NEW TABLES OF THE PKÜBABILITY INTEGKAL". 



By w. f. SHEPPAKD, iM.A., j.l.m. 



Description of the Tables. 



1. The " probability integral" expresses the area of the normal curve, or 

 curve of error, whose eqiuition is 



z= ^L-e-5'' (1). 



The abscissa x is measured from the central ordinale, about which the curve 

 is s3-mmetrical, and its unit of measurement is the Standard deviation (square 

 root of niuan S(|nare of deviation). The wholc area of the curve is uuity. If tliis 

 whole area be divided by the ordinate z, at distance x from the central Ordinate, 

 into portions i(l+a) and i(l— «), then 



i(l + a)=j' zdx, i{l-a)= j'^zdx (2), 



a = 2| zdx (2a), 



J 



where z has the value given by (1). 



Tables I. and II. give the values of z and of ^ (1 + a) for any value of x fi'oni 

 •00 to 6'00; and therefore, the curve beiug synimetrical about the central ordinate, 

 they enable us to determine the values of i (1 + a), ^ (1 — a), and z, for any value 

 of X betweeu — 6'00 and + 6'00. Tables III. and IV. give the values of x and of z 

 for any value of o from '00 to '80 ; and therefore for any value of a between 

 -•80 and +-80. 



If X denotes the measurement of an organ common to a large number N 

 of individuals, and if the different values of X are distributcd according to the 

 normal law about a niean value m with meau Square of deviation a-, then the 



* [In the prospectus of Biometrika, the Editors promised to provide " numcrical table« tending 

 to reduce the labour of Statistical arithmetic." The first instaluieut of such taUes by Mr I'alin Eklerton 

 was given in Vol. i. This second instahnent provides for the widely feit want of probability integral 

 and normal curve data calculated on the basia of the Standard deviation and not on that either of 

 the modulus or of the probable error. Emtoks.] 



