Reflexion and Refraction of Light. 423 



Eliminating (F + G) from (39) and (42) ; and (F-G) from 

 (40), (41) we find two equations for C and C, ; and then (39), 

 (40) give (F + G), (F — G) ; and thus we find our four un- 

 known quantities. The resulting formulas are greatly sim- 

 plified by the assumption of equal rigidities (B = B y ) adopted 

 by Green on account of its simplicity, and proved by Lorentz 

 and Rayleigh to be necessary, in the incompressible-solid 

 theory, to get any approach to agreement with observation. 

 It seems equally, or almost equally, necessary in the other 

 extreme form of the elastic solid theory which I am now sug- 

 gesting ; but at all events I adopt it for the present on account 

 of its simplicity. It gives, by the elimination of (F — G) from 

 (40) and (41), 



A(X 2 + m 2 )C=A / (V + ^ 2 )C / .... (43), 

 or, by (37), 



?C=?A (44): 



whence, by elimination of (F + G) from (39) and (42), and by 

 (37), 



XC + Xfl^ lf + l* _!,-$ 



\v 



hence 



6 — l£dk' c ' =m M • • • (46) - 



This, used in (40), and (45) in (39), give 



F+G=| (48). 



These (46), (47), (48), with (34),(35), and (32), express the 

 complete solution of our problem. 



15. To interpret it remark that (32) represent the compo- 

 nents of three distinct waves in the upper medium, and two in 

 the lower, of which the directions of propagation make angles 

 with the normal to the interface equal respectively to i,j, i n j t ; 

 LUi h*ii Dem g given in terms of i by (25) and (38)] ; and 

 of which the amplitudes are as follows : — 



incident wave (distortional) <y . F//3 \ 



distortional reflected wave eo . G//3 



condensational-rarefactional reflected wave . co.C/ot J- (49). 



distortional refracted wave co . l//3 ; 



condensational-rarefactional refracted wave . co.CJuj 



