GIFT OF MICHAEL REESE 66 V THE PATTERN MAKER'S ASSISTANT: EMBRACING LATHE WORK, BRANCH WORK, CORE WORK, SWEEP WORK, FBiOTIOAL GEAE CONSTRUCTION; PREPARATION AND USE OF TOOLS ; TOGETHER WITH A LABGB COLLECTION OF USEFUL AND VALUABLE TABLES. SECOND EDITION. BY JOSHUA ROSE, M. E., w * AUTHOR OK "COMPLKTK PRACTICAL MACHINIST." WITH 250 ILLUSTRATIONS. NEW YORK : D. VAN NOSTRAND, PUBLISHER, & MURRAY STREET & 27 WARREN STREET. LONDON: E. & F. N. SPON, 48 CHARING CROSS. r 8. COPYRIGHT, 1877. BY D. VAN NOSTRAND STEREOTYPED AND PRINTED BY THE NATIONAL PRINTING CO., 13 CHAMBERS STREET, NEW YORK. PREFACE. THE object of this book is to impart a knowledge of Pattern Making that shall be useful to apprentice Pattern Makers, and also to practical machinists, because the draw- ings of the designer do not as a rule give any instructions as to the construction of the patterns, while at the same time that construction may affect to a considerable degree, the manipulations of the machinist. Furthermore, it often occurs in the experience of a gen- eral machinist, that he is required to make a pattern either in iron or wood, and the complete isolation which usually exists between the pattern shop and the machine shop, is an effective bar to the acquisition of knowledge by obser- vation. The information is given from actual pattern shop prac- tice, and in the ordinary workshop parlance. The tables have been selected with a view to a collec- tion comprising all that the Pattern Maker of the widest experience requires ; arranged for his convenience, although in as compact a form as possible. CONTENTS. CHAPTER I. PAGE. General Remarks, - 11 Selection of Wood, - 15 Warping of Wood, 17 Drying of Wood, 18 Plane-irons, 20 Grinding Plane-irons, 21 Descriptions of Plauca, 24 Chisels, - 33 Gouges, 36 Compasses, 38 Squares, 39 Gages, 42 Trammels, 44 Winding-strips, - 45 Screw-driver, 47 48 49 CHAPTER II. 51 Lathe Hand-rest, 51 Lathe Head, - 54 Lathe Tail-stock, - 56 Lathe Fork, 57 Lathe Chucks, 58 Gonge, - - 66 Skew-chisel, - 68 Turning Tools, . . - - 70 CHAPTER III. Molding Flask, . ~ . . - 73 How a Pattern is Molded, - 74 &nar> Flash. 76 V CONTENTS. CHAPTER IV. Description of Cores, ..... Core-boxes, ---.... Examples of Cores, ..... Swept Core for Pipes, etc., - .... CHAPTER V. Solid Gland Pattern, - ... Molding Solid Gland Pattern, Gland Pattern without Core-print, . . Gland Pattern made in Halves, - Bearing, or Brass Pattern, - - ' I Rapping Patterns, . - . Example in Turning, Sand-papering, - ... Pattern Pegs, - .... Pattern Dog, or Staple, - - Varnishing, - ... Hexagon Gage, - - Scriber, CHAPTER VI. Example in T-joints. or Branch Pipes, Example in Angular Branch Pipes, .... Core-box for Branch Pipes, CHAPTER VII. Double-flanged Pulley, - .... Molding Double-flange Pulley, - Building up Patterns, - ... Shooting-board, - - . . Jointing Spokes, - . - . . CHAPTER VIII. Pipe Bend, - - - 143 Core-Box for Pipe Bend, - 147 Swept Core for Pipe Bend, - 150 Staving, or Lagging, - - - 151 Lagging Steam Pipes, - 156 CONTENTS. V CHAPTER IX. PAGE - Globe Valve, Chucking Globo Valve, Core-boxes for Globe Valve, CHAPTER X. Bench, and Bench-stop, Bench-hoot, Mortise and Tenon, - Half-lap Joint, Dovetail Joint, Mitre-box, Pillow Block, CHAPTER XI. 17S Square Column, Block for Square Column, Ornaments for Square Column, Cores for Square Columns, Patterns for Round Columns, - CHAPTER XII. Thin Work, Window Sill, .... Blocks for Window Sill, CHAPTER XIII. Sweep and Loam-work, Sweeping up a Boiler, Sweep Spindle, Sweeping up an Engine Cylinder, CHAPTER XIV. 199 Gear-wheels, - Construction of Pinion, Construction of Wheel-teeth, Gage for Wheel-teeth, Bevel Wheels, ^ Building up Bevel- wheels, viii CONTENTS. CIIAPTEK XIV. Continued. PAGE. Worm Patterns, - - 213 Turning-screw of Worm Pattern, - - - 213 Cutting Worm by Hand, - 216 Wheel Scale, - ..... 218 CHAPTER XV. Patterns for Pulleys, - - 221 Section Patterns, - - 222 CHAPTER XVI. Cogging, - - . 225 Woods Used for Cogging, - - 226 Templates for Cog-teeth, - - . - 227 Sawing Out Cogged Teeth, - 228 Boring Cogged Teeth, - 231 CHAPTER XVII. Machine Tools for Pattern Making, - - 234 Face Lathe, 236 Jig Saw, - - 237 Band Saw, - .... 240 Circular Saw, - - 241 Planing Machine, 242 Glue Pot, - 243 CHAPTER XVIII. Shrinkage of Solid Cylinders, 244 Globes, - - 244 " Disks, - - - 245 " Round Square Bars, - - 245 " Rectangular Tubes, 245 " U-shaped Castings, - - 246 l ' Wedge-shaped Castings, - - 246 " Ribs on Plates, - - 246 General Laws of Shrinkage, - 246 Table of Shrinkage, - - 247 Calculating Thickness of Thin Pipes, - 248 Calculating Thickness of Cylinders for Hydraulic Presses, 249 Calculating Rims of Fly-wheels, - - 249 CONTENTS. ix TABLES OF USEFUL INFORMATION. PACK. Mixtures of Metals, 250 Melting Points of Metals, 250 Weight of Patterns and Castings, 251 Weight of Timber, - 251 " Cast Metals, 251 Weight of a Lineal Foot of Flat Cast Iron, - - 255 Weight and Strength of Ropes and Chains, 255 Weight of Wire per Lineal Foot, - 257 Weight of Metal Plates per Square Foot, 258 Weight of Water in Pipes, - 259 Measures of Length, - 260 Square Measure, ... . 261 Solid, or Cubic Measure, - ... 261 Avoirdupois Weight, - - 262 Troy Weight, 262 Ale and Beer Measure, - 263 Wine Measure, 263 Foreign Measures of Length, compared with United States, 264 French Measures of Length, 265 Conversion of English Inches into Centimetres, - - 265 " Centimetres into English Inches, 266 " English Feet into Metres, - 266 ' Metres into English Feet, 266 " French Measure in United States, - - 267 Decimal Equivalents for Avoirdupois Weight, - 268 " " Troy " - - 268 " " Long Measure, 268 Weight of Water in Decimal Equivalents, - - 269 " at Different Temperatures, - 269 Diametral Pitch, - 270 Sizes of Paper, ..... 271 " Sheet Iron and Zinc, ... - 271 " Penny Nails, ----- 271 X CONTENTS. TABLES OF USEFUL INFORMATION.-Coutinucd. PAGE. Sizes of Tapping-boles, - 272 " Taps for Machine Screws, - - 272 41 Iron Washers, - 273 " Iron Wire Rope, - 273 Tables of Diameters, Circumferences, and Scale of Equal Squares, 274 Tables of Squares, Cubes, Square Roots and Cube Roots of Numbers, -, - 284 Tables of Diameters, Circumferences and Areas of Circles/ and the Contents in Gallons, at a foot in depth, - 297 Tables of Decimal Equivalents, - 300 Conversion of Vulgar Fractions into Decimals, - 300 " Fractious of an Inch into Decimals of a Foot, 301 " Inches and Fractions into Decimals of a Foot, 3?1 " Inches into Decimals of a Yard, - 301 Decimal Equivalents of Pounds and Ounces Avoirdupois, 301 Scantling and Timber Measure, - 302 To find the Chordial Pitch of Teeth, - - 307 Table of the Radii, Number of Teeth, and Pitch of Gear Wheels, from to 1 inch Pitch, 308 Table of the Radii, Number of Teeth, and Pitch of Gear Wheels, from 1 to 3 inches Pitch, - - - 314 THE PATTERN MAKER'S CHAPTER I. PATTERN MAKING. THOSE savans who have read our old earth's unwritten history in and from its strata, tell us that, in ages far remote, men made tools and contrivances of bronze, which, being an alloy, necessitated the fusion and casting of the metal. This casting involves the use of patterns, and pattern making may therefore lay claim to the highest antiquity. But the modern idea of the division of labor has exalted it to be a distinctive art ; in the last generation, for instance, a good machinist (or rather engineer or millwright, for those terms were then applied to builders of machinery,) was required to be alike expert in working upon both wood and metal. He constructed his framing of wood, and made the patterns for his cast metal work ; he was to-day a lathe hand, to-morrow a vise hand. As, however, the present age of iron dawned, it became apparent that working in wood and in metal must be sepa- rated, not only because the handiwork could be more cheaply produced by reason of the increased skill arising from con- tinuous practice, but also because the amount of knowledge required to make an artisan skillful in either the manu- facture of wood or of iron, was too great to be thoroughly mastered in the working lifetime of an ordinary, or even an unusually expert workman. Hence modern intelligence 12 PATTERN MAKER'S ASSISTANT. soon discovered that better as well as cheaper work could be obtained by a practical education in one particular 1 1 branch of usefulness, and hence pattern making has taken its place as a specialty. The field of usefulness of cast iron ; Jia;s deVklbipted I to, a remarkable extent during the last twenty yeafs/and the same remark applies to cast steel during the last ten years j both of these materials are steadily encroaching upon the domain of usefulness of wrought iron, stone, and bricks and mortar. So that the field of application for pattern making is stretching out- ward and onward, to the discomfiture of its rivals. From these considerations, we may readily perceive that a real proficiency in pattern making will exercise to the utmost the skill of the workman, on account of the unceasing va- riety of the patterns, in form and in the purposes for which they are designed ; and the advantage of a retentive mem- ory is evident when we consider that years may elapse ere the same pattern maker may be called upon to exercise his skill upon the same or a similar piece of work. In this art, there are to be considered many details that are seldom or never shown in drawings; such, for instance, as the amount necessary to allow on the pattern for finishing certain parts of a casting, and on what part such allow- ance is required j and the method which has been proved by experience to be the safest and most expeditious in molding from a certain kind of pattern. But above all these considerations lies the fact that drawings merely show the shape which the finished pattern is required to have, leaving it entirely to the judgment of the pattern maker to elect in what way the various pieces of wood (of which the pattern is constructed) shall have the grain lie, and how they shall be fastened or held together. There is, it is true, an unwritten practice which has obtained universal observ- ance in particular branches of pattern making 5 but in the newer fields into which the art has advanced and is ad- UNIV PATTERN MAJQNG^^C/IM 13 vaneing, this unwritten practice is merely in the process of formation, which state of things must continue so long as casting is discovered to have new arenas of application. A goodly store of well remembered experience is therefore invaluable to the pattern maker ; and this being so, the quicker it is obtained the better. Hence the learner should always keep a record of the work which falls under his observation, in which record the sizes and proportions of the work, the method of putting it together, the time taken in its production, and (if possible) whether the castings were satisfactory, noting the defects in the latter, if any, together with suggestions for the remedy of those defects. A pen and ink sketch of the pattern made in the margin will add to the usefulness of the record, besides accustom- ing the hand to making correct sketches and elucidating the explanation. The operative's intelligence will be much exercised in the shaping and building-up of patterns, de- pending as this does on the strength of the material of which the casting is to be made, the strength of the pattern itself, and the desirability of its molding well. Dr. An- drews has well said (in the English Mechanic) : " The cor- rect forms to be given to the materials employed in the construction of tools or machinery depend entirely upon natural principles. Natural form consists in giving to each part the exact proportion that will enable it to fulfill its assigned duty with the smallest expenditure of material, and in placing each portion of the materials under the most favorable conditions of position that the circumstances will admit of. Such natural form is not only the most economi- cal, but, strange to say, it is always correct in every respect, and is invariably beautiful and lovely in its outlines." I may now mention the qualifications necessary to en- able an artisan to become a good pattern maker : First : As the idea of the size and contour of the article or work required will be conveyed to him by drawings, it is neces- 14 PATTEllN MAKEK'S ASSISTANT. sary that he should be conversant with the principles of mechanical and architectural drawing ; and it may be of great advantage to him, though it is not absolutely neces- sary, to be able to make such drawings. It is too often the case that the apprentice pattern maker gains his knowl- edge of drawing from the drawings from which he operates, which, being simple in the first case, and becoming compli- cated only after the lapse of two or three years, makes the acquisition of a knowledge of drawing possible without either study or application ; but the result is that, so soon as he is called upon in a new field of action, upon a descrip- tion of work different from that to which he has been ac- customed, he becomes timid, gets confused, finds it neces- sary to ask many questions upon and concerning various parts of the drawings, and then does not obtain credit for the amount of ability to which his skill in handling his tools perhaps entitles him. Furthermore, a knowledge of draw- ing will enable him to learn his trade in a comparatively short space of time, and give him confidence in, and a re- tention of, that which he has already learned. Secondly : He should be perfectly familiar with the operations of the brass and iron founder, as it is by him that patterns will be used to produce the required forms. The pattern must be so made that a mold can be made from it, and that it may be made in the most expeditious manner. The pattern maker, it must be remembered, determines how the mold- er is to mold the pattern, so that the latter is controlled in his operations by the former. For the benefit of those who have been unable to devote sufficient time to the work of the foundery, it will be necessary, as we proceed, to explain the operations of molding different kinds of pat- terns, selecting those which will best serve as a key to the whole. Thirdly : The pattern maker must be acquainted with some, at least, of the properties of the metals of which the castings from his patterns are to be madej such, SELECTION OF WOOD. 15 for instance, as how they behave in passing from the fluid, to the solid state, the strains to which a casting is sub- ject during this transition, to what extent those strains may be modified by alterations of proportion or shape in the pattern, the shrinkage of castings, and the alteration in form which takes place in the cooling of castings of various sizes and shapes. Fourthly : He should, if pos- sible, add to the above qualifications a general knowledge of the manner of fitting up the different kinds of work for which patterns are used. With regard to the first requirement, it is not my purpose to enter into the subject of mechanical drawing, which is treated of in books devoted exclusively to that subject. With regard to the second, I shall, as already stated, refer to it hereafter. The third I shall consider after I have treated upon timber, and tools ; and the fourth can only be obtained by watchfulness on the part of the student as to what is being done in the workshop in which he is engag- ed. This latter may seem a trivial matter j but I have on several occasions, by watching where certain castings re- quired to be most operated upon in the machine or vise, had a pattern altered, making it apparently of an incorrect form, with the result that the time necessary to fit the work was reduced by one half. This subject, however, will be treated upon in its proper place. Of the different kinds of wood serviceable to the pattern maker, pine is, for many reasons, usually employed. It should be of the best quality, straight-grained, and free from knots ; it is then easy to work in any direction, possessing at the same time sufficient strength for all but the most del- icate kinds of work, and having besides the quality of cheap- ness to recommend it. Care taken in its selection at the lum- ber yard will be amply repaid in the workshop. When it is straight-grained, the marks left by the saw will show an even roughness throughout the whole length of the plank; 16 PATTERN MAKER'S ASSISTANT. and the rougher the appearance, the softer the plank. That which is sawn comparatively smooth will be found hard and troublesome to work. If the plank has an une- ven appearance that is to say, if it is rough in some parts and smooth in others the grain is crooked. Such timber is known to the trade as catfaced. In planing it, the grain tears up, and a nice smooth surface cannot be obtain- ed. Before purchasing timber, it is well to note, what con- venience the yard possesses for storing. Lumber on the pile, though it be out in all weathers, does not deteriorate, but becomes seasoned; nevertheless its value is much in- creased if it has an extemporized roof to protect it from the sun and rain j but as it is not convenient to visit the pile for every customer, quantities are usually taken down to await sale, and for such, a shelter must be provided, otherwise it will be impossible to insure that the lumber is dry, sound, and fit for pattern making ; it being obvious that the foregoing remarks on the storage of lumber apply to all woods. The superiority of pine for pattern making is not, how- ever, maintained when we come to fine delicate patterns or patterns requiring great durability. When patterns for fine work, from which a great many castings are to be made, are required, a pattern wherefrom to cast an iron pattern is improvised, because, if pine were employed, it would not only become rapidly worn out, but would soon warp and be- come useless. It is true that a pine pattern will straight- en more easily than one made of a hard wood ; but its sphere of usefulness in fine patterns is, for the above rea- sons, somewhat limited. Iron patterns are very desirable on account of their durability, and because they leave the sand easily and cleanly, and because they not only do not warp, but are also less liable than wooden ones to give way to the sand, while the latter is being rammed around them by the molder a defect that is often experienced with light PATTERN MAKING. 17 patterns, especially if they are made of pine. Iron patterns, however, are expensive things to make, and therefore it is that mahogany is extensively employed for fine or durable pattern work. Other woods are sometimes employed, be- cause they stand the rough usage of the molding shop better and retain the sharp corners, which, if pine be used, in time become rounded, impairing the appearance of the casting. Mahogany is not liable to warp, nor subject to decay 5 and is for these reasons the most desirable of all woods employed in pattern making, providing that first cost is not a primary consideration. There are various kinds of this beautiful wood, that known as South Ameri- can mahogany being chiefly used for patterns. Next to mahogany we may rank cherry, which is a very durable wood, but more liable to twist or warp than mahog- any, and it is a little harsh to the tool edge. If, however, it is stored in the workshop for a length of time before be- ing used, reliable patterns may be made from it. In addi- tion to these woods, walnut, beech, and teak are some- times employed in pattern making. The one property in all timber to be specially guarded against is its tendency to warp, bend, expand, and con - tract, according to the amount of humidity in the atmos- phere. Under ordinary conditions, we shall be right in supposing a moisture to be constantly given off from all the exposed surfaces of timber j therefore planks stored in the shop should be placed in a rack so contrived that they do not touch one another, so that the air may circulate be- tween the planks, and dry all surfaces as nearly alike as possible. If a plank newly planed be lying on the bench on its flat side, the moisture will be given off freely from the upper surface, but will, on the under surface, be con- fined between the bench and the plank : the result being that a plank, planed straight and left lying as described, will be found, even in an hour, to be curved, from the con- 18 PATTERN MAKER'S ASSISTANT. traction of the upper surface due to its extra exposure j aud therefore it is that lumber newly planed should be stored on end or placed on edge. Lumber expands and contracts with considerable force across the grain ; hence if a piece even of a dry plank, be rigidly held and confined at the edges, it will shrink and rend in twain, often with a loud report. There is no appreciable alteration length- wise in timber from the above causes; and if two pieces be glued together so that the grain of one crosses that of the other, they can never safely be relied upon to hold. Hence they had better be screwed, so that there will be a little liberty for the operation or play of the above forces, while the screws retain their hold. The shrinkage, expansion, and warping of timber may perhaps be bet- ter understood by considering as follows : The pores of wood run lengthwise, or with its grain, and hence the moisture contained in these passes off more readily endwise or from any surface on which the pores terminate. Then again the wood shrinks precisely in proportion in which the moisture leaves it ; and if we have full knowledge of the direction of the grain, and of the position in which a piece of timber stands or lies, we can (all other things be- ing equal, that is to say, supposing there to be no artificial heat or other disturbing cause operating on one more than on another side of it) predicate in what direction it will warp. Thus, let A, Fig. 1, be a piece of timber having the direction of its grain as denoted by the lines ; then its surface, B B, which has the grain and pores terminating upon it, would al- low free exit of the moisture, and that face would dry first WARPING OF WOOD. 19 (especially if it lay uppermost) and would contract the most, so that after a time the shape of the piece would be curved, as shown in Fig. 2. Now if it had been placed to lay with the face, 0, uppermost, the warping would have been much less, because the extra porosity of the face, B B, would have been counteracted by the lack of circulation of air. If, on the oth- er hand, it was placed endwise, the warping, though it would have taken place, would have been appreciably less. It must not be supposed that thoroughly seasoning the timber will remove the tendency to warp, for timber, however long and carefully it has been dried or seasoned, undergoes con- siderable transformation of shape so soon as much of its outer surface is removed, making it appear that the season- ing or drying process takes place mainly at and near the outer surfaces, and is renewed every time an entirely new surface is presented to the action of the atmosphere. Thus, if we take a thoroughly seasoned piece of wood 3 inches square and 1 foot long, and cut it into strips 1 inch square and 1 foot long, the pieces will warp in a day or so ; and if, after a few days, we take those inch strips and cut them into strips i^ inch square and 1 foot long, these latter will again warp ; and no matter what pains might be taken with these last strips to season them and let them assume then? new shape, were we to cut them into thin veneers the warping process would again set in. It is well, therefore, hi particular work, to cut out roughly the various parts of the pattern, so that, while some parts are being operated upon, the others may be assuming their new shape, and thus become not so liable to warp after being worked up in the pattern. 20 PATTERN MAKER'S ASSISTANT. TOOLS, ETC. One of our first requisites in the way of tools and appli- ances will be a carpenter's bench, which may be made as follows : Three pieces of stuff, 2x5 inches and 3 feet long, will serve for supports for the top. Two 12 inch boards, 12 feet long and 1 inch thick, will do for the sides. Nail these side boards firmly to the 2x5 inch cross pieces, and put on a top of suitable material, and the bench is ready for the legs. Now take four pieces of stuff, 2x5 inches, and of the requi- site hight for the legs, and frame a piece 1x3 inches across each pair of legs, about G inches from the bottom, placing the legs at the distance apart necessary for the width of the bench. Then cut a fork or slit in the top end of each leg, so as to straddle the cross piece at the ends, and put a bolt 3^x|^ inches through each leg and through the side boards, and the bench will be complete ; and it will possess the advantage that it can be taken down in a few minutes by removing the bolts from the legs. The jack plane is employed for roughing off the surface timber ; the stock is made of beech and the blade of cast steel. The blade acts most effectively when it is ground well away toward the corners, thus producing a curved edge, as shown in Fig. 3. When the blade is placed in the stock, and in position to cut off the largest amount of stuff, its cut- ting edge should protrude through the face of the stock TOOL GRINDING. 21 about a sixteenth of an inch, while the corners, A B, are about level with the face of the stock. The beveled face should stand at about an angle of 50 to the flat face. The grindstone should be kept true and liberally supplied with water; the straight face should not be ground away, nor indeed touched upon the stone. The pressure with which the blade is held against the grindstone should be slight at and toward the finishing part of the grinding process, so as not to leave a long ragged burr on the end of the blade, as is sure to be the case if much pressure is applied ; and it will occur to a slight extent even with the greatest of care. The blade should not be held still upon the grindstone, no matter how true, flat, or smooth the latter may be j but it should be moved back and forth across the width of the stone, which will not only grind the blade bevel even and level, but will also tend to keep the grindstone in good or- der. If a grindstone is in excellent condition (that is, true, flat, and level, or slightly rounding), as it should be, it tempts the workman to grind the plane blade with the stone running toward him, as shown in Fig. 4, for the following reasons : If the stone, A, travels in the direction of the arrow, 0, the plane blade, B, will relieve the abrasion of the stone at the cutting edge first, thus leaving it clean and with no tendency to leave a long ragged edge ; but if the blade were 22 PATTERN MAKER'S ASSISTANT. held on the other side of the stone, that is to say, with the stone running from the operator, as shown in Fig. 5, the re- sult will be a long ragged edge on the plane blade, espe- cially if much pressure be placed on the blade. In Fig. 5, A represents the grindstone, B the plane blade, and C the direction in which the grindstone is supposed to revolve : in which case it becomes evident that the plane blade will receive at its edge some pressure in the direction of the arrow, D 5 and the metal at the cutting edge of the blade, being very thin, gives way to this pressure and bends back instead of abrading off, leaving a long feather edge, as shown in Fig. 6, from A to B. This edge breaks off in many cases further back than it should do, and in- evitably breaks off when the blade is applied to the oil- stone, leaving upon the face of the oilstone particles of steel which must be removed before a good edge can be secured to the tool. As a rule, however, this feather edge is broken off by tapping the blade on the palm of the hand, or it may TOOL GRINDING-. 23 be removed by passing the edge lengthwise on a piece of wood. It is, however, better to hold the blade as shown in Fig. 4 ; but there are other considerations which sometimes render this impracticable. For instance, if the stone is out of true, the high spots will strike against the cutting edge, and render it impossible to hold the blade steadily, and hence impossible to grind it true. If the stone has soft spots in it, as most stones have, the blade will dig in those soft spots, and will also be thrown off the stone when en- countering an unusually hard spot. If, in consequence of digging in a soft spot, the blade catches, the cutting edge will be ground completely off; so that it is only under ex- ceptional and unusual circumstances that the blade can be ground in the position shown in Fig. 4. It is better, there- fore, to grind it in the position shown in Fig. 5, which is saf- er and surer. In oilstoning a plane blade, the straight face should be held quite level with the face of the oilstone, so that the cutting edge may not be beveled off. Not much appli ca- tion to the oilstone is necessary to the straight face, because that face is not ground upon the grindstone, and it only requires to have the .wire edge or burr removed, leaving an oilstone polish all along the cutting edge. The oilstoning should be performed alternately on the flat and beveled faces, the blade being pressed very lightly on the oilstone toward the last part of the operation, so as to leave as fine a wire edge as possible. The wire is the edge or burr which bends or turns over at the extreme edge of the tool, in con- sequence of that extreme edge giving way to the pressure of the abrading tool, be it a grindstone or an oilstone. This wire edge is reduced to a minimum by the oilstone, and is then so fine that it is practically of but little account ; to re- move it, however, the plane blade or iron may be buffed backwards and forwards on the palm of the hand. The iron being sharpened, we may screw the cover on, ad- justing it so that its edge stands a shade below the corners 24 PATTERN MAKER'S ASSISTANT. of the iron, and then screwing it tight ; the blade or iron and the cover must now be placed in the mouth of the plane stock, and adjusted in the following manner : The plane iron should be passed through the mouth of the stock until as much in depth of it is seen to protrude from the bottom face of the stock as is equal to the thickness of shaving it is intended to cut : to estimate which, place the back end of the plane upon the bench, holding the stock in the left hand with the thumb in the plane mouth, so as to retain the iron and wedge in position, the wedge being turned toward the workman. A glance down the face of the stock will be sufficient to inform the operator how much or how little the cutting edge of the iron protrudes from the face of the plane stock, and hence how thick his shaving will be. When the distance is adjusted as nearly as possible, the wedge may be tightened by a few light blows of the hammer. If, after tightening the wedge, the blade is found to protrude too much, a light blow on the fore end of the top face of the plane will cause it to retire. The wedge should be tight- ened by a light blow after it is finally adjusted. In using a jack plane, we commence each stroke by ex- erting a pressure mostly on the forepart of the plane, com- mencing at the end and towards the edge of the board, and taking off a shaving as long as the arms can conveniently reach. If the board is longer than can be reached without moving, we pass across the board, planing it all across at one standing ; then we step sufficiently forward, and carry the planing forward, repeating this until the jack planing is completed. To try the level of the board, the edge or corner of the plane may be employed 5 and if the plane is moved back and forth on the corner or edge, it will indent, and so point out the high place. The fore plane (or truing plane, as it is sometimes called) is made large, so as to cover more surface, and therefore to cut more truly. It is ground and set in the same manner OILSTONING. 25 as the jack plane, with the exception that the corners of the iron or blade, for about one eighth inch only, should be ground to a very little below the level of the rest of the cutting edge, the latter being made perfectly straight (or as near so as practically attainable) and square with the edge of the iron. If the end edge of the cover is made square with the side edge, and the iron is ground with the cover on, the latter will form a guide whereby to grind the iron edge true and square j but in such case the cover should be set back so that there will be no danger of the grind- stone touching it. The oilstoniiig should be performed in the manner described for the jack plane, bearing in mind that the object to be aimed at is to be able to make as broad and fine a shaving as possible without the corners of the plane iron digging into the work. The plane iron should be so set that its cutting edge can only just be seen projecting evenly through the stock. In using the fore or truing plane, jt is usual, on the back stroke, to twist the body of the plane so that it will slide along the board on its edge, there being no contact between the cutting edge of the plane iron and the face of the board, which is to preserve the cutting edge of the plane iron from abrasion by the wood ; as it is obvious that such abrasion would be much more destructive to the edge than the cutting duty performed during the front stroke would be. The face of the fore plane must be kept perfectly flat on the under side, which should be square with the sides of the plane. If the under side be hollow, the plane iron edge will have to protrude further through the plane face to compensate for the hollowness of the latter ; and in that case it will be impossible to take fine shavings off thin stuff, because the blade or iron will protrude too much, and as a consequence there will be an unnecessary amount of labor incurred in setting and reset- ting the plane iron. The reason that the under surface should be square, that is to say, at a right angle to the sides 26 PATTERN MAKER'S ASSISTANT. of the body of the plane, is because the plane is sometimes used on its side on a shooting board. When the under surface of the plane is worn out of true, let the iron be wedged in the plane mouth, but let the cut- ting edge of the iron be well below the surface of the piano stock. Then, with another fore plane, freshly sharpened and set very fine, true up the surface, and be sure the sur- face does not wind, which may be ascertained by the appli- cation of a pair of winding strips, the manner of applying which will be explained hereafter. If the mouth of a fore plane wears too wide, as it is apt in time to do, short little shavings, tightly curled up, will fall half in and half out of the mouth, and prevent the iron from cutting, and will cause it to leave scores in the work, entailing a great loss of time, in removing them at every few strokes. The smoothing plane is used for smoothing rather than truing work, and is made shorter than the truing plane, so as to bo handier in using. It is sometimes impracticable to make a surface as smooth as desirable with a truing plane, because of the direction of the grain of the wood. Thus in Fig. 7, let E represent a piece of stuff requiring to be planed on the upper surface, and let us plane it, cutting in the direc- tion of the arrow, D. It is evident that the edge of the plane iron, when cutting the surface from B to A, will strike against the edge or end of the grain of the wood, tend- ing to rough it up; whereas, while passing from A to C, the tendency of the pressure of the iron edge would PLANES. 27 be to smooth the grain of the wood downwards, the difference between the two tendencies being sufficient to make it necessary in many cases to use a smoothing plane, cutting in both directions, as shown in Fig. 7, first from A to B, cutting in the direction of the arrow, F, and then from A to C, cutting in the direction of the arrow, G. Thus the cutting will be at all times performed in the direction tending to smooth down and not rough up the grain of the wood. That this method of planing is neces- sary is demonstrated in planing across the end grain of wood, for which purpose the smoothing plane is almost in- dispensable, and in which operation it is necessary to use it, on small surfaces, with a side as well as with a forward sweep, thus producing a curved motion, the most desirable direction of which is determined by the direction of the gram of the wood. Fig. 8 represents an ordinary compass plane, which is a necessary and very useful tool for planing the surfaces of hollow sweeps. This tool is sometimes made adjustable by means of a piece dovetailed in the front end of the plane, as shown in Fig. 9, at A; which, by being lowered, alters the sweep and finally converts it from a convex to a concave. There is now, however, in the market a compass plane, the 28 PATTERN MAKER'S ASSISTANT. body of which is made of malleable iron with a sole made of a blade of spring steel, which, by the operation of two screws, can be set to any curvature, either concave or con- vex, within the capacity of the instrument. Kff.9. *J Another very useful species of plane is the router, shown in Fig. 10 ; which represents one of these planes in opera- FifflO. tion, A being the router, and B the work. The use of this tool is to plane out recesses (exactly to any given depth) such PLANES. 29 as are required to receive rapping plates. Tlie wood in the plane stock is cut away just over the edge of the iron, to give clearance for the shavings, and so that the cutter may be seen at work. BID VIEW Rabbet planes are narrow planes having the sole or side of a conformation to suit the work. Fig. 11 represents a rab- Fuji. \s bet plane to suit a round edge, Fig. 12, a similar plane for a groove, and Fig. 13 a side rabbet plane. The latter is, how- ever, very seldom used, but is especially useful in planing hard wood cogs fitted to iron wheels, or the teeth of wheel 30 PATTERN MAILER'S ASSISTANT. patterns, or other similar work. One or two flat bottomed ones will also be required. Small thumb rabbet planes, having an iron stock, with the blade near the front end, are now supplied, and are very useful for cutting out half checks that are not cut right across the stuff. Fig. 14 is an end, and Fig. 15 a side, view of a core box plane, suitable for planing semicircular grooves out of the solid. The principle of its construction and use is that the angle in a semicircle is a right angle. Suppose, for example, that Fig. 16 represents a piece of wood having a semicircular groove in it, and we mark off on the groove the points, a, fc, c, dj Cj and strike from, each of these a line direct to each corner of the groove. We shall thus find that the two lines struck will be at a right angle to each other, the two lines, A A, meeting at the point, a, being at a right angle. The two side faces, CC, of the plane in Fig. 14 are made to stand at a right angle to each other ; and while the plane is in position (as shown in Fig. 14) to bear against the corners of the core PLANES. 31 box, a semicircle (the apex of the plane, D, in Pig. 14) must be in the semicircle, and will only cut away the wood in the form of the circle, no matter in what position rJ6. a the plane stands, so long as its sides touch the corners of the semicircle. This being the case, the first operation in using this plane is to cut out the required semicircle to the necessary width, which may be done with a rabbet plane. The core box plane may thus be employed to cut out the semicircle, commencing at each of the corners and planing on each side down to the center of the depth of the RffJl semicircle. As this plane is intended to finish the work, it is desirable to cut away as much of the stuff as possible before employing it, the work appearing as shown in Fig. 17. These planes have one disadvantage. They are apt 32 PATTERN MAKER'S ASSISTANT. Fig. A. Fig. B. to abrade the corners of the work ; hence great care should be exercised in their use, and care must also be taken that the extreme point of the plane iron stands just at the apex of the angle of the body of the plane ; for if it be in advance or not up to it, the work will not be semicircular. Of late years there have been introduced planes having a stock of iron, the advantage being that the mouth docs not wear larger, the soles keep true, and all parts are interchange- able. The blade of the block plane, shown in Fig. A, is set at a greater angle, as is ne- cessary for planing the end gram of wood. The circular plane, shown in Fig. B, is an especially desirable tool, be- cause the solo can be set to any desir- ed curve, either con- cave or convex, and the plane can be used clear up to the edge of the curve ; in which respect it possesses an advantage over the plane Fin C ^*s> shown in Figs. 8 and 9. jm In Figs. O and D are smoothing and jointer planes of this class; and it may be mentioned that the blades can be altered in adjustment while the plane is being operated. There is a sense of flatness in using these planes, that is S? Of THf UNIVF PLANES. 33 very desirable for true work. The manner in which the iron fits to the blade is shown in Fig. E, the iron being fig.D. Fly. E. curved to insure that it shall touch the blade close to the cutting edge, supporting and stiffening it so that thinner blades can be used, the latter being easier to grind and oilstone. Of chisels, the principal kinds used are the paring chisel, used entirely by hand pressure, and the lirmer chisel, for use with the mallet. The difference between the two is that the paring chisel is the longer. A paring chisel, worn to half its original length, will however answer for use as a firmer chisel, because, when so worn, it is sufficiently long for the duty. A chisel should not, however, be used indiscriminately as a paring and firmer chisel, for the rea- son that the paring chisel requires to bo kept in much bet- ter order than the firmer chisel does. It is necessary to have several sizes of chisels, varying in width from an eighth of an inch to an inch and a half. A paring chisel for general use is shown in Fig. 18. Its width is about one and a half inch, and its handle should be exactly of the form shown in the engraving ; the total length of handle 2* 34 PATTERN MAKER'S ASSISTANT. being six inches, from A to B being one and a half inch, and the diameter at O, and from B upwards, being one and a half inch. The hollow below B is of three-eighths inch FiaJS. B" B- JO C -( A J radius, and the diameter at D is one inch . This shape and size gives a good purchase, especially from A to B, where the hand is most often applied, the end, E, being against CHISELS. 35 the operator's shoulder. A firmer chisel having a handle of the ordinary pattern is shown in Fig. 19. Chisels are sharpened in the same manner as plane irons; but being usually narrower, they require special attention in the grinding, as they should be held against the grind- stone with an amount of pressure proportionate to their width. In describing Figs. 5 and 6, it was explained how a long feather edge may be given to a tool in the grinding ; and these remarks apply especially to chisels. Hence, to- wards the finishing part of the grinding operation, the chisel should be held very lightly against the stone ; the flat face of the chisel should never be ground, but should be kept straight and even, otherwise the whole value of the tool will be impaired. In setting the edge of a chisel upon an oilstone, it is necessary to exercise great care that the hands are not elevated so as to oilstone the blade at a different bevel to that at which it was ground, and not to allow the movement of the hands to be such as to round off the bevel face at and near the cutting edge an error which, from lack of experience, is very apt to occur. The position in which the bevel of the chisel should be pressed to the oilstone should be such that the marks made by the oilstone will lie from the back of the bevel to the cutting edge, but be shown more strongly at and towards the cut- ting edge. The motion of the hands of the operator should not be simply back and forth, parallel with the length of the oilstone, but partly diagonal, which will greatly assist in keeping the bevel level with the oilstone. Very little pressure should be applied to the chisel during the latter part of the process of oilstoning; and the flat face of the chisel should be held level with the face of the oilstone, and moved diagonally under a light pressure, sufficient only to remove the wire edge. After the setting is complete, the chisel should be lapped upon the hand, to remove the fine wire edge left by the oilstone. 36 PATTERN MAKER'S ASSISTANT. The next tool is the gouge, of which there are several kinds. Those having the bevel on the concave side are termed inside gouges ; and when the bevel is on the convex side, they are called outside gouges. Gouges, like chisels, are also classed into firmer and paring gouges, the distinc- tion between the two being the same as in the case of chisels. It is not necessary to possess a full set of each kiisd of gou- ges ; half a set each of inside and outside will suffice. Fig. "20 represents a paring, and Fig. 21 a firmer, outside gouge. The inside gouge may be ground ;i little keener than the chisel or plane iron, and requires care in the operation, since it has generally to be ground on the corner of the grindstone, which is rarely of the same curve as the gouge requires. ID. oilstouiug a gouge, what is called a slip is employed. Slips are wedge-shaped pieces of oilstone, of various curves and shapes, to suit the purposes for which they are applied. The gouge should be held in the left hand, and the slip in the right, the latter being supplied with clean oil. The back or convex side of the gouge must be laid level on the face of the oilstone, and the handle worked to and from the workman, who must roll it at the same time, so as to bring every part of the curve of the gouge in contact with the face of the oilstone. All the remarks upon grinding and oilstoniug chisels apply with greater force to gouges, be cause the small amount of the surface of the gouge, in con- tact with either the grindstone or oilstone, renders it ex- tremely liable to the formation of a feather edge in grinding, and a wire edge in oilstoniug. In grinding outside gouges, a new feature steps in $ for if the gouge be kept at the same inclination throughout the grinding, as in the case of all the tools heretofore mentioned, the center of the gouge will be keener than the corners j to avoid which the gouge is given a rolling motion to bring every part against the action of the grindstone, while at the same time lowering the back hand as the corners of the gouge approach the stone. This SQUARES. 37 if evenly performed, gives an equal keenness to all parts of the cutting edge. The same rising and falling motion of the back hand is necessary in oilstoning the convex side of the gouge. The concave side is to be rubbed with an oilstone slip, taking care to let the slip be flat in the trough of the gouge and not elevated at the near end ; for if once a habit of beveling, however slightly, the flat faces of tools is con- tracted, it tends to increase, so that the tools finally lose their characteristics, and are in fact ruined, so far as their application to good work is concerned. Several sizes of squares are necessary to the pattern mak- er, because his work necessitates in many cases that the blade be short, in order to admit of its application to the Fw.ZZ. 'iff. work. Fig. 22 represents an ordinary try square j the blade should be of sawblade, and the back of hard wood, the in- side and outside edges of the back being covered with sheet metal, to prevent undue wear. In Fig. F is shown a try square which can be used as a simple square or as a mitre square. By simply changing the position of the handle, and bringing the mitred face at 38 PATTERN MAKER'S ASSISTANT. the top of the handle against one edge of the work in hand, a perfect mitre, or angle of forty-five degrees, can be struck from either edge of the blade. Fig.F. Tl 1 "1"" 1 E, \ \"- \ 4 1 IT \ \ \ \ \ 2 fia.23. J In addition to this, however, a bevel square is required ; and it is best to have one with a slid- ing blade, so that the length it projects from the square back, on eith- er side, may be adjusted to suit the work. Such a bevel square is illus- trated in Fig. 23. Of compasses there are two kinds, one being plain, and having no means of permanent adjustment, as shown in Fig. 24. This is used for casual measurements or marking. The other has an attachment by which it may be COMPASSES. 39 permanently set, as shown in Fig. 25, in which A represents a thumb screw employed to set one leg firmly against the radius piece, 7 and B being an adjusting screw for finally adjusting the compass points after the thumb screw, A, is fastened, the spring, D, operating to keep the leg, E, firm- ly against the face of the screw, B j so that, when the ad- justment of the compass points is once properly made, the compasses may be laid upon the bench and used from time to time without danger of the adjustment being altered by handling or by a slight blow. 40 PATTERN MAKER'S ASSISTANT. An excellent attachment for compass points has lately come into use; it is for the purpose of fastening to the marking leg a pencil, to avoid scratching the surface of the work with the compass point. This device and its mode of application are shown in Fig. 26, in which A represents a thin tube with the feet, G G, on it, and provided with the split, B. C is a clainp ? provided with a thumbscrew, E. Fiti.27. D represents one of the compass legs. F is a piece of lead pencil which passes through the tube, A. The attachment is slipped on the compass leg, and the screw is tightened up, clamping that leg to the feet, G G ; and clamping at the same time the pencil in the tube. Another of these attach- ments, in which the pencil point is adjustable in a direction GAGES. 41 other than that in which the compass point stands, is shown in Fig. 27, the pencil tube being swiveled at A, and i> representing the compass leg. The points of compasses should be forged out when they get thick from wearing short, and they should be tempered lo a blue color. For marking small holes, compasses are too cumbersome for fine work, and spring dividers are preferable. A recent improvement in these tools consists in making the spring helical, as shown in Fig. 20, instead of making it broad, flat, and thin, as formerly. Of gages for drawing marking lines at any regulated distance from the finished edge or edges of the work, there are several kinds. First we have that shown in Fig. 29, which is the kind ordinarily sold; others have, instead of the set screw, a wedge running lengthwise, as shown in Fig. 30. A better gage, however, than either of these is that shown in Fig. 31, in which A represents the tightening wedge, standing at a right angle to the rod of the gage. The advantage of this design is that it requires only one hand to work it, inasmuch as the w^edge may be loosened or tightened by striking it, as if it were a hammer, against 2** PATTERN MAKER'S ASSISTANT. anything that may happen to lie on the bench. Thus the gage may be set and adjusted with one hand, while the oth- er is holding the work, as is often necessary when marking small work. The marking point should be a piece of steel wire fitted tightly in the stem, the protruding part being ground or filed to a wedge, with the two facets slightly rounding, and whose broad faces stand at a right angle to the stem of the gage ; the point or edge only projecting suf- ficiently to produce a line clear enough to work by ; other- v/ wise it will not be suitable for accurate work. The mortise gage is similar to the above as regards the stem and slid- ing piece, but it is provided with two marking points, their distance apart being adjustable. Fig. 32 represents the gage referred to, the head screw working hi brass nuts. On account of the narrowness of the base afforded by the sliding piece on the common gage, there is not sufficient GAGES. 43 steadiness to gage to aiiy great width, so that for widths above ten or eleven inehes we must have recourse to the gage shown in Fig. 33. It is called the panel gage ; its sliding piece may be seven inches long, and the stem two fur 33. feet ; the rabbeting at A forms a steadying base, the part of the rod about the marking point being raised to corre- spond with the distance from the rabbet to the stem nut. Next we have the cutting gage, shown in Fig. 34, in which a steel cutter takes the place of the marking point, being wedged in position. It is employed to cut thin strips of wood ; that is to say, of thicknesses up to about a quarter of an inch. The cutter point should be tempered to a dark straw color. In Fig. G is shown a gage in which one side has a fixed Fig. G. point, and the other an adjustable one for mortise and oth- er similar work, the movable point being operated by the thumbscrew shown at the end. 44 PATTERN MAKER'S ASSISTANT. For marking off curves or large circles, we require a pair of beam compasses or trammels, as shown in Fig. 35. They are composed of two sliding sockets, made of either wood or metal, fitted, at a sliding fit, to a staff. They are made of various designs, to suit the taste of the maker, and are often made by the pattern maker himself during his term of probation. The style shown in Fig. 35 is one very easily made. A A represents a staff of any desired length, com- posed of common pine. B and C are the two sliding sock- ets or holders ; the mortises in them arc made to fit the thickness of the staff, but they are longer than they are wide, to admit of the fastening wedge. They may be made of some hard wood, such as maple. The lower parts being turned and fitted with brass ferrules, a small hole is then drilled up the turned end of each, into which brad- awls of large size are driven they are then pointed on a grindstone. The wedges are made with a gib head on the small end, so as to prevent them from flying out when tap- ped back to loosen the sliding sockets from the staff, for TRAMMELS. 45 adjustment. If maple be used for the sockets, then the wedges may be made of a dark colored wood, sandpapered and varnished two or three times, which will give them a neat appearance. Made as above described, the trammels will be light and almost everlasting 5 and as the materials are always at hand, the cost is a minimum. In place of the wedge, a screw may be, and sometimes is used, in which case a packing piece of either wood or sheet brass should be inserted, as shown in Fig. 36, at A, which will protect the staff from being indented by the end of the screw when the latter is tightened up. Our next requirement is the straight edge, which, for small work, is better of steel than of wood. A straight edge is a piece of stuff whose edges are straight and par- allel to each other, which is necessary because they are sometimes used in conjunction with the square. A pair of Straight edges, termed winding strips, are indispensable ; their use is shown in Fig. 37, in which A is a piece of work requiring to have its edge true; B B are the winding strips, placed on the work as shown, so that by casting the eye along the upper edge of one strip, and leveling the head so that the edge of one strip will be brought nearly horizontally level with the other, it will readily be perceived whether the two are level one with the other, and hence whether the face of the work is true. Winding strips are simply 46 PATTERN MAKER'S ASSISTANT. pieces, of wood made parallel and true, and generally about two feet long, three or four inches wide, and about five-eighths of an inch thick. When the edges have been made as straight as possible with the truing plane, one of these should be lightly chalked on its edge face and laid upon the other, and then moved back and forth through a distance of about one-half inch. The upper one should not be pressed to the lower, but allowed to lie of its own weight j otherwise it will spring to suit the outline of t lie lower one, or bear upon it at the points pressed by the hands. Before separating the two, take a blacklead pen- cil and make a mark on one side of each, so as always to bo able to bring the pieces together in the same way. Then separate them and ease away the high places, con- tinuing the truing operation until they bear all over. In placing thorn upon the work, be careful that they stand parallel to each other ; that is to say, that the distance between them is about the same at each end, otherwise the eye will bo misled in sighting them when on the work. SC11EW DRIVER. 47 IfaSft In Fig. 38, we have an ordinary screwdriver, the point of which should be shaped as shown at A, in Fig. 39, and not as shown at B, as is usually the case, because if the part entering the screw head is tapered, it not only raises a burr on the screw head, but it is liable to slip out, even from a screw that drives easily, and much more from one that drives hard. To grind it to the shape shown at A, it should be ground on that side of the stone in which the latter is running toward you, the length of the screwdriver being at a right angle to the plane of the stone and the handle held in one hand, while the driving end is held in the other, which should be supported by the grindstone rest. If the stone is a small one, the screwdriver, while being ground in this position, should be moved a little, so that fir3t one corner and then the other will approach the stone, so as to prevent the grinding from being hol- low, which would weaken the screwdriver point by thinning it in the middle. Screw- drivers should be made of cast steel, and tempered at the point to a blue color. The mallets should be of hickory, and of the form shown in Fig. 40 ; the sizes being, one 2^x3x5 inches long, and an- other about 3x3^x5^ inches long, the handles being mortised and properly wedged to the head. Of oilstones there should properly be two, one for rough- ing and one for finishing. Wichita or Arkansas stones are even in grain and cut well, and are the best for our pur- pose. In addition to the large oilstone, a number of slips of oilstone are necessary, some being flat, others half round 1 48 PATTERN MAKER'S ASSISTANT. and flat, with round edges, their uses being for gouges and other tools in which the cutting edges are hollow or curved. The. general oilstone should be kept with a flat face, other- wise it will be impossible to properly set plane blades, firmer and paring chisels, and other similar tools upon it. With this object in view, the workman should set small tools upon the ends, so as to prevent the stone from be- coming hollow in the middle. When it becomes necessary to grind the face of the oilstone, it may be done upon the grindstone ; but a better plan is to take a flat board and liberally supply it with clean sand and water, and then grind the oilstone on it by hand, leaving the face a little rounding in its length, by easing it off at each end, but leaving it flat across the face, by which means it will last longer without regrinding. There are some stones which are used with water instead of oil j they do not cut, as a rule, very freely, but the finer grades of them will cut unusually smooth. These are the descriptions used by the Japanese workmen, who use two stones, one to rough cut, which cuts very freely; the other to finish, which seems to grip the metal firmly, rendering it easy to keep the tool at the ne- cessary angle and level, while at the same time it cuts very finely indeed. The first is a bright yellow stone, the latter is of a green slate color hot water being used on both of them. Aside from those already mentioned, we have the Turkey stone, a close-grained and amber-colored stone, which cuts CALIPERS. 49 freely or fine, according to the grade of the stone. For all ordinary purposes the Arkansas stone will suffice, and it is obtaianble at almost every hardware store. The oil- stone for general use should be fitted into a block of wood, having a margin outside of the stone of one half inch on each side, and about an inch at each end, the block being hollowed on the bottom face so that it will stand firmly and not rock when in use. It should also be provided with a cover, to prevent dust and dirt from accumulating upon it. Two pairs of inside and three pairs of outside calipers are necessary to the pattern maker, the smallest of each pair being large enough to take in diameter up to four inches, the largest from four up to about ten inches. The other pair of outside calipers may be large enough to use upon diameters from ten to eighteen inches. For bores above ten inches a wire gage may be used, by bending a piece of wire as shown in Fig. 41, which may be shortened by being bent more, or lengthened by being straightened. It is preferable to make an adjustable gage, such as shown in Fig. 42, in which A and B represent two sliding pieces of steel ? and and D screws and nuts. It is obvious that, when the screws are loosened sufficiently to just let the sliding pieces move by a slight tap, the gage may be ex- tended by striking the ends, E, or either of them, their in- 3 50 PATTERN MAKER'S ASSISTANT. side edges being rounded off to prevent them from burring. It is better to set them at first a little below the required size, and to perform the adjustment by opening them, so as not to require to strike the point at all. The points should, however, in any event, be tempered to a blue. It is an ex- cellent plan to file away the screw heads on two sides, a little, say ^ inch, thus forming a sliding piece under each head to fit into the slot of the gage, which will prevent the screws from turning when screwed or unscrewed, and in the end save much annoyance. A small machinist's square and a steel rule are also necessary for small fine work, the wooden ones being too clumsy. The edges of the rule should be trued so that it may be used as a straight edge. OHAPTEE II. LATHE LATHE CHUCKS, AND LATHE TOOLS. To give the required form to various patterns, recourse must frequently be had to that useful machine, the lathe. The lathe adapted for pattern work is strong and steady in the framework, to avoid the tremor resulting from the high speed at which it is driven. It should be of good and durable workmanship, and should also be handy ; that is to say, the parts requiring frequent adjustment should be provided with the readiest means for accomplishing that end ; and especially is this the case with the hand rest and the manner of holding it to the lathe bed, as it is, in the progress of a piece of work, almost constantly changed in position. Fig. 43 shows the method, still followed by many wood turners, of holding the hand rest ; it is a prim- 52 PATTERN MAKER'S ASSISTANT. itive arrangement, but the tightening and loosening of the wedge, E, is found to take less time than screwing up the nut D. In Fig. 43, A is the hand rest, B B the lathe shears, the clamp, and D the nut upon the bolt, E, the head of which slides in a groove running along the foot of the hand rest. It will be observed that the nut, being be- neath the lathe shears, is somewhat unhandy to get at, and the wrench may not perhaps at the moment be at hand ; while, in any event, screwing up a nut with a wrench is a slow process. In some cases there is substituted, for the nut, a wheel with a tapped hole in its center ; but it is still not perfect, because the workman, in slacking it off, gives the wheel a twist ; and while his attention is absorbed in the intricacy of his work, the momentum of the rim of the wheel has kept it turning, so that it either unscrews itself altogether and falls off, or runs so far back that it requires handling twice to bring it home when refastening it. A much better method is now in many cases adopted; it is shown in Fig. 44, in which A A represents the lathe shears, B the hand rest, the fastening bolt, D a piece hinged at each end and having through its center a hole to receive the fastening bolt, and a countersink or recess to receive the nut and prevent it unscrewing. E represents a hinged plate, and F a lever having a cam at its pivoted end. A slot for the fastening bolt to pass through is pro- vided in the plate, E. In this arrangement, a very moder- ate amount of force applied to bring up the cam lever will cause the plate, D, to be pressed down, carrying with it the nut. This arrangement is simple, cheap, durable, and very handy, and may be applied on any existing lathe to the hand rest, slide rest, or tail stock. There are other simple and useful contrivances devised for the same pur- pose 5 but generally speaking, the lathe requires to be de- signed to accommodate them, and they are not superior in action to the system above described. THE LATIIB. 53 The running head of the lathe requires particular men- tion. The mandrel should always be of steel, turned true, hardened, and trued by an emery wheel, after the harden- ing process. It should be well fitted to its bearing ; for if it is not, an unpleasant jarring noise will be produced when the latter is set in motion. Hard steel coned bearings are very desirable, and will work perfectly when properly made, lasting practically un- impaired for years. They are, however, expensive to make j and in view of the present active competition in producing cheaply, most mechanics, knowing the difficulty attending the proper fitting of this style of mandrel, feel more or less dubious as to the perfection of such lathes until they have been well tried. Next to a hard steel coned bearing, we should prefer a cylindrical one of hard brass ; that is to say, a mixture of five parts copper, one part tin, 54 PATTERN MAKER'S ASSISTANT. and one quarter part zinc. The length of the journal should be three times its diameter j the brasses should be made in halves, and adjusted so that the faces of the brasses are butted when the cap screws are tightened home, and the journal is at a neat working fit in the bearings. It will then be a long time before the brasses will require letting together for adjustment. If, however, the joint faces of the brasses are left open, the cap screws are apt to slack back, there being no pressure on them, to retain them in their places. It is an advantage to have the man- drel bored nearly through its length, say within one inch of the tail pin or screw, whose coned end forms the bear- ing for that end of the mandrel. The size of the hole re- ferred to should be as large as consistent with the strength of the mandrel. This arrangement is shown in. Fig. 45. The usefulness of this bore or hole is that when a number of small pieces require to be turned, a nipping chuck can be screwed on the mandrel, and a long piece of stuff can be THE LATHE. 55 pushed up the hole, and the projecting end to be operated upon nipped in the chuck j then, when a piece is finished, all we have to do is to advance our long piece of stuff and proceed again. The method ordinarily employed is to drive a plug into the mandrel, and form the projecting end to the shape re- quired. By this plan more stuff is lost than is used ; and if the plug is not well fitted and driven, it loosens while be- ing operated upon, to say nothing of the trouble of extract- ing the stub from the mandrel when the work is cut off. Another purpose served by the long bore is that it will form a guide for a boring bar. The cone pulleys should be as light as possible for a pow- er lathe. ITard wood is very suitable for them, the manner of fastening to the mandrel being shown in Fig. 45. The cone pulley, A, is bored to fit the mandrel, B, tightly, and secured at the end to receive the light brass bush, 0, which is keyed to the mandrel and screwed to the pulley. The reason for making the cone pulley of wood is that, if it were of iron, and consequently heavy, it would, from its weight, require time to get up to its full speed ; and from its momentum, it .would take some little time to stop in both cases, especially if the work were heavy. The tail stock should, in addition to the hand wheel be provided with an arm ; and a lever, to give rapid motion to the spindle when used for boring purposes, should be added, the ar- rangement being as illustrated in Fig. 46, in which A rep- resents the arm or fulcrum, and B the lever, which is ap- plied after the hand wheel is removed. The end of the screw must be cut like a double eye. The long hole or slot in the middle of the line is to allow for the difference in the di- rection of the motion, since the lever moves from its end as a center, while the tail stock spindle moves in a straight line. The supporting frames of the lathe need not be very heavy, but should be well braced to the shears or bed, and 56 PATTERN MAKER'S ASSISTANT. screwed fast to the floor. It is not an uncommon thing, when an unusually large job is being done in the lathe, to KrJB. y -J brace or shore the lathe by means of braces placed between the lathe shears and the floor, wall, and ceiling. Of this arrangement it is sufficient to say that it is merely a make-shift, and is only resorted to when the floor is springy. In cases where it is necessary to use one lathe for both large and small work, the countershaft overhead should be so placed that the belt will run quarter-cross when the lathe head is placed across the bed, in which position there will be full swing for large work from floor to ceiling. It remains now to provide, for large work, a means of supporting the hand rest. The handiest is the portable tripod rest shown in Fig. 47. The legs, A A A, are curved so as to get the rest close up to a large chuck. Heavy weights, in the form of a U, as shown at B B B, may be clamped, by means of the set screw, to the legs, to give ad- ditional steadiness if required ; but if good spread be given to the legs, so that they may form an angle of about GO to the floor (taken from the point of the foot to where the leg joins the hub), the weights may be dispensed with ; and THE LATHE. 57 at the same time more space will be occupied, so that it may not be possible at all times, on account of surround- ing objects, to get such a broadly spread rest in- to the position required ; hence a narrower spread in conjunction with the weights, is, under such condition, the most desi- rable. We come now to the various chucking contriv- ances employed by the pattern maker. In Fig. 48, A represents a fork center, the taper part of which fits into the lathe mandrel in place of a center, the extreme end, B, being a flat projection, providing that there is a recess in the mandrel to receive it, as there should be. But if the lathe mandrel is bored up a great distance, then the extra length which may be given to the conical part of the fork will cause adhesion suf- cient to drive the work. The broad part is wedge-shaped on the edge view, the center point, C, being turned conical, similar to a common center. The cen- ter, C, acts to keep the work true, and as a guide in taking the work in and out of the lathe, while the prongs, D and E, drive it. This tool, 3* 58 PATTERN MAKER'S ASSISTANT. .o Jiq. J 49 however, is only to be depended upon for small work; for larger work, center plates are used. They are made of metal and screwed firmly to the work. Of these cen- ter plates, one has a slot in it, so that it may be used in conjunction with the fork; while another has a conical hole in the center, which hole is made to fit the back center of the lathe. They may be made of hard wood, , . screwed to a small iron face plate; such plates are made useful for a variety of pur- poses. A pair of such center plates are shown in Fig. 49 N ' x A being that to receive the back center, and B that for the fork center. Another driv- ing chuck for small work is shown in Fig. 50, the part, A, having an internal screw to fit the driving screw on the lathe spindle, and the point, B, being a coarse screw intend- ed to screw into the work ; which latter should have a small hole bored up it to pre- vent (especially in the case of hard woods) the pressure of the screw from splitting the work. From the appliances for turn- ing work between the centers, we pass to those for holding work independent of the back center of the lathe by means of chucks, the name by which such appliances are generally known. view of a face plate, to which work may be held by screws ; the usual method, however, is to screw to the face plate a disk of wood, and then to true the wood across the Fiff.50. Fig. 51 is a back THE LATHE CHUCK. 59 face and on the diameter. The work is then fixed to the new surface thus obtained. Many good purposes are serv- ed by the intervention of the disk of wood (or chuck, as it is usually termed) between the metal plate and the work. For instance, it is a guard which effectually prevents the turning tools from touching the metal of the face plate. It supports the work (being nearly of the same size) when required, and obviates the necessity of having more than three or four face plates of metal. Its surface is readily made to conform to the shape of the work, and furthermore it is very readily trued up. When we have to deal with large sizes, a mere disk of wood will not serve, as it will be too weak across the grain: and here it may be remarked that the work often supports the chuck, and therefore we should always, in fixing, make the grain of the work cross that of the chuck, because the centrifugal force due to the high velocity is so great that both the chuck and the work have before now been rent asunder by reason of the non-observance of this apparently small matter. When it is considered that the chuck has not sufficient strength across the grain, battens should be screwed on at the back; but a chuck so strengthened will require truing frequently, on account of the strains to which its fibers will be subjected from the unequal expan- 60 PATTERN MAKER'S ASSISTANT. sion or contraction of its component parts. Fig. 52 shows the back of a chuck strengthened by the battens, A A A. Another method of making a chuck is shown in Fig. 53. It is considered superior to the former, from its greater ability to resist outward strains in every direction, while the strains to which it must necessarily be subject, from variations of temperature and humidity, are less than in the former. It will also be found that it can be trued with greater facility, especially on the diameter, as the turning tool will uot be exposed to the end grain of the wood. To make one of these chucks about 2 feet in diameter, we pro- ceed as follows : Procuring two bars for the back, say 4x2 llff.53. inches and 2 feet long, we plane them all over ; then hi the middle of each we cut out the recess (shown at A in Fig. 53) to a depth equal to half the thickness, the width of the recess being equal to that of the bar ; this process is term- ed half checking. We next fasten these bars together by gluing and screwing them at the center, driving the screws thightly home while the glue is warm. Upon the cross thus formed, we superpose the segments shown in the front view of Fig. 53, at B B B j these may be of almost any thick- ness, say from to 1J inch. They should be planed on the back, and should not extend to the center, but leave f\ CHUCKS. 61 an open space (as shown in Fig. 53, at C) of about 4 or 5 inches. This opening can be filled, if desired, by screwing on a square piece. If the segments were carried to the cen- ter, they would be too weak to bear a screw near that point j and again, in large chucks we very seldom require to use the part about the center. Chucks of very large size that is to say, from 4 feet up wards will require more support than is afforded by the four arms of the cross. Three bars can be put together, so as to give six arms, which will an- swer probably for a G or 7 feet chuck. For still larger sizes, it is necessary to cast a strong circular plate to form the middle of the chuck, and to then bolt the requisite number of arms to it. The strength of the chuck will of course depend upon the number of arms and their depths j and unless the chuck is very substantial, a difficulty will be ex- perienced in turn- ing, on account of the tremor. A chuck having the middle of iron and the out- side of wood, sup- ported by arms, is shown in Fig. 54. In shops where the size of the work necessitates the em- ployment of chucks of so large a diame- ter, a special lathe is of great advantage, because a lathe having an elevated bed is so tremulous and shaky j while those having large solid heads are too cumbersome, and are not belted to run at a sufficiently high rate of speed. In such cases, the arrange- 62 PATTERN MAKER'S ASSISTANT. ment shown in Fig. 55 is an excellent one. A represents a lathe head bolted firmly to two uprights, B B, which are firmly fixed to the joists, C, and to the flooring at D, right over and upon the joists supporting the flooring, or else upon beams provided for the purpose. By this means the work may, if the lathahead is fixed midway upon the posts, B B, be as large as the space between the ceiling and the flooring will admit, a movable tripod rest, such as shown in Fig. 47, being employed for a tool rest. Fig. 56 represents a side and face view of a very useful chuck, suitable for holding core boxes while boring them. It is shown attached to one of the metal plates that fit the CHUCKS. 63 mandrel of the lathe, and is usually made of hard wood ; but for a large sized one, say 15 or more inches in diameter, the disk portion, A, may be made of pine wood. The Fia.56. two sides, B B, are firmly fixed to the disk, their inner edges being planed at an acute angle to it. The work is held by driving the wedges, C, and may be truly chuck- ed by them in a comparatively short space of time. Another very useful chuck is shown in Fig. 57. It will answer the same purposes as that shown in Fig. 56. It is, however, made entirely of metal, somewhat similar to a machinist's dog chuck, but much lighter. Pieces of wood may be screwed on the jaws at A A, and bored to the cur- vature of any round piece of wood an advantage which the chuck shown in Fig. 56 does not possess. Or the jaws may be turned round in their places, so that the faces, A A, will stand outwards, and the wooden pieces screwed thereon may be made to fit a hole. This chuck will be found to save much time over the plan of screwing work to the common face plate. Y pieces of wood may be fixed to the jaws, and a piece of work in the rough held by them during the process of facing, boring, and turning the pro- 64 PATTERN MAKER'S ASSISTANT. jecting part. The work can then be reversed in the chuck, and similar operations performed on the opposite end 5 and the work can be taken from the lathe and tried as to either fit or conformation, and, if necessary, restored in a mo- ment to its original position in the chuck, so as to run quite true ; but at the same time, for first-class work, it is better not to use the V's on finished surfaces. For holding bits and small work, neat little chucks may be purchased at the hardware stores, and they act similarly to the nip- ping arrangements applied to boring braces. These chucks can be supplied to screw on the lathe mandrel ; or they will, with a taper shank, fit into the taper holes provided to fit the lathe centers. It is well to have one of each, so as to be able to use one of them in place of the still lathe center, to operate upon work already chucked on the face plate of the lathe. A simple and very useful chuck still remains to be de- scribed, being what is known as the cement chuck, which is made as follows : A disk of hard wood is screwed to a metal plate, where it should remain permanently j but if the face plate cannot be spared, bore a slightly taper hole cncrcKS. C5 through the disk, a little smaller than the diameter of the screw of the lathe mandrel, and partly through the disk. Then screw the disk on the mandrel, working the disk backwards and forwards to form a thread in the bore of the disk, and then turn and face it perfectly true. Then bore a small hole in its center, and drive in a piece of soft steel wire, leaving a short length projecting from the face, and turn it to a point, as shown in Fig. 58. The object of this chuck is to drive thin, delicate work, which it would be difficult to screw or clamp by ad- hesion, and this is accomplished as follows: We first prepare a wax, composed of 8 parts of resin to 1 of the best beeswax, melted and well stirred together, and run into tubes of paper or other suitable molds. To chuck the work, we take a stick of the wax, and press its end against the face of the chuck while the lathe is running, and then place the cen- ter of the piece of work on the steel point, applying sufficient pressure to cause the steel point to force its way into the work. Just before the work touches the wax surface, we throw the lathe belt on to the loose pulley ; and the momentum of the lathe, combined with a moderately heavy pressure, will generate, by fric- tion, sufficient heat to melt the wax and cause the work to adhere to the chuck. The work may be detached, when necessary, by inserting behind it a thin wedge or blade. TURNING TOOLS. The turning work necessary in making patterns is usu- ally done by hand; although on small and plain work. 3** 66 PATTERN MAKER'S ASSISTANT. such as simple boring and facing, slide rest tools may be used to advantage, inasmuch as they will operate quicker than hand tools. Since, however, pattern lathes are not usually provided with slide rests, we shall confine our remarks to hand tools. For roughing out, the turning gouge, shown in Fig. 59, is used. In grinding this gouge, it is necessary to lower the back hand when grinding at and towards the outside corners, so that the cutting edges may be formed, by the junction of two faces, at as acute an angle as those forming the cutting edge in the centre of the width of the tool. It is always the custom to reduce the work in the lathe to nearly the re- quired form by this tool, the finishing tools being (with one exception) sim- ply scraping tools, and not, properly speaking, cutting tools 5 hence it is evidently inadvisable to leave much for them to take off. The manner of holding the gouge is shown in Fig. 00. One band grasps the handle near the end, while the other grasps the gouge near the cutting point, that is to say, as near as the hand rest will permit. It is sometimes, however, necessary to slightly vary the manner of holding, by passing the forefinger of one hand around the hand rest while the gouge is confined between tbe thumb and forefinger, thus gripping the gouge end to the rest. This is advisable when turning a piece of work that is not completely round, as, for instance, tipping off the teeth of a gear wheel, in which case gripping the gouge THE LATHE. 67 to the hand rest will steady it and prevent it from digging into the work. The gonge is shown, in Fig. 60, to be cut- ting from right to left ; it will, however, cut equally 1 Iff. 60. well if used from left to right, in which case the position of the hands must be reversed, the left hand gripping the gouge edge. near the In either cutting case. however, the gouge is not held horizontally level, but is tilted to one side, the lower side being the cutting one, other- wise the tool would rip into the work. Fig. 61 shows the sec- tion of the tool and the tilt of the tool when cut- ting from right to left; while that of the tool, A, shows tilt when cutting from left to right. The reasons for this are as follows : The face of the gouge, on its hollow side and FUT.6L \J R a cutting near the edge, receives the strain which is ne- cessary to curl the shaving, that is to say, which is ne- cessary to force it out of the straight 68 PATTERN MAKER'S ASSISTANT. line. But if we were to place the gouge in the position shown in Fig. 61, at 0, the whole of this strain would be placed upon the gouge, tending to force it forward and into the cut, as denoted by the direction of the arrow ; and as a consequence, the gouge would run forward and dig into the work, in spite of all endeavors to prevent it. When, however, the gouge is held in the positions relative to its line of travel to its cut, shown in Fig. 61, at A and B, there is but little ten- dency for it to run forward, and it can be fed easily to its cut. In ad- dition to its use as a roughing tool, the gouge makes a very efficient finishing tool for hollows, though it is not often employed as such by pattern makers. In this case, however, great care must be taken in controlling its posi- tion to the work, as shown in Fig. 61. For finishing plain work, we have the tool shown in Fig. G2, which is the exception noted previously as being a finishing and, at the same time, a cutting tool. It is called a skew chisel, because its cutting edge is ground at an angle or askew to the center line of its length. Fur- thermore, it is beveled at the cutting end on both sides (as shown in the edge view), being ground very keen. It is THE LATHE. employed for finishing straight or parallel surfaces, and for dressing down the ends or down the sides of a collar or shoulder. When used for finishing straight or parallel surfaces, it performs its cutting in the center of the length of its cutting edge only, as shown at A, in Fig. 63, and is held in the position relative to the work shown in Fig. 62. When nicely sharpened it leaves a polish, unlike other finishing tools 5 but with these advan- tages, it has a draw- back (and a serious one) to learners, as it seems to have a terrible propensity for tearing into the work, whether it is used upon the cir- cumference or facing the shoulders of the work. This difficulty can only be over- come by practice, and the reason lies in the difficulty of learning how to handle the tool with dexterity. It must be held almost flat to the work ; and yet, if it should get quite flat against the work, the cutting edge would cut along its whole length, and the pressure of the cut would be sufficient to force the tool edge deeper into the work than is intended, which process would continue, causing the tool to rip in and spoil the work. The face of the chisel nearest to the face of the work being operated upon, stands almost parallel, with 70 PATTERN MAKER'S ASSISTANT. just sufficient tilt of the tool to let the cutting edge meet the work in advance of the inside face of the tool 5 or in other words, the amount of the tilt should be about that of the intended depth of the cut ; so that, when the cutting edge of the tool has entered the wood to the requisite depth, the flat face will bear against the work and form a guide to the cutting edge. The corner of the chisel which is not cutting must be kept clear of the work. Fig. C3 will convey the idea, the arrows showing the direction in which the chisel is, in each case, supposed to be traveling. The short lines, A and B, under the arrows, and those touching the collar, at C and D, show the tilt or incline of the chisel to the work. In turning the circumference, the obtuse corner of the chisel is the cut- ting one 5 while in turning down a side face, it is the acute angle. Most pattern makers, however, do not often use the skew chisel for finishing straight cylindrical work, because it is liable to make the surface of the work more or less wavy. It is, however, almost al- ways used for cut- ting off and for cutting down shoulders, for which purpose it is highly ad- vantageous. For circumferential work on cylindrical sur- THE JLATltE. 71 A B D faces, an ordinary chisel is mostly employed, the position in which it is held to the work causing it to scrape rather than cut. A worn-out paring chisel is as good as any. Such a chisel is shown in Fig. 64, the position in which it is held being illustrated by A, which represents a section of a piece of cylindrical work ; B representing the chisel, and C the hand rest. Some pattern makers prefer to in- crease the keenness of this tool by holding it so that the plane of its length lies in the direction denoted by the dot- ted line, D ; this, however, renders it more likely to rip into the work, and pj~ or the position shown is all that is necessary, providing the cut- ting edge be kept properly sharpened. This chisel is also used on side faces. Still another tool, sometimes used for finishing plain cylin- drical surfaces and side faces, is that shown in Fig. 65, at A. It is used in the same manner and re- lative position as the chisel shown above, in Fig. 64. For finishing hol- lows, which should first be roughed out with the gouge, the form of tool shown at B, in Fig. 65, should be used. Several of these tools, of various sizes, should be kept ; they are used in the same position as the 72 PATTERN MAKER'S ASSISTANT. finishing chisel, shown in Fig. 64. The tool shown at C, in Fig. 65, is used upon large work, and is advantageous be- cause it presents less surface of cutting edge in proportion to the depth of the cut than the gouge ; and, in consequence, it is less liable to cause the work to jar or tremble. It is usually made about 2 feet long, which enables the opera- tor to hold it very firmly and steadily. It is used with its top face lying horizontally, and should be kept keen. D, in the same figure, represents a similar tool, with a round nose ; this latter is not, however, made long, and may be used in a handle. For boring and shouldering purposes, the tools shown in Fig. 66 are employed ; those shown at A and B, having their cutting edges at C and D, are therefore right and left hand tools. When, however, the hole is too small to admit of those tools being used, that shown at E may be employed, its cutting edge being at F. The temper of all these tools should be drawn to a light brown color, and the instruction given for grinding bench tools should be rigidly observed hi grinding and oilstoning these turning tools. CHAPTER nr. THE FOUND R.Y. HOW A PATTERN IS MOLDED. IT has been already remarked that the operations of the molder are, to a large extent, predetermined by the pat- tern maker; hence it becomes necessary that the latter shall have a knowledge of foundry work, otherwise he is likely to make the patterns very expensive and awkward to mold. In learning the trade, an apprentice is usually put to work and distinctly instructed as to the required form of his work, without knowing anything of the reasons therefor. In this way he attains a practical knowledge of how different classes of patterns should be, or are, usually made; but it takes him years to become an expert me- chanic, for the reason that, having learned by rote, he is in- capable of meeting new conditions to the best advantage, until his experience has included both observations in the foundry and, in some cases, consultations with foundry- men. Before entering, therefore, into the method of put- ting together different kinds of pattern work, it will be well to take a glance at the foundry, and examine the contrivances and the operations of the workmen, so that our operations in pattern work may be intelligently made from the beginning. The floor of the foundry first demands our attention. It is composed of a layer of molding sand of sufficient depth to imbed patterns of the size usually cast in that foundry. For Exceptionally large work, there is usually a place where the natural earth has been excavated to a greater depth 5 the cavity is filled with molding sand. This place is usually within easy reach of the crane (which commands 4 74 PATTERN MAKER'S ASSISTANT. almost every part of the floor) and the threshold of the melting furnace or cupola. We next observe the capa- cious oven for baking cores and drying molds for such special work as may require these operations ; but the particular contrivance with which the pattern maker has now to concern himself is represented in Fig. 67. It is called a flask, and is composed of two or more parts (two only being shown in the engraving). The lower part is called the nowel, and the tipper the cope. Each part is simply a strong rectangular frame of wood or iron. The sides, being continued past the rectangles, are roughly shaped for use as handles. The cope is provided with several crossbars, which embrace the pattern, as it were, being roughly shaped like it in contour and approaching THE FOUNDRY MOLDING. 75 it in size, being about lialf an inch larger all round. These bars, by their adhesion, support the body of the sand in the cope, and in this they are frequently assisted by nails driven nearly half way into them. When an intermediate part is used with the two parts shown in Fig. 07, the con- trivance is called a three-part flask ; with two intermedi- ates it is called a four-part flask, and so on. As the cope is provided with crossbars, so also the intermediates, hav- ing to lift a ring of sand, are provided with wings ; that is to say, as much crossbar as will extend from tlie sides to within about half an inch of the pattern. The parts are guided, in their position one to the other, by taper pins on one part fitting into eyes fixed to the other part, as shown in Fig. 67, in which the cope is shown with the side hav- ing the two pins exposed to view, while the opposite side of the nowel, having one eye, is visible. In many cases, and for large work, the nowel is dispensed with, and the foundry floor is used in its stead, in which case the cope is guided to, and retained in, its place by stakes driven into the floor sand, as shown in Fig. 08, so that, when lifted to admit of the pattern being drawn from the mold, the cope may be returned to its exact proper and former position. In Fig. 08, A represents the pattern whose impression in the floor sand, at M, forms a part of the mold. B repre- sents the cope j for the word cope is usually applied to the upper part of the mold as well as to that portion of the flask which contains it. The top print, C, of the pattern, has formed its impression in the cope at P. B is a round taper peg, which leaves a hole in the cope at r, through which hole the molten metal is poured. It also leaves an indentation at r 1 ; and from this latter a gutter is made by the in older to communicate with the mold, M, as shown. The stakes referred to above are marked S. The dots, shown around the impression of the top pattern print, C, hi the cope, are small holes made in the sand (after the 76 PATTERN MAKER'S ASSISTANT. molding is finished) by a piece of fine wire, and are for the purpose of giving vent to the air and gases which must escape when the metal is poured in. It will be seen that, when a mold is made in the flask we have described, it can perform no further duty until the casting has been made; for every mold, therefore, we re- quire a flask, and hence the pile of these appliances we always see in a foundry. For light work, however, a com- paratively modern and greatly improved device has come into general use. It is termed a snap flask, each part hav- ing a hinge at one corner and a latch at the diagonally op- posite one ; so that, after the mold is made, it can be THE FOUNDRY MOLDING. 77 detached from the perfected mold and can be used to make another. Sometimes, though rarely, it happens that a casting is required of such form that the patterns cannot be constructed so as to be molded with a flask of the or- dinary kind. The flask requires to come to pieces and the mold to be parted side wise ; this adds greatly to the labor of the niolder, and the pattern maker should so construct the pattern as to avoid this, whenever he can devise any means of so doing. Even when the pattern is molded in the floor, the mold is sometimes of necessity made to part on one or more of its sides, and these partings are termed drawbacks. By watching the operations of a molder, we shall observe that, in the case of a solid pattern that is to say, a pattern not made in halves he always endeavors to have as little of the pattern in the cope as possible, and in this respect the pattern maker should supplement his efforts. The rea- son is obvious : the cope has to be lifted while as yet there has been no opportunity to loosen the pattern in the mold. It is true that, in some cases, a bar is passed through the cope and driven into the pattern, and by rapping it the loosening is accomplished ; but it is not well to have re- course to such an expedient, because, wherever the bar passes, the cope is damaged, and must be mended ; and when a mold has to be mended, it is doubtful if the cor- rect form, such as the pattern would have given it, will be left. Furthermore, it is all work in the dark 5 for the effect or extent of the rapping cannot be scrutinized, and it may therefore produce an undue distortion in one direction, while in another it may not have been effectual. Perhaps the bar may have descended at a place in the pattern where it is comparatively weak, from crossgrain of the wood or from some other cause. This measure is, there- fore, on account of these difficulties, seldom resorted to ; and it may be generally disregarded in the calculations of 78 PATTERN MAKER'S ASSISTANT. the pattern maker. The cope, then, being, as we may say, a dead lift, and with nothing to guide the operator in moving it, either horizontally or vertically, any part of the mold contained in it is much more liable to break down than is the other part of the mold. In extracting the pat- tern from the lower part of the mold, the eye lends to the molder great assistance. The pattern can be loosened in .70. the sand before extraction, and is furthermore less cum- bersome to handle than is the cope : all of which circum- stances tend to preserve the lower part of the mold from damage during the extraction of the pattern. Rapping a pattern tends to alter the form of the mold from that calcu- THE FOUNDRY MOLDING^ 79 lated upon. A circle becomes slightly oval, a square be- comes an oblong, and so on : and this cannot in most cases be avoided, because it is necessary to rap the pattern so as to enable the moldcr to extract the pattern without draw- ing out the sand with it ; all that can be done in this direc- tion is to rap the pattern as little as possible, and equal- ly in all directions. When a flask nowel is used, the labor involved in mak- ing a parting of the mold is facilitated. Fig. G7 shows a board cope and nowel for an ordinary straight parting ; but it is evident that the parts of the flask may be made to show a crooked, a curved, or irregular line at the joint, if it is required, in which case the bed board must be made of similar conformation. The process of molding with a flask independently of the floor, is illustrated in Figs. 70 and 71. If it be required to mold the pattern illustrated in Fig. GO, which is made in halves, the joint being de- noted by the line, A A, one of the halves is taken and laid with its flat face upon the molding board, B, shown in Fig. 70. The nowel, N, is then placed upon the board, so that the half of the pattern will be in about the middle of the flask nowel. Sand is then rammed tightly in the nowel j and when the latter is filled with the sand, it is turned upside down, showing the flat face of the half pattern, the rest of the half pattern being imbedded in the sand. The other half of the pattern is then placed upon the one in the sand, its proper position being determined and regulated by pegs fitting into holes, provided in the first part, to re- ceive them. The next operation is to put on the cope, as shown in Fig. 71, the taper pins being fast to the cope lugs shown on the sides, fitting into holes provided in the nowel lugs, similarly shown, serving to hold the cope in position and prevent it from moving. The cope is then filled with sand, lightly rammed, the taper pin, E, Fig. 68, being inserted to leave in the mold the hole, E, Fig. 71, 80 PATTERN MAKER'S ASSISTANT. through which to pour the melted metal. The cope is now lifted vertically ; and as the pattern is made in halves, the top half lifts with the sand in the cope. In some cases a screw is fixed into the top half of the pattern, the head of the screw projecting into the cope: the object being to insure that the top half of the pattern shall lift with the cope. - The next procedure is to extract the two halves of the patterns from the molds, and perform any trimming or repairing that the mold may require, after which the cope is again placed upon the nowel, and the mold is com- plete, ready to have the metal poured in. THE FOTJNDRY MOLDING. 81 In Figs. 76 and 77, we have another example of flask molding, but for a pattern of different shape to our pre- vious one. The pattern is, in this case, not made in halves, its flanges on one side being left loose. In Fig. 76, one half of the pattern is shown on the molding board, and the nowel placed thereon and rammed with sand; '#. 77. jjfjj^jjj^ljj^ m while in Fig. 77, the pattern is shown molded and ready to have the cope taken off, A representing one of the crossbars fitted into the cope, and following the outline of the pattern. CHAPTER IV. THE FOUNDRY. ON COUES. COEES are projecting bodies of sand, either left iii the mold by the pattern itself or else made in a separate device called a core box. They are placed, after being dried, in position in the mold. The purpose of a core of the latter description is to leave a hole or recess of such a peculiar shape or in such a position that it is impracticable to make the mold of the necessary conformation by the use of the pattern alone. The use of these cores also per- mits us to modify the shape of a pattern that would other- wise be difficult to mold. For example, Fig. 78 represents Jiar. 78. \ a plate of such length that it is necessary to mold it in the direction indicated by the arrow ; as the pendants, which are long and narrow, with their projections at the extrem- THE FOUNDRY CORES. 83 ities, would lock the pattern in the mold. Three methods present themselves whereby to overcome the difficulty. First, we may make the projection loose, the vertical line, A, being the joint j it is held in position by vertical dove- tails or by horizontal wires, as shown in Fig. 78. In the latter case, the inolder, when ramming the sand, with- draws the wires ; and when the pattern is withdrawn from the mold, the two different projecting pieces are left in the mold, and are subsequently retracted horizontally, and then lifted out. It is obvious that this can only be done when there is sufficient space to accommodate the project- ing piece as it is withdrawn from its recess in the sand, and to admit of its being raised to the surface. To this method there is the objection that the recess left by the projecting piece in the mold cannot be, in many cases, either inspected or dressed, if any reparation is required. A second plan would be to make the projecting piece join the pattern at the horizontal line, B, in Fig. 78, but sepa- rable from it; but in this case a three-part flask would have to be used, entailing double work for the molder. The third method is to affix the core prints, C C, to the sides of the pattern, leaving those sides smooth and even ; and the pattern will then draw easily out of the mold. If we then core away all we have added to the pattern, as shewn by the dotted lines in Fig. 78, the casting will retain the correct shape of the pattern. To effect this cor- ing away, we make dry sand cores of the shape of the core prints, C C, and place them in the mold. Ordinary dry sand cores are composed of a mixture of sand and flour moistened with water, and they are molded to the requisite shape in the core boxes already mentioned. They are then baked, becoming sufficiently strong to han- dle ; but previous to the baking they are so weak that they cannot be handled without being in some way supported. It is, therefore, as great a consideration to the 84 PATTERN MAKER'S ASSISTANT. pattern maker how the core is to be taken from the box as it is how a pattern shall be drawn from the mold. We may divide cores molded in a core box into three classes : First, those that lie as they are made ; second, those that require turning over ; and third, those that not only re- quire turning over, but require also a bed of sand made for them to lie upon during the process of baking. Figs. 72 ? 73, and 74 are examples of the first, in which the cores are represented by C. The core boxes, being made hi halves and loose at two of the opposite corners, can be drawn away from the cores, C, leaving them standing, just as they were made, on an iron plate ready for removal to the oven. In a core box made as in Fig. 74, it is neces- sary to bore in the ends a couple of small holes for the in- sertion of wires to effect ventilation. In cases where sulfi- THE FOUNDRY CORES, cient draft or taper can be allowed on the core, the core box need not be made in halves, but may be made solid, as shown in section in Fig. 75. While it is the aim of the pattern maker to form his core boxes to work hi the simple manner illustrated in our examples, there are very large classes of cores with which such easy methods are impracticable. This, for instance, is the case with all round cores that are of such length that they are not able to support themselves on end, and with those having branches, as shown in Fig. 70, which re- presents a core for a straight faucet. If it were attempted to make this core in a vertical position, its overhanging branches would fall away immediately after separating the two halves of the box ; hence it is made horizontally, and generally in separate halves, which, after being baked, are 86 PATTERN MAKER'S ASSISTANT. pasted together and again dried, thus forming the full round core. In cases, however, where great numbers of such cores are required, as in steam fitters' work, they are usually lifted from the box whole j but it is a delicate operation, involving much practice. We need not, how- ever, go into this, the subject only being mentioned to show how a pattern maker decides whether he shall make a full core box or only half a one ; for if the halves of the core are to be made separate, and one part is exactly similar to the other, then a half core box is all that is necessary. Suppose, for instance, the core of a faucet, shown in Fig. 79, to be alike at the branches, C and D ; then, it being made in two halves, meeting in a point represented by the line A B, the core box may be made to mold the half, E ; and two of such halves, pasted together as described, will form the whole core. In this particular example, however, there is yet another way of making the core, providing the branches, C and D, are parallel in diameter, and that is, to punch holes in the main part of the core, through holes provided in the core box, using a piece of wood for the purpose. Fig. 80 is an illustration of a square core for a baluster ; its four sides being curved, it is necessary to make it in separate halves, dividing it diagonally across the corners, as denoted by the lines A B. 87 We have now to give an example of the third class of core, which will not stand on end and does not present a flat surface on any of its four sides, neither can it be readily divided, as in the former case. Fig. 81 is an illustration 88 PATTERN MAKER'S ASSISTANT. Ify.89. of probably the simplest kind of this class, which will re- quire a core box that must part in all directions in order to enable us to extract the core, which will require, in addi- tion to this, what is called a turnover box. Fig. 82 is an end sectional view of this core box, having four joint- ed sides and a bottom, with holes cut in them where the projections are to be formed on the core. The top, in this case, is simply two bars that cross the box where the projections occur ; and holes are cut in these bars to form the projections. The box is retained together and kept in position by the taper pegs, shown at the junction of the sides. The ends of the box are recessed to receive the sides, but all is removable. In using this box, after ramming up the top, the crossbars are removed, and in their place is mounted the turnover box, shown in section in Fig. 83, at A, which is a simple square frame, made taper. It rests on the outer edge of the core box, so as to give a bed of sand somewhat larger than the core itself. Small blocks nailed to the under side, B B, keep it in posi- tion. The frame is then carefully filled with ordinary molding sand, so as not to disturb the projecting parts of the core, and the sand on the outside is then struck off level. An iron plate is then placed on the top of all, and the whole is turned upside down. The bottom of the core box, which has now become the top, is first removed, and then the sides and ends. Thus the turnover box affords a bedding of sand, on which the core may rest without suf- fering injury from its own weight. THE FOUNDRY CORES. 89 It would be a costly matter to make core boxes for long cylindrical cores, such as are used for pipe and similar cast- ings ; hence, for such purposes, a core is made as shown in Fig. 84, in which C represents a core for a pipe, having a . 83. socket at one end. It is prepared as follows : Upon the two tressels, A A, is mounted the long tube, D D, which is perforated throughout its entire length with numerous small holes, and which is provided at one end with a crank handle, by means of which it may be revolved as it rests in the two rude V bearings, provided hi the top of the tres- sels, as shown. Upon this tube a layer of rudely twisted straw rope, sufficient to make its diameter assume, from end to end, nearly the required diameter of the core, is coiled. Outside the straw rope there is then applied a coating composed of a mixture of loam and other material sufficient to increase the diameter from end to end, some- what above finished size. To round up the core even, and make it of the necessary size, the core or loam board, B B, is employed. It is simply a board ranging in thickness 4** PATTERN MAKER'S ASSISTANT. from seven eighths inch upwards, according to its length. One of the edges is cut to the conformation of the required core ; and all but about three sixteenths of an inch of the thickness of this edge is beveled off at an angle of about 30. This board is laid upon the tressels with the beveled edge uppermost, and is held in position by weights placed upon it over the tressels. The core is then revolved by the 84. handle in the direction of the arrow, as show n in Fig. 85, in which A represents the tube, B the straw rope, C the loam coating, and D the board. It follows that, as the loam is added, the board will level it off, leaving the sur- face round and true, and to whatever shape the edge of the board may be made. It is customary to mix with the coating of loam, horse dung, or a substitute therefor, the object of which is as follows : It will be readily perceived that it is a difficult matter in a long casting to give vent to and permit the escape of the air and the gases formed in the mold by the molten metal j but by mixing in with the loam a combustible material, the latter becomes con- THE FOUNDRY CORES. 91 sinned during the baking of the core, leaving the latter porous, so that the air and gases can pass from the mold through the loam coating and thence through the straw rope, and find exit through the hollow tube upon which the latter is wound. CHAPTER V. EXAMPLES OF SIMPLE LATHE WORK. WE may now commence a series of examples, accompa- nying each example with the explanations and considera- tions necessary to, and governing the method of, the construction chosen. Fig. 86 represents a drawing of a gland for which a pattern is required. Now this is a very simple pattern, and yet there are at least six different methods of mak- ing it, any of which may be followed, as will ap- pear more clearly to the reader by his glancing over Figs. 87, 89, 90, 92, 93, and 94. The first question is how to deter- mine which method is the most suitable. Let us suppose the pattern mak- er to be uninformed of the purpose the casting is to serve, or how it is to be treated: in such a case he is guided partly by his knowledge of the use of such patterns, and a consideration of being on the safe side. The form shown in Fig. 87 would suggest itself as being a very ready method of making the pattern; by coring out the hole it can be made parallel, which the drawing seems to require. The advantage of leaving the LATHE WORK. 93 hole parallel is that less metal will require to be left for boring, in case it should be necessary 5 because-, if the hole is made taper, the largest end of the bore will require to have the proper amount of allowance to leave metal suf- ficient to allow the hole to be bored out true, and the smaller end would, therefore, have more than the neces- sary amount : while just the least taper given to the ex- terior would enable the molder to withdraw the pattern from the mold. Made in this way, it would be molded as shown in Fig. 88, with the flange uppermost, be- cause almost the whole of the pattern would be imbedded in the lower part of the flask, the top core print being all that would be contained in the cope 5 and even this many be omitted if the hole requires to be bored, since the lower core print will hold the core sufficiently secure in small work, unless the core is requir- ed to be very true. The parting of the mold (at C D, in Fig. 88) being level with the top face of the flange, much taper should be given to the top print (as shown in Fig. 87), so that the cope may be lifted off easily. Were this however the only reason, we might make the top print like the bottom one, providing we left it on loose, or made it part from the pattern and adjust to its place on the pattern by a taper pin j but another advantage is gained by well tapering the top print, in that it necessitates the tapering of the core print at that end; so that, when the two parts of the mold are being put together that is to say, when the cope is being put in place if the core has 94 PATTERN MAKEK/S ASSISTANT. not been placed quite upright, its tapered end may still arrive and adjust itself in the conical impression, and thus correct any slight error of position of the core. The size of the core print should be, at the part next the pattern, 55;. the size of the core required; for if the extremities are made of the size of the core, and the taper or draft is in excess, there will be left a useless space around the core print, as shown in A B in Fig. 88, into which space the metal will flow, producing on the casting around the hole and projecting from the end face a useless web, which is called a fin, which will of course require to be dressed off the casting. We will now suppose that our piece, when cast, is to be turned under the flange and along the outside of the hub or body, and that the hole also is to be bored. In this case the pattern made as above would still be good, but could be much more easily made and molded if it has to leave its own core its shape being as shown in Fig. 80 because the trouble of making a core is obviated, and the core is sure to be in the center of the casting, which it seldom is when a core is used. We must, however, allow more taper or draft to a hole in a pattern than is necessary 011 the LATHE WORK. 95 outside; about one sixteenth inch on the diameter for every inch of hight on work of moderate size is sufficient. The allowance for boring should be one sixteenth inch at the large end of the hole, providing the diameter of the hole is not more than five or six inches, slightly exceeding this amount as the diameter increases; whereas, if the pattern had been made with core prints, an allowance of one eighth inch for small, and three six- teenths inch for larger work would be required. These are the advantages due to making the pattern leave its own core. We have still to bear in mind, however, that, if the casting require a parallel hole, a core must be used; and furthermore, if the hole is a long one, we have the following considerations : The separate dry sand core is stronger, and therefore better adapted to cases where the length of the hole greatly exceeds the diameter. Then again, if the hole require to be bored parallel, it can be more readily done if the hole is cast parallel, because there will be less metal to cut out. The casting also will be lighter, entailing less cost, pro- viding it has to be paid for by the pound, as is usually the case. The molder is given more work by making the core; but the saving in metal and in turning more than compensates for this, provided the length of the hole is greater than the diameter of the bore. Let it now be required that the casting is to be finished all over, such as for a gland for a piston rod. It would in that case be preferred that, if the casting should contain any blow or air holes, they should not be on the outside face of the flange; and this will necessitate that the 90 PATTERN MAKER'S ASSISTANT. piece be molded the reverse way to that shown hi Fig. 88 that is to say, it must be molded as shown in Fig. 90 with the flange downwards; for it may be here noted that the soundest part of a casting is always that at the bottom of the mold; and furthermore, the metal there is more dense, heavier, and stronger than it is at the top, for the reason that the air or gas, which does not escape from the mold, leaves holes in the top of the casting, or as near to the top as it can by reason of the shape of the casting rise. The bottom metal also has the weight of the metal above it, compressing it, and mak- ing an appreciable difference in its density. It must therefore be remembered, that faces requiring to be particularly sound, should be cast downwards or at least as near the bottom of the mold as they conveniently can. Following this principle, our gland will require to be mold- ed as shown in Fig. 91, P P representing the line of the parting of the mold ; so that, when the cope is lifted off, the loose hub, A, will rise with it, leaving the flange imbed- ded in the lower half of the mold. It is evident that in LATHE WOftK. 97 this case the pattern must be made as shown in Fig 90, the body and core prints being in one piece and the flange in another, fitting to an easy fit on to a parallel part on one end, and adjoining the core print, as shown at A. .^raw\\\\\vc^i fillip I^'SS^E For glands of moderate size, this method is usually adopt- ed, and it answers very well for short pieces j but in cases where the length of the body approaches say three dia- meters, the horizontal position is the best, and the pat- tern should be made as shown in Figs. 92, 93, or 94. Even in short pieces, when the internal diameter approaches that of the external, this plan is the best, because it is dif- ficult for the molder to tell when his core is accurately set in position. 5 98 PATTERN MAKER'S ASSISTANT. For a pattern to be molded horizontally, Fig. 93 shows the best style in which it can be made. Its diameters are 1 Fig. 93. turned parallel; the required draft is given by making the rim of the flange a little thinner than at the hub, and by making the end faces of the hub and the core prints slightly rounding. If the hub is very small as, say, a half inch or less, and the flange does not much exceed it the pattern may be made solid, as shown in Fig. 92 5 but if the hub be small and the flange large, it should be made as shown in Fig. 94. LATHE WORK. 99 To construct the pattern shown in Fig. 87 we proceed as follows : From a piece of plank we saw off a piece of wood a little larger and thicker than the required flange, measuring with a contraction rule that is to say, a rule specially made for the pattern maker, and having its measurements larger than the actual standard ones, in the proportion of one eighth inch per foot : so that a foot on a contraction rule is 12i standard inches, and an inch is IgL standard inches. The reason for this is, that when the metal is poured into the mold it is expanded by heat, and as it cools it contracts 5 and a casting is therefore, when cold, always smaller than the size of the mold in which it was made. Brass castings are generally said to be smaller than the patterns, in the proportion of one eighth inch per foot, and cast iron castings one tenth inch per foot ; and so, to avoid frequent calculations and possible errors, the contraction rule has the necessary allowance in every division of the foot and of the inch. It is not how- ever to be supposed that the possession of such a rule renders it possible for the pattern maker to discard all further considerations upon the contraction of the casting j because there are others continually occurring. Such, for example, is the fact thatthecontractionwill not be equal all over, but will be the greatest in those parts where the casting contains the greatest body of metal. If we are requir- ed to make a pattern for a brass, such as -B shown in Fig. 95, its bore being six inches in diameter and its length ten niches, we shall find that the diameter of the casting will be less at A B than can be accounted for 100 PATTERN MAKER'S ASSISTANT. on the basis of a contraction of one eighth inch per foot ; and furthermore, the projection in the middle of the brass, which is sometimes provided instead of flanges to prevent the brass from moving endwise in the box, will cause the sides of the hexagon to cast hollow in. their lengths; so that a straight edge, placed along the bevel from C to D, would touch the brass at each end, and not in the middle. In the smaller sizes of patterns, however, such as those of G and less inches in diameter, there is another and a more important matter requiring attention, which is, that after a inolder has imbedded the pattern in the sand, and has rammed the sand closely around it, it is held firmly by the sand and must be loosened before it can be extracted from the mold. To loosen it, the moldsr drives into the exposed surface of the pattern a pointed piece of steel wire, which he then strikes on all sides, causing the pattern to compress the sand away from the sides of the pattern in all directions; and as a result, the mold is larger than the pattern. In many kinds of work, this fact may be and is disregarded ; but where accuracy is concerned, it is of great importance, especially in the matter of our example (brasses for journals), for they can be chipped and filed to fit their places much more rapidly than they can be planed, and it is necessary to have the castings as nearly of the correct conformation as possible. In cases where it is necessary to have the castings of the correct size with- out any work done to them, the shake of the pattern in the sand is of the utmost importance. If he is required to cast a piece of iron 3 inches long and 1 inch square, supposing the pattern were made to correct measure by the contrac- tion rule, the molder, by rapping the pattern (as the loos- ening it in the mold is termed), would, by increasing the size of the mold above that of the pattern, cause the cast- ing to be larger than the pattern; that is to say, it would CONTRACTION OF ^C A&TItfGS; , "V \ J ' i \ 103 be longer and broader, and therefore, in those two direc- tions, considerably above the proper size, since even the pattern was too large to the amount allowed for contraction. The depth, however, would be of correct size, because the loosening process, or rapping, does not drive the pattern any deeper in the mold. It follows that, to obtain a cast- ing of as nearly the correct size as possible, the pattern must be made less in width and in length than the proper size, to the amount of the rapping ; and to insure that the inolders shall always put the pattern in the sand with the same side uppermost, the word " top" should be printed on the face intended to lie uppermost in the mold. The amount to be allowed for the rapping depends upon the size of the pattern, and somewhat upon the molder, since some molders rap the patterns more than others : hence, where a great number of castings of accurate size are re- quired, it is best to have two or three castings made, and alter tbe pattern as the average casting indicates. For castings of about 1 inch in size, the patterns may be made ^2 inch too narrow and the same amount too short 5 but for sizes above 6 inches, allowance for rapping may be dis- regarded. In patterns for small cast gears, the rapping is of the utmost consequence. Suppose, for instance, we have 6 rollers of 2 inches diameter, requiring to be connected together by pinions, and to have contact one with the other all along the rollers : if we disregarded the allowance for rapping, the pinions will be too thick, and we shall require to file them down, entailing a great deal of labor and time, besides the rapid destruction of files. To resume, then : having sawn out our piece of wood for the flange, we plane up one side, and set a pair of com- passes to the radius of the required flange, and mark a circle upon the piece of wood, and then saw off the corners nearly to the circle. We then true up a facing chuck in MAKER'S ASSISTANT. the lathe, and fix the flange to it by screws passing through the chuck from the back, placing them far enough from the center to avoid their coming into contact with the hole which we shall require to bore in the flange. We then dress off the face of the flange to nearly the required thickness, using the gouge to rough it out with, and the scraping chisel to finish. It is not necessary to finish right down to the center, but merely down to a diameter some- what smaller than the hole in the flange will be. Our next procedure is to mark the size of the hole, which is done by setting the compasses to the required diameter, and then holding them with one leg resting upon the hand rest j and by bringing the point into contact with the face of the work, we may describe upon the latter a true circle, some- what smaller in diameter than that required. This circle will serve as a guide to us while we hold both compass points against the work to describe a circle of the correct diameter, which will be done by keeping the compass points at equal distances, one on each side of the circle first de- scribed. We must, in the last operation, hold the compass points lightly against the work until we can see that the Hue described by one point falls in the same line as that de- scribed by the other, and then we may make a deep mark. This method is quite as easy an operation as setting the compasses to the radius of the hole, and, putting one leg in the center of the work, describing a circle with the other 5 and this process is also more exact when the wood is rough. We next take a chisel of about i inch wide, and cut out the hole at one cut, by forcing the chisel light- ly through the thickness of the flange, taking care to cut the hole nearly ^ inch too small, so as to allow finishing with the diamond point or side tool. The hole being fin- ished, we may turn the outside diameter of the flange with a very sharp gouge, leaving about 3^ inch for finishing, which may be done with the scraper. When the scraping LATHE WORK. 103 chisel as indeed all scraping tools is in proper order, a slight burr can be felt on the top face of the tool, which is caused by oilstoning the beveled face of the chisel last. To form the body of the pattern, we take a piece of tim- ber of sufficient size to make the hub and core prints in one piece, and, with an ax, we hack off the corners, so as to save lathe work. We then i>lace it in the lathe between the centers, using the fork shown in Fig. 48 as the run- ning center and to drive the piece of wood, and screwing up the back center sufficiently firm to hold the wood tightly. The large diameter is turned to its size with the gouge and scraper, using the latter to finish with, and bearing in mind that the wood is apt to become loose be- tween the lathe centers, by reason of the latter becom- ing imbedded in the wood 5 and it is ne- cessary, therefore, during the earlier portion of the turn- ing, to try the back center and screw it up into the work, if necessary. Then, with the skew chisel, we cut two recesses, as shown in Fig. 96, the dis- tance from A to B being the length of the body or hub of the pattern, and the small diameter of the recess be- ing a little above the re- quired diameter of the core prints. We next turn down the core prints to the re- quired sizes, and turn the part shown at C, in Fig. 97> to fit the hole tight to the flange 5 and it will be perceived Fia.97. 104 PATTERN MAKER'S ASSISTANT. that, by leaving a longer end outside of the recess or nick at one end than at the other, we have left room for the flange, and so kept the core prints of equal length at each end, as shown in Fig. 97. The part that protrudes through the flange will in this case be for the top print, and it is therefore given an excess of taper, for reasons before explained. The hub or body of the pattern is also made taper, being a little the smallest at the end farthest from the flange (A, in Figs. 87 and 96), because this hub, being cast endwise, requires draft to permit it to bo extracted easily from the mold. Having brought our pattern, as nearly as possible, to the requisite size and form with the cutting tools, it is ne- cessary to consider those final processes which so much add to the appearance and smoothness of pattern work. The first of these processes is termed sand-papering or glass- papering. Sand-paper is a sort of Will-o'4he-wisp to the beginner, luring him on to scamp his work, under the im- pression that sand-paper will hide the defects, and bring it all right, while the fact is nearer the reverse ; for, let a pat- tern be ever so truly shaped and turned, if the sand-pa- pering be injudiciously performed, the sharpness of its outline will be destroyed, and very likely its size and shape be seriously interfered with. It is true that it is scarcely possible to do much damage to large surfaces ; but that is merely because of the great disproportion that would exist between an error engendered by sand-papering and the whole size of the pattern itself. If we have an inch cube to sand-paper, and should take -^ inch more off one side than off another, our error would amount to the -ff of the length of the pattern; but had the same thing been done upon a 12-inch cube, the error arising therefrom would only amount to yj^ of the length of the pattern. Again, to remove -^ inch from one side of each of these respective cubes, we should have 144 times as SAND-PAPEKINa. 105 much wood to abrade away in the one case as in the other ; so that it will be readily perceived that the difficulties at- tending the sand-papering of a pattern, so as to preserve its true form and size, increase in a two-fold ratio as the size of pattern diminishes, until at last it becomes imprac- ticable. Exactly where this point is reached, it is not possi- ble to state ; it will, however, vary with the capabilities of the workman, the steadiness of his eye and hand, and the nature and material of tbe work. It must have happened to many that they have made patterns so small that they dared not attempt; to sand-paper them, and that they have turned intricate details upon a piece of work which could not be preserved in its sharpness under the abrasion of sand-paper. While, therefore, we respect sand-paper, let us respect our tools more, and let the pattern or core box, as the case may be, be brought as nearly to the form re- quired as practicable with the cutting instrument, and then let the sand-paper be applied, not by folding it together and rubbing it upon the work, but by considering the shape we intend to finish, and preparing a piece of wood to correspond to the shape. Such a piece of wood is called a rubber. A flat surface requires a flat rubber, a convex sur- face a concave rubber, and vice versa. Eubbers are made of a size suitable to hold in the hand, and in length range up to 12 inches. Longer than this would be use- less for one sheet of sand-paper, and that is all that is generally used at a time. Turned cyl- inders make good rub- bers for core boxes that are semicircular, up to about 3 inches in diameter ; above that size, the turned rubber be- comes clumsy, and a piece flat on one side and planed to suit the curve is used. Such a piece is shown in Fig. 98. 5* 106 PATTERN MAKER'S ASSISTANT. To use it, place one fold of sand-paper only around the rubber ; and applying it to the work, move it over the sur- face of the work, and across the grain of the timber, if it is possible. If the size of the work is smaller than the rubber, we must take short strokes, so as to be able to move the latter steadily, and not round off the work at and toward the edges. A very good plan, where extra care is required, is to either glue the sand-paper to the rubber, or else fasten it with a few tacks. Sand-paper glued to a flat board is very useful for small surfaces ; but in this case, we rub the work upon the paper, and not the paper upon the work. The grades of sand-paper ,used upon pattern work range from No. i up to No. 2, Nos. 1 and 1-J being most commonly employed. The surfaces of the hub or body of our gland pattern being straight in their outlines, we sand-paper them in the lathe, with the paper wrapped once around a flat rubber, applying the paper lightly to the work, and moving it very slowly over the work, in the manner in which a file is used. We next fasten the flange to the body by gluing it, by using finishing nails, or by both. If finishing nails are used, care must be taken to use a bradawl before insert- ing the nails, for fear of splitting the wood. To make the pattern in the manner shown in Fig. 90, the method of procedure is the same as the above, with the exception that the tapering of the core prints must be vice versa, as in this case the core print the farthest from the flange will be the top one in the mold, and must therefore be given the most taper. And since the body of the pat- tern will lift with the cope, while the flange will remain in the nowel of the flask when the mold is taken apart (as shown in Fig. 91), the flange of the pattern must be made an easy fit to its place on the body or hub, and must not be left of a tight fit, as in the former case. A pattern of the form shown in Fig. 92 may be turned, flange and all, out PTCGS. 107 of a solid piece of wood 5 or, if too large for this, we may plane up a piece for the flange, and glue a hub to it ; and when the glue is dry, turn up the whole pattern at one chucking in the lathe. The construction shown in Figs. 92, 93, and 94 is so nearly the same, and the slight difference is so obvious, that an explanation of Fig. 94 will cover the ground. For Fig. 94 we plane up a piece over twice as long and more than half the size of the required flange, and out of this piece cut the two half flanges. If, however, the flange is of sufficient size to make it necessary to study economy, the two half flanges may be set out on the plank, lapping each other, as shown hi Fig. 99. We next, with a flat scriber, draw a line on the chuck exactly through its cen- ter, and set the half flanges to this line, and then screw them to the chuck, and turn them as if they were solid. By setting the halves exactly true to the line, it is insured that the flange shall part exactly at the center. To make the pattern shown in Fig. 93, we take two pieces of wood long enough to make the two halves, and allow about half an inch or an inch to turn off each end, so that the impressions of the fork and center may not appear on and disfigure the finished work, and for other reasons hereafter to be mentioned. We plane these pieces on one edge and on one face, making them of equal thickness. We make the flat surfaces which come together, true, trying them with the winding strips shown in Fig. 37, to detect any twist. Our next operation is to insert the pegs, 108 PATTERN MAKER'S ASSISTANT. and we may, for this purpose, adopt either of the two fol- lowing methods, the more ready of which we will take first : Clamping the two jointed faces together, as shown in Fig. 100, we bore two holes right through the top piece and into the bottom, one to a little greater depth than the hight to which the pin is intended to project, as shown by the dot- ted lines. We then plane up a piece of hard wood, about two and a half feet long, to fit the holes tightly. It is just as easy to plane a long piece as a short one, and what is left over will serve for a future occasion. A useful tool for preparing pin stuff is illustrated in Fig. 101, which repre- PEGGING. 109 sents a hardened plate of steel, pierced with holes of the sizes of the pins usually required. The wood for the pins having been planed up to the required size, is driven with a mallet through the plate, saving a great deal of time, and making the pins more nearly round than is possible by hand work. In some of these plates the holes are made taper, as shown at A, in Fig. 101; this, however, is detrimental, and the parallel hole is the best, because it guides and supports the stick, while it does not impede the cutting action of the tool. A hollow formed around the edge of the hole, as shown in the sectional view, at B B, would improve that action; or it might be still further improved by inserting bushes in the plate, with a portion left projecting above the plate and beveled off to resemble a chisel, as shown at C. The pin stuff being prepared and inserted into one half of the pattern, the jjrojecting end is then tapered off, as shown in Fig. 102. The formation of this projecting pin may secin a very i simple matter ; but if sufficient consid- eration is not given to it, a great deal of annoyance is caused to the molder, and the castings will be imperfect. If we reflect for what purpose these pins are inserted, we shall find the proper shape. First, with regard to the projecting length, some workmen seem to be guided by the diameter of the pin, making it project to a distance equal to its diameter ; but it is obvious that a short peg or pin will govern the position as well as a long one, and will be less liable to stick in the loose half of the pattern : hence it is better to let the protruding end stand out from three sixteenths to one half inch, and let 110 PATTERN MAKER'S ASSISTANT. from one sixteenth to one eighth inch of the large part tit the hole, the nut being tapered off so as to be sure that the pin can be released easily. These conditions inevita- bly bring us to the parabolic form shown in Fig. 102. An- other point to be observed is to make the pin of as large a diameter as is consistent with the work ; for th(3 larger the pin, the longer it will remain free from shake. Above all, it is essential that the pin be perfectly round at the part that fits the hole j and if these elements are neglected, castings will be produced of which the halves will not match, which is always very unsightly. Nothing is gained by making the pins to a tight fit in the loose half of the pattern, as they will not work that way ; and the molder will enlarge the holes with a red hot rod, and then, after a little while, the charred part around the hole falls out, and the pin becomes too slack. After inserting our pins, the two halves of. our patterns are to be fastened firmly together ; and this may be readi- ly done by brushing the end faces with hot glue for a breadth of one half or one inch, according to the amount we have allowed our pieces to be larger than the finished work. Then we hold them firmly together with a screw clamp, leaving them until they are perfectly dry. If there is not time for the gluing, the two halves may be screwed together 5 and indeed, if the job be a heavy one, it will not be safe to trust entirely to glue, but to use screws or dogs. Dogs are a kind of square staple, made of steel, and of the form shown in Fig. 103 $ and two of them driven in each end of a pattern will hold its loose halves very firmly together. While very handy, however, on large or small work, they are FigJOS. LATHE WORK. Ill cumbrous ; aiid the gluing or screwing is preferable. The work can now be mounted in the lathe, and turned as though it were solid. Care must be taken that the center points are exactly in the joint, and it was to ascertain if this was the case that our two halves were planed of equal thickness ; for if, in the process of turning, one flat is seen to be narrower than the other, as shown in Fig. 104, at A B, it is proof that the centers are not in the joint ; and unless the error is corrected, one half of the finish- ed pattern would be thicker than the other. To remedy this error, we tap at the pattern lightly with a hammer in the requir- ed direction, and then screw up the lathe centers a little more, continuing the process until the flat sides upon the pattern, when very nearly trued up as shown in Fig. 104, at C are equal, and finally disappear simultaneously. Our pattern being then turned and sand-papered, as already directed, the next proceeding is to stop up all holes or cracks that are not desired to appear, with either bees- wax or putty. This is a simple process, but it may have been noticed that some workmen take a much longer time over it than others, at least when beeswax is the stopping material. One who is expert at this work guesses just the proper amount necessary for each hole or crack ; then he forms the wax into a worm-like shape, and with a warm chisel (that is not hot enough to make the wax run but only to cut it easily) he presses the wax into the hole, and seldom leaves any surplus to remove. The same knack is necessary in filleting, that is, in filling in an internal square 112 PATTERN MAKER'S ASSISTANT. sharp corner, when it is thought too small to be filled in with wood ; for if the worm or string of wax of the right size be laid along the corner, the pressure of a warmed gouge will cause it to expand to the required fillet ; while if too much wax is inserted, much time will be occupied in trimming off the surplus. . The third and last of the finishing processes is the appli- cation of two or more coats of spirit varnish, which adds to the appearance of the pattern, and increases its durabil- ity by giving it a surface impervious to water, and by pro- ducing that smoothness so necessary for its easy extraction from the sand. A varnished pattern escapes much of the rough usage commonly bestowed upon patterns, because the molder does not rap it so much as he otherwise would do. Several thin coats of varnish give a much finer ap- pearance than fewer and thicker ones. The first coat fills up the pores of the wood and fixes the fibrous projections left by the sand-paper ; and after the first coat is dry, fine sand-paper is again applied to remove the fibers so fixed. The second and succeeding coats give the gloss. The pattern maker invariably mixes his own varnish, which he does in the following manner : The varnish pot should be of stone, and not of iron, which would discolor the varnish. The cover should be of thick leather, having through the middle a hole of such size that the brush han- dle, forced through it, will be suspended, and will not pass through to the bottom of the pot. The object of making the cover of leather is that the varnish collects around the lid and sticks the cover down, requiring sometimes so much force to remove it that wood would be liable to split. In the pot is placed so much shellac, and there is added just sufficient alcohol to cover the shellac, the whole being occasionally stirred with a piece of stick, and not with the brush. The consistence should be that of raw linseed oil j and to hasten the mixing, a little warmth may be applied. VARNISHING. 113 The color of the varnish used is, strictly speaking, optional. The usual plan, however, is to use clear varnish for the pattern, and black for core prints and the insides of core boxes, which thus distinguishes them. The black is made by adding the best dry ivory black to the clear varnish. A very durable varnish may be made by adding powdered oxide of iron to the clear varnish, which gives a hard var- nish with a reddish brown color. In mixing colored var- nishes, however, we must remember, that the lighter the pigment, the easier they work. Ivory black is the lightest {riginent, and so always pervades the varnish, and does not readily settle to the bottom ; hence it does not often re- quire stirring. Oxide of iron requires frequent stirring, even in the course of varnishing one pattern, if it be a large one ; because it settles so rapidly that a perceptible difference in the coat is apparent, unless the varnish is stirred previously to each insertion of the brush. The brush should never go to the bottom of the pot, and the pot should always be kept covered when not in actual use. Varnishing lathe work cannot be done while running the lathe ; but after the work is varnished, running the lathe hastens the drying. . Work should always, if possible, be varnished on a dry day ; for if the air is damp, the varnish becomes what is technically termed chilled that is, it as- sumes a soapy or milky appearance, as though it had ab- sorbed water and hence is spotty when dry. Having thus finished our example, we may now explain the process of putting pins in patterns, which we omitted to do when speaking upon that subject, to avoid digression. There are many cases in which it is not suitable for the pin hole to show on the outside of the pattern; and again, in large work, the holes would require to be bored so deep, and the pins made so long, that it would be too elaborate an affair altogether. In such circumstances, lines are re- sorted to, being drawn in the following manner : Place the 114 PATTERN MAKER'S ASSISTANT. pieces side by side, with the planed edges touching and the ends fair, as shown in Fig. 105, the line, G, representing the edges; and make two fine notches at A B. Then sepa- rate the pieces, and square the very fine lines, C 0, D D, )' i across with a knife. Then set a gage to half the width of the pieces, and mark the intersecting lines, E F ; and tho centers for the respective pin holes will be the intersection of the lines, E and D F. If, however, we have no planed edge to work from, and the job is of such size as to in- volve so much labor as not to admit of planing, we may take two small brads or finishing nails (or as many as we desire to have pins), and drive them almost entirely into one piece of the wood, in the spots where the pins are ultimately to be, and then file the projecting part of each to a point. By then resting the other half in its proper relative position upon the filed points, and, when adjusted, applying a little pressure to it, the nail points will enter the top piece and mark the corresponding centers for the holes to receive the pins. We may then extract the brads or nails, and pro- ceed to bore the holes and insert the pins. Another method of marking the pin holes, is to provide some ordinary lead shot, and make shallow holes with a brad-awl, slightly less in diameter than the shot. Where LATHE WORK. 115 pins are to be inserted, place the shot in the hole, so that they project beyond the surface, and then proceed as de- scribed for the brad points the latter being the more expe- ditious method of the two. Our second example, Fig. 106, is a design for another kind of gland, such as is often fitted to glands for pump rods and spindles. For the small sizes, the glands are usually cast solid, and the hole is drilled out in the lathe ; in which case, providing the gland is not very deep, it would be molded vertically, with the head in the nowel, and would be turned out of the solid piece of wood in the style of our previous example, treating for the moment the hexagonal part as a flange, whose diameter must be turned to the size of the hexagon across the corners. After the turning is done, we mark the hexagon as follows. We set a pair of compasses as nearly as possible to the radius of the turned piece that is to form the hexagon, and divide that piece off into six divisions, in the manner shown in Fig. 107 for the radius of a circle will divide its circum- ference into six equal parts so that, if the compasses are correctly set, one trial will be sufficient ; but if not, we must readjust the compasses, and go around again. Then, from these points, we square lines, as shown in Fig. 107, at 1, 2, 3, 4, 5, C ; and then, with the paring chisel, we pare off the 116 PATTERN MAKER'S ASSISTANT. sides to the lines. It is not necessary to actually draw the hexagon on the circumference, by joining the lines of division on the top of the flange ; for a straight edge being applied as the par- ing proceeds, will be all that is necessary to produce a true hexagon. Neverthe- less it ib possible that error may have crept in, though we have performed the above .operation with the greatest of care ; it is there- fore imperative upon us to apply correcting tests to our work, such as a pair of calipers, to try if each pair of the opposite sides are parallel ; also the bevel, to verify if each angle of the figure contains 120. Hexagon shapes are so common that a special hexagon gage is very useful ; and such a gage, of the most approved form, is shown in Fig. 108, together with its method of application, the edges, A B ? being to try the hexagon, and C D to square the edge to HEXAGON GAGE. 117 the face, and the edge, F, being used as a straight edge. If, however, we have not such a gage, we may set the bevel square, shown in Fig. 23, in the following manner: Take a piece of board, planed on one side and on one edge, and let A B, in Fig. 109, represent the planed edge, from which we mark with the gage the line, G D. Then tak- ing any point, such as I, in the line D, as a center? at a convenient distance, we describe with a pair of com- passes the arc, F G. We then take the compasses, and, without shifting their points at all, we rest one point on the intersection of the lines, D and F G, and then mark the arc, H. If then we draw a line from he intersec- tion of the arc, F G, and the arc, H, to the center, I, upon which the arc, F G, has struck, the lines, H I, I C, form the angle required j and we may apply the stock <>f the bevel square to the planed edge, A B, and set the blade to the line, I H, as denoted by the dotted lines. The bevel being set, we test the work as it proceeds, first cutting down one hexagonal side, and then applying the bevel to gage the angle of the oth- ers; and as the diametrically op- posite sides are finished, we ap- ply the calipers. The lines of divi- sion upon all good pattern work are made very fine, in fact, merely dis- tinguishable ; and the instrument by which they are drawn is shown in Fig. 110. It is called a cutting scriber, and the end at A is beveled off at both sides, like a skew 118 PATTERN MAKER'S ASSISTANT. chisel, forming a knife edge. The end, B, is ground to a point, and both ends are finished on an oilstone. The point end is for drawing lines along the grain, while the cutting edge, A, is for drawing lines across the grain of the wood. The wooden handle in the center is to enable the operator to hold it more firmly. It sometimes happens that the size of the hexagon is given across the flat sides instead of over the angle; and when that is so, we proceed as follows: We describe upon a piece of board, as in Fig. Ill, a circle of a diameter equal to the given distance between the flat sides. We then take a hexagon gage, or else set the bevel square to an angle of 120 ; and applying it to the planed edge of the board, we draw the line, C D, in Fig. Ill, in which figure A is the circle of the size of the flat sides of the hexagon, and B E are the planed edges of the board. We next reverse the bevel ; and from the opposite edge of the board we strike the line, F D, cutting D at the point D, where both the lines cut the circumference of the circle, A. Then from the center of the circle A, we draw the LATHE WORK. 119 circle G, intersecting the point D. The diameter of G will be the size of the hexagon across the corners. If the gland is a long one, it will be better to make it in halves, letting it part across two corners, as shown in Fig. 112. When a gland of this kind is made in halves, the corners at the parting are liable, from their weakness, to chip off, and it is therefore proper to make it of hard wood. CHAPTER VI. EXAMPLES OF T PIPE AND JOINT WORK. OUR next example is what is called a T, a drawing for which is shown in Fig. 113. It is shown with flanges on the main body, and a hexagon on the branch. Sometimes a flange is employed instead of the hexagon, but this de- pends npon the connections to which it is to be attached. Patterns of this class are often made so that either round flanges or hexagonal connections may be put on at will ; and it is in that style that we propose to make our example. It is apparent that the pattern will be the most easily molded with its body and branch both lying horizontally in the mold j so that, if we suppose the surface of this paper to re- present the surface of the mold, the engraving shows just how the pattern will lie in it. It will be advisable, there- fore, to make the pattern in halves. PIPE AND JOINT WORK. 121 We first prepare the body and flanges, in the same manner as described for the body of our gland; the only difference being that we have, in this case, to fit a flange on each end. The same method is pursued in making the branch, with the exception that we only require a core print on one end, the other end abutting against the body. The first question that arises is, How long shall we make the branch 1 and this depends upon how far the branch follows the curvature of the body. In our example, the branch and body are of the same diameter, and therefore the branch will follow exactly half way around the body. We turn up the branch piece, then, to its requisite diameter, and make its length equal to the diameter to which it should stand out from the body, added to half the diameter of the body. The pieces we have made, then, are those shown in Fig. 114, in which A represents the piece for the body, and C, the piece for the branch. Our next proceeding is to cut out the abutting end of the branch to fit to the curvature of the body, and this we perform as follows : We first set the bevel square to an angle of 45, by the process shown in Fig. 109, and then, taking the branch halves apart, and 6 122 PATTERN MAKER'S ASSISTANT. placing the bevel square with its back across the end face of the branch (the blade lying on the joint face of the half branch), we mark the two lines, A B, in Fig. 115, which must meet exactly in the center of the branch and at the extreme end, as shown in Fig. 11G. Wo then pare off the angular piece, C D, down to the lines, A B. If, before we do the paring, however, we give our half branch a quarter turn around, it will appear as shown in Fig. 116 j the curve formed by the intersection of the plane surface (just made) with the round surface of the piece, is the true curve of the body of the T. Turning to the other half of the branch, we perform upon it the same operation ; and we may then cut away with the gouge the intervening timber from between the curve lines. Our two halves will be of the proper curve at the end, to fit exactly to the body of the T, as shown in Fig. 117, in which A represents a sectional view of the body of the T, and B are the two halves of the branch ; while the view D shows the body of the T lying horizontally, with the branch attached. PIPE AND JOINT WORK. 123 We have now to fasten the branch to the body of the T ; and here we must pause to consider whether the pattern is required to serve simply for the production of a few cast- ings 5 whether it is to be cast aside after the first casting, never to be used again (which is often the case), or whether it is intended for standard or continuous use. For a tem- porary purpose, a few screws will be sufficient ; but for a permanent pattern, a much stronger joint may be made as follows : Brush with hot glue the ends of the branch piece, and let them stand until the glue has been absorbed into the pores of the wood. This is called sizing, and is always necessary in gluing end wood, as it is called meaning the end grain of wood. The reason that sizing is in that case necessary is, that the pores of the wood all meet the surface in the end grain, and the sizing is necessary to fill them. We then take a truly planed piece of board, and lay one half of the body down upon it, placing a piece of thin paper between the body and the board, so that any glue that may run out may not touch the board : otherwise it may glue the work so fast to the board that, in parting them, some of the fibers of the wood may get torn out. Then we fasten temporarily the half body to the board, and lay one half of the branch with its flat surface on the same board, and glue it to its place, drawing it well up to the body piece with dogs or clamps, at the same time observing that it is close down to the board, and fixing it temporarily there, as shown in Fig. 118, and allowing it to remain until the glue 124 PATTERN MAKER'S ASSISTANT. is dry. In putting on the second half of the branch, the board need not be used, since the first half, already in posi- tion, will serve as a guide. A piece of paper must, how- ever, be placed between the two halves of the branch, to prevent them from adhering together. When all is dry, put a strong screw in the position denoted at A, in Fig. 110, cut out a recess on the flat face of each half, and let in a piece of hard wood, as shown by the dotted lines in the same figure. us now suppose that, in our ex- ample, the diameter of the branch had been smaller than that of the body of the T. In that case we must first ascertain its proper length by the process illustrated in Fig. 120, which represents a piece of board, upon which we strike the line A B ; and from the point 0, we make the semicircle D, which must be of the same radius as the body of the pattern. Then, parallel with the line A B, we draw the line D E the distance between these two lines being equal to half the diameter of the branch of the pattern. Then from the junction of the line D E with the semicircle D, we strike the line D F, at a right angle to A B ; and then from F to G, added to the distance which the branch requires to stand out from the edge of the body, is the length we require to make the branch. To draw the curve on this branch so as to cut it out to fit the body, we proceed as follows : Fig. 121 represents the application of a peculiar trammel, designed for this and similar purposes. It enables the operator to strike a true circle upon a round or uneven surface. It is com- posed of the turned bar or rod of metal, A, of about half an inch diameter, and upon it slides the piece of brass tube, B, upon which is contrived a support for the sliding O Jf G PIPE AND JOINT WOKK. 125 arm, 0, as Welt as a set screw for fastening the arm, 0, in any desired position. At the end of the arm, O, is placed an arrangement for fastening the scriber, D, so that we may set the scriber at any requisite distance from the rod, A, by adjusting and fastening the arm, 0, and revolve it about while lifting or lowering it upon the rod, A. When properly made, this is a most useful tool ; and if not in use, it may be taken apart in an instant, and it occupies but very little room in a tool box. If the stand, E, pierced with holes for screwing down, is provided, it will be a very useful addition, but it may be dispensed with; whereas the tool proper, or some improvised substitute for it, is absolutely neces- sary, for the curve must be struck somehow. If the pipe or branch is large say even six inches in diameter to attempt to fit it by guessing and trying, is the work of a novice and not of a workman. To apply this tool to our branch, we proceed as follows : Taking a planed board, we gage a line upon it, and at a point on this line we describe W 722 a c * rc k 11 P OU it of the size of the foot k 2L of the instrument. We then make two V blocks, such as shown in Fig. 122, to carry the branch. We then place these V blocks with the apex of the V exactly over the gaged line, and place the branch in the V ? s. We then set the point of the scriber at a distance from the rod of the trammel equal to the dia- 120 PATTERN MAKER'S ASSISTANT. meter of the branch, which may be readily clone if the size of the rod be known. We next mark upon the top of the branch, as it lays in the V's (with the joint of the two halves standing vertically), the distance it requires to be cut out to form the curve, which distance will correspond to the distance of F G, in Fig. 120. We then draw the branch forward, until this mark falls exactly under the scriber, keeping the joint faces vertical ; and this adjustment being made, we fix temporarily the branch to the piece of board whereon it and the V's rest. Then we move the arm, 0, in Fig. 121, a half circle; and letting the point of the scriber contact with the branch, we draw the necessary line. It will be found, however, that it is requisite to mark the lines while lifting the arm, to prevent the scriber from digging into the wood. Thus one side of the branch will be marked, and we must then turn it upside down on the Vs, set the joint vertically again, adjust the mark to the scriber point, and proceed as before to mark the other side of the branch. We may then cut out the corners to the lines, which may be most rapidly performed by a baud saw, sawing exactly to the line the branch being held on a board, as it was when being marked. In fact, a piece of wood should be fitted underneath, where the saw cut will come, so as to prevent the fibers of the wood from being torn out at the edge, showing a ragged cut as it is very apt to do, especially if the band saw is not in first-class order. Should the branch be re- quired to stand obliquely to the body of the pattern, as shown in Fig. 123, it may be struck out in the same manner ; but instead of being set square with the rod of the trammel, as in the former PIPE AND JOINT WORK. 127 case, it must be set at the bevel at which it is to be fixed upon the body of the pattern. When marking one side, the branch must make an angle with the upright equal to the angle at A, in Fig. 123 ; while, when mark- ing the other side, it must form an angle equal to that at B, in the same figure. It will pay, where two or three pattern makers are employed, to have this marking appa- ratus always standing ready for use upon aboard, with the degrees of angles marked thereon ; so that a workman could mark off his job in five minutes, and cut it out with a band saw. Cutting out with a gouge, and trying to its place, may take four or five hours. It must be borne in mind that too much care cannot be given to striking out the piece accurately, and to sawing them true to the lines. The saw must be sharp, and of a width suitable to the curve, and not tremble, or " dither," as band sawers say. By attending to these matters, a fit may be obtained with a minimum of labor to the workman j and this is desirable in itself, and is an item of profit in the cost of the pattern. We need not dwell upon the half core box, which is ne- cessary for this pattern if the branch stands at a right angle to the body ; or the full one, necessary if it is required to stand obliquely. When the body of the T is much larger in diameter than is the branch, we may joint the two in a simpler way, which, so long as it does not entail a great weakening of the body, will be found more advantageous than the method described. This simpler method is : Hav- ing found the amount of the length of the branch necessary to allow for curvature of the body (by the process shown in Fig. 116), we turn upon the branch end an additional projection or stem, as shown in Fig. 124, somewhat smaller 128 PATTERN MAKER'S ASSISTANT. in diameter than the branch itself ; and we then cnt in the body a recess to receive the branch and turned stem or projection, which recess may be either cut out with a gouge or turned out in the lathe, the latter being, for obvious reasons, the best method. For this latter operation, we take a chuck, similar to that described in Fig. 58, as a cement chuck ; and having verified that the point and the face of the chuck run quite true, we draw a center line across it, set the apexes of the two V blocks exactly over this line, and then fasten them. Having marked upon the body the center of the branch, we find a point diametrically opposite to it upon the body, and place the body so that the steel center point enters the point so found, at the same tune as the body rests in the Vs. We then fix it in this position by thin straps of hoop iron, or any other contrivance that will not project so as to pre- vent the lathe rest (or tool rest, as it may be more pro- perly termed) from being brought close to the work. The work must be securely screwed to the chuck, on account of the high velocity of the lathe in turning. To cut out the recess, we commence by placing a center bit in the back lathe center, and boring a hole, as large as convenient and very nearly to the required depth. A screw bit is not available for this purpose, for it would in many cases be right through the work before there was time to stop the lathe, which is not usually sufficiently under control. We may next take a turning tool, and turn out the recess to fit the end of the branch ; and after taking the job from the lathe, we fasten each half of the branch by gluing and screws. In connection with this method, there is yet another advantage : it is, that by cutting away the body instead of the branch, it renders us indifferent as to PIPE AND JOINT WORK. 129 . fiffJZS. whether the shape of the body be spherical, as in a globe valve, or elliptical, or even vase-shaped : because, in this case, the shape adds nothing to the difficulty of the job. Should it occur that one end of the T is larger than the other, we may find the height necessary for each of the V pieces (whereon the body rests during the turning process) as follows : Draw upon a piece of board the line A D, in Fig. 126, which will represent the plane of the chuck ; and let the point C represent the center point of the lathe. Then, from C, we square up the line D 5 and we set the compasses to the radius of the body of the pattern at the center of the place where the branch is to be. We take a radius from 0, and about T x inch up from the line A B, and with this radius we mark on the line D, the point E. From this point, as a center, we strike the axes, E and F, whose radii correspond to the unequal sizes of the pattern, where the V ? s are required to be. Then we draw tangents to each of these arcs, and complete the forms of the V blocks, as shown in Fig. 127, in which half of each V block is shown. We have now to make a core box for our T; and for clearness of illustration we will make the drawing some- what larger than those for the T itself. Fig. 127 repre- sents three views of the core box j that portion which pro- jects below the line, at B, may be made separately, and need not, therefore, be given any consideration. Having drawn the plan of the box, as shown in Fig. 127 at 1, we draw the end and side views, as shown at 2 and 3, and divide these latter into courses of a thickness to suit the stuff at hand, from which the core box is to be made. The courses may be made of equal or unequal depth. Courses 1 and 2 are got out of the full size of the box, while courses 6* 130 PATTERN MAKER'S ASSISTANT. 3 and 4 must be of the length of the box, bnt their width will differ according to the curvature of the half circle of the core, as shown in Fig. 127, at 2 and 3 ; 5 and 6 will be similar to 3 and 4, and may be marked iroin them. All these pieces must be planed to a true surface and glued together, each course being allowed to dry before the next one is put on ; but for greater expedition, nails, in addi- tion to the glue, may be used, in which case care must be taken that they do not come so close as to interfere with the cutting out of the half circle. The part A B, if very short, say under 3 inches, may be made in one piece ; but if over 3 inches and not over 6 inches, we take two pieces of the required length and width, and of half the thick- ness, and chuck them in the manner previously explained for making flanges in halves ; then we place the work in the lathe, and bore a hole for the core, then take them from the chuck and glue them, first together and next to the body of the core box. We next turn the body part of the core to a semicircle of the required size, and all that will then remain to be cut is that part of the branch that PIPE AND JOINT WORK. 131 is above the line A B. If, however, the part below A B, in Fig. 127, should be required still longer, then it had better be built up in the same manner as the other part. The lengths of the pieces forming the courses will be the same, and may be measured on Fig. 127, from A B out- wards. The widths will differ, and may be measured from E or F, inwards. This separate portion, from the grain of the wood being enduric, cannot be firmly fixed to the main body of the box with glue ; we must, therefore, in addition, place battens below the box, and let in pieces of hard wood or metal above, as represented in Fig. 127, at G and H. CHAPTER VII. WHEEL AND PULLEY WORK. Our fourth example is a double flanged pulley, shown in section in Fig. 128 ; and our first consideration is, how it shall be molded. It evidently should He in the sand in the position shown in Fig. 129; but it will be observed that the sand is confined between two flanges, rendering it practically impossible to retract the pattern from the mold, if it is made in one piece. We say practically im- possible, meaning that it cannot be done economically ; for strictly speaking, an expert molder with every requisite appliance, can mold almost anything, as any one will conclude who examines the various works of art in bronze which appear in art exhibitions and elsewhere. Our pat- tern must, for ease of molding, be made in two parts. If the disk (or spokes, if it be a spoke- wheel) be sufficiently WHEEL AND PULLEY WORK. 133 thick to allow it, the division may be made at the center, that is to say, on the line A P, in Fig. 128. The operation of the molder may be understood from Fig. 129, three dis- tinct beds of sand being necessary. It may be that a part of a flask is used for each bed, or it may be arranged as shown in Fig. 129, it being a matter of indifference to the pattern maker. In either case, however, draught should be allowed both inside and outside, that is to say, both the interior and exterior diameters of the pattern should be made smallest at the line of parting, the diameters in- creasing slightly as they approach the flanges. The hubs also should, in like manner, be slightly tapered. Inside sharp corners should be avoided ; they should, in fact, al- ways be rounded by cutting them out with a round-nosed tool. To construct this pattern, we proceed as follows: For a small pattern, we take two pieces, somewhat thicker than half the thickness of the finished pattern, and large enough to allow for turning. We then chuck them, as shown in Fig. 130j and turn them up. The recesses, shown at the center by the dotted lines, must be made of equal size in the halves of the pattern ; and we prepare a chuck with a projection across the center to fit into the recess, and thus rechuck the pieces, and turn out the opposite sides, cutting the hubs out of the solid. We may then fit a plug into the recess in one half of the pattern, and glue it fast, allowing it to project so as to fit into the recess in the other half ; and the pattern is complete, unless the hole in the hub is to be cored, hi which case it will be necessary to fix core prints on the top and bottom, in the manner described in our first example. 131 PATTERN MAKER'S ASSISTANT. A useful hint may here be given to the effect that when it is decided to fix prints in the center of a piece of turned work, a slight recess may be made to receive the print, which is then sure to stand true 5 and sho ild it at any time get accidentally knocked off, as prints often do, another may be immediately affixed without the trouble of linding the center. The pattern now supposed to be made, though good enough for many purposes, has one great defect which will be readily perceived when we bear in mind our remarks on the properties of timber. It is, that it will gradually be- come oval ; and to avoid this, we must have recourse to what is termed building up, a process which must in any event be used, if the pattern is a large one. To build up such a pattern, we proceed as follows : After drawing the pulley in section and in plan, as shown in Fig. 131, we divide the whole height of the section into courses, the WHEEL AND PULLET WORK. 135 number of courses being regulated so as to have each of a convenient thickness. It is advisable, however, to have at least two courses in the flange, which will greatly increase its strength. After dividing one of the circles in the plan view into six parts, we draw lines from the points of division to the center, as shown ; and then we make a template of one division, as shown at A, which must be made a little larger than the division, and this forms a template where- by to cut out the segments forming the courses which make up the flanges. A similar template, cut out somewhat larger than the space devoted to B, in Fig. 131, will serve to cut out the sections to be used in forming the body of the pattern. The flanges being made in two courses each, and there being six sections in each course, we shall require 20 pieces of the size of the large template ; and allowing each half of the body likewise to consist of two courses, we shall require the same number, to form the body of the pattern, of the size of the small template. Our templates being made, we plane up some pieces of board a trifle thicker than the courses are intended to be. It is easier to plane up the pieces of the board while yet square, than to plane up the segments separately. From the template, with a black lead pencil, we mark off on the planed pieces of board the requisite number of segments, and cut them out with a band or jig saw. We now proceed to building up, for which purpose we employ a chuck as a base whereon to build. It will save time, however, to have two chucks, building one half of the pattern on each, and both halves simultaneously, which will give suflicient time for each course to dry, without requiring nails or pegs to assist the glue in holding them together. The two chucks having been prepared, we glue to them strips of paper at intervals where the points of the segments will come, as shown in Fig. 132 ; and if the segments are very long, we glue another strip between 136 PATTERN MAKER'S ASSISTANT. each of these strips, so that the segment may lie level on the chuck. As the building proceeds, the end of each segment must be planed; and for this purpose, we re- quire what is called a shooting board, which is a simple FjffJS, contrivance, made in the following manner i We take a piece of board about 2 feet long, 8 or 9 inches wide, and nearly 1 inch thick, and also a piece of the same length, but 6 inches wide, and f inch thick; and after planing them up straight, we screw one to the other, as shown in Fig. 133, at A B. S is a raised piece called a stop, and it should be recessed about f inch into B, and dove- tailed. It should not be glued, as the shooting board is useful for other purposes besides dressing segments : and it may be necessary to change the stop for one of a dif- ferent height. In Fig. 133, the segment is shown in posi- tion for being dressed; while in Fig. 132 attern when the excess in length referred to is turned oif. We next prepare, in the same way, two more pieces, to form the two halves of the branch, shown at B, in Fig. 150, for which, however, one peg only will be necessary. These pieces must be somewhat wider than the size of the required hexagon across the corners that is, supposing the hexagon is to be solid with the branch otherwise we must make them a little wider than the diameter of the hub of the flange or of the round part of the hexagonal pieces. Their lengths must be such as to 160 PATTERN MAKER'S ASSISTANT. afford a good portion to be let into the ball or body of the pattern (as shown by the dotted lines in Fig. 149), which is necessary to give sufficient strength. The two pieces must be firmly fixed together, and then turned in the lathe. During the early stages of the turning, or, in other words, during the roughing out, we must occa- sionally stop the lathe and examine the flat places on the body; for unless these places disappear evenly, the work is not true, and one half will be thick- er than the other, so that the joint of the pattern will not be in the middle. It was to insure this, that the pieces were directed to be planed of equal thickness, since, if such is the case, and the flat sides dis- appear equally and simultaneous- ly during the turn- ing, the joint or parting of the pat- tern is sure to be central. If the lathe centers are not exactly true in the joint of the two pieces, they may* be made so by tapping the work on the side having the GLOBE VALVES. 161 Hu/M narrowest flat place, the process being continued, and the work being trued with the turning tool at each trial, until the flat places become equal. By this means we insure, without much trouble, two exact halves hi the pattern, which is very important in a globe valve pattern, on ad- count of the branches and other parts, not to mention the molding. Having turned the body of the pattern to the requisite outline, and made while in the lathe a fine line around the center of the ball where the center of the branch is to come, as shown in Fig. 149, by the line A, we make a prick point (with a scriber) at each crossing of the line A and the joint or parting of the pattern. We then mount the body upon a lathe chuck, in the manner shown in Fig 151. A point center should be placed in the lathe, and should come exact- ly even with the line A. In Fig. 151, V V are two V blocks made to receive the core prints. These V's are screwed to the lathe chuck, and the pattern is held to them by two thin straps of iron placed over the core prints and fastened to the Y's by screws. If the chuck and center point run true, the V blocks are of equal height, and the core prints are equal hi diameter, the prick point opposite to the one placed to the center point will run quite true ; and we may face off the ball or body to the required dia- 7*t 1G2 PATTERN MAKER'S ASSISTANT. ineter of branch, and bore the recess to receive the same. We make the holes in the flanges of the same size as the core prints; but we should not check in the print, because, if a flange with a different length of hub were substituted, it would be a disadvantage. To obtain the half flanges, we take a chuck and face it off true in the lathe; then, with a fine scriber point, we mark the center while the chuck is revolving. We then stop the lathe, and placing a straight-edge to intersect the chuck center, we draw a straight line across the chuck face. We then take two pieces suitable for the half flanges, and plane up one flat side and one edge of each piece. If the flanges are not large ones, they may be planed all at once in a long strip. We place the pieces in pairs, and mark on each pair a cir- cle a little larger than the required finished size of flange. We then fix each pair to the chuck, with the planed faces against the chuck, and the planed edges placed in con- tact, their joint coming exactly even with the straight line marked on the chuck face, and we may then turn them as though they were made in one piece and to the requisite size. In Fig. 152, we have a representation of one half of a suitable core box, the other half being exactly the same, with the exception that the position of the internal parti- tion is reversed. To get out this core box, we plane up GLOBE VALVES. 163 two pieces of exactly the same size and length as the pat- tern, and of such width and thickness as will give suffi- cient strength around the sphere, allowing space for the. third opening. After pegging these two pieces together, we gage, on the joint face of each, lines representing the centers of the openings and the center of the sphere. We then chuck them (separately) in the lathe, and turn out the half sphere. We next place the two halves together, and chuck the block so formed in the three positions ne- cessary to bore out the openings ; or, if preferred, we may pare them out. The partition. (A, in Fig. 152) follows the roundness of the center hole, and is on that account more difficult to extract from the core, than if it were straight and vertical. When, however, the partitions are of this curved form, the pieces of which they are formed are coin- posed of metal, brass being generally preferred. Patterns have in this case to bo made, wherefroin to cast these pieces, and they may be made as follows: First, two half pieces, such as shown in Fig. 153, are turned 5 each is then cAit away so as to leave the shape as shown at O, in the same figure, and is then fitted into the spheri- cal recess in the core box, letting each down until both are nearly but not quite level. The two pieces, A and B, in Fig. 153, are then fastened on, and this pattern is com- plete. When the pieces are cast, they must be filed to fit the core box, and finished off level with its joint face, a small hole being drilled in the center, and a pin being driven through the piece and into the box, to steady the 164 PATTERN MAKER'S ASSISTANT. corners. We then saw the pieces in halves with a very fine saw. If the partition, instead of following the roundness of the valve seat, is made straight, the construction of the core box is much more simple. In this case, a zigzag mor- tise is made clear through each half of the box, its size and shape being that of the required partition. Fig. 154 repre- sents a half core box of this kind. A piece of wood, A, is fixed as shown to the partition, to en- able the core maker to draw it out before removing the core from the box. The mortise for the partition should be turned out before the half spherical re- cess the mortise being temporarily plugged with wood, to render easy the operation of turning. In very large valves (say 10 or 12 inches) a half core box is generally made to serve, by fitting the two half parti- tions, shown at 0, in Fig. 153, to a half core box, and keeping them in position by means of pegs j a half core be- ing made first with one, and then one with the other in the core box. It is often necessary to form a raised seat in the body of an angle valve, such as shown in Fig. 155, which represents a section of such a body. It is shown with flanged openings, though in small valves hexagons, to receive a wrench, would be substituted. Fig. 156 is a plan of half the core box necessary for forming the raised seat. From this construction it will be seen that the large core, though solid with the branch GLOBE VALVES. 165 core, is not solid with that forming the hole in the seat and the part below itj therefore the core prints on the body pattern must be left extra long, to give suffi- cient support in the mold for the overhanging cores. The loose round plug, P, is made of the size of the outside of the seat, and fitted to the box. The part outside the box is a roughly shaped handle to draw it out by. The di- minished part, D, is a print, and into the im- pression left by it is in- serted the core made in box, shown in Fig. 157. The print, D, is of the same diameter as the hole in the I seat 5 and the print on the pattern is of the size of the increased di- ameter below the seat. Large an- gle valves are made with half a core box, by making a branch open- ing in the box right and left, a semi- circular plug being provided. Two half cores are made with the plug, first in one and then in the other branch open- ing. The plug, P, should be in this case only half round. CHAPTER X JOINTS, AND EXAMPLES IN BENCH WORK. Turning now for a space from examples requiring so much lathe work, we come to deal more particularly with the bench, and the devices and operations connected with it. A good bench is a great assistance to a pattern maker. It should be perfectly true on its upper surface, which is best made of hard wood, and covered with a coat of varnish to prevent dust or drippings of glue from adhering to it, so that it is always cleanly in appearance. The vise, when screwed close to the bench, should come level with its top, and the butt or stop for work to press against, should be so constructed that its height may be readily altered, as this will have to be done perhaps fifty times a day. In the absence of a well contrived mechanical stop, which always admits of re-adjustment without stooping, I should recommend a stop of wood made by placing two wedges together, as shown at A and B, JVftfJGS. Fig. 158. A pin is fixed tightly in the wedge A, which slides in a groove, in B, for a short dis- tance j this prevents the wedges from falling apart when loos- ened. A light tap on B loosens, and one on A tightens the stop. The ordinary contrivances used at the bench, in addition to the workman's tools, are the shooting board (already described), the mitre box, and the bench hook. The mitre box is a contrivance to enable a workman to saw moldings, pipe patterns, etc., to an angle of 45. It is simply a trough JOINTS. 167 with saw cuts made at the required angle. The stuff to be cut is laid in the trough and pressed to one of its sides, the saw being guided by the saw cut. The bench hook is a piece of wood sawn to the shape shown in Fig. 159, and is used as a butt ; for timber, in cross-cutting work, should not be sawn directly on the bench. Figs. 160, 161, and 162, are illustrations of different methods of jointing pieces of wood together so as to form a square or any angle. Fig. 160 represents a tenon arid mortise joint, made as follows : The two pieces, A and B, having been planed or other- wise made to size as required, are marked for the position and length of the mortise in one case, and for the length of the tenon in the other ; both pieces are now gaged with a mortise gage, both being marked alike ; and then from the face side we mark a tenon or mortise of the size required, which is generally a third of the thickness of the stuff. Where the mortise approaches the end of the piece, a provision has to be made to insure strength, by adding the extension denoted in Fig. 160 by the dotted lines. This practice, however, though often adopted in carpentry, is rarely ad- missible in pattern work ; and in its stead, the tenon, or 168 PATTERN MAKER'S ASSISTANT. the piece B, is diminished in width, as shown in Fig. 163, the mortise being made to correspond. In order to avoid breakage during the cutting of the mortise, the piece A, Fig. 160, is got out an inch or two longer, which excess is sawn off after the glue is dry. An excess of -J- to i an inch should also be allowed on the tenon, as it is ne- cessary to chamfer off the corners of the tenon, so that in driving it may not damage the mortise. To prevent the tenon from, in time, working out, the mortise is slightly tapered that is, made wider on the side remote from the piece carrying the tenon. Then the tenon is provided with two saw cuts, one on each side, near the edge ; and after being driven home, wedges are driven into these cuts, thus locking the joint. A joint, more commonly in use among pattern makers, is the half lap, shown hi Fig. 161, which has been already described. When this joint occurs away from the end of the pieces, the mortise need not, and should not, extend through the piece. This joint, besides being glued, may be fastened with screws, or if very thin, riveted with short pieces of lead wire. A very superior method of jointing is the dovetail, shown in Fig. 164, which is serviceable for connecting the ends and sides of a box, or any article in that form. The strength of the corner formed in this way is only limited by that of the material itself; therefore, it JOINTS. 169 should be preferred, when available, in making standard patterns, or for work too thin to admit nails or screws. The corner formed by this joint is not limited to 90 or square, so called, but may form any angle. Nor is it imperative that the sides or ends of the box or other article be parallel. They may incline towards one another like a pyramid j a mill hopper is a familiar example of this. If it be required to dove- tail a box together, get out four pieces for the sides and ends, to be of the full length and width of the box outside, respectively. They are to be planed all over, not omitting the ends. The gage, that is already set to the thickness of the stuff, must now be run along the ends, marking a line on both sides of each piece. Then mark and cut out the pins as on the piece A ; the dovetail openings, in B, are traced from the pins in A. The pieces, having been tried and found to go together, are finally brought into contact and held in their places with glue. Fig. 162 is a mitre joint the only one serviceable to moldings, pipes, and other curved pieces. It is not a strong form of joint, and is only used where the preceding kinds are inapplicable. It is made with glue, the pieces having been previously sized ; and as an additional pre- caution, if the work will admit, nails, brads, or screws, are inserted at right angles to one another. In Fig. H is shown a mitre box exceedingly useful as a shop fixture, but of course, being made of iron, it is not intended to form a part of a journeyman pattern maker's kit of tools, but rather from its superiority to dispense with the necessity for the same. The saw blade is guided 8 170 PATTERN MAKER'S ASSISTANT. by the rolls shown upon the upright spindles, and leaden rolls below regulate the depth to which the saw will cut, Mg. H and thus preserve the saw teeth from contact with the iron frame. This mitre box can be used with a back saw or a panel saw equally well. If a back saw is used, both links which connect the rollers, or guides, are left in the upper grooves, and the back of the saw is passed through under the links. If a panel saw is used, the link which connects the rollers on the back spindle is changed to the lower groove ; and then the blade of the saw will be stiffly supported by both sets of rollers, and 1x3 made to serve as well as a back saw. As an example, to make the pattern for a pillow block, as shown in Fig. 1G5. This pattern will be more easily molded with the base up ; that is to say, it will lie in the sand in the reverse position to what it is drawn in Fig. 105. Prints will be required for the bolt holes, square prints for the recesses in the block intended to be cored out to receive the heads of the cap bolts, round prints on the tops of the cheeks, and oval prints on the base. We first plane a piece for the base, B B, to the correct size, allowing y^ inch to the foot for the contraction of the casting in cooling. We next draw center lines upon it on both sides. BENCH WORK. 171 It must now be observed that a hollow or filleted corner appears where the cheeks of the block meet the base j and further, that the recess in the block to receive the brasses is drawn to a depth coinciding with the height of the hollow or fillet. It will be advisable, therefore, ^ to prepare a piece of 7 1 the length from C to C, and to shape the ends to the outline of the cheeks, and, forming in this piece all the fillet, the cheeks may next be prepared of a thick- ness from the line A to D. These must be strongly fastened, and are best mortised clear through the base, and glued fast. Two semicircular pieces must be turned for the portions out- side the lines A A, and three-cornered pieces must be fitted in the square recess, to make it octagonal as required. Nothing now remains but to attach the core prints, and make a suitable core box. A half box will suffice for the cap bolt-holes, and a whole one for the holes in the base, as the cores for these latter will stand on end. To make the cap, we take a piece of timber large enough to make that portion of the cap that is above the line C C ; and we line or mark out the form of the cap on both sides (using a center line to make the two sides cor- respond), and pare away the surplus wood down to the lines. The pieces below the line C are to be afterwards glued and nailed on. It is advisable to cut out a recess in the top of the cap, as shown in Fig. 166, at A B, to afford 172 PATTERN MAKER'S ASSISTANT. convenience to the machinist in using the wrench upon the nuts. Fig. 107 is a sectional view of a pattern for the brasses ; and this pattern requires great care in its making, for the following reasons : Brasses of this kind, and of a size not larger than is required for a journal about ten inches in diameter, can be fitted in much quicker by chip- ping and filing than by any other method ; and in any event, a great deal of labor and metal can be saved by constructing the pattern of the necessary shape. Since, however, to give the required shape without the reasons therefor, would not convince the reader of the correctness of the method, I will fully explain the two. It has been stated in former remarks that brass castings are smaller than the patterns from which they are cast, by an amount of inch per foot, which is due to the contraction of the metal in cooling. Now, in addition to this contraction, the casting of a brass also contracts across the bore. Sup- pose, for example, that, in Fig. 106, A A represents a loco- motive axle box, and that B represents the brass for the same, the two being shown in section, while C represents the casting for the brass. Beginning, then, with the cast- ing, C, we have the following considerations : The diameter BENCH WORK. 173 of the brass across D will be less than it should be, because such castings always close in that direction more than is due to the contraction in cooling. As a consequence of this, the top of the bevels, as denoted by the dotted line, E, becomes less than it should be ; and when the brass is fitted on the sides, and let down in the box ready to fit on the crown and on the bevels, the bottom of the brass will bed, and the bevels will not, as shown in the illustration. Now supposing the angles to be at the top ^ of an inch from the bevels of the box, then it will require about i of an inch to be taken off the bottom of the brass to let the sides come to a fit j whereas if, when the bevels of the brass contact with the bevels of the box, the bottom of the brass were -g- inch from the bottom of the box, -f-g inch taken off the bevels would let the bottom come home. It is then easy to see that the pattern maker should make the pat- tern so as to allow for the shrinkage across D, and at the same time insure that the bevels of the brass shall contact with the box before the bottom does. Then, by the time that the machinist has taken sufficient off the bevels of the brass to fit them to the bevels of the box, the crown will come home ; and the best way to insure this is to make the bevels of the brass of the same shape as those in the box, and then take a certain amount off the crown face of the brass (G, in Fig. 166). What this amount should be, depends upon the angle of the bevels. For bevels of 45 the proportions should be, for brasses of two and less inches bore, a full -^ inch ; for brasses having a bore of from two to four inches, T a inch will answer ; while, if the bore is from four to seven inches diameter, inch will be a good proportion. If, however, the bevel is greater, these proportions may be increased. This is an important matter, and should never be overlooked or neglected, since it reduces the labor of fitting the brasses by at least one half. 174 PATTERN MAKER'S ASSISTANT. The method to be pursued to make the pattern for the brass, is as follows : Take a piece of wood of sufficient size to form the body of the brass, and make it of the necessary size and form, observing the direction above given as to the bevels ; and make the flanges by turning the two halves in one, as explained in a previous example, omitting to turn out the inside, as this would effect no saving, and such boring would weaken the flange, and render it liable to split in attaching it to the body of the pattern. To fasten the flanges, glue them on ; and when dry insert brads, setting the flanges by lines. Then pare out the flange even with the bore of the brass. In many cases brasses are dispensed with, and Babbitt metal is employed in their stead. The requisite form of casting for this pur- pose is shown in Fig. 1G7, the Babbitt metal being cou- tained within the thin ridges which extend all around the edges of the half circular bearing. In addition to this, however, the machinist sometimes drills small holes in the cavity for the Babbitt metal. The ridges are cast solid with the box, and the two at the end (D and E, in Fig. 107) make no difference to the molding, since they will leave the sand readily and easily. But the ridges or strips that extend lengthwise of the bearing, must be made detachable BENCH WOKE. 175 from the pattern, the strips referred to being held in posi- tion by the dovetails shown at C. The recesses to receive the dovetails are first cut out, and the dovetails are made to a neat fit therein. Then we take the strips required to form the ridges, and having just spotted the faces of the dovetails with glue, while they are in their places, we press the strips against them for a moment, and adjust the strips and leave them in position for the glue to dry. By this means the dovetails are fastened to the strips exactly in the required position. When dry, the strips with the at- tached dovetails may be withdrawn from the pattern, and should then be more securely fastened together by the addi- tion of screws or nails. In many cases, wires are employed in place of the dovetails j they being inserted, as shown in Fig. 167, at F ; and when they are used, it becomes a consideration whether the molder can conveniently extract them. If he can, they are preferable to the dovetails, as these latter are sometimes apt to stick. Bearings of this class (Babbitt metal) are often formed in the framework of a machine, or in other patterns that do not permit of being molded in the direction suitable for the above example. Fig, 168 represents such an example, which requires to be molded in the direction denoted by the arrow. It will be ad vis- able to core out the whole space for the cap and bear- ing, the core box in this case being fitted with the strips in a manner similar to that above described for the Babbitted pillow block. The pattern in this case is made as shown in Fig. 169, the space for the bearing being blocked up, and the block extending through, as shown 176 PATTERN MAKER'S ASSISTANT. at A, to form a core print. The core box shown beneath may be, in the smaller sizes, cut out of the solid wood, the part B being made thick, because it includes the thick- ness of the ridge on that end, and also the depth of the print, as shown at A. The reason that the block or core print protrudes at C, is, that a ridge may be formed in the mold to steady the core while inserting it in the mold ; and the depth of the core box, at E, must be made to suit it. It will be noted that the core prints, at F F, are carried to the top of the pattern j and it will be readily perceived that they must be so made in order that the pattern may lift from the Band. Then, after the mold is made, the core for the hole is first inserted, and then a small core is fitted into the recess in the mold ; and thus is the top part of the recess (above the core print) stopped off. The circles marked on the faces of the prints, F, are to be painted on the pattern in black varnish, and their purpose is to denote that the core proper is round. If these black circles were not made, the pattern maker would BENCH WORK. 177 require to make a similar circle and cross marks with chalk or pencil, that the molder may know how the core is to be left. Fig. 170 is a representation of a pattern for a slide ; it has the projections simply set on with pegs, to prevent the pattern being locked in the sand. In molding this piece, a false core is laid between these projections. After the cope is lifted, the plate A may be taken out j and after removing the false core, the pieces B B can be withdrawn. 8* CHAPTER XL EXAMPLES IN COLUMN PATTERNS. Our next example shall be for a square or rectangular column, which, though very simple in construction, yet necessitates a departure from the ordinary method pur- sued in pattern making the object being to save the making of an entirely new pattern for every required column. In view of the thousands of columns of this kind that have been cast, it is not to be wondered at tbat measures have been taken to cheapen the cost of the pattern, and lessen the labor hi preparing the mold; but it is to be remarked that no one has been able to invent a permanent mold for this class of work. In cast iron columns, the strict rules of architecture are not rigidly followed. The slight but graceful curve prescribed for every column and pilaster is frequently neglected, and various parts of the column are modified in their contour to their detriment, as may be easily seen by comparing the details of a stone building with those of an iron one. Square iron columns are usually made parallel through- out their lengths ; while, on the end view, two of the sides incline towards one another, on account of the draft or taper given to the pattern. Round column patterns are not made parallel, but are smaller at the cap than at the base. The curve above mentioned is given to the shaft ; but as the pattern is made to serve for all lengths of columns of that diameter, the curve can only, in most cases, be an approximation. In foundries that make a specialty of this class of work, numbers of blocks of various sizes and lengths are kept, and they simply require the addition of such ornaments as the design comprises, COLUMN PATTERNS. 179 which ornaments such as moldings, flutings, and the like are often ready to hand, to complete the column pat- tern. These blocks are, for small columns, made solid j but for large columns they are constructed like boxes or troughs, with pieces filled in at short distances to give strength. (See Fig. 172.) Fig. 171 is a perspective view of a block, mounted with moldings and other ornamentation, so as to form a column pattern ready to go into the sand. The base, B, and its moldings, a and &, are to be cast solid with the shaft of the column j this, however as may be inferred from what has been said is not compulsory. It will be seen that the base forms a guide for the stop- ping-off blocks, A A, at that end 5 at the other end of the column the guides, O, are attached. The distance be- tween the stopping-off blocks, A A, is of course the length of the column, plus shrinkage and plus the amount left for cutting off to square up the ends of the cast column. The wires shown are for the pur- pose of holding the ornaments in position, upon the block. The ornaments on the face 180 PATTERN MAKER'S ASSISTANT. are held by loose pegs, except the cabling, D, and the paneling, E, which are made fast on the face by nails or screws. Let it be required to prepare a pattern for a column 12 feet long, of 12 inches face, and 14 niches deep, to be of the style shown in Fig. 171. Select a block similar to that shown in Fig. 172, in which the top piece is shown removed, so that the distance pieces may be seen. _. We will suppose our column ty ^~r*z^S^ to require mounting on the face and one side; then i inch or |- inch will be taken up on the face and side by the margins, E, which form, with their moldings, the paneling : therefore, if \ inch margins are used, the block should measure 11J by 13J inches, and \ less if f margins are employed. The length of the block is immaterial, so that it be not less than 20 inches longer than the column. This excess is for core prints at the ends of the pattern. Lay off upon the block the length of the column pattern j this will be 12 feet -f ig inch for shrinkage + \ or T 3 inch at each end for squaring up. Space off upon the block the position of the various members, and apply them as directed. It must be noted that the moldings and base pieces on the face overrun those upon the side, and also extend according to their contour over the side that is not mounted (see Figs. 171 and 173). The reason of this is that by removing these face moldings and base pieces, except the cabling and paneling (which are fast), the in older can make a bevel parting. When the parting MOLDING COLUMNS. 181 is made, the pieces are then replaced, and will be taken up again by the cope. A rectangular column is invari- ably molded with the face up, because of the facility such a position gives for supporting the main core by means of the cores which make the openings always formed at the back of these columns. For stopping off the column to the right length, we simply prepare four pieces, as shown at A, Fig. 171, of a length equal to the depth of the column at the ends, not iucludiug the base piece, as that will be stopped off in the cope. In ramming up the column, when in the sand, these pieces are bedded in, in the position shown. Some provision is necessary .to prevent them from being ram- med out of the perpendicular. This is provided in this case by the base pieces, B ; but at the other end of the column temporary strips are braddedto the block, as shown at 0. To find the place for these guiding strips, add to the length of the column pattern the thickness of the stopping- off piece, square a line at this point down each side of the block, and nail on the guides outside this line, but with one edge touching it. Columns are often cast without bases or caps these latter being cast thin, and attached by screws after the columns are set up. The ornamentation of columns is varied constantly, de- pending upon the taste of individuals ; therefore, it is im- possible to lay down precise directions hi this matter. It is thought, however, that the above remarks will be of service ; and I may add that, in place of cabling, fluting is often employed. This is never to be cut out of the block, but formed in extra pieces. The cabling on the side is made by fastening the strips to a piece of board, and this is attached to the block by wires. Fig. 174 shows this arrangement. Baked or dry sand is not used for the main core of square columns, and we proceed to describe 182 PATTERN MAKER'S ASSISTANT. the method of making the green sand core now invariably adopted. Fig. 175 shows a sort of universal core bore, em- ployed for making these cores. A is a cast iron plate, laid upon the floor of the foundry, generally in close prox- imity to the mold ; upon this are set up two stout boards, B, about two niches thick. These boards are adjustable, so as to take in any breadth of face, by the brackets, D, moving along slots in the plate. Nipping screws in the brackets admit of the boards being pressed together on the end pieces, which must be changed for every width of column ; the height of the core is regulated by means of the strike, E. On account of the exceedingly fragile na- ture of a green sand core, it is necessary to imbed within it a strong bar of cast iron, called a core bar, such as is re- presented at F, Fig. 175. It consists of a strong center bar with pieces cast solid with it, ranged on each side, called wings 5 the bar itself is made to taper off to a narrow ridge towards the under part, as also are the wings which taper at the edges. The sand, being rammed between these wings, is able not only to sustain itself, but also a MOLDING COLUMNS. 183 small portion extending beyond them namely, to the correct outline of the core. The bar is generally from half an inch to one inch smaller than the core, as will be seen in the sectional end view, Fig. 177. A notch is cut out of each wing, to admit of the insertion of a perforated tube on each side, for ventilation. The core bar, F, and the perforated tubes, G G, are shown in Fig. 175, imbedded in the core. As there are not any core prints required to form the openings at the back of the column, the cores for these openings are made in a box not thicker than the intended thickness of metal in the column. Such a box is shown in Fig. 178 ; though for the sake of cheapness, when the columns are not more than half an inch thick, the core box is sawn out of one piece. Fig. 179 is an end view of the core box, with core, shown in Fig. 175, but with the addition of the wooden binder, which serves to assist the brackets in holding the 184 PATTERN MAKER'S ASSISTANT. sides, B, of the core box together, which is necessary when the core box is very deep. Round columns are either plain, fluted, or of a mixed design, to agree with the square columns in the same building. Fig. 180 represents a plain round column ; but it must be remembered that, even thougli the shaft be plain, the design of the base and cap may be modified according to taste. In the case of so simple a one as wo have illustrated, it would probably be cast solid, as repre- sented ; though if of very large size as those in the crypts of churches, perhaps 18 inches in diameter a great deal of metal would be saved by simply casting a plain round shaft with the moldings, N and O, upon it, and of a length measured from the lower part of the base to the top of the cap. This casting takes the weight of the building. The base, B, with its molding, B M, and the cap, C, with its molding, C M, are thin castings fixed to the column by screws. P P are the core prints. Little need be said as to the method of preparing a pattern of this description. If small, it will be turned from the solid wood ; and if large, it will be lagged or staved up, as we have described in examples of lagging and staving. In any case, the pattern must be made in halves. Some foundries require a half core box ; while in others, the core is struck up in the manner described on pages 89, 90. We may now pass to the consideration of the fluted column, shown in Fig. 181. D is a plan of the peculiar cap required for this kind of column j it is neither square nor round, but of a shape which harmonizes beautifully with the carved work below, all of which, including the cap, is added afterwards, the column being cast a plain round above the member marked N, and also below that marked O. The extension, A, is the part which passes between the joists of the flooring ; it is often flattened to admit of this, as shown at C, Fig. 182. B is a section of J?t be thin, the heat will radiate rapidly in that direction, causing the outer or top side to sot first; the under side, setting later, will drag the top side over with it, causing it to round up on top and dish in the bottom. Or if the pattern bo not perfectly true in every direction, the strains first spoken of will cause any curved portion to become more exagger- ated. If the pattern bo perfectly true, cop and drag of the same thickness, and both rammed evenly, there is no reason why the plate should not come out perfectly true, the strains being all self-contained in the same plane and balanced. If the plate, however, have an ogee molding projecting downward around the edge, it will likely be de- pressed on the top surface when cast. This is due to all the surfaces being set alike and at the same instant, excepting the metal within the corners, which, containing the most metal in a mass, will shrink last of all. When this does shrink, its tendency is to pull over the top side of the molding toward the plate, which being soft, although sot, will bo forced downward at tho edges, giving a chance for the strains within the plate, as above described, to aid in tho distortion. ROUND AND SQUARE BARS. These strains are similar in both, and are already treated of under solid cylinders. There is another feature, not before spoken of, which is rather curious. If two bars of the same dimensions and mixture of iron be heated to the same temperature, the one allowed to cool in the mold, the other plunged while hot into water, tho latter will be found to have shrunk the most. This is due to tho particles about the surface having been enabled, by the softness of the interior metal, to get closer to each other than they could have done if the material had cooled slowly. RECTANGULAR TUBES. These are usually cast with a core, which has a tendency to retain the shape of tho casting ; still the flat sides will show a tendency to bulge up slightly at the middle. This is due to much of the same 246 PATTEKN MAKER'S ASSISTANT. causes the outer surface is cooled instantly by the wall of the mold, and is set ; the inner surface is not cooled quite so rapidly, owing to the core being of harder material, and not so good a conductor f heat. When this does cool it will pull inward the outer skin of the casting, forming a slight curve ; each side acting for itself, will pro- duce the same effects. GUTTER, OR U-SHAPED CASTINGS. These are usually made thinner at the edges than at the middle, because the pattern has been made with draught. When castings of this shape are taken from the mold, they will be found rounded over in the direction of their length, the legs being on the curved side. This is explained by the mold cooling and setting the legs first ; then when the back or round shrinks, it pulls upward the two ends of the casting. WEDGE-SHAPED CASTINGS. In parallel castings of any length, having a cross section similar to a wedge or similar to a "knife" in paper-mill work the thick side will invariably be found concave and the thin edge curved. This is due to the same causes as explained above. The thin edge is set as soon as cast ; the thick edge, cooling later, shrinks and draws the ends of the casting upward, and with them the thin edge, which acts as a pillar to resist further shrinkage. RIBS ON PLATES. All ribs have a tendency to curve a plate, if they bo thicker or of the same thickness as the plate, owing to the fact that whatever shrinkage strain they possess is below the general plane of the shrink- age of the plate itself. If the ribs be thinner than the plate, they will cool first ; and by resisting the shrinkage of the bottom of the plate, cause it to curve upwards, or " dish " on top. GENERAL LAWS REGARDING SHRINKAGES. The most metal in a mass always shrinks last ; hence if a casting be composed of irregular thickness, it will bo liable to be broken by the forces contained within itself. It is, therefore, especially neces- sary that columns and castings supporting or resisting great pres- sures, should be so designed as to prevent this great error. Mold- ings on columns are often so badly designed with regard to this mat- ter, that the columns are excessi vely weak where they should be the SHRINKAGE, ETC. 247 strongest. As a rule, moldings should seldom be cast on a column, but rather bolted on. Much of the irregularity of flat castings and those of irregular shapes, could be remedied by a proper attention to cooling the castings while in the mold. To be sure, this is done to a certain extent, though few moiders know why they do so. They know that by removing the sand from a particular casting, it will straighten in the shrinking. This is but the result of experience, not of thought, or any attempt to know why they so act. It is useful to know, also, that all shrinkage takes place while the casting is chang- ing from a red to a black heat. SHRINKAGE OP CASTINGS. In locomotive cylinders ^ inch in a foot. Inpipes " " Girders, beams, etc | " 15 in. Engine beams, connecting rods | " 16 in. In large cylinders, say 70 in. diameter, 10 ft. stroke, the contraction of diameter is about f "at top^ " " " " i "at bottom Shrinkage of length is | " in 16 in. InThinbrass " 10" "Thickbrass i " 12" " Zinc ft " 12" "Lead ft " 12" " Copper A 12 " "Tin. A " 12" 248 PATTERN MAKER'S ASSISTANT. TO CALCULATE STRENGTH OF PIPES OR OTHER THIN CYLINDERS. RULE : Multiply the inside diameter of the pipe or cylinder in inches by the pressure in Ibs. per square inch that is to act inside of it, and divide the product by 10,000. To this result add a sufficiency to insure a good casting, and to enable the pipe to stand handling ; and this will give the total thickness. NOTE ; The amount to be added varies with the diameter of the pipe. On a 4" pipe, and under, allow ^ 6 " over 4" " $ 8 " " 6 allow -fV 12 " " 8 " | 30 " " 12 " $ 4$ " 30 " 70 " " 48 " 100 " ' 70 " EXAMPLE : What must be the thickness of a 25 inch cylinder for a Bteam engine, so that it may stand CO Ibs. per square inch ? 25 -1- CO = 1500 ~ 10000 = & or & of an inch ; add to this | = i inch -f- ~h> Add another for reboring. MOLESWORTIFS RULE for calculating the necessary thickness of metal for cylinders or pipes, is as follows: RULE : Multiply the inside diameter of the pipe or cylinder by the pressure in Ibs. per square inch it is to bear, and divide the product by 4000. The last product to be increased one half. It is to be noted, however, that the rules for calculating the neces- sary thickness of a cylinder to withstand a given pressure, do not give the thickness that the pattern maker requires, because the num- ber of times allowed for reboriug the cylinder, its situation as to its being subjected to oxidation, and other similar considerations, have caused the existence in actual practice of greater thicknesses than those given by any of the rules ; and in a general way specific kinds of cylinders are made to conform in thickness to that which practice has demonstrated to suit the requirements of the duty; this latter term including more than mere strength. THICKNESS OF CYLINDERS, ETC. 249 TO CALCULATE THE THICKNESS OF METAL FOR CYLIN- DERS FOR HYDRAULIC PRESSES. RULE : Multiply the constant number given below for the material of which the cylinder is to be made by the pressure in tons per square inch, and by half the internal diameter of the cylinder. EXAMPLE: A 10-inch cylinder is to bear a pressure of 3 tons per square inch ; what must be its thickness in cast iron ? CONSTANTS : Cast iron Gun metal -22 [> -41 + 3 = 1-23 + 5 = 6'15 or 6. Wrought iron Steel EXAMPLE : A steel cylinder of 5 inches internal diameter is to bear a pressure of 35 tons per square inch ; what must bo its thickness? 0-G X 35 = 2-10 X 2-5 = (Ana.) 5-25, or 5J inches. TO CALCULATE THE WEIGHT OF RIMS FOR FLY WHEELS. RULE : 2542FS U 2 X 2 f F = Constant force in pounds, or mean, force on piston ; S = Stroke in feet; W Weight in pounds of fly wheel ; x = Radius of center of gyration in feet ; n = No. of revolutions per minute ; f=-05. Multiply the area of the cylinder by the mean pressure on the pis- ton in Ibs. per square inch, by the stroke in feet, and by 500, and divide by the product of the number of revolutions per minute, mul- tiplied by the radius of the fly wheel, measured at the inside of the rim. 11* TABLES OF USEFUL INFORMATION. MIXTURES OF METALS. CASTINGS FOR Copper. Tin. Zinc. Lead. Antim'y. Bismuth. Brass bearings 10 H I Brass val ves - 9 r I Bell metal 15 5 \ ello w brass for castings . . - Gun metal .... .... ... 36 9 '4 17 --- .... Fine solder 1 1 Plumber's solder . 1 2 Solder for cast irou . . 1 Babbitt's metil 1 10 j Metal to expand in cooliu r . 9 2 1 Metal to heat and cool without loss of size or alteration of shape, must contain 9 parts of copper and 1 of aluminium. MELTING POINTS OF METALS. Cast iron from 1900 to 2900" Fahr. Antimony 812 Lead 620 Aluminium 1292 Copper 1994 Tin 442 Zinc.. . 773 WEIGHT OF MATERIALS AND CASTINGS. ESTIMATING WEIGHT OF CASTINGS FROM THE WEIGHT OF THE PATTERN, In presenting a table wherefrom to estimate the weight of a casting from the weight of the pattern, it must bo understood that the calcu- lation is only approximate; and in all cases in which there are core prints or battens to sustain the pattern, or other extraneous parts which exist upon the pattern and not upon the casting, the weight WEIGHT OF MATERIALS AND CASTINGS. 251 of these parts must be estimated, or calculated, and deducted from the weight of the pattern. A PATTERN WEIGHING 1 LB. AND CAST IN Cast iron. WILL WE Zinc. IGH WHEN Copper. CAST IN Yellow brass Gun metal. Mahogany, Nassau Ibs. 10-7 12-9 8-5 12-5 16-7 14-1 Ibs. 10-4 12-7 8-2 12-1 16-1 13-6 Ibs. 12-8 15-3 10-1 14-9 19-8 16-7 Ibs. 12-2 14-6 9-7 14-2 19 16 Ibs. 12-5 15-0 9-9 14-6 19-5 16-5 " Honduras . . . t( Spanish Pine, Red " White " Yellow WEIGHT OF TIMBER. WEIGHT OF if < 4 S a <"~ WEIGHT OF !l 11 < Ash Ibs. 45 Ibs. j 026 Maple Ibs. 49 Ibs. 025 Beech ... W 025 Oak, Red American . . f>3 03 Box . 80 046 Oak, White American 49 028 Hornbeam 47 027 Pine, Red . . . - 36 021 Li tr num-vita3 83 048 < it 41 024 Mahogany, Nassau 42 024 " White 97 015 <% Honduras 35 02 (i 34 02 *' Spanish 53 031 " Yellow W> 018 . WEIGHT OF CAST METALS. Metal. Specific gravity. Weight per cubic foot. Weight per cubic inch. Aluminium 2-56 Ibs. 159-8 Ibs. 096 Antimony . 6-72 419-5 242 Copper . . 8-G07 537-3 31 Iron, from . . 7 437- 252 " to . 7-6 474-4 273 " average 7-23 451- 26 Lead 11-36 708-5 408 Steel . 8 499- 288 Tin 7-291 455-1 262 Zinc - -. 7- 437- 252 Gun Metal 10 copper, 1 tin. . . Babbitt metal 8-561 7-31 534-42 456-32 308 263 Average composition (bearing), brass 524-88 30375 252 WEIGHT OF CAST IRON PIPES. TABLE Qf the Weight of Copper Bolts, from \ to 2J in. Diameter, and 12 inches long. Diameter. Pounds. Diameter. Pounds. Diameter. Pounds. | 189 T* 1-998 and! 5-723 1 296 7 2-318 and T \ 6-255 I 425 H 9-661 and ^ 6811 1 10 579 3-016 and ft 7-390 i 757 and -jV 3-417 andf 7-933 A 958 and| 3-831 and f 9270 1 1*182 and fV 4-269 and I 10-642 H 1-431 and 4-730 2 12061 I 1-703 and ^r 5-214 2 and| 13668 TABLE Of the Weight of a Lineal Foot of Cast Iron Pipes, in Ibs., from 1 inch to 30 inches Bore. Bore. Thickness. Wcisrht. Bore. Thnkiie. Weight. Bore. Thickness. Weight. Inches. Inches. Pounds. Inches. Inches. Pounds. Inches. Inc ies. Poun.ls. 1 * 3-06 3| k 20-90 I 63-18 1 5-05 26-83 7 36-66 H i 3-67 33-07 46-80 1 6- 4 22-05 56-96 U 1 6-89 28-28 67-60 i 9-80 34-94 78-39 1| 7-80 4* 2335 n 39-22 11-04 29-85 ' 49-92 2 8-74 36-73 60-48 12-28 4i 24-49 71-76 IN 9-65 31-40 83-28 13-48 38-58 8 41-64 *i 10-57 4| 25-70 52-68 14-66 32-91 64-27 19-05 40-43 76-12 2! 11-54 5 26-94 88-20 15-91 34-34 8i 44-11 20-59 42-28 f 56-16 3 12-28 5J 29-40 1 68- 17-15 3744 1 80-50 22-15 45-94 1 93-28 2756 6 31-82 9 i 46-50 3* 18-40 4056 1 58-92 2372 49 60 ! 71-70 29-64 58-96 I 84-70 3* i 19-66 6* 3432 97-98 1 25-27 43 68 91 \ 4898 \ 31-20 5330 ! 62-02 * NOTE : These weights do not include any allowance for spigot and faucet ends. WEIGHT OF CAST IKON PIPES. 253 Bore. Thick less. Weight. Bore. Thickness. Weight. | Bore. rhickness. Weight. Inches. Inches. Pounds. Indies. Inches. Pounds. Inches. Inches. Pound.. N I 75-32 14 89-61 19 145-20 88-98 108-46 170-47 102-90 127-60 195-92 10 1 51-46 147-03 20 126-33 f 65-08 14* 73 72 152-53 I 7899 9266 17902 | 93-24 112-10 205-80 1 108-84 131 86 21 13250 10J 1 53-88 151-92 159-84 f 68-14 15 75-96 187-60 I 82-68 95-72 215-52 I 97-44 115-78 22 13860 1 112-68 136-15 167-24 11 i 56-34 156-82 196-46 t 71-19 15* 78-40 22538 1 86-40 98-78 23 144-77 101-83 119-48 174-62 117-60 140-40 204-78 rii 58-82 161-82 235-28 74-28 16 80-87 24 150-85 90-06 101-82 181-92 106-14 123-14 213-28 122-62 144-76 245-08 12 61-26 166-60 25 156-97 77-36 16* 83-30 189-28 93-70 104-82 221-94 110-48 126-79 254-86 127-42 149-02 26 196-62 12* 63-70 171-60 230-56 80-40 17 85-73 264-66 97-40 107-96 27 204-04 114-72 130-48 239-08 132-35 153-30 274-56 13 66-14 176-58 28 211-32 83-46 17* 88-23 247-62 101-08 111-06 284-28 118-97 134-16 29 218-70 137-28 157-59 256-20 13J 68-64 181-33 294-02 86-55 18 t . 114-10 30 I 226-20 104-76 1 137-84 1 264-79 123-30 I 161-90 1 303-86 142-16 186-24 u 343-20 14 1 71-07 19 f 120-24 The above table is found to be of great use in making out correct estimates of cast iron pipes. For instance, suppose it is required to know the weight of a range of pipes, 324 feet long, 8$ inches diam- 254 WEIGHT OF DIFFERENT METALS. eter of bore, and metal f of an inch thick. The table shows the weight of 1 foot of such pipe to be 56' 16 Ibs : Then, 56'16X 324=18195-84 Ibs., or 9 T V tons, very nearly. TABLE, Showing the Weight of Solid Cylinders of Cast Iron, 12 inches long, in Avoirdupois Pounds. Diameter in Inches. Weight in Ibs. Diameter in Inches. Weight in IDS. Diameter in Inches. Weight in Ibs. Diameter in Inches. Weight in IBs. 1 1-394 2* 15-492 4i 50-193 8 158-638 5 1-897 2| 17-080 4| 55-926 8| 179-087 1 in. 2-478 2| 18-745 5 61-968 9 200-774 H 3-137 2| 20-488 5k 68-319 94 223-704 I* 3-873 3 22-308 5* 74-981 10 247-872 if 4-686 3J 24-206 5| 81-952 lOi 273-278 U 5-577 3* 26-181 6 89-234 11 299-925 if 6-545 3| 28-234 6* 96-825 114 327-811 II 7-591 84 30-364 6i 104-726 12 356-935 ii 8-714 3f 32-572 61 112-936 13 418-903 2 9-915 3f 34-857 121-457 14 485-830 2| 11-193 3| 37-219 n 130-287 15 557-712 2i 12-548 4 39-660 n 139-428 16 634-552 2 13-981 4* 44-771 7f 148-878 NOTE. Cubic inches of cast iron X '263 =lbs. avoirdupois. Circular inches of cast iron X -2065= Ibs. avoirdupois. TABLE, Showing the Capacity and Weight of Cast Iron and Lead Balls, from 1 inch to 8i Diameter. Diam. inches. Capacity in Cubic Inches. Cast Iron Pounds. Lead Pounds. Diam. j Capacity in inches. Cubic Inches. Cast Iron Pounds Lead Pounds. 1 523 136 215 5 65-450 17-063 26-843 4 1-767 461 725 5i 87-114 22-721 35-729 2 1-189 1-092 1-718 6 113-097 29-484 46-385 *J 8-181 2-133 3-355 6i 143-793 37-453 58-976 3 14-137 3-685 5-798 7 179-594 46-820 73-659 3,V 22-449 5-852 9-207 7J 220-893 57-587 90-598 4 33-510 8-736 13-744 8 268-082 69-889 109-552 a 47-713 12-439 19-569 ^ 321-555 83-840 131-883 TABLE, Showing the Number of Nails and Spikes to the Pound, of Various Sizes, as manufactured at the Troy Iron and Nail Factory, N. Y. S,ze of Na!l. No, to the Ib. Boat Spikes. Diameter of Rod. No. Spikes to the Ib. Ship Spikes. Diameter ot Rod. No. Spikes to the Ib. 3 penny 600 No. 4 i 13 No. 4 A 8 4 360 " 5 IT 8 ' 5 6 6 200 " 6 1 5 ' 6 5 8 110 11 7 1 4 ' 7 3 10 88 * 8 i 3 12 68 ' 9 T 9 * 2 20 40 " 10 A 1* WEIGHT OP DIFFERENT METALS. 255 WEIGHT OF A FOOT IN LENGTH OF FLAT CAST IRON. Width of iron. Thick, ' i-4th inch. Thick, 3-8th inch. Thick, i-a inch. Thick, 5-8th inch. Thick. 3-4th inch. Thick, 7-8th inch. Thick, i inch. Inches. Pounds. Pounds. Pounds. Pounds. Pounds. Pounds. Pounds. 2 1-56 2-34 3-12 3-90 4-68 5-46 6-25 2i 1-75 2-63 3-51 4-39 5-27 6-15 7-03 24 1-95 2-92 3-90 4-88 5-86 6-83 7-81 2| 2-14 3-22 4-29 5-37 6-44 7-51 8-59 3 2-34 3-51 4-68 5-85 7-03 8-20 9-37 3* 2-53 3-80 5-07 6-34 7-61 8-88 10-15 s| 2-73 4-10 5-46 6-83 8-20 9-57 10-93 3f 2-93 4-39 5-85 7-32 8-78 10-25 11-71 4 3-12 4-68 6-25 7-81 9-37 10-93 12-50 4 3-32 4-97 6-64 8-30 9-96 11-62 13-28 4i 3-51 5-27 7-03 8-78 10-54 12-30 14-06 4f 3-71 5-56 7-42 9-27 11-13 12-98 14-84 5 3-90 5-86 7-81 9-76 11-71 13-67 15-62 5^ 4-10 6-15 8-20 10-25 12-30 14-35 16-40 5* 4-29 6-44 8-59 10-74 12-89 15-03 17-18 5| 4-49 6"73 8-98 11-23 13-46 15-72 17-96 6 4-68 7-03 9-37 11-71 14-06 16-40 18-75 TABLE OF THE RELATIVE WEIGHT AND STRENGTH OF ROPES AND CHAINS. ^ c 1 ^ l g 2 i a & 5 I ^' i 3 2 i- I if. n*s g 1 I 1 2, S * 2, z 2 i i! ^ f i * S. 1 I i 5 1 I | " S i 1 * * s' = =' = i 5 s 5 * inches. u, s . inches/ H>s. tons. cwts. inches. 11)8. inches. 11)8. tons. cwts. 3 21 'ft 5J 1 5i ' 10 23 I 43 10 4 1 41 8 - 1 16| ! 10J 28 if 49 11 11 5 5f T lOi 2 10 ll t 30 1 56 13 8 p . 7 9* 111 f Tf 14 18 22 *^ f A. ' 4 3^ ! 5 2 13 T 13J 36 39 45 ii b 63 71 79 14 18 16 14 18 11 8 15 14 27 6 4 14^ 48 i^. 87 20 8 8| 19 21 t 32 37 7 7 8 13 1 16 56 GO if 6 96 106 22 13 24 18 TABLE 781 1-756 3-125 4-881 7-031 9-568 12-520 15-818 19-531 23631 28125 33-009 38-281 43-943 50-000 56-443 63-281 70-506 78-125 86131 94-531 103-318 112-500 122-058 OF THE WEIGHT, IN LBS. Of afoot in length of Cast Iron. liuieofthe s< juare or Square, diameter. 2-703 4-225 6-085 8-281 10-815 13-990 16-900 20-450 24-340 28-565 33-131 38-031 43-271 48-353 54-768 61-021 67-515 74-549 81-815 89-421 97-368 650 1-471! 2-603 4-065 5-856 7-971 1 10-412; 13-168: 16-256 19-671 23-412 27-475 31-818 36-581; 41-881: 46-990 52-681 58-696 65-040 71-701 78-696 86-015 93-656 105-640 101-621 612 1-387 2-454 3-854 5-521 7-515 9-815 12-425 15-337 18-559 22-087 25-921 30-065 31-512 39-268 44-331 49-700 55-375 61-359 67-709 74-243 81-126 88-354 95-871 132-031 142-381 153-125 161-256 175-781 187-693 200-000 212-693 225-781 23i>-256 266-781 282-031 410-281 Hex 'on. Oct'gon. 114-271 123-231 109-948 118-534 132-528 127-478 136-743 142-1(52 152-037 177-071 207-078 199-127 253-125 2J9 078 210-721 29G-968 257-105 247'315 233-318 312-500 270-471 328-318 284- 159 273-341 v~-s-/^x-xx"*y> .. Circle. J 146-337 138-056 102449 156-259 147-415 173-099 166-503 157-078 184-087 177-071 167-049 195-412 187-365 177-328 187-912 199-203 231-418 222-600 210-800 244-100 234-793 221-506 344-531 298 193 286-828 270-593 351-131 312-559 300-646 283-633 378- 125- 327-268 314-7 393-216 342-31 103-696 111-825 120-372 128-986 260-163245-437 257-859 TABLE THE WEIGHT OF A CUBIC FOOT OF VARIOUS SUBSTANCES, In common use for Building. Sand (solid) ................... 112-5 " (loose) ................... 95 Earth ..................... 93-75 Common soil .................. 124 Strong soil ................... 127 Clay ..................... 120tol35 Clay and stone .................. 153 Brick ..................... 119 Granite ..................... 169 Marble ..................... 166tol69 ? Sand, 1 cubic yard, ................ 3037 ] Common soil, 1 cubic yard .............. 3429 WEIGHT OF WIRE. 257 WEIGHT OF WIRE PER LINKAL FOOT. American Gage. Size of each number. Wrought Irou. Steel. Copper. Braam. NOA inch. Ibs. Ibs. Ibs. Ibs. 0000 .46000 .560740 .566030 .640513 .605176 000 .40964 .444683 .448879 .507946 .479908 00 .36480 .352659 .355986 .402830 .380666 .32495 .279665 .282303 .319451 .301816 1 .28930 .221789 .223891 .253342 .239353 2 .25763 .175888 .177548 .200911 .189818 3 .22942 .139480 .140796 .159323 .150522 4 .20431 .110616 .111660 .126353 .119376 5 .18194 .087720 .088548 .100200 .094666 6 .16202 .069565 .070221 .079462 .075075 7 .14428 .055165 .055685 .063013 .059545 8 .12849 .043751 .044164 .049976 .047219 9 .11443 .034699 .035026 .039636 .037437 10 .10189 .027512 .027772 .031426 .029687 11 .090742 .021820 .022026 .024924 .023549 12 .080808 .017304 .017468 .019766 .018676 13 .071961 .013722 .013851 .015674 .014809 14 .064084 .010886 .010989 .012435 .011746 15 .057068 .008631 .008712 .009859 .009315 16 .050820 .006845 .006909 .007819 .007587 17 .045257 .005427 .005478 .006199 .005857 18 .040303 .004304 .004344 .004916 .004645 19 .035390 .003413 .003445 .003899 .003684 20 .031961 .002708 .002734 .003094 .002920 21 .028462 .002147 .002167 .002452 .002317 22 .025347 .001703 .001719 .001945 .001838 23 .022571 .001350 .001363 .001542 .001457 24 .020100 .001071 .001081 .001223 .001155 25 .017900 .0008491 .0008571 .0009699 .0009163 20 .01594 .0006734 .0006797 .0007692 .0007267 27 .014195 ,0005340 .0005391 .0006099 .0005763 28 .012641 .0004235 .0004275 .0004837 .0004570 29 .011257 .0003358 .0003389 .0003835 .0003624 30 .010025 .0002663 .0002688 .0003042 .0002874 31 .008928 .0002113 .0002132 .0002413 .0002280 32 .007950 .0001675 .0001691 .0001913 .0001808 33 .007080 .0001328 .0001341 .0001517 .0001434 34 .006304 .0001053 .0001063 .0001204 .0001137 35 .005614 .00008366 .00008445 .0000956 .00009015 3G .005000 .00006625 .00006687 .0000757 .0000715 37 .004453 .00005255 .00005304 .00006003 .00005671 33 .003965 .00004166 .00004205 .00004758 .00004496 39 .003531 .00003305 .00003336 .00003775 .00003566 40 .003144 .30002620 .00002644 .00002992 .00002827 485.87 490.45 554.988 524.16 The specific gravities to determine the weights, were taken and made by CHAS. H. HASWELL. 11 258 WEIGHT OF METAL PLATES. WKIGHT OF METAL PLATES PER SQUARE FOOT. American Gage, Wrought Iron. Steel. Copper. Bras?. Nos. no, Ibs. Ibs. Ibs. 0000 17.25 17.48 20.838 19.688 000 15.3615 15.5663 18.5567 17.5326 00 13.68 13.8624 16.5254 15.6134 12.1823 12.3447 14.7162 13.904 1 10.8488 10.9934 13.1053 12.382 2 9.6611 9.7899 11.6706 11.0266 3 8.6033 8.7180 10.3927 9.8192 4 7.6616 7.7638 9.2552 8.7445 5 6.8228 6.9137 8.2419 7.787 6 6.0758 6.1568 7.3395 6.9345 7 5.4105 5.4826 6.5359 6.1752 ' 8 4.8184 4.8826 5.8206 5.4994 9 4.2911 4.3483 5.1837 4.8976 10 3.8209 3.8718 4.6156 4.3609 11 3.4028 3.4482 4.1106 3.8838 12 3.0303 3.0707 3.6606 3.4586 13 2.9985 2.7345 3.2598 , 3.0799 14 2.4032 2.4352 2.9030 2.7428 15 2.1401 2.1686 2.5852 2.4425 16 1.9058 1.9312 2.3021 2.1751 17 1.6971 1.7198 2.0501 1.937 - 18 1.5114 1.5315 1.8257 1.725 19 1.3459 1.3638 1.6258 1.5361 20 1.1985 1.2145 1.4478 1.3679 21 1.0673 1.0816 1.2893 1.2182 22 .95051 .96319 1.1482 1.0849 23 .84641 .8577 1.0225 .96604 24 .75375 .7638 .91053 .86028 25 .67125 .6802 .81087 .76612 26 .59775 .60572 .72208 .68223 27 .53231 .53941 .64303 .60755 28 .47404 .48036 .57264 .54103 29 .42214 .42777 .50994 .48180 30 .37594 .38095 .45413 .42907 31 .3348 .33926 .40444 .38212 32 .29813 .3021 .36014 .34026 33 .2655 .26904 .32072 .30302 34 .2364 .23955 .28557 .26981 35 .21053 .21333 .25431 .24028 36 .1875 .19 .2265 .2140 37 .16699 .16921 .20172 .19059 38 .14869 .15067 .17961 .1697 39 .13241 .13418 .15995 .15113 40 .1179 .11947 .14242 .13456 WEIGHT OF WATER. 259 TABLE SHOWING THE WEIGHT OF WATER IN PIPES FOR VARIOUS DIAMETERS ONE FOOT IN LENGTH. Diameter lu Inches. Weigl t in 1'ounds. Diameter iu Inches. Weight in Pounds. \ Diameter In Inches. Weight in Pounds. 3 3 HI r 45 20 136i Ht 3i llf 47 20! 143i * 31 4: 12 49 21 150^ 3f 4 12 51 211 1571 4 5 121 53^ 22 165 4i 6; 12| 551 22! 172! 41 7 13 571 23 180i 4f 7J 13j 59f 23! 1884 5 & 131 621 24 106} 3 9< te 14 66f 24! 25 204! 213 5* 11 14^ 69^ 25! 221! 6 141 711 26 230! I 13" 14 J ; 14f 74i 15 761 26! 27 239! 248! 6| 151 15> 79i 27! 257| 7 161 82 28 267i 74 18 15f 841 281 276| 7} 8 m 16 11 87i 90 1 29 286J 29! 296! 30 306| 83- 23^ 161 95! 30 ^ 3174 81 241 17 981 31 327 -i 8| 26 r?T 1011 31! 338J 9 171 104! 32 349 9^ 17 f 107! 32! 360 91 18 110! 33 37 H 9f 18i 1131 331 38-2! 10 34 181 116! 34 394 10^ 351 18f 119-J 341 405| 101 371 19 123 35 417 1 lOf 39^ 1 Q4- 126i 35! 429! 11 414 191 129! 36 441| Si 43i 132 UNITED STATES WEIGHTS AND MEASURES. MEASURE OF LENGTH. 3 barleycorns - = 1 inch. 12 inches - - - = 1 foot. 3 feet - - - =1 yard. 5 yards or 1G ft. = 1 rod or pole. 40 rods or 220 yds. = 1 furlong. 8 furlongs or ? t ., 1760yds. ! =lmile. GO geo. miles = 1 degree. Ropes and Cables. 6 feet = 1 fathom. 120 fathoms = 1 cable's length. SPECIAL MEASURE OF LENGTH. Land Measure. 7-92 inches - - - = 1 link. 100 links or22 yards = 1 chain. 80 chains - - - = 1 mile. 60-121 miles - - - - = 1 geographical degree. Nautical Measure. 1 nautical mile == 6082-66 feet. 3 miles = 1 league. 20 leagues = 1 degree. 360 degrees the earth's circumference. NOTE. Bowditch gives 6120 feet in a sea mile, which, if taken as the length, will make the divisions 51 feet and 5 1-10 feet fur the knot and fathom. Pendulums. 6 points = 1 line. 12 lines = 1 inch. 2\ inches 4 nails 4 quarters CLOTH MEASURE. 1 nail. 1 quarter. 1 yard. 3 quarters 1 Flemish ell. 5 quarters = 1 English ell. 6 quarters = 1 French ell. COMPARATIVE MEASURE OF LENGTH. 3 miles 1 league, marked lea. 2f " = 1 French league. 3f " =1 Spanish league. 4 " = 1 German mile. 3J " =1 Dutch mile. mile = 1 Italian mile. " = 1 Russian verst. " =1 Scotch mile. " =1 Irish mile. WEIGHTS AND MEASURES. 261 MEASURE OF SURFACE, OR SQUARE MEASURE. 144 square inches = 1 square foot. 9 272$ 30i 40 4 640 feet = 1 feet = 1 yards = 1 rods = 1 roods = 1 acres = 1 yard. rod or pole. pole. rood. acre. mile. SPECIAL MEASURE OF SURFACE. For Land. 62-7264 square inches = 1 square link. 10,000 " links =1 " chain. 10 " chains = 1 acre. NOTE. By these tables, land measure and artificers' work arc computed. MEASURE OF SOLIDITY OR CUBIC MEASURE. j. i & 21 il 9 H 11 A 2^ 9 i n I 14 A 2J u 9 H u A 14 4 3 H 9 5 ^ il 12 i 3^ if 9 U it f 12 A 3^ if 8 f 12 iV if 8 If H ii 12 4 M 8 2 IRON WIRE ROPE. HOISTING HOPE, 19 WIRES TO THE STRAND. Trade number. Circumference in inches. Diameter. i Trade number. Circumference in inches. J)inmeter. 1 6f s* 8 3i 1 2 6 2 9 2f | 3 6* If 10 2 4 5 5 4f 1| H a 2 If ,1 6 4 li 10f II i 7 34 H ROPE, WITH 7 WIRES TO THE STRAND. Trade number. Circumference in inches. Diameter. Trade number. Circumference in inches. Diameter. 11 4f u 20 H i 12 4i If 21 If , 7 6 13 3f H 22 li f 14 H U 23 H A 15 3 i 24 1 A 16 M i 25 1 17 2f f 26 f 3 7 2 18 i fl 27 f Ml 19 H f -- -- TABLE, Containing the Diameters, Circumferences, and Areas of Circles, and the Sides of an Equal Square from -^ Inch up to 26 Feet. Pinm. Circum. Area. Kide of i equal square. ' l)iam. Circum. Area. H.hYof equal square. Inch. J. 1963 0030 2* in. JL 6-6759 6-8722 3-5465 3-7582 1-8831 I 3927 5890 0122 0276 1107 I 7-0686 7-2640 3-9760 4-2001 1-9939 I 7854 9817 0490 0767 2155 I 7-4613 7-6576 4-4302 4-6664 2-1047 A 1-1781 1-3744 1104 1503 3223 ? A 7-8540 8-0503 4-90o7 5-1573 2-2155 ? -iHr 1-5708 1-7671 1963 2485 4311 8-2467 8-4430 5-4119 5-6727 2-3262 s 1-9635 2-1598 3068 3712 5438 A 8-6394 8-8357 5-9395 6-2126 2-4370 1 2-3562 2-5525 4417 5185 6646 A 9-0321 9-2284 6-4918 6-7772 2-5478 Y 2-7489 6013 7756 44 2-9452 6903 3 in. 9-4248 7-06-i6 2-6586 i Q-6'21 1 7-*?fifi9 1 in. JU 3-1416 3-3379 7854 8861 8862 i 9-8175 10-0138 7-6699 7-9793 2-7694 V Jg 3-5343 3-7306 9940 1-1075 9969 v X 10-2120 10-4065 8-2957 8-6179 2-8801 f A 3-9270 4-1233 1-2271 1-3529 1-0775 i 10-6029 10-7992 8-9462 9-2806 2-9909 TV 4-3197 4-5160 1-4848 1-6229 1-2185 -JTT KF9956 11-1919 9-6211 9-9678 3-1017 V i l r 4-7124 4-9087 1-7671 1-9175 1-3293 I 11-3883 11-5846 10-3206 10-6796 3-2124 ^ 5-1051 5-3014 2-0739 2-2365 1-4401 ? U 11-7810 11-9773 11-0446 11-4159 3-3232 1 5-4978 5-6941 2-4052 2-5801 1-5508 4 12-1737 12-3700 11-7932 12-1768 3-4340 i rc.oqnr: 2-761 1 1-6616 M 6-0868 2-9483 4 in 12-5664 12-5664 3-5448 JL 12-7627 12*9622 2 in. fe 6-2832 6-4795 3-1416 3-3411 1-7724 ] 6 i 12-9591 13-1554 13-3640 13-7721 3-6555 TABLE OF THE CIRCUMFERENCES, ETC., OF CIRCLES. 275 Diam. Circum. Area. Side of equal square. Diam. Circum. Area. bide ot equal square. 4i in. At 13-3518 13-5481 14-1862 14-6066 3-7663 7-Hn. X 22-3839 22-5802 39-1783 40-5469 6-3142 13-7445 13-9408 15-0331 15*4657 3-8771 ? -A- 22-7766 22-9729 41-2825 41-9974 6-4350 '/ i 14-1372 14-3335 15-9043 16-3492 3-9880 I 23-1693 23-3656 42-7184 43-4455 6-5358 4 14-5299 14-7262 16-8001 17-2573 4.0987 I 23-5620 23-7583 44-1787 44-9181 6-6465 * 44 14-9226 15-1189 17-7205 18-1900 4-2095 4 23-9547 24-1510 45-6636 46-4153 6-7573 A 15-3153 15.5716 18-6655 19-1472 4-3202 ? if 24-3476 24-5437 47'1730 47-9370 6-8681 7 24-7401 4H-7070 fi-9787 15-7080 19-6350 4-4310 A 24-9364 49-4833 i 1 r; .Q04'* on- 1 2QO t 16-1007 16-2970 20-6290 21-1252 4-5417 8 iu. JU 25-1328 25-3291 50-2656 51-0541 7-0897 J i' A 16-4934 16-6897 21-6475 22-1661 4-6525 I 25-5255 25-7281 51-8468 52-8994 7-2005 i 16-8861 17-0824 22-6907 23-2215 4-7633 1 JL 25-9182 26-1145 53-4562 54-2748 7-3112 f 17-2788 17-4751 23-7583 24-3014 4-8741 * A 26-3109 26-5072 55-0885 55-9138 7-4220 H 17-6715 17-8678 24-8505 25-4058 4-9848 1 26-7036 26-8999 56-7541 57-5887 7-5328 A 18-0642 18-2605 25-9672 26-5348 5-0956 ? tt 27-0963 27-2926 58-4264 59-7762 7-6436 1 18-4569 18-6532 27-1085 27-6884 5-2064 4 27-4890 27-6853 60-1321 60-9943 7-7544. Y 27-8817 61-8625 7-8651 6 in 18-8496 28-2744 5-3172 4 28-0780 62-7369 1Q-04 r Q oa.Qe IB' i 19-2423 19-4386 29-4647 30-0798 5-4280 9 in. A 28-2744 28-4707 63-6174 64-5041 7-9760 f A 19-6350 19-8313 30-6796 31-2964 5-5388 4 28-6671 28-8634 65-3968 66-2957 8-0866 ! 20-0277 20-2240 31-9192 32-5481 5-6495 1 29-0598 29-2561 67-2007 68-1120 8-1974 I A 20-4204 20-6167 33-1831 33-8244 5-7603 fa 29-4525 29-6488 69-0293 69-9528 8-3081 | 20-8131 21-0094 34-1747 35-1252 5-8711 ? trr 29-8452 30-0415 70-8823 71-8181 8-4190 if 21-2508 21-4021 35-7847 36-4505 5-9819 I 30-2379 30-4342 72-7599 73-7079 8-5297 1 21-5985 21-7948 37-1226 37-8005 6-0927 j it 30-6306 30-8269 74-6620 75-6223 8-6405 7 QI O9'}1 7fi >r 8H7 Q.7P11Q 7 in. 21-9912 38-4846 6-2034 A 31-2196 77-5613 A- 22-1875 39-1749 276 TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES, - Circum. Area. Side of equal Square. Diana. Circura. Area. Sit't tfi ecual SqW. 10 in. i I 31-416 31-808 32-201 32-594 QO.QQfi 78-540 80-515 82-516 84-540 Qfi.r:oft 8-8620 8-9728 9-0836 9-1943 Q.OA^I 15^in. f f 5 48-694 49087 49-480 49-872 188-692 191-748 194-828 197-933 13-736 13-847 13-957 14-068 i 33-379 33-772 34-164 88-664 90-762 92-885 9-4159 9-5267 9-6375 16 in. k i 50-265 50-658 51-051 51-443 201-062 204-216 207-394 210'597 14.179 14-290 14-400 14-511 11 in. i [ 1 34-557 34-950 35-343 357JJ5 95-033 97-205 99-402 101-623 i ni-RfiQ 9-7482 9-8590 9-9698 10-080 1 A.I Ql i 51-836 52-229 52-621 53014 213-825 217-077 220-353 223-654 14-622 14-732 14-843 14-954 f I 36-521 36-913 37-306 106-139 108-434 110-753 10-302 10-413 10523 17 in. 53-407 53-799 54-192 54-585 226-980 230-330 233-705 237-104 15-065 15-176 15-286 15-397 12 in. i i 37-699 38-091 38-484 38-877 00.07/1 113-097 115-466 117-859 120-276 10-634 10-745 10-856 10-966 H-077 54-978 55-370 55-763 56-156 240-528 243-977 247-450 250-947 15-508 15-619 15-730 15-840 I I 39-662 40-055 40-448 125-184 127-676 130-192 11-188 11-299 11-409 18 in. 56-548 56-941 57-334 57-726 254-469 258-016 261-587 265-182 15-951 16-062 16-173 16-283 13 in. i i I 40-840 41-233 41-626 42-018 132-732 135-297 137-886 140-500 1 /1Q-1 ^Q 11-520 11-631 11-742 11-853 H.QftO 58-119 58-512 58-905 59-297 268-803 272-447 276-117 279-811 16-394 16-505 16-616 16-727 i 42-804 43-197 43-589 145-802 148-489 151-201 12-074 12-185 12-296 19 in. 59-690 60-083 60-475 60-868 283-529 287-272 291-039 294-831 16-837 16-948 17-060 17-170 14 in. i j i 43-982 44-375 44-767 45-160 153-938 156-699 159-485 162-295 12-406 12-517 12-628 12-739 1 61-261 61-653 62-046 62-439 298-648 302-489 306-355 310-245 17-280 17-391 17-502 17-613 i i I i 4O-OOJ 45-045 46338 46731 LoO'loU 167-989 170-873 173-782 12 960 13-071 13-182 20 in. i * | 62832 63-224 63617 64-010 314-160 318-099 322-063 326-051 17-724 17-834 17-945 18*056 15 in. i i 47 124 47-516 47-909 48-302 176-715 179-672 182-654 185-661 13-293 13-403 13-514 13-625 i f f J 64-402 64-795 65-188 65-580 330-064 334-101 338-163 342-250 18-167 18-277 18-388 18-499 TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES. 277 Diam. Ciroum. Area. Side of equal Square. Dram. Circum. Area. Side ot equal Square. 23-484 23-595 23-708 23-816 21 in. * t 1 i I 1 1 65-793 66-366 66-759 67-151 67-544 67-937 68-329 68-722 346-361 350-497 354-657 358-841 363-051 367-284 371-543 375-826 18-610 18-721 18-831 18-942 19-053 19-164 19-274 19-385 26iin. i 1 5 83-252 83-645 84-037 84-430 551-547 556-762 562-002 567-267 27 in. k * 1 I f ! 1 84-823 85-215 85-608 86-001 86-394 86-786 87-179 87-572 572-556 577-870 583-208 588-571 593-958 599-370 604-807 610-268 23-927 24-038 24-149 24-259 24-370 24-481 24-592 24-703 22 in. k I i i f ! I 69-115 69-507 69-900 70-293 70-686 71-078 71-471 71-864 380-133 384-465 388-822 393-203 397-608 402-038 406-493 410-972 19-496 19-607 19-718 19-828 19-939 20-050 20-161 20-271 28 in. 1 i 1 f 1 I 87-964 88-357 88-750 89-142 89-535 89-928 90-321 90-713 615-753 021-263 626-798 632-357 637-941 643-594 649-182 654-839 24-813 24-924 25-035 25-146 25-256 25-367 25-478 25-589 23 in. i i i f I i 72-256 72-649 73-042 73-434 73-827 74-220 74-613 75-005 415-476 420-004 424-557 429-135 433731 438-333 443-014 447-699 20-382 20-493 20-604 20-715 20-825 20-936 21-047 21-158 29 in. i i 1 f i I 91-106 91-499 91-891 92-284 92-677 93-069 93-462 93-855 660-521 666-227 671-958 677-714 683-494 689-298 695-128 700-981 706-860 712-762 718-690 724-641 730-618 736-619 742-644 748-694 25-699 25-810 25-921 26-032 26-143 26-253 26-364 26-478 24 in. I i i 1 I 1 75-398 75-791 76-183 76-576 76-969 77-361 77-754 78-147 452-390 457-115 461-884 466-638 471-436 476-259 481-106 485-978 21-268 21-379 21-490 21-601 21-712 21-822 21-933 22-044 30 in. i i i \ f ! I 94-248 94-640 95-033 95-426 95-818 96-211 96-604 96-996 26-586 26-696 26-807 26-918 27-029 27-139 27-250 27-361 25 in. i i i i I ! i 78-540 78-932 79-325 79-718 80-110 80-503 80-896 81-288 490-875 495-796 500-741 505-711 510-706 515-725 520-769 525-837 22-155 22-265 22-376 22-487 22-598 22-709 22-819 22-930 31 in. k i I 1 1 I 97-389 97-782 98-175 98-567 98-968 99-353 99-745 100-138 754-769 760-868 766-992 773-140 779-313 785-510 791-732 797-978 27-472 27-583 27-693 27-804 27-915 28-026 28-130 28-247 26 in. i * 81-681 82-074 82-467 82-859 530-930 536-047 541-189 546-356 23-041 23.152 23-062 23-373 278 TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES. Oiarn. Circum. Area. Side of equal Square. Diam. Circum. Area. Side of equal Square. 32 in. i i 1 100-531 100-924 101-316 101-709 1 H9- 1 09 804-249 810-545 816-865 823-209 090. cyo 28-358 28-469 28-580 28-691 OO.OAl 37Hn I f 5 117-810 118-202 118-595 118-988 1104-46 1111-84 1119-24 1126-66 33-232 33-343 33-454 33-564 I 1 I 102-494 102-887 103-280 835-972 842-390 848-833 28-912 29-023 29-133 38 in. ft i 119-380 119-773 120-166 120-558 1134-11 1141-59 1149-08 1156-61 33-675 33-786 33-897 34-008 33 in. i * 103-672 104-055 104-458 104-850 855-30 861-79 868-30 874-84 29-244 29-355 29-466 29-577 9Q-RS7 ft 1 1 I 120-951 121-344 121-737 122-129 1164-15 1171-73 1179-32 1186-94 34-118 34-229 34-340 34-451 i i f 105-636 106-029 106-421 888-00 894-61 901-25 29-798 29-909 30-020 39 in. ft i f 122-522 122-915 123-307 123-700 1194-59 1202-26 1209-95 1217-67 34-561 34-672 34-783 34-894 34 in. ft i 106-814 107-207 107-599 107-992 907-92 914-61 921-32 928-06 30-131 30-241 30352 30-463 OA.C'V.^ i $ 1 i 124-093 124-485 124-878 125-271 1225-42 1233-18 1240-98 1248-79 35-005 35-115 35-226 35-337 i. f ! I 108-777 109-170 109-563 yo4: ax 941-60 948-41 955-25 30-684 30-795 30-906 40 in. ft i 125-664 126-056 126-449 126-842 1256-64 1264-50 1272-39 1280-31 35-448 35-558 35-669 35-780 35 in. ft i 109-956 110-348 110-741 111-134 962-11 968-99- 97590 982-84 31-017 31-128 31-238 31-349 ft 1 I I 127-234 127-627 128-020 128-412 1288-25 1296-21 1304-20 1312-21 35-891 36-002 36-112 36-223 5 f I i o^o 111-919 112-312 112-704 yoy-yu 996-78 1003-7 1010-8 dl 4OU 31-571 31-681 3T792 41 in. ft i 128-805 129-198 129-591 129-983 1320-25 1328-32 1336-40 1344'51 36-334 36-445 36-555 36-666 36 in. ft 113-097 113490 113883 114-275 1017-87 1024-95 1032-06 1039-19 31-903 32-014 32-124 32-235 qo.Q.1 c i 1 I i 130-376 130-769 131-161 131-554 1352-65 1360-81 1369-00 1377-21 36-777 36-888 36-999 37-109 115061 115453 115846 1053-52 1060-73 1067-95 32-457 32-567 32-678 42 in. ft i 131-047 132-339 32-732 33-125 1385-44 1393-70 1401-98 1410-29 37-220 37-331 37-442 37'52 37 in. i i 116239 116631 117-024 117-417 1075-21 1082-48 1089-79 1097-11 32-789 32-900 33-011 33-021 ft f 1 133-518 133-910 134-303 134-696 1418-62 1426-98 1435-36 1443-77 37-663 37-774 37-885 37-996 TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES. 279 Diam. Circum. Area. Side of equal Square. Diam. Circum. Area. Side of ' equal Squaw.. 43 in. ft i 1 i f ! 5 135-088 135-481 135-874 136-266 136-659 137-052 13-7-445 137-837 1452-20 1460-65 1469-13 1477-63 1486-17 1494-72 1503-30 1511-90 38-106 38-217 38-328 38-439 38-549 38-660 38-771 38-882 48in. f f I 152-367 152-760 153-153 153-545 1847-45 1856-99 1868-55 1876-13 42-980 43-091 43-202 43 313 49 in. 1 i 1 i 1 1 I 153-938 154-331 154-723 155-116 155-509 155-901 156-294 156-687 1885-74 1895-37 1905-03 1914-70 1924-42 1934-15 1943-91 1953-69 43-423 43534 43-645 43-756 43-867 43-977 44-088 44-199 44 in. k i 1 1 \ f 138-230 138-623 139-015 139-408 139801 140-193 140-586 140-979 1520-53 1529-18 1537-86 1546-55 1555-28 1564-03 1572-81 1581-61 38-993 39-103 39-214 39-325 39-436 39-546 39-657 39-768 50 in. i \ i 157-080 157-865 158-650 159-436 1963-50 1983-18 2002-96 2022-84 44-310 44-531 44-753 44-974 45 in. i i \ t f 1 141-372 141-764 142-157 142-550 142-942 143-335 143-728 144-120 1590-43 1599-28 1608-15 1617-04 1625-97 1634-92 1643-89 1652-88 39-879 39-989 40-110 40-211 40-322 40-432 40-543 40-654 51 in. i \ f 160-221 161-007 161-792 162-577 2042-82 2062-90 2083-07 2103-35 45-196 45-417 45-639 45-861 52 in. i ft f 163-363 164-148 164-934 165-719 2123-72 2144-19 2164-75 2185-42 46-082 46-304 46-525 46-747 46 in. t i 144-513 144-906 145-299 145-691 146-084 146-477 146-869 147-262 1661-90 1670-95 1680-01 1689-10 1698-23 1707-37 1716-54 1725-73 40-765 40-876 40-986 41-097 41-208 41-319 41-429 41-540 53 in. i h f 166-504 167-290 168-075 168-861 2206-18 2227-05 2248-01 2269 06 46-968 47-190 47-411 47-633 54 in. i i f 169-646 170-431 171-217 172-002 2290-22 2311-48 2332-83 2354-28 47-854 48-076 48-298 48-519 47m. 147-655 148-047 148-440 148-833 149-226 149-618 150-011 150-404 1734-94 1744-18 1753-45 1762-73 1772-05 1781-39 1790-76 1800-14 41-651 41-762 41-873 41-983 42-094 42-205 42-316 42-427 55 in. i i 172-788 173-573 174-358 175-144 2375-83 2397-48 2419-22 2441-07 48-741 48-962 49-184 49-405 48 in. 150-796 151-189 151-582 151-974 1809-56 1818-99 1828-46 1837-93 42-537 42-648 42-759 42-870 56 in. i i 175-929 176-715 177-500 178-285 2463-01 2485-05 2507-19 2529-42 49-627 49-848 50-070 50-291 280 TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES. Diam. Circum. Area. Side of equal Square. Diam. Circum. Area. Side of equal Square. 57 in. i i i 179-071 179-850 180-642 181-427 2551-70 2574-19 2596-72 2619-35 50-513 50-735 50-956 51-178 67 in. * 4 210-487 211-272 212-058 212843 3525-66 3552-01 3578-47 360503 59-375 59-597 59-818 00-040 58 in. i * 1 182212 182-998 183-783 184-569 2042-08 2004-91 2087-83 2710-85 51-399 51-621 51-842 52-064 68 in. i i f 213-628 214-414 215-199 215-985 3631-63 3658-44 3085-29 3712-24 00-201 00-483 00-704 00-926 59 in. i i i 185-354 186-139 186-925 187-710 273397 2757-19 2780-51 2803-92 52-285 52-507 52-729 52-950 69 in. I i 1 216-770 217555 218-341 219-126 373928 3766-43 3793-67 3821-02 61-147 61-369 61-591 61-812 60 in. i i * 188-490 189-281 189-006 190-852 2827-44 2851-05 2874-70 2898-50 53-J72 53393 53-615 53-836 70 in. i i f 219-912 220697 221 482 222-268 384846 3875-99 390363 3931-36 62-034 62-255 62-477 62-968 61 in. * i 191-637 192423 193208 193-993 2922-47 2940-47 2970-57 2994-77 54048 54-279 54-501 54723 71 in. i i I 223053 223-839 224-624 225-409 3959-20 3987-13 4015-16 4043-28 09-920 03-141 63-363 63-545 62 in. i i I 194-779 195-504 196-350 197-135 301907 3043-47 300790 309250 54-944 55-166 55-387 55609 72 in. * i 1 226-195 226-980 227-766 228-551 4071 51 4099-83 1128-25 4156-77 63-806 64-028 64-249 64-471 63 in. * i i 197-920 198-700 199-491 200-277 3117-25 3142-04 3100-92 3191-91 55-830 56-052 56-273 56-495 73 in. k I ! 229336 230122 230907 231-693 4185-39 4214-11 424292 4271-83 61-692 64-914 65-135 65-357 61 in. i i 1 201-002 201-847 202633 203-418 3216-99 3242-17 3267-40 3292-83 56-710 50-938 57-159 57-381 74 in. i * f 75 in. i i i 232-478 233-263 234-049 234-834 4300-85 432995 4359-16 1388-47 65-578 05-800 00-022 00-243 65 in. i i 1 204-204 204-989 205-774 206 500 3318-31 3343-88 3309-50 3395-33 57-003 57-824 58-046 58-207 235-620 230-405 237-190 237-976 4417-87 4447-37 4476-97 4500-07 66-465 66-080 06-908 67-129 66 in. i i ! 207-345 208-131 208-910 209701 3421-20 3447-10 3473-23 3499-39 58-489 58-710 58-932 59-154 76 in. i h i 238-761 239-547 240-332 241-117 4530-47 4500-30 4590-35 4020-44 07-351 67-572 67-794 68-016 TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES. 281 Diam. Circura. Area. Side of equal Square. Diam. Circum. Area. Side of cnual Square. 77 in. L 4 241-903 242-638 243-474 244259 4656-63 1636-92 4717-30 1747-79 68-237 68-459 68-680 68-902 93 in. 1 292-168 293-739 6792-92 6866-16 82-416 82-859 83-302 83-746 84-189 84-632 94 in. 295-310 296-881 6939 79 7013-81 7088-23 7163-04 78 in. 1 1 ! 245-044 245-830 246-615 247-401 4778-37 4809-05 4339 83 1870-70 69-123 69-345 69-566 69-783 95 in. h 293-452 300-022 eet. in. 8 1 2 3 4 5 6 7 8 9 10 11 eet. in. 25 11 25 45- 25 7 7 S 25 11 26 21 26 51 26 8 26 111 27 21 27 5! 27 9 23 01 feet. 50-265 51-317 52-381 53-456 54-541 55-637 56-745 57-862 58-992 60-132 61-282 62-444 eet. in. 7 01 7 If 7 2J 7 3| 7 4| 7 51 7 6| 7 71 7 81 7 91 7 91 7 10! 79 in. i 1 f 80 in. 218-186 243-971 249-757 250-542 251-323 252-893 4901-63 1932-75 1963-92 1995-19 70-003 70231 70453 70-674 5026-56 5089-58 70-896 71-339 8 1 in. 1 254-469 256-040 5153-00 5216-82 71-782 72-225 82 in. 1 257-611 259-182 r >281-02 5345-62 72-668 73-111 83 in. 1 260-752 262-323 5410-62 5476-00 73-554 73-997 9 1 2 3 4 5 6 7 8 9 10 11 28 31 28 6 28 91 29 Of 29 3| 29 7 29 101 30 11 30 4} 30 71 30 lit 31 If 63-617 64-800 65-995 67-200 68-416 69-644 70-882 72-130 73-391 74-662 75-943 77-236 7 11| 8 01 8 11 8 21 8 31 8 41 8 5 8 5& 8 61 8 7| 8 81 8 91 8 101 8 111 9 01 9 1 9 11 9 2! 9 3| 9 41 9 5| 9 61 9 71 9 81 84 in. 1 263-894 265-465 267-036 268-606 5541-78 5607-95 74-440 74-884 75-327 75770 85 in. 1 5674-51 5741-47 86 in. 1 270-177 271-748 5808-81 5876-55 76-213 76-656 87 in. 88 in. k 273-319 274-890 5944-69 6013-21 77-099 77-542 77-985 78-428 276-460 278-031 6082-13 6151-44 10 1 2 3 4 5 6 7 8 9 10 11 31 5 31 81 31 Hi 32 2| 32 51 32 8| 32 11! 33 2| 33 61 33 91 34 0| 34 31 78-540 79-854 81-179 82-516 83-862 85-221 86-590 87-969 89-360 90-762 92-174 93-598 89 in. 279-602 281-173 6221-15 6291-25 78-871 79-315 90in. 1 282-744 284-314 6361-74 6432-62 79-758 80-201 91 in. 1 285-885 287-456 6503-89 6573-56 80-644 81-087 92 in. 289-027 290-598 6647-62 6720-07 81-530 81-973 12* 282 TABLE OF THE CI11CUMFERENCES, ETC. OF CIRCLES, Diara. Circurn. Area. Side of equal Square. Diam. Circum* Area. Side of equal Square. feet. 10. 11 1 2 eet. in. 34 6f 34 9f 35 0| feet. 95-033 96-478 97-934 aet. in. 9 85 9 95 9 10! eet. in. 14 9 10 11 eet. in. 46 4 46 71 46 111 feet. 70-873 72-809 74-756 eet. in. 13 11 13 if 13 2| 3 4 5 6 7 8 9 10 11 35 41 35 71 35 101 36 H 36 41 36 7f 36 10| 37 2| 37 51 99-402 100-879 102-368 103-869 105-379 106-901 108-434 109-977 111-531 9 111 10 01 10 If 10 21 10 31 10 4 10 5 10 55 10 6! 15 1 2 3 4 5 6 7 8 47 11 47 4| 47 7* 47 105 48 21 48 51 48 81 48 llf 49 2f 76-715 78-683 80-663 82-654 84-655 86-668 188-692 190-726 192-771 13 31 13 4f 13 5J 13 61 13 71 13 8 13 81 13 91 13 101 13 1 2 37 8| 37 ll| 38 2f 113-097 114-673 116-260 10 7f 10 8& 10 9| 9 10 It 49 51 49 81 50 194-828 196-894 198-973 13 11* 14 OS 14 11 3 4 5 6 7 8 9 10 11 38 5! 38 8 39 39 3i 39 6 39 91 40 Of 40 31 40 65 117-859 119-467 121-087 122-718 124-359 126-012 127-676 129-350 131-036 10 101 10 111 1 1 05 1 15 1 2| 1 3| 1 41 11 5| 16 1 2 3 4 5 6 7 8 9 50 31 50 61 50 91 51 01 51 3! 51 61 51 10 52 11 52 41 52 7f 201-062 203-161 205-272 207-394 209-526 211-670 213-825 215-989 218-166 22Q-353 14 21 14 3 14 35 14 45 14 5| 14 6| 14 71 14 8! 14 91 14. ini 13 1 40 10 41 11 132-732 134-439 11 61 11 71 10 11 52 101 53 If 222-551 224760 14 11 14 HI 2 3 4 5 6 7 8 9 10 11 41 4f 41 71 41 10| 42 If 42 45 42 8 42 111 43 2t 43 5J 43 8| 136-157 137-886 139-626 141-377 143-139 144-911 146-694 148-489 150-294 152-110 11 81 11 8| 11 9f 11 10$ 11 llf 12 Ol 12 Ig 12 2 12 31 12 4 17 1 2 3 4 5 6 7 8 9 53 45 53 8 53 11 J 54 21 54 5| 54 8* 54 llf 55 25 55 6 55 91 226-980 229-210 231-452 233-705 235-968 238-243 240-528 242-824 245-131 247-450 15 Of 15 If 15 2f 15 3 15 4| 15 51 15 61 15 7 15 75 15 8! 14 1 43 11! 44 25 153-938 155-775 12 45 12 5| 10 11 56 0| 56 31 249-778 252-118 15 9} 15 101 2 3 4 5 6 7 8 44 6 44 91 45 01 45 31 45 6f 45 9| 46 0} 157-625 159-485 161-355 163-237 165-130 167-033 168-947 12 61 12 71 12 8| 12 9 12 101 12 111 13 18 1 2 3 4 5 6 56 61 56 9| 57 Oi 57 4 57 71 57 101 58 1| 254-469 256-830 259-203 261-587 263-980 266-386 268-803 15 11| 16 Of 16 11 16 21 16 31 16 35 16 4} TABLE OF THE CIRCUMFERENCES, ETC. OF CIRCLES. 28? Diun. Circuiu. Area. Side of equal Square. Diam. Circum. Area. bide ot equal Square. feet. in. 18 7 8 9 10 11 feet. in. IS 44 58 7-g 58 10- 53 2 59 5J feet. 271-229 273667 276-117 278-576 281-047 feet. iu. 16 5| 16 6J 16 7 16 8i 16 9| feet. in. 22 3 4 5 6 7 8 9 10 11 feet. in. 69 10! 70 Ig 70 5 70 8i 70 Hi 71 2* 71 51 71 81 71 115 feet. 388-822 391-738 394-668 397-608 400-558 403-520 406-493 409-475 412-470 feet. in. 19 8| 19 94 19 10| 19 lli 20 Oi 20 li 20 2 20 25 20 3J JO 1 2 3 4 5 6 7 8 9 10 11 59 8* 59 114 60 2-5 60 5S 60 8! 60 11| 61 31 61 6i 61 94 62 62 31 62 6f 283-529 288-021 288-524 291-039 293-564 296-110 298-648 301-205 303-774 306-355 308-944 311-546 16 10 16 11 16 ll 17 Of 17 1| 17 24 17 31 17 4i 17 6i 17 6 17 7 17 11 23 1 2 3 4 5 6 7 8 9 10 11 72 3 72 6i 72 9| 73 0:, 73 3f 73 6f 73 9 74 1 74 4i 74 7i 74 10J 75 If 415-476 418-491 421-519 424-557 427-605 43G-665 433-737 436-817 439-910 443.014 446-127 449-253 20 44 20 54 20 61 20 7| 20 8} 20 9i 20 10 20 10^ 20 H| 21 Of 21 14 21 2| 20 1 2 3 4 5 6 7 8 9 10 11 21 1 2 3 4 5 6 7 8 9 10 11 22 1 2 62 9 63 li 63 41 63 7{f 63 11* 64 11 64 4! 64 7 64 11 65 2i 65 5 65 8} 314-160 316-782 319-417 322-063 324-718 327385 330-064 332-752 335-452 338-163 340-884 343-617 17 8| 17 9| 17 I0i 17 11| 18 Oi 18 li 18 2 18 2| 18 3| 18 4| 18 5| 18 64 24 1 2 3 4 5 6 7 8 9 10 11 75 4| 75 7J 75 11 76 2 76 6i 76 8A 76 llf 77 21 77 51 77 9 78 Oi 78 3i 452-390 455-536 458-694 461-864 465-042 468-234 471-436 474-647 477-871 481-106 484-350 487-607 21 3i 21 4j 21 5 21 6 21 65 21 7| 21 8j 21 94 21 lOf 21 Hi 22 Oi 22 1 65 11| 66 2$ 66 5 66 9 67 0^ 67 3 1 67 61 67 9| S8 Oii 68 31 68 7 68 10i 346-361 349-114 351-880 354-657 357-443 360-241 363-051 365-869 368-701 371-543 374-394 377258 18 7i 18 8| 18 9a l 18 10 18 10 18 111 19 01 19 If 19 24 19 3 19 4i 19 5i 25 1 2 3 4 . 5 6 7 8 9 10 11 78 6| 78 94 79 Of 79 3| 79 7i 79 Hi 80 li 80 4| 80 7| 80 10! 81 U 81 5 490-875 494-151 497-441 500-741 504-051 507-373 510706 514-048 517403 520769 524-144 527531 22 If 22 2| 22 3| 22 4| 22 54 22 6 22 7i 22 8i 22 9 22 95 22 10| 22 llf 69 1| 69 44 69 7| 380-133 383017 385-914 19 5| 19 6& 19 71 USB OP THE ABOVE TABLE. To find, by inspection, the area of any circle, from i to 100 inches, of which the diameter is given : Calling the diameters feel, the area *ill be feet ; if rods, or yards, the area will be of a corresponding denomination. 284 TABLE Of Squares, Cubes, Square and Cube Roots of Numbers. Number. Square. Cube. Square Root. Cube Root. 1 1 1 1-0 1-0 2 4 8 1-414213 1-25992 3 9 27 1-732050 1-44225 4 16 64 2-0 1-58740 5 25 125 2-236068 1-70997 6 36 216 2-449*89 1-81712 7 49 43 2-645751 1-91293 . 8 64 512 2-828427 2-0 9 81 720 3-0 2-08008 10 100 1000 3-162277 2-15443 11 121 1331 3-316624 3-22398 12 144 1728 3-464101 2-28942 13 169 2197 3-605551 2-35133 14 196 2744 3-741657 2-41014 15 225 3375 3-872983 2-46621 16 256 4096 4-0 2-51984 17 289 4913 4-123105 2-57128 18 324 5832 4-242640 2-62074 19 361 6859 4-358898 2-66840 20 400 8000 4-472136 2-71441 21 441 9261 4-582575 2-75892 22 484 10648 4-690415 2-80203 23 529 12167 4-795831 2-84386 24 576 13824 4-898979 2-88449 25 625 15625 5-0 2-92401 26 676 17576 5-099019 2-96249 27 729 19683 5-196152 30 28 784 21952 5-291502 3-03658 29 841 24389 5-385164 3-07231 30 900 27000 5-477225 3-10723 31 961 29791 5-567764 3-14138 32 1024 32768 5-656854 3-17480 33 1089 35937 5-744562 3-20753 34 1156 39304 5-830951 3-23961 35 1225 42875 5-916079 3-27106 36 1296 46656 6-0 3-30192 37 1369 50653 6-082762 3-33222 38 1444 54872 6-164414 3-36197 39 1521 59319 6-244998 3-39121 40 1600 64000 6-324555 3-41995 41 1681 68921 6'403124 3-44821 42 1764 74088 6*480740 3-47602 ' 43 1849 79507 6-557438 3-50339 44 1936 85184 6-633249 3-53034 45 2025 91125 6-708203 3-55689 46 2116 97336 6-782330 3-58304 47 2209 103823 6-855654 3-60882 48 2304 110592 6-928303 3-63424 49 2401 117649 7-0 3-65930 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Root. 50 2500 125000 7-071067 3-68403 51 2601 132651 7-141428 3-70843 52 2704 140608 7-211102 3-73251 53 2809 148877 7-280109 3-75628 54 2916 157464 7-348469 3-77976 55 3025 166375 7-416198 3-80295 56 3136 175616 7-483314 3-82586 57 3249 185193 7-549834 3-84850 58 3364 195112 7-615773 3-87087 59 3481 205379 7-681145 3-89299 60 3600 216000 7-745966 3-91486 61 3721 226981 7-810249 3-93649 62 3844 238328 7-874007 3-95789 63 3969 250047 7-9372G3 3-97905 64 4096 262144 8'0 4-0 65 4225 274625 8-062257 4-02072 66 4356 287496 8-124038 4-04124 67 4489 300763 8-185352 4-06154 68 4624 314432 8-246211 4-08165 69 4761 328509 8-306623 4-10156 70 4900 343000 8-366600 4-12128 71 5041 357911 8-426149 4-14081 72 5184 373248 8-485281 4-16016 73 5329 389017 8-544003 4-17933 74 5476 405224 8-602325 4-19833 75 5625 421875 8-660254 4-21716 76 5776 438976 8-717797 4-23582 77 5929 456533 8-774964 4-25432 78 6084 474552 8-831760 4-27265 79 6241 493039 8-888194 4-29084 80 6400 512000 8-944271 4-30887 81 6561 531441 9-0 4-32674 82 6724 551368 9-055385 4-34448 83 6889 571787 9-110433 4-36207 84 7056 592704 9-165151 4-37951 85 7225 614125 9-219544 4-39683 86 7396 636056 9-273618 4-41400 87 7569 658503 9-327379 4-43104 88 7744 681472 9-380831 4-44796 89 7921 704969 9-433981 4-46474 90 8100 729000 9-486833 4-48140 91 8281 753571 9-539392 4-49794 92 8464 778688 9-591663 4-51435 93 8649 804357 9-643650 4-53065 94 8836 830584 9-695359 4-54683 95 9025 857375 9-746794 4-56290 96 9216 884736 9-797959 4-57785 97 9409 912673 9-848857 4-59470 98 9604 941192 9-899494 4-61043 286 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Root. 99 9801 970299 9-949874 4-62606 100 10000 1000000 10-0 4-64158 101 10201 1030301 10-049875 4-65701 102 10404 1061208 10-099504 4-67233 103 10609 1092727 10-148891 4-68754 104 10816 1124864 10 198039 4-70266 105 11025 1157625 10-246950 4-71769 106 11236 1191016 10-295630 4-73262 10? 11449 1225043 10-344080 4-74745 108 11664 1259712 10-392304 4-76220 109 11881 1295029 10-440306 4-77685 110 12100 1331000 10-488088 4-79142 111 12321 1367631 10-535653 4-80589 112 12544 1404928 10-583005 4*82028 113 12769 1442897 10-630145 4-83458 114 12996 1481544 10*677078 4-84880 115 13225 1520875 10-723805 4-86294 116 13456 1560896 10-770329 4-87699 117 13689 1601613 10-816653 4-89097 118 13924 1643032 10-862780 4'94086 119 14161 1685159 10-908712 4*91868 120 14400 1728000 10-954451 4-93242 121 14641 1771561 iro 4*94608 122 14884 1815848 11-045361 4'95967 123 15129 1860867 11-090536. 4*97319 124 15376 1906624 H'135528 4*98663 125 15625 1953125 11-180339 5'0 126 15876 2000376 11 '224972 5"01329 127 16129 2048383 11-269427 5*02652 128 16384 2097152 11-313708 5-03968 129 16641 2146689 11-357816 5*05277 130 16900 2197000 11-401754 S'06579 131 17161 2248091 11-445523 5*07875 132 17424 2299963 11-489125 5*09164 133 17689 2352637 11-532562 5*10446 134 17956 2406104 11-575836 5*11723 135 18225 2460375 11-618950 5*12992 136 18496 2515456 11-661903 5'14256 137 18769 257135S 11-704699 5*15513 138 19044 2628072 11-747344 5'16764 139 19321 2685619 11-789826 5'18010 140 19600 2744000 11-832159 5*19249 141 19881 2803221 11-874342 5*20482 142 20164 28G3288 11-916375 5'21710 143 20449 2924207 11-958260 5*22932 144 20736 2985984 12-0 5"24148 145 21025 3048625 12-041594 5*25358 146 21316 311213d 12-083046 526563 147 21609 317G523 12-124355 5*27763 148 1 21904 3241792 12-165525 5*28957 SQUARES, CUBES, AND ROOTS 287 W umoer. Square. Cube. 149 22201 3307949 12-206555 5-30145 150 22500 3375000 12-247448 5-31329 151 22801 3442951 12-288205 5-32507 152 23104 3511808 12-328828 5-33680 153 23409 3581577 12-369316 5-34848 154 23716 3652264 12-409673 5-36010 155 24025 3723875 12-449899 5-37168 156 24336 3796416 12-489996 5-38323 157 24649 3869893 12-529964 5-39469 158 24964 3944312 12-569805 5-40612 159 25281 4019679 12-609520 5-41750 160 25600 4096000 12-649110 5-42883 161 25921 4173281 12-688577 5-44012 162 26244 4251528 12-727922 5-45136 163 26569 4330747 12-767145 546255 164 26896 4410944 12-806248 5-47370 165 27225 4492125 12-845232 5-48480 166 27556 4574296 12-884098 5-49586 167 27889 4657463 12-922848 5-50687 168 28224 4741632 12-961481 5-51784 169 28561 4826809 13-0 5-52877 170 28900 4913000 13-038404 5-53965 171 29241 5000211 13-076696 5-55049 172 29584 5088448 13-114877 5-56129 173 29929 5177717 13*152946 5-57205 174 30276 5268024 13-190906 5-58277 175 30625 5359375 13-228756 5-59344 176 30976 5451776 13-266499 5-60407 177 31329 5545233 13-304134 5-61467 178 31684 5639752 13 341664 5-62522 179 32041 5735339 13-379088 5-63574 180 32400 5832000 13-416407 5-64621 181 32761 ' 5929741 13-453624 5-65665 182 33124 6028568 13-490737 5-66705 183 33489 6128487 13-527749 5-67741 184 33856 6229504 13-564660 5-68773 185 34225 6331625 13-601470 5-69801 186 34596 6434856 13-638181 5-70826 187 34969 6539203 13-674794 5-71847 188 35344 6644672 13-711309 5-72865 189 35721 6751269 13-747727 5-73879 190 36100 6859000 13-784048 5-74889 191 36481 6967871 13-820275 5-75896 192 36864 7077888 13-856406 5-76899 193 37249 7189057 13-892444 5-77899 194 37636 7301384 13-928388 5-78896 195 38025 7414875 13-964240 5-79889 196 38416 7529536 14'0 5-80878 197 38809 7645373 14-035668 5-81864 198 39204 7762392 14-071247 5-82847 288 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Root. 199 39601 7880599 14-106736 5-83827 200 4QOOO 8000000 14-142135 5-84803 201 40401 8120601 14-177446 5-85776 202 40804 8242408 14-212670 5-86746 203 41209 8365427 14-247806 5-87713 204 41616 8489664 14-282856 5-88676 205 42025 8615125 14317821 5-89636 206 42436 8741816 14-352700 5-90594 207 42849 8869743 14-387494 5-91548 208 43264 8998912 14-422205 5-92499 209 43681 9123329 14-456832 5-93447 210 44100 9261000 14-491376 5-94391 211 44521 9393931 14-525839 5-95334 212 44944 9528128 14-560219 5-96273 213 45369 9663597 14-594519 5-97209 214 45796 9800344 14-628738 5-98142 215 46225 9938375 14-662878 5-99072 216 46656 10077696 14-696938 6-0 217 47089 10218313 14-730919 6-00924 218 47524 10360232 14-764823 6-01836 219 47961 10503459 14-798648 6-02765 220 48400 10648000 14-832397 6-03681 221 48841 10793861 14-866068 6-04594 222 49284 10941048 14-899664 6-05504 223 49729 11039567 14-933184 6-06412 224 50176 11239424 15-966629 6-07317 225 50625 11390625 15-0 6-08220 226 51076 11543176 15-033296 6-09119 227 51529 11697033 15-066519 6-10017 228 51984 11852352 15-099668 6-10911 229 52441 12008989 15-132746 6 11803 230 52900 12167000 15-165750 6-12692 231 53361 12326391 15-198684 6-13579 232 53824 12487168 15-231546 6-14463 233 54289 12649337 15-264337 6-15344 234 54756 12812904 15-297058 6-16223 235 55225 12977875 15-329709 6-17100 236 55696 13144256 15-362291 6-17974 237 56169 13312053 15-394804 6-18846 238 56644 13481272 15-427248 6-19715 239 57121 13651919 15-459624 6-20582 240 57600 13824000 15-491933 6-21446 241 58081 13997521 15-524174 6-22308 242 58564 14172488 15-556349 6-23167 243 59049 14348907 15-588457 6-24025 244 59536 14526784 15-620499 6-24880 245 60025 14706125 15-652475 6-25732 246 60516 14886936 15-684387 6-26582 247 61009 15069223 15-716233 6-27430 248 61504 15252992 15-748015 6-28276 SQUARES, CtJBES, AND ROOTS. 280 Numbec Square. Cube. Square Root. Cube Root. ~249 62001 15438249 15779733 6-29119 250 62500 15625000 15-811388 6-29960 251 63001 15813251 15-842979 630799 252 63504 16003008 15-874507 631635 253 64009 16194277 15-905973 632470 254 64516 16387064 15937377 633302 255 65025 16581375 15968719 634132 256 65536 16777216 160 6-34960 257 66049 16974593 16031219 6-35785 258 66564 17173512 16-062378 6-36609 259 67081 17373979 16093476 6-37431 260 67600 17576000 16 124515 6-38250 261 68121 17779581 16-155494 6-39067 262 68644 17984728 16-186414 6-39882 263 69169 18191447 16-217274 6-40695 264 69696 18399744 16-248076 6-41506 265 70225 18609625 16-278820 6-42315 260 70756 18821096 16-309506 6-43122 267 71289 19034163 16-340134 6-43927 263 71824 19248832 16-370705 6-44730 269 72361 19465109 16-401219 6-45531 270 72900 19883000 16-431676 6-46330 271 73441 19902511 16-462077 6-47127 272 73934 20123648 16-492422 6-47922 273 74529 20346417 16-522711 6-48715 274 75076 20570824 16-552945 6-49506 275 75625 20796875 16-583124 6-50295 276 76176 21024576 16-613247 6-51082 277 76729 21253933 16-643317 6-51868 278 77284 21484952 16-673332 6-52651 279 77841 21717639 16-703293 6-53433 280 78400 21952000 16-733200 6-54213 281 78961 22188041 16-763054 6-54991 282 79524 22425768 16-792855 6-55767 283 80089 22665187 16-822603 6-56541 284 80656 22906304 16-852299 6-57313 285 81225 23149125 16-881943 6-58084 286 81796 23393656 16-911534 6-58853 287 82369 23639903 16-941074 6-59620 288 82944 23887872 16-970562 6-60385 289 83521 24137569 170 6-61148 290 84100 24389000 17-029386 661910 291 84681 24642171 17-058722 6-62670 292 85264 24897088 17-088007 6-63428 293 85849 25153757 17-117242 6-64185 294 86436 25412184 17-146428 6-64939 295 87025 25672375 17-175564 6-65693 296 87616 25934336 17-204650 6-66444 297 88209 26198073 17-233687 6-67194 298 88804 26463592 17-262676 6-67941 13 290 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Root. 299 89401 26730899 17-2U1616 6-68688 300 90000 27000000 17-320508 6-69432 301 90601 27270901 17-349351 6-70175 302 91204 27543608 17-378147 6-70917 303 91809 27818127 17-406895 6-71656 304 92416 28094464 17-435595 6-72395 305 93025 28372625 17-464249 6-73131 306 93636 28652616 17-492855 6-73866 307 94249 23934443 17-521415 6-74599 308 94864 29218112 17-549928 6-75331 309 95481 29503629 17-578395 6-76061 310 96100 29791000 17-606816 6-76789 311 96721 30080231 17-635192 6-77516 312 97344 30371328 17-663521 6-78242 313 97969 30G64297 17-691806 6-78966 314 98596 30959144 17-720045 6-79688 315 99225 31255875 17-748239 6-80409 316 99856 31554496 17-776388 6-31128 317 100489 31855013 17-804493 6-81846 318 101124 32157432 17-832554 6-82562 319 101761 32461759 17-860571 6-83277 320 102400 32768000 17-888543 6-83990 321 103041 33076161 17-916472 6-84702 322 103684 33386248 17-944358 6-85412 323 104329 33698267 17-972200 6-86121 324 104976 34012224 18-0 6-86828 325 105625 34328125 18-027756 6-87534 326 106276 34645976 18-055470 6-88238 327 106929 34965783 18-083141 6-88941 328 107584 35287552 18-110770 6-89643 329 108241 35611289 18-138357 6-90343 330 108900 35937000 18-165902 6-91042 331 109561 36264691 18-193405 6-91739 332 110224 36594368 18-220367 6-92435 333 110889 36926037 18-248287 6-93130 334 111556 37259704 18-275666 6-93823 335 112225 37595375 18-303005 6-94514 336 112896 37933056 18-330302 6-95205 337 113569 38272753 18-357559 6-95894 338 114244 38614472 18-384776 6-96581 339 114921 38958219 18-411952 6-97268 340 115600 39304000 18-439088 6-97953 341 116281 39651821 18-466185 6-98636 342 116964 40001688 18-493242 6-99319 343 117649 40353607 18-520259 7-0 344 118336 40707584 18-547237 7-00679 345 119025 41063625 18-574175 7-01357 346 119716 41421736 18-601075 7-02034 347 120409 41781923 18-627936 7-02710 348 121104 42144192 18-654758 7-03385 SQUARES, CUBES, AND ROOTS. 291 Number. Square. Cube. Square Root. Cube Root. 349 121801 42508549 18-681541 7-04058 350 122500 42875000 18-708286 7-04720 351 123201 43243551 18-734994 705400 352 123904 43614208 18-761663 7-06069 353 124609 43986977 18-788294 7-06737 354 125316 44361864 18-814887 7-07404 355 126025 44738875 18-841443 7-08069 356 126736 45118016 18-867962 708734 357 127449 45499293 18-894443 7-09397 358 128164 45882712 18-920887 7-10058 359 128881 46268279 18-947295 7-10719 360 129600 46656000 18-973666 7-11378 361 130321 47045881 19-0 7-12036 362 131044 47437928 19-026297 7-12693 363 131769 47832147 19-052558 7-13349 364 132496 48228544 19-078784 7-14003 365 133225 48627125 19-104973 7-14656 366 133956 49027896 19-131126 7-15309 367 134689 49430863 19-157244 7-15959 368 135424 49836032 19-183326 7-16609 369 136161 50243409 19-209372 7-17258 370 136900 50653000 19-235384 7-17905 371 137641 51064811 19-261360 7-18551 372 138384 51478843 19-287301 7-19196 373 139129 51895117 19-313207 7-19840 374 139876 52313624 19-339079 7-20483 375 140625 52734375 19-364916 7-21124 376 141376 53157376 19-390719 7-21765 377 142129 53582633 19-416487 7-22404 378 142884 54010152 19-442222 7-23042 379 143641 54439939 19-467922 7-23679 380 144400 . 54872000 19-493588 7-24315 381 1451 01 55306341 19-519221 7-24950 382 145924 55742968 19-544820 7-25584 383 146689 56181887 19-570385 7-26216 384 147456 56623104 19-595917 7-26848 385 148225 57066625 19-621416 7-27478 386 148996 57512456 19-646882 7-28107 387 149769 57960603 19-672315 7-28736 388 150544 58411072 19-697715 7-29363 389 151321 58863869 19-723082 7-29989 390 152100 59319000 19-748417 7-30614 391 152881 59776471 19-773719 7-31238 392 153664 60236288 19-798989 7-31861 393 154449 60698457 19-824227 7-32482 394 155236 61162984 19-849433 7-33103 395 156025 61629875 19-874606 7-33723 396 156816 62099136 19-899748 7-34342 397 157609 62570773 19-924858 7-34959 398 158404 63044792 19-949937 7-35576 2U2 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Root. 399 159201 63521199 19-974984 7-36191 400 160000 64000000 20-0 7-36806 401 160801 64481201 20-024984 7-37419 402 161604 64964808 20.049937 7-38032 403 162409 65450827 20074859 7-38643 404 163216 65939264 20-099751 7-39254 405 164025 - 66430125 20-124611 7-39863 406 164836 66923416 20-149441 7-40472 407 165649 67419143 20-174241 7-41079 408 166464 67917312 20-199009 7-41685 409 167281 68417929 20-223748 7-42291 410 168100 68921000 20-248456 7-42895 411 168921 69426531 20-273134 7-43499 412 169744 69934528 20-297783 7-44101 413 170569 70444997 20-322401 7-44703 414 171396 70951944 20-346980 7-45303 415 172225 71473375 20-371548 7-45903 416 173056 71991296 20-396078 7-46502 417 173889 72511713 20-420577 7-47099 418 174724 73034632 20-445048 7-47696 419 175561 73560059 20-469489 7-48292 420 176400 74038000 20-493901 7-48887 421 177241 T46 18461 20-518284 7-49481 422 178084 75151448 20-542638 7-50074 423 178929 75686967 20-536963 7-50666 424 179776 76225024 20-591260 7-51257 425 180625 76765625 20-615528 7-51847 426 181476 77308776 20-639767 7-52436 427 182329 77854483 20-663978 7-53024 428 183184 78402752 20-688160 7-53612 429 184041 78953589 20-712315 7-54198 430 184900 79507000 20-736441 7-54784 431 185761 80062991 20-760539 7-55368 432 186624 80621568 20-784609 7-55952 433 187489 81182737 20-808652 7-56535 434 188356 81743504 20-832666 7-57117 435 189225 82312875 20-856653 7-57698 436 190096 82881856 20-880613 7-58278 437 190969 83453453 20-904545 7-58857 438 191844 84027672 20-928449 7-59436 439 192721 84604519 20-952326 7-60013 440 193600 85184000 20-976177 7-60590 441 194481 85766121 21-0 7-61166 442 195364 86350888 21-023796 7-61741 443 196249 86938307 21-047565 7-62315 444 197136 87528384 21-071307 7-62888 445 198025 88121125 21-095023 7-63460 446 198916 88716536 21-118712 7-64032 . 447 199809 89314623 21-142374 7-64602 448 200704 89915392 21-166010 7-65172 SQUARES, CUBES, AND ROOTS. 293 Number. Square. Cube. Square Root. Cube Root. 449 201601 90518849 21-189620 7-65741 450 202500 91125000 21-213204 7-66309 451 203401 91733851 21-236760 7-66876 452 204304 92345408 21-260291 7-67443 453 205209 92959677 21-283796 7-68008 454 206116 93576664 21-307275 7-68573 455 207025 94196375 21-330729 7-69137 456 207936 94818816 21-354156 7-69700 457 208849 95443993 21-377558 7-70262 458 209764 96071912 21-400934 7-70823 459 210881 96702579 21-424285 7-71384 460 211600 97336000 21-447610 7-71944 461 212521 97972181 21-470910 7-72503 462 213444 98611128 21-494185 7-73061 463 214369 99252847 21-517434 7-73618 464 215296 99897344 21-540659 7-74175 465 216225 100544825 21-563858 7-74731 466 217156 101194696 21-587033 7-75286 467 218089 101847563 21-610182 7-75840 468 219024 102503232 21-633307 7-76393 469 219961 103161709 21-656407 7-76946 470 220900 103823000 21-679483 7-77498 471 221841 104487111 21-702534 7-78049 472 222784 105154048 21-725561 7-78599 473 223729 105823817 2 L -748563 7-79148 474 224676 106496424 21-771541 7-79697 475 225625 107171875 21-794494 7-80245 478 226576 107850176 21-817424 7-80792 477 227529 108531333 21-840329 7-81338 478 228484 109215352 21-883211 781884 479 229441 109902239 21-886068 7-82429 480 ' 230400. 110592000 21-908902 7-82973 481 231361 111284641 21-931712 783516 482 232324 111980163 21-954498 7 84059 483 233289 112678587 21-977261 7-84601 484 234256 113379904 22-0 7-85142 485 235225 114084125 22-022715 7-85682 486 236196 114791256 22-045407 7-86222 487 237169 115501303 22-068076 7-86761 488 238144 116214272 22-090722 7-87299 489 239121 116930169 22-113344 7-87836 490 240100 117649000 22-135943 7-88373 491 241081 118370771 22-158519 7-82909 492 242064 119095488 22-181073 7-89444 493 243049 119823157 22-203603 7-89979 494 244036 120553784 22-226110 7-90512 495 245025 121287375 22-248595 7-91046 496 246016 122023936 22-271057 7-91578 497 247009 122763473 22-293496 7-92110 498 248004 123505992 22-315913 7-92640 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Hoot. 499 249001 124251499 22-338307 7-93171 500 250000 125000000 22-360679 7-93700 501 251001 125751501 22-383029 7-94229 502 252004 126506008 22-405356 7-94757 503 253009 127263527 22-427661 7-95284 504 254016 128024064 22-449944 7-95811 505 255025 128787625 22-472205 7-96337 506 256036 129554216 22-494443 7-96862 507 2.57049 130323843 22-516660 7-97387 503 258064 131098512 22-538855 7-97911 509 259081 131872229 22-561028 7-98434 510 260100 132651000 22-583179 7-93956 511 261121 133432831 22-605309 7-99478 512 262144 134217728 22-627417 8-0 513 263169 . 135005697 22-649503 8-00520 514 264196 135796744 22-671568 8-01040 515 265225 136590875 22-693611 8-0155'J 516 266256 137388096 22-715633 8-02077 517 267289 138188413 22-737634 8-02595 518 268324 138991832 22-759613 8-03112 519 269361 139798359 22-781571 8-03629 520 270400 140608000 22-803508 8-04145 521 271441 141420761 22-825424 8-04660 522 272484 142236643 22-847319 8-05174 523 273529 143055667 22-869193 8-05688 524 274576 143877824 22-891046 8-06201 525 275625 144703125 22-912878 8-06714 526 276676 145531576 22-934689 8-07226 527 277729 146363183 22-956480 8-07737 528 278784 147197952 22-978250 8-08248 529 279841 148035889 23-0 8-08757 530 280900 148877000 23-021728 8-09267 531 281961 149721291 23-043437 8-09775 532 283024 150568768 23-065125 8-10283 533 284089 151419437 23-086792 8-10791 534 285156 152273304 23-108440 S'11298 535 286225 153130375 23-130067 8-11804 536 287296 153990656 23-151673 8-12309 537 288369 154854153 23-173260 8-12814 538 289444 155720872 23-194827 8-13318 539 290521 156590819 23-216373 8-13822 540 291600 157464000 23-237900 8-14325 541 292681 158340421 23-259406 8-14827 642 263764 159220088 23-280893 8 15329 543 294849 160103007 23-302360 8-15830 514 295936 160989184 23323807 8-16330 545 297025 161878625 23-345235 8-16830 546 298116 162771336 23-366642 8-17330 547 299209 163667323 23-388031 8-17828 548 300304 164566592 23-409399 8-18326 SQUARES, CUBES, AND ROOTS. 295 Number. Square. Cube. Square Root. Cub. Root. 549 301401 165469149 23-430749 8-18824 550 302500 166375000 23-452078 8-19321 551 303601 167284151 23-473389 8-19817 552 304704 168196608 23-494680 8-20313 553 305809 169112377 23-515952 8-20808 554 306916 170031464 23-537204 8-21302 555 308025 170953875 23-558438 8-21796 556 309136 171879616 23-579652 8-22289 557 310249 172808693 23-600847 8-22782 558 311364 173741112 23-622023 8-23274 559 312481 174676879 23-643180 8-23766 560 313600 175616000 23-664319 8-24257 561 314721 176558481 23-685438 8-24747 562 315844 177504328 23-706539 8-22237 563 316969 178453547 23-727621 8-25726 564 318096 179406144 23-748684 8-26214 565 319225 180362125 23-769728 8-26702 566 320356 181321496 23790754 8-27190 567 321489 182284263 23-811761 8-27677 568 322624 183250432 23-832750 8-28163 569 323761 184220009 23-853720 8-28649 570 324900 185193000 23-874672 8-29134 571 326041 186169411 23-895606 8-29619 572 327184 187149248 23-916521 8-30103 573 328329 188132517 23-937418 8-30586 574 329476 189119224 23-958297 8-31069 575 330625 190109375 23-979157 8-31551 576 331776 191102976 24-0 8-32033 577 332929 192100033 24-020824 8-32514 578 334084 193100552 24-041630 8-32995 579 335241 194104539 24-062418 8-33475 580 336400 195112000 24-083189 8-33955 581 337561 196122941 24-103941 8-34434 582 338724 197137368 24-124676 8-34912 583 339889 198155287 24-145392 8-35390 584 341056 199176704 24-166091 8-35867 585 342223 200201625 24-186773 8-36344 586 343396 201230056 24-207436 8-36820 587 344569 202262003 24-228082 8-37296 588 345744 203297472 24-248711 8-37771 589 346921 204336469 24-269322 8-38246 590 348100 205379000 24-289915 8-38720 591 349281 206425071 24-310491 8-39194 592 350464 207474688 24-331050 8-39667 593 351649 208527857 24-351591 8-40139 594 352836 209584584 24-372115 8-40611 595 354025 210644875 24-392621 8-41083 596 355216 211708736 24-413111 8-41554 597 356409 212776173 24-433583 8-42024 598 357604 213847192 24-454038 8-42494 296 SQUARES, CUBES, AND ROOTS. Number. Square. Cube. Square Root. Cube Root. 599 358801 214921799 24-474476 8-42963 600 360000 216000000 24-494897 8-43432 601 361201 217081801 24-515301 8-43900 602 362404 218167208 24-535688 8-44368 603 363603 219256227 24-556058 8-44836 604 364816 220348864 24-576411 8-45302 605 366025 221445125 24-596747 8-45768 606 367236 222545016 24-617067 8-46234 607 368449 223648543 24-637370 846699 60S 369664 224755712 24-657656 847164 609 370881 225866529 24-677925 8-47628 610 372100 226981000 24-698178 848092 611 373321 228099131 24-718414 848555 612 374544 229220928 24-738633 849018 613 375769 230346397 24-758836 849480 614 376996 231475544 24-779023 8-49942 615 378225 232608375 24-799193 8-50403 616 379456 233744896 24-819347 8-50864 617 380689 234885113 24-839484 8-51324 618 381924 236029032 24-859605 8-51734 619 383161 237176659 24-879710 8-52243 620 384400 238328000 24-899799 8-52701 621 385841 239483061 24-919871 8-531GO 622 386884 240641848 24-939927 8-53617 623 388129 241804367 24-959907 8-54074 624 389376 242970624 24 979992 8-54531 625 390625 244140625 25-0 8-5*987 626 391876 245314376 25-019992 8-55443 627 393129 24G491883 25-039968 8-55899 628 394384 247673152 25-059928 8-5G353 629 395641 248858189 25-079872 8-56808 630 396900 250047000 25-099800 8-57261 631 398161 251239591 25-119713 8-57715 632 399424 252435968 25-139610 8-58168 633 400689 253636137 25-159491 8-58620 634 401956 254840104 25-179356 8-59072 635 403225 256047875 25-199206 8-59523 636 404496 257259456 25-219040 8-5997'l 637 405769 258474853 25-238858 8-60425 638 407044 259694072 25-258661 8-60875 639 408321 260917119 25-278449 8-61324 640 409600 262144000 25-298221 8-61773 641 410881 263374721 25-317977 8-G2222 642 412164 264609288 25-337718 8-62670 643 413449 265847707 25357444 8-63118 644 414736 267089984 25-377155 8-63565 645 416025 268336125 25396850 8-64012 646 417316 269586136 25-416530 8-64458 647 418609 270840023 25-436194 8-64904 648 419904 272097792 25-455844 8-65349 TABLE Of Diameters, Circumferences, and Areas of Circles, and the Contents in Gallons (of 231 Cubic Inches) at 1 Foot in Depth. Diam. Circum. Area. Gallons. Diam. Circum Area. Gallons. 1 in Indies. 3-1416 Inches. 7854 04084 6|in Inches. 20-420 Inches. 33-183 1-72552 i 3-5343 9940 05169 4 20-813 34-471 1-79249 3-9270 1-2271 03380 A 21-205 35-784 1-86077 1 4-3197 1-4848 07717 I- 21-598 37-122 1-93034 I 4-7124 1-7671 09188 7 in 21-991 38-484 2-00117 5-1051 2-0739 10782 1 22-383 39-871 2-07329 5-4978 2-4052 12506 22-776 41-282 2-146C6 1 5-8905 2-7611 14357 .g. 23-169 42-718 2-22134 2 in 6-2832 3-1416 16333 ^ 23-562 44-178 2-29726 | 6-6759 3-5465 .18439 f 23954 45-683 2-37448 7-0686 3-9760 20675 24-347 47-173 2-45299 1 7-4613 4-4302 23036 1 24-740 48-707 2-53276 I 7-8540 4-9087 25522 8 in 25-132 50-265 2-61378 I 8-2467 5-4119 28142 i 25-515 51-848 2-69609 1 8-6394 5-9395 30883 i 25-918 53-456 2-77971 1 9-0321 6-4918 33753 23-310 55-088 2-86458 3 in. 9-4248 7-0686 38754 I 26-703 56-745 2-95074 i 9-8175 7-6699 39879 f 27-096 58-426 3-03815 i 10-210 8-2957 43134 27-489 60-132 3-12886 I 10-602 8-9462 46519 1 27-881 61-832 3-21682 JL ^ 10-995 9-6211 50029 9 in. 28-274 63-617 3-30808 f 11-388 10-320 53664 i 28-667 65-396 3-40059 I 11-781 11-044 57429 29-059 67-200 3-49440 1 12-173 11-793 61324 .| 29-452 69-029 3-58951 4 iii. 12-566 12-566 65343 -^ 29-845 70-882 3-68586 i 12-959 13;364 69493 f 30-237 72-759 3-78347 I 13-351 14-185 73767 30-630 74-662 3-88242 13-744 15-033 78172 i 31-023 76-588 3-98258 ^ 14-137 15-904 82701 10 in. 31-416 78-540 4-08408 f 14-529 16-800 87360 i 31-808 80-515 4-18678 I 14-922 17-720 92144 32-201 82-516 4-29083 1 15-315 18-665 97058 j. 32-594 84-540 4-39608 5 in. 15-708 19-635 1-02102 JP 32-936 86-590 4-50268 i 16-100 20-629 1-07271 1 33379 88-664 4-61053 16-493 21-647 1-12564 33-772 90.762 4-71962 | 16-886 22-690 1-17988 .J 34-164 92-885 4-82846 ^ 17-278 23-758 1-23542 11 in. 34-557 95-033 4-94172 1 17-671 24-850 1-29220 i 34-950 97-205 5-05466 f 18-064 25-967 1-35028 35-343 99-402 5-16890 i 18-457 27-108 1-40962 f 35-735 01-623 5-28439 6 in. 18-849 28-274 1-47025 38.128 03-8C9 5-40119 i 19-242 29-464 1-53213 I 36.521 06-139 5.51923 i 19-635 30-679 1-59531 36.913 08-434 5.63857 f 20-027 31-919 1-65979 1 37.306 10-753 5.75916 13* 298 TABLE OF DIAMETERS OF CIRCLES, ETC. Diam. Circum. Area. Gallons. Diam. Circum. Area. Gallons. Ft. In. Ft. In. Feet Ft. In. Ft. In. Feet. 1 3 1| 7854 5-8735 5 15 84 19-6350 146-8384 1 1 3 4f 9217 6-8928 5 1 15 111 20-2947 151-7718 1 2 3 8 1-0690 7-9944 5 216 2f 20-9656 156-7891 3 3 11 1-2271 9-1766 5 316 5f 21-6475 161-8886 4 4 24 1-3962 10-4413 5 4 16 9 22-3400 167-0674 5 4 &f 1-5761 11-7866 5 5 17 04 23-0437 172-3300 6; 4 8 1-7671 13-2150 5 6 17 3^ 23-7583 177-6740 7 4 llf 1-9689 14-7241 5 7 17 6| 24-4835 183-0973 8 5 2f 2-1816 16-3148 5 817 9| 25-2199 188-6045 i y 5 51 2-4052 17-9870 5 9 18 0* 25-9672 194-1930 1 10 5 9 2-6398 19-7414 5 1018 3| 26-7251 199-8610 1 11 6 2i 2-8852 21-4830 5 11 18 74 27-4943 205-6133 2 6 3f 3-1416 23-4940 6 18 104 28-2744 211-4472 2 1 6 6i 3-4087 25-4916 6 319 74 30-6796 229-4342 2 2 6 9f 3-6869 27-5720 6 620 41 33-1831 2481564 2 3 7 Of 3-9760 29-7340 6 921 22 35-7847 267-6122 2 4 7 31 4-2760 32-6976 7 21 m 38-4846 287-8032 2 5 7 7 4-C869 34-3027 7 322 9| 41-2825 308-7270 2 C 7 10i 4-9087 38-7092 7 6 ! 23 G| 44-1787 330-3859 2 7 8 1| 5-2413 39-1964 7 924 44 47-1730 352-7665 2 8 8 44 5-5850 41-7668 8 25 11 50-2656 375-9062 2 9 8 7| 5-9395 44-4179 8 325 11 53-4562 399-7668 2 10 8 10i 6-3049 47-1505 8 626 8| 56-7451 424-3625 2 11 9 If 6-6813 49-9654 8 927 5| 60-1321 449-2118 3 9 5 7-0686 52-8618 9 28 31 63-6174 475-7563 3 1 9 81 7-4666 55-8382 9 329 Of 67-2007 502-5536 3 2i 9 11| 7-8757 58-8976 9 629 104 70-8823 530-0861 3 310 2A 8-2957 62-0386 9 930 74 74-C620 558-3522 3 410 5f 8-7265 65-2602 10 31 5 78-5400 587-3534 3 510 8f 9-1683 68-5193 10 332 2| 82-5160 617-0876 3 6 10 111 9-6211 73-1504 10 632 11| 86-5903 647-5568 3 7 11 3 10-0846 75-4166 10 933 91 90-7627 678-2797 3 811 64 10-5591 78-9652 11 34 61 95-0334 710-6977 3 911 9f 11-0446 82.5959 11 335 44 99-4021 743-3686 3 1012 5 11-5409 86-3074 11 6 36 14 103-8691 776-7746 3 1112 12-0481 90-1004 11 9 36 101J 108-4342 810-9143 4 12 6| 12-5664 93-9754 12 37 8|113-0976 848-1890 4 112 91 13-0952 97-9310 12 338 51117-8590 881-3966 4 2|13 1 13-6353 101-9701 12 639 31122-7187 917-7395 4 313 44 14-1862 103-0300 12 9 40 Of 127-6765 954-8159 4 413 7i 14-7479 110-2907 13 40 10 1132-7326 992-6274 4 5 ! 13 10.] 15-3206 114-5735 13 341 74 1 137 -8867 1031-1719 4 614 if 15-9043 118-9386 13 642 411143-1391 1070-4514 4 714 4 16-4986 123-3830 13 9 43 21 148-4696 1108-0645 4 8; 14 71 17.1041 127-9112 14 J43 111153-9384 1151-2129 4 914 11 17.7205 132-5209 14 344 94159-4852 1192-6940 4 1015 24 18.3476 137-2105 14 645 6f 165-1303 1234-9104 4 1115 5i 18.9858 142-0582 14 9 46 4 1170-8735 1277-8615 TABLE OF DIAMETERS OF CIRCLES, ETC. 299 Diam. Circum. Area. Gallons. 1321-5454 1365-9634 1407-5165 1457-0032 1503-6250 1550-9797 1599-0696 1647-8930 Diam. Circum. Area, Gallons. Ft. In. 15 15 3 15 6 15 9 16 16 3 16 6 16 9 Ft. In. Feet. 47 H 176-7150 47 10l 182-6545 48 8^188-6923 49 5f 194-8282 50 3i 201-0624 51 1 207-3946 51 10 (213-8251 52 7|220-3537 Ft. In. 17 17 3 17 6 17 9 18 18 3 18 6 18 9 Ft. In. Feet. 53 4|226-98061697-4516 54 2f '233-7055 1747-7431 54 llf 240-5287 1798-7698 55 9f247-4500 1850-5301 56 6i 254-4696 1903-0254 57 4 261-58721956-2537 58 If 268-8031 2010-2171 58 10f276-11712064-9HO DECIMAL EQUIVALENTS. FRACTIONS OF A LINEAL INCH CONVERTED INTO DECIMALS. 8ths. |fc = .8125 } = .9375 ff = .90625 |i = .96875 t = .453125 H = .484375 & = .125 1 = .515625 =.25 3 = .375 32nds. 64ths. = .546875 = .578125 | = .50 ^ = .03125 ^=.015625 = .609375 f = .625 & = .09375 ^f = .046875 = .640625 4 = .75 JO = .15625 ^ = .078125 = .671875 I = .875 j = .21875 ^=.109375 & = . 703125 tV = .28125 ^ = .140625 ft = .734375 # = .34375 ^i = . 171875 = .765625 16ths. -^ = .0625 4 = .40625 # = .46875 # = .53125 Jf = .203125 ^ = .234375 If = .265625 = .796875 - = .828125 - = . 859375 ft = .1875 # = .59375 If = .296875 - = .890625 tV = .3125 f | = .65625 * = .328125 = .921875 -ft = .4375 ft = .71875 || = .359375 = .953125 -^=.5625 U = .6875 H- = .78125 If = .84375 f = .390625 |j = . 421875 = .984375 1 Q W -* CONVERSION OF VULGAR FRACTIONS INTO DECIMALS. Fractions. Decimals. Fractions. Decimals. 1:2 .5 7:8 .875 1:3 .33333 5:12 .41666 2:3 .66666 7:12 .58333 1:4 .25 11:12 .925 3:4 .75 1:24 .04166 1:5 .2 5:24 .28333 3:5 .6 7:24 .29166 1:6 .16666 11:24 .45833 5:6 .83333 13 : 24 .54166 1:8 .125 17:24 .70833 3:8 .375 19:24 .79166 5:8 .625 23:24 .95833 DECIMAL EQUIVALENTS. 301 CONVERSION OF FRACTIONS OF AN INCH INTO DECIMALS OF A LINEAL FOOT. ^r Inch = 0-001375 feet, -sfe =0-00265 " -ji, =0-005208 - " =0-01041 ' : -]- * =0-02083 " Inch = 0-03125 feet. i " =0-04166 " =0-05208 " | =0-0625 " i " =0-07291 " CONVERSION OF INCHES AND FRACTIONS (UP TO 12 INCHES) INTO DECIMALS OF A LINEAL FOOT. Inches % X H % H K H 1 .08333 .09375 .10416 .11458 .125 .13541 .14588 .15639 2 .16066 .17707 .1875 .19792 .20832 .21873 .22914 .23965 3 .25 .26041 .270 .28125 .29166 .30208 .3125 .32291 4 .33333 .34375 .35416 .364 .375 .38541 .39588 .40639 5 .41666 .42707 .437 .44792 .45832 .46873 .47914 .48965 6 .5 .51041 .520 .53125 .54166 .55208 .2625 .57291 7 .58333 .593/5 .60416 .614 .625 .63541 .64588 .65639 8 .66666 .67707 .685 .69792 .70832 .71773 .72914 .73965 9 .75 .76041 .770 .78125 .79169 .80208 .8425 .82291 10 .83333 .84375 .85416 .864 .875 .88541 .89588 .90639 11 .91666 .92707 .937 .94792 .95832 .96873 .97914 .98965 12 1 foot. foot. foot. foot. foot. foot. foot. foot. CONVERSION OF INCHES INTO DECIMALS OF A LINEAL YARD. 1 inch = -0277 yard. 2 inches = -0555 " 3 " =-0833 " 4 " =-1111 " 5 inches = '1389 yard. 6 =-1666 " 7 " ='1944 " 8 " =-2222 " 9 inches = -25 yard. 10 " =-2778 " 11 " =-3055 " 12 " =-3333 " DECIMAL EQUIVALENTS OF POUNDS AND OUNCES AVOIRDUPOIS. Ozs. Ibs. \ = -015625 I = -03125 | = -046875 1 =-0625 1$ = -09375 2 =-125 2 -15625 Ozs. Ibs. 3 =-1875 3=-21875 4 ='25 41 = -28125 5 =-3125 5| = -34375 6 -373 Ozs. Ibs. Gi = -40625 7 =-4375 7 = -46875 8 =-5 8 = -53125 9 =-5625 9 -59375 Ozs. Ibs. 10 =-625 lOJ = -65625 11 =-6875 11 = -71875 12 =-75 12i = -78125 13 -8125 Ozs. Ibs. 13| = -84375 14 =-875 14 = -90625 15 =-9375 15 = -96875 16 =-1 302 SCANTLING AND TIMBER MEASURE. SCANTLING AND TIMBER, Accurately reduced to Inch Board Measure* EXPLANATION. The length of any piece of scantling, or timber, will be found in the left-hand column, under the side dimensions. The breadth and depth (or side dimensions), in inches, will be found at the head or center of each column of computations. Thus, on page 261, a piece of scantling 2h by 11 inches, side dimension, and 16 feet long, is shown to contain 36 feet and 8 inches, of board measure. On page 263, a piece of scantling 4 by 10 inches, side dimension, and 17 feet long, is shown to contain 56 feet 8 inches of board measure. The answer sought for, in all cases, will be found directly on the right of the length, and under the side dimensions. If a piece of scantling, or stick of timber, should exceed in length any provision which has been made in these tables, its contents would be shown by taking twice what is shown for half its length. Thus, a stick of timber, or piece of scantling, 46 feet long, would contain twice as many feet, board measure, as is shown in the table to be the contents of a stick 23 feet long. So also, one 39 feet long would contain as many feet, board measure, as these tables show opposite to 22 and 17 feet long, or 3 times the contents of one 13 feet long. TABLES. a by a. j] a by 3. 8 by 4-. a by 5. a by 6. a by 7. lo 1 0-4 -51 0-6 | o l 0-8 u o-io t 1 1- G. 1 1-2 J2 0-8 s2 I- 2 1-4 2 1-8 j2 2- "2 2-4 "*3 1- 3 1-6 J 3 2- 3 2-6 3 3- J 3 3-6 4 1-4 4 2- 4 2-8 4 34 4 4- 4 4-8 5 1-8 5 2-6 5 34 5 4-2 5 5- 5 5 ; 10 6 2- 6 3- 6 4- 6 5 6 6- 6 7- 7 2-4 7 3-6 7 4-8 7 5-10 7 7- 7 8-2 8 2-8 8 4- 8 5-4 8 6-8 8 8- 8 9-4 9 3- 9 4-6 9 6- 9 7-6 9 9- 9 10-6 10 3-4 10 5- 10 6-8 10 8-4 10 10- 10 11-8 11 3-8 11 5-6 11 7-4 11 9-2 11 il- 11 12-10 12 4- 12 6- 12 8- 12 10- 12 ia- 12 14- 13 4-4 13 6-6 13 8-8 13 10-10 13 13- 13 15-2 14 4-8 14 7- 14 9-4 14 11-8 14 14- 14 16-4 15 5- 15 7-6 15 10- 15 12-6 15 15- 15 17-6 16 5-4 16 8" 16 10-8 16 13-4 16 16- 16 18-8 17 5-8 17 8-6 17 11-4 17 14-2 17 17- 17 19-10 18 6- 18 9- 18 12- 18 15- 18 18- 18 21- 19 6-4 19 9-6 19 12-8 19 15-10 19 19- 19 22-2 20 6-8 20 10- 20 134 20 16-8 20 20- 20 23-4 21 7- 21 10-6 21 14- 21 17-6 21 21- 21 24-6 22 7-4 22 II- 22 14-8 22 18-4 22 22- 22 25-8 23 7-8 23 11-6 23 15-4 23 19-2 23 23- 23 26-10 24 8- 24 12- 24 16- 24 20- 24 24- 24 28- SCANTLING AND TIMBER MEASURE. 303 a by 8. 3 by U. 3 by 1O. 3 by 11. 3 by 5. 3 by 6. 12 1-4 2-8 14 1-6 3 fa 1-8 34 j\ 1-10 38 = 2 1-1 2-1 t 1 2 1-3 2-6 "'s 4- J 3 4-6 3 5 5-6 J 3 3-2 3 3-9 4 5-4 4 6- 4 68 4 7-4 4 4-2 4 5- 5 6-8 5 7-6 5 8-4 5 9-2 5 5-3 5 63 6 8- 6 9- 6 10- 6 11- 6 6-3 6 76 7 9-4 7 10-6 7 11-8 7 12-10 7 7-4 7 8-9 8 10-8 8 12- 8 13-4 8 14-8 8 8-4 8 10- 9 12- 9 136 9 15- 9 16-6 9 9-5 9 11-3 10 134 10 15- 10 16-8 10 18-4 10 10-5 10 12-6 11 14-8 11 166 11 18-4 11 20-2 11 11-6 11 13-9 12 16- 12 18- 12 20- 12 22- 12 12-6 12 15- 13 174 13 19-6 13 21-8 13 23-10 13 137 13 16-3 14 18-8 14 21- 14 23-4 14 25-8 14 14-7 14 17-6 15 20- 15 22-6 15 25- 15 27-6 15 15-8 15 18-9 16 21-4 16 24- 16 268 16 29-4 16 16-8 16 20- 17 22-8 17 256 17 28-4 17 31-2 17 17-9 17 21-3 18 24- 18 27- 18 30- 18 33- 18 18-9 18 22-6 19 25-4 19 28-6 19 318 19 34-10 19 19-10 19 23-9 20 26-8 20 30- 20 33-4 20 36-8 20 20-10 20 25- 21 28- 21 31-6 21 35- 21 38-6 21 21-11 21 26-3 22 29-4 22 33- 22 36-8 22 40-4 22 22-11 22 276 23 30-8 23 34-6 23 38-4 23 42-2 23 24- 23 28-9 24 32- 24 36- 24 40- 24 44- 24 25- 24 30- 3by 7. 3 A by 8. 3by9. 'A\ by 10. 34 by 11. a i by 13. Sl 1-6 -=1 1-8 f 1 l-ll "= 1 2-1 -Sl 2-4 -'1 26 jf 2-11 |2 3-4 If 3-9 l2 4-2 = 2 4-7 12 5. 3 4-5 *^3 5- Q 5-8 **3 6-3 3 7- ^3 7-6 4 5-10 4 6-8 4 7.6 4 8-4 4 9-2 4 10- 5 7-4 5 8-4 5 9-5 5 10-5 5 11-6 5 12-6 6 8-9 6 10- 6 11-3 6 12-6 6 13-9 6 15- 7 10-3 7 11-8 7 13-2 7 14-7 7 16- 7 17-6 8 11-8 8 13-4 8 15- 8 16-8 8 18-4 8 20- 9 13-2 9 15- 9 16-11 9 18-9 9 20-8 9 22-6 10 14-7 10 16-8 10 18-9 10 20-10 10 23- 10 25- 11 16-1 11 18-4 11 20-8 11 22-11 11 25-3 11 27-6 12 17-6 12 20- 12 226 12 25- 12 27-6 12 30- 13 19- 13 21-8 13 24-5 13 27-1 13 29-10 13 32-6 14 20-5 14 234 14 26-3 14 29-2 14 32-1 14 35- 15 21-11 15 25- 15 28-2 15 31-3 15 34-4 15 376 16 23-4 16 26-8 16 30- 16 33-4 16 36-8 16 40- 17 24-10 17 28-4 17 31 11 17 355 17 39- 17 42-6 18 26-3 18 30- 18 339 18 37.6 18 11 3 18 45- 19 27-9 19 31-8 19 358 19 39-7 19 43-7 19 47-6 20 29-2 20 33-4 20 376 20 41-8 20 45-10 20 50- 21 30-8 21 35- 21 395 21 43-9 21 48-2 21 526 22 32-1 22 36-8 22 41 3 22 45-10 22 50-5 22 55- 23 33-7 23 38-4 23 432 23 47-11 23 52-9 23 57-6 24 35- 24 40- 24 45- 24 50- 24 55- 24 GO- 304 SCANTLING AND TIMBER MEASURE. 3 by 3. || 3 by 4. 3 by 5. 3 by 6. 3 by 7. 3 by 8. i 0-9 1-6 la I- 2- Si 2 1-3 2-6 fa 1-6 3- F 1-9 3-6 |4 2- 4- 2-3 3 3- **3 3-9 3 4-6 Q 5-3 J 3 6- 4 3- 4 4- 4 5- 4 6- 4 7- 4 8- 5 3-9 5 5- 5 6-3 5 7-6 5 8-9 5 10 6 4-6 6 6- 6 7-6 6 9- 6 10-6 6 12- 7 5-3 7 7- 7 8-9 7 106 7 12-3 7 14- 8 6- 8 8- 8 10- 8 12- 8 14- 8 16- 9 6-9 9 9- 9 11-3 9 13-6 9 15-9 9 18 10 7-6 10 10- 10 12-6 10 15- 10 17-6 10 20- 11 8-3 11 Il- 11 13-9 11 166 11 19-3 11 22- 12 9- 12 ia- 12 15- 12 18- 12 21- 12 24- 13 9-9 13 13- 13 16-3 13 19-6 13 22-9 13 26- 14 10-6 14 14- 14 17-6 14 21- 14 24-6 14 28- 15 11-3 15 15- 15 18-9 15 22-6 15 26-3 15 30- 16 12- 16 16- 16 20- 16 24- 16 28- 16 32- 17 12-9 17 17- 17 21-3 17 25-6 17 29-9 17 34- 18 13-6 18 18- 18 22-6 18 27- 18 31-6 18 36- 19 14-3 19 19- 19 23-9 19 28-6 19 33-3 19 38- 20 15- 20 20- 20 25- 20 30- 20 35- 20 40- 21 15-9 21 21- 21 26-3 21 31-6 21 36-9 21 42- 22 16-6 22 22- 22 27-6 22 33- 22 38-6 22 44- 23 17-3 23 23- 23 28-9 23 34-6 23 40-3 23 46- 24 18- 24 24- 24 30- 24 36- 24 42. 24 48- 3 by 9. || 3bylO. 3 by 11. 3 bv 13. 4- by. 4:. 4: by 5. 1 23 5 1 2-6 *l 2-9 ^1 3- j= l 1-4 -s 1 1-8 la 4-6 2 5- ! 3 5-6 fo J* 6- 2 2-8 2 3-4 5 3 6-9 ^3 7-6 J 3 8-3 J 3 9- 3 4- J 3 5- 4 9- 4 10- 4 11- 4 12- 4 5-4 4 6-8 5 11-3 5 12-6 5 13'9 5 15- 5 6-8 5 8-4 6 13-6 6 15- 6 16-6 6 18- 6 8- 6 10- 7 15-9 7 17-6 7 19-3 7 21- 7 9-4 7 11-8 8 18- 8 20- 8 22- 8 24- 8 10-8 8 13-4 9 20-3 9 22-6 9 24-9 9 27- 9 12- 9 15- 10 22-6 10 25- 10 27-6 10 30- 10 13-4 10 16-8 11 24-9 11 27-6 11 30-3 11 33- 11 14-8 11 18-4 12 27- 12 30- 12 33- 12 36- 12 16- 12 20- 13 293 13 32-6 13 35-9 13 39- 13 17-4 13 21-8 14 31-6 14 35- 14 38-6 14 42- 14 18-8 14 23-4 15 339 15 37-6 15 41-3 15 45- 15 20- 15 25- 16 36- 16 40- 16 44- 16 48- 16 21-4 16 26-8 17 38-3 17 42-6 17 46-9 17 61- 17 22-8 17 28-4 18 40-6 18 45- 18 49-6 18 54- 18 24- 18 30- 19 42-9 19 47-6 19 52-3 19 57- 19 25-4 19 31-8 20 45- 20 50- 20 55- 20 60- 20 26-8 20 33-4 21 473 21 52-6 21 57-9 21 63- 21 28- 21 35- 22 49-6 22 55- 22 60-6 22 66- 22 29-4 22 36-8 53 51-9 23 57-6 23 63-3 23 69- 23 30-8 23 38-4 24 64- 24 60- 24 66- 24 72- 24 32- 24 40- SCANTLING AND TIMBER MEASURE. 303 4r by 6. 4: by 7. 4rby8. 4 by 9. 4: by 10. 4:byll. jj 2- A I 2-4 41 2-8 sl 3- J| 3-4 5 1 38 F2 4- h 4-8 I 2 5-4 I2 6- 2 6-8 I2 7-4 *^3 6- ^3 7- 8- J 3 9- ^3 10- ^3 11- 4 8- 4 9-4 4 10-8 4 12' 4 13-4 4 14-8 5 10- 5 11-8 5 13-4 5 15- 5 16-8 5 18-4 6 12- 6 14- 6 16- 6 18- 6 20- 6 22- 7 14- 7 16-4 7 18-8 7 2i* 7 , 23^ 7 25-8 8 16- 8 18-8 8 21-4 8 M 8 26-8 .9 29-4 9 18- 9 21- 9 24- 9 27- 9 30- 9 33 10 20- 10 23-4 10 26-8 10 30- 10 334 10 :*68 11 22- 11 25-8 11 29-4 11 33- 11 36-8 11 404 12 24- 12 28- 12 32- 12 36- 12 40- 12 44- 13 26- 13 30-4 13 34-8 13 39- 13 43-4 13 47-8 14 28- 14 32-8 14 37-4 14 42- 14 46-8 14 51-4 15 30- 15 35- 15 40 15 45- 15 50- 15 55- 16 32- 16 37-4 16 42-8 16 48- 16 53-4 16 58-8 17 34- 17 39-8 17 45-4 17 51- 17 56-8 17 62-4 18 36- 18 42- 18 48- 18 54- 18 60- 18 66- 19 38- 19 44-4 19 50-8 19 57- 19 63-4 19 69-8 20 40- 20 46-8 20 53-4 20 60- 20 66-8 20 73-4 21 42- 21 49- 21 56- 21 63- 21 70- 21 77- 22 44- 22 51-4 22 58-8 22 66- 22 73-4 22 80-8 23 46- 23 53-8 23 61-4 23 69- 23 76-8 23 84-4 24 48- 24 56- 24 64- 24 72' 24 80- 24 88- 4: by 12. 5 by 5. 5 by 6. 5 by 7. 5 by 8. 5 by 9. f 1 4- 41 2-1 S 1 2-6 41 2-11 4 1 3-4 t'\ 39 |2 8- =2 4-2 g2 5- 2 5-10 l2 6-8 2 7-6 Q 12- 3 63 J 3 7-6 ^3 8-9 ^3 10- 3 11-3 4 16- 4 8-4 4 10- 4 11-8 4 13-4 4 15- 5 20- 5 10-5 5 12-6 5 14-7 5 16-8 5 18-9 6 24- 6 12-6 6 15- 6 176 6 20- 6 22-6 7 28- 7 14-7. 7 17-6 7 20-5 7 23-4 7 26-3 8 32- 8 16-8 8 20- 8 23-4 8 26-8 8 30- 9 36- 9 18-9 9 22-6 9 26-3 9 30- 9 33-9 10 40- 10 20-10 10 25- 10 29-2 10 33-4 10 37-6 11 44- 11 22-11 11 27-6 11 32-1 11 36-8 11 41-3 12 48- 12 25- 12 30- 12 35- 12 40- 12 45- 13 52- 13 27-1 13 32-6 13 37-11 13 43-4 13 48-9 14 56- 14 29-2 14 35- 14 40-10 14 468 14 52-6 15 60- 15 31-3 15 37-6 15 43-9 15 50- 15 56-3 16 64- 16 33-4 16 40- 16 46-8 16 53-4 16 60- 17 68- 17 35-5 17 42-6 17 49-7 17 56-8 17 63.9 18 72- 18 37-6 18 45- 18 52-6 18 60- 18 67-6 19 76- 19 39-7 19 47-6 19 55-5 19 63-4 19 71-3 20 80- 20 41-8 20 50- 20 58-4 20 66-8 20 75- 21 84- 21 43-9 21 52-6 21 61-3 21 70- 21 78-9 22 88- 22 45-10 22 55- 22 64-2 22 63-4 22 82-6 23 92- 23 47-11 23 57-6 23 67-1 23 76-8 23 86-3 24 96- 24 50- 24 60. 24 70- 24 80- 24 90- 13** 306 SCANTLING AND TIMBER MEASURE. 5 by 10. GbyG. Gby 7. 6 by 8. 7 by 7. 7 by 8. a,l 4-2 41 3 .5! 3-6 f 1 4- 51 4-1 .5! 4-8 8-4 |2 6- l2 7- S2 8- 12 8-2 |2 9-4 3 12-6 "^3 9- J 3 10-6 J 3 12- J 3 12-3 ^3 14- 4 16-8 4 12- 4 14- 4 16- 4 16-4 4 18-8 5 20-10 5 15- 5 17-6 5 20- 5 205 5 24-4 6 25- 6 18- 6 21- 6 24- 6 24-6 6 28- 7 29-2 7 21- 7 24-6 7 28- 7 28-7 7 328 8 33-4 8 24- 8 28- 8 32- 8 32-8 8 37-4 9 37-6 9 27- 9 31-6 9 36- 9 36-9 9 42- 10 41-8 10 30- 10 35- 10 40- 10 40-10 10 4G-8 11 45-10 11 33- 11 38-6 11 44- 11 44-11 11 51-4 12 50- 12 36- 12 42- 12 48- 12 49- 12 56- 13 54-2 13 39- 13 45-6 13 52- 13 53-1 13 60-8 14 58-4 14 42- 14 49- 14 56- 14 57-2 14 65-4 15 62-6 15 45- 15 52-6 15 60- 15 61-3 15 70- 16 66-8 16 48- 16 56- 16 64- 16 65-4 16 74-8 17 70-10 17 51- 17 59-6 17 68- 17 69-5 17 79-4 18 75- 18 54- 18 63- 18 72- 18 73-6 18 84- 19 79-2 19 57- 19 66-6 19 76- 19 77-7 19 88-8 20 83-4 20 60- 20 70- 20 80- 20 81-8 20 93-4 21 87-6 21 63- 21 73-6 21 84- 21 85-9 21 98- 22 91-8 22 66- 22 77- 22 83- 22 89-10 22 102-8 23 95-10 23 69- 23 80-6 23 92- 23 93-11 23 107-4 24 100- 24 72- 24 84- 24 96- 24 98- 24 112- 7 by 9. 8 by 8. 8 by 9. j 8 by 10. 9 by 9. 9 by 10. c 1 5-3 5 I 5-4 fl 6- 1 G-8 -Si 6-9 l 7-6 k 10-6 15-9 k 10-8 16- k 12- 18- !* 13-4 20- la *3 13-6 20-3 15- 22.6 4 21- 4 21-4 4 24- 4 2G-8 4 27- 4 30 5 26-3 5 26-8 5 30- 5 33-4 5 33-9 5 37-6 6 31-6 6 32- 6 36- 6 40- 6 40-G 6 45- 7 36-9 7 37-4 7 42- 7 46-8 7 47-3 7 52-6 8 42- 8 42-8 8 48- 8 53-4 8 54- 8 60- 9 473 9 48- 9 54- 9 60- 9 609 9 67-6 10 52-6 10 53-4 10 60- 10 668 10 676 10 75- 11 57-9 11 58-8 11 66- 11 73-4 11 743 11 82-6 12 63 12 64- 12 72- 12 80- 12 81- 12 90- 13 68-3 13 69-4 13 78- 13 86-8 13 87-9 13 97-6 14 73-6 14 74-8 14 84- 14 93-4 14 946 14 105 15 78-9 15 80- 15 90- 15 100- 15 101 3 15 112-6 16 84- 16 85-4 16 96- 16 10G-8 16 108 16 120- 17 89-3 17 90-8 17 102- 17 113-4 17 1149 17 127-6 18 94-6 18 96- 18 108- 18 120- 18 121 6 18 135 19 99-9 19 101-4 19 114- 19 126-8 19 128-3 19 142-6 20 105- 20 1068 20 120- 20 133-4 20 135- 20 150- 21 110-3 21 112- 21 126- 21 140- 21 141-9 21 157-6 22 115-6 22 117-4 22 132- 22 146-8 22 148-6 22 165 23 120-9 23 122-8 23 138 23 153-4 23 155-3 23 172-6 24 126- 24 128- 24 144- 24 160- 24 162- 24 180- TO FIND THE CHORDIAL PITCH OF ANY GIVEN WHEEL. Wo take the number of degrees in a circle, 360, and divide that number by the number of teeth iu the wheel, which gives us the number of degrees and minutes to the arc pitch ; of this amount, whatever it may be, we take one half and look in a table of natural sines for the sine of the half arc pitch. Then multiply the s'ue so found by 2 and by the radius in inches, and the product is the chordial pitch. EXAMPLE : What will be the chordial pitch of a pinion 8 inches in diameter and to contain 12 teeth I 360o-r-12 (No. of teeth) =30; take half =15; now the sine of 15 in the table is '2588X2 = .5176x6 (radius of pin- ion) = 2.0706 : which is the true chordial pitch. l*g. Sine. Deg. Siiie. Deg. Sine. Deg. Sine. 00 12 20791 24 40673 35 57357 1 01745 13 22495 25 4-^261 36 58778 2 03489 14 24192 26 438:37 37 60181 3 -05233 15 - -25881 27 45399 38 61566 4 06975 16 27563 28 46947 39 62932 5 08715 17 29237 | 29 48480 40 64278 6 10452 18 39901 ! 30 50000 41 65605 7 12186 19 32556 31 51503 42 66913 8 13917 20 34202 32 52991 43 68199 9 =15643 21 35836 33 54463 44 69465 10 17364 22 37460 34 55919 45 70710 11 .19080 23 39073 TABLE OF THE PROPORTIONAL RADII OF WHEELS. Fro m to I Inch. No. of' I7 teeth. [ % H K H Z /4 7 A l 10 0-405 0-607 0-809 1-011 1-214 1-416 1-618 11 0-444 0-666 0-887 1-109 1-331 1.553 1-775 12 0-483 0-724 0-966 1-207 1-449 1-690 1-932 13 0-522 0-783 1-045 1-306 1-567 1-828 2-089 14 0-562 0-843 1-123 1-404 1-685 1-966 2-247 15 0-601 0-902 1-202 1-503 1-804 2-104 2-405 16 0-641 0-961 1-281 1-G02 1-922 2-243 2-563 17 0-680 1-020 1-361 1-701 2-041 2-381 2-721 18 0-720 1-080 1-440 1-800 2-160 2-519 2-879 19 0-759 1-139 1-519 1-899 2-278 2-658 3-038 20 0-799 1-199 1-598 1-998 2-397 2-797 3-196 21 0-839 1-258 1-677 2-097 2-516 2-935 3-355 22 0-878 1-318 1-757 2-196 2-635 3-074 3-513 23 0-918 1-377 1-836 2-295 2-754 3-213 3-672 24 0-958 1-437 1-915 2-394 2-873 3-352 3*831 25 0-997 1-496 1-995 2-493 2-992 3-491 3-989 26 1-037 1-556 2-074 2-593 3-111 3-630 4-148 27 1-077 1-615 2-154 2-692 3-230 3-769 4-307 28 1-116 1-675 2-233 2-791 3-349 3-908 4-466 29 1-156 1-734 2-312 2-890 3-468 4-047 4-625 30 1-196 1-794 2-392 2-990 3-588 4-186 4-783 31 1-236 1-853 2-471 3-089 3-707 4-325 4-942 32 1-275 1-913 2-551 3-188 3-826 4-464 5-101 33 1-315 1-973 2-630 3-288 3-945 4-603 5-2GO 34 1-355 2-032 2-710 3-387 4-064 4-742 5-419 35 1-394 2-092 2-789 3-486 4-183 4-881 5-578 36 1-434 2-151 2-868 3-586 4-303 5-020 5-737 37 1-474 2-211 3-948 3-685 4-403 5-159 5-896 38 1-514 2-271 3-027 3-784 4-541 5-298 6-055 39 1-553 2-330 3-107 3-884 4-660 5-437 6-214 40 1-593 2-390 3-186 3-983 4-780 5-576 6-373 41 1-G33 2-449 3-266 4-082 4-899 5-715 6-532 42 1-673 2-509 3-345 4-182 5-018 5-854 6-691 43 1-712 2-569 3-425 4-281 5-137 5-994 6-850 44 1-752 2-628 3-504 4-381 5-257 6-133 7-009 45 1-792 2-688 3-584 4-480 5-376 6-272 7-168 PROPORTIONAL RADII OP WHEELS. 309 No. of teeth. fc X K S A k "A l 46 832 2-748 3-663 4-579 5-495 6-411 7-327 47 871 2-807 3-743 4-679 5-614 6-550 7-486 48 911 2-867 3-822 4-778 5-734 6-689 7-645 49 951 2-927 3-902 4-877 5-853 6-828 7-804 50 991 2-986 3-982 4-977 5-972 6-968 7-963 51 2-031 3-046 4-061 5-076 6-092 7-107 8-122 52 2-070 3-105 4-141 5-176 6-211 7-246 8-281 53 2-110 3-165 4-220 5-275 6-330 7-385 8-440 54 2-150 3-225 4-300 5-375 6-449 7-524 8-599 55 2-190 3-284 4-379 5-474 6-569 7-663 8-758 56 2-229 3-344 4-459 5*573 6-688 7-803 8-917 57 2-269 3-404 4-538 5-673 6-807 7-942 9-076 58 2-309 3-463 4-618 5-772 6-927 8-081 9-235 59 2-349 3-523 4-697 5-872 7-046 8-220 9-395 60 2-388 3-583 4-777 5-971 7-165 8-359 9-554 61 2-428 3-642 4-856 6-070 7-285 8-499 9-713 62 2-468 3-702 4-936 6-170 7-404 8-638 9-872 63 2-508 3-762 5-015 6-269 7-523 8-777 10-031 64 2-548 3-821 5-095 6-369 7-643 8-916 10-190 65 2-587 3-881 5-175 6-468 7-762 9-055 10-349 66 2-627 3-941 5-254 6-568 7-881 9-195 10-508 67 2-667 4-000 5-334 6-667 8-000 9-334 10-667 68 2-707 4-060 5-413 6-767 8-120 9-473 10-826 69 2-746 4-120 5-493 6-866 8-239 9-612 10-985 70 2-786 4-179 5-572 6-965 8-358 9-752 11-145 71 2-826 4-239 5-652 7-065 8-478 9-891 11-304 72 2-866 4-299 5-731 7-164 8-597 10-030 11-463 73 2-905 4-358 5-811 7-264 8-716 10-169 11-622 74 2-945 4-418 5-890 7-3G3 8-836 10-308 11-781 75 2-985 4-478 5-970 7-463 8-955 10-448 11-940 76 3-025 4-537 6-050 7-562 9-074 10-587 12-099 77 3-065 4-597 6-129 7-631 9-194 10-726 12-258 78 3-104 4-657 6-209 7-761 9-313 10-865 12-417 79 3-144 4-716 6-288 7-860 9-432 11-004 12-577 80 3-184 4-776 6-368 7-960 9-552 11-144 12-736 81 3-224 4-836 6-447 8-059 9-671 11-283 12-895 82 3-263 4-895 6-527 8-159 9-790 11-422 13-054 83 3-303 4-955 6-607 8-258 9-910 11-561 13-213 84 3-343 5-015 6-686 8-358 10-029 11-701 13-372 85 3-383 5-074 6-766 8-457 10-148 11-840 13-531 86 3-423 5-134 6-845 8-556 10-268 11-979 13-690 87 3-462 5-194 6-925 8*656 10-387 12-118 13-849 88 3-502 5-253 7-004 8-755 10-506 12-258 14-009 89 3-542 5-313 7-084 8-855 10-626 12-397 14-168 90 3-582 5-373 7-163 8-954 10-745 12-536 14-327 91 3-622 5-432 7-243 9-054 10-864 12-675 14-486 92 3-661 5-492 7-323 9-153 10-984 12-815 14-645 93 3-701 5-552 7-402 9-253 11-103 12-954 14-804 310 PROPORTIONAL RADII OF WHEELS. No. of teeth. K % X X * H 1 94 3-741 5-611 7-482 9-352 11-223 13.093 14-963 95 3-781 5-671 7-561 9-452 11-342 13-232 15-122 96 3-820 5-731 7-641 9-551 11-461 13-371 15-282 97 3-860 5-790 7-720 9-650 11-581 13-511 15-441 98 3-900 5-850 7-800 9-750 11-700 13-650 15-600 99 3-940 5-910 7-880 9-849 11-819 13-789 15-759 100 3-980 5-969 7-959 9-949 11-938 13-928 15-918 101 4-019 6-029 8-039 10-048 12-058 14-068 16-077 102 4-059 6-089 8-118 10-148 12-177 14-207 16236 103 4-099 6-148 8-198 10-247 12-297 14-346 16-396 104 4-139 6-208 8-277 10-347 12-416 14-485 16-555 105 4-178 6-268 8-357 10-446 12-535 14-625 16-714 106 4-218 6-327 8-436 10-546 12-655 14-764 16-873 107 4-258 6-387 8-516 10-645 12-774 14-903 17-032 108 4-298 6-447 8-596 10-744 12-893 15-042 17-191 109 4-338 6-506 8-675 10-844 13-013 15-182 17-350 110 4-377 6-566 8-755 10-943 13-132 15-321 17-509 111 4.417 6-626 8-834 11.043 13-251 15-460 17-669 112 4-457 6-685 8-914 11-142 13-371 15-599 17-828 113 4-497 6-745 8-993 11-242 13-490 15-738 17-987 114 4-536 6-805 9-073 11341 13-609 15-878 18-146 115 4-576 6-864 9-153 11-441 13-729 16-017 18-305 116 4-616 6-924 9-232 11-540 13-848 16-156 18-464 117 4-656 6-984 9-312 11-640 13-968 16-295 18-623 118 4-696 7-043 9-391 11-739 14-087 16.435 18-782 119 4-735 7-103 9-471 11-839 14-206 16-574 18-942 120 4-775 7-163 9-550 11-938 14-326 16-713 19-101 121 4-815 7-222 9-630 12-037 14-445 16-852 19-260 122 4-855 7-282 9-710 12-137 14-564 16-992 19-419 123 4-895 7-342 9-789 12-236 14-684 17-131 19-578 124 4-934 7-402 9-869 12-336 14-803 17-270 19-737 125 4-974 7-461 9-948 12-435 14-922 17-410 19-896 126 5-014 7-521 10-028 12-535 15-042 17-549 20-056 127 5-054 7-581 10-107 12-634 15-161 17-688 20-215 128 5-093 7-640 10-187 12-734 15-280 17-827 20-374 129 5-133 7-700 10-267 12-833 15-400 17-966 20-533 130 5-173 7-760 10-346 12-933 15-519 18-106 20-692 131 5-213 7-819 10-426 13-032 15-638 18-215 20-851 132 5-253 7.879 10505 13-132 15-758 18-384 21-010 133 5-292 7-939 10-585 13-231 15-877 18-523 21-170 134 5-332 7-998 10-664 13-331 15-997 18-663 21-329 135 5-372 8-058 10-744 13-430 16-116 18-802 21-488 136 5-412 8-118 10-824 13-529 16-235 18-941 21-647 137 5-452 8-177 10-903 13-629 16-355 19-080 21-806 138 5-491 8-237 10-983 13-728 16-474 19-220 21-965 139 5-53L 8-297 11-062 13-828 16-593 19-359 22-124 140 5-571 8-356 11-142 13-927 16-713 19-498 22-284 141 5-611 8-416 11-221 14-027 16-832 19-637 22-443 PROPORTIONAL RADII OP WHEELS. 311 No. of teeth. # H K H X ft 1 142 5-650 8-476 11-301 14-126 16-951 19-777 22-602 143 5-690 8-535 11-381 14-226 17-071 19-916 22-761 144 5-730 8-595 11-460 14-325 17-190 20-055 22-920 145 5-770 8-655 11-540 14-425 17-309 20-194 23-079 146 5-810 8-714 11-619 14-524 17-429 20-334 23-238 147 5-849 8-774 11-699 14-623 17-548 20-473 23-398 148 5-889 8-834 11-778 14-723 17-668 20-612 23-557 149 5-929 8-893 11-858 14-822 17-787 20-751 23-716 150 5-969 8-953 11-938 14-922 17-906 20-891 23-875 151 6-009 9-013 12-017 15-021 18-026 21-030 24-034 152 6-048 9-072 12-097 15-121 18-145 21-169 24-193 153 6-088 9-132 12-176 15-220 18-264 21-308 24-352 154 6-128 9-192 12-256 15-320 13-384 21-448 24-512 155 6-168 9-252 12-335 15-419 18-503 21-587 24-671 156 6-207 9-311 12-415 15-519 18-622 21-726 24-830 157 6-247 9-371 12-494 15-618 18-742 21-865 24-989 158 6-287 9-431 12-574 15-718 18-861 22-005 25-148 159 6-327 9-490 12-654 15-817 18-980 22-144 25-307 160 6-367 9-550 12-733 15-917 19-100 22-283 25-466 161 6-406 9-610 12-813 16-016 19-219 22-422 25-626 162 6-446 9-669 12-892 16-115 19-339 22-562 25-785 163 6-486 9-729 12-972 16-215 19-458 22-701 25-944 164 6-526 9-789 13-052 16-314 19-577 22-840 26-103 165 6-566 9-848 13-131 16-414 19-697 22-979 26-262 168 6-605 9-908 13-211 16-513 19-816 23-119 26-421 167 6-645 9-968 13-290 16-613 19-935 23-258 26-580 168 6-685 10.027 13-370 16-712 20-055 23-397 26-740 169 6-725 10-087 13-449 16-812 20-174 23-536 26-899 170 6-764 10-147 13-529 16-911 20-293 23-676 27-058 171 6-804 10-206 13-609 17-011 20-413 23-815 27-217 172 6-844 10-266 13-688 17-110 20-532 23-954 27-376 173 6-884 10-326 13-768 17-210 20-651 24-093 27-535 174 6-924 10-385 13-847 17-309 20-771 24-233 27-694 175 6-963 10-445 13-927 17-409 20-890 24-372 27-854 176 7-003 10-505 14-006 17-508 21-010 24-511 28-017 177 7-043 10-564 14-086 17-607 21-129 24-650 28-172 178 7-083 10-624 14-166 17-707 21-248 24-790 28-331 179 7-123 10-C84 14-245 17-806 21-368 24-929 28-490 180 7-162 10-744 14-325 17-906 21-487 25-068 28-649 181 7-202 10-803 14-404 18-005 21-6C6 25-207 28-808 182 7-242 10-863 14-484 18-105 21-726 25-347 28-968 183 7-282 10-923 14*563 18-204 21-845 25-486 29-127 184 7-321 10-982 14-643 18-304 21-964 25-625 29-286 185 7-361 11-042 14-723 18-403 22-084 25-764 29-445 186 7-401 11-102 14-802 18-503 22-203 25-904 29-607 187 7-441 11-161 14-882 18-602 22-323 26-043 29-763 188 7-481 11-221 14-961 18-702 22-442 26-182 29-923 189 7-520 11-281 15-041 18-801 22-561 26-321 30-082 312 PROPORTIONAL RADII OF WHEELS. No. of teeth. */4 H K X H H 1 190 7-560 11-340 15-120 18-901 22-681 26-461 30-241 191 7-600 11-400 15-200 19-000 22-800 26-600 80-400 192 7-640 11-460 15-280 19-099 22-919 26-739 30-559 193 7-680 11-519 15-359 19-199 23.039 26-878 30-718 194 7-719 11-579 15-439 19-298 23-158 27-018 30-877 195 7-759 11-639 15-518 19-398 23-277 27-157 31-037 196 7-799 11-698 15-598 19-497 23-397 27-296 31-196 197 7-839 11-758 15-677 19-597 23-516 27-436 31-355 198 7-879 11-818 15-757 19-696 23-636 27-575 31-514 1*9 7-918 11-877 15-837 19-796 23-755 27-714 31-673 200 7-958 11-937 15-916 19-895 23-874 27-853 31-832 201 7-998 11-997 15-996 19-995 23-994 27-993 31-991 202 8-038 1-2-056 16-075 20-094 24-113 28-132 32-151 203 8-077 12-116 16-155 20-194 24-232 28-271 32-310 204 8-117 12-176 16-234 20-293 24-352 28-410 32-469 205 8-157 12-236 16-314 20-393 24-471 28-550 3-2-6-28 206 8-197 12-295 16-394 20-492 24-f>90 28-689 32-787 207 8-237 12-355 16-473 20-591 24-710 28-828 3-2-946 208 8-276 12-415 16-553 20-691 24-829 28-967 33-106 209 8-316 12-474 16-632 20-790 24-948 29-107 33-265 210 8-356 12-534 16-712 20-890 25-068 29-246 33-424 211 8-396 12-594 16-791 20-989 25-187 29-385 33-583 212 8-436 12-653 16-871 21-089 25-307 29-524 33-742 213 8-475 12-713 16-951 21-188 25-4-26 29-664 33-901 214 8-515 12-773 17-030 21-288 25-545 29-803 34-060 215 8-555 12-832 17-110 21-387 25-665 29-942 34-220 216 8-595 12-892 17-189 21-487 25-784 30-081 34-379 217 8-634 12-952 17-269 21-586 25-903 30-221 34-538 218 8-674 13-011 17-349 21-686 26-023 30-360 34-697 219 8-714 13-071 17-420 21-786 26-142 30-499 34-856 220 8-754 13-131 17-508 21-885 26-261 30-638 35-015 221 8-794 13-190 17-587 21-984 26-381 30-778 35-174 222 8-833 13-250 17-667 22-084 26-500 30-917 35-334 223 8-873 13-310 17-746 22-183 26-620 31-056 35-493 224 8-913 13-369 17-826 22-282 26-739 31-195 35-652 225 8-953 13-429 17-906 22-382 26-858 31-335 35-811 226 8-993 13-489 17-985 22-481 26-978 31-474 35-970 227 9-032 13-548 18-065 22-581 27-097 31-613 36-129 228 9-072 13-608 18-144 22-680 27-216 31-752 36-289 229 9-112 13-668 18-224 22-780 27-336 31-892 36-448 230 9-152 13-728 18-303 22-879 27-455 32-031 36-607 231 9-191 13-787 18-383 22-979 27-574 3-2-170 36.766 232 9-231 13-847 18-463 23-078 27-694 3-2-309 36-925 233 9-271 13-907 18-542 23-178 27-813 32-449 37-084 234 9-311 13.966 18-622 23-277 27-933 3-2-588 37-243 235 9-351 14-026 18-701 23-377 28-052 32-727 37-403 236 9-390 14-086 18-781 23-476 28-171 3-2-867 37-562 237 9-430 14-145 18-860 23-576 28-291 33-006 37-721 PROPORTIONAL RADII OF WHEELS. 313 xo. of T/ ,, teeth. A H % ft % H 1 238 9-470 14-205 18-940 23-675 28-410 33-145 37-880 2^9 9-510 14-265 19-020 23-774 28-.? 29 33-284 38-039 240 9-550 14-324 19-099 23-874 28-649 33-424 38-198 241 9-589 14-384 19-179 23-973 28-768 33-563 38-357 242 9-629 14-444 19-258 24-073 28-887 33-702 38-517 243 9-669 14-503 \ 19-338 24-172 29-007 33-841 38-676 244 9-709 14-563 19 417 24-272 29-126 33-981 38-835 245 9-749 14-623 19-497 24-371 29-246 34-120 38-9^ 246 9-788 14-682 1 19-577 24-471 29-365 34-259 39-lo 247 9-828 14-742 \ 19-656 24-570 29-484 34-398 39-312 248 9.868 14-802 19-736 24670 29-604 34-538 39-472 249 9-908 14-861 19-815 24-769 29-723 34-677 39-631 2CO 9-947 14-921 19-895 24-869 39-842 34-816 39-790 2U 9-987 14-981 19974 24-968 29-962 34-955 39-949 252 10-027 15-041 20-054 25-068 30-081 35-095 40-108 253 10-067 15-100 20-134 25-167 30-200 35-234 40-267 254 10-107 15-160 20-213 i 25-267 30-320 35-373 40-426 255 10-146 15-220 20-293 25-366 30-439 35-512 40-586 2C6 10-186 15-279 20-372 25-465 30-559 35-652 40-745 257 10-226 15-339 20-452 25-565 30-678 35-791 40-904 258 10-266 15-399 20-532 25-664 30-797 35-930 41-063 219 10-306 15-458 20-611 25-764 30-917 36-Oo9 41-222 2(50 10-345 15-518 20-691 25-863 31-036 36-209 41-381 261 10-385 15-578 20-770 25-963 31-155 36-348 41-540 262 10-425 15-637 20-850 26-062 31-275 36-487 41-700 263 10-465 15-697 20-929 26-162 31-394 36-626 41-859 264 10-504 15-757 21-009 26-261 31-513 36-766 42-018 265 10-544 15-816 21-089 26.361 31-633 36-905 42-177 266 10-584 15-876 21-168 26-460 31-752 37-044 42-336 267 10-624 15-936 21-248 26-560 31-872 37-183 42-495 268 10-664 15-995 21-327 26-659 31-991 37-323 42-655 269 10-703 16-055 21-407 26-759 32-110 37-462 42-814 270 10-743 16-115 21-486 26-858 32-230 37-601 42-973 271 10-783 16-175 21-566 26-958 32-349 37-741 43-132 272 10-823 16-234 21-646 27-057 32-468 37-880 43-291 273 10-863 16-294 21-725 27-156 32-588 38-019 43-450 274 10-902 16-354 21-805 27-256 32-707 38-158 43-609 275 10-942 16-413 21-884 27".<55 3^-826 38-298 43-769 278 10-982 16-473 21-964 27-455 32-946 38-437 43-928 277 11022 16-533 22-043 27-554 33-065 38-576 44-087 278 11-062 16-592 22-123 27-654 33-185 38-715 44-246 279 11-101 16-652 22-203 27-753 33-304 38-855 44-405 280 11-141 16-712 22-282 27-853 33-423 38-994 44-564 281 11-181 16-771 22-362 27-952 33-543 39-133 44-724 282 11-221 16-831 22-441 28-052 33-662 39-272 44-883 283 11-260 16-891 22-521 28-151 33-781 39-412 45-042 284 11-:?00 16-950 22-600 28-251 33-901 39-551 45-201 285 11-340 1 17-010 22-680 28-3CO 34-020 39-690 45-360 14 314 PROPORTIONAL RADII OF WHEELS. No. of 1 teeth. X # % ft & X l 286 11.380 17-070 22-760 28-450 ! 34-139 39-829 45-519 8K7 11-420 17-129 22-839 28-549 34-259 ! 39-969 45-678 288 11-459 17-189 2-919 28-648 34-378 40-108 45-838 289 11-499 17-249 22-998 28-748 34-498 40-247 45-997 290 11-539 17-308 23-078 28-847 34-617 40-386 46-156 291 11-579 17-368 23-158 28-947 34-736 40-526 46-315 292 11-619 17-428 23-237 29-046 34-856 40-665 46-474 293 11-658 17-488 23-317 29-146 34-9.75 40-804 46-633 294 11-698 17-547 23-396 29245 35-094 40-943 46-792 295 11-738 17-607 23-476 29-345 35-214 41-083 46-952 296 11-778 17-667 23-555 29-444 35-333 41-222 47-111 297 11-817 17-726 23-635 29-544 35-452 41-361 47-270 298 11-857 17-786 23-715 29-643 35-572 41-500 47-429 299 11-897 17-846 23-794 29-743 35-691 41-640 47-588 300 11-937 17-905 23-874 29.842 35-811 41-779 47-747 TABLE OF THE PROPORTIONAL RADII OF WHEELS. From 1) to 3 Inches Pitch, No. Of! l y teeth. : 1* IX 2 2K 1% 3 15 3-006 3-607 4-209 4-810 5-411 6-012 7-215 16 3-204 3-844 4-485 5-126 5-767 6-407 7-689 17 3-401 4-082 4-762 5-442 6-122 6-803 8-163 18 3-599 4-319 5-039 5-759 6-479 7-198 8-638 19 3-797 4-557 5-316 6-076 6-835 7-594 9-113 20 3-995 4-794 5-593 6-392 7-192 7-991 9-589 21 4-193 5-032 5-871 6-710 7-548 8-387 10.064 22 4-392 5-270 6-148 7-027 7-905 8-783 10-540 23 4-590 . 5-508 6-426 7-344 8-262 9-180 11-016 24 4-788 5-746 6-704 7-661 8-619 9-577 11-492 25 4-987 5-984 6-981 7-979 8-976 9-973 11-968 26 5-185 6-222 7-259 8-296 9-333 10-370 12-444 27 5-384 6-460 7-537 8-614 9-691 10-767 12-921 28 5-582 6-699 7-815 8-931 10-048 11-164 13-397 29 5-781 6-937 8-093 9-249 10-405 11-561 13-874 30 5-979 7-175 8-371 9-567 10-763 11-958 14-350 31 6-178 7-413 8-649 9-885 H-120 12-356 14-827 32 6-376 7-652 8-927 10-202 11-478 12-753 15-303 33 6-575 7-890 9-205 10-520 11-835 13-150 15-780 34 6-774 8-128 9-483 10-838 12-193 13-547 16-257 PROPORTIONAL RADII OF WHEELS. 315 No. of teeth. 1JC 1% IK 2 2% v/ z 3 35 6-972 8-367 9-761 11-156 12-550 13-945 16-734 30 7-171 8-605 10-040 11-474 12-908 14-342 17-211 37 7-370 8-844 10-318 11-972 13-266 14740 17-688 38 7-569 9-082 10-596 12-110 13-623 15-137 18-164 3D 7-767 9-321 10-874 12-428 13-981 15-534 18-641 40 7-966 9-559 11-152 12-746 14-339 15-932 19-118 41 8-165 9-798 11-431 13064 14-696 16-359 19-595 42 8-363 10-036 11-709 13-382 15-054 16-727 20-072 43 8-562 10-275 11-987 13-700 15-412 17-124 20-549 44 8-761 10-513 12-265 14-018 15-770 17-522 21-026 45 8-960 10-752 12544 14-336 16-128 17-920 21-503 46 9-159 10-990 12-822 14-654 16-485 18-317 21-981 47 9-357 11-229 13-100 14-972 16-843 18-715 22-458 48 9-556 11-467 13-379 15-290 17-201 19-112 22-935 49 9*755 11-706 13-657 15-608 17-559 19-510 23-412 50 9-954 11-945 13-935 15-926 17-917 19-908 23-889 51 10-153 12-183 14-214 16-244 18-275 20-305 24-366 52 10-351 12-422 14-492 16-562 18-633 20-703 24-843 53 10550 12-660 14-770 16-880 18-990 21 100 25-320 54 10-749 12-899 15-049 17-198 19-348 21-498 25-798 55 10-948 13-137 15-327 17-517 19-706 21-896 26-275 56 11-147 13-376 15-605 17-835 20064 22-293 26-752 57 11-346 13-615 15-884 18-1:3 20-422 22-691 27-229 58 11-544 13-853 16-162 18-471 20-780 23-089 27-706 59 11-743 14-092 16-441 18-789 21-138 23-486 28-184 60 11-942 14-330 16-719 19-107 21-496 23-884 28-661 61 12-1-11 14-569 16-997 19-425 21-854 24-282 29-138 62 12-340 14-808 17-276 19-744 22-212 24-680 29-615 63 12-539 15-046 17-554 20-062 22-570 25-077 30-093 64 12-738 15'-285 17-833 20-380 22-928 25-475 30-570 5 12-936 15-524 18-111 20-698 23-285 25-873 31-047 66 13-135 15-762 18-389 21-016 23-643 26-270 31-525 67 13-334 16-001 18-668 21-335 24-001 26-668 32-002 68 13-533 16-240 18-946 21-653 24-359 27-066 32-479 69 13-732 16-478 19-225 21-971 24-717 27-464 32-956 70 13-931 16-717 19-503 22-289 25-075 27-861 33-434 71 14-130 16-956 19-781 22-607 25-433 28259 33-911 72 14-328 17-194 20-060 22-926 25-791 28-657 34-388 73 14-527 17-433 20-338 23-244 26-149 29-055 34-866 74 14-726 17-671 20-617 23-562 26-507 29452 35-343 75 14-925 17-910 20-895 23-880 26-865 29-850 35-820 76 15-124 18-149 21-174 24-198 27-223 30-248 36-298 77 15-323 18-387 21-452 24-517 27-581 30-646 36-775 78 15-522 18-626 21-731 24-835 27-939 31-044 37-252 79 15-721 18-865 22-009 25-153 28-297 31-441 37-730 80 15-920 19-103 22-287 25-471 28-655 31-839 38-207 81 16-118 19-342 22-566 25-790 29-013 32-237 38-684 82 16-317 19-581 22-844 26-108 29-371 32.635 39-162 316 PROPORTIONAL RADII OF WHEELS. No. of teeth. i# iK iK 2 iy 4 iy 2 3 83 16-516 19-820 23-123 26-426 29-729 33-033 39-639 84 16-715 20-058 23-401 26-744 30-087 33-430 40-116 85 16-914 20-297 23-680 27-063 30-445 33-8-28 40-C94 86 17-113 20-536 23-958 27-381 30-803 34-226 41-071 87 17-312 20-774 24-237 27-699 31-161 34-624 41-548 88 17-511 21-013 24-515 28-017 31-519 35-022 42-026 89 17-710 21-252 24-794 28-335 31-877 35-419 42-503 90 17-909 21-490 25-072 28-654 32-235 35-817 42-981 91 18-107 21-729 25-350 28-972 32-593 36-215 43-458 92 18-306 21-968 25-629 29-290 32-952 36-613 43-935 93 18-505 22-206 23-907 29-608 33-309 37-011 44-413 94 18-704 22-445 26-186 29-927 33-668 37-408 44-890 95 18-903 22-684 26-464 30-245 34-026 37-808 45-367 96 19-102 22-922 26-743 30-563 34-384 33-204 45-845 97 19-301 23-161 27-021 30-881 34-742 38-602 46-32^ 93 19-500 23-400 27-300 31-200 35-100 33-000 46-800 99 19-699 23-638 27-578 31-518 35-458 39-397 47-277 100 19-898 23-877 27-857 31-836 35-816 39-795 47-754 101 20-097 24-116 28-135 32-155 36-174 40-193 48-232 102 20-295 24-355 28-414 32-473 33-532 40-591 48-709 103 20-494 24-593 28-692 32-791 36-890 4D-989 49-187 104 20-693 24-832 28-971 33-109 37-248 41-387 49-664 105 20-892 25-071 29-249 33-428 37-606 41-784 50-141 106 21-091 25-309 29-528 33-746 37-964 42-182 50-619 107 21-290 25-548 29-806 34-064 38-322 42-580 51-096 108 21-489 25-787 30-084 34-382 38-680 42-978 51-573 109 21-688 26-025 30-363 34-701 39-038 43-376 52-051 110 21-887 26-264 30-641 35-019 39-396 43-774 52-528 111 22-086 26-503 30-920 35-337 39-754 44-171 53-006 112 22-285 26-742 31-198 35-655 40-112 44-569 53-483 113 22-484 26-980 31-477 35-974 40-470 44-967 53-960 114 22-682 27-219 31-755 36-292 40-828- 45-365 54-438 115 22-881 27-458 32-034 36-610 41-186 45-763 54-915 116 23-080 27-696 32-312 36-928 41-544 46.161 55-393 117 23-279 27-935 32-591 37-247 41-903 46-558 55-870 118 23-478 28-174 32-869 37-565 42-261 46-956 56-347 119 23-677 28-412 33-148 37-883 42-619 47-354 56-825 120 23-876 28-651 33-426 38-202 42-977 47-752 57-302 121 24-075 28-890 33-705 38-520 43-335 48-150 57-780 122 24-274 29-129 33-983 38-838 43-693 48-548 58-257 123 24-473 29-367 34-262 39-156 44-051 48-945 58-735 124 24.672 29-606 34-540 39-475 44-409 49-343 59-212 125 24.871 29-845 34-819 39-793 44-767 49-741 59-690 126 25-070 30-083 35-097 40-111 45-125 50-139 60-167 127 25-268 30-322 35-376 40-429 45-483 50-537 60-644 128 25-467 30-561 35-654 40-748 45-841 50-935 61-122 J29 25-666 30-800 35-933 41-066 46-199 51-333 61-599 130 25-865 31-038 36-211 41-384 46-557 51-730 62-077 PROPORTIONAL RADII OF WHEELS. 317 No. of -i i/ teeth. A/ * IY 2 1# 2 2# 2K 3 131 26-064 31-277 36-490 41-703 46-915 52-128 62-554 132 26-263 31-516 36-768 420^1 47-274 52-526 63-031 133 26-462 31-754 37-047 42-339 47-632 52-924 63-509 134 26-661 31-993 37-325 42-657 47-990 53-322 63-986 135 26-860 32-232 37-604 42-976 48-348 53-720 64-464 136 27-059 32-471 37-882 43-294 48-706 54-118 64-941 137 27-258 32-709 38-161 43-612 49-064 54-515 65-418 138 27-457 32-948 38-439 43-931 49-422 54-913 65-896 139 27-656 33-187 38-718 44-249 49-780 55-311 66-373 140 27-855 33-426 38-996 44-567 50-138 55-709 66-851 141 28-053 33-664 39-275 44-885 50-496 56-107 67-328 142 28-252 33-903 39-553 45-204 50-854 56-505 67-806 143 28-451 34-141 39-832 45-522 51-212 56-902 68-283 144 28-650 34-380 40-110 45-840 51-570 57-300 68-760 145 28-849 34-619 40-389 46-159 51-928 57-698 69-238 146 29-048 34-858 40-667 46-477 52-286 58-096 69-715 147 29-247 35-096 40-946 46-795 52-645 58-494 70-193 148 29-446 35-335 41-224 47-113 53-003 58-892 70-670 149 29-645 35-574 41-503 47-432 53-361 59-290 71-148 150 29-844 35-813 41-781 47-750 53-719 59-687 71-625 151 30-043 36-051 42-060 48-068 54-077 60-085 72-102 152 30-242 36-290 42-338 48-387 54-435 60-483 72-580 153 30-441 36-529 42-617 48-705 54-793 60-881 73-057 154 30-639 36-767 42-895 49-023 55-151 61-279 73-535 155 30-838 37-006 43-174 49-341 55-509 61-677 74-012 156 31-037 37-245 43-452 49-660 55-867 62-075 74-490 157 31-236 37-483 43-731 49-978 56-225 62-472 74-967 158 31-435 37-722 44-009 50-296 56-583 62-870 75-444 159 31-634 37-961 44-288 60-615 56-941 63-268 75-922 160 31-833 38-200 44-566 50-933 57-299 63-666 76-399 161 32-032 38-438 44-845 51-251 57-658 64-064 76-877 162 32-231 38-677 45-123 51-569 58-016 64-462 77-354 163 32-430 38-916 45-402 51-888 58-374 64-860 77-832 164 32-629 39-155 45'680 52-206 58-732 65-258 78-309 165 32-828 39-393 45-959 52-524 59-090 65-655 78-786 166 33-027 39-632 46-237 52-843 59-448 66-053 79-264 167 33-226 39-871 46-516 53-161 59-606 66-451 79-741 168 33-425 40-109 46-794 53-479 60-164 66-849 80-219 169 33-623 40-348 47-073 53-797 60-522 67-247 80-696 170 33-822 40-587 47-351 54-116 60-880 67-645 81-174 171 34-021 40-826 47-630 54-434 61-238 68-043 81-651 172 34-220 41-064 47-908 54-752 61-596 68-440 82-129 173 34-419 41-303 48-187 55-071 61-954 68-838 82-606 174 34-618 41-542 48-465 55-389 62-313 69-236 83-083 175 34-817 41-780 48-744 55-707 62-671 69-634 83-561 176 35-016 42-019 49-022 56-026 63-029 70-032 84-038 177 35-215 42-258 49-301 56-344 63-387 70-430 84-516 178 35-414 42-497 49-579 56-662 63-745 70-828 84-993 318 PROPORTIONAL RADII OF WHEELS. So. of teeth. 179 35-613 42-735 49-858 56-980 64-103 71-226 85-471 180 35-812 42-974 50-136 57-299 64-461 71-623 85-948 181 ! 36-011 43-213 50-415 57-617 64-19 72-021 86-425 182 i 36-210 43-451 50-693 57-935 65-177 72-419 86-903 183 ! 36-408 43-690 50-972 58-254 65-535 72*817 87-380 184 36-607 43-9-J9 51-250 58-572 65-893 73-215 87-858 185 36-806 44-108 51-529 58-890 66-251 73-613 88-335 186 37-005 44-406 51-807 59-208 66-610 74-011 88-813 187 37-204 44-645 52-086 59-527 66-968 74-408 89-290 188 37-403 44-884 52-364 59-845 67-326 74-806 89-768 189 37-602 45-123 52-643 60-163 67-684 75-204 90-245 190 37-801 45-361 52-921 60-482 68-042 75-602 90-722 191 38-000 45-600 53-200 60-800 68-400 76-000 91-200 192 38-199 45-839 53-478 61-118 68-759 76-398 91-677 193 38-398 46-077 53-757 61-437 69-116 76-796 92-155 194 38-597 46-316 54-035 61-755 69-474 77-194 92-632 195 38-796 46-555 54-314 62-073 69-832 77-591 93-110 196 38-995 46-794 54-593 62-391 70-190 77-999 93-587 197 39-194 47-032 54-871 62-710 70-548 78-387 94-065 198 39-393 47-271 55-150 63-028 70-907 78-785 94-542 199 39-591 47-510 55-428 63-346 71-265 79-183 95-019 200 39-790 47-748 55-707 63-665 71-623 79-581 95-497 201 39-989 47-987 55-985 63983 71-981 79-979 95-974 202 40-188 48-226 56-264 64-301 72-339 80-377 96-452 203 40-387 48-465 56-542 64-619 72-697 80-774 96-929 204 40-586 48-703 56-821 64-938 73-055 81-172 97-407 205 40-785 48-942 57-099 65-256 73-413 81-570 97-884 206 40-984 49-181 57-378 65-574 73-771 81-968 98-362 207 41-183 49-420 57-656 65-893 74-129 82-366 98-839 208 41-382 49-658 57-935 66-211 74-487 82-764 99-317 209 41-581 49-897 58-213 66-529 74-845 83-162 99-794 210 41-780 50-136 58-492 66-848 75-204 83-560 100-271 211 41-979 50-374 58-770 67-166 75-562 83-957 100-749 212 42-178 50-613 59-049 67-484 75-920 84-355 101-226 213 42-377 50-852 59-327 67-803 76-278 84-753 101-704 214 42-576 51-091 59-606 68-121 76-636 85-151 102-181 215 42-774 51-329 59-884 68-439 76-994 85-549 102-659 216 42-973 51-568 60-163 68-757 77-352 85-947 103-136 217 43-172 51-807 60-441 69-076 77-710 86-345 103-614 218 43-371 52-046 60-720 69-394 78-068 86-743 104-091 219 43-570 52-284 60-998 69-712 78-426 87-140 104-568 220 43-769 52-523 61-277 70-031 78-784 87-538 105-046 221 43-968 52-762 61-555 70-349 79-143 87-936 105-523 222 44-167 53-000 61-834 70-667 79-501 88-334 106-001 223 44-366 53-239 62-112 70-986 79-859 88-732 106-478 224 44'565 53-478 62-391 71-304 80-217 89-130 106-956 225 44-764 53-717 62-669 71-622 80-575 89-528 107-433 226 44-963 53-955 62-948 71-940 80-933 | 89-926 107-911 PROPORTIONAL RADII OF WHEELS. 319 No. of n TX teeth. *'* IK 1% 1 2 ; 2^ t l / z 3 227 45-162 54-194 63-226 72-259 81-291 90-323 108-388 228 45-361 54-433 j 63-505 72-577 81-649 90-721 108-866 229 45-560 54-672 63-783 72-895 82-007 91-119 109-343 2)50 45-759 54-910 64-062 73-214 82-365 91-517 109-820 231 45-957 55-149 64-340 73-532 82-723 91-915 110-298 5J32 46-156 55-388 64-619 73-850 83-082 92-313 110-775 '233 46-355 55-626 64-897 74-169 83-440 92-711 111-253 234 46-554 55-865 65-176 74-487 83-798 93-109 111-730 235 46-753 56-104 65-454 74-805 84-156 93-506 112-208 236 46-952 56-343 65-733 75-123 84-514 93-904 112-685 237 47-151 56-581 66-012 75-442 84-872 94-302 113-163 238 47-350 i 56-820 66-290 75-760 85-230 94-700 113-640 *39 47-549 57-059 66-569 i 76-078 85-588 95-098 114-117 240 47-748 57-297 66-847 76-397 85-946 95-496 114-595 241 47-947 57-536 67-126 76-715 86-304 95-894 115-072 242 48-146 57-775 67-404 77-033 86-662 96-292 115-550 243 48-345 58-014 67-683 77-352 87-020 96-689 116-027 244 48-544 58-252 67-961 i 77-670 87-379 97-087 116-505 245 48-743 58-491 68-240 i 77-988 87-737 97-485 116-982 246 48-942 58-730 68-518 78-306 88-095 97-883 117-460 247 49-140 58-969 68-797 78-625 88-453 98-281 117-937 248 49-339 59-207 69-075 78-943 88-811 98-679 118-415 249 49-538 59-446 69-354 79-261 89-169 99-077 118-892 250 49-737 59-685 69-632 79-580 89-527 99-475 119-369 251 49-936 59-923 69-911 79-898 89-885 99-872 119-847 252 50-135 60-162 70-189 80-216 90-243 100-270 120-324 253 50-334 60-401 70-468 80-535 90-601 100-668 120-802 254 CO-533 60-640 70-746 80-853 90-959 101-066 121-279 255 50-732 60-878 71-025 81-171 91-318 101-464 121-757 256 50-931 61-117 71-303 81-489 91-676 101-862 122-234 257 51-130 61-356 71-582 81-808 92-034 102-260 122-712 258 51-329 61-595 71-860 82-126 92-392 102-658 123-189 259 51-528 61-833 72-139 82-444 92-750 103-055 123-667 260 51-727 62-072 72-417 82-763 93-108 103-453 124-144 261 51-926 62-311 72-696 83-081 93-466 103-851 124-621 262 52-125 62-549 72-974 83-399 93-824 104-249 125-099 263 52-323 62-788 73-253 83-718 94-182 104-647 125-576 264 52-522 63-027 73.-531 84-036 94-540 105-045 126-054 265 52-721 63-266 73-810 84-354 94-898 105-443 126-531 266 52-920 63.504 74-088 84-673 95-257 105-841 127-009 267 53-119 63-743 74-367 84-991 95-615 106-239 127-486 268 53-318 63-982 74-645 85-309 95-973 106-636 127-964 269 53-517 64-221 74-924 85-627 96-331 107-034 128-441 270 53-716 64-459 75-202 85-946 96-689 107-432 128-919 271 53-915 64-698 75-481 86-264 97-047 107-830 129-396 272 54-114 64-937 75-760 86-582 97-405 108-228 129-873 273 54-313 65-175 76-038 86-901 97-763 108-626 130-351 274 54-512 65-414 76-317 87-219 98-121 109-024 130-828 320 PROPORTIONAL RADII OF WHEELS. No. of teeth. IK i# IK 2 2# 2M 3 275 54.711 65-653 76-595 87-537 98-479 109-422 131-306 276 54-910 65-892 76-874 87-856 98-837 109-819 131-783 277 55-109 66-130 77-152 88-174 99-196 110-217 132-261 278 55-308 66-369 77-431 88-492 99-554 110-615 132-738 279 55-507 66-608 77-709 88-810 99-912 111-013 133-216 280 55-705 66-847 77-988 89-129 100-270 111-411 133-693 281 55-904 67-085 78-266 89-447 100-628 111-809 134-171 282 56-103 67-324 78-545 89-765 100-986 112-207 134-648 283 56-302 67-563 78-823 90-084 101-344 112-605 135-125 284 56-501 67-801 79-102 90-402 101-702 113-002 135-603 285 56-700 68-040 79-380 90-720 102-060 113-400 136-080 286 56-899 68-279 79-659 91-039 102-418 113-798 136-558 287 57-098 68-518 79-937 91-357 102-776 114-196 137-035 288 57-297 68-756 80-216 91-675 103-135 114-594 137-513 289 57-496 68-995 80-494 91-993 103-493 114-992 137-990 290 57-695 69-234 80-773 92-312 103-851 115-390 138-468 291 57-894 69-473 81-051 92-630 104-209 115-788 138-945 292 58-093 69-711 81-330 92-948 104-567 116-185 139-423 293 58-292 69-950 81-608 93-267 104-925 116-583 139-900 294 58-491 70-189 81-887 93-585 105-283 116-981 140-377 295 58-690 70-427 82-165 93-903 105-641 117-379 140-855 296 58-888 70-666 82-444 94-222 105-999 117-777 141-333 297 59-087 70-905 82-722 94-540 106-357 118-175 141-810 298 59-286 71-144 83-001 94-858 106-715 118-573 142-287 299 59-485 71-382 83-279 95-177 107-074 118-971 142-765 300 59-684 71-621 83-558 95-495 107-432 119-869 143-242 INDEX. A di ustablo gages, 38, 41, 42, 43, 49 Adjustable hand rest, 53, 56 " plane for curves, 28, 32 Adjusting bevel square, 33 33 Babbitt metal, bearing for, 174, 175, 17G Bearing castings, shape of, 172 Bearing for Babbitt metal, 174,175,176 Bearing castings, contraction of, 172, 173 Bench stop, 1GG Bench lor pattern making, ICG Bench hook, 1G Bevel gage setting, 11 Bevc) gearwheels, 206 to 213 Bevel pinion, Bovcl wheel, building up, 211 Boycl square, 38 Boiler, how to sweep up a, 193 Boiler, or pan, mold for, 193 Building pulley patterns, 133 to 142 Calipers, 4 Castings, contraction in cooling of, 99 Cement chuck, 65 Cement, mixture of, 65 Center plates, 68 Chisel handles, shape of, 34 Chisel, paring, 33 Chisel sharpening, 35 Chuck cement, 65 Chucking contrivances, 57 Chuck for thin work, 65 Chuck, methods of making, C9 to 63 Chuck screw, 6i Chuck wood faced, 69 Cog teeth for gear wheels, 225 to 233 Column patterns, blocks for, 178 cores for, 181, 182, 183 ornaments for, 181 how to make, 180 " round, 184 to 183 Column patterns, square, 178 Compasses, 39 pencil attachment for, 40 Compass plane, 27 Contraction of brass castings, 172 Conversion of English inches into centimetres, 2(55 14* Conversion of centimetres into English inches, 266 Conversion of metres into English foct, 2GG Conversion of English foot into metres, 266 Conversion of French square measure into English, 267 Conversion of French cubic meas- ure into English, 267 Conversion of French lineal meas- ure into English, 267 Cope of foundry ilask, 74 Cores, use of, 82 '' kiuds of, 83 " for globe valve, 1G2, 163, 1G4, 165 Core boxes, 82, 83, 84, 85, 86, 87, 83, 89 " boxes for T patterns, 130 " boxes for pipe benda or T's, 146, 147, 148, 149 Core box plane, 30 Cores for pipe work, 90 " sweeping for pipe bends, 149, 150 Decimal eqiiivalents for avoirdu- pois weight, 268 Decimal equivalents for cubic measure, 261 Decimal equivalents for inches and fractions, 300, 301 Decimal equivalents for long measure, 268 Decimal equivalents for square measure, 261 Decimal equivalents for troy weight, 268 Diametral pitch, 270 Diameters, circumferences, areas, etc., of circles, 274 to 283 Diameters, areas, etc. of circles and contents in gallons, at one foot in length or depth, 297 to 299 Dog for holding work, 110 Dovetailed joints, 167 Dovetailing pinion teeth, 200 E Endless screw, to cut in the lathe, 213, 214, 216 " to cut by hand, 2J6 to 218 322 INDEX. Face lathes, 61, 235, 236 Face plate, 53 Flasks for molding, 74, 75, 7G Fly wheels, calculating weight of, 249 Fore plane, how to use, 24 Foundry floor, 73 Foundry operations, 73 to 87, ami 193 to 193 Fork center, 67 Gage hexagon, 116 Gages for sawing out cog teeth, 227, 228, 229, 230, 231, 232 Gages, 41, 42, 43 Gage, adjustable, 49 Gear wheel teeth, marking out, 201, 202, 203, 204 Gear wheel teeth cutting out, 204 " " frame for, 204 " " " adjusting and fastening, 205 Gear wheels, bevel, 200 to 213 Gear worm screw, pattern for, 213, 214 Gear wheel patterns, construc- tion of, ' 199 to 213 Gear wheel patterns made in sec- tions, 205 Gear wheel patterns, solid pin- ions, 200 Gear wheel patterns, turning, 200 Gear wheel pinions, dividing off, 200 Gear wheel patterns, how to make, 199 to 213 Gear worm screw, cutting in the lathe, 214, 215 Gear worm screw, cutting by hand, 21G, 217, 218 Gear wheel teeth, scale for, 218 Gear wheel teeth, how to use scale for, 219, 220 Gear wheels, patterns for, 199, Gear wheel patterns, wood for, 200 Gear wheels, cog teeth for, 225 to 233 Gland patterns, how to make, 99 to 111, and 115 to 118 Gland patterns, kinds of, 92 to 98 Globe valve, 158 to 1C5 Gluing end wood, 123 Gluing segments, 137, 138 Glue pot, 243 Gluing wheel teeth, 205 Gouge turning, 66 Gouge, grinding a, 36 Gouge, concave and convex, 36 Gouge, how to hold, 66 H Half lap joint, 168 Hand rest, fastening, 50, 51, 52, 53 " " movable tripod, 59 Hexagon brasses, bevels of, 172, 173 Hexagon gage, 116 I Holding dog, no I Holding turning gage, 66, 67 " skew chisel, 68 Holes, marking, for pegging, 108 Jack plane, how to use, 24 Jig saw, " 237, 238, 239 Joint, half lap, 168 Jointing spokes, 140, 141 Joints, tenon and mortise, 167 Journal, brass limits on patterns for, 9J, 172, 173 Lathe for pattern work, 50 Lathes for facing, 63 Lathe, fastening rest upon, 50, 51,52,53 Lathe, cono pulley of, 55 Lathe rest, adjustable or movable, 56 Lathe, tailstock of, 66 " running head of, 53 " tools, 6(5, 67, 68, 69, 70, 71, 72 Lagging or staving, 190 Loam work, 193 Mallet, 47 Marking pin or peg holes, 114 Mitre box, ICG, 169 Mitre joint, 169 Mixtures of metals, 250 Mixing varnish, 112 Molds, construction of, 73 to 81 Molding with sections of pat- terns, 222, 223, 224 Moldiug boards for thin work, cores for columns, 191, 192 cored gland pattern, 94 cylinders by sweeps, 1G9 by section patterns, 221-224 cores for*pipe bends, 149, 150 pulleys, Mortise and tenon joint, 169 o Oilstones use of, 23 Oilstones truing, 48 Oilstones kinds of, 47 Paring chisel, 33 Parallel strip, 46 Patterns for Babbitted boxes, 174 to 176 bearing boxes, 99 bevel gears, 206 to 212 bevel pinions, 210, 211 branch pipes, 126 columns, 178 to 184 cylinders, 197 glands, 93 INDEX. 323 Patterns for gear wheels, 199 to 207, and 225 to 234 globe valves, 158 to l 62 pulleys, 132, 133, 134, 135 pillar block, 170, 174 pipe bends, 143 T's 120 window sill, -worm screw, 213 to 217 Patterns, sweep, Patterns, loosening in the inoiild, 100 Pattern, varnishing, Pegs or pins, 107, 108, 103 Peg or pin, making tool, 103 Peff, shape of, 109 Pitch, diametral, 270 Piu or peg holes, marking, 114 Planes, 20 to 32 Plane iron grinding, 20, 2 1 Planing machine, 242 Pulleys, patterns for, 132, 221 Pulleys, molding in sections, 222 Rabbit planes, 29 Rapping patterns, 78, 100, 101 Router plane, 28 Rubbers for sand-paper, 105 Rule to calculate thickness of cylinders and pipes, 248 Rule to calculate cylinders for hydraulic presses, 249 Rules to calculate weight of fly- wheel, 249 Sand-papering, 104, 105 Saw, band, 240 8aw, circular, 241 Saw, jig, 237,238,239 Scriber, 117 Screw-driver, 47 Screw chuck, 58 Section patterns, 222 Section molding, 222, 223, 224 Shape of chisel handles, 34 Shrinkage in castings, 244 " bars, 245 " cylinders, 244 disks, 245 general laws of, 246, 247 globes, 244 journal brasses, 245 " ribs on plates, 247 " table of, 245 " tubes, 24G U-shaped castings, 240 " wedge-shaped cast- ings, 246 Shooting board, 137 Ske\v chisel, how to use, 68, 69 Staving or lagging, 151 to 157 Snap flask, 76 Spindle for sweep work, 139 Spokes, jointing, 140,141 Square, Steam cylinders, sweeping up, 196 Strength of cylinders, rules to cal- culate the, 248, 249 Swept cores, 149, 150 Sweep and loam work, 193 Sweep, operation of, 193, 194, 195, 196 Tables of weight, avoirdupois weight, 262 Tables of weight, troy weight, 262 " "* of water, de- cimal equivalents for, 269 Tables of the weight of cast iron bars, 256 Tables of the weight of cast iron cylinders, 254 Tables of the weight of cast metals, 251 pipes, 252, 253 Tables of the weight of cast iron and lead balls, 254 Tables of the weight of copper bolts, 252 Tables of the weight of flat cast iron, 255 Tables of the weight of various kinds of wire, 257 Tables of the weight of nails and spikes, 254 Tables of the weight of water in decimal equivalents, 269 Tables of the weight of water in pipes, 259 Tables of the weight of water at different temperatures, 263 Tables of the weight of various substances, 256 Tables of the weight of ropes and chains, 255 Tables of the weight of timber, 251 patterns and castings, 251 Tables of the weight of metal plates per square foot, 258 Tables of Measure : Ale and beer measure, 263 American and English meas- ures, 261 Comparative measures of length, 260 Cloth measure, 260 Dry measure, 261 Foreign measures of length compared with U. 8., 264 Land measure, 260 Measures of length, 260 Miscellaneous measures, 261 Nautical measure, 260 Pendulums, 260 Solid or cubic measure, 261 Square measure, 361 324 INDEX. Tables of Measure. Continued : Timber measure, Wine measure, Table of the sizes of drawing paper, *,* Table of the sizes of tracing paper, 271 " iron washer* " penny nails, " taps tor ma- chine screws, Table of the sizes of tapping holes for pipe taps, Table of tho sizes of sheet iron and zinc, Table of the sizes of wire rope, " diameters and number of teeth iu wheels of various pitches, i Table of mixtures of metals, " melting points of metals, 230 " squares, cubes, square roots, cube roots, etc., of num- bers, 284 Table of diameters, areas and circumferences of circles, 274 Table of scantling and timber measure, 302 Table of natural sines, " decimal equivalents, 269, and 3i T pattern, T pattern, core boxes for, T pattern, how to make, 121 T pattern, skew, Thickness for cylinders, jure*, lydraulic press, cylinders, Thin patterns, Timber drying, Timber, selection of, Teeth, dovetailed. Teeth of gear wheels, how to make, 200 Tools, bevel squares, " block plane. " boring, Tools, chisels, 33, 34, G8, 69, 70, 71 302 " compasses, 39 263 r " compass plane, 27, 32 " core box wlane, 30, 31 271 " fore plaui , 24 er, 271 " for cuttiu j endless screws S, 273 or worms, 214, 215, 21 G 271 " gages, 36, 41, 42, 43, 40, 50 272 r 1 1 gouges, 33, 34, 35, 66, 67 " jack plan 20,21 ' jointer pi' ic, 32,33 272 1 machine, 234 to 212 l " parallel sti 's, 46 271 " plane blad 20 273 " rabbet plan 29 " router plain 28 I " smoothing i ane, 32 to 320 " square, 37 250 " trammels, 44, 45 llS,250 " trammel gage for T's, 125 ) " tool for pin Making, 108 " turning, 71 to 296 Tripod hand-rest, 56 to 283 to 306 307 Useful numbers in calculating useful weights an 1 measures, 264 265 to 00, 301 *^ 121 Varnish, pot for, 112 130 ' colors of, 113 to 129 application of, 114 126 248 "W* 248 Wheels, making teeth for, 199 to 213, and 225 to 233 249 Wheel teeth dovetailed, advan- 189 17 15, 16 tages of, 210 Window sill, molding block for, 189 Window sill, pattern for, 189 212 Wire edge of tools, 23 ce, 200 Wood, facing chuck, 59 to 210 Wood, selecting, is 38 32 72 Wood, shrinkage of, 18 Wood, storage of, 16 Wood, warping of, 17 RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (510)642-6753 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date. 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