•118 Prof. Potter on the Definition of the Temperature of Bodies f 



strictly scientific definition of the measurements of both caloric 

 and temperature, and the latter only imperfectly. At page 20 

 of his Thcorie Analytique de la Chaleur, he defines the unit of 

 caloric to be the quantity which will convert a unit of mass of ice 

 at the freeziug-point into water at the same temperature; and if 

 a number C of these units will raise a unit of mass of any body 

 or substance through a temperature from to 1, then C is the 

 specific capacity for heat of that substance; and if a quantity of 

 caloric ^C (where z may be positive or negative) is communicated 

 to the body, then z is the temperature communicated to it, and 

 i?> generally proportional to the change of the volume of the body, 

 but not universally. 



TThen we come to great ranges of temperature, we shall see 

 that the above definition of their measurement is not complete. 

 Now we have tw T o mathematical expressions which involve tem- 

 peratures, and w 7 hich have received a general assent as to their 

 accuracy, from which we may deduce the definitions which have 

 been tacitly assumed in their formation, and w r hich we may call 

 the statical and dynamical definitions of the measurements of 

 temperatures. The first, furnishing the statical definition, is 

 the formula by which the specific heat of bodies is calculated; 

 and the second, giving the dynamical definition, is the formula 

 for the velocity of cooling of bodies in a vacuum. 



We defiue the specific heat of a body, or its capacity for caloric, 

 to be measured by the quantity of caloric necessary to be com- 

 municated to, or abstracted from, a unit of mass of the body in 

 order to raise or low T er respectively its temperature one degree. 

 Putting c for this capacity, then the quantity which will raise a 

 mass m through one degree is m . c, and the quantity which wil 

 raise the mass m through t degrees is m.c.t, for which we put 

 T, or 



r=?ra. c»t 



• /° — 



• • V — 



m. c 



where it is supposed that c has not changed sensibly in the 

 interval t° of temperature. 



If we put y for Y when £ =1° and wz = l, we have 



c 



Now c is found to be different for different substances at the same 

 temperature, and to vary for the same substance at different 

 temperatures; and 7 must vary directly as c varies. As the 

 capacities of bodies for caloric are found to increase with their 

 temperatures, then at very low temperatures, where c may be 



