TO THE MOVEMENT OF MACHINES. 513 



6. If the electric curi'ent is divided into several branches, the lengths 

 of which, reduced in an inverse ratio to their diameter, may be expressed 

 by /, t, l', &C., the total action will be the same as if there were only a 

 single connecting wnre whose length is expressed by the equation 



— = — + — + —, &c. Therefore having n wires of the same length, 



the total force of the current will be expressed by 

 I'E n?i'dd'E 



A = 



I r' I' «' rid' -\- r' I' d nn'' 



nd d' 



As we can avail ourselves of the magnetizing power of each unity of 

 length of the connecting wire by coiling it round bars of the same di- 

 mension, the total power gained by a connecting wire I will be 

 4_ InnJdd'E 

 rld'+ t'V d n n'' 

 From this formula the limits of the action of the current may be de- 

 duced, which cannot be increased by the number or the surface of the 

 voltaic pairs, by the length, the diameter, and the number of the connect- 

 ing branches. Increasing only the surface of the pairs d', the limit of 



n n' d E 

 the total power of the current will be ^ = ; increasing the 



Id' E 

 number n', this limit is ^ = , , . 

 r' I' 



Again this limit will be, by increasing the length of the wire /, 



A = ; the thickness of the wire d, Az=. — — — ; the number of 



r r V 



the connecting branches «, ^ = — —- • 



rv 



In general, in order to increase the force of the current to any 

 degree, it is necessary to enlarge the surface of the plates, and at the 

 same time the thickness of the connecting wire or the number of the 

 branches. The increase of the number of the pairs requires that of the 

 length of the connecting wire, in order to attain the same end. 



The experiments, as accurate as they are numerous, which M.Fechner 

 has made on this subject, and which he has published in his work "Maass- 

 bestimmungen iiber die galvanische Kette (1831)," leave no doubt as to 

 the justness of these laws, which express in a very simple manner all the 

 relations of the different elements which constitute the voltaic pile. 

 Tliese experiments have been made for the most part by employing the 

 method of oscillations, which M. Biot was the first to apply ingeniously 

 to this kind of experiments. 



9. 



In admitting at first that the chemical effects which take place in the 

 v(jltaic pile, and which represent the expense attending the magnetic 



