Method of reducing Experimental Results, 103 



that <j)(x) can be expanded in ascending powers of x is by 

 no means universally true." * This fact tells to a certain 

 extent in favour of methods (such as Mr. Pickering's) in 

 which no such assumption is made. 



Exception is taken to Mr. Pickering's " dealing with an 

 abscissa of 50*06998 .... and a corresponding ordinate of 

 1*404296 " f . It may be freely conceded that as regards the 

 abscissa, the last two figures cannot affect the diagram, but 

 it may be presumed that the actual experiments have some 

 value apart from the present application. Mr. Lupton appears 

 to have momentarily forgotten that Mr. Pickering's chart 

 refers to the first differential. He will find if he looks again 



at the table J, that in the values of -=- the figures in the 



sixth decimal place have been deliberately omitted. The 

 figures in the fifth place would tell, even on the small scale 

 of the published diagram. 



It is a little hard too on Mr. Pickering that he should be 

 attacked for his use of the term " differentiation," in which 

 he is only following others, when he so carefully explains 

 what he means by it § . He notes the distinction between 

 differences and differentials, and even goes so far as to call 

 attention to the fact that irregularities will be caused if the 

 intervals are not equal. It is interesting to notice that if the 

 curves dealt with are parabolas whose equation is of the form 



y^a + bx + cx 2 , the value of — — — (called by Mr. Pickering 



x 2 —x l S 



a differential) is actually the same as that of ~ (the true dif- 

 ferential coefficient) at the point whose abscissa is 1 9 2 . 



Before concluding these remarks I wish to call attention to 

 what is really the strongest, though not perhaps the most 

 striking argument in favour of Mr. Pickering's conclusions : 

 the general agreement of the results obtained from the study 

 of various properties, and the apparent absence of any in- 

 explicable discrepancy in special cases. It is strange that 

 Mr. Lupton should not only have ignored this aspect of the 

 question, but should even have used an expression || which 

 would seem to imply that there was an absence of confirma- 

 tory evidence derived from different sources. The importance 

 of the omission can scarcely be overrated. 



* P. 421. t P. 420. 



% " Nature of Solutions," p. 142. § Id. p. 67. 



|| "In the hurry of modern life " (experimentalists) "are apt to omit 

 the test of accuracy afforded by obtaining the same results by several 

 different methods/ 1 p. 419. 



