Revolving Liquid under Capillary Force. 163 



If, as in fig. I, the curve meets the axis, (3) must be 

 satisfied by x = 0, dy/ds = Q. The constant accordingly dis- 

 appears, and we have the much simplified form 



dy a(o 2 x z p x ,-. 



37 = ~8T~ + 2T W 



At the point A on the equator dyjds=l. If OA = a, 



~8T~ + 2T ; 

 whence eliminating p and writing 



<TG) 2 a 3 



" = ^f T -, (6) 



we get dy 



a? ,. ~, x 



In terms of y and # from (7) 



■ <fy \ <»' / . /ON 



or if we write 



*2/a 2 =l-~, (9) 



2<fy 1-flj 



adz~ x /z. v / {l + 2(l-~)n-z(l-z)W} 



=(i-n+|H 3 >^-|OH .... (io) 



when we neglect higher powers of O than H 2 . Reverting 

 to a,', we find for the integral of (10) 



±f-(i-n +W (l-#-£(i-#, (ii) 



no constant being added since y = when # = a. 

 If we stop at 12, we have 



2 2 



^ + a 2 (i-n) 2=1 • : • ■ (12) 



representing an ellipse whose minor axis OB is a (1 — XI). 

 When fl 2 is retained, 



OB = (l-n + n 2 )a (13) 



The approximation in powers of 12 could of course be con- 

 tinued if desired. 



M2 



