390 THE WORLD MACHINE 



apparent existence of distinct star clusters like the Pleiades 

 and others, rendered it highly possible that there are, as it 

 were, clumps of stars. This might be true over vast areas. 



It was evident that a mere count of the stars could not 

 settle the question. It was needful to gain some idea of their 

 distance. This alone might give some clue as to their relative 

 spacing. But in Herschel's time no reliable measures of parallax 

 could be made. He therefore conceived a simple method of 

 determining relative, if not actual distance. This lay in com- 

 parisons of brightness or magnitude. 



If the radiance of the suns be equal, it is obvious that the 

 light that comes to us from them will be in proportion to their 

 distance, more precisely in inverse proportion to the square of 

 the distance. A star twice as far as another will send one- 

 fourth the light it will seem just one-fourth as bright. Then, to 

 determine their relative distance, all that remained then was to 

 find some method of accurately determining the light of the stars. 



Herschel found this in a fairly satisfactory way in the use 

 of telescopes of different powers. In reflecting telescopes 

 at least, the amount of light transmitted to the eye of an 

 observer is in proportion to the square of the diameter of the 

 reflecting mirror. It follows that, on the average, a star four 

 times the distance of another will appear of equal brightness 

 with the other viewed through a telescope four times as large. 

 This, of course, assumes that the stars are of equal size and 

 emit light with equal intensity. We know now, of course, 

 that the stars vary in size as greatly as the members of the 

 solar system that is to say, in proportions all the way from the 

 sun itself down to the minor satellites of a minor planet. We 

 know, too, that their light-giving power varies as widely, let 

 us say, as from an incandescent electric lamp to an arc light. 

 Nevertheless, bunching them by the millions, it is probable 

 that the assumption of an equal average size for each " magni- 

 tude " is fairly justified, and Herschel's larger telescopes easily 

 showed twenty or thirty millions of suns. 



It was on this basis that Herschel estimated that, on the 

 average, a star is distant in proportion to its magnitude, and 

 that his forty-foot reflector therefore revealed the existence of 

 stars 2800. times the distance of Sirius, the brightest of the 

 heavens. He assumed, of course, that there is no extinction 

 of light across this distance. 



