108 A NEW METHOD OF DETERMINING 
and reducing by means of 
Z=an+ By, 
we have 
ped ZL He 
A= “+ (+m) * + Zecosi, 
or 
V2, on ae i 
de = Oe + be = Z GOS 2. 
V2, 
Fae given above, 
Comparing this with the other expression for ~ 
we haye 
da da dp dy __ Z 2 
Fie Tein Tach Gia a 
0 ° dz, 0 
From this equation, and the value of ak since 
¢ 
d 2S Sep 
2 yi =kv pl =e 
we find 
da. 
Fi =—hrcosisinv Z, 
dp 
da hrcostcosv Z. 
a 
d 
Substituting these values in the expressions for = and “! ae 
we have 
dp dp 
7 =hrcostsin (v— 2) Z, 
= = hr cost cos (v— Qo) Z. 
