1891.] vibrating electrical system, and its radiation. 175 



The relative magnitudes of the two terms in the numerator 

 of A 2 have to be estimated ; the terms to be compared are of the 

 orders 



uAA 2 , X Xv 



— , and w or — , 



that is WX h and 10 7 \, roughly. 



For light waves, X is of the order 10~ 4 , so that neither of these 

 terms can be neglected compared with the other ; and the com- 

 pletion of the solution will correspond to the somewhat com- 

 plicated circumstances of the metallic reflexion of light. 



But for waves comparable to a centimetre in length, or longer, 

 the second term is negligible ; and then 



^- s sr^' 



and B 1 = — A 1 . 



The wave is therefore reflected clean but with opposite phase. 

 And the value of n 2 given above shews that the longer the waves 

 the slighter is their penetration into the conductor ; so that even 

 for a curved surface like that of a wire this solution has an 

 application. 



The meaning of this approximation is that the first surface 

 condition, in the form it assumes when n 2 is very great, supplies 

 all the necessary data for the motion in the dielectric. That 

 surface condition is equivalent to the statement that F is zero 

 in the dielectric along the surface, and therefore so is the tan- 

 gential displacement. 



Thus the tangential surface conditions suffice in this case to 

 give a full account of the dielectric phenomena, the normal con- 

 ditions being simply left to take care of themselves. 



The function V by which the adjustment is made in the 

 conductor to obtain the normal displacement at the surface which 

 shall satisfy the condition of zero condensation is derived from 

 the characteristic equation V 2 V=0, the same equation as that 

 for the pressure in a homogeneous massless fluid ; it of course 

 indicates instantaneous adjustment to an equilibrium value 

 throughout the volume. 



(3) On the Theory of Discontinuous Fluid Motions in two 

 dimensions. By A. E. H. Love, M.A., St John's College. 



This paper contains an exposition of a modification of Mr 

 Michell's method published in Phil. Trans. R. 8., A. 1890. The 

 motion of the fluid is supposed to take place in the plane of a 

 complex variable z, and to be given by means of a velocity-potential 



