560 REPOKT — 1891. 



Now. since the differentiation of/ with respect to t is partial only, we may use 

 the substitution 



Hence differentiating d/ldt with respect to 2 we find 



J) df eCB'F 



which gives an electromotive force in the direction of y of amount 



~4ndz' 

 Hence we have finally 



dG fCa'F dy}^ 



the two first terms on the right making up — dQjdt. 

 We have therefore 



dQ_ 3^ eil d^F 

 dt -~dt^ ~4n dtdz'' 



But the displacement current in the direction of ;/ is dtfjdf, and thus is K/4rr. 

 dQidt. Also, by the equations of currents dffldt - - I/^tt/x . o^G/9s^. Therefore we 

 have the equation 



KdQ_dj_ 1 d"Ct 



in dt~dt~~47rixdz^ 



•which would in the equation already found for oQldf yield 



d-G 1_8^G e^a^F 



d8f'-Kf.d^~4Kdt-dzi 



Similarly for the other component in the case of circularly polarised light we 

 find the equation 



arF_j_a^ eca^G 



dt^ -K^dz^ ^47rdid^' 



These two equations are identical in form with those given by the gyrostatic 

 theory, and of course lead to the same results ; that is to say, the plane of polari- 

 sation of an electromagnetic beam will show a turning efl^ect when the beam is 

 transmitted along the lines of force in a magnetised medium.^ 



3. On an Experiment on the Velocitij of Light in the neighbourhood of 

 Eapiclhj-moving Matter. By Professor Oliver J. Lodge, F.B.S, 



An apparatus was described which had been constructed to apply Michelsons 

 interference method to a beam of light sent round and round by mirrors between a 

 pair of circular saws clamped together and rotating rapidly. The results were, at 

 present, negative. 



4. The Action of Electrical Radiators, with a Mechanical Analogy. 

 By J. Larmor. 



In an electrical vibrator of rapid period the currents in the metallic parts are 

 confined to the surface ; the periodic times are therefore independent of the metals 



' It ought to be stated that I understand from a reference In M. Poincare's ' The- 

 ories de Maxwell' that a similar theory has been proposed by M. Potier in a note to 

 his French translation of 'Maxwell's Electricity.' I have not seen M.Potier's inves- 

 tigations, which may have completely anticipated the present note. 



