THE INTERNAL CONSTITUTION OF BODIES. 463 



(III)" 9=Qo+~^(ffr,,+fq^) 



3 k 



where the sums S are to be extended to all the molecules, including tlie 

 first. 



Tliis last equation determines what the density of the aether must be 

 at each point .r t/ z, in order that it may be in equilibrium when it is 

 submitted to the action of the spherical molecules of matter. The value 

 of this density consists of different terras, each of which is due to a par- 

 ticular molecule, and represents its proper atmosphere. As the quan- 

 tity of aether diffused through the immensity of space may be considered 

 as infinite, the atmosphere formed by each molecule for itself is always 

 the same, and its density is only superadded to that wliich the aether in 

 the same places owes to other causes. According to the nature of the 



molecular actions, the value of the coefficient a = \ / — j^ should 



be considered as very great : hence it follows that the density of each 

 atmosphere will be incomparably greater when quite near or in con- 

 tact with the molecule, and will decrease very rapidly as its distance 

 from the molecule increases. This circumstance enables us to deter- 

 mine with ease, by approximation, the value of q , or the density of the 

 aether at the surface of any molecule whatsoever, on the supposition 

 that the molecules are not too near each other. If, for instance, we 

 make r = S in the term answering to the first molecule, and r, ^ r„ 

 r^ = r.2 . . . 7- = r^^ in the other terms, all these will be very small 

 in comparison with the first, and by neglecting them we shall have 

 very nearly 



4 



whence we derive 



<i = 9o+ 3^(^^ +/q)^' 



• , 4 TT »o 



6. We arc now in a condition to consider the equilibrium of any 

 molecale whatever, such as it is given by the equations (II). 



The (juantity e under the double integral in these equations must be 

 replaced 'oy ^ k q-. Let us represent the coordinates x, y, z, so far as 

 they belong to the points in contact with the surface of the molecule, 

 by X -}- i, y + 7j. z -(- ^ ; x, y, z being the coordinates of its centre : 

 by developing the expression for q, and stopping, because of the small- 

 ncss of the molecule, at the first terms, we shall be able to take 



' \f\ r/v flz 



