634 Proceedings of Royal Society of Edinburgh. [sess. 
The moment of momentum generated in any one of the molecules 
is rAMcosfl, where 9 denotes the inclination of the axes 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 differences. These differ- 
ences will be different for different molecules, because of the 
different values of 6 for their different orientations. Hence each 
bright line is not split into two sharp lines, but is broadened to an 
extreme breadth corresponding to the value 0 = 0. Ho simplifying 
suppositions as to the character of the molecule, such as symmetry 
of forces and moments of inertia round the axes of the ring, can 
possibly give Zeeman’s normal results of the splitting of a bright 
line into two sharp lines circularly polarised in opposite directions, 
when the light is viewed from a direction parallel to the lines of 
magnetic force ; and the dividing of each bright line into three, 
each plane polarised, when the light is viewed from a direction 
perpendicular to the lines of force. Hence, although from 1856 
till quite lately I felt satisfied in knowing that it sufficed to 
explain Faraday’s magneto-optic discovery, I now, in the light of 
Zeeman’s recent discovery, discard my old tempting gyrostatic 
hypothesis for an irrefragable reason, which is virtually the same 
as that stated by Larmor * in the following words | — “ Hence a 
principal oscillation which is thus magnetically tripled must be 
capable of being excited with reference to any axis in the molecule ; 
otherwise there would be merely hazy broadening or duplication 
instead of definite triplication.” 
§ 8. It now seems to me that the theory of H. A. Lorentz 
(of Leyden), as expressed by equations (1) in Zeeman’s first paper 
“ On the Influence of Magnetism on the Hature of the Light 
emitted by a Substance,” t is essentially true. 
§ 9. Though it cannot explain Zeeman’s discovery, the mole- 
cular rotation caused by the institution of a magnetic field, which 
is the subject of the present communication, may, however, be 
considered as interesting, not only because the idea of it seems 
to be new in electromagnetic theory, but also because it may 
* Phil. Mag., vol. xliv., 1897, “ On the Theory of the Magnetic Influence on 
Spectra,” p. 507, line 3. 
t Phil. Mag., vol. xliii., 1897, p. 226. 
