306 CLAUSIUS ON THE CONSTITUENTS OP THE ATMOSPHERE 



water are formed which remain floating in the air, and hence 

 the assumption is in no way forced, that even in serene weather 

 some extremely fine bladders are present. Such a vesicle con- 

 sists of a film of water which is bounded by two spherical sur- 

 faces, and fulfils the above condition the more completely the 

 finer it is. Thus by fine vesicles of this kind the direct propa- 

 gation of light will be almost totally undisturbed, while the 

 reflexion, inasmuch as each ray has to cross four limiting sur- 

 faces in passing through each bladder, will be considerable. 

 For the reason last mentioned, a comparatively small number 

 of such vesicles would be sufficient to produce the total re- 

 flexion which occurs in the atmosphere. The assumption al- 

 luded to is the following : — that the reflexion in the atmosphere 

 is produced by vesicles of water, and it has in the first place 

 proved itself satisfactorily by the explanation which it furnishes 

 of the phaenomena above mentioned. 



We now turn to the more general consideration of masses 

 whose limiting surfaces are not parallel but inclined in any 

 way to each other, in order to determine the dispersion pro- 

 duced by them and to compare the results with what actually 

 exists. 



In the case of such masses, we may either assume that all 

 possible inclinations are present without exception, or that 

 definite inclinations obeying any laws whatever are predominant. 

 The latter case would naturally have as a consequence peculiar 

 optical atmospheric phaenomena, as for example, those of the 

 halo and mock suns, which may be explained on the assump- 

 tion of crystals of ice, whose angles of inclination, in the majority 

 of cases, amount to 60°. It would, however, be superfluous 

 to enter more fully upon such particular cases ; the impossibility 

 will be evident when the other assumption, that all possible 

 angles of inclination are present, has been completely examined. 

 We shall therefore reserve these, and to exclude every limita- 

 tion, we will proceed at once from the assumption, that the shape 

 of the reflecting masses, and hence also the position of their 

 limiting surfaces, are altogether arbitrary and subjected to pure 

 chance. 



With respect to the effect of a great number of bodies arbi- 

 trarily formed, we can reduce them to the action of an equal 



