198 Prof. Kelland on Mr. Earnshaw’s Reply to the 
The sum of this function will depend on the distance be- 
tween two consecutive particles: when that distance is exceed- 
2 
ingly small (e) it is os (abstracting from sign), as I shall have 
to prove in the prosecution of my arguments in reply to 
the two remaining objections to Newton’s law of molecular 
action. 
4. Mr. Earnshaw explains his equations which he asserts 
I have misunderstood. ‘1 fear it will give to my letter an 
air of great sameness if I again accuse the Professor of misun- 
derstanding what he attempts to criticise.” ‘The equations in 
their first form (Phil. Mag. for May, p. 373) are the same as 
Cauchy’s well-known ones. But the coefficients, it appears, 
are very different. M.Cauchy’s depend on the direction of 
transmission, Mr. Earnshaw’s do not. This was the ground 
of my objection to the latter. Let us see the reply. “I ask 
how does the Professor know that these coefficients are not 
equal?” ‘Does it depend upon the direction of transmis- 
sion? This question and a similar one for each of the other 
coefficients M. Cauchy has not answered, but I have answered 
it for myself in the negative, on experimental grounds.” 
It is quite true that Cauchy does not (in the Memoir al- 
luded to) answer the question, for a most obvious reason. 
He could never have conceived it to admit of doubt. What 
is the problem they are solving? It is this: To find the vi- 
brations which are capable of being transmitted, when the posi- 
tion of the plane of the wave is ‘given. Had it turned out that 
the coefficients are independent of the position of the plane 
of the wave, one of two consequences must have followed ; 
either,—1, that any vibrations whatever may be transmitted 
along a given direction or with a given wave; or 2, that only 
certain vibrations can be transmitted, whatever be the plane 
of the wave; both of which are contrary to experiment. I 
say then that Cauchy could not conceive it possible that his 
coefficients should be independent of the plane of the wave. 
But I add, that although he did not g2ve their values, he left 
only one step tobe supplied for their determination, The co- 
efficients D, E, and F, are expressed at p. 38 (equations 70),viz. 
D=2Rbch, E=2Rackh, F=2RadbP, 
Peds sie 2 Spee’ ah 
Balt Ba 
that is, these coefficients are reciprocally proportional to the 
cosines of the angles which the perpendicular to the plane of 
the wave makes with the coordinate axes. It is evident there- 
fore that they depend on the position of the plane of the 
wave. Since, then, Mr. Earnshaw’s do nof, are we to con- 
