DETERMINING THE CONSTANTS OF A VOLTAIC CIRCUIT. 
305 
spending decrease in its resistance ; in a thermo-electric arrangement the resistance 
is in general small, because the circuit is entirely metallic, while in a voltaic element 
the resistance of the liquid is always considerable. 
Any interposed resistance weakens the force of the current, but less so as it is 
smaller in proportion to the other resistances in the circuit. Hence in two circuits, 
both producing currents of equal force, when the same resistance is introduced, the 
strength of the two currents may be weakened in very different proportions. A single 
voltaic element, -^r, and a series consisting of any number of such elements, form 
circuits in which the currents have the same force, but very different results will be 
obtained according as the added resistance is great or small compared with the 
original resistances in the circuits ; if it be small, the effects of the two circuits will 
remain sensibly the same ; but if it be large, the resistance that weakens to a very 
great extent the current in the circuit of the single element produces but a trifling 
diminution in that of the series. This explains the necessity of employing a series to 
overcome considerable resistances. The same remarks will apply to the comparison 
of a thermo-electric with a voltaic circuit. 
The following is the general formula for the force of the current in a voltaic circuit 
when completed by a connecting wire ; the metallic plates of the voltaic elements 
being parallel to each other and of equal size : 
p _ .... 
1 ?iRD rl 
F is the force of the current, E the electro-motive force of a single element, n the 
number of elements, R the specific resistance of the liquid, D the thickness of the 
liquid stratum or distance of the plates, S the section of the plates in contact with 
the liquid, r the specific resistance of the connecting wire, / its length, a- its section. 
Expressed in words we have the following laws : — 
The electro-motive force of a voltaic circuit varies with the number of the ele- 
ments, and the nature of the metals and liquids which constitute each element, but is 
in no degree dependent on the dimensions of any of their parts. 
The resistance of each element is directly proportional to the distance of the plates 
from each other in the liquid, and to the specific resistance of the liquid, and is also 
inversely proportional to the surface of the plates in contact with the liquid. 
The resistance of the connecting wire of the circuit is directly proportional to its 
length and to its specific resistance, and inversely proportional to its section. 
The limits of this communication will not allow me to dwell longer on the conse- 
quences of Ohm’s theory of the electric circuit ; for further developments I must refer 
to the author’s work, ‘Die Galvanische Kette mathematisch bearbeitet,’ Berlin 1827, 
a translation of which has appeared in Taylor’s Scientific Memoirs, vol. ii. ; to his 
various other memoirs published in Schweigger’s ‘ Jahrbuch der Physik;’ and to the 
