Arguments against Newton's Theory of Molecular Action. 119 
P.S. Should any of my readers be desirous of seeing a 
proof of the inequality of the three expressions, elsewhere than 
in my own writings, they will find it at p. 301 of the Exercices 
@ Analyse of M. Cauchy. In a paper, part of which is already 
in the hands of the Editor, I have proved that my equations 
give rise, by the most simple process, to M. Cauchy’s results. 
This is a sufficient guarantee for their correctness, and a strong 
illustration of the importance of the method which I have 
adopted. —— 
P.S. Jan. 4, 1843.—The Philosophical Magazine for this 
month, with the united reply of Mr. Earnshaw and Mr. 
O’Brien, has just reached me. The object of the arguments 
in that paper is to show that what I termed a misprint or mis- 
transcription, is in reality a mistake. Now suppose I grant 
them this for the sake of getting along, what do they gain by 
it? DoTI thereby “confess that my fundamental equations 
are essentially erroneous” (O’Brien, p. 22)? No such thing, 
I confess no more than this—that there is an error in the 
equations, which error has never been propagated to other 
parts of my writings, and which has been corrected by myself 
in the Philosophical Magazine for May 1837. If then these 
gentlemen choose to call it a mistake, let them do so, and we 
will proceed to our arguments. But let not my readers be 
deceived by assertions. If this zs an error in my fundamental 
equations, I again demand, where are these erroneous equa- 
tions used by me? ‘The case then stands between us as be- 
fore. ‘To follow their three positions:—1. I have never ad- 
mitted the three 7’s as equal, although in the place in ques- 
tion they were denoted by the same letter. 2. I have never 
applied the equations without the limitation (relative to the 
direction of transmission) which they deem necessary. And 
3. I have taken, and do still take, the blame of leading these 
gentlemen astray to myself. 
In their P.S. is exhibited what is more tangible, an argu- 
ment against the theory, and another against the consequences 
which I drew. They are,—1, that because v? + v2 + uv’? = 0, 
v=0,v' = 0,v"=0. Every one is aware that there are two 
ways of satisfying these equations, viz. (1) by the method which 
they give, and (2) by supposing that one (or two) of the quan- 
tities is impossible. Now the first cannot be true, for the na- 
2 
ture of the function > m( raf be ) sin? mel is such that 
’ ha 
in some cases it must depend on the relation of dy to d. 
And further, M. Cauchy, in the place cited above, has de- 
termined the value of this function, and based an important 
