Theory of Molecular Action according to Newton's Law. 267 



at all in confirming the theory, if the formulae were of necessity 

 capable of producing correct results from correct or incorrect 

 data indifferently?" 



In answering this question, I must premise that I fear I do 

 not rightly understand what Mr. Earnshaw means by " from 

 correct or incorrect data indifferently." Perhaps I shall make 

 the matter more clear by putting an hypothetical case. The 

 formula being general, admitting as many arbitrary constants 

 as you please, is sufficient to satisfy any numerical results con- 

 tinuous and not inconsistent with each other. This I presume 

 will be allowed. Suppose, then, the results had been exactly 

 the converse of what they are : suppose /n to have increased 

 with A. The formula, then, could probably never have been 

 made apparently applicable; and, although sufficient, would 

 assuredly have been held as not at all probably true. By re- 

 versing the process, and showing that a formula not only sa- 

 tisfies the requisite demand, but does so in the most simple 

 manner, we certainly add weight to its authority, and strengthen 

 the process on which it is founded. 



I proceed now to the consideration of the other objections 

 which Mr. Earnshaw has adduced, for the most part to my 

 own results, in the same paper. They all originate in one 

 and the same error which Mr. Earnshaw has fallen into in 

 deducing his equations at p. 47. I dare say Mr. Earnshaw 

 has himself discovered the oversight ere now, and, but that he 

 has wielded the erroneous results to which it led him in dealing 

 blows most at my conclusions, I should have left it to himself 

 to supply the correction : but as Mr. Earnshaw has set his 

 conclusions in opposition to the truth of my deductions, and 

 those, too, of the most important kind, I cannot delegate the 

 power of replying to his own convictions. The error I allude to 

 is this. Mr. Earnshaw says, " We are now at liberty, without 

 affecting the generality of our investigations, to suppose that 

 the axes of symmetry were the coordinate axes employed in my 

 former paper ; in which case D = E = F = 0," &c. (p. 47). 

 Now it is not at all true that because the axes are axes of 

 symmetry therefore D = E = F = 0. The method which 

 Mr. Earnshaw has employed in his former paper (Phil. Mag. 

 May, p. 373) to obtain his equations, is more similar to that 

 which M. Cauchy uses to obtain the same equations in his 

 recent publications, than to his original method. In his Nou- 

 veaux Exercises, p. 4, for instance, he makes 



as Mr. Earnshaw does, without giving explicitly the value of F. 



