r,()(j PROFESSOR KELLAND ON THE THEORY OF WAVES. 



Now, the moving force on the solid PN 



/- + -« / dz \ 1 A + -« / , <'" \ 



" 'lygg [z +;^«-yj +2?y„ dy [u^ + 2 u j-^a "^ + i^ 



=Jj dygg (z-i/) 

 -f:^^'''dygg(z+'^£a-y^+Qjjdyu^^<'- 



.We have omitted the part s?/ '''" dyu^ + q^ + Q, from the circmnstance 



that it does not depend on the difference of velocity or of resistance, and, there- 

 fore, is no part of our force. 



Perhaps it woiild be well to call p the horizontal pressure, instead of the 

 whole pressure, as by this means we should have been spared the apparent in- 

 correctness of omitting a part of the results ; but I have prefeiTed retaining the 

 above, as the more usual mode of proceeding. 



By integrating the above expression between limits, we o))tain for tlie 

 moving force 



1 , 1 / rf^ \^ du 



and the mass m Qaz; hence the accelerating force is 



/du\ dz du 



{}i7) = -^d-.'-"d^' 



du 



where -r- is the total differential coefficient of u with respect to t. 

 By substituting for ii its value 



ca . 27r ca . n 



— . sm -^— ct—x or — . sin f 

 h X li 



we obtain 



(dx\ 27ra -, 27rac 



c — — ) =^.^-— .cos O — u -—-— cos 

 dl) \ Xh 



'Invca n / dx\ 2'Ka a 2irac 



— ^ — . cos ( 



by equating coefficients, we obtain j-=ff as the first part, and the other part is an 



identity. 



7. We may vary the last part of the process in the following manner. 

 Since the moving force is 



n pdy- 1'^^'°' pdy. 



I 



