146 Dr Olbers on the Transparency of Space. 



blaze upon us with solar brightness. If we suppose, for ex- 

 ample, that the degree of transparency be such, that of 800 rays 

 which emanate from Sirius, 799 attain the distance at which we 

 are placed from that planet, this would suffice, and more than 

 suffice, to make us see the system of fixed stars such as we ac- 

 tually see it. 



Since rays proceed in all directions from every point of the 

 surface of luminous bodies, we may represent to ourselves this 

 light as composed of cyHndrical fasciculi, themselves formed of 

 parallel rays. The lustre of the radiating bodies will be pro- 

 portional to the density of the hght in these fascicuh. Accord- 

 ing to the law of the diminution of the hght which traverses 

 homogeneous substances, not entirely transparent, the diminu- 

 tion of the density of this hght for each infinitely small degree 

 erf its progress, is proportional to this very density. Let «/, 

 then, be the density of light at the distance x from the radiating 

 body ; for every space d x which it traverses in its passage from 

 the body, it undergoes a diminution d «/, and we have d «/ = — 

 ay di X, or integrating, log y = const ■ — ax. The constant 

 quantity will be determined by remarking, that y = A, for ex- 

 ample, when X = o; and we shall thus obtain the equation. 



Log -^ = — « zr ; or log ^ is anatural logarithm, «, the measure 



of the defect of the transparency of space ; -, the subtangent 



a 



of the logarithmic curve, of which the decreasing ordinates mea- 

 sure the diminution of brightness which the luminous object 

 undergoes when its distance increases. Besides, in the calcula- 

 tion, we may employ for log -— the artificial logarithm, keep- 

 ing in mind, that then a, multiphed by 0.43429448, is the 

 measure of the opacity. 



Let us now find what wiU be the value of a, on the supposi- 

 tion (entirely arbitrary) that the light of a star, placed at the 



distance of Sirius, becomes weakened in the proportion of -— 

 in coming to us. Let r be the distance of Sirius, 



