144 THE LAWS OF 



3.5.7...2ft + 



1.2.3... % r^v "- 3. 5. ..2ft 



n 2 . n .. 



= 2 



2. 4. ..2*' 

 1.2.3... i n-l .n 



1.3.5...2ft-l 3. 5.. ..2ft +2' + 2 



ST. 



2. 4. ..2 f 



since by what Laplace has shown (Ifec. (7e?. Liv. iii. No. 17) 



2 /1. 2. 3... 



If now we restore to //, the accents with which it was origi- 

 nally affected, and multiply the resulting quantity by r'"" 1 , we 

 shall have when r < r 



r 1 



J-i l l 



, 1.2.3... ft gn-l.n + l...n + 2ft + 2*'-3 

 * 1 . 3 . 5 ... 2ft - 1 3.5... 2ft + 2*' + 1 



W-2.W ... w + 2'-4 



2. 4. ..2*' 



and in order to deduce the value of the same integral when / < r, 

 we shall only have to change r into r', and reciprocally, in the 

 formula just given. 



We may now readily obtain the value of F 4 (i by means of 

 the formula (8). For the density corresponding thereto being 



it follows from what has been observed in the former part of the 

 present article, that f^r** 9 * may always be reduced to a rational 



