of the Modulus of Errors. 505 



alluded to. Here the interval represented by our 2i is two 

 inches, and the remaining data are : — 



n 1 = 64591, w_!=76157, 



n 2 = 25500, n_ 2 = 36989, 



n B = 6358, w_s= 9871, 



n_ 4 = 1674, 

 rc = 94450, 

 S/i = 315620. 



Taking as the centre of the highest compartment, I find, 

 as a superior limit of the mean-square-of-error, 7' 6. This is 

 a very serviceable approximation, considering that the real 

 value of this quantity (as given directly by Prof. Unwin's 

 reduction, and indirectly from a copious anthropometrical 

 experience) is 6*9. Instead of the real modulus 3*1, we have 

 the assumed modulus 3*9. In employing the latter constant to 

 investigate whether certain classes, e. g. savants or artizans, are 

 materially taller or shorter than the general population, we 

 shall neither overrate nor seriously underrate the evidence in 

 favour of a* significant distinction. 



As an example of i variable, I have taken the following 

 summary of anthropometrical observations, cited fromM. Bodio 

 by Dr. Baxter : — 



320 



370 



100 



21 



58 



60 



67 



71 



Here the figures below the horizontal line represent inches 

 of height*; the figures above the corresponding numbers of 

 men. There are, for instance, 370 men whose height is 

 between 64 and 67 inches. The total number of men is 

 1000. An inspection of the data suggests the advisability of 

 taking O at the extreme left corner of the highest compart- 

 ment. Employing the formula, mutatis mutandis, I find, as a 

 superior limit for the assumed modulus, 4*2. 



Our method requires modification when the Centre of 

 Gravity and Greatest Ordinate are far from coinciding, as when 

 the data assume the accompanying form. In this case it is 



* It should be observed that in this and the preceding example the 

 bases of the outmost compartments have not been given. I have assumed 

 that they may be regarded as each equal to 2 inches. 



73 



