164 A NEW METHOD OF DETERMINING 
Thus we have 
€ d a b 
V/ ih I // > 
+1.351 —1.21T5nt --.856 +3.2376nt ; 
and hence 
(“e wb ud — Lea wd —ub 
uw Wy} V1 1] Pet VT 
-+1.351 3.2376 —1.2175nt —.856 —1.2175 —3.2376nt 
or, since w is unity, 
dt a VI 1] 
+4.59 —1.2175nt —2.07 —3.2376. 
In case of the term (2 — 0), u is E. 
In the way indicated we derive the values of ndz, and ». In the case of sont 
we have the values at once without another integration as was necessary for ndz and v. 
In the value of W given above the arbitrary constants of integration have not 
been applied. 
We give these constants in the form 
It) + hk, cos y + ky sin y + 7) k, cos 2y + yk, sin Zy + ete. 
1dW 
Then in case of —3 7, We have 
r 
$k, sin y — $k, cos y + 7) ky, sin 2y — 7 k, cos 2y 4 ete. 
Having W from the integration of ae we form W from the value of W and 
converting y into g. 
We thus have from the equation 
9 
ait W+e() , 
Selah, 
+(1”.351 + %,) cosg ~ + (0’.856 + k,) sin g 
-— 1”.2175nt cos g + 3/.2376nt sin g 
+ (—'.284 + 7 k,) cos 2g + (0.589 + 74 hk.) sin 2g 
—'’.0488nt cos 2g + ’.1298nt sin 2g 
+ ete. + ete. 
