108 Mr. A. G. Girdlestone on the condition 



6. they are so situate as not to be intersected by any one 

 ellipse whatever — the distinction being similar to that which 

 exists between four points, which may be either such as to have 

 passing through them as well ellipses as hyperbolas, or else to 

 have passing through them hyperbolas only. 



I remark that the limitation of the theorem to the case of a 

 quartic curve without nodes or cusps is necessary, at any rate as 

 regards the nodes. We may in fact find a quartic curve having 

 a single node which is met by every line in at least two real 

 points, and which is therefore not the projection of any finite 

 curve; for if we imagine two hyperbolas so situate that each 

 branch of the one cuts each branch of the other, then it may be 

 seen that there exists a quartic curve approaching everywhere 

 very nearly to the system of two hyperbolas, but having, instead 

 of the four nodes of the system, only a single node, which is 

 such that every line meets it in at least two points. 



Cambridge, December 15, 1864. 



XVII. On the condition of the Molecules of Solids. 

 By A. G. Girdlestone, Magdalen College, Oxford*. 



THAT gases are bodies whose particles are moving in straight 

 lines is now no hypothesis, but a fact resting on physical 

 demonstration, derived from the phenomena of diffusion, heat, 

 &c. In like manner the motion of the particles of liquids may 

 be demonstrated. The object of the present paper is to give the 

 same certainty to the hypothesis of the molecular motion of 

 solids. 



Now there are certain prima facie difficulties in the way of 

 such an hypothesis, e. g. the cohesion of solids, the fact that 

 they exert no chemical action, that they do not transmit pres- 

 sure equally in all directions, their inertia, &c, which, however, 

 on further consideration are the most convincing confirmatory 

 evidence that these molecules, equally with those of liquids and 

 gases, are in motion. 



For if we adopt the idea that they rotate on their own axes, 

 just as atop does, these phenomena must ensue, as will be seen. 

 Let us imagine first a single top spinning (the gyroscopic top 

 furnishes an apt illustration); this, when in rapid rotation, 

 strongly resists any change of its plane of rotation, and if sup- 

 posed free from gravity and external forces, would continue to 

 do so. Now if a mass composed of such tops under such con- 

 ditions be imagined, the axes of rotation lying in every conceiv- 

 able plane, (a) the phenomenon called cohesion would be ob- 



* Communicated bv the Author. 



