118 REPORT—1865. 
no other effect than the current, and the work done by the current must 
therefore be=W, or equivalent to that done in moving the conductor against 
the force f; but, by equation (3), W=C°R, and hence 
VSL 
ar ins See OM ofl ella test RIS he, 2 (8) 
It has already been shown that C and S can be obtained in absolute mea- 
sure; hence the second member of equation (8) contains no unknown quantities, 
and, by the experiment described, the absolute resistance (R) of a wire might 
be determined. One curious consequence of these considerations is, that the 
resistance of a conductor in absolute measure is really expressed by a velo- 
city ; for, by equation (8), when SL=C we have R=V, that is to say, the 
resistance of a conductor may be expressed or defined as equal to the velocity 
with which it must move, if placed in the conditions described, in order to 
generate a current equal to the product of the length of the conductor into 
the intensity of the magnetic field ; or more simply, the resistance of a circuit 
is the velocity with which a conductor of unit length must move across a mag- 
netic field of unit intensity in order to generate a unit current in the circuit. 
Moreover it can be shown that this velocity is independent of the magnitude 
of the fundamental units on which the expression of the magnetic intensity of 
the field or strength of the current is based, and hence that electrical resist- 
ance really is measured by an absolute velocity in nature, quite independently 
of the units of time and space in which it is expressed. (Appendix C, § 39.) By 
equation (8) we have cake , but by equation (1) at hence 
i= VSG ge ele oe 5 ont ae (9) 
that is to say, the electromotive force produced between two ends of a 
straight conductor moved perpendicularly to its own length and to the lines 
of force of a magnetic field is equal to the product of the intensity of the 
field into the length of the conductor and the velocity of the motion ; or, more 
simply, the unit length of a conductor moving with unit velocity perpendicu- 
larly across the lines of force of a magnetic field will produce a unit electro- 
motive force (or difference of potential) between its two ends. This was by 
Weber made a fundamental equation, in place of equation (3), first shown 
by Thomson and Helmholtz to be consistent with Weber’s electromagnetic 
equation. These simple and beautiful relations between inductive effects and 
the simple voltaic effects first described are well adapted to show the rational 
and coherent character of the absolute system. 
The experiment last described, as a method of finding the absolute resistance 
of a conductor by measuring the velocity of motion of a straight wire, would 
be barely practicable; but it will be easily understood that we can, by cal- 
culation, pass from this simple case to the more complex case of a circular 
coil of known dimensions revolving with known velocity about an axis in a 
magnetic field of known intensity. Weber, from these elements, determined 
the absolute resistance of many wires; but this method requires that the in- 
tensity of the magnetic field be known ; and the determination of this element 
is laborious, while its value, for the earth at least, is very inconstant. A 
method due to Professor Thomson, by which a knowledge of this element is 
rendered unnecessary, has therefore been adopted in the experiments of the 
Sub-Committee at King’s College. In this plan a small magnet, screened 
from the effect of the air, is hung at the centre of a revolving coil, which is 
divided into two parts to allow the suspending fibre to pass freely. 
By calculation it can be shown that when the coil revolves round a vertical 
