THE GREAT STAR MAP 241 



the abruptness of class division being entirely artificial. But 

 it will make the argument simpler and obscure nothing 

 if for the moment we suppose these class divisions made 

 quite abruptly : let us imagine all the stars in each class to 

 be exactly of the average brightness of the class, instead of 

 grading off by small stages into the classes above and below. 

 Now there is overwhelming evidence that these differences 

 in brightness are partly actual differences in the stars them- 

 selves and partly the effect of distance. It is certain that the 

 stars are not all at the same distance from us ; it is just as 

 certain that, if they were, they would not appear of the same 

 brightness. Taking any particular star of magnitude 2 say 

 and distance 10, we could make it appear of the 3rd magnitude 

 by removing it to distance 16, of the 4th magnitude by 

 removing it to distance 25, of the 5th to distance 40 and so 

 on. Let us suppose spherical surfaces described about the 

 earth with radii proportional to 



10 16 25 40 6^ 100 160 250 etc. 



[This series is determined by the convention about star 

 magnitudes and we need not stop to explain it : but it will be 

 noticed that after five terms it is repeated on ten times the 

 scale ; there is no difficulty in continuing it indefinitely both 

 ways by means of this principle.] And now let us suppose 

 all the stars in the neighbourhood of these successive surfaces 

 to be actually collected upon them, which will save us the 

 inconvenience of intermediate grades. Then if the stars had 

 happened to be all of the same intrinsic brightness, those on 

 the first surface (with radius 10) would appear to us of the 

 2nd magnitude; on the second surface (16) of the 3rd; on 

 the third surface (25) of the 4th and so on. The difference 

 in magnitude would be purely apparent and simply an effect 

 of distance. This, as already remarked, is far from being the 

 case ; but before dismissing the possibility we will consider 

 an important consequence of it. 



The number of stars on the successive surfaces will increase 

 rapidly outwards. The surfaces themselves increase in area 

 and the distances between them also increase : so that if the 

 stars are scattered through space impartially, the number due 

 to each surface will increase from both causes. A little 



