Absorbing Powers of different Bodies for Light and Heat 5 



infinitely near unity. From the theory of the colours of thin 

 plates, it follows that 



r=p sm^; 



where p indicates a magnitude proportional to the thickness of 

 the plate, and independent of \, and p a magnitude independent 

 of the thickness of the plate. The former equation then becomes 



d\{e-e>)p*sm 4 £- = 0. 



And since this equation holds good whatever be the thickness of 

 plate P, that is, whatever be the value of p, it may be deduced 

 that whatever X may be, 



6-^ = 0. 



In order to prove this, in the above equation for sin 4 ^ substitute 



itSValue i(cos4f-4co 8 2f+3), 



and differentiate twice with respect to p } we then have 



\*ik —^ p 2 (cos 4| - cos 2|) = 0. 



o 



Let - = a and (e-e l )p <2 =fa. Then 



A 



1 dot fa (cos 2/?a— cosjoa) =0. 



And since when <f>a is any function of a, 



I da (j>a cos 2pa = ^\ da$( ^J cos pa, 



as will be seen if ^ be substituted for a, the above equation may 

 be written as follows: 



\ dc V i — 2/«)cos^«=0. 



Multiply this equation by dp cos xp, where x is any magnitude 

 whatever, and integrate from p = to p = x . Then by Fourier's 

 formula, that 



1 



4» cos px I da$(a) cos pa = -^ </>\, 



o */o 



