Wave- Mot ion in an Elastic Solid. 391 



We have 



therefore j. (93) g 



a J _ (u g /K a -f-2)^/yo> t E^ »(a + c) | 



6 _7 ~ W 3 /<^ + 2 ' TM! ' 2tT&C ' J 



This ease is supremely important in respect to molecular 



sources of light. 



§40. Let c be very small in comparison with a + b*/a. 



We have 



E . a 9 /b + b .be* 2 . 



— = — ^ ; yo>== 2 ■ ;i i nm 2 =fc . . (91). 



§ 41. Let c=2o . We have 



— = —— . ; ryco = b ; ma)* = a . . . (95). 

 no 'lirb ' 



This is the simple case of a rigid globe of mass m embedded 

 firmly in the elastic solid, and no other elasticity than that of 

 the solid around it brought into play. It is interesting in 

 respect to Stokes' and Rayleigh's theory of the blue sky. 

 § 42. Let w=oo . We have 



; - ^i^ : -iy 6 = <^ • • ( fl6 >- 



This case is of supreme interest and importance in respect to 

 the Dynamical Theory of Light. 



§ 43. Take now the particular example suggested in the 

 addition of March 6, 1899 (§33 above], which is specially 

 interesting as belonging to cases intermediate between those 

 of § 38 and § 39 ; a vast mass of granite with a spherical 

 hollow of ten centimetres diameter acted on by an internal 

 simple harmonic vibrator of 1006^ periods per second, 



/ being 1000 a/1? Y This makes <y 2 = 40 x 10 6 , q*a> 2 = 1 0*, 



g) = 6324, <?&> = 31620. Now the velocities of the equi- 

 voluminal and the irrotational waves in granite* are about 

 2'2, and 4 kilometres per second ; so we have u = 2*2 x iO 5 , 

 v = A x 10 5 . Hence ; and by (80) and {91), 



— =6-958; -^ 2 =48-4; ~^-.=r2343; 

 qto q'o) 1 q co 4 



—=12-657; -|^ = 160; -|^- 4 = 25600; ,(97). 



qo) q'oi' q*(i) 



J = 11-96; a = 189 1xQco 2 ; 6 = 25-88 x Qa> 2 ; r =7'307 



b 



* Gray and Milne, Phil. Mag-. Nov. 1881. 



