ON PRESSURE AND EQUILIBRIUM. 45 



he could only have displaced the earth insensibly by the properties of his 

 machines ; and without any such support, when he threw rocks upon the 

 ships of Marcellus, he actually caused the walls of Syracuse and the island 

 of Sicily to move northwards, with as much momentum as carried his pro- 

 jectiles southwards against the Roman armaments. 



LECT. VI. ADDITIONAL AUTHORITIES. 



Centre of Gravity. Wallis de Centre Gravitatis Hyperbolae, Ph. Tr. 1672, p. 

 5074. Roberval on the Centres of Gravity of Solids, Hist, et Mem. de Par. vi. 270, 

 282. Lahireon the Motion of the Centre of Inertia, ibid. ix. 175. Laura Bassion 

 ditto, Com. Bon. iv. O. 74. Varignon on the Centre of Gravity of Spheres, 

 Hist, et Mem. de Paris, x. 508. Clairaut on Finding the Centre of Gravity, ibid. 

 1731, p. 159. Bossut on the Centres of Gravity of Cycloidal Surfaces and Solids, 

 Mem. Presentes, Paris, iii. 603. Gr. Fontana on the Axis of Equilib. and the 

 Centre of Gr. Atti dell' Academia di Siena, 4to, vi. 177. L'Huillier's Theorem 

 respecting the Centre of Gravity, Nov. Act. Petrop. 1786, 4to, H. 39. Kramp on 

 the Centre of Gravity of Sph. Triangles, Hindenburg's Archiv. ii. 296. 



LECTURE VII. 



ON PRESSURE AND EQUILIBRIUM. 



WE have now examined the principal cases in which a simple force is 

 employed in the production of motion ; it is of equal consequence to attend 

 to the opposition of forces, where they prevent each other's action. A 

 force counteracted by another force, so that no motion is produced, becomes 

 a pressure : thus we continually exert a pressure, by means of our w r eight, 

 upon the ground on which we stand, the seat on which we sit, and the bed 

 on which we sleep ; but at the instant when we are falling or leaping, we 

 neither exert nor experience a pressure on any part. 



It was very truly asserted by the ancients, that pressure and motion are 

 absolutely incommensurable as effects ; for according to the definition of 

 pressure, the force appears to be what is called in logic a potential cause, 

 which is not in a state of activity : and since an interval of time must elapse 

 after the removal of the opposite force, before the first force can have 

 caused any actual motion, this effect of a finite time cannot with justice be 

 conceived to bear any proportion to the pressure, which is as it were a 

 nascent effect only. It is true that a large weight pressing on a spring, 

 may keep it bent, in exactly the same place into which a smaller weight, 

 falling on it with a certain velocity, would inflect 'it : but, to retain a 

 spring in a certain position, and to bend it into that position, are effects 

 absolutely incommensurable ; the one being a measure of the constant 

 repulsive force of the spring, bent to a certain point, the other of the sum of 

 the effects of the same spring in various degrees of flexure, for a certain 



