342 Mr. R. Hargreaves on Radiation 



on the aether. The expression in brackets is for one principal 

 polarization always negative for some part of the range of n; 

 for the other principal polarization this is true if /a 2 < 2. The 

 integral for either or for a mean of both is positive in the upper 

 range of /i, and when /x. is infinite has the limit which belongs 

 to perfect reflexion; but it is negative for a finite though 

 short range of fi starting from /i=l. It seems difficult to 

 accept an interpretation which gives a back pressure from the 

 dielectric on the sether, or involves the attraction of a 

 dielectric by impinging waves, if fi has a value below a 

 certain limit (different for the two polarizations if taken 

 separately), and for higher values a repulsive action. [Of 

 course entry into an infinite dielectric is in question, not the 

 resultant of actions on entry and emergence.] 



§ 15. In the original argument it appeared that the result 

 of differ entiating the equations giving the laws of reflexion 

 and refraction, was a connexion between cubes of periods, 

 which was then altered by the use of the factors 



/>(l-U/V)==p'(i-TJ'/V)==w; 



and the possibility of using 



/{p(l-U/V)}=/{ P '(l-U'/V)}=/( OT ) 



in place of the linear factor was just mentioned, cf. § 3. We 

 now examine the consequences of supposing this done, 

 the method remaining in other respects as before. The 

 relations between p, p f , and tsr, when only iu exists, then 

 become 



p*(\ 2 vdv(l-3rv)f{p(l-rv)}=p / *CA 2 vdv(l + 3rv)f{p(l + rv)}> | 



J ° J ° « K52) 



/I B 2 vdv(l-Zrv)f{p(l-rv)}=*T*f{*7)\ B*vdv. 



Jo Jo J 



With first-order workf{p(l — rv) } =f(p) —prvf(p) ; i. e. 



f P A*vdv{f(p) -nrQflp) +pf(p))i=P' d f tfvdv{f(p f ) + rv(?>f(p') +p'f(p'))} 

 or 

 A lP y(p)-rA,(3pH(p) + P *f(p))=A i p"f(p')+rA 2 (Zp«>f(p') +p' i f(p')). 



If now p' =p(l + e'), 



p'W) =Mp) +*Vp°Ap)+P l f(p)); 



and therefore 



(8p , /(p) + pV , (p))(2rA 1 + e'A 1 )=0; 



