On the Transparency of the Ether. 13 



not followed until a further diminution in amplitude, the rela- 

 tive coloration between the nearer and remoter stars, depend- 

 ing on the distance, would only be the more marked, since 

 the differential effect would be less for the nearer than for the 

 remoter stars. 



As the light must pass through our own atmosphere, a 

 further absorption must take place, which also varies with 

 the wave-length. It will be necessary to include this effect 

 in the relative coloration to determine what the resultant 

 appearance would be. 



Let 



^^yl~['i'Wy + 'i>Wy'] (18) 



represent the law of absorption, v/here '>^{\)y corresponds 

 to the exponents in I., II., III., and (f>(X)j'' is the corre- 

 sponding exponent for atmospheric absorption through any 

 thickness y'. As both -»/r and are approximately indepen- 

 dent of the amplitude, they are interchangeable as regards 

 sequence in absorption, and we may suppose the atmospheric 

 absorption to have taken place first. Hence in every case, we 

 can leave out of consideration this effect and simply apply 

 I., II., and III. to spectra as they are seen, to determine 

 the relative coloration produced by absorption in space alone. 

 We have now to apply I., II., and III. to a normal spectrum 

 to determine the amount of energy absorbed when coloration 

 is perceptible. In plate I., the curve A^ represents approxi- 

 mately the distribution of energy in the visible portion of the 

 normal solar spectrum for different wave-lengths at high sun, 

 according to Langlcy.^ The effect of space-absorption on the 

 solar spectrum would be inappreciable. Let now such a 

 spectrum be carried to a very great distance ; suppose the 

 rays parallel, and absorption present. The loss of energy can 

 be represented graphically by plotting curves with values 

 obtained from I., II., and III. The intensity is proportional 

 to the square of the amplitude or in I. and II. to 



1 Researches on Solar Heat, Plate I. Prof, papers of U. S. S. S., No. XV. 



13 



