THE EXTENT OF THE UNIVERSE 331 



which the universe is situated into concentric spheres drawn 

 at various distances around our system as a centre. Here 

 we shall take as our standard a distance 400,000 times that 

 of the sun from the earth. Regarding this as a unit, we 

 imagine ourselves to measure out in any direction a dis- 

 tance twice as great as this then another equal distance, 

 making one three times as great, and so indefinitely. We 

 then have successive spheres of which we take the nearer 

 one as the unit. The total space filled by the second sphere 

 will be 8 times the unit ; that of the third space 27 times, and 

 so on, as the cube of each distance. Since each sphere 

 includes all those within it, the volume of space between 

 each two spheres will be proportional to the difference 

 of these numbers that is, to I, 7, 19, etc. Comparing 

 these volumes with the number of stars probably within 

 them, the general result up to the present time is that 

 the number of stars in any of these spheres will be about 

 equal to the units of volume which they comprise, when 

 we take for this unit the smallest and innermost of the 

 spheres, having a radius 400,000 times the sun's distance. 

 We are thus enabled to form some general idea of how 

 thickly the stars are sown through space. We cannot 

 claim any numerical exactness for this idea, but in the 

 absence of better methods it does afford us some basis 

 for reasoning. 



Now we can carry on our computation as we supposed 

 the farmer to measure the extent of his wheat-field. Let us 

 suppose that there are 125,000,000 stars in the heavens. This 

 is an exceedingly rough estimate, but let us make the suppo- 

 sition for the time being. Accepting the view that they are 

 nearly equally scattered throughout space, it will follow 

 that they must be contained within a volume equal to 125,- 

 000,000 times the sphere we have taken as our unit. We 

 find the distance of the surface of this sphere by extracting 

 the cube root of this number, which gives us 500. We may, 

 therefore, say, as the result of a very rough estimate, that 

 the number of stars we have supposed would be contained 

 within a distance found by multiplying 400,000 times the dis- 

 tance of the sun by 500; that is, that they are contained 

 within a region whose boundary is 200,000,000 times the 



