29 
the pair of third terms, each separately and of necessity, 
satisfies the criterion of a spherical surface potential, viz. ; 
that— 
d(Ysin'?i) _ dX 
du d\ 
We are now prepared to examine the writer’s next step 
in which, combining the criterion just mentioned with the 
assumption that and making the new assumption 
CIO dX 
that (Ysinu) is a product of (U), a function of u only, into 
^ function of the time onty, he obtains the results — = 
Ysm« = U^^’ and X = T^^, 
dd du 
results which have a most delusive appearance of generality. 
As we have remarked above, this last assumption is con- 
sistent with each of the terms of equation (8), after multi- 
plication by sinu, providing T is made a function of the 
local time instead of the absolute time, and d(0 + A) be 
substituted for dfl, when the results become — ■ 
Ysim( = U 3 ^^, and (9) 
d(0 + X) du ^ ’ 
But, in combination, only the first and second terms are 
consistent with the assumption, and the adoption of the 
latter necessitates that I and J should each be zero or that 
K should be zero. Thus, the assumptions — 
Idd d\’ 
clY^dY 
dd dX 
and 
Ysinz^ = U 
dT 
d{6 + X) 
] 
have caused the potential of nature to dwindle away, in the 
first case, till only two independent constants are left in it, 
and, in the last case, till only four such constants are left ; 
in other words, if we suppose the time factors in the original 
potential to have each involved four co-efficients {p, q, p, q) 
112 2 
of its own, thirty-two arbitrary co-efficients have, by as- 
sumptions that will not bear close examination, been cut 
