PHYSICS: C. BARUS 
13 
by an application of the second law of thermodynamics." " All we need is an 
expression for dS, the increment in the entropy caused by motion of the pis- 
ton. If <p is the change in the energy of the system which accompanies the 
transference of each electron from the hot body to the surrounding enclosure, 
then 
dS = - [d{n v <p) + pdv]," etc. 
In writing this equation, which is fundamental to his argument, Richardson 
treats the case of a metal emitting electrons precisely as one treats the case of 
a body of water giving off steam to push against a piston. That is, he treats 
the emission of electrons as a process strictly comparable with evaporation. 
But there is an important difference between the two processes. In evapora- 
tion the thing given off is of the same substance as that left behind. In the 
emission of electrons this is not true. Evaporation leaves the constitution 
of the remaining liquid unchanged. Emission of electrons continually changes 
the constitution of the emitting metal, unless other electrons are put into the 
body to make good the loss. When a body emits a certain mass m of electrons 
under the conditions described by Richardson, the system under discussion 
takes in something more than heat energy; it takes in substance, the mass m 
of electrons. There is no analogue to this in the process of evaporation, and 
it remains to be shown that the equation which I have quoted from Richard- 
son, an equation that holds beyond question for the case of evaporation, holds 
also for the case of emission of electrons. 
One cannot, according to my view, meet this difficulty by supposing the body 
of metal made very large, so large that the static charge produced on it by the 
emission of a mass m of electrons without compensation would be negligibly 
small. For, if the loss of the electrons is not made good, the mass-law, re- 
quiring that n e X n { shall remain constant within the metal, will cause ioni- 
zation there proportional to m, without regard to the amount of the metal; 
and this ionization will introduce a consumption of heat for which Richardson 
has made, I think, no provision. 
ON THE EQUATIONS OF THE RECTANGULAR INTERFEROMETER 
By Carl Barus 
Department of Physics, Brown University 
Communicated December 8, 1917 
1. Auxiliary Mirror. — It is desirable to deduce the fundamental equations 
more rigorously than has heretofore 1 seemed necessary. Figure 1 is supplied 
for this purpose, and represents the more sensitive case, where in addition to 
the mirrors M,M', N,N f (all but M being necessarily half silvers), there is an 
