The Reflection of Diverging Waves by a Gyrostatic Medium 



By R. V. L. HARTLEY 



{Manuscript Received Feb. 28, 1950) 



This paper furnishes the basis for a companion one, which discusses the pos- 

 sibility of describing material particles as localized oscillatory disturbances in a 

 mechanical medium. If a medium is to support such disturbances it must reflect 

 a part of the energy of a diverging spherical wave. It is here shown that this 

 property is possessed by a medium, such as that proposed by Kelvin, in which 

 the elastic forces are of gyrostatic origin. This is due to the fact that, for a 

 small constant angular displacement of an element of this medium, the restoring 

 torque, instead of being constant, decreases progressively with time. 



Introduction 



IN A companion paper it is pointed out that it may be possible to de- 

 scribe the behavior of material particles as that of moving patterns of 

 wave motion, provided a medium can be found which is capable of sus- 

 taining a localized oscillator^' disturbance. In most media this is not possible, 

 for the energy of the disturbance would be propagated away in all directions. 

 Something special in the way of a medium is therefore called for. It must 

 be capable of trapping the wave energy released from a central source. 

 Kelvin proposed a mechanical medium, the equations of which, for small 

 disturbances, were identical with those of Maxwell for free space. The 

 medium derived its elasticity from gyrostats. He recognized that, for finite 

 disturbances, the restoring torque depends on the time as well as the angular 

 displacement. It is the present purpose to show that this time dependence 

 imparts to his medium exactly the energy trapping property required. 



The GYROST.A.TIC Ether 



The concept of an ether with stiffness to rotation originated with Mac- 

 CuUagh- in 1839, and was further developed by Kelvin^ in 1888. MacCullagh 

 showed that certain optical phenomena associated with reflection could not 

 be represented by the elastic solid ether of Fresnel, but required for their 

 mechanical representation a medium in which the potential energy is a func- 

 tion of what is now called the curl of the displacement. Fitzgerald'* remarked 

 in 1880 that its equations are identical with those of the electromagnetic 



^ R. V. L. Hartley, Matter, a ^Mode of Motion — this issue of the Bell System Technical 

 Journal. 



^ Collected Works of James MacCullagh, Longmans Green & Co., London, 1880, p. 145. 



^ Alathematical and Physical Papers of Sir William Thomson, Vol. HI, Art. XCIX, 

 p. 436, and Art. C, p. 466. 



'' Phil. Trans. 1880, quoted by Larmor, Ether and Matter, Cambridge U^niv. Press, 

 1900, p. 78. 



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