452 mossotti on the forces which regulate 



Analysis. 



3. If several material moleculeS; which mutually repel each other, 

 are plunged into an elastic fluid, the atoms of which also mutually repel 

 each other, but are at the same time attracted by the material mole- 

 cules, and if these attractive and repulsive forces are all directly as the 

 masses, and inversely as the square of the distance, it is proposed to 

 determine whether the actions resulting from these forces are sufficient 

 to bring the molecules into equilibrium, and keep them fixed in that 

 state. The object of this inquiry, as may be perceived, is to complete 

 the deductions from the hypothesis of Franklin and iEpinus. It is al- 

 ready known that the conditions of equilibrium which it furnishes, in 

 reference to questions of statical electricity, are in accordance with the 

 phaenomena : it remains to be ascertained, whether the molecular ac- 

 tions which result from it are also in accordance with those which de- 

 termine the interior constitution of bodies. An agreement of this 

 kind would add greatly to the probability that the hypothesis in ques- 

 tion is well founded, and afford us a glimpse of the means by which we 

 should be enabled to consider all physical phaenomena in one and the 

 same point of view. 



Let/ be the accelerative force of repulsion existing among the atoms 

 of the asther at a distance taken as unity; q the density at a point a; 3/ 2, 

 and £ the measure of the elastic force or pressure at the same point, 

 referred to the superficial unit. Let g be the accelerative force of at- 

 traction between the atoms of the aetlier and the matter of the molecules 

 at a distance equal to unity, and ra- the density at the point ij ? of a 

 molecule which we suppose to be possessed of a certain though very 

 small extension. 



By putting 



p^n f q' dx' dy' dz' 



_ /y /. gadldtjd^ 



JJJ {i.^-^r-+(-o-yy-+{^-^)'}^' 



G = 



the triple integral F being extended to the whole space from x', y', z', 

 equal to — 00, as far as x', y\ z', equal to = co (the small parts occu- 

 pied by the molecules being excepted), and the triple integral G being 

 extended to all the values of 0, ij, ?, that answer to the points occupied 

 by the molecule, we shall have for the equilibrium of the aether the 

 equations 



dB IF dG ^ dO, dG., dG, 



dx^-'i'dU^'idl^ ^'ilUc ^'i'dx +'?177+^*'=- 



