1] 



Introduction 



XV 



at P of the plane which (by the method of least squares) most nearly passes 

 through the four points of the surface vertically above A, B, G, D. We have then 



Ux,,t = i (Mi.,0 + «i,o + "0,1 + «i,i) + i («i,o - «o,o + «i,i - "0,1) (* - '5) 



+ h («o,i - "11,0 + wi,i - «i,o)(y - 'o) (ix), 



but by trial it has been found that this formula gives occasionally worse results 

 than that for first differences, using only three points. To find by the methods 

 of simple interpolation (with first or first and second differences) the points 

 a and h, and then interpolate P between them, generally gives a fairly good 

 result ; but this result usually differs somewhat from that obtained by first simply 



1) 



F 



G 





H 



I 



© 



© 





© 



© 



-1, -1) 



(0, -1) 





(1, -1) 



(2, - 



(-1,0) 



(0, 0) 





(1,0) 



(2, 0) 



E 



A -^ . 



■ ^- a 



B 



J 



© 



® 



.... X .. 



© 



© 



! 

 y 

 I 

 © p. 



x/ 



© © X ® ® 



,S' D h C K 



(-1, 1) (0, 1) (1, 1) (2, 1) 



© © © © 



H N M L 



(-1,2) (0,2) (1,2) (2,2) 



interpolating e and / and then interpolating between e and /*. Various other 

 methods for interpolation in n-dimensioned space will be found discussed by Palin 

 Elderton in Bio7netrikaf. The ideal method can hardly yet be said to be known, 

 and it may well vary from table to table and from one part of the same table 

 to another. One or other of the above methods will, however, suffice in practice 

 for most statistical purposes. 



I consider now the individual tables. 



Table I (p. 1) 



Table of Deviates of the Normal Curve for each Permille of Frequency. (Calcu- 

 lated by Sheppard and published by Galton in Biometrika, Vol. v. p. 405.) 



If N be the total number in a population, zhx the frequency between x and 

 x + hx, <T the standard-deviation, then the frequency curve of the population 

 assuming its distribution to be Gaussian or normal will be : 



.(ix) 



* B. A. Report, Dover 1899. Tables of G {r, i-) -Integrals, Report of the Committee (Drawn up 

 by K. Pearson). j- Vol. vi. p. 94. 



