OF NATURAL PHILOSOPHY. 93 towards the parts on which B lies ; arid in free spaces, to go forward in infmitiim with a motion perpetually accelerated ; which is absurd and contrary to the first Law. For, by the first Law, the system ought to per severe in its state of rest, or of moving uniformly forward in a right line : and therefore the bodies must equally press the obstacle, and be equally attracted one by the other. I made the experiment on the loadstone and iron. If these, placed apart in proper vessels, are made to float by one another in standing water, neither of them will propel the other ; but, by being equally attracted, they will sustain each other's pressure, and rest at last in an equilibrium. So the gravitation betwixt the earth and its parts is mutual. Let the earth FI be cut by any plane EG into two parts EGF and EGI, and their weights one towards the other will be mutually equal. For if by another plane HK, parallel to the former EG, the greater partFJ EGI is cut into two parts EGKH and HKI. whereof HKI is equal to the part EFG, first cut oft', it is evident that the middle part EGKH, will have no propension by its proper weight towards either side, but will hang as it were, and rest in an equilibrium betwixt both. But the one extreme part HKI will with its whole weight bear upon and press the middle part towards the other extreme part EGF : and therefore the force with which EGI, the sum of the parts HKI and EGKH, tends towards the third part EGF, is equal to the weight of the part HKI, that is, to the weight of the third part EGF. And therefore the weights of the two parts EGI and EGF, one towards the other, are equal, as I was to prove. And in deed if those weights were not equal, the whole earth floating in the nonresisting aether would give way to the greater weight, and, retiring from it, would be carried off in infinitum. And as those bodies are equipollent in the congress and reflexion, whose velocities are reciprocally as their innate forces, so in the use of mechanic instruments those agents are equipollent, and mutually sustain each the contrary pressure of the other, whose velocities, estimated according to the determination of the forces, are reciprocally as the forces. So those weights are of equal force to move the arms of a balance; which during the play of the balance are reciprocally as their velocities upw ards and downwards ; that is, if the ascent or descent is direct, those weights are of equal force, which are reciprocally as the distances of the points at which they are suspended from the axis oi the balance : but if they are turned aside by the interposition of oblique planes, or other ob stacles, and made to ascend or descend obliquely, those bodies will be equipollent, wThich are reciprocally as the heights of their ascent and de scent taken according to the perpendicular ; and that on account of the determination of gravity downwards.