62 Dr. Herschel on the Power of 



As the difference, between these and the stars of the preceding 

 order, is much less striking than that between the stars of the 

 first and second magnitude, we also find that the expressions 



=== ., , and , 2 , are not in the high ratio of 4 to 1 , but only 



as g to 4, or i\ to 1 . 



Without tracing the brightness of the stars through any 

 farther steps, I shall only remark, that the diminution of the 

 ratios of brightness of the stars of the 4th, 5th, 6th, and 7th 

 magnitude, seems to answer to their mathematical expressions, 

 as well as, from the first steps we have taken, can possibly be 

 imagined. The calculated ratio, for instance, of the brightness 

 of a star of the 6th magnitude, to that of one of the 7th, is but 

 little more than ii to 1 ; but still we find by experience, that 

 the eye can very conveniently perceive it. At the same time, 

 the faintness of the stars of the 7th magnitude, which require 

 the finest nights, and the best common eyes to be perceived, 

 gives us little room to believe that we can penetrate much 

 farther into space, with objects of no greater brightness than 

 stars. 



But, since it may be justly observed, that in the foregoing 

 estimation of the proportional distance of the stars, a consider- 

 able uncertainty must remain, we ought to make a proper 

 allowance for it; and, in order to see to what extent this should 

 go, we must make use of the experimental sensations of the 

 ratios of brightness we have now acquired, in going step by 

 step forward : for, numerical ratios of brightness, and sensa- 

 tions of them, as has been noticed before, are very different 

 things. And since, from the foregoing considerations, it may be 

 concluded, that as far as the 6th, 7th, or 8th magnitude, there 



