390 



Lord Kelvin on the Production of 



This ought to agree with the work done by ye per period, 

 being 



i 



dt e ye, which, by (84), is 



iTyM >[(i + t)' + (iy\ . . . ( 89). 



The agreement between (89) and (88) is secured by (85), 

 § 36. By (87) (89), and Ttu = 27r, and (86) (85), we find 



E _ m mco' 2 _a(a + c) + b* 

 no ry 2iry(o "lirbc 



(90), 



which, as we shall see, is a very important result, in respect 

 to storage of energy in vibrators for originating trains of 

 waves. 



§ 37. Remark now that a, b, c are each of the dimensions 

 of a " longitudinal stiffness," that is to say Force -^-Length, or 

 Mass-r-(Time) 2 ; and for clearness write out the full expres- 

 sions for a and b, from (72') and (72") as follows : — 



9»<V ,u 2 + 2v 2 



a = Q< 



2 _ „2 v 2 4 Mt , 



qrco" J g 2 o) 2 



U 2 + 2v 2 ~^\ 2 ru + 2 V \ 2 





v 2 } 



r*+w_iY + F±*-) 



V (Tar / \ 00) J 



b=Qco 



2u fW_ ^ j. i^ j. v ( 9 " 4 3m 2 \ 

 2 £aA^a> 4 + q*<0* + ) + qco(q^ 4 + qW + L ) 



y (91). 



/ u 2 + 2v 2 _ \ 2 / u + 2v \ 2 

 \ qW J V qo) ) 



§ 38. Let qco be very large in comparison with the larger 

 of u or v (Case I. of § 32). We have 



a == Q« 



2 4?w — v 2 



b = Q< 



qco 



therefore 



"=0- E — h 



b no ' 2ttc 



(92). 



This case is interesting in connexion with the dynamics of 

 waves in an elastic solid, but not as yet apparently so in 

 respect to light. 



§ 39. Let qco be very small in comparison with the smaller 

 of m or v (Case IV. of § 32). 



