By Professor Pell. 9 



perature, the whole heat per atom will be the same for both ; 

 and if <t and o-j be their specific heats at the absolute zero of 

 temperature, we have 



M cr = Ml 0-1 

 which acords with what is called the constancy of the atomic heat 

 of simple substances in the solid state. For such substances we 

 should have Mtr = x, where x is constant. If it were possible for 

 two atoms M and Mi to become united into a single atom, and s 

 were the absolute specific heat of the compound, we should have 

 (M + Ml) s = X. But when two equivalents are chemically com- 

 bined it is found that (M + MJ s = 2k; and if there be^ of one 

 and q of the other 



[pM. + gMi) s = [p + q) 71 

 This is what might be inferred from the above considerations, for 



■^- i — ^ is the average mass of an atom of the compound, and 



^ i — ^ s, the average heat per atom to produce a rise of 1° 



p + q 



from the absolute zero, and therefore equal to x. 



This subject is very fully treated in a valuable memoir by Kopp 

 in the Philosophical Transactions. He points out that the circum- 

 stance that K is nearly the same for most simple solids, does not 

 indicate necessarily that they are really simple, but that they are 

 of the same order of composition. There is some difiiculty in the 

 theory however, for Kopp remarks, that the known change of 

 specific heat with change of temperature is not sufficient to 

 account for the observed differences in the values of x, even for 

 those substances which nearly satisfy the law. This difficulty 

 disappears, I think, when we observe that the quantity estimated 

 and recorded as the atomic heat is 



M 0- (1 + £t), 

 and although e is very small, it is different for different sub- 

 stances, and T being the absolute temperature is considerable. If 

 we had the means of reducing the observations with certainty to 

 the absolute zero, it is probable that the discrepancies would 

 disappear. 



The most general case which I have yet attempted to investigate 

 in connection with the motion of atoms, is that o^n atoms in a 

 straight line. This is far, of course, from being an arrangement 

 which the atoms of a molecule would really assume and main- 

 tain ; but it is a theoretically possible combination, and having 

 some generality, its consideration may enable us to form by 

 analogy, an idea of the nature of molecular arrangements, and lead 

 the way to something better. 



