10 Carl C. Engbcrg 



genius. Nevertheless, in his apphcation to a special case, he 

 destroys the usefulness of his results by using seven-place 

 logarithms and computing the constants to six decimal places. 

 Four-place tables are as accurate as any statistics we have, or 

 ever can obtain on the subject, and, using these, the work of 

 computing the constants may be done in hours where Professor 

 Pearson's method requires days, and the results would be as 

 reliable as the data warrant. 



VIT 



In vol. I, part III, of Biomctrika, Professor Pearson shows 

 how to fit Makeham's curve to mortality statistics, a work of 

 great advantage to actuaries, as it gives a general rule for fitting. 

 Makeham's formula is 



X 



where I.v denotes the number who attain the age of x, and k, s, g, 

 and c are constants to be determined from known data. 



Here, even if we take the origin at the middle of the range, x 

 will still receive values as large as 30 or 35, and hence great 

 accuracy is necessary. Professor Pearson, in fact, carries out his 

 approximations to twelve decimal figures, using a large Bruns- 

 viga, as logarithm tables are necessarily out of the question. A 

 comparison of the values of some of the constants derived by 

 different processes gives us results which Avould be ludicrous 

 were they not pathetic. 



For c, Professor Pearson finds : 



<:=i.098,096,393,273, 

 while King and Hardy, by a method of averages, get : 



^=1.095,612,204. 

 Now putting 



/3^ 



r 20^3 3M1 1 



I' ~ 

 96 



