698 KEPOEi — 1893. 



The minimum value of ^ + V is - , where - must be determined from the initial 



P P P 



conditions, 



Further R, 6 are such that 



r = E. sin ^, 

 s-Z = Rcos^. 



The whole motion depends on the following constants : — 



(1) The radius of the sphere c. 



(2) The uniform velocity 2. 



(3) The minimum value of ^+ V,viz., 



P P 



4. On the Magnetic Shielding of Two Concentric Spherical Shells. 

 By A. W. RtJCKER, F.B.S. 



The formulae were found which express the shielding of two concentric perme- 

 able spherical shells, and several special cases were discussed. The result was 

 reached that if the smallest and largest radii and the volume of the permeable 

 matter are given, the shielding is a maximum for a given portion of the empty- 

 shell. If the magnetic field is produced by a small magnet placed at the common 

 centre of the shells, if the empty space is small and the matter highly permeable, 

 the best position is that in which the volume enclosed by the 'crack' is the 

 harmonic mean of the volumes included by the outermost and innermost surface. 



5. On the Equations for Calculating the Shielding of a Long Iron Tube 

 on an Internal Magnetic Pole. By Professor Gr. F. FitzGerald, M.A., 

 F.B.S. 



Attention was called to the desirability of having the integrals of the form 



— ' plotted or tabulated, as it would very much facilitate the calculation of 



\/P' + «' 

 this and other cases to which Bessel's functions were applicable but were com- 

 plicated in appUcation. 



6. On the Equations for Calculating the Effect of a Hertzian Oscillator 

 on Points in its Neighbourhood. By Professor G. F. FitzGerald, 

 M.A., F.B.S. 



Attention was recalled to the error made by Maxwell when he assumes that for 

 variable electrification it is legitimate to assume that A-\//- = at points of space 

 where there was no electrification. The true expression is A^\//- = Kfi . yjr. The 



rcos u d}L 

 evaluation of the integrals — =^ was also advocated in order to facilitate 



J s/P' + u- 

 the calculation of the efiects of a linear Hertzian vibrator on points in its neigh- 

 bourhood, The elliptic motion of the electric force in the neighbourhood of such 

 an oscillator follows at once from the fact that the vector potential is parallel to 

 the oscillator, and may be taken as A = t'F. From this we get that the magnetic 

 force is H = VaA, and thence the electric force 2 = VaH. 



If the vibration on the oscillator be simply periodic it is easy to see that the 

 form of E is 



E=EiCos?!L* + E, sin%^, 

 T r 



where Ei and E, are two vectors, so that E is the vector of an ellipse. 



In determining the period of vibration of an oscillator the difficulty arises that 

 the energy is being dissipated by radiation, and that some impressed forces must 



