On the Production of Waoe-Motion in an Elastic Solid. 227 



It is not at all difficult to get the apparatus to work 

 properly, and I have no doubt but that it could be made to 

 work on quite a small scale with a good photographic objective 

 of rather long focus. The objective of a good-sized spy-glass 

 would also give good results. Toepler was, I believe, of the 

 opinion that he got more uniform results with an influence- 

 machine than with the coil. He certainly found the time- 

 interval between the two sparks to be more constant. This, 

 however, is no object in photographic work, for the wide 

 variation is the very thing that makes the pictures interesting. 



Physical Laboratory of the University of Wisconsin, 

 Madison, May 20th. 



XXII. On the Application of Force within a Limited Space, 

 required to produce Spherical Solitary Waves, or Trains of 

 Periodic Waves, of both Species, Equivoluminal and Irro- 

 tational, in an Elastic Solid. By Lord Kelvin, G.G.V.O., 

 P.R.S.E. 



[Concluded from the May Number.] 



§ 21. rilHE strictly equivoluminal motion thus represented 



JL in equations (58) consists of outward-travelling 



waves, having direction of vibration in meridional planes, and 



very approximately * perpendicular to the radial direction, 



and amplitude of vibration equal to §/i - sin 6, where 6 denotes 



the angle between r and the axis. The gradual change from 

 the simple motion f =/isin cot at the surface of the rigid globe, 

 through the elastic solid at distances moderate in comparison 

 with q, out to the greater distances where the motion is very 

 approximately the pure wave-motion represented by (58), is a 

 very interesting subject for detailed investigation and illus- 

 tration. The formulas expressing it are found by putting 

 u=oo in (45), and using this equation to determine F 2 (£) in 

 terms of F : (f); then using (47) to determine F x (£) in terms of 

 $(f) given by (51); and then using (55) and (56), for which 

 r=co makes t 2 = t, to determine £, rj, £. They are as 

 follows: — 



< t)x '-\r) 2-Ll 1 ~^) sinft, ' + ?^ sm& " 1 -^; C0S ^J 



, 2 3A u a Zh . 



a — cos o)£i.+ — v sin wi, 

 2 qco r 2 



t) = B(r, t)xy ; £= B(r, i)xz 



an 



* Rigorously so, if the wave-length and q are each infinitely small in 

 comparison with r. 



