36 C. V. L. Charlier 



d f 



Put, in (57), instead of ^ its value from the fundamental equation 



then 



(58) ^ = (1) + (2) + (3) + (4) + (5) + (6), 



where 





dû, 







u ^ + 



^ dx 



IK — 



' 82/ 









yA 





Q ds^ dil . 



. (4)= fV{/\)QdB,dii, 



(ö)= / □ (A) (t> rfsi , 

 (6)= iQf^ds^dQ. 



Consider (2) ! As, in the differentiations regarding the coordinates, the velocities 

 are to be kept constant, we have 



(2) = - [(^ + ^ + ^) Q d-., dil 

 ^ ' ]\ dx ^ dy dz I ^ ' 



, }\ dx dy dz j ^ 



+ 



If, however, n denotes the outwardly , directed normal of the limiting surface, 

 then, as is well known from the potentialtheory, 



dil = |m, J\ Q cos {xn) ds,^ do , 



where o is an element of the limiting surface. 

 Consequently we get 



dx ' dy ' dz ' 



ds. dil 



= ^do ds^ f\ Q^ (?Y.j cos xn + cos yn + i(\ cos zn) 



