246 SCIENCE PROGRESS 



the greater we make this ratio. Hence this is, so far as it 

 goes, a reason for moderation, though it must be admitted 

 that the first argument is not very conclusive. 



The second and more serious consideration is that, however 

 far we extend the " solar cluster," we do not remove the chief 

 difficulty. The ratio of the number of stars of any magnitude, 

 to that of one magnitude brighter, obstinately refuses to rise 

 up to 4, however far we count. The counting soon becomes 

 very laborious, as may be seen from the figures already quoted : 

 we have over 5,000 stars of the 6th magnitude, which means 

 approximately 20,000 of the 7th, 80,000 of the 8th and so on ; 

 two more steps take us into the millions. It will cause no 

 surprise that the counting has then to be done by inference 

 from samples in diff'erent parts of the sky and is no longer 

 complete; but even the imperfections of the counting fail to 

 suggest any escape from the conclusion that the ratio is 

 sensibly less than 4. Does then the " solar cluster " extend 

 indefinitely ? This would be only another way of saying that 

 the whole universe is arranged with reference to our sun and 

 its system. A few centuries ago it was natural to put ourselves 

 at the centre of all things and to regard the universe as a 

 mere appendage : but we have out-grown this instinct and we 

 now feel suspicious of any suggestion which assigns special 

 importance to our own position. The evidence of the star 

 counts is very striking : but before accepting it as conclusive 

 we feel bound to inquire whether it may not be susceptible 

 of another interpretation. 



One such interpretation at least is open to us and our 

 familiar experiences in a fog are enough to suggest it. We 

 know how a moderate fog limits our visible universe in all 

 directions : in front, behind, to the right, to the left, upwards— 

 downwards the earth anticipates the limit but from a balloon 

 the exception would be removed—in all directions there seems 

 to come an end to our surroundings at about the same distance. 

 If we move about, objects appear suddenly within this charmed 

 circle in front and leave it as suddenly behind us. Were it 

 not for our independent knowledge, we might believe that 

 we were the centre of all things : as it is, we attribute the 

 appearance of centrality to the fog. Even if the fog were not 

 in other ways obvious— if, for instance, it were night-time 

 and the fog were too thin to irritate our nostrils— we might 



