of falling bodies are as the square roots of the heights through which they fall, the square root of 16.087 will be to the square roots of the height of the fall, as 32-174 to a fourth number, which will be the velocity of the water. Therefore the velocity of the water may be always found by multiplying 32.174 by the square root of the height of the fall, and dividing that product by the square root of 16.087. Or it may be found more easily by multiplying the height of the fall by the constant number 64.348, and extracting the square root of the product, which, abstracting the effects of friction, will be the velocity of the water required. 3. Take one-half of the velocity of the water, and it will be the velocity which must be given to the float-boards, or the number of feet they must move through in a second, in order that the greatest effect may be produced. 4. Divide the circumference of the wheel by the velocity of its float-boards per second, and the quotient will be the number of seconds in which the wheel revolves. 5. Divide 60 by this last number, and the quotient will be the number of revolutions which the wheel performs in a minute. Or the number of revolutions performed by the wheel in a minute, may be found by multiplying the velocity of the float-boards by 60, and dividing the product by the circumference of the wheel, which in the present case is 47.12. 6. Divide 90 (the number of revolutions which a mill-stone five feet diameter should perform in a minute) by the number of revolutions made by the wheel in a minute, and the quotient will be the number of turns which the mill-stone ought to make for one revolution of the wheel. 7. Then, as the number of revolutions of the wheel in a minute is to the number of the revolutions of the mill-stones in a minute, so must the number of staves in the trundle be to the number of teeth in the wheel, in the nearest whole numbers that can be found. 8. Multiply the number of revolutions performed by the wheel in a minute, by the number of revolutions made by the mill-stone for one of the wheel, and the product will be the number of revolutions performed by the mill-stone in a minute. In this manner the following table has been calculated for a water-wheel 15 feet in diameter, which is a good medium size, the mill-stone being five feet in diameter, and revolving 90 times in a minute. DR. BREWSTER'S MILL-WRIGHTS' TABLE. In which the velocity of the wheel is three-sevenths of the velocity of the water, and the effects of friction on the velocity of the stream reduced to computation. THE OPERATIVE MECHANIC TREATISES ON MILL-WORK. Känsliche abriss Allerhand, Wasser, Wind-ross, und Hand-muhlen, &c., von Jacob. de Strada a Rosberg, 1617. Georg. Christoph Luerner Machina toreutica nova; oder beschreibung der neu erfundenen Drehmühlen, 1661. Theatrum Machinarum Novum; das ist, neu vermehrter Schauplatz der Contenta discursus Mechanici, concernentis Descriptionem Optimæ formea Dissertatio Historica de Molis, quam præside Joh. Phil. Treuer defend. Martin Marten's Wiskundige beschouwinge der Wind of Wadermoolens, vergeleken met die van den heer Johann Lulofs Amsterdam 1700. Vollständige Mühlen-baukunst, von Leonhard Christoph. Sturm, 1718: Joh. van Zyl Theatrum Machinarum Universale of Groot Algemeen, Moolenbock, &c., Amsterdam, 1734. Jo. Caral. Totens Disser. de Machinis Molaribus optime construendis, Lugd. Batav. 1734. Kurze, aber Deutliche anweisung zur construction der Wind und Wassermuhlen, von Gottfr. Kinderling, 1735 Desagulier's Experimental Philosophy, 2 vols. 4to. 1735, 1744. Mr. W. Anderson, F. R. S. Description of a Water-wheel for Mills. Phil. Leonh. Euleri, De Constructione aptissima Molarum alatarum disp. Nov. Com. Acad. Petrop. tom. 4, 1752. Mémoire dans lequel on démontre que l'Eau d'une Chûte, destinée à faire mouvoir quelque Moulin ou autre Machine, peut toujours produire beaucoup plus d'effet en agissant par son poids qu'en agissant par son choc, et que le roues à pots qui tournent vite, relativement aux chûtes et aux dépenses d'eau, par M. de Parcieux, Acad. Roy. Paris, 1754. Jo. Alberti Euleri Enodatio Questionis: quo modo vis Aquæ aluisve fluidi cum maximo lucro ad Molas circumagendas, aliave opera perficienda impendi possit, præmio à Societate Regia. Sci. Gotting. 1754, An experimental Inquiry concerning the Natural Powers of Wind and Water to turn Mills and other Machines depending on Circular Motion, by Mr. J. Smeaton, F. R. S. Phil. Trans. 1759. This, and Mr. Smeaton's other papers are republished with his Reports, 1813, in 4to. Mémoire dans lequel on prouve que les Aubes de Roues mues par les courans de grandes Rivières feroient beaucoup plus d'effet si elles étoient inclinées aux rayons, qu'elles ne font étant appliquées contre les rayons mêmes, comme elles sont aux Moulins pendans et aux Moulins sur Bateaux qui sont sur les Rivières de Seine, de Marne, de Loire, &c. par M. de Parcieux. Mem. Acad. Roy. Paris, 1759. Joh. Albert Euler's Abhandlung von der bewegung ebener Flachen, wen sie vom Winde Getrieben Werden, 1765. Schauplatz des Mechanischen Mühlenbaues, Darinnen von Verschiedenen Hand, Trett, Ross, Gewicht, Wasser, und Wind-mühlen Gehandelt Wird, durch Johan Georg. Scopp. J. C. iter Theil, 1766. Theatrum Machinarum Molarium, oder schauplatz der Mühlenbaukunst, als der Neunte theil von des sel hrn Jac. Leopolds, Theatro Machinarum, von Joh. Mathias Beyern, 1767, 1788, 1802. A Memoir concerning the most advantageous Construction of Water-wheels, &c. by Mr. Mallet of Geneva, Phil. Trans. 1767. Mémoire sur les Roues Hydrauliques, par M. le Chevalier de Borda, Mem. Acad. Roy. Paris, 1767. Kurzer unterricht, allerley arten von Wind und Wasser-mühlen auf di vortheilhafteste weise zu erbauen, nebst einigen gedanker über die verbesserung des räderwerks, an den Mühlen, von Joh. König, 1767. G. G. Bischoff's Beyträge zur Mathesis der Mühlen, 1767. Détermination générale de l'Effet des Roues mues par le Choc de l'Eau, par M. l'Abbé Bossui, Mem. Acad. Roy. Paris, 1769. Andreas Kaovenhöfer, Deutliche abhandlung von den rädern der Wassermühlen, und von dem einrandigen werke der Schneidemühlen, 1770. Manuel du Meunier et du Charpentier des Moulins, redigé par Edm. Bequillet, 1775. Remarques sur les Moulins et autres Machines, où l'Eau tombe en dessus de la Roue, par M. Lambert. Expériences et Remarques sur les Moulins que l'Eau meut par en bas dans une Direction horizontale, par M, Lambert. Remarques sur les Moulins et autres Machines, dont les Roues prenant l'Eau à une certaine Hauteur, par M. Lambert, (The three last articles are inserted in Mem. Acad. Roy. Berlin, 1775. Ausführliche erklärung der Vorschläge für die Längere dauer de Muhlenwerk, nebst ähnlichen gegenstander, in ein gespräch verfasset, von Johann Christian Fullmann Muhlenmeister, 1780. Tratado de los Granos y Modo de Molelos con Economie de la Conservacion de Astos y de las Harinas; escr. en Fr. par M. Beguillet y extract. y trad. al Cast. con algun Notas y un Supplem. por Ph. Marescaulchi, Madrid, 1786, Suite de l'Architecture Hydraulique, par M. Fabre, 1786. Mémoires sur les Moyens de perfectionner les Moulins, et la Mouture économique, par C. Bucquet, 1786. Manuel ou Vocabulaire des Moulins à Pot, à Amst., 1786. Die Nothigsten Kenntnisse zur Anlegung, Beurtheilung, und Berechnung der Wasser-mühlea, and zwar der Mahl, Oehl, und Säge-Muhlen, sür Anfänger und Liebhaber der Mühlenbaukunst, von Joh. Christ. Huth, 1787. An Essay proving Iron far superior to Stone of any kind for breaking and grinding of Corn, &c. by W. Walton, 1788. Mühlenpraktik, oder unterricht in dem Mahlen der Brodfrüchte, für Polizeybeamte, Gaverksleute und Hauswirthe, von L. Ph. Hahn, 1790. The Young Mill-wright and Miller's Guide, by Oliver Evans, Philadelphia, 1790. Manuel du Meunier, et du Constructeur des Moulins à Eau et à Grains, par C. Bucquet, 1791. Praktische anweisung zum Mühlen bau, von Lr. Clausen, 1792. Beschreibung zweir Machinen zur Reinigung des Korns, von Lr. Clausen, 1792. Instructions sur l'Usage des Moulins à Bras, inventés et perfectionnés par les Citoyens Duraud, Père et Fils, Méchaniciens, 1793. Theoretisch-praktische abhandlung über die Besserung der Mühlräder, von dem Verfasser der Zweckmässigen, Luftreiniger, &c. 1795. A Treatise on Mills, in four parts, by John Banks, 1795. Handbuck der Maschinenlehre, sur prakiker und akademische lehrer, von Karl Christian Langsdorf, 1797, 1799. On the Power of Machines; including Barker's Mill, Westgarth's Engine, Cooper's Mill, Horizontal Water-wheel, &c. by John Banks, 1803. The Experienced Mill-wright, by Andrew Gray, Mill-wright, 1804. The Transactions of the Society of Arts and Manufactures; several of the volumes of which contain improvements in Mill-work. See also the Repertory of Arts, first series 16 vols. and second series 31 vols, WINDMILLS. THE windmill derives its name from the motion it receives from the impulse of the wind. The date of its invention is not precisely known, though authors generally concur in believing it to have taken place at no very distant period of time. Some state it to have been first used in France in the sixth century: others, on the contrary, assert, that at the time of the crusades it was introduced into Europe from the east, where scarcity of water gave the impetus that led to its discovery. Windmills are of two kinds, horizontal and vertical. THE VERTICAL WINDMILL CONSISTS of a strong shaft, or axis, inclining a little upwards from the horizon, with four long yards, or arms, fixed to the highest end, perpendicular to the shaft, and crossing each. other at right angles. Into these arms are mortised several small cross-bars, and to them are fastened two, three, or four, long bars, running in a direction parallel with the length of the arms; so that the bars intersect each other, and form a kind of lattice work, on which a cloth is spread to receive the action of wind. These are called the sails, and are in the shape of a trapezium, usually about nine yards long and two wide. As the direction of the wind is very uncertain, and perpetually changing, it becomes necessary to have some contrivance for bringing the windshaft and sails into a position proper for receiving its impression. To effect this, two methods are in general use: the one called the post-mill; the other the smock-mill. POST-MILLS. In the post-mill it is accomplished by driving perpendicularly into the earth the trunk of a strong tree, that is held securely upright by several oblique braces, which extend from a platform on the ground to the middle of the tree, leaving 10 or 12 feet of the upper part free from the braces. The part thus left free from obstruction is rounded, and made to pass through a circular collar, formed in the flooring of the lower chamber, and to enter into a socket fixed into the flooring of the upper chamber, and to one of the strongest cross-beams, which must sustain the. whole weight of the mill-house, so that, by means of a pivot, or gudgeon, fastened on that part of the post which enters into the socket, the whole machine can turn about horizontally to face the wind. A strong |