150 ME. C4EOKGE W. WALKER ON THE INITIAL ACCELERATED 



(X, Y, Z) is discontinuous because the tangential component of (a, /3, y) is discontinuous 

 and measures the surface current. To avoid this discontinuity of aether strain 

 tangentially, I consider the possibility that the tangential component of (X, Y, Z) is 

 continuous. It follows at once that for a perfect conductor we must have either the 

 condition (l) that the tangential component of (X, Y, Z) vanishes, or the condition 

 (2) that the tangential component of (X', Y', Z') vanishes, just outside the surface. 



The motion we propose to consider is not, however, steady, but is supposed to be 

 variable. The condition inside the conductor remains the same, and on the basis of 

 continuity of tether strain tangentially we again get condition (1). The argument by 

 which condition (2) is established for steady motion does not appear to me quite so 

 satisfactory when the motion is variable. An experimental difficulty arises to my 

 mind in this connection. We know that a copper sphere can be set in rotation by a 

 rotating magnetic field, and that the motion of a copper plate is rapidly damped in a 

 magnetic field. If condition (2) holds generally for variable motion, the tangential 

 forces that actually exist in these experiments are not explained. Condition (l), 

 however, provides an explanation, because it gives a tangential component of (X', Y', Z') 

 at the surface. 



I cannot claim to have proved condition (l), nor am I convinced of its correctness; 

 and, on the other hand, condition (2) seemed to present difficulties. The position 

 seemed to call for reservation of judgment, and the only course was to work out the 

 cases for both conditions. 



The distinction is, of course, immaterial when squares of the velocity are neglected. 



In dealing with large velocities the question of LoBENTZ 1 hypothesis, that a body 

 contracts in the direction of the motion in the proportion (1 ^/0")% naturally arose. 



So far, no dynamical explanation of such a hypothesis has been obtained, and 

 considerable doubt still exists as to whether it is really necessary. In dealing with a 

 varying velocitv the hypothesis would clearly introduce complications of a somewhat 

 unsatisfactory nature from u dynamical point of view, if from no other, and 1 have 

 therefore decided to exclude it from the problem. 



The method of investigation to be pursued was suggested by reading LOVE'S paper 

 on " The Mode of Decay of Vibratory Motions" (' Proc. Lond. Math. Soc.,' ser. 2, 

 vol. 2). In that paper an exceedingly elegant method of dealing with the vibrations 

 of a fixed electrified spherical conductor is established. The electrification is initially 

 constrained to be proportional to a zonal harmonic, and the constraint is then removed. 

 It appears that rapidly damped harmonic or exponential trains of waves are produced, 

 and equations for the determination of the constants are obtained. 



On examination of the expression for an initial zonal distribution of the first order, 

 it appeared that if the sphere carried, in addition, a constant surface charge, then a 

 mechanical force, due to the radiation, was exerted in the direction of the axis of the 

 harmonic, and the force vanished only when the vibrations had subsided. It was 

 thus argued conversely, that if a charged sphere was initially at rest and an 



