SECT. IV.] THREE SPECIFIC COEFFICIENTS. 465 



placed by a given condition, which expresses the state of the 

 surface, whether constant, variable or periodic. 



433. The differential equations of the movement of heat are 

 mathematical consequences analogous to the general equations of 

 equilibrium and of motion, and are derived like them from the 

 most constant natural facts. 



The coefficients c, h, k, which enter into these equations, must 

 be considered, in general, as variable magnitudes, which depend 

 on the temperature or on the state of the body. But in the appli 

 cation to the natural problems which interest us most, we may 

 assign to these coefficients values sensibly constant. 



The first coefficient c varies very slowly, according as the tem 

 perature rises. These changes are almost insensible in an interval 

 of about thirty degrees. A series of valuable observations, due to 

 Professors Dulong and Petit, indicates that the value of the specific 

 capacity increases very slowly with the temperature. 



The coefficient h which measures the penetrability of the sur 

 face is most variable, and relates to a very composite state. It 

 expresses the quantity of heat communicated to the medium, 

 whether by radiation, or by contact. The rigorous calculation of 

 this quantity would depend therefore on the problem of the move 

 ment of heat in liquid or aeriform media. But when the excess 

 of temperature is a sufficiently small quantity, the observations 

 prove that the value of the coefficient may be regarded as constant. 

 In other cases, it is easy to derive from known experiments a 

 correction which makes the result sufficiently exact. 



It cannot be doubted that the coefficient k, the measure of the 

 permeability, is subject to sensible variations; but on this impor 

 tant subject no series of experiments has yet been made suitable 

 for informing us how the facility of conduction of heat changes with 

 the temperature 1 and with the pressure. We see, from the obser 

 vations, that this quality may be regarded as constant throughout 

 a very great part of the thermometric scale. But the same obser 

 vations would lead us to believe that the value of the coefficient 

 in question, is very much more changed by increments of tempera 

 ture than the value of the specific capacity. 



Lastly, the dilatability of solids, or their tendency to increase 

 1 Reference is given to Forbes experiments in the note, p. 84. [A. F.j 

 F. H. 30 



