438 Mr. S. U. Pickering on the Recognition of 



one " point " for diagrammatic purposes. The mean error of 

 each of these points was determined in the usual way by the 

 equation 



V n (n-\ 



1) 



in which a, /3, &c. are the differences between the individual 

 observations and the arithmetical mean of them, and n the 

 number of those observations. 



To determine the relative acceptability of any drawing as a 

 representation of series of experiments, several considerations 

 must be taken into account : — 



(1) The actual magnitude of the average apparent error of 

 the points as compared with the drawing. 



(2) The number of points represented by it as showing an 

 exceptionally large and improbable error. 



(3) The grouping together of errors with like signs. 



(4) The equivalence of the sum of the minus errors to that 

 of the plus errors. 



As far as I know, no method has been proposed for taking 

 proper account of any of these points except the first, still less 

 for combining them so as to get a single value to represent the 

 general acceptability of the drawing ; and although the method 

 which I have adopted in the following pages might be improved 

 in abler mathematical hands, I think that it will be found to 

 approximate closely to a mathematically correct method, and 

 it is at any rate convenient, and seems to lead to results which 

 are fair from all points of view. I may mention that it was 

 not till after I had adopted this method under the impression 

 that, though fair, it was entirely arbitrary, that I found that 

 it could be justified mathematically. 



1. The Average Error. — There is no difficulty about this ; 

 I represent it by e r It is generally the form of error which 

 is alone considered ; but I think that it is of less importance 

 than the others, for it is possible to make a palpably unjusti- 

 fiable drawing which yet attributes no more than the average 

 experimental error to the points. 



2. Judging from experimental results, the number of points 

 which may reasonably be expected to show an error greater 

 than tw'ice the average experimental error is, in a case where 

 each point is the mean of several determinations, between 

 1 and 2 in every ten, or a proportionately smaller number 

 showing greater errors. On this principle the excessive 

 errors may be estimated by 



s — m2e 



e 2 = — i > 



Arte 



in which s is the arithmetical sum of those errors which exceed 



