io”) 
Dr. H. A. Bumstead on the 
for the refractive index of the plate. This gives for the 
retardation 
dp’ 
aes —= 
é (1 il a ), 
and for the best thickness of the plate this must be equal to 

d ae 
EN) or — $M a according as a grating or prism is used to 
dr 
produce the spectrum. 
6. We are so much accustomed to regard the homogeneous 
wave as the simplest element into which all wayve-motions 
may be resolved that we sometimes overlook the fact that the 
phenomena of white light may all be reproduced by a single 
disturbance of short duration. ‘There are cases, and the phe- 
nomenon of Talbot’s bands may serve as a conspicuous example, 
where the consideration of the combined group yields to a 
simpler treatment than the resolution into homogeneous waves. 
I have shown in my paper on “ Interference Phenomena” 
how group velocities may be used to determine the conditions 
of achromatism. Considerations similar to those used in that 
paper may perhaps be usefully employed to simplify the treat- 
ment of achromatized interference-bands. 



II. On the Variation of Entropy as treated by Prof. Willard 
Gibbs. By H. A. Bumsrgzap, Ph.D., Assistant Professor 
of Physics, Yale University *. 
iB the August number of the Philosophical Magazine 
Mr. 8. H. Burbury has discussed certain difficulties 
which present themselves in Chapter XII. of the “ Principles 
of Statistical Mechanics,” by the late Prof. J. Willard Gibbs. 
Unless I have misunderstood Mr. Burbury’s statement, I 
believe these difficulties may be surmounted, and shall en- 
deavour to give, as briefly as possible, my reasons for this 
belief. For the sake of brevity I shall assume that the 
reader has Mr. Burbury’s paper before him, and shall refrain 
from quoting from it unless it seems necessary for clearness 
of statement. | 
The first difficulty (which may be more conveniently dis- 
cussed in terms of the hydrodynamical analogue than in 
terms of the ensemble of systems) is in regard to Prof. 
Gibbs’s statement that ‘‘one may perhaps be allowed to say 
that a finite amount of stirring will not affect the mean 
square of the density of the colouring matter, but an infinite 
amount of stirring may be regarded as producing a condition 
* Communicated by the Author. 
