294 



PROFESSOR K. PEARSON AND MR. L. N. G. FILON 



Then as a step towards the determination of other probable errors, the standard 

 deviation and utnbral equation* for y = m l + nh were found 



This led to 



2, = 6-3085, 



Xv = Antl. l'091,2932 Xwi + Antl. 1'947,5528 X , V 



R yra , = -9312, 



y, = '9888, 



R y ,, = 7848. 



By aid of these auxiliary results the probable errors of all the algebraical and 

 " physical " constants were determined. 



PROBABLE Error Table. 



Now it will be clear from an examination of these results that all the " physical " 

 constants are determined with great accuracy, t The mean is subject to less probable 

 error than the mode, the modal frequency has a slightly less probable error than the 

 mean, and as it is less than 1*4 per cent, in the former case, either are closely 

 known. The skewness and distance from mean ta mode are known respectively 

 with less than 5'1 and with 5 '6 probable errors. Thus they are both significant 

 constants. In other words, the curve differs significantly from a normal curve, and 

 it is erroneous to represent the frequency by such a normal curve. The range which 

 ought to be such that there is no frequency at 1 gland, gives no frequency at 



* See footnote, p. 286, and later, p. 305. It may be as well to remind the reader that here, as in the 

 other illustrations, logarithms of the full, not the cited values, were used in the calculations. 



t The probable percentage errors in^, m } , a L , 3 are high, but this, as we have several times pointed 

 out, is of small importance, as, owing to their high correlation, the actual shape of the curve is not 

 changed sensibly by large changes in ii and m t . 



