748 

 Wliic'li integral is 1 Tor — P <^ f/ "^ /' 



and for y <^ — p and For 7 ^ + />. 



Now if we put /) =z s and t/ = iy,. cos [i -\- .s, and if we make .v 

 to increase indefinitely, tlie integral appears to become 1 for x\co.sn <^() 

 and for 0,. cos (i ^ 0. 



Thus we finally find for the force wliicli the liquid above the 

 plane ^ = exerts per surface unity on tiiat below it: 





^la — — — -^- I ',(u,- u^)st„ ycos^i i ((',- r^).mt y.nn^-\- {n\-?(\)ro.sy\' X 



• , ^^«)') 



(( (( 



As fic, and (/j, will be in general very small compared with «i 

 and fi^, we may write for the first exponential factor under the 

 integral sign : 



11 I - ' '«1 '+•■+"•>-) 



1 ^ 2(1 (^/, e , f i(,z J f f<, <} ros y) U =^- 

 ( « ) 



When we substitute this in the integral, the term 1 between the 



accolades in (6) will furnish after integration : it is the value of 



2a 

 the force of friction for (^ = 0. The integrals with — ^i u^ and 



2a 

 - z^ii, will become equal, but of opposite sign, so that they cancel 



'la 

 (( 



each other, and the integral with n, a cos y only remains. 



((^ 



z^ 

 When we now divide by a, and when we still put- = -', and 



o 



- = u\ "=:w\i(fp=:z(f and ~' = ,y'. and when we then 



tc a a 



again omit the accents, we get : 



') The minus sign has been written for this, because i '• cos a is negative, while 

 UiL' number of collisions are naturally positive, and the sign of expression (3) 

 stioulil properly speaking be reversed. 



