338 REPORT — 1893. 



are respectively [L], [L'T~^], [LT"'^]. The term actually employed by 

 MacCuUagh to illustrate that action was the statical one with k^ for 

 coefficient. 



Dynamical Illustrations, 



4. The first direct dynamical investigation bearing on tbe subject is 

 by Lord Kelvin.' He points out that the elastic reaction of a homo- 

 geneously strained solid has a character essentially devoid of all helicoidal 

 and of all dipolar asymmetry. It therefore follows that the helicoidal 

 rotation of the plane of polarisation by quartz, turpentine, etc., must be 

 due to elastic reactions dependent on the heterogeneity of the strain 

 through the space of a wave. 



Then with regard to the magnetic or unipolar rotation the well- 

 known paragraph occurs, quoted by Maxwell ('Treatise,' § 831) as 'an 

 exceedingly important remark,' of which his own theory of molecular 

 vortices, and also its outcome, the conception of the working model 

 which led to the electric theory of light, is an expansion. On reversing 

 the light the magnetic rotation is not reversed : therefore it depends on 

 some outside influence of a vector character, exerted on the system 

 which transmits the light. This influence makes the free period of a 

 circular motion differ, according as it rotates in one direction or the 

 opposite one. If the purely elastic forces maintaining the motion are 

 supposed similar in the two cases, it will follow that ' the laminiferous 

 circular motions are only components of the whole motion.' There 

 must be another dynamical system present, linked with the one which 

 transmits the light, and possessing motion of rotation round the lines of 

 magnetic force, or some other motion directed with respect to those 

 lines ; and the kinetic reaction between these two systems will account 

 for the magnetic rotation. 



The influence which is exerted on the free periods of a vibrating 

 system by linking it on to another system which is in rotation may be 

 illustrated by some dynamical problems. If the angular velocity of the 

 rotating system is supposed to be maintained constant, such illustrations 

 admit of comparatively simple analytical treatment. We can determine 

 the change produced by the rotation in the free period of the original 

 system. If that system is one member of a chain or solid continuum, 

 we can deduce the velocity of propagation of waves of given length from 

 a knowledge of this change of period ; for it is the velocity which would 

 carry the undulation over a wave-length in the free period. A typical 

 example of this kind, which is treated in the paper, is the motion of a 

 Blackburn's pendulum, suspended from a horizontal bar which is made 

 to spin round a vertical axis with angular velocity w. The equations of 

 motion are 



Writing 



(Py „ ^ dx q 



-l(r+£).-^^'=l(f-|). 



' W. Thomson, ' Dynamical Illustrations of the Magnetic and the Helicoida 

 Rotatory Effects of Transparent Bodies on Polarised Light,' Proc. Roy. Soc, 1856. 



