xlvi Tables for Statisticians and Biometricians [XXVI — XXVIII 



actually these values are negative and must be subtracted from log?/o, i.e. 1-.592,621; 

 the resulting values are given in the third columu. In column (iv) are given 

 the antilogarithms of the numbers in column (iii), and these must be plotted to 

 the values in column (i) to obtain the graph of the curve which is a good fit. 



(i) (ii) (iii) (iv) 



x=aX ;)[logj„(l + A')-.Yloge]* 



log;/ 



' 



- 9-77 2 



474,991 



- -882,370 



-13 



- 8-88 1 



923,630 



- -331,009 





47 



- 7-99 1 



472,368 



•120,253 



1 



32 



- 7-11 1 



103,755 



•488,866 



3 



08 



- 6-22 



804,557 



■788,064 



6 



14 



- 5-3.3 



564,456 



1-028,165 



10 



67 



- 4-44 



375,287 



1-217,334 



16 



49 



- 3-55 



230,493 



1^362,128 



23 



02 



- 2-67 



124,683 



1-467,938 



29 



37 



- 1-78 



053,386 



1-539,235 



34 



61 



- 0-89 



012,888 



1 -579,733 



38 



00 



0-00 



000,000 



1-592,621 



39 



14 



0-89 



012,039 



1 -580,582 



38 



07 



1-78 



046,713 



1 -545,908 



35 



15 



2-67 



101,957 



1 -490,664 



30 



95 



3-55 



176,074 



1-416,547 



26 



09 



4-44 



267,482 



1-325,139 



21 



14 



5-33 



374,828 



1-217,793 



16 



51 



6-22 



496,920 



1-095,701 



12 



47 



7-11 



632,702 



-959,919 



9 



12 



7-99 



781,189 



-811,432 



6 



48 



8-88 



941,509 



-651,112 



4 



48 



9-77 1 



112,905 



-479,716 



3 



02 



10-66 1 



294,689 



-297,932 



1 



99 



11-55 1 



486,196 



-106,425 



1 



28 



12-44 1 



686,831 



- -094,210 





80 



13-32 1 



896,111 



- -303,490 





50 



14-21 2 



113,510 



- -520,889 





30 



15-10 2 



338,613 



- -745,992 





18 



15-99 2 



570,963 



- -978,.342 



-11 



Once the reader is used to the process it will be found to work readily, and the 

 same multipliers are kept on the mechanical calculator throughout. 



Tables XXVII and XXVIII (pp. 38—41) 



Tables of the Povjers and Sums of the Powers of the natural numbers from 1 to 

 100. (W. Palin Elderton, Biometrika, Vol. ii. p. 474.) 



These tables can be used in a great variety of ways, for example in finding the 

 roots of equations, or in fitting parabolae of various orders to curves. 



Illustration (i). Find the positive root of the equation : 

 <f) (r) = -002,72G?-" + ■0.57,149?-« + •017,192?-'' 



+ -0S3,.578r-' + -088,,3:31?-» + •1:34,717?-= + r - -500,386 = 0. 

 * Actually these values are negative, and are therefore subtracted from log j/„ to give (iii). 



