xiv.] FORBES' SCIENTIFIC WO UK. 473 



* Take a simple case, n = 4. 



3) _6 _ 11 6 



2 ' 



Pllt i (P~ 2 ) 4 1 ?4_ 32 16 

 p 4 p ' 2/ P* " P 4 



a totally different thing ; having (when p is very large) 

 to the former the ratio of 4 to 3. 



' And why is this ? Simply because the large term 

 goes out, and you take a false mean for the standing 

 terms. If p is very large, and n very small, 



n- 



P 



will be very nearly correct, but only when n is very small 



pared withjp. 



4 -nd. You ask for the logarithms of e, and of 

 4254602 and 4254372. Now, I am not very skilled 

 in computing logarithms to 12 places, and I am afraid 

 of committing an error. But I will, instead, give you the 

 process (which you can repeat, for I fear errors of mul- 

 tiplication and division) of finding the value of [your 

 expression itself, which involves the ratio only of these 

 large numbers the calculation follows]. I hope you 

 wifl find this correct. It is more laborious than either 

 difficult or complicated. It is, in fact, a mere matter of 

 multiplication and division.' 



From SIR WILLIAM THOMSON. 



1 August I5th, 1850. 



' .... In the first place, if we consider what we 

 mean by a " physical connection " between two stars, we 

 find that unless we are to speculate upon the cause of 

 their being created near one another, or at least to 

 speculate as the nebular theorists have done, it means 

 merely the stars being near enough to sensibly influence 

 one another's motions by their mutual ,-ittraction, and not 

 h,-i\ i in their relative motions to cause 



time an norniously greater separation 



