190 Prof. A. Anderson on the Mutual 



We may now inquire what time is required for the accu- 

 mulation of energy equal (say) to one quarter of the limiting- 

 value. This occurs when e~^ = ^ or by (5) when 



^loK^jogijr (12) 



q p.kr.Zircr*' 



The energy propagated in time t across the area S of primary 

 wave-front is ( ; Theory of Sound,' § 215) 



iSo-aPa 2 ^ ... . (13) 



where a is the velocity of propagation, so that p=-ak. If we 

 equate (13) to one quarter of (9j and identify t with the 

 value given by (12), neglecting the distinction between M 

 and M', we get 



S= ^ _ ?i 2 (id.}* 



21og2.* 8 87TlOir2- ' ' ' ^V 



o 



The resonator is thus able to capture an amount of energy 

 equal to that passing in the same time through an area of 

 primary wave-front comparable with \ 2 /V> an area which 

 may exceed any number of times the- cross-section of the 

 resonator itself. 



XVIII. On the Mutual Magnetic Energy of two Moving 

 Point Charges. By Prof. A. Anderson f. 



THE method here given of finding the mutual magnetic 

 energy of two moving point charges of electricity is 

 elementary. It does not claim to have the elegance of 

 Heaviside's method. It is, however, a confirmation of his 

 result by simple mathematics, in which there are no vector 

 potentials, no curls of any kind, and no trouble of adjusting 

 the vector potential to make the space integral of the scalar 

 product of it and the magnetic force vanish for the polar, or 

 displacement, currents in the medium. 



Consider, first, the case of two charges, e 1 and e 2 , at A and 

 B moving along parallel lines AL and BM with velocities 

 Wi and iv 2 , AB being perpendicular to AL and BM (tig. 1). 



Let P be any point in space. Draw the plane PLM 

 perpendicular to AL and BM and join PA, PB. 



* log 2=0-693. 



t Communicated by the Author. 



