30 CLAUSIU8 ON THE MECHANICAL EQUIVALENT 



ones ; and although the system of bodies exposed to the action 

 of the electricity was thus increased, still the increase could 

 scarcely be regarded as an actual lengthening of the connecting 

 arc, and was therefore, as in former cases, neglected. In the 

 series of experiments now before us, however, each additional 

 new battery was placed behind the others, so that its intervening 

 wire must be regarded as an actual lengthening of the connecting 

 arc. 



From this it follows that the assumption formerly made, when 

 the connecting arc remained the same, that the heat generated 

 at a single place is proportional to the totality of action, cannot 

 be extended to the case where, by increasing the elements of a 

 cascade battery, the total action is increased ; but that, on the 

 contrary, the heat generated in this case ought to be somewhat 

 under the quantity which would flow from the above assump- 

 tion. Now, as according to the above equations, the total 

 action, or the increase of the potential, if the members of a higher 

 order in respect to k be neglected, is proportional to the number 

 of elements discharged, an electrical thermometer introduced 

 into the circuit, where the number of elements is gradually in- 

 creased, ought to show temperatures which are something less 

 than the series of whole numbers expressive of the gradual 

 increase of the elements. 



In Dove's experiments* this difference is indeed not obser- 

 vable, inasmuch as with four batteries he found the heat gene- 

 rated to be expressed by the whole numbers 1, 2, 3, 4. The 

 experiments of Riessf^ on the contrary, show considerable diver- 

 gences, for with four jars he found the numbers to be as 1 to 

 3 instead of 1 to 4; and with three jars he found, . instead of 

 1 to 3, the rates of 1 to 2'5. A definite law cannot of course 

 be expected here, inasmuch as the results must greatly depend 

 on the nature of the battery made use of, and of its connexions. 



The correctness of the assumption made above, that every 

 combination of every two elements is to be regarded as an actual 

 lengthening of the circuit, is particularly evident from the fact, 

 that, according to the observations of both physicists, the heating 

 of the wire connecting the elements takes place in the same 

 manner as in the principal connecting arc ; and that by intro- 

 • Pogg. Ann. vol. Ixxii. p. 408. f Pogg. Ann. vol. Ixxx. p. 351. 



