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XXVI. On the Longitudinal Component in Light. By 

 Prof. George Francis FitzGerald, M.A., Se.B., F.R.S., 

 F.T.C.D* 



IN most investigations on the propagation of light attention 

 has been concentrated on the transverse nature of the 

 vibration. Longitudinal motions have been relegated to the 

 case of pressural waves, and investigators have devoted them- 

 selves to separating the two as much as possible. In Sir George 

 Stokes's classical paper on Diffraction, and in Lord Kelvin's 

 Baltimore Lectures, the existence of a longitudinal component 

 is mentioned ; but it is mentioned only to show that it is very- 

 small and that the motion is mostly transverse. Now the 

 longitudinal component is no doubt generally small except in 

 the immediate neighbourhood of a source ; but it by no means 

 follows that, as a consequence, the actual direction of motion 

 is transverse at all points in a wave. In every complicated 

 wave there are points and often lines along which the trans- 

 verse component vanishes, and at all these places the small 

 longitudinal component may be, and often is, of great relative 

 importance, so that the actual motion is largely in the direc- 

 tion of wave propagation at these places. 



I. The simplest case is that of a simple oscillator whose 

 theory has been completely worked out by Hertz. There are 

 two kinds of oscillator, an electric and a magnetic one. They 

 are exactly complementary, the magnetic forces in one cor- 

 responding exactly with the electric forces in the other. 



if the oscillator be taken as an electric one parallel to z, 

 we have for the components of the vector potential 



F = G=0, H = H OOS ^-^ ; 

 and the components of the electric force, which are in general 



P = A 2 F-^, Q = A 2 G-^, R = A 2 H-^, 

 dx 7 ^ dy 9 dz' 



where T _ d¥ dG dK 



~ dx dy dz 

 become in this case 



dzda? ^~ dsdtf dx 1 + dy 2 ' 



It is particularly to be observed that P and Q arise entirely 

 from J, which was dismissed by Maxwell as not coming into 

 consideration in cases of wave propagation on account of 

 there being no varying electrification. This is true as regards 

 * Communicated bv the Author. 



