The cause occupied several days, during which time the court house was continually crowded with an intelligent audience.
The questions were, first, whether the granter was confined to the use of simple apertures of the dimensions mentioned in the deed, when it was apparent from the opinions of men of science, and from the experiments made before the jury, that through such openings it was not possible for him to draw more than 65 and 2/3d per cent. of the water contracted for, (it being a law of nature that when a fluid is drawn from a simple aperture or opening, the stream or vein is contracted so as to form the figure of a cone;) or whether the grantee was entitled, at all events, to his 300 inches of water, and had a right to affix adjutages to overcome this law of nature, and restore things to the state they were supposed to be in by the parties, if, when they contracted, they were ignorant of this principle. Second. The defendant having contracted for as much water as "can pass" through metalic apertures of given sizes, whether he was entitled, provided he did not increase the size of the openings, nor increase the head, so to adjust the adjutages as to draw more water than 300 square inches; for it was proved by another set of experiments that, by reason of the adjutages at the defendant's mill, he had contrived, not only to overcome the vena contracta or contracted vein, but to draw off more water than would have passed through a plain opening if the vena contracta did not exist.
When a vessel is filled with a homogeneous fluid, and it is in equilibrium, all the particles of the fluid are pressed equally in all directions. This law was known to Archimedes, and its knowledge enabled him to detect the fraud committed by the gold smith upon Hiero, King of Syracuse. The first regular work upon Hisdrodynamics was written by Sextus Julius Frentinus, inspector of the public fountains at Rome under the Emperors Nerva and Trajan. He laid down the law, that water which flows in a given time, from a given orifice, does not depend merely upon the magnitude of the orifice, but upon the head or height of the fluid in the vessel. From that period until the 17th century none of the principles upon which this cause depends, were much studied, nor the doctrine of fluids much known. At length Gallileo the astronomer, by his discovery of the uniform acceleration of gravity, paved the way for a rapid improvement in hydrodynamics. Gallileo was acquainted with the fact that water could not be made to rise more than a certain height in a common pump; but he was entirely unacquainted with the reason. His pupil, Torricelli, and his friend, Viviani, discovered that it was owing to the pressure of the external air, and thus the problem was solved. Mariotte, who introduced experimental philosophy into France, was the first who announced that fluids suffer a retardation from the friction of their particles against the sides of tubes; and he shewed that this was the case even though the tubes were made of the smoothest glass. From his works, which were published after his death, in 1684, it appears that though he was thus acquainted with the principle upon which it is explained, he was unacquainted with the vena contracta. About that time this subject began to be much more studied in Italy. Dominic Guglielmini, a celebrated engineer, in 1697, published a very learned work upon the friction and resistance of fluids; and from that period to this the learned of all nations have admitted, that this resistance and retardation of fluids, owing to their friction, did take place in a moving fluid. This work, as connected with the motion of rivers and water in open canals, is one of deep interest in natural philosophy; and it is one, which in this age of improvements, should not be neglected in this country. Sir Isaac Newton, whose capacious mind grasped at every kind of knowledge, struggled hard to detect the reason of this resistance. In his 2nd book of his "Principia," propositions 51, 52 and 53, he lays down certain hypotheses, from which it results, that the filaments (as he calls them,) of a fluid, in a pipe, will be kept back by their adhesion to the sides of the tube, and that the next filaments will be kept back, though in a less degree, by their adhesion to the first filaments, and so on, until the velocity of the fluid will be greatest at the centre. Now if we apply this principle to the discharge of a fluid through a plain aperture, we will perceive that the parts of the water next to the sides of the opening, being liable to the greatest friction, will be the most retarded; and that those in the centre, being liable to the least friction, will be most in advance; and that the friction decreasing gradually from the extremities to the centre, the water will be always flowing in the form of a cone, with the smallest end in advance. This is the exact form of the vena contracta or contracted vein!
When the pipes are very small, this attraction of the sides of the pipes to the fluid operates so as to suspend the whole mass, when it is called capillary attraction. This appears to be the extent to which Newton was acquainted with the laws that govern the vena contracta, at the time he published the first edition of his Principia; but in his second edition, published in 1714, he discloses the doctrine of the contracted vein with his usual intelligence.
Every body is acquainted with the splendid experiments of the Abbe Bossut, which were published successively in 1771, 1786 and 1796, and any one desirous of examining this interesting subject will consult them at large.
Poleni first discovered, that by applying an additional cylindrical pipe to the orifice, of the same diameter, the expenditure of the fluid was increased. This discovery was followed up, first, by Mr. Vince; secondly, by Doctor Matthew Young; and lastly, by Venturi. This last named gentleman published his work on hydraulics in 1798; it was immediately translated and published in Nicholson's Journal of Natural Philosophy, where all the different adjutages, including the one used by the defendant in this action, are accurately drawn and described. They are also noticed, though not in as ample a manner, in Gregory's Mechanics, pages 438, 445 and 447.
From all which it was contended, that every one making a contract, must be presumed to be acquainted with the principles of the vena contracta, and of the methods used to overcome it, and that this party had a right to use these adjutages without incurring the risk of a suit.
[We understand that the suit, the foregoing interesting sketch of which has been obligingly furnished by one of the counsel, is still, in the language of the lawyers, sub judice; the jury having found a verdict subject to the opinion of the court. We are promised a full report of the trial and decision, for a subsequent number.]—ED.
For the Southern Literary Messenger.