162 
A NEW METHOD OF DETERMINING 
Having the values of the coefficients of (+ y + 7g + 7g’), both for W and —<, 
we have next to find those of (vy + 7 + 7g’), and of (Oy + 7g + 7q) in the case 
Uu 
cosa 
The expressions for this purpose 
7? = 
7) =— 
vo) = 
yO = 
For Althzea we find 
log. 7 = 8.60309 log 
e. n® = 7.388368 
are 
aly _1 9 
te — le — se 
Bis ILS at 
se 1T28@ 
le 
— (ge + =4e + etc.) 
lox. 1 = 9.081960 
We multiply the coefficients of ( y + ig + 79’) by 7, and 7, respectively, 
to find those of (+ 2y + tq + 79’), 
(= 3y + 9 + 19’). 
In case of (Oy + zg + vg’) in the expression for <= we add the coefficients of 
(+ y + tg + 19’) to those of (— y + 2g + vg) and multiply the sum by 7. 
dw 
We will give a few examples to show the formation of WW, and — 4—. 
dy 
With these two we give at once also their integrals, which are néz and v respec- 
tively. 
= 1W 
Ww = i° 
> ihe 
(O—) 
cos sin sin cos 
ida W ” W 
ail =O  —=890909 =E.0988 +16.3486 +-.0494 
— 2 2— 0 0190 —-.0017 + .0190 +.0017 
—32.7162 +.0511 
” wu 
—32.7162 -.0511nt 
