I 



1822.] Mr. Herapath's Reply to X. 31 



imagine I could act with such palpable absurdity. Let him look 

 at the passage again, and he will find I have neither expressed 

 nor imphed such a variance of my theory with experiment, much 

 less have I confessed it. 



His seventh paragraph of his first paper charges me with a 

 mathematical error. By the theorem 1 have given, p. 57, AnnaU 



for July, 1816, E a ^^jr^ and -,^, supposing the volume V 



constant. In this theorem, T is the true temperature, E the 

 elasticity, N the number of particles in the air, and W the 

 weight or specific gravity, taking V as constant. Now p being 

 the mass of a particle, W = p N ; and, therefore, E a 



I!J!L* a a T^ N : for in one and the same air, as in 



Prop. 8, we are speaking of, j[9 is a constant quantity. This v^rill 

 satisfy X. that the error does not lie on my side. Indeed from 

 the obviousness of the thing, I was surprised he should have 

 advanced such a charge ; and still more so at his not rectifying 

 it in his last paper. 



X. says : " If the temperature be in the subduphcate ratio of 

 the volume, that when the temperature is nothing, the volume 

 itself is nothing." This, I grant, is a correct inference, and 

 would have weight had I not provided against it. In the enun- 

 ciation of my Prop. 7, of the first paper, I have distinctly drawn 

 my inference on the supposition of ** the particles being indefi- 

 nitely small." Again, in p. 103 of the last volume, I have said : 

 •^ Had Mr. Dalton applied his views of fluid expansion to gases," 

 (that is, that the squares of the temperature are as the increments 

 of expansion from their greatest density), he would have anti- 

 cipated the general law of temperature I have given." These 

 and other passages of the kind published before X.'s first paper 

 appeared, clearly show that I was perfectly aware of what 1 was 

 writing, and did not write without thinking. It is strange, there- 

 fore, that X. should have drawn the inference he has about 

 *' nonentities and nascent existencies." But let us take X. on 

 his own grounds ; and supposing I had not had an eye to this point • 

 of greatest density, let us see how much my determination of 

 the real zero might err " on that account. By our best experi- 

 ments, steam is about 1400 times lighter than water, and nine 

 times heavier than hydrogen. Now if hydrogen be 50 times 

 lighter than phosgene gas, we may certainly conceive it possible 

 for a gas to be eight or ten times lighter than hydrogen. In 

 such a case, the volume of the body in the aeriform state would 

 be in round numbers about 100000 times greater than in the 

 liquid or solid, supposing the same law to hold good as in the 

 condensation of vapour. Again, experiment teaches us that 

 the same laws of expansion and contraction by temperature are 

 true under one compression as under another. Let us, therefore, 

 instead of a compression of 30 inches of mercury to the inch 



