128 REPORT—1862. 
length alone. In the second or electro-static system, the series of units is 
fixed by the unit of quantity, which Weber defines as that quantity which 
attracts another equal quantity at the unit distance with the unit force. 
Starting from these two distinct definitions, Weber, by the relations 
defined above, has framed two distinct systems of electrical measurement, 
and has determined the ratio between the units of the two systems—a matter 
of great importance in many researches; but the electro-magnetic system is 
more convenient than the other for dynamic measurements, in which currents, 
resistances, &c., are chiefly determined from observations conducted with the 
aid of magnets. 
As an illustration of this convenience, we may mention that the common 
tangent galvanometer affords a ready means of determining the value in 
electro-magnetic units of any current y in function of the horizontal com- 
ponent of the earth’s magnetism H, the radius of the coil R, its length L, 
and the deflexion 6. 
RH 
y=tang. 6 a re 
In this Report, wherever Professor Weber’s, or Thomson’s, or the absolute 
system is spoken of, the electro-magnetic system only is to be understood as 
referred to. The immense value of a coherent system, such as is here described, 
can only be appreciated by those who seek after quantitative as distinguished 
from merely qualitative results. The following elementary examples will 
illustrate the practical application of the system. 
It is well known that the passage of a current through a metal conductor 
heats that conductor; and if we wish to know how much a given conductor 
will be heated by a given current in a given time, we have only to multiply 
the time into the resistance and the square of the current, and divide the 
product by the mechanical equivalent of the thermal unit. The quotient 
will express the quantity of heat developed, from which the rise of tempera- 
ture can be determined with a knowledge of the mass and specific heat of the 
conductor. 
Again, let it be required to find how much zine must necessarily be con- 
sumed in a Daniell’s cell or battery to maintain a given current through a 
given resistance. The heat developed by the consumption of a unit of zine 
in a Daniell’s battery has been determined by Dr. Joule, as also the mechanical 
equivalent of that heat; and we have only to multiply the square of the 
current into the resistance, and divide by the mechanical equivalent of that 
heat, to obtain the quantity of zinc consumed per unit of time. 
Again, do we wish to calculate the power which must necessarily be used 
to generate by a magneto-electric machine a given current of (say) the strength 
known to be required for a given electric light. 
Let the resistance of the circuit be determined, and the power required will 
be simply obtained by multiplying the resistance into the square of the current. 
Again, the formula for deducing the quantity of electricity contained in the 
charge of a Leyden jar or submarine cable from the throw of a galyanometer 
needle depends on the relation between the unit expressing the strength of 
current, the unit of force, and the unit magnet-pole. When these are expressed 
in the above system, the quantity in electro-magnetic measure is immediately 
obtained from the ballistic formula. In estimating the value of the various 
insulators proposed for submarine cables, this measure is of at least equal 
importance with the measure of the resistance of the conductor and of the 
insulating sheath; and the unit in which it is to be expressed ge be at 
once settled by the adoption of the general system described. 
