144 Mr. S. H. Burbury on the 



for infinite values of w } and is not altered by changing the 

 sign of x, so that 



j f{x) dx = 1. 

 f(x)xdx=0. 



Let 



/»O0 



%) — < 



r 



T[X)X CLX — X • 



%. 



Let there be N, a very great number, of such magnitudes, 

 each independent of all the others, denoted by x^ x 2 • • • 

 Let it be required to find the chance that 



VN 



shall lie between c and c + dc, and let this chance be ¥{c)dc. 

 Then by the known method we find 



in which C is constant and 



X= dxf{x)e VN fa 



«/ — oo 



= I f{x)dx 



— — I xf(x)dx (which is zero as stated) 



VN J -00 



+ 



1 2 P 00 



I x 2 f(x) dx 



N 



+ terms involving 3 &c. 



1 — 6 2 

 s 1 — =^^ 2 — + terms involving 3 &c. 



_i~ 2 - 



se""^ 2 + terms involving 3 &c, 



and therefore _ N Lj?f 



X =e 2 + &c. 



