50 Professor Hamitton’s Zhird Supplement 
py 
\ being a multiplier introduced for the purpose of treating the variations of oruryzy 
as independent ; and to determine the value of this multiplier we have, by the condi- 
tion of homogeneity (B'), 
Bu 
(vo — 2 )=041=1: (R*) 
the coefficients of Q of the first order are therefore known, and we have for example, 
1 
ao SA . 
3 a= ee 6 (S°) 
ra ou 
Again, for the second order, 
8 
p= 3.5 + d, (8v © 2, — &e.); | 
p= 8AS + a(S e— &e); | 
6Q éu 
BS = Bd + As (Rv —5* 8 — &e); 
6Q ou ou 
8 = — BAT + A (30-5 bo — &e.); (T’) 
6Q 38 
a a Xs (80 =* 6 — &e.); 
gS? = sam + 2,(8 Sas — ae); | 
20 oh tak, | 
O35 =- 85 + Xi (80 — a — &e.) J 
in which, by (C'*) (0°) (Q°), the multipliers \,...; have the following values, 
Mar (ods sd). r®, 
meA(oetre).ar®; | 
waa (seer e)a; | 
MEA (ee tre):a eee: (U") 
ANIA (of+rg) ago’, 
EA (oo 4-2).a2 ue, 
m= A( oes re) ARN 
