87 



state of motion. It might be doubted, therefore, whether the con- 

 clusions arrived at were applicable to any substances except gases, 

 or very limpid liquids, in which the mutual actions of the atoms are 

 similar in all directions. 



To remedy this defect the present paper has been prepared, in 

 which no definite supposition is made respecting the arrangement of 

 the atomic centres, the distribution of their atmospheres, or the 

 form of the orbits which the particles of those atmospheres describe. 

 If the hypothesis, therefore, is a sound one, the conclusions are 

 applicable to all substances. It will be seen that they are all con- 

 sistent, and for the most part identical with those deduced from the 

 more limited supposition. The most important are the following : — 



Let Q denote the mechanical value of the quantity of heat, that 

 is to say, the mechanical power corresponding to the vis-^iva of the 

 molecular revolutions, in unity of weight of a substance. Let h be 

 the specific elasticity of the atomic atmosphere of the substance ; k, 

 a specific constant depending on the nature of the substance ; r, its 

 absolute temperature as measured by a perfect-gas thermometer, and 

 reckoned from a point 274°* 6 centigrade = 494°-28 Fahrenheit, be- 

 low the temperature of melting ice ; and x, a constant depending on 

 the thermometric scale, and the same for all substances in nature. 

 Then 



h k 



— is the real specific heat of the substance. 



The expansive pressure of any body is composed of two parts ; 

 one depending jointly on density and heat, the other a function of 

 density alone. Let P be the total expansive pressure, p the part 

 depending jointly on density and heat, and V the volume of unity 



of weight of the substances, so that =^ is its mean density. Then 



P=p +/(V) 

 Let (/, be the weight of the atmospheric part of an atom ; M, the 

 total weight ; G^, a certain function of the density ; and G'^, Q'\, 

 &c., the successive differential co-efficients of that function with re- 

 spect to the hyperbolic logarithm of V. Also let 



„ X G, ^2 G', ^ x^ G'\ . . . . 

 H, = i K-^ H o-^ — &c., ad. mf. 



