42S OHM ON THE GALVANIC CIRCUIT. 



follows that the one combination is most active in those cases 

 where the other ceases to be so^ and vice versa. If therefore 

 we are in possession of a certain number of simple circuits in- 

 tended to act upon the portion whose reduced length is A, 

 much depends on the way in which they are placed, in order 

 to produce the greatest effect of current ; whether all be 

 side by side, or all in succession, or whether part be placed 

 by the side of each other, and part in series. It may be mathe- 

 matically shown that it is most advantageous to form them into 

 a voltaic combination, of so many equal parts, that the square of 



A A 



this number be equal to the quotient -y-. When y- is equal to, 



or smaller than A, they had best be arranged by the side of each 

 other, and in succession when -j- is equal to, or larger than the 



jLa 



square of the number of all the elements. We see in this de- 

 termination the reason why in most cases a simple circuit, or I 

 at least a voltaic combination of only a few simple circuits, is 

 sufficient to produce the greatest effect. If we bear in mind, 

 that since the quantity of the cun'ent is the same at all places of 

 the circuit, its intensity at the various places must be in inverse 

 proportion to the magnitude of the section there situated, and 

 if we grant that the magnetic and chemical effects, as well as the 

 pho2nomena of light and heat in the circuit, are direct indica- 

 tions of the electrical current, and that their energy is deter- 

 mined by that of the current itself, then a detailed analysis of the 

 current, here indicated merely in outline, will lead to the perfect 

 explanation of the numerous and partially enigmatical anoma- 

 lies observed in the galvanic circuit, in as far as we are justified 

 in considering the physical nature of the circuit as invariable*. 

 Those great differences which are frequently met with in the 

 statements of various observers, and which are not consequences 

 of the dimensions of their different apparatus, have undoubtedly 

 their origin in the double capability of change of the hydro-cir- 

 cuits, and will therefore cease when this circumstance is taken 

 into consideration on a repetition of the experiments. 



The remarkable variability in the circle of action of one 

 and the same multiplier in various circuits, and of different 

 niultiphers in the same circuit, is completely explained by the 



* See Scliweigger's Jahrhich, 1826, Part 2, where I l;;ive given a somewhat 

 more detailed explanation of the separate points. 



