388 



Journal of Agricultv.ral Research 



Vol. IV, No. s 



Now, if we let x take all possible values, we have as the probability 

 that the group recorded with the strength m^ + ry is at least stronger 

 than the other the double integral 



(•4769)^ 



r.r^Tc 



-IT \^ L u \dx. 



dh. 



Designating this probability by p and letting '^' ^ (wj — mi + ;c + /i) = ^, 



''1 

 we shall have the equation 



.4769 /'' /"^-C^l^ e-^^dx.dL 



-{mi—mi-'ri+k) 



By breaking this integral into two, we may write our equation as follows: 



rj J e-'' dx.dt. 



^-VAj^Te-'' dx.dt. 



The first of these integrals can be evaluated by a well-known method in 

 definite integrals. Its value is %. The second integral we shall call q. 

 Then placing m^ — m^-^-h^k, we obtain the following: 



'e-^' dx.dt 



[^47691'] 



1=^ / ^-'"'"■[(^)'H^")i*. 



or 





r 



ft/ — w 



Now, by putting .4769 ( ^ V^i +^2 _|. — . ^ ) = w 



we shall have 



Jg .4769 



dk K^r^^ + r^^ 



£ 



(.4769^)- , 



