C'or. 3. The pressure exerted upon the sides of a vessel, perpenclicular.to its base, is equal to the weight of a rec tangular prism of the fluid, whose height is equal to that of the fluid, and whose base is a parallelogram, one side of which is equal to the height of the fluid, and the other to half the perimeter of the vessel.
Cor. 4. The pressure against one side of a cubical ves sel is equal to half the pressure against the bottom ; and the pressure against the sides and bottom together, is equal to three-times the pressure against the bottom alone. Hence, by Cor. 1. the pressure against both the sides and bottom together, is equal to three times the weight of fluid in the vessel.
Cor. 5. The pressure exerted upon the surface of a hemisphere full of fluid, is equal to the product of that surface multiplied by its radius.
Car. 6. The pressure sustained by different parts of the sides of a vessel are as the squares of their depths below the surface. Hence, these pressures will be represented by the ordinates of a parabola, when the depths are repre sented by its abscissa.
The preceding experiments of our author are not only the most numerous, but the most correct, that have been made on capillary attraction, and have been appealed to by La Place as a proof of the accuracy of his own theory. The opinions of Hawksbee respecting the cause of capil lary attraction were equally correct. He ascribed the as cent of the fluid to the attraction of the whole surface of the tube ; and he considered the attractive force of the glass as extending, like the refracting force, only to insensible distances.
In the year 1718, Dr James Jurin communicated to the Royal Society his Inquiry into the Cause of the Ascent and Suspension of Water in Capillary Tubes. This paper con tains many new and ingenious experiments ; but its author was unfortunate in the erroneous explanation which he gives of the phenomena. " Since in every capillary tube," says he, " the height to which the water will spontaneously ascend is reciprocally as the diameter of the tube, it fol lows that the surface, containing the suspended water in every tube, is always a given quantity ; but the column of water suspended is as the diameter of the tube ; therefore, if the attraction of the containing surface be the cause of the water's suspension, it will follow that equal causes pro duce unequal effects, which is absurd." " Having shewn," continues he, " the insufficiency of this hypothesis, I come now to the real cause of the phenomenon, which is the at traction of the periphery or section of the surface of the tube to which the tipper surface of the water is contiguous and collet es. For this is the only part of the tube from which the water most recede upon its subsiding, and con sequently the only one which by the force of its cohesion or attraction opposes the descent of the water. This is also a cause proportional to the effect which it produces, since that periphery and the column suspended are both in the same proportion as the diameter of the tube." Dr Jurin afterwards accounts for the spontaneous ascent of the wa ter. lie supposes that the water which first enters a ca pillary tube, when its orifice is immersed in the fluid, has its gravity taken off by the attraction of the periphery with which its upper surface is in contact : Hence it must ne cessarily rise higher, partly by the pressure of the stag nant water, and partly by the attraction of the periphe ry immediately above that which is already contiguous to it. These opinions Dr Jul in endeavoured to support by the experiment represented at E, F, G in Fig. 5. of Plate
CX. and described under CAPILLARY ATTRACTION• (See Phil. Trans. vol. xxx. p. 739.) In a subsequent pa per he inquires into the cause of the suspension of water in tubes of glass, and seems to adopt the opinion, that the cohesion may depend on the pressure of a medium subtle enough to penetrate the receiver. " For though such a medium," says he, 66 will pervade the pores of the water as well as those of the glass, yet it will act with its entire pressure on all the solid particles, if I may so call them; of the surface of the water in the cistern ; and whereas so many of the solid particles of the water in the tube, as hap pen to lie directly under the solid particles of the water above them, will thereby be secured from this pressure, and consequently there will be a less pressure of this me dium on any surface of the water in the tube below the capillary, than in an equal surface of the water in the cis tern ; so that the column of water suspended in the tube may be sustained by the difference between these two pressures." The subject of capillary attraction was treated at great length by George Bernhard Bullfinger, in a dissertation en titled De Tubulis dissertatio experimentalis, which appeared in the Commentarii Acad. Petropolitance for 1727. This paper contains an examination of the different hypotheses which had been employed to explain the pheno menon of capillary attraction, and several new experiments illustrative of his own opinion. He found that the relative ascent of spirit of wine, red wine, and water, were as 4,•7 and 12. He seems, upon the whole, to prefer the hypo thesis of Dr Jurin, although he states a number of difficul ties which attend it. Dr Jurin replied to this paper of Bullfinger's in the volume of the Commentarii Acad. Pe trolzolitanx for 1728; and his paper is published with the annotations of Bull finger. After examining all the objec tions which had been stated, and apparently to the satisfac tion of Bullfinger, Dr Jurin begs that he will no longer con sider his explanation as a hypothesis, but as a true and established theory.* When M. IluIllinger exhibited his experiments before the Academy or St Petersburgh, his colleague, the cele brated Daniel Bernoulli, who was at that time unacquaint ed with the speculations of his uncle on the same subject, proposed a new theory of capillary attraction. In order to get over the difficulty respecting the ascent of the water under the receiver of an air pump, he ascribed the pheno menon, not to the unequal pressure of the air, as his uncle had done, but to the unequal pressure of an ethereal fluid. He considered the base of the Iluicl as contiguous to the surface of the water ; but he supposed that it was not so full at the sides of the pipe as in its axis ; or, in other words, that the e=ther stood at a greater distance from the glass than water did, or was less dense in the neighbour hood of the glass. This effect he attributed to the parti cles of the tether being greater than those of water. This hypothesis, which differs in no respect from that of James Bernoulli, excepting in the substitution of e=ther for air, has the advantage of surmounting the difficulty already mentioned. But, in other respects, it is more inadmissible. Daniel Bernoulli attempted to chew that it explained many of the common experiments, and that the proportion be tween the magnitude of the particles of different fluids might be deduced from the height of their ascent in capil lary tubes. He inferred, from a rude and erroneous expe riment, that the particles of mercury were twice as small as those of water.