68 
earth, and the method by which he has thought proper to 
estimate the magnitude of powerful induction currents.* 
The intensity of a voltaic current, as represented by the 
mathematical theory of Ohm, is equal to the electro-motive 
force, divided by the internal resistance of the battery ; and 
from this theory it is inferred that an electro-motor, in order 
to overcome a great external resistance, must itself possess 
a correspondingly great internal resistance. A further conse- 
quence deduced from this theory is, that the maximum 
useful effect of a given electro-motor is obtained when the 
external and internal resistances are equal. 
Now, this mode of estimating the magnitude of an electric 
current does not apply to the circuits on the armatures of 
the machines invented by the author. Taking, for example, 
the results obtained from the quantity armature of a 
10-inch machine. The dimensions of the coil of this arma- 
ture may be represented by a bar of pure copper 67 feet 
long, and having a sectional area of 1*6 square inches; so 
that the resistance which this circuit presents to the passage 
of a current, when compared with that of the liquids in a 
voltaic battery, is practically null. When the coil is in full 
action it will melt 15 inches of thin iron wire *035 of an 
inch in diameter, or the same length of \ inch iron rod with 
equal certainty ; and will electrolize acidulated water in at 
least 16 voltameters in series : so that the resistance outside 
the circuit, whether estimated by the 15 inches of thin wire 
melted, or by the number of electrolizing cells in series is 
more than a hundred times greater than that of the coil in 
which the current is generated. 
Moreover, the author has found that whenever a voltaic 
battery and a magneto-electric machine will melt an equal 
length of wire, the power which these electro-motors have 
to overcome external resistance, as measured by the number 
of voltameters in series, is also equal. And generally the 
power of an electro-motor (whether voltaic or magneto- 
* Philosophical Magazine , August, 1868. 
