PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 253 



hammer was 1.166 metre; tlie recoil of the same after impact 0.087 metre; the 

 recoil of the anvil after impact 0.103 metre. Ilenco the living force which the 

 iron hammer had attained in falling was, 



L=350- 1.166=408.100 metre-kilograms; 

 but the living force with which hammer and anvil after the blow recoiled from one 

 another was, 



Z=0.103 (941-f2.95) + 0.087- 350 = 127-677 metre-kilograms; 

 the living force, therefore, expended in the compression of the lead is, 

 L—?=408.100— 127.677=280.423 metre-kilograms. 

 In order to determine the quantity of heat which was developed through the 

 compression of the lead, the latter, after receiving Fis- 8. 



the blow, was quickly withdrawn from between the 

 hammer and anvil, and by means of two threads, 

 W'hich had been already attached to it, was sus- 

 pended in the manner shown at Fig. 8. Into the 

 cavity of the compressed piece of lead, 18.5 

 grams of water at0° C. were poured, and the tem- 

 perature thereof, which very quickly became the 

 same with that of the lead, was ascertained by 

 means of an immersed thermometer. This tempera- 

 ture w'as: 



4 minutes after the impact 12°.10 



8 minutes after the impact .... 11°. 75 

 Thus in four minutes, from the end of the fourth 



minute to the end of the eighth, the cooling amounted to 0°.35. If we assume, 

 now, what may at least be accepted as an approximation, that the rate of cooling, 

 during the first four minutes after the blow, was maintained during the following 

 four minutes, we have 11.75 : 0.35 = 12.1 : x; whence results a;=0.36. Since, 

 therefore, the temperature of the lead had, at the moment of compression, been 

 12°.10-|-0°.36=12°.46,the calefaction from the blow would be 12°.46 — 7°.87= 

 4°.59 ; consequently, the quantity of heat developed through the collision is, 

 4°.59 • 2.948 • 0.03145-|-12.46 • 0.0185=0.656 units of heat, since 0.03145 is 

 the specific heat of lead. 



If we divide the work spent in the compression of the lead, 280.423 metre- 

 kilograms, by the coiTesponding quantity of heat, 0.656 thermic units, we obtain 

 the work necessary for producing one thermic unit, 



280.423 .„„ , , ., 

 ——-—-- = 427 metre-kilofjrams. 

 0.656 =' 



Instead of this number, however, 425.2 is the result, if the cooling of the lead 

 is not calculated approximately, as above, but by exact formulas, 



IV. — EQUIVALENCE OF HEAT AND WORK. 



As a mean, there results, from the best experiments which have been made 

 on this subject, 424 metre-kilograms as the mechanical equivalent of heat, or, to 

 use a more accurate expression, the ivork equivalent of the unit of heat ; and tho 

 quantity of heat A, which corresponds to the unit of work, is 



^=—=0.002358 units of heat; 

 424 



that is to say, the caloric equivalent of tho work unit is 0.002358 units of heat; 

 by the expenditure of one metre-kilogram, therefore, 0.002358 miits of heat may 

 be generated. 



