196 Prof. Kelland on Mr. Earnshaw’s Reply to the 
any manner ‘whatever, no force is put in play on the one which 
is not moved. But Mr. Earnshaw refers to Art. 4 for proof. 
E 4 AV . . : 
There is nothing about Tf in that article, so I suppose this 
‘ Ll, Cig CA Pee 
is a misprint for Art. 3, where are said to be equal to Owhen 
the position of the pointis one of xeutral attraction, i. e. when 
WA. yd “ge 
the force (ZF) is 0. But why it is also 0 when the point is 
in a position of equilibrium (a very different thing from neu- 
tral attraction when the other particles are not in their positions 
of rest), does not appear. If any one doubts whether spor the 
force parallel to an axis be really 0 or not, in such circum- 
stances, I refer him to M. Cauchy’s demonstration, that it is 
not in the Nouveaux Exercices,p. 190, or the Lxercices d Ana- 
lyse, p. 304. 
But that I am justified in my misconception (in supposing 
that Mr. Earnshaw’s Memoir has reference to equilibrium), 
will, 1 hope, be admitted by any one who reads the hypothe- 
sis on which it is based. ‘It is assumed that the other con- 
sists of detached particles; each of which zs im a position of 
equilibrium, and when slightly disturbed is capable of vibrating 
in any direction.” Further, a point of neutral attraction and 
a position of equilibrium are used as synonymous, Arts. 3, 4, 
6, 11, &c. And moreover, if equilibrium is a failing case in 
his objection (Art. 15), that “the equilibrium can only be 
stable in one plane,” I am at a loss to know what the objection 
itself amounts to. 
2. I turn now to the second portion of Mr. Earnshaw’s Re- 
ply (p. 438). It is quite unconnected with the former. Rela- 
tive to the first four paragraphs, I beg to direct attention to 
the previous objection of my opponent and to my Reply. ‘The 
objection is this (Phil. Mag. for July, 1842, p. 47): the 
2 3 hives - i 
equation 2 =? (+) = 3(A, sine) is such “that its right- 
hand member involves ) implicitly, in a manner which depends 
upon the arrangement of the molecules of zther, &c. Hence 
ifthere be dispersion in a medium on the finite interval theory, 
there must be dispersion im vacuo also.” To this I replied by 
stating that this expression in a medium “ must contain a term 
due to the action of the particles of matter.” (Phil. Mag. for 
Oct. 1842, p. 264.) Mr. Earnshaw’s argument assumes that 
it does not. Now in the Reply before me, it is attempted to 
be shown that the action of the particles of matter is included. 
