238 Lord Kelvin on Magnetism and Molecular Rotation. 



be connected with the surrounding ether by springs, having 

 sufficient resilience to store up in themselves the total energy 

 thus radiated out. Taking now as gyrostat our electric 

 doublet of vitreously electrified rigid hollow ring filled with 

 fluid resinously electrified, consider what must be the nature 

 of the elastic communication between it and a rigid lining of 

 a spherical hollow in ether around it, to fulfil some of the 

 known conditions of radiant molecules. 



§ 6 (a). Let the spring connexion be equivalent to a simple 

 force between I, the centre of inertia of ring and fluid, and 

 0, the centre of the spherical sheath, varying directly as the 

 distance between those points. The gyrostatic influence will 

 be inoperative, and the result will be precisely the same as if 

 we had a single Maxwell-Sellmeier material point at 1, of 

 mass equal to that of ring and fluid together. 



(b). Let points on the ring be connected by springs with 

 points on the sheath. Supposing now the sheath to be held 

 rixed, the stiffnesses and the tensions of these springs may be 

 adjusted to give 21 arbitrary values for the coefficients in the 

 quadratic for the potential energy of any infinitesimal dis- 

 placement specified by three components of linear displace- 

 ment of I, and three components of rotational displacement 

 round axes through I. The well-known solution of the 

 problem of infinitesimal vibrations about a position of equili- 

 brium of a rigid body, modified in respect to moments of 

 inertia to take into account the fluidity of the incompressible 

 fluid in the ring, gives us immediately the periods and geo- 

 metrical specifications of six fundamental modes of simple 

 harmonic vibration. Hence our combination, serving as a 

 radiant molecule, without magnetic force, would give six 

 bright lines (understood of course that each of the six periods 

 is within the range of light-periods). Suppose now avast 

 number of such molecules, all equal and similar in every 

 respect, but with different orientations, to be scattered through 

 a flame. Each molecule, whatever its orientation, will give 

 six lines of the same periods, though of different intensities 

 when seen in any particular direction, according to the 

 chances of orientation and of impulses. Hence each of the 

 six bright lines will be perfectly sharp. 



§ 7. Now suppose a magnetic field to be suddenly instituted. 

 The moment of momentum generated in any one of the 

 molecules is rAM cos 6, where 6 denotes the inclination of the 

 axis of its ring to the lines of force. The gyrostatic influence 

 will split each of our six fundamental modes of vibration into 

 two, greater than it and less than it by equal very small 



