PROFESSOR KELLAND ON THE THEORY OF WAVES. 137 



a a 



Hence ^ =**'' 2 



a_y TC 





3 



X\*'~o/ ' ^" -^^ J <^~ ' 2 X 



2a^(6-y) 

 4 



^' 2 (--s 



\^_ a 



~1 



or if x--=rcos6 



i 



x + =r / cos & 



m 



we get 



b y = rsin6 = r' sin & 



t 2 /cos 6 cos 0' 



_ bg t ( cos 6 ___ cos fl' ^ ?_ a /sin 2 (9 sin 2 



rfy~ir I r ~^ 6" V r 2 ~^ 



d(f)_bff((sin6 sin^ jr if 2 /cos 2 cos 2 fl'\ 



^""^FlT" ~7" "T'V""! 5 " r' 2 ) 



. --- 

 dt Trl 2 \ r / 



These formulcfi are very elegant and symmetrical. 



d 2 d> 

 COR 1. + 



We know that this equation holds true approximately for the surface : it ap- 

 pears from the results above, that at the very beginning of the motion the equa- 



VOL. XV. PART I. 00 



