J. H. K. IIaldank 205 



Henoo /* « ^T - '8800, and the cniHs-ovcr valur in 12 00 7^, 



and the ca)culate<] cx|x»ct4\tioii is 



4821'7^A., 392-:}/?/. f\^2:\hL, VM-ylU, 

 against obeen'iKl niitnb<>rs 



4881 BL, 390 m, :\m\ bL, VXIH hi. 



We have now t-<i calculate the probable errors of the values ol 

 T, Py X, and Y^ obtained above. 



The probability of any value T -^ a of t varies as 





^ r.a 



But the coefficient of a in the exponent vanishes, and a may b 

 neglected in compjirison with T or 1 — T unless n is small, hence th^ 

 probability varies as 



Hence the probable error of T is 



/iT(2+T){l-T) 



That of P is x-p of this, or 



^^V (r+2P=)» <^>- 



The probable error of X is 



or, when X is large, approximately 



•6745(X+1)a/^ "^-^ (JO. 



That of r is 



■-('•^../"■■^m?,:/-^' 



or, when 1' is large, approximately 



(i745<''+'»'^ ,n.. 



