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



spond with the values given by a probability-curve, namely, 

 2, 6*7, 12, 17*1, 23*3, and 38*9, average 16*7 ; and it must 

 be remembered that all numbers below a certain value, de- 

 pending on the scale used, will count as in the practical 

 examination of results. It was found in this way that the 

 average value of the coefficient of n, when the total number 

 of points examined was 9 to 18, was a little over 4, so that 

 the 5 which I have taken leaves some margin beyond the 

 average value. The nature of the e z error is obviously such 

 that it may lead to wrong conclusions in some cases: judging 

 from the results with dice, I should say that with the co- 

 efficient 5 we might expect e B to be rather greater than unity 

 in 14 cases out of 50, but that in only 2 cases out of 50 would 

 it reach the value 2. 



4. The equivalence or otherwise of the sum of the opposite 

 errors need not, I think, be taken into consideration. With 

 the mathematical method here adopted we ought to get an exact 

 equivalence ; and if in using the graphic method we make a 

 drawing in which there is a great want of equality, that draw- 

 ing must be rejected, and a better one made. At the same 

 time I do not think that strict equality should be sought, for, 

 unless the number of points available is very large (some 

 hundreds), the equal balancing of the majority of the errors 

 of different signs may be upset by an accidentally large error 

 in one or two of them. In this respect T think that the 

 graphic method is superior to the mathematical one ; for 

 making the sum of the errors of opposite signs equal may 

 be a distinct source of inaccuracy. Thus, if eighteen out of 

 twenty points lie evenly about a straight line, we ought gene- 

 rally to accept a straight line as a representation of them ; 

 the mathematical method would, however, lead to the adoption 

 of a curve in nearly every case of this description. Similarly, 

 a curve deduced mathematically from a given number of 

 experimental points will, when produced, nearly always de- 

 viate much farther from the points beyond those utilised, than 

 will a curve drawn with the lath. 



The total error, E, of a drawing or formula is taken to be 

 the product of e v e 2 , and e 3 ; and in any good representation 

 this product will differ very little from e x , and, consequently, 

 very little from the ascertained experimental error. 



Opinions will no doubt differ as to the relative importance 

 of the three errors ; but whatever be the demerits of the 

 method adopted, it will, I think, be found to be fair, and it 

 will also be found that we shall generally arrive at the same 

 qualitative, if not quantitative "*, estimate of the relative merits 



* The e lf e 2 , and e 3 errors will naturally have different relative values 

 according to the different peculiarities of the figures under investigation. 



