yo Mr. Gwyther on a 



Consider, first, the disturbance generally, represented by 







;;2(;;^ + i)rw + 2)^ + 3):^"'^ 



7;z(w — i):r'"~^2; (;;/ + \){m + 2)^'"2' 



V8/lsin/(^/-r) 



- i):r'"-^2; (;;/ + i)(;;2 + 2)^'"^ , /, v „ 



TM^i ^ %. ^ |/2/.cos^(/;/-r) + &c. 



with a similar expression for ^, in accordance with (2) which 

 represents a displacement along parallels of spheres having 

 the axis of x for pole. 



The resultant displacement represented by the leading 



term is — '"—^ri — > the constant which we may call the 



stre7igth of the pole being taken as units to avoid constant 

 repetition of it. 



Let us imagine that on a sphere of radius c this dis- 

 placement is broken up and replaced by a series of secondary 

 waves in the usual manner. 



Let P be the point at which we are going to consider the 

 integral displacement, and let the distance of P from the 

 origin be written p, and let the direction cosines of the 

 radius of P and the tangents to the meridians and parallel 

 through P of a concentric sphere be given by the scheme. 



cosa . sina cos/3 . sinasin/3 

 sina . - cosocos/3 . - cosa sin/3 

 . sin/3 . - cos/3 



and let these lines be considered as a new set of axes. 



Let OP meet the surface of the sphere of radius c \\\ P>, 

 and let the pole of the meridians and parallels be A. 



Let O be any point on the sphere, <:cos0, rsinOcos</). 

 <:sin0sin<^ its co-ordinates referred to the new axes, and let 

 another set of axes through O be drawn in the direction of 

 the radius produced and tangents to the meridians and 

 parallels through O referred to axis of .t as axis. 



