XXVII— XXVIII] 



Introduction 



xlvii 



The positive root is less thau '56, but the term in r 2 shows that it must be less 

 than -.52. Take "52 and '50 as trials. From Table XXVII we have 



1st -520,000 and 500,000, 



2nd -270,400 „ -250,000, 



3rd -140,608 „ -125,000, 



4th -071,162 „ -062,500, 



5th -038,020 „ -031,250, 



6th 019,771 „ -015,625, 



7th -010,281 „ -007,813. 



Multiply out by the coefficients of <f> (r), retaining the products always on the 

 arithmometer. We find 



<j> (-52) = + -016,384. 



$ (-50) = - -008,990. 



Interpolating r = "52 — Hff| x 2 = '5071, 



which is correct to last figure. 



Illustration (ii). Fit a cubic parabola to the data below, giving the average 

 age of husband to each age of wife in Italy (see Biometrika, Vol. II. p. 20). We 

 will suppose each observation to be of equal weight, — this is of course not the fact, 

 but it will illustrate the general method of fitting parabolic curves. In the paper 

 just cited illustrations are given up to parabolae of the sixth order. The object 

 here is to show the use of Table XXVII. 



The ages of groom have been taken as approximate means. Now we can take 

 our axis of x, the age of bride through 30'5, and the age of groom to be measured 

 from 32'0. x will accordingly range from —15 to +15, and the age 32 + y of 

 groom will range from y = - 7 to y=ll"5. We can now re-arrange the above 

 table in a form suitable for working on the following table. Then the squares, 

 cubes, and if necessary, higher powers of x are taken from Table XXVII, p. 38, 

 and are given as Columns (iii) and (iv) below. The entries in Column (i) are then 

 multiplied by those in (ii), (iii) and (iv) by continuous process on the machine, and 



