198 LECTURE XXI. 



face of a fluid must always be perpendicular to the direction of the joint t 

 results of all the forces which act on it ; and since the earth turns round 

 on its axis, the centrifugal force resulting from its motion is combined with 

 that of gravity, in determining the position of the general surface of the 

 ocean. 



A similar combination of a centrifugal force with gravitation may be 

 observed when a bucket is suspended by a rope, and caused to turn round 

 on its axis by twisting the rope : the direction of the joint forces is such 

 that the surface, in order to be perpendicular to it, must assume a parabolic 

 form. When also any number of different fluids are made to revolve in 

 the same manner, or when they are inclosed in a glass globe and turned by 

 means of the whirling table, the surfaces which separate them, acquire 

 always the forms of parabolic conoids, when the axis remains in a vertical 

 position ; but if the axis be in any other position, the situation of the sur- 

 face will be of more difficult determination. (Plate XIX. Fig. 240.) 



In all these cases the equilibrium is stable ; for if any part of the fluid 

 be raised above the surface, it will immediately tend to return to its level. 

 But if a heavier fluid were contained in a bent tube or siphon, with its 

 legs or branches opening downwards, and immersed in a lighter fluid, the 

 equilibrium would be tottering, since, if it were once disturbed, it would 

 never be restored. (Plate XIX. Fig. 241.) 



From these principles, we may infer that the pressure of a fluid on every 

 particle of the vessel containing it, or of any other surface, real or im- 

 aginary, in contact with it, is equal to the weight of a column of the fluid 

 of which the base is equal to that particle, and the height to its depth below 

 the surface of the fluid. Thus if we have a vessel of water one foot deep, 

 each square foot of the bottom will sustain the pressure of a cubic foot of 

 water, or nearly 1000 ounces : if we have a vessel of mercury an inch in 

 depth, each square foot will sustain a pressure of one twelth part of a cubic 

 foot of mercury, or 1130 ounces ; the atmosphere presses on each square 

 foot of the earth's surface with a force of about 34,000 ounces, which is 

 equivalent to the pressure of a column of mercury 30 inches high. The 

 pressure of the water on a small portion of the lowest part of the side of the 

 vessel containing it, is also equal to the weight supported by an equal por- 

 tion of the bottom ; but we cannot estimate the force sustained by any 

 large portion of the side, without considering the different depths below the 

 surface at which its different parts are situated. 



It is obvious that if we conceive a fluid to be divided by an imaginary 

 surface of any kind, the particles contiguous to it are urged on either side 

 by equal forces, the fluid below resisting them, and pressing them upwards 

 with as much force as the fluid above presses them downwards, their own 

 weight being comparatively inconsiderable, for without this equality of 

 pressures they could not possibly remain at rest. And if we employ a 

 vessel of such a form as to occupy the place of any superior portion of the 

 fluid, the pressure against that part of the vessel which is thus substituted 

 will be the same that before supported the weight of the fluid removed ; 

 and in order that all may remain in equilibrium, the vessel must itself 

 exert an equal pressure on the fluid below it ; so that the pressure on the 



