81 Lord Kelvin on 



particles are essential to the result ; and to include these we 

 shall have to use the formula 



*=^2p^] 8 .... (3), 



where 2 f)~ denotes the sum of ^ for 



all the particles in a cubic centimetre. 



§ 56. Supposing now the number of suspended particles 

 per cubic wave-length to be very great, and the greatest 

 diameter of each to be small in comparison with its distance 

 from next neighbour, we see that the virtual density of the 

 ether vibrating among the particles is 



D + tT(D'-D) (4); 



and therefore, if u and it' be the velocities of light in pure 

 ether, and in ether as disturbed by the suspended particles, 

 we have (Lecture VIII. p. 80) 



u^[l + 2 T ^~^ ] . . . . 



(5). 



Hence, if fi denote the refractive index of the disturbed ether, 

 that of pure ether being 1, we have 



, = [1 + 2 ZW=^)J (6); 



and therefore, approximately, 



^-l = S T ^'-^ (7). 



§ 57. In taking an example to illustrate the actual trans- 

 parency of our atmosphere, Eayleigh says * ; " Perhaps the 

 " best data for a comparison are those afforded by the varying 

 " brightness of stars at various altitudes. Bouguer and others 

 " estimate about '8 for the transmission of light through the 

 " entire atmosphere from a star in the zenith. This corre- 

 '' sponds to 8*3 kilometres (the " height of the homogeneous 

 " atmosphere " at 10° Cent.) of air at standard pressure:" 

 Hence for a medium of the transparency thus indicated we 



* Phil. Mag. April 1899, p. 382. 



