246 Researches in the Theory and Calculus of Operations. 



been placed by the Creator in this status of eternal gene- 

 ration, production, destruction and reproduction (or action, 

 production and restitution) in which man finds it in this our 

 present world, and extends the same law in contemplation 

 to the remotest bounds of the telescopic universe. 



5. Place a homogeneous sphere (fig. 4), of unit diameter 

 and unit mass, upon a smooth plane horizontal table. It re- 

 mains at rest, exactly as if it were completely inert; and yet 

 it is the embodiment of nothing less than an infinite force, 

 that would require infinite power to annihilate it; but the 

 equal components of this infinite force are mutually ba- 

 lanced in pairs by opposition of direction, and the resultant 

 is mathematical equilibrium H =0 (Oken). On the ho- 

 rizontal line passing through the centre of the sphere, the 

 sum of the energies of the atoms on the right hand radius 

 tend to move the body in that direction, but are equally 

 opposed by the energies of the atoms of the left hand radius 

 exerted in the direction opposite to the former ; and so of 

 every other pair of opposing radii in the sphere. The op- 

 posing radii cannot.be parted at the centre, because the 

 central atom holds to those on all sides with the highest in- 

 tension; so there is no call for the hooks of Democritus. 

 The repulsive force of a solid body is infinite at the point 

 of contact, and null at a sensible distance therefrom. 



The ball being in repose, let a unit of impulsive force be 

 applied at A, directed through the centre ofgravity O. Dur- 

 ing the short interval or instant of time consumed in the 

 impulsive contact, the atomic forces which were pulling from 

 O in the direction OA and equilibrated by the equal atomic 

 forces which were pulling from in the opposite direction 

 OA', is destroyed by the impulsion, leaving the latter amount 

 OA' unequilibrated, and therefore ready to take effect in 

 moving the ball in the left hand direction at the beginning 

 of the next instant of time, and thus the motion is begun. 

 Spherical equilibrium is instantly restored from the centre 

 to both extremities of the diameter, by the emanative con- 



