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XXVIII. On the Fundamental Equations of Electrodynamics 

 and Cremieu's Experiment. By H. C. PoCKLLNGTON, M.A., 



D.Sc* 



1. npHE object of this paper is to deduce the equations of 

 JL the electromagnetic field from the results of experi- 

 ment combined with the simplest possible assumptions, and 

 to use them to discuss the question whether a moving charge 

 produces a magnetic field, and whether the sudden charging 

 of a rotating disk will cause an induced current in a coil 

 surrounding it (Cremieu's experiment). The results of the 

 investigation are that Hertz's form of Maxwell's equations 

 can be obtained with the aid of assumptions so simple as to be 

 almost beyond doubt, and with them the theorem that a 

 moving charge produces a magnetic field, but that it is some- 

 what doubtful whether an induced current should theoretically 

 be observed in Cremieu's experiment. The assumption that 

 the phenomena are mechanical and therefore satisfy certain 

 reciprocal relations is not made, and no assumptions are made 

 as to the equations that are to be satisfied at the surface of a 

 moving body or in its substance. We use Quaternions on 

 account of the difficulty of expressing in Cartesians some of 

 the ideas involved. 



2. We shall consider the electric force first. 



I. Experimental Fact. The cetlier is homogeneous and 

 isotropic. — This follows from the independence of the pheno- 

 mena of light, electrostatics and current electricity on any 

 direction or position fixed in space. 



II. Assumption. The electric force satisfies differential 

 equations. — The analogous proposition is true for the case of 

 the motion of an elastic solid or of a membrane. It is not 

 true for the motion of the surface of a liquid oscillating under 

 gravity. 



III. Experimental Fact. The differential equations are 

 linear. — For otherwise two trains of waves of light could 

 not be propagated through the same space independently of 

 each other. 



IV. Experimental Fact. The velocity of propagation 

 of all leaves is the same. — This is shown by experiments on 

 the velocity of light of different wave-lengths. 



V. Experimental Fact. Waves are propagated through 

 the 03ther without suffering absorption. — Otherwise the ratio 

 of the magnitudes of two stars, one near the pole of the 

 ecliptic, the other near the ecliptic, would depend on the time 

 of year when the observation was made. 



* Communicated by the Author. 



