The Artisan, or, Mechanic's instructor : containing a popular, comprehensive and systematic view of the following sciences ... also biographical notices of eminent scientific men, enriched by portraits : with many interesting and valuable articles relating to the mechanical and useful arts : the whole intended as a companion to the institutes
Carey, George G
/, Qr '/ , y . / </A /.X? / ;££ />!..<’ *-»•* • ^v' 7 ^ •- / "' /r/zZC. * 7) i r ^v,- Digitized by the Internet Archive' in 2015 https://archive.org/details/artisanormechaniOOcare Isaac Hewisn, -*?V2£ / J s QL V /rr/s/Ss’ ' Sr? i THE ARTISAN; OR, MECHANICS INSTRUCTOR: CONTAINING A POPULAR, COMPREHENSIVE, AND SYSTEMATIC VIEW OF THE FOLLOWING SCIENCES : GEOMETRY, MECHANICS, HYDRODYNAMICS, PNEUMATICS, OPTICS, CHEMISTRY, ASTRONOMY, ARCHITECTURE, PERSPECTIVE, ELECTRICITY, MAGNETISM, ALGEBRA. biographical Notice# of eminent Scientific Jtten, ENRICHED BY PORTRAITS: WITH MAttY INTERESTING AND VALUABLE ARTICLES RELATING TO THE MECHANICAL AND USEFUL ARTS. THE WHOLE INTENDED AS A COMPANION TO THE INSTITUTES. VOL. I. LONDON : PRINTED FOR WILLIAM COLE, (LATE HODGSON AND CO.) 10, NEWGATE-STREET. PREFACE Nothing tends so much to the successful cultivation of scientific knowledge, as forming clear and accurate ideas of the Elements, or first principles, of those sciences which form the basis of all physical know- ledge. Convinced of the truth of this observation, and of the value of scientific knowledge to the Artisans and Mechanics of this commercial and manufacturing country, the Editor of the following work has endea- voured to render the various subjects contained in it as plain and as easily understood as the nature of them would permit. In pure Geometry, it is scarcely possible to abridge the steps of a demonstration, without rendering the truth of the proposition less appa- rent; it has therefore been deemed more advantageous to the Geome- trical student, to present him with the Propositions of Euclid’s Elements, without attempting any abridgement or alteration of them. He will, however, find many observations and useful remarks, on a number of the propositions, that are not to be found in the common editions of the Elements. The science of Mechanics, though more intricate and complex than Geometry, may nevertheless be very much simplified in many of its most useful and practical branches, by explaining the laws and prin- ciples upon which they rest, in common language , instead of expressing them in mathematical and algebraical symbols. This has been particu- larly attended to, in delivering the general doctrines of this science in the following work, as well as in treating of the power and effects of particular machines-. The same rule has been observed in treating of Hydrodynamics, Pneumatics, Optics, and Astronomy, though they are strictly mixed mathematical sciences, and have hitherto been treated in the most abstract and mathematical manner, even in works pretending to be purely elementary. IV PREFACE. The science of Chemistry is also rendered as simple and amusing as it is possible to make it; and the most accurate and modern improve- ments which have been introduced into that science have been noticed. To render the work useful and amusing, not only to the scientific student, but to the general reader, an extensive miscellaneous depart- ment has been added, including memoirs of the lives of men who have distinguished themselves, either by the improvements they have made in the Sciences, or the discoveries they have made in the Arts. Another important feature of this department of the work is, a comprehensive and popular view of the beautiful and elegant science of Architecture, illustrated by neatly engraved specimens of the various orders of build- ing, both ancient and modern. The other subjects introduced into the Miscellaneous part of the work, are perhaps as numerous as in some other works, which are appropriated solely to subjects of this nature. And, upon examination, they will be found not only interesting and useful at the 'present time, but to be of such a nature, as to render them equally useful at any future period. The mathematical and philosophical questions contained in the work may, perhaps, be considered by some as of too abstruse and intricate a nature to be generally understood; but the reason for devoting a small portion of the work to subjects of this kind, was to render it interesting, and, if possible, valuable to the mathematician, and the philosopher, as well as the tradesman and the mechanic. The Copper-plate portraits which are given along with the work, are of the very first order in point of execution; the same may be said of the numerous Wood engravings interspersed through it. But a care- ful perusal of the whole, and a comparison with other works that treat of the same subjects, will afford the best criteria , for determining both the comparative and real value of the work now offered to the public. INDEX GEOMETRY. Friction of Wheels - Page 245 Angles, various kinds of - - Page 5 , Method of diminishing 245 — , exterior, Property of - - 83 Fulcrum, what - 55 - — — , vertical, ditto - - 82 Gravity, what - 7 Axioms - - - 17 ■ , centre of - 53 Book 1st. - - 4 Hook's Universal Joint - 278 Book 2d. - - 273 Inclined Plane, of the ns Book 3d. - - 369 Lever, of the - - 54. 84 Circle - - - 5 of Lagaroust _ 277 Contrary Propositions, what - - 18 Machine in which all the Mechanical Corollary, what - 17 Powers are united _ 279 Converse Propositions, what - -  Machinery, Regulation of _ 307 Enunciation, what - 18 Matter, what - _ 6 Geometry, Definition of - - 4 Mechanics 6, 21, 51, 84, 115, 148, Lemma, what - - 17 179, 212, 243, 276, 307, 340 Parallelogram, Definition of " - 177 Mechanical Agents - - ' - 276 • , Properties of - 178 Contrivances 277 Parallel Lines, what - - 6 Powers 54 Properties of * - 146 Mobility, what. 7 Pons Asinorum - - 20 Motion, various kinds of - 8 Postulates - - - 17 , 1st. Law of - 21 Problem, what * - 17 2d ditto - 22 Proposition, Definition of - - 17 , 3d ditto - 23 Propositions, Book 1st. 18, 49, 81, Pinion, what - 86 113, 145, 177, 209, 241 Pulley, of the - - 115 Propositions, Book 2d. 273, 305, 337 Screw, of the - - 149 Propositions, Book 3d. - - 369 Smeaton's Machine for Experiments Rectangle, what - - 273 on Rotatory Motion _ 341 Reductio ad Absurdum - - - 17 Specific Gravity, what _ 8 Square, Definition of - - 6 Steelyard, what - _ 181 Superficies, what - 4 Time, how expressed 8 — — Plane, ditto - - - 4 Velocity, various rates of - _ 21 Theorem, what - - 17 Vis Inertia - 7 Triangles, various kinds of - - 5 Wedge, of the -. 148 MECHANICS. Weight, what - _ 7 Animals, Strength of _ - 276 Wheel and Axle, of the - - 85 Atwood's Machine, Description of - 309 Windlass - - 86 Balance, of the - - 179 HYDRODYNAMICS. — — - Fraudulent - _ - 181 Archimedes’s Screw _ 151 Ball and Socket - - 278 Barker’s Mill - _ 312 Belts or Bands - - 277 Capillary Tubes, effects of _ 56 Capstan - - 86 Suspension _ 57 Crank, various kinds of. - - 278 Columnaria, what 87 Density, what - - 8 Equilibrium of Indifference 26 Divisibility, what - - 7 Stable — Unstable - „ 27 Dynamics, Definition of - - - 6 Fluids, Bodies floating in _ 26 Extension, Definition of - - - 76 — issuing through Apertures _ 57 Falling Bodies * - 51 pressure of - - 87 Figure, what - - 6 how conveyed in Pipes - 87 Forces, various kinds of - - 21 percussion and resistance of 119 Composition and Resolution of 24 Fountain, Hungarian _ 217 Friction, account of, - - 212 — of Schemnitz and Hiero 217, 218 of Surfaces - - 212 Hydraulics 87, 118, 151, 183, 216, — of Axles - > - 214 247, 280, 311, 343 of Wheel Carriages _ - 215 Hydraulic Ram - - 216 of Ropes - - - 243 Hydrostatics - - - 9, 25 , 56 — of Pivots - - - 244 Hydrostatical Balance and Paradox 9 nn INDEX. Montgolfier’s Ram - - Page Pump Chain ..... • — — Cellular .... Pump, Paternoster - ■ Rope - Pump, Spiral Shower Bellows .... Spanish Noria - Specific Gravity defined ... — method of Determining - — Table of ... Stopcock,  form of the dead Machines for discharging ■ Machines moved by the re- action of ... Machines for measuring the velocity of - Machine for raising Machines raised by changes in the air - running in Canals - Screw ..... Snail — Velocity of - Wheels, comparative effects of Waves, formation and Extent of ; Velocity of - Wheels, Breast ----- Chain - Horizontal - Persian - Scoop - Overshot - Smeaton’s - Undershot .... at right angles to the Stream Besant’s - ... Bossut’s ... Pitot’s .... • Smeaton’s - with Spiral float-boards Whitehurst’s Engine - Zurich Machine - PNEUMATICS. Air, Condensed - — — Effects of on bodies in motion - Elasticity of Experiments Avith - Gun described - Properties of - . Pressure of ~ Pump described Resistance of - Temperature of Weight of - Anemoscope - - - Barometer, Mensuration of heights by Bellows, wind - - - Diving Bell - Experiments with Air Pump - Experiments on the weight of the Air 67 * on Resistance of ditto - 97 — on Elasticity of Air - 98 _ Miscellaneous on ditto - 99 Lift-tenter described ... 226 Parallel Motion described - - 259 Pistons of Pumps - - - 133 of Steam Engines - - 195 Pneumatics 10, 33, 67, 97, 131, 161, 195, 225, 259, 289, 321, 353, 385  _ - 195 Maudslay’s - 289, 322 Newcomen’s - - 195 Savery’s Watt’s - - 195 _. 196 Worcester’s. 165 Steam Gauge. - 228 Navigation - - 322 Sun and Planet wheels. - 227 Symington’s Boat. 323 Vacuum Gas Engine - _ 259 Valve, Safety ... - 353 Throttle _. 226 Wind Mill. 354 Chariot _ - 385 Waggon - - 386 OPTICS. Camera Lucida. 264 Obscura. - 228 Catoptrics - - _ - 11 Colour, what - - 102 of Natural Bodies - _ 136 of the Atmosphere - - 199 Concave Glass, what. - 13 Properties, of - - 39 Mirrors, of - - 72 Convex Glass, what -. - 13 — Properties of - - 37 Dioptrics - - 11 Eye, Description of the - - 39 Defects of the -. 70 Focus, what - - - -. 37 Glasses, various kinds of _. 13 Incidence, angle of -. - 12 Light, opinions respecting - - 21 of various colours of - - 102 Polarization of -. - 163 Magic Lantern - -. 229 Medium, what _ _ 12 Megascope ... _ 229 Meniscus Glass, what - - 13 Microscopes, various kinds of - - 70 — — Magnifying power of - 71 Mirror, Cylindrical - - 199 Multiplying Glass - 101 Optics, 36, 70, 101, 134, 163, 197. ,228, 263, 291, 324, 357, 388 Optics, Division of - 11 Optigraph, Description of - 386 Phantasmagoria, what - 263 Phatometry, what - 388 Plano Concave Glass, what - 13 — - — Convex Glass, what - - 13 216 183 184 184 153 152 343 153 10 10 25 89 34 343 59 89 88 59 121 343 311 313 151 218 89 152 151 89 311 118 119 153 250 284 183 183 247 249 280 283 281 281 281 281 284 184 152 131 34 95 67 131 10 67 34 97 11 10 386 33 • 387 132 67 INDEX; Prism, Description of - Page Rainbow, account of - Lunar, ditto - Rays, Parallel - Coloured - Diverging - - - Homogeneous - Reflected — Refracted Reading Glasses - Refraction, Angle of - Double - unusual, of the Atmos- phere - Refractive Power of Substances Solar Spectrum - Telescope, of the - - Achromatic - Astronomical - — Brewster’s ... Cassegrainian - Dolland’s - Galilean ... ■ Gregorian ... Herschel’s - ■ Newtonian - Reflecting kind Refracting ditto — Tremors of CHEMISTRY. Affinity, what - Elective - Alloys, what - Amalgam, what - Azote, what - ... how procured Combinations of ■ Properties of - Carbon, what — How procured - Properties and Combinations Carburetted Hydrogen Gas Charcoal, Preparation of - Properties of - Chemistry IB, 40, 73, 103, 138, 166, 200, 230, 267, 294, 327, 359, Etymology of - _ ; - — - History of Chlorine, how obtained - - — Combinations of Properties of - Uses of Compound Bodies - Diamond, nature and Properties of - Gold ..... 361, Oxides and Properties of 361, Hydrogen Gas - — — how procured — — — Combinations of — . Properties of Iodine, Combinations of - — Discovery of - - how procured ... — Properties of - Lutes, their use - Metals, account of - Calces of ... Classification of - — ____ General Properties of - Metals, History of - Page 227 Imperfect ... 3G0 Oxides of ... 229 Perfect .... 3 go Table of 361 • Uses of .... 327 Muffle, what .... 105 Muriatic Acid .... 230 absorbed by Water - 232 how procured - - 231 • Properties of - 231 Oxygen Gas, how obtained - 41 — its Properties - - 42 Phosphorus, Description of 105 how procured - - 105 Properties of - - 139 Phosphoric acid .... 139 Phosphuretted Hydrogen - - 139 Platina, history of ... 391 Simple Bodies, what - - - 40 Sulphur, account of - - 166 — • — Combinations of - 166 Combustion of - - - 167 Properties and Purification of 166 Wolf’s Apparatus, representation of - 232 ASTRONOMY. Astronomical definitions - - - 78 Astronomy 16, 27, 44, 76, 106, 140, 169, 202, 233, 270, 296, 330, 362, 394 History of - - -  ...... 395 Clouds, formation of ... 394 Comets, account of - - -169 Copernican system - -  of the Moon - - - 331 of Jupiter’s Satellites - 233 Jupiter, description of - 109,. 140 Light, an account of ... 362 Mars, description of 108 Mercury, description of - - - 107 Moon, description of ... 203 apparent size of 234 Harvest - 233 Motions >of - 204 Mountains of, &c. - -  296 their distance and number - 297 Sun, of the ----- 78 heat  103 13 103 12 70 12 165 197 165 102 265 357 266 325 292 357 266 291 324 293 291 365 357 40 43 330 330 209 200 201 200 75 104 104 75 76 390 40 13 267 268 268 269 40 105 390 362 73 74 75 74 295 294 294 294 42 327 229 360 328 INDEX. Uranus, or Georgium Sidus Page  317 — Catanarian - 317 Various kinds of - - 317 Architecture, Civil - - 253 Definitions - 175 — Division of - - 154 — Gothic - - 253 History of - - 154 — Military and Naval - 154 Architecture 154, 174, 188, 205, 221, 236, 253, 286, 317 Architrave, what -  Entablature ■ - - 175 Facades, what — Frieze - - 175 King’s Chapel, Cambridge, view of - 254 Mouldings, various kinds of - - 286 Order, what - •• 175 Composite - - 236 Corinthian - - 221 Doric - 188 Ionic - - 205 Tuscan - - 188 Pedestal, what — Plinth - - - 175 Shaft - - - 175 Tri glyph, what - - 205 Volute, what - 175 BIOGRAPHY. Life of Agnesi, M. - - - 154 Archimedes - - 30 Bacon, Lord Francis - - 193 — Bacon, Roger - - - 314 Copernicus - - 122 Davy, Sir H. - - 65 — Emerson, W. - - 251 Euclid _ - 59 — - — - Euler, Leonard - - 345 Ferguson, James - - 235 Franklin, Dr. - - 366 Galileo - - 172 Hutton, Dr. Hypatia - - 257 - - 333 Mayer, J. Tobias v - - 397 Newton, Sir I. - - 3 Playfair, Professor - - 218 Ramsden, Mr. - - 185 Saunderson, Nicholas - 298 Simpson, Thomas - - 90 Watt, James - - 129 Questions and Solutions 32, , 48, 63, 80, 95, 112, 127, 144, 1G0, 175, 191, 207, 223, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 399 END OF MISCELLANEOUS. Alcohol, quantity in Porter Page 23S Apartments, method of warming - 302 Aquatinta Engraving - - - 32 Balloons, construction of - 238 improvement of - » 351 Bell’s Apparatus, description of - 301 Bridges, suspension - 159 Carey’s Arithmetic reviewed - - 318 Celestial Atlas, account of 235 Chinese Year, on the - - ■■ 143 Clocks, oil for 94 Cloth, how embroidered - 303  Fixed Stars, pamphlet on the - - 303 Galvanism and Fermentation, on - 237 Gases, correction for temperature - 126 Gilding with Gold - 206 - — — on Brass, &c. - 207 on Leather - • - 238 Glass, to etch designs on - - 191 — to stain .... 206 Gunter’s Scale, description of - 347, 380 Heat, singular application of - - 63 Hydraulic Ram, of the  - - 158 Medical pump - 286 Moon, conjectures respecting the - 94 Mosaic, manufacture of - 239 Mountains, heights of - - - 61 Nautical eye tube - 158 Nitre, preparation of - - - 157 Optics, on the study of - - 62 Pendulum, Kater on the - 142 application of - - 155 Perpetual motion impossible - - 222 Printing, on Lithographic - - 159 Queries, answers to - - - 111 Query, Philosophical - - - 32 Rain, the cause of ... 207 Refraction of the atmosphere - - 156 Safety Lamp ----- 125 Seamen, apparatus for saving - - 349 Sea, temperature of the - - 158 Starch, preparation of - - - 191 Stars, change in the place of - - 157 Steam, force of - 159 Sulphur, action of on Iron - -158 Trees, representation of - - - 287 Trigonometrical Survey, on the - 80 Vernier Scale described - - 205 Water, electric effects of - 319 Weights, new French - - - 111 Weights, &c., uniformity of - 281, 398 Wind, intensity of - 190 VOL. I. Printed by W\ Cole , in, Newgatc-street. Stye artisan; OR, MECHANIC’S INSTRUCTOR: BEING A COMPANION TO THE INSTITUTES. INTRODUCTION. The value of scientific knowledge is now so generally known and appre- ciated in this country, that any attempt to point out the advantages resulting from an acquaintance with it, would be quite superfluous. It must, however, be admitted, that the value of this species of knowledge is more generally understood than the principles upon which it is founded. The effects produced by it are seen and acknowledged by all; but com- paratively few are acquainted with the mode of producing them. Every one has seen and must admire both the structure and powerful effects of the Steam-engine ; but few are acquainted either with the scientific prin- ciples upon which its construction depends, or with the nature of the extraordinary fluid by which its surprising effects are produced. Being fully convinced of the truth of these observations, and of the great importance of scientific knowledge to every individual engaged in the cultivation of the Arts, the Conductors of the present Publication have resolved to devote the greater part of the work to the developement and explanation of the fundamental principles of those Sciences which form the basis of the Mechanical Arts. Particular care will, therefore, be taken to give a comprehensive and connected view of the most useful branches of Mathematics, Mechanics, Hydrostatics, Pneumatics, Optics, Astronomy, and Chemistry. In treating of these sciences, the greatest pains will be taken to render them as plain and easily understood as their nature will admit ; — and in order to render the work of permanent utility, not only to those who are beginning the study of these sciences, but to those who are already well acquainted with them, a regular and systematic arrangement of the various parts of each will be preserved, and no part omitted which can be considered of real value. Mathematical knowledge being the foundation of all physical science, as well as most of the mechanical arts, has certainly the first claim to attentive observation; a portion of “ Euclid's Elements" will therefore be given in each Number of the “ Artisan," in a more simple and popular form than that celebrated work has ever yet assumed : for although we are perfectly aware that “ there is no Royal Road to Geometry," yet we do think that many of the Propositions in that work may be made more intelligible to mathematical Students than they are, as they stand in the most popular editions of the Elements. It will, therefore, be the parti- Yol. I. B 2 INTRODUCTION. cular care of the Conductors of the “ Artisan,” to make this part of the work as easily understood as possible, knowing that little progress can he made in any of the physical sciences without possessing a tolerable share of mathematical knowledge. This is a fact so well knowh to those who have made those sciences their particular study, that no arguments can be employed to give additional weight to it. And though it may be impos- sible to give an adequate idea of the usefulness of mathematical know- ledge to those who are wholly unacquainted with it, yet it may atford some satisfaction to those who are about to commence the study to observe, that mathematical knowledge supplies most of the means by which, the business of society is carried on, and its comfort secured. To mathematical principles the skilful Architect necessarily resorts for the means of contriving and executing his plans ; and to them every building, from the cottage to the palace, owes its existence. By mathematical knowledge the mariner shapes his course through the wide and pathless ocean, the intrepid soldier plans his operations for the protection of his country, the skilful miner contrives his subterraneous excavations, and procures for our use most of the substances employed in the arts of civilized life. Having here stated, in general terms, some of the uses of mathematical science, it is unnecessary to make any observations on the other sciences to be introduced in the present publication, because the utility of these are much more apparent to the generality of mankind, than the science upon which they immediately depend. But though this be the case, the sciences themselves are necessarily as little known as the elementary branches of mathematics. It will, therefore, be the study of the Conductors of the “ Artisan v to present their readers with a regular and comprehen- sive view of the various branches of Natural Philosophy, as far as they are known at the present day. And to render their work of general interest, part of each Number will be devoted to giving an account of any discovery or improvement that may be made in the Arts ; with biogra- phical notices of men who have contributed to the advancement either of the Arts or Sciences. The Editors will therefore receive with gratitude short and authentic communications relative to every species of useful knowledge ; but they have resolved to exclude every thing of a speculative nature, and to con- fine their work entirely to the promulgation of facts founded on experi- ment and observation. By thus selecting and condensing their materials, and by endeavouring to give a popular form to the various subjects that come under their notice, the Conductors of the “ Artisan” trust that they may, in some degree, advance the interest of science, by promoting its general diffusion, at a time when there is so much anxiety shown by every class of the community to acquire a knowledge of the accurate sciences. The Editors also trust that the plan here adopted, of giving a clear and connected view of each of the Sciences contained in the present Number, will be considered the most effectual mode of aiding the laudable exertions now making by the operative Mechanics of this Country, to acquire a knowledge of the principles upon which their respective arts depend. They are, therefore, not without hopes that their exertions may suc- cessfully contribute to the diffusion of scientific knowledge, as well as to the advancement of the useful Arts. 3 BIOGRAPHICAL MEMOIR OF SIR ISAAC NEWTON, Sir Isaac Newton, one of the greatest mathematicians and philosophers that ever lived, was born in Lincolnshire, in 1642. Having made some proficiency in the clas- sics, &c. at the grammar school at Grantham, he (being an only child) was taken home by his mother (who was a widow) to be her companion, and to learn the manage- ment of his paternal estate : bnt the love of books and study occasioned his farming concerns to be neglected. In 1660 he was sent to Trinity College, Cambridge : here he began with the study of Euclid, but the propositions of that book being too easy to arrest his attention long, he passed rapidly on to the Analysis of Des Cartes, Kepler’s Optics, &c. making occasional improvements on his author, and entering his ob- servations, &c. on the margin. His genius and attention soon attracted the favourable notice of Dr. Barrow, at* that time one of the most eminent mathematicians in England, who soon became his steady patron and friend. In 1664 he took his degree of B.A. and employed himself in speculations and experiments on the na- ture of light and colours, grinding and polishing optic glasses, and opening the way for his new method of fluxions and infinite series. The next year, the plague which raged at Cambridge obliged him to retire into the country ; here he laid the foundation of his universal system of gravitation, the first hint of which he received from seeing an apple fall from a tree ; and subsequent reasoning induced him to conclude, that the same force which brought down the apple might possibly extend to the moon, and retain her in her orbit. He afterwards extended the doctrine to all the bodies which compose the solar system, and demonstrated the same in the most evident manner, confirming the laws which Kepler had discovered, by a laborious train of observation and reasoning ; namely, that u the planets move in elliptical orbits,” that “ they describe equal areas in equal times and that the squares of their periodic times are as the cubes of their distances. Two years after, his friend Dr. Barrow resigned to him the mathematical chair ; he became a member of parliament in 1688 ; and through the interest of Mr. Montagu, Chancellor of the Exchequer, who had been educated with him at Trinity College, our author obtained in 1696 the appointment of Warden, and three years after that of Master, of the Mint : he was elected in 1699 member of the Royal Academy of Sciences at Paris ; and in 1703 President of the Royal Society, a situation which he filled during the remainder of his life, with no less honour to himself than benefit to the interests of science. In 1705, in consideration of his superior merit, Queen Anne conferred on him the honour of knighthood : he died on March 20th, 1727, in the 85th year of his age. His works, collected in 5 volumes, 4to. with a valuable Commentary by Dr. Horsley, were published in 1784, b 2 4 THE ARTISAN. GZSOMZSTZt'Sr. Geometry is that branch of the Mathema- tics which treats of figure and extension ; and is divided* into Plane and Solid.* Plane Geometry being the foundation, not only of solid Geometry, but of most of the other branches of the Mathematics, it naturally falls to be considered before any of the other branches; — and as Euclid’s Elements is generally allowed to be the best system of Geometry that has yet made its appearance in the world, we shall adopt that celebrated work as our text-book in treating of Geometry, in this and the suc- ceeding Numbers of the Artisan. In attempting to illustrate, or explain, the following definitions and propositions, we are perfectly aware that many of our expressions and illustrations will be ob- jected to by the speculative and rigid mathematician ; but, as we have already stated elsewhere, our object is simplicity ; and to convey a knowledge of the sciences to those who are wholly unacquainted with them. DEFINITIONS.! 1. A Mathematical point is that which hath no parts nor magnitude. 2. A line is length without breadth. 3. The extremities of a line are points. It is evident that there is nothing in na- ture agreeing with, or corresponding to, a point or a line taken in the sense of the first and second definition ; but still they may be comprehended by the mind, for they may be conceived to mark the position where a real point or a line may be formed. In the case of a real distance between two places, which is certainly a line, no enquiry is ever made about the breadth of that distance. 4. A straight line joining any two points upon a plane, or surface, lies wholly on that surface. 5. A superficies is a space which has only length and breadth, or it is a surface, with- out thickness. In speaking of the superficies, or surface, of a table, a wall, or a field, the thickness is laid out of the question. 6. The extremities or boundaries of a superficies are lines, which may be either straight or curved.— A circle is bounded only by one line. * The word Geometry is formed from two Greek words; and literally signifies to measure tta earth. t Though some of Euclid’s definitions are omitted, as being unnecessary, yet those which are intro- duced here are numbered as in Dr. Simpson’s Euclid, which is the one we intend to use in the present work. 7. A plane superficies is that in which any two points being taken, the straight line joining them lies wholly in that super- ficies. This will perhaps be better understood by considering the nature of a curved su- perficies; as the surface of a globe, for example. If two points be taken on its surface, the straight line that joins them does not lie wholly in that superficies, and therefore, the surface of a globe is not a plane superficies. 9, A plane rectilineal angle is the incli- nation of two straight lines to each other, meeting in a point. Or, it is the opening, or diverging, of two straight lines from a point. If there be only one angle at a point, as at A, then it may be expressed by one letter placed at the angular point. But when several angles are formed at the same point, it is necessary to employ three letters, to express any one of these angles; and the letter which is at the angular point is put between the other two letters.* Thus the angles at the point B, which is formed by the lines B C and B D, is named the angle CBD or DBG; and the angle formed by the lines B D and B E, is named the angle DBEorEBD. When two angles are separated from each other only by a straight line, as the angles CBD and DBE, they are called adjacent angles. 10. When a straight line standing on another straight line makes the adjacent angles equal to one another, each of these angles is called a right angle; and the * A straight line is usually expressed by placing a letter at each end of it. THE ARTISAN. line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A circle is a plane figure contained by one line, which is called the circum- ference ; and is such, that all straight lines drawn from the centre to the circumference are equal to one another.* 14. A diameter of a circle is a straight line drawn through the centre, and termi- nated both ways by the circumference. 15. A semi-circle is that part of a circle contained between the diameter and cir- cumference. * A plane surface included by one or more lin is called a mathematical figure, as a triangle , square, &c. 16. A segment of a circle is that part of the circle contained between part of the circumference, and a straight line which cuts off that part of the circumference. 17. Rectilineal figures are those which are contained by straight lines. 18. Trilateral figures, or triangles, are contained by three straight lines,. 19. Quadrilateral figures by four straight lines. 20. Multilateral figures, or polygons, by more than four straight lines. 21. An equilateral triangle is that which has three equal sides. 22. An isosceles triangle, is that which has two sides equal. 23. A scalene triangle, is that which has three unequal sides. 24. A right angled triangle, is that which has a right angle in it. THE ARTISAN. 25. An obtuse angled triangle, is that which has an obtuse angle in it. 26. An acute angled triangle, is that which has three angles acute. 30. A rhomboid, is that which has its opposite sides equal to one another, but none of its angles are right angles All other four- sided figures besides these are called trapeziums. Parallel straight lines, are such as are in the same plane, and though produced ever so far both ways, do not meet. 27. Of four-sided figures,— a square is that which has all its sides equal, and all its angles right angles. 28. An oblong, or rectangle, is that which has all its angles right angles, but not all its sides equal. 29. A rhombus, is that which has all its sides equal, but none of its angles are right angles. MECEAH€S-a Mechanics, is a mixed mathematical sci- ence, which treats of the nature, produc- tion, and change of motion. When bodies are free to obey the im- pulses communicated to them, that branch of Mechanics which treats of their motion is called Dynamics. Dynamics is the most elementary branch of the doctfine of motion, and is also the most general in its principles. Previous to entering upon the explana- tion of the general laws of motion, or what is termed the composition and resolution of forces , it will be necessary to state a few of the general properties of matter, as well as to explain a few terms which frequently occur in treating of philosophical subjects. Matter is a substance, the object of our senses, in which are always united the following properties : extension, figure, solidity, mobility, divisibility, gravity, and inactivity. Extension may be considered in three points of view : 1st. As simply denoting the part of space which lies between two points, in which case it is called distance. 2d. As implying both length and breadth, w hen it is denominated surface or area. 3d. As comprising three dimensions, length, breadth, and thickness ; in which case it may be called bulk, solidity, or content. When considered as a property of matter, it is used in the last of these senses. Figure , is the boundary of extension : for all bodies are included by one or THE ARTISAN. 7 more boundaries, and consequently possess figure ; they have also the capacity of receiving an indefinite variety of figures. Some bodies receive new figures with diffi- culty, but maintain them easily ; such are the bodies usually called solid. Others receive any figure easily, but cannot main- tain it without the assistance of other bo- dies ; fluid bodies are of this kind. Many bodies have figures that are pecu- liar to them in their natural state. This is the case not only with plants and animals, but with certain mineral productions called crystals, which are usually bounded by plane surfaces. Mobility , or a capacity of being moved from one place to another, is a quality found to belong to all bodies upon which we can make suitable experiments ; hence we conclude that it belongs to all bodies. Divisibility signifies a capacity'of being separated into parts. That matter is thus divisible, our daily experience convinces us. How far the divi- sion can actually be carried is not so easily ascertained : we are., however, certain that many bodies can be divided into very mi- nute parts. Of this we have examples in the gilding of silver wire, in the propaga- tion of odours, ^and in the colours produced by chemical solutions, &c. These, and other considerations, lead us to conclude that the division of matter is carried to a degree of minuteness far exceeding the bounds of our comprehension ; and it seems not unreasonable to suppose, that this capability of division is without limit, or as it is usually expressed, ad infinitum. That any portion of extension is divisible into parts which become less and less without end, may easily be perceived, by a moment’s consideration of the following figure. Suppose the line AB is to be divided into as minute parts as possible. It will soon be perceived, that if the line A C be extended indefinitely, and that an unli- mited number of points, as E, F, G, &c. may be taken in it ; and if straight lines be drawn from these points to the point D, the line A B will be divided into an inde- finite number of parts. Hence it appears that the division of the line A B may be continued ad infinitum. Gravity is the tendency which all bodies have to the centre of the earth. That all bodies have this tendency expe- rience convinces us ; for we see that when a body is supported, its pressure is exerted in that direction ; and when every impe- diment is removed, it always descends in that direction. The weight of a body is its tendency to the earth, compared with the like tendency of some other body, which is considered as a standard. The weight of a given body may, therefore, be employed to measure the weights of all other bodies. From these definitions it appears, that gravity must be distinguished from weight ; for the force of gravity is the same in all bodies ; that is, all bodies have an equal tendency to the earth, and would fall at the same rate to the ground were the resistance of the air removed ; but it is well known that the weight of all bodies are not the same. As gravity is a property belonging to every particle of matter, however minute, the weight of a body is the sum of the gravities of all its particles ; or it is the product of all its particles, multiplied by a single particle. Inactivity may be consi- dered in two lights : 1st. As an inability in matter to change its state, whether it be at rest or in motion. 2d. As that quality by which it resists any such change. In this latter sense it is usually called the force of inactivity , the inertia, or the vis inertice. That a body resists any change in its state of rest, or uniform rectilinear motion, is known from constant experience. We cannot move the least particle of matter without some exertion ; nor can we destroy any motion without perceiving some re- sistance.* Thus we see, in general, that inertia is a property inherent in all bodies with which we are acquainted ; different indeed in different cases, but existing, in a greater or less degree, in all. These properties, which are always found to exist together in the same sub- stance, have sometimes been said to be essential to matter. Whether they are or are not necessarily united in the same sub- stance, it is impossible to decide, nor does it concern ns to inquire. Our business is not to find out what might have been the constitution of nature, but to examine what it is in fact, and to account for the pheno- mena, or appearances, which fall under our observation, from those properties of * This resistance is quite distinct from, and inde- pendent of , gravity ; because it is perceived where gravity produces no effect : as when a: wheel is turned round its- axis, or a body moved along a horizontal plane. THE ARTISAN. 8 matter which we know by experience that it possesses. The density of a body is measured by the quantity of matter it contains in a given bulk; and the quantity of matter in any body is always proportional to its weight. That is, a body which is double the weight of another body contains double the quan- tity of matter. The specific gravity of a body is the weight of a given bulk of it, compared with an equal bulk of another body, which is assumed as a standard of comparison.— Water has been generally assumed as this standard ; hence it is said that the specific gravity of gold is 19, which signifies that any given bulk of gold is as many times the weight of an equal bulk of water. By motion we understand the act of a body constantly changing its place ; and is generally considered of two kinds, absolute and relative. A body is said to be in absolute motion, when it is actually transferred from one place to another ; and to be relatively in motion , when its situation is changing with respect to the bodies around it. These two kinds of motion often coin- cide ; as for example, when a person walks from any given place to another, he changes his place both absolutely and relatively with respect to the first place ; but if another person walks by his side all the time, he has no relative motion with respect to him. When a body passes over equal parts of space, in equal portions of time, its motion is said to be uniform. When its motion continually increases, it is said to be acce- lerated ; and when it continually decreases, to be retarded. If it increases or decreases uniformly, it is said to be equally accele- rated, or retarded. When a body falls from any considerable height, its motion is uniformly accelerated, or its velocity increases proportionally to the time ; but if a body be projected directly upwards, its motion will be uniformly re- tarded, or its velocity will decrease pro- portionally to the time it has been in motion. In measuring the velocity of bodies, it is necessary to take a certain portion of time as the unit, or standard, to which all other portions of time may be referred. The unit generally employed for this purpose is one second. 