114 Prof. D. J. Korteweg on a General Theorem of 
11 To the third term of the right-hand side of this equation 
we apply the theorem of Green. With respect to the boun- 
dary conditions (4), it then takes the form 
- 4/a J (V V 2 m + v r \/h- + w'V 2 w ) dx dy dz. 
" In virtue of (1), this may be written 
or, by partial integration, 
which expression is identically zero, having regard to the 
equation of continuity. 
"In the last term of the equation (6) the multiplications 
must be effected. By partial integration we then can give 
it the form 
, v r( 5 2 »o , SVq _ 8% _ &i'o \ 
\8ySx 8y8x 8x* 8~' J 
" By means of the equation of continuity this may be 
reduced to 
2(i J (V V\) + t/V% + «/ V 2 w>o) rfa? rfy <fe, 
which expression has already been seen to vanish. Therefore 
A=Ao + A' (7) 
"Now, if we effect quite similar transformations with the 
terms of the expression for A', 
fr/W Sr'V , /&«' 8u/\\/Bv f 8u'Vl , 
