CHAP. IV. Origin and Progress of Hydrodynamics. Ir the science of mechanics, which relates to solid bodies, were so slowly formed, that of hydrodynamics must have been much more slowly established: for, supposing that the conditions of equilibrium and motion for any system of solid bodies were geometrically determined, the same method could not be applied directly to a fluid mass, the elements of which are not known, either with regard to number, figure, or magnitude. It was necessary, therefore, that experience, or some property peculiar to fluids, fhould form a bridge of communication as it were from one science to the other. Then, the fundamental bases of hydrodynamics being once established, the problems depending on them are capable of being referred to geometry, and to the general laws of equilibrium and motion, like those of the mechanics of solids. Archimedes is the first, likewise, who established the fundamental laws of hydrostatics, or that part of hydrodynamics which treats on the equilibrium of fluids. The work he wrote on this subject has reached us only through the medium of an arabic version, whence it has been translated into latin. In this state it is entitled De Humido Insidentibus, of Bodies floating on a Fluid,' and is divided into two books. Archimedes assumes as a fundamental principle, that, the molecules of a fluid being supposed equal, and equally equally heavy, they will remain each in it's place, or all the mass will be in equilibrio, when each particular molecule is equally pressed upon in every direction. This equality of pressure, on which he makes the state of equilibrium essentially depend, is demonstrated by experiment. The author afterward examines the conditions, which are requisite to produce and preserve the equilibrium of a solid floating on a fluid. He shows, that the centre of gravity of the whole body, and that of the immersed part of it, must be in the same vertical line; and that the whole weight of the body is to the weight of the quantity of fluid displaced, as the specific gravity of the fluid is to that of the floating body. This general theory he illustrates by various examples taken from the triangle, the cone, the paraboloid, &c. We readily perceive by the 7th proposition of the first book, that two bodies equal in bulk, and immersed in a fluid lighter than either of them, lose equal quantities of their weight; or inversely, that two bodies, when they lose equal quantities of their weight in a fluid, are of equal volume. I cite this theorem, because it is the general opinion of mathematicians, that Archimedes employed it to solve a well known problem, proposed to him by king Hiero on the following occasion. For this monarch a goldsmith of Syracuse had made a crown, which, by the terms of the agreement, was to have been of pure gold. But the king suspecting, that silver had been mixed with it, had recourse to Archimedes, to discover the truth without injuring the crown. It is very probable, that Archi medes medes accomplished it in this manner. He began by forming two ingots, one of pure gold, the other of pure silver, each of them equal in bulk to the crown; weighing the three bodies, that is the crown and the two ingots, one after the other in water, and diminishing or enlarging the ingot of gold, and the ingot of silver, till each lost in water the same weight as the crown. This preliminary operation being performed, Archimedes weighed the same three bodies separately out of the water, or in the air and having found, that the crown weighed less than the ingot of gold, but more than the ingot of silver, he concluded, that the crown was neither pure gold, nor pure silver, but a mixture of the two. All that was wanting to complete the solution of the problem was, to discover the proportion of the metals. This he effected by a very simple arithmetical calculation, which consists in estimating the proportion of the gold to the silver in the ratio of the excess of the weight of the crown over the ingot of silver to that of the weight of the ingot of gold over the crown. Some authors say, that Archimedes being in the bath when these ideas presented themselves to his mind, he immediately leaped out in a transport of joy, and, without thinking of the condition in which he was, ran through the streets of Syracuse, exclaiming I have found it! I have found it!' I have no intention to detract from this ingenious discovery, which would be as unjust as misplaced: but for the sake of some of my readers I shall observe, that, if the crown, instead of containing merely merely silver and gold, as was supposed, had contained more than two metals, as gold, silver, and copper, for instance, the crown might have been made of the same weight, though these three metals had been combined in several different proportions, which could not have been detected in this manner*. The screw of Archimedes, as it is called, is a very simple hydraulic engine, and very convenient for raising water to a small height. According to Diodorus Siculus, Archimedes invented this machine when on his travels in Egypt, and it was employed for draining marshes, rivers, &c.: but Vitruvius, a contemporary of Diodorus, does not include it among the discoveries of Archimedes, of whom however he was a great admirer. Claude Perrault, the translator and commentator of Vitruvius, observes, that the remarkable use assigned to this machine by Diodorus, that of having contributed to render Egypt habitable, by draining off the water with which it was formerly inundated, may lead us to presume, that it was much more ancient than the time of Archimedes. Vit. book x, chap. 11. If this conjecture have any foundation, let us not mix with the legitimate property of Archimedes an invention, his title to which may be disputed he is too rich in other respects, for us to hesitate about sacrificing an equivocal claim. About a century after Archimedes, two mathematicians of the alexandrian school, Ctesibius and his To this may be added, that the specific gravity of a compound of two metals in many cases differs from the mean of the two simple metals composing it, and sometimès considerably. T. disciple Hero, invented pumps, the siphon, and the fountain which plays by the compression of the air and still retains the name of Hero. A. C. 150. We are indebted more especially to Ctesibius for a machine of the same kind, composed of a sucking and a forcing pump, which are so disposed, that by their alternate action the water is continually drawn up and forced through a tube ascending between them. At present we know, that the medium through which the moving principle is applied to all these machines is the pressure of the atmosphere, which forces the water up into the vacuum made by the piston in ascending or descending: but the effects produced by them are very curious, and must have appeared at first not a little extraordinary. Accordingly the ancients, not knowing to what they were ascribable, had recourse to their grand scheme of occult qualities, so convenient for explaining the phenomena of nature. The water, said they, ascends in the pump, because Nature abhors a vacuum, so that the moment the piston is raised, the place it quits must be occupied by the water. The natural philosophy of the ancients was full of these secret powers, which were infinitely diversified according to the occasion. The ideas of hatred and affection were transferred from the moral to the physical world; celestial or terrrestrial bodies had a sympathy or antipathy with respect to each other; and a phenomenon was supposed to be explained, if it could be any way brought under the dominion of these chimerical agents. The |