pon 
VIL. 
ON THE REFLECTION OF ELECTRIC WAVES BY A MOVING PLANE 
CONDUCTOR. 
By ARTHUR W. CONWAY, M.A., F.R.U.I., Professor of Mathematical Physics, 
University College, Dublin. 
[Read, January 19, 1904. ] 
Tue following paper deals with the simplest case of the problem stated in 
the title—the case of direct reflection at the surface of a perfect conductor 
bounded by a plane face, and moving in any yariable manner without 
rotation. It will first be necessary to obtain the conditions to be satisfied at 
the boundary. The following method of deducing them is founded on the 
method used by Macdonald* for the case of conductors at rest. Take axes 
of w and y in the tangent plane of the surface, and the axis of 2 normal ; 
and let the origin of coordinates which moves with the surface have velocities 
in these directions uw, v, w respectively. Conceive that the current (4, J, Js), 
in place of being confined to the surface, takes place in a shell of very small 
thickness, and has a volume distribution (7%, %, #3). The current includes both 
conduction and convection currents which are to be estimated along axes fixed 
in space which for the moment coincide with the moving axes; also we 
suppose that essential magnetic singularities are absent. ‘The fundamental 
equations now become within this thin shell—- 
ae OX aX as, = % _ 0B 
a” Ge oy ” be ay Ga” 
Or 8 BI a da dy 
sey 2 Prem tae tek 5 ian Shed re Osh ee Me ec a 
us E ag i Gaal 7 Te UE eS Bk 
*H. M. Macdonald, ‘‘ Electric Waves,’ Cambridge, 1900, p. 12. 
TRANS. ROY. DUB. SOC., N.S., VOL. VIII. PART VII. 
