Wave-Motion in an Elastic Solid. 

 and by (19) directly used in (2) we find 



485 



,-JJV V,l¥ l^U^' M+Ml 

 n -*SJ$" W+1M 15 </>\,*" 3 *\ 3 H 



Remark here how by the summation of these three formulas 

 we find for e+f-\-g the value given for 8 in (22). 



§ 9. These formulas (22) and (23), used in (5), give the 

 force-components per unit area at any point of the boundary 

 (S of § 1) of a hollow of any shape in the solid, in order that 

 the motion throughout the solid around it may be that expressed 

 by (19). Supposing the hollow to be spherical, as proposed 

 in § 2 ; let its radius be q. We must in (23) and (5) put 



x— qX; y = qp- i z = qv . . . (24) ; 



and putting v = 0, we have, as in (7), the two force-com- 

 ponents for any point of the surface in the meridian z = 0, 

 expressed as follows : — 



X = (/j-f?7)0 2 X 2 -^{2X 2 A + 2(2\ 2 + l)B + (A. 2 +l)C 1 } 

 Y = (*-|n)'C 2 V-nX^(2A + 4B + 1 ) 



where 



_ d>"' G<£" 15$' 15$ 1 



(25), 



B 



<J>" 3<£' 3* 





(26), 



C,= 



U 2 



^V 3 ^ 2 y 2 



<t> and ^ denoting and F with q for r. 



§ 10. Returning now to (19), consider the character of the 

 motion represented by the formulas. For brevity we shall 

 call XX" simply the axis, and ihe plane of YY', Z Z' the 

 equatorial plane. First take y = Q, £ = 0, and therefore x = r. 



Phil Mag. S. 5. Vol. 47, No. 288. May 1899. 2 L 



(23) 



