118 Prof. Kelland’s Supplementary Remarks on certain 
3. Do I not make an axis of coordinates to coincide with 
the direction of transmission ? On this depends the correct- 
ness of my equations. Their very,form is determined by the 
fact that Ido. It has been shown above that they assume an 
essentially different form in the contrary case. 
At p. 161, I say “...we might at once suppose the direction 
of transmission to be the axis of y, and put dy for 6 @; this, 
however, I shall not do, as it does not appear necessary, and 
it is convenient to retain the symbol p, on other accounts to be 
noticed hereafter. The above remarks will be mainly useful 
in pointing out to us what are the quantities to be rejected in 
our equations of motion.” J refer to this when I say (p. 162) 
‘bearing in mind the remark above made with respect to p.” 
Now I am quite sensible this might have been better and 
more clearly stated. But the reason why I did not put the 
symbol y for p, or rather why I changed y into g, as I actually 
did, was this: I wished to retain a symbol which might be 
converted into a, y, or z at pleasure; and my readers will 
find I made g to represent in succession x and x at p. 166, 
and y at p. 179. I will add further, that I never changed it 
into anything else. I never supposed it to incline to the axes. 
But the most satisfactory way of ascertaining how I understood 
my equations, will be to inquire how I interpreted and used 
them. I assert—always as having an axis of coordinates along 
the axis of transmission. Let my opponents point out one 
place in all my writings where I have done otherwise. It 
would be tedious for me to go over all I have written, and ex- 
tract every passage where the form occurs. It will suffice that 
I point out a few. Trans. Camb. Phil. Soc. vol. vi. pp. 179, 
239, 245, &c.; Phil. Mag. for May, 1837, p. 336; Theory of 
Heat, p. 146. In all these places, and in every other in which 
these equations occur, the direction of transmission coincides 
with one of the axes of coordinates. 
I proceed, now, in conclusion, to answer Mr. Earnshaw’s 
questions at p. 444 of the Magazine for this month (Dec.), or 
rather to answer one of them, so as to render the rest nu- 
gatory. 
1. * Does Professor Kelland admit that I have satisfactorily 
proved that the quantity used in his memoir on dispersion, 
is equal to zero?” 
I answer no. And wherefore? Because the proof rests 
on the assumption that three quantities are equal, which are 
essentially and necessarily not so. One of them must be dif- 
ferent from the others. If any one thinks otherwise, let him 
prove that they are equal, or let him point out an error in my 
proof of their inequality. 
Edinburgh, December 6, 1842. 
