27 1 Mr. T. S. Davies on Mr. Herapatli's Dcmondmlion. 



no such values of v and /• had even been in the most distant 

 manner suggested), was not only the most natural course, but 

 seemed to be tar the least objectionable mode of proceeding. 

 It is true the title of the article led us at once to see the ulti- 

 mate object of the inquiry ; but it by no means intimated that 

 in the stage at which we had arrived, a different class of values 

 from that we had been previously considering was to be given to 

 the indices. It is not usual to employ quantities in an elemen- 

 tary investigation with a new import, without expressly stating 

 that the import of them is changed at that step, nor can a due 

 regard to perspicuity be consistent with such an omission. 

 Every one conversant with subjects of this nature must be aware 

 how vaguely and imperfectly the mere title of a paragraph 

 must necessarily define the character of the symbols which 

 are introduced into an investigation. It will be recollected that 

 not the slightest intimation had been given that it was con- 

 cerning the symbols r and v that the ultimate results were 

 sought J and in reality, the passage quoted by P. Q. in sup- 

 j)ort of those symbols having been introduced as fractions, ap- 

 pears quite as much like an extension of the signification 

 which they had previously possessed, — if indeed that be the 

 meaning which Mr. Herapath himself wished to convey by it. 



However, it is a matter of little importance what construc- 

 tion the passage will bear, or even which is its most obvious 

 interpretation ; it is as little, perhaps, in reference to the prin- 

 ciple tor which I contend, — whether Mr. Herapath has failed 

 in his usual precision of expression, or whether through haste 

 or misconception I have mis-stated his processes. It is suffi- 

 cient, in the present case, if when the most favourable state- 

 ment of l)oth views is made, that my principle equally applies, 

 and that the example which I have selected of its application 

 is equally pertinent, whichever interpretation of the selected 

 process we may fix upon. If I can show that under the in- 

 terpretation of P. Q. the demonstration is even more faulty 

 than that I had already considered, then I think a step will 

 be gained in the application of a great and pervading princi- 

 ple, — of a principle in itself so obvious, that I am astonished it 

 was not adopted when experiment was made the basis of menUd 

 disquisition, even though it had escaped notice when Natural 

 Philosojihy was first placeil upon the same foundation : and 

 still more surprised am I to find that it is not unhesitatingly 

 admitted amongst our very axioms in this talented and in- 

 (juiring age. It is not a little remarkable that the only relics 

 of the metaphysics of Pythagoras and Plato are to be found 

 inv.oven with the principles of that science which claims for 



itself 



