regard to the Dark or Heat-producing Rays of the Spectrum. 171 



NjoV, N 2 oV, N s oV, &c. denote the same constants for the body 

 N for the thickness St 1 . It is here supposed that, for exceed- 

 ingly small thicknesses of the substances M and N, the radia- 

 tion (and consequently the absorption) is proportional to the 

 thickness. This will only hold good when such thicknesses 

 absorb only a very small proportion of the incident heat. It is, 

 however, possible that there are some kinds of heat which are 

 greatly absorbed even by a single set of particles. If there be 

 such rays, they may be supposed to be excluded from this inves- 

 tigation, as the test to which it refers, and which is furnished 

 by plates of sensible thickness supposed capable of passing heat, 

 is evidently in their case quite inapplicable. 



8. Conceive now the plate M to be composed of a great num- 

 ber of slices laid side by side, the thickness of each slice being 

 St ; also let N be composed of the same number of slices, the 

 thickness of each being St 1 . Let us denote the total thickness 

 of M by t, and that of N by t 1 . 



The quantity of the heat A, which will be absorbed by the 

 first elementary slice of M will be = A^St, while, again, the 

 quantity of the same heat which will be radiated by the same 

 slice will be =MjOt. Hence (art. 4) M 1 £t=A 1 « 1 oY, and 



.*. MjSrA^. 



In like manner, 



M 2 =A 2 0, 



rt>J (i) 



&c. 

 Also with regard to N, we have, similarly, 



N 2 =AA/ f (2) 



&c. J 



9. Now if the quality of the heat radiated by a particle of M 

 is the same as that radiated by a particle of N, we have 



Mj : M 2 : M 3 , &c. ; : If, : N 2 : N 3 , &c. ; 



hence, (1) and (2), 



A 1 « l : A 2 « 23 &c. : : A 1 i 1 : A 2 # 2 , &c. ; 

 hence also 



a l :b l : '.a^'.b^'.'.a^: b s , &c. 



Take a l T=b l T l , hence 



t : t ! : : b Y : a x : : b 2 : « 2 , &c. 

 Hence 



N2 



