312 LEXZ ON THE VARIOUS CONDUCTING POWERS 



ranging one fourth of these, or twenty-five particles, then there will only 

 remain seventy-five to be arranged by any increase of power. Let us 

 now suppose we have another wire of the same length, whose section 

 contains only twenty-five atoms ; it is obvious that this battery will be 

 able to arrange more than one fourth of this number, so that the ratio 

 of the conducting powers cannot be as one to four, but will be found 

 by actual experiment a very different ratio. If we increase the size of 

 the battery, suppose the size of the plates to be doubled, then it is ob- 

 vious we shall not double the deflecting power. For out of one hun- 

 dred particles there are only seventy-five remaining, a part of which 

 only can be arranged by the increased part of the battery. Hence the 

 deflecting force increases very slowly with the increased size or energy 

 of the battery," 



That this view of Ritchie's is wrong may easily be proved by ex- 

 periments, of which the numerical determinations of Fechner afford 

 numerous examples. There are, in fact, some arrangements, particu- 

 larly in closed galvanic series, which show such a relation between the 

 pile and the connecting wires, that the increase of the plates does not 

 perceptibly increase the strength of the current in the wire. This 

 would, according to Ritchie's opinion, prove the whole of the fluid to 

 be already entirely disposed of, and that it would be impossible to pass 

 any more fluid through the same wire. But this is by no means the 

 case ; for if, instead of doubling the number of plates, their size be 

 doubled, the force will be almost exactly double. This proves, there- 

 fore, that the whole of the fluid has not yet been disposed of, and that 

 another arrangement of the voltaic pile only was required to produce 

 the arrangement of a double number of particles of the fluid. Besides, 

 Ritchie's theory does not explain the difference of effect produced by 

 a voltaic pile of many plates, and by one of fe^er plates but of larger 

 size. 



Ohm however several years ago furnished us with a theory of the gal- 

 vanic battery which supplies this deficiency ; but being only published 

 in German, it is unknown both in France and in England. This theory 

 explains perfectly the difference between Barlow's results and those of 

 other natural philosophers who have occupied themselves with this 

 subject, as well as the doubts of Ritchie. The latter says, in his paper 

 above quoted, that " The conducting power of a wire must be a func- 

 tion of all the quantities concerned in the experiment. These quantities 

 are obviously the diameter of the wire, its length, the size of the battery, 

 and the strength of the acid." Had he, instead of the term " conducting 

 power" used that of strength of the current, he would have been nearer 

 the mark, and gi'en a proper explanation of those apparent anomalies. 



Before quoting the simple formula of Ohm we must observe, that 

 this philosopher always uses the terra conducting resistance instead of 



