42 Prof. Clausius on the Reflection of 



I cannot admit that this conclusion is correct ; for the numbers 

 resulting from my calculation caunot be used in the sense in which 

 they have here been taken, but the comparison of observation 

 with theory must be made in a totally different manner. 



In adducing my numbers I have expressly stated* that they 

 do not simply depend upon the hypothesis that the reflection is 

 occasioned by the vesicles of water, but that in calculating them, 

 several other assumptions have been made, of which I may men- 

 tion the following as the most important. In my general for-* 

 mulse a coefficient occurs which depends on the degree of trans- 

 parency of the atmosphere. This coefficient may at different 

 times and in different places have very different values, since 

 even when the sky is supposed to be cloudless (which is the case 

 in the formula?) the degree of transparency may vary consider- 

 ably. Hence the coefficient must be especially determined for 

 each series of observations which is to be compared with the 

 results of theory. At the conclusion of my paper I have even 

 said that this coefficient must be different for different kinds of 

 rays, since the atmosphere does not transmit rays of all colours 

 with equal facility. It is well known that the blue rays of the 

 atmosphere are less readily transmitted by the atmosphere than 

 the red ones ; and it must therefore be assumed that the chemi- 

 cally active rays, which are even more refrangible than the blue 

 ones, must be still less readily transmitted than these. In the 

 numerical calculation which I have carried out, to give an example 

 of the application of the general formulae, I have chosen a value 

 for the coefficient which has been obtained from observations on 

 radiant heat as an approximate mean ; but this value is not to be 

 regarded as universally applicable. 



If in a theoretical determination of the luminous intensities in 

 the atmosphere all cooperating circumstances are to be taken 

 into account, the calculation becomes very tedious, and I shall 

 therefore restrict myself to an approximation. 



The quantity of light which a horizontal unit of surface of the 

 earth would receive from the sun, if the sun were in the zenith 

 and there were no atmosphere, may serve as unit. Taking, then, 

 the sun at any given height 3, and again assuming that there 

 is no atmosphere, the quantity of light which the unit of surface 

 would receive under these circumstances is represented by 



sinS. 



Assuming, finally, that the atmosphere is present, the sun's 

 light in passing through it will be weakened, and the unit of 

 surface will therefore receive less light from the sun. If, for 

 the sake of simplicity, it be assumed that the light of the sun is 



* Poggendorff's Annalen, vol. lxxii. p. 308. 



