ON STANDARDS OF ELECTRICAL RESISTANCE. 139 
the conductor in virtue of which it prevents the performance of more than a 
certain amount of work in a given time by a given electromotive force is 
called its electrical resistance. The resistance of a conductor is therefore 
inversely proportional to the work done in it when a given electromotive 
force is maintained between its two ends; and hence, by equation (5), it is 
inversely proportional to the currents which will then be produced in the 
respective conductors. But it is found by experiment that the current pro- 
duced in any case in any one conductor is simply proportional to the electro- 
motive force between its ends; hence the ratio C will be a constant quantity, 
to which the resistance as above defined must be proportional, and may with 
convenience be made equal; thus 
E 
Bigger thtcansntiilly theo taalesniet «if 
an equation expressing Ohm’s law. In order to carry on the parallel with 
the pipes of water, the resistance overcome by the water must be of such 
nature that twice the quantity of water will flow through any one pipe when 
twice the head is applied. This would not be the result of a constant me- 
chanical resistance, but of a resistance which increased in direct proportion 
to the speed of the current; thus the electrical resistance must not be looked 
on as analogous to a simple mechanical resistance, but rather to a coefficient 
by which the speed of the current must be multiplied to obtain the whole 
mechanical resistance. Thus if the electrical resistance of a conductor be 
called R, the work, W, is not equal to CRt, but Cx CR xt, or 
W=C*Rt * . . . . ° . . . . . (7) 
where C may be looked on as analogous to a quantity moving at a certain 
speed, and CR as analogous to the mechanical resistance which it meets with 
in its progress, and which increases in direct proportion to the quantity con- 
veyed in the unit of time. 
18. Measurement of Electric Currents by their Action on a Magnetic 
Needle.—In 1820, Oersted discovered the action of an electric current upon 
a magnet at a distance, and one method of measurement may be based on 
this action. Let us suppose the current to be in the circumference of a 
vertical circle, so that in the upper part it runs from left to right. Then a 
magnet suspended in the centre of the circle will turn with the end which 
points to the north away from the observer. This may be taken as the 
simplest case, as every part of the circuit is at the same distance from the 
magnet, and tends to turn it the same way. The force is proportional to 
the moment of the magnet, to the strength of the current as defined by 
§ 15, to its length, and inversely to the square of its distance from the 
magnet. 
Let the moment of the magnet be ml, the strength of the current C, the 
radius of the circle &, the number of times the current passes round the 
circle n, the angle between the axis of the magnet and the plane of the 
circle @, and the moment tending to turn the magnet G, then 
G=mlC.2enk >,0088,- 2. 2... (8) 
which will be unity if m/,C,%, and the length of the circuit be unity, 
and if @=0°. 
* By equation (5) we have W=CEz; but by equation(6)R =e hence W =C?R¢,—Q.E.D. 
