Motion of a Viscous Incompressible Fluid. 337 



b are positive. Thus 



Sitidrj 



C«*dv__C a dr, C» d v 



_ C'W - ti*)dv C b W-h*)dy „.C' _Mi£ 

 "Jo T7+W Jo W + tf)" " Jo W + 



♦•£«?&' ■ ■ w 



and it suffices to show that I * 2+ \{J cannot vanish. 

 A short table makes this apparent. 



Table II. 



n- 



<? a — / 2 



(V+'i 9 ) 3 - 





Sums of 

 fourth column. 



•l 



-r l'OOO 



1000 



4-1000 



1-000 



•3 



+ 0-997 



1002 



4- -995 



1-995 



•5 



+ 0951 



1042 



4- -913 



2-908 



*7 



+ 0-581 



1-399 



4- '415 



3323 



•9 



- 0-569 



2989 



- 191 



3132 



1-1 



- 3-982 



16*60 



- -240 



2-892 



1-3 



- 6155 



72-25 



- -085 



2-807 



1-5 



4- 4-38 



485-8 



4- -009 



2-816 



1-7 



4- 57-9 



36600 



4- -OK) 



2-832 



1-9 



+ 119-0 



317000 



4- 004 



2-836 



2-1 



- 2550 



3140000 



- 001 



2-835 



23 



-18540 



353x10-* 



- -ooi 



2-834 



2-5 



- 6160 



45x10-6 



- 000 



2834 



The fifth column represents the sums up to various values 



of r). The approximate value of 



I 



(*i 



o* 



h 2 )d v 



is 



thus 



•2x 2*834 or '567. The true value of this integral is 

 (D'/D) sin 60° or '571, as we see from (30) and (19), (20). 



We couclude that (37) cannot be satisfied with any values 

 of y 2 and ??i. 



When the value of X is not sufficiently great to justify 

 the substitution of (37) for (31) in the general case, we may 

 still apply the argument in a rough manner to the special 

 case (7?2 + 7 ?i = 0) °f (32), at any rate when r) 2 is moderately 

 great. For, although capable of evanescence, the functions 

 8i3 hi s 2) h increase in amplitude so rapidly with rj that the 

 extreme value of tj may be said to dominate the integrals. 



Phil. Mag. S. 0. Vol. 30. No. 177. Sept. 1915. Z 



