138 PROFESSOR KELLAND ON THE THEORY OF WAVES. 



tion holds true at all points. It is, however, accurately true when I has a value 



sin 2 6 sin 2 6' 



only in the case in which : -, =0, that is, for the surface, or at least 



near it. 



Con. 2. When x lies between ~ and , b-y is zero at the commencement 



A & 



of the motion ; 



.-. when t=Q, and by=Q 



-7^= - bff, which we know to be correct. 

 Still supposing b y=Q, we get 



. ... j* 



d<t> 2-TT/a 2 



-77=0 when t 2 = ( -r- - 

 dt ct\4: 



nr a 

 = at the origin. 



This gives the time at which the surface has attained the statical level. 

 COR. 3. If b-y be neglected in comparison with of, we have 



^ 

 4 



or if x be large, y (2 (* y) =*' 2 



^ 2 = 77T at the surface. 



?( 6 ) 



This expression gives the time at which the swell has attained its maximum. 

 COR. 4. The height to which it attains is approximately 



,d(f> bfft 2 a 



~~ ' 



dz 



x 2 



4 



ba & ba 



27r(6) 



a 



2~7T 



This result is curious, inasmuch as it shews that the swell depends on the extent 

 of surface disturbed, and not on the magnitude of the disturbance. 



