Arguments against Newton’s Theory of Molecular Action. 117 
2. Does it follow from the arguments I have used that they 
ought to be equal ? 
3. Do I make an axis of coordinates to coincide with the 
direction of transmission ? 
1. I say it does not follow from any hypothesis that these 
quantities should be equal; nor even that the equations should 
assume the form assigned to them at p. 162, unless one of 
the axes of coordinates be that of transmission. This I sup- 
pose my opponents will admit, at least Mr. O’Brien himself 
points out the fact, when he says (Phil. Mag. for June, 1842, 
p. 485), “ I assert that the equations at the foot of p. 162 of the 
Transactions of the Camb. Phil. Soc. are essentially erroneous ; 
they ought to have been in the form,” &c. He explains him- 
self afterwards, (Phil. Mag. for November, p. 345, P.S.) by 
making me exclude the case (the only one I did not exclude) 
in which an axis of coordinates coincides with the direction of 
transmission. Mr. O’Brien then admits (what is quite correct) 
that even the form of the equations, to say nothing of the 
equality of the quantities themselves, is not a necessary conse- 
quence of the hypothesis of molecular forces. I may add that 
the true form corresponding with the case supposed by Mr. 
O’Brien, will be found in the Transactions of the Camb. Phil. 
Soc. p. 331. Any arguments, then, levelled at the Newtonian 
Law through the supposed equality of these quantities, fall to 
the ground. 
2. But does it follow from the arguments I have used that 
they ought to be equal? If it does, no consequences will fol- 
low, except the obvious one, that I have committed an error 
in one proposition. But this clearly does not follow from my 
arguments. ‘The quantities are doubtless denoted by the same 
letter 2; and Cauchy designates them by the same letter s, 
almost always. At p.139o0f the Hvercices d Analyse, we find 
s = E,s* = E + FP’, the one directly under the other. 
But it may be urged that I have myself apparently sanctioned 
the supposition that the quantities are equal, by what I say at 
p- 163. Ihave already twice over admitted that some little 
confusion appears in this place. But if this be insufficient, I 
think the right way to determine whether I did consider the 
quantities to be equal or not, is to turn to where I have ap- 
plied them. It will be found that, far from supposing this to 
be the case, I have proved them to be unequal. Let me point 
out where. In the Trans. of the Camb. Phil. Soc. pp. 179- 
180, and p. 268, for v differs from 2 only by a constant mul- 
tiplier: in the Philosophical Magazine for May, 1837, p. 340, 
and in my Theory of Heat, p. 155. I assert, moreover, that 
I have never treated the three quantities as equal—if I have, 
let my opponents say where. 
