Determination of the Earth's Horizontal Magnetic Force. 389 



average experiment which formed one of the couple usually made. 

 This would give for the probable error in the value of a " constant " 

 based on one experiment only, the value 



8,/ = (2)%", 



where Sy" is the arithmetic mean of the probable errors 8y" found in 

 the cases where two experiments were made. 



In the few cases where constants were based on three independent 

 experiments, one could, of course, have calculated the probable errors 

 8y"', and found their mean. The number of such cases appeared, how- 

 ever, too small to give a satisfactory mean value. 



§ 21. Taking first the moment of inertia, I examined seventy-one 

 cases in which two independent determinations had been made. 

 Employing 2SK to represent the difference between the two observed 

 values, whose arithmetic mean is K, I found 



Mean SK/K = 0*00041. 



The corresponding mean probable error is given by 



8K"I% = 0-000277, 



and answering to this the probable error in X is 



SX = 0-000138X. 



Ascribing to X the value 0*18 C.G.S. unit — which is not far from 

 the present mean value in Great Britain — we should have 



SX = 0*000025, approx. 



Taking the same value 0*18 for X, I also determined the law of inci- 

 dence of the probable error in the seventy-one cases examined. 

 The results were as follows : — 



Table X. 



TO 3 5 1 2 3 4 greater 



(Prob. error) x 10 5 between < than 



LO-5 1 2 3 4 5 5 

 Number of magnets 18 8 13 14 4 6 8 



As measurements of horizontal force are usually taken to 1 x 10~ 5 

 C.G.S. unit, we see that error in the moment of inertia may be 

 expected to affect the last significant figure, in these latitudes, in fifty- 

 three cases out of seventy-one, or practically in two cases out of three. 

 In one-ninth of the total number of cases the probable error in X shown 

 by Table X reached or exceeded five units in the last significant figure. 



