0.00042 



Arm» 



51.6 (200 and 150) 
50.8 (200 and 100) 
50.0 (150 and 100) 
50.8 



1 Wiedemann*! Annalen, XLM., 1892. 



366 



C. R. MANN, 



[Vol. 111. 



These two tables are seen to be very similar. Therefore it is very 
probable that these long cylinders act very similar to their corre- 
sponding ellipsoids, as has always been assumed;^ and hence I 
felt warranted in assuming the value I did for N^^? 

Having this for a starting point, the values of N for the other 
curves are easily calculated by formula 4. 

The measurements on bundles of wire were conducted simulta- 
neously with those on the second short cylinder. The wire used 
was 0.0801 cm. in thickness, and cut into lengths of 9.8 cm. 



1400 

oiaoo 




It 


'^ 


^ 


jiii- 




^^ 


J^ 


09_ 




Wi/, 


V 


y 


,/ 




^ 


-^ 










^iiii 


// 


/ 




/ 
















/J 


/ 


/ 
















&•" 




A 


/ 


















u 400 

kl 






r y/ 











































SO 100 1BOa00300a008B0400 

MAGNETIZING FORCE OC 

Fig. 3. 
Magnetization Cunres for Wire Bundles. 



900 



These lengths were bound into cylindrical bundles, and the mag- 
netization curves (given in Fig. 3) determined as for solid cylinders. 
The size of the bundles varied from a single wire, for which 
w = 122.5, to 171 wires, for which ^=9.37. The value of N^^ for 
the wire bundles was of course that for a cylinder of the form of 
a single wire; i,e, the value corresponding to w = 122.5. This 
factor was taken from the table of N for solid cylinders. In 
interpolating and comparing the observations, the factor N alone 
was not used, but rather the expression Nnfi, as this latter serves 
much better for this purpose. Figure 4 contains the curves 

^ Maxwell, Electricity and Magnetism, § 438. 

^ It is probable that it should be a trifle smaller, say 0.00070 ; but this difference of 
0.00005 is not appreciable for the shorter cylinders. 



No. 5.] 



DEMAGNETIZATION FACTORS. 



367 



Nm^^f{fn) for solid cylinders, ovoids, and wire bundles. The 
points represent the various observations. 



80 



ao 



Nmt 




















— 












,^p 


^ 




















<^ 






















>d 


> 




















w 




















■i 


r 






















1 
























I 
























1 
























1 

























00 78 100 125 150 ITS 

Fig. 4. 
Nw? as a function of m. 



aoo 



225 



275 «, 300 



The following table gives corresponding values of m, N, and 
Nm^ for the three cases: 



Cylindera. 


Ovoids. 


Wire Bundles. 


m 


iV 


A^m* 


AT 


Arm* 


JV 


Arm» 


5 


0.68000 


17.0 


0.7015 


17.5 


^^ 


^^ 


10 


0.25500 


25.5 


0.2549 


25.5 


0.22750 


22.8 


15 


0.14000 


31.5 


0.1350 


30.4 


0.12580 


28.3 


20 


0.08975 


35.9 


0.0848 


34.0 


0.08225 


52.5 


25 


0.06278 


39.3 


0.0579 


36.2 


0.05680 


35.5 


30 


0.04604 


41.4 


0.0432 


38.8 


0.04213 


37.9 


40 


0.02744 


43.9 


0.0266 


42.5 


0.025% 


41.5 


SO 


0.01825 


45.6 


0.0181 


45.3 


0.01760 


44.0 


60 


0.01311 


47.2 


0.0132 


47.5 


0.01277 


46.0 


70 


0.00988 


48.4 


0.0101 


49.5 


0.00951 


47.8 


80 


0.00776 


49.7 


0.0080 


51.2 


0.00768 


49.1 


90 


0.00628 


50.8 


0.0065 


52.5 


0.00623 


50.5 


100 


0.00518 


51.8 


0.0054 


54.0 


0.00515 


51.5 


150 


0.00251 


56.5 


0.0026 


58.3 


— 


— 


200 


0.00152 


60.8 


0.0016 


64.0 


— 


— 


300 


0.00075 


67.5 


0.00075 


67.5 


— 


— 



368 



C. R. MANN, 



[Vol. III. 



The column N for ovoids was calculated from formula (2). 
They are good for all values of |. 

When I calculated the value of Niox cylinders and wu*es from the 
observations by formula (4) under the supposition ^^3^3= 0.00075, I 
found that iV remains practically constant only for | < 800. Hence 
the numbers given in the table are obtained by calculating from 
the observations the value of N for every round hundred of | from 
300 to 800, and taking the mean. They are, therefore, called mean 
demagnetization factors, and are good only until | reaches the value 
800 c.g.s. 

It will be seen from the curves that for | > 800 the magnetiza- 
tion curves fall off rapidly from the curve i fgr which ;/« = 300, 
causing a correspondingly rapid increase in the values of N, This 
same effect has been noted by Lehmann ^ in experiments on radi- 
ally cut rings. The wire bundles lie intermediate between cylin- 
ders and ellipsoids in this respect, the demagnetization factors 
remaining constant longer than those of their corresponding 
cylinders. 

The following table for |, with the corresponding value of 
N^ will illustrate the point in hand : 





N 


S 


N 


I 


m= 46.30 
wires. 


m = 20.60 
cylinders. 


m- 46.30 
wires. 


in«= 20.60 
cylinders. 


300 
400 
500 
600 
700 
800 


0.02167 
0.01907 
0.02024 
0.01984 
0.01976 
0.01%2 


0.04718 
0.04822 
0.04873 
0.04870 
0.04892 
0.04735 


900 
1000 
1100 
1200 
1300 


0.01950 
0.02085 
0.02480 
0.03287 
0.05181 


0.05166 
0.05877 
0.07964 
0.09768 
0.12777 



The results may be summed up as follows . 

The mean magnetization of a cylinder does not differ greatly 
in amount from the magnetization of the corresponding ellipsoid 
for values of | < 800 c.g.s. For | > 800 an ellipsoid assumes 
a much stronger magnetization for the same magnetizing force 
than its corresponding cylinder. 

* Wiedemann's Annalcn, XLVIIL, p. 406, 1893. 




No. 5.] DEMAGNETIZATION FACTORS. 369 

Wire bundles assume, when | < 800, a much stronger magneti- 
zation for the same magnetizing force than either their corre- 
sponding ellipsoids or cylinders. The ellipsoid has, however, 
greater susceptibility for higher values of |. 

Cylinders whose length is from 20 to 30 times their diameter 
differ most from the corresponding ellipsoids in their reaction 
towards induced magnetization.^ 

These values of N for cylinders, when used in formula (3), 
will give the correct value of /c, provided only that | < 800 c.g.s. 

This result is practically of value, as it enables us to determine 
K from observations made by the ordinary magnetometric method 
on cylinders. 

The above investigation was carried on in the physical labora- 
tory of the Berlin University, under the direction of the late 
Professor Kundt and Professor Warburg, whose kindness and 
assistance I wish here gratefully to acknowledge. 

University op Chicago, January, 1896. 

1 a. Tanakadate, Philosophical Magazine, 5 Series, Vol. XXVI., p. 453, 18S8. 



370 CAROUNE W, BALDWm. [Vol. III. 



A PHOTOGRAPHIC STUDY OF ARC SPECTRA. I. 

By Caroline Willard Baldwin. 

Introduction. 

IN the course of his investigation of the Infra-Red Spectra of 
the Alkalies, Professor Snow ^ has shown the remarkable effect 
produced upon the arc spectrum when the alkalies were present 
in the carbons. He found that the curve obtained from his 
bolometric measurements was materially changed by the metals. 
While in the ordinary arc he had several very strong maxima 
in the ultra-violet and in the visible spectrum, he discovered that 
upon introducing the metals, these intense regions disappeared 
and strong maxima were now observed only in the infra-red. 

The maxima in the violet and ultra-violet are the well-known 
characteristic, bright groups of the arc spectrum. These are 
produced by a peculiar crowding together of fine lines in the 
regions X=3450 to X=3590, X = 3700 to X = 3885, and X = 4030 
to X =42 1 1. The disappearance of these and other similar groups 
would amount to a practical obliteration of the arc spectrum and 
substitution in its stead of the line spectrum of the particular 
metal used. 

The phenomena seemed worthy of further study, and as the 
bright groups lie in the regions to which the photographic plate 
is most sensitive, it was thought worth while to try the applica- 
tion of photography to determine whether the disappearance noted 
was complete, or whether the bright regions were only so much 
reduced in intensity as to escape detection by bolometric obser- 
vation. 

As a matter of fact, the work was extended beyond its original 
limit, and in the end it assumed the form of a photographic study 
of the spectrum obtained from different regions of the arc under 

1 B. W. Snow, Physical Review, Vol. I., p. 28. 




No. 50 



STUDY OF ARC SPECTRA. 



371 



different conditions, and of the effect of the metallic spectra upon 
the original carbon arc spectrum. 

Apparatus. 

The spectrum to be photographed was produced by means of 
a Rowland concave grating, which was arranged in the usual way 
upon a Brashear mounting. The latter consisted of a strong iron 
frame, which carried two tracks, SG and SC, Fig. i, at right 
angles to one another. At their point of intersection 5, the slit 
was placed. The carriage G^ which contained the grating, moved 
on one track, and the carriage C, for the camera box, on the other. 
These two carriages were connected by an iron rod to which they 



t' 




Fig. 1. 

were clamped in such a position as to keep the rod in the common 
normal to the grating and photographic plate. A screw on the 
camera box permitted the finer adjustments of position to be 
made. 

The width of the slit was adjusted by means of a micrometer 
screw, o. i mm. being the width ordinarily used. The length of 
the slit was gauged by means of a diaphragm having a wedge- 
shaped opening. A frame which held the slit could be turned by 
means of a screw and spring so as to place the slit accurately par- 
allel to the lines of the grating. 

The grating was of six-foot radius, and 14,000 lines to the 
inch. 

Celluloid films were used, and, as these could be readily bent to 



372 CAROLINE W, BALDWm, [Vol. III. 

any curvature, the film holder was curved to conform to the focus 
of the concave grating. A fence work of horizontal and vertical 
bars placed back of the film kept it from curving longitudinally, 
and yet permitted the spectrum to be seen from the back, so that 
a cleared film could be used for focussing. 

The light used was obtained from a Thomson and Houston arc 
lamp, which was hung so that the arc could be kept nearly in 
the horizontal plane in which lay the center of the grating and the 
central points of the slit and camera box. The carbons were 
I. cm. in diameter, unplated, and were made with a soft core 
.3 cm. in diameter. To produce the arc spectra of the metals, the 
cores were removed and the space was filled with the metallic salt 
well pounded in. 

In order to prevent fogging of the photographic plates, the 
lamp Z, Fig. i, was placed in the outer of two dark rooms, and 
the light was reflected into the inner room, which contained the 
grating, by means of a large concave mirror {M), This mirror 
was mounted so as to be adjustable about both a horizontal and a 
vertical axis. Its radius of curvature was twelve feet. The arc 
light was placed nearly at the center of curvature of the mirror, 
which was so adjusted that a real, slightly enlarged image was 
formed on the slit (5). This arrangement was also of advantage, 
inasmuch as it did away with the use of a converging lens. The 
arrangement of the apparatus is given in Fig. i, to which refer- 
ence has already been made. 

The opening between the two rooms was closed on the outer 
side by a slide provided with a circular opening, and on the inner 
side by a solid slide, by means of which the light could be entirely 
shut out. 

A screen near the lamp cut off the direct rays of the opening 
between the rooms ; and another screen was placed a short dis- 
tance in front of the slit, to intercept the scattered light. 

Outline of the Work. 

The image of the arc, as examined by the eye, shows sheaths 
of different colors. The arc is slightly cone-shaped, the apex 




No. 5.] 



STUDY OF ARC SPECTRA, 



373 



resting on the negative carbon. The central portion (i), which is 
of a violet tint, connects the two bright points of the carbons. 
Outside of this is a sheath of dull blue (2), which is 
most brilliant at the negative carbon, where it extends 
across in such a way as to hide the violet portion. The 
outer sheath (3) is yellow, shading into orange at the 
cooler outer edge; this last part includes the greater 
portion of the flame of the arc, and extends well up 
around the positive carbon. The different divisions are 
shown in Fig. 2. 

The investigation may be considered as divided into four 
parts: 

I. Photographs were taken with the slit extending vertically 
through the arc in six different positions : first, through the center 
of the violet portion ; second, at the line of separation between 




Fig. 2. 






Fig. 3. 



Fig. 4. 



Fig. 5. 



the violet and blue ; third, in the blue ; fourth, between the blue 
and the yellow; fifth, in the yellow; and sixth, at the extreme 
outer edge of the yellow (see Fig. 3). 

II. Photographs were also taken with the slit extending horizon- 
tally through the image of the arc. Three positions were chosen 



374 CAROLINE W, BALDWIN. [Vol. III. 

for these: first, near the tip of the negative carbon; second, 
half-way between the carbons ; and third, near the positive carbon. 

III. The flame was blown out from between the carbons by 
means of a horseshoe magnet. Under these circumstances the 
violet part does not change much in its position, but is slightly 
extended on the side away from the magnet ; while the blue and 
yellow are blown out nearly three centimeters beyond the edge of 
the carbons. The appearance of the arc was as shown in Fig. 4. 
Photographs were taken with the slit extending vertically through 
this image in nine different places (Fig. 5) : first, at the inner 
edge of the arc; second, in the center between the tips of the 
carbons ; third, in the outer part of the violet ; fourth, at the edge 
of the carbons ; fifth, outsilie of the carbons through the blue and 
yellow ; sixth, in the yellow ; seventh, at the extreme end of the 
flame ; eighth and ninth, at the edge of the carbons, giving the 
extent of the flame in the first place at the side toward the nega- 
tive carbon, and in the second place at the positive carbon. 

One hundred and thirty photographs were taken by these 
methods, from which the study of the ordinary arc spectrum has 
been made. 

IV. Metals were introduced into the arc, and similar sets of 
photographs were taken. 

The metallic salts used were lithium carbonate, sodium nitrate 
and chloride, potassium chloride, calcium chloride, strontium oxide, 
barium chloride, copper sulphate, silver nitrate, zinc chloride, and 
cadmium chloride. Sodium and zinc were studied by all three 
methods, the others only by the first two. This series included 
one hundred and fifty photographs. 

All of these photographs were taken in the primary spectrum, 
as there was less confusion due to overlapping of spectra. The 
ultra-violet of the second spectrum, which extended to the green 
of the first, could be easily cut off by means of a glass plate placed 
in front of the slit. This gave a pure spectrum in the region to 
which the plates were sensitive. 

In order to have the negatives evenly exposed, and the intensity 
as nearly as possible the same for different parts of the spectrum, 
four positions were chosen for photographing. First, the ex- 



No. 5.] STUDY OF ARC SPECTRA. 375 

treme ultra-violet, including the first bright group (X = 2263 to 
X = 3600) ; second^ the region of the three principal bright 
groups (X = 3450 to X=42ii); third, from the brightest of the 
groups to the D lines, or from X=38oo to X=:S9CX); dmA fourth, 
with a very long exposure, the region between X =450x3 and 
X=6400. The exposures varied in length from thirty seconds 
in the violet to five or ten minutes in the extreme ultra-violet, and 
fifteen to twenty minutes in the red of the spectrum. 

On account of the motion of the arc it was necessary to have 
a movable screen, by means of which the light could be cut off 
whenever the arc moved so as to throw the wrong part of the 
image upon the slit. This movement of the arc caused so much 
trouble that it was difficult to obtain ^ood photographs of the 
different sheaths in the regions of the spectrum which required 
long exposure. Hence the study of the spectra of different parts 
of the arc has been confined to the region between X=3oio and 
X=55oo; and toward the ends of this region photographs were 
taken only in the violet, blue, and yellow sheaths of the image. 
A slightly longer exposure was given in the outer part of the arc 
than was needed in the violet and blue portions. 

The length of the arc used was about 1.4 cm. 

I. 

Results obtained with the Ordinary Arc. 

The distinctive features of the arc spectrum are the bright 
groups^ from X=3S20 to X=3590,. X=38oo to X=3885 men- 
tioned by Kayser and Runge, Drude and Nunst, Nichols and 
Franklin, etc.; one from X=4400 to X=46o4; the carbon bands ^ 
given by Kayser and Runge and others, X=468o to X=4737, 
X=4746 to X=5i65, and X=5530 to X=5635; together with 
a host of periodically placed fine lines. The bright groups 
appear to be due to a crowding together of these numerous fine 
lines. The strong lines of the various metals, which are present 

* Snow, Physical Review, Vol. I., p. 28 ; Kayser and Runge, Wied. Ann., 
XXXVIIL, p. 81, 1889; Drude and Nunst, Wied. Ann., XLV., p. 460, 1892; Nichols 
and Franklin, Am. J. (3), p. 106, 1889. 

' Kayser and Runge, Ueber die Spectren der Elemente, Zweiter Abschnitt 



376 CAROUNE fV, BALDWIN, [Vol. III. 

as impurities in the carbons, are superposed upon this under spec- 
trum. The arc spectrum thus seems to consist of two spectra. 

The general arrangement of the periodic lines is worthy of 
note. They are finer and nearer together toward the violet end of 
the spectrum ; the bright groups are also nearer together in the 
regions of greater refrangibility. In each group, however, the 
lines are finer and nearer together toward the red of the spectrum, 
the maximum being toward the longer wave lengths, on which 
side the termination of the g^oup is sudden. Each of the groups 
shows secondary maxima, and between each of these the same 
general law is followed, as in the case of the group as a whole. 
We shall speak of these groups hereafter under the general 
name of the band spectrum. 

Many of the metallic lines are stronger near the negative car- 
bon and are weak or invisible at the positive carbon,^ while the 
lines of the band spectrum are strongest at the positive carbon. 

As we pass from the center of the arc to the edge, the band 
spectrum grows fainter and finally disappears. This is also true 
of many of the metallic lines, while other metallic lines seem to 
be equally bright in all parts of the arc, and a considerable 
number are relatively stronger in the outer sheath. This effect 
is enough to change the entire aspect of the spectrum in many 
places. The lines which show the last effect do not belong 
exclusively to any one metal, neither do all the lines of a metal 
seem to act thus. In the case of the calcium lines, all the trip- 
lets of the 2d series given by Kayser and Runge * are strongest 
in the center, while the pairs 

396«t'(-nd 3737.08) 

3933.83) 3706.18J 

and certain other lines as \= 4226.91 are much stronger in the 

yellow part of the arc flame. A few of the triplets of the first 

series are stronger toward the edge. Such are 



4318.80 
4302.68 
4299.14 



3644.4s 
and 3630.82 
3624.15 J 



1 Lockycr, Proc. Roy. Soc., XXVIII., 1879. 

* Kayser and Range, Ueber die Spectren der Elemente. 



No. 5.] STUDY OF ARC SPECTRA. 377 

In the carbon band, ending at ^=4735, the maxima remain 
the same as we pass from center to edge of the flame, but the 
law seems to be changed. In the outer sheath the maximum 
intensity is toward the violet and the strongest maximum is 
X=4645. The shading of the band is thus completely reversed. 
Another band with maxima toward the violet is seen in the outer 
sheath from X=4840; the maxima being X = 4840, X= 4865 and 
X=4892. The strongest part of the group at 3590 becomes 
the weakest in the outer part of the arc, and many groups 
have the faintest lines at the center, the strongest at the edge. 

When the photographs are taken giving the spectrum of the 
flame as blown out from between the carbons by the agtion of 
a magnet, the slit extends across the different sheaths of the arc, 
and those lines which are stronger in the outer parts of the arc 
reach through the spectrum with their brightness undiminished or 
increased at the edges, while the bands and many of the metallic 
lines appear only in the central part. 

When the slit is arranged to pass through the image of the arc 
horizontally, this effect is more marked, owing to the greater 
steadiness of the flame. In watching the developing of the nega- 
tives, it was observed that many of the lines, as 4226, 3583, 
3571, were first visible at the edge and then gradually extended 
toward the center, while the fine lines of the band spectra and 
most of the other lines appeared first at the center and then 
extended part way to the edge. The photographs taken by the 
three methods thus show complete agreement in their results. 

Since the spectrum of the arc has already been mapped with 
more powerful apparatus than that used in these experiments, 
only such points will be given as may serve to indicate the differ- 
ences between the spectra of the different sheaths. 

(A) Region lying between 2263 and 31CX). 

135 lines were mapped between 2263 and 3016, all of which 
belonged to the central violet sheath [(i) Fig. 2]. 

The first lines which could be detected in the blue and yellow 
sheaths lay between 3018 and 3099; eleven lines among the 
nineteen mapped were visible in the blue and four in the yellow. 



378 CAROLINE W, BALDWIN. [Vol. III. 

(B) Region lying between 3100 and 3440. 

72 lines were mapped, all of which were confined to the central 
blue sheath. 

(C) Region lying between 3440 and 3928. 

135 lines were mapped, of which 

125 were present in the violet, 
96 were present in the blue, 
58 were present in the yellow. 

Of those which were invisible or very faint in the central violet 
sheath, although strong in the outer sheaths, the following are 
readily placed in Rowland's Standard List : ^ 

3812.12^ 3832.4s Mg. 

3812.20 >C. 3834.36 Fe. 

3812.34J 3838.43 Mg. 

3815.98 Fe. 3841.19 FeMn. 

3820.59 FeC. 3856.52 Fe. 

3827.03 Fe. 3860.05 FeC. 

(D) Region lying between 3930 and 4550. 

Throughout this region photographs were taken in the five posi- 
tions indicated in Fig. 3, as a, 2, 3, 5, and 6. 
213 lines were mapped, of which 

211 lines were visible in central violet sheath (/z), 
200 lines were visible in outer violet sheath (2), 
179 lines were visible in blue sheath (3), 

175 lines were visible in inner yellow sheath (5), 
57 lines were visible in outer yellow sheath (6). 

The two lines absent from the central violet appear to be 

1 Rowland, Astrophysical Journal, I., p. 29, 1895. 




No. 5.] STUDY OF ARC SPECTRA, 379 

(E) Region lying between 4550 and 4960. 

Photographs were taken in three regions (i, 2, and 3, Fig. 2). 
129 lines were mapped, of which 

129 lines were visible in the violet sheath, 
103 lines were visible in the blue sheath, 
95 lines were visible in the yellow sheath. 

(F) Region lying between 4960 and 6042. 

IIS lines were mapped, of which 

1 1 5 lines were visible in the violet sheath, 
42 lines were visible in the blue sheath. 

If we sum up these data, we find 

Total lines mapped 799,^ 

Visible in central violet 787, 

Visible in blue 431, 

Visible in yellow 232. 

Attempts to classify these lines according to their sources led 
to no satisfactory results. A study of the photographs, however, 
showed that the lines of the arc spectrum may be grouped as 
follows : 

\,a. Lines which grow gradually weaker as we move from the 
center to the edge, and are usually invisible in the outer sheath. 

\.b. Lines which preserve about the same intensity in the center 
and blue of the arc, but are suddenly much weaker or invisible in 
the yellow. 

Forty lines of this class were counted. They were distributed 
throughout the spectrum from 3024 to 5616. 

The lines of the band spectra grow fainter through the blue, but 
disappear quite suddenly there, not being seen in the yellow. 

Lr. Faint lines which are only found in the first two positions 
(a and 2, Fig. 3). Invisible in the blue. One hundred and sixteen 
of these were counted. 

1 Exclusive of Uie fine lines of Uie band spectrum which were not counted. 



380 CAROUNE W. BALDWIN. [Vol. III. 

\\,a. Lines which appear equally strong in all parts of the arc. 
Seventy such lines were counted. 

II. *. Lines which become stronger as we go out from the center. 
Seventy-nine of these lines were mapped. 

II. r. Lines which are not visible or exceedingly faint at the 
center of the arc. There are eighteen of these, of which exact 
positions for twelve have been given in a previous paragraph. 

\\,d. Lines which have their maxima in other sheaths, 2 or 3, 
rather than in the center or at the edge of the arc. There are 
sixteen such lines upon the photographs.^ 

11.^. Lines which have more than one maximum. Six such 
lines were noted. 

The lines of division I. are as a rule stronger at the positive 
carbon^ while the lines of II. are usually stronger at the negative 
carbon. W.b. and II. r. are especially strengthened at the negative 
carbon, 11.^. to a less extent. 

The calcium lines 4581.66 and 4586.12 appear as single lines 
at the negative carbon, but at the positive they seem to be double. 

^ There is reason to think that at least ten of these are titanium lines, but the evidence 
is not conclusive. 

{Tb be coHcluded^ 



No. 5.] 



SURFACE TENSION OF UQU/DS, 



381 



MINOR CONTRIBUTIONS. 

The Surface Tension of Liquids. 
By Arthur L. Foley. 

IN the Philosophical Magazine of November, 1893, Mr. T. Proctor Hall 
describes some " New Methods of Measuring the Surface Tension of 
Liquids.'* Two years ago, at the suggestion of Professor Michelson of the 
Chicago University, I undertook to repeat and to extend the investigation. 
In the present article, I shall confine myself to a brief statement of the 
results obtained by using Mr. Hall's method c^ the maximum-weight 
method.* 

Let a (Fig. i) be an end face of a rectangular parallelopiped suspended 
from one arm of a balance, with its lower face horizontal, and therefore 
parallel to the liquid surface 
Ox. Call w^ the weight of 
the frame (block) in this posi- 
tion. Lower the frame until it 
touches the liquid, and bring 
it again to the first position, 

as in ^. The weight of the 

frame is now increased by the 
weight of the liquid raised 
above the level surface. As 
the frame is raised, the weight increases for a time, then suddenly de- 
creases, passing through a distinct maximum. Call w^^ the total maximum 
weight. The net maximum weight is 



.=^_ 



-^ 



^ 



V 



Fig. 1. 



w = w*^— w*= 2 T' sin a + pfy, 



(I) 



where T= the surface tension in grams per centimeter; 

a = the angle between the ^-axis and the tangent to the liquid 

surface at the edge of the frame ; 
/ = the thickness of the frame ; 
p = the density of the liquid ; 

y = the height of the frame above the liquid surface ; 
/= the length of the frame, one centimeter. 

^ Philosophical Magazine, NoYember, 1893, p. 402. 




382 ARTHUR L. FOLEY. 


[Vol. III. 


^^* Tsma^pyjdx, 


(2) 


dx 7" cos a 
da py 




Placing ^^ = — , and f emembering that -^ = tan a, 
p ax 

dy__^sma . 
da y 




y = — 2^^cosa + >&. 




When >' = 0, a = 0, and ^ = 2 r*. 




/i — cos a . a 

'2 2 


(3) 



cos 



2 ^ 4^ 



2r^-/ 

cos a = --«^» 

2r 



(4) 
(5) 



U7 



Let us now suppose that the frame has vertical 
legs (as in Fig. 2) extending downward into the 



L y liquid. Let / be the length between the legs. 
Pj 2 Equation (i) becomes 

2e/= 2r(/--/)sina4-p/?K, 
= 2 p(^(J — /) sin a 4" 2 Itpc sin -< 



(6) 



dw 



. When 2t/ is a maximum, —-=0. Let /be very small compared with /, theo 
da 



2 c cos a-\-t cos - = o. 
2 



Eliminating a by (4) and (5), and inserting the value of r, 



^ /. 8 \2p 64 



When / is small, a near approximation is 
Supplying this value of j' in (6), and solving for T, 



(7) 



T= 



2{/ 






No. s] 



SURFACE TENSION OF UQUIDS. 



383 



Table II. gives the value of T' calculated by the above formula for mica 
frames varying in thickness from 0.0013 cm. to 0.02067 cm. 

Mr. Hall, in his investigation, used glass frames (made of cylindrical 
glass rods) of the shape indicated in Fig. 3. He deduced for them equa- 
tions corresponding to (6), (7), and (8). He admits, 
however, that these equations are so complicated as 
to be almost unmanageable, and that the correction is 
obtained more easily by determining the constants of 
a frame by using frames of different length and of the 
same diameter, and again, of the same length but of 
different diameters. It is very difficult indeed to 
make such frames, and to use them after they are made. 

The chief objections to glass frames may be summed 
up as follows : — 




Fig. 3. 



The value of ^, and hence the correction that must be applied to 
the maximum weight in order to obtain the true film weight which 
measures the tension, depends in a very complicated way upon the 
diameters of the rods of the frame. 

This correction forms a considerable part of the total maximum 
weight (see Table I.). Frames cannot be made sufficiently rigid 
and less than 0.03 cm. in diameter. Hence the correction is at least 
10 per cent of the whole. 

The frames are difficult to make and they require delicate handling 
at every stage. 

With cylindrical end rods the actual length of the film surface is 
uncertain. 



It occurred to me that these troublesome corrections and inaccuracies 
might be partially avoided by using a different kind of frame. After 

^ experimenting with frames of various materials, 

among which I may mention thin sheet glass, 
mamamtmmammmma^ platinum, aluminum, and mica, I found that 

I the latter offered decided advantages over 

glass. The general shape of the mica frame is 
given in Fig. 4. The frame is supported by a 
forked glass stem, and the method of using is exactly as with a glass 
frame. 

My first frames were made by cutting the mica sheet as it lay under a 
steel rule upon a piece of plate glass. I afterwards had made two heavy 
steel plates of the exact shape of the frame desired. The inner surface of 
each plate was ground plane with emery dust upon plate glass. A sheet 



Fig. 4. 



384 



ARTHUR L, FOLEY. 



[Vol. III. 



of mica was clamped between them and cut to their dimensions. The 
advantages of frames made in this way are : 

The steel plates are accurately ground; the frames are corre- 
spondingly regular. 

The mica does not split along the cut edge. 

The edge is of the same thickness as the plate itself; there is no 
bur. Very thin frames are easily made, but it is difficult to work with 
them when they are much less than 0.002 cm. thick. 

A difficulty experienced with the mica frame, as also with those of 
platinum and aluminum, is that the fluid does not readily and equally wet 
all portions of the surface. It has a tendency to collect in drops, rendering 
the after-weighing uncertain. This difficulty was entirely overcome by 
roughing the surface (darkened in Fig. 4) of the plate near the edge by 
rubbing very lightly with the finest French emery paper. Both weights 
could then be taken again and again with a variation of only a few hun- 
dredths of a milligram. 

The advantages claimed for the mica frame are as follows : 

1. They are easily made, and do not require careful handling. 

2. They are of even thickness, with straight edges and square comers. 
Hence the film length is not so uncertain as with glass frames. 

3. They can be made less than one-tenth of the thickness of a glass 
frame, reducing the correction correspondingly. Table I. gives the relative 
corrections for glass and mica frames, obtained by determining the maxi- 
mum weight for a soap solution, and then weighing the film itself. The 
film weight divided by twice the length of the frame gives the surface- 
tension. But with many liquids it is impossible to obtain the film weight, 
as the film breaks immediately after it is formed. The maximum weight 
can be determined in almost every case, and the film weight by correction. 
It is evident that a slight error in the value of this correction will be 
lessened by reducing the total correction, as is done by using the mica 
frame. 

Table I. 



Kind of frame. ! 


/ 


/ 


w 


Film weight. 


Percent 
difference. 


Glass ... 1 


6.346 


0.0405 


0.39226 


0.34100 


15 


Glass - . . ! 


7.584 


0.0510 


0.48283 


0.40302 


19 


Glass ... 


10.163 


0.0620 


0.65420 


0.53700 


21 


Glass . . . 


7.475 


0.0920 


0.52480 


0.39660 


32 


Mica ... 1 


6.012 


0.0030 


0.31202 


0.30697 


1.6 


Mica - . . 


5.301 


0.0051 


0.27776 


0.27092 


2.5 


Mica . . . 


5.140 


0.0079 


0.27222 


0.26260 


3.7 



A fresh solution was used in the last three measurements. 



No. 5.] 



SURFACE lEJVS/OAT OF LIQUIDS. 



385 



4. The correction varies directly as the thickness of the frame; Fig. 5. 
Observations with two frames of varying thickness are sufficient to deter- 
mine the actual film weight and hence the tension. 



5 

uno 


/ 
















A 


A 


7^ 


^ 




5 
1.010 

5 
liXK) 










y 


/ 


/ 


/ 


/- 










5 








7^ 


/ 


X-MA 
y-TH 


KIMUM 
ICKNE8 


WEIQH- 
lOFMI 


' IN OR 
CAFRA 


AM8 
ME INC 


ENTIMI 


TERS. 




J60 

5 

J60 




/ 


A 






















/ 
























X 



JXa Mi M» JJfB 



.012 JOU 

Fig. 5. 



M6 i)i8 joao 



joa 



JOU a» 



5. In the case of thin frames the tension can be determined at once 
from the maximum weight uncorrected, with results that vary less than do 
those obtained by the method of capillary tubes. For example, compare 
Table II. with I'able III., the latter giving selected results obtained by 
Quincke by the capillary tube method.^ 

6. As y and / are small, a small error in the assumed value of p will not 
appreciably affect the calculated value of T, Eq. (6). 

y being small, the film is much narrower than with a glass frame. There- 
fore there is less temperature change due to evaporation from the film 
surface, and less absorption of gases and impurities from the air. 

7. The equations for w and y are not so complex that they cannot be 
used. In Table II. are given the values of T' deduced by formula (8). It 
will be noted that the last frame is about sixteen times as thick as the first, 
yet the greatest difference in these values is but a little more than one part 
in two hundred. Of the results for the first four frames, the greatest dif- 

^ Wiedemann's Annalen, No. 5, 1894, p. 14. 




3«6 



ARTHUR L. FOLEY. 



[Vol, III. 



ference is (me part in seven hundred. The thicker frames cannot be 
expected to give such consistent results, as the water tends to creep in 
between the thin layers of which the mica sheet is made up. 

Table II. 



/ 


w 


T by formula. 

^%7 


T by equation (8). 


Temperature 
of water. 


0.00130 cm. 


0.9826 g. 


007396 


0.07365 


20<^.7C. 


0.00190 


0.9842 


0.07408 


0.07374 


20^.7 


0.00352 


0.98791 


0.07437 


0.07372 


20^.7 


0.00516 


0.99094 


0.07458 


0.07365 


20^.7 


0.00928 


0.99991 


0.07527 


0.07352 


20^.8 


0.01206 


1.00592 


0.07572 


0.07355 


20°.8 


0.01536 


1.01358 


0.07630 


0.07345 


20°.9 


0.01828 


1.01973 


0.07676 


0.07339 


21<^.0 


0.02067 


1.02468 


0.07713 


0.07332 


21^.0 



Table III. 

(Temperature i8°.) 



Kind of glass. 



Common Jena glass 
Common Jena glass 
English flint glass . . 
English flint glass . . 
Fusible (soft) Jena glass 
Fusible (soft) Jena glass 



Diameter of 
tube. 


Ai^e of tube. 


T 


0.5832 


Ohr. 


0.07528 


0.5851 


24hrs. 


0.07336 


0.5390 


2 mos. 


0.07490 


0.5740 


Ohr. 


0.07411 


0.6440 


Ohr. 


0.07258 


0.9106 


12hrs. 


0.07480 



In this experiment I used distilled water from the Chemical Laboratory. 
Subsequent tests showed that this water contained considerable organic 
matter. 

I have almost completed an investigation of the temperature coefficient 
of the surface tension of water by the maximum weight and mica frame 
method. I hope to give the results of this work in a subsequent paper. 



Physical Laboratory of the Indiana Universfiy. 



No. 5.] THE RESISTANCE OF TIN-FOIL, 387 

The Resistance of Tin-foil as Changed by 
Electric Waves. 

By C. D. Child. 

THE results of recent investigations of the effect of electric waves on 
the resistance of tin-foil by Haga * and Mizuno * differ from the con- 
clusions of Aschkinass,^ who first observed this phenomenon. He found 
that the resistance of a grating made of tin-foil decreased when subjected 
to electric waves, and was again brought back to its original resistance 
when jarred or heated. He attributed this to a change in the tin-foil itself. 
The others ascribe the variation of resistance to a change of contact 
between consecutive strips. In this they confirm my own experience as 
given at the Springfield meeting of the A. A. A. S., 1895, ^^^ briefly 
reviewed in the Electrical World for Sept. 14, 1895, P- 284. At that time 
I expressed the hope that the method might be made quantitative. I 
have failed thus far in carrying out my desires in this respect, but think 
that it may not be amiss to give the results of my work. 

The waves with which I worked were generated from an exciter of the 
type used by Righi, and were about 5 cm. in length. The exciter was 
placed at the focus of a parabolic mirror for receiving the waves. The 
resistance was made by fastening a piece of tin-foil on a block of wood and 
slitting it in such a way that the current must follow a zigzag path back and 
forth across it. When the tin- foil was cut so that there was considerable 
distance between consecutive strips, there was no effect whatever ; when it 
was cut with a sharp knife, so that the consecutive strips were almost in 
contact, the effect was large. 

Several resistances were tried, made in these two ways, but no change of 
resistance was observed which could not be ascribed to a change of con- 
tact between consecutive strips. 

To make doubly sure, I folded a narrow strip of tin-foil back and forth 
on itself with very thin pieces of tissue paper laid between the folds of tin- 
foil, so that there could be no actual contact between consecutive strips. 
In this way I folded the tin-foil until it made a pile 2.5 cm. high, but was 
unable to detect any change of resistance. 

Having satisfied myself that the effect was entirely due to change of 
contact between adjacent strips, I next endeavored to secure more regular 
effect in order to make quantitative measurements by this means. There 
is no doubt but that such a change of resistance affords the most sensitive 
method of detecting electric waves. The use of iron filings by Lodge and 

* Wiedemann's Annalen, Vol. LVI., p. 571. ^ Philosophical Magazine, Vol. 40, p. 497. 
• Wiedemann's Annalen, VoL LIV., p. 103. 



388 C. D. CHILD, [Vol. III. 

others have shown this conclusively, but the action of the filings has been 
found to be quite irregular. I found that the regularity of the action of 
the tin-foil depended largely on the material with which it was fastened to 
the block of wood. For this purpose I tried several substances, such as 
shellac, paraffin, mucilage, and beeswax. In order to get good results, it 
seemed to be necessary that the substance should hold the tin-foil rather 
firmly, and yet not rigidly. Of those used, beeswax gave the best results. 
Better results were obtained by having the strips of tin-foil perpendicular 
to the direction of the electric oscillations. 

The pieces of tin-foil used were 2.5 cm. square. I first made them of 
this size because I thought that there might be a resonance effect How- 
ever, difference in size did not seem to affect the results, and I continued to 
make them of this size for convenience. It was not possible to tell cer- 
tainly whether one size was better than another, because no two pieces 
ever worked alike even when they were of the same size, — except that 
most of them were equally bad. Many of them would be constantly vary- 
ing in resistance even when there was no mechanical jar nor electrical dis- 
turbance that could be detected ; and even the best seemed to deteriorate 
with age. 

For qualitative work, such as lecture experiments, the method can be 
made to give excellent results. Some of the pieces of tin-foil worked with 
considerable regularity, where the intensity of the oscillations was large, 
but when the intensity was small, the action was very irregular. I was 
attempting to work with an effect analogous to that got by a diffraction 
grating in light It was not at all difficult to detect such an effect, but one 
could not be certain of the point at which a maximum was obtained, 
because of the irregularity in the working of the tin-foil. Unfortunately 
I could not be sure that the trouble was not largely with the exciter. The 
exciter was worked by an induction coil with an ordinary magnetic make 
and break. However, the very great difference between different pieces 
of tin-foil showed that the trouble was not all with the exciter. Moreover, 
one could scarcely expect the action to be regular. The resistance was 
connected so as to be one arm of a Wheatstone's bridge, and by keeping 
the connections closed at the same time that the tin-foil was being acted 
upon by the electric waves, one could easily watch the effect. In general, 
the effect was greater the longer the time during which the waves acted 
iipon it, but there was by no means a constant change. A large change 
would often take place very suddenly, as indicated by the throw of the 
galvanometer needle. This was no doubt caused by some more violent 
oscillation of the exciter, and if it were possible to have exactly the same 
action of the exciter at all times, the change in the tin-foil would have 
been regular. One spark larger than usual would often produce a greater 



No. 5.] THE RESISTANCE OF T/N-^FO/L. 389 

effect than would be produced at another time by long-continued action of 
the exciter, and a method of detecting electric waves can hardly be relied 
upon, when some slight irregularity in the exciter is liable to produce such 
large effects. 

However, to show of what the method is capable, two series of readings are 
given below, taken when endeavoring to measure wave-lengths by means of 
a diffraction grating. By watching the galvanometer indicating the resist- 
ance of the tin-foil, it was usually possible to bring it back to its original 
resistance. I would measure its resistance, allow it to be acted upon for 
six seconds, and again measure its resistance. While the oscillations were 
occurring, the connections to the tin- foil were broken as near to it as pos- 
sible ; for I found that otherwise waves were liable to be caught up by the 
wires running to the bridge and its connections, and brought to the tin- foil, 
thus making its action still more irregular. In one case the initial resist- 
ance was 7.3 ohms. The changes in fivQ consecutive readings, when the 
circumstances were apparently the same, were approximately 0.98, 0.71, 
0.73, 1. 18, 0.62 ohms. At another time, when the intensity of the waves 
was not so great, the resistance decreased as follows, 0.28, 0.38, 0.66, 0.79, 
0.38. These are measurements which I took on the effect through a 
grating, which we may call a diffraction grating. They are rather better 
than the average. 

My conclusion is that the method is an excellent one for qualitative 
but not for quantitative work. 




390 ^r£lV books, [Vol. III. 



NEW BOOKS. 

Hydrodynamics. By Horace Lamb, F.R.S. Cambridge, Univer- 
sity Press, 1895. 

It is not difficult to understand the attraction which the study of fluid 
motion appears always to have had for mathematicians. Whether we look 
at the practical or theoretical importance of its problems, the mathematical 
difficulties involved in many of them, the beautiful simplicity of the solution 
of certain most complex motions, — as, for instance, the motion of ellip- 
soidal masses of fluid under their own attraction, or of two-dimensional jets 
with free surfaces, — and, at the same time, the large field for investigation 
still open, the reason for this interest is not far to seek. 

The first connected treatise on the subject of any worth, in English, was 
Lamb*s Treatise on the Motion of Fluids, published in 1879. This was 
followed, in 1888, by Basset's well-known and valuable Treatise on Hydro- 
dynamics , and now we have what is practically a revised and greatly enlarged 
edition of Lamb's original treatise, but so altered that the author has thought 
it well to make a change in its title. The 258 pages of the original have 
expanded to 604. The chief additions are in the treatment of the Motion 
of Solids through Liquids (from 36 pages to 105 pages). Wave Motion (42 
pages to 230 pages), Viscosity (16 pages to 84 pages), and a new chapter 
on the Motion of Rotating Masses of Liquid. It will thus be seen that the 
bulk of the new matter is on Wave Motion. So great, indeed, is this increase 
that this portion may be regarded as a monograph on the subject. It is, 
perhaps, to be regretted that the extension should be so one-sided, as the 
author has thereby been compelled, in order to bring the book within 
reasonable compass, to omit much important matter in other branches. 
The due selection of matter from such a wealthy storehouse of results, is 
not easy, and each writer will have his own preferences. In any text-book, 
general principles must, in any case, take a prominent place. In this 
respect, the treatise is a model of clearness, and cannot be too highly 
praised. But a mathematical text-book ought not to be a mere repertory 
of known facts, but an armory of weapons for further investigations. Two 
canons should then govern the selection of matter : is the result important 
in itself? does it exemplify a method? Many a problem, of small interest 
in itself, becomes of importance as an example of a particular method. 



No. 5.] NEW BOOKS, 39 1 

One could wish that, in this last respect, the treatment had been fuller. 
Clebsch's representation of the velocity by three functions, ^, w, ^, where 

udx + vdy -h wdz = d<l>-\- mt/ip, 

is wanting. The general method of curvilinear co-ordinates, and the 
method of images, are only slightly touched on. The only example of 
Lagrange's method of dealing with fluid motion is the artificial wave form 
of Gerstner, whilst in Dirichlet and Dedekind's treatment of the motion of 
an ellipsoidal mass of fluid, a most striking illustration might have been 
given. In Chapter IV., it would have been preferable to deduce solutions 
instead of taking functions satisfying vV = o> and seeing what boundary 
conditions they satisfy. For instance, in the case of the elliptic cylinder, 
the opportunity is lost of introducing the method of elliptic curvilinear 
co-ordinates, and deducing from the general solution of y^ = o, in these 
co-ordinates, the proper form for translation, rotation, or any surface 
motion whatever. We could have dispensed with much of the new matter 
on waves if thereby we could have had Kirchoff'*s treatment of the motion 
of a solid of revolution, a much fuller treatment of the motion of two 
bodies, of vortex motion, and especially of the motion of ellipsoidal masses 
of fluid. The author has apparently made it a rule to omit any investiga- 
tion in which elliptic functions enter. This is unfortunate, as many solu- 
tions are most elegantly expressed in these functions — witness the motion 
of two parallel cylinders ; it is also unnecessary, as a knowledge of the 
elements, at least, of these functions is possessed nowadays by all mathe- 
maticians. 

One most valuable feature of the book is the number of diagrams of 
stream lines introduced. Nothing gives a clearer idea of what is taking 
place than this translation of formulae into visible form. Compare, for 
instance, the stream lines for the cylinder given on pages 86 and 87 with 
those for the sphere on pages 137 and 265 ; or examine the lines of motion 
of a symmetrical body in a plane, in which for the first lime the correct 
form is given. The diagram illustrating the effect of viscosity on wave 
motion of a finite depth, again, is most instructive. Most of these are due 
to the author himself. In fact, the reader already acquainted with the 
subject is not only pleased with the way in which old friends are intro- 
duced, but with frequently occurring bits of new work which the author 
modestly allows him to pick out for himself. 

The two or three deviations from ordinary usage introduced by the 
author are scarcely to be commended. It is always a gi-eat advantage, not 
only in working out results, but also in interpreting them, to choose func- 
tions which have a definite physical meaning, a magnitude which is mentally 
seeable, and which has a direct reference to the subject we are dealing with. 



392 ^TEW BOOKS. [Vol. III. 

Professor Lamb confesses that it is with some hesitation that he has used 
throughout the reversed sign for the velocity potential His reason b that 
thereby it represents, when multiplied by the density, the impulsive pressure 
which will generate the motion from rest, and also that it is then analogous 
to the magnetic potential But by the old usage it represents the flow of 
liquid along a line between two points, or the momentum per sectional area 
in a small uniform tube between the points. It follows at once that to 
generate this an impulse must be applied equal to the momentum. We can 
therefore much more clearly form a visual picture of the distribution of its 
value, and interpret results more easily with this conception, than with the 
new one. That it may have an analogy with the magnetic potential is no 
help whatever in hydrodynamical work. By all means seek for analogies ; 
but for actual use in investigations let us employ the simplest ideas natural 
to the subject in hand. These remarks are illustrated again by the new 
definition given to a source or sink. Surely the natural measure of a 
source is the number of cubic centimeters or the number of grams issuing 
from it per second. But this would spoil the analogy with electrostatics. 
Therefore it is proposed that the unit source shall be one which delivers 
1 2.566- •• cubic centimeters per second. It is a curious inversion of the 
4 7r-mania from which some eminent electricians suffer. These, instead of 
taking the idea natural to their subject, and defining the unit of electricity 
so that two units at a distance of one centimeter repel with a force of one 
dyne, desire to alter it so they shall repel with a force of 1/16 11^ dynes, and 
this to make the electrostatic unit analogous to a source. For the same 
purpose of analogy with a foreign subject also, the letters F.G.H. are used 
to denote the component of the vector potential, in place of L.M.N, intro- 
duced by Helmholtz, and used by all writers in hydrodynamics since. As 
in the former case, mutual courtesy should induce the 4 7r-electricians to use 
L.M.N, instead of F.G.H. 

On the contrary, the author conforms to common usage in one respect 
in which a change might be desirable. Stokes' stream function is defined 
as the total flux through a circle divided by 2 tt, so that the velocities are 
given by i ,/^ , ^^ 

rar r dy 

There is much to be said in favor of defining it as the flux itself. ^ then 
has a definite meaning. It is clear at once that, since the energy due to a 
thin vortex (juidS) is that due to the initiating impulse on the diaphragm 
filling its aperture: 

The energy 

= impulse x change of flux, 

= momentum in closed uniform tube bent round the vortex x flux, 

= circulation x flux = i^dS x ^. 



No. 5.] ATEIV BOOKS. 393 

Wherever ^ enters, it tells its own tale. The only argument for the usual 
definition is that the expressions for the velocities are simplified. This is 
so, but only with the effect of complicating other expressions by bringing 
in 2 IT where it has no meaning ; e^, the energy is now 2 irtnt^dS, 

After all, perhaps, these points are merely matters of taste. There is no 
doubt that in the book before us Professor Lamb has produced a most 
valuable addition to mathematical literature which should find a place in 
every mathematical library. 

W. M. Hicks. 



Elements of the Matheinatical Theory of Electricity and Magnetism, 
By J. J. Thomson, F.R.S. 8vo. pp. 510. Cambridge, The University 
Press, 1895. 

The program, admirably carried out in this elementary treatise, is stated 
in the introduction. "For in the simple cases," says the distinguished 
author, " the absence of analytical difficulties allows attention to be more 
easily concentrated on the physical aspects of the question, and thus gives 
the student a more vivid idea and a more manageable grasp of the subject 
than he would be likely to attain if he merely regarded electrical phenomena 
through a cloud of analytical symbols." 

The mathematical apparatus employed is of the simplest kind, and it is 
employed, not for the purpose of enabling the student to obtain results 
quickly by making short cuts in his physical reasoning, but only as a record 
of the results obtained by a purely physical method of analyzing physical 
phenomena. His attention is rjveted upon the physical law describing 
what is going on in the elements of space and time, and not upon the 
differential equation, which is only a symbolic stategient of this law, and 
hence " eine Nebensache," as the German saying goes. 

The passage from the infinitesimal elements of the phenomena to the 
phenomena themselves, such as we perceive them, is not treated as a mere 
mathematical process of integration. The student is trained to build up 
synthetically the finite from the infinitely small by examining carefully what 
is going on in every one of the elements which he is summing up. For 
instance, the theorems concerning transformations of surface integrals into 
line integrals, or of volume integrals into surface integrals, are valuable labor- 
saving machines in the hands of an advanced mathematical physicist. To 
a young student of mathematical physics they are perplexing puzzles, unless 
he has been taught first how, for instance, to build up the magnetomotive 
force around a finite closed curve from the currents which pass through the 
various elementary «nreas of a surface bounded by that curve, etc. It is 
this sjrnthetic building-up which Professor Thomson substitutes in place of 



394 ^^^ BOOKS. [Vol. III. 

abstract mathematical theorems. Such a treatment keeps die student con- 
tinually in touch with the phenomena ; it makes him a mathematician by 
teaching him how to apply physics to mathematics. 

The classification of the phenomena is the usual one ; it is in accordance 
with the historical order of development The statical phenomena are dis- 
cussed first, the current comes next, and the phenomena of electromagnetic 
induction in conductors and dielectrics follow last More than half of the 
book is devoted to statics. This will probably displease the engineering 
student ; but it should be remembered that our knowledge of the two most 
important physical constants of the electromagnetic field, that is, of specific 
inductive capacity and magnetic permeabihty, is derived from these statical 
phenomena. Besides, tubes of induction, especially those of electric induc- 
tion, have a much deeper meaning in Professor Thomson's view of electro- 
magnetic phenomena, and play a much more significant part than is usually 
attributed to them. Our ideas concerning these tubes can be derived most 
easily from a study of statical phenomena. Those who have followed care- 
fully Professor Thomson's investigations within the last few years will be 
delighted with his electrostatics and magnetostatics as given in this ele- 
mentary treatise. 

The phenomena of electrolysis, and Faraday's laws relating to these 
phenomena, form the foundation on which Professor Thomson builds what 
one may call the mechanical model of the electric current. Those who 
are acquainted with his theory of moving electrostatic tubes, which, as a 
rule, have their ends attached to the atomic charges, would naturally expect 
him to emphasize the intimate relation between the electric current and 
the chemical effects accompanying it. A very forcible and exceedingly 
clear statement of this relation will be found in the chapter on electric 
currents. ^ 

The discussion of the magnetic field which accompanies an electric 
current is very brief, but, nevertheless, it is clear and complete. The same 
may be said of the discussion of magneto-electric induction in conductors. 
The application of the fundamental laws of induced electromotive and of 
the magnetomotive force to the theory of alternating currents will probably 
be considered as too brief to satisfy the needs of electrical engineering 
students. It may be answered, however, that this is not a book on elec- 
trical engineering, and that a student who has mastered this book will find 
no difficulty whatever in rushing through any one of the many voluminous 
treatises on alternating current generators, transformers, and motors. The 
distribution of alternating electric and magnetic forces in the interior of 
conducting masses is beautifully worked out, and will be much appreciated. 
This is probably the first time that this extremely interesting subject has 
been discussed in an elementary treatise. 




No. 5.] NEW BOOKS, 395 

The chapter on electrical units is not shrouded in that sepulchral gloom 
which generally accompanies every discussion of units. This is due to the 
fact that the interesting theory of the various methods of absolute measure- 
ment has been assigned to this chapter. 

The chapter containing Maxwell's electromagnetic theory in general, and 
the electromagnetic theory of light in particular, is so interesting that the 
young student will undoubtedly regret that Professor Thomson has not 
made this chapter longer. But he can console himself with the idea that 
if this book has not given him the whole story of the modem achievements 
of the electromagnetic theory, it has certainly prepared him to hear and 
appreciate this story. 

An elementary book like this, by so eminent an authority as Professor 
Thomson, contributes almost as much to the progress of science as an 
important discovery. Teachers and students of electricity should not be 
without it. 

M. I. PUPIN. 



Crystallography y a Treatise on the Morphology of Crystals, By N. 
Storv-Maskelyne, M.A., F.R.S. i2mo, pp. 521 4- xii. Oxford, Claren- 
don Press, 1895. 

As indicated by the sub-title, the author's aim is a complete discussion 
of the external form of crystals ; and it may be said at the outset that 
nothing in English equals this book as regards detailed treatment of 
geometrical crystallography. 

In the first chapter is given a very brief sketch of the general properties 
of crystals. This serves as an introduction to the more special study of 
their forms. 

Chapters II., III., IV., and V. deal with crystal planes and axes, and with 
the mutual relations of the same. The treatment, as required by the nature 
of the case, is almost purely mathematical. It is in most respects clear 
and thorough, and will be found very useful to those who wish to supple- 
ment an elementary knowledge of the subject. The foundation here laid 
is, naturally, specially adapted to use in the later portions of the book ; 
yet the discussion of Miller's symbols and of the possible kinds of crystal 
symmetry will be appreciated by any who wish to consider these subjects 
apart from the rest of the book. 

The following chapter is divided into two sections, — one devoted to 
mero-symmetry (a term coined to designate all kinds of symmetry except 
six, viz., the highest symmetry possible in each of the six systems) and the 
other to twin crystals. It seems unfortunate that two subjects which are 
so pre-eminently matters of crystal structure should be treated firom the 




396 ITEIV BOOKS. [Vol. III. 

staDdpoint of their external form, but this is in accord with the plan of 
the book, and the author is consistent in carrying it out. 

In Chapter VII., which occupies 200 pages, the six crystal systems are 
described in detail. All the possible crystal forms are classified and 
named. At the end of the description of the forms in each system, several 
articles are devoted to the subject of twin crystals. Though no mention is 
made of ogdohedrism (the author would call it ogdo-symmetry), neverthe- 
less this pecuHar type of symmetry is duly noticed under the heading 
" Tetarto-systematic Haplohedral Forms " in the hexagonal system. 

Chapter VIIL, on the measurement and calculation of the angles of crys- 
tals, contains a very good description of some kinds of goniometers and 
their use, as well as methods of calculation which may be of service to such 
as desire help in this line. 

The final chapter presents an extremely satis^tory resume of the various 
methods of representing crystals, though parts of it may be found rather 
too condensed to be appreciated by the beginner. 

The book as a whole may be characterized as independent and thorough. 
Its independence lends fi-eshness and interest, to be sure, though in several 
respects it may also be found by some to detract fi-om its value as a book 
of reference. For instance, no allusion is made to the symbols used by 
Naumann, Weiss, L^vy, or Dana in designating the position of planes on a 
crystal, although all these are simpler than Miller's. This is no oversight. 
The author simply (and rightly) considers Miller's method the best, and 
uses it. Yet three of the above-mentioned systems of symbols are still in 
use by crystallographers, and the fourth is found of service to beginners. 

The terras hemihedral and hemihedrism are not discussed. They are 
replaced by words designating the symmetry. The new nomenclature can 
hardly be said to be an improvement on the old, so far as the significance 
of its derivation is concerned, as there is no more reason for calling the 
symmetry of calcite a partial symmetry, than there would be for designat- 
ing the symmetry of axinite in the same way. Each substance crystallizes 
with the /^^/7 symmetry belonging to itself, without reference to the greater 
or less symmetry which may be manifested by other substances. 

The authcr's use of the words merohedral (p. 159) and clinopinakoid 
(p. 358) in a sense entirely new is certainly not defensible, and the omis- 
sion of all reference to alternative names for the six systems may also be 
criticized, especially in the case of the sixth, which is much more generally 
called triclinic than anorthic. Yet only the latter name appears in the 
book. Reference may also be made to the employment of the Greek 
letters i, 1;, and { instead of the more usual a, )3, and y, in designating the 
angles between the axes. On the whole, the book may be said to lose 
more than it gains by its independence in the matter of terminology. Yet 



No. 5.] NEW BOOKS. 397 

the words haplohedral and diplohedral, denoting the absence or presence of 
parallel planes in a crystal form, would seem to have good reason for 
existence. 

In the matter of clearness the book is frequently at fault through a com- 
bination of long sentences with cumbersome technical words. More rarely 
a misprint or a word wrongly used is responsible for the difficulty. An 
example may be quoted from p. 156. " When we turn to the natural poly- 
hedra presented in crystals in order to determine to what extent these 
actually accord in their geometrical characters with the crystalloid systems 
hitherto considered, we cannot fail to recognize that whereas the crystal- 
lographer, guided heretofore solely by observation and experience, referred 
every crystal to one or other of six crystallographic systems, those systems 
furnish precisely the several types of symmetry which coincide in their dis- 
tinctive features with the six crystalloid types of symmetry resulting from 
the above principle ;" viz., that there are only four possible varieties of 
isogonal zones in a crystalloid system. If the above sentence was not 
intended to call attention to the coincidence between the independent 
results of the crystallographer and of the mathematician in establishing six 
cr)'stal systems, the reviewer has not yet fathomed it. 

A. C. Gill. 



Electricity and Magnetism, a Mathematical Treatise for Advanced 
Undergraduate Students, By Francis E. Nipher. 8vo, pp. 426. St. 
Louis, Boland Book Co., 1895. 

This book occupies a field in electrical science that is of fundamental 
importance, but which has not been covered satisfactorily by existing liter- 
ature. The older treatises, of which that of Mascart and Joubert may be 
taken as an example, were based upon objects and methods that antedated 
the remarkable development of electrical applications during recent years. 
It might be said that the science of electricity, considered from the purely 
mathematical or physical standpoint, is entirely independent of practical 
applications ; nevertheless the fact remains that this progress, commercial 
though it may be, has produced the greatest stimulating effect that any 
science ever received. Even in such apparently abstract subjects as 
those of rational units and definite terminology, their appreciation and 
general adoption are due far more to this influence than to all others 
combined. Furthermore, many of the most earnest and most successful 
students of electrical science are those who are preparing themselves for 
a career in its engineering branches ; therefore it is reasonable to expect 
that the instruction not only in technical schools, but also in courses of 
pure science, shall be in harmony with and lead up to the practical applica- 



398 NEIV BOOKS. [Vol. III. 

tions. Even those students who intend to devote themselves to the theo- 
retical side of electricity are much benefited by and are usually anxious to 
acquire at least a general knowledge of the dynamo, motor, and transformer. 
There are many works on special subjects which are essentially mathe- 
matical in character, but so far as the reviewer is aware, this book is the 
first general treatment of the mathematical principles of electricity and 
magnetism which leads directly up to electrical engineering, but only goes 
into it to the extent of giving a few practical examples. Professor Nipher 
therefore deserves credit as a pioneer in a most important direction. His 
work is also to be commended for features which show ability and experience 
in the art of teaching. For example, the subjects of potential and energy 
are introduced and explained in connection with gravitation. This not only 
gives a definite and well-grounded conception, but also broadens the view 
of the electrical student, who is apt to think that potential is confined to 
his particular science. The frequent use of concrete numerical examples 
is still another great aid to the student as well as to the instructor. The 
scope of this book shows good judgment; that is to say, the point at 
which it begins and the previous knowledge assumed, as well as the limits 
reached, are well suited to the majority of students who are Ukely to use it. 

Nevertheless, there are several features which are open to question or 
criticism. The most prominent of these is the excessive amount of matter. 
While four hundred pages is not an unusually large number for a text-book, 
nevertheless the subject is somewhat difficult and is given in condensed 
form, so that it would not be practicable to cover more than a few pages 
in one lesson. Moreover, it would have been perfectly possible to con- 
siderably reduce the length without sacrificing anything essential. For 
example, in the chapter on electrostatics some of the cases of potential, 
distribution of charge, etc., under various conditions, might have been 
omitted. 

The old-fashioned conceptions and methods relating to magnetism, such 
as susceptibility, magnetic moment, etc., might have been abridged with- 
out material loss. In fact, the modern way of treating the magnetic circuit 
in terms of flux, M.M.F., and reluctance is not incorporated in the book as 
freely and completely as present custom warrants. In this connection, the 
idea of surface charge or distribution of magnetism used by Professor 
Nipher is unnatural and perpetuates the geometrical methods of treating 
this subject, including poles, straight lines of force, and other conditions 
which rarely if ever exist and differ so radically fi-om the more modem 
views of the ** closed loops " of Faraday. 

The author's definition of current in terms of its magnetic effect is ver}' 
abrupt and hardly satisfactory to the majority of minds, and the same is true 
of the manner in which the subject of alternating currents is introduced. 



No. 5.] NEIV BOOKS. 399 

The book would have been improved by giving references to authorities 
and sources of information, not only to assist and encourage those who 
wish to pursue their studies further, but also in simple justice to writers 
from whom much material was derived. The fact that it is an elementary 
and not an advanced treatise is not a valid answer to this criticism. 

In spite of these objections this book is a fairly successful attempt in a 
new and yet very important direction, and should be welcomed by those 
interested in education in electrical science, particularly when it forms part 
of an engineering course. 

F. B. Crocker. 



Notes on the Nebular Theory. By William Ford Stanley. 8vo. 
pp. 260. London, Kegan Paul, Trench, Trubner & Co., 1895. 

This book of 260 pages contains the speculations upon the Nebular 
Theory of a gentleman not a professional astronomer, who has evidently 
devoted much thought to the subject. Nevertheless, it is difficult to regard 
the work as a positive contribution to our knowledge of cosmogony. The 
author states in the preface that he has been led " to the conclusion that a 
modified form of the Nebular Theory of Laplace might be established on 
some new ideas which I had formed, and by certain calculations that I felt 
sure the actual conditions warranted." 

The treatment of the subject is not mathematical, and, except for some 
fifteen pages of historical notes upon the theories of Wright, Kant, Laplace, 
and later philosophers of cosmogony, the book is merely a statement — 
and not always a clear one — of the numerous ideas that have occurred to 
its author. It cannot be said that these ideas are based upon our present 
knowledge of astronomy, mathematics, and physics, to the degree that 
would be expected in a book upon such a subject as this. The strong 
confirmation of the general theory of Laplace that has been furnished by 
recent spectroscopic researches seems to have been overlooked. A chap- 
ter is given to a " discussion of the mechanical principles upon which our 
solar-planetary system may have been formed,'* but many of the views ad- 
vanced cannot be harmonized with the laws of mechanics. Although the 
margins of the reviewer's copy of the book are quite fully occupied with 
exceptions taken to the author's statements, yet it seems hardly worth while 
to cite them in detail here. 

The author's style is not lucid ; in fact, his language is so greatly clogged 
with words that it is often very difficult to grasp the idea presented, even 
after repeated readings of the passage. We give an example, without 
selecting an especially conspicuous one. " In this case, with proportional 
time-condensation, under the increasing amount of tangential impulse due 



400 NEIV BOOKS, [Vol. III. 

to centralized condensation into gravitation, which produces the law of 
orbit, the distances of the planets from the sun and their separate masses 
would be symmetrically proportional, in accordance with the pull of gravi- 
tation and the tangential momentum of the amount of the condensed 
matter" (p. 66). On p. 105, the term iridescence is used where irradia- 
tion is obviously the phenomenon referred to. 

Under the chapter devoted to " Comets considered as Ordinary Gravita- 
tive Matter in Rotation constructively as a Part of the Planetary System," 
we read : " These ideas will be now reproduced, with some extenuations 
that appear to me necessary in reconsidering the subject." Among the 
ideas requiring ** extenuation," we cite this : " If the comet depart through 
some disturbance from its law of original construction, its matter may pre- 
sent afterward only what we may term a specialized confusion, too compli- 
cated to discuss by the most advanced science" (p. 127). 

Something more than the last third of the book is occupied with geologi- 
cal theories, upon which the reviewer can express no opinion, although 
decided exceptions must be taken to the astronomical speculations upon 
which the succession of geological periods is based, in the chapter entitled 
" Periodic Conditions of Earth-formation produced by effects incidental to 
the Nebular Clouding at Inferior Planetary Formation, and at Critical Tem- 
peratures of Matter surrounding the Sun." 

The typographical appearance of the book is excellent. 

Edwin B. Frost. 

Mechanics and Hydrostatics, By R. T. Glazebrook, F.R.S. 8vo. 
pp. 244, 176, and 208. Cambridge, The University Press, 1895. 

This volume consists of three parts, — Dynamics, Statics, and Hydrostat- 
ics, each with its own paging. The parts may also be obtained separately. 
A notice of the series and a review of Dynamics has been given in the 
Physical Review, Vol. III., No. 3. 

Analytical Chemistry. By N. Menschutkin. Translated by James 
Locke. 8vo, pp. xii, 511. London, Macmillan & Co., 1895. Received. 

Elementary Mensuration. By F. H. Stevens, pp. 243. Macmil- 
lan & Co., 1895. (^Received.) 

Elements of Physics: a College Text-Book. By Edward L. 
Nichols and Wiluam S. Franklin. In three volumes. Vol. I., Me- 
chanics and Heat. pp. 228. Macmillan & Co., 1895. 

Vol. II. (Electricity) and Vol. III. (Sound and Light) are in preparation. 



Volume III. May-June^ i8g6. Number 6. 



THE 

PHYSICAL REVIEW. 



SOLIDS AND VAPORS. 
By Wilder D. Bancroft.^ 

WHEN a substance, having no appreciable vapor-pressure of 
its own, is dissolved in a liquid, the vapor-pressure of the 
solution is less than that of the pure solvent. From this it follows 
that if two beakers, one containing a salt solution and the other 
pure water, be placed under a bell-jar, the water will all distill over 
into the beaker containing the solution,^ provided that we leave out 
of account any effect due to gravity. A further conclusion is that 
all substances are deliquescent in presence of the saturated vapor 
of a liquid in which they are soluble. As a striking example of 
this I have taken the blue double salt, CuCl^ 2 KCl 2 H2O. This 
salt was placed in a test-tube above absolute alcohol, so that any 
liquid that condensed upon it might flow back into the bottom of 
the test-tube again. The result was that the cupric chloride was 
dissolved out, leaving the white potassium chloride behind. 

As the vapor-pressures of pure water and of a saturated salt 
solution are functions of the temperature only, it follows that, if 
the other conditions are kept constant, water must condense on the 
salt solution at an uniform rate so long as any of the solid salt is 

1 In my paper on the Chemical Potential of the Metals, Physical Review, Vol. III., 
p. 253, 1896, 1 overlooked very carelessly the definite assumption of Nemst, Zeitschr. L 
phys. Chem., 4, p. 149, 1889, in regard to the anion. 

^ Cf. Beyerinck, Zeitschr. f. phys. Chem., 9, p. 264, 1892. 

401 



402 WILDER D, BANCROFT. [Vol. III. 

present I tried the experiment at first very roughly by putting a 
little ammonium chloride in a small porcelain crucible, which was 
then placed in a desiccator containing water instead of sulfuric 
acid. The whole was left at room temperature ; the crucible was 
weighed from time to time, and the gain in weight noted. While 
there could be no doubt but that the ammonium chloride would 
absorb water, I was not at all sure that the amount absorbed in a 
given time would be enough to make the experiment of any value. 
In this I was agreeably surprised, as I found that under these cir- 
cumstances the salt gained water at the rate of about twelve milli- 
grams per hour. The rate of absorption is dependent on the dif- 
ference of pressure between the solvent and the solution, on the 
areas of the evaporating and condensing surfaces, and on the rate 
of diffusion of water-vapor under the conditions of the experiment. 
Whether there is also an effect due to the specific nature of the 
dissolved substance apart from the vapor-pressure of its saturated 
solution is not known. Such an effect would be entirely contrary 
to our present ways of looking at things ; but that does not prove 
its non-existence. With so many factors to be taken into account, 
it is very difficult to make absolute measurements. On the other 
hand, it is a comparatively simple matter to make relative deter- 
minations which are entirely satisfactory for a great many pur- 
poses. The uncertainty as to the amount of surface of the solid 
salt can be obviated by having a saturated solution in a cylindrical 
vessel so that the condensation takes place on a liquid surface 
only. By setting up the apparatus always in the same way, it 
would not be necessary, so far as purposes of direct comparison 
go, to know the areas of the evaporating and condensing surfaces 
nor the term due to the rate of diffusion. Mr. Parker has kindly 
made one set of determinations for me at constant temperature to 
show that under uniform conditions one actually gets a constant 
reaction-velocity. The salt taken was ammonium chloride, and 
the temperature was 35°. The results are given in Table I. The 
last determination was made when the solution was no longer 
saturated, all the salt having been dissolved. As was to be ex- 
pected, the rate of condensation has decreased, owing to the in- 
creased vapor-pressure of the solution. 




No. 6.] 



SOUDS AND VAPORS. 



403 



Table I. 



No. of hours. 


Gain per hour. 


No. of hours. 


Oain per hour. 


24 


0.039 g. 


49 


0.044 g. 


25 


0.040 


23 


0.041 


71 


0.036 


25 


0.042 


48 


0.042 


24 


0.042 


71 


0.042 


25 


0.031 



The results agree as well as one could wish under the circum- 
stances. It would doubtless be possible to get more accurate 
results by stirring the solution so that there should be no differ- 
ences of concentration in the liquid. This method gfives an easy 
and fairly accurate measurement of vapor-pressures of salt solu- 
tions, and I hope before long to communicate some interesting 
applications of it. 

We are now able to state* the conditions under which deliques- 
cence will take place. An anhydrous salt is permanent if the concen- 
tration of the water-vapor is equal to or less than the vapor-pressure 
of its saturated solution. It is deliquescent if the pressure exceeds 
that value. With hydrated salts the case is a little different, 
because they can .also lose water. It is well known that below a 
certain pressure of water-vapor they effloresce. If the concentra- 
tion of water in the vapor space becomes greater than that corre- 
sponding to the saturated solution, they will deliquesce. Do these 
two concentrations coincide, or is there an interval over which the 
salt is permanent and in indifferent equilibrium with the vapor i 
In other words, does a hydrated salt have the same vapor-pressure 
as the solution with which it is in equilibrium? I have been 
unable to find any definite statement on the subject in the text- 
books of Ostwald or of Nernst ; but the impression which I get 
from their writings is that they would probably apply the law of 
the Substitution of Phases to this case, and would say that the two 
phases, hydrated crystals and saturated solution, being in equi- 
librium with each other, must have the same vapor-pressure.^ I 
am the more inclined to believe that this is a fair statement of 

^ Cf. Zeitschr. f. phys. Chem., i, p. 205, 1887. 



404 



WILDER D, BANCROFT. 



[Vol. IIL 



their views, because there is no question but that Planck holds 
this view. He says : ^ "All coexisting solid and liquid phases send 
out the same vapor." This is the more remarkable because there 
is abundant evidence that this is not true. Van 't HofiF^ has 
shown that slightly effloresced sodium sulfate has a less vapor- 
pressure than the saturated solution; Roozeboom* has stated that 
the solution and the hydrate cannot have the same vapor-pressure 
except at the inversion temperature ; and Lescoeur, while disput- 
ing the accuracy of Roozeboom's generalization, brings forward a 
long series of observations to show that it is true in a great many 
cases. In Table II. I tabulate some of Lescoeur's measurements 
on the vapor-pressures of hydrated salts and their saturated solu- 
tions.* It will be noticed that the differences between the two are 
often enormous. The pressures are given in millimeters of mer- 
cury ; the temperature is 20°. 

Table II. 





Pressure la mm. 




PrsMure in mm. 




Hg. 




Hg. 




Solution. 


Salt. 


Solution. 


Sslt. 


CaQzeHjO. . . . 


5.4 


2.3 


NajCOslZHjO . *. 


16.0 


10.1 


SrOaeHzO. 








11.4 


5.6 


NajSOilOHjO . . 


15.7 


13.9 


Mna2 4HsO 








8.0 


3.8 


Na2S04 7H20 . . 


15.0 


10.5 


NiaseHsO. 








8.0 


4.6 


MgS04 7H20 . . 


14.5 


7.3 


C0CI2 6 H2O 








9.0 


4.0 


CUSO45H2O. . . 


58.0 


30.0 


NaBr4HaO. 








9.6 


7.6 


Mga26H20. . . 


5.7 


1.8 


SrBraeHjO. 








9.1 


1.7 


NaI4H20. . . . 


5.4 


1.5 



It is generally assumed that two phases in equilibrium must 
give off the same vapor, or that it would be possible to make a 
perpetual motion machine, but this conclusion is not necessary. 
Suppose we have a system composed of hydrated salt, solution, 
and vapor. If the solution has a greater vapor-pressure than the 

1 Grundriss d. Thermochemie, p. 125. 

2 Zeitschr. f. phys. Chem., i, p. 185, 1887. 
»C. r. no, p. 134, 1890. 

* Ann. chim. phys. (6), 19, p. 533, 21, p. 511, 1890; (7), 2, p. 78, 1894. 




No. 6.] SOLIDS AND VAPORS. 405 

hydrated salt, there will be a tendency for water to precipitate on 
the crystals ; but the effect of this will be to cause some of the salt 
to go into solution, and at the same time water will evaporate to 
restore the vapor-pressure of the saturated solution, precipitating 
the same quantity of salt which has just dissolved. No change 
has taken place in the system, and there is no surplus energy with 
which to run a machine. The matter can be seen even more 
clearly in the limiting case, that of an anhydrous salt in equilib- 
rium with a saturated solution and the vapor thereof. Here there 
can be no question that we have a solid and a liquid phase coexist- 
ing, and that they do not give off the same vapor. With calcium 
chloride, and still more strikingly with the hydrates of ferric 
chloride, Roozeboom^ has shown that the same hydrate can be in 
stable equilibrium with two different solutions, one containing 
more water than the crystals, the other less. As the vapor-pres- 
sures of the two solutions are not the same, it follows that at least 
one is different from the value for the hydrated salt, which is suffi- 
cient to prove the point. The case does not rest on this alone. 
We may reach the same conclusion in another way. If we add to 
a saturated solution of a hydrated salt a second salt having differ- 
ent ions, we shall have more of the first salt go into solution. The 
solution will now have a less vapor-pressure than before. If the 
vapor-pressure of the hydrated salt had been equal to the vapor- 
pressure of its saturated solution, it would be greater than that of 
the new solution, and the crystals would effloresce, no matter how 
small the added quantity of the second salt was. In general this 
is not the case, and I conclude that the vapor-pressure of a 
hydrated salt is not necessarily the same as that of the solution 
with which it is in equilibrium. It has been overlooked by every 
one except Roozeboom and van 't Hoff that in the system, salt, 
solution, and vapor, there are two kinds of equilibrium repre- 
sented, the stable and the indifferent. A given solution can have 
only one vapor-pressure at a given temperature; the concen- 
tration of water vapor in equilibrium with an anhydrous or a 
hydrated salt may have any value between two limits. The reason 
for this difiference is that the concentration of the solution can 

1 Zeitschr. f. phys. Chem., 4, p. 34, 1889; ^^*^'* lo* P* 4^6? 1S92. 




4o6 



WILDER D, BANCROFT, 



[Vol. 111. 



vary continuously, that of the hydrate cannot The vapor-pressure 
of a system containing hydrate, water vapor, and a third phase will 
depend therefore on the nature of the third phase. The experi- 
ments of Roozeboom^ show that this is so.^ In Table III. I give 
his determinations of the vapor-pressures at which CaCl^ 6 HjO is 
in equilibrium with different phases, the pressures being in milli- 
meters of mercury. 

Table III. 



Temperature. 


o* 


»• 


20* 


«5- 


CaQz 6 HiO, solution, vapor . . . 
CaGa 6 HjO, CaQj 4 HjOo, vapor . 
CaCla 6 H2O, CaQ, 4 HjO/S. vapor . 


1.9H 

0.92 

0.76 


3.456 

1.92 

1.62 


5.616 

3.78 

3.15 


6.696 

5.08 

4J2 



As will be seen, not only is the vapor-pressure of the saturated 
solution different from that when there is a solid phase present, 
but there is a marked difiference between the values for the 
systems CaClj 6 HjO, CaClg 4 HgOa, vapor, and CaClg 6 H3O, 
CaCl2 4 HjOA vapor. This discrepancy is a real one, being 
greater than the probable error of the measurements. The ques- 
tion suggests itself, in view of these facts, whether it is proper to 
speak of the vapor-pressure of a hydrated salt ; in other words, 
whether it has a true vapor-pressure independent of the nature of 
the third phase. There is such a value as we may see from the 
following considerations : Suppose that water and the salt under 
consideration could form a continuous series of mix crystals, as is 
the case with the alums. For a given temperature and a given 
concentration of the solid phase the pressure would be definitely 
fixed, just as is the case when the equilibrium is between a liquid 
solution and its vapor. That value is the true vapor-pressure of 
that crystal. If we bring in discontinuity, we increase the range 
of pressures at which the hydrate can be in equilibrium, but we 
do not change the fact that one particular pressure differs from 
the others, because the equilibrium in that case is independent of 
the discontinuity in the solid phase. I define the true vapor- 

1 2^itschr. f. Chem., 4, p. 42, 1889. 

^ This has been overlooked by Nernst, Theor. Chem., p. 491. 



No. 6.] SOLIDS AND VAPORS - 407 

pressure of a given hydrate at a given temperature as the pressure 
at which it would be in equilibrium if it were one term in a con- 
tinuous series of mix crystals. This is probably the same as the 
vapor-pressure of the system containing hydrate, anhydrous salt, 
or lower hydrate, solution, and vapor in equilibrium, the number 
of the components in the solution not being limited.^ If this be 
true, it follows that as yet only in the cases where the measure- 
ment has been made at the inversion temperature can we be sure 
that we have determined the true vapor-pressure of the hydrated 
salt, for there is no reason to assume that this value coincides with 
that usually measured for the equilibrium between hydrate, efflo- 
resced product, and vapor. 

The fact that the saturated solution often has a greater vapor- 
pressure than the hydrated salt which crystallizes from it is of 
great interest as throwing light on some of the peculiarities which 
have been discovered in regard to the inversion temperature of 
salts. It is clear that if we add to a saturated solution enough of 
any substance to bring the vapor-pressure of the solution below 
that of the hydrated salt in respect to which the solution is satu- 
rated, the salt must effloresce. The simplest way to do this is to 
add a salt having no common ion. The only instance of this 
which I can now recall is the case cited by Meyerhoffer,^ that the 
double salt CuCljKCl crystallizes out of solutions containing acetic 
acid, instead of the double salt, CuClj 2 KCl 2 HjO. As I shall 
have occasion to discuss the mechanism of this reaction more fully 
under another head, I will only point out that the hydrated double 
salt ceases to be stable as soon as, by the addition of acetic acid, 
the partial pressure of the water-vapor in equilibrium with the 
solution becomes less than the true vapor-pressure of the hydrated 
double salt. That this instance might not seem an isolated, 
abnormal case, I have made a few qualitative experiments on 
other hydrated salts, and have found the phenomenon to be 
entirely general. 

Another means of obtaining the same result, namely dehydra- 
tion, is to add a substance which increases the number of re- 

1 Cf. Vriens, Zeitschr. f. phys. Chem., 7, p. 208, 1891. 
« Zeitschr. f. phys. Chem., 3, p. 339, 1889. 




408 WILDER D. BANCROFT, [Vol. III. 

acting weights in solution, though decreasing the solubility of the 
hydrated salt. This effect may be produced by a non-electrolyte 
in which the salt is insoluble, or by a salt having a common ion, 
though it by no means follows that either of these must do it 
The dehydrating effect of alcohol on many salts with water of 
crystallization is too familiar to need more than a reference. That 
salts crystallize in a more or less completely dehydrated condition 
from solutions containing an excess of acid is also well known. 
This has been used as a method for obtaining salts having less 
crystal water than is normal at the temperature of the experiment^ 
This means that the inversion temperature of that particular 
hydrate in respect to the solution has been changed, and this 
phenomenon has been noticed often without any very satisfactory 
explanation having been gfiven. The reaction 

MgS04 7 H2O = MgSO^ 6 H jO 4- H3O 

takes place at 48^.2 when no other salt is present; at 47*^.2,* if an 
excess of K^Mg(S04)2 6 HjO be present, and at 29^.8,* if the solu- 
tion be also saturated in respect to potassium chloride. Loewen- 
herz* has noticed that the inversion temperature is lowered to 25° 
if, to a saturated solution of magnesium sulfate, magnesium chloride 
be added in such quantities that the solution contains 73 units of 
anhydrous magnesium chloride to 1000 units of water, or if mag- 
nesium chloride and potassium chloride be added in such propor- 
tions as to give concentration of 62 units of MgCl2 and 16 units of 
KCl per 1000 units of water. We have in all these cases the same 
phenomenon, addition of another salt or salts reducing the vapor- 
pressure of the solution below that of the hydrated salt, which 
thereupon effloresces. The difference in the effect produced by 
magnesium chloride and by Schonite is due chiefly to the greater 
solubility of the former, though the relative influence on the solu- 
bility of the magnesium sulfate is also a factor. The change of 
Schonite into potassium astrakanite, corresponding to the reaction 

K2Mg(S04)2 6 H2O = K^MgCSO^)^ 4 H^O 4- 2 HjO, 

1 Cf. Ditte, Ann. chim. phys. ($), 22, p. 560. * Ibid., 13, p. 489, 1894. 

2 Zcitschr. f. phys. Chem., 12, p. 426, 1893. * Ibid^ 13, p. 480, 1894. 



No. 6.] SOLIDS AND VAPORS, 409 

occurs at 92° if there is an excess of potassium sulfate present, 
and at 72° in presence of an excess of the magnesium sulfate with 
six units of water.^ If the solution is not saturated in respect to 
MgCla 6 HjO, the inversion temperature may be made to lie any- 
where between these two temperatures, depending on the amount 
of magnesium sulfate in solution. There is no doubt in my mind 
that still other inversion temperatures could be found by adding 
other salts to a saturated solution of Schonite. As is well known, 
Na2S04 10 HjO changes into the anhydrous salt at about 33"^ if 
there is nothing else in solution. If an excess of 

Na,Mg(SO,)a4H20 

be added, the inversion temperature falls to 26°, while an excess of 
NaCl and MgS04 7H20 carries it down to 15°.^ The double 
salts of copper and potassium chlorides have been studied by 
Meyerhofifer,* who found that the reaction which takes place is 
represented by the equation 

CUCI32 KCl 2 H20 = CuCl2KCl4-KCl4-2 H^O. 

This change takes place at 92° if the solution is saturated in 
respect to KCl; at 55"^ if saturated in respect to CuCl2 2HjO. 
Here, as before, the greater solubility of the cupric chloride is the 
cause of this change in the stability of the hydrated double salt. 
This reaction differs from the others which we have considered in 
that we do not get a simple case of dehydration as we should 
expect, but have the formation of a new salt with separation of 
potassium chloride. The reason for this seems to be that the 
anhydrous salt CuClg 2 KCl is unstable and goes over into the 
form CuCljKCl and KCl.' Why this should be so is not known. 
I have let the blue double salt effloresce over strong sulfuric acid, 
but the product seems to be the red double salt and potassium 
chloride. It would be very interesting to know whether double 
salts of this type, where the two components are held together by 
the water of crystallization, differ in any other properties from 
hydrated double salts which do not show this peculiarity. 

1 Zeitachr. f. phys. Chem., 12, p. 417, 1893. 

« Ibid., I, p. 176, 1887. « IHd., 3, p. 336, 1889. 



ai 



4IO WILDER D, BANCROFT, [Vol. III. 

The cases which we have examined so far have all been alike in 
one respect, that the hydrated salt which it was proposed to make 
effloresce was stable below the inversion temperature. This is 
not necessary, and in astrakanite we have the reverse order of 
things. 

MgS04 7 H3O + Na,S04 10 H2O = Na2Mg(S04)a 4 H^O + 1 3 H3O. 

Here the double sulfate crystallizes out above 21**. 5, the single 
salts below that temperature. Adding a salt which will increase 
the number of ions in solution will therefore raise the inversion 
temperature, while the addition of a salt which decreases the num- 
ber of ions will lower it. In other words, we shall have our previ- 
ous effects reversed. Both these cases have been realized by van *t 
Hoff.^ In the presence of an excess of MgCl2 6 H3O the inversion 
temperature is raised to 31°, while saturating the solution with 
sodium chloride produces the opposite effect, the inversion tem- 
perature becoming +5°. For the first time we get a marked 
effect, due to the different precipitating power of two salts. The 
addition of either magnesium or sodium chloride should cause a 
decrease in the solubility of the double salt ; but in the first case 
the precipitation is so slight that the number of ions in solution is 
increased, and in the second it is so great that the vapor-pressure 
of the solution rises. 

Having shown that in general the vapor-pressure of a partially 
effloresced salt is less than that of its saturated solution, it is worth 
while to consider whether the two can be equal except at the 
inversion temperature. In Table IV. I give some of Lescceur*s 
measurements.^ The pressures are in millimeters of mercury. 

1 Zeitschr. f. phys. Chem., i, pp. 170, 176, 183, 1887. 
^ Ann. chim, phys., (7), 2, p. 78, 1894. 



No. 6.] 



SOUDS AND VAPORS. 



411 



Table IV. 



BaBrj 2 HjO 
BaBra 2 H2O 
MgBrj 6 HaO 
MgBraeHsO 
CdBrj4HaO 
CdBra4HsO 
BaIa6H20 . 
BaIa6H20 . 
MnBra 4 H2O 
MnBra4HaO 



Pressure. 



Solution. 



10.7 

124.0 

3.4 

166.0 

10.0 

122.0 

8.4 

58.0 

5.0 

202.0 



Salt. 



10.6 
124.0 

33 
166.0 

9.0 
124.0 

8.4 
60.0 

5.0 
200.0 



Temperature. 



60° 
20° 

100° 
20° 
60° 
20° 
60° 
20° 

100° 



We have in all these cases equality between the two vapor- 
pressures, and that over a considerable range of temperature. A 
more interesting confirmation is furnished by Joannis ^ in his meas- 
urements of the vapor-pressure of saturated solutions of sodam- 
monium and of the partially effloresced product. 

Table V. 



lg.NH8Xa+ 1.669 g.NHs . 
1 g. NHsNa -I- 0.460 g. NHs . 
0.971 g. NHjNa + 0.029 g. Na 
0.487 g. NHsNa + 0.513 g. Na 
0.108 g. NHsNa -f- 0.892 g. Na 
0.(M3 g. NHsNa -|- 0.957 g. Na 
1 g. NHsNa -I- 0.46 g. NH, . 
0.7 g. NHsNa + 030 g. Na . 
0.39 g. NHsNa -|- 0.61 g. Na . 
0.19 g. NHsNa + 0.81 g. Na . 



Pressure. 



169.7 mm. 

169.7 

169.7 

169.7 

169.7 

169.65 

117.0 

1173 

117.0 

117.1 



Temperature. 



0° 

0° 

0° 

0° 

0° 

0° 

-10° 

-10° 

-10° 

-10° 



The agreement is perfect, and as the compound is stable at 
H-22®, the objection of Roozeboom that the measurements had 
been made in the neighborhood of the inversion temperature 
ic. r., no, p. 238, 1890. 



412 WILDER D. BANCROFT. [Vol. III. 

cannot be sustained. I see at present no theoretical reason why 
the dissociation-pressure of a hydrated salt may not be the same as 
that of its saturated solution, and I do not agree with Roozeboom 
when, after describing the usual diagram for the equilibrium be- 
tween different hydrates and water, he says:^ "II en resulte que la 
tension de dissociation est toujours plus petite que celle de sa solu- 
tion satur6e, sauf dans le point C. Ainsi ce point represente la tem- 
perature et la pression unique ou il y a coexistence des deux corps 
solides avec la solution et la vapeur d'eau." At the inversion tem- 
peratiure there come together three vapor-pressures,^ that of the 
hydrate, of its saturated solution, and of the saturated solution of 
the anhydrous salt, and all that can be predicted is that the vapor- 
pressure of the stable saturated solution is greater than that of the 
solution saturated in respect to the labile modification. How 
rapidly the curves for the true vapor-pressure of the hydrate and 
its saturated solution diverge, or whether they necessarily diverge 
at all, is a question which has no bearing on the inversion tempera- 
ture. They may intersect before the inversion temperature is 
reached, in which case the salt melts and there is no formation of 
a new solid phase. 

In speaking of the stable and the labile modifications, it must 
be kept in mind that these terms are to be reversed if we are con- 
sidering the vapor-phase. When we refer to the solution, the 
more stable modification is the less soluble one. When we refer 
to the vapor-phase, it is the one having the lesser vapor-pressure. 
Below 33*^, for instance, the saturated solution of anhydrous 
sodium sulfate has a smaller vapor-pressure^ than the solution in 
equilibrium with the hydrated salt, and is therefore more stable in 
that respect. If we place the two saturated solutions in the two 
limbs of an inverted U-tube, water will distill from the one contain- 
ing the hydrated salt into the other. We can go still further, and 

»C r.. no, p. 135, 1890. 

^ U there are no other components, the dissociation curve intersects here. The true 
\aiK>i picssure of the hydrate will always lie between the pressure of the saturated solu- 
iivu Aiul the dissociation pressure. 

'^ VKycihortcr's diagram is wrong. (Phasenregel, p. 28.) His curves for the \2.'pox- 
luv >nuica <A Na^SO^^ solution, vapor, and of Na2S04 10 H2O, solution, vapor, if continued 
kv> a^ u> ic^uv:keut the labile equilibria, are in contradiction with the facts. 



No. 6.] SOLIDS AND VAPORS. 413 

say that if the system hydrated salt, anhydrous salt, vapor, has 
a greater vapor-pressure than the system anhydrous salt, solu- 
tion, vapor, the hydrated salt will effloresce, and the water will con- 
dense in the beaker containing the saturated solution of the an- 
hydrous salt. We shall thus have the spontaneous formation of 
the less stable system at the expense of the more stable. I tried 
to realize this with sodium sulfate at a temperature of about thirty 
degrees, and it looked once as if I had succeeded, but I cannot be 
certain of this. The great difficulty in carrying out the experiment 
is, of course, the spontaneous appearance of the more stable modi- 
fication in the solution. It may be that this experiment is theoreti- 
cally impossible for the reason that the vapor-pressure of the 
system hydrate, anhydrous salt, vapor, may be necessarily less 
than that of the saturated solution of the unstable modification. 
This is the case with the saturated solutions of CaCl2 4H20a and 
CaCl^ 4 HjO/S.i This would be very interesting if true. In that 
case Roozeboom would be entirely correct in the remarks of his 
which I have just quoted. While this may be true, it has not yet 
been shown by any one so far as I am aware. 

While I was in Amsterdam, Professor van 't Hoff showed me a 
very pretty lecture experiment which consisted in putting clear 
pieces of crystallized calcium sulfate in mixtures of sulfuric acid 
and water of different proportions. In the solutions containing 
much sulfuric acid, the crystals became cloudy, and in those con- 
taining much water they remained clear. The concentration at 
which the first dehydration took place could be determined with 
great accuracy by the eye. The method in this form is adapted 
only to sulfates insoluble in water, and is therefore incapable of 
general application. This is easily remedied by bringing the crys- 
tals in contact with the vapor of the solution instead of with the 
liquid itself. In this way one can use any salt which forms clear 
crystals, and one can equally use any other drying agent. Theo- 
retically there are objections to be made. For instance, it would 
not be proper to say that with sodium carbonate there was no 
formation of sodium sulfate ; but this reaction runs so slowly that 
the experiment is ended long before this effect becomes noticeable. 
1 Zeitschr. f. phys. Chem., 4, p. 43, 1889. 



414 WILDER D. BANCROFT, [Vol. III. 

This might not be the case were one to use strong hydrochloric 
acid as the drying agent. I have made a few measurements on 
copper and magnesium sulfates with rather surprising results. 
Frowein ^ found the vapor-pressure of partially effloresced copper 
sulfate to be equal to 10.9 mm. of mercury at 30*^.2 ; I find that 
copper sulfate just begins to effloresce when placed over a solution 
containing 48 per cent of sulfuric acid by weight, the temperature 
being 30°. This corresponds to a vapor-pressure of about 13 mm.* 
of mercury, or over two millimeters more than the value found by 
Frowein. This is beyond the limits of experimental error, as 
my measurements are accurate to within one-half a per cent of 
H2SO4, while the value of 10.9 mm. corresponds to a solution 
containing 51.5 per cent of sulfuric acid by weight. The same 
thing was noticed with magnesium sulfate. At 30°, Frowein's 
measurements give for the vapor-pressure of partially effloresced 
MgS04 7H2O the value (by interpolation) of 17.5 mm. Hg corre- 
sponding to the vapor-pressure of a solution containing 40.7 per 
cent HSO by weight. The direct experiment shows that mag- 
nesium sulfate effloresces over a 38 per cent solution of sulfuric 
acid, which has a vapor-pressure of 19.2 mm. As the vapor- 
pressure of an 84.5 per cent solution is only about 0.23 mm. at 
30°, there is no appreciable error in assuming the whole vapor- 
pressure of sulfuric acid solutions at that temperature to be due 
to water-vapor. The experiments just cited force upon us the 
conclusion that the equilibrium between a hydrated salt and water- 
vapor is affected by the presence of other substances. This shows 
that the minute quantity of sulfuric acid present as vapor does not 
behave as a so-called " indifferent " gas, and the same will be true 
of alcohol vapor and of the vapors of all substances capable of 
forming a solution with water at that temperature of the experi- 
ment. This has never been recognized. Nernst^ says: "Haben 
wir das Gleichgewicht zwischen Wasserdampf und wasserhaltigem 
Aether einmal untersucht, so ergibt umgekehrt die Bestimmung 
der Wassermenge, die einem krystallwasserhaltigen Salze von 
Aether entzogen wird, die Dissociationsspannung des Salzes.** 

1 Zeitschr. f. phys. Chem., i, p. 5, 1887. 

2 Landolt and Bernstein's Tables, p. 65. « Theoretische Chemic, p. 524. 



No. 6.] SOLIDS AND VAPORS. 415 

Linebarger^ has based a method of measuring vapor-pressures 
on this. 

This method can give good results only in cases where the 
effects due to the other liquid fall within the experimental error. 
This seems to be the case with ether, which is not surprising, 
though I have little doubt that a careful series of determinations 
would show that the results from the indirect method were larger 
than those by direct measurement. This would certainly be the 
case if alcohol or methyl alcohol were taken.^ The importance 
of this is that we can no longer assume that the same amount of 
work is done in compressing a given quantity of water-vapor 
from one volume to another in the two cases when we have the 
water-vapor alone and when we have alcohol-vapor present also, 
but work with a piston permeable to alcohol. 

Since it is not necessarily true that a solid and a liquid phase 
when in equilibrium must have the same vapor-pressure, it seems 
worth while to ask whether two liquid layers in equilibrium must 
give off the same vapor. Ostwald has given a proof of Konowa- 
low*s Law, which I quote : ^ " Denken wir uns namlich einen ring- 
formigen Hohlraum, Fig. i, der bei A etwa eine gesattigte Losung 
von Wasser in Ather, bei B eine solche von Ather und Wasser 
und in C den Dampf der Fliissigkeiten cnthalte, so wiirde, falls 
der Dampf iiber A eine andere Spannung als bei B hatte, oder 
anders zusammengesetzt ware, eine fortdauemde Destination oder 
Diffusion von der einen Seite zur anderen stattfinden, ohne dass 
jemals ein Stillstand eintrate, da auch die Fliissigkeiten sich durch 
Diffusion immer wieder ausgleichen wiirden. Wir batten also ein 
Perpetuum mobile was unmoglich ist." This sounds most con- 
vincing ; but let us examine this so-called " perpetuum mobile *' a 
little more closely. For the purposes of argument, let us assume 
that the vapor given off by the ether layer contains more ether 
than the vapor given off by the water layer and that the second 
vapor contains more water than the first. Ether will therefore 

' Zcitschr. f. phys. Chcm., 13, p. 500, 1894. 

^ I ventured to point out to Mr. Linebarger, nearly a year ago, this source of error; 
but he replied that the reasoning on which the method was based was free from hypoth- 
esis and as certain as the laws of thermodynamics. 

* Lchrbuch, I., p. 644. 



41 6 WILDER D, BANCROFT. [Vol. UI- 

distill from AtoB, and water from B to A, The water condens- 
ing at A will sink through the less dense ether layer ; the ether 
which condenses at B will become saturated with water, and we 
shall have as the second step in the process three liquid layers, 
the solution of water in ether at A, the solution of ether in water 
at By and an infinitely thin film of a solution of water in ether on 
top of the aqueous layer. Both free surfaces having the same 
composition, there is no need nor possibility of any further dis- 
tillation if we neglect the effect due to gravity.^ In other words, 
it is conceivable that we may have two liquid layers with different 
vapor-pressures and not assume the possibility of a perpetual- 
motion machine. Whether such a case really exists is an experi- 
mental problem, for which there are as yet no data. It is true 
that two liquid layers such as benzol and water, ether and water, 
have different boiling points, but this evidence is capable of 
another interpretation and is not conclusive. Of course, if it is 
shown that two liquid layers do not, as a rule, have the same 
vapor-pressure, that part of my argument on the difference be- 
tween solvent and solute, which is based on the contrary assump- 
tion,2 falls to the ground. 

The results of this paper, most of which are contained implicitly 
or explicitly in Roozeboom's articles, may be summed up : 

(i) Anhydrous salts are permanent till the pressure of the water- 
vapor in the gaseous phase becomes greater than the vapor-pressure 
of the saturated solution, after which they deliquesce. 

(2) Hydrated salts deliquesce when the pressure of the water- 
vapor becomes greater than the vapor-pressure of the saturated 
solution, effloresce when it becomes less than the vapor-pressure 
of the system containing hydrated and anhydrous salt, and are 
permanent when the value lies between these limits. 

(3) The vapor-pressure of a hydrated salt is usually less than 
the vapor-pressure of its saturated solution. 



^ Professor Trevor pointed out to me some time ago that, assuming the two liquid 
layers had the same vapor-pressure when at the same level, the effect of gravity would 
cause distillation till the system was symmetrical and the two free surfaces at the same 
level. This experiment has since been tried in his laboratory with the predicted result 

2 Physical Review, III., p. 203, 1895. 



No. 6.] SOLIDS AND VAPORS. 417 

(4) The vapor-pressure of a hydrated salt is a£fected by the 
nature of the effloresced salt. 

(5) The true vapor-pressure of a hydrated salt is probably known 
in few cases. 

(6) The equilibrium between a hydrated salt and water-vapor is 
affected by the presence of sulfuric acid. 

(7) Two liquid layers in equilibrium need not have the same 
vapor-pressure. 

May I, 1895. 



4l8 C. E. UNEBARGER. [Vol.111. 



T 



ON THE HEAT EFFECT OF MIXING LIQUIDS. 

By C. £. LiNEBARGER. 

Introductory, 
HE wide-reaching analogy between gases and solutions, first 



clearly pointed out by van 't Hofif, has proven very fruitful 
when applied to the elucidation of the phenomena presented by 
solutions. The fact that the laws which have been established for 
gaseous matter are by a little extension applicable to dissolved 
matter has been of great service in getting at the nature of solu- 
tion. While these laws are strictly true for gaseous and dissolved 
matter only in states of great rarefaction or dilution, they may, 
when properly modified, be employed in the investigation of gases 
or solutions of any degree of condensation. Especially is this true 
in the case of such substances as do not suffer molecular polymeri- 
zation, for the complexity caused by the introduction of considera- 
tions relative to the association and dissociation of the molecules is 
in such cases not present. In the case of normal liquids, a close 
continuity may be expected, not only in the passage from the 
liquid to the gaseous state, but also in the properties of the two 
states, and such differences as may be found in the liquid state 
compared with the gaseous state may be accounted for by com- 
paratively simple assumptions. 

An important property of different portions of matter is their 
possible inter-diffusibility or miscibility with one another. A 
characteristic of the gaseous state is unlimited miscibility. All 
liquids which do not suffer any alteration in the size of their 
molecules on passing into the gaseous condition are also perfectly 
miscible ; at least, no exception to this statement, so far as I know, 
has yet been found. Many associated liquids, however, do not 
mix in all proportions under certain conditions, but a certain 
degree of miscibility may always be observed, which, through 



No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS. 419 

changes in temperature and pressure, may become perfect. 
Solids, also, are not generally found to be capable of forming 
homogeneous mixtures under ordinary conditions ; yet by suitable 
changes of these conditions, it is probable that they may be made 
to mix. Van der Waal's law — "All substances can mix with one 
another if subjected to sufficient pressure"^ — is without doubt 
true of any system of bodies whatever, no matter what their state 
of aggregation ; seeming contradictions must, and doubtless will, 
be cleared away by future experimentation. 

To mix substances requires energy. The kinds of energy ex- 
pended in effecting the mixing are principally heat, volume, and 
chemical energy ; in the case of liquids and solids, surface and 
osmotic energy also come into play ; in all but exceptional cases 
electrical energy and light energy play no part. When the sum 
of the volumes of the unmixed substances is equal to the volume 
of the mixture, the mechanical energy, which is mainly evident in 
the overcoming of the pressure of the atmosphere, is equal to zero, 
and in many cases the changes of volume that occur during the 
mixing are so slight that the concomitant changes of mechanical 
energy vanish in comparison with the quantities of other kinds of 
energy brought into action. Heat energy plays by far the most 
important rdle in the mixing of substances. 

In nearly all work, both experimental and theoretical, on the 
heat changes occurring during solution, materials have been em- 
ployed which can exhibit the phenomenon of saturation or a 
limited degree of miscibility, and only one side of the question is 
taken into account. In the case of aqueous solutions of salts, 
which have as yet received the most attention, the solution of the 
salt in the water is alone thought of, although it is just as proper 
to say that the water dissolves in the salt, as that the salt dissolves 
in the water. This view of the subject is probably due to the cir- 
cumstance that the salt alone undergoes a change in its state of 
aggregation ; it becomes liquid, while the water remains liquid. But 
in reality solution is just as truly reciprocal in this case as in the 
case of dissolving liquids in liquids. This last-named phenomenon 

1 Die ContinaitSt des gasnSrmigen und flOssigen Zustandes. Roth's Gennan transla- 
tion, p. 146. 



420 C. E, UNEBARGER, [Vol. III. 

— solution of liquids — has received but little attention, especially 
when the liquids are normal. But as normal liquids approximate 
closely to gases in their behavior, and as gases present the simplest 
phenomena, it may be expected that investigation of the thermal- 
behavior of normal liquids will yield the simplest possible results, 
and give some indications as to the best means of getting a clear 
understanding of the general question of solution. 

The object of this paper is, accordingly, the determination and 
discussion of the heat effect of mixing normal liquids. 

Historical. 

H. Sainte-Claire Deville^ determined the "heat produced by 
twenty-five different mixtures of water and sulphuric acid.'* No 
experimental details are given, and the method employed is incapa- 
ble of giving very accurate results. Deville believed that his data 
were in corroboration of certain theoretical views that he advanced, 
and, when the latter were subjected to some animadversions on the 
part of Jamin,^ he protested energetically.^ To this, Jamin * made 
a rather detailed reply, giving some experimental determinations 
of the changes of temperature occurring when alcohol and water 
are mixed, as corroborative of a theory of his own in contradiction 
to that of Sainte-Claire Deville. Still the latter was not convinced, 
and maintained his old opinions.^ It is not necessary to enter into 
the consideration of the theoretical views advanced by these two 
scientists, as none of them have proven to be correct. 

Favre ® determined, by the mercury calorimeter, the heat effect 
of mixing, in several proportions, water with sulphuric acid, with 
alcohol, with acetic acid, and with glycerine ; alcohol with glycer- 
ine, and with acetic acid ; and acetic acid with sulphuric acid. His 
results showed that, in the mixing of these liquids, heat was either 
evolved or absorbed. As he puts it, having, as he did, the idea 
that solution was an example of a kind of chemical affinity : " Deux 
ordres d'actions semblent se produire simultan^ment et marcher de 
front; une action d*attraction r^ciproque des molecules h^tiro- 

1 Comptes Rendus, 50, p. 534, i860. ♦ Ibid.^ 71, p. 23, 1870. 

2 Ibid,, 70, p. 1309, 1870. * Ibid., 71, p. 30, 1 870. 

« Ibid., 70, p. 1379, 1870. • Ibid., 50, p. 1150, i860, and 51, p. 316, l86a 



No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS, 42 1 

gdnes qui sont raises en contact et qui est accompagn6 d'un 
degagement de chaleur, et une action de diffusion qui produit 
un abaissement de temperature. Le nombre foumi par Texp^ri- 
cnce est positive ou negative suivant que la premiere ou la seconde 
de ces actions predomine." His data cannot be well compared 
with later ones, as he has omitted to give the details necessary for 
a reliable comparison. 

Bussy and Buigfnet^ determined the changes of temperature 
brought about by mixing, in various proportions, alcohol with 
carbon bisulphide, chloroform, ether, and essence of terebenthine ; 
water with acetic acid, and alcohol ; ether with carbon bisulphide, 
essence of terebenthine, and chloroform; and carbon bisulphide 
with essence of terebenthine. The results of their experiments are 
similar to those obtained by Favre,^ although his researches are 
not mentioned. This induced Favre ^ to call attention to his work, 
and, in so doing, to communicate some new results on the thermal 
effect of mixing water with methyl alcohol, and of mixing ethyl 
alcohol with methyl, amyl, and caprylic alcohols, as well as glycol. 
This claim of priority was recognized by Bussy,* who stated that 
he had been ignorant of the work by Favre, but that, anyhow, he 
had taken different liquids, of a simpler nature than Favre had. 

In a subsequent paper, Bussy and Buignet^ determined the 
specific heats of many of the mixtures, the change of temperature 
caused by the mixing of which they had previously observed,^ thus 
permitting the calculation in heat units of the thermal effect. 

Guthrie ^ determined, by rather a crude method, the changes of 
temperature occasioned by mixing alcohol with ether, carbon bisul- 
phide, chloroform, and benzene; ether with carbon bisulphide, 
amylene, chloroform, and benzene; carbon bisulphide with amy- 
lene, chloroform, and benzene ; amylene with chloroform, and ben- 
zene ; and chloroform with benzene. The changes in the volume 
of these liquids, when mixed, were also measured, it being found 
that, when the mixing was accompanied with a rise of temperature, 

1 Comptcs Rendus, 59, p. 673, 1864, and Annales de chimie et de physique, (4), 4« 
p. I, 1865. 

* he. cit. * Ihid,, 64, p. 330, 1 867. 

• Comptei Rendus, 59, p. 783, 1864. • he. cit. 

^ Ibid., 59, p. 785, 1864. ^ Philosophical Magazine, (5), 18, p. 495, 1884. 



422 C. E, UNEBARGER. [Vol. III. 

contraction in volume occurred, while, when there was a fall in 
temperature, expansion took place. These generalizations are, 
however, based on too narrow a field of inquiry, and Guthrie's 
paper contains very little that is really novel, at least, along these 
lines. 

W. Alexejew,^ in summing up his work on the solubility of liquids 
in liquids, communicates some data as to the amount of heat ab- 
sorbed in mixing benzene and aniline in several proportions. This 
he finds to be quite insignificant, and states in this connection: 
"Fiir ein Gemisch von 68.5 Proc. Benzol und 31.5 Toluol bei 14°, 
z. B. ist sie gleich — 13.7 cal." As he states later that the possible 
error of a determination may amount to 5 cal., and as he does not 
give the absolute masses of the liquids taken, the absorption of 
heat given by him for this case may even be less than — 8.7 cal. 

Experimental Details, 

Of the common methods of carrying out thermochemical meas- 
urements, the one in which use is made of a Bunsen*s ice calorimeter 
has been preferred, mainly for the reasons that accurate results can 
be obtained with small quantities of material, and because it is un- 
necessary to know the specific heats of the liquids mixed. 

The ice calorimeter employed was of rather large size, permitting 
of the introduction of about 1 5 c.c. of liquid. The amount of mer- 
cury expelled or drawn into the outer chamber by the formation or 
melting of ice was determined by weighing, as recommended by 
Schiiller and Wartha;^ indeed, the disposition of the apparatus 
was very similar to that adopted by these investigators, there being 
an outer cylindrical vessel filled with pure water, around the walls 
of which was a layer of ice, etc. The calorimeter was set in an 
ice box, and covered, with the exception of the top of the inner 
tube and the mercury tube, with clean snow or ice. The room in 
which the work was done was nearly all the time at the tempera- 
ture of freezing water, and the temperature never rose above 5° 
or 6°. 

After the calorimeter had been brought into normal working 
condition, it was found that the mercury was continually moving 

1 Wiedemann's Annalen, 28, p. 322. * /^-^.^ 2, p. 359, 1877. 




No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS, 423 

in one direction or the other, according to external conditions. As 
the amounts of heat evolved or absorbed by the mixing of non- 
associated liquids are generally quite small, it was necessary to 
keep strict account of this movement of the mercury; as the 
degree and direction of the movement changed very slightly in 
intervals of time long in comparison with the time occupied for the 
performance of an experiment, this could be done both easily and 
accurately in a way to be described later. 

The cooling of the liquids to o**, and their subsequent mixing, 
was accomplished as follows : A thin glass tube, closed at one end, 
and of such external diameter as to permit of its being slipped 
easily, but snugly, into the inner tube of the calorimeter, was taken 
of such length that about an inch of it projected out of the calo- 
rimetric tube. A pipette fitting easily into the above tube had its 
outlet directly below its cylindrical bulb, and was closed by means 
of a glass rod running axially up through the pipette and ground 
accurately into the outlet. A bit of thin rubber tubing was slipped 
over this glass rod and pushed down between the upper stem of 
the pipette and the rod, thus closing the pipette above. By means 
of a good cork the pipette was held within the tube mentioned at 
the beginning of this paragraph. 

A rectangular piece of aluminium foil was for about two-thirds 
of its length cut into in several places on each side to near the 
middle, and the parts thus formed were so bent that, when the 
uncut portion of the foil was rolled into cylindrical shape and 
slipped over the lower part of the bulb of the pipette, where it was 
held securely by its own elasticity, they formed a number of small 
paddles, some directed upwards and some downwards. This 
stirring device proved to be very efficient, the mixing of two 
liquids being brought about rapidly and perfectly. 

To make a determination, a certain amount of one liquid was 
drawn up into the pipette and weighed to o.cxx)i gram. The other 
liquid was weighed in the tube, which was corked during the 
operation. The aluminium stirring contrivance was then slipped 
over the bulb of the pipette, and the latter passed into the tube, 
where it was held in place by a tightly fitting cork, and was so 
adjusted that its orifice would be above the level of the liquid after 



424 C. E. UNEBARGER, [Vol. III. 

the mixing had been done, while the paddles reached to the bottom 
of the tube. 

A weighed dish of mercury was always placed to catch the 
expelled mercury for exactly half an hour just before the tube and 
pipette with their contents were placed in the inner tube of the 
calorimeter ; in this way a calorimeter correction was obtained just 
before the performance of an experiment. The weighed dish of 
mercury was then exchanged for an unweighed one, and the tube 
and pipette which had been standing in the ice box, so that they 
had already attained the temperature of o**, were placed in the 
calorimetric chamber. In a half-hour or so a weighed dish of 
mercury was placed under the mercury tube, and the amount of 
mercury moved during another half-hour determined. Again a 
weighed dish of mercury was placed in position, and without delay 
the cork holding the pipette was lifted a little and its contents 
made to run out into the tube. The pipette was then tightly closed 
and moved around and a little up and down for a minute or so, in 
order to thoroughly mix the two liquids. The cork was again 
inserted in the tube and the whole left undisturbed for just half 
an hour. At the expiration of that time another weighed dish of 
mercury was substituted for the last one and left there for another 
half-hour, when the mercury vessel, as well as the tube and pipette, 
were removed. The amount of mercury moved during this last 
half-hour should, if the thermal equilibrium disturbed by the heat 
evolved or absorbed by the mixing of the liquids has reestablished 
itself, and if there has supervened no change in the velocity of the 
movement of the mercury, be equal to the amount moved in the 
half-hour before the introduction of the liquids, and in the half- 
hour elapsing just before they are mixed. This was generally the 
case, the deviation always being very slight, and the average of 
these amounts was taken as the true correction to be applied. 

All weighings were made with great care, since an error of one 
milligram entails an error of several hundredths of a heat unit. 
It is believed that the results of the experiments are accurate to 
within less than one-half of a calorie. 

The calorimetric unit employed is defined by the amount of heat 



No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS. 



425 



required to melt a volume of ice equal to that occupied by 0.01544 
gram of mercury at 0°. 

The liquids used as material for the investigation had all been 
carefully purified; in foot-notes are indicated the methods of 
purification and their boiling-points (uncorr.). 

Experimental Results, 

When a pair of liquids was taken for the determination of the 
heat effect of mixing them, about equal quantities of each were 
weighed out for the first estimation. If the thermal effect proved 
to be less than that capable of detection by the apparatus, com- 
monly no other mixtures were examined, it having been found that 
the maximum heat effect was produced when the amounts of the 
liquids mixed were about the same. An evolution or absorption 
of heat might nevertheless have been found if other proportions 
had been investigated, although this is not very probable. Such 
mixtures as did not appear to exhibit any heat effect are given 
first. The minus sign before a number indicates an absorption 
of heat ; the positive sign, an evolution of heat. 



Table I. 

HEAT EFFECT OF MIXING MONOCHLORBENZENEi AND TOLUENE.^ 





I. 


11. 


Chlorbenzene 


3.0028 g. 

4J032 
-0.0013 
-0.0018 
-0.0005 
-0.032 


3.7715 g. 

4.2190 
-0.0014 
-0.0020 
-0.0006 
-0.033 


Toluene 

Calorimeter correction in weight of mercury . . 

Weight of mercury moved 

Weight of mercury moved due to mixing liquids 
Heat effect in calories 



1 Commercial, chemically pure monochlorbenzene was distilled in fractions until nearly 
half of it boiled at I3i°.8 to 131*^.9, under a pressure of 757 mm. of mercury. 

^ The toluene had been fractionally distilled until more than a pound of it boiled con- 
stantly at 1 10^. I, under a pressure of 758 nmi. of mercury. 



426 



C. E, UNEBARGER. 



[Vol. III. 



Table II. 

HEAT EFFECT OF MIXING MONOBROMBENZENE » AND TOLUENE.* 



I. 


n. 


4.9530 g. 


1.1611 g. 


43680 


73887 


-0.0009 


-0.0010 


-0.0020 


-0.0005 


-0.0011 


+0.0005 


-0.072 


+0.032 



Brombenzene 

Toluene 

Calorimeter correction in weight of merciuy . . 

Weight of mercury moved 

Weight of mercury moved due to mixing liquids 
Heat effect in calories 



Table III. 

HEAT EFFECT OF MIXING ETHYL ETHER* AND TOLUENE.* 

Ether 6.9858 grams. 

Toluene 3.7256 ** 

Calorimeter correction in weight of mercury . —0.0033 " 

Weight of mercury moved —0.0033 ** 

Weight of mercury moved due to mixing liquids 0.0000 " 
Heat effect in calories 0.000 



Table IV. 

HEAT EFFECT OF MIXING ETHYL IODIDE* AND TOLUENE.* 

Ethyl iodide 7.8668 grams. 

Toluene 6.1445 " 

Calorimeter correction in weight of mercury . —0.0130 " 

Weight of mercury moved —0.0129 " 

Weight of mercury moved due to mixing liquids -1-0.0001 ** 

Heat effect in calories +0.006 

Since the freezing-point of benzene is higher than that of water, 
it was impossible to employ it in the ice calorimeter in the pure 
state; accordingly a mixture containing 97.37 per cent of the 

^ Of about a pound fractionally distilled, nearly 150 grams were obtained, boiling at 
1 54°. 3 to I54°.5f under a pressure of 761 mm. of mercury. 

2 The toluene had been fractionally distilled, until more than a pound of it boiled con- 
stantly at iio°.i, under a pressure of 758 mm. of mercury. 

• The ethyl ether had been washed repeatedly with water, dried over fused calcium 
chloride, and finally distilled from phosphoric anhydride. Almost the whole of it boiled 
at a constant temperature. 

* Rectified over phosphoric anhydride, the ethyl iodide boiled at 72^.5, under a 
pressure of 757 mm. of mercury. 



No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS 427 

hydrocarbon and 2.63 per cent of monochlorbenzene was pre- 
pared, and it was with this mixture that the determination recorded 
in Table V. was made. 

Table V. 

HEAT EFFECT OF MIXING CHLORBENZENEi AND BENZENE.' 
Mixture benzene and chlorbenzene .... 3.0208 grams. 

Chlorbenzene 63470 " 

Calorimeter correction in weight of mercury . —0.0013 ** 

Weight of mercury moved —0.0030 " 

Weight of mercury moved due to mixing liquids —0.0017 ** 

Heat effect in calories —0.101 

The rest of the mixtures examined showed so appreciable ther- 
mal effects that several proportions of the liquids were mixed, and 
in the following tables are recorded the results. In order to 
obtain a uniform means of comparison, the quantities of liquids 
mixed are calculated in molecular per cents, and the amounts of 
heat increased so as to correspond to these masses. In this way, 
the numbers representing the amounts of heat change when cer- 
tain numbers of gram-molecules are mixed, come out over a hun- 
dred times greater than those actually determined. Accordingly, 
it must be borne in mind that the units and tens of the numbers 
communicated have hardly any significance. 

Table VI. 

HEAT EFFECT OF MIXING ETHYL IODIDE* AND ETHYL ETHER.* 



Oramt 
C,H.. 


Oramt 
C.H,„0 


Per cent 
C,H,I. 


Molec. per 
cent CiHs. 

10.955 
40.146 
55.616 


Mercury 
moved. 


Calorimeter 
correction. 


Calories. 


Gal. per 
molt. 


2.4240 

83683 

13.8745 


9.3465 
5.9185 
5.2520 


20.595 
58.573 
72.543 


-0.0110 
-0.0053 
-0.0300 


0.0000 

+ 0.0125 

0.0000 


-0.71 
-1.18 
-1.92 


- 632 

- 863 
-1215 



1 G>inmercia]» chemically pure monochlorbenzene was distilled in fractions until nearly 
half of it boiled at 131^.8 to I3i°.9, under a pressure of 757 mm. of mercury. 

' G>mmercially pure benzene was treated with sulphuric acid to remove thiophene, 
fractionally crjrstallized to constant melting-point, viz. 5^.42, and distilled over sodium. 
Boiling-point was 8o°.i, under a pressure of 757 mm. of mercury. 

« Rectified over phosphoric anhydride, the ethyl iodide boiled at 72^.5, under a 
pressure of 757 mnL of mercury. 

* The ethyl ether had been washed repeatedly with water, dried over fused calcium 
chloride, and finally distilled from phosphoric anhydride. Almost the whole of it boiled 
at a constant temperature. 




428 



C E. UNEBARGER. 



[Vol. III. 



Table VII. 

HEAT EFFECT OF MIXING CARBON BISULPHIDE i AND TOLUENE.* 



Qramt 
CtH,. 


Gramt 
CS.. 


Per cent 
CtH.. 


Molec. per 
cent CtH«. 


Mercury 
moved. 


Calorimeter 
correction. 


Calories, 


Gal. per 
molt. 


1.6035 


13.2050 


10.829 


9.117 


-0.(H20 


+0.0080 


-3.22 


-1695 


3.6267 


12.4130 


22.610 


19.443 


-0.0871 


+ 0.0061 


-6.00 


-2971 


6.8225 


7.0721 


49.101 


44350 


-0.1105 


+0.0095 


-7.81 


-4648 


10.6800 


1.8372 


85J22 


82.766 


-0.0605 


-0.0020 


-3.80 


-2701 


10.5282 


0.5040 


95.518 


94.517 


-0.0050 


+0.0065 


-0.76 


- 615 



Table VIII. 

HEAT EFFECT OF MIXING CHLOROFORM » AND TOLUENE.* 



Grama 
CtH.. 


Gramt 
CHCl.. 


Per cent 
CtHs. 


Molec. per 
cent CrHg. 


Mercury 
moved. 


Calorimeter 
correction. 


Calories. 


Cal.per 
mols. 


0.6075 


6.8166 


8.182 


10.375 


+0.0708 


-0.0010 


+ 4.53 


+ 7.101 


2.8565 


6.1682 


31.562 


37.560 


+0.1%2 


-0.0038 


+ 12.91 


+ 15,669 


2.1741 


3.1679 


40.698 


47.120 


+0.1215 


-0.0072 


+ 8.33 


+ 16,493 


6.0145 


2.0438 


74.637 


79.264 


+0.1108 


-0.0038 


+ 7.40 


+ 8,9% 


7.0400 


0.6445 


91.619 


93.406 


+0.0110 


-0.0030 


+ 0.50 


+ 636 



Table IX. 

HEAT EFFECT OF MIXING CARBON TETRACHLORIDE* AND TOLUENE.* 



Grams 
C,H,. 


Grams 
CCI4. 


Per cent 
CtH.. 


Molec. per 
cent C6I4. 


Mercury 
moved. 


Calorimeter 
correction. 


Calories. { 


Cal.per 
mols. 


0.4200 


7.2987 


5.441 


8.785 


-0.0080 


-0.0042 


1 
-0.25 ! 


- 474 


1.3662 


6.9568 


16.415 


24.735 


+0.0005 


-0.0057 


-0.41 1 


- 666 


3.7530 


6.5552 


36.408 


48.937 


+0.0050 


-0.0114 


+ 1.13 1 


+ 1272 


5.1212 


4.2560 


54.613 


71.717 


+0.0162 


-0.0066 


+ 1.51 1 


+ 15(H 


6.0023 


1.8523 


76.418 


84.434 


+0.0070 


-0.0066 


+0.88 1 


+ 1139 


6.3920 


0.8978 


87.684 


93.320 


-0.0102 


-0.0042 


-0.32 1 


- 419 



1 The carbon bisulphide was dried over phosphoric anhydride and distilled over 
mercury; it boiled constantly at 46^.25, under a pressure of 756 mm. of mercury. 

* The toluene had been fractionally distilled until more than a pound of it boiled con- 
stantly at 1 10^. I, under a pressure of 758 mm. of mercury. 

* The chloroform had been fractionated to constant boiling-point, and was finally dis- 
tilled over phosphoric anhydride; its boiling-point was 61^.3, under a pressure of 759 mm. 
of mercury. 

* The sample had been fractionally distilled over phosphoric anhydride, and boiled at 
76^.7, under a pressure of 754 mm. of mercury. 




No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS, 



429 



Table X. 

HEAT EFFECT OF MIXING CARBON TETRACHLORIDE 1 AND 
CHLOROFORM.^ 



Oramt 

ecu. 


Oramt 
CHCl.. 


Per cent 

ecu. 


Molec.per 
cent CHCl, 


Mercury 
moved. 


Calorimeter 
correction. 


Calories. 


Cal.per 
mofs. 


0.7632 


11.9765 


5.986 


4.713 


-0.0210 


-0.0151 


-0.45 


- 369 


13275 


6.2995 


16.649 


14.053 


-0.0302 


-0.0190 


-0.71 


-1193 


8.9100 


5.2060 


63.120 


57.046 


-0.0892 


-0.0052 


-5.42 


-5353 


12.5720 


2.6480 


82.599 


78.643 


-0.0750 


-0.0213 


-3.41 


-3289 


11.8203 


1.6395 


87.820 


84.838 


-0.0580 


-0.0180 


-2.59 


-2786 


11.3480 


03600 


97.199 


96.072 


-0.0364 


-0.0152 


-1.40 


-1799 



Discussion of Results, 

In a paper "On the Vapor Tensions of Mixtures of Volatile 
Liquids,"^ I have had occasion to discuss the mixing of liquids 
without the production of any appreciable thermal effect, in con- 
nection with considerations on their vapor tensions, and in this 
present paper more experimental data are given in corroboration of 
the views stated in that place. It may be added here, to what was 
said there, that it is not probable that absolutely no heat change 
occurs when certain liquids are mixed. The amount of heat evolved 
or absorbed is, however, so slight that it escapes detection ; with 
more delicate instruments, no doubt, its amount could be ascertained. 

In regard to whether heat will be evolved or absorbed in appre- 
ciable measure, there seems to be no criterion. Thus, it seems 
probable, if two liquids A and B each mix with another liquid C, 
without a measurable heat effect, that these two liquids will mix 
with one another without giving rise to any evolution or absorption 
of heat. This is, however, not the case, for both ethyl ether and 
ethyl iodide mix with toluene without a thermal change (Tables 
III. and IV.), and yet, when mixed with each other, give a not 
inconsiderable heat effect (Table VI.). A curious result is ob- 

1 The chloroform had been fractionated to consUnt boiling-point, and was finally dis- 
tilled over phosphoric anhydride; its boiling-point was 61^.3, under a pressure of 759 mm. 
of mercury. 

2 The sample had been fractionally distilled over phosphoric anhydride, and boiled at 
76°. 7, under a pressure of 754 mm. of mercury. 

« Journal of the American Chemical Society, Vol. XVII., August, 1895. 



430 C, E, LINEBARGER. [Vol. III. 

tained with mixtures of chloroform, carbon tetrachloride, and tolu- 
ene. When carbon tetrachloride and chloroform are mixed, heat 
is absorbed, and, indeed, the heat absorption reaches a maximum 
when about equal quantities of each liquid are mixed. The mixing 
of chloroform and toluene gives, on the other hand, an evolution of 
heat, attaining its maximum when about the same number of mole- 
cules of each liquid is taken. With mixtures of carbon tetrachlo- 
ride and toluene, an entirely different behavior is found. If a 
small proportion of either of the liquids be added to the other, 
heat is absorbed; when, however, the proportions in which the 
liquids are mixed become more nearly equal, an evolution of heat 
is observed. This difference of behavior in the three liquids is 
enigmatical. Chloroform and carbon tetrachloride being so simi- 
lar, both chemically and physically, it might be expected that they 
would behave more similarly, as regards their thermal effects, 
when mixed with toluene, a liquid which had shown itself to give 
very simple results when mixed with ether, ethyl iodide, etc. Our 
knowledge of the subject does not at present permit us to get at 
the secret of the affair. 

When carbon bisulphide and toluene are mixed, heat is absorbed, 
no matter what the relative proportions of the two liquids, and the 
amount of heat is greater than that absorbed in the mixing of 
ethyl iodide and ether. This greater absorption of heat, occa- 
sioned by the mixing of the first two liquids, may be due to the 
fact that carbon bisulphide is slightly associated ; and it is proba- 
ble that heat is required to break up the associated molecules. 

Influence of Temperature upon the Heat Effect of Mixing Normal 

Liquids. 
It is of some interest to consider what influence a change of 
temperature exercises upon the amount of heat absorbed or evolved 
when liquids are mixed. It may be that the absolute amount of 
heat brought into play is different at various temperatures, and in 
some cases the mixing of liquids will occasion an evolution of 
heat at one temperature, and an absorption of heat at another. 
Certain energetical considerations will afford us a relation between 
the heat efifects of mixing liquids at different temperatures and the 




No. 6.] THE HEAT EFFECT OF MIXING LIQUIDS, 431 

specific heats of the mixed and unmixed liquids, and by its aid and 
comparison with experimental data on the specific heats of mix- 
tures of liquids, we will obtain a definite answer to our question. 

Let two liquids A and B be mixed at the temperature T^, whereby 
a positive or a negative heat efifect amounting to ± is occasioned ; 
for the sake of simplicity, we will assume the heat efifect to be posi- 
tive, as such a supposition is in nowise a restriction to the generality 
of the results. The mixture is now heated to the temperature T^, 
in which operation an amount of heat equal to (TJj"" ^1)^1 ^^ needed, 
c^ representing the specific heat of the mixture in the temperature 
interval (T'g— 7\). At the temperature T^ the two liquids are 
separated, the act of separation being accompanied by an absorp- 
tion of heat amounting to Q^. The separated liquids are now 
cooled down to the original temperature, when {T^— ^1)^2 units of 
heat are given out, if c^ represents the sum of the heat capacities 
of the liquids. As the cycle of operations is now completed, we 
may, in accordance with the law of the conservation of energy, 
form the following equation : 

or(i) Q«C',= ^^. 

Accordingly the difference between the specific heats of the pure 
liquids and their specific heats when mixed is equal to the increase 
of the heat effect of mixing them per degree of rise of temperature. 

Now it results from the experiments of J. H. Schiiller,^ of W. 
Alexejew,^ and of F. L. Perrot,^ that the difference between the 
specific heats of mixed and unmixed normal liquids is less than 
that due to unavoidable experimental errors ; a normal liquid pre- 
serves its specific heat in mixture. From this experimental fact it 
follows that the first member of equation (i) is equal to zero in the 
case of mixtures of normal liquids, and hence the second member is 
equal to zero also. A change of temperature, then, has no appreci- 
able influence upon the thermal effect of mixing normal liquids. 

Chicago, January 24, 1896. 

* Pogg. Ann. Erganzungsband, V., p. 210, 1871. 

3 Wiedemann's Annalen, 28, p. 322, 1886. 

« Arch, des sciences physiques ct naturelles, 32, pp. 145, 254, and 337, 1894. 




432 MAI^y CHILTON NOYES. [Vol. III. 



THE INFLUENCE OF HEAT, OF THE ELECTRIC 
CURRENT, AND OF MAGNETIZATION UPON 
YOUNG'S MODULUS. 

By Mary Chilton Noyes. 

IN the Physical Review for January-February, 1895,^ an article 
was published describing a series of experiments which had 
been made in the physical laboratory of Cornell University, to 
determine the effect of temperature upon Young's modulus for a 
piano wire. An electric current was used as the source of heat, 
and a series of different temperatures employed. The experi- 
ments showed very clearly that Young's modulus for a piano wire 
decreases as the temperature is raised from 15° to 180° C, and 
that the decrease is nearly, if not exactly, proportional to the 
increase in temperature. The value of the thermal coefficient was 
likewise determined. 

There were, however, other questions which were raised rather 
than settled by the experiments. When the wire was heated by 
an electric current through a helix surrounding it, the results were 
quite regular ; but when the current was sent through the piano 
wire itself, results were obtained which were so irregular that no 
certain conclusions could be drawn from them. Some of them 
seemed to indicate that the current through the wire had a very 
perceptible effect upon the elasticity; others made it doubtful 
whether there was any effect aside from that due to the heat It 
seemed desirable to conduct a series of experiments by the same 
general method, but so planned as to distinguish between the 
effects due to the heat, to the longitudinal magnetization, and to 
the electric current through the wire. For this purpose apparatus 
similar in all essential particulars to that used at Cornell, and 
described in the previous article, was arranged in the physical 
laboratory of Western Reserve University. A solid block of oak 
1 Physical Review, Vol. II., No. 10, p. 277. 



No. 6.] YOUNG'S MODULUS, 433 

of sufficient length was placed upon a stone pier which was 
isolated from the floor so as to avoid jars from other parts of the 
building. The wire was passed through a glass tube, attached to 
a support at one end, and passed over an Atwood wheel at the 
other. Every precaution was taken to avoid drafts of air or any- 
thing which would cause variation of temperature. A large cloth 
screen was placed between the apparatus and the hot-air register ; 
the Atwood wheel was carefully covered with a cloth, and the wire 
at the other end was protected in a similar way. 

When the wire was heated by a current through the helix 
around the tube, the temperature was determined by three ther- 
mometers placed inside the tube, but so arranged as not to touch 
it. Before using the thermometers, a table of corrections was 
made for them. To do this they were compared with a standard 
thermometer between 0° and icx)^ ; the freezing and boiling 
points were determined ; and the stems between icx)° and 2CX)° 
were calibrated by using a thread of mercury and comparing with 
the parts between 0° and icx)°. The corrections so determined 
were applied to all the readings taken. When the wires were 
heated by a current through them, the temperatures were deter- 
mined by the elongation, the coefficient of linear expansion being 
previously determined by noticing the elongation when the wires 
were heated by tfte current around them. Sometimes the highest 
temperature used in a series of observations was determined both 
by noticing the elongation when the wire was heated and the sub- 
sequent contraction after the current had stopped; the results 
usually agreed within a fraction of a degree. Some experimenters 
have found that an electric current through a wire produces a 
greater elongation than would be caused by the same temperature 
produced in some other way. The difference is, however, so small 
that it has not seemed necessary to take it into account in deter- 
mining the temperatures. 

The micrometer heads of the microscopes had fifty divisions ; in 
all the readings half-divisions were used. It was found that 4080 
half-divisions were equal to one millimeter. The diameters of the 
wires were measured by two or three micrometer wire gauges and 
the average results taken. 




434 MARY CHILTON NOYES. [Vol, III- 

The wires were stretched by a weight equal to about one-half 
the breaking weight for twenty-four hours or longer before the 
first observations were made, and the maximum weight used in the 
determinations was a little less than the stretching weight With 
the piano wires, the same weights were always used for the same 
kind of wire, so that the results obtained in the different experi- 
ments might be comparable. In determining the modulus,, all the 
weight added was put on at once instead of using intermediate 
weights, as had been done in most of the previous work. The 
additional weight was always put on and taken off before the first 
reading was taken, and the readings were made as soon as possible 
after placing the weights. Usually the weight was put on and 
removed three times for one determination, so that the result was 
the average of six values ; in many cases a larger number of obser- 
vations was taken. The attempt was made to secure so steady a 
temperature that the readings before placing the weights and after 
removing them would not vary more than one or two half-divisions, 
but it was not always found possible to obtain this condition. If 
the variations were a little more, but all in the same direction and 
of the same amount, showing that the change in temperature was 
regular, it was thought that the average result could not be far 
wrong. The matter was tested by comparing the average result 
when there was a considerable, but regular, change in the read- 
ings with that obtained a little later with the same current but after 
the temperature had become steady ; the results usually differed 
only about one-tenth of one per cent. 

The wires were measured to one one-hundredth of a millimeter 
with a standard meter rule. In computing the moduli, this length 
was corrected for the elongation corresponding to each tempera- 
ture employed. 

With the first wire used, the elongation for one degree was 
found to be o.oi 137 mm. ; the length of the wire was 952.00 mm., 
making the coefficient of expansion 0.000012. The same coeflfi- 
cient was used in determining the change in the cross-section with 
change of temperature, and this correction was also used in making 
the calculations. 



No. 6.] YOUNG'S MODULUS. 435 

Experiment i. 

A piece of number six piano wire was used in this series of 
observations. It was heated alternately by the magnetizing cur- 
rent and by the current through the wire itself. The lowest 
weight used was 3.5 Kg., and the additional weight used to 
produce the elongation was i.o Kg. A number of observations 
made before the adjustments were sufficiently perfect to give 
concordant results were discarded. 

Observations were first made with current through the magnet- 
izing helix, then with current in the wire itself. The set with 
the current through the wire are somewhat irregular, but with a 
single exception are higher than those that had been previously 
obtained with the magnetizing helix. When the magnetizing 
current was again used, the values found fall between those of 
the first and second sets. A final set, with the current again 
through the wire, are more regular than the first set obtained 
in the same way, and are on the whole higher than any of the 
preceding sets. 

The results show an increase from heating the wire alternately 
by the two methods; but there is little to indicate whether the 
effect is due to the heat alone, to the current, or to the mag- 
netization. 

In order to see if a continuation of the current would change 
the modulus, a number of determinations were made with an 
interval between the sets of observations, but making no change 
in the conditions. The results differed no more than the probable 
errors of observation. 

Experiment 2. 

Another piece of the same kind of wire as had been used in the 
previous experiment was adjusted and heated in a similar way, 
only the current through the wire was used first, and afterwards 
the magnetizing current. The following table gives the numerical 
results obtained, and (Fig. i) represents them graphically. 




436 



MABY CHILTON NOYES, 



[Vol. III. 



Table I. 

Current left to ri^t, throoffa wire. 



No. 


Dmte. 


TeflBperftture* 


Bloo. for I Kg. 


No.ofobe. 


Modulus. 


1 


March 14 


23°.5 


1442.44 


7 


21,234 


2 


« 15 


24°.9 


1140.50 


6 


2i;268 


3 


" 15 


27°.2 


1145.50 


6 


21.173 


4 


" 15 


34^.1 


1145.05 


4 


21,179 


5 


" 15 


43°.2 


1150.63 


6 


21,075 


6 


" 15 


50°J 


1157.63 


8 


20.947 


7 


« 15 


63^.6 


1160.23 


6 


20,896 


8 


" 15 


83^.0 


1172.28 


6 


20,676 


9 


" 15 


97^.9 


1189.90 


6 


20366 


10 


- 16 


33°.8 


1146.56 


12 


21.152 


11 


" 16 


45^.8 


114833 


8 


21,118 


12 


" 16 


640.9 


1155.00 


4 


20,992 


13 


« 16 


9P.4 


1172.27 


6 


20,675 


14 


" 16 


112°.7 


1186.85 


8 


20,416 


15 


- 16 


137°1 


1200.87 


3 


20,171 





Current right to left, through wire. 






16 


March 18 


270.2 


1131.98 


5 


21,426 


17 


" 18 


76^.7 


1158.67 


12 


20,920 


18 


" 18 


930.1 


117236 


8 


20,672 


19 


" 18 


II60.O 


1191.90 


4 


20,328 


20 


" 18 


157°.8 


1209.15 


4 


20,028 


21 


" 18 


183°.5 


1231.42 


10 


19,654 


22 


" 19 


770.1 


1155.40 


4 


20,979 (?) 


23 


« 19 


950.0 


1176.47 


6 


20,599 


24 


« 19 


1110.6 


1182.01 


8 


20,500 


25 


" 19 


1230.8 


1186.58 


10 


20.418 


26 


« 19 


15003 


1198.60 


8 


20,207 


27 


" 19 


I660.6 


1209.78 


8 


20,014 


28 


«* 20 


1303 


1134.07 


6 


21,394 



Current right to left, through magnetizing helix. 



29 


March 20 


280.8 


1134.78 


8 


21373 


30 


" 20 


370.4 


1140.03 


7 


21,272 


31 


« 20 


420.7 


1140.50 


8 


21,262 


32 


" 20 


50O.4 


1142.59 


10 


21,223 


33 


" 21 


3305 


1134.66 


8 


21374 


34 


" 21 


5 10.0 


1139.20 


8 


21,286 


35 


" 21 


680 1 


1153.45 


4 


21,018 


36 


« 21 


8503 


1157.50 


3 


20,939 




No. 6.] 



YOUNG'S MODULUS, 



437 



Table I. (continued). 

Current left to ris^ht, through magnetizing helix. 



No. 


Date. 


Temperature. 


Elon. for x kg. 


No. of Obi. 


Modulus. 


37 


March 22 


39°.l 


1137.76 


8 


21,315 


38 


" 22 


61^.5 


1148.98 


5 


21,102 


39 


*• 22 


86^.9 


1154.60 


6 


20,993 


40 


" 22 


90^.3 


1165.00 


4 


20,804 


41 


" 22 


105°.l 


1169.03 


6 


20,728 


42 


« 23 


15^.6 


1128.84 


7 


21,498 



Current left to right, through wire. 



43 


March 23 


39°.9 


1133.37 


6 


21,398 


44 


«« 23 


58°.2 


1137.53 


4 


21,315 


45 


" 23 


90°.5 


1159.90 


4 


20,895 


46 


" 25 


77°.3 


1147.70 


8 


21,120 


47 


" 25 


93°.4 


1157.28 


5 


20,942 


48 


" 25 


150^.0 


1199.63 


6 


20,188 


49 


" 26 


19^.8 


1129.27 


6 


21,481 


50 


« 26 


34^.2 


1138.87 


6 


21,295 


51 


" 26 


42^.5 


1147.29 


7 


21,136 


52 


" 26 


51^.2 


1139.35 


4 


21,282 


53 


" 26 


76°.2 


1146.63 


6 


21,141 


54 


" 26 


92°.5 


1155.68 


8 


20,971 


55 


" 26 


113°.9 


1172.90 


8 


20.657 


56 


" 26 


150^.0 


120232 


10 


20,143 



L = 954 mm. at 18°. Q - 0.16046 sq. mm. at 18°. i> = 1 Kg. 




Fig. 1. 




438 MARY CHILTON NOYES. [Vol. III. 

The values found for the first set of observations show a 
gradual increase in the modulus as the heating is repeated ; some 
of the later values fall very nearly in the same line as those of 
the next set, which were obtained with the magnetizing current 
Most of the final set, when the current was again sent through 
the wire, are higher than either of the preceding sets. There is 
the same progressive increase in elasticity with the alternate 
methods of heating that had been found in the preceding 
experiment. 

Experiment 3. 

A third piece of the number six piano wire was taken, and 
the same order used in the methods of heating as in the first 
experiment. 

After a few readings had been obtained, it was discovered that 
the cloth used to protect the Atwood wheel from drafts of air 
touched the wire, making the results uncertain ; hence the values 
for the first heating were rejected. The subsequent results were 
more regular than in either of. the previous experiments, and the 
results obtained in the third and fourth sets fall almost exactly 
in the same line, which seems to indicate that the wire had 
reached a condition such that its elasticity would not have been 
much modified by further repetition of the heating or of the 
magnetization. 

The three experiments all show that the elasticity of a piano 
wire is increased by heating it alternately by a magnetizing cur- 
rent and by a current through the wire itself. The fact that the 
order in which the two methods are used makes no essential 
difference in the result, makes it probable that the efifect is due 
to the heat alone. 

In this, as in several of the other experiments, both the mag- 
netizing current and the current through the wire were reversed 
a number of times; no difference in the effect of the current 
could be detected. This fact furnishes additional evidence that 
neither the longitudinal nor the circular magnetization is the cause 
of the change in the elasticity. 



No. 6.] 



YOUNG'S MODULUS, 



439 



Experiment 4. 

A larger piano wire was used for this experiment in order to 
make it more certain that the results obtained did not depend 
upon any peculiarity in the particular specimen of wire employed. 
The results obtained are much the same as those that had been 
found with the smaller wire, but the increase in elasticity from 
the heating is less than in the other cases, and a condition in 
which a repetition of either form of heating produced no further 
change was sooner reached. 

Experiment 5. 

In order to determine with greater certainty whether heat alone 
was the cause of the increase in the modulus produced by alter- 
nating the two methods of heating, 
a double coil was so arranged that 
the current flowed through one part 
in one direction and the other part 
in the opposite direction, thus mak- 
ing it non-inductive. This coil was 
used for heating another piece of 
the number six wire. Figure 2 
shows the results obtained by this 
method. There is the same kind of 
increase in elasticity with each 
alternation of the method of heat- 
ing that had been found when using 
the magnetizing helix. The conclusion seems inevitable that the 
longitudinal magnetization at least has no appreciable effect upon 
the result. 

Experiment 6. 

The results of each of the previous experiments showed a 
change in the modulus produced by repeated heating. It there- 
fore seemed desirable to compare the moduli obtained with the 
different methods of heating applied to a wire that had already 
been heated and cooled so many times that further repetition of 
the treatment would produce no change in the elasticity. For 




Fig. 2. 



440 



AfA/^y CHILTON NOYES. 



[Vol. Ill, 



this purpose a piece of the number six piano wire was placed in 
the tube inside the magnetizing helix, and was repeatedly heated 
by a current through the helix. 

Some of the results obtained in the previous year indicated the 
possibility that repeated magnetization might modify the eflfects 
produced in a wire by a current through it. The plan of this 
experiment made it possible to test this point also. 

After heating and magnetizing the wire a number of times, a 
series of values for the modulus was found when it was heated 
by the magnetizing current, and the following day a correspond- 
ing series when it was heated by 
a current through the wire itself. 
The results are plotted in Fig. 3. 
They all fall very close to a 
straight line, with no appreci- 
able difference in the results ob- 
tained by the two methods of 
heating. These results show 
that if there is any difference in 
the effects produced upon the 
elasticity of a piano wire by 
magnetizing it longitudinally and 
circularly, that difference is too 
small to be detected with any certainty by this method of experi- 
ment. 

Since the results of the fifth experiment, compared with those 
of the first three experiments, showed that the heating effects 
produced by a non-inductive current and by a magnetizing current 
are the same, the proof seems conclusive that neither longitudinal 
magnetization nor a current through a wire produce any appre- 
ciable effect upon Young*s modulus aside from that which is due 
to the accompanying heat. 

From the results obtained in the first three experiments, it was 
computed that the permanent increase in elasticity due to repeated 
heating is about 1.45 per cent of the value found for the modulus 
by producing the line passing through the first set of results until 
it intersects the zero line. The corresponding change found in 















Ex 


>.6 






• 


\ 


















21600 


\ 


L 
















20600 




X 


K 














Mod 


])n«_ 






k 




















• 


\ 










20900 










— V 


\ 








ueoo 




(2)x< 


purre 
burrc 


nt li 

Dtit 


bell 
wlr 


fT" 


\ 




















\ 




_s 


)• < 


)• € 


TEMPEfM 


TURC 

^0* IS 


0- 1 


li 


i( 


k 



Fig. 3. 



No. 6.] YOUNG'S MODULUS. 441 

the fifth experiment is 1.90 per cent of the value at o®; the 
greater increase may be due to the fact that higher temperatures 
were secured in this case with the current around the wire than 
had been used in the earlier experiments ; the cooling took place 
much more slowly after stopping the current through the helix 
than when the current was through the wire itself; this more 
gradual cooling might easily account for the larger increase in 
elasticity. 

The thermal coefficient was determined in connection with the 
different experiments by drawing lines which would correspond 
to the average decrease of the modulus with the increase of tem- 
perature, and comparing that decrease with the zero value corre- 
sponding to the final set of results. The average value found 
in this way from experiments i, 2, 3, and 5, is 4.65 per cent 
for 100°. The value found in a similar way from the results 
of the sixth experiment is 4.55 per cent. This result is more 
probable than any of the others, since it is difficult to draw a line 
satisfactorily through the results obtained before the wires had 
been heated sufficiently to reach a permanent condition. Giving 
equal weight to the average of the four results and to the result 
of the sixth experiment, we get a value of 4.60 per cent for the 
thermal coefficient. This is a little smaller than the value found 
in the previous investigation already cited for the larger wire 
experimented with, but is just the same as that found for the 
smaller wire. 

A few results which were obtained with this wire at tempera- 
tures ranging from 300° to 600°, showed a continued decrease in 
the modulus with the increasing temperature. The decrease was 
apparently at about the same rate as that found between 15° and 
180°; but these high temperatures could not be determined with 
sufficient accuracy to be sure that the thermal coefficient remains 
constant. 

Experiment 7. 

A piece of the number six piano wire was annealed by heating 
it inside a glass tube, through which a current of coal gas was 
passing so as to prevent oxidation. The modulus of the wire was 



442 



MAI^y CHILTON NOYES. 



[Vol. III. 



then determined when it was heated by the non-inductive current 
and by a current through the wire. Another piece of the same 
kind of wire was heated while covered with powdered charcoal, to 
prevent oxidation. The modulus was then determined when it 
was heated by the non-magnetizing current, by a current through 
the wire, and by a magnetizing current. The results, which were 
entirely analogous to those of the previous experiments, make it 
safe to conclude that with an annealed wire, as with the unan- 
nealed, there is no appreciable effect except that due to heat 
The thermal coefficient is smaller for the annealed than for the 
unannealed wire, being only 3.4 per cent for 100°. 

Experiment 8. 

A piece of silver wire 0.48 mm. in diameter was used for this 
experiment. Young's modulus was determined when the wire 

was heated by a current through the 
non-inductive coil, and when it was 
heated by a current through the wire 
itself. Figure 4 shows the results. The 
observations are numbered so that the 
progressive change in the modulus may 
be traced more clearly. Comparing 
numbers i, 4, and 7, we see an increase 
in the modulus each time the wire was 
heated. The still greater change be- 
tween numbers 7 and 16 was probably 
due to the fact that in determining 
number 15 the wire was stretched 
beyond its elastic limit. All of the 
results from the sixteenth through the 
twenty-fourth are close to the same 
line. Between numbers 21 and 22 there was an interval of about 
a month during which the wire had remained unstretched ; a 
comparison of results obtained before and after that time shows 
no appreciable change in the elasticity. 

Number 15, and some of the other results obtained at the higher 
temperatures, are somewhat uncertain. No appreciable change in 




Fig. 4. 



No. 6.] 



YOUNG'S MODULUS, 



443 



the elastic limit with the increase in temperature had been antici- 
pated, and the weights chosen were those found suitable at the 
temperature of the room. It was found, however, that at about 
80"^ the larger weight that had been used at the lower temperature, 
2.9 Kg., slightly exceeded the elastic limit ; and at 88° the heaviest 
weight that could be used was 2 Kg. These facts led to an 
investigation of the change in the elastic limit with change of 
temperature. The results ob- 
tained are shown in Fig. 5. 
Numbers i to 5 were obtained 
one day, and numbers 6 to 12 two 
or three days later, while num- 
ber 13 was twenty-four hours 
after number 12. There was 
not time to contrive any very 
accurate method of determining 
the elastic limit that could be 
employed with the apparatus 
in use, and the results are not 
as definite as could be desired. 
They seem, however, to show plainly that the elastic limit 
decreases with increasing temperature, and also that between 20° 
and 115° the decrease is nearly, if not exactly, proportional to 
the increase in temperature. They also show a decrease in the 
elastic limit with the repeated heating and stretching. 

Determinations of the modulus made after numbers 5 and 13 in 
the elastic-limit series, gave the values 7605 at 23°, and 7954 at 
25°. These values, and also number 16, previously referred to, 
show a permanent increase in the elasticity produced by stretching 
the wire beyond the elastic limit while that limit was temporarily 
lowered by heating. 



X 


t 






Elai 


ticli 


mltc 


faU 


er^ 


ice 


-8b8- 












Ex>.8 






X. 




\, 
















1 ft-. 




V 

s. 


<. 
















7 


1 


N 


•• 


*^^ 










1 4- 




8 




^ 


^^ 




'*''.. 
















S 


10 — " 






*•» 


.l_n 


Lin 


lit In 


kg8. 








^ 


:i" 




















"^ 


^ 




4 


)* 


T« 


PERA 


URE 
i 


}• 


1)0' 





Fig. 5. 



Experiment 9. 

A piece of copper magnet-wire 0.64 mm. in diameter was heated 
by the same methods that had been employed with the silver wire. 
The results were somewhat affected by the application of unsuita- 



444 



MARY CHILTON NOYES. 



[Vol. III. 



ble weights, but they suflSced for the computation of the thermal 
coefficient of the modulus. 

It was found to be 13.3 per cent for 100° ; whence 

iW;=J/o( I -0.00133/). 

The elastic limit was also determined at three temperatures. 
The results show a decrease which is proportional to the increase 
in temperature. (See Table III.) 

The coefficient of linear expansion of the wire was determined 
when it was heated by using the non-inductive coil, and this coeffi- 
cient was employed in determining the temperatures when heating 
by the other method. The coefficient found was 0.0000153. This 
is smaller than the coefficient usually given; the low value is 
probably due to the quality of the copper wire tested. The small 
value found for the modulus may perhaps be accounted for in a 
similar way. 

Experiment 10. 

A smaller piece of copper magnet-wire was used for this experi- 
ment. Its diameter was 0.50 mm. The following table gives the 





r t! 


1 


























I? 


Sv 


• a 




















^» 






( 


OPJH 


rwt 


e 




'isk- 


» 


\ 




ft 


£1 


utlc 


llnUt 


ofc 


>ppe 


•wlr 


B 


r^ 


fcLi 






Exp 


10 










^ 


e 


n 




Ex 


J.10 








MOOQ 


P 


\_ 










T-ft- 








^ 


^ — 
















^ 


S" 


x» 
















^ 


xu 












uaoo 

Kod 

loeot^ 




4 


f? 


^ 






Vit- 


Lin 


it, J 


Lte 






N 


V 














— \Y 


— "N 

• 
10 


\ 


It 
















N 


V 








ilus- 










^ 


fcS— 
















s 


V 








S'on- 

CUIT 


uductive 
•nt in wlr 


CUITf 


nt 




















> 


\ 




4 


)* 


TEMP 

s 


:rati re 


0* 




_J 


)• 


J 


r 


TEl 


PCRA 


'URE 
1^ 


0* 


2 


»' 


a 


^ 



Fig. 6. 



Fig. 7. 



results that were obtamed, and Figs. 6 and 7 represent them 
graphically. 



No. 6.] 



YOUNG'S MODULUS 



445 



Table II. 

Non-inductive Current. 



No. 


Date. 


Tempera- 
ture. 


Blon. for 
o.6Kg. 


No. of 
oba. 


Modulus. 


Elastic 
limit. 


No. 
(Elastic 

limit 
series). 


1 


June 14 


25°5 


983.60 


6 


11,841 






2 


« 14 


40^.8 


990.73 


6 


11,754 






3 


" 14 


40^.2 


988.56 


10 


11,780 






4 


" 14 


62^.8 


1020.87 




11,402 






5 


" 15 


24<^.7 


979.80 




11,887 


2.60 Kg. 


1 


6 


" 15 


40^.3 


981.37 




11,866 


2.60 


2 


7 


« 15 


62^.9 


998.84 




11,653 


2.55 


3 


8 


" 15 


82^.8 


1025.80 




1U45 


2.50 


4 


9 


" 15 


97^.9 


1027.29 




1U27 


2.45 


5 


10 


" 15 


11P.6 


1(H5.30 




11,129 


2.30 


6 


11 


" 15 


98^.8 


1036.30 


6 


11,228 







Current through wire. 



12 


June 17 


25°.l 


973.93 


6 


11,959 


2.6 


7 


13 


« 17 


330.3 


978.50 


4 


11,901 


2.6 


8 


14 


" 17 


550.0 


984.30 


6 


11,827 


2.5 


9 


15 


u 17 


%o.O 


1019.76 


5 


11,409 


2.4 


10 


16 


" 17 


1120.9 


1036.77 


6 


11,218 


2.3 


11 


17 


" 17 


250.0 


972.05 


4 


11,982 


2.6 


12 


18 


" 18 


1070.0 


1014.60 


6 


11,465 






19 


" 18 


1490.3 


1057.33 


6 


10,994 


2.15 


13 


20 


" 18 


I880.3 


1146.63 


6 


10,132 


1.85 


14 


21 


" 18 


2480.8 


1050.09 


9 


9,209 


1.60 


15 



Q = 0.1998 sq. mm. 



L = 950.91 at 250.5. 



/'=0.6Kg. 



If we notice numbers i, 5, 12, and 17, all of which were 
obtained at the temperature of the room, we see an increase in 
the elasticity after each time that the wire was heated, although 
the change from 12 to 17 was very slight. The increase may have 
been partly due to stretching the wire in determining the elastic 
limit, and not wholly to the heat ; the irregularity of the values 
after the seventeenth is probably due to the same cause. 

The results found for the elastic limit show a decrease which is 
very nearly proportional to the increase in temperature. As was 



i 



446 



MA/^y CHILTON NOYES. 



[Vol. III. 



found to be true with the silver wire, the elastic limit decreased 
slightly with repeated heating and stretching, while the elasticity 
was increased by the same treatment. 

The following table gives a comparison of the results obtained 
with the copper wires tested in this and the preceding experiment : 

Table III. 



Coefficient of Expansion . . . 
Thermal coefficient of elasticity . 

Modulus at 25° 

Thermal coefficient of elastic limit 



0.0000153 
0.00133 
10020 
0.0034 



0.0000164 
0.000698 
11980 
0.00165 



As the table shows, the differences in all of the properties tested 
are very marked. The thermal coefficient of elasticity, and also of 
the elastic limit, are nearly twice as large in the first case as in 
the seycond. Such results serve rather to call attention to the wide 
variations in the properties of apparently similar specimens of 
wire than to fix the values of the coefficients determined. 

Conclusion, 
The following table gives a summary of results obtained from 
the experiments described in this article and the one previously 
published. The results for the piano wires are for temperatures 
ranging from about 15° to 180°, for the silver wire and the first 
copper wire the range was from 20° to 80° or 90° : 

Table IV. 



Kind of wire. 


Diam. 


Per cent of 

change in 

modulus for 

xoo'. 


Per cent of 
permanent 
change in 
modulus. 


Per cent of 

change in 

elastic limit 

for xoo*. 


Piano wire 

Piano wire 

Piano wire 

Piano wire 

Average for piano wire . . 
Annealed piano wire . . . 

Silver wire 

Copper wire 

Copper wire 


0.40 mm. < 
0.26 
0.45 
0.49 

0.45 
0.48 
0.64 
0.50 


5.0 
4.6 
4.6 
4.3 
4.6 
3.4 
8.2 
13.3 
7.04 


1.5 

1.27 

1.8 

1.15 


69.2 
33.9 
16.8 



No. 6.] YOUNG'S MODULUS. 447 

The results obtained show that neither magnetization nor an 
electric current through a wire produces any appreciable efifect 
upon the size of Young's modulus aside from that which can be 
attributed to the accompanying heat. All the wires show a per- 
manent increase in elasticity produced by heating them, the in- 
crease being gi:eatest for the silver and least for the copper wire. 

The thermal coefficient of elasticity is somewhat smaller for 
annealed than for unannealed piano wire. The values found for 
the thermal coefficients of silver and copper wire are much larger 
than those that have been found by others who have worked upon 
this subject.^ Perhaps the weights which my method of experi- 
ment made necessary were heavier than those used by other 
experimenters ; the thermal coefficient may be quite different for 
weights nearly as large as the elastic limit from what it would be 
with smaller weights. 

The temporary effects of heat upon the elastic limit of silver and 
copper wires are very marked. In some electric circuits for Vhich 
copper wire is employed, it has been found that the wire stretches 
much more during the summer than it contracts when the cold 
weather returns. This is doubtless because the elastic limit is so 
decreased by the summer heat that the weight of the wire between 
the points of support stretches it beyond this limit. The fact that 
copper wires vary so much in the effect of heat upon the elastic 
limit may need to be considered in selecting wires for telephone 
circuits or other purposes for which long wires are to be employed. 

(These experiments were made under the direction of Professor 
Frank P. Whitman, and the paper was presented as part of a 
thesis for the degree of Ph.D.) 

' N. Katzcnelsohn, BeibUtter XII., p. 307, 1888. H. Tomlinson, Pro. Roy. Soc, 
XL. p. 343, 1886. 




448 CAROUNE W, BALDWIN. [Vol. 111. 



A PHOTOGRAPHIC STUDY OF ARC SPECTRA. \\} 

By GlROLINE WiLLARD BALDWIN. 
II. 

Metallic Spectra. 

CERTAIN metals when introduced into the arc tend to obscure 
the band spectrum, e.g, Na, Li, K, Sr, Ba, Ca ; while others, 
as Zn, Cd, Cu, Ag, give the band spectra with equal or increased 
brilliancy. In no case was the band spectrum entirely invisible, 
but it was so much weakened by the alkalies that it is not strange 
that in their presence the carbon bands were not detected by the 
bolometric measurements of Professor Snow. 

In the ensuing paragraphs the results obtained by photograph- 
ing the arc when cores of the carbons were filled with various 
alkalies are briefly described and tables of the lines are given. 

Lithium Carbonate, 

Lithium gives an almost homogeneous carmine-colored arc. 
The spectrum has much the same general appearance as the 
spectra from the outer sheaths of the arc, with the addition of 
the lithium lines, and at a very short distance from the center of 
the arc the band spectrum is entirely invisible. However, the 
bright groups are faintly visible in the photographs taken from the 
center of the arc. 

Lithium does not materially affect the other metallic lines 
present in the ordinary arc spectrum. The lines which are most 
brilliant in the outer sheaths of the original arc are, with but few 
exceptions, the strong lines present when lithium is introduced. 
The carbon lines 3585.99, 3586.04, and 3590.52 are much fainter 
than in the yellow of the ordinary arc, and are not visible at 
1 Concluded from the Physical Review, March-April, 1896. 




No. 6.] 



STUDY OF ARC SPECTRA, 



449 



all when the slit is at a little distance from the center of the image, 
while a line at 3583 is very sharp in all the photographs. The 
calcium lines 4299.14, 4302.68, 4318.80, 4425.61, 4435.86, and 
4456.81 are stronger than in the yellow of the arc, being nearly 
as strong as 4307.91 ; but Ca 4527.17 is fainter in comparison to 
surrounding lines. Line 4527.17 is in fact hardly visible. 

Lithium lines photographed.^ 



X = 2741.39 


X = 3794.9 


X = 3985.94 


X = 4602.37 


3232.77 


3838.3 


4132.44 


4972.11 


3670.6 


3915.2 


4273.44 


6103.77 


3718.9 









Sodium Nitrate, 

When sodium is in the arc the flame is homogeneous and quite 
dense; the band spectrum is not so faint as when lithium is 
present, still it is much reduced in brilliancy. All of the calcium 
lines are strengthened. Calcium seems to have been present as 
an impurity in a number of the salts used. The Z^-lines were re- 
versed both when the nitrate and chloride were used. 



Sodium lines photographed. 



X = 2512.23 


X = 4343.7 


X = 4546.03 


X = 5153.72 


2543.85 


4390.7 


4665.2 


5670.40 


2593.98 


4393.7 


4669.4 


5675.92 


2680.46 


4420.2 


474836 


5682.90 


2852.91 


4423.7 


4752.19 


5688.26 


3302.47 


4494.3 


4979.30 


5890.19 


3303.07 


4500.0 


4983.53 


5896.16 


4325.7 


4542.75 


5149.19 





1 The wave lengUis of Uie metallic lines are taken from Kayser and Runge, Ueber 
die Spectnmi der Elemente, with whose measurements the scale readings agreed quite 
accurately. These tables are not given to establish wave lengths, but to show which of 
the lines already catalogued were found in these photographs. 




450 



CAROLINE W. BALDWIN. 



[Vol. III. 



Potassium Chloride. 

Potassium easily gives a long arc which is homogeneous and 
very clear, so as to be hardly visible between the carbons. It is of 
a less intense color than the arc of sodium or of lithium, and seems 
to be surrounded by a considerable mass of cooler vapor. The 
carbons are not at a very high temperature. The band spectrum 
is absent except very near the positive carbon. The strong me- 
tallic lines from the original arc are present The metallic lines 
appear much as when sodium and lithium are used. 



Potassium lines photographed. 



X = 3217.76 


X = 4(H7.36 


X = 4956.8 


X = 5112.68 


3446.49 


4870.8 


4965.5 


5782.67 


3447.49 


4943.1 


5084.49 


5802.01 


4044.29 


4952.2 







Calcium Chloride. 

When calcium is in the carbons, they are as highly incandescent 
as carbons which contain no metallic salt. The heat of the arc 
does not seem to be so much diminished as in the preceding 
cases. The arc shows a more varied formation. There is a blue- 
violet center, which is decidedly blue near each carbon. This is 
surrounded by a dark part, while the outer sheath is of an orange 
tint. The dark part diminishes as the carbons become heated. 

In the spectrum the strength of the bands is less affected than 
by the other metals yet studied; but their hazy appearance is 
removed, and the fine lines are more sharp. As soon as we pass 
into the outer sheath, the bands disappear with the exception of a 
slight indication of the one which terminates at X=3885. The cal- 
cium lines remain exceedingly sharp and brilliant in the outer sheath. 

As in the ordinary arc, the calcium lines 4581.66 and 4586.12, 
also lines of unknown origin near 4603., 4586., and 4581., are 
clearly seen at the negative carbon only, while lines at 4604. and 
4576. are visible only at the positive carbon. Line 4226.91 was 
strongly reversed. 



No. 6.] 



STUDY OF ARC SPECTRA, 



451 



Calcium lines photographed. 



X = 2398.66 


X = 3630.82 


X = 4318.80 


X = 5189.05 


2995.06 


3644.45 


4355.41 


5260.58 


2997.42 


3653.62 


4425.61 


5261.93 


2999.76 


3706.18 


4435.13 


5262.48 


3006.95 


3737.08 


4335.86 


5264.46 


3140.91 


3933.83 


4454.97 


5265.79 


3150.85 


3949.09 


4456.08 


5270.45 


3158.98 


3957.23 


4456.81 


5349.66 


3179.45 


3968.63 


4508.04 


5513.07 


3181.40 


3973.89 


4509.89 


5582.16 


3209.68 


4092.93 


4512.73 


5588.96 


3215.15 


4095.25 


4527.17 


5590.30 


3225.74 


4098.82 


4578.82 


5594.64 


3344.49 


4226.91 


4581.66 


5598.68 


3350.22 


4240.58 


4586.12 


5601.51 


3361.92 


4283.16 


4685.40 


5603.06 


3468.68 


4288.51 


4833.85 


5857.77 


3474.98 


4299.14 


4847.22 


6102.99 


3487.76 


4302.68 


487834 


6122.46 


3623.15 


4307.91 


5041.93 





Strontium Oxide, 



With strontium the arc has a pear-shaped purple center, the 
larger end of which rests on the positive carbon. The central 
part is bluish at each carbon. The outer sheath is of a brilliant 
red color, and the line between the two parts is very sharp and 
bright. The carbons are not very hot. They are, indeed, scarcely 
more than at a red heat. The effect on the spectrum is similar to 
that of calcium, and the same arrangement of lines at the positive 
and negative carbon is emphasized. The band spectrum is about 
as strong as when calcium is present, but it does not disappear 
quite so completely as in the outer sheaths of the arc. 

The number of strontium lines in the vicinity of the bands 
tends to obscure their character. 



452 



CAROUNE W. BALDWIN. 



[Vol. III. 





Strontiuin lines photosrapbed. 




X = 2931.98 


X = 3547.92 


X = 431939 


X = 4784.43 


X = 515637 


3199.1 


3628.62 


4326.60 


4812.01 


5222.43 


3200.4 


365322 


4338.00 


4784.43 


522535 


3301.81 


3705.88 


4361.87 


4812.01 


5229.52 


3307.64 


3940.91 


4412.82 


4832.23 


5238.76 


332232 


3969.42 


4438.22 


485527 


5257.12 


3330.15 


3970.15 


4480.96 


4868.92 


5451.08 


335135 


4030.45 


4531.54 


4869.41 


5481.15 


3366.43 


' 4032.51 


4607.52 


4872.66 


548637 


3380.89 


4077.88 


467839 


487635 


5504.48 


3464.58 


4161.95 


4722.42 


489220 


5522.02 


3475.01 


4215.66 


4729.93 


4%2.45 


5535.01 


347733 


4305.60 


4742.07 


4968.11 


554028 


3499.40 


4308.49 


4755.59 


4971.85 


5543.49 


3504.70 











Barium Chloride. 

When barium is present, the arc has a large round center, which 
shades from rose pink through lemon yellow to lime green at the 
edge. Next to each carbon it is of a brilliant lemon yellow color. 
The carbons are not very highly heated. 

The barium lines come out easily, and are very strong ; but the 
bands and all but the strongest lines in the original spectrum are 
so weak that they are almost invisible. 



Barium lines photographed. 



X = 2304.32 


X = 3662.62 


X = 408535 


X= 4407.10 


X= 4636.80 


233533 


3664.76 


4087.90 


4413.% 


464238 


2596.89 


3689.28 


4110.46 


4432.13 


4673.69 


2702.78 


3701.87 


4130.88 


446736 


4691.74 


3281.96 


3794.77 


4132.60 


4489.50 


4700.64 


3357.00 


3861.87 


4166.24 


4493.82 


4724.98 


3420.48 


3889.45 


4179.57 


4506.11 


4726.63 


3501.29 


3891.97 


4224.11 


4523.48 


4877.99 


3525.23 


3892.97 


4239.91 


4525.19 


4900.13 


3544.94 


3900.54 


4242.83 


455421 


4903.11 


3577.79 


3906.20 


4264.45 


4574.08 


4934.24 


3579.97 


3910.04 


4283.27 


4579.84 


4947.50 


3586.64 


3917.42 


4323.15 


4589.82 


5424.82 


3588.33 


3935.87 


4325.38 


4591.88 


5437.66 


3593.58 


3938.09 


4333.04 


4600.02 


551937 


3599.60 


3993.60 


4350.49 


4605.11 


5535.69 


3611.17 


3995.92 


4359.80 


4620.19 


5777.84 


3637.10 


4079.56 


4402.10 


4628.45 


5853.91 



No. 6.] 



STUDY OF ARC SPECTRA. 



Zinc Chloride, 



453 



The band spectrum is better than was obtained under any other 
circumstances. The bands are greatly extended and very distinct. 
The arrangement of lines in different parts of the arc is especially 
marked in the flame spectra. All of the calcium and aluminium 
lines are very clear in the outer sheath of the arc and near the 
negative carbon. The bands cling closely to the positive carbon, 
but the zinc lines cross the arc with nearly equal brilliancy in all 
parts. Only the carbon bands are seen in the region having a 
wave length greater than X=4862. 

The ** grating effect" is continuous from X=3400. to \=S635. 
The effect of the zinc seems to be to obscure all but the 
strongest of the other metallic lines, and to increase the intensity 
of the band spectrum. 

Zinc lines photographed. 



X = 2802.11 


X= 3072.19 


X = 3515.26 


X = 4293.02 


2823.27 


3075.99 


3572.90 


4298.54 


2833.13 


3282.42 


3671.71 


4630.06 


2863.43 


3302.67 


3683.63 


4680.38 


2873.39 


3303.03 


3740.12 


4722.26 


2913.63 


3345.13 


4019.75 


4810.71 


3018.50 


3345.62 


4058.02 


5182.20 


3035.93 


3346.04 


4101.94 





Cadmium Chloride, 

The spectrum obtained when cadmium is present in the arc is 
similar to that with zinc. 





Cadmium lines 


photographed. 




X = 2677.65 


X = 2%1.64 


X =3466.33 


X = 3981.92 


2712.65 


2980.75 


3467.76 


4306.98 


2733.97 


2981.46 


3500.09 


44)3.23 


2763.99 


3081.03 


3595.64 


4662.69 


2775.09 


3133.29 


3610.66 


4678.37 


2837.01 . 


3252.63 


3613.04 


4800.09 


2868.35 


3261.17 


3649.74 


5086.06 


2880.88 


3299.11 


3729.21 


5154.85 


2881.34 


3403.74 







454 



CAROUNE W, BALDWIN, 



[Vol. III. 



Copper, 

Copper gives an arc which has a bluish-green center with 
bright green near the carbons. This is surrounded by a dark 
part, which is again enclosed by a yellow outer sheath. 

The spectrum appears almost like that obtained from the center 
of the original arc, with the addition of the lines due to copper. 
The variation in brightness of certain lines at the positive and 
negative carbons is very noticeable, and is more easily observed 
owing to the £act that the copper lines are all strongest about 
half-way between the carbons, at which point they show a decided 
enlargement. In the band spectrum only the fine, grating-like 
lines are seen. The indications of the strong lines are seen at the 
negative carbon, while the lines of the band spectrum are strong 
for the whole width of the arc. 



Copper lines photographed. 



X= 3771.96 


X = 4123.38 


X = 4378.40 


X = 4674.98 


3860.64 


4177.87 


4397.42 


4697.62 


4003.18 


4242.42 


4415.79 


4704.77 


4010.% 


4249.21 


4480.59 


5105.75 


4015.80 


4253.53 


4507.62 


5144.35 


4022.83 


4259.63 


4509.60 


5153.33 


4056.80 


4267.48 


4513.39 


5218.45 


4062.54 


4275.32 


4531.04 


5220.25 


4063.50 


4329.00 


4539.98 


5292.75 


4073.28 


4336.17 


4587.19 


5700.39 


4080.70 


4354.91 


4651.31 


5782.30 



Silver, 
The appearance of silver in the arc, and its eflfect upon the 
spectrum, are almost identical with that of copper. 



Silver lines photographed. 



X = 3280.80 


X = 3841.30 


X = 4055.44 


X = 4616.03 


3383.00 


3907.63 


4212.10 


4668.70 


3542.67 


3914.47 


4311.28 


4678.04 


3557.30 


3940.30 


4379.45 


5209.25 


3681.80 


3943.10 


4396.49 


5465.66 


3710.10 


3981.87 


4476.29 


5471.72 


3810.60 


3991.90 


4556.13 





No. 6.] 



STUDY OF ARC SPECTRA. 



455 



Remarks. 

As has been noted in a previous paragraph, the lines of the 
ordinary arc which are strongest at the negative carbon increase 
in intensity in the outer sheaths, while the reverse is true with 
the lines from the positive carbon. When the metals K, Na, Li, 
Ba, Sr, and Ca are introduced, the lines from the positive carbon 
are weakened. The effect is most marked in the case of potas- 
sium. Barium reduces the carbon bands the most. 

The metals Cu and Ag, from the group I. b, give the spectrum 
in about its normal condition, with the lines due to the especial 
metal added ; while the metals Cd and Zn increase the intensity 
of the bands and diminish the strength of the metallic lines 
originally present near the negative pole. 

It has been frequently observed by others who have worked 
with metallic spectra by this method, that it is necessary to have 
added resistance in the circuit which supplies the arc, when metals 
are used, in order to maintain a constant length of arc. The 
amount that had to be added in the course of these experiments 
varied very much with the different metals. 

In a circuit of such electromotive force that 3 ohms resistance 
were necessary to give the ordinary arc its normal voltage (48 v), 
it was found that the following resistances would restore the arc 
to its proper condition: 



Metal. 


Retittance. 


Metal. 


Resistance. 


Silver 

Copper 

Zinc 

Barium 

Strontium 


3.1 
3.8 
5.6 
5.6 

5.8 


Cadmium 

Potassium 

Sodium 

Lithium 

Calcium 


5.8 
9.1 
9.5 
9.7 
9.9 



When the metals were used, the temperature of the carbons 
was apparently much less than with the pure carbon points. 
The temperature of the positive carbon was most affected, and it 
did not waste so rapidly in proportion to the negative as when 
no metallic salt was in the core. 



456 CAROUNE W. BALDWIN. [Vol. III. 

It might be thought that the changes observed were due to 
the fact that the temperature is not high enough to render all 
the lines visible. This view would be strengthened if the lines 
of metals which require the highest temperature for fusing and 
vaporization were strongest in those parts of the arc which are 
hottest. But this does not seem to be the case, for although 
K, Na, and Li, metals of low melting points, are strengthened at 
the negative carbon, so also are Ba, Sr, and Ca, which have 
relatively high melting points. The Cu and Ag lines extend 
across the arc with nearly even intensity, and the same is true 
of Zn and Cd. 

It does not seem that the diminished intensity of the carbon 
bands in the presence of certain metals can be wholly due to 
the density of the gases of the flame; as there is no direct 
relation between the amount of weakening of the bands and the 
density of the metallic vapor. Neither does the change seem 
to depend in any simple way upon the atomic weight of the 
metals. Barium and potassium obscure the bands most ; and 
they are respectively the highest and lowest in atomic weight of 
the metals studied. 

There are many reasons for believing that there is an electro- 
lytic action in the arc. This belief is strengthened by the fact 
that the metallic lines appear at the negative carbon, and the 
carbon bands are strongest at the positive. It is also true that 
the metals K, Na, Li, Ba, Sr, Ca, which are highly electropositive, 
are more strengthened at the negative carbon than are Cd, Zn, 
Cu, Ag, which are less positive. 

In studying the efifect of the metals upon the lines of the 
original spectrum, we may consider the need of increased resist- 
ance in the outer circuit to be due to diminished resistance of 
the arc, or to a change in the counter electromotive force. In 
the former case, the list of resistance given should have the 
same order as the resistance of the various metallic vapors. The 
arrangement, however, is not that of the respective metals as 
we know them at ordinary temperatures. 





_ 


*^ _ 


-»^ 


;j 


'_/■ 


^ ^^ 












_T 









C. W. BALDWIN ARC SPECTRA. 



No. 6.] STUDY OF ARC SPECTRA, 457 

Summary. 

(i) The spectrum obtained from the electric arc is not the 
same for all parts of the arc and the surrounding flame. On the 
contrary, there is z. decided difference in the spectrum of the 
several sheaths. The difference is largely due. to a fading out of 
the carbon bands and of all lines from the positive carbon, and an 
increase of intensity in the outer sheath of those lines which are 
most brilliant near the negative carbon. Certain lines and bands 
which are invisible in the center are seen in the outer part of the 
flame. 

(2) The total number of metallic lines diminishes rapidly, as 
we explore the arc from the center outwards. 

(3) When the spectrum is changed by the introduction of 
metals into the carbons, it is observed that the more positive 
metals, such as K, Na, Li, and Ba, Ca, Sr, greatly weaken, but 
do not destroy, the characteristic band spectrum of the arc. The 
lines which are most affected by these metals are those which in 
the ordinary spectrum are strongest near Xht positive carbon. 

Certain metals, as silver and copper, do not materially alter the 
original arc spectrum, while others, as zinc and cadmium, affect 
the lines near the negative carbon, and thus give the band spec- 
trum, which is no longer obscured by the metallic lines usually 
present, an unwonted brilliancy. 

The causes of the phenomena are not easily discovered, but it is 
hoped that the points brought out in this paper may throw some 
light upon the intricacies of this complex problem. 



458 C. H, SHARP. [Vol. III. 



MINOR CONTRIBUTIONS. 

A Method for the Use of Standard Candles 
IN Photometry. 

By Clayton H. Sharp. 

THE fundamental assumption on which is based all American and Eng- 
lish practice in the use of candles as a standard of light in photometry 
is that the intensity of light emitted by a candle is, within certain arbitrary 
limits, proportional to the rate at which the material of the candle is con- 
sumed. Supposing this assumption to be in a measure justifiable, we 
could scarcely imagine it to be rigorously exact. The purity and hygro- 
metric state of the air, which Liebenthal ^ has recentiy shown to have such 
a large influence on the intensity of the Hefiier light, can scarcely be of 
inappreciable influence on the candle flame.* 

But no matter how nearly this assumption approximates to the true state 
of affairs, the fundamental and inevitable difficulty with this definition of 
the light unit still remains. It is this : what we ought to know is not the 
mean rate of consumption during the period over which the measurements 
extend, but the rate at the instant at which a photometer setting is made. 
Since it is impracticable to determine this quantity, the mean rate has been 
used for correcting observations. 

That this cannot be a proper method of procedure on the assumption 
made, is shown by a study of the enormous and quick variations to which 
the quantity of light emitted by a candle is subject. Curves * showing 
these instantaneous variations have been obtained by the use of a sensitive 
bolometer which, when exposed to the radiation of a candle flame, would 
respond to every change in the intensity of that radiation. It is quite 

* Liebenthal, " Ueber die Abhangigkeit der Hefnerlampe und der Pentanlampe von 
der BeschafTenheit der umgebenden Luft" 

Elektrotechnische Zeitschrift, XVI., p. 655, 1895. 

2^itschrift f&r Instrumentenkunde, 15, p. 147. 

Electrical World Digest, XXVI., p. 220 and p. 500, 1895. 

* For evidence conBnning this statement see an article by John Methven read before 
the Southern District Association of Gas Engineers and Managers, London Gas World, 
1889, p. 572. A translation into German will be found in Dingler's Polytechnisches 
Journal, 1890, Vol. 277, p. 276. 

8 Sharp and Turnbull, " A Bolometric Study of Light Standards," Physical Review, 
Vol. II., p. I. This article will be referred to frequently. 



No. 6.] USE OF STAISTDARD CANDLES TN PHOTOMETRY, 459 

possible that a series of photometric settings should be made in such a 
way that their mean would give a value considerably lower than the mean 
ordinate of an intensity curve covering all the time between two weighings 
of the candle. 

Moreover, in the bolometric investigation it was found that corrections to 
the mean ordinates of the various curves for deviations from the normal 
rate of consumption did not serve to reduce these ordinates to a common 
value ; or, in other words, that the energy radiated was not proportional to 
rate. Since the radiant efficiency of a candle flame does not change with 
its size, — provided that it does not smoke, — this would be true for luminous 
radiation as well as for total radiation. This is in accord with the obser- 
vations of Tyndall * and the results of von Jolly, who showed that on a 
mountain summit candles have a shorter flame and diminished intensity, 
with the same rate of consumption. 

Recognizing these facts, the German photometrists have insisted that the 
flame height is the significant factor, and that candle measurements should 
be made only with a standard height of flame. They would clean the wick 
of the candle, wait until the flame height becomes normal, and then set the 
photometer.^ 

There are certain objections to this method of procedure although it 
undoubtedly gives better results than the English practice. In the first 
place, it must be a dme-wasting and patience-trying operation. Moreover, 
it is very doubtful if snuffing the wick of a standard candle is an allowable 
operation, since the shape of the flame depends on the particular curl which 
the wick assumes, and is normal only when the wick has its natural curl. 

A more desirable method would be to measure, at the instant the pho- 
tometer setting is made, the height of the candle flame ; then, knowing a 
relation between the height of the flame and the intensity of light emitted, 
to reduce the instantaneous intensity to the intensity at normal flame 
height. 

The first question then becomes: Does any definite relation exist 
between these quantities ? Giroud has shown that the slender, pointed flame 

1 Tyndall, " Heat as a Mode of Motion." Also Dr. Franklmnd, Philosophical Transac- 
tions, 1861. 

* In the original directions for the proper use of the German Vereinskerze, however, 
it is stated that snuffing is unallowable, and that measurements should be made only when 
the quietly burning flame has reached a height of 50 mm. See *^ Beschluss der Versamm- 
lung des Vereines des Gas- und Wasserfachmanner Deutschlands," etc. Dingler's 
Polytechnisches Journal, 206, p. 329. This is a reprint from the Journal fik Gasbelcucht- 
ung und Wasserversorgung, 1872, Nov. 12. 

On the other hand, see the report of a committee of the Verein von Gat- und Wasser- 
iacminnen as transcribed in La Lumi^re Electrique, 34, p. 178. Here snuffing the 
wick is recommended. See also KrUss' book, Elektrotechnische Photometrie. 




460 



C H, SHARP. 



O'OL. III. 




Fig. 1. 
Cunres by Liebenthal. 



of his bee-bougie varies at the rate of about 2 per cent per millimeter, the 
relation between flame height and intensity being nearly linear. Liebenthal^ 
has drawn curves (see Fig. i) showing this relation in the case of the 
Hefner lamp and of the English standard candle. For the former the 

relation is approximately 
linear for small variations 
and shows for variations be- 
tween 35 mm. and 45 mm., 
2.6 per cent per miUime- 
ter. The two English can- 
dle curves are practically 
i ••1 y/^ straight lines for all ordi- 

i 1 / ij^^jy variations, and show 

2.1 per cent and 1.9 per 
cent per millimeter respec- 
tively, for variations be- 
tween 40 mm. and 50 nmi. 
The present experiments were suggested by the results of the bolometric 
tests of candles. They were undertaken first for the purpose of investi- 
gating this relation between flame height and intensity, and, second, to 
determine whether the use of this relation would not make it possible to 
get more consistent results than can be obtained by correcting for rate of 
consumption. 

Two methods were employed to determine the flame height-intensity 
ratio. In the first method the intensity of the radiation of the candle was 
measured by the bolometer in the way previously described. To measure 
the height of the flamej a long camera was constructed, having its lens and 
ground-glass plate at a fixed distance from each other. The ground-glass 
plate was graduated empirically to read directly in millimeters the height 
of objects focussed upon it. The candle was placed on a pan attached to 
a spiral spring of such a length that its elongation would be just equal to 
the length of the candle. By this arrangement the top of the candle was 
kept at a constant height above the floor, and when once the image of the 
base of the flame had been accurately adjusted on one of the lines of the 
camera screen (to facilitate which the screen was capable of a slight vertical 
movement), it remained there during a considerable period of time. Hence, 
to measure the height of the flame at any instant, it was necessary only to 
glance at the image of the top of the flame and to note its position on the 
screen. It will be noticed that this camera device is, to a certain extent, 
a modification of Krtiss' optical flame measure which has been in use a 

* Liebenthal, " Photometrische Untersuchungen fiber die von Hefner- Altensck'sche 
Uchtcinhert," Elektrotechnische Zeitschrift, 9, p. 96, 1888. 



No. 6.] USE OF STANDARD CANDLES IN PHOTOMETRY, 461 

number of years. Extended to take in the bottom of the flame, and com- 
bined with the spring balance, it enables measurements to be made with 
great quickness, and with a sufficient degree of accuracy, by an observer 
who is located so far from the flame as to leave it entirely undisturbed by 
his movements. 

The magnifying power employed was about two, and heights were 
measured only to 0.5 mm. Greater closeness of measurement was deemed 
unnecessary on account of the ill-defined nature of the base and tip of the 
flame. The actual base of a candle flame is difficult to observe, on account 
of the small quantity of light which it emits. The procedure adopted 
was to set on the line of demarkation between the charred and uncharred 
portions of the wick, since this was found usually to mark the base of the 
flame. In case a close inspection of the candle showed the base of the 
flame to be slightly above this point, a further adjustment of the screen was 
made. 

In order to insure great steadiness of the flame, the candle was placed 
in a roomy, well-ventilated box having a glass window. Having put the 
candle in position before the bolometer, and having adjusted the camera 
properly, the bolometer screen was raised and simultaneous observations 
were made of galvanometer deflections and flame heights. These readings 
were corrected for any change in sensitiveness of the bolometer and any 
drift of the galvanometer needle, and were plotted, using flame heights and 
galvanometer deflections as coordinates. 

In the second method a Lummer-Brodhun photometer was used. At 
one end of a photometer bar 200 in. long was placed a no-volt glow-lamp. 
This was maintained at a voltage of 100 by means of a storage battery. 
Being run at low efficiency, its color was about the same as that of a candle, 
and its change in candle power during the time it was in use was too small 
to be detected. 

At the other end of the bar was the candle, supported by its adjusted 
spring. The candle was always placed so that the curl of the wick was 
perpendicular to the axis of the bar.* The arrangement for measuring 
flame heights is shown in Fig. 2, which represents a projection of the 
apparatus on a horizontal plane. B is the photometer bar, C the candle, 
M a mirror placed behind the candle in such a way as to reflect the rays 
from it through the lens Z, which projected them on a graduated screen »S 
placed immediately behind the bar. The mirror was carried on a movable 
support so as to admit of an adjustment of focus. 

This arrangement was adopted, since by its use one observer could do 

1 For the variation of the intensity of candle as a function of the azimuth of the 
plane of the wick, see Methven, he, cit,; also an article by Sugg, in the Journal for Gas 
Lighting, which is reprinted in the Scientific American Supplement, No. 484, p. 7726. 



462 



C. H, SHARP. 



[Vol. III. 



all the work. The method was simply to make a rather quick photometer 
setting, and then instantly to note the position of the top of the flame on 
the screen, reading the position of the photometer afterwards. 

In some of the earlier measurements a kerosene lamp with an Argand 
burner similar to the ordinary student-lamp burner was used as a secondary 
standard. The upper part of the chimney was covered by a closely fitting 
cylinder of ferrotype iron in such a way that the top of the flame was 
entirely hidden. This furnished a very steady source of light after it had 
been burning long enough for the parts to become thoroughly warmed, and 



^-J. 



^ \ 



s 



.V. 



0= 



Fig. 2. 
Arrangement of Photometer. 

its intensity was imaflected by slight adjustments of the height of the flame, 
provided only that the flame was always high enough. Unfortunately, its 
intensity varied enough from day to day to make its indications unreliable 
without a daily calibration, and it was replaced by the more convenient 
and accurate glow-lamp. Observations of variation of intensity with 
flame height are not affected by this fact. 

The observations were treated in the following manner: The various 
observed values of flame height were collected in such a way that heights 
of 41.0 mm., 41.5 mm., and 42.0 mm., formed one group; 42.5 mm., 43.0 
mm., and 43.5 mm., another, etc. The mean height of each group was 
found, and also the mean bar-reading corresponding to it. The candle 
power of the standard was found by taking the mean of aD the heights and 
bar-readings, and reducing, by means of an approximate correction, to a 
standard flame height of 45 mm. Using this value for the intensity of the 
glow-lamp, the intensity of the candle corresponding to each group was 
computed. By means of a curve plotted from these values the percentage 
variation per millimeter of flame height was determined. 

In order to find the relative accuracy of this and of the ordinary method 
of using candles, the following observations were made : A candle burn- 
ing normally was weighed by the " method of transits," was transferred to 
the spring balance, and ten or more photometer settings made — the flame 



No. 6.] USE OF STANDARD CANDLES IN PHOTOMETRY, 463 

heights also being noted. The candle was then weighed again, and another 
group taken. A number of such sets of observations were made on several 
days, and since the glow-lamp was used as a reference standard, these sets 
are comparable with each other. 

The mean value of the candle power of the glow-lamp given by each of 
these sets of observations was corrected for rate in the ordinary way, and 
was also corrected by reducing from the mean flame height to the standard 
height of 45 mm., using the mean value of the relation between intensity 
and flame height as determined from all the observations, both bolometric 
and photometric. The deviation of each value obtained for the candle 
power of the glow-lamp from the mean value obtained from all the obser- 
vations was computed, and this deviation was reduced to per cent. A 
comparison of the percentage deviations given by the two methods shows 
their relative accuracy, while the absolute values of the percentages show 
the error which one is liable to make in using candles in either of the two 
ways. 

Table I. 



8|3 


Qalvanometer 
deflection. 


Flame 
height 
(mm.). 


Qalvanometer 
deflection. 


Flame 
height 
(mm.). 


Qalvanometer 
deflection. 


48.0 


29.0 


44.0 


26.7 


43.0 


25.8 


48.5 


29.5 


45.0 


27.5 


44.0 


27.0 


49.5 


30.3 


45.5 


283 


Wick of 


candle 


48.0 


29.2 


43.5 


27.0 


clea 


ned. 


47.0 


28.2 


43.5 


27.0 


55.0 


37.2 


47.5 


28.8 


44.5 


27.5 


46.5 


30.6 


45.5 


27.5 


44.5 


27.5 


47.5 


3U 


46.5 


28.0 


45.0 


28.3 


48.0 


32.0 


46.5 


28.2 


44.5 


27.7 


49.0 


32.7 


46.5 


28.0 


43.5 


26.5 


49.0 


32.6 


45.0 


27.0 


43.5 


27.0 


49.5 


32.8 


45.5 


27.6 


43.0 


26.5 


50.5 


33.7 


45.5 


27.8 


42.5 


26.0 


50.0 


33.0 


44.5 


26.5 


43.5 


26.8 


50.0 


33.0 


42.0 


25.8 


42.5 


25.5 


50.0 


33.2 


43.0 


26.8 


43.5 


26.0 


49.0 


32.6 


43.0 


26.0 


44.0 


26.3 


47.0 


30.4 


43.5 


26.7 


43.5 


26.0 


48.5 


30.0 


44.0 


26.8 


43.5 


26.2 


48.5 


31.0 


44.5 


27.1 


44.0 


26.7 


47.0 


30.0 


44.5 


27.2 


44.5 


27.0 


46.5 


30.0 


43.5 


26.4 


44.0 


26.8 


46.5 


30.0 



464 



C. H. SHARP. 



[Vol. lU. 



Table IL 



Flame 
height 


Photometer 
her. 


Fleme 
height 


Photometer 
her. 


Flame 
height. 


Photometer 
bar 


(mm.). 




(mm.). 




(mm.). 




45.5 


702 


41.5 


713 


53.0 


686 


46.5 


699 


43.0 


707 


48.0 


700 


48.0 


700 


43.0 


708 


48.5 


695 


49.0 


693 


44.0 


706 


46.0 


704 


51.5 


690 


44.0 


707 


45.0 


708 


53.0 


697 


45.0 


705 


44.0 


707 


44.5 


709 


44.0 


709 


44.0 


711 


46.0 


705 


44.0 


710 


46.0 


707 


49.0 


694 


43.0 


713 


43.0 


713 


46.0 


699 


45.0 


708 


46.0 


708 


48.0 


698 


End of 


wick 


44.5 


710 


48.0 


693 


cut 


off. 


44.0 


711 


49.0 


691 


40.0 


712 


46.0 


711 


45.5 


700 


44.0 


708 


45.5 


708 


44.0 


707 


47.0 


698 


46.0 


712 


45.5 


699 


48.0 


696 


42.5 


716 


48.0 


697 


50.0 


693 


42.0 


715 


46.0 


698 


54.0 


688 


43.0 


715 


46.5 


6% 


53.0 


688 


44.0 


714 


45.0 


700 


51.0 


693 


45.0 


711 


45.0 


701 


50.0 


694 







Table III. 



Bolometric. 


Per 
cent. 


Photometric. 


Per 
cent. 


Photometric. 


Per 
cent. 


1894. Nov. 29 . 


. 2.2 


1895. July 27. 




3.3 


1895. Dec 3 


El 




Dec. 5 . . 


2.7 


Oct. 30 . 




3.4 




F 


2.3 


1895. Feb. 23, I 


2.2 


Nov. 1 


I. 


3.3 




Gj 


II 


2.5 




IL 


3.3 




HJ 




UI 


. 3.2 


Nov. 6 


I. 


2.2 


Dec. 4 


\^ 




March 21, I 


^ 3.1 




II. 


2.7 




J 




II 


Nov. 27 


I. 


2.7 




K 


2,6 


Oct.4 . . 


2.7 




II. 


2.9 




L 






Dec. 2, A.M 


.Al 
B J 


2.7 




M 

N. 








Dec.2,P.M. 


.c 

D ^ 


2.8 








Mean . . . 


2.7 




D' 




Weighted mean 


of all 


2.7 



No. 6.] USE OF STANDARD CANDLES IN PHOTOMETRY, 465 



Table IV. 



Name of 

group of 

observationt. 


Rate 

(grams 

per 
hour). 


1 

C. p. of 
Flame glow- 
height Tamp 
(mm.), uncor- 

. rected. 


C.P. 
cor- 
rected 
for 
rate. 


C.P. 

cor- 
rected 

for 
flame 
height. 


Devia- 
tion from 

mean 

corrected 

for rate. 


Devia- 
tion from 

mean 

corrected 

for 

height. 


Percent- 
age 
deviation. 
Rate. 


Per- 
centage 
devia- 

tion. 
Height. 


A 
B 
C 
D 
E 
F 
G 
H 
I 

J 
K 
L 
M 

N 


7.601 
8320 
6.981 
8.100 
7.157 
7.863 
8.030 
7.330 
8.422 
7.271 
7.367 
7.440 
7.137 
7301 


43.0 

45.15 

44.95 

46.1 

46.4 

44.7 

44.8 

44.05 

44.3 

47.1 

46.15 

45.6 

42.3 

44.2 


6.11 

5.785 

6.01 

6.09 

5.52 

5.67 

5.72 

5.80 

5.65 

5.35 

5.50 

5.64 

6.00 

5.79 


5.99 
6.20 
5.41 
6.35 
5.09 
5.74 
5.91 
5.47 
6.13 
5.02 
5.22 
5.41 
5.52 
5.45 


5.78 
5.80 
6.00 
6.25 
5.73 
5.62 
5.69 
5.66 
5.54 
5.65 
5.67 
5.73 
5.56 
5.67 


4-035 
+0.56 
-0.23 
+ 0.71 
-0.55 
+0.10 
+0.27 
+0.17 
+0.49 
-0.62 
-0.42 
-0.23 
-0.12 
-0.19 


+0.04 
+ 0.06 
+0.26 
+0.51 
-0.01 
-0.12 
-0.05 
-0.08 
-0.20 
-0.09 
-0.07 
-0.01 
-0.18 
-0.07 


% 
+ 6.0 
+ 9.8 

- 4.25 
+ 12.6 

- 9.8 
+ 1.6 
+ 4.8 
+ 3.0 
+ 8.5 
-11.0 

- 7.6 

- 4.25 

- 23 

- 3.5 


% 
+0.7 
+ 1.0 
+4.5 
+ 8.7 
-0.2 
-2.1 
-0.9 
-1.4 
-3.5 
-1.6 
-1.2 
-0.2 
-3.2 
-1.2 


Means, disre- 
garding signs 


7.594 


44.9 


5.76 


5.64 


5.74 


0.36 


0.125 


635 


2.16 


Nov. 6, I. 

II. 
Nov. 11 
Nov. 12, 1. 

II. 
Dec. 2, D' 




45.5 
46.3 
43.1 
44.1 
42.9 
493 


5.60 
5.79 
6.17 
5.87 
6.20 
5.36 




5.68 
6.00 
5.85 
5.73 
5.85 
5.99 




-0.09 
+ 0.23 
-0.08 
-0.04 
-0.08 
+0.22 




-1.6 
+ 4.0 
-1.4 
-0.7 
-1.4 
+3.8 


Means of all, 
disregard- 
ing signs 




45.0 


5.78 




5.77 


Last six 
only. 


0.123 




2.14 



Results. 

Table I. gives a characteristic set of data obtained by the use of the 
bolometer, 1894, March 21. Table XL is a similar set of photometric 
data obtained 1895, November 6. The data of Table I. and Table II. 
are shown reduced and plotted in Fig. 3 and Fig. 4 respectively. Table 
III. gives values found for the variation in intensity of candles expressed 
in per cents per millimeter. Table IV. shows, in the way described 
above, the comparative accuracy of the two methods of reducing candle 
observations. Figure 5 shows plots obtained from groups of observations 



466 



C H, SHARP, 



[Vol. III. 



designated by Ay By C^ * • • N, Figure 6 shows plots from three suc- 
cessive sets of bolometric observations. 

.\n inspection of the tables and curves will show that while the relation 
between dame height and intensity is a fairly definite one for any given 






5. 





























^ 


>^ 
















































^^ 


^ 


^ 






















^ 




^ 






















■^a 
























fc-^ 




^" 


























y^ 


































































1 


LAME 


HEIQ 


ITIN 


AiLUljlETERls 











Fig. 3. 
Bolometer Curve. 

iiUHip oi observations, there is a considerable range of variation in the 
^a/.ujk tor it as obtained from different groups. Moreover, the relation 
NoaK tunes changes during one burning of the candle. Figure 6 illustrates 
10. V {vvuluuity in that there is a group of points marked [T] which lie 
vvavivicuiMv below the Une plotted to represent all the observations; and 
loai liu' moik: of the flame height-intensity curve plotted from the points 



1 


1 














• _- 






• 


=^ 


1 

1 


r - 
1 










,— • *** 


1^ 


r 










1 


-^ 


^- 


^ 


^^ 


® 
















"■ 




F 


.AME 


^EIQ^ 


TINR 


IILLIM 


ETER 


\ 









Fig. 4. 
Photometer Ciirves. 

^ 'ii^itciKilly different from that obtained from other groups 

I M.A 'na> be due to a change in the shape of the wick. The 

^ ^. u.iHi is iK>t absolutely constant does not vitiate the pro- 

. .icaiui^ caudle observations; for since the deviations of 




No. 6.] USE OF STANDARD CANDLES IN PHOTOMETRY. 467 



flame height from 45 mm. is seldom more than 10 per cent, if our assumed 
value for this relation is in error by as much as 20 per cent, our reduced 
value for candle power would be in error by no more than 2 per cent. 
Table IV. shows that the mean deviation from the mean of observations 



z 

IM 

few 



















_r-*ll 


^•- 


r^^ 














^ 


m^^' 


^ 




• 












Li^ 


'X^ 


r^ 


^^ 




















.« 




































FUUM 


EHEH 


mTl^ 


MILL 


METE 


R8 











U tf 10 i7 

Fig. 5. 
Photometer Curve. 



corrected in this way is a little over 2 per cent, and that fourteen out of 
twenty values were in error by 2.1 per cent or less. In the case of cor- 
rections for rate, the mean deviation is over 6 per cent, while but one out 



C!49 

M 
O 

S 38 

z 































L.^ 


























L.''-* 


W 


I*' ' 






















^^ 




:^ 






















,^ 


> 


"X' 

^ 






















.^ 


























^ 


^ 


5>^ 


r 


















---«' 


i^f 


^ 


> 


y 




















'^ 


^- 


■^s 




" 




























































1 


LAME 


HEIQI 


IT INI 


IILLIM 


ETER 


\ 











41 ^ «8 

Fig. 6. 
Bolometer Curve. 



of fourteen values deviated by less than 2 per cent, and only four by less 
than 4 per cent. 

In other words, by correcting for flame height an error of less than 
2 per cent may reasonably be expected, and the probability of making an 



468 



C. H. SHARP, 



[Vol. III. 



error greater than 4 per cent is small ; while in correcting for rate, errors of 
8 per cent and 9 per cent are of common occurrence. 

The values corrected for rate might, perhaps, be more consistent if the 
rule were followed to reject all observations in which the rate fell below 
114 or above 126 grains per hour. Similarly, the errors in the values 
corrected for flame height might be smaller if observations made at extreme 
flame heights were to be rejected. Indeed, it is one of the chief advan- 
tages of the method that the observed flame height furnishes a criterion for 
the rejection of any observation which is regarded as doubtful. In this 
discussion, however, in order to be equally fair to both methods, no obser- 
vations have been rejected. 

The results of these photometer observations confirm fully those obtained 
by the use of the bolometer in determining the variations of light standards, 
and show very conclusively that the fundamental assumptions on which the 
bolometric tests were based, were entirely justifiable. If we compute from 
Table IV. the mean value of the flame height-intensity ratio, as determined 



1 1 






H- 
I- 


FLAME 

INTENI 


HEMHl 
ITYOF 


INMIU 
CANOU 


JMETEI 


8 




H 






1 1 














y 


^ 


' ^ 


_^ 


\, 








1 — J 


U_, 


»•-"? 


N^-^J 


1^ 




~~ ^ 


r- 


I 1 


'^ 


1 


OJ 


^ 


7^ 


^ 


r^ 


• 


t 


r 








^ 


» 


r^ 








Tl 


ME IN 


PERV* 


L8 











Fig. 7. 

Variation of flame-height (//) and intensity (/) of English candles. Dotted line shows Intensi^ 
reduced to standard flame-height. 



by the bolometer, we find that it is just the same as the mean value from 
a// the observations. 

In the " Bolometric Study of Light Standards " it was shown that the 
English candle is subject to sudden variations in intensity which are some- 
times as large as 15 per cent. Many of these sudden drops were noticed 
while making the photometer observations, and they all had the same 
characteristics as are shown by the bolometer curves. Figure 7 shows a 
group of these observations — group F in the tables. Assuming that the 
time intervals between the various photometer settings were equal, points 
were plotted showing the relation between intensity of the candle and time 
and between flame height and time. It will be seen at once that the two 
curves are of very similar characters. The flame height gradually increased, 



No. 6.] USE OF STANDARD CANDLES IN PHOTOMETRY. 469 

and with it the intensity, until, when the height of 48 mm. had been reached, 
there was a sudden drop, the change in intensity amounting to 1 2 per cent. 

These curves evidently show in an imperfect way variations precisely 
similar to those which are so faithfully reproduced by the galvanometer 
needle. In view of these qualitative and quantitative results, it would seem 
to be impossible to doubt the reliability of the bolometer as an instrument 
for making such tests. 

Another interesting consequence of these candle measurements is the 
very careful standardization of the glow-lamp. Its intensity has been 
measured in terms of the Hefner light also, and by this means a good 
determination has been made of the candle power of the Hefner light. 
This result, together with previous determinations of the same ratio, 
appears in Table V. 

Table V. 



Observer. 


Hefner. 


BngUth candle. 


SharD. candles reduced for rate 


0.872 


Sharp, candles reduced for flame height 


0.892 


Sharp and Tumbull, integration of energy curves ^ 

Violle 


0.941 
0.98 


Reichsanstatl investigations, mean value ^ 

'N#>therland Photometrv Commission * 


0.876 
0.921 


S. Schiele, mean value * 


0.881 







The value 0.94 is taken from curves made in the bolometer tests, and 
rests on the assumption that the radiant efficiencies of the candle and 
Hefner flames are equal. Since the Hefaer flame is distinctly redder in 
color than the candle flame, its radiant efficiency is probably smaller, and 
consequently the value 0.94 is too large. A difference in the radiant effi- 
ciencies of the two sources of less than 0.2 per cent would serve to bring 

* Loc. ciL 

* This is the mean of a long series of determinations made by different observers at 
different times, using candles from various sources. The measurements were taken at 
normal flame height of 45 mm. See *' Beglaubigung der Hefnerlampe "; Zeitschrift flir 
Instrnmentenkunde, 13, p. 257. 

' An abstract in German by Krflss will be found in the Journal f^ Gasbeleuchtung and 
Wasscrvcrsorgung. 1894. 

^ Schiele, Report of Committee on the Comparison of the Hefner lamp and Ger- 
man and English candles. Journal fUr Gasbeleuchtung und Wasserversorgung, Band 32, 
1889, p. 757; also Dingler's Poly tech nisches Journal, 274, p. 540. The measurements 
were made at normal flame height of 45 mm. 



470 HAROLD N, ALLEN, [Vcl. 111. 

this value down to 0.88. The preponderance of evidence in favor of the 
value 0.88 is very great. It is probably true that the very best way we 
have at the present time of determining candle power is to use the Hefner 
lamp and then to reduce by the use of this ratio. 

The writer desires in conclusion to express his obligations to Mr. C. P. 
Matthews for timely assistance in making some of the above observations. 

Cornell University, Ithaca, N.Y., 
January, 1896. 

The Graphical Representation of Magnetic Theories. 
By Harold N. Allen. 

THE induction theory of magnetism, introduced by Faraday, is now 
looked upon by all physicists as correct. The older theory which 
assumes the existence of magnetic fluids covering the ends of the magnet 
is in some cases mathematically simpler, and is for this reason often made 
use of. This, however, is apt to breed confusion as to the true nature of 
the induction or polarization in any given case. The difficulty Tyndall 
experienced in accepting Faraday's views as to diamagnetism, is accounted 
for by the fact that he was thinking in terms of the fluid theory, while 
Faraday was considering the magnetic polarization in the diamagnetic 
substance. 

The object of this paper is to insist again upon the distinction between 
these two theories, and at the same time to consider some points in the 
induction theory itself. A number of diagrams will be described which 
illustrate the different aspects of the induction theory. They show how 
the molecules of the magnet are supposed to be polarized, and how this 
polarization is continued in the surrounding ether. The tubes of force, or 
" polarization tubes," and the equipotential surfaces are drawn in each case 
according to Maxwell's method. The figures must be revolved about the 
horizontal axis, so that the lines drawn will trace out, some the bounding 
surfaces between the tubes, and others the equipotential surfaces. 

It has been found convenient to give the name polarization tube to a 
tube of force consisting of a bundle of 4 x induction tubes. The polar- 
ization at any point is measured by the number of polarization tubes 
passing through a square centimeter of a surface, which cuts them at 
right angles, just as the induction is measured in the same way by means 
of the induction tubes. 

If D^ is the magnetic polarization, 

B^ the magnetic induction, 
H^ the magnetic field intensity, 



No. 6.] MAGNETIC THEORIES, 47 1 

the following relations will hold : 

A polarization cell or energy cell is a portion of the medium bounded on 
the sides by the walls of a polarization tube, and at the ends by two equipo- 
tential surfaces, differing from one another in value by unity. It is possible 
to regard each of these cells as containing half a unit (erg) of energy. 
This energy is to be regarded as in some way directed along the lines of 
force, as the energy of a bullet is directed along the line of its flight, or the 
energy of rotation of a fly-wheel is directed along its axis. 

The length of the cell in a uniform field being 

I _ /x dn 

H^^^^D^" dv: 

and the area of its section being -^, 



the volume will be 



Thus the density of the directed energy is 2 icD^ in a medium of unit 
permeability. 

According to one statement by Maxwell, the energy density in a medium 

of permeability fi is ^^ "* . Ampere's theory of magnetism, however, 

implies, as will be shown, a much larger energy density than this. 

In the first part of his treatise. Maxwell seems practically to assume that 
the polarization in a paramagnetic substance is made up of two parts, the 
polarization of the iron molecules or the intensity of magnetization /, 
and the polarization of the ether which occupies the same space = Z?' 

= — , where H^ is the field intensity in the substance ; that is, in a long 
47r 

uniform crevice, the direction of which coincides with that of the induction 

tubes. 

Thus the total polarization is 

/?« = - + /, 

47r 

or i?« = Z?'-h/, 

or in more familiar terms, 

^^ = ^'4-4^7. 

The two polarizations are regarded as being superimposed, so that in some 
way they occupy the whole of the same space at the same time. 

In Diagram II., Fig. i, are shown the equipotential surfaces and polar- 



472 



HAROLD N. ALLEN, 



[Vol. III. 







1 


1 


III IV 


















































c__ 




. — 






d 










--^ 


-i-i.—.. _,_ 












ipSS 










A 




















B 



















J 

87r 



J 

27r 



5 

87r 



Fig. 1. Half size. 



ization tubes produced, when an infinite cylinder of constant permeability, 
fi = 2, is placed with its axis parallel to a uniform field of force H— i. 

Diagram I., Fig. i, is a representation of the field before the introduc- 
tion of the cylinder. The polarization tubes in these diagrams are bounded 

by the cylinders generated by the hori- 
zontal lines when the figure is rotated 
about AB, The line CD traces out 
the surface of the paramagnetic cylin- 
der. The equipotential surfaces in the 
cylinder are simply continuations of 
those in the outside field. The polar- 
ization tubes are twice as numerous 
in the cylinder as outside. 

Half of the tubes are supposed to 
pass through the ether, just as if the 
iron were not present; the other half 
go through the iron molecules, which 
are supposed to fill out the whole volume of the cylinder. 

The energy density in the air is — , in the iron — . The polarization 
J J Stt 47r 

is — in the air, and — in the cyHnder. 

47r 27r ^ 

Maxwell does not say anything about the energy density according to 
Ampere's theory of elementary current magnets. From the nature of the 
case any exact determination seems impossible, but some idea can be 
obtained by making certain assumptions with regard to the distribution 
of the elements, and supposing that the amount of conducting material is 
very small. 

Suppose that the cylinder is saturated, and that all the elements are set 
at right angles to the field of force. In order to obtain a minimum value 
for the directed energy density we will assume that the elementary mag- 
nets consist of thin wires of infinite conductivity, bent into square or hex- 
agonal circuits, which, for the sake of simplicity, are taken as arranged 
regularly in long hnes side by side so as to form square or hexagonal 
magnetic solenoids. These latter are to fit together so as to leave only 
very narrow cracks between them. The permeability of the ether between 
the conductors and of the conductors themselves is unity. 

Then the polarization inside each solenoid due to the currents in the 
elementary circuits is /, and to this must be added D\ the polarization 
which would exist there if the iron were not present. Thus the total polar- 
ization is Z> = Z>' -h /. In the very narrow cracks between the solenoids 
the polarization is D\ the same as that in the space outside, and the dis- 



tance between the equipotential surfaces is 



4 7rZ>' 



The equipotential 



No. 6.] MAGNETIC THEORIES. 473 

surfaces in the cracks are then sinaply continuations of the plane equipo- 
tential surfaces in the air around the iron. The energy density in the 
crack is 2 -nD^, The distance between the equipotential surfaces inside 

the solenoids is — ^, and this is to the distance in the outside field in the 
4 7rZ> 

ratio D' : D. 

The density of the energy directed parallel with the field inside the 
solenoid is 2 ttZ^. 

Since the cracks are very narrow, this will be the density of the directed 
energy in the iron. 

With an induction of 20,000 lines per square centimeter, this gives 
about 16,000,000 ergs per cubic centimeter, or about four- tenths of a 
calorie. 

An attempt is made to represent the equipotential surfaces and polar- 
ization tubes according to this hypothesis in Diagram III., Fig. i. The 
fiill vertical lines represent equipotential surfaces, both within and without 
the iron, while the dotted lines are additional equipotential surfaces inside 

the solenoids, /x = 2, ^' = i, 2>' = — , 2> = — • Energy density in air 

4- 'T 2 TT 

= ^— , in iron = — , or twice as great as in Diagram II. Length of polar- 

OTT 2 TT 

ization cell in air and in cracks = one centimeter, length in solenoids = half 
a centimeter. 

It is certain that the elementary circuits do not fill out the space in this 
way. If they did, the induction would soon reach a limit, beyond which it 
could not rise. For each of the elementary circuits is a perfect conductor, 
and on being turned round so that its axis is parallel to the field, will 
prevent any additional lines from passing through it, if there is an increase 
in the field. 

The facts of saturation seem to indicate that the space guarded from 
the entrance of external lines by the elementary magnets is very small. 

The molecules of magnetized iron are in all probability distributed very 
irregularly, but the problem can be simplified by assuming that they form 
long solenoids when the iron is saturated, and that these solenoids only 

occupy -th of the whole volume. The following results can be deduced. 
ft 

The polarization Z>" inside these solenoids remains constant fi-om the 
moment they are formed, the current in the elementary magnets decreasing 
as the external field increases. 

The average polarization of a cubic centimeter of the iron is 

n n 



474 HAROLD N. ALLEN, [Vol. III. 

The quantity known as intensity of magnetization is defined by the 
equation 

Thus 7= -^"-^: 

n 
or / diminishes after the constant value of 2>" has been reached, the 

diminution being -th of the increase of D\ If n is large, this diminution 
ft 

will be small, and /will be fairly constant throiigh a large range if « = loo. 

The amount of energy in a cubic centimeter will be 



2 IT 

n 



jym , 2Tr{n- l) j^n 



Taking certain results of Ewing on induction in iron in high magnetic fields 
and making «= loo, the amount of energy in one cubic centimeter is 
found to be 45 calories. This may perhaps be regarded as a maximum 
value. 

In Diagram IV., Fig. i, the condition of a portion of a very long 
cylinder in a uniform field I/= i is indicated, on the assumption that 
« = 2, and /x the ratio between the average polarization of the paramag- 
netic substance and that in the intermolecular spaces is also two. The 

polarization outside the cylinder is — , while the average polarization 

I ^^ 

inside is — , as in the two former cases. 
27r 

One half of the space is occupied by the solenoidal molecular chains^ 
which are represented in the figure, suitably divided by the polarization 
tubes and equipotential surfaces. These are of course much nearer 
together inside the solenoids than outside. 

The polarization inside the solenoids is -^' Each of the cells shown, 

4^ Air 

the volume of which is 4 ir c.c. outside the solenoids, and — c.c. inside, 

9 
contains half an erg of energy; so that the energy density outside the 

solenoids is ^— • Inside it is —-, and the average energy density in the 

O TT O TT 

cylinder is ^, as against 3— in the surrounding field, — inside the cyl- 

O TT OTT 2 IT 

inder of Diagram III., and — in Diagram II. 

4ir 

Diagram V., Fig. 2, shows the result, according to the ordinary induc- 
tion theory, of placing a sphere of radius 4 and permeability 2 in a unit 
field -5'= I. Inside the sphere are shown the equipotential surfaces 

F' = — ^— — which are 4 cm. apart. At right angles to these run the 



No. 6.] 



MAGNETIC THEORIES. 



475 



tubes of polarization, which are bounded by the cylindrical surfaces traced 
out by the horizontal lines, when the figure is revolved about the horizontal 
diameter of the sphere. Of these there are 

^ B xuiB' X 

Z> = — = — ——-, — 7 = TT- per square centimeter. 
47r 47r(/i-|-2) Stt 

Hence through the i6ir square centimeters of the equatorial plane there 
pass six of these polarization tubes, while in the original field, before the 
sphere was introduced, four tubes passed through the same area. 

The polarization tubes outside the sphere are continuous on the surface 
with those inside, and at a distance from the sphere they become identical 




Energy density mV = -2-, VI = -^. VII =-^. VIII =-|-. 
64ir 32ir 64ir I28ir 

Fig. 2. Half size, 
with those due to the field H^ — B^ = i. The intensity of magnetization 
is — r— , and the polarization of the ether in the sphere is also — ^, making 
a total polarization of ^ in the sphere as compared with - — in the air at 

a distance. The energy density is only 7-^ in the sphere, while it is ^— 

04 7 ow 

in the original field. 

Diagram VI., Fig. 2, shows the same problem treated so as to represent 
Ampere's theory, the molecular circuits being supposed to fill out the whole 
volume, as is also the case in Diagram III., Fig. i. The dotted lines 
represent equipotential surfaces inside the solenoids, but not in the narrow 
cracks between them. 

The energy density is twice as great as in the former case, being 

9 



2irL^ = 



32 TT 



476 



HAROLD N, ALLEN. 



[Vol. III. 



In Diagram VII., Fig. 2, the molecular chains or solenoids are only 
supposed to occupy one-third of the volume of the sphere. 

In reality of course these solenoids must be supposed to be very narrow 
in comparison to their length, and the difficulty observed in the diagram, 
with regard to the connection between the tubes inside the sphere and 
those outside, does not occur. 

If these solenoids could exist without the presence of the external field, 
they would send tubes back in the negative direction through the empty 
spaces between them, so that the polarization in these spaces when the 

external field is present is only -^, whereas in the distant parts of the 
external field it is — • Inside the molecular solenoids the polarization is 
-^. The total flow of polarization through the sphere is the same in Dia- 

grams V., VI., and VII. The energy density in the sphere is in this last case 

27 

- -^, or 50 per cent greater than in Diagram VI. 
64 T 

Diagram VIII., Fig. 2, shows a sphere of insulating material, the dielec- 
tric constant of which is unity. The electrical density on its surface is 

<r = -r- • cos $. 

lOTT 

The sphere is suspended in a uniform electrostatic field B\ = i, so that 
the line ^ = o points along the direction of the field. 

Outside the sphere the electrostatic equipotential surfaces and polariza- 
tion tubes are geometrically identical with the magnetic lines in the 

previous cases. Within the 
sphere the equipotential surfaces 
are identical with those of Dia- 
gram V. 

The electrostatic field inten- 
sity inside the sphere is only 
I H\ and the polarization is 

-^-' The energy density is only 
Three of the six tubes 




Fig. 3. Half size. 



128 TT 

which come to the surface of the 
sphere on the negative side end 
in the three units of negative 
electricity distributed over that 



side, while three of the six tubes that start firom the positive side, have 
their origin in the three units of positive electricity on that side. The 
remaining three tubes fi-om the external field pass through the sphere. 



No. 6.] THE ALTERNATING CURRENT DYNAMO. 477 

The reason for the fact that the field in the sphere is smaller than that 
at a distance, is of course that the given electrical distribution would, if 
acting by itself, produce inside the sphere a field in the negative direction, 
as indicated in Fig. 3, the field intensity being — \ H\ This is the 
" demagnetizing effect of tlie ends " of which we hear when instead of 
electric charges " free magnetisms " are supposed to exist on the surface 
of the sphere. It seems as though it would be almost worth while to treat 
all problems in which this mathematical method is simplest by means of 
the electrostatic analogy. That is, never to speak of free magnetism, but 
to work out the electrostatic problem, and to state that the required mag- 
netic field is mathematically the same as the electrostatic field, wherever 
the permeability is unity. 

While there may be nothing very new in what precedes, it is hoped 
that the diagrams with their explanations may prove of some use to those 
who, like the author, have experienced difficulty in keeping the different 
magnetic theories clearly separated. 

Universtty of Nebraska. 



On the Alternating Current Dynamo. 

By W. E. GOLDSBOROUGH. 

CONSIDER the case of a simple alternator having but one armature 
coil that rotates in a magnetic field of uniform intensity about an 
axis at right angles to the direction of the lines of force. If successive 
instants of time during one revolution of the coil are counted from the 
instant that the coil passes a line drawn through its axis of rotation and 
perpendicular to both the axis of rotation and the direction of the magnetic 
flux, the value of the induction piercing the coil at any instant during one 
cycle is expressed by the equation 

iV^=iVni«coso)/, • (i) 

in which N^^^ equals that portion of the flux that passes through the coil 
at the instant the plane of the coil is at right angles to the direction of the 
lines of force, and to represents its angular velocity. The instantaneous 
value of the E.M.F. generated in the coil will be, by Faraday's law, 

^ = = (tfiVL^ sin <i)/= ^ sin w/, (2) 

dt 

since its maximum value E = inN^^, (3) 

If the coil is closed through a circuit of resistance R\ inductance Z' 
and capacity C\ the resistance and inductance of the coil itself being R 



478 W^. E, GOLDSBOROUGH, [Vol. III. 

and Z respectively, a current i will begin to circulate, and we can write the 
equation of E.M.F.'s of the circuit in the form 



. = (^ + iP'),+(Z + Z')|+M 



From this expression we can derive the equation of the current in terms 
of the constants of the circuit and the maximum value of the E.M.F. 
developed in the coil and obtain 



which expresses the instantaneous value of i as soon as a condition of 
cyclic stability has been attained. 

Equations (i), (2), and (4) are the general equations that cover the 
working of alternating current dynamos; they have been subjected to 
graphical analysis, the results of which are exhibited in Fig. i, and are 
discussed in the following paragraphs : 

Suppose a circuit in which the inductance is zero, the capacity infinite, 
and the resistance variable, to be subjected to the influence of a simple 
harmonic E.M.F. that is generated by an alternator having a constant 
armature inductance for all values of armature current, a constant field 
excitation and a constant speed. Under these conditions, the virtual value 
of the E.M.F. at the brushes of the alternator just before the circuit is 
closed will be 

-£'=<«>^«n«-f-V2, (S) 

which is represented by the vector OA in the figure. The vector ON is 
laid off at right angles to OA to represent the value of the M.M.F. pro- 
ducing N^aaji' It is drawn 90"* in advance of the E.M.F. it induces in 
accordance with the relation exhibited in equations (i) and (2). At the 
time of closing the circuit, suppose the external variable non-inductive 
resistance to have a value R\ and that the constant armature resistance 
has a value R^ and the constant armature inductance a value Z. Then 
the equation of the current will assume the form 

E 

(VR+'R'y-^L^^^ 



i = ^ sin To,/ - tan-^ it^^I (6) 



and its virtual value /= =^ , ( 7) 

V(*-hi^')* + ZV 



No. 6.] 



THE ALTERNATING CURRENT DYNAMO. 



479 



Zo> 



which we can represent* by the vector OBo lagging tan~* ^ degrees 

R •\- R 

behind OA. This armature current will react upon the magnetizing forces 









\ i \ 



/' 1/ ! '- r 

'ii p /! ^^+ — -• — ^iPi 




A 



Rg. 1. 

* The subscript letter (o) refers to the initial condition. 
The subscript letter (r) refers to changes in the line resistant e. 
The subscript letter (/) refers to changes in the line inductatue. 
The subscript letter (r) refers to changes in the capacity of the line 



480 H^. E, GOLDSBOROUGH. [Vol. III. 

due to the constant field excitation, and by virtue of the inductance of the 
armature will produce an M.M.F. in phase with itself which is represented 
by the vector NNq, drawn parallel to the current vector from the positive 
extremity of ON. This armature M.M.F. sets up a cychc magnetization 
developing a counter E.M.F. OD© lagging 90° behind the current, and 
there is a loss of effective E.M.F. due to the armatm-e resistance that is 
shown by the short E.M.F. vector in phase with OBq ; therefore the total 
loss of E.M.F. in the armature will be the resultant of these two vectors or 
OAo. The effective E.M.F. that overcomes the resistance of the non- 
inductive external circuit will be the vector AqA, since it completes the 
E.M.F. triangle on OA and is in phase with the current OBo. The 
total effective E.M.F. (OCo) that overcomes the total ohmic resistance 
(^-f-^') of the circuit, is due to the cyclic magnetization set up by 
the M.M.F. vector ON©. ONo is the resultant of ON and NNq, and as 
shown by the geometry of the figure, it is 90® in advance of the current, 
and therefore of AoA, as it should be. The projection of NN© on ON is 
the component of the armature M.M.F. that acts against the field magnet- 
ization, /.^. it is a measure of the armature reaction. The projection of 
NNo on OA is likewise a measure of the cross-magnetizing action of the 
armature. 

Having constructed the initial diagram, we can now follow out what 
takes place when the resistance of the external circuit is varied. Suppose 
R* is reduced to a value R^, The current vector head ^ will move out 
along the semicircle OBqB, until equilibrium is again established in the 
circuit by the current reaching its maximum possible value under the new 
conditions.^ The vectors OA and ON retaining their positions, all the 
other vectors involved will reach their final values corresponding to the new 
current by following the arcs of the circles passing through their positive 
extremities to the positions designated by the common subscript letter (r). 
The correctness of the variations indicated can be readily verified by an 
inspection of the geometry of the figure in connection with equation (7). 

In the present case, R^ has been reduced to zero ; in other words, the 
subscripts (r) indicate what takes place when a machine whose armature 
inductance is large, as well as constant, is short-circuited. Ao moves up to 
A, and the E.M.F. at the brushes is zero. The current assumes an angle 
of lag of almost 90° behind the total internal armature E.M.F. OA, the 
armature reaction almost counterbalances the M.M.F. of the fields, and 
the resultant M.M.F. ON^ is just sufficient to develop the E.M.F. OC, that 
overcomes the resistance of the armature. 

Returning to the initial conditions, suppose we increase the value of 
V from zero to some value Z,, i,e, suppose we introduce inductance into 

1 See Bedell and Crehore^s Alternating Currents, p. 223. 



No. 6.] THE ALTERNATING CURRENT DYNAMO. 48 1 

the external circuit. The virtual value of the current will then be expressed 
by the equation 

/= , ^_ , (8) 

_ i • 

and it will lag behind the internal E.M.F. E or OA by an angle 

Referring to the figure, the new positions assumed by the variable vectors, 
owing to the introduction of Li, are designated by the subscript letter (1). 
The current will decrease and its vector head move along the circle 
OBcBqBiO until a state of equilibrium exists between the forces involved. 
The E.M.F. that overcomes the resistance and inductance of the armature 
will decrease also and move to the position 0A|, its vector head following 
the circle OAcAoA,0, and the E.M.F. at the collector rings will first 
decrease and then increase to a final value AiA. The introduction of 
inductance into the external circuit brings the E.M.F. at the collector 
rings and the total internal E.M.F. (OA) more nearly into phase ; it how- 
ever causes a lag angle FjOBi to be introduced between the collector 
'E.M.F. and the current. The inductance E.M.F. of the armature de- 
creases along the circle ODcDoDjO to a value OD^, and the inductance 
E.M.F. of the external circuit increases from zero along the circle 
YQcOQiY to a value OQ,. The resultant M.M.F. will be ON,, and it is 
seen that while the armature reaction has remained very nearly constant, 
the cross-magnetizing effect has been reduced about fifty per cent. 

From our initial conditions as indicated by the subscript letter (o), we 
can also study the effects produced by the introduction of capacity into the 
external circuit. If the value of C is reduced from infinity to some value 
Ce, the virtual value of the current will change to 

7= ^ ( 10) 

and the angle between OA and the current will have a value 

In consequence of this change the current vector will assume the position 
OBc, and the other variable vectors will move to their corresponding posi- 
tions shown by the subscript letter (c). The current in its new position 
is not only in advance of the E.M.F. (A^O) at the brushes, but is also in 



482 W. E. GOLDSBOROUGH, [Vol. 111. 

advance of the E.M.F. OA, since it has moved from £0 to a maximum 
value when passing OA, and then decreased in value.* 

The collector E.M.F., on the other hand, steadily increases as the 
capacity decreases, till it reaches a value AeA much greater than the open 
circuit E.M.F. of the machiqe. A resonant effect comes into play here 
after the capacity of the line neutralizes the inductance of the armature 
that is very well illustrated by the figiu-e ; the line AcA will be a maximum 
when it passes from A through the center of the circle OAgAoAiO, and 
will represent the greatest difference of potential that can possibly exist 
between the brushes so long as R and R^ remain unchanged in value. 
This rise in potential is due to the current being in advance of the vector 
OA, for the position of the armature M.M.F. vector is also advanced, and 
NNc increases the total flux in the air gap instead of diminishing it. The 
cross-magnetizing action of the armature, however, remains approximately 
the same. 

The introduction of capacity into the line causes the inductance E.M.F. 
of the armature to move to the position Dc and the reactance E.M.F. of 
the external circuit to decrease through zero and then increasing, assume 
a position QgO, considerably in advance of the collector E.M.F., and 90° 
in advance of the current OB^. 

The arrows indicate the relative direction of motion of the vectors as 
the resistance is varied from infinity to zero, or as the reactance is carried 
from zero capacity to an infinite inductance. 

By following out a similar line of constructions the effects produced by 
variations of the armature inductance can be studied, and by successively 
varying the resistance, inductance, capacity, and frequency constants, and 
constructing corresponding diagrams, a large variety of problems involving 
the simultaneous variation of several terms can be successfully treated. 

^ See Bedell and Crehore's Alternating Currents, p. 297. 




No. 6.] NEW BOOKS. 483 



NEW BOOKS. 

A New View of the Origin of Daltotis Atomic Theory : A Contri- 
bution to Chemical History y together with Letters and Documents concern- 
ing the Life and Labours offohn Dalton^ now for the first time published 
from Manuscript in the Possession of the Literary and Philosophical 
Society of Manchester, By Henry E. Roscoe and Arthur Harden. 
8vo, pp. x-h 191. London and New York, Macmillan & Co., 1896. 

The happy discovery, in the rooms of the Literary and Philosophical 
Society of Manchester, of a number of manuscript volumes in the hand- 
writing of John Dalton, has thrown a new light upon the genesis of his 
ideas. The precious documents comprise an extensive series of laboratory 
notes, beginning with the year 1802, and continuing to Dalton 's latest 
years, bound in twelve volumes, as well as lecture notes of six lectures 
delivered in 181 o by Dalton at the Royal Institution, London. The 
laboratory note-books contain an almost unbroken record of the experi- 
mental work conducted in the rooms of the Manchester Society, and which 
supplied him with the materials embodied in his great work, A New 
System of Chemical Philosophy, 

It has hitherto been supposed that it was the experimental discovery of 
the law of combination in multiple proportions that led Dalton to conceive 
of the chemical combination of atoms having definite weights, the atomic 
theory being thus adopted to explain the facts ascertained by chemical 
analysis. But an examination of the newly found papers shows that Dalton 
approached the atomic theory from a physical standpoint, he being an 
adherent of the Newtonian doctrine of the atomic constitution of matter. 

The first part of the volume contains details of the evidence on which 
the above conclusion is founded ; this is followed by a short epitome of 
Dalton's daily laboratory notes from 1802 to 1808, and by a discussion of 
the successive series of numbers given by Dalton as representing the atomic 
weights of the elements. The following table of atomic weights was written 
out Sept. 6, 1803, and is probably the earliest constructed : 

Ult. at hydrogen LOO I Ult. at nitrous oxide 13.66 

" oxygen 5.66 ' " nitric acid 15.32 



azot 4.00 

carbon (charcoal) .... 4.50 

water 6.66 

ammonia 5.00 

nitrous gas 9.66 



sulphur 17.00 

sulphurous acid 22.66 

sulphuric acid 28.32 

carbonic acid 15.80 

oxide of carbone . . . . 10.20 



484 ^E^ BOOKS. [Vol. III. 

Chapter V. contains letters written and received by Dalton ; among the 
latter are a few from Berzelius, Thomas Thomson, and Davy. The book 
is well printed, and the facsimiles of Dalton's MS. add to the interest of a 
valuable contribution to the history of chemistry. There is no index. 

H. Carrington Bolton. 



A Laboratory Course in Experimental Physics. By W. J. Loudon 
and J. C. McLennan. 8vo, pp. 302. Macmillan & Co., 1895. 

A little more than a quarter of a century ago, the first laboratory guide- 
book in physics was published in Leipzig. The author was Friedrich 
Kohlrausch, and his Leitfaden is still a standard for most of the teachers 
of physics who have studied in Germany. But the book is so solid, so 
compact, that the elementary student who has no supplementary instruc- 
tions is sure to be discouraged by its use, whether he employs the German 
edition or the English translation. It was natural, therefore, after labora- 
tory methods had become generally introduced, that new guide-books 
should come forth to compete for popular favor, such as the well-known 
manuals by Pickering, Stewart, and Gee, and Glazebrook and Shaw. At 
present, we may safely look for one or more new ones each year. 

Every such guide-book is the outcome of the author's own experience 
and necessities, and is published in the belief that its sphere of usefulness 
may extend beyond the laboratory for which it was primarily intended. It 
would be interesting to examine statistical returns, if such were available, 
with a view to ascertaining to what extent any such book is systematically 
employed in any laboratory with which the author has no immediate con- 
nection. The case is quite different from that of a class text-book, in which 
lessons are assigned for which the student is held responsible, or which is 
assumed as the accompaniment of a systematic course of lectures. In 
every college, a course of practical laboratory exercises in physics is given 
as the needful preparation for subsequent work of investigation; and a 
majority of the students never advance beyond this prescribed course in 
manipulation. Most generally this work is done under the supervision of 
an instructor who has but little leisure, and each exercise is undertaken by 
the students in rotation. The immediate object of a laboratory manual is, 
therefore, to economize the students* time and the instructor's labor. In- 
stead of giving the same oral instruction, in succession, to scores of stu- 
dents, it is best to write out what the student needs, and let this specific 
instruction, on paper or cardboard, be found with the apparatus to which 
it refers. The expenditure of breath and of patience is thus reduced to a 
minimum. Such instruction-cards can be so prepared as to leave room for 



No. 6.] NEW BOOKS. 485 

the exercise of ingenuity and thought on the part of the student ; but such 
directions as they convey must be explicit, and adapted to the exact appa- 
ratus which the student is about to handle. 

No two laboratories are alike in equipment. Whatever is written for one 
will be found, for any other, to be lacking in many indispensable details, 
and overburdened with much unavailable material. A variety of laboratory 
manuals must be at hand for reference-books, but not one of them can 
alone be a satisfactory guide. Most of them will receive but scant atten- 
tion from the ordinary student if his instruction- cards have been well pre- 
pared. He will frequently consult tables of constants, and, in studying out 
the construction of an unfamiliar instrument, printed descriptions are often 
valuable. But such a description is quite as apt to be found in a dealer's 
catalogue, or a comprehensive text-book, as in any one of an assortment of 
laboratory guide-books. 

Every laboratory instructor, therefore, finds it necessary to write his own 
guide-book, either in part or in whole. In doing so, he will naturally con- 
sult other guide-books, but adopt none. The volume by Loudon and 
McLennan is, doubtless, well suited for the students in the Toronto labora- 
tory, where the collection of expensive and historical apparatus is evidently 
uncommonly fine. Part L is devoted to an elementary course in which 
very excellent instructions are given for the standar4 beginner's exercises, 
such as measurements of length, volume, and density ; but no discussion or 
guidance is offered regarding the measurement of mass. Quite probably, 
the students for whom the book was prepared receive training in the 
chemical laboratory, and thus acquire some familiarity with the use of the 
physical balance before beginning physical laboratory work. If so, this 
removes the necessity for teaching anything about the sensibility of the 
balance, and the precautions required for accurate weighing ; but, for other 
laboratories, such an omission in a guide-book is serious. Exercises are 
provided for the testing of Boyle's law, the determination of capillary 
constants, specific heat, and heat of fusion, and quite a number in relation 
to mirrors, lenses, and photometry. 

Part II. is a more advanced course devoted to work in acoustics, heat, 
magnetism, and electricity, followed by an appendix on the determination 
of gravity, and on the torsion-pendulum. The portion devoted to acoustics 
is exceptionally large, more than half as much as that assigned to electricity. 
It includes theoretical discussion and quantitative work in relation to pitch 
and musical quality, harmonic motion, optical methods of tuning, and 
several methods of measuring the velocity of sound. The Toronto labora- 
tory is evidently well provided with Konig's best apparatus, including such 
pieces as the expensive Helmholtz outfit for synthesis, and Regnault's con- 
trivance for studying the velocity of sound in gases. What is more remark- 



486 ATEW BOOKS. [Vol. III. 

able is that this apparatus is actually used, instead of being kept merely on 
display for historical purposes. Of late years, acoustics has been so gener- 
ally relegated to the background, to make room for electricity, that the 
exhibition of serious interest in it, in an American college, is a refreshing 
evidence of scientific courage and unselfish zeal. 

The list of advanced experiments in heat covers considerable ground, 
and implies the possession of such instruments as Favre and Silbermann*s 
calorimeter, and Regnault's apparatus for hygrometry, specific heat of 
gases, and energy of change of state. These may be legitimately regarded 
as laboratory luxuries. Access to them is impossible for perhaps a majority 
of those who read the book. Important as was the work of these distin- 
guished physicists, it may be questionable whether the exact duplication of 
such historic apparatus is now really to be desired in a student-laboratory. 
If the student undertakes similar research, the outlay would, perhaps, better 
be spent in the construction of appliances due to his own adaptation of 
means to ends. In the repetition of what is historic, there should be wide 
room for variation. 

The section assigned to electricity and magnetism is made unnecessarily 
diffuse by the introduction of much material that is better introduced in a 
lecture course of general instruction. It is fair to assume that elementary 
definitions, such as that " two magnetic poles of the same kind repel," are 
unnecessary for the student who is at all fit to enter the physical laboratory. 
There is, possibly, room for difference of opinion about the extent to which 
qualitative observation may be accepted in lieu of quantitative measure- 
ment in the student-laboratory, but there are few, to-day, who think that 
even the simplest laws of nature should be rediscovered by elementary 
students. The last thirty pages of the section contain an excellent exposi- 
tion of methods in the electrical laboratory ; but, of the preceding sixty 
pages, the greater part belongs more properly to the general text-book 
than to the laboratory guide. 

Throughout the book, it may be said that the discussion of general prin- 
ciples has occupied space that would better have been devoted to precau- 
tions for securing accuracy, and to the consideration of numerical examples. 
As an aid to those who prepare their own laboratory instruction-cards, this 
volume will be found very useful, and it is a welcome addition to the 
laboratory book-shelf; but, as a practical guide to the ordinary student, in 
an ordinary laboratory, its usefulness will be less wide than one may natu- 
rally wish on account of its general attractiveness. 

W. LeConte Stevens. 



No. 6.] NEiV BOOKS. 487 

A Primer of the History of Mathematics, By W. W. Rouse Ball. 
8vo, pp. 146. Macmillan & Co., 1895. 

Of all sorts and conditions of books that fall to the lot of the reviewer, 
one of this kind is the most difficult to fairly judge. One cannot say that 
it is unscientific, for it makes no pretensions to be otherwise ; neither can 
one say that it is wanting in seriousness, for it will at once assert that 
seriousness is the farthest from its thoughts. If you assert that it gives no 
adequate view of mathematics of this century, it replies that that is not its 
humble mission, and, if you say that it wastes its pages in story-telling, it at 
once retorts that it caters to readers who must be brought to better things 
by just that diet. And the critic who sets his " five wits on the stretch " to 
demolish the work at the stroke of the pen finds himself helplessly repeat- 
ing, " Is one mocked by an elf ? " before he has fairly begun. 

The fact is, for what the work pretends to be, it is well written, and may 
be called a decided success. A multum in parvOy it supplies, at a trifling 
expense, a handbook that will serve the purposes of elementary students 
and teachers who cannot afford the more elaborate and expensive treatises. 

The first thing liable to impress the reader unfavorably is the apportion- 
ment of matter. Forty per cent of the pages have to do with mathematics 
before the Renaissance, and one-seventh of the work is devoted to the 
mediaeval period, both being entirely disproportionate allowances. But 
when it is considered that this is a handbook for students who are reading 
the mere elements of the subject, and that these elements were largely 
developed before the Renaissance, the fault seems less prominent. 

Nevertheless, it cannot be denied that here is the real weakness of the 
book, and the more one considers it the more serious it becomes. One 
feels that a line apiece to familiar names like Monge, Camot, and Poncelet, 
and not a syllable for Mobius, fits hardly with a page on Roger Bacon, and 
a considerable setting forth of tradition about Thales, Pythagoras, Archi- 
medes, and other worthies. And when one reads the further gossip, inter- 
esting but not very valuable, about Kepler's trouble with his first wife, and 
his method of courting his second, and about Tartaglia, Lagrange, Laplace, 
and others, he wonders if, after all, the elementary reader might not be 
better served by the mention of a few of the many familiar names which 
are omitted. As examples of names, almost every one of which finds place 
in text-books of quite an elementary grade, and for which readers of the 
Primer will seek information in vain, the following may be mentioned : 
Argand, Galois, Horner, Wilson, Plticker, Gudermann, Bezout, Vander- 
monde, Sarrus, Cramer, Landen, Malfatti, Matthew Stewart, Arbogaste, 
Mascheroni, L'Huilier, Maupertuis, Gergonne, Quetelet, Bellavitis, Clifford, 
with many others. 



488 NEW BOOKS. [Vol. III. 

Furthermore, out of all proportion to the importance of their contribu- 
tions are the apportionments between certain individuals. Jordanus gets 
fifteen times as much space as De Moivre, Roger Bacon eighteen times as 
much as Roger Cotes, and Regiomontanus twenty times as much as Ponce- 
let. While Pacioli gets two pages, Von Staudt gets a quarter of a page ; 
while Pascal gets three pages and a half, and certainly deserves generous 
treatment, Cayley, Riemann, and Steiner get along with half a page each. 

The mathematics of the present century can hardly expect any generous 
treatment in a work of this nature. But such common names as those of 
Brianchon and Feuerbach in elementary geometry, or Lobachevsky and 
Bolyai in the non- Euclidean, or those of the creators of the recent geom- 
etry of the triangle, — Lemoine, Brocard, Tucker, and others; or Klein, 
Fuchs, Hermite, and Sylvester, — since living writers are not wholly 
excluded ; or Clebsch and Hesse, — one cannot reconcile the omission 
of typical names like these, representing movements more or less familiar 
to all, with the presence of names of lesser note. 

Of course, the work has its share of misprints, which is merely another 
way of saying that it is still in its first edition. Among them are : iscosa- 
hedron (p. 7) ; octrahedron (p. 7); Swa/it? (p. 32) ; 162 1, for 1620, as the 
date of Harriot's death (p. 68) ; 1576, for March 5, 1574-5, as the date 
of Oughtred's birth (p. 68) ; improper spacing between the E's and F's in 
the index, etc. These dates are all right in the second edition of the 
author's larger history, and so are manifestly misprints here. 

There are also some chronological errors which cannot be so easily 
explained away. That Abel's theorem was "written in 1828 " is true, but 
it was not first written in that year. It was in Abel's possession as early as 

1825, the year in which he first went to Paris, and it was made pubHc in 

1826. In cases of uncertainty of date, the author usually and commenda- 
bly resorts to the word " about " or " circa "/ but, in the case of Girard, 
he says "i 590-1 633," though each date is quite uncertain; similarly, for 
several other dates, including that of Lord Brouncker's birth, which, unless 
Mr. Ball has found some new documentary evidence, is also quite doubtfiil. 
Documentary evidence suggests the case of the date of Briggs's birth. 
The author and, rather strangely. Cantor, who is usually very exact in 
details, give 1556. The older writers all give that date, some with a circa. 
Since Whittaker's sketch in the Dictionary of National Biography^ in which 
it is stated that Briggs was born "in February, 1 560-1, according to the 
entry in the Halifax parish register," the recent encyclopedias have 
adopted this date. It would be interesting to know if there is longer any 
doubt about the matter. A rather strange error which has run through 
each edition of the larger work, and which now appears in the Primer^ is 
the statement that "the only regular polygons which can be constructed by 



No. 6.] ATEIV BOOKS. 489 

elementary geometry are those of which the number of sides is 2*(2* -|- i), 
where m and n are integers, and 2* -|- i is a prime." This excludes the 
pentedecagon, and, unless zero be reckoned an integer, the triangle, penta- 
gon, and others. 

It must be confessed, however, that the essential features of criticism are, 
largely, matters of judgment which depend upon the point of view. It is 
doubtful if any one else would have succeeded better in the selection of 
matter, or would have presented the subject in as happy a style as that 
which characterizes all of Mr. Ball's contributions to the history of mathe- 
matics. 

David Eugene Smtth. 

Michigan State Normal School, Ypsilanti. 



Etude Analytique et Graphique des Courants Altematifs, Par 
F. Bedell et A. C. Crehore. Traduit par J. Berthon, Ing^nieur des 
Arts' et Manufactures. 8vo, pp. 261. fiditeur, Georges Carr^, 3 Rue 
Racine, Paris, 1895. 

Tluorie der Wecliselstrome in analytischer und graphischer DarsteU 
lung. Von Dr. Frederick Bedell and Dr. A. C. Crehore. Uebersetzt 
von Alfred H. Bucherer. Svo, pp. 266. Berlin, Julius Springer, 
and Mlinchen, R. Oldenbourg, 1895. 

Perhaps the best proof that the theoretical work of American scientists 
is gaining recognition abroad is the fact that American treatises are now 
l)eing translated into the Continental languages. That a mathematical 
work, even though pertaining to practical applications, should be deemed 
worthy of translation into the French and German languages, already rich 
in works of this nature, and particularly upon the alternating current, must 
be gratifying to the authors ; for though perhaps not the birthplace of the 
alternating current, the Continent may justly be looked upon as the father- 
land of the commercial applications. Both translations follow the original 
very closely, the intention evidently being to give the original authors full 
credit for their work. On many points there may arise a divergence of 
opinion, as, for instance, when the translators choose for the word medium 
the German mittel and the French milieu, while medium in German and 
medium in French express the English meaning of medium exactly. Pro- 
fessor Foeppl, a German authority on electro-mathematics, uses the word 
medium in his theoretical demonstrations, while, on the other hand, Mr. 
Vashy, the well-known French theorist, uses milieu. Mr. Bucherer adopts 
the English style of denoting the arc of tangent by tang"*, instead of the 
more common German arc-tang, while Mr. Berthon seems to prefer the 




490 N-EW BOOKS, [Vol. III. 

latter denomination. Drs. Bedell and Crehore followed Mr. Steinmetz*s 
example in denoting V — i by j instead of /, which is of importance in a 
treatise like the one under consideration, where the instantaneous value of 
the current, usually denoted by /*, occurs so frequently. Mr. Bucherer 
seemed to be more radical in his views, and accepted the given hint, while 
Mr. Berthon avoids committing himself by clinging throughout to V— i. 
When it comes to the solution of the linear differential equations for the 
current, Mr. Bucherer follows the authors verbally, naturally omitting the 
references to Johnson's Differential Equations Mr. Berthon hesitated to 
follow this practice, which seems creditable, as Johnson's book is not known 
to any extent in France and Germany; he pronounces the American 
authors' method somewhat "peculiar," and applies a method commonly 
taught in Continental treatises of analysis, avoiding even a repetition of the 
solution by using a different one on each occasion. In the second part of 
the book, the graphical treatment, the originality of the American authors 
is strictly preserved. The careful work of the translators, and the original 
merit of the treatise, should ensure a hearty reception to the work which 
naturally must add to the appreciation and regard for American works in 
general. 

F. J. DOMMERQUE. 



CompJitation Rules and Logarithms, with Tables of Other Useful 
Functions, By S. W. Holman. pp. xlv -|- 73. Macmillan & Co., 1896. 

In the selection and arrangement of the material for this book, the 
author has shown exceeding care. The attention given by him to cor- 
rectness in mechanical detail, adds not only to the pleasing effect produced 
by the book, but also to its efficiency and the facility with which it may 
be used. The logarithms (4 and 5 place) and other tables have been 
arranged with reference to rapidity in their use with minimum mental 
effort, type and spacing being selected with this end in view. 

The first portion of this book gives directions for the rejection or reten- 
tion of significant figures and other computation rules and directions for 
the use of the tables. B. 



A Text-book of Gas Manufacture, For students. By John 
Hornby, pp. xii-h 261. London, George Bell & Sons, 1896. {Re- 
ceived,) 



INDEX TO VOLUME HI. 



Absorption of heat experiment, lo. 
Admittance in oscillating currents, 341. 
Air effect in polarization, 96. 
Allen, H. N., The graphical representation 

of magnetic theories, 470. 
Alternating current : 

An experimental study of inductive 

phenomena in, Millis^ 351. 
Galvanometer for photographing, 

Hotchkiis and MilHs^ 49. 
Dynamo, Goldsborough^ 477. 
When the electromotive force is of a 
zigzag wave type, Rimmington^ loO. 
Angstrom, K., On a simple method of 
photographically registering the 
infra-red energy spectrum, 137. 
Appleton, J. H., EH IV. Blake, 226. 
Arago^s explanation of polarization by 

emission, 85. 
Arc spectra, A photographic study of, 

Baldwin^ 370, 448. 
Austin, L. W., On a new form of water 
battery, 309. 



Baldwin, Caroline W., A photographic 

study of arc spectra, 370, 448. 
Ball, W. W. R., A Primer of the History 

of Mathematics^ 487. 
Bancroft, W. D. : 

On ternary mixtures, 21, 114, 193. 
Solids and vapors, 401. 
The chemical potential of the metals, 
250. 
Barium spectrum, 452. 
Battery, water, On a new form of, Austin 

and Thwing, 309. 
Bauer, L, A., On the secular motion of a 
free magnetic needle, II., 34. 



Bedell, F.: 

J^tude Analytique et Graphique des 

Courants Aiternatifs, 489. 
Holman's Computation Rules and Log- 
arithmSf with Tables of Other Use- 
ful Functions^ 490. 
Theorie der Wechselstr'dme in analy- 
tischer und graphischer DarsteUung^ 
489. 
Blake, E. W., Appleton^ 226. 
Bolton, H. C, Roscoe and Harden*s A 
New View of the Origin ofDaltoh's 
Atomic Theory , 483. 
Book Reviews: 

A Laboratory course in experimental 

physics, Loudon and McLennan^ 

484. 

A new view of the origin of Dalton's 

atomic theory, Roscoe and Harden^ 

483- 

A primer of the history of mathemat- 
ics. Ball, 487. 

A text -book of gas manufacture, 
Hornby, 491. 

American Association for the Advance- 
ment of Science, 226. 

Analytical chemistry, Menschutkin, 400. 

Computation rules and logarithms, with 
tables of other useful functions, 
Holman, 490. 

Crystallography, a treatise on the mor- 
phology of crystals, Story-Maske- 

(k«^ 395- 
Electric waves, Hert%, 234. 
Electricity and magnetism, Nipher, 397. 
EHementary lessons in electricity and 

magnetism, Thompson, 78. 
Elementary mensuration, Stevens, 400. 
Elements of the mathematical theory of 

electricity and magnetism, Tkomp^ 

son, 393. 



491 



492 



INDEX. 



Book Reviews {continuecT) : 

Elements of physics, I., Nichols and 
Franklin, 400. 

£tude Analytique et Graphique des 
Courants Alternatifs, Bedell and 
Crehore, 489. 

Grundzfige der Matematischen Chemie, 
Helm, 152. 

Hydrodynamics, Lamb, 390, 

Industrial photometry, Poiaz, 317. 

Mechanics, Glazebrook, 239. 

Mechanics and hydrostatics, Glaze- 
brook, 400. [399- 

Notes on the nebolar theory, Stanley, 

OberflUchen- oder Schillerfarben, Wal- 
ter, 319. 

Ostwald*s Klassiker der exacten Wis- 
senschaften, 154. 

Polyphase motors, Thompson, 316. 

Popular science lectures, Mach, 158. 

Principien der mechanik. Hertz, 73. 

Principles of physics, Daniell, 311. 

Proceedings of the Electrical Society 
of Cornell University, 152. 

Solution and electrolysis, Whetham, 

315- 
Standard methods in physics and elec- 
tricity criticised, Naber, 160. 
Steam and the marine steam engine, 

Yeo, 180. 
The Herschels and modem astronomy, 

Gierke, 319. 
Theorie der Wechselstrome in analy- 
tischer und graphischer Darstellung, 
Bedell and Crehore, 489. 
Briggs, L. J. , On the electrolytic conduc- 
tivity of concentrated sulphuric 
acid, 141. 
Bru^re, Alice H., A comparison of two 

concave Rowland gratings, 301. 
Buckingham, E., Helm's GrundzUge der 

Mathematischen Chemie, 152. 
Bunsen*s ice calorimeter, 422. 

C. 

Cadmium spectrum, 453. 

Calcium spectrum, 450. 

Candles in photometry, A method for the 

use of standard, Sharp, 458. 
Capacity in oscillating currents, 340. 



Caachy*s formulae for metallic reflection, 

181. 
Chemical potential of the metals, Bancrofts 

250. 
Child, C D. : 

The resistance of tinfoil as changed by 

electric waves, 387. 
Thermal conductivity of copper, II., I. 
Qerke, Agnes M. The Herschels and 

Modern Astronomy, 319. 
Color phenomena, A new apparatus for 

the study of, von Hardroff, 306. 
Colored lights, on the photometry of dif- 
ferently, and the " Flicker " photom- 
eter, Whitman, 241. 
Concentration, its effect on £. M. F. of a 

cell, 264. 
Conductivities and viscosities, 332. 
Conductivity, Electrolytic, of concentrated 

sulphuric acid, Guthe and Briggs^ 

141. 
Conductivity of copper. Thermal, II., Quick^ 

Child, and Lanphear, i. 
Conductivity of metallic wires in different 

dielectrics, Sanford, 161. 
Cooley, L. C, Daniell's Principles of 

Physics, 311. 
Copper spectrum, 454. 
Copper, Thermal conductivity of, II., Quick, 

Child, and Lanphear, i. 
Crehore, A. C. : 

£tude Analytique et Graphique des 

Courants Alternatifs, 489. 
Experiments with a new polarizing 

photo-chronograph, as applied to 

the measurement of the velocity 

of projectiles, 63. 
Theorie der Wechselstr'dme in ana- 

lytischer und graphischer Darstel- 

lung, 489. 
Croker, F. B., Nipher's Electricity and 

Magnetism, 397. 
Current, dynamo. On the alternating, 

Goldsborough, ^11, 
Currents, oscillating, Notes on the theory 

of, Steinmetz, 335. 

D. 

Daniell, Principles of Physics, 311. 
Deliquescence, 403. 



INDEX. 



493 



Demagnetization factors for cylindrical 
rods, Mann^ 359. 

Dielectrics, Variation in electric conductiv- 
ity of metallic wires in dififerent, 
Sanfordt 161. 

Discharges in oscillating currents, 344. 

Dissociation theory, the relation of freez- 
ing-points to, 284. 

Dommerque, F. J. : 

Bedell and Crehore*s Atude Analytique 
et Graphiqtte des Couranis Alterna- 
Hfs, 489. 
Theorie der Wechsehtr'dme in analyti- 
scher und graphischer Darsiellung, 
489. 

Durand, W. F., Yeo*s Steam and the Ma- 
rine Steam Engine, 80. 

Dynamo, Alternating current, Goidsbor- 
^Hi^* 477- 

E. 

Elastic limit, 447. 

Electric current, influence of, upon Young's 
V modulus, Noyes, 432. 

p Electrolytic conductivity of concentrated 
sulphuric acid, GutAe and Briggs, 
141. 

Electro-motive force of a cell, 250. 

Engine cylinder, variation of temperature 
of, 60. 

F. 

** Flicker" photometer, On the photome- 
try of differently colored lights and. 
Whitman , 241. 

Fluid pressure, experimental demonstra- 
tion of a law of, Humphreys, 71. 

Foley, A. L., The surface tension of 
liquids, 381. 

Franklin, W. S., Elements of Physics, I., 400. 

Freezing-points of dilute aqueous solutions, 
Loomis^ 270, 293. 

Fresnel's formulae for vitreous reflection, 
177. [181. 

Fresnel's formulae for metallic reflection. 

Frost, E. B., SUnley's Notes on the Nebu- 
lar Theory, 399. 

Q. 

Galvanometer for photographing alternat- 
ing current curves, Hotchkiss and 
Millis, 49. 



Gill, A. C, Story-Maskelyne*s Crystallogra- 
phy, a Treatise on the Morphology 
of Crystals, 395. 

Glazebrook, R. T. : 
'Mechanics, 239. 
Mechanics and Hydrostatics, 400. 

Goldsborough, W. E., On the alternating 
current dynamo, 477. 

Gratings, A comparison of two Rowland's 
concave, Bruere, 301. 

Guthe, K. E., On the electrolytic conduc- 
tivity of concentrated sulphuric 
acid, 141. 

H. 

Harden, A., A New View of the Origin of 

Dalton's Atomic Theory, 483. 
Heat effect of mixing liquids, Linebarger, 

418. 
Heat, influence of, upon Young's modulus, 

Noyes, 432. 
Hefner light, 469. 
Helm, G., GrundzUge der Mathematischen 

Chemie, 152. 
Hertz, H.: 

Die Principien der Mechanik, 73. 
Electric Waves, 234. 
Hicks, W. M., Lamb's Hydrodynamics, 

390. 

Holman, S. W., Computation Rules and 
Logarithms, with tables of other use- 
ful functions, 490. 

Hornby, J., A Text-Book of Gas Manu- 
facture, 491. 

Hotchkiss, H. J., A galvanometer for 
photographing alternating current 
curves, 49. 

Humphreys, W. J., Experimental demon- 
stration of a law of fluid pressure, 

71- 
Hydrate of sulphuric acid, electrolytic 
properties of, 149. 



I. 

Incandescent solid and liquid surfaces, A 
study of the polarization of the 
light emitted by, Millikan, 81, 
177- 



494 



INDEX, 



Inductance of oscillating currents, 339. 

Inductive phenomena in alternating car- 
rent circuits, An experimental study 
of, MiUis, 351. 

Infra-red energy spectrum. On a simple 
method of photographically regis- 
tering, Angstrdm, 137. 

Impedance of oscillating currents, 339, 

343. 
Iron wires. On the changes in length pro- 
duced by magnetization. More, 210. 



Jackson, D. C, Thomson's EUmentary 
lessons in Electricity and Magnet- 
ism, 78. 

L. 

Laboratory at Lille, The new Physics, 

Nichols^ 232. 
Lamb, H., Hydrodynamics, 390. 
Lanphear, B. S., Thermal conductivity of 

copper, II., I. 
Lawrence, H. E., Glazebrook*s Mechanics, 

239. 

Light emitted by incandescent solid and 
liquid surfaces, A study of the po- 
larization of, Millikan, 81, 177. 

Lille, The new Physics Laboratory at, 
Nichols, 232. 

Linebarger, C. E., On the heat effect of 
mixing liquids, 418. 

Liquids, On the heat effect of mixing, 
Linebarger, 418. 

Lithium spectrum, 448. 

Locke, J., Translation of Menschutkin's 
Analytical Chemistry ^ 400. 

Loomis, E. H., On the freezing-points of 
dilute aqueous solutions, 270, 293. 

Loudon, W. J., A Laboratory Course in 
Experimental Physics, 484. 

M. 

Mach, E., Popular Science Lectures, 158. 

Mackenzie, A. S., Mach's Popular Science 
Lectures, 158. 

Magnetic Theories, The graphical repre- 
sentation of, Allen, 470. 



Magnetization: 

Its influence on Young's modolus, 

Noyes, 432. 
On the changes in length produced in 
iron wires by. More, 210. 

Mann, C R., Demagnetization £&ctors for 
cylindrical rods, 359. 

McLennan, J. C, A Laboratory Course in 
ExperimenUU Physics, 484. 

Menschutkin, N., Analytical Chemistry^ 
400. 

Merritt, £., Naber's Standard Methods in 
Physics and Electricity Criticised^ 
160. 

Metals, The chemical potential of, Ban- 
croft, 250. 

Metallic spectra, 448. 

Millikan, R. A., A study of the polariza- 
tion of the light emitted by the 
incandescent solid and liquid sur- 
faces, 81, 177. 

MiUis, F. E. : 

A galvanometer for photographing al- 
ternate current curves, 49. 
An experimental study of inductive 
phenomena in alternating current 
circuits, 351. 

Muctures, Ternary, Bancroft, 21, 114, 193. 

Moore, B. E, On the viscosity of certain 
salt solutions, 321. 

More, L. T., On the changes in length 
produced in iron wires by magnet- 
ization, 210. * 

N. 
Naber, H. A., Standard Methods in Physics 

and Electricity Criticised, 160. 
von Nardroff, E. R., A new apparatus for 
the study of color phenomena, 306. 
Needle, Secular motion of a free magnetic, 

II., Bauer, 34. 
Nichols, E. L. : 

Elements of Physics, I, 400. 
Palaz's Industrial Photometry^ 317. 
Walter's Die Oberflachen- oder Schil- 
ler farben, 319. 
Qerke's The Herschels and Modern 

Astronomy, 319. 
The new Physics Laboratory at Lille, 
232. 



INDEX. 



495 



Niphcr, F. E., EUctricity and Magnetism, 

397- 
Noycs, Mary C, The inflaence of heat, of 
the electric current, and of magnet- 
ization upon Young's modulus, 432. 

O. 

Oscillating currents, Notes on the theory 
of, SieinmefMf 335. 



P. 

Palaz, Industrial Photometry, 317. 
Patterson, G. W., and M. R., Translation 
of Palaz's Industrial Photometry, 

3>7- 

Photo-chronograph as applied to the meas- 
urements of the velocity of projec- 
tiles, Crehore and Squire, 63. 

Photographic study of arc spectra. Bald- 
win, 370, 448. 

Photographically registering the infra-red 
energy spectrum, Angstrdm, 137. 

Photographing alternate current curves, 
Hotchkiss and Millis, 49. 

Photometer, "Flicker," On the photome- 
try of different colored lights and, 
Whitman, 241. 

Photometry : 

A method for the use of standard candle 

in. Sharp, 458. 
Of different colored lights and the 
"Flicker" photometer. Whitman, 
241. 

Pitch for the human voice. The limits of, 
Stevens, 230. 

Polarization of the light emitted by incan- 
descent solid and liquid surfaces, 
A study of, Millikan, 81, 177. 

Polarizing photo-chronograph as applied to 
the measurements of the velocity of 
projectiles, Crehore and Squire, 

63. 

Potassium spectrum, 450. 

Potential, Chemical, of the metals. Ban- 
croft, 250. 

Pressure, Fluid, experimental demonstra- 
tion of a law of, Humphreys, 71. 

Projectiles, Polarizing photo-chronograph 



as applied to the measurements 
of the velocity of, Crehore and 
Squire, 63. 
Pupin, M. I., Thomson*s Elements of the 
Mathematical Theory of EUctricity 
and Magnetism, 393. 

Q 

Quick, R. W., Thermal conductivity of 
copper, 11^ I. 



Reflection, 

Fresnel's formulae for, 177. 
Cauchy's formulae for, 181. 

Resistance of tin-foil as changed by elec- 
tric waves. Child, 387. 

Rimmington, £. C, Alternating currents 
when the electromotive force is of 
a zigzag wave type, 100. 

Rods, Demagnetization factors for cylin- 
drical, Mann, 359. 

Roscoe, W. E., A New View of the Origin 
of Dalton's Atomic Theory, 483. 

Rowland's gratings, A comparison of two 
concave, Bruere, 301. 

Ryan, H. J., Thompson's Polyphase Motors, 
316. 

S. 

Salt solutions, On the viscosity of, Moore, 
321. 

Sanford, F., Variation in electric conduc- 
tivity of metallic wires in different 
dielectrics, 161. 

Secular motion of a free magnetic needle, 
Bauer, 34. 

Self-induction, Experimental study of, 351. 

Sharp, C. H., A method for the use of 
standard candles in photometry, 458. 

Sheldon, S., Whetham's Solution and Elec- 
trolysis, 315. 

Silver spectrum, 454. 

Smith, D. E., Ball's A Primer of the His- 
tory of Mathematics, 487. 

Snow, B. W., Ostwald's Klassiker der ex- 
acten Wissenschaften, 154. 

Sodium spectrum, 449. 

Solids and vapors, Bancroft, 401. 

Solution of liquids in liquids, 21. 



496 



INDEX. 



Solutions, certain salts, On the viscosity of, 
Moore ^ 321. • 

Solutions, dilute, aqueous, On the freezing- 
points of, Loomis, 270, 293. 

Spectra, arc, A photographic study of, I., 
Baldwin^ 370, 448. 

Spectrum, the infra-red, On a simple 
method of photographically regis- 
tering, Angstrdm^ 137. 

Squier, G. O., The photo- chronograph as 
applied to the measurement of the 
velocity of projectiles, 63. 

Standard candles in photometry, Sharp, 
458. 

Stanley, W. F., Notes on the Nebular 
Theory, 399. 

Steinmetz, C P., Notes on the theory of 
oscillating currents, 335. 

Stevens, F. H., Elementary Mensuration, 
400. 

Stevens, W. L. : 

Loudon and McLennan's A Laboratory 
Course in Experimental Physics, 
484. 
The limits of pitch for the human voice, 
230. 

Story-Maskelyne, N., Crystallography, a 
Treatise on the Morphology of Crys- 

^^» 395- 

Strontium spectrum, 451. 

Sulphuric acid, concentrated, On the elec- 
trolytic conductivity of, Guihe and 
Briggs, 147. 

Surfaces, incandescent solid and liquid, A 
study of the polarization of the light 
emitted by, Millikan^ 81, 177. 

Surface tension of liquids, Foley, 381. 



Temperature : 

Co-efl5cient of copper wire, 2. 
Its influence on the heat effect of mix- 
ing normal liquids, 430. 

Tension of liquids. Surface, Foley, 381 . 

Ternary mixtures, Bancroft, 21, 114, 193. 

Thermal conductivity of copper, II., Quick, 
Child, and Lanphear, i. 

Thomson, J. J., Elements of the Mathe- 
matical Theory of Electricity and 
Magnetism, 393. 



Thompson, S. P. : 

Elementary Lessons in Electricity and 

Magnetism, 78. 
Polyphase Motors, 316. 
Thwing, C B., On a- new form of water 

battery, 309. 
Tin-foil, Resistance of, as changed by elec- 
tric waves. Child, 387. 
Transformer, Oscillating currents, 348. 

U. 

Uranium glass, Polarization of light from, 
97. 

V. 

Vapors and solids, Bancroft, 401. 
Voice, The limits of pitch for, Stevens, 230. 
Viscosity of certain salt solutions, Moore^ 
321. 

W. 

Walter, B.,Die OberflSchen- oder Schiller- 

farben, 319. 
Wave type. Alternating currents when the 

electromotive force is of a zigzag, 

Rimmington, loo. 
Waves, electric. The resistance of tin-foil as 

changed by, Child, 387. 
Webster, A. G. : 

Hertz's Die Principien der Mechanik^ 

73. 
Hertz's Electric Waves, 234. 
Whetham, W. C. D., Solution and EUc-- 

trolyns, 315. 
Whitman, F. P., On the photometry of 

different colored lights and the 

"Flicker" photometer, 241. 
Wires, metallic, in different dielectrics. 

Variations in electric conductivity 

of, Sanford, 1 61. 

Y. 

Yeo, John, Steam and the Marine Steam 
Engine, 80 

Young's modulus. Influence of heat, of the 
electric current, and of magnetiza- 
tion upon, Noyes, 432. 



Z. 



Zinc spectrum, 453.