400 Hydrodynamics. 



Let CD, as before, be represented by , and DG by c, then 

 EH = a sin x cos #, and DK = c cos x 2 . Hence the impulsive 

 force is expressed by a sin x cos x c cos x 2 . But, as before, 

 the number of particles of fluid which strike against the plane is 

 diminished in the ratio of rad. to sin a?, wherefore the whole 

 force against the sail will be expressed by 



(a sin x cos x c cos x 2 ) sin x. 



Let sin a; = */, then cos x = y'l y 2 , 

 and 



(a sin a? cos a? c cos a: 2 ) sin a? = (ay \/l y 2 c(l y 2 )) y> 

 By taking the differential of this quantity we obtain 



y* c (1 y 2 )) dy = ; 

 and dividing by dy, we have 



. 

 or 



But 



fZT^ tan * 2 : 



wherefore 



1 \ c 



2 tang x 2 + ^3 . ^) - tang a? = o ; 



\ sm x^x a 



and, by reducing this equation of the second degree, we have 



1 



tang x = 



3 r 



sm 



X 



