Feb. IS, 1915 



Fitting Logarithmic Curves 



419 



how this combination has been carried out, and also the calculation of 

 the moments from ordinates at irregular intervals. Since in this instance 

 the four ordinates at each end are regularly spaced, Elderton's formula 

 V may be used. W-hen the end ordinates are not regularly spaced, this 

 is not applicable, and the ordinates may without serious loss of accuracy 

 be left unmodified. 



Table III. 



-Calculation of moment! for data on HoUtein-Friesian cows, with grouping 

 of certain ordinates 



From Table III we have the following values: Mo= 11,315.45; M,= 

 158,369-77; M2^2,8o3,263.i9; M3 = 55,479,430.81 ; / + 7=26.5; /=26; 

 ?=o.5- 



Substituting these values in the equations xi to xiv, we obtain: 



d = 0.000096940 (20M3—810A/2 + 8907M,— 2 1,829. 5M„) = 245.67899. 



= 0.000025250 (6A'/,— 162M, + 755.5M|,) + o.oo24io2(f= —0.1338. 



6 = 0.00034137 (2M, -27M„)- 27c- o.044239(i= -3.425. 



a = 0.03846 1 5 A/„— I3.5&— 238.583333c— 1.0221 1 id= 262.26. 



The final equation then becomes — 



j/= 262. 26- 3.425X- 0.1338*- + 245.679 logio^;. 



Table IV compares the fit of the two curves calculated by the method 

 of moments with that of the curve fitted by the method of least squares. 

 It is apparent that the two methods give results of substantially the same 

 accuracy. By the method of moments the root mean-square error is 

 greater, and the mean error less than by that of least squares. Neither 

 difference is, however, large. 



