108 REPORT— 1885. 
of a current is accompanied by an alteration in the velocity of flow, 
the acceleration of the positive electricity will, if we take Fechner’s. 
hypothesis, be equal and opposite to that of the negative ; but since there 
is a part of the force due to the moving electrified body which changes. 
sign both with the electrification and “the acceleration, the force due to 
the acceleration of the positive electricity will be equal in all respects 
to that due to the acceleration of the negative, so that there will bea 
resultant force on a unit of positive electricity at b, and this force is the 
electromotive intensity at b due to the alteration of the intensity of the 
current ina. In this way we can explain the induction due to the varia- 
tion of the current in the primary circuit. 
Theories of this kind have been given by Gauss, Weber, Riemaun,. 
and Clausius, and these writers have given expressions for the force 
between two electrified particles moving in any way. We shall after- 
wards consider these expressions in detail, but we may remark in passing 
that the theories of Gauss, Weber, and Riemann have much in common ; 
among other things they all lead to impossible results. In addition 
Clausius has shown that, unless we make Fechner’s hypothesis about a. 
current, viz. that it consists of equal quantities of positive and negative 
electricity moving with equal speeds in opposite directions, a current would 
on these theories exert a force on an electrified body at rest. 
The question of the forces due to moving electrified bodies is 
interesting in connection with electrolysis. Taking the ordinary view 
that the current is carried by the ions, we know from Hittorf’s researches 
that the anion and the cation move at different rates, so that the forces 
produced by these will be different ; hence we should expect an electrolyte: 
conveying a current to exert a force on a charged particle at rest. 
We shall now go on to consider the various theories separately. 
Gauss’s Theory.' 
Gauss assumes that the force between two particles separated by a 
distance r and charged with quantities of electricity e and e’ is along the 
line joining the particles and equal to 
ee! 1 2 3 dr 2 
Sita ye s(t) } 3 
where w is the relative velocity of the two particles and ¢ is a constant. 
This law will, if we make Fechner’s hypothesis, explain the mechanical. 
force between two circuits; but, since it contains no term depending on 
the acceleration, it cannot explain the E.M.F. produced by the variation 
of the strength of the current inthe primary ; it is also inconsistent with 
the principle of the Conservation of Energy, and so we need not consider 
it any further. 
W. E. Weber's Theory.” 
Weber assumes that the force between two charged particles, using” 
the same notation as before, is 
. or dir 
S{ital? we? a) DE 
1 Gauss’s theory was published after his death in his collected works, G6ttingen 
edition, vol. v. p. 616. See also Maxwell's Electricity and Magnetism, 2nd edit. vol, 
li, p. 440. 
2 Weber’s theory was published in 1846 in dbhandlungen der Koniglich-Sach— 
