Decembee 9, 1898.] 



SCIENCE. 



809 



(16) 



Thus, with the exception of the electrical 

 currents ii, v, w on the left of equation (15) 

 and the negative sign in (16), we have com- 

 plete analogy between the electrical and 

 magnetic equations. In these equations 

 neither the electric nor magnetic potentials 

 nor the vector potentials appear, and we are 

 concerned only with the two field intensities, 

 which have a more tangible existence than 

 the potentials. While equations (15) are 

 identical with (8), equations (16) take the 

 place of (9) and (]0),for if we difierentiate 

 equations (10) according to the time, and 

 substitute on the right for the time-deriva- 

 tives of -F, G, H, their values from (9), we 

 obtain (16). 



In order to obtain the result of propaga- 

 tion with finite velocity, let us consider a 

 non-conductor, where u, v, w are zero, and 

 let us suppose £, /^ to be constants. Differ- 

 entiating the third of equations (16) accord- 

 ing to y and subtracting from the second 

 differentiated according to z gives 



di\^^ 'dz \~ dx" ~^ "dy"' + dz" 

 _ d IdX dY dZ) 

 dx 1 3.1; '^ dy "^ dz ] ' 



Substituting the value of the parenthesis 

 in the left from the first of equation (15), 

 after making use of equations (11) and (12) 

 and assuming that the parenthesis on the 

 right vanishes, since there is no free elec- 

 tricity, gives 



32 X 



' dt^ 



3'X B^x .'d^Z 

 '' dx' "*" dy' "*" 3^2 ' 



which is the equation for the propagation of 

 waves, as we have it in the theories of sound 

 and light. The velocity of propagation 



is 1_ 



The last paper of the series of Hertz treats 

 of the equations to be used in connection 



with moving bodies, and besides introducing 

 terms accounting for the remarkable dis- 

 covery by Rowland of the magnetic effect 

 of a moving charge of electricity suggests 

 several matters not yet verified by experi- 

 ment. Still deeper into the theory goes an 

 elaborate paper by Heaviside on the 'Forces, 

 Stresses and Fluxes of Energy in the Elec- 

 tro-magnetic Field,' published in the Philo- 

 sophical Transactions of 1892. In this paper 

 Heaviside deals with matters which are 

 still open to controversy. 



The last contributions of Helmholtz to 

 the theory were his paper on the ' Principle 

 of Least Action in Electrodynamics,' pub- 

 lished in 1893, in which he seeks to deduce 

 all the electrical equations from this funda- 

 mental mechanical principle, and his paper 

 on the ' Electro-magnetic Theory of Disper- 

 sion,' in which he adapts his beautiful expla- 

 nation of this complicated optical phenom- 

 enon to the electro magnetic theory. 



I have time here only to mention re- 

 searches on electro- and magneto striction, 

 or change of form and shape of bodies in 

 electric or magnetic fields, to which contri- 

 butions have been made by Helmholtz, 

 Boltzmann, Kirchhoff, Stefan, Lorberg, 

 Adler, Cantone and Duhem, and on the 

 magnetic effects produced by the motion of 

 electrical charges, upon which subject papers 

 have appeared by J. J. Thomson, Heaviside 

 and Searle. 



Before closing I must, however, mention 

 several elaborate papers bj^ Larmor, begun 

 in the Philosophical Transactions for 1894, 

 in which the attempt is made to propound 

 a dynamical theory of the ether, which shall 

 not only give a suitable explanation of light, 

 but also a dynamical theory of all electric 

 and magnetic phenomena, including the 

 electro-magnetic theory of light. For this 

 purpose the old theory of McCullagh is 

 found to be available and is developed with 

 extremely interesting results, while a great 

 variety of phenomena are dealt with. 



