ON ELECTRICAL THEORIES. 109 
This formula is not inconsistent with the principle of the Conservation of 
Energy ; making Fechner’s hypothesis, it will explain the mechanical force 
between circuits conveying currents ; it will also explain induction due 
both to the motion of the primary and the alteration in the strength of the 
current in the primary. We shall see, however, that it makes a body 
under certain circumstances behave as if its mass were negative; 7.e. if it 
were acted on by a force in a direction opposite to that in which it is 
moving, its velocity would continually increase. 
Riemann’s Theory. 
This is explained in his ‘Schwere Electricitiit und Magnetismus,’ 
edited by Hallendorff, p. 327. According to this theory the force be- 
tween two electrified bodies is not altogether along the line joining them, 
but consists of the following parts :— 
1. A force along the line joining the particles equal with the same 
notation as before to 
2. A force on the first particle parallel to its velocity relative to the 
second equal to 
cr? dt 
3. A force on the first particle parallel to its acceleration relative to 
the second equal to 
2ee! f 
cr * 
where f is the relative acceleration of the particles. 
There are of course similar forces acting on the second particles, and 
we see from the form of the expressions of the forces that the force on the 
first particle is equal and opposite to the force on the second. Riemann’s 
law of force is not inconsistent with the principle of the conservation of 
energy, and it explains the mechanical force between two circuits; hence 
it must explain the induction of currents. We shall see, however, that it 
is open to the same objection as Weber’s theory, viz. that it makes an 
electrified particle under certain circumstances behave as if its mass were 
negative. 
Clausius’ Theory. 
If x, y, 2 are the co-ordinates of the first electrified particle, a’, y', z’ 
those of the second, then according to this theory the z component of the 
force on the first particle is equal to 
er ee ashi a Sf ae 
ee Vd vv cos ¢/o?)— = als 7) | 
With similar expressions for the components parallel to y and z, here 
sischen Gesellschaft der Wissenschaften, 1846, p- 211; it is reprinted in Zlectro- 
dynamische Maassbestimmungen, 1871. A good account of the theory is given in 
Maxwell’s Electricity and Magnetism, 2nd edit. vol. ii. chap. xxiii. 
’ This theory is given in Crelle, vol. 82, p. 85. There is also a full abstract in 
Wiedemann’s Beiblatter, vol. i. p. 143. 
