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 



E 

 which oppose themselves to the passage of the current, or ^ =-„• 



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 £!, 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 r the resistance of the connecting wire, we 



rl 

 shall have —r for the resistance of a wire, of a length I, and of a thick- 



r' V 

 ness d ; —jf will likewise be the resistance of the liquid conductor, the 



surface and thickness of which are respectively expressed by d' I'. There- 

 fore the action of the current, or the quantity of electricity passing 



through the pile, will be^ = — = r-=- 



r I r V' 



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 r' in- 

 creases in the same proportion. Having one pile of w' pairs, the force 



n' E 

 of the current will be expressed by .4 = —. ; — - 



— r T • 



d d' 



