ON STANDARDS OF ELECTRICAL RESISTANCE. 113 
have been adopted ; but when a word has once been generally accepted, it is 
undesirable to introduce a new word to express the same idea. The object 
or use of the absolute system of units may be expressed by saying that it 
avoids useless coefficients in passing from one kind of measurement to 
another. Thus, in calculating the contents of a tank, if the dimensions are in 
feet, the cubic contents are given in cubic feet, without the introduction of any 
coefficient or divisor ; but to obtain the contents in gallons, the divisor 6:25 
is required. If the power of an engine is to be deduced from the pressure on 
the piston and its speed, it is given in foot-pounds or metre-kilograzimes per 
second by a simple multiplication ; to obtain it in horse-power, the coefficients 
33,000 or 550 must be used. No doubt all the natural relations beiween 
the various magnitudes to be measured may be expressed and made use of, 
however arbitrary and incoherent the units may be. Nevertheless the intro- 
duction of the numerous factors then required in every calculation is a very 
serious annoyance, and moreover, where the relations between various kinds of 
measurement are not immediately apparent, the use of the coherent or ab- 
solute system will lead much more rapidly to a general knowledge of these 
relations than the mere publication of formule. 
The absolute system is, however, not only the best practical system, but 
it is the only rational system. Every one will readily perceive the absurdity 
of attempting to teach geometry with a unit of capacity so defined that the 
contents of a cube should be 61 times the arithmetical cube of one side, or 
with a unit of surface of such dimensions that the surface of a rectangle 
would be equal to 0:000023 times the product of its sides; but geometry so 
taught would not be one whit more absurd than the science of. electricity 
would become unless the absolute system of units were adopted. 
In determining the unit of electrical resistance and the other electrical 
units, we must simply follow the natural relation existing between the various 
electrical quantities, and between these and the fundamental units of time, 
mass, and space. ‘The electrical phenomena susceptible of measurement are 
four in number—current, electromotive force, resistance, and quantity. The 
definitions of these need not now be given, but will be found in the Appen- 
dix (C. 14, 15, 16, and 17). Their relations one to another are extremely 
simple, and may be expressed by two equations. 
First, by Ohm’s law, experimentally determined, we have the equation 
E 
C=, o 8 OP de he Sloe oe wo Ch) 
where C=current, E=electromotive force, and R=resistance. From this 
formula it follows that the unit electromotive force must produce the unit 
current in a circuit of unit resistance ; for if units were chosen bearing any 
: E 
other relation to each other,C would be equal to RP where « would be a useless 
and absurd factor, complicating all calculation, and confusing the very simple 
conception of the relation established by Ohm’s law. 
Secondly, it has been experimentally proved by Dr. Faraday that the 
statical quantity of electricity conveyed by any given current is simply pro- 
portional to the strength of the current, whether electromagnetically or 
electrochemically measured, and to the time during which it flows; hence, in 
mathematical language, we have the equation 
QC no 2.8 botnets aon emia Le) 
where t=time, and Q=quantity. From this equation it follows that the unit 
of quantity must be the quantity conveyed by the unit current in the unit of 
I 
. 
