484 Prof. Clausius on the Dynamical Theory of Gases. 
the preceding values of N,, N,, N., D be substituted, the required 
percussion Q will be obtained as a function of the data of the 
problem ; that is to say, of the three arms «, 8, y of inertia of 
the body, of the given forces and couples Xo, Yo, Zo, Lip, Mo; No 
which animate it, and of the three coordinates x, y, z of the 
point C of the body where the obstacle is presented. 
13. The form of the above expressions shows that, in virtue 
of the applied forces and couples, the actual percussion of the 
body is composed of the percussions which would be produced 
upon the same point if each of these given forces and couples 
acted separately, and this should clearly be the case. 
It may also be remarked, that all these general formule may 
be verified by applying them to the particular cases treated in 
the first two chapters. By so doing the reader may convince 
himself of the perfect accordance between our results. 
In conclusion, it will be well to add a short remark with 
respect to the precise nature of the obstacle considered in the 
problem which has just been solved. It is simply a fixed point 
which is supposed to be capable of suddenly and totally arresting 
the point C of the body which strikes it; that is to say, of re- 
taining it for an instant in the same position in space, just as if 
this point C of the body had, for an instant, fallen into the inte- 
rior of a hollow and resisting sphere of infinitely small radius. 
It must also be borne in mind that, after the shock, this obstacle 
is supposed to disappear entirely ; for after the shock the body 
merely retains a rotation around a spontancous axis passing 
through C, and therefore becomes incapable of striking an ob- 
stacle presented at this point. 
By means of its new motion, however, the body is capable of 
striking with any other point C’; and the new percussion may be 
found from the same formule on replacing the old forces by the 
new ones: we are thus led naturally to the theory of the singular 
motions known as ricochets. 
LVII. On the Dynamical Theory of Gases. 
By Professor Cuavustus. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, | 
oe January Number of your Journal contains a very valu- 
able paper by Professor Maxwell, entitled “Illustrations 
of the Dynamical Theory of Gases,’ in which occurs (see 
Prop. X.) a result opposed to an assertion made by me in a pre- 
viously published paper*. Having waited in vain for the pro- 
* Phil. Mag. February 1859. 
