the paper on Sound, in the February Number. 409 



to think when he speaks of a cubical or spherical form, as the 

 actual form of an atom. By the laws of mechanics, however, in 

 the case of such balancing forces as we have cousidex-ed, we know 

 that when the atoms have freedom of motion, as in liquids and 

 gases, the only arrangement for equilibrium must be one of 

 symmetry, or what is meant by a cubical arrangement of the 

 atoms. The supposition of equilibrium is, however, only ap- 

 proximate, because bodies are perpetually changing their tem- 

 perature, and hence, also, the relative positions of the atoms are 

 perpetually changing in liquids and gases, although their relative 

 distances change only in such a degree as not to affect largely, 

 in general, the result of other impressed actions in the fluid. 

 Mr. Haughton has omitted to see that, in using the words " cube 

 attributed to the atom," I meant what I have explained above, 

 expecting that any reader of the Philosophical Magazine who had 

 studied natural philosophy would be familiar with what is meant 

 by the " atomic constitution of bodies." 



Now in solving any problem, we are. at liberty to take the 

 simplest mode of solution ; and to take it for any possible case ; 

 when necessary, making the corrections upon it afterwards if 

 they are only small. Thus in flnding the expression for the 

 ])ressure acting in any direction upon an atom in vibratory motion, 

 I was evidently at liberty to consider contiguous atoms as situated 

 in the line of that direction ; but I was not at liberty to consider 

 the fluid as reduced to such a line of atoms in discussing the 

 equation of motion for that atom, unless the result could be 

 shown to be the same as for a mass of fluid. 



Mr. Haughton^s mathematical investigations in the last Num- 

 ber of the Magazine are for a line of atoms only, and are what I 

 arrived at myself in my preliminary investigations, when I ac- 

 cordingly thovight, as he still does, that the introduction of the 

 doctrine of atoms made no change in the solution of the problem 

 of sound. 1 soon, however, saw that it was not a legitimate 

 method, but that the atom must be considered one in a mass of 

 fluid, and not one in a line of atoms. This showed me, that, in 

 deducing the pressure acting upon an atom from that upon a 

 unit of area in a fluid, a definite area must belong to that atom 

 in whatever direction the pressure were considered ; the law of 

 the equalization of density being involved in the expressions 

 always hitherto used for gases. This value of the area for pres- 

 sure, considered as the face of a cube or otherwise, is consequently 

 correctly put i^'^^yf in my pa])er on Sound in the February 

 Number, and my result is the true one. 



As to Mr. Stokes's objection to my using Boyle's law, it is 

 based on Poisson's assum|)tion discussed by me in the last Num- 

 ber, and its value is to be taken accordingly. 

 London, April 10, 1851. 



