Apparatus for freezing Water by the aid of Sulphuric Acid, 133 allow of the slightest leakage. If a pump has been used previously for freezing, by the vaporization of ether, it will not be competent for the experiment in question, unless it be taken apart and cleaned. Cocks of the ordinary construction are rarely if ever perfectly airtight, and their imperfection always increases with wear. Under these impressions, having cleansed my air pump, and put it into the best order possible; for the purpose of obviating leakage through the cocks associated with the instrument, I closed the hole in the centre of the air pump plate by a screw, and for a receiver made use of a bell glass with a perforated neck furnished with a brass cap and a female screw, by means of which one of my valve cocks was attached. A communication between the bell and the chambers of my pump was established through the valve cock and a flexible lead pipe, in a mode analogous to that already described in the account of the valve cock. In this way I succeeded in preserving the vacuum, longer than when the cocks of the air pump were employed in the process; and accomplished the congelation of water by means of the vacuum and sulphuric acid. Latterly I have used an apparatus which is represented by the adjoining figure, in which a brass cover is made to close a large glass jar so as to be quite tight. In operating, the bottom of the jar was covered with sulphuric acid, and another jar, with feet, also supplied with acid enough to make a stratum half an inch deep on the bottom, was introduced as represented. The bottom of the vessel last mentioned, was, by means of the feet, kept at such a height above the surface of the acid in the outer jar, as not to touch it. Upon the surface of the glass vessel, a small piece of very thin sheet brass was placed, made concave in the middle, so as to hold a small quantity of water. The brass cover was furnished with three valve cocks, one communicating with the air pump, another with a barometer gauge, and the third with a funnel supplied with water. Under these circum stances, having made a vacuum on a Saturday, I was enabled to freeze water situated on the brass, and to keep up the congelation till the Thursday following. As the water in the state of ice evaporates probably as fast as when liquid, during the night the whole quantity frozen would have entirely disappeared, but for the assistance of a watchman whom I engaged to supply water at intervals. At a maximum I suppose the mass of ice was at times about two inches square, and from a quarter to a half an inch thick. The gradual introduction of the water, by aid of the funnel and valve cock, also of the pipe represented in the figure, by which it was conducted to the cavity in the sheet brass, enabled me to accumulate a much larger mass than I could have produced otherwise. The brass band which embraces the inner jar near the brim, with the three straps proceeding from it, serves to keep this jar in a proper position; that is in fact concentric with the outer jar. In this last mentioned experiment, I employed an air pump upon a new construction, which I have lately contrived, and of which I shall soon publish a description. ART. XV.—On the general principles of the Resistance of Fluids, in a notice of the Fifth Article of No. XV of the Southern Review;* by Lewis R. GIBBES, Columbia, S. C. THE works selected as the subjects of the review are, "Remarks on Canal Navigation, &c. by W. Fairbairn, Lond. 1831," and "A new Theory of the Resistance of Fluids, &c. by T. Tredgold, article 41st of Phil. Mag. April, 1829." The first portion of the review is occupied by remarks on the great utility, and indeed necessity, of uniting sound theoretical knowledge with practical information. Fairbairn's work, the reviewer observes, shows the want of this combination, while Tredgold's works, particularly his "Treatise on rail roads and carriages," evince the superiority derived from it. The reviewer next proceeds to state the experiments detailed in Fairbairn's work. The results of these are, that when boats, single or twin, were drawn on a canal with different velocities, from five to thirteen miles an hour, * PROF. SILLIMAN: Dear Sir-Ever since the publication of the article, "Remarks on Canal Navigation and the Resistance of Fluids," in the eighth volume of the Southern Review, (fifth article of No. 15,) I have been expecting, with no little interest, to see or hear of some notice of it, but as yet none has come to my knowledge. At this I am somewhat surprised, as from the principles the able writer of itt has demonstrated, it is peculiarly valuable to the science of hydrodynamics, so much cultivated during the last half century by the French and Italians. Perhaps, from the comparatively small extent of circulation enjoyed by that work, the article has been seen by few to whom it would prove interesting, and has therefore met with no attention, especially as theory has lent but little aid to the practical engineer in this branch of science. I am induced, therefore, to give the following short notice of the contents of the article referred to, in the hope that it may meet the eyes of others, who with abilities far beyond mine, will duly appreciate the subject, and do it full justice. I have annexed a few of the simplest results of the important theorem furnished by the article, which will illustrate the difference between it and the theorem usually given in books on the subject. If you think the whole worth inserting in your Journal, by so doing you will oblige your obedient servant, LEWIS R. GIBBES. + Rev. James Wallace, Prof. Math. Astron. in South Carolina College. the wave or surge that rose in front of the boats, at velocities from five to ten miles an hour, diminished rapidly or ceased altogether at the higher velocities, from ten to thirteen miles. This result Mr. Fairbairn considers as "very anomalous and contrary to all previous theory," because it does not accord with the theorem that the resistances increase as the squares of the velocities, but the reviewer points it out as affording an instance of the necessity of uniting theory with practice, and assigns a sufficient reason for it afterwards. He then proceeds to lay down the general laws and principles on which inquiries concerning the resistance of fluids depend. His first theorem is the well known one, "If a non-compressible fluid act upon a plane opposed perpendicularly to the direction of its motion, the force with which it impels the plane, or acts upon it, will be as the square of the velocity of the fluid." Under this, he remarks the corrections necessary to be observed in experimenting on this subject. The next theorem is the one to which, particularly, I wish to call attention, as it is an extremely important correction of a theorem which has been adopted in all scientific works, from Newton's to the present day. The old theorem is well known. It is this: "If the inclination of the plane to the direction of the motion of the fluid vary, the resistance perpendicularly to the plane will vary as the square of the sine of angle of inclination." The demonstration is as follows. Since the particles of the fluid strike the plane obliquely, their force perpendicularly to the plane will vary as the sine of angle of inclination, by resolution of forces. The breadth of the column of fluid, and consequently the number of particles striking the plane, also varies as the sine of same angle; the breadth being estimated perpendicularly to the direction of the fluid. The resistance in a direction perpendicular to the plane, which depends on the number of particles multiplied by their force in that direction, will therefore vary as the square of the sine of angle of inclination. The theorem of Mr. Wallace is this: "If the inclination of the plane vary, the resistance perpendicularly to the plane will vary as the SINE of the angle of inclination. His demonstration may be thus expressed. Since the particles strike the plane obliquely, their force perpendicularly to the plane, as in the former theorem, will vary as the sine of angle of inclination. But the number of particles striking the plane, he argues, does not depend on the breadth of the column, but on the surface of the plane, because the particles that act on the plane are those in contact with it, and therefore their number is as its superficial area. As the surface of the plane, by supposition, does not vary, the number of particles acting on it, therefore, does not vary, and the resistance, consequently, is as the sine of the angle of inclination-the number of the particles being the same at all inclinations, and the force of each, varying as the sine of angle of inclination. Mr. Wallace, to whom this correction is entirely due, then cites authors to show that his theory agrees more nearly with experiments than the old one. All authors agree that the resistance obtained by experiment is greater than that deduced from the old theory, and as much greater as the angle of inclination is less, in both of which points does the new theory coincide with experiments. Indeed, Prof. Robison, in speaking of the French experiments, (in the Art. Resistance, in Encyc. Brit.) makes this remarkable observation: "The theoretical law, (the squares of the sines,) agrees tolerably with observation in large angles of incidence; that is, in incidences not differing very far from the perpendicular; but in more acute prows, the resistances are more nearly proportional to the sines of the angles of incidence than to their squares,"—thus actually recognizing this law, without even hinting at the reason of it. The reviewer next observes, that the force perpendicular to the plane may be resolved into two others, one in the direction of the motion, which will vary as the square of sine of inclination, (by the old theory it is as the cube of the sine,) and one perpendicular to the direction of the motion, which will vary as the product of the sine and cosine of same angle. This latter force in boats moving on the surface of the water, acts in a direction contrary to gravity, and being unopposed, tends to raise them out of the fluid, and diminish the surface immersed. This upward force, "which," says the reviewer, "appears to be entirely overlooked by writers on this subject," accounts for the diminution of the surge in Fairbairn's experiments, and shows the incorrectness of an observation of Dr. Lardner, (in Vol. XVII of the Cabinet Cyclopedia,) on the advantages of rail roads over canals, which is quoted by the reviewer. Ꮖ To illustrate the theorem of Mr. Wallace, I will investigate a few of its simplest results in the resistance of fluids to bodies moving in them. To find the resistance to a solid of revolution, moving in the direction of its axis of revolution. Let x and y be the coördinates of the curve, whose revolution generates the surface of the solid, their origin being at the extremity of the axis. By the theorem, the number of particles that act on a surface is as its area, while only their force varies with the inclination. The number of particles, thereVOL. XXVII.-No. 1. 18 |