Mathematics to Chemistry. 275 



force proportional to its distance from the centre s; hence, 

 if the atom a were left to the action of this resultant, un- 

 disturbed by any other influence or obstacle, it would move 

 to the centre by a velocity determined by this law. The 

 same reasoning applies to any other atom h, in the sphere ; 

 therefore, both would, in the absence of all obstacles, or 

 other force on each other, approach, and at the same time 

 meet in the centre, and always their distances from each 

 other would be proportional to that of either from the 

 centre : but this measures their accelerating force, which 

 is, therefore, as their distance. 



But, besides the mutual actions, which alone would pro- 

 duce the above motions, the atoms a and h act independently, 

 and directly on each other, by an accelerating force, in- 

 versely, proportional to the square of their distance, 

 (1st prin.) ; this must, therefore, be compounded with the 

 former; thus, the force between them varies as the dis- 

 tance, directly, and as the square of the distance, inversely; 

 that is, as the distance inversely. 



Again, since one of the centres of every two contiguous 

 atoms is within the sphere of repulsion of the other ; the 

 force, here investigated is a repelling force ; which also ap- 

 pears from this, that if the compressing force were removed 

 the atoms would separate : hence, the proposition is true, 

 when the ethereal atoms are of one kind. But, if any num- 

 ber of these be removed, and their places supplied by other 

 atoms, in such manner, that exactly the same equilibrium 

 may be maintained, we shall still have the same conclusion. 



Prop. 3. If the absolute forces or spheres of repulsion 

 of the tenacious atoms be increased or diminished, the 

 resultant repelling force, as determined in the last pro- 

 position, will not be altered : provided that none of the 

 atmospherules of tenacious atoms are penetrated by the 

 centres of others, so as to displace the atmospherules on 

 the contiguous sides ; that is, on the parts between the two 

 tenacious atoms. 



For their tendency to separate depends, not on their 

 absolute forces, or spheres of repulsion, as is evident from 

 the last proposition ; but on the law of force, and the given 

 pressure, and these remaining, the repelling force between 

 the atoms a and h will also remain unaltered. 



T 2 



