320 
NATURE 
[ Feb. 1, 1883 
It is found exper‘mentally by measuring with a delicate 
electrometer that, between any two cross-sections 4 and 
B of a homogeneous wire, in which a uniform current of 
electricity is kept flowing by any means, there exists a 
difference of potentials, and that if the wire be of uniform 
section throughout, the difference of potentials is in direct 
proportion to the length of wire between the cross-sections. 
It is found further that if the difference of potentials 
between 4 and & is kept constant, and the length of wire 
between them is altered, the strength of the current varies 
inversely as the length of the wire. The strength of the 
current is thus diminished when the length of the wire is 
increased, and hence the wire is said to oppose vesestance 
to the current ; and the resistance between any two cross- 
sections is proportional to the length of wire connecting 
them. Ifthe length of wire and the difference of poten- 
tials between 4 and & be kept the same, while the cross- 
sectional area of the wire is increased or diminished, the 
current is increased or diminished in the same ratio; and 
therefore the resistance of a wire is said to be inversely 
as its cross-sectional area. Again, if for any particular 
wire, measurements of the current strength in it be made 
for various measured differences of potentials between 
its two ends, the current strengths are found to be in 
simple proportion to the differences of potential so long 
as there is no sensible heating of the wire. Hence we 
have the law, due to Ohm, which connects the current C 
flowing in a wire of resistance A’, between the two ends 
of which a difference of potential / is maintained, 
Lines! S 
Ca Ss ard) 
In this equation the units in which any one of the three 
quantities is expressed depend on those chosen for the 
other two. We have defined unit current, and have seen 
how to measure currents in absolute units; and we have 
now to show how the absolute units of / and & are to be 
defined, and from them and the absolute unit of current 
to derive the practical units—volt, ampere, coulomb, and 
ohm, 
We shall define the absolute units of potential and 
resistance by a reference to the action of a very simple 
but ideal magneto-electric machine, of which, however, 
the modern dynamo is merely a practical realisation. 
First of all let us imagine a uniform magnetic field of 
unit intensity. The lines of force in that field are every- 
where parallel to one another: to fix the ideas let them 
be vertical. Now imagine two straight horizontal metallic 
rails running parallel to one another, and connected to- 
gether by a sliding bar, which can be carried along with 
its two ends in contact with them. Also let the rails be 
connected by means of a wire so that a complete con- 
ducting circuit is formed. Suppose the rails, slider, and 
wire to be all made of the same material, and the length 
and cross-sectional area of the wire to be such that its 
resistance is very great in comparison with that of the 
rest of the circuit, so that, when the slider is moved with 
any given velocity, the resistance in the circuit remains 
practically constant. When the slider is moved along 
the rails it cuts across the lines of force, and so long as it 
moves with uniform velocity a constant difference of 
potentials is maintained between its two ends, and a 
uniform current flows in the wire from the rail which is 
at the higher potential to that which is at the lower. If 
the direction of the lines of force be the same as the 
direction of the vertical component of the earth’s magnetic 
force in the northern hemisphere, so that a blue pole 
placed in the field would be moved upwards, and if the rails 
run south and north, the current when the slider is moved 
northwards will flow from the east rail to the west through 
the slider, and from the west rail to the east through the 
wire. If the velocity of the slider be increased the differ- 
ence of potentials between the rails, or, as it is otherwise 
called, the electromotive force producing the current, is 
increased in the same ratio; and therefore by Ohm’s law 
so also is the current. Generally for a slider arranged as 
we have imagined, and made to move across the lines of 
force of a magnetic field, the difference of potentials pro- 
duced would be directly as the field intensity, as the 
length of the slider, and as the velocity with which the 
slider cuts across the lines of force. The difference of 
potentials produced therefore varies as the product of 
these three quantities ; and when each of these is unity, 
the difference of potentials is taken as unity also. We 
may write therefore /= 7Zv, where / is the field in- 
tensity, Z the length of the slider, and ~@ its velocity. 
Hence if the intensity of the field we have imagined be 
I C.g.s. unit, the distance between the rails 1 cm., and the 
velocity of the slider 1 cm. per second, the difference of 
potentials produced will be 1 c.g.s. unit. 
This difference of potentials is so small as to be incon- 
venient for use as a practical unit, and instead of it the 
difference of potentials which would be produced if, every- 
thing else remaining the same, the slider had a velocity 
of 100,000,000 cms. per second, is taken as the practical 
unit of electromotive force, and is called one vo/éA It is 
a little less than the difference of potentials which exists 
between the two insulated poles of a Daniell’s cell. 
We have imagined the rails to be connected by a wire 
of very great resistance in comparison with that of the 
rest of the circuit, and have supposed the length of this 
wire to have remained constant. But from what we have 
seen above, the effect of increasing the length of the wire, 
the speed of the slider remaining the same, would be to 
diminish the current in the ratio in which the resistance 
is increased, and a correspondingly greater speed of the 
slider would be necessary to maintain the current at the 
same strength. We may therefore take the speed of the 
slider as measuring the resistance of the wire. Now 
suppose that wher the slider 1 cm. long was moving at 
the rate of 1 cm. per second, the current in the wire was 
I c.g.s. unit; the resistance of the wire was then I ¢.g.s. 
unit of resistance. Unit resistance therefore corresponds 
to a velocity of 1 cm. per second. This resistance, how- 
| ever, is too small to be practically useful, and a resistance 
1,000,000,000 times as great, that is, the resistance of a 
wire, to maintain I ¢c.g.s. unit of current in which it would 
be necessary that the slider should move with a velocity 
of 1,000,000 000 cms. (approximately the length of a 
quadrant of the earth from the equator to either pole) per 
| second, is taken as the practical unit of resistance, and 
called one cfm. : 
In reducing the numerical expressions of physical 
quantities from a system involving one set of funda- 
mental units to a system involving another set, as for 
instance from the British foot-grain-second system, 
formerly in use for the expression of magnetic quantities, 
to the c.g.s. system, it is necessary to determine, accord- 
ing to the theory first given by Fourier, and extended to 
electrical and magnetic quantities by Maxwell, for each a 
certain reducing factor, by substituting in the formula, 
which states the relation of the fundamental units to one 
another in the expression of the quantity, the value of the 
units we are reducing from in terms of those we are 
reducing to. For example, in reducing a velocity say 
from miles per hour, to centimetres per second, we have 
to multiply the number expressing the velocity in the 
former units by the number of centimetres in a mile, and 
divide the result by the number of seconds in an hour ; 
that is, we have to multiply by the ratio of the number of 
centimetres in a mile to the number of seconds in an hour. 
The multiplier therefore, or change-ratio as it bas been 
called by Professor James Thomson, is for velocity 
simply the number of the new units of velocity equi- 
valent to one of the old units, and may be expressed by the 
formula 2 where Z is the number of new units of length 
contained in one of the old, and 7 is the corresponding 
number for the unit of time. In the same way the 
