20 A NEW METHOD OF DETERMINING 
The value of g, is found from 
= 23 
n= (23) 
The quantities g, g,, Q can be expressed in another manner. The equations (22) 
give 
ig Q= a .tg # 
7 
Ga fia SI Bet fi ely aCOS els 
from which we derive 
Q =F ao a sin 27 =— $ G = .sin 47’ -+ ete. 
ql SEG ' 
log. = log. f + 3 log. (&". sin *#’ + 7” cos °F). 
Since y and y” agree up to terms of the third order, the equations for & and 7’ 
give 
ef RON ac ie) 
Sp i Ve vie 
or, 
rar = ue io Me 3) 
ra = th a ae (2%. as ) cos 2” 
Further 
£? sin °F 4+ 7” cos*H=14 2 - (yz. sin °*L— 7’ cos °F’) — (4) 
and 
4 log. (&° sin >2’+ x” cos “PY = Fs C (x sin’ “F— yx cos “F’) 
= “(x sin °L’—y’ cos “F’)°—4$ (A) 
Substituting the values of y, y’, C, given before, we find 
at i Yo 12 es 9 
(Xx sin “H— 7’ cos °#’) = ey ae + S cos 2 
fo 7 es 
Ce) cos Af 
