392 On the Production of Wave-Motion in an Elastic Solid. 

 And by (85), (86), (90); with for brevity c^sQa?, 

 25-88.. s 2 ,. Q 1 



"7 ft) 



xQ< 



(189-1 -M) 2 4 (3698 



m _ [189-l(189-l-M)+6698]* _ 



Q """ (189* l + s) 2 + 6698 



E 7-307(189-1 +s) + 25-88 /.,__ 

 — as — — =l'lbo + 



TIO Z7TS 



y 



(98). 



234 



§44. As a first sub-case take (§ 41) c=x>; we find 

 by (95), (97), 



m = 189-1 Q ; and E/rw = 1-163. 



Tbese numbers show that the kinetic energy of m at each 

 instant of transit through its mean position supplies only 

 1 - 163 of the energy carried away in the period by the outward 

 travelling waves ; though its mass is as much as 189 times 

 that of granite enough to fill the hollow. Hence we see that 

 if the moving force ye were stopped, the motion of m would 

 subside very quickly, and in the course of six or seven 

 times t it would be nearly annulled. The not very simple 

 law of the subsidence presents an extremely interesting problem 

 which is easily enough worked out thoroughly according to 

 the methods suitable for § 25 above. Meantime we confine 

 ourselves to cases in which E/nr is very large. 



§ 45. Such a case we have, under §§ 39, 41 ; if instead of 

 1006^ periods per second we have only 1*0065, which makes 

 v 9 a, 2 = 1000; </&> = 10 v '10 = 31-620; and by (93), (95) with 

 still our values of u and v for granite, 



Wft ) 8 = rt=l-892xl0 8 xQ(» 2 : y=7395 ; -- = 1177. (99). 



t> TIC 



Hence the kinetic energy of m in passing through the 

 middle of its range is nearly 12ll0 times the work required to 

 maintain its vibration at the rate of 1*0065 periods per 

 second ; and the value found for a, used in (95), shows that 

 m, a rigid globe filling the hollow, must be 189 million times 

 as dense as the surrounding granite, in order that this period 

 of vibration can be maintained by a force in simple pro- 

 portion to velocity. It is now easy to see that if the main- 

 taining force is stopped, the rigid globe will go on vibrating 

 in very nearly the same period, but subsidentially according 

 to the law 



he mm s i u __ 



T 



. (100); 



