298 On the KineticTheory of the Dissipation of Energy. 

 Now by hypothesis 



and therefore 



a 



2 



a + b 



10' 



b 

 a + b 



8 

 " 10 ; 



abilitj 



r is 



226> 



CIO 12 



10 



LO 13 * 



Call this =j^j and let log denote common logarithm. We have 



log N=10 13 -26 x 10 12 x log 2= (10-26 log 2) x 10 12 = 2173220 x 10 6 . 



This is equivalent to the result stated in the text above. The 

 logarithm of so great a number, unless given to more than 

 thirteen significant places, cannot indicate more than the 

 number of places of whole numbers in the answer to the pro- 

 posed question, expressed according to the Arabic notation. 



The calculation of T £J when i and n—i are very large 

 numbers, is practicable by Stirling's theorem, according to 

 which we have approximately 



1.2... i=i i+ h ^2^ 

 and therefore 



n(n — 1) ...(n—i + 1) _ n n+ i 



1.2 ... i ' V2iri i+ -{n-i) n - i ^' 



Hence for the case 



a 

 n 



a + b' 



which, according to the preceding formulae, gives T^ its 

 greatest value, we have 



T<= 1 



\^2irnef 

 where 



a+b J a+b 



Thus, for example, let n—2 x 10 12 ; 



e = % /=-8, 

 we have 



1 1 



T,= 



800000 Vtt M18000 



