474 EEPORT— 1888. 



the specific heat being sensibly constant for an interval of one degree. 

 When no mass is mentioned unit mass is understood. 



The conditions referred to above may be various as to pressure and 

 volume of the body, but in practice only two are necessary to discuss, 

 viz., (1) -when the body is kept at constant pressure, e.g., that of the 

 atmosphere ; (2) when the body is kept, or reckoned as kept, at constant 

 volume. 



The necessity for taking account of these two conditions is most 

 obvious in the case of bodies in the state of gas or vapour, the change of 

 volume of bodies in the liquid and solid conditions being comparatively 

 small ; but as the liquid and the gaseous states merge one into the other, 

 there are circumstances in which the change of volume cannot be 

 neglected in the case of bodies in the liquid state. 



Experiment enables the mean capacity for heat to be determined from 

 0° C. to t° C, giving a numerical value for Q/t. A number of similar 

 determinations may he made for other temperatures ; referring the results 

 to unit mass of the body we thus get a number of mean specific heats 

 between 0° and ii°, 0° and t.,°, 0°and <3°, and so on. From a sufficient 

 number of such determinations, if the intermediate temperatures tj°, 

 t./, . . . are fairly uniformly distributed between 0° and t° it is possible 

 to find an interpolation formula Qlt=C° + at + ht-+ . . . for the 

 heat-capacity of the body between 0° and t°, where t is any temperature 

 between 0° and the extreme limit of temperature in the set of experi- 

 ments. Hence we can deduce the specific heat of the body at any such 



temperature ; for, for unit mass, '-^ is this specific heat ; if we call this 



Coat 0° and C at i,° wehave, Q,=Ct,t + at'^ + U^+ . . .; whence fZQ/tZi! 

 (or C)=Co + 2a<+3Z/<M- • . . 



This is the principle of the method by which from experimental 

 results formulas are obtained, giving approximately the specific heat of a 

 body for a range of temperatures more or less extended, from 0° C, and 

 from which curves can be drawn representing the relation of specific 

 heat to temperature in the case of each body. 



It is evident, from what has been said, that it is not always a matter 

 of indifference what temperature is chosen at which to compare solid 

 bodies, simple or compound, as to specific heat ; for, although for most 

 solids the temperature is not required to be known accurately, the 

 variation in specific heat being very slow, in others the variation of this 

 with the temperature is sufficient to make it a matter of importance 

 whether the specific heat used be that at ordinary, or at lower, or higher 

 temperatures. 



For the present this part of the subject may be dismissed, to be 

 reconsidered later on. 



Specific Heats — Solids. 



In the introduction to a series of memoirs on this subject, Regnault ' 

 says that although the subject had been attacked by many physicists 

 before Dulong and Petit, it is to these last, with the exception of some 

 very careful and accurate experiments by Lavoisier and Laplace, that we 

 are indebted up to his time for any accurate determinations of the heat- 



' Arm. Chim. (2), 73, 1840, p. 5. 



