OF MOLECULAR FORCES. 103 



tides. If the position of equilibrium be such, that one of them, as 

 d) V, is evanescent, then, F being evanescent also, for small displace- 

 ments parallel to the axis of at, the particle will be unattracted. An 

 example of this is afforded in the case of a particle placed within a 

 hollow elliptic or circular cylinder of indefinite length. The displace- 

 ment of particles placed in such positions as those here considered 

 would not bring into action any forces of restoration ; on which account 

 the particles would not vibrate. It is evident, therefore, that the phe- 

 nomena of light and sound are not due to the motions of particles 

 placed in such positions : and as the purpose of this paper is to ex- 

 amine the constitution of media supposed to be capable of transmitting 

 light, a phenomenon due to vibration, we shall, in what follows, always 

 suppose that none of the quantities d} V, d 2 g V, d\ V are evanescent : 

 under which supposition also, they cannot be equal, since their sum 

 = 0. 



9. Since the force which urges a displaced particle acts in the 

 direction of a normal to the parametric surface in which the particle is 

 at any moment situated, there are in general only three directions in 

 which a particle can be displaced, so that the force called into play 

 may act in the direction of the displacement. These directions coincide 

 with the principal axes of the parametric hyperboloids. The exceptions 

 to this are, when the constitution of the system is such, that two of 

 the three quantities, (P f V, d\ V, d\ V, are equal ; in which case the asymp- 

 totic cone has a circular base, and the exterior parametric hyperboloid 

 becomes the hyperboloid of revolution of one sheet : and since the normals 

 to this surface, corresponding to points in that principal section which 

 is perpendicular to the axis of revolution, all pass through the centre, 

 the force of restitution will always act in the line of displacement, when 

 the particle is disturbed in any direction in this plane. This is the only 

 exception. 



10. It is very important to remark, that since the parametric sur- 

 faces cannot be spherical in any case, the constitution of a medium, 

 composed of detached attractive particles, can never be such that the 

 force of restitution called into play by a disturbance in any direction 



