THE INTERNAL CONSTITUTION OF BODIES. 451 



tlie latter be spherical, they are surrounded by an atmosphere the den- 

 sity of which decreases according to a function of the distance which 

 contains an exponential factor. The diiferential equation which deter- 

 mines the density being linear, is satisfied by any sum of these functions 

 answering to any number of molecules. Whence it follows that their 

 atmospheres may overlay or penetrate each other without disturbing 

 the equilibrium of the sether. Proceeding in the next place to the con- 

 ditions of equilibrium of the molecules, I observed that, for a first ap- 

 proximation (which may be sufficient in almost all cases), the recipro- 

 cal action of two molecules and of their surrounding atmospheres is 

 independent of the presence of the others, and possesses all the charac- 

 teristics of molecular action. At first it is repulsive, and contains an 

 exponential factor which is capable of making it decrease very rapidly : 

 it vanishes soon after, and at this distance two molecules would be as 

 much indisposed to approach more nearly as they would be to recede 

 further from each other ; so that they would remain in a state of steady 

 equilibrium. At a greater distance the molecules would attract each 

 other, and their attraction would increase with their distance up to a 

 certain point, at which it would attain a maximum : beyond this point 

 it would diminish, and at a sensible distance would decrease directly as 

 the product of their mass, and inversely as the square of their distance. 



This action, possessing all the properties witii M'hich we can pre- 

 sume that molecular action is endued, is the more remarkable as it has 

 been deduced from those forces only whose existence was already ad- 

 mitted by philosophers, and whose law is characterized by such extra- 

 ordinary simplicity. When tested in the explanation of the varied 

 phaenomena which are proper to it, it must lead, in case of failure, to 

 the exclusion of those forces from amongst physical principles ; or, in 

 case of success, establish their reality ; and thus mark in a striking man- 

 ner the admirable ceconomy of nature. 



To apply the formulae which we have found, for the purpose of re- 

 presenting molecular action, to the phaenomena of the interior consti- 

 tution of bodies, requires methods of calculation which are not yet 

 developed, and which must become still more complicated when the 

 arrangement of the molecules, their form and their density, are taken into 

 consideration. I have thought it advisable, however, in consideration 

 of tin; use to which it might be applied by able geometers, not to post- 

 pone the publication of this mode of viewing molecular action. It is a 

 subject which appears to me entitled to the gi'eatest attention, because 

 the discovery of the laws of molecular action must lead mathematicians 

 to estaljlish molecular mechanism on a single principle, just as the dis- 

 covery of the law of universal attraction led them to erect on a single 

 basis the most splendid monument of human intellect, (he mechanism of 

 the heavens. 



