296 Journal of the Asiatic Society of Bengal. [N.S., XVIII, 
Fig.l. 
——a 
£-axis 
Hy A H- axis 
Fig Hl. 
f- axis 


Hy, Hy H-axis 
(ii) Two degrees of freedom ; ordinary Newtonian ellipse: 
phase-integrals :-— 
Ig dt. 8H=h:; {¢ dp.Sp=h. 
What has been said respecting the case of one degree of 
freedom will apply equally in this case to the phase-integral 
[pau Hak 
But fresh phases come up by reason of the fact that, keeping 
H and T constant, we can vary p or the azimuth. The phases 
bronght up by variation of azimuth have no necessary relation 
with those depending on time-difference, for although in this 
case f dp is an absolute constant, in the case of the relativistic 
ellipse it is a function of p while 7 is a function of H. Having 
regard therefore to the proposition that the space-total of phases 
of different systems having the same p, 7, and H would be 
equal to the time-total of phases of a single system we inte- 
grated df over the complete period. Subsequent integration 
with respect to p, therefore, accounts for all phases which can 
arise through these causes. 


