308 CLAUSIUS ON THE CONSTITUENTS OF THE ATMOSPHERE 



the case of arbitrary bodies as 2 : 'v/2, and if the angles of 

 deflection be not sufficiently small, another but similar ratio 

 exists. 



If this be taken into account, it is only necessary to confine 

 our attention to the effects of spherical bodies, without thereby 

 limiting the assumption as to the true shape of the bodies 

 which actually exist; it is not even necessary to dwell upon 

 the circumstance, that in many cases where single masses sepa- 

 rate freely from each other the spherical form is in reality the 

 most probable. 



Let it therefore be assumed in the following, that the reflexion 

 of light in the atmosphere is due to the fact that numerous 

 transparent spherical bodies float in it. The refraction which 

 accompanies the reflexion may then be accurately calculated. 



In these considerations it makes an important difference 

 whether the refractive force of the spheres, as compared with that 

 of the surrounding medium, be regarded as considerable or as 

 very inconsiderable, that is to say, the index of refraction very 

 nearly =1, In the first case, a superficial calculation suffices to 

 show that phaenomena would thereby be produced which are 

 so very different from those which actually exist, that the as- 

 sumption must be rejected at once; while the second case, on 

 the contrary, needs a somewhat closer examination. 



To finish with the first case, we will assume, for example, that 

 in the atmosphere solid spheres of w-ater float so that the re- 

 fractive index, with which we have to do, amounts to 1*333. 

 With the aid of this value and Fresnel's reflexion formula, we 

 can calculate how much of the light which proceeding, say from 

 the sun, falls upon such a sphere is reflected at its forward and 

 hinder surfaces. We thus find the value 0*12 when the inci- 

 dent is taken as the unit. Now Bouguer and Lambert have 

 made experiments to ascertain how much light is lost in serene 

 weather by its passage through the atmosphere. If the strength 

 of the light of the sun beyond the atmosphere be set =1, and 

 the sun is conceived to occupy the zenith so that his rays pass 

 perpendicularly through the atmosphere, then the intensity of 

 the light on reaching the surface of the earth is, 



According to Bouguer 0*81 



According to Lambert 0*59 



