262 On Mr. Herapath's Second Attack 



theoretical investigation in order to secure its appearance in the 

 Transactions of that Society, I chose in preference to send it to 

 Newcastle, and to take this most respectable channel for pre- 

 senting it to the public, knowing that it will be extensively cir- 

 culated among men of science, as well as that in these days it 

 does not require the aid of authority to support the cause of 

 truth ; while, recollecting the state of hydrodynamical science 

 as it appears in books written for the use of University stu- 

 dents, we know that when authority has not truth to propa- 

 gate, it does not hesitate to teach that which is known to be 

 erroneous. 



Having opened a new path in this difficult subject of the 

 motion of fluids, it was not in my nature to stand still ; the ef- 

 flux of fluids, the impulse on bodies placed in a moving fluid, 

 and various other inquiries followed. These, as my health per- 

 mils, will be presented to the world. Thomas Tredgold . 



XLII. On Mr. Herapath's Second Attack on Lagrange's 



Method. 

 [" AGRANGE's method still charged with failure ! In re- 

 -*- i turning to this subject it was incumbent on Mr. Herapath, 

 as a man of an ingenuous mind, to acknowledge the mistake he 

 has already committed ; of which he says not a word, although 

 it was so clearly pointed out to him. Who, that felt the spirit 

 of Science within him, could bear the thought of having made 

 a charge of failure in consequence of a mistake of his own, 

 without hastening to apologize to his living readers, and to the 

 illustrious dead from whose fame he had detracted ! The former 

 argument, which was to overturn Lagrange's method, origi- 

 nated in the erroneous notion that every one of the three parts 

 of the integral considered, must separately satisfy the diffe- 

 rential equation ; whereas it is the aggregate of all the three 

 parts which satisfies that equation*. The matter is so very 



* At the bottom of p. 23, of this Journal for January, Mr. Herapath 

 gives the value of/?, which he has computed. Taking this value, it is ob- 

 vious that his p y u is the same with the first part of the integral in p. 96 of 

 this Journal for February. The other two parts of the same integral are 

 of course identical with p { y 2 and p. 2 y^ t all the parts being derived from 

 one another by interchanging the roots. Mr. Herapath's expression of y, 

 viz. py x -f- p { y 2 -f Piya is therefore the very same with the integral in 

 p. 96 of this Journal for February. This being established, however surpris- 

 ing it may appear, yet we must infer, from what he says of the integral just 

 mentioned, and from the very confident postscript to his article, that he is 

 not acquainted with what he has himself computed. The truth is, that care 

 was taken not to change his expressions in the slightest degree. God knows 

 what would have been the consequence, if, in explaining this gentleman's 

 mistakes, any one had presumed to alter one tittle of his formulas ! 



plain, 



