PLEASURES OF THE TELESCOPE. 745 



ing power of the star as compared with the sun. The first tiling 

 to do is to multiply the earth's distance from the sun, which may 

 be taken at 93,000,000 miles, by 206,265, the number of seconds of 

 arc in a radian, the base of circular measure, and then divide the 

 product by the parallax of the star. Performing the multiplica- 

 tion and division, we get the following : 



19.182.645,000,000 



r^ '- = 1,065,790,250,000,000. 



The quotient represents miles ! Call it, in round numbers, a thou- 

 sand millions of millions of miles. This is about 11,400,000 times 

 the distance from the earth to the sun. 



Now for the second part of the calculation: Tlie amount of 

 light received on the earth from some of the brighter stars has 

 been experimentally compared with the amount received from 

 the sun. The results differ pretty widely, but in the case of Arc- 

 turus the ratio of the star's light to sunlight may be taken as 

 about one twenty-five-thousand-millionth i. e., 25,00(),0(0,()00 

 stars, each equal to Arcturus, would together shed upon the earth 

 as much light as the sun does. But we know that light varies in- 

 versely as the square of the distance ; for instance, if the sun was 

 twice as far away as it is, its light would be diminished for us to 

 a quarter of its present amount. Suppose, tlien, that we could re- 

 move the earth to a point midway between the sun and Arcturus, 

 we should then be 5,700,000 times as far from the sun as we now 

 are. In order to estimate how much light the sun would send 

 us from that distance we must square the number 5,700,000 and 

 then take the result inversely, or as a fraction. We thus get 



representing the ratio of the sun's light at half 



32,490,000,000,000, ^ ^ 



the distance of Arcturus to that at its real distance. But wliile 



receding from the sun we should be approaching Arcturus. We 



should get, in fact, twice as near to that star as we were before, 



and therefore its light would be increased for us fourfold. Now, 



if the amount of sunlight had not changed, it would exceed the 



light of Arcturus only a quarter as much as it did before, or in 



the ratio of ^^^^^'^^'^'^''^'^^ = 6,250,000,000 to 1. But, as we have 



seen, the sunlight would diminish through increase of distance to 

 one 32,490,000,000,000th part of its original amount. Hence its 

 altered ratio to the light of Arcturus would become 6,250,000,000 

 to 32,490,000,000,000, or 1 to 5,198. 



This means that if the earth were situated midway between 

 the sun and Arcturus, it would receive 5,198 times as mucli light 

 from that star as it would from the sun ! It is quite probable, 

 moreover, that the heat of Arcturus exceeds the solar heat in the 

 same ratio, for the spectroscope shows that although Arcturus is 



