TJIANSACTIONS OF SECTION A. 



619 



the vibration by hand, the weight will hang down at rest, the pin drawn out to a 

 certain degree; and the distance dra\>.. out will be simply proportional to the 

 weifrlit huiiff on, as in an ordinary spring balance. 



Here, then, out of matter possessing rigidity, but absolutely devoid of elasticity 

 we liave made a perfect model of a spring in 1 ;!»' form of a spring balance. Connect 

 millions of millions ot particles by pairs of rouP such as these of this spriii"- balance 

 and we have a group of particles constituting an elastic solid; exactly^fulfillin.' 

 the mathematical ideal worked out by Navier, Poisson, and. Cauchy, and many 

 other inathematicianswho, following their example, have endeavoured to found a 

 theory of the elasticity of solids on mutual attraction and repulsion between a 

 group of material particles. All that can possibly be done by this theory with 

 its assumption of forces acting according to any assumed law of 'relation to distance 

 is- done by the gyrostatic system. But the gyrostatic system does, besides, what 



the sy.steni of naturally acting material particles can^iot do: it constitutes an 

 elastic solid which can have the Faraday magneto-opt ".c rotation of the plane of 

 polarisation of light ; supposing tlie application of our solid to be a model of the 

 luniiniferous ether for_ illu'^trating the undulatory theory of light. The gyrostatic 

 model spring balance is arranged to have zero moment" of momentum as a whole, 



tic 



and therefore to_ contribute nothing to the Faraday rotat ion ; witli this arrange 

 ment the model illustrates tiie luniiniferous ether in a field 'uiailecteil by magnetic, 

 force. But now let there Iw a diflerent rotational velocity imparted to the jointed 

 square round the axisof the two projecting hooked rods,su(li as to give a resultant 

 moment of momentum roiuid any given line througii the cent e of inertia of the 

 system, and let pairs of the liooked rods in the model thus altered, which is no 

 longer a model of a mere spring-balance, be a])plied as comiections lietween millions 

 of pairs of particles as before: with the lines of resultant moment of momentum all 

 similarly directed. We now have a model elastic solid which will have the property 

 that the direction of vibration in waves of rectilinear vibrations propagated through 



