-I 



Functions, Disgregation, and Real Specific Heat. 409 



in which v is the volume of the substance, and p its elastic 

 pressure. 



4. In the value of the metamorphic function F which I gave 

 in the Transactions of the Royal Society of Edinburgh for 

 1850-51, I proceeded on the supposition that every substance 

 is capable of passing into the state of perfect gas at every tem- 

 perature. If such is the fact, the value of F is as follows : — 



** ; « 



5. Professor Clausius points out that, if the substance under 

 consideration is at any temperature incapable of passing into the 

 state of perfect gas, the preceding value of the integral of equa- 

 tion (2) is incomplete, and requires the addition of a function of 

 the temperature to complete it. The value which he gives in 

 units of mechanical work for the function which he calls " dis- 

 gregation " (being that which corresponds, in his researches, to 

 the " Metamorphic Function " in mine) is as follows, 



HS-H^ • • • • (4) 



in which A is the thermic equivalent of a unit of work (or reci- 

 procal of Joule's mechanical equivalent of a unit of heat), and I 

 denotes the internal work done during change of temperature, 

 at the volume corresponding to the lower limit of integration 

 with respect to dv. 



6. The first term of equation (4) is what constitutes the differ- 

 ence between my value of the " metamorphic function" F and 



Professor Clausius' s value of the " dis&Tegation " -r- Professor 



° D A 



Clausius observes that, for substances which at all temperatures 



are capable of passing into the perfectly gaseous state, that term 



vanishes, and the two functions become identical ; but that for 



substances which at any temperature are incapable of passing 



into the perfectly gaseous state, the term in question has some 



value, and the two functions are no longer absolutely identical. 



I admit that Professor Clausius is right in both those assertions ; 



and that, in assigning the value to F which is given by equation (3), 



I did not contemplate the existence of substances which at any 



temperature are incapable of passing into the perfectly gaseous 



condition. 



7. Whether such substances exist or not is a question which 

 experiment alone can decide. I cannot agree, however, with 

 Professor Clausius in thinking it difficult to conceive that such 

 substances as iron can pass into the perfectly gaseous state at 

 low temperatures. Iron, copper, tin, zinc, and lead at low tem- 



Phil. Mag. S. 4. Vol. 30. No. 205. Dec. 1865. 2 E 



