2. FLUIDS have been already treated of in general, with respect to the effect they have upon solid bodies moving in them[262]; now we must consider them in reference to the operation of the power of gravity upon them. By this power they are rendered weighty, like all other bodies, in proportion to the quantity of matter, which is contained in them. And in any quantity of a fluid the upper parts press upon the lower as much, as any solid body would press on another, whereon it should lie. But there is an effect of the pressure of fluids on the bottom of the vessel, wherein they are contained, which I shall particularly explain. The force supported by the bottom of such a vessel is not simply the weight of the quantity of the fluid in the vessel, but is equal to the weight of that quantity of the fluid, which would be contained in a vessel of the same bottom and of equal width throughout, when this vessel is filled up to the same height, as that to which the vessel proposed is filled. Suppose water were contained in the vessel A B C D (in fig. 109.) filled up to E F. Here it is evident, that if a part of the bottom, as G H, which is directly under any part of the space E F, be considered separately; it will appear at once, that this part sustains the weight of as much of the fluid, as stands perpendicularly over it up to the height of E F; that is, the two perpendiculars G I and H K being drawn, the part G H of the bottom will sustain the whole weight of the fluid included between these two perpendiculars. Again, I say, every other part of the bottom equally broad with this, will sustain as great a pressure. Let the part L M be of the same breadth with G H. Here the perpendiculars L O and M N being drawn, the quantity of water contained between these perpendiculars is not so great, as that contained between the perpendiculars G I and H K; yet, I say, the pressure on L M will be equal to that on G H. This will appear by the following considerations. It is evident, that if the part of the vessel between O and N were removed, the water would immediately flow out, and the surface E F would subside; for all parts of the water being equally heavy, it must soon form itself to a level surface, if the form of the vessel, which contains it, does not prevent. Therefore since the water is prevented from rising by the side N O of the vessel, it is manifest, that it must press against N O with some degree of force. In other words, the water between the perpendiculars L O and M N endeavours to extend itself with a certain degree of force; or more correctly, the ambient water presses upon this, and endeavours to force this pillar or column of water into a greater length. But since this column of water is sustained between N O and L M, each of these parts of the vessel will be equally pressed against by the power, wherewith this column endeavours to extend. Consequently L M bears this force over and above the weight of the column of water between L O and M N.