The Reflection of Diverging Waves by a Gyrostatic Medium

1 A it is pointed out that it be possible to deINscribecompanion paperofa material can be foundthatmaymoving patternssusthe behavior particles as of of wave motion, provided medium which is capable of taining a localized oscillatory 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. T H E GYROSTATIC ETHER The concept of an ether with stiffness to rotation originated with MacCullagh 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 function of what is now called the curl of the displacement. Fitzgerald remarked in 1880 that its equations are identical with those of the electromagnetic 2 3 1