1821.] Further Remarks upon Mr. Herapath's Theory. 391 



allude to ; and I shall not trouble your readers with further par- 

 ticulars. 



I will now proceed to a few further remarks, which I have been 

 led to make partly from reading the continuation of Mr. H.'s 

 communications, since the date of my former paper (which was 

 sent in hopes of having it inserted in the Annals for August), 

 and partly because some of my friends have thought that my 

 observations on Mr. H.'s use of the term temperature needed a 

 little further explanation. The substance of what I wish to ob- 

 serve respecting his law of temperature will, I hope, be distinctly 

 understood if I state it thus : 



He finds that, within a certain range, gases go on expanding 

 nearly as the squares of a certain set of numbers. 



According to his theory he considers it proved that gases 

 expand as the squares of their temperature ; that is, defining the 

 temperatures to be the momentum of their particles. He, there- 

 fore, concludes, that that set of numbers represents the tempera- 

 tures thus defined. 



Now within the same range, the expansions are also nearly as 

 the simple ratio of another set of numbers : that set of numbers 

 are the common Fahrenheit temperatures ; therefore, within this 

 range, little evidence is gained either for or against his theory ; 

 and this range includes the temperatures at which almost all 

 experiments are tried. 



Again : he finds that the set of numbers first alluded to are 

 such as are obtained in a given way from the Fahrenheit tem- 

 peratures : hence he finds a point in Fahrenheit's scale which 

 corresponds to a temperature of 0, or a point at which there will 

 be no motion in the particles of a gas, and at which the volume 

 of the gas will be also. 



If experiments agree with this progression of temperatures, 

 what they prove is this, that the zero is fixed at such a point of 

 Fahrenheit as to make the law of temperature agree with experi- 

 ments within a certain range ; that is, that the one hypothesis is 

 so framed as to be consistent with the other. They prove that 

 the theory of temperature agrees with observation, provided the 

 amount of observation be measured according to a standard pre- 

 viously fixed, and fixed upon the assumption of that theory ; for 

 he is led to fix the zero where he does, by taking the ratio of the 

 volumes of gas at the temperatures of freezing and boiling water; 

 and assuming that the law of expansion and temperature holds 

 good down to that point where the progression would end. 



Unless it can be proved that such a state as absolute cold 

 really exists, it cannot be admitted that these numbers represent 

 the real temperatures, or absolute quantities of heat in the gases, 

 or absolute intensities of motion reckoned from a point of abso- 

 lute rest in their particles. They will only measure the temper- 

 ature above a certain point, and not above real zero. None of 

 the experiments which Mr. II. has mentioned prove the existence 



