Please handle this volume with care. The University of Connecticut Libraries, Storrs » ^ » ^-^ » ^ » " ^ ^ ~W^ ■ i .i.i.i.i.i. ii . i . i . i .i.i.i.i, i , i ii ,iiiiiiiiiiiiiii|i III III 3 ^153 onaatflT 2 m So to i; This Book may be kept out TIFO fFEEKS only and is subject h THE CELEBRATED Steel Squares MANUFACTURED BY SARGENT & CO. /RE THE RECOq;^IZ;ED ^TAfiDJ^Y{D^, fAADZ f^^^ UJMEXCELX-ED jVIy^TEFJI/I-^ /ND OJM IJVIPr^OVEF ]Vl/CHIJ^(ERY OF DEJ-ICATj: /DJU^T/VlflJMT. NOJ\r£ GENUINE UNLESS STAMPED ALL SUCH SQUARES FULLY WARRANTED, FOR SALE BY ALL HARDWARE DEALERS. "Decidedly the most convenient Square for the operative workman in the market." — Hodgson. r)i A Steel Squares AND THEIR USES. BEING A DESCRIPTION OF THE VARIOUS STEEL SQUARES AND THEIR USES IN SOLVING A LARGE NUMBER OF MECHANICAL PROBLEMS IN Constructive Carpentry, Joinery, Sheet Metal Work, Cut Stone and Brick Work. ALSO SHOWING HOW MANY GEOMETRICAL AND OTHER PROBLEMS MAY BE SOLVED BY THE USE OF THE STEEL SQUARE. BY FRED. T. HODGSON, Editor of " The Builder and Woodworker.'' Author of "The Carpenter's Steel Square and its Uses ;" "The Builder's Guide and Estimator's Price Book;" •'Practical Carpentry; " "Stair Building Made Easy;" "Hand Saws — Their Carb AND Use ; " " Plaster, How to Make and How to Use;" etc., etc. FULLY ILLUSTRATED WITH NUMEROUS ENGRAVINGS AND DIAGRAMS. NEW YORK: THE INDUSTRIAL PUBLICATION COMPANY. 1890. GopyrigM, Secured, 1890, hy John Fhin. JtHrU Tif^ STEEL SQUARES AND THEIR USES. ■^.A^IFLT II. THIS BOOK IS DEDICATED TO MY SON, FRED. ALBERT HODGSON, WHOSE DEVOTION, KINDLY ASSISTANCE AND PLEASING COMPANIONSHIP HAVE MADE THE WRITING OF THIS LITTLE WORK A LABOR OF PLEASURE. THE AUTHOR. PREFACE, The great demand for the first volume of ''The Steel Square and Its Uses" convinced the writer that a second volume on the same subject would be sure to meet with a fair reception. The 150,000 readers of Vol. I. will want to see and know more of what may be done by the aid of the Steel Square and a little mental effort. The present volume, like the first, contains but little of bewildering mathematics, and is brought down as near to the operative workman's standard as possible. Perhaps many readers of this book will find between its covers some things they have known for years or have seen employed by some fellow workmen ; they will, however, find many things and problems they have never seen, and some little ** dodges" they have not heard of before, any one of which will be worth to them the whole price paid for the book. Indeed, the writer considers the matter and illustrations pre- sented in this work of much more importance to the advanced PREFACE. workman than that which appeared in the first, and feels assured his labors on The Square would not be complete without the present treatise. At this writing (1890) over 150,000 copies of the first volume have been sold, and the demand is still brisk, thus showing there was a want of a work of this kind ; and as the first volume did not nearly exhaust the subject, it became the duty of the author to supplement it with the present one, which it is thought will pretty nearly cover the ground. Never, perhaps, in the history of technical literature has a work exceeded 50,000 or 60,000 of a circulation, and it is both flattering to the author and gratifying to the publishers to find that their efforts to aid the workman in acquiring technical knowledge have been so generously appreciated. It is hoped their present eff"orts in the same direction will do as much good and deserve a like appreciation. THE AUTHOR. New York, May, 1890. CONTENTS. PAGB Dedication. vii Preface . ix Contents xi Preliminary 15 Advice to Students 15 Polygons 15 Equal and Uni^qual Squares 15 Pentagons 16 Scientific way of forming Pentagons 16 Pentagons by the "Square " 16 Hexagon Figure 17 How to Construct Hexagons 18 Figure of Heptagon 18 How to Construct Heptagons 18 Figure of Octagon 19 To Construct Octagons 19 To Construct an Octagon by the Square 19 Advice to Young Workmen 20 Figure of Nonagon 20 How to Construct Nonagon with the Square 20 To lay off Octagon in a Square 21 Figure of Square and Octagon 21 Octagon described from edge 21 Xil CONTENTS. PACK To lay off Octagon on a given side 21 Making a Square stick Octagonal 21 To find the side of an Octagon when side of Square is given. ... 22 When the side of an Octagon is given, to find the square width. . 22 Figure showing application of Square for constructing Octagon ... 22 Octagonal and Hexagonal Roofs 22 Figure of Octagon Roof. 23 Side Bevels Octagonal Roof 23 Backing Hips for Octagonal Roofs 23 Jack Rafters for Octagonal Roofs 23 Hexagonal Roof 24 Hips and Jack Rafters for Hexagonal Roof 24 Hexagonal and Octagonal Boxes or Hoppers 24 Cuts and Bevels for Octagonal and Hexagonal Hoppers 25 Figure of Hopper 25 To test a Square 25 Diagram of Test 26 How to find the centre of a Circle with the Square 26 Figure showing method 26 Three points not in a straight line being given, to find the centre of a circle which will pass through them 26 To find a circle equal in area to two or more circles 27 Diagram showing how done 27 Rule applied to other Figures 27 To find the .side of a square of half the area of a given square . . 28 Equilateral Triangle 28 Figure of Equilateral Triangle 28 Bisecting Angles by using the Square 29 Two Diagrams showing manner of Bisecting. 29 Method of dividing Angles 30 Figure with Bisected Angles 30 CONTENTS. Xlll PAGE Obtuse and Acute Angles Bisected 31 Diagram showing method 31 Method of finding Angles 32 Two Diagrams 32 Angles of 30*^ and 60", and how found 33 Protractor made by Square 33 Tangent Problem 34 To find a Tangent 35 Good for Stair-builders 35 Finding a lost Centre 36 Diagram showing how found 37 Practical applications of rule 38 Proportioning Columns 39 Method illustrated 39 Diagonal Scale 41 Diagram of Scale 42 Scale and uses explained. . , 43 To make Flared or Splayed Circular Work 44 Two Diagrams in explanation 44 Steel Squares generally 45 The No. 100 Square 46 The No. 200 Square 46 The Crenelated Square 47 Directions for using 48 A Combination Square 49 Seven illustrations of Combination Square 50 Useful applications of the Steel Square ' i Combination Diagram 52 Length of Chords 53 Division of Circles 55 Construction of Unequal Squares. ,,,,.,.., 57 Xiv CONTENTS. PAGB Circumferences of Circles 59 Degrees and Angles obtained by using the Square 61 Hip, Valley, Mansard and other Roofs 62 To cut a Purlin against a Valley Rafter 63 Another method 64 To Timber a Hexagon Roof 65 Lines for Hip Roofs 66 Valley Rafters and Cripples 67 Rule for Valley Rafters 67 Pyramidal Frame Work 67 Diagram of Battered Frame 68 Make a Pyramid 68 Windmill Frame 69 Backing Corner Posts 70 Two Diagrams of Post Bevels 70 Mansard and French Roofs 71 Manner of making Mansard Roof 72 Another style of Mansard Roof 73 Another form of Roof. 73 Concerning Hoppers 73 Diagram of Roof 74 Hopper Lines 75 A Constant Diagram 76 Butt Joints for Hoppers 7^ Mitres for Hoppers 7^ Hoppers with unequal Flares 77 Novel method of cutting Hopper Joints 78 Hexagonal Hoppers 79 Diagram of Hexagonal Hopper Sc Steel Squares AND THEIR USES. Preliminary. — Every angle or cut for rafters, hoppers, raking mouldings ,or mitres, is some angle of a polygon or right-angled triangle ; therefore it is fitting this work should open with rules for finding the inclination of sides, construction and angles of same. It is thought the methods shown herewith will prove both new and useful to many mechanics, and will be a valuable addition to the literature of the Steel Square. The student is earnestly advised to construct polygons of all sorts by the usual method, then make a table of the figures required to construct the figures and find the angles. The following methods will give an idea of how the angles and lines may be found by using the steel square. Polygons. — Polygons are nearly as much used in the con- structive arts as ellipses or circles, and I think it quite fitting to begin real work in this book with these figures. A square figure whose sides are equal, or unequal, as the case may be, if all the angles are right, requires no descrip- tion, as every workman knows how to construct such a figure ; §0 I will begin by showing how a pentagon, or five-sided i6 STEEL SQUARES figure, may be constructed. There are several methods of forming this figure, but I prefer the following : On a given line let A B, Fig. i, be the length of one side ; divide this into two equal parts, marking it as at 2. From B square up a line, and make B N equal to A B ; then with 2 as a centre and 2 N as radius, describe the arc, cutting the line A B at 3. Now take A 3 for radius, and from A and B as centres make Fig. I. the intersections at D ; then from D, with a radius equal to A B, describe an arc as shown ; then using A and B for centres, intersect the arc in E and C ; connect these points together with straight lines, and the pentagon is complete. This is a scientific way of forming this figure, but it may be obtained much easier by the square. It may be necessary to explain that in regular equal-sided AND THEIR USES. 17 polygons the angles are equal, so any side of a regular polygon may be used for a base line. Let this fact be remembered, as it is important the student should keep it in mind when dealing with any problem connected with polygons, where the steel square is used : By a careful examination of Fig. i it will be seen that the outer edge of the tongue of the square is in line with one side, A E, of the pentagon, measuring down below the base line, A B, six inches ; then the 2 1 inch mark on the outer edge of the square will also touch the base line, A B. This position of the square then gives the exact inclination of the side of the pentagon with the base. Now if we reverse the square and place the 6 in. mark at B, and the 21 in. mark on he line A B, we get three sides of the figure. Now make the distance from A to E the same as A B, and we have the length ol that side. Perform the same operation with B C. Then using A E and B C as base lines, we can form the figure com- i8 STEEL SQUARES plete. This shows how any pentagon having equal sides can be formed with the square. The method of obtaining the mitres or cuts suitable for cutting joints in mouldings and other works, for this and all other polygons, will be shown further on. Now remember that 6 in. on the tongue and 21 in. on the blade gives the proper angle for forming pentagons. Fig. 3- To make a Hexagon, Fig. 2, take seven inches on the tongue and twelve inches on the blade, and apply as shown on a base line which forms a square around the figure. Fig. 3 shows a Heptagon, or seven-sided figure, and the manner in which it is obtained. To get the angle as shown, form a square in accordance with dimensions required ; then inscribe a circle as shown ; then place the square as repre- sented, using the base line of the outside figure having the AND THEIR USES. 19 tongue running in a line with the centre, keeping the 7 in. mark on the base line ; then on the blade the 14 in. mark will be over the base line. Hence, 7 in. on the tongue and 14 in. on the blade gives the figures for finding the lines for a heptagon. Perhaps there is no one of the polygons so much used as the octagon, Fig. 4, with the exception, of course, of the square or four-sided figure. In consequence of this fact, I Fig. 4- think it necessary to say more of it than of the other polygons. An octagon, as my readers know, is an eight-sided figure, and may be obtained by many different methods, among which are those shown at Figs. 6, 7 and 8, of which more will follow. In Fig. 4 it will be seen that the figure may be easily formed by using the square as shown. Take seven inches on the tongue and seventeen on the blade, and apply on the base line, and the angles are readily obtained. It will be seen that 20 STEEL SQUARES nearly all kinds of polygons may be obtained by using the square, and any workman may discover for himself the figures on the square to apply by constructing a polygon of any num- ber of sides, and then applying the square in such a manner as to understand its application for the formation of any similar figures. The following, which relates to octagons particularly, will be found of much service to the younger workmen; and I Fig. 5- would advise them to master all these little "kinks," and to procure a copy of the first part of the work on this subject, ^nd study up all that is said there on the subject of polygons, and I am sure they will thank me for bringing the matter to their notice. Fig. 5 exhibits a nonagon, a figure having nine sides. It is but seldom used, but may be wanted sometimes, so it ig AND THEIR USES. 21 as well to have it described. Five inches on the tongue and thirteen inches on the blade will give the angle from the base line. To lay off an Odagon in a Square. — Fig. 6. Draw the diagonals e and/! Mark ofF the distance from the centre g, on all the sides, measuring from the corners. The resulting marks give the corners of the octagon. Fig. 7. Another method is to measure off the side of the square on its diagonal k. Square from a side to the point thus found on the diagonal, and n is the distance to be guaged from each corner, to mark the corners of the octagon. Fig. 6. Fig. 7, To lay off an Odagon on a given side. — Fig. 8. Prolong the ^iven side a b, and lay off an angle of 45° at both a and b. The lines i, 2 are squared up from the given side, also lines 3 and 4. By applying the square to the other lines we get the remaining sides. To make a square stick odagonal. — Fig. 9. Lay the square or two-foot rule diagonally across the stick so as to measure two feet on it, letting the corners on the same side of the blade or rule touch the edges of the stick. Make marks at the 7 in. and the 17 in marks. Measure thus at each end of the stick. 22 STEEL SQUARES Lines struck through these points show what is to come off to make it octagonal. To find the side of an Octagon when the side of the square is given. — Multiply the side of the square by 5 and divide by 12 The quotient is the side of the inscribed octagon. When the side of the Octagon is given, to find the square width. — Suppose the side of the octagon is to be 16 ft. ; take half this or 96 in. for the square, 16 in. on both tongue and blade taken 6 times, giving 11 ft. 3J in., which, being doubled and added to the side of the octagon, gives the square width. 7^ % ^<^ \~ A \ >^A ^ V 1^ \ ^ ~VL \ ^ ik Fig. 9. Octagonal and Hexagonal Roofs. — Fig. 10 represents an octagonal roof In its construction the suggestions on octa- gons, herein made, must be referred to. The length of hips is found as usual from rise and run, the run being half the diagonal of the octagon. Cut the first pair full length AND THEIR USES. 23 to butt against each other ; the next pair are to be set up at right angles to these, and each is to be cut shorter than the first pair by half the thickness of first pair, measured square back from the down bevel. The third and fourth pairs are to be cut shorter than the first by half the diagonal of a square whose side is the thickness of the first rafters. If the thickness of the first pair is 2 in., then the third and fourth pairs are shortened by i-^^, as 2-J-0. is the diagonal of a square whose side is 2. The first and second pairs have no side bevels ; the side bevels of the third and fourth run back on both sides from Fig. 10. the middle of the rafter. Find this bevel by taking the original length of rafter on the blade and its run on the tongue, when the blade shows the cut. The backing of the hips obtain by taking -^ of the rise on the tongue and the length of hip on blade, the latter giving the cut ; for the side of an octagon is -^ its square width. Half the square width is the run of the middle jack-rafter, from which and its rise we get its length. From the length deduct the same amount as from the third and fourth pairs of hips. If there are to be two jacks between the middle one 24 STEEL SQUARES and the corner, we divide the length of side into three parts, also the rise, whence are obtained as before the distance ol rafters apart, and the rise of shortest jack. Divide half the square width of octagon by three to find the run of shortest jack. Just as the square is laid on to find the length of a jack, it gives the down and lower end bevels ; while the side bevel is obtained by taking length of middle jack on blade and half one side of the octagon on the tongue ; the blade giving the cut. A Hexagonal Roof. — The side of a hexagon equals the radius of the circumscribing circle. The square width is determined from two parallel sides ; a diagonal of the figure, is a line from opposite angles. The first pair of hips are set up as in the octagonal roof. The second and third pairs have a side bevel. To find this, take half the side of the hexagon on the tongue and half the square width added to the gain of the hip-rafter in running that distance, on the blade. The tongue gives the cut. Strike the bevel across the rafter. Now, the second and third pairs are to be measured back shorter than the first pair, on their middle lines, just half the length of this bevel. The third pair has the bevel cut on both sides from the centre. The backing of the hips is found by taking y-j^^- the rise of roof on the tongue and the length of hip on blade ; the latter gives the cut. The side of a hexagon is -^-^ its square width, or apothem. The lengths and bevels of the jack-rafters are found as in octagonal roofs. Hexagonal and Octagonal Boxes or hoppers. — The cuts for the edges of the pieces of a hexagonal hopper are found by subtracting the width of one piece at the bottom, viz., the width of same at top, and taking the remainder on the tongue. AND THEIR USES. 25 and depth of side on blade. The tongue gives the cut. For the cut on the face of the sides, take -^ of the rise on the tongue, and the depth of side on the blade. The tongue gives the cut. The bevel for the top and bottom edges is found by taking the rise on the blade and the run on the tongue. The latter gives the cut. To find the cut of an octagonal hopper (Fig. 11) for the face of the board and also the edge, subtract the rise from the width of side ; take the remainder on the tongue and width of Fig. 11. side on blade ; the tongue gives the cut. The edge of the stuff is to be square when applying the bevel. The bevel for the top and bottom edges of the sides is found by taking the rise on the blade and run on the tongue, the latter giving the cut. This makes the edges horizontal. The edges are not to be beveled till the four sides are cut. To test a square with the compasses, draw the two con- centric arcs, d and c, Fig. 12, with radii of 6 and 8 in. Set the compasses to 10 in., and inserting one point anywhere on the outer arc, as c, mark the exact distance on the inner arc, as at d. Connecting these points with the centre of the two arcs, we have an exact right angle with which to compare 26 STEEL SQUARES the square. To test a framing square, it is best to draw arcs of 12 and 1 6 in. radius, laying off 20 in. between c and d. The square may be more quickly tested by laying it on a wide board, placing the blade parallel to one edge, which must be planed perfectly straight, and drawing a fine line along the tongue. The square is then turned over, so as to rest in a reversed position on the opposite side of the line just drawn. If the square now exactly coincides with the line and the board-edge, it is a perfect right angle. A great recom- mendation of this method is that an inaccuracy of the scale is doubled by the reversing, and so made more apparent. If the square is not true, it should be set in a vise and draw filed. I! i^ Fig. 12. Fig. 13. To find the centre of a Circle with the Square. — Fig. 1 3. Lay the square on the circle with the corner at the circumference. Mark where outer edge of tongue and blade cut the circle, and draw a line connecting these points. This line is always a diameter, and by drawing in like manner a diameter in another direction, the intersection of the two gives the centre. Three points not in a straight line bei?ig given, to find the centre of a circle which will pass through them. — Fig. \\. Let i, 2 and 3 be the points. Connect them by straight lines, and square from half the distance between them as at d and e. The intersection of these perpendiculars is the centre. This will be discussed at length further on. AND THEIR USES. 27 To find a Circle equal in area to two or more Circles. — Fig. 1 5. Let A be f in. in diameter, and B ij in. Measure across from the | in. on one arm of the square to the \\ in. on the other ; this distance is the diameter of the required circle, C. 5 c-' Fig. 14. If there were three circles, we should set the diameter of the third on the tongue and that of C on the blade ; and the diagonal distance between these points would be the diameter of a circle equal to the three, and so on for any number. Fig. IS. This applies to squares also. By this simple rule we can find the size of one pipe equal to two or more, and square spouts in like manner. Similar figures of all kinds may be worked by this method — triangles, rectangles, hexagons, octagons, etc., taking similar dimensions only; that is, if the shortest 28 STEEL SQUARES side of one triangle is taken, the shortest side of the other must be taken also, and the answer gives the shortest side of the required triangle. To find the side of a square of half the area of a given square. — Fig. 1 6. Let G be the given square; half its diagonal gives the side of the smaller square. A square constructed on the diagonal of G would contain double the area. Fig. i6. Equilateral Triangle. — An equilateral triangle may be AND THEIR USES. 29 obtained by the use of the square, if the length of one side is given : suppose B C, Fig. 16, the length of one side, then take 10 inches on the blade and 17 inches on the tongue of Fig. 17. *he square and apply on a line, as at B C, resting the 10 inch mark at the point B. Draw a line from B to A. Reverse the square and place 10 inches at the point C, then on the Fig. 18. tongue keep the 17 inch mark on the line B C, and draw the line C A until it cuts the line B A ; then will B A be equal to the line A C, which is equal to the line B C. 30 STEEL SQUARES Of course this figure, when within the range of a pair of compasses, may be constructed very simply, as follows : Take the length of one side of the triangle on compass, place one foot on C, describe an arc at A ; then with one foot of the compass at B describe the arc A, and the three points of the figure are given ; join A B, B C, and A C ; the figure will then be complete. Method of Dividing Angles.— K B C, Fig. 17, is an acute angle. We wish to divide it. Measure up from B to A any distance, make B C the same distance, place the square on the points A and C as shown, keeping the distance on the blade and tongue the same, then the heel or corner of the square, S, will give the points through which to draw a line AND THEIR USES. 31 passing through the angle at B, and the division will be com- plete. Again : Let Fig. 18 be an obtuse angle ; make B A and B C equal. Apply square as shown, keeping equal distances on blade and tongue at the points of contact A and C. The point E on the heel of sc^uare will be one point 32 STEEL SQUARES from which to draw a line through B, which forms the division of the angle. At Fig. 19 I show a number of angles, which are treated same as foregoing. At the junction of the lines drawn from the angles B B B, the centre of the triangle is found at P. B Fig. 21. This method of bisecting an angle is very useful, inasmuch as the ''cut " or mitre of any mouldings placed at any angle on a flat surface may be obtained. This is shown at Fig. 20, which may be a panel or other like surface. This diagram Fig. 22. shows that angles of any form and in any position may be equally divided by a proper use of the steel square. Suppose we want to find the angle 45° on a board, we mark any two points A C, Fig. 21, on the edge of a board ; AND THEIR USES. 33 apply the square as shown, keeping its sides on A C ; then the distance on each side of the square being equal, measuring Fig. 23. from its heel or corner B gives the angle 45°. H this portion be cut out it will form a templet or set square which is very Fig. 24. useful in drawing. The lines A B and C B are true mitres, or angles of 45*, with the line A C as their base. 34 STEEL SQUARES A, B, C, R at Fig. 22 show the lines for forming a set-square having 60° on the line A R, and 30° on C R. This figure is formed with compasses, as follows ; Make A C length of base line ; let B be half the distance between A C. From C B as centres and radius make the intersection at R, then by joining A R and C R the angles 30° and 60° are formed. This is the AND THEIR USES. 35 principle. To do all this with the square, simply take the length of the square — 24 inches — on the blade and thirteen inches on the tongue, and place these points on the line ABC, Fig. 23, and you have the angles at once. If the figure required is greater than the square can cover, then continue the line A D to the length required ; then square down until the line cuts ABC, and the work is done. If a smaller figure is wanted, measure off on A D, or A B C, and square over. At Fig. 24 I show a quarter of a circle trisected or formed into angles of 30, 60 and 90 degrees ; 12 and 7 by the square will give 30° and 12 and 21 will give the angle of 60°. These are things to remember, as the carpenter and joiner will find them very useful in his everyday work. To find a Tangent. — To find a Tangent to the arc of a circle, divide the chord A C (Fig. 25) in B ; from B square up a line cutting in K, giving it as a point, through which draw square with K A as shown cutting in R, making K S equal K R ; draw from S through A, and the line is tangent to the arc at point A. The steel square may be used as shown, to good advantage. This problem is very useful to stair-builders and other practical workmen operating on circular work, where tangents must be found to make proper lines for joints. To find a point that will be the centre of a circle touching any three points not in a straight line : Let ABC, Fig. 26, be three points through which 4t is desired to describe a circle or seg- ment of a circle ; connect B C, also B A ; divide A B at i ; then square down at i with the steel square, and continue the line indefinitely. Divide B C also equally at 2, then square down at this point as shown ; continue the line until it crosses the line starting from i B A. At the junction of these lines 36 STEEL SQUARES set one leg of the compass and extend the other to either of the points ABC; describe a circle, and it will be found that AND THEIR USES. 37 its circumference will touch the points ABC exactly. The same problem is shown at Fig. 27, where the lines starting from I and 2 are continued to S, which is the centre of the circle whose circumference touches the points ABC. 38 STEEL SQUARES This method of finding a centre of any segment, such as part of a circle, is one of the most useful known in the art of constructive carpentry, as it enables the workman to get the exact sweep of any circle, arch, window or door-head, if he has but the width of the opening and the rise or height of the arch given him. As an illustration, I show at Fig. 28 a portion of a door- way with a segmental head. Suppose the doorway to be three feet and six inches wide, and the rise to be nine inches only. Now set off the width as shown, then the height from the spring line A C at equal distances from each point, connect A B and B C, proceed as in the other problems, and the centre of the circle will be found at S. In many cases it will be impossible to use compasses or even an ordinary trammel, for in large openings or arches for bridges or other work the trammel could not be used. When such is the case a tape line, or sometimes a strong cord may be used, or even a surveyor's chain. In making centres for bridge work or for large openings in buildings, the angles of the voussoirs and key stones may be obtained and laid off on the sides of the centres, or they may be marked off and AKD THEIR USIS. 39 measured and placed on paper or on the drawing board until required. This problem may be applied to many cases m carpen- ter's work, sheet metal work, and in laying out curves of any sort ; and I would advise the young mechanic to learn it thoroughly and apply it as often as possible. It frequently happens that the skilful carpenter or joiner is called upon to perform some work which justly belongs to the architect, but which in many instances the architect him- self does not know how to practically operate. For instance : Fig. 29. It is a well known fact, that if a column is formed with a straight line down its side in the direction of its length, when completed it will appear as though it was made concave, or of less relative diameter half way down, than it really is. This peculiarity was well known to the Egyptians and provided for, but it remained for the Greeks to discover the ''why and wherefore " and apply a scientific remedy. Of course, many columns are now made with straight tapering sides, or parallel from base to neck, but this is not the best or most scientific manner, and I now propose to show how a line 40 STEEL SQUARES may be obtained by the use of the square and a rod, that will be conoidal, which is the name given to a curve described as I am about to show. Take the square and place as shown at A and B, Fig 29. Draw a line, G, which must be straight with the lower edge of the blade B. Then measure the height of the column on the outside edge of the blade, A — in scale, of course — and draw the line I at right angles to A. On the line, G, measure a distance equal to half of the diameter of the base, and on line I measure a distance equal to half the diameter of the top of column. Then take a rod, C, and make a hole in one end, to hold a pencil, D ; from the centre at D measure a distance equal to half the diameter at base, and drive in a nail, E. Now bring the pencil, D, to I and make the nail, E, touch the edge of the blade, A. This done, drive in a nail, F, so that it will just touch the edge of the blade, B, or the line G. All is now ready : move the pencil, D, to G, being care- ful to see that the nails slide along smoothly on the edges of the square, and the pencil, D, will describe the curve desired. In case a full-sized templet or curve is required, all that has to be done is simply to nail down on a clean floor two strips of wood in imitation of a large square, making sure the strips are long enough to make the curve as long as the column required. The rest is quite easy. A templet of this kind can be reversed and made con- cave, so as to try on the work as it progresses. Sometimes the curve obtained by this method is designated as "the curve of diminution." Among architects, however, the curve, or rather the swelling of a column or pillar or newel post, in the centre is known as Entasis. There are many other ways of getting this curve, but I AND THEIR USES. 41 do not know of any that is better than the one shown, or so easily understood by the operative workman. The Diagonal Scale. — In the first volume of The Steel Square and its Uses, I gave a brief account of the diagonal scale as shown on the No. lOO square. I propose here to dwell at length on this department of the tool, and show to what extent this scale may be employed. On Fig. 30 I show a diagram of the scale enlarged and Fig. 30. lettered for this occasion ; and I may here state that the workman will find no difficulty in adapting the diagrams and what follows to the scale as depicted on his own square. From the numerous inquiries I have had I am led to believe that the diagonal scale is not so well understood or appreciated as it ought to be, which is certainly to be regretted. This scale is intended for minute measurements, and when a thorough knowledge of its properties are understood, it is not a very difficult operation to so employ it that the 500th part of an inch may be obtained, and for the practical work- man this is, perhaps, minute enough, though to the advanced scientist this would be considered a trifling operation, when such minute measurements are used as the 5000th part of an inch. 42 STEEL SQUARES In actual practice the scale is never used to find the smaller measurements, but, it may sometimes happen that the workman may want to measure a plan or take a distance on a map pretty accurately, then a fine subdivision will be found useful. In order to give the reader a fair understanding of the principles on which this scale is founded, I illustrate its construction and the manner in which it is used, and in doing so I will, for convenience sake, quote from an excellent authority on the subject : HH ' ' Let us draw a diagram, Fig. 3 1, say three times the size of the first division of the scale as shown on the square. Imagine the short distance from A to B to represent ten inches ; it will be evident to any one that to divide that short space into ten equal parts would simply confuse the whole diagram ; but if we adopt another plan and divide it into ten parts on its length, as shown, and then draw a diagonal line from B to C, we have the distance A B divided into ten parts. The numbers shown in the diagram indicate the fractional parts of the line A B, and if we take our compasses and place one leg on the line A C, at number five, and the other leg where the diag- onal line cuts the line five ; that distance will be found to be just one-half of the distance between A and B. There is a difference of one-tenth of the whole distance between A B, at every point where the diagonal cuts the cross lines. Or in other words, where the diagonal crosses the horizontal lines, the point of juncture is one inch nearer to the line A C, than the next point lower down." This is the principle on which the diagonal scale is based, Fig. 31 ANDTHEIRUSES. 43 and it will be seen that any fraction of a foot or an inch may be so divided by diagonals that the most minute subdivisions may be obtained. The measurements, of course, are always taken along the horizontal lines, and measured from the perpendicular to the diagonal. With a thorough knowledge of the foregoing it will be easy to understand that the perpendicular is not necessarily limited. It may be made twice or four times the length, and divided into twice or four times the number of parts which would render the diagram to make reading of 200ths and 400ths respectively. If twelfths of an inch or foot are wanted, all that is required is to divide the height into twelve parts instead of ten, draw the diagonal, and the twelfths are there. In using this scale let us examine it at Fig. ^o, and we will see that the other divisions are in inches, so to apply the rule we proceed as follows : For instance, we want one inch and forty-six one-hundredths, place one leg of the com- pass on the one inch mark and the other leg where the diag- onal cuts the line at 4, on the sixth division up. This gives the length required. The foregoing description and explanation applies to the diagonal scale that generally accompanies a case of drawing instruments, as well as to the scale on a steel square. It may be well to state here that some new squares recently placed in the market, and known to the trade as No. 200, have, in place of the diagonal, a graduated line or scale, with the subdivisions of the inch marked off in looths. This innovation is said by the manufacturer to be "an improve- ment." If it is, the "improvement," in my opinion, is a questionable ©ne. 44 STEEL SQUARES To Make Flared Circular Work. — This problem will some- times be found useful to the wood-worker, but it is more par- ticularly adapted for the use of tin and sheet-metal workers - .^ Fig. 32. Place the square as shown at Fig. 32, A, B, i and 17. Do not alter the position of the square, but lay off one-half the large diameter of the work in hand, at A B. Then measure Fig. 33. from A to I the depth of the work ; now move the square down to I as shown and draw a line ; on this line mark off the distance of half the small diameter of work, as at i, 8; AND THEIR USES. 45 draw line from B to 8 until it crosses line at 17; now set compasses at 17 and 8, and describe circle at h, Fig. 33 ; then set compass at 17 and B and draw circle z', Fig. -i^i) draw the line/, Fig. 'i^'}, ; divide the circumference into any number of pieces — I show these in this case — and take a piece of cardboard or other flexible material, and measure off on the line h the number of divisions. Draw radial lines to centre as shown. Allow extra material for joining. Any flaripg piece of work on a circular plan can be made by this method. Steel Squares Generally. — The Frontispiece exhibits three different styles of steel squares — the bridge-builder's square, the machinist's square and the carpenter's square. The pecu- liarity of the bridge-builder's square is that the blade is three inches wide, having a slot twenty-one inches long and one inch wide down its centre. It will be easy to see how useful this square is, as it may be used for 2 in. or 3 in. mortises with either 2 or 3 in. shoulders, or, when occasion requires, it may be used for one inch mortises or one inch tenons. One and a half inch mortises and tenons may be laid out with the blade of the square. This square also has other useful features which will readily be seen by the practical workman. Nearly all of the problems shown in this volume may be solved by this square, but it does not possess for the regular workman that usefulness which is attributed to the carpenter's square. The small square shown is made specially for machinists, and is very handy for men who have charge of wood-working machinery. It is also very useful as a bench square, and should find its way into every carpenter's and joiner's kit. The No. 100 square shown is the carpenter's square, and is the one by which all the problems shown in this work have been solved. An exhaustive description of all the figuring on this square may be found in my first treatise on The Steel 46 STEEL SQUARES Square and its Uses, a copy of which the reader of this should obtain, if he has not already secured one. There is a square made, the blade of which is 1.7 in. wide and twelve inches long ; the tongue is nine inches long and one inch wide. It is figured in inches, half inches, quarters, eighths and sixteenths. It is a very handy square, and often useful where either a larger or smaller one would be of no service. Besides the squares mentioned in the foregoing there are several others, such as the stonecutter's square, which has a blade thirty inches long and two inches wide, and a tongue two feet long and one and a half inches wide. The blade and tongue are marked into one-eighths, quarters, half inches and inches. They are excellent tools for stonecutters, some of whom are quite expert in their use. The price of these squares is about three dollars and fifty cents. There is also a square made called * * The Flat Steel Square, " which is often found useful for some sorts of work. It is similar to the ordinary carpenter's square, but is not tapered in its thickness, nor is it figured the same, showing only eighths, quarters, halves and inches. There is also an iron square made which sells for about $1.50, and which is generally used by blacksmiths, brick- layers and some wagon makers. Why these mechanics should use such inferior tools as this is, I cannot understand, unless it is on the scale of economy, which in this case is certainly misapplied. A new square, called " The Crenelated Steel Square," has lately come into use, which has little notches cut along the inside edge of the tongue. I give herewith an illustration of it. Fig. 34, and quote from the inventor's circular the object of the invention : AND THEIR USES. 47 *' This SQUARE is invaluable to the mechanic. It is designed to facilitate the operation of marking timber for mortises or the 'Maying off a frame." At the same time it secures the utmost accuracy. It excels all other squares for carpenters' Fig. 34- THE CRENELATED STEEL SQUARE. or builders' use. Turning the timber is nearly dispensed with, as three sides can be marked while it remains in the same position, 4§ STEEL SQUARES "By the use oi this square one man can lay off more timber in the same length of time than two men can in the ordinary way. ''You can mark on either side or overhead." Directions /or Use. — Take the square in the left hand, lay the tongue of the square upon the surface to be marked, for a tenon or mortise, lower the end of the main arm of the square next to you, say about two or three inches from the upper surface, place the awl, held in the right hand, in the notch designating the distance you wish to have the mortise or tenon from the outer surface, gently press the square against the timber, and with one toward movement the mark is made. Replace the square as before, place the awl in the notch desired, for width of mortise or tenon, and again mark as before. For a mortise, replace again, place the awl in a notch equidistant from marks already made, and again mark, for guide to the augur, doing away with witness marks. In using a pencil, after having marked, move the square back a trifle before moving the right hand, to avoid breaking the pencil. The same rules apply to its use in marking on the sides of timber or overhead, and the square in either hand. I may also add that the square is so figured that almost every problem shown in either of the works on the steel square can be solved with it if skilfully handled. As this work is intended to discuss the Steel Square and ITS Uses only, I do not feel called upon to say anything about other kinds of squares, of which there are many, all useful for the purposes for which they were designed. I show at Fig. 35 a combination tool in which the square is the most prominent feature. The intelligent workman will AND THEIR USES. 49 have no difficulty in adapting the tool to a great variety of work, and while it is somewhat cumbersome and scarcely adapted for the everyday uses of the carpenter, many foremen and master builders may find it of great service. The device, I believe, was patented some years ago, by Mr. P. O. King, of Valley City, Dakota. Fig. 35. By a proper adjustment of the various parts of this com- bination tool, angles and lengths of all sorts of braces and struts may be obtained. The steel square, A (Fig. 35), is formed with longitudinal dovetail grooves in the faces of its arms to receive sliding screws. The 36 in. rule, B, has a longitudinal slot through its t Fig. 38. face for the sliding screws to work in ; this slot extends to within 2 in. of one end and within 5 in. of the other end. One side of the rule is divided into inches and twelfths, and the other side has lumber measurements indicating 12, 14, 16, and 1 8 ft., or other lengths. The sliding screws (Fig. 38) are so constructed as to form scribers. A T-square (Fig. 36) 50 STEEL SQUARES may be formed by sliding the head-piece, D, on one end of the rule ; the square may also be used as a gauge by fitting the rule with the grooved sliding metal block S, Fig. 39. Fig. 36. When the square and rule are combined, as shown in Fig. 35, the tool may be used for giving the angle and length of differ- ent kinds of rafters and braces. The rule can be readily Fig. 39' taken off and put on, and when once set will be held firmly by the set screws. When the tool is to be used for levelling, as in Fig. 40, the supports F, which screw into the rule or Fig. 40. pass around it, may or may not be used. The method of using the tool as a level is clearly shown in the drawing ; when used as a plumb (Fig. 37), the string is placed in th^ AND THEIR USES. 51 slit E, as in Fig. 41. The yard rule may also be used as a plumb by attaching the string as shown in Fig. 41. Fig. 39 shows the tool arranged to be used also as a beam compass. If this instrument is in the market, I can not find it. I have made inquiries at many of the large dealers in such kind of tools, but up to writing I have been unable to find this one. The description as given in the foregoing is taken from the inventor's circular, and may be relied upon, as I have examined the tool closely — on paper — and find its capabili- ties far beyond those the inventor claims. Fig. 37. c- Fig. 4i Useful Applicatio7is of the Square. — At Fig. 42 I show a very useful quality of the square or right angle, when used in combination with the quadrant, and equilateral triangle. One property of the circle is that its radius will divide its circumference into approximately six parts. This fact gives us the idea that a scale may be so constructed that it will 52 STEEL SQUARES divide a circle into any number of parts we may desire. The construction is as follows : Through E draw a tangent line at right angles with B E ; on the radius A B form the equilateral triangle intersecting in Fig. 42. C-^then A C divides the circumference of this circle into six parts ; produce the lines from A B to cut the tangent in D and J— make J N equal E D. This gives E N for one of the divisions on the tangent line ; the others being equal to AND THEIR USES. 53 E N, forms a scale by which the circumference of the circle may be divided into as many parts as may be desired from one to twenty. For example, let seven be the number required. Draw the line A N; this cuts the perpendicular in P, giving B P as the length of a chord that will divide the circumference into seven equal parts. Suppose the radius A B to measure by a J inch scale, nine feet one inch, and the length of the chord B P, by the same scale, 7 ft. 11 in., which would be the length, it will be seen the method produces results correct enough for all practical purposes. If we wish to divide the circumference of a circle into eight parts proceed as follows : Draw from A to the point below 8 in the figure, which gives B R as the length of chord for eight divisions. For nine divisions : Draw from A to the point below 10 ; this gives us B T as the length of the chord. Ten divisions may be made by drawing from A to the point below lo ; this gives B T, which is the length of chord required. For eleven divisions, draw from A to the point below 1 1 ; this gives B H the proper length of chord. For twenty divisions draw from A to the point below 20, which gives B S as the length of chord for twenty parts. This useful and elegant construction was first introduced by the celebrated Peter Nicholson nearly 100 years ago and was elaborated and improved by the late Robert Riddell, of Philadelphia, of whom I have many pleasant remembrances. The following figure, which is based on the principles con- tained in the foregoing, has been known to advanced work- men for many years, and although it has appeared in several publications during the last twenty years, is not so well known among workman as its merit for usefulness deserves 54 STEEL SQUARES Suppose the lines A J and A 8 (Fig. 43), to be the blade and tongue of the square shown in Fig. 44, then construct along the blade divisions as shown atJHFEDCBA. This is merely an example, and any divisions desired may be used if the proper bevels are used. Now take the distance from A to J, on your compasses, and describe a large circle, with A (Fig. 44), as a centre. With H A as radius, describe a second circle. With F A describe a third circle. With E A, as a radius, describe a Fig. 43. fourth circle, D A is the radius for the fifth circle, and C A for the sixth, and B A gives the radius of the mner circle. This figure (44) is only half-size, being J inch scale, while Fig. 43 for convenience sake is made on a scale of J inch ; so the operator must bear this in mind when working this problem. By keeping this fact m view the following solutions may be easily rendered. The large circle having the radius A J, its circumference is required to be divided into ten equal parts ; these are found by setting a bevel to 5^ inches on the blade of the square, and 3f inches on the tongue. The bevel as now set must be applied to J (Fig. 43), and a straight edge placed against the AND THEIR USES. 55 blade of bevel, it will show a straight line cutting the tongue of blade at 7, giving P 7 for length of chord required which stepped around the larger circle will divide it into ten equal parts. Fig. 44. The next circle having the radius A H, is to be divided into nine equal parts. Proceed as before by setting bevel on 5^ inches on blade, and 3^ inches on tongue. Now apply at H 56 STEEL SQUARES (Fig. 43), run line on blade of bevel to point 6, giving P 6 for length of chord wanted. Now take third circle A F, the circumference of which we will divide into seven parts. Set the bevel to 5 J inches on blade and 4f inches on the tongue. Apply at F (Fig. 43), apply- straight edge as before, and it will give you the point 8, then P 8 will be the length of chord sought, and will divide the circle into seven equal parts. The next circle, with A E for radius, is required to be divided into nine parts ; we set our bevel at 5 J on the blade of square, and at 3^ on the tongue. Apply at E (Fig. 43), use straight edge as before which will give you point 5 ; thus P 5 is the length of chord required, and will divide the cir- cumference into nine equal parts. It will be seen that the bevel is at the same angle for A E, as it was for A H, and that each of these circles are divided into nine equal parts, though the diameters are unequal, hence it will be seen that the same angles divide any sized circle into same number of parts. The circle whose radius is A D, is to be divided into eleven parts. Set the bevel to 5f inches on blade of square and 3 inches on tongue, proceed as before, cutting point 4 on Fig. 43 ; P 4 will then be length of chord required. The circle having radius A C, is to be divided into thirteen parts ; we set blade of bevel on 6 inches on blade of square, and 3^ inches on tongue, and proceed as before. Cut the line at 3 and P 3 will be the chord sought for, being 1-13 the circumference of circle. The inner circle described with radius A B, is divided into seventeen parts as follows : Set bevel to 6 inches on blade of square, and 2J inches on tongue ; set to B on Fig. 43, and place straight edge against blade cutting the line P 3, then AND THEIR USES. 57 P 3 at 3 will be the chord sought. This distance stepped round the circle A B will divide it thirteen times. This problem, or rather rule, may be worked to any extent and the operator will soon find the figures to make any number of divisions he may require. Figure 45 shows a method of constructing two unequal K Fig. 45. squares so that the surface of the larger shall be double that of the smaller. Let A B C D be a square of any size. Draw from B through D, and from C through A ; make L H and L K equal B D and A C ; completing the other sides with the square as shown, then the square L H N K is just twice as large as A B C D. This is a very useful problem and may be brought into use by the active workman in the solution of many things that present themselves from time to time. 58 STEEL SQUARES Suppose we have a post 4x4 inches supporting a given weight, and we wish to replace it with another, which is required to sustain double the weight, we simply form a square 4x4 inches, and proceed as shown in the diagram, and the larger square is the sectional area of the required post or column. Of course this may be solved in a somewhat simpler manner, either with or without the square. It will be seen on examination of the diagram that it is the diagonal or the line running across the corners of the smaller square that gives the sides of the larger one ; hence, simply measuring across the corners with a rule will give the length of side, or by using the square and measuring across, at the figures Fig. 46. representing the size of the smaller square ; for example, as in the post mentioned, measure from 4 inches on blade to 4 inches on tongue, and so on for any dimensions within the scope of the square. Reduction of sizes may be found by simply reversing the rule, indeed, the thinking workman will find in his experience dozens of cases where this rule may be of use in some form or other. Figure 46 shows how the circumference of a circle may be obtained by the square, the diameter being given. The solu- tion of this problem by the use of the steel square has been AND THEIR USES. 59 attempted by a number of writers on carpentry. Payne, Nicholson and Robert Riddell have all tried their hands at it, besides a number of lesser lights, with varying success. Riddell, perhaps, came the nearest to a correct solution. It is not claimed that absolute correctness is obtained in this way, but it is claimed for this-^method that it is the nearest approach to correctness Vi&tr'm ad e by using the steel square. The method is not Wew, it having been employed for more than ten years. Let A. D represent a straight edge of a board, say I o in. or 12 in. wide ; place the end of the blade of square at A, and let D on tongue be 7 15-32 inches. Take three Fig. 47- diameters from A to C, and square down a line from C, cutting A D at E ; then A E equals the circumference. A circle whose diameter is eight inches would have a circumference equal to the line from A to D by this rule. It will be seen by this that any right angle whose base is 24, and having an altitude of 7 15-32, forms a constant by which siny circumference may be obtained by spacing three times the diameter on the line A B, and squaring down as at C, the hypothenuse being the required answer. The line A B may be continued indefinitely, being careful to retain the proper angle as shown in diagram. Fig. 47 shows a method by which the circumference of a circle may be obtained from the diameter. This will be found 6o STEEL SQUARES very convenient in almost all the trades ; particularly is it so for sheet-metal workers, carpenters, plasterers and coopers. Describe a circle in some proportion to the actual work, say one inch to the foot ; then apply the heel of the square at the centre of the circle, as at A ; then project the lines A B and A C as shown. Now connect the points where the radial lines touch the circle by the line B C, and from the middle point of this line draw the line D E to the circumference. To obtain the circumference of the circle, add to three times Fig. 48. the diameter the distance D E, which will give the desired result practically correct. At Fig. 48 I give a practical illustration. Suppose we have a circular tank or cistern, or a sheet metal vessel of any sort that requires to be eight feet in diameter. Draw a circle eight inches in diameter. This is one inch to the foot ; place the square with the heel on the centre as at A, draw lines along side blade and tongue as shown, cutting circumference, then at the junction of these lines draw a line same as B C in Fig. AND THEIR USES. 6l 47, then draw the short line from the centre of the line B C Fig. 47 and you have the circumference near enough for all practical purposes. It will be seen at once how useful this method may prove to the mechanic, and how easily applied. For getting the length of hoops, or the number and breadth of staves for a circular tub, it will prove quite a useful method. At Fig. 49 is shown a diagram from which the different angles — in degrees — are shown in such a manner as to be obtained at once by the square. The figures in the left column give the angles in degrees from 5° to 90°. The column on the right shows the figures in inches, so as to enable the operator to get the different pitches. For example, if quarter pitch is wanted take 12 in. on the blade and 6 in. on the tongue, as shown in the sixth space of the column, counting from the top. If you want degrees, say for example a pitch of 30°, take 12 in. on the blade and 6 15-16 on the tongue and the line along the blade will have an inclination of 30°, and the angle on the line of the tongue will be 60°. This diagram will often be found useful to the carpenter and joiner in obtaining degrees, for as a rule a protractor is seldom found in a workman's kit. Fig. 50 shows a method of squaring the circle, which may be of use occasionally. Erect a perpendicular as shown in diagram at A B, then from the centre of the circle D space off any distances of equal length, as at A and B. Use A as a centre and draw the arcs 5 and 6, then, using B for a centre, draw the arcs 7 and 8, then draw line C C, cutting centre of arcs and running through centre of circle at D. The lines from I, 2, 3, 4, as shown, will square the circle. The cir- cumference may be described before or after the operation of squaring. 62 STEEL SQUARES Hip, Valley, Mansard and Other Roofs.^k work of this kind would not be complete if it did not embrace something in regard to hip roofs, therefore I deem it proper to insert a few examples of roofs of this kind, showing how the bevels and lines for working out same may be obtained. The question of hip roofs was pretty thoroughly discussed in the first volume of The Steel Square and its Uses, also my work on Prac- tical Carpentry, so I will only give here a few examples that are not included in the works mentioned. AND THEIR USES. 63 T0 cut a Purlin against a Valley Rafter.— Lti ABC (Fig. Fig. 50- 51) be the eaves of the roof, D F and F E the ridges, B F the F J D Fig. 51* ,alle5r on plan, H E the rise pf the roof, and B E the pitch of 64 STEEL SQUARES the roof. From B describe the arc E I ; draw I J parallel to H F, and draw B J ; then the bevel C B J will apply on the top of valley. From H draw H K square to B E, and from H describe the arc K L ; draw K N and L M parallel to H F, and draw N M parallel to F D ; draw M F, then the bevel L M F will apply on the side of the valley. At Fig. 52 I show another method of finding the bevels. Fig. 52. Let A B C be the eaves of roof, D F and F E the ridges, B F the valley or plan, H E the pitch of roof. Mark the purlin I J K to a large scale — full size, if possible — and draw I L, J M, and K N all parallel to E F ; make M O equal to J K ; draw O P, and draw N P parallel to D F ; join M P ; and the bevel J M P will apply on the side of valley. Make AND THEIR USES. 65 S R equal to J I ; draw L R ; join MR; and the bevel J M R will apply on top of valley. The method given here will apply to hips as well as valleys, and the square may be used in finding the angles where the pitches are given. It is better, however, in cases of this kind, to work out the bevels and angles by diagrams as shown in the two figures, as it saves time and insures accuracy. To Timber a Hexagon Roof. — On the line i 2, Fig. 53, Fig- 53. is the seat of the hips, 3 4 will be the rise. On the line i S, say at O, draw a line touching the line i 2 square from i S, which is the seat of a jack rafter. Make P H equal P F ; square from O P draw the line O H : this gives the bevels 66 STEEL SQUARES and length for plumb cut of jack rafter. From C 7 draw the line 8 9 indefinitely ; set the compasses to i 4 and from the point 4 intersect 9 8. Repeat from 7 8, which is the covering for one side of roof, the intermediate lines being the lengths of jack rafters and bevels for side-cut. On the line i 2, say at B, take B for a centre, touching the line 4 2, for radius, describe the arc B C, through B, at right angles to i 2, draw the line D E, and from C to E and C to D will be found the bevels for backing of the hips. This rule will apply to any sort of a roof having its plates on the same plane, and is particularly adapted to polygons of any kind. The method is an old one, having been invented by Peter Nicholson, from whose works this and the two pre- vious examples are taken. It will be new to many of my readers, for I have never seen it reproduced in any American work or publication. It is exceedingly simple and, withal, accurate. Fig. 54 illustrates a very thorough and simple manner of obtaining the lines, cuts and bevels for a Hip roof Suppose the lines A B and B C represent the walls at the angle of a building : B E shows the seat of the hip rafter, and G F the seat of a jack rafter. Draw E H at right angles to B E, and make it equal to the rise of the roof; join B and H, and H B will be the length of the hip rafter, and the bevel shown on the lines E H and H B will be the plumb cut for same. Through E draw D I at right angles to B C ; upon B, with the radius B H, describe the arc H I, cutting D I in I ; join Band I, and extend G F to meet B I in F ; then G J will be the length of the jack rafter. The length of each jack rafter is found in the same manner by extending its seat to cut the lines B I. From F draw F K at right angles to F G, also F L at right angles to B E ; make F K equal to F L by the arc L K, or make G K AND THEIR USES. 67 equal to G F by the arc F K ; then the angle at F will be the top bevel of the jack rafters and the bevel at K will be the plumb cut. Valley rafters and "cripples" connected with them may all be obtained by this same method. This method will apply to any sort of hip roof, be the angles right, acute or obtuse, with very slight variation of lines. I introduce at this point a piece of pyramidal frame work, or battered frame work, as some carpenters term it. Since sending out the first volume of The Steel Square and its Uses, I have had hundreds of letters asking questions about this kind of a structure and for information regarding the 68 STEEL SQUARES manner of construction. I have also received many letters asking for more information regarding the manner of con- structing hip roofs and the lines for splayed work, such as hoppers, carriage seats and similar work. All this class of work is based on one principle, of which the pyramid is the central example. Fig. 55- If the young workman wishes to grasp the hard-pan prin- ciples that underlie this question or questions, let him make a rough pyramid, say with a base 4x4 feet on the ground plan, and 2x2 feet at the top, and four feet high. Now try ANDTHEIRUSES. 69 and fit a base board around this pyramid. Make one corner a butt joint ; see that it fits accurately. This will give an idea of what is wanted, and if careful notice is taken of this joint, the workman will be better able to understand anything I may say on the subject in hand. After making a good butt joint and finding out the " why and wherefore" of the change in angles of a perpendicular base and an inclined base in the "butts," a mitre joint should be tried, which will further enlighten the student. The young man who tries this once, and thoroughly investi- gates the operation and examines closely the difference between splayed and square work, will never be at a loss to make a hopper, put on a hip roof, or erect a tapering structure similar to that shown at Fig. 55, for hoppers and tapering structures are hip roofs, and hip roofs are perfect hoppers inverted, or a hopper is a part of a hip roof inverted, which- ever you will. Fig. 55 shows a side of a frame suitable for a windmill or for other similar purposes. The posts incline two inches to the foot^that is, two inches from the plumb line to every foot in the length of the post, and this incline is both ways. The length of post and bevels at the foot and top of posts may be found by applying the square as shown at R — that is, 24 in. on the blade and 4 in. on the tongue, or 2 in. on the tongue and 12 in. on the blade, which is the same thing, so far as the bevels are concerned. These same figures also answer for the ends of the joists, S S. I show at Fig. 56 the manner in which the bevels at the foot of the post are marked. The dotted lines show the bevels on all sides, for, as the post leans two ways, the post must be beveled two ways. This, of course, will present itself to the workman as he proceeds. Let us suppose the foot of the post to have no tenon, but is intended to rest 70 STEEL SQUARES flat-footed on the sills. This being the case, it gives us an opportunity of getting the backing of the post, for, like a hip rafter — which it is — it requires to be backed, if it is intended Fig. 56. to be enclosed or boarded, and we will suppose it is so intended. From an examination of Fig. 57 we can see how the backing of the post may be obtained by using the square Fig. 57- and applying it on the foot after it has been beveled. The overwood at E is to be removed. It will be noticed that the square is placed on the angles O and P, with its heel at E. The distance from E to P is the same as from E to O. The ANDTHEIRUSES. 71 overwood shown in this is somewhat exaggerated purposely, to give a clear idea of the requirements. The braces shown in this sketch will give the student an opportunity to figure. The lengths and bevels may be obtained either by using the square or by taking them from a drawing, or by calculation. I may observe at this point, that the posts in this structure are simply like the hips in a very steep roof or spire, and may be treated as such, and the angles and backing can be obtained in the same manner. A very full and clear explanation of forming hip roofs is given in ^'Practical Carpentry," pub- lished by the same Company that publish this work ; but to insure the student's possession of the practical rules required to build hip roofs of every description, I have embodied in this work a number of excellent rules for that purpose. Mansard Roofs. — I have frequently been asked to show how the cuts and lengths of the corners and rafters of a Man- sard or French roof may be obtained. I herewith exhibit a method of finding the lengths and bevels of a curved roof, with the manner of construction, style and method of attaching cornice, and rule for getting curve of angle rafter : Suppose A D to be the seat line (Fig. 58), A being the lowest point of curve, draw X Y parallel to A D ; at right angles to A D draw A W, F N, G O, H P, J Q and K L ; make Y Z equal W Q ; place the thickness of the angle rib as shown at M X ; at right angles to IM L draw L V, Q U, P T, O S and N R ; make N R equal to E F ; make O S equal B G ; make P T equal C H, and Q U equal D J ; through U T S R M trace the curve of the angle rib ; make U V equal J K. The position of the upper and lower plates in connection with the angle rib is shown at V and 2. These ribs may be got out of plank ten inches wide, as the curvature takes but six inches from the ^lS3 72 STEEL SQUARES width. Although the radius for the curve, 20 feet, is given yet for all practical purposes the curve of the rib may be made RADIUS 20 Ft. Fig. 58. by first laying out the plank, as it connects with cornice plates and rafter, then bending a rod and marking the curve from AND THEIR USES. 73 the points given to the depth 3, 4, as required. If the angle rib is drawn and placed as here shown it will not require to be backed ; but if for any reason backing the rib is required, the rule for finding the lines for this purpose may be found under the head of Hip Roofs. A Mansard roof is really a hip roof as far as it goes, or it may be called an inverted hopper, and, as both these questions are considered in this work, it is quite unnecessary to say more on these matters here. It will be seen on examination of the diagram that the bevel may be obtained by the square, though really there is not much gain in time by using it for this kind of work, though I might say that in some cases, particularly when the rafter is not curved, the square may be applied to advantage. Figure 59 shows another style of French roof with only a portion of the rafter curved, it also shows full details of con- struction both of roof and cornice. In this instance the curved part of the rafter may be nailed on as shown at A B. CD shows the side of the rafter. The same method may be observed at the angle rib E F, which may be nailed to the hip H G. The rules given in the previous illustration are applicable to this. The radius shown is given here merely as an example. Any radius may be used. Figure 60 shows a very useful form of roof plan, with a method of finding the butt joint for the straining beam and principal. The line O O is the line of joint. A A show how the square is applied ; the points A A are equi-distant from S, through which point the joint line is drawn, having the point at the heel of the square in line. Concerning Hopper Bevels. — Since the first volume of The Steel Square and its Uses was published I have had quite a number of inquiries regarding Fig. ^Z of the first part and the explanation thereto. .--^ Fig. 59. AND THEIR USES. 75 It appears the explanation is not sufficiently clear to enable all minds to grasp it, yet it is simple and to my mind the best method ever produced for obtaining the bevels of all ordinary hoppers. I reproduce it in this volume with a more lengthy explanation, and give some examples so that the workman may more readily see how to apply the method. In Fig. 6 1 the whole thing may be worked out. Let S S be the edge of a board any width, and O O the other edge of the board. Make the line A B the same bevel as the flare of Fig. 60. the hopper desired. Place the square with the blade so as to coincide with the line A B, and mark by the tongue the line B C, as shown, then square up from the edge of the board the line B D. Now we have a figure that will, when properly applied by the steel square, give the cuts for a hopper of any flare, either with butt or mitre joints. Suppose A B to be 8J inches, then B C will be 12 J inches and A D 10 inches and D C 5 inches. Now A B or 8| inches on the blade, and A D or 10 inches on the tongue, will give 16 STEEL SQUARES bevel for face cut ; this seems self-evident. Now take B C or 12J inches on the blade, and A D or 10 inches on tongue and you have the mitre cut. Again take D C or 5 inches on blade, and A D or 10 inches on tongue and you have the butt cut. This is an example only and any style of hopper built at right angles on its base, and having sides of equal flare, may have all its cutting angles found by this method. Let A B always be the guiding line, and the one from which all the others take their positions, making that line equal in length the width of the side of intended hopper. Fig. 61. I recapitulate the rule : To find bevel to cut across face of board : Take A B on blade and A D on tongue ; bevel of tongue is line required. To find mitre : Take B C on blade and A D on tongue ; line of tongue is bevel sought. For butt joint : Take D C on blade and A D on tongue, and line of tongue gives joint required. I now exhibit a method of obtaining the bevels for a hopper having diff'erent flares : The rise to the foot being given, find the bevels of the opposite sides having the lesser rise to the foot. Apply the square to a straight-edge, taking 1 2 in. on the blade and the AND THEIR USES. n lesser rise to the foot, on the tongue. Mark by the blade, A B, Fig. 62, make B C perpendicular to A C D, and equal to the greater rise to the foot. Draw B D perpendicular to A B. Apply the square to the line A C D. Taking A C on the blade and 1 2 in. on the tongue, mark by the blade for C E. Make D E perpendicular to A C D. Apply the square to the line A C D, taking A B on the blade and 1 2 in. on the tongue, which will denote the surface bevel. Apply the square, taking B D on the blade and D E on the tongue, which will give the line for mitre joint. For butt joints take B D on the blade and 1 2 in. on the tongue, which will give the bevel required. The same results may be obtained by geometrical con- struction. Make B D, Fig. 62, equal to 12 in. Draw A F. Make B G equal to B D, and draw F G. Make D H equal to B D, and draw E H. Then the acute angle at F is the angle of the surface bevel, and the obtuse angle at F is the bevel for butt joints. The angle E is the bevel for mitre joints. To find the bevels of the opposite sides having the greater rise to the foot, proceed in the same manner, being careful to yS STEEL SQUARES supersede lesser rise for greater rise, and greater rise for lesser rise. The principles involved in the foregoing examples cover the whole field of hopper cuts, and their study is as interesting as instructive. In connection with the subject of hoppers, I present the following illustration, Fig. 6^, taken from ''Carpentry and Fig. 63. Building. " This shows how the butt cut for any sort of a regular hopper may be cut by those having a band-saw at their disposal. It is perhaps more curious than available. In order to make this department complete, I herewith give a method by which the cuts or bevels may be obtained for a flaring hopper having only three sides. In other words. Fig. 64 gives bevels for a box whose top and bottom form two unequal equilateral triangles : Make the triangle C E F, then from the middle point of E F let fall the perpendicular B D, then draw A B parallel and equal to C D, also A C parallel and equal to B D, thus forming the rectangle A, B, C, D. Now draw C H to the same inclination from C D, that a side pf the box when AND THEIR USES. 79 finished will show from the perpendicular line ; then draw L D perpendicular to C H, and, with C as a centre and a radius C L, make an intersection at I, and connect I and A, and at A is the bevel for the mitre at the ends. Again, with D for a centre and a radius D L, make an intersection at K, and connect K and B ; and at B is the bevel for the down or cross cut. To find the Bevels required to Mitre together the Flared Sides of a Hexagonal Box, — Let N E (Fig. 65) be in the plane of ihe bottom of the box, and E J the inclination of the sides ; continue G D to B indefinitely ; through J draw J O parallel to Q D ; through O draw A C at right angles to J O ; make E M equal E J ; through M draw L C parallel to Q D ; make F H equal F J ; draw H A parallel to Q D ; through F draw F B parallel to L C ; connect C D, and the bevel at D will give the angle for the face joint ; connect B A, and the bevel at B will give the angle for the mitre on the sq'iare edge. This rule may be applied to other figures, such as pentagons, pptagons, or other similar hoppers, where the flares are equal 8o STEEL SQUARES. Sometimes the student may get in a little maze when working out the angles and bevels for hopper work, as the operation is often perplexing, and, like the rules for stair- building, requires patience and steadiness. There is no reason. Fig. 65. however, because of these matters appearing difficult at first, that they should not be thoroughly understood by any ordinary workman, after two or three trials. Established 1870. STANDARD BOOKS PUBLISHED AND FOR SALE BY THE INDUSTRIAL PUBLICATION CO. New York. These books will be sent, postpaid, to any address in any accessible part of {he world, on receipt of price. — Full Descriptive Catalogues may be had free. — Neio Catalogues, with additions of new books, are issued from time to time, and will be sent to any address on request. — Address, IXDUSTRLAX PUBLICATION CO., New York. THE STEEL SQUARE AND ITS USES. Being a Description of the Square and Its Uses in Obtaining the Lengths and Bevels of all kinds of Rafters, Hips, Groins, Braces, Brackets, Purlins, Collar-Beams, and Jack-Rafters. — Also, its Application in Obtaining the Bevels and Cuts for Hoppers, Spring Moldings, Octagons, Stairs, Diminished Stiles, &c. — By Fred. T. Hodgson, author of "Practical Carpentry," "The Builders' Guide," &c. — Third Edition, Revised and Greatly Enlarged. — Illustrated by Nearly One Hundred Fine Engravings. — Cloth, gilt. . . $1 This is the only practical work on the steel square and its uses ever published. It is thorough, accurate, clear, and easily understood. Confounding terms and scientific phrases have been religiously avoided where possible ; and everything in the book has been made so plain that a boy of twelve years of age, possessing ordinary intelligence, can understand it from end to end. This new edition, just issued, is illustrated by nearly one hundred handsome engi'aviugs, showing how the square may be used for solving nearly every problem in the whole art of carpentry. The carpenter who possesses this book need not waste time and material " cutting and trying." He can lay out his work to a hair's breadth, and "cut to the line." And, in these days, the workman who can not lay out his work accurately at the first attempt stands no show. The book is absolutely indispensable to every person who may have to use a carpenter's square. Joiners, cabinet-makers, bricklayers, stonecutters, plasterers, lumber-dealers, amateurs, and all who build a fence, tinker a gate, or make a chicken-coop will find something in this little volume that will help and aid them to do their work better and more intelligently than they could without a knowledge of its contents. Many difficult and troublesome mathematical problems can be solved by the use of this tool, and the methods of solving them are shown in this book. It describes how painting, plastering, and brickwork can be measiired, and how many mechan- ical difficulties can be overcome with gi-eat ease. It explains how ellipses, parabolas, octagons, circles, and many other figiires, may be described by the steel square. It is safe to say that this dollar book will easily enable any intelligent mechanic to save ten dollars in time and material during the first three months that he has it i» use. . . ,. CATALOGUE OF INDUSTBIAL BOOKS. STEEL SQUARES AND THEIR USES. Being a Descriptiou of the Various Steel Squares and Their Uses in Solving a large number of Mechanical Problems in Constructive Carpentry, Joinery, Sheet-metal Work, Cut-stone or Brick-work. Also, showing how many Geometrical and other Problems may be solved by the use of the Steel Square. — By Fred. T. Hodgson, author of "The Steel Square and Its Uses," "The Slide-Rule, and Its Uses," "Practical Carpentry," "The Builders' Guide," (fee- Finely Illustrated. — Cloth $1 This fonns Part II of " The Steel Square and Its Uses," and is not in any sense a substitute for the First Part, which still remains what it always has been— a neces- sity to every intelligent workman. Part II is an extension and enlargement of the First Part, giving new problems, new methods, and new wrinkles for shortening the labor and increasing the accuracy of the workman. It is illustrated in the same handsome manner which characterizes the First Part, to which it foims a companion volume. With these two volumes in his possession the workman has at command the entire practical mathematics of construction, and is prepared to lay out any piece of work more easily, quickly, and accui-ately than it can be done by any other method. PRACTICAL CARPENTRY. Being a Guide to the Correct Working and Laying-out of all kinds of Carpenters' and Joiners' Work, with the Solutions of the Various Problems in Hip-Roofs, Gothic Work, Centering, Splayed Work, Joints and Jointing, Hingeing, Dovetailing, Mitering, Timber- Splicing, Hopper-work, Skylights, Raking Moldings, Circular Work, &c. — To which is prefixed a thorough treatise on "Car- penters' Geometry."— By Fred. T. Hodgson, author of "The Steel Square and Its Uses," " The Slide-Rule, and How to Use It," "The Builders' Guide," &c. — Illustrated by over Three Hundred Engravings. — Cloth, gilt $1 This is the most thorough book of the kind ever published. It is thoi-ough, practical, and reliable ; and at the same time is written in a style so plain that any workman or apprentice can easily understand it. STAIR-BUILDING MADE EASY. Being a Full and Clear Description of the Art of Building the Bodies, Carriages, and Cases for all kinds of Stairs and Steps. — Together with Illustrations Sliowing the Manner of Laying Out Stairs, forming Treads and Risers, building Cylinders, preparing Strings; with Instructions for making Carriages for Common, Platform, Dog-legged, and Winding Stairs.— To which is added an Illustrated Glossary of Terms used in Stair-Building, and Designs for Newels, Balusters, Brackets, Stair-Moldings, and Sections of Pland-Rails.— By Fred. T. Hodgson, author of " The Steel Square and Its Uses," &c.— Illustrated by over One Hundred and Twenty Engravings, many of them full-page size. — Cloth, gilt. . . . $1 This work takes hold at the very beginning of the subject, and carries the student along by easy stages until tlie entire subject of stairbuilding has been un- folded, so far as ordinary practice can ever require. This book, and the following gue on Sand-Railing, cover nearly the whole subject of Stair-Building. CATALOGUE OF INDUSTRIAL BOOKS. A NEW SYSTEM OF HAND-RAILING. Or, How to Cut Haud-Railing for Circular and other Stairs, square from the Plauk, without tlie aid of a Falling Mould. — By An Old Stairbuilder. — Edited and corrected by Fred. T. Hodgson, author of "Stair-building Made Easy," &e. — Cloth, gilt. . . $1 The sj'stem is new, novel, economic, and easily learned. Rules, instructions, and working drawings for building rails for seven different kinds of stairs are given. THE BUILDERS' GUIDE, and Estimators' Price-Book. Being a Compilation of Current Prices of Lumber, Hardware, Glass, Plumbers' Supplies, Paints, Slates, Stones, Limes, Cements, Bricks, Tin, and other Building Materials. Also, Prices of Labor and Cost of Performing the Several Kinds of Work Required in Building; together with Prices of Doors, Frames, Sashes, Stairs, Moldings, Newels, and other Machine-work. — To which is ap- pended a large number of Building Rules, Data, Tables, and Useful Memoranda, with a Glossary of Architectural and Building Terms. — Bv Fred. T. 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Pemberton, Draughtsman and Mechanical Engineer. — Illustrated by numerous engravings. — Cloth, gilt. $1 This is a simple but thorough book, by a draughtsman of twenty-five years' experience. It is intended for beginnei's and self-taught students, as well as for those who pursue the study under the direction of a teacher. DRAWING INSTRUMENTS. Being a Treatise on Draughting Instruments, with Rules for their Use and Care; Explanations of Scales, Sectors, and Protractors. Together with Memoranda for Draughtsmen; Hints on Purchasing Instruments, Paper, Ink, Pencils, &c. Also, a Price-list of all Mate- rials required by Draughtsmen. — Illustrated with twenty-four Explan- atory Illustrations.— By Fred. T. Hodgson.— Paper. ... 25 cents. CATALOGUE OF INDUSTRIAL BOOKS. THE SLIDE-RULE, AND HOW TO USE IT. Being a Compilation of Explanations, Rules, and Instructions, suitable for Mechanics and others interested in the Industrial Arts. — Compiled and arranged by Fred. T. Hodgson. — 25 cents. Rules are given for the measurement of all kinds of boards and planks, timber in the round or square, glaziers' work and painting, brickwork, paviors' work, tiling and slating, the measurement of vessels of various shapes, the wedge, inclined planes, wheels and axles, levers, the weighing and measurement of metals and all solid bodies, cylinders, cones, globes, octagon rules and formulae, the measurement of circles, and a comparison of French and English measures, with much other informa- tion useful to builders, carpenters, bricklayers, glaziers, paviors, slaters, machinists, and other mechanics. Possessed of this little book and a good slide-rule, mechanics might carry in their pockets some liundreds of times the power of calculation that they now have in their heads, and the use of the instrument is very easily acquired. THE ENGINEER'S SLIDE-RULE, and Its Applications. A Complete Investigation of the Principles upon which the Slide- Rule is constructed; together with the Method of its Application to all the Purposes of the Practical Mechanic. — By William TONKES. — Paper 25 cents. THE LIGHTNING CALCULATOR. Practical Hints on Lightning Calculating. — To which are added Rules, Tables, Data, Formulae, and Memoranda, for making rapidly those everyday calculations that are required in business, mechan- ics, and agriculture. — Paper 20 cents. A CENTURY OF INVENTIONS. An exact reprint of the famous "Century of Inventions" of the Marquis of Worcester (first published in 1663). — With au Intro- duction, Notes, and a Life of the Author. — With Portrait after a Painting by Van Dyke. — Edited by John Phin.— Cloth. . . . $1 This is one of the most extraordinary books ever published. The famous "Century of Inventions" is of more than mere historical interest. It contains nu- merous hints and suggestions of what might be accomplished, and will be found of great interest and value to every one interested in mechanics. Many persons claim that the Marquis of Worcester anticipated many of our most important modern inventions and discoveries. Great care has been taken to reprodtiee exactly (so far as modern type, &e., could do it) the edition published by the Marqixis himself. It has been entirely out of print for many years. THE ELECTRICIAN'S POCKET COMPANION. Electrical Rules, Tables, Tests, and Formulae.— By Andrew Jamieson, C.E., F.R.S.E.— Fully illustrated.— Cloth 75 cents. This is the most compact and thorough work in the market for the practical eleeti'ieian. It contains minute directions for all calculations, tests, &c., with clear engravings of the apparatus employed. The following list of contents will give an idea of its scope : — Formulae of the Absolute Units,— Practical, Electrical, and Mechanical. Heat and Light Units. Electro-chemical Equivalents, Electrolysis, Heat and Energy of Combustion. Practical Methods of Electrical Measurements. Electric Conductors: Copper, &c.— Insulators: Guttapercha, &c. Submarine Cables.— Aerial Land-lines. Electric Lighting, and Transmission of Power. CATALOGUE OF INDUSTRIAL BOOKS. LECTURES IN A WORKSHOP -By t. p. Pemberton, formerly Associate Editor of The Technologist; author of "The Student's Illustrated Guide to Practical Draughting." — With an Appendix containing the famous papers by Whitworth ''On Plane Metallic Surfaces of True Planes"; *'0n the Uniform System of Screw-Threads"; ''Address to the Institution of Mechanical En- gineers, Glasgow"; "On Standard Decimal Measures of Length." Cloth, gilt $1 We have here a sprightly, fascinating book, full of valuable hints, interesting anecdotes, and sharp sayings. It is not a compilation of dull sermons or dry math- ematics, but a live, readable book. The papers by Whitworth, now first made readily accessible to the American reader, form the basis of our modern systems of accurate work. THE NEW POCKET CYCLOPEDIA. A Compendium of General Knowledge, Useful and Interesting Facts, Valuable Statistics, and Practical Information. — 16mo., cloth 50 cents. This is a handy volume of 164 pages, printed in small but clear type on very fine thin paper, so that the book may be readily carried in the pocket or trunk. It con- tains all those facts and figures which are most commonly referred to in eveiyday life, great care being taken to secure accuracy and clearness. It is not a collection of "curious information" made up from newspaper clippings, but a thoroughly arranged manual of the most useful general knowledge. HOW TO BECOME A GOOD MECHANIC. Intended as a Practical Guide to Self-taught Men: Telling What to Study; What Books to Use; How to Begin; What Difficulties will be met ; How to Overcome Them. In a word, how to carry on such a course of self-instruction as will enable the young mechanic to rise from the bench to something higher. — Paper, 15e. This is not a book of "goody-goody" advice, neither is it an advertisement of any special system, nor does it advocate any hoblay. It gives plain practical advice in regard to acquiring that knowledge which alone can enable a young man engaged in any profession or occupation connected with the industrial arts to attain a po- sition higher than that of a mere workman. CEMENTS, GLUE, AND PASTE. A Practical Treatise on the Preparation and Use of all kinds of Cements, Glue, and Paste. — By John Phin, author of "How to Use the Microscope." — Paper 25 cents. Every mechanic and householder will find this volume of almost every-day use. It contains nearly two hundred recipes for the preparation of cements for almost every conceivable pui-pose. HINTS FOR PAINTERS, DECORATORS, AND PAPER-HANGERS. Being a Selection of Useful Rules, Data, Memoranda, Methods, and Suggestions for House, Sliip, and Furniture Painting; Paper- Hanging, Gilding, Color-Mixing, and other matters useful and instructive to painters and decorators. — Prepared with special reference to the wants of amateurs. — By An Old Hand. — Paper 25 cents. CATALOGUE OF INDUSTRIAL BOOKS. THE HARDWOOD FINISHER: With Rules and Directions for finishing in Natural Colors, and in Antique, Mahogany, Cherry, Birch, Walnut, Oak, Ash, Redwood, Sycamore, Pine, and all other Domestic Woods. Finishing, Filling, Staining, Varnishing, and Polishing. Also, Miscellaneous Rules for Dyeing, Gilding, and Bronzing. — Compiled and Edited by Fred. T. Hodgson, late Editor of T}ie Builder and Woodworker, and of The Cabinetmaker and Upholsterer. — ]2mo, cloth. . . $1 In this country the art of using wood for almost every purpose has gone far beyond anj'thing that has ever been attempted by any other people. The modera houses of the Americans are finished with a richness and beauty in the woodwork of which our fathers, not to speak of our grandfathers, had little idea. The car- penter, builder, or painter who does not fully understand the best methods of finishing the hard woods so as to preserve and increase their beauty is behind the times. The object of this book is to aid him in acquiring the knowledge necessary to this end; and the author has certainly succeeded in producing an exhaustive treatise on the subject. THE ENGINEER'S HANDY-BOOK: Containing a series of Useful Calculations for Engineers, Tool- makers, Millwrights, Draughtsmen, Foremen in Engineering Es- tablishments, and for the better class of Mechanics and Artizans generally. Also, Rules to determine the Proportion of Wheels for Screw-cutting by a Lathe, &c. — From the fifth London edition, with American additions. — 32mo, cloth 50 cents. PLAIN DIRECTIONS FOR THE CONSTRUCTION AND ERECTION of LIGHTNING- RODS. — ^y John Phin, C.E., author of "Chemical History of the Six Days of Creation," "How to Use the Microscope," &c. Enlarged and fully illustrated. — Third edition. — 12mo, cloth, gilt title 75 cents. This is a well-known and standard work. It is simple and pi'actical, intended to convey just such information as will enable every property-owner to decide whether or not his buildings are thoroughly protected. It is the only book on this subject published in this country that has not been written in the interest of some patent or some manufacturing concern. By following its directions any ordinarily skillful mechanic can put up a rod that will afford perfect protection, and that will not infringe on any patent. Every owner of a house or barn ought to procure a copy. TRADE "SECRETS" AND PRIVATE RECIPES. A Collection of Recipes, Processes, and Formulas that have been offered for sale at prices varying from 25 cents to $500. With Notes, Corrections, Additions, and Special Hints for Improve- ments. — Edited by John Phin, assisted by an experienced and skillful pharmacist. — Cloth, gilt title 60 cents. This work was prepared by the author for the purpose of collecting and pre- senting in a compact form all those recipes and so-called "trade secrets" which have been so extensively advertised and offered for sale. It is by no means a claptrap book, though it' exposes many claptraps. It contains a large amount of valuable information that can not be readily found elsewhere ; and it gives not only the formulae, &c., for manufacturing an immense variety of articles, but important and trustworthy hints as to the best way of making money out of them. Even as a book of recipes* it is worth more than its price to any one who is interested in the subject on which it treats. CATALOGUE OF IXDUSTBIAL BOOKS. A PRACTICAL GUIDE TO SUCCESS IN THE USE OF RECIPES, Formulae, &c., with Hints on Chemical and Mechanical Manipula- tion. — Intended as a supplement to all books of recipes. — By John Phin. — 12mo, paper 25 cents. While it is an undoubted fact that many of the recipes published in the ordinary collections are erroneous, either from original blunders on the part of the authors or from mistakes in copying, failure in the use of others frequently arises from defective information and vicious methods on the part of those who attempt to put them in practice. The object of the present book is to give such hints and cautions as will enable the worker to secure success where success is possible ; and where the products are intended for sale it gives special and valuable advice as to the best methods of putting them on the market. A MANUAL OF INSTRUCTION IN THE ART OF WOOD ENGRAVING. With a Description of the necessary Tools and Apparatus, and Concise Directions for their Use ; Explanations of the Terms used and the Methods employed for producing the various classes of Wood Engravings.— By* S. E. Fuller.— Fully illustrated -with engravings by the author, separate sheets of engravings for trans- fer and practice being added. — New edition, neatly bound. 50 cts. A really thorough and practical work, written for those who want to learn the art without the aid of a teacher. A GUIDE TO COLLODIO ETCHING.-By Rev. Benjamin Hartley. — Illustrated by the author. — 12mo, cloth $1.00 This volume gives complete and minute instmctions for one of the most delight- ful of amateur arts. It is fully illustrated by woodcuts of all the apparatus used (which is very simple and easily made), and also by actual photo-prints of the etchings themselves. THE PRACTICAL POCKET COMPANION. A Cyclopedia of the most useful Facts, Figures, and General Information required by everybody in everyday life. — Edited by John Phin, author of "How to Use the Microscope," "The Work- shop Companion," "Chemical History of the Six Days of Crea- tion," &e. — Numerous illustrations = 10 cents. Contents.— Abbreviations in Common Use— Business Laws and Commercial Rules— Acceptances— Agencies— Bills of Eschange—Cheeques— Common Carriers— Corporations— Law of Finding— Indorsements— Innkeepers— Negotiable Instruments —Partnerships— Promissory Notes — Protests— Receipts— Concrete Walls for Houses —Copyrights— Rules for Correspondence— How to treat Accidents to the Eye— Fac- tors of Safety— Best Methods of Extinguishing Fires— Language of Flowers— Sig- nificance of Gems and Precious Stones— Periods of Gestation and Incubation— Legal Holidays— Homestead Law— Distinguishing Characteristics and Anxious Periods of Infectious Diseases— Prevention of Attacks of Insects— Knots, and How to Tie Them, with full page of illustrations— Genei-al Rules— Single Draw-knot— Galley- knot — Square-knot, or Reefing-knot— Weaver's-knot, or Sheet-bend-knot— Half hitch —Two Half -hitches— Clove-hitch— Timber-hitch— Bowline-knot — Fisherman's-knot —Whipping or Binding— Tying Parcels— Care of Leather— Lightning-rods, general rules for— Best Materials— Proper Size and Best Shapes of Rod— Painting— Points, or Air-Terminals— Ground Connections— Arrangement and Mode of Attaching the Rod to the House— Value of Moneys of Foreign Nations— Passports— Patents— Anti- dotes for Poisons— Postal Rules aiid Rates— Railroad and Steamboat Signals— Rules for Spelling and the Use of Capitals— Trade-marks— Weather Indications, &c. CATALOGUE OF IIWUSTRTAL BOOKS. WHAT TO DO AND HOW TO DO IT IN CASE OF ACCIDENT.— A book for everybody.— Cloth, gilt. 50 cts. This is one of the most useful books ever published. It tells exactly what to do iu case of accidents, such as severe cuts, sprains, dislocations, broken bones, burns with tire, scalds, burns with corrosive chemicals, sunstroke, suffocation by foul air, hanging, drowning, frost-bite, fainting, stings, starvation, lightning, poisons, accidents from machinei-y and from the falling of scaffolding, gunshot wounds, &c. It ought to be in every house, for young and old are liable to accident, and the directions given in this book might be the means of saving many a valuable life. COMMON SENSE IN THE POULTRY-YARD. A Story of Failures and Successes, including a full account of 1,000 hens and what they did. With a complete description of the houses, coops, fences, runs, methods of feeding, breeding, market- ing, &c., and many new wrinkles and economical dodges. — By J. P. Haig. — With numerous illustrations.— Cloth, gilt title. $1 This is a lively and entertaining work, which embodies the actual experience of many years in the keeping of poultry in large and small numbers. It is the most thoroughly practical work on poultry in the market, and contains an amount of solid information which, to even the keeper of a dozen fowls, will make it worth many times its cost. A DICTIONARY OF PRACTICAL BEE-KEEPING. With Notes and Practical Hints.— By John Phin, author of **How to Use the Microscope," &c. — Numerous illustrations. — Cloth, gilt 50 cents. This work discusses thoroughly nearly five hundred subjects. Gives in con- densed form an immense amount of valuable information under the different head- ings. Under the heads Bee. Comb, Glucose, Honey, Race, Species. Sugar, Wax, and others, it brings together a large number of important facts and figures now scat- tered through our bee literature and costly scientific works, and are not easily found when wanted. Here they can be referred to at once under the proper head. PLAIN DIRECTIONS FOR ACQUIRING THE ART OF SHOOTING ON THE WING. With Useful Hints concerning all that relates to Guns and Shoot- ing, particularly in regard to the art of loading so as to kill. To which has been added several valuable and hitherto secret recipes, of great practical importance to the sportsman. — By An Old Game- keeper.— 12mo, cloth 75 cents. This book contains a novel and most valuable feature found in no other work on this subject. This is a series of graduated lessons by which the self-taught young sportsman is enabled to advance step by step from such easy marks as a sheet of pa- per nailed on a fence to the most difficult trap-shooting and the sharpest snap-shots. THE PISTOL AS A WEAPON OF DEFENCE, In the House and on the Road.— 12mo, cloth. ... 50 cents. This work aims to instruct peaceable and law-abiding citizens in the best means of protecting themselves from the attacks of the brutal and the lawless, and it is the only practical book published on this subject. Its contents are as follows :— The Pistol as a Weapon of Defence— The Carrying of Firearms— Different kinds of Pistols in Market— How to Choose a Pistol— Ammunition, different kinds : powder, . caps, bullets, copper cartridges. &c. — Best form of Bullet— How to Load— Best Charge for Pistols— How to Regulate the Charge— Care of the Pistol : how to clean it— How to Handle and Carry the Pistol— How to Learn to Shoot— Practical Use of the Pistol— How to Protect Yourself and Disable your Antagonist. CATALOGUE OF INDVSTTtlAL BOOKS. CHEMICAL HISTORY of the SIX DAYS of CREATION By John Phin, author of "How to Use the Microscope," &c. 12mo, cloth 75 cents. In this volume an attempt is made to trace the evolution of our globe from the primeval state of nebulous mist, "without form and void," and existing in "dark- ness," or with an entire absence of the manifestation of the physical forces, to the condition in which it was fitted to become the habitation of man. While the state- ments and conclusions are rigidly scientific, it gives some exceedingly novel views of a rather hackneyed subject. THE SUN: A Familiar Description of his Phenomena. By Rev. Thomas William Webb, M.A., F.R.A.S., author of ''Celestial Objects for Common Telescopes." — With numerous illustrations. — 12mo, cloth 40 cents. This work gives, in a delightfully popular style, an account of the most recent discoveries in regard to the sun. It is freely illustrated. HOW TO USE THE MICROSCOPE. A Book of Practical Hints on the Selection and Use of the Microscope. Intended for beginners. — By John Phin, editor of The American Journal of Microscopy. — Sixth edition. Greatly enlarged, with over eighty engravings in the text, and eight full- page engravings, printed on heavy tint paper. — 12mo, cloth. $1.25 This work has been received with such general favor that it has passed through five large editions in a few years. It gives a full account of the different kinds of microscopes; of the various accessories, and of the best methods of using them; of the best methods of collecting, preparing, and preserving objects, and preparing slides and cabinets. Many of the illustrations, devices, and methods used, are original with the author, although they have been freely copied and appropriated without credit by several other writers. A BOOK FOR BEGINNERS WITH THE MICROSCOPE. Being an abridgement of ''How to Use the Microscope." — By John Phin. — Fully illustrated, and neatly and strongly bound in cloth 50 cents. This book was prepared for the use of those who, having no knowledge of the use of the microscope,— or, indeed, of any scientific apparatus, — desire simple and practical insti'uction in the best methods of managing the instrument and preparing objects. THE MICROSCOPE.— By Andrew Ross.— Fully illustrated. 12mo, cloth, gilt title 75 cents. This is the celebrated article contributed by Andrew Ross to "The Penny Cyclo- pedia," and quoted so frequently by writers on the microscope. Carpenter and Hogg, in the latest editions of their* works on the microscope, and Brooke, in his treatise on Natural Philosophy, all refer to this article as the best source for full and clear information in regard to the principles upon which the modem achromatic microscope is constructed. It should be in the library of every person to whom the microscope is more than a toy. It is written in simple language, free from abstruse teclmicalities. CATALOGUE OF INDUSTRIAL BOOKS. THE ANGULAR APERTURE OF MICROSCOPE OBJECTIVES. By Dr. George E. Blackham.— Eighteen full-page illustrations. Printed on extra fine paper. — 8vo, cloth $1.25 This is the elaborate paper on Angular Aperture read by Dr. Blackham before the Microscopical Congress, held at Indianapolis. SECTION-CUTTING FOR THE MICROSCOPE. A Practical Guide to the Preparation and Mounting of Sections for the Microscope, special prominence being given to the subject of Animal Sections. — By Sylvester Marsh, M.D. — Reprinted from the London edition. — With illustrations. — 12mo, cloth, gilt title 75 cents. This is undoubtedly the most thorough treatise extant upon section-cutting in all its details. The American edition has been greatly enlarged by valuable explanatory notes ; and also by extended directions, illustrated with engi-avings, for selecting and sharpening kuives and razors. THE MARVELS OF POND LIFE. A Year's Microscopic Recreations among the Polj^s, Infusoria, Rotifers, Water-Bears, and Polyzoa. — By Henry J. Slack, F.G.S., F.R.M.S., &c. — Seven full-page plates, and numerous wood en- gravings in the text.— Second edition. — 12mo, cloth, gilt. . $1 DIATOMS.— Practical Directions for Collecting, Pre- serving, Transporting, Preparing, and Mounting Diatoms.— By Prof. A. Mead Edwards, M.D., Prof. Christopher Johnston, M.D., PEof. Hamilton L. Smith, LL.D.— ]2mo, cloth. 75 cents. This volume contains the most complete series of directions for collecting, preparing, and mounting diatoms, ever published. The directions given are the latest and best. BACTERIA: FORMS AND MODES OF GROWTH. A Series of Papers on the Exliibits at the Biological Laboratory of the Health Exhibition, under the charge of Watson Cheyne. Reprinted from the London Lancet. — Illustrated with over thirty engravings, showing the forms and modes of growth of the various species, and the apparatus used in the different "cultures." — 12mo, paper 25 cents. TRICHINyC SPIRALIS: How to Detect Them and How to Avoid Them.— -^ Popular Account of the Habits, Modes of Propagation, and Means of Dissemination of Pork- worms or Flesh- worms. — By John Phix, author of "How to Use the Microscope." — Fully illustrated. — Paper. , , , 25 cents. CATALOGUE OF INDUSTRIAL BOOKS. HANDBOOK OF URINARY ANALYSIS, Chemical and Microscopical.— For the Use of Physicians, Medical Students, and Clinical Assistants. — By Frank M. Deems, M.D., Laboratory Instructor in the Medical Department of the Univer- sity of New York; Member of the New York County Medical Society; Member of the New York Microscopical Society, &c. — Second edition. — Greatly enlarged, and fully illustrated. — Cloth. $1 This manual presents a plan for the systematic examination of liquid urine, urinary deposits, and calculi. It is compiled with the intention of supplying a concise guide, which, from its small compass and tabulated arrangement, renders it admirably adapted for use, both as a bedside reference-book and a work-table companion. The author is well known as one who has had for several j^ears a very extended experience as a teacher of this important branch of physical diagnosis, and lie has compiled a manual which will serve to lessen the difficulties in the way of thd beginner, and save valuable time to the practitioner. THE MICROSCOPIST'S ANNUAL FOR 1879 Contains a list of all the microscopical societies in the country, with names of officers, days of meeting, &c.; alphabetical and classified lists of all the manufac- turers of microscopes and objectives, dissecting apparatus, microscopic obje3ts, materials for microscopists, «fec., in Europe and America; postal rates, rules and regulations, prepared expressly for microscopists. Weights and measures, with tables and rules for the conversion of different measures into each other; customs dnties and regulations in regard to instruments and books; value of the moneys of all countries in United States dollars; value of the lines on Nobert's test-plates ; t:ible of Holler's probe-platte, with the number of lines to inch on the several diatoms, &c.; focal value of the objectives of those makers who number their objectives (Hartnack. Nachet, &c.); focal value of tlie eyepieces of different makers; magnifying power of eyepieces and objectives, &c The whole forming an indis- pensable companion for svery working microscopist.— Limp cloth, gilt. 25 cents. A BOOK ABOUT BOOKS; or, Practical Notes on the Selection, Use, and Care of Books. Intended as a popular guide for bookbuyers, students, and all lovers of good reading. — Cloth 40 cents. This is a readable, gossipy book, full of literary anecdotes, and containing also a great deal of practical information, useful to every one that owns or expects to own books. The directions for binding, repairing, preserving, and handling books, should receive the careful attention of every one that desires to keep his books in sood condition ; but even if regarded as mere ]tleasant reading for a leisure hour, tliere are few more readable and interesting books than this, witli its gossip, chat, and stories. It is illustrated with three full-page engravings, one being a reproduc- tion of the first wood engraving of which there is any record; the second is an exceedingly curious woodcut representing the birth of' Eve ; and the third is an engraving of one of the curious "hornbooks" of the seventeenth centuiy. RHYMES OF SCIENCE: WISE AND OTHERWISE. By Oliver Wendelli Holmes, Bret Harte, Ingoldsby, Prof. Forbes, Prof. J. W. McQ. Rankine, Hon. R. W. Raymond, and others.— With illustrations. Cloth, gilt title 50 cents. THE YOUNG SCIENTIST.— Tins journal was devoted to amateur Science and Art, and was deservedly a favorite with young people. We have a few bound volumes for sale. Pnce 75 cents each. THE AMERICAN JOURNAL OF MICROSCOPY. A few bound volumes for sale. Price $1 each. IMPORTANT ANNOUNCEMENT TO AECHITECTS, CONTRACTORS AND BUILDERS. For many years past there has been a want by the building fraternity of a good and reliable book on Estimating, one that will give prices of materials and labor lor every department of building, so far as this is possible. Such a book, the pub- lishers believe, has at last been produced, and is now offered to those interested. THE BUILDER'S GUIDE, AND ESTIMATOR'S PRICE BOOK. By FRED. T. IIODGSOIV. HANDSOMELY BOUND IN CLOTH, GILT TITLE. PRICE, - $2.00. Current Prices of Lumber, Hardware, Glass, Plumbers' Supplies, Paints, Slates, Stones, Limes, Cements, Bricks, Tin and other Building Materials; also, Prices of Labor, and Cost of Performing the Several Kinds of AVork Ilequired in Building'. Together with Prices of Doors, Frames, Sashes, S J airs. Mouldings, Newels, and other Machine \Vork. To Avhich is appended a 1 irge nvimber of Building Rules, Data, Tables and Useful Memoranda, Avith a Glossary of Architectural and Bviilding Terms. Tliis is an entirely new work, and gives Prices of Labor and Materials down to a recent date, and is, therefore, the most reliable book in the market on the subject of prices of labor and materials required for building-. The work con- tains, besides Prices, Data, Rules, and Several Hundred Tables and Hints on Building, a blank column where the prices of Labor, or Material may be written in pencil, where such prices differ from those given in the book. There is also a very complete Glossary of Building and Architectural Terms appended to the work, which is a useful and valuable addition for practical builders. The work is really a Cyclopgedia of Prices and Builder's Tables, Data and :Memoranda, and is necessarily a large work, having over 330 pages, each page being 7i x 4|, and covered with closely printed matter. In order to give an idea of what the work contains, we give the following brief SY]\OI»SIS OF CO.lfTEIVTS: Part L— Contains Hints and Rules for Correct Estimatino;.— Forms for Taking Estimates, Quantities, Prices, and Mannerof Computation.— General Memoranda of Items for Estimates.— Excavations.— Foundations.— Drains.— Iron Work.— Baths and Water Closets.— Brick Walls.— Carpenter's Work.— Joiner's Work.— Mantels, Grates, Stove Fittings, etc.— Pantry, Closets, Kitchens and Appurten- ances.— Bell Hanging, Gas Fixing and Fixtures.— Stairs and Staircases.— Roofs, (Gutters and Conductors.— Porches, Verandas and Fences.— Framing; Cost of same.— Cost of Painting, Plastering, Shingling, Slating, Tinning, Finishing, (rlazing, Building Chimneys, and other Brick Work.— Rules for Measurins; all kinds of Hip and other Roofs, with Cost of same.— Rou^h Boarding. Shino'ling, Siding, Laying Floors, and other Work.— Cost of Material and Labor for Stairs, Newels, Balusters, Rails, Doors, Mouldings, Sliding and Folding Doors, Windows of all kinds. Blinds, Wainscoting, Baseboards, Finials, Cresting, Plumbing, Floor- ing, and everything else used about a Building. Part II.— Contains an Extensive Schedule of Builder's Prices, for Digging, Shovelling, Ramming in Loose Earth, Clay and Gravel.— Cost of Masonry, Rubble, Hammer-Dressed Work, Rough Rock Work, Reveals, Ashler Work, Re- SYNOPSIS OF CONTENTS (Continued). pairs, Arches, Plain Work, Rubbed Work, Beaded Work, Fluting, Reeding, Throating, Grooving, Rebating, Leading in Work, Sunken Work, Mortising, etc.— Prices of all kinds of Native Stones per Cubic Foot.— Prices of Cements; Portland, Rosendale, Keene's, Lime of Teil, Lime, Lath, Slate, etc.— Bricklay- ing; Price per 1,000, Laborer's Wages, Prices of Bricks of Different Grades, Cir- cular and Elliptical Work, Brick Paving of all kinds. Laid Dry or in Mortar,— Drain Pipes, Cost and QuaUty; Terra-Cotta Chimney Tops, Cresting, Tiles and Mouldings, etc.— Colored Bricks, Tuck Pointing, Setting in Sash and Door Frames, Taking Down Old Work, Rebuilding wifh Old Bricks, Firebricks, Tile Work, Quality and Prices of Bricks from Various Localities, Prices of Peerless Brick Company's Colored Bricks, Colored Mortars and Cements, Odd-Shaped Bricks.— Plasterer s Work, Scaffolding, Lathing, Mortars for all kinds of Work, Cements for Walls and Ceilings, Cornices and Stucco Work, Plaster-of-Paris Flower and Ornamental Work, Kalsomining and Washes of all Kinds.— Carpen- ter's and Joiner's Work ; Wages, Prices of Lumber, Prices of Made-up Stuff of all Kinds.— Hard-wood Work, Nails, Screws. Locks, Butts and other Hardware.— Stairs of all Kinds, Table for Finding the Run and Rise of Treads and Risers, Turned Work for Stairs and other Work.— Painting, Colors, Prices for Different Kinds of Work, Ladders, Scaffolding, Tools, Graining, Painting Iron Work, Staining, Repairing Old Work. Numerical Work, Tarnishing, Lettering, Oihng, Sash and Door Painting, Mixing Colors, Prices of Colors, Miscellaneous Re- marks.— Roofing Materials of all Kinds, with Prices and Cost of Laying ; Bell- Hanging Materials, Skylights, Tubs, Sinks, Sheet Iron. Pumps, Tanks, Registers, Ventilators, Wire Ropes, and other matters required in Building. Part III.— Contains Rules for Builder's Bookkeeping, Form of Balance Sheet, Rules for Measuring Artificer's Work, including Excavation, Drains, Shoring, Concreting, and Labor in General ; also Methods of Measuring all Kinds of Ma- terials for Brick, Stone, or Wood Work.— Elements of the Mechanics of Archi- tecture, Strength of Materials, Rules for Obtaining Same ; Iron, Wood, Stone and Brick, Crushing Loads for Various Building Materials, Columns, Iron, Wood, Stone.— Tables for Computing the Strength of "Materials, Factors of Safety, Rolled-Iron Beams and Girders.— Bricks and Brick Piers, Terra-Cotta, Strength and Qualities of Cements and Mortars, Fire-Brick, Colored Mortars, Granite and other Stone. Part IV.— Miscellaneous Tables.— Weight of Iron, Lead, Brass, Copper and Cast Iron, per Foot Superficial or in Bars ; Strength of Round Ropes, Weight of Boiler Iron, AVrought-Iron Pipes, Flat and Round Wire Ropes for Elevators. Iron Roofing, Lead Pipes, Nails, Foreign Weights and Measures, Force of Wind, Square Measure, Long Measure, Equivalents, Arithmetical and other Signs, Ex- pansion by Heat, Force of Explosives, Number of Shingles, Slates, Tiles and other Covering Required for 100 feet of Roofing, Number of Bricks Required for Given Wall, Strength of Woods, Loads for Bridges, Strains on Bridges and Trusses, Specific Gravities. Part V.— Mensuration of Superfices, Areas of Squares, Cubes, Triangles, Multi-sided Figures, etc.; Measurements of Solids, Cubes, Cones, Cylinders, Splieres, etc.; Squares and Cubes of Numbers, Table of Spherical Contents, Diameters, Circumferences and Areas of Circles, Board and Plank ;Measure, Scantling Measure, Wages Table, Sizes and Capacities of Cribs, Boxes and Tanks. Part VI.— Mechanics' Lien Laws of Alabama, Arkansas, Connecticut, Cali- fornia, Colorado, District of Cohunbia, Delaware, Florida, Georgia. Indiana, fowa, Illinois, Kansas, Kentucky, Maine, Louisiana, Massachusetts, Maryland, Mississippi, Michigan, Missouri', New Jersey, Nevada, Nebraska, New Hamp- shire, North Carolina, New York, Oregon, Ohio, Pennsylvania, Rhode Island, South Carolina, Texas, Tennessee, Vermont, Virginia, West Virginia, Wisconsin, Ontario. Part VII,— Schedule of Architect's Charges, Drawings, Superintendence, Per- centage on Public Buildings.— Architect's Rules and Methods of Charging for Services Rendered.— Leading Architectural and Building Journals.— Glossary of Architectural and Building Terms. (This "Glossary" covers some fifty-seven pages, and deals with over One Thousand Terms used in Architecture and Building). AJ A\/ r% ^ YO/IA