512 PROF. JACOBI ON THE APPLICATION OF ELECTRO-MAGNETISM 
adopt it, in order to obtain from it a general basis for the arrangement of 
the different elements of the magnetic apparatus. I may be permitted 
here to state the fundamental principles of this theory. 
1. In a closed voltaic circuit the same quantity of electricity passes 
across each section which is perpendicular to the direction of the 
current, whatever be the form or the matter of the different parts of 
the circuit. 
2. Whatever change is made in one part of the circuit, this change 
affects the entire action of the pile, and is not confined merely to the 
place where the change takes place. 
3. The voltaic action, in whatever manner measured, is in the direct 
ratio of the electro-motive power, and inversely as the resistances 
which oppose themselves to the passage of the current, or A == 
4. The resistances are composed of — 
a) the resistance of the solid conductor or of the connecting wire. 
For the same substance this resistance is directly as the length of the 
wire, and inversely as the transversal section or as its thickness. 
b) the resistance of the liquid conductor: this is in the direct“ratio 
of the thickness of the liquid stratum which separates the positive and 
negative plates, and inversely as its transversal section, which coin- 
cides generally with the surface of the plates. During the action of 
the pile this last resistance increases, and at the same time the elec- 
tro-motive power, or F, is affected by it. This is caused by chemi- 
cal effects which take place and change by degrees the nature of the 
liquids, the surface of the metals, and the electric tension. But 
fixing any state of the pile, the law cited always exists. The 
difficulty of making electro-magnetic experiments comparable with 
each other, and the still greater difficulty in obtaining absolute mea- 
sures, consist principally in the continual change of these elements. 
Thus in expressing by 7 the resistance of the connecting wire, we 
shall have = for the resistance of a wire, of a length /, and of a thick- 
U il! 
ness d ; ao will likewise be the resistance of the liquid conductor, the 
surface and thickness of which are respectively expressed by d! 7’. There- 
fore the action of the current, or the quantity of electricity passing 
through the pile, will be A oS 
ata 
5. The electromotive force is in the direct ratio of the number of 
voltaic pairs united in a pile, and at the same time the resistance 7’ in- 
creases in the same proportion. Having one pile of x! pairs, the force 
a FE 
rl nr! 
eee 
of the current will be expressed by A = 
