500 Sir William Thomson on Reflexion 



to the equation of E a , viz. 



E.= s — > • • • (400) 



-4ttK + ^ [^(JU-J/GC^)]-' 



from which we see that it is Jma = that now makes the 

 external field vanish. 



78. This concludes my treatment of electromagnetic waves 

 in relation to their sources, so far as a systematic arrangement 

 and uniform method is concerned. Some cases of a more 

 mixed character must be reserved. It is scarcely necessary 

 to remark that all the dielectric solutions may be turned 

 into others, by employing impressed magnetic instead of 

 electric force. The hypothetical magnetic conductor is re- 

 quired to obtain full analogues of problems in which electric 

 conductors occur. 



August 10, 1888. 



LVII. Note by Sir W. Thomson on his Article on Reflexion 

 and Refraction of Light in the November Number. 



YESTERDAY evening, in Cambridge, Mr. Glazebrook 

 pointed out to me that the assumption of equal rigidities 

 (§ 14) adopted for the purpose of obtaining agreement with 

 observation, "or at all events on account of its simplicity," 

 is necessary for stability, on the peculiar assumption of zero 

 velocity for condensational-rarefactional wave which 1 intro- 

 duce. This, which I had not noticed previously, is most 

 satisfactory. It is satisfactory to find an assumption, which 

 was adopted arbitrarily for the sake of results, thus now de- 

 monstrated as an essential of the theory. The proof of insta- 

 bility unless B = B' is obvious if we consider, for example, a 

 globe of elastic solid of quality (A', B') embedded in an infi- 

 nite solid of quality (A, B). Let the interfacial spherical 

 surface be caused to expand infinitesimally from radius a to 

 radius a(l-fe), and be held so by force applied to it, with the 

 matter all in equilibrium outside and inside ; while we calcu- 

 late the force required to hold it so. Taking coordinates from 

 the centre as origin, we have, for the component displace- 

 ments of the matter within the interface, 



u = x(l + e), v=y(l + e), w = z(l + e); 



whence, by (7) of § 9, we find for the force per unit area with 



