300 Lord Kelvin on 



prismatically analysed direct sunlight reduced by passage 

 through a narrow slit ; and the results were therefore not 

 vitiated by unequal absorptions of direct sunlight in the 

 apparatus. A translation of the author's own account of his 

 conclusions is published in the Philosophical Magazine for 

 August 1902 ; by which it will be seen that the blueness of 

 the sky, even when of most serene azure, was always much 

 less deep than the true Rayleigh blue defined by the X~ 4 law. 

 Hence, according to Rayleigh's theory (see § 53 above) much 

 of the light must always have come from particles not ex- 

 ceedingly small in proportion to the wave-length. Thus 

 in Zettwuclr's researches we have a large confirmation of the 

 views expressed in §§ 54, 58, 61, 74 above, and §§ 78, 79 

 below. 



§ 78. Through the kindness of Professor Becker, I am now 

 able to supplement Bouguer's 170-year old information with 

 the results of an admirable extension of his investigation by 

 Professor Miiller of the Potsdam Observatory, in which the 

 proportion (denoted by p in the formula below) transmitted 

 down to sea-level of homogeneous light entering our atmo- 

 sphere vertically is found for all wave-lengths from 4*4 . 10 -5 

 to 6' 8 . 10~ 5 , by comparison of the solar spectrum with the 

 spectrum of a petroleum flame for different zenith distances 

 of the sun. It is to be presumed, although I do not find it so 

 stated, that only the clearest atmosphere available at Potsdam 

 was used in these observations. For the sake of comparison 

 with Rayleigh's theory, Professor Becker has arithmetically 

 resolved Muller's results into two parts ; one constant, and 

 the other varying inversely as the fourth power of the wave- 

 length, expressed in the following formula* modified to 

 facilitate comparison with §§ 57-59 above: 



p = e -C0887 + -0772^) = . 91 5 2e --0772^ _ § ( (33^ 



where c = X-f-'6 . 10~ 5 . In respect to the two factors here 

 shown, we may say roughly that the first factor is due to 

 suspended particles too large, and the second to particles not 

 too large, for the application of Rayleigh's law. For the case 

 of X=6 . lO" 5 (z = l) this gives 



7; = e -co887+-o772) = . 9152 ..9258 = -847 . . (34). 



§ 79. Taking now the last term in the index and the 

 last factor shown in (34) and dealing with it according to 

 §§ 57-59 above, and still, as in § 55, using k to denote the 

 * Miiller, Die Photometrie der Gestirne, p. 140. 



