4 Carl C. Ell gb erg 



We then get for the vahies of the constants : 



r= 68.78 



£=24 -.s 



b= 74.14 

 in\-=i 2.757 

 a\-=^ 3.056 

 jj/„=i883 



The centroid vertical is at 18.97 years. 



Carrying the work out to six decimal figures, Protessor Pear- 

 son finds for these constants : 



/^2— 4-070554, /i3=7-598i96, Mi=69. 379605 

 3^1— 2^2+6=. 1935 

 r= 72.28642 d^=^ .98643 



e^ 259.78912 A^=^ .488922 



b=^ 77.28312 

 wi= 2.79291 7^2=67. 49351 



^1= 3.07801 ^2=74.20511 



j>/o=i890.83 



The centroid vertical is at 18.9691 years; i. e., .29382 unit 

 from 15-20. To compute the run of a disease to a twenty-thou- 

 sandth part of a year is rather fine work, especially when five 

 years is the unit. 



A comparison of the two sets of results shows a considerable 

 difiference in the values of the constants. Theoretically the latter 

 is the more correct set of values ; practically the former is the 

 better. The equations given above apparently necessitate a high 

 degree of approximation, for high powers of the moments and 

 other constants are involved, and the successive powers of an 

 approximate decimal fraction are correct to fewer and fewer 

 decimal places; so that, if we want the values of the constants 

 correct to two or three decimals, we must start with at least six 

 decimal figures in the values of the moments. This is true if we 

 are dealing with six-place data, but suppose we have before us 

 only three-place data? We can then at best make a guess at the 

 fourth figure, but can tell absolutely nothing about the following 



90 



