28 
up a general system which is to have far-reaching conse- 
quences. But let us see what are the limitations that they 
require us to admit as probable as to the nature of the 
potential itself First we must have — 
= Icos'W-[sin(0 + a)cosX + cos(0 + a)sin\} 
+ Jcos2z^{sin(0 + /3)cos\ + cos(0 +/3)sinX]- ■ (0) 
+ Ksin2it|sin2(0 + y)cos2X + cos2(0 + y)sin2X]- ^ 
a, /3, 7 being constant angles and I, J, K constant numbers, 
or 
=lcos'i^sin(0 + a + X) + Jcos22^sin(0 + /3 + X) + 
Ksiii2i^sin(0 + y + X) 
that is, we must suppose — 
(1) that A==0. 
} (7) 
( 2 ) 
(3) 
(0 
(5) 
( 6 ) 
(7) 
and (8) 
B 1 
- = - -(pcosd + gsin0) = lsia(0 + o), 
^ IB IB 
C 
a 
D = 0 
- - (^cos0 + 3 'sin 0 ) = lcos(0 + a), 
1C IG 
-3® 
a 
- (pcos0 + gsiii0) 
IE IB 
Jsin(0 + /3), 
F 3 
— 3 ' = — (paond + 2 'sin 0 ) = J cos(0 + /3), 
Cl Cl ij’ IP 
- 3^ = “ -(jocos20 + ^sin20) = Ksin2(0 + y), 
Cl Cl 2G 2G 
“ “(^cos20 + 2'sin20) = Kcos2(0 + y). 
CC 2H 2H 
And a similar and related set of restrictions must be made 
with respect to Y^, so that it shall become — 
(8) 
= lcos(0 + a + X) + jcosi^cos(0 + (3 + X) + 2Ksm2^cos2(0 + y + X) 
Observing, now, that the part (d + X) of the angles in 
equations (7) and (8) may be regarded as a single variable— 
the local time, we see from those equations that the 
restricted values of and (Y^sin^^) consist each of three 
terms, each of which is the product of a function of u into 
a function of the local time. And the pair of first terms in 
and (Y^sinu) respectively, the pair of second terms, and 
