158 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
Writing (8’) in the form y= zw, + 2’w, + aw, + &e. (3”) 
and assuming y” = 2”(y,) + c ay (¥,) + &e. (4) 
Where (»,) obviously equals w,”, and (,), (,), &., are functions 
v— y—l 
of &,7 to be determined, we have, from (4), vy ; _ =z vw) 
v2 
t+ar.vt1.(4)+ae .»+2.(,)+ &e. (5) 
from (3”), = e®.1lwta'.2w,+2?.3w, + &e. | (6) 
d cae 
from (3”, 5),» y’. 2 =2"((,)yw,) +e (yew) y+1.u,) 
+2 (Gay +) ofl. uy +) 2 2.0) + &e. 
d ; < 
from (4,6), y”. - = 2(,) w, +2 fe (¢,)» . 2w, ot (,)y . 1w,)) 
se OES i Sey a ney att 1w,) + &e. 
" 0O=(%). »—-0.w+,).0-—1.y, 
0=0,).2—0.u,+().¥—1.u,+0,).0—2.u, 
0=6,).383—0.4,+().22—1.u,+ ©) .¥—-2.4, 
+(%).0—3.%, ° 
O=().m—0.u,4,+%).(m—1)¥—1.u, 
+ (»,).(m — 2)» —2.w,—,+() . (m— 3) »— 38. u,_-, 
+...+(%,).0—m.u, 
