80 A NEW METHOD OF DETERMINING 
we have 
dx = —d sin «de 
dy = d COS >. COS ede. 
é 
Then since 
dg = ” de, ee, “dy, “oe he as 
dz hr? Vv. 
using the values of sin «, cos ¢, in terms of sin f, cos f, we find 
dx ae ke sin f dy __ cos fe, 
Ge = 1/ Det dz ~~ V Po 
And these give 
bsinf _ _ da V Bo 
VP sae VP 
k cos f __ dy VP. key 
vp ae yp VP 
— dy YR her _ (% Sr dt 
dz VP VPs Pp 
The equations (8) then become 
= ao da dz “V/ Do sin f 2 
~+ =[d+% ver] = == S42 Gaya 
~—dy st Ge V Po — : cos fe, : 
Yue dz [ato ) dt eS eye) ae 
(9) 
MEN qo : 5 
the constant — Ye being included in the integral. 
J 
pe will now voor equations (9), and for this purpose we multiply the first 
by 2 7, the second by oe “ , and noting that 
