18 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



observable, from the great difference in the numbers, how con- 

 siderable the quantity of work expended by the spark, in cases 

 when difficulties are presented to its passage, may be. An exact 

 measure of this work cannot be deduced from the experiments ; 

 and such a measure, in my opinion, we do not yet possess, even 

 for the simplest and most important case where the spark passes 

 through air. 



At first sight it might be imagined that the quantity of work ex- 

 pended must, when the density of the air is uniform, he proportional 

 to the thickness of the layer. When, however, the nature of the 

 circuit or of the charge is changed, the distance across which the 

 spark passes remaining unaltered, such differences are observed, 

 even in the exterior manifestations of the spark, its noise and 

 magnitude, that such sparks cannot be regarded as alike, in 

 respect to the quantity of work which they have consumed. 



Further, it might be perhaps concluded from some of the ob- 

 servations communicated by Riess*, that the work consumed by 

 a spark in passing through the air is so small that it might be 

 neglected. Riess has conducted the experiments with the little 

 discs and balls before mentioned, bringing them first into con- 

 tact, and then within different distances of each other, so that in 

 the first case the electricity passed without a spark, and in the 

 latter case with a spark ; for each of these cases he observed the 

 quantity of heat developed in the connecting wire under the 

 same conditions of experiment. In these instances the quantity 

 of heat developed when the discs were separated by an interval 

 of air, was only a little less than by actual contact ; and in some 

 cases it was actually greater, which was the more extraordinary, 

 inasmuch as a residue here remained in the battery, while in 

 those cases where contact was established a complete discharge 

 took place. I believe, however, that these observations would 

 not justify the foregoing conclusion. 



sumption of work, but the contrary; and this seems to involve a contradiction. 

 I believe, however, that this assumption, even although it is as yet incapable 

 of being firmly established, is not to be regarded as contrary to common sense. 

 For with regard to the quantity of work expended, we have not only to take 

 into account the bodies which were penetrated, but also the manner in which 

 the penetration is effected, and this latter will certainly be affected by the con- 

 ducting body introduced between the cards. 

 * Fogg. uinn. vol. xliii. p. 78. 



