64- Mr. Herapatli on M. Laplace's Thcorij 



will pass over. Granting that the caloric of the surrounding 

 molecules acts in some way by its re[nilsion to make the central 

 molecule radiate, it is plain by the course M. Laplace himselt' 

 takes, that he considers this action proportional to the quantity 

 of caloric acted on, and to the intensity of repulsion of the 

 surrounding caloric. The radiation must dierefore be as 

 cxgcf {>•) nearly * ; r being the distance of two molecules, and 

 'P (r) the intensity of repulsion of a particle of caloric at the 



distance r. But a being some constant r = ^—', find there- 

 fore by M. Laplace's own principles his equation 2 should be, 



§c^M^/7)=?'^(0 (A) 



instead of, qr = qn{t). 



In the third part of his paper, M. Laplace introduces the 

 function ^ (r); but drops it in the final equation without giving 

 any reason whatever. From what I can perceive, he seems to 

 involve it in the constant coefficient q. If so, it appears to me 

 to be utterly repugnant to his own principles and definition of 

 this supposed constant; for he distinctly tells us that q is 

 " un facteur constant dependant de la nature de la molecule 

 ou du gaz;" and therefore it ought to be the same for every 

 density of the same gas ; since neither the nature of the mole- 

 cule or gas is changed by a change of density. 



It is the error of neglecting this function which has enabled 

 the marquis to bring out his conclusions independently of the 

 law of repulsion in his 2nd part, and of the laws of repvdsion 

 and attraction in the 3rd part — conclusions which at the first 

 glance of his paper forcibly struck me as strongly indicative 

 of errors somewhere. That we are not justified in neglecting 

 that part of A which depends on ^y, will appear from the con- 

 sideration, that a molecule of gas is made, by M. Laplace's 

 views, to radiate its caloric by the repulsion of the caloric of 

 other molecules surrounding that molecule. And as he assumes 

 that this sphere of repulsion is insensibly small, the entire 

 action of the whole molecules within this sphere must be some 

 function of r, the distance of two molecules; and therefore 

 some function of the density q. 



Equation A combined with 1, would produce results at 



* The correct value of the factor depending on (p{r) is 2'7rfr''-(prdr taken 

 from r-=o to r=io . 



I mi;^lit here make a remark very useful in investigations of this kind, and 

 which I do not remember to have seen elsewhere. If <p (r) be such a func- 

 tion of r that it is sensible only with insensible values to r; and if y(') he 

 any other function of r, finite always when r is finite, and such that the 

 value of/(c) x (p (/) decreases as )• increases, //(;■), (p {>■). d r=o when r=ao . 



variance 



