Digitized by the Internet Archive in 2016 https://archive.org/details/cyclopediaofdraw01 keni Main Building, Armour Institute of Technology CYCLOPEDIA OF DRAWING MECHANICAL DRAWING By Ervin Kenison, S. B. Department of Mechanical Drawing, Massachusetts Institute of Technology. SHADES AND SHADOWS By Harry W. Gardner, S. B. Assistant Professor of Architecture, Massachusetts Institute of Technology. PERSPECTIVE DRAWING By William H. Lawrence, S. B. Associate Professor of Architecture, Massachusetts Institute of Technology. FREEHAND DRAWING By Herbert E. Everett Department of Architecture, University of Pennsylvania. PEN AND INK RENDERING By David A. Gregg Department of Architecture, Massachusetts Institute of Technology. RENDERING IN WASH By Herman V. von Holst, A. B., S. B. Architect, Chicago ARCHITECTURAL LETTERING By Frank Chouteau Brown. Architect, Boston Compiled from the Instruction Papers in the Architectural Course of the American School of Correspondence at Armour Institute of Tech- nology :::::::::::::: Chicago , Illinois Edited by ALFRED E. ZAPF, S. B. Secretary American School of Correspondence Copyright 1 005 by American School of Corresiondence Entered at Stationers' Hall , London All Rights Reserved y THIS VOLUME CONSISTS OF NINE OF THE FIFTY REGULAR INSTRUCTION PAPERS IN THE ARCHITECT- URAL COURSE OF THE AMERICAN SCHOOL OF CORRES- PONDENCE, INDEXED AND BOUND TOGETHER IN CON- VENIENT FORM FOR READY REFERENCE, BUT NOT IN THE ORDER USUALLY STUDIED. THE INSTRUCTION PAPERS OF THE AMERICAN SCHOOL OF CORRESPONDENCE ARE PREPARED EXCLU- SIVELY FOR THE USE OF ITS STUDENTS BY MEN OF ACKNOWLEDGED PROFESSIONAL STANDING, AND REPRE- SENT YEARS OF SPECIAL PREPARATION NECESSARY TO ADAPT THEM TO THE NEEDS OF PERSONS OBLIGED TO STUDY WITHOUT THE DIRECT ASSISTANCE OF A PERSONAL TEACHER. THE CHIEF AIM OF THIS WORK IS TO ACQUAINT THE PUBLIC WITH THE STANDARD, SCOPE, AND PRACTICAL VALUE OF THESE PAPERS THROUGH AN OPPORTUNITY FOR PERSONAL EXAMINATION; AND IT IS HOPED THAT SUFFICIENT MATERIAL IS GIVEN HERE TO AROUSE IN THE READER A DESIRE TO KNOW MORE. ALTHOUGH PUBLISHED PRIMARILY TO SHOW THE CHARACTER OF THE INSTRUCTION OFFERED BY THE AMERICAN SCHOOL OF CORRESPONDENCE, AND REPRE- SENTING ONLY A SMALL PORTION OF THE COMPLETE COURSE, IT IS CONFIDE NTI Y BELIEVED THAT THIS VOL- UME HAS IN ITSELF ENOUGH CONDENSED, PRACTICAL INFORMATION TO MAKE IT OF IMMEDIATE VALUE TO THE DRAFTSMAN, STUDENT, OR TEACHER. EXAMINATION QUESTIONS FOLLOWING EACH SECTION ARE THE QUES TIONS OR PLATES WHICH CONSTITUTE THE REGULAR EXAMINATION OF THE AMERICAN SCHOOL OF CORRESPONDENCE. THEY OFFER THE READER A MEANS OF TESTING HIS KNOWLEDGE OF THE SUBJECTS TREATED. INABILITY TO ANSWER THESE QUESTIONS, OR TO SOLVE THE PROBLEMS, WILL SERVE TO SHOW THE NECESSITY FOR FURTHER STUDY. THE READER IS URGED TO SOLVE EVERY PROBLEM, CHECKING HIS RESULTS WHEREVER POSSIBLE WITH SIMILAR PROBLEMS IN THE PRECEDING PAGES. THIS WILL AFFORD AN EX- CELLENT MEANS FOR FIXING THE MATTER IN HIS MIND. STUDENTS PREPARING FOR COLLEGE OR CIVIL SERVICE EXAMINATIONS WILL FIND THESE QUESTIONS OF GREAT VALUE FRAGMENTS FROM ROMAN TEMPLE AT CORI, ITALY. One of the most interesting examples of architectural rendering in existence. Original drawing by Emanuel Brune. Reproduced by permission of Massachusetts Institute of Technology . MECHANICAL DRAWING* The subject of mechanical drawing is of great interest and importance to all mechanics and engineers. Drawing is the method used to show graphically the small details of machinery; it is the language by which the designer speaks to the workman; it is the most graphical way to place ideas and calculations on record. Working drawings take the place of lengthy explana- tions, either written or verbal. A brief inspection of an accurate, well-executed drawing gives a better idea of a machine than a large amount of verbal description. The better and more clearly a drawing is made, the more intelligently the workman can com- prehend the ideas of the designer. A thorough training in this important subject is necessary to the success of everyone engaged in mechanical work. The success of a draftsman depends to some extent upon the quality of his instruments and materials. Begin- ners frequently purchase a cheap grade of instruments. After they have become expert and have learned to take care of their instruments they discard them for those of better construction and finish. This plan has its advantages, but to do the best work, strong, well-made and finely finished instruments are necessary. INSTRUflENTS AND HATERIALS. Drawing Paper. In selecting drawing paper, the first thing to be considered is the kind of paper most suitable for the pro- posed work. For shop drawings, a manilla paper is frequently used, on account of its toughness and strength, because the draw- ing is likely to be subjected to considerable hard usage. If a finished drawing is to be made, the best white drawing paper should be obtained, so that the drawing will not fade or become discolored with age. A good drawing paper should be strong, have uniform thickness and surface, should stretch evenly, and should neither repel nor absorb liquids. It should also allow con- siderable erasing without spoiling the surface, and it should lie smooth when stretched or when ink or colors are used. It is, of 7 4 MECHANICAL DRAWING. course, impossible to find all of these qualities in any one paper, as for instance great strength, cannot be combined with fine surface. In selecting a drawing paper the kind should be chosen which combines the greatest number of these qualities for the given work Of the better class Whatman’s are considered by far the best. This paper is made in three grades; the hot 'pressed has a smooth surface and is especially adapted for pencil and very fine line drawing, the cold pressed is rougher than the hot pressed, has a finely grained surface and is more suit- able for water color drawing ; the rough is used for tinting. The cold pressed does not take ink as well as the hot pressed, but erasures do not show as much on it, and it is better for general work. There is but little difference in the two sides of Whatman’s paper, and either can be used. This paper comes in sheets of standard sizes as follows: — Cap, Demy, Medium, Royal, Super-Royal, Imperi al, 13 X 17 inches. 15 X 20 “ 17 X 22 “ 19 X 24 “ 19X27 “ 22 X 30 “ Elephant, Columbia, Atlas, Double Elephant, Antiquarian, Emperor, 23 X 28 inches. 23 X 34 “ 26 X 34 “ 27 X 40 “ 31 X 53 “ 48 X 68 “ The usual method of fasteningpaper to a drawing board is by means of thumb tacks or small one-ounce copper or iron tacks. In fastening the paper by this method first fasten the upper left hand corner and then the lower right pulling the paper taut. The other two corners are then fastened, and sufficient number of tacks are placed along the edges to make the paper lie smoothly. For very fine work the paper is usually stretched and glued to the board. To do this the edges of the paper are first turned up all the way round, the margin being at least one inch. The whole surface of the paper included between these turned up edges is then moistened by means of a sponge or soft cloth and paste or glue is spread on the turned up edges. After removing all the surplus water on the paper, the edges are pressed down on the board, commencing at one corner. During this process of laying down the edges, the paper should be stretched slightly by pulling the edges towards the edges of the drawing board. The drawing board is then placed horizontally and left to dry. After the*paper has become dry it will be found to be as smooth and tight as a MECHANICAL DRAWING. 5 drum head. If, in stretching, the paper is stretched too much it is likely to split in drying. A slight stretch is sufficient. Drawing Board. The size of the drawing board depends upon the size of paper. Many draftsmen, however, have several boards of various sizes, as they are very convenient. The draw- ing board is usually made of soft pine, which should be well sea- soned and straight grained. The grain should run lengthwise of the board, and at the two ends there should be pieces about 1 J or 2 inches wide fastened to the board by nails or screws. These end pieces should be perfectly straight for accuracy in using the T-square. Frequently the end pieces are fastened by a glued matched joint, nails and screws being also used. Two cleats on the bottom extending the whole width of the board, will reduce the tendency to warp, and make the board easier to move as they raise it from the table. Thumb Tacks. Thumb tacks are used for fastening the paper to the drawing board. They are usually made of steel either pressed into shape, as in the cheaper grades, or made with a head of German silver with the point screwed and riveted to it. They are made in various sizes and are very convenient as they can be easily removed from the board. For most work however, 9 6 MECHANICAL DRAWING. draftsmen use small one-ounce copper or iron tacks, as they can be forced flush with the drawing paper, thus offering no obstruction to the T-square. They also possess the advantage of cheapness. Pencils. In pencilling a drawing the lines should be very fine and light. To obtain these light lines a hard lead, pencil must be used. Lead pencils are graded according to their hardness, and are numbered by using the letter H. In general a lead pencil of 5H (or HHHHH) or 6H should be used. A softer pencil, 4H, is better for making letters, figures and points. A hard lead pencil should be sharpened as shown in Fig. 1. The wood is cut away so that about i or | inch of lead projects. The lead can then be |rb| sharpened to a chisel edge by rubbing it I If against a bit of sand paper or a fine file. I I It should be ground to a chisel edge and I/ the comers slightly rounded. In making the straight lines the chisel edge should be used by placing it against the T-square or triangle, and because of the chisel edge the lead will remain sharp much longer than if sharpened to a point. This chisel edge enables the draftsman to draw a fine line exactly through a given point. If the drawing is not to be inked, but is made for tracing or for rough usage in the shop, a softer pencil, 3H or 4H, may be used, as the lines will then be somewhat thicker and heavier. The lead for compasses may also be sharpened to a point although some draftsmen prefer to use a chisel edge in the compasses as well as for the pencil. In using a very hard lead pencil, the chisel edge will make a deep depression in the paper if much pressure is put on the pencil. As this depression cannot be erased it is much better to press lightly on the pencil. Erasers. In making drawings, but little erasing should be necessary. However, in case this is necessary, a soft rubber should be used. In erasing a line or letter, great care must be exercised or the surrounding work will also become erased. To prevent this, some draftsmen cut a slit about 3 inches long and J to ^ inch wide in a card as shown in Fig. 2. The card is then 10 MECHANICAL DRAWING. 7 placed over the work and the line erased without erasing the rest of the drawing. An erasing shield of a form similar to that shown in Fig. 3 is very convenient, especially in erasing letters. It is made of thin sheet metal and is clean and durable. For cleaning drawings, a sponge rubber may be used. Bread C Fig. 2. crumbs are also used for this purpose. To clean the drawing scatter dry bread crumbs over it and rub them on the surface with the hand. T-Square. The T-square consists of a thin straight edge Fig. 4. called the blade, fastened to a head at right angles to it. It gets its name from the general shape. T-squares are made of various materials, wood being the most commonly used. Fig. 4 shows an ordinary form of T-square which is adapted to most work. In Fig. 5 is shown a T-square with edges made of ebony or mahogany, as these woods are much harder than pear wood or maple, which is generally used. The head is formed so as to fit against the left- hand edge of the drawing board, while the blade extends over the surface. It is desirable to have the blade of the T-square form a right angle with the head, so that the lines drawn with the T- square will be at right angles to the left-hand edge of the board. This, however, is not absolutely necessary, because the lines drawn with the T-square are always with reference to one edge of the ll 8 MECHANICAL DRAWING. board only, and if this edge of the board is straight, the lines drawn with the T-square will be parallel to each other. The T- square should never be used except with the left-hand edge of the board, as it is almost impossible to find a drawing broad with the edges parallel or at right angles to each other. The T-square with an adjustable head is frequently very con- venient, as it is sometimes necessary to draw lines parallel to each Fig. 5 . other which are not at right angles to the left-hand edge of the board. This form of T-square is similar to the ordinary T-square already described, but the head is swiveled so that it may be clamped at any desired angle. The ordinary T-square as shown in Figs. 4 and 5 is, how ever, adapted to almost any class of drawing. Fig. 6 shows the method of drawing parallel horizontal lines with the T-square. With the head of the T-square in contact with the left-hand edge of the board, the lines may be drawn by moving the T-square to the desired position. In using the T-square the upper edge should always be used for drawing as the two edges may not be exactly parallel and straight, and also it is more convenient to use this edge with the triangles. If it is neces- sary to use a straight edge for trimming drawings or cutting the paper from the board, the lower edge of the T-square should be used so that the upper edge may not be marred. For accurate work it is absolutely necessary that the working edge of the T-square should be exactly straight. To test the Fig. 6. 12 MECHANICAL DRAWING. 9 straightness of the edge of the T-square, two T-squares may be placed together as shown in Fig. 7. This figure shows plainly that the edge of one of the T-squares is crooked. This fact, how- ever, does not prove that either one is straight, and for this deter- mination a third blade must be used and tried with the two given T-squares successively. Triangles. Triangles are made of various substances such as wood, rubber, celluloid and steel. Wooden triangles are cheap but are likely to warp and get out of shape. The rubber tri- angles are frequently used, and are in general satisfactory. The transparent celluloid triangle is, however, extensively used on ac- count of its transparency, which enables the draftsmen to see the work already done even when covered with the triangle. In using a rubber or celluloid triangle take care that it lies perfectly flat or is hung up when not in use ; when allowed to lie on the drawing board with a pencil or an eraser under one corner it will become warped in a short time, especially if the room is hot or the sun happens to strike the triangle. Triangles are made in various sizes, and many draftsmen have several constantly on hand. A triangle from 6 to 8 inches on a side will be found convenient for most work, although there are many cases where a small triangle measuring about 4 inches 13 10 MECHANICAL DRAWING. on a side will be found useful. Two triangles are necessary for every draftsman, one having two angles of 45 degrees each and one a right angle ; and the other having one angle of 60 degrees, one of 30 degrees and one of 90 degrees. The value of the triangle depends upon the accuracy of the angles and the straightness of the edges. To test the accuracy of the right angle of a tri- angle, place the triangle with the lower edge rest- ing on the edge of the T-square, as shown in Fig. 8. Now draw the line C D, which should be perpendicular to the edge of the T-square. The same triaaigle should then be placed in the position shown at B. If the right angle of the triangle is exactly 90 degrees the left-hand edge of the triangle should exactly coincide with the line C D. To test the accuracy of the 45-degree triangles, first test the right angle then place the triangle with the lower edge resting on the work- ing edge of the T-square, and draw the line E F as shown in Fig. 9. Now without moving the T- square place the triangle so that the other 45-degree angle is in the position occupied by the first. If the two 45-degree angles coincide th&y are accurate. Triangles are very convenient in drawing lines at right angles to the T-square. The method of doing this is shown in Fig. 10. Triangles are also used in drawing lines at an angle with the horizontal, by placing them on the board as shown in big. 11. Suppose the line E F (Fig. 12) is drawn at any angle, and we wish to draw a line through the point P parallel to it. 14 * — i~ 2 - — i A TYPICAL ARCHITECT’S DRAWING. This shows the conventional manner of indicating the over-all dimensions of the house, the size and shape of the rooms, the finish, the location of light and other fixtures, the swing of the doors, etc. ; also the conventional style of lettering. MECHANICAL DRAWING. 11 First place one of the triangles as shown at A, having one edge coinciding with the given line. Now take the other triangle and place one of its edges in contact with the bottom edge of triangle A. I [olding the triangle B firmly with the left hand the triangle A may be slipped along to the right or to the left until the edge of the triangle reaches the point P. The line M N may then be drawn along the edge of the triangle passing through the point P. In place of the tri- angle B any straight edge such as a T-square may be used. A line can be drawn perpendicular to another by means of the triangles as follows. Let E F (Fig. IB) be the given line, and suppose we wish to draw a line perpendicular to E F through the point D. Place the longest side of one of the triangles so that it coincides with the line E F, as the triangle is shown in posi- tion at A. Place the other triangle (or any straight edge) in the position of the triangle as shown at B, one edge resting against the edge of the triangle A. Then holding B with the left hand, place the tri- angle A in the position shown at C, so that the longest side passes through the point D. A line can then be drawn through the point D perpendicular to E F. In previous figures we have seen how lines may be drawn making angles of 30, 45, GO and 90 degrees with the horizontal. If it is desired to draw lines forming angles of 15 and T5 degrees the triangles may be placed as shown in Fig. 14. In using the triangles and T-square almost any line may be drawn. Suppose we wish to draw a rectangle having one side 15 12 MECHANICAL DRAWING. horizon tal. First place the T-square as shown in Fig. 15. By moving the T-square up or down, the sides A B and D C may be drawn, because they are horizontal and parallel. Now place one of the triangles resting on the T-square as shown at E, and hav- ing the left-hand edge passing through the point D. The vertical line D A may be drawn, and by sliding the triangle along the edge of the T-square to the position F the line B C may be drawn by using the same edge. These positions are shown dotted in Fig. 15. If the rectangle is to be placed in some other position on the drawing board, as shown in Fig. 1G, place the 45-degree triangle F so that one edge is parallel to or coincides with the side D C. Now holding the triangle F in position place the triangle H so that its upper edge coincides with the lower edge of the triangle F, By holding H in position and sliding the triangle F along its upper edge, the sides A B and D C may be drawn. To draw the sides A I) and B C the triangle should be used as shown at E. Compasses. Compasses are used for drawing circles and arcs of circles. They are made of various materials and in various sizes. The cheaper class of instruments are made of brass, but they are unsatisfactory on account of the odor and the tendency to tarnish. The best material is German silver. It does not soil 16 MECHANICAL DRAWING. 18 readily, it lias no odor, and is easy to keep clean. Aluminum in- struments possess the advantage of lightness, hut on account of the soft metal they do not wear well. The compasses are made in the form shown in Figs. 17 and 18. Pencil and pen points are provided, as shown in Fig. 17. Either pen or pencil may he inserted in one leg by means of a shank and socket. The other leg is fitted with a needle point which is placed at the center of the circle. In most instru- ments the needle point is separate, and is made of a piece of round steel wire having a square shoulder at one or both ends. Be- low this shoulder the needle point projects. The needle is made in this form so that the hole in the paper may he very minute. In some instruments lock nuts are used to hold the joint firmly in position. These lock nuts are thin discs of steel, with notches for using a wrench or forked key. Fig. 19 shows the detail of the joint of high grade instruments. Both legs are alike at the joint, and two pivoted screws are inserted in the yoke. This permits ample movement of the legs, and at the same time gives the proper stiff- ness. The flat surface of one of the legs is faced with steel, the other being of German silver, in order that the rubbing parts maybe of different metals. Small set screws are used to prevent the pivoted screws from turning in the yoke. The contact surfaces of this joint are made cir« cular to exclude dust and dirt and to prevent rusting of the steel face. Figs. 20, 21, and 22 show the detail of the socket; hi some D T \ \ !\E N ' L_A .N - — ‘C !\F\ L.N Fig. 15. 17 14 MECHANICAL DRAWING. r instruments the shank and socket are pentagonal, as shown in Fig. 20. The shank enters the socket loosely, and is held in place by means of the screw. Unless used very carefully this arrange- ment is not durable because the sharp corners soon wear, and the pressure on the set screw is not sufficient to hold the shank firmly in place. In Fig. 21 is shown another form of shank. This is round, having a flat top. A set screw is also used to hold this in posi- tion. A still better form of socket is shown in Fig*. 22 : the hole O Fig. 17. is made tapered and is circular. The shank fits accurately, and is held in perfect alignment by a small steel key. The clamping screw is placed upon the side, and keeps the two portions of the split socket together. Figs. 17 and 18 show that both legs of the compasses are jointed in order that the lower part of the legs may be perpen- dicular to the paper while drawing circles. In this way the needle point makes but a small hole in the paper, and both nibs of 18 A beautiful example of rendering in wash, showing conventional method of representing plan and surrounding grounds. This is usually done in strong contrasting colors. The black rectangles indicate statuary; the crossed lines arbors. Note how the shadows of the building, terraces, statuary, etc. , help to give interest to the drawing. Contrast this plan with the^ one rendered in pen and ink page 421. See also “Rendering in Wash’’ page 453. MECHANICAL DRAWING. 15 the pen will press equally on the paper. In pencilling circles it is not as necessary that the pencil should be kept vertical; it is a good plan, however, to learn to use them in this way both in pen- cilling* and inking. The com- passes should be held loosely be- tween the thumb and forefinger. If the needle point is sharp, as it should be, only a slight pres- sure will be required to keep it in place. While drawing the circle, incline the compasses slightly in the direction of revolution and press lightly on the pencil or pen. In removing the pencil or pen, it should be pulled out Fi £- 19 - straight. If bent from side to side the socket will become en- larged and the shank worn; this will render the instrument inac- curate. For drawing large circles the lengthening bar shown in When using the lengthening bar the Fig. IT should be used. rr~bE =a e Fi is an exercise in free-hand lettering. The finished exercise, with all guide lines erased, should have the appearance shown in Fig . ^ of PLATE I. The guide lines are drawn as shown in Fig. 37. First draw the center line E F and light pencil lines Y Z and T X, | inch from the border lines. Now, with the T- square, draw the line G, i inch from the top line and the line H, ^ inch below G. The word “ LETTERING- ” is to be placed between these two lines. Draw the line I, ^ inch below H. The lines I, J, etc., to K are all ^ inch apart. We now practice the lower-case letters. Draw the line L, inch below K and a light line l inch above L to limit the height of the small letters. The space between L and M is inch. The lines M and N are drawn in the same manner as K and L. The space between N and O should be l inch. The line P is drawn ^ inch below O. Q is also A inch below P. The lines Q and R are drawn inch apart as are M and N. The remainder of the lines S, U, V and W are drawn g 5 2 - inch apart. The center line is a great aid in centering the word “ LETTERING^” the alphabets, numerals, etc. The words U TIIE” and “ Proficiency ” should be indented about -| inch as they are the first words of paragraphs. To draw the guide lines, mark off distances of 1 inch on any line such as J and with the 60-degree triangle draw light pencil lines cutting the parallel lines. The letters should be sketched in pencil, the ordin- ary letters such as E, F, H, N, R, etc. being made of a width equal to about | the height. Letters like A, M and W are wider. The space between the letters depends upon the draftsman’s taste but the beginner should remember that letters next to an A or an L should be placed near them and that greater space should be left on each side of an I or between letters whose sides are parallel; for instance there should be more space between an N and E than between an E and FI. On account of the space above the lower line of the L, a letter following an L should be close to it If a T follows a T or the letter L follows an L they should be placed near together. In all lettering the letters should be placed so that the general effect is pleasing. After the four figures are 86 MECHANICAL DRAWING. 31 completed, the lettering for name, address and date should be pencilled. With the T-square draw a pencil line inch above the top border line at the right-hand end. This line should be about 3 inches long. At a distance of inch above this line draw another. line of about the same length. These are the guide lines for the word PLATE I. The letters should be pencilled free hand and the student may use the 60-degree guide lines if he desires. The guide lines of the date, name and address are similarly drawn in the lower margin. The date of completing the drawing should be placed under Fig. 3 and the name and address at the right under Fig. 4* The street address is unnecessary. It is a good plan to draw lines -fa inch apart on a separate sheet of paper and pencil the letters in order to know just how much space each word will require. The insertion of the words “ Fig. 1 ,” “ Fig. 2” etc., is optional with the student. He may leave them out if he desires ; but we would advise him to do this extra lettering for the practice and for convenience in reference. First draw with the T-square two parallel line ^ inch apart under each exercise ; the lower line being Ag inch above the horizontal center line or above the lower border line. Inking. After all of the pencilling of PLATE I has been completed the exercises should be inked. The pen should first be examined to make sure that the nibs are clean, of the same length and come together evenly. To fill the pen with ink use an ordi- nary steel pen or the quill in the bottle, if Higgin’s Ink is used. Dip the quill or pen into the bottle and then inside between the nibs of the line pen. The ink will readily flow from the quill into the space between the nibs as soon as it is brought in contact. Do not fill the pen too full, if the ink fills about ^ the distance to the adjusting screw it usually will be sufficient. If the filling has been carefully done it will not be necessary to wipe the outsides of the blades. However, any ink on the outside should be wiped off with a soft cloth or a piece of chamois. The pen should now be tried on a separate piece of paper in order that the width of the line may be adjusted. In the first work where no shading is done, a firm distinct line should be used. The beginner should avoid the extremes : a very light line makes 37 32 MECHANICAL DRAWING. the drawing have a weak, indistinct appearance, and very heavy lines detract from the artistic appearance and make the drawing appear heavy. In case the ink does not flow freely, wet the finger and touch it to the end of the pen. If it then fails to flow, draw a slip of thin paper between the nibs (thus removing the dried ink) or clean thoroughly and fill. Never lay the pen aside without cleaning. In ruling with the line pen it should be held firmly in the right hand almost perpendicular to the paper. If grasped too firmly the width of the line may be varied and the draftsman soon becomes fatigued. The pen is usually held so that the adjusting screw is away from the T-square, triangles, etc. Many draftsmen incline the pen slightly in the direction in which it is moving. To ink Fig. i, place the T-square with the head at the work- ing edge as in pencilling. First ink all of the horizontal lines moving the T-square from A to D. In drawing these lines con- siderable care is necessary ; both nibs should touch the paper and the pressure should be uniform. Have sufficient ink in the pen to finish the line as it is difficult for a beginner to stop in the middle of the line and after refilling the pen make a smooth con- tinuous line. While inking the lines A, E, F, G, H, I, etc., greater care should be taken in starting and stopping than while pencib Hng. Each line should start exactly in the pencil line A D and stop in the line B C. The lines A D and B C are inked, using the triangle and T-square. Fig. 2 is inked in the same manner as it was pencilled ; the lines being drawn, sliding the triangle along the T-square in the successive positions. In inking Fig. 3, the same care is necessary as with the pre- ceding, and after the oblique lines are inked the border lines are finished. In Fig. Jj. the border lines should be inked in first and then the border lines of the plate. The border lines should be quite heavy as they give the plate a better appearance. The intersections should be accurate, as any running over necessitates erasing. The line pen may now be cleaned and laid aside. It can be 38 RLATE MECHANICAL DRAWING. 33 cleaned by drawing a strip of blotting paper between the nibs or by means of a piece of cloth or chamois. The lettering should be done free-hand using a steel pen. If the pen is very fine, accu- rate work may be done but the pen is likely to catch in the paper, especially if the paper, is rough. A coarser pen will make broader lines but is on the whole preferable. Gillott’s 404 is as fine a pen as should be used. After inking Fig. 4, the plate number, date and name should be inked, also free-hand. After ink- ing the words “ Fig. 1 ,” “ Fig. 2” etc., all pencil lines should be erased. In the finished drawing there should be no center lines, construction lines or letters other than those in the name, date, etc. The sheet should be cut to a size of n inches by 15 inches, the dash line outside the border line of PLATE /indicating the edge. PLATE II. Pencilling. The drawing paper used for PLATE //should be laid out as described with PLATE 1, that is, the border lines, center line and rectangles for Figs. 1 and 2. To lay out Figs. 3, Ij, and 5 proceed as follows : Draw a line with the T-square parallel to the horizontal center line and | inch below it. Also draw another similar line 4| below the centerline. The two lines will form the top and bottom of Figs. 3, ^ and 5. Now measure off 2L inches on either side of the center on the horizontal center line and call the points Y and Z. On either side of Y and Z and at a distance of L inch draw vertical parallel lines. Now draw a vertical line A D, 4L inches from the line Y and a vertical line B C 4| inches from the line Z. We now have three rectangles each 4 inches broad and 4| inches high. Figs. 1 and 2 are pen- reined in exactly the same way as was Fig. 1 of PLATE /, that is, horizontal lines are drawn i inch apart. Fig. 3 is an exercise to show the use of a 60-degree triangle with a T-square. Lay off the distances A E, E F, F G, G H, etc. to B each L inch. With the 60 degree triangle resting on the upper edge of the T-square, draw lines through these points, E, F, G, H, I, J, etc., forming an angle of 30 degrees with the hori- zontal. The last line drawn willfbe A L. In drawing these lines move the pencil from A B to B C. Now find the distance 41 34 MECHANICAL DRAWING. between the lines on the vertical B L and mark off these distances on the line B C commencing at L. Continue the lines from A L to N C. Commencing at N mark off distances on A D equal to those on B C and finish drawing the oblique lines. Fig. £ is an exercise for intersection. Lay off distances of -i inch on A B and A D. With the T-square draw fine pencil lines through the points E, F, G, H, I, etc., and with the T-square and triangle draw vertical lines through the points L, M, N, O, P, etc. In drawing this figure draw every line exactly through the points indicated as the symmetrical appearance of the small squares can be attained only by accurate pencilling. The oblique lines in Fig. 5 form an angle of 60 degrees with the horizontal. As in Figs. 3 and Jf mark off the line A B in divisions of 1 inch and draw with the T-square and 60-degree triangle the oblique lines through these points of division moving the pencil from A B to B C. The last line thus drawn will be A L. Now mark off distances of ^ inch on C D beginning at L. The lines may now be finished. Inking. Fig. 1 is designed to give the beginner practice in drawing lines of varying widths. The line E is first drawii. This line should be rather fine but should be clear and distinct. The line F should be a little wider than E ; the greater width being obtained by turning the adjusting screw from one-quarter to one- half a turn. The lines G, H, I, etc., are drawn ; each successive line having greater width. M and N should be the same and quite heavy. From N to D the lines should decrease in width. To complete the inking of Fig. 1 , draw the border lines. These lines should have about the same width as those in PLATE I. In Fig. 2 the first four lines should be dotted. The dots should be uniform in length (about inch) and the spaces also uniform (about -Jg- inch). The next four lines are dash lines similar to those used for dimensions. These lines should be drawn with dashes about £ inch long and the lines should be fine, yet distinct. The following four lines are called dot and dash lines. The dashes are about | inch long and a dot between as shown. In the regular practice of drafting the length of the dashes depends upon the size of the drawing — 1 inch to 1 inch being common. The last lour lines are similar, two dots being used between the 4 2 MECHANICAL DRAWING. 35 dashes. After completing the dot and dash lines, draw the border lines of the rectangle as before. In inking Fig. 3, the pencil lines are followed. Great care should be exercised in starting and stopping. The lines should begin in the border lines and the end should not run over. The lines of Fig. If must be drawn carefully, as there are so many intersections. The lines in this figure should be lighter than the border lines. If every line does not coincide with the points of division L, M, N, O, P, etc., some will appear farther apart than others. Fig. 5 is similar to Fig. 3 , the only difference being in the angle which the oblique lines make with the horizontal. After completing the five figures draw the border lines of the plate and then letter the plate number, date and name, and the figure numbers, as in PLATE I. The plate should then be cut to the required size, u inches by 15 inches. PLATE III. Pencilling. The horizontal and vertical center lines and the border lines for PLATE ILL are laid out in the same manner as were those of PLATE II. To draw the squares for the six figures, proceed as follows : Measure off two inches on either side of the vertical center line and draw light pencil lines through these points parallel to the vertical center line. These lines will form the sides A D and B C of Figs. 2 and 5. Parallel to these lines and at a distance of I inch draw similar lines to form the sides B C of Figs. 1 and If and A D of Figs. 3 and 6. The vertical sides A D of Figs. 1 and If and B C of Figs. 3 and 6 are formed by drawing lines perpen- dicular to the horizontal center line at a distance of 6 ^ inches from the center. The horizontal sides D C of Figs. 1 , 2 and 3 are drawn with the T-square I inch above the horizontal center line. To draw the top lines of these figures, draw (with the T-square) a line 4J inches above the horizontal center line. The top lines of Figs. If, 5 and 6 are drawn 1 inch below the horizontal center line. The squares are completed by drawing the lower lines D C, 41 inches below the horizontal center line. The figures of PLATES I and II 43 36 MECHANICAL DRAWING. were constructed in rectangles ; the exercises of PL A TE III are, however, drawn in squares, having the sides 4 inches long. In drawing Fig. 1, first divide A D and A B (or DC) into 4 equal parts. As these lines are four inches long, each length will be 1 inch. Now draw horizontal .lines through E, F and G and vertical lines through L, M and N. These lines are shown dotted in Fig. 1 . Connect A and B with the intersection of lines E and M, and A and D with the intersection of lines F and L. Similarly draw D J, J C, I B and I C. Also connect the points P, O, I and J forming a square. The four diamond shaped areas are formed by drawing lines from the middle points of A D, A B, B C and D C to the middle points of lines A P, A O, O B, I B etc., as shown in Fig. 1. Fig . 2 is an exercise of straight lines. Divide A D and A B into four equal parts and draw horizontal and vertical lines as in Fig . i. Now divide these dimensions, A L, M N, etc. and E F, G B etc. into four equal parts ( each ^ inch ) . Draw light pencil lines with the T-square and triangle as shown in Fig. 2. In Fig. 3 , divide A B and A D into eight parts, each length being 1 inch. Through the points H, I, J, K, L, M and N draw vertical lines with the triangle. Through O, P, Q, R, S, T and U draw horizontal lines with the T-square. Now draw lines con- necting O and H, P and I, Q and J, etc. These lines can be drawn with the 45-degree triangle, as they form an angle of 45 degrees with the horizontal. Starting at N draw lines from A B to B C at an angle of 45 degrees. Also draw lines from A D to D C through the points O, P, Q, R, etc., forming angles of 45 degrees with D C. Fig . ^ is drawn with the compasses. First draw the diagonals A C and D B. With the T-square draw the line E H. Now mark off on E H distances of | inch. With the compasses set so that the point of the lead is 2 inches from the needle point, de- scribe the circle passing through E. Witli H as a center draw the arcs F G and I J having a radius of 1| inches. In drawing these arcs be careful not to go beyond the diagonals, but stop at the points F and G and I and J. Again with H as the center and a radius of li inches draw a circle. The arcs K L and M N are drawn in the same manner as were arcs F G and I J ; tha 44 PLATE JANUARY* /A, / 90/. HELP BURT U HA NHL BP CH/BAOO, MECHANICAL DRAWING. 37 radius being li inches. Now draw circles, with H as the center, of 1, -J, | and ^ inch radius, passing through the points P, T, etc. Fig. 5 is an exercise with the line pen and compasses. First draw the diagonals A C and D B, the horizontal line L M and the vertical line E F passing through the center Q. Mark off dis- tances of 1 inch on L M and E F and draw the lines NN' O O' and N R, O S, etc., through these points, forming the squares N R R'N', O S S' O', etc. With the bow pencil adjusted so that the distance between the pencil point and the needle point is 1 inch draw the arcs having centers at the corners of the squares. The arc whose center is N will be tangent to the lines A L and A E and the arc whose center is O will be tangent to N N' and N R. Since P T, T T', T' P' and P' P are each 1 inch long and form the square, the arcs drawn with Q as a center will form a circle. To draw Fig. 6 , first draw the center lines E F and L M. Now find the centers of the small squares A L I E, L B F I etc. Through the center I draw the construction lines HIT and RIP forming angles of 30 degrees with the horizontal. Now adjust the compasses to draw circles having a radius of one inch. With I as a center, draw the circle H P T R. With the same radius (one inch V draw the arcs with centers at A, B, C and D. Also draw the semi-circles with centers at L, F, M and E. Now draw the arcs as shown having centers at the centers of the small squares A L I E, L B F I, etc. To locate the centers of the six small circles within the circle H P T R, draw a circle with a radius of -A inch and having the center in I. The small circles have a radius of -A- inch. Inking. In inking this plate, the outlines of the squares of the various figures are inked only in Figs. 2 and 3. In Fig. 1 the only lines to be inked are those shown in full lines in PLATE III. First ink the star and then the square and diamonds. The cross hatching should be done ivithout measuring the distance be- tween the lines and without the aid of any cross hatching device as this is an exercise for practice. The lines should be about -A inch apart. After inking ’erase all construction lines. In inking Fig. 2 be careful not to run over lines. Each line should coincide with the pencil line. The student should 47 38 MECHANICAL DRAWING. first ink the horizontal lines L, M and N and the vertical lines E, F and G. The short lines should have the same width but the border lines, A B, B C, C D and D A should be a little heavier. Fig. 3 is drawn entirely with the 45-degree triangle. In ink- ing the oblique lines make F I, R K, T M, etc., a light distinct line. The alternate lines O II, Q J, S L, etc., should be some- what heavier. All of the lines which slope in the opposite direc- tion are light. After inking Fig. 3 all horizontal and vertical lines (except the border lines) should be erased. The border lines should be slightly heavier than the light oblique lines. The only instrument used in inking Fig. 4 is the compasses. In doing this exercise adjust the legs of the compasses so that the pen will always be perpendicular to the paper. If this is not . done both nibs will not touch the paper and the line will be ragged. In inking the arcs, see that the pen stops exactly at the diagonals. The circle passing through T and the small inner circle should be dotted as shown in PLATF III. After inking the circles and arcs erase the construction lines that are without the outer circles but leave in pencil the diagonals inside the circle. In Fig. 5 draw all arcs first and then draw the straight lines meeting these arcs. It is much easier to draw straight lines meet- ing arcs, or tangent to them, than to make the arcs tangent to straight lines. As this exercise is difficult, and in all mechanical and machine drawing arcs and tangents are frequently used we advise the beginner to draw this exercise several times. Leave O all construction lines in pencil. Fig. 6 , like Fig. 4 , is an exercise with compasses. If Fig. 6 has been laid out accurately in pencil, the inked arcs will be tan- gent to each other and the finished exercise will have a good appearance. If, however, the distances were not accurately measured and the lines carefully drawn the inked arcs will not be tangent. The arcs whose centers are L, F, M and E and A, B, C and D should be heavier than the rest. The small circles may be drawn with the bow pen. After inking the arcs all construction lines should be erased. 48 DETAILS * OF* IONIC* CAPITAL W////////M Section throvgh ROLL ON LINE XX FACE -DF 'CAPITAL' — 6 -+- 3 .Si| -^rX ±b &.S- -) - 7 .S--J l? <6 -f to \ V 'PIATT OF' CAPITAL' 6 - 4 - • 139 6 PC 1 3 .S^- 2 .S'-*Z s[ t I t rv !? \ 0 / ioo\' r\ ■ " * i 1 i 5;SJ A a\ 1?.S l_ -•i-2.5 I- 0 6.5- ^ A . J _ of AIDE ' OF' CAPITAL' One Half Eru |Q |?~ | | | | ^ ^ ^ O' ' ' 2 15~^ ^ ^ ^ ^ S.y ^ ^ 4|Q, , . F’E. , , A 0 IONIC CAPITAL. A Study in Orthographic Projection. MECHANICAL DRAWING, PART II. GEOHETRICAL DEFINITIONS. A point is used for marking position ; it lias neither iengtli breadth nor thickness. A line has length only ; it is produced by the motion of a point. A straight line or right line is one that has the same direction throughout. It is the shortest distance between any two of its points. A curved line is one that is constantly changing in direction. It is sometimes called a curve. A broken line is one made up of several straight lines. Parallel lines are equally distant from each other at all points. A horizontal line is one having the direction of a line drawn upon the surface of water that is at rest. It is a line parallel to the horizon. A vertical line is one that lies in the direction of a thread suspended from its upper end and having a weight at the lower end. It is a line that is perpendicular to a horizontal plane. Lines are perpendicular to each other, if when they cross, the four angles formed are equal. If they meet and form two equal angles they are perpendicular. An oblique line is one that is neither vertical nor horizontals In Mechanical Drawing, lines drawn along me edge of the T square, when the head of the T square is resting against the left-hand edge of the board, are called horizontal lines. Those drawn at right angles or perpendicular to the edge of the T square are called vertical. If two lines cut each other, they are called intersecting lines , and the point at which they cross is called the point of intersection. 51 4 MECHANICAL DRAWING. ANGLES. An angle is formed when two straight lines meet. An angle is often defined as being the difference in direction of two straight lines. The lines are called the sides and the point of meeting is called the vertex . The size of an angle depends upon the amount of divergence of the sides and is independent of the length of these lines. Y_ RIGHT ANGLE. ACUTE ANGLE. OBTUSE ANGLE. If one straight line meet another and the angles thus formed are equal they are right angles. When two lines are perpendic- ular to each other the angles formed are right angles. An acute angle is less than a right angle. An obtuse angle is greater than a right angle. SURFACES. A surface is produced by the motion of a line; it has two dimensions, — length and breadth. A plane figure is a plane bounded on all sides by lines ; the space included within these lines (if they are straight lines) is called a polygon or a rectilinear figure, TRIANGLES. A triangle is a figure enclosed by three straight lines. It is a potygon of three sides. The bounding lines are the sides, and the points of intersection of the sides are the vertices. The angles of a triangle are the angles formed by the sides. A right-angled triangle, often called a right triangle, is one that has a right angle. An acute-angled triangle is one that has all of its angles acute. An obtuse-angled triangle is one that has an obtuse angle. In an equilateral triangle all of the sides are equal. 52 MECHANICAL DRAWING. 5 If all of the angles of a triangle are equal, the figure is called an equiangular triangle. A triangle is called scalene, when no two of its sides are equal. In an isosceles triangle two of the sides are equal. RIGHT ANGLED TRIANGLE. ACUTE ANGLED TRIANGLE. OBTUSE ANGLED TRIANGLE. The base of a triangle is the lowest side ; however, any side may be taken as the base. In an isosceles triangle the side which is not one of the equal sides is usually considered the base. The altitude of a triangle is the perpendicular drawn from the vertex to the base. EQUILATERAL TRIANGLE. ISOSCELES TRIANGLE. SCALENE TRIANGLE. QUADRILATERALS. A quadrilateral is a plane figure bounded by four straight lines. The diagonal of a quadrilateral is a straight line joining two opposite vertices. A trapezium is a quadrilateral, no two of whose sides are parallel. A trapezoid is a quadrilateral having two sides parallel. 53 6 MECHANICAL DRAWING. The bases of a trapezoid are its parallel sides. The altitude is the perpendicular distance between the bases. A parallelogram is a quadrilateral whose opposite sides are parallel. The altitude of a parallelogram is the perpendicular distance between the bases which are the parallel sides. There are four kinds of parallelograms: RECTANGLE. SQUARE. RHOMBUS. A rectangle is a parallelogram, all of whose angles are right angles. The opposite sides are equal. A square is a rectangle, all of whose sides are equal. A rhombus is a parallelogram which has four equal sides; but the angles are not right angles. A rhomboid is a parallelogram whose adjacent sides are unequal ; the angles are not right angles. POLYGONS. A polygon is a plane figure bounded by straight lines. The boundary lines are called the sides and the sum of the sides is called the perimeter . Polygons are classified according to the number of sides. A triangle is a polygon of three sides. A quadrilateral is a polygon of four sides. A pentagon is a polygon of five sides. A hexagon is a polygon of six sides. A heptagon is a polygon of seven sides. An octagon is a polygon of eight sides. A decagon is a polygon of ten sides. A dodecagon is a potygon of twelve sides. An equilateral polygon is one all of whose sides are equal. An equiangular polygon is one all of whose angles are equal. A regular polygon is one all of whose angles are equal and all of whose sides are equal. 54 MECHANICAL DRAWING. 7 CIRCLES. A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center. The curve which bounds the circle is called the circumference. Any portion of the circumference is called an arc. The diameter of a circle is a straight line drawn through the center and terminating in the circumference. A radius is a straight line joining the center with the circumference. It has a length equal to one half the diameter. All radii (plural of radius) are equal and all diameters are equal since a diameter equals two radii. O PENTAGON. HEXAGON. OCTAGON. An arc equal to one-half the circumference is called a semi- circumference and an arc equal to one-quarter of the circumfer- ence is called a quadrant . A quadrant may mean the sector, arc or angle. A chord is a straight line joining the extremities of an arc. It is a line drawn across a circle that does not pass through the center. A secant is a straight line which intersects the circumference in two points. A tangent is a straight line which touches the circumference at only one point. It does not intersect the circumference. The point at which the tangent touches the circumference is called the point of tangency or point of contact . 55 8 MECHANICAL DRAWING. A sector of a circle is the portion or area included between an arc and two radii drawn to the extremities of the arc. A segment of a circle is the area included between an arc and its chord. Circles are tangent when the circumferences touch at only- one point and are concentric when they have the same center. CONCENTRIC CIRCLES. INSCRIBED POLYGON An inscribed angle is an angle whose vertex lies in the cir- cumference and whose sides are chords. It is measured by one- half the intercepted arc. A central angle is an angle whose vertex is at the center of the circle and whose sides are radii. An inscribed polygon is one whose vertices lie in the circum- ference and whose sides are chords. MEASUREnENT OF ANGLES. To measure an angle describe an arc with the center at the vertex of the angle and having any convenient radius. The por- tion of the arc included between the sides of the angle is the measure of the angle. If the arc has a constant radius the greater the divergence of the sides, the longer will be the arc. If there are several arcs drawn with the same center, the intercepted arcs will have different lengths but they will all be the same fraction of the entire circumference. In order that the size of an angle or arc may be stated with- 56 MECHANICAL DRAWING. 9 out saying that it is a certain fraction of a circumference, the cir- cumference is divided into 360 equal parts called degrees. Thus we can say that an angle contains 45 degrees, which means that it is ^g 5 -Q = | of a circumference. In order to obtain accurate measure- ments each degree is divided into 60 equal parts called minutes and each minute is divided into 60 equal parts called seconds. Angles and arcs are usually measured by means of an instrument called a protractor which has already been explained. SOLIDS. A polyedron is a solid bounded by planes. The bounding planes are called the faces and their intersections edges. The intersections of the edges are called vertices. A polygon having four faces is called a tetraedron ; one having six faces a hexaedron ; of eight faces an octaedron ; of twelve faces a dodecaedron, etc. PRISM. RIGHT PRISM. TRUNCATED PRISM. A prism is a polyedron, of which two opposite faces, called bases, are equal and parallel ; the other faces, called lateral faces are parallelograms. The area of the lateral faces is called the lateral area. The altitude of a prism is the perpendicular distance between the bases. Prisms are triangular , quadrangular , etc., according to the shape of the base. A right prism is one whose lateral edges are perpendicular to the bases. 57 10 MECHANICAL DRAWING. A regular prism is a right prism having regular polygons for bases. A parallelopiped is a prism whose Bases are parallelograms. If the edges are all perpendicular to the bases it is called a right parallelopiped. A rectangular parallelopiped is a right parallelopiped whose bases are rectangles ; all the faces are rectangles. 0 PARALLELOPIPED. RECTANGULAR PARALLELOPIPED. OCTAEDRON. A cube is a rectangular parallelopiped all of whose faces are squares. A truncated prism is the portion of a prism included between the base and a plane not parallel to the base. PYRAMIDS. A pyramid is a polyedron one face of which is a polygon (called the base) and the other faces are triangles having a com- mon vertex. PYRAMID. REGULAR PYRAMID. FRUSTUM OF PYRAMID. The vertices of the triangles form the vertex of the pyramid. The altitude of the pyramid is the perpendicular distance from the vertex to the base. A pyramid is called triangular, quadrangular, etc., accord- ing to the shape of the base. A regular pyramid is one whose base is a regular polygon 58 MECHANICAL DRAWING. 11 and whose vertex lies in the perpendicular erected at the center of the base. A truncated pyramid is the portion of a pyramid included between the base and a plane not parallel to the base. A frustum of a pyramid is the solid included between the base and a plane parallel to the base. The altitude of a frustum of a pyramid is the perpendicular distance between the bases. CYLINDERS. A cylindrical surface is a curved surface generated by the motion of a straight line which touches a curve and continues parallel to itself. A cylinder is a solid bounded by a cylindrical surface and two parallel planes intersecting this surface. The parallel faces are called bases. Q CYLINDER. RIGHT CYLINDER. INSCRIBED CYLINDER. The altitude of a cylinder is the perpendicular distance between the bases. A circular cylinder is a cylinder whose base is a circle. A right cylinder or a cylinder of revolution is a cylinder gen- erated by the revolution of a rectangle about one side as an axis. A prism whose base is a regular polygon may be inscribed in or circumscribed about a circular cylinder. The cylindrical area is call the lateral area. The total area is the area of the bases added to the lateral area. CONES. A conical surface is a curved surface generated by the motion of a straight line, one point of which is fixed and the end or ends of which move in a curve. 59 12 MECHANICAL DRAWING. A cone is a solid bounded by a conical surface and a plane which cuts the conical surface. The plane is called the base and the curved surface the lateral area. The vertex is the fixed point. The altitude of a cone is the perpendicular distance from the vertex to the base. An element of a cone is a straight line from the vertex to the perimeter of the base. A circular cone is a cone whose base is a circle. CONE. A right circular cone or cone of revolution is a cone whose axis is perpendicular to the base. It may be generated by the revolution of a right triangle about one of the perpendicular sides as an axis. A frustum of a cone is the solid included between the base and a plane parallel to the base. The altitude of a frustum of a cone is the perpendicular distance between the bases. SPHERES. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center. The radius of a sphere is a straight line drawn from the 60 MECHANICAL DRAWING 13 center to the surface. The diameter is a straight line drawn through the center and having its extremities in the surface. A sphere may be generated by the revolution of a semi-circle about its diameter as an axis. An inscribed polyedron is a polyedron whose vertices lie in the surface of the sphere. An circumscribed polyedron is a polyedron whose faces are tangent to a sphere. A great circle is the intersection of the spherical surface and a plane passing through the center of a sphere. A small circle is the intersection of the spherical surface and a plane which does not pass through the center. A sphere is tangent to a plane when the plane touches the surface in only one point. A plane perpendicular to the extremity of a radius is tangent to the sphere. CONIC SECTIONS. If a plane intersects a cone the geometricrd figures thus formed are called conic sections. A plane perpendicular to the base and passing through the vertex of a right circular cone forms an isosceles triangle. If the plane is parallel to the base the intersection of the plane and conical surface will be the circum- ference of a circle. Fig. 1. Fig. 2. Fig. 3. Fig. 4. Ellipse. The ellipse is a curve formed by the intersection of a plane and a cone, the plane being oblique to the axis but not cutting the base. If a plane is passed through a cone as shown in Fig. 1 or through a cylinder as shown in Fig 2, the curve of intersection will be an ellipse. An ellipse may be defined as being a curve generated by a point moving in a plane , the sum of the distances of the point to two fixed points being always constant . The two fixed points are called the foci and lie on the 01 14 MECHANICAL DRAWING. longest line that can be drawn in the ellipse. One of these points is called a focus . The longest line that can be drawn in an ellipse is called the major axis and the shortest line, passing through the center, is called the minor axis. The minor axis is perpendicular to the middle point of the major axis and the point of intersection is called the center An ellipse may be constructed if the major and minor axes are given or if the foci and one axis are known. VERTEX ELLIPSE. PARABOLA. Parabola. The parabola is a curve formed by the inter- section of a cone and a plane parallel to an element as shown in. Fig. 3. The curve is not a closed curve. The branches approach parallelism. A parabola may be defined as being a curve every point of which is equally distayd from a line and a point. The point is called the focus and the given line the directrix. The line perpendicular to the directrix and passing through the focus is the axis. The intersection of the axis and the curve is the vertex. Hyperbola. This curve is formed by the intersection of a plane and a cone, the plane being parallel to the axis of the cone as shown in Fig. 4. Like the parabola, the curve is not a closed curve ; the branches constantly diverge. An hyperbola is defined as being a plane curve such that the difference of the distances from any point in the curve to two fixed points is equal to a given distance . 62 MECHANICAL DRAWING. 15 The two fixed points are the foci and the line passing through them is the transverse axis. Rectangular Hyperbola. The form of hyperbola most used in Mechanical Engineering is called the rectangular hyperbola because it is drawn with reference to rectangular co-ordinates. This curve is constructed as follows : In Fig. 5, O X and O Y are the two co-ordinates drawn at right angles to each other. These lines are also called axes or asymptotes. Assume A to be a known point on the curve. In drawing this curve for the theoretical indicator card, this point A is the point of cut-off. Draw A C parallel to O X and A D perpendicular to O X. Now mark off any convenient points on A C such as E, F, G, and H ; and through these points draw EE', FF', GG', and II IF perpendicular to O X. Connect E, F, G, H and C with O. Through the points of inter- section of the oblique lines and the vertical line AD draw the horizontal lines LL', MM', NN', PP' and QQ'. The first point on the curve is the assumed point A, the second point is R, the intersection of LL' and EE'. The third is the intersection S of MM' and FF'; the fourth is the intersection T of NN' and GG'. The other points are found in the same way. In this curve the products of the co-ordinates of all points are equal. Thus LR X RE' = MS X SF'= NT X TG'. ODONTOIDAL CURVES. The outlines of the teeth of gears must be drawn accurately because the smoothness of running depends upon the shape of the teeth. The two classes of curves generally employed in drawing gear teeth are the cycloidal and involute. Cycloid. The cycloid is a curve generated by a point on the circumference of a circle which rolls on a straight line tangent to the circle. The rolling circle is called the describing or generating circle Y ,4 E r o H c 03 1G MECHANICAL DRAWING. and the point, the describing or generating point. The tangent alongf which the circle rolls is called the director. O In order that the curve may be a true cycloid the circle must roll without any slipping. Epicycloid. If the generating circle rolls upon the outside of an arc or circle, called the director circle , the curve thus gener- ated is called an epicycloid. The method of drawing this curve is the same as that for the cycloid. Hypocycloid. In case the generating circle rolls upon the inside of an arc or circle, the curve thus generated is called the hypocycloid. The circle upon which the generating circle rolls is called the director circle. If the generating circle has a diameter equal to the radius of the director circle the hypocycloid becomes a straight line. Involute. If a thread or fine wire is wound around a cylinder or circle and then unwound, the end will describe a curve called an involute. The involute may be defined as being a curve generated by a point in a tangent rolling on a circle known as the base circle. The construction of the ellipse, parabola, hyperbola and odontoidal curves will be taken up in detail with the plates. 64 MECHANICAL DRAWING. 17 PLATE IV. Pencilling. The horizontal and vertical center lines and the border lines for PLATE IV should l:e laid out in the same manner as were those for PLATE I. There are to be six figures on this plate and to facilitate the laying out of the work, the fol- lowing lines should be drawn : measure off inches on botli sides of the vertical center line and through these points draw vertical lines as shown in dot and dash lines on PLATE IV In these six spaces the six figures are to be drawn, the student placing them in the centers of the spaces so that they will present a good appearance. In locating the figures, they should be placed a little above the center so that there will be sufficient space below to number the problem. The figures of the problems should first be drawn lightly in pencil and after the entire plate is completed the lines should be inked. In pencilling, all intersections must be formed with great care as the accuracy of the results depends upon the pencilling. Keep the pencil points in good order at all times and draw lines exactly through intersections. GEOMETRICAL PROBLEMS. The following problems are of great importance to the mechanical draughtsman. The student should solve them with care ; he should not do them blindly, but should understand them so that he can apply the principles in later work. PROBLEM I. To Bisect a Given Straight Line. Draw the horizontal straight line A G about 3 inches long. With the extremity A as a center and any convenient radius (about 2 inches) describe arcs above and below the line A C. With the other extremity C as a center and with the same radius draw short arcs above and below A C intersecting the first arcs at D and E. The radius of these arcs must be greater than one-half the length of the line in order that they may intersect. Now draw the straight line D E passing through the intersections D and E. This line cuts the line A C at F which is the middle point. A F = F C 65 18 MECHANICAL DRAWING. Proof. Since the points D and E are equally distant from A and C a straight line drawn through them is perpendicular to A C at its middle point F. PROBLEM 2. To Construct an Angle Equal to a Given Angle. Draw the line O C about 2 inches long and the line O A of about the same length. The angle formed by these lines may be any convenient size (about 45 degrees is suitable). This angle A O C is the given angle. Now draw F G a horizontal line about 2L inches long and let F the left-hand extremity be the vertex of the angle to be constructed. With O as a center and any convenient radius (about 1| inches) describe the arc L M cutting both O A and OC. With F as a center and the same radius draw the indefinite arc O Q. Now set the compass so that the distance between the pencil and the needle point is equal to the chord L M. With Q as a center and a radius equal to L M draw an arc cutting the arc O Q at P. Through F and P draw the straight line F E. The angle EF G is the required angle since it is equal to A O C. Proof. Since the chords of the arcs L M and P Q are equal the arcs are equal. The angles are equal because with equal radii equal arcs are intercepted by equal angles. PROBLEM 3. To Draw Through a Given Point a Line Parallel to a Given Line. First Method. Draw the horizontal straight line A C about 3| inches long and assume the point P about It inches above A C. Through the point P draw an oblique line F E forming any convenient angle with A C. (Make the angle about 60 degrees). Now construct an angle equal to P F C having the vertex at P and one side the line E P. (See problem 2). This may be done as follows: With F as a center and any con- venient radius, describe the arc L M. With the same radius draw the indefinite arc N O using P as the center. With N as a center and a radius equal to the chord L M, draw an arc cutting the arc N O at O. Through the points P and O draw a straight line which will be parallel to A C. 66 plate: V" /^. /0O/. /-y^r/=?^yEr/=?7 r ‘ £?/-/^\A/-Z7 /LjE~^? Z7/V/<03 £?£?, //L/L. MECHANICAL DRAWING. 19 Proof. If two straight lines are cut by a third making the corresponding angles equal, the lines are parallel. PROBLEM 4. To Draw Through a Given Point a Line Parallel to a Given Line. Second Method. Draw the straight line A C about 3L inches long and assume the point P about IT inches above A C. With P as a center and any convenient radius (about 21 inches) draw the indefinite arc E D cutting the line A C. Now with the same radius and with D as a center, draw an arc P Q. Set the com- pass so that the distance between the needle point and the pencil is equal to the chord P Q. With D as a center and a radius equal to P Q, describe an arc cutting the arc E D at H. A line drawn through P and H will be parallel to A C. Proof. Draw the line Q H. Since the arcs P Q and II D are equal and have the same radii, the angles P H Q and H Q D are equal. Two lines are parallel if the alternate interior angles are equal. PROBLEM 5. To Draw a Perpendicular to a Line from a Point in the Line. First Method. When the point is near the middle of the line. Draw the horizontal line A C about 3^ inches long and assume the point P near the middle of the line. With P as a center and any convenient radius (about 1^ inches) draw two arcs cutting the line A C at E and F. Now with E and F as centers and any convenient radius (about 2L inches) describe arcs inter- secting at O. The line O P will be perpendicular to A C at P. Proof. The points P and O are equally distant from E and F. Hence a line drawn through them is perpendicular to the middle point of E F which is P. PROBLEM 6. To Draw a Perpendicular to a Line from a Point in the Line. Second Method . When the point is near the end of the line. Draw the line A C about 3J inches long. Assume the given point P to be about ^ inch from the end A. With any point D as a center and a radius equal to D P, describe an arc, cutting A C at E. Through E and D draw the diameter E O. A line from O to P is perpendicular to A C at P. 69 20 MECHANICAL DRAWING. Proof. The angle O P E is inscribed in a semi-circle ; hence it is a right angle, and the sides O P and P E are perpendicular to each other. After completing these figures draw pencil lines for the lettering. The words “ PLATE IV" and the date and name should be placed in the border, as in preceding plates. To letter the words “ Problem 1,” “Problem 2,” etc., draw horizontal lines i inch above the horizontal center line and the lower border line. Draw another line -j 3 g inch above, to limit the height of the P, b and l. Draw a third line inch above the lower line as a guide line for the tops of the small letters. Inking. In inking PLATE IV the figures should be inked first. The line A C of Problem 1 should be a full line as it is the given line; the arcs and line D E, being construction lines should be dotted. In Problem 2, the sides of the angles should be full lines. Make the chord L M and the arcs dotted, since as before, they are construction lines. In Problem 3, the line A C is the given line and P O is the line drawn parallel to it. As E F and the arcs do not form a part of the problem but are merely construction lines, drawn as an aid in locating P O, they should be dotted. In Problems 4, 5 and 6, the assumed lines and those found by means of the construction lines should be full lines. The arcs and construction lines should be dotted. In Problem 6, the entire circumference need not be inked, only that part is necessary that is used in the problem. The inked arc should however be of sufficient length to pass through the points O, P and E. After inking the figures, the border lines should be inked with a heavy line as before. Also, the words 4 PLATE IV" and the date and the student’s name. Undereach problem the words “Problem 1,” “Problem 2,” etc., should be inked; lower case let- ters being used as shown. PLATE V. Pencilling. In laying out the border lines and centre lines follow the directions given for PLATE IV The dot and dash lines should be drawn in the same manner as there are to be six problems on this plate. 70 PLATE MECHANICAL DRAWING. 21 PROBLEM 7. To Draw a Perpendicular to a Line from a Point without the Line. Draw the horizontal straight line A C about 3^ inches long. Assume the point P about 1L inches above the line. With P as a center and any convenient radius (about 2 inches) describe an arc cutting A C at E and F. The radius of this arc must always be such that it will cut A C in two points; the nearer the points E and F are to A and C, the greater will be the accuracy of the work. Now with E and F as centers and any convenient radius (about 2i inches) draw the arcs intersecting below A C at T. A line through the points P and T will be perpendicular to A C. In case there is not room below A C to draw the arcs, they may be drawn intersecting above the line as shown at N. When- ever convenient, draw the arcs below A C for greater accuracy. Proof. Since P and T are equally distant from E and F, the line P T is perpendicular to A C. PROBLEM 8. To Bisect a Given Angle. First Method. When the sides intersect. Draw the lines O C and O A forming any angle (from 45 to 60 degrees). These lines should be about 8 inches long. With O as a center and any convenient radius (about 2 inches) draw an arc intersecting the sides of the angle at E and F. With E and F as centers and a radius of lj or 1| inches, describe short arcs intersecting at I. A line O D, drawn through the points O and I, bisects the angle. In solving this problem the arc E F should not be too near the vertex if accuracy is desired. Proof. The central angles A O D and DOC are equal because the arc E F is bisected by the line O D. The point I is equally distant from E and F. PROBLEM 9. To Bisect a Given Angle, Second Method . When the lines do not intersect. Draw the lines A 0 and E F about 4 inches long and in the positions as shown on PLATE V Draw A' C' and E' F' parallel to A C and E F and at such equal distances from them that they will intersect at O. Now bisect the angle C' O F' by 73 22 MECHANICAL DRAWING. the method of Problem 8. Draw the arc G H and with G and H as centers draw the arcs intersecting at R. The line O R bisects the angle. Proof. Since A' C' is parallel to A C and E' F' parallel to E F, the angle C' O F' is equal to the angle formed by the lines A C and E F. Hence as O R bisects angle C' O F' it also bisects the angle formed by the lines A C and E F. PROBLEM 10. To Divide a Given Line into any Number of Equal Parts. Let A C, about 3-J inches long, be the given line. Let us divide it into 7 equal parts. Draw the line A J at least 4 inches long, forming any convenient angle with A C. On A J lay off, by means of the dividers or scale, points D, E, F, G, etc., each i inch apart. If dividers are used the spaces need not be exactly 1 inch. Draw the line J C and through the points D, E, F, G, etc., draw lines parallel to J C. These parallels will divide the line A C into 7 equal parts. Proof. If a series of parallel lines, cutting two straight lines, intercept equal distances on one of these lines, they also intercept equal distances on the other. PROBLEM 11. To Construct a Triangle having given the Three Sides. Draw the three sides as follows : A C, 2| inches long. E F, 1L|- inches long. M N, 2^ inches long. Draw R S equal in length to A C. With R as a center and a radius equal to E F describe an arc. With S as a center and a radius equal to M N draw an arc cutting the arc previously drawn, at T. Connect T with R and S to form the triangle. PROBLEM 12. To Construct a Triangle having given One Side and the Two Adjacent Angles. Draw the line M N 3^ inches long and draw two angles A O D and E F G. Make the angle A O D about 30 degrees and E F G about 60 degrees. Draw R S equal in length to M N and at R construct an 74 MECHANICAL DRAWING. 23 angle equal to A O D. At S construct an angle equal to E F G by the method used in Problem 2. PLATE V shows the neces- sary arcs. Produce the sides of the angles thus constructed until they meet at T. The triangle R T S will be' the required triangle. After drawing these six figures in pencil, draw the pencil lines for the lettering. The lines for the words “ PLATE V” date and name, should be pencilled as explained on page 20. The words “ Problem 7,” “ Problem 8,” etc., are lettered as for PLATE IV. Inking. In inking PLATE V the same principles should be followed as stated with PLATE IV. The student should apply these principles and not make certain lines dotted just because they are shown dotted in PLATE V. After inking the figures, the border lines should be inked and the lettering inked as already explained in connection with previous plates. PLATE VI. Pencilling. Lay out this plate in the same manner as the two preceding plates. PROBLEM 13. To describe an Arc or Circumference through Three Given Points not in the same straight line. Locate the three points A, B and C. Let the distance between A and B be about 2 inches and the distance between A and C be about 2| inches. Connect A and B and A and C. Erect perpendiculars to the middle points of A B and A C. This may be done as explained with Problem 1. With A and B as centers and a radius of about 1| inches, describe the arcs inter- secting at I and J. With A and C as centers and with a radius of about 1J inches draw the arcs, intersecting at E and F. Now draw light pencil lines connecting the intersections I and J and E and F. These lines will intersect at O. With O as a center and a radius equal to the distance O A, describe the circumference passing through A, B and C. Proof. The point O is equally distant from A, B and C, since it lies in the perpendiculars to the middle points of A B and 75 24 MECHANICAL DRAWING A C. Hence the circumference will pass through A, B and C. PROBLEM 14. To inscribe a Circle in a given Triangle. Draw the triangle L M N of any convenient size. M N may be made 3f inches, L M, 2f inches, and L N, 31 inches. Bisect the angles M L N and L M N. The bisectors MI and L J may be drawn by the method used in Problem 8. Describe the arcs A C and E F, having centers at L and M respectively. The arcs intersecting at I and J are drawn as already explained. The bisectors of the angles intersect at O, which is the center of the inscribed circle. The radius of the circle is equal to the perpen- dicular distance from O to one of the sides. Proof. The point of intersection of • the bisectors of the angles of a triangle is equally distant from the sides. PROBLEM 15. To inscribe a Regular Pentagon in a given Circle. With O as a center and a radius of about It inches, describe the given circle. With the T square and triangles draw the cen- ter lines A C and E F. These lines should be perpendicular to each other and pass through O. Bisect one of the radii, such as O C, and with this point H as a center and a radius H E, describe the arc E P. This arc cuts the diameter A C at P. With E as a center and a radius E P, draw arcs cutting the circumference at L and Q. With the same radius and a center at L, draw the arc, cutting the circumference at M. To find the point N, use either M or Q as a center and the distance E P as a radius. The pentagon is completed by drawing the chords E L, L M, MN,NQ and Q E. PROBLEM 16. To inscribe a Regular Hexagon in a given Circle. With O as a center and a radius of If inches draw the given circle. With the T square draw the diameter A D. With D as a center, and a radius equal to O D, describe arcs cutting the circumference at C and E. Now with C and E as centers and the same radius, draw the arcs, cutting the circumference at B and F. Draw the hexagon by joining the points thus formed. To inscribe a regular hexagon in a circle mark off chords equal in length to the radius. 76 F’LsA TE MECHANICAL DRAWING, 25 To inscribe an equilateral triangle in a circle the same method may be used. The triangle is formed by joining the opposite vertices of the hexagon. Proof. The triangle O C I) is an equilateral triangle by construction. Then the angle C O D is one-third of two right angles and one-sixth of four right angles. Hence arc C D is one- sixth of the circumference and. the chord is a side of a regular hexagon. PROBLEM 17. To draw a line Tangent to a Circle at a given point on the circumference. With O as a center and a radius of about 1^ inches draw the given circle. Assume some point P on the circumference Join the point P with the center O and through P draw a line F P perpendicular to P O. This may be done in any one of several methods. Since P is the- extremity of O P the method given in Problem 6 of PLATE IV ] may be used. Produce P O to Q. With any center C, and a radius C P draw an arc or circumference passing through P. Draw E F a diameter of the circle whose center is C and through F and P draw the tangent. Proof. A line perpendicular to a radius at its extremity is tangent to the circle. PROBLEM 18. To draw a line Tangent to a Circle from a point outside the circle. With O as a center and a radius of about 1 inch draw the given circle. Assume P some point outside of the circle about 21- inches from the center of the circle. Draw a straight line passing through P and O. Bisect P O and with the middle point F as a center describe the circle passing through P and O. Draw a line through P and the intersection of the two circum- ferences C. The line P C is tangent to the given circle. Simi- larly P E is tangent to the circle. Proof. The angle P C O is inscribed in a semi-circle and hence is a right angle. Since P C O is a right angle P C is per- pendicular to C O. The perpendicular to a radius at its extremity is tangent to the circumference. Inking. In inking PLATE VI the same method should be 79 26 MECHANICAL DRAWING. followed as in previous plates. The name and address should be lettered in inclined Gothic capitals as before. PLATE VII. Pencilling. PLATE VII should be laid out in the same manner as previous plates. Six problems on the ellipse, spiral, parabola and hyperbola are to be constructed in the six spaces. PROBLEM 19. To draw an Ellipse when the Axes are given. Draw the lines L M and C D about 3| and 2i inches long respectively. Let C D be perpendicular to M N at its middle point P. Make C P — P D. These two lines are the axes. With C as a center and a radius equal to one-half the major axis or equal to L P, draw the arc, cutting the major axis at E and F. These two points are the foci. Now mark off any convenient distances on P M, such as A, B and G. With E as a center and a radius equal to L A, draw arcs above and below L M. With F as a center, and a radius equal to A M describe short arcs cutting those already drawn as shown at N. With E as a center and a radius equal to L B draw arcs above and below L M as before. With F as a center and a radius equal to B M, draw arcs intersecting those already drawn as shown at O. The point P and others are found by repeating the process. The student is advised to find at least 12 points on the curve — 6 above and 6 below L M. These 12 points with L, C, M and D will enable the student to draw the curve. After locating these points, a free hand curve passing through them should be sketched. PROBLEM 20. To draw an Ellipse when the two Axes are given. Second Method. Draw the two axes A B and P Q in the same manner as for Problem 19. With O as a center and a radius equal to one-half the major axis, describe the circumference A C D PI F B. Similarly with the same center and a radius equal to one-half the minor axis, describe a circle. Draw any radii such as O C, O D, O E, O F, etc., cutting both circumferences. These radii may be drawn with the 60 and 45 degree triangles. At the 80 MECHANICAL DRAWING. *27 points of intersection of the radii with the large circle C D E and F, draw vertical lines and from the intersection of the radii with the small circle C', D', E', and F( draw horizontal lines intersect- ing the vertical lines. The intersections of these lines are points on the curve. • As in Problem 19, a free hand curve should be sketched pass- ing through these points. About five points in each quadrant will be sufficient. PROBLEM 21. To draw an Ellipse by means of a Trammel. As in the two preceding problems, draw the major and minor axes, U Y and X Y. Take a slip of paper having a straight edge and mark off C B equal to one-half the major axis, and D B one-half the minor axis. Place the slip of paper in various positions keeping the point D on the major axis and the point C on the minor axis. If this is done the point B will mark various points on the curve. Find as many points as necessary and sketch the curve. PROBLEM 22. To draw a Spiral of one turn in a circle. Draw a circle with the center at O and a radius of 11 inches. Mark off on the radius O A, distances of one-eighth inch. As O A is 1| inches long there will be 1 2 of these distances. Draw circles through these points. Now draw radii O B, O C, O D etc. each 30 degrees apart (use the 30 degree triangle). This will divide the circle into 12 equal parts. The curve starts at the center O. The next point is the intersection of the line O B and the first circle. The third point is the intersection of O C and the second circle. The fourth point is the intersection of O D and the third circle. Other points are found in the same way. Sketch in pencil the curve passing through these points. PROBLEM 23. To draw a Parabola when the Abscissa and Ordinate are given. Draw the straight line A B about three inches long. This line is the axis or as it is sometimes called the abscissa. At A and B draw lines perpendicular to A B. Also with the T square draw E C and F D, 11 inches above and below A B. Let A be 83 28 MECHANICAL DRAWING. the vertex of the parabola. Divide A E into any number of equal parts and divide E C into the same number of equal parts. Through the points of division, It, S, T, U and V, draw horizontal lines and connect L, M, N, O and P, with A. The intersections of the horizontal lines with the oblique lines are points on the curve. For instance, the intersection of A L and the line V is one point and the intersection of A M and the liue U is another. The lower part of the curve A D is drawn in the same manner. PROBLEM 24. To draw a Hyperbola when the abscissa E X, the ordinate A E and the diameter X Y are given. Draw E F about 3 inches long and mark the point X, 1 inch from E and the point Y, 1 inch from X, With the triangle and T square, draw the rectangles A B D C and O P Q R such that A B is 1 inch in length and A C, 3 inches in length. Divide A E into any number of equal parts and A B into the same num- ber of equal parts. Draw L X, M X and N X; also connect T, U and V with Y. The first point on the curve is the intersection A ; the next is the intersection of T Y and L X ; the third the intersection of U Y and M X. The remaining points are found in the same manner. The curve X C and the right-hand curve P Y Q are found by repeating the process. Inking. In inking the figures on this plate, use the French or irregular curve and make full lines for the curves and their axes. The construction lines should be dotted. Ink in all the construction lines used in finding one-half of a curve, and in Problems 19, 20, 23 and 24 leave all construction lines in pencil except those inked. In Problems 21 and 22 erase all construction lines not inked. The trammel used in Problem 21 may be drawn in the position as shown, or it may be drawn outside of the ellipse in any convenient place. The same lettering should be done on this plate as on previous plates. PLATE VIII. Pencilling. In laying out Plate VIII, draw the border lines; and horizontal and vertical center lines as in previous plates, to divide the plate into four spaces for the four problems. 84 AP. /0O/. /-/£r/=?&£7/=?T £?/S^A/JJl- £T/=? C‘/~//C'yA GO. //LZ_. MECHANICAL DRAWING. 29 PROBLEM 25. To construct a Cycloid when the diameter of the generating circle is given. With 0' as a center and a radius of inch draw a circle, and tangent to it draw the indefinite horizontal straight line A B. Divide the circle into any number of equal parts (12 for instance) and through these points of division C, D, E, F, etc., draw hori- zontal lines. Now with the dividers set so that the distance between the points is equal to the chord of the arc C D, mark off the points L, M, N, O, P on the line *A B, commencing at the point H. At these points erect perpendiculars to the center line G O'. This center line is drawn through the point O' with the T square and is the line of centers of the generating circle as it rolls along the line A B. Now with the intersections Q, R, S, T, etc., of these verticals with the center line as centers describe arcs of circles as shown. The points on the curve are the inter- sections of these arcs and the horizontal lines drawn through the points C, D, E, F, etc. Thus the intersection of the arc whose center is Q and the horizontal line through C is a point I on the curve. Similarly, the intersection of the arc whose center is R and the horizontal line through D is another point J on the curve. The remaining points, as well as those on the right-hand side, are found in the same manner. To obtain great accuracy in this curve, the circle should be divided into a large number of equal parts, because the greater the number of divisions the less the error due to the difference in length of a chord and its arc. PROBLEM 26. To construct an Epicycloid when the di= ameter of the generating circle and the diameter of the director circle are given. The epicycloid and hypocycloid may be drawn in the same manner as the cycloid if arcs of circles are used in place of the horizontal lines. With O as a center and a radius of | inch describe a circle. Draw the diameter E F of this circle and pro- duce E F to G such that the line F G is 2|^ inches long. With G as a center and a radius of 2 ^ inches describe the arc A B of the director circle. With the same center G, draw the arc P Q which will be the path of the center of the generating circle as it rolls along the arc A B. Now divide the generating circle into 87 30 MECHANICAL DRAWING. any number of equal parts (twelve for instance) and through the points of division H, I, L, M, and N, draw arcs having G as a center. With the dividers set so that the distance between the points is equal to the chord H I, mark off distances on the director circle A F B. Through these points of division R, S, T, U, etc., draw radii intersecting the arc P Q in the points IT, S', T', etc., and with these points as centers describe arcs of circles as in Problem 25. The intersections of these arcs with the arcs already drawn through the points H, I, L, M, etc., are points on the curve. Thus the intersection of the circle whose center is IT with the arc drawn through the point H is a point upon the curve. Also the arc whose center is S' with the arc drawn through the point I is another point on the curve. The remaining points are found by repeating this process. PROBLEM 27. To draw an Hypocydoid when the diam= eter of the generating circle and the radius of the director circle are given. With O as a center and a radius of 4 inches describe the arc E F, which is the arc of the director circle. Now witli the same center and a Radius of 3-^ inches, describe the arc A B, which is the line of centers of the generating circle as it rolls on the director circle. With O' as a center and a radius of | inch describe the generating circle. As before, divide the generating circle into any number of equal parts (12 for instance) and with these points of division L, M, N, O, etc., draw arcs having O as a center. Upon the arc E F, lay off distances Q R, R S, S T, etc., equal to the chord Q L. Draw radii from the points R, S, T, etc., to the center of the director circle O and describe arcs of circles having a radius equal to the radius of the generating circle, using the points G, I, J, etc., as centers. As in Problem 26, the inter- sections of the arcs are the points on the curve. By repeating this process, the right-hand portion of the curve may be drawn. PROBLEM 28. To draw the Involute of a circle when the diameter of the base circle is known. With point O as a center and a radius of 1 inch, describe the base circle. Now divide the circle into any number of equal parts 16 for instance) and connect the points of division with the cen* 88 MECHANICAL DRAWING. 31 ter of the circle by drawing the radii 0 C, O D, O E, O F, etc., to O B. At the point D, draw a light pencil line perpendicular to the radius O D. This line will be tangent to the circle. Similarly at the points E, F, G, H, etc., draw tangents to the circle. Now set the dividers so that the distance between the points will be equal to the chord of the arc C D, and measure this distance from D along the tangent. Beginning with the point E, measure on the tangent a distance equal to two of these chords, from the point F measure on the tangent three divisions, and from the point G measure a distance equal to four divisions on the tangent G P. Similarly, measure distances on the remaining tangents, each time adding the length of the chord. This will give the points Q, R, S and T. Now sketch a light pencil line through the points L, M, N, P, etc., to T. This curve will be the involute of the circle. Inking. The same rules are to be observed in inking PLATE VIII as were followed in the previous plates, that is, the curves should be inked in a full line, using the French or irregular curve. All arcs and lines used in locating the points on one-half of the curve should be inked in dotted lines. The arcs and lines used in locating the points of the other half of the curve may be left in pencil in Problems 25 and 26. In Problem 28, all construction lines should be inked. After completing the problems the same lettering should be done on this plate as on previous plates. 89 PIERCED- 11011 THREE-COARTER-OCALE-DETAIL'OF'CUT -3TONE -WORK- CENTRAL PAVILION ■ EASTERN- PARKWAY- ELEVATION- BROOKLYN.'* INSTITUTE.* k?kim*hlad*an°*whitc *a£ckt:5- i DRAWING h angle, equal in length and width to the length and width respec- tively of the prism, and as the prism stands with its base on H, the elevation, showing height above H, must have its base on the ground line. Observe carefully that points in elevation are verti- cally over corresponding points in plan. The second drawing in Fig. 5 represents a prism of the same size lying on one side on the horizontal plane, and with the ends parallel to V. The principles which have been used thus far may be stated as follows, — MECHANICAL DRAWING. 7 1. If a line or point is on either plane, its other projection must be in the ground line. 2. Height above H is shown m elevation as height above the ground line, and distance in front of the vertical plane is shown in plan as distance from the ground line. 3. If a line is parallel to either plane, its actual length is shown on that plane, and its other projection is parallel to the ground line. A line oblique to either plane has its projection on that plane shorter than the line itself, and its other projection oblique to the ground line. No projection can be longer than the line itself. 4. A plane surface if parallel to either plane, is shown on Fig. 6. Fig. 7. that plane in its true size and shape ; if oblique it is shown smaller than the true size, and if perpendicular it is shown as a straight line. Lines parallel in space must have their V projec- tions parallel to each other and also their H projections. If two lines intersect, their projections must cross, since tli9 point of intersection of the. lines is a point on both lines, and therefore the projections of this point must be on the projections of both lines, or at their intersection. In order that intersecting lines may be represented, the vertical projections must intersect in a point vertically above the intersection of the horizontal pro- 95 8 MECHANICAL DRAWING. jections. Thus Fig. 6 represents two lines which do intersect as C v crosses D v at a point vertically above the intersection of C h and D 71 . In Fig. 7, however, the lines do not intersect since the inter- sections of their projections do not lie in the same vertical line. In Fig. 8 is given the plan and elevation of a square pyramid standing on the horizontal plane. The height of the pyramid is the distance A B. The slanting edges of the pyramid, AC, AD, etc., must be all of the same length, since A is directly above the center of the base. What this length is, however, does not appear in either projection, as these edges are not parallel to either V or H. Suppose that the pyramid be turned around into the dotted posi- tion C, Dj E, F ( where the horizontal projections of two of the slanting edges, A C, and A E, are parallel to the ground line. These two edges, having their horizontal projections parallel to the ground line, are now parallel to V, and therefore their new vertical projections will show their true lengths. The base of the pyra- mid is still on H, and therefore is projected on V in the ground line. The apex is in the same place as be- fore, hence the vertical projection of the pyramid in its new position is shown by the dotted lines. The vertical projection A C, v is the true length of edge A C. Now if we wish to find simply the true length of A C, it is unnecessary to turn the whole pyramid around, as the one line A C will be sufficient. The principle of finding the true length of lines is this, and can be applied to any case : Swing one projection of the line par- allel to the ground line, using one end as center. On the other projection the moving end remains at the same distance from the ground line, and of course vertically above or below the same end in its parallel position. This new projection of the line shows its true length. See the three Figures at the top of page 9. 96 MECHANICAL DRAWING. 9 Third plane of projection or profile plane. A plane perpen- dicular to both co-ordinate planes, and hence to the ground line, is called a profile plane . This plane is vertical in position, and may be used as a plane of projection. A projection on the profile plane is called a profile view, or end view , or sometimes edge view, and is often required in machine or other drawing when the plan and elevation do not sufficiently give the shape and dimensions. A projection on this plane is found in the same way as on the V plane, that is, by perpendiculars drawn from points on the object. Since, however, the profile plane is perpendicular to the ground line, it will be seen from the front and top simply as a 97 to MECHANICAL DRAWING. straight line ; in order that the size and shape of the profile view may be shown, the profile plane is revolved into V using its inter- section with the vertical plane as the axis. Given in Fig. 9, the line A B by its two projections A v B w and A h B 71 , and given also the profile plane. Now by projecting the line on the profile by perpendiculars, the points A* B, v and B, 71 A, 71 are found. Revolving the profile plane like a door on its hinges, all points in the plane will move in horizontal circles, so the horizontal projections A, 71 and B/ 1 will move in arcs of circles with O as center to the ground line, and the vertical projections B, v and A, v will move in lines parallel to the ground line to positions directly above the * revolved points in the ground line, giving the profile view of the line A p B p . Heights, it will be seen, are the same in profile view as in elevation. By referring to the rectangular prism in the same figure, we see that the elevation gives vertical dimensions and those parallel to Y, while the end view shows vertical dimensions and those perpendicular to Y. The profile view of any object may be found as shown for the line A B by taking one point at a time. In Fig. 10 there is repre- sented a rectangular prism or block, whose length is twice the width. The elevation shows its height. As the prism is placed at an angle, three of the vertical edges will be visible, the fourth one being invisible. In mechanical drawing lines or edges which are invisible are drawn dotted. The edges which in projection form a part of the outline or contour of the figure must always be visible, hence always full lines. The plan shows what lines are visible in eleva- tion, and the elevation determines what are visible in plan. In Fig. 10, the plan shows that the dotted edge A B is the back edge, and in Fig. 11, the dotted edge C D is found, by looking at the elevation, to be the lower edge of the triangular prism. In general, Fig. 10. 98 Mechanical drawing. n if in elevation an edge projected ivithin the figure is a back edge, it must be dotted, and in plan if an edge projected within the outline is a lower edge it is dotted. Fig. 12 is a circular cylinder with the length vertical and Fig. 11. with a hole part way through as shown in elevation. Fig. IB is plan, elevation and end view of a triangular prism with a square hole from end to end. The plan and elevation alone would be insufficient to determine positively the shape of the hole, but the end view shows at a glance that it is square. In Fig. 14 is shown plan and elevation of the frustum of a square pyramid, placed with its base on the horizontal plane. If the frustum is turned through 30°, as shown in the plan of Fig. 15, the top view or plan must still be the same shape and size, and as the frustum has not been raised or lowered, the heights of all points must appear the same in elevation as before in Fig. 14. The elevation is easily found by projecting points up from the plan, and projecting the height of the top horizontally across from the first elevation, because the height does not change. The same principle is further illustrated in Figs. 16 and 17. The elevation of Fig. 16 shows a square prism resting on one edge, and raised up at an angle of 30° on the right-hand side. The 99 12 MECHANICAL DRAWING. plan gives the width or thickness, | in. Notice that the length of the plan is greater than 2 in. and that varying the angle at Fig. 12. Fig. 13. which the pri«m is slanted would change the length of the plan. Now if the prism be turned around through any angle with the vertical plane, the lower edge still being on H, and the inclination Fig. 14. Fig. 15. of 30° with II remaining the same, the plan must remain the same size and shape. If the angle through which the prism be turned is 45°, we 100 MECHANICAL DRAWING. 13 have the second plan, exactly the same shape and size as the first. The elevation is found by projecting the corners of the prism ygv- Fig. 16. tically up to the heights of the same points in the first elevation. All the other points are found in the same way as point No. 1. Fig. 17. Three positions of a rectangular prism are shown in Fig. 17. In the first view, the prism stands on its base, its axis therefore 101 14 MECHANICAL DRAWINGS is parallel to the vertical plane. In the second position, the axis is still parallel to V and one corner of the base is on the horizontal plane. The prism has been turned as if on the line l /l ~i v as an axis, so that the inclination of all the faces of the prism to the vertical plane remains the same as before. That is, if in the first figure the side A B C D makes an angle of 30° with the vertical, the same side in the second position still makes 30° with the ver- tical plane. Hence the elevation of No. 2 is the same shape and size as in the first case. The plan is found by projecting the corners down from the elevation to meet horizontal lines projected across from the corresponding points in the first plan. The third posi- tion shows the prism with all its faces and edges making the same angles with the horizontal as in the second position, but with the plan at a different angle with the ground line. The plan then is the same shape and size as in No. 2, and the elevation is found by projecting up to the same heights as shown in the preceeding elevation. This principle may be applied to any solid, whether bounded by plane surfaces or curved. This principle as far as it relates to heights, is the same that was used for profile views. An end view is sometimes necessary before the plan or elevation of an object can be drawn. Suppose that in Fig. 18 we wish to draw the plan and elevation of a tri- angular prism 3" long, the end of which is an equilateral triangle 102 MECHANICAL DRAWING. 15 \y on each side. The prism is lying on one of its three faces on H, and inclined toward the vertical plane at an angle of 30°. We are able to draw the plan at once, because the width will be 1^ inches, and the top edge will be projected half way between the other two. The length of the prism will also be shown. Before we can draw the elevation, we must find the height of the top edge. This height, however, must be equal to the altitude of the triangle forming the end of the prism. All that is necessary, then, is to construct an equilat- eral triangle on each side, and measure its altitude. A very convenient way to do this is shown in the figure by laying one end of the prism down on H. A similar construction is shown in Fig. 19, but with one face of the prism on V instead of on H. In all the work thus far the plan has been drawn below and the elevation above. This order is sometimes inverted and the plan put above the elevation, but the plan still remains a top view no matter where placed, so that after some practice it makes but little difference to the draughtsman which method is employed. SHADE LINES. It is often the case in machine drawing that certain lines or edges are made heavier than others. These heavy lines are called shade lines, and are used to improve the appearance of the draw- ing, and also to make clearer in some cases the shape of the object. The shade lines are not put on at random, but according to some system. Several systems are in use, but only that one which seems most consistent will be described. The shade lines are lines or edges separating light faces from dark ones, assuming the light always to come in a direction parallel to the dotted diagonal of the cube shown in Fig. 20. The direction of the light, then, may be represented on H by a line at 45° running 103 16 MECHANICAL DRAWING. backward to the right and on Y by a 45° line sloping downward and to the right. Considering the cube in Fig. 20, if the light comes in the direction indicated, it is evident that the front, left- hand side and top will be light, and the bottom, back and right- hand side dark. On the plan, then, the shade lines will be the back edge 1 2 and the right-hand edge 2 3, because these edges are between light faces and dark ones. On the elevation* since the front is light, and the right-hand side and bottom dark, the edges 3 T and 8 7 are shaded. As the direction of the light is represented on the plan by 45° lines and on the elevation also by 45° lines, Fig. 20. we may use the 45° triangle with the T-square to determine the light and dark surfaces, and hence the shade lines. If the object stands on the horizontal plane, the 45°- triangle is used on the plan, as shown in Fig. 21, but if the length is perpen- dicular to the vertical plane, the 45° triangle is used on the eleva- tion, as shown in Fig. 22. This is another way of saying that the 45° triangle is used on that projection of the object which shows the end. By applying the triangle in this way we determine the light and dark surfaces, and then put the shade lines between them. Dotted lines, however, are never shaded, so if a line which is between a light and a dark surface is invisible it is not MECHANICAL DRAWING. 17 shaded. In Fig. 21 the plan shows the end of the solid, hence the 45° triangle is used in the direction indicated by the arrows. This shows that the light strikes the left-hand face, but not the back or the right-hand. The top is known to be light with- out the triangle, as the light comes downward, so the shade edges on the plan are the back and right-hand. On the elevation two faces of the prism are visible ; one is light, the other dark, hence the edge between is shaded. The left-hand edge, being between a light face and a dark one is a shade line. The right-hand face is dark, the top of the prism is light, hence the upper edge of this face is a shade line. The right-hand edge is not shaded, because by referring to the plan, it is seen to be between two dark surfaces. In shading a cylinder or a cone the same rule is fol- lowed, the only difference being that as the surface is curved, the light is tangent, so an element instead of an edge marks the separation of the dark from the light, and is not shaded. The elements of a cylinder or cone should never be shaded, but the bases may. In Fig. 23, Nos. 3 and 4, the student should carefully notice the difference between the shading of the cone and cylinder. 105 18 MECHANICAL DRAWING. If in No. 4 the cone were inverted, the opposite half of the base would be shaded, for then the base would be light, whereas it is now dark. In Nos. 7 and 8 the shade lines of a cylinder and a circular hole are contrasted. In No. 7 it is clear that the light would strike inside on the further side of the hole, commencing half way where the 45° lines 5 6 7 8 Fig. 23. are tangent. The other half of the inner surface would be dark, hence the position of the shade line. The shade line then enables us to tell at a glance whether a circle represents a hub or boss, or depression or hole. Fig. 24 represents plan, elevation and profile view of a square prism. Here as before, the view showing the end is the one used to determine the light and dark surfaces, and then the shade lines put in accordingly. 100 MECHANICAL DRAWING. 19 In putting on the shade lines, the extra width of line is put inside the figure, not outside. In shading circles, the shade line o' o' is made of varying width, as shown in the figures. The method of obtaining this effect by the compass is to keep the same radius, but to change the center slightly in a direction parallel to the rays of light, as shown at A and B in No. 2 of Fig. 24. No. 2. INTERSECTION AND DEVELOPHENT. If one surface meets another at some angle, an intersection is produced. Either surface may be plane, or curved. If both are plane, the intersection is a straight line ; if one is curved, the intersection is a curve, except in a few special cases ; and if both are curved, the intersection is usually curved. In the latter case, the entire curve does not always lie in the same planes. If all points of any curve lie in the same plane, it is called a plane curve. A plane intersecting a curved surface must always give either a plane curve or a straight line. In Fig. 25 a square pyramid is cut by a plane A parallel to the horizontal. This plane cuts from the pyramid a four-sided figure, the four corners of which will be the points where A cuts the four slanting edges of the solid. The plane intersects edge o b at point 4^ in elevation. This point must be found in plan vertically below on 107 20 MECHANICAL DRAWING. the horizontal projection of line o b , that is, at point 4A Edge o e is directly in front of o b, so is shown in elevation as the same line, and plane A intersects o e at point in elevation, found in plan at 1A Points 3 and 2 are obtained in the same way The intersection is shown in plan as the square 1 2 3 4, which is also its true size as it is parallel to the horizontal plane. In a similar way the sections are found in Figs. 26 and 27. It will be seen that in these three cases where the planes are parallel to the bases, the sections are of the same shape as the bases, and have their sides parallel to the edges of the bases. It is an invariable rule that when such a solid is cut by a plane parallel to its base, the section is a figure of the same shape as the base. If then in Fig. 28 a right cone is intersected by a plane .parallel to the base the section must be a circle, the center of which in plan coincides with the apex. The radius must equal o d. In Figs. 29 and 30 the cutting plane is not parallel to the base, hence the intersection will not be of the same shape as the bas6. The sections are found, however, in exactly the same manner as in the previous figures, by projecting the points where the plane intersects the edges in elevation on to the other view of the same line. INTERSECTION OF PLANES WITH CONES OR CYLINDERS. Sections cut by a plane from a cone have already been de- fined as conic sections. These sections may be either of the fol- lowing: two straight lines, circle, ellipse, parabola, hyperbola. All except the parabola and hyperbola may also be cut from a cylinder. Methods have previously been given for constructing the 108 MECHANICAL DRAWING. 21 22 MECHANICAL DRAWING. ellipse, parabola and hyperbola without projections ; it will now be shown that they may be obtained as actual intersections. In Fig. 31 the plane cuts the cone obliquely. To find points on the curve in plan take a series of horizontal planes Fig. 3L x y z etc., between points cv and d v . One of these planes, as w , should be taken through the center of c d. The points c and d must be points on the curve, since the plane cuts the two contour elements at these points. The horizontal projections of the contour elements will be found in a horizontal line passing through the center of the base ; hence the horizontal projection of c and d will be found on this center line, and will be the extreme ends of the curve. Contour elements are those forming the outline. 110 MECHANICAL DRAWING. 23 The plane x cuts the surface of the cone in a circle, as it is parallel to the base, and the diameter of the circle is the distance between the points where x crosses the two contour elements. This circle, lettered x on the plan, has its center at the horizontal projection of the apex. The circle x and the curve cut by the plane are both on the surface of the cone, and their vertical projec- tions intersect at the point 2. Also the circle x and the curve must cross twice, once on the front of the cone and once on the back. Point 2 then represents two points which are shown in plan directly beneath on the circle x, and are points on the re- quired intersection. Planes y and z, and as many more as may be necessary to determine the curve accurately, are used in the same way. The curve found is an ellipse. The student will readily see that the true size of this ellipse is not shown in the plan, for the plane containing the curve is not parallel to the horizontal. In order to find the actual size of the ellipse, it is necessary to place its plane in a position parallel either to the vertical or to the horizontal. The actual length of the long diameter of the ellipse must be shown in elevation, dv, because the line is parallel to the vertical plane. The plane of the ellipse then may be revolved about cv d v as an axis until it becomes parallel to V, when its true size will be shown. For the sake of clearness of construction, c*> c? u is imagined moved over to the position c' d\ parallel to cv d*. The lines 1 — 1, 2 — 2, 8 — 8 on the plan show the true width of the ellipse, as these lines are parallel to H, but are projected closer together than their actual distances. In elevation these lines are shown as the points 1, 2, 3, at their true distance apart. Hence if the ellipse is revolved around its axis c*> the distances 1 — 1, 2 — 2, 3 — 3 will appear perpendicular to cv d v , and the true size of the figure be shown. This construction is made on the left, where 1' — 1', 2 r — 2' and 3' — 3' are equal in length to 1 — 1, 2 — 2, 3 — 3 on the plan. In Fig. 32 a plane cuts a cylinder obliquely. This is a simpler case, as the horizontal projection of the curve coincides with the base of the cylinder. To obtain the true size of the section, which is an ellipse, any number of points are assumed on the plan and projected up on the cutting plane, at 1, 2, 3, etc. Ill 24 MECHANICAL DRAWING. The lines drawn through these points perpendicular to 1 7 are made equal in length to the corresponding distances 2 f — 2', 8' — 3' etc., on the plan, because 2' — 2' is the true width of curve at 2. If a cone is intersected by a plane which is parallel to only one of the elements, as in Fig. 33, the resulting curve is the parabola, the construc- tion of which is exactly simi- lar to that for the ellipse as given in Fig. 31. If the intersecting plane is parallel to more than one element, or is parallel to the axis of the cone, a hyperbola is produced. In Fig. 34, the vertical plane A is parallel to the axis of the cone. In this instance the curve when found will appear in its true size, as plane A is parallel to the vertical. Observe that the highest point of the curve is found by drawing the circle X on the plan tangent to the given plane. One of the points where this circle crosses the diameter is projected up to the contour element of the cone, and the horizontal plane X drawn. Intermediate planes Y, Z, etc., are chosen, and corresponding circles drawn in plan. The points where these -circles are crossed by the plane A are points on the curve, and these points are projected up to the elevation on the planes Y, Z, etc. DEVELOPHENTS. The development of a surface is the true size and shape ot the surface extended or spread out on a plane. If the surface to be developed is of such a character that it may be flattened out Fig. 32. 112 MECHANICAL DRAWING. 25 without tearing or folding, we obtain an exact development, as in case of a cone or cylinder, prism or pyramid. If this cannot be done, as with the sphere, the development is only approximate. In Older to find the development of the rectangular prism in Fig 35, the back face, 1 2 7 6, is supposed to be placed in contact Fig. 33. with some plane, then the prism turned on the edge 2 7 until the side 23 8 7 is in contact with the same plane, then this continued until all four faces have been placed on the same plane. The rectangles 1 4 3 2 and 6 7 8 5 are for the top and bottom respec- tively. The development then is the exact size and shape of a covering for the prism. If a rectangular hole is cut through the prism, the openings in the front and back faces will be shown in the development in the centers of the two broad faces. The development of a right prism, then, consists of as many 113 26 MECHANICAL DRAWING. rectangles joined together as the prism has sides, these rectangles being the exact size of the faces of the prism, and in addition two polygons the exact size of the bases. It will be found helpful in developing a solid to number or letter all of the corners on the projections, then designate each face when developed in the same way as in the figure. If a cone be placed on its side on a plane surface, one element will rest on the surface. If now the cone be rolled on the plane, the vertex remaining stationary, until the same ele- ment is in contact again, the space rolled over will represent the development of the convex surface of the cone. A, Fig. 86, is a cone cut by a plane parallel to the base. In B, let the vertex of the cone be cone coincide with Y A I. The length of this element is taken from the elevation A, of either contour element. All of the elements of the cone are of the same length, so when the cone is rolled each point of the base as it touches the plane will be at the same distance from the vertex. From this it follows that the development of the base will be the arc of a circle of radius equal to the length of an element. To find the length of this arc which is equal to the distance around the base, divide the plan of the circumference of the base into any number of equal parts, as twelve, then 114 MECHANICAL DRAWING. 'M with the length of one of these parts as radius, lay off twelve spaces, 1 ....13, join 1 and 13 with Y, and the sector is the development of the cone from vertex to base. To represent on the development 8 6 Fig. 35. the circle cut by the section plane, take as radius the length of the element from the vertex to D, and with Y as center describe an arc. The development of the frustum of the cone will be the portion of the circular ring. This of course does not include the 115 28 MECHANICAL DRAWING. development of the bases, which would he simply two circles the same sizes as shown in plan. A and B, Fig. 87, represent the plan and elevation of a regular triangular pyramid and its development. If face C is placed on the plane its true size will be shown at C in the devel- opment. The true length of the base of triangle C is shown: in the plan. The slanting edges, however, not being parallel to the vertical, are not shown in elevation in their true length. It be- comes necessary then, to find the true length of one of these edges as shown in Fig. 6, after which the triangle may be drawn in its full size at C in the development. As the pyramid is regular, three equal triangles as shown developed at C, D and E, together with the base F, constitute the development. If a right circular cylinder is to be developed, or rolled upon a plane, the elements, being parallel, will appear as parallel lines, and the base, being perpendicular to the elements, will develop as a straight line perpendicular to the elements. The width of the development will be the distance around the cylinder, or the cir- cumference of the base. The base of the cylinder in Fig. 88, is divided into twelve equal parts, 12 8, etc. Commencing at point 1 on the development these twelve equal spaces are laid along the straight line, giving the development of the base of the cylin- der, and the total width. To find the development of the curve cut by the oblique plane, draw in elevation the elements corre- sponding to the various divisions of the base, and note the points 116 MECHANICAL DRAWING. 29 where they intersect the oblique plane. As we roll the cylinder beginning at point 1, the successive elements 1, 12, 11, etc., will appear at equal distances apart, and equal in length to the lengths of the same elements in elevation. Thus point number 10 on the development of the curve is found by projecting horizontally across from 10 in elevation. It will be seen that the curve is symmetri- cal, the half on the left of 7 being* similar to that on the right. 7 O O The development of any curve whatever on the surface of the cylinder may be found in the same manner. The principle of cylinder development is used in laying out elbow joints, pipe ends cut off obliquely, etc. In Fig. 39 is shown plan and elevation of a three-piece elbow and collar, and develop- ments of the four pieces. In order to construct the various parts making up the joint, it is necessary to know what shape and size must be marked out on the flat sheet metal so that when cut out and rolled up the three pieces will form cylinders with the ends fitting together as required. Knowing the kind of elbow desired, we first draw the plan and elevation, and from these make the developments. Let the lengths of the three pieces A, B and C be the same on the upper outside contour of the elbow, the piece B at an angle of 45°; the joint between A and B bisects the angle between the two lengths, and in. the same way the joint between B and C. The lengths A and C will then be the same, 117 30 MECHANICAL DRAWING. and one pattern will answer for both. The development of A is made exactly as just explained for Fig. 38, and this is also the development of C. It should be borne in mind that in developing a cylinder we must always have a base at right angles to the elements, and if the cylinder as given does not have such a base, it becomes neces- sary to cut the cylinder by a plane perpendicular to the elements, and use the intersection as a base. This point must be clearly understood in order to proceed intelligently. A section at right angles to the elements is the only section which will unroll in a straight line, and is therefore the section from which we must work in developing other sections. As B has neither end at right angles to its length, the plane X is drawn at the middle and per* pendicular to the length. B is the same diameter pipe as C and A, so the section cut by X will be a circle of the same diameter as the base of A, and its development is shown at X. From the points where the elements drawn on the elevation of A meet the joint between A and B, elements are drawn on B, 118 MECHANICAL DRAWING. 0 t 01 which are equally spaced around B the same as on A. The spaces then laid off along X are the same as given on the plan of A. Commencing with the left-hand element in B, the length of the upper element between X and the top corner of the elbow is laid off above X, giving the first point in the development of the end of B fitting with C. The lengths of the other elements in the elevation of B are measured in the same way and laid off from X. The development of the other end of the piece B is laid off below X, using the same distances, since X is half way be- tween the ends. The development of the collar is simply the de_ velopment of the frus- tum of a cone, which has already been explained, Fig. 86. The joint be- tween B and C is shown in plan as an ellipse, the construction of which the student should be able to understand from a study of the figure. The intersection of a rectangular prism and pyramid is shown in Fig. 40. The base b c d e of the pyramid is shown dotted in plan, as it is hidden by the prism. All four edges of the pyramid pass through the top of the prism, 1, 2, 3, 4. As the top of the prism is a horizontal plane, the edges of the pyramid are showm passing through the top in elevation at xv g*> kv i v . These four points might be projected to the plan on the four edges of the pyramid; but it is unnecessary to project more than one, since the general principle applies here that if a cone, pyramid, prism or cylinder be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point xv is there- fore projected down to a b in plan, giving xh, and with this as a v 119 32 MECHANICAL DRAWING. one corner, the square xh gh i h kli is drawn, its sides parallel to the edges of the base. This square is the intersection of the pyramid with the top of the prism. The intersection of the pyramid with the bottom of the prism is found in like manner, by taking the point where one edge of the pyramid as a b passes through the bottom of the prism shown in elevation as point m», projecting down to m h on ah bh, and drawing the square mh n Jl oh ph parallel to the base of the pyramid. These two squares constitute the entire intersection of the two solids, the pyramid going through the bottom and coming out at the top of the prism. As much of the slanting edges of the pyramid as are above the prism will be seen in plan, appearing as the diagonals of the small square, and the rest of the pyramid, being below the top surface of the prism, will be dotted in plan. Fig. 41 is the development of the rectangular prism, show- ing the openings in the top and bottom surfaces through which the pyramid passed. The development of the top and bottom, back and front faces will be four rectangles joined together, the same sizes as the respective faces. Commencing with the bottom face 5 6 7 8, next would come the back face 6127, then the top, etc. The rectangles at the ends of the top face 1 2 3 4 are the ends of the prism. These might have been joined on any other 120 MECHANICAL DRAWING 33 face as well. Now find the development of the square in the bottom 5 6 7 8. As the size will be the same as in projection, it only re- mains to determine its position. This position, however, will have the same relation to the sides of the rectangle as in the plan. The center of the square in this case is in the center of the face. To transfer the diagonals of the square to the development, extend them in plan to intersect the edges of the prism in points 9, 10, 11 and 12. Take the distance from 5 to 9 along the edge 5 6, and lay it on the development from 5 along 5 6, giving point 9. Point 10 located in the same way and connected with 9, gives the position of one diagonal. The other diagonal is obtained in a similar way, then the square constructed on these diagonals. The same method is used for locating the small square on the top face. If the intersection of a cylinder and prism is to be found, we may either obtain the points where elements of the cylinder pierce the prism, or where edges and lines parallel to edges on the sur* face of the prism cut the cylinder. A series of parallel planes may also be taken cutting curves from the cylinder and straight lines from the prism ; the intersec- tions give points on the intersection of the two solids. Fig. 42 represents a triangular prism intersecting a cylinder. The axis of the prism is parallel to V and inclined to H. Starting with the size and shape of the base, this is laid off at a { b h c h , and the altitude of the triangle taken and laid off at a v c v in elevation, making right angles with the inclination of the axis to H. The plan of the prism is then constructed. To find the intersection of the two solids, lines are drawn on the surface of the prism parallel to the length and the points where these lines and the edges pierce the cylinder are obtained and joined, giving the curve. The top edge of the prism goes into the top of the cylinder. This point will be shown in elevation, since the top of the cylinder is a plane parallel to H and perpendicular to V, and therefore projected on V as a straight line. The upper edge, then, is found to pass into the top of the cylinder at point o, o v and o h . The intersection of the two upper faces of the prism with the top of the cylinder will be straight lines drawn from point o and will be shown in plan. If we can find where another line of the surface o a h 14 pierces the upper base of the cylinder, this point joined 121 Fig. 43. 34 MECHANICAL DRAWING. with o will determine the intersection of this face with the top of the cylinder. A surface may always be produced, if necessary, to find an intersection. Edge a b pierces the plane of the top of the cylinder at point d , seen in elevation ; therefore the line joining this point with o is the intersection of one upper face of the prism with the upper 122 MECHANICAL DRAWING. 35 base of the cylinder. The only part of this line needed, of course, is within the actual limits of the base, that is o 9. The intersec- tion o 8 of the other top face is found by the same method. On the convex surface of the cylinder there will be three curves, one for each face of the prism. Points b and 9 on the upper base of the cylinder, will be where the curves for the two upper faces will begin. The point d is found on the revolved position of the base at t?,, and d { b is divided into the equal parts d { — e p e x — /j, etc., which revolve back to d\ e h ,f h and g h . The divisions are made equal merely for convenience in developing. The vertical pro- jections of d, e , etc., are found on the vertical projection of a b, directly above d h , e\ etc., or may be found by taking from the revolved position of the base, the perpendiculars from d x e , etc., to c h b h and laying them off in elevation from b v along b v a v . Lines such as f 12, m 5, etc., parallel to a o are drawn in plan and eleva- tion. Points i h k h m h n h are taken directly behind d h e h f h g h hence their vertical projections coincide. Points n x m, /q and z, are formed by projecting across from n h m h Jc h and i h . The convex surface of the cylinder is perpendicular to H, so the points where the lines on the prism pierce it will be projected on plan as the points Avhere these lines cross the circle, 14, 13, 12, 11 .3. The vertical projections of these points are found on the corresponding lines in elevation, and the curves drawn through. The curve 3, 4.. ..8 must be dotted, as it is on the back of the cylinder. The under face of the prism, which ends with the line b c, is perpendicular to the vertical plane, so the curve of intersec tion will be projected on V as a straight line. Point 14 is one end of this curve. 3 the other end, and the curve is projected in elevation as the straight line from 14 to the point where the lower edge of the prism crosses the contour element of the cylinder. Fig. 43 gives the development of the right-hand half of the cylinder, beginning with number 1 . As previously explained, the distance betAveen the elements is shown in the plan, as 1 — 2, 2 — 3, 3 — 4 and so on. These spaces are laid off in the development along a straight line representing the deA^elopment of the base, and from these points the elements are drawn perpendicularly. The lengths of the elements in the development from the base to the curve are exactly the same as on the elevation, as the 183 36 MECHANICAL DRAWING. elevation gives the true lengths. If then the development of the base is laid off along the same straight line as the vertical projec- tion of the base, the points in elevation maj^ be projected across with the T-square to the corresponding elements in the develop- ment. The points on the curve cut by the under face of the prism are ou the same elements as the other curves, and their vertical projections are on the under edge of the prism, hence these points are projected across for the development of the lower curve. In Fig. 44 is given the development of the prism from the right-hand end as far as the intersection with the cylinder, begin- 14 ning at the left with the top edge a o, the straight line a b c a being the development of the base. As this must be the actual distance around the base, the length is taken from the true size of the base, a, b h c h . The parallel lines drawn on the surfaces of the prism must appear on the development their true distances apart, hence the distances a x d r d l e,, etc., are made equal to a d, de, etc. on the development. The actual distances between the parallel lines on the bottom face of the prism are shown along the edge of the base, b h c h . Perpendicular lines are drawn from the points of division on the development. The position of the developed curve is found by laying off the true lengths on the perpendiculars. These true lengths (of the parallel lines) are not shown in plan, as the lines are not parallel to the horizontal plane, but are found in elevation. The length oa on the development is equal to a v d 10 to d v 1 0, and 124 MECHANICAL DRAWING 37 so on for all the rest. Point 9ys found as follows: on the projec- tions, the straight line from o to d passes through point 9, and the true distance from o to 9 is shown in plan. All that is necessary, then, is to connect o and d on the development, and lay off from o the distance 0 h 9. Number 8 is found in the same way. ISOMETRIC PROJECTION. Heretofore an object has been represented by two or more projections. Another system, called isometrical drawing, is used to show in one view the three dimensions of an object, length (or height), breadth, and thickness. An isometrical drawing of an object, as a cube, is called for brevity the “ isometric ” of the cube. Fig. 45. To obtain a view which shows the three dimensions in such a way that measurements can be taken from them, draw the cube in the simple position shown at the left of Fig. 45, in which it rests on H with two faces parallel to V ; the diagonal from the front upper right-hand corner to the back lower left-hand corner is indicated by the dotted line. Swing the cube around until the diagonal is parallel with V as shown in the second position. Here the front face is at the right. In the third position the lower end of the diagonal has been raised so that it is parallel to H, becoming thus parallel to both planes. The plan is found by the principles of projection, from the elevation and the preceding plan. The front face is now the lower of the two faces shown in the elevation. From this position the cube is swung around, using the corner 125 38 MECHANICAL DRAWING resting on the H as a pivot, until the diagonal is perpendiculai to V but still parallel to H. The plan remains the same, except as regards position; while the elevation, obtained by projecting across from the previous elevation, gives the isometrical projection of the cube. The front face is now at the left. In the last position, as one diagonal is perpendicular to V, it follows that all the faces of the cube make equal angles with V, hence are projected on that plane as equal parallelograms. For the same reason all the edges of the cube are projected in elevation in equal lengths, but, being inclined to V, appear shorter than they actually are on the object. Since they are all equally foreshortened and since a drawing may be made at any scale, it is customary to make all the isometrical lines of a drawing full length. This will give the same proportions, and is much the simplest method. Herein lies the distinction between an isomet- rical projection and an isometric- drawing. It will be noticed that the figure can be inscribed in a circle, and that the outline is a perfect hexagon. Hence the lines showing breadth and length are 30° lines, while those showing height are vertical. Fig. 46 shows the isometric of a cube, 1 inch square. All of the edges are shown in their true length, hence all the surfaces appear of the same size. In the figure the edges of the base are inclined at 30° with a T-square line, but this is not always the case. For rectangular objects, such as prisms, cubes, etc., the base edges are at 30° only when the prism or cube is supposed to be in the simplest possible position. The cube in Fig. 46 is supposed to be in the position indicated by plan and elevation in Fig. 47, that is, standing on its base, with two faces parallel to the vertical plane. If the isometric of the cube in the position of Fig. 48 were required, it could not be drawn with the base edges at 30° ; neither 126 MECHANICAL DRAWING 39 would these edges appear in their true lengths. It follows, then, that in isometrical drawing, true lengths appear only as 30° lines or as vertical lines. Edges or lines that in actual projection are either parallel to the ground line or perpendicular to V, are drawn in isometric as 30° lines, full length; and those that are actually vertical are made vertical in isometric, also full length. In Fig. 45, lines such as the front vertical edges of the cube and the two base edges are called the three isometric axes. The isometric of objects in oblique positions, as in Fig. 48, can be con- Fig. 47. Fig. 48. strutted only by reference to their projections, by methods which will be explained later. In isometric drawing small rectangular objects are more satis- factorily represented than large curved ones. In woodwork, mor- tises and joints and various parts of framing are well shown in isometric. This system is used also to give a kind of bird's-eye view of the mills or factories. It is also used in making sketches of small rectangular pieces of machinery, where it is desirable to give shape and dimensions in one view. In isometric drawing the direction of the ray of light is parallel to that diagonal of a cube which runs from the upper left corner to the lower right corner, as 4 V -7 V in the last elevation of Fig. 45. This diagonal is at 30° ; hence in isometrical drawing the direction of the light is at 30° downward to the right. From 127 40 MECHANICAL DRAWING this it follows that the top and two left-hand faces of the cube are light, the others dark. This explains the shade lines in Fig. 45. In Fig. 45, the top end of the diagonal which is parallel to the ray of light in the first position is marked 4, and traced through to the last or isometrical projection, 4 V . It will be seen that face 3 V 4 V 5 V 8 V of the isometric projection is the front face of the cube in the first view; hence we may consider the left front face of the isometric cube as the front. This is not absolutely necessary, but by so doing the isometric shade edges are exactly the same as on the original projection. f Fig. 49 shows a cube with circles inscribed in the top and two side faces. The isometric of a circle is an ellipse, the exact construction of which would necessitate finding a number of points; for this reason an approximate construction by arcs of circles is often made. In the method of Fig. 49, four centers are used. Considering the upper face of the cube, lines are drawn from the obtuse angles f and e, to the centers of the opposite sides. The intersections of these lines give points g and A, which serve as centers for the ends of the ellipse. With center g and radius g a , the arc a d is drawn; and with/* as center and radius f d , the arc d c is described, and the ellipse finished by using centers h and e. This construction is applied to all three faces. Fig. 50 is the isometric of a cylinder standing on its base. 128 MECHANICAL DRAWING 41 Notice that the shade line on the top begins and ends where T-square lines would be tangent to the curve, and similarly in the case of the part shown on the base. The explanation of the shade is very similar to that in pro- jections. Given in projections a cylinder standing on its base, the plan is a circle, and the shade line is determined by applying the 45° triangle tangent to the circle. This is done because the 45° line is the projection of the ray of light on the plane of the base. In Fig. 49, the diagonal m l may represent the ray of light and its projection on the base is seen to be k l , the diagonal of the base, a T-square line. Hence, for the cylinder of Fig. 50, apply tangent to the base and also to the top a line parallel to the projection of the ray of light on these planes, that is, a T-square line, and this will mark the beginning and ending of the shade line. In Fig. 49 the projection of the ray of light diagonal m l on the right-hand face is e Z, a 30° line; hence, in Fig. 51, where the base is similarly placed, apply the 30° triangle tangent as indi- cated, determining the shade line of the base. If the ellipse on the left-hand face of the cube were the base of a cone or cylinder extending backward to the right, the same principle would be used. The projection of the cube diagonal m l on that face is m n, a 60° line; hence the 60° triangle would be used tangent to the base in this last supposed case, giving the ends of the shade line at points o and r. Figs. 52, 53 and 54 illustrate the same idea with respect to prisms, the direction of the projection of the ray of light on the plane of the base being used in each case to determine the light and dark faces and hence the shade lines. 120 42 MECHANICAL DRAWING In Fig. 52 a prism is represented standing on its base, so that the projection of the cube diagonal on the base (that is, a T-square line) is used to determine the light and dark faces as shown. The prism in Fig. 53 has for its base a trapezium. The projection of the ray of light on this end is parallel to the diagonal of the face; hence the 60° triangle applied par- allel to this diagonal shows that faces a c db and a g hb are light, while c e f cl and g e f h are dark, hence the shade lines as shown. The application in Fig. 54 is the same, the only difference being in the position of the prism, and the consequent difference in the direction of the diagonal. Fig. 55 represents a block with smaller blocks projecting from three faces. Fig. 56 shows a framework of three pieces, two at right angles and a slanting brace. The horizontal piece is mortised into the upright, as indicated by the dotted lines. In Fig. 57 the isometric outline of a house is represented, show- ing a dormer window and a partial hip roof; a b is a hip rafter, c d a valley. Let the pitch of the main roof be shown at B, and let m be the middle point of the top of the end wall of the house. Then, by measuring vertically up a distance m l equal to the vertical height a n shown at B, a point on the line of the ridge will be found at l. Line l i is equal to b h, and i h is then drawn. Let the pitch of 130 MECHANICAL DRAWING 43 the end roof be given at A. This shows that the peak of the roof, or the end a of the ridge, will be back from the end wall a distance equal to the base of the triangle at A. Hence lay off from l this distance, giving point a, and join a with b and x. The height k e of the ridge of the dormer roof is known, and we must find where this ridge will meet the main roof. The ridge must be a 30° line as it runs parallel to the end wall of the house 131 44 MECHANICAL DRAWING and to the ground. Draw from e d line parallel to b h to meet a vertical through h at f This point is in the vertical plane of the end wall of the house, hence in the plane of i Ti. If now a 80° line be drawn from f parallel to x b , it will meet the roof of the house at g. The dormer ridge and f g are in the same horizontal plane, hence will meet the roof at the same distance below the ridge a i. Therefore draw the 80° line g c, and connect c with d. In Fig. 58 a box is shown with the cover opened through 150°. The right-hand edge of the bottom shows the width, the left-hand edge the length, and the vertical edge the height. The short edges of the cover are not isometric lines, hence are not shown in their true lengths; neither is the angle through which the cover is opened represented in its actual size. The corners of the cover must then be determined by co- ordinates from an end view of the box and cover. As the end of the cover is in the same plane as the end of the box, the simple 132 MECHANICAL DRAWING 45 end view as shown in Fig. 59 will be sufficient. Extend the top of the box to the right, and from c and d let fall perpendiculars or a b produced, giving the points e and f. The point c may be located by means of the two distances or co-ordinates b e and e c. and these distances will appear in their true lengths in the isometric view. Hence produce a ' b r to e ' and f' ; and from these points draw verticals e r c' and f' d ’ ; make b' e' equal to b e, e' c' equal to e c; and similarly for d ' . Draw the lower edge parallel to c' d' and equal to it in length, and connect with b ' . It will be seen that in isometric draw- ing parallel lines always appear parallel. It is also true that lines divided propor- tionally maintain this same relation in isometric drawing. Fig. 60 shows a block or prism with a semicircular top. Find the isometric of the square circumscribing the circle, then draw the curve by the approximate method. The centers for the back face are found by projecting the front centers back 30° equal to the thickness of the prism, as shown at a and b. The plan and elevation of an oblique pentagonal pyramid are shown in Fig. 61. It is evident that none of the edges of the pyramid can be drawn in isometric as either vertical or 30° lines; hence, a system of co-ordinates must be used as Fig. 60. 133 46 MECHANICAL DRAWING shown in Fig. 58. This problem illustrates the most general case; and to locate some of the points three co-ordinates must be used, two at 80° and one vertical. Circumscribe, about the plan of the pyramid, a rectangle which shall have its sides respectively parallel and perpendicular to the ground line. This rectangle is on H, and its vertical projection is in the ground line. The isometric of this rectangle can be drawn at once with 30° lines, as shown in Fig. 62, o being the same point in both figures. Fig. 61 . The horizontal projection of point 8 is found in isometric at 3 h , at the same distance from o as in the plan. That is, any distance which in plan is parallel to a side of the circumscribing rectangle, is shown in isometric in its true length and parallel to the corre- sponding side of the isometric rectangle . If point 3 were on the horizontal plane its isometric would be 3 h , but the point is at the vertical height above H given in the elevation ; hence, lay off above 3 h this vertical height, obtaining the actual isometric of the point. To locate 4, draw 4 a parallel to the side of the rectangle; then lay 134 MECHANICAL DRAWING 47 off o a and a 4 h , giving what may be called the isometric plan of 4. Next, the vertical height taken from the elevation locates the iso- metric of the point in space. In like manner all the corners of the pyramid, in- cluding the apex, are located. The rule is, locate first in isometric the horizontal pro- jection of a point by one or two 30° co-ordinates ; then vertically, above this point, its height as taken from the elevation. The shade lines cannot be determined here by applying the 30° or 60° triangle, owing to the obliquity of the faces. Since the right front corner of the rectangle in plan was made the point o in isometric, the shade lines must be the same in isometric as in actual projection; so that, if these can be de- termined in Fig. 61, they may be applied at once to Fig. 62. The shade lines in Fig. 61 are found by a short method which is convenient to use when the exact shade lines are de- sired, and when they cannot be deter- mined by applying the 45° triangle. A plane is taken at 45° with the horizontal plane, and parallel to the direction of the ray of light, in such a position as to cut all the surfaces of the pyramid, as shown in 135 48 MECHANICAL DRAWING elevation. This plane is perpendicular to the vertical plane; hence the section it cuts from the pyramid is readily found in plan by projection. This plane contains some of the rays of light falling upon the pyramid; and we can tell what surfaces these rays strike and make light, by noticing on the plan what edges of the section are struck by the projections of the rays of light. That is, rs,st, and t u receive the rays of light; hence the surfaces on which these lines lie are light, r s is on the surface determined by the two lines passing 136 MECHANICAL DRAWING 49 through r and s, namely, 2—1 and 1 — 5; in other words, r s is on the base; similarly, s t is on the surface 1 — 5 — 6; and t u on the surface 4 — 6 — 5. The other surfaces are dark ; hence the edges which are between the light and dark faces are the shade lines. Whenever it is more convenient, a plane parallel to the ray of light and perpendicular to H may be taken, the section found in elevation, and the 45° triangle applied to this section. The same method may be used to determine the exact shade lines of a cone or cylinder in an oblique position. Figs. 63 to 70 give examples of the isometric of various objects. Fig. 65 is the plan and elevation, and Fig. 66 the Fig. 69. Fig. 70. isometric, of a carpenter’s bench. In Fig. 70, take especial notice of the shade lines. These are put on as if the group were made in one piece ; and the shadows cast by the blocks on one another are disregarded. All upper horizontal faces are light, all left-hand (front and back) faces light, and the rest dark. OBLIQUE PROJECTIONS. In oblique projection, as in isometric, the end sought for is the same — a more or less complete representation, in one view, of any object. Oblique projection differs from isometric in that one face of the object is represented as if parallel to the vertical plane of projection, the others inclined to it. Another point of 137 50 MECHANICAL DRAWING difference is that oblique projection cannot be deduced from orthographic projection, as is isometric. In oblique projection all lines in the front face are shown in their true lengths and in their true relation to one another, and lines which are perpendicular to this front face are shown in their true lengths at any angle that may be desired for any particular case. Lines not in the plane of the front face nor perpendicular to it must be determined by co-ordinates, as in isometric. It will be seen at once that this system possesses some advantages over the isometric, as, for instance, in the representation of circles, as any circle or curve in the front face is actually drawn as such. The rays of light are still supposed to be parallel to the same diagonal of the cube, that is, sloping downward, toward the plane of projection, and to the right, or downward, backward and to the right. Figs. 71, 72 and 73 show a cube in oblique projection, 138 MECHANICAL DRAWING 51 with the 30°, 45° and 60° slant respectively. The dotted diagonal represents for each case the direction of the light, and the shade lines follow from this. The shade lines have the same general position as in isometric drawing, the top, front and left-hand faces being light. No matter what angle may be used for the edges that are perpendicular to the front face, the £>rojection Q f the diagonal of the cube on this face is always a 45° line; hence, for determining the shade lines on any front face, such as the end of the hollow cylinder in Fig. 74, the 45° line is used exactly as in the elevation of ordinary projections. Figs. 75, 76, 77 and 79 are other examples of oblique projections. Fig. 77 is a crank arm. The method of using co-ordinates for lines of which the true 139 52 MECHANICAL DRAWING lengths are not shown, is illustrated by Figs. 78 and 79. Fig. 79 represents the oblique projection of the two joists shown in plan and elevation in Fig. 78. The dotted lines in the elevation (see Fig. 78) show the heights of the corners above the horizontal stick. The feet of these perpendiculars give the horizontal dis- tances of the top corners from the end of the horizontal piece. In Fig. 79 lay off from the upper right-hand corner of the front end a distance equal to the distance between the front edge of the inclined piece and the front edge of the bottom piece (see Fig. 78). From this point draw a dotted line parallel to the Fig. 78. length. The horizontal distances from the upper left corner to the dotted perpendicular are then marked off on this line. From these points verticals are drawn, and made equal in length to the dotted perpendiculars of Fig. 78, thus locating two corners of the end. LINE SHADING. In finely finished drawings it is frequently desirable to make the various parts more readily seen by showing the graduations of light and shade on the curved surfaces. This is especially true of such surfaces as cylinders, cones and spheres. The effect is obtained by drawing a series of parallel or converging lines on the surface at varying distances from one another. Sometimes draftsmen vary the width of the lines themselves. These lines are farther apart on the lighter portion of the surface, and are closer together and heavier on the darker part. 140 MECHANICAL DRAWING 53 Fig. 80 shows a cylinder with elements drawn on the surface equally spaced, as on the plan. On account of the curvature of the surface the elements are not equally spaced on the elevation, but give the effect of graduation of light. The result is that in elevation the distances between the elements gradually lessen from the center toward each side, thus showing that the cylinder is convex. The effect is intensified, however, if the elements are made heavier, as well as closer together, as shown in Figs. 81 to 87. Cylinders are often shaded with the light coming in the usual way, the darkest part com- mencing about where the shade line would actually be on the surface, and the lightest portion a little to the left of the center. Fig. 81 is a cylinder showing the heaviest shade at the right, as this method is often used. Considerable practice is necessary in order to obtain good results; but in this, as in other portions of mechanical drawing, perseverance has its reward. Fig. 82 represents a cylinder in a horizontal position, and Fig. 83 represents a section of a hollow vertical cylinder. Fig. 81. Fig. 82. Fig. 83. Figs. 84 to 87 give other examples of familiar objects. In the elevation of the cone shown in Fig. 87 the shade lines should diminish in weight as they approach the apex. Unless this is done it will be difficult to avoid the formation of a blot at that point. 141 54 MECHANICAL DRAWING LETTERING. All working drawings require more or less lettering, such as titles, dimensions, explanations, etc. In order that the drawing may appear finished, the lettering must be well done. No style of lettering should ever be used which is not perfectly legible. It is generally best to use plain, easily-made letters which present Fig. 84. Fig. 85. a neat appearance. Small letters used on the drawing for notes or directions should be made free-hand with an ordinary waiting pen. Two horizontal guide lines should be used to limit the height of the letters; after a time, however, the upper guide line may be omitted. 142 mechanical drawing 00 In the early part of this course the inclined Gothic letter was described, and the alphabet given. The Roman, Gothic and block letters are perhaps the most used for titles. These letters, being of comparatively large size, are generally made mechanically; that is, drawing instruments are used in their construction. In order that the letters may appear of the same height, some of them, owing to their shape, must be made a little higher than the others. This is the case with the letters curved at the top and bottom, such as C, O, S, etc., as shown somewhat exaggerated in Fig. 88. Also, the letter A should extend a little above, and V a little below, the guide lines, because if made of the same height as the others they will appear shorter. This is true of all capitals, whether of Roman, Gothic, or other alphabets. In the block letter, however, they are frequently all of the same size. There is no absolute size or proportion of letters, as the dimensions are regulated by the amount of sj)ace in which the letters are to be placed, the size of the drawing, the effect desired, etc. In some cases letters are made so that the height is greater than the width, and sometimes the reverse; sometimes the height and width are the saipe. This last proportion is the most common. Certain relations of width, however, should be observed. Thus, in whatever style of alphabet used, the W should be the widest letter; J the narrowest, M and T next widest to W, then A and B. The other letters are of about the same width. In the vertical Gothic alphabet, the average height is that of B. D. E, F, etc., and the additional height of the curved letters and of the A and V is very slight. The horizontal cross lines of such letters as E. F. H. etc., are slightly above the center; those of A, G and P slightly below. For the inclined letters, 60° is a convenient angle, although they may be at any other angle suited to the convenience or fancy of the draftsman. Many draftsmen use an angle of about 70°. The letters of the Roman alphabet, whether vertical or inclined, are quite ornamental in effect if well made, the inclined Roman being a particularly attractive letter, although rather difficult to make. The block letter is made on the same general plan as the Gothic, but much heavier. Small squares are taken as 143 56 MECHANICAL DRAWING. u Inclined Gothic Capitals. MECHANICAL DRAWING 57 the unit of measurement, as shown. The use of this letter is not advocated for general work, although if made merely in outline the effect is pleasing. The styles of numbers corresponding with the alphabets of capitals given here, are also inserted. When a fraction, such as 2§ is to be made, the proportion should be about as shown. For small letters, usually called lower-case letters, abcdefghijklmn opqrstuvwxyz Fig. 89. obcc/efgh/jk/mn opqrs tuv wyyz Fig. 90. abcdefghijklmn opqrstuvwxyz Fig. 91. » the height may be made about two-thirds that of the capitals. This proportion, however, varies in special cases. The principal lower-case letters in general use among drafts- men are shown in Figs. 89, 90, 91 and 92. The Gothic letters shown in Figs. 89 and 90 are much easier to make than the Roman letters in Figs. 91 and 92. These letters, however, do not 145 AB C D E F G HI JKLMN 58 MECHANICAL DRAWING. Inclined Homan Capitals. MECHANICAL DRAWING 59 give as finished an appearance as the Roman. As has already been stated in Mechanical Drawing, Part I, the inclined letter is easier to make because slight errors are not so apparent. One of the most important points to be remembered in letter- ing is the spacing. If the letters are finely executed but poorly spaced, the effect is not good. To space letters correctly and rapidly, requires considerable experience; and rules are of little value on account of the many combinations in which letters are abode fg hijklmn opqrs tuvwxy z Fig. 92. found. A few directions, however, may be found helpful. For instance, take the word TECHNICALITY, Fig. 93. If all the spaces were made equal, the space between the L and the I would appear to be too great, and the same would apply to the space between the I and the T. The space between the H and the _N and that between the N and the I would be insufficient. In general, when the vertical side of one letter is followed by the verti- cal side of another, as in H E, H B, I R, etc., the maximum space TECHNICALITY Fig. 93. should be allowed. Where T and A come together the least space is given, for in this case the top of the T frequently extends over the bottom of the A. In general, the spacing should be such that a uniform appearance is obtained. For the distances between words in a sentence, a space of about 1^ the width of the average letter may be used. The space, however, depends largely upon the desired effect. 147 60 MECHANICAL DRAWING For large titles, such as those placed on charts, maps, and some large working drawings, the letters should be penciled before inking. If the height is made equal to the w T idth considerable time and labor will be saved in laying out the wx>rk. This is especially true with such Gothic letters as O, Q, C, etc., as these letters may then be made with compasses. If the letters are of sufficient size, the outlines may be drawn with the ruling pen or compasses, and the spaces between filled in with a fine brush. The titles for working drawings are generally placed in the lower right-hand corner. Usually a draftsman has his choice of Block Letters. letters, mainly because after he has become used to making one style he can do it rapidly and accurately. However, in some draft- ing rooms the head draftsman decides what lettering shall be used. In making these titles, the different alphabets are selected to give the best results without spending too much time. In most work the letters are made in straight lines, although we frequently find a portion of the title lettered on an arc of a circle. In Fig. 94 is shown a title having the words CONNECTING ROD lettered on an arc of a circle. To do this work requires considerable patience and practice. First draw the vertical center 148 MECHANICAL DRAWING 61 line as shown at C in Fig. 94. Then draw horizontal lines for the horizontal letters. The radii of the arcs depend upon the general arrangement of the entire title, and this is a matter of taste. The difference between the arcs should equal the height of the letters. After the arc is drawn, the letters should be sketched in pencil to find their approximate positions. After this is done, draw radial lines from the center of the letters to the center of the arcs. BEAM ENGINE SCALE 3 INCHES = 1 FOOT PORTLAND COMPANY’S WORKS JULY 10, 1894 F'ig. 94. These lines will be the centers of the letters, as shown at A, B, D and E. The vertical lines of the letters should not radiate from the center of the arc, but should be parallel to the center lines already drawn; otherwise the letters will appear distorted. Thus, in the letter N the two verticals are parallel to the line A. The same applies to the other letters in the alphabet. 149 62 . MECHANICAL DRAWING Tracing. Having finished the pencil drawing, the next step is the inking. In some offices the pencil drawing is made on a thin, tough paper, called board paper, and the inking is done over the pencil drawing, in the manner with wdiich the student is already familiar. It is more common to do the inking on thin, trans- parent cloth, called tracing cloth, which is prepared for the pur- pose. This tracing cloth is made of various kinds, the kind in ordinary use being what is known as “ dull back,” that is, one side is finished and the other side is left dull. Either side may be used to draw upon, but most draftsmen prefer the dull side. If a drawing is to be traced it is a good plan to use a 3H or 411 pencil, so that the lines may be easily seen through the cloth. The tracing cloth is stretched smoothly over the pencil draw- ing and a little powdered chalk rubbed over it with a dry cloth, to remove the slight amount of grease or oil from the surface and make it take the ink better. The dust must be carefully brushed or wiped off with a soft cloth, after the rubbing, or it will inter- fere with the inking. The drawing is then made in ink on the tracing cloth, after the same general rules as for inking the paper, but care must be taken to draw the ink lines exactly over the pencil lines which are on the paper underneath, and which should be just heavy enough to be easily seen through the tracing cloth. The ink lines should be firm and fully as heavy as for ordinary work. In tracing, it is better to complete one view at a time, because if parts of several views are traced and the drawing left for a day or two, the cloth is liable to stretch and warp so that it will be difficult to complete the views and make the new lines fit those already drawn and at the same time conform to the pencil lines under- neath. For this reason it is well, when possible, to complete a view before leaving the drawing for any length of time, although of course on views in which there is a good deal of work this cannot always be done. In this case the draftsman must manipu- late his tracing; cloth and instruments to make the lines fit as best he can. A skillful draftsman will have no trouble from this source, but the beginner may at first find difficulty. Inking on tracing cloth will be found by the beginner to be quite different from inking on the paper to which he has been accustomed, and he will doubtless make many blots and think at 150 TYPICAL ARCHITECT’S DRAWING SHOWING DETAILS OF WINDOW FRAME. MECHANICAL DRAWING 63 first that it is hard to make a tracing. After a little practice, however, he will find that the tracing cloth is very satisfactory and that a good drawing can be made on it quite as easily as on paper. The necessity for making erasures should be avoided, as far as possible, but when an erasure must be made a good ink rubber or typewriter eraser may be used. If the erased line is to have ink placed on it, such as a line crossing, it is better to use a soft rubber eraser. All moisture should be kept from the cloth. Blue Printing, The tracing, of course, cannot be sent into the shop for the workmen to use, as it would soon become soiled and in time destroyed, so that it is necessary to have some cheap and rapid means of making copies from it. These copies are made by the process of blue printing in w T hich the tracing is used in a manner similar to the use made of a negative in photography. Almost all drafting rooms have a frame for the purpose of making blue prints. These frames are made in many styles, some simple, some elaborate. A simple and efficient form is a flat sur- face usually of wood, covered with padding of soft material, such as felting. To this is hinged the cover, which consists of a frame similar to a picture frame, in which is set a piece of clear glass. The whole is either mounted on a track or on some sort of a swinging arm, so that it may readily be run in and out of a window. The print is made on paper prepared for the purpose by having one of its surfaces coated with chemicals which are sensi- tive to sunlight. This coated paper, or blue-print paper, as it is called, is laid on the padded surface of the frame with its coated side uppermost; the tracing laid over it right side up, and the glass pressed down firmly and fastened in place. Springs are frequently used to keep the paper, tracing, etc., against the glassy With some frames it is more convenient to turn them over and remove the backs. In such cases the tracing is laid against the glass, face down; the coated paper is then placed on it with the coated side against the tracing cloth. The sun is allowed to shine upon the drawing for a few minutes, then the blue-print paper is taken out and thoroughly washed in clean water for several minutes and hung up to dry. 153 (54 MECHANICAL DRAWING If the paper has been recently prepared and the exposure properly timed, the coated surface of the paper will now be of a clear, deep blue color, except where it was covered by the ink lines, where it will be perfectly white. The action has been this: Before the paper was exposed to the light the coating was of a pale yellow color, and if it had then been put in water the coating would have all washed off, leaving the paper white. In other words, before being exposed to the sunlight the coating was soluble. The light penetrated the trans- parent tracing cloth and acted upon the chemicals of the coating, changing their nature so that they became insoluble; that is, when put in water, the coating, instead of being washed off, merely turned blue. The light could not penetrate the ink with which the lines, figures, etc., were drawn, consequently the coating under these was not acted upon and it washed off when put in water, leaving a white copy of the ink drawing on a blue background. If running water cannot be used, the paper must be washed in a sufficient number of changes until the water is clear. It is a good plan to arrange a tank having an overflow, so that the water may remain at a depth of about 6 or 8 inches. The length of time to which a print should be exposed to the light depends upon the quality and freshness of the paper, the chemicals used and the brightness of the light. Some paper is prepared so that an exposure of one minute, or even less, in bright sunlight, will give a good print and the time ranges from this to twenty minutes or more, according to the proportions of the various chemicals in the coating. If the full strength of the sun- light does not strike the paper, as, for instance, if clouds partly cover the sun, the time of exposure must be lengthened. Assembly Drawing. We have followed through the process of making a detail drawing from the sketches to the blue print ready for the workmen. Such a detail drawing or set of drawings shows the form and size of each piece, but does not show how the pieces go together and gives no idea of the machine as a whole. Consequently, a general drawing or assembly drawing must be made, which will show these things. Usually two or more views are necessary, the number depending upon the complexity of the machine. Very often a cross-section through some part of the 154 MECHANICAL DRAWING G5 machine, chosen so as to give the best general idea with the least amount of work, will make the drawing- clearer. The number of dimensions required on an assembly drawing depends largely upon the kind of machine. It is usually best to give the important over-all dimensions and the distance between the principal center lines. Care must be taken that the over-all dimensions agree with the sum of the dimensions of the various details. For example, suppose three pieces are bolted together, the thickness of the pieces according to the detail drawing, being one inch, two inches, and five and one-half inches respectively; the sum of these three dimensions is eight and one -half inches and the dimensions from outside on the assembly drawing, if given at all, must agree with this. It is a good plan to add these over-all dimensions, as it serves as a check and relieves the mechanic of the necessity of adding fractions. FORMULA FOR BLUE=PRINT SOLUTION. Dissolve thoroughly and filter. Red Prussiate of potash * 2*4 ounces, Water . . ...o.... 1 pint, Ammonio-Citrate of iron 4 ounces, B ' Water , . 1 pint. Use equal parts of A and B. FORHULA FOR BLACK PRINTS Negatives. White lines on blue ground; prepare the paper with Ammonio-Citrate of iron. . 40 grains, Water 1 ounce. After printing wash in water. Positives. Black lines on white ground; prepare the paper with: Iron perchloride 616 grains, Oxalic Acid 308 grains, Water 14 ounces. T Gallic Acid. 1 ounce, Develop in 1 Citric Acid 1 ounce, ( Alum 8 ounces. Use 1^ ounces of developer to one gallon of water. Paper is fully exposed when it has changed from yellow to white. 155 66 MECHANICAL DRAWING PLATES. PLATE SX. The plates of this Instruction. Paper should be laid out at the same size as the plates in Parts I and II. The center lines and border lines should also be drawn as described. First draw two ground lines across the sheet, 3 inches below the upper border line and 3 inches above the lower border line. The first problem on each ground line is to be placed 1 inch from the left border line; and spaces of about 1 inch should be left between the figures. Isolated points are indicated by a small cross X, and projections of lines are to be drawn full unless invisible. All construction lines should be fine dotted lines. Given and required lines should be drawn full. Problems on Upper Ground Line: 1. Locate both projections of a point on the horizontal plane 1 inch from the vertical plane. 2. Draw the projections of a line 2 inches long which is parallel to the vertical plane and which makes an angle of 45 degrees with the horizontal plane and slants upward to the right. The line should be 1 inch from the vertical plane and the lower end inch above the horizontal. 3 Draw the projections of a line 1J inches long which is parallel to both planes, 1 inch above the horizontal, and f inch from the vertical. 4. Draw the plan and elevation of a line 2 incnes long which is parallel to H and makes an angle of 30 degrees with V. Let the right-hand end of the line be the end nearer V, ^ inch from V. The line to be 1 inch above H. 5. Draw the plan and elevation of a line 1^ inches long which is perpendicular to the horizontal plane and 1 inch from the vertical. Lower end of line is \ inch above H. 6. Draw the projections of a line 1 inch long which is perpendicular to the vertical plane and 1^ inches above the horizontal. The end of the lino nearer V, or the back end, is | inch from V. 156 EEBRUARY /7, 190/. HERBERT CHANDLER , CH/CAGO, ILL. ELATE MECHANICAL DRAWING G7 7. Draw two projections which shall represent a line oblique to both planes. Note. Leave 1 inch between this figure and the right-hand border line. Problems on Lower Ground Line : 8. Draw the projections of two parallel lines each 1-J inches long. The lines are to be parallel to the vertical plane and to make angles of GO degrees with the horizontal. The lower end of each line is \ inch above H. The right-hand end of the right-hand line is to be 2f inches from the left-hand margin. 9. Draw the projections of two parallel lines each 2 inches long. Both lines to be parallel to the horizontal and to make an angle of 30 degrees with the vertical. The lower line to be § inch above H, and one end of one line to be against V. 10. Draw the projections of two intersecting lines. One 2 inches long to be parallel to both planes, 1 inch above H, and f inch from the vertical; and the other to be oblique to both planes and of any desired length. 11. Draw plan and elevation of a prism 1 inch square and 1| inches long. The prism to have one side on the horizontal plane, and its long edges to be perpendicular to V. The back end of the prism is J inch from the vertical plane. 12. Draw plan and elevation of a prism the same size as given above, but with the long edges parallel to both planes, the lower face of the prism to be parallel to H and \ inch above it, The back face to be J inch from V. PLATE X. The ground line is to be in the middle of the sheet, and the location arid dimensions of the figures are to be as given. The first figure shows a rectangular block wdth a rectangular hole cut through from front to back. The other two figures represent the same block in different positions. The second figure is the end or profile projection of the block. The same face is on H in all three positions. Be careful not to omit the shade lines. The figures given on the plate for dimensions, etc., are to be used but not repeated on the plate by the student. 159 68 MECHANICAL DRAWING PLATE XI. Three ground lines are to be used on this plate, two at the left 4 \ inches long and 3 inches from top and bottom margin lines ; and one at the right, half way between the top and bottom margins, 9| inches long. The figures 1, 2, 3 and 4 are examples for finding the true lengths of the lines. Begin No. 1 finch from the border, the vertical projection If inches long, one end on the ground line and inclined at 30°. The horizontal projection has one end \ inch from V, and the other inches from V. Find the true length of the line by completing the construction commenced by swinging the arc, as shown in the figure. Locate the left-hand end of No. 2 3 inches from the border, 1 inch above H, and § inch from V. Extend the vertical projection to the ground line at an angle of 45°, and make the horizontal pro- jection at 30°. Complete the construction for true length as commenced in the figure. In Figs. 3 and 4, the true lengths are to be found by complet- ing the revolutions indicated. The left-hand end of Fig. 3 is f inch from the margin, 1\ inches from V, and If inches above H. The horizontal projection makes an angle of 60° and extends to the ground line, and the vertical projection is inclined at 45°. The fourth figure is 3 inches from the border, and represents a line in a profile plane connecting points a and b. a is If inches above H and f inch from V ; and b is \ inch above H and inches from V. The figures for the middle ground line represent a pentagonal pyramid in three positions. The first position is the pyramid with the axis vertical, and the base § inch above the horizontal. The height of the pyramid is 2\ inches, and the diameter of the circle circumscribed about the base is 2\ inches. The center of the circle is 6 inches from the left margin and If inches from V. Spaces between figures to be f inch. In the second figure the pyramid has been revolved about the right-hand corner of the base as an axis, through an angle of 15°. The axis of the pyramid, shown dotted, is therefore at 75°. The method of obtaining 75° and 15° with the triangles was shown in 160 II A 3-1 y-73 EEBRUAR Y 27 y /90/. HERBERT CHANDLER CH/CAGO, /LL MECHANICAL DRAWING G9 Part I. From the way in which the pyramid has been revolved, all angles with V must remain the same as in the first position ; hence the vertical projection will be the same shape and size as before. All points of the pyramid remain the same distance from V. The points on the plan are found on T-square lines through the corners of the first plan and directly beneath the points in elevation. In the third position the pyramid has been swung around, about a vertical line through the apex as axis, through 30°. The angle with the horizontal plane remains the same; consequently the plan is the same size and shape as in the A second position, but at a different angle with the ground line. Heights of all points of the pyramid have not changed this time, and hence are projected across from the second elevation. Shade lines are to be put on between the light and dark surfaces as determined by the 45° triangle. PLATE XII. Developments. On this plate draw the developments of a truncated octagonal prism, and of a truncated pyramid having a square base. The arrangement on the plate is left to the student; but we should suggest that the truncated prism and its development be placed at 163 TO MECHANICAL DRAWING the left, and that the development of the truncated pyramid be placed under the development of the prism ; the truncated pyramid may be placed at the right. The prism and its development are shown in Fig. 96. The prism is 3 inches high, and the base is inscribed in a circle 2J inches in diameter. The plane forming the truncated prism is passed as indicated, the distance A B being 1 inch. Ink a suffi- cient number of construction lines to show clearly the method of finding the development. The pyramid and its development are shown in Fig. 97. Each side of the square base is 2 inches, and the altitude is 3J inches. A Fig. 97. The plane forming the truncated pyramid is passed in such a position that A B equals If inches, and A C equals 2 \ inches. In this figure the development may be drawn in any convenient position, but in the case of the prism it is better to draw the development as shown. Indicate clearly the construction by inking the construction lines. PLATE XIII. Isometric and ObSique Projection. Draw the oblique projection of a portable closet. The angle to be used is 45°. Make the height 3| inches, the depth 1^ inches, and the width 3 inches. See Fig. 98. The width of the closet 164 MARCH V, /90/ HERBERT CHANDLER CH/CAGO, /LL. MECHANICAL DRAWING 71 is to be shown as the left-hand face. The front left-hand lower comer is to be 1 inch from the left-hand border line and 2 inches from the lower border line. The door to be placed in the closet should be 1§ inches wide and 2| inches high. Place the door centrally in the front of the closet, the bottom edge at the height of the floor of the closet, the hinges of the door to be placed on the left-hand side. In the oblique drawing, show the door opened at an angle of 90 degrees. The thickness of the material of the closet, door, and floor is J inch. The door should be hung so that when closed it will be flush with the front of the closet. Make the isometric drawing of the flight of steps andend walls as shown by the end view in Fig. 99. The lower right-hand corner is to be located 2 \ inches from the lower, and 5 inches from the right-hand, margin. The base of the end wall is 3J- inches long, and the height is 2 \ inches. Beginning from the back of the wall, the top is horizontal for § inch, the remainder of the outline being composed of arcs of circles whose radii and centers are given 167 72 MECHANICAL DRAWING in the figure. The thickness of the end wall is § inch, and both ends are alike. There are to be five steps; each rise is to be f inch, and each tread | inch, except that of the top step, which is | inch. The first step is located § inch back from the corner of the wall. The end view of the wall should be constructed on a separate sheet of paper, from the dimensions given, the points on the curve being located by horizontal co-ordinates from the vertical edge of the wall, and then these co-ordinates transferred to the isometric drawing. After the isometric of one curved edge has been made, the others can be readily found from this. The width of the steps inside the walls is 3 inches. PLATE XIV. Free=hand Lettering. On account of the importance of free-hand lettering, the student should practice it at every opportunity. For additional practice, and to show the improvement made since completing Part I, lay out Plate XIV in the same manner as Plate I, and letter all four rectangles. Use the same letters and words as in the lower light-hand rectangle of Plate I. PLATE XV. Lettering. First lay out Plate XV in the same manner as previous plates. After drawing the vertical center line, draw light pencil lines as guide lines for the letters. The height of each line of letters is shown on the reproduced plate. The distance be- tween the letters should be J inch in every case. The spacing of the letters is left to the student. He may facilitate his work by lettering the words on a separate piece of paper, and finding the center by measurement or by doubling the paper into two equal parts. The styles of letters shown on the reproduced plate should be used. 168 F'LyATE ! IN Ld CO GC O i i DETAIL FROM TEMPLE OF MARS VENGEUR. An example of classic lettering, conventional shadows and rendering, Reproduced by permission of Massachusetts Institute of Technology. SHADES AND SHADOWS, 1. The drawings of which an architect makes use can be divided into two general kinds: those for designing the building and illustrating to the client its scheme and appearance; and “working drawings” which, as their name implies, are the draw- ings from which the building is erected. The first class includes “ studies,” “ preliminary sketches,” and “ rendered drawings.” Working drawings consist of dimensioned drawings at various scales, and full-sized details. 2. It is in the drawings of the first kind that “shades and shadows” are employed, their use being an aid to a more truthful and realistic representation of the building or object illustrated. All architectural drawings are conventional; that is to say, they are made according to certain rules, but are not pictures in the sense that a painter represents a building. The source of light casting the shadows in an architectural representation of a building is sup- posed to be, as in the “picture” of a building, the sun, but the direction of its rays is fixed and the laws of light observed in nature are also somewhat modified. The purpose of the architect’s draw- ing is to explain the building, therefore the laws of light in nature are followed only to the extent in wdiich they help this explanation, and are, therefore, not necessarily to be followed consistently or completely. The fixed direction of the sun’s rays is a further aid to the purpose of an architectural drawing in that it gives all the drawings a certain uniformity. 3. Definitions. A clear understanding of the following terms is necessary to insure an understanding of the explanations which follow. 4. Shade: When a body is subjected to rays of light, that portion which is turned away from the source of light and which, therefore, does not receive any of the rays, is said to be in shade. See Fig. 1. 5. Shadow: When a surface is in light and an object is 173 4 SHADES AND SHADOWS placed between it and the source of light, intercepting thereby some of the rays, that portion of the surface from which light is thus excluded is said to be in shadow. 6. In actual practice distinction is seldom made between these terms “shade” and “ shadow,” and “shadow” is generally used for that part of an object from which light is excluded. 7. TJmbra: That portion of space from w T hich light is excluded is called the umbra or invisible shadow. (a) The umbra of a point in space is evidently a line. (b) The umbra of a line is in general a plane. (c) The umbra of a plane is in general a solid. (d) It is also evident, from Fig. 1, that the shadow of an object upon another object is the intersection of the umbra of the first object with the surface of the second object. For example, in Fig. 1, the shadow of the given sphere on the surface in light is the intersection of its umbra (in this case a cylinder) with the given surface producing an ellipse as the shadow of the sphere. 8. Ray of light: The sun is the supposed source of light in “ shades and shadows,” and the rays are propo- gated from it in straight lines and in all directions. Therefore, the ray of light can be represented graph- ically by a straight line. Since the sun is at an in- finite distance, it can be safely assumed that the rays of light are all par- allel. 9. Plane of light : A plane of light is any plane containing a ray of light, that is, in the sense of the ray lying in the plane. 10. Shade line: The line of separation between the portion of an object in light and the portion in shade is called the shade line. 11. It is evident, from Fig. 1, that this shade line is tlie boundary of the shade. It is made up of the points of tangency of rays of light tangent to the object. 12. It is also evident that the shadow of the object is the space enclosed by the shadow of the shade line. In Fig. 1, the 174 SHADES AND SHADOWS shade line of the given sphere is a great circle of the sphere. The shadow of this great circle on the given plane is an ellipse. The portion within the ellipse is the shadow of the sphere. NOTATION. 13. In the following explanations the notation usual in orthographic projections will be followed: H = horizontal co-ordinate plane. Y == vertical co-ordinate olane. a = point in space. a y = vertical projection (or elevation) of the point. a h = horizontal projection (or plan) of the point. a ws = shadow on V of the point a . « hs = shadow on II of the point a. R = ray of light in space. R v = vertical projection (or elevation) of ray of light. R h — horizontal projection (or plan) of ray of light. GL= ground line, refers to a plane on which a shadow is to be cast, and is that projection of the plane which is a line. 14. In orthographic projection a given point is determined by “project- ing” it upon a vertical and upon a horizontal plane. In representing these planes upon a sheet of drawing paper it is evident, since they are at right angles to each other, that when the plane of the paper represents V( the vertical “co-ordinate” plane), the hor- izontal “co-ordinate” plane H, would be seen and rep- resented as a horizontal line, Fig. 2. Vice versa , when the plane of the paper represents H(the horizontal co- ordinate plane) , the vertical co-ordinate plane V, would be seen and represented by a horizontal line, Fig. 2. 15. In architectural drawings having the eleva- tion and plans upon the same sheet, it is customary to place the “elevation,” or vertical projection, above the plan, as in Fig. 2. It is evident that the distance between the two ground lines can be that which best suits convenience. 16. As the problems of finding the shades and shadows of objects are problems dealing with" points, lines, surfaces, and solids, they are dealt with as problems in Descriptive Geometry. It is assumed that the student is familiar with the’ principles of orthographic projection. In the following problems, the objects are referred to the usual co-ordinate planes, but as it is unusual in architectural drawings to have the plan and elevation on the same sheet, two ground lines are used instead of one. 17. Ray of Light. The assumed direction of the conven- tional ray of light R, is that of the diagonal of a cube, sloping downward, forward and to the right; the cube being placed so FIG* 2 Vertical Co-ordinate plane blang L-V plane Horizontal Co-orainate plane 6 SHADES AND SHADOWS that its faces are either parallel or perpendicular to H and Y. Fig. 3 shows the elevation and plan of such a cube and its diagonal. It will be seen from this that the II and V projections of the ray of light make angles of 45° with the ground lines . The true angle which the actual ray in space makes with the co-ordinate planes is 35° 15’ 52' This true angle can be determined as shown in Fig. 4. Revolve the ray parallel to either of the co-ordinate planes. In Fig. 4, it has been revolved parallel to Y, hence T is its true angle. FIG‘3 18. It is important in the following explanations to realize the difference in the terms “ray of light,” and “projections of the ray of light.” SHADOWS OF POINTS. 19. Problem I. To find the shadow of a given point on a given plane. Fig. 5 shows the plan and elevation of a given point a . It is required to find its shadow on a given plane, in this case the Y plane. The shadow of the point a on Y will be the point at which the ray of light passing through a intersects Y. Through the II projection of the given point, draw R h until it intersects the lower ground line. This means that the ray of light through a has pierced Y at some point. The exact point will be on the perpendicular to the ground line, where R v drawn through a v intersects the perpendicular. The point a YS is, therefore, the shadow of a on the Y plane. R v is also the Y projection of the umbra of the point a and it will be seen that the shadow of a on Y is the intersection of its umbra with Y. 176 SHADES AND SHADOWS 7 20. Fig. 6 shows the construction for finding the shadow of a point a on H. 21. Fig. 7 shows the construction for finding the shadow of a point a , which is at an equal distance from both Y and II. Its shadow, therefore, falls on the line of intersection of Y and II. 22. Fig. 8 shows the construction for finding the imaginary shadow of the point a , situated as in Fig. 5, that is, nearer the Y plane than the H. The actual shadow would in this case fall on Y, but it is sometimes necessary to find its imaginary shadow on H. The method of determining this is similar to that explained in connection with Fig. 5. Draw R v until it meets the ground line of H. Erect a perpendicular at this point of intersection. Draw R h . The intersection a hs , of the latter and the perpendicular, is the required imaginary shadow on H of the point a . 23. The actual shadow of a given point, with reference to the two co-ordinate planes, will fall on the nearer co-ordinate plane. 24. Fig. 9 shows the construction for finding the shadow of 8 SHADES AND SHADOWS a given point a on tlie Y plane projections of the point are given. 25. In general, the finding o on a given plane is the same as th< section of its umbra with that pla\ when the vertical and profile f the shadow of a given point i finding of the point of inter - xe. To obtain this, one projec- tion of the given plane must be a line and that is used as the ground line . It is neces- sary to have a ground line to which is drawn the projection of the ray of light, in order that we as pierced the given plane. SHADOWS OF LINES. 26. Problem II. To find the shadow of a given line on a given plane. A straight line is made up of a series of points. Rays of light passing through all of these points would form a plane of light. The intersection of this plane of light with either of the co-ordinate planes would be the shadow of the given line on that plane. This shadow would be a straight line because two planes always intersect in a straight line. This fact, and the fact that a straight line is determined by two points, enables us to cast the shadow of a given line by simply casting the shadows of any two points in the line and drawing a straight line between these points of shadow. In Fig. 10, a v b v and a h b h are the elevation and plan respectively of a given line ab in space. Casting the shadow of the ends of the line a and b by the method illustrated in Problem 1 and drawing the line a ws b vs , we obtain the shadow of the given line ab on Y. 27. Fig. 11 shows the construction for finding the shadow of the line ab when the shadow falls upon II. 178 SHADES AND SHADOWS 9 28. Fig. 12 shows the construction for finding the shadow of a line so situated that part of the shadow falls upon V and the remainder on H. To obtain the shadow in such a case, it must be found wholly on either one of the co-ordinate planes. In Fig. 12, it has been found wholly on Y, a ys being the actual shadow of that end of the line, and J vs being the imaginary shadow of the end b on Y. Of the line a vs b vs we use only the part & vs c vs , that being the shadow wdiich actually falls upon Y. The point where the shadow leaves Y and the point where it begins on H are identical, so that the beginning of the shadow on H will be on the lower ground line directly below the point c vs ; c hs will then be one point in the shadow of the line on H, and casting the shadow of the end b we obtain £ hs . The line i i i i ► i i i p' i o v s v j i n${p b ! ! 1 1 1 1 i i ! ! b — i / ab , the part ac falls on the plane mnop and the remainder, cb , on the plane nrso. To find the shadow of ac on the left-hand plane we must first determine our ground line. The ground line will be that pro- jection of the plane receiving the shadow which is a line. In this example the vertical projection of the plane mnop is the rectangle m y n y o y p y . This projection cannot, therefore, be used as a GU The plan, or H projection, of this plane is, however, a line m h n h . This line, therefore, will be used as the ground line for finding the shadow of ac on mnop. 180 SHADES AND SHADOWS 11 We find the shadow of a to be at a s and the shadow of c at 0 s , Problem I. The line a s c s is, therefore, a part of the required shadow. The remaining part, c s b s is found in a similar manner. 34. The above illustrates the method of determining the O GL when the shadow falls upon some plane other than a co-ordinate plane. In case neither projection of the given plane is a line, the shadow must be deter- mined by methods which will be ex- ! • , X \ FIG-17 plained later. !> \ ' SHADOWS OF PLANES. 35. Problem III. To find the shad= ow of a given plane on a given plane. Plane surfaces are bounded by straight or curved lines. Find the shadows of the bounding lines by the method shown in Problem II. The resulting figure will be the required shadow. 3G. In Fig. IT, the plane ale is so situated that its shadow falls wholly upon Y. The shadows of its bounding lines, ah , be, ca have been found by Problem II. That portion of the shadow hidden by the plane in elevation is cross-hatched along the edge of the shadow only. This method of indicat- ing actual shadows © which are hidden by the object is to be fol- lowed in working out the problems of the examination plates. 37. Fig. 18 shows the construction of the shadow 7 of a plane on the co-ordinate plane to which the given plane is parallel. (In this case the vertical plane.) It is to be observed that the shadow is equal in size and shape to the given plane. Fig. 19 shows that, in case of a circle parallel to one of the FIG-18 181 12 SHADES AND SHADOWS co-ordinate planes, it is only necessary to find the shadow of the center of the circle and w T ith that point as a center construct a circle of the same radius as that of the given circle. NOTE: 39. Any point, line, or plane lying in a surface is considered to be its own shadow on that surface. 40. A surface parallel to a ray of light is considered to he in shade. 41. In the above problems the points, lines and planes have been given in vertical and horizontal projection. The methods for finding their shadows are, in general, equally true when the points, lines and planes are given by vertical and profile projection or horizontal and profile projection. SHADOWS OF SOLIDS. 42. The methods for finding the shadows of solids vary with the nature of the given solid. The shadows of solids which are bounded o by plane surfaces, none of which are parallel, or perpendicular, to the co-ordinate planes, can in general, be found only by finding the shadows of all the bounding planes. These will form an enclosed polygon, the sides of which are the shadows of the shade lines of the object, and the shade lines of the solid are deter- mined in this way. The following is an illustration of this class of solids. 43. Problem IV. To find the shade and shadow of a polyhedron, none of whose faces are parallel or perpendicular to theco=or= dinate planes. Fig 20 shows a poly- hedron in such a position and of such a shape that none of its faces are per- pendicular or parallel to the co-ordinate planes. It is impossible, therefore, to apply to this figure the projections of the rays of light and determine what faces are in light and w T hat in shade. Consequently we cannot determine the shade line whose shadows would form the shadow of the object. 18 g SHADES AND SHADOWS 13 Under these circumstances we must cast the shadows of all the boundary edges of the object . Some of these lines of shadow will form a polygon, the others will fall inside this polygon. The edges of the object whose shadows form the bounding lines of the polygon of shadow are the shade lines of the given object. Know- ing the shade lines, the light and shaded portions of the object can now be determined, since these are separated by the shade lines. In a problem of this kind care should be taken to letter or number the edges of the given object . 44. The edges of the polyhedron shown in Fig. 20 are ab , be, cd, da, ac and bd. Cast the shadows of each of these straight lines by the method shown in Problem II. We thus obtain a polygon bounded by the lines b vs c YS , c YS a YS , a ys b ws , and this polygon is the shadowof the given solid. The lines which cast these lines of shadow, b YS c xs , c YS a ws , and a YS U s are therefore the shade lines of the object, and, therefore, the face abc is in light and the faces abd, bed and acd are in shade. The shadows of the edges bd, dc, and ad falling within the polygon, indi- cate that they are not shade lines of the given object, and, therefore, they separate two faces in shade or two faces in light. In this example bd and cd separate two dark faces. In architectural drawings the object usually has a sufficient number of its planes perpendicular or parallel to the co-ordinate planes, to permit its shadow being found by a simpler and more direct method than the one just explained. 45. Problem V. To find the shade and shadow of a prism on the co-ordinate planes, the faces of the prism being perpen= dicular or parallel to the V and H planes. In Fig. 21 such a prism is shown in plan and elevation. The FIG* 21 183 14 SHADES AND SHADOWS elevation shows it to be resting on H, and the plan shows it to be situated in front of Y, its sides making angles with V. Since its top and bottom faces are parallel to H and its side faces per- pendicular to that plane, we can apply the projections of the rays of light to the plan and determine at once which of the side faces are in light and which in shade. The projections of the rays R 1 and R 2 show that the faces abgf and adif receive the light directly, and that the two other side faces do not receive the rays of light and are, therefore, in shade. The edges bg and di are two of the shade lines. R 3 and R 4 are the projections of the rays which are tangent to the prism along these shade lines. Applying the projection R 5 in the elevation makes it evident that the top face of the prism is in light and the bottom face is in shade since the prism rests on H. This determines the light and shade of all the faces of the prism, and the other shade lines would therefore be be and ed. Casting the shadow of each of these shade lines, we obtain the required shadow on Y and H. It is evident that the shadows of the edges bg and di on H will be 45° lines since these edges are perpendicular to H (§ 31) Also, their shadows on Y will be parallel to the lines themselves since these shade lines are parallel to Y. (§ 30) 46. In general, to find the shadow of an object whose planes are parallel or perpendicular to II or Y : (1) Apply to the object the projections of the ray of light to determine the lighted and shaded faces. (2) These determine the shade lines. (3) Cast the shadows of these shade lines by the method fol- lowed in Problem II. 47. Problem VI. To find the shade and shadow of one object on another. In Fig. 22 is shown in plan and elevation a prism B, resting on II and against Y. Upon this prism rests a plinth A: To find the shadow of the plinth on the prism and the shadow of both on the co-ordinate planes. Since these objects have their faces either perpendicular to, or parallel to, the co-ordinate planes, we can deter- mine immediately the light and shade faces and from them the shade lines. 184 SHADES AND SHADOWS 15 48. Considering first tlie plinth A, it is evident that its top, left-hand and front faces will receive the light, that the lower and right-hand faces will be in shade. The back face resting against the Y plane will be its own shadow on Y. (§ 39) The shade lines of A will be, therefore, cf^fg^ go and cd . Cast the shadows of these lines. A rests against Y and part of its shadow will fall on Y ; also, since it rests on B the remainder will fall on B. Begin with the point until it intersects the line a p ^ p , the profile projection of the front face. From this point qf draw a horizontal line across until it meets the vertical projection of the ray drawn through q y . From ^ v , the shadow of q v w y on the front face will be parallel to q y w y , for that line is parallel to that face; therefore draw q?zf 188 An example of conventional shadows and rendering. Reproduced by permission of Massachusetts Institute of Technology. SHADES AND SHADOWS 19 N ow that the visible shadows on the chimney itself have been determined, its shadow on the roof can be found as explained in the first part of this problem. A portion of the shade line of the flat band, w Y n y , etc., falls beyond the chimney on the roof, as shown by the line z s w s , w s n 3 , etc. 52. It is to be noted in the shadow on the roof that: (a) The shadows of the vertical edges of the chimney make angles with a horizontal line equal to the angle of the slope of the roof { in this case 60°). i(b) The horizontal edges which are parallel to V cast shadows which are parallel to these same edges in the chimney. (c) The horizontal edges which are perpendicular to V cast shadows which make angles of 45° with a horizontal line. 53. The above method would also be used in finding shad- ows on sloping surfaces when the objects are given in elevation and side elevation, as, for example, a dormer window. 54. Problem IX. To find the shades and shadows of a hand rail on a flight of steps and on the ground. Fig. 24 shows the plan and elevation of a flight of four steps situated in front of a vertical wall, with a solid hand rail on either side, the hand rails being terminated by rectangular posts. At a smaller scale is shown a section through the steps and the slope of the hand rail. This problem amounts to finding the shadow of a broken line, that is to say, the shade line, on a series of planes. Each of the planes requires its own ground line, which in the case of each plane will be that projection of the plane wdiich is a line. Since the planes of the steps and rails, with one exception, are all parallel or perpendicular to the co-ordinate planes we can determine at once what planes are in light and what in shadow and thus deter- mine the shade line. 55. An inspection of the figure will make it evident that the “treads” of the steps, A, B, C, D and the “ risers,” M, N, O, P are all in lio-ht. Of the hand rail it will be evident also that the left- o hand face, the top, and the front face of the post are in light. The remaining faces are in shade. This is true of both rails; there- fore, in one case we must find the shadow of a broken line, dbcdef on the vertical wall and on the steps, and then find the shadow of 191 20 SHADES AND SHADOWS the broken line mnojpqr on the vertical wall and on the ground. 56. Beo-inninor with the shadow of the left-hand rail, the shadow of the point a on the wall is evidently ce Y , since a lies in the plane of the vertical wall (§ 39) The line ab is perpendicular to Y hence its shadow will be a 45° line, the point b ys being found by Problem I. The shadow of be , the sloping part of the rail, will fall partly on the vertical wall and partly on the treads and risers. We have already found the shadow of the end b on Y in the point b ys . The shadow of c 192 SHADES AXD SHADOWS 21 on V, found by Problem I will be c ys . Tbe portion b vs y YS is the part of tbe shadow of this line be that actually falls on the wall, the steps preventing the rest of the line from falling on V. The line of shadow now leaves the vertical wall at the point vs and p vs respectively to the perimeter of the top and base. Their points of intersection m v , n y , 6> v and are the ends of the shade elements in the elevation. They can be found in plan by projection. An inspection of the figure will make it evident what portions of the cylindrical surface between these shade elements will be light and what in shade. 71. In this problem it will be seen that the shadow does not fall wholly upon. Y. The shadow leaves Y at the points x vs and y vs and will evidently begin on H at points directly below, as .£ hs and y hs . 197 26 SHADES A HD SHADOWS If projections of the ray are drawn back to the object in plan and elevation from these points, a? vs , y ys , x hs , and y hs , they will determine the portion of the shade line which casts its shadow on H. It is evident that in this particular object it is that portion of the shade line of the top between the points p and y and the portion xp, of one of the shade elements. The shadows of these lines are found on H by Problem II. USE OF AUXILIARY PLANES. 72. In finding shadows on some of the double-curved sur- faces of revolution, such as the surface of the spherical hollow, the scotia and the torus, we can make use of auxiliary planes to advantage, when the plane of the line whose shadow is to he cast is parallel to one of the co-ordinate planes . 73. Problem XIII. To find the shadow in a spherical hol= low. Fig. 29 shows in plan and elevation a spherical hollow whose plane has been assumed parallel to Y. Applying to the elevation, the projections of the ray II, we determine the amount of the edge of the hollow which will cast a shadow on the spherical surface inside. The points of tangency a y and h y are the lim- its of this shade line a y c y h y . The remaining portion of the line a y d y h y is not a shade line since the light would reach the spherical surface adjacent to it and also reach the plane surface on the other side of a y d y h y outside the spherical hollow. We must now cast the shadow of the line a y c y h y on the spher- ical surface of the hollow, and having no ground line, (since neither Lie Y nor the H projection of the spherical hollow is a line,) we use auxiliary planes. If we pass through the spherical hollow, parallel to the plane SHADES AND SHADOWS 27 of the line acb (in this case parallel to Y) an auxiliary plane P, it will cut on the spherical surface a line of intersection xy\ in elevation this will show as a circle x v if , whose diameter is oh- tained from the line x h y h in the plan. This line of intersection will show in plan as a straight line, x h y h . Cast the shadow of the line acb on this auxiliary plane P. This is not difficult because the plane P was assumed parallel to acb 9 and in this particular case, a*c v b v is the arc of a circle. To cast its shadow on P it is only necessary to cast the shadow of its center has pierced the scotia surface. If now the plane P is revolved back to its original posi- tion, this point a' vs will move in a horizontal line in elevation to the point a ys , and the point a ys thus obtained is the shadow of the point a Y on the surface of the scotia and is also the highest point of the shadow. FIG > 32 77. The remainder of the process is, from now on, similar to the method just explained in the previous problem. See Fig. 32. We pass auxiliary planes, A, B, C, etc., (in this case parallel to IT) through the scotia. We determine in plan their respective lines of intersection with the scotia: they will be circles. Cast the shadow of the arc x h a h y h on each of these auxiliary planes. This is done by casting the shadow of its center O and drawing arcs equal to x h a h y h . 202 SHADES AND SHADOWS 31 The points of intersection, 2 h , 3 h , 4 h , 5 h , 6 h , etc., are points in the required shadow in plan. The points l h and 10 h are the ends, where the shadow leaves the scotia, and these are determined by tak- ing one of the auxiliary planes at the line MX. The points l v , 2 V , 3 V , etc., are obtained in the elevation by projection from the plan. The shade of the lower fillet is determined by Problem XI. 78. In case the fillets are conical instead of cylindrical sur. faces, as is sometimes the case in the bases of columns where the scotia moulding is most commonly found, care must be taken to first determine the shade elements of the conical surface. This supposition of conical surfaces w T ould mean a larger arc for the shade line than the arc x h a h y h . U5E OF PLANES OF LIGHT PERPENDICULAR TO THE COORDINATE PLANES. 79. Another method often necessary and convenient in casting the shadows of double- curved surfaces is the use of yjlanes of light perpendicular to the co-ordinate plagues. These auxiliary planes of light are passed through the given object. They will cut out lines of intersection with the object and to these lines of inter- section can be applied the projections of the rays of light which lie in the auxiliary planes of light. The points of contact or tangency, as the case may be, of the projections of the rays and the line of intersection are points in the required shadow. 80. The use of this method will be illustrated by finding the shadow of a sphere in the following problem. The shadow of the sphere serves to illustrate this method well, but a more aceur- FIG A 33 203 32 SHADES AND SHADOWS ate and convenient method is given later in Problem XXIX for determining the shade line of the sphere and its shadow. 81. Problem XV. To find the shade line of a sphere. In Fig. 33 is shown the plan and elevation of a sphere. Through the sphere in plan, pass the auxiliary jplane of light P, perpendicular to H. This cuts out of the sphere the ‘‘line of in- tersection,” shown in the elevation. This “line of intersection” is determined by using the auxiliary planes A, B, C, D, etc., each To this line of intersection made by the plane of light plane giving two points in the line. PIG 4 34 r ^ -L—A i V- ) A i \ 1 p is in tlie light, and that the ray is tangent to its lower edge 1 ack line. PLATE I. 99. See directions on plate. PLATE II. 100. Find the shadows of lines ah, etc., in Problems XIV. XVI. 101. In Problem XVII find the shadow of line ah on the planes A, B, and C. 102. In Problem XVIII find the shadow cf plane abed. PLATE III. 103. See directions on plate. PLATE IV. 101. See directions on plate. PLATE V. 105. In Problem XXV find all the shadows on the steps and the shadows on the co-ordinate planes in plan and elevation. Letter carefully the various planes in elevation and plan. 106. In Problem XXVI find all the shades and shadows of the cylinder and its shadows on the co-ordinate planes. PLATE VI. 107. In Problems XXVIII and XXIX find the shades and shadows of objects and their shadows on the co-ordinate planes. 108. In Problem XXX, C is a square projection or fillet on the V plane. Below this fillet and also applied to the V plane are portions of two cylinders, DD, which support the fillet C. Find the shades and shadows in elevation only. 48 SHADES AND SHADOWS PLATE VII. 109. Problem XXXI, given a spherical hollow, its plane parallel to Y, find its shadow. 110. Problem XXXII, given a scotia moulding, the upper fillet of which is the frustum of a cone, the lower fillet is a cylin- der. Find its shadow in elevation and plan. * PLATE VIII, 112. Problem XXXIII shows a series of pediment mould- ings applied to a vertical wall A. Find the shadows on the mould- ings and the shadows of the mouldings on the vertical plane A. PLATE IX. 113. In Problem XXXIY find the shadows of a given window. 114. In Problem XXXY find the shadows of the given key- block and the shadow of the keyblock on the vertical wall to which it is applied. Use the short methods of construction and use the plan only from which to take distances. PLATE X. 115. Problem XXXVI. Given the upper portion of a Doric order, the column being engaged to the vertical wall Y, see plan. The entablature breaks out over the column, see plan. Find all the shadows, using the short methods of construction and use the plan only to obtain required distances. PLATE XL 116. Problem XXXVII. Given a rectangular niche, as shown by the plan, having a circular head as shown by the eleva- tion. Situated in the niche is a pedestal in the form of truncated square pyramid. This pedestal has on its four side faces projections as shown in the elevation and plan. On the pedestal rests a sphere. Find all the visible shadows in the elevation. Use the short methods of construction and use the plan only for determining distances. 117. Problem XXXVIII. Given a niche in the form of a spherical hollow. The profile of the architrave mouldings is shown at A. Find all the shadows. Use the short methods of construction. PLATE XII. 118. Problem XXXIX. Given the lower part of a column standing free from a vertical wall, and resting on a large square base, the base having a moulded panel in its front face. At the foot of the vertical wall is a series of base mouldings, the lower ones cutting into the side of the square base on w T hich the column stands, see plan. Find all the visible shadows, using the short methods of construction. * Optional. 222 SHADES & SHADOWS PLATE I ~1 DATE NAME SHADES & SHADOWS PLATE II rind shade of objects and shadows on V and H . •19- -20- DATE NAJAE SHADES & SHADOWS PLATE IV DATE, NA7AE SHADES &, SHADOWS PLATE V DATE NAME SHADES &, SHADOWS PLATE VII DATE NAME SHADES & SHADOWS PLATE IX Kle vaXion of Side Key block ElevaJton SHADES &, SHADOWS PLATE X DATE SHADES &, SHADOWS PLATE XI DATE [ DATE NA7AE /^IPf Kdvf rv B v i Id i y \$ A STUDY IN PEN AND INK RENDERING (For a different treatment of the same build’iig, see page 406.) PERSPECTIVE DRAWING DEFINITIONS AND GENERAL THEORY. 1. AYhen any object in space is being viewed, rays of light are reflected from all points of its visible surface, and enter the eye of the observer. These rays of light are called visual rays. They strike upon the sensitive membrane, called the retina, of the eye, and form an image. It is from this image that the observer receives his impression of the appearance of the object at which he is looking. 2. In Fig. 1, let the triangular card abc represent any object in space. The image of it on the retina of the observer’s eye will be formed by the visual rays re- flected from its sur- face. These rays form a pyramid or cone which has the observer’s eye for its apex, and the object in space for its base. 3. If a transparent plane M, Fig. 2, be placed in such a position that it will intersect the cone of visual rays as shown, the intersection will be a projection of the object upon the plane M. It will be noticed that the projecting lines, or projectors, instead of being perpendicular to the plane, as is the case in orthographic projection,* are the visual rays which all converge to a single point coincident with the observer’s eye. * In orthographic projection an object is represented upon two planes at right angles V* each other, by lines drawn perpendicular to these planes from all points on the edges or contour of the object. Such perpendicular lines intersecting the planes give figures which are ailed projections ( orthographic ) of the object. a 249 4 PERSPECTIVE DRAWING. 4. Every point or line in the projection on the plane M will appear to the observer exactly to cover the corresponding point or line in the object. Thus the observer sees the point a Y in the projection, apparently just coincident with the point a in the object. This must evidently be so, for both the points a v and a lie on the same visual ray. In the same way the line a v b v in the projection must appear to the observer to exactly cover the line ab in the object ; and the projection, as a whole, must present to him exactly the same appearance as the object in space. 5. If the projection is supposed to be permanently fixed upon the plane, the object in space may be removed without affecting the image on the retina of the observer’s eye, since the visual rays which were originally re- flected from the sur- face of the object are now reflected from the projection on the plane M. In other words, this projection may be used as a substitute for the object in space, and when placed in proper relation to the eye of the observer, will convey to him an impression exactly similar to that which would be produced were he looking at the real object. 6. A projection such as that just described is known as a perspective projection of the object which it represents. The plane on which the perspective projection is made is called the Picture Plane. The position of the observer’s eye is called the Station Point, or Point of Sight. 7. It will be seen that the perspective projection of any point in the object, is where the visual ray, through that point, pierces the picture plane. 8. A perspective projection may be defined as the represen- 250 PERSPECTIVE DRAWING. tation, upon a plane surface, of the appearance of objects as seen from some given point of view. 9. Before beginning the study of the construction of the perspective projection, some consideration should be given to phenomena of perspective. One of the most important of these phenomena, and one which is the keynote to the whole science of perspective, has been noticed by everyone. It is the apparent diminution in the size of an object as the distance between the object and the eye increases. A railroad train moving over a long, straight track, furnishes a familiar example of this. As the train moves farther and farther away, its dimensions apparently become smaller and smaller, the details grow more and more indistinct, until the whole train appears like a black line crawling over the ground. It will be noticed also, that the speed of the train seems to diminish as it moves away, for the equal distances over which it will travel in a given time, seem less and less as they are taken farther and farther from the eye. 10. In the same way, if several objects having the same dimensions are situated at different distances from the eye, the nearest one appears to be the largest, and the others appear to be smaller and smaller as they are farther and farther away. Take, for illustration, a long, b straight row of street- lamps. As one looks along the row, each succeeding lamp is ap- parently shorter and smaller than the one before. The reason for this can easily be explained. In estimating the size of any object, one most naturally compares it with some other object as a stand- ard or unit. Now, as the observer compares the lamp-posts, one with anothar, the result will be something as follows (see Fig. 3). If he is looking at the top of No. 1, along the line ba , the top of No. 2 is invisible. It is apparently below the top of No. 1, for, in order to see No. 2, he has to lower his eye until he is looking in 251 6 PERSPECTIVE DRAWING, the direction ba v He now sees the top of No. 2, but the top of No. 1 seems some distance above, and he naturally concludes that No. 2 appears shorter than No. 1. As the observer looks at the top of No. 2, No. 3 is still invisible, and, in order to see it, he has to lower his eye still farther. Comparing the bottoms of the posts, he finds the same apparent diminution in size as the distance of the posts from his eye increases. The length of the second post appears only equal to the distance mn as measured on the first post, while the length of the third post appears only equal to the distance os as measured on post No. 1. 11. In the same way that the lamp-posts appear to diminish in size as they recede from the eye, the parallel lines («, a Y , a 2 , etc., and c, c v lane belongs. Qe') As the intersection of two planes is a line lying in both , the vanishing point of this intersection must lie in the vanishing traces of both planes, and hence, at the point where the vanishing traces of the two planes cross. In other words, the vanishing point 10 PERSPECTIVE DRAWING. of the intersection of two planes must lie at the intersection of the vanishing traces of the two planes. 22. The five axioms in the last paragraph are the statements of purely imaginary conditions which appear to exist, but in reality do not. Thus, parallel lines appear to converge and to meet at a point at infinity, but in reality they are exactly the same distance apart throughout their length. Parallel planes appear to converge as they recede, but this is a purely apparent condition, and not a reality ; the real distance between the planes does not change. 23. The perspective projection represents by real conditions the purely imaginary conditions that appear to exist in space. Thus, the apparent convergence of lines in space is represented by a real convergence in the perspective projection. Again, the vanishing point of a system of lines is a purely imaginary point which does not exist. But this imaginary point is represented in perspective projection by a real point on the picture plane. From § 14, the vanishing point of any system of lines lies upon the visual element of that system. This visual element may be considered to be the visual ray which projects the vanish- 256 PERSPECTIVE DRAWING. 11 mg point to the observer’s e}^e. Hence, from § T, the intersection of this visual element with the picture plane will be the perspective of the vanishing point of the system to which it belongs. This is illustrated in Fig. 6. The object in space is shown on the right of the figure. If the observer wishes to find the vanishing point of the oblique line ab in the object in space, he imagines a line parallel to ab to enter his eye, and looks along this line (§ 13). Where this line along which he is looking pierces the picture plane, will be the perspective of the vanishing point. Further- more, the perspective of the line ab has been found by drawing the visual rays from a and b respectively, and finding where these rays pierce the picture plane (§ 7). These points are respectively, a F and b p , and the straight line drawn between a? and b v is the perspective of the line ab. The perspective of the line a l b l which is parallel to ab , has been found in a similar way, and it will be noticed that its perspective projection ( a\ 6f) actually converges towards a v b v in such a manner that if these two lines are pro- duced they will actually meet at the perspective of the vanish- ing point of their system. Note. — It is evident that the perspective of a straight line will always be a straight line , the extreme points of which are the perspec- tives of the extremities of the given line. 24. Thus, the five axioms of perspective may be applied to Perspective Projection as follows : — (ci) Parallel lines do converge and meet at the vanishing point of their system. (b) Parallel planes do converge and meet at the vanishing trace of their system. (c) The vanishing point of any line lying in a plane will be found in the vanishing trace of the plane. Therefore , the vanishing points of all horizontal lines will be found in the horizon (§ 20). ( d ) The vanishing trace of any plane will be determined by the vanishing points of any two lines that lie in it, and must con- tain the vanishing points of all lines that lie in it. ( e ) The vanishing point of the intersection of two planes will be found at the intersections of the vanishing traces of the two planes. 257 12 PERSPECTIVE DRAWING. To the five axioms of perspective projection already stated may be added the following three truths concerning the construc- tion of the perspective projection : — • (/) The perspective of any point in space is where the visual ray through the point pierces that picture plane (§7). (g) The perspective of the vanishing point of any system of lines is where the visual element of that system pierces the j)ic- ture plane. Rule for fi7iding the perspective of the vanishing point of any system of lines : — Draw an element of the system through the ob- server’s eye , and find where it pierces the picture plane. (h) Any point, line, or surface which lies in the picture plane will be its own perspective, and show in its true size and shape. 25. Knowing how to find the perspective of any point, and how to find the vanishing point of any system of lines, any prob- lem in perspective may be solved. Therefore, it may be said that the whole process of making a perspective projection reduces itself to the problem of finding where a line pierces a plane. Before proceeding farther, the student should review the first twenty-five paragraphs by answering carefully the following questions : — (1) What does a perspective projection represent? (2) What is a visual ray? (3) How is a perspective projection formed ? (4) How does a perspective projection differ from an ortho graphic projection ? (5) What is the plane called on which the perspective pro jection is made ? (6) What is meant by the term Station Point? (7) What is the most important phenomenon of perspective (8) What is meant by a system of lines ? (9) What is meant by a system of planes ? (10) What is a visual element? (11) Define vanishing point. (12) Define vanishing trace. (13) Describe the position of the vanishing point of any sy^ tem of lines. 258 PERSPECTIVE DRAWING. 13 (14) Give the five axioms of perspective. (15) Do parallel lines in space really converge? (16) Do the perspective projections of parallel lines really converge? (17) Where will the perspective projections of parallel lines meet? (18) How is the perspective of any point found? (19) How is the perspective of the vanishing point of any system of lines found ? (20) What will be the perspective of a straight line? (21) What is meant by the horizon ? (22) What is meant by the plane of the horizon ? THE PLANES OF PROJECTION. 26. Two planes of projection at right angles to one another, one vertical and the other horizontal, are used in making a per- spective. In Fig. 7 these two planes are shown in oblique pro- jection. The vertical plane is the picture plane (§ 6 and Fig. 7) on which the perspective projection is made, and corresponds exactly to the vertical plane, or vertical coordinate used in ortho- graphic projections. 259 14 PERSPECTIVE DRAWING. 27. The horizontal plane, or plane of the horizon (§ 20 and Fig. 7), always passes through the assumed position of the observer's eye , and corresponds exactly to the horizontal plane or horizontal coordinate used in orthographic projections. 28. All points, lines, surfaces, or solids in space, the per- spective projections of which are to be found, are represented by their orthographic projections on these two planes, and their per- spectives are determined from these projections. 29. Besides these two principal planes of projection, a third plane is used to represent the plane on which the object is sup- posed to rest (Fig. 7). This third plane is horizontal, and is called the plane of the ground. Its relation to the plane of the horizon determines the nature of the perspective projection. To illustrate : The observer’s eye must always be in the plane of the horizon (§ 27), while the object, the perspective of which is to be made, is usually supposed to rest upon the plane of the ground. In most cases the plane of the ground will also be the plane on which the observer is supposed to stand, but this will not always be true. The observer may be standing at a much higher level than the plane on which the object rests, or he may be standing below that plane. It is evident, therefore, that if the plane of the ground is chosen far below the plane of the horizon, the observer’s eye will be far above the object, and the resulting per- spective projection will be a “ bird’s-eye view.” If, on the other hand, the plane of the ground is chosen above the plane of the horizon, the observer’s eye will be below the object, and the re- sulting perspective projection will show the object as though being viewed from below. This has sometimes been called a “ worm’s-eye view,” or a “ toad’s-eye view.” Usually the plane of the ground is chosen so that the dis- tance between it and the plane of the horizon is about equal (at the scale of the drawing) to the height of a man. This is the posi- tion indicated in Fig. 7, and the resulting perspective will show the object as though seen by a man standing on the plane on which the object rests. 80. The intersection of the picture plane and the plane of the horizon corresponds to the ground line used in the study of pro- jections, in Mechanical Drawing. For more advanced work, how- 260 PERSPECTIVE DRAWING. 15 ever, there is some objection to this term. The intersection of the two coordinate planes has really no connection with the ground, and if the term “ ground line ” is used, it is apt to result in a confusion between the intersection of the two coordinate planes, and the intersection of the auxiliary plane of the ground, with the picture plane. 31. The intersection of the two coordinate planes is usually lettered VH on the picture plane, and HPP on the plane of the horizon. (See Fig. 7.) That is to say : When the vertical plane is being considered, VH represents the intersection of that plane with the plane of the horizon. It should also be considered as the vertical projection of the plane of the horizon. See Mechani- cal* Drawing Part III, page 5, paragraph in italics. All points, lines, or surfaces lying in the plane of the horizon will have their vertical projection in VH. 32. On the other hand, when the horizontal plane is being considered, HPP represents the intersection of the two planes, and also the horizontal projection of the picture plane. All points, lines, or surfaces in the picture plane will have their horizontal projections in HPP. Thus, instead of considering the inter- section of the two coordinate planes a single line, it should be considered the coincidence of two lines, i.e. : First, the vertical projection of the plane of the horizon ; second, the horizontal projection of the picture plane. 33. The plane of the ground is always represented by its intersection with the picture . plane (see VH t Fig. 7). Its only use is to determine the relation between the plane of the horizon and the plane on which the object rests (§ 29). The true distance between these two planes is always shown by the distance between VH and VH X as drawn on the picture plane. 34. To find the perspective of a point determined by its vertical and horizontal projections. Fig. 8 is an oblique projection showing the two coordinate planes at right angles to each other. The assumed position of the plane of the ground is indicated by its vertical trace (VH,). 261 16 PERSPECTIVE DRAWING. Note. — The vertical trace of any plane is the intersection of that plane with the vertical coordinate. The horizontal trace of any plane is the intersection of that plane with the horizontal coordinate. The assumed position of the station point is indicated by its two projections, SP V and SP H . Since the station point lies in the plane of the horizon (§ 27), it is evident that its true position must coincide with SP H , and that (§ 31) its vertical projection must be found in VH, as indicated in the figure. Let the point a represent any point in space. The perspective of the point a will be at a p , where a visual ray through the point a pierces the pic- ture plane (§ 24). We may find a v in the following manner, by using the orthographic projections of the point a T , instead of the point itself. a n represents the horizontal projection, and a Y repre- sents the vertical projection of the point a . A line drawn from the vertical projection of the point a to the vertical projection of the station point, will represent the vertical projection of the visual ray , which passes through the point a. In Fig. 8 this vertical projection is represented by the line drawn on the picture jfiane from a Y to SPV A line drawn from the horizontal projection of a to the hori- zontal projection of the station point will represent the horizontal projection of the visual ray , which passes through the point a. In Fig. 8, this horizontal projection is represented by the line drawn on the plane of the horizon from a H to SP H . Thus we have, drawn upon the planes of projection, the vertical and horizontal projections of the point a , and the vertical and horizontal projec- tions of the visual ray passing between the point a and the station point. 35. We must now find the intersection of the visual ray with the picture plane. This intersection will be a point in the picture plane. It is evident that its vertical projection must coin- cide with the intersection itself, and that its horizontal projection must be in HPP (§ 32). But this intersection must also be on the visual ray through the point a, and consequently the horizon- tal projection of this intersection must be on the horizontal pro- jection of the visual ray. Therefore, the horizontal projection of this intersection must be the point m n , where the line between k */62 Fi g. 9a PERSPECTIVE DRAWING. 17 SP H and a H crosses HPP. The vertical projection of this inter- section must be vertically in line with this point, and on the line drawn between SP V and a Y , and hence at m v , Since the vertical projection of the intersection coincides with the intersection itself, a v (coincident with ra v ) must be the perspective of the point a . 36. This is the method of finding the perspective of any point, having given the vertical and horizontal projections of the point and of the station point. The method may be stated briefly as follows : — Draw through the horizontal projection of the point and the horizontal projection of the station point, a line representing the horizontal projection of the visual ray, which passes through the point. Through the intersection of this line with HPP, draw a vertical line. The perspective of the point will be found where this vertical line crosses the vertical projection of the visual ray, drawn through SP V and a Y . 37. It would evidently be inconvenient to work upon two planes at right angles to one another, as shown in Fig. 8. To avoid this, and to make it possible to work upon a plane sur- face, the picture plane (or vertical coordinate) is supposed to be revolved about its intersection with the plane of the horizon, until the two coincide and form one surface. The direction of this revolution is indicated by the arrows and s 2 . After revo- lution, the two coordinate planes will coincide, and the vertical and horizontal projections overlap one another, as indicated in Fig. 9. It will be noticed that the coincidence of the two planes in no way interferes with the method given in § 36, of finding the perspective (a p ) of the point a, from the vertical and horizontal projections of the point. Thus, the horizontal projection of the visual ray through the point will be seen, drawn from SP H to a H f and intersecting HPP in the point m H . The vertical projection of the visual ray through the point will be seen passing from SP V to a v . And a v is found upon the vertical projection of the visual ray, directly under m K . It will readily be understood that in a complicated problem, the overlapping of the vertical and horizontal projections might 265 18 PEESPECTIYE DRAWING. result in some confusion. It is, therefore, usually customary, after having revolved the two coordinate planes into the position shown in Fig. 9, to slide them apart in a direction perpendicular to their line of intersection, until the two planes occupy a position similar to that shown in Fig. 9a. 38. It will be remembered from the course on projections which the student is supposed to have taken, that horizontal pro- jections must always he compared with horizontal, and never with vertical proj ections, and that in the same way, vertical projections must always he compared ivith vertical, and never with horizontal projections. It is evident that in sliding the planes apart, the relations between the projections on the vertical plane will not be disturbed, nor will the relations between the projections on the horizontal plane, and consequently it will make no difference how far apart the two coordinate planes are drawn, provided that horizontal and vertical projections of the same points are always kept in line. Thus, in Fig. 9a, it will be seen that in drawing the planes apart, a Y has been kept in line with a n , m Y with m K , SP V with SP H , etc. 39. It will be observed that in sliding the planes apart, their line of intersection has been separated into its two projections (§§ 31 and 32). II PP, being on the plane of the horizon or hori- zontal coordinate, is the horizontal projection of the intersection of the two planes, while VII, being on the picture plane or vertical coordinate, is the vertical projection of the intersection of the two planes. In the original position of the planes (Fig. 9) these two projections were coincident. The distance between II PP and VH always represents the distance through which the planes have been slid. This distance is immaterial, and will have no effect on the perspective drawing. VHj represents the vertical trace of the plane of the ground. In this figure, as in the case of Fig. 9, the student should follow through the construction of the perspective of the point a, applying the method of § 36. 40. Fig. 10 shows the position of the two coordinate planes and of the plane of the ground, as they are usually represented on the drawing board in making a perspective drawing. It is essentially the same thing as Fig. 9a, except that the ] atter was 266 PERSPECTI V E DR AWI N( i . shown in oblique projection in order that its development from the original position of the planes (Fig. 8) might he followed more readily. The two coordinate planes are supposed to lie in the plane of the paper. HPP represents the horizontal projection of the picture plane, and YI1 represents the vertical projection of the plane of the horizon. As horizontal projections are never compared with vertical projections (§ 38), HPP may he drawn as far from, or as near, YII as desired, without in any way affecting the resulting per- spective drawing. HPP and YH were coincident in Fig. 9, and the distance between them in Fief. 10 simply shows the distance that the two planes have been slid apart, as illustrated in Fig. 9a. As already stated, this distance is immaterial, and may be made whatever is most convenient, according to the nature of the problem. If HPP should be placed nearer the top of the sheet, a n and SP H , both being horizontal projec- tions, would follow it, the relation between these horizontal projec- tions always being preserved. On the other hand, SP V , a v , a}\ YII, and YH 1? all being pro- jections on the vertical plane, must preserve their relation with one another, and will in no way be affected if the group of projections on the horizontal coordinate is moved nearer or farther away. It must be borne in mind, however, that, in all cases, the vertical and horizontal projections of corresponding points must be kept vertically in line. Thus, a H must always be vertically in line with a Y . The vertical distance between these two projections does not matter, provided the distance from a K to HPP, or the distance from a Y to YII, is not changed. This point cannot be too strongly emphasized. 267 20 PERSPECTIVE DRAWING. 41. Suppose it is desired to determine from Fig. 10 how far the station point lies in front of the picture plane. This is a horizontal distance, and therefore will he shown by the distance between the horizontal projection of the station point and the horizontal projection of the picture plane, or, in other words, by the distance between SP H and HPP. 42. The point a is a certain distance above or below the plane of the horizon. This is a vertical distance , and will be shown by the distance between the vertical projection of the point a and the vertical projection of the plane of the horizon; in other words, by the distance between a Y and YH. It will be seen that in Fig. 10 the point a lies below the plane of the horizon. 43. If it be desired to find how far in front or behind the picture plane the point a lies, this is a horizontal distance , and will be shown by the distance between the horizontal projection of the picture plane and horizontal projection of the point a , that is, by the distance between HPP and a 11 . In Fig. 10 the point a lies behind the picture plane. 44. The distance between the plane of the ground and the plane of the horizon is a vertical distance, and will be shown by the distance between the vertical projection of the plane of the horizon and the vertical projection of the plane of the ground ; i.e., the distance between YH and YH X . The distance between the observer’s eye and the jfiane 0 f the ground is also a vertical dis- tance, and will be shown by the distance between SP V and YH X ; but as SP V must always be found in YH, the distance of the observer’s eye above the plane of the ground will always be shown by the distance between VH and YH X . 45. To find the perspective of the point a, Fig. 10, draw the visual ray through the point, and find where this visual ray pierces the picture plane (§ 24/). The horizontal projection of the visual ray is shown by the line R H drawn through the horizontal projection SP H of the observer’s eye and the horizontal pro- jection a H of the point a. The vertical projection of the visual ray is shown by the line R v drawn through the vertical projec- tion SP V of the observer’s eye and the vertical projection a Y of the point a. This visual ray pierces the picture plane at the point a p on R v vertically in line with the point where 268 PERSPECTIVE DRAWING. 21 R H crosses HPP (§§ 35 and 36). a v is the perspective of the point a. Note. — To find where any line, represented by its horizon- tal and vertical projections, pierces the picture plane, is one of the most used and most important problems in perspective projec- tion. The point where any line pierces the picture plane will always be found on the vertical projection of the line, vertically above or below the point where the horizontal projection of the line crosses HPP (§§ 35 and 36). NOTATION. 46. In order to avoid confusion between the vertical, hori- zontal, and perspective projections of the points and lines in the drawing, it becomes necessary to adopt some systematic method of lettering the different points and lines. The following method will be found convenient, and has been adopted in these notes. If the student will letter each point or line as it is found, in accordance with this notation, he will be able to read his drawings at a glance, and any desired projection of a point or line may be recognized instantly. The picture plane (or vertical coordinate) is indicated by the capital letters PP. The plane of the horizon (or horizontal coordinate) is indi- cated by the capital letter H. A point in space is indicated by a small letter. The same small letter with an index v , H , or p , indicates its vertical , horizontal , or perspective projection, respectively. A line in space is indicated by a capital letter, usually one of the first letters in the alphabet. The same capital letter with an index v , H , or r , indicates its vertical , horizontal , or perspective projection, respectively. All lines which belong to the same system may be designated by the same letter, the different lines being distinguished by the subordinate v 2 , 3 , etc., placed after the letter. The trace of a plane upon the picture plane is indicated by a capital letter (usually one of the last letters in the alphabet) with a capital V placed before it. 269 22 PERSPECTIVE DRAWING. The same letter preceded by a capital IT indicates the trace of the plane upon the horizontal coordinate. The perspective of the vanishing trace of a system of planes is indicated by a capital letter preceded by a capital T. The perspective of the vanishing point of a system of lines is indicated by a small v with an index corresponding to the letter of the lines which belong to the system. PP = vertical coordinate, or picture plane. HPP = horizontal trace of the vertical coordinate, or picture plane. H = horizontal coordinate, or plane of the horizon. VH =s vertical trace of the horizontal coordinate, or plane of the horizon. H 1 = plane of the ground. VH 1 = vertical trace of the plane of the ground. a = point in space. a Y = vertical projection of the point. q H S horizontal projection of the point. a? = perspective projection of the point. A = line in space. A v = vertical projection of the line. A p = perspective projection of the line. VS = trace of the plane S upon PP (vertical trace). ITS = trace of the plane S upon H (horizontal trace). TS = perspective of the vanishing trace of the plane S. (See Note I below.) v A = perspective of the vanishing point of a system of lines, the elements of which are lettered A 1? A 2 , A 3 , A 4 , etc. (See Note 2 below.) Note 1. — A plane in space may also be designated by the letters of any two lines which lie in it. Thus, the plane AH would be a plane determined by the two lines A and B. TAB would indicate the perspective of the vanishing trace of the plane. Note 2. — A straight line may be designated by the letters of any two points which lie in it. Thus, the line ab would be a straight line determined by the two points a and b. v ab would indi- cate the perspective of the vanishing point of the line. It is some- times convenient to use this notation in place of the general one. 270 PERSPECTIVE DRAWING. ELEMENTARY PROBLEMS. 47. PROBLEM I. Fig. 11. To find the perspective of a point. The point to be situated behind the picture plane, and above the plane of the horizon. The observer’s eye to be in front of the picture plane. First assume HPP and VH (§ 40). These lines may be drawn anywhere on the paper, HPP usually being placed some distance above VH, in order to avoid confusion between horizontal and vertical projections. The position of the point with respect to the coordinate planes must now be established by means of its verti- cal and horizontal projections. a Y located above VH will rej>- resent the vertical projection of the point. Its horizontal projection must be vertically in line with a Y ; and since the point is to be behind the picture plane, its horizontal projection must be behind the horizontal projection of the picture plane, i.e., i" behind HPP. Next establish the position of the observer’s eye, or station point. Its vertical projection (SP V ) may be assumed anywhere in VH. Its horizontal projection (SP H ) must be verti- cally in line with SP V and J" in front of HPP. The perspective of the point a will be where the visual ray through the point pierces the picture plane. A line R H drawn through SP H and & H will be the horizontal projection of this visual ray. Its verti- cal projection will be the line R v drawn through SP V and a Y . The perspective a v of the point will be found on R v vertically in line with the intersection of R H and HPP (§ 45, note). Com- pare with the construction shown in Fig. 10 and Fig 8. 271 24 PERSPECTIVE DRAWING. 48. Figs. 12, 13, and 14 illustrate this same problem. In Fig. 12, the point a, as shown by its vertical and horizon- tal projections, is situated below the plane of the horizon and 1" behind the picture plane. a v is the perspective of the point. HPP Fig. 13 HFF Fig. 14 In Fig. 13, the point a is above the plane of the horizon and in front of the picture plane, a? is its perspective. In Fig. 14, the point a is below the plane of the horizon and 4" in front of the picture plane. a p is its perspective. 49. PROBLEM II. Fig. 15. To find the perspective of a line, the line being determined by its vertical and horizontal projections. Let HPP and VH be given as indicated in the figure. Let A H represent the horizontal projection of the line, its two ex- tremities being represented by a n and 6 H , respectively. Similarly, let A v be the vertical projec- tion of the line, a Y and b Y being the vertical projections of its extremities. Let the position of the observer’s eye be as indicated by SP V and SP H . The perspective of the point a has been found by Problem I. at a ¥ . The per- spective of the point b has been found by Problem I. at b T . The line (A p ), joining a v and 6 P , will be the perspective of the given line. (See note under § 23.) 272 PERSPECTIVE DRAWING. 50. PROBLEM III. Fig. 16. Having given the vertical and horizontal projection of any line, to find the perspective of its vanishing point. Let the line be given by its vertical ancl horizontal projections (A v and A H ), as indicated in the figure. SP V and SP H represent the position of the observer’s eye. To find the perspective of the vanishing point of any line, draw through the observer’s eye an element of the system to which the line belongs, and find where this element pierces the picture plane (§ 24 rf). Through SP H draw A X H parallel to AH, and through SP V draw A x v parallel to A v . A X H and A x v represent the two projections of a line passing through the observer’s eye and parallel to A H A V . This line pierces the picture plane at v K , giving the perspective of the required vanish- ing point (§ 45, note). The perspectives of all lines parallel to A V A H will meet at v K . Figs. 17 and 18 illustrate this same problem. 51. In Fig. 17, the line, as shown by its two projections, is a horizontal one ; hence, A \ drawn through SP V coincides with YH, and the vanishing point for the system of the lines must be found on YH at as indicated (§ 24 c ). Note. — Systems of lines which vanish upward will have their vanishing points above YH. Systems of lines which vanish downward will have their vanishing points below YH (§ 16). HPP Fig. 18 SP" VH A V !- V A < § 273 26 PERSPECTIVE DRAWING. 52. In Fig. 18, the given line is perpendicular to the picture plane ; hence, A x v must be a jioint coincident with SP V ; and as v K will always he found on A x v , the vanishing point of the line must coincide with SPV Note. — In a perspective drawing, the vanishing point for a system of lines perpendicular to the picture plane will always coincide with the vertical projection of the observer’s eye. METHOD OF THE REVOLVED PLAN. 58. PROBLEM IV. Fig. 19. To find the perspective of a rectangular block resting upon a horizontal plane 1" below the level of the eye, and turned so that the long side of the block makes an angle of 3o° with the picture plane. The block is shown in plan and elevation at the left of the figure. The. first step will be to make an auxiliary horizontal pro- jection of the block on the plane of the horizon, showing the exact position of the block as it is to be seen in the perspective projec- tion. This auxiliary horizontal projection is really a revolved plan of the object, and is called a Diagram. It is the general rule, in making a perspective projection, to place the object behind the picture plane with one of its principal vertical lines lying in the picture plane (24 li ). HPP is usually drawn near the upper edge of the paper, leaving just room enough behind to place the auxiliary plan or diagram. In the figure the diagram is shown in the required position, i.e., with one of its long sides ( ccbfe ) making an angle of 30° with the picture plane. The vertical edge ( ae ) of the block is supposed to lie in the picture plane. VH may now be drawn parallel to HPP at any convenient distance from it, as indicated. YH L , the vertical trace of the plane on which the block is supposed to rest, should be assumed in accord- ance with the given data, i.e., 1" below YH (§ 44). The position of the observer’s eye should next be established. SP H is its horizontal projection, and shows by its distance from HPP the distance in front of the picture plane at which the ob- server is supposed to stand. SP V is its vertical projection, and must always be found in YH. In this problem the station point is 1 in front of the picture plane. 274 PERSPECTIVE DRAWING. Note. — As a general rule, it is well to assume the station point on a vertical line half way between two lines dropped from the extreme edges of the diagram, as indicated. This is not necessary, but, as will be explained later,. it usually insures a more pleasing perspective projection. Next find the vanishing points for the different systems of lines in the object (§ 12). There are three systems of lines in the block, formed by its three sets of parallel edges. 1st. A system formed by the four horizontal edges vanishing to the right : ab , ef, dc , and kg. 2d. A system formed by the four horizontal edges vanishing towards the left: ad, ek , be, and fg. 3d. A system formed by the four vertical edges. First find the vanishing point for the system parallel to ab by drawing through the station point a line parallel to ab and finding where it pierces the picture plane (24 g). A 11 drawn through SP ir is the horizontal projection of such a line. Its ver- tical projection (A v ), drawn through SP V , will coincide with VII, and its vanishing point will be found on VH at v ab (§51). All lines in the perspective of the object that are parallel to ab will meet at v ah (§ 24 a). In a similar manner find v &d , which will be the vanishing point for all lines parallel to ad. 54. If the method for finding any vanishing point is applied to the system of vertical lines, it will be found that this vanishing point will lie vertically over SP V at infinity. That is to say, since all vertical lines are parallel to the picture plane, if a ver- tical line is drawn through the station point, it will never pierce the picture plane. Therefore (24 g'), the perspective of the van- ishing point of a vertical line cannot be found within any finite limits, but will be vertically over SP V , and at an infinite distance from it. In a perspective projection all vertical lines are drawn actually vertical , and not converging towards one another. Note. — This is true of all lines in an object which are parallel to the picture plane. Thus, the perspective of any line which is parallel to the picture plane, ivill actually be parallel to the line itself ; and the perspectives of the elements of a system of lines parallel to the picture plane, will be drawn parallel to, and not con- verging towards , one another. That this must be so, is evident, 28 PERSPECTIVE DRAWING. since, if the perspectives of such a system of lines did converge towards* one another, they would meet within finite limits. But it has just been found that the perspective of the vanishing point of such a system is at infinity. The perspectives of the elements of any system can meet only at the perspective of their vanish- ing point, and must, therefore, in a system parallel to the picture plane, be drawn parallel to one another. The directions of the perspectives of all lines in the object have now been determined, and will be as follows : All lines parallel to ah will meet at v ab . All lines parallel to ad will meet at v* a . All vertical lines will be drawn vertical. Since the point e is in the base of the object, it lies on the plane of the ground, and also, since the line ae lies in the picture plane, the point e must lie on the intersection of the plane of the ground with the picture plane. Therefore, the point e must lie in VH , and must be vertically under the point e in the diagram. Since the point e lies in the picture plane, it will be its own per- spective ; and e v will be found on VI/, vertically under e in the diagram, as shown in the figure. From e v the perspective of the lower edges of the cube will vanish at v Ah and v ad , respectively, as indicated. / p is the perspective of the point/, and will be found on the lower edge of the block, vertically under the intersection of HPP with the horizontal projection of the visual ray drawn through the point / in the diagram. Similarly, Jc v is found on the lower edge of the block, verti- cally under the intersection of HPP and the visual ray drawn through the point k in the diagram. Vertical lines drawn through / p , e v , and & p , will represent the perspectives of the visible vertical edges of the block. The edge e v a v being in the picture plane will be its own per- spective, and show in its true size (§24 A). Therefore, a v may be established by making the distance e v a v equal to e Y a v as taken from the given elevation. From a F two of the upper horizontal edges of the block will vanish at v ah and v ad , respectively, estab- lishing the points h v and c2 p , by their intersections with the vertical edges drawn through k v and / p , respectively. Lines drawn through 278 PERSPECTIVE DRAW I XG. 20 p o p equal to the true height of the block, as given by the elevation. Two lines drawn through o p and p F respectively, and vanishing at v ad , will represent the perspectives of the upper and lower edges of the face cbf \ produced. The perspective (6 P ), of the point b, will be found on the perspective of the upper edge of the face cbf, verti- cally below the intersection of HPP with the horizontal projection of a visual ray drawn through the point b in the diagram. A ver- tical line through b v will intersect the lower horizontal edge of the face cbf in the point / p . Lines drawn respectively through b T and / p , vanishing at v ab , will establish the perspectives of the upper and lower horizontal edges of the face abfe The points a F and e F will be found vertically under the points a and e in the diagram. The remainder of the perspective projection may now easily be determined. 5T. The perspectives of any points on the faces of the block may be found by means of the diagram and one of the lines of measures. Let the points g Y , h Y , k Y , and l Y , in the given elevation, de- termine a square on the face abfe of the block. Let the points g, h, k, and l, represent the position of the square in the diagram. Extend the upper and lower horizontal edges of the square, as shown in elevation, until they intersect the vertical edge a Y e Y in the points t Y and v Y . To determine the perspective of the square, lay off on a F e F , which is a line of measures for the face abfe , the divisions t F and v F taken directly from the elevation. Two lines drawn through t F and v F respectively, vanishing at v ab , will represent the perspectives of the upper and lower edges (pro- duced) of the square. g F will be found on the perspective of the upper edge, vertically under the intersection of HPP with the horizontal projection of a visual ray drawn through the point g in the diagram. The position of k F may be established in a similar manner. Vertical lines drawn through g F and k F respectively, will complete the perspective of the square. 58. The auxiliary line of measures o F p ? might have been used instead of a F e F . In this case, o F p> F should be divided by the points iv F and y F , in the same way that ae, in elevation, is divided 280 PERSPECT IYE DR A WING. 31 by the points t and v. Through w v and y v , draw horizontal lines lying in the plane cbf, for which cPpP is a line of measures. These lines will vanish at v ad , and intersect the vertical edge b l f v of the block. From these intersections draw horizontal lines lying in the plane abef, vanishing at v* h , and representing the upper and lower edges of the square. The remainder of the square may be determined as in the previous case. In a similar manner, the auxiliary line of measures m l 'n v might have been used to determine the upper and lower edges of the square. This construction has been indicated, and the student should follow it through. 59. It sometimes happens that no line in the object lies in the picture plane. In such a case there is no principal line of measures, and some vertical plane in the object must be extended until it intersects the picture plane, forming by this intersection an auxiliary line of measures. Fig. 21 illustrates such a case. A rectangular block, similar to those shown in Figs. 19 and 20, is 283 PERSPECTIVE DRAWING. situated some distance behind the picture plane, as indicated by the relative positions of HPP and the diagram. Its perspective projection will evidently be smaller than if the vertical edge ae were in the picture plane, as was the case in Figs. 19 and 20, and the perspective of ae will evidently be shorter than the true length of ae. There is, therefore, no line in the object that can be used for a line of measures. It becomes necessary to extend one of the vertical faces of the block until it intersects the picture plane, and shows by the intersection its true vertical height. Thus, the plane abfe has been extended, as indicated in the diagram, until it intersects the picture plane in the line mn. This intersection is an auxiliary line of measures for the plane abfe , and m F n F shows the true vertical height of this plane. Either of the other vertical faces of the block, as well as the face abfe, might have been extended until it intersected the picture plane, and formed by this intersection a line of measures for the block. The vanishing points for the various systems of lines have been found as in the previous cases. From m F and n F , the horizontal edges of the face abfe vanish to v ah . a F will be found on the upper edge of this face, vertically below the intersection of HPP with the horizontal projection of the visual ray through the point a in the diagram. A vertical line through a F will represent the perspective of the nearest verti- cal edge of the block, and will establish the position of e F . In a similar manner, b F will be found vertically below the intersection of HPP with the horizontal projection of the visual ray through the point b in the diagram. A vertical line through b p will establish f F , and complete the perspective of the face abfe. Having found the perspective of this face, the remainder of the block may be determined as in the previous problems. Note. — Instead of being some distance behind the picture plane, the block might have been wholly or partly in front of the picture plane. In any case, find the intersection with the picture plane of some vertical face of the block (produced, if necessary). This intersection will show the true vertical height of the block. At this point the student should solve Plate II. 284 PERSPECTIVE DRAWING. 33 00. PROBLEM V. Fig. 22. To find the perspective of a house, the projections of which are given. The plan, front, and side elevations of the house are shown in the figure. The side elevation corresponds to the projection on the profile plan, used in the study of projections. This prob- lem is a further illustration of the method of revolved plan and of the use of horizontal vanishing points and auxiliary lines of measures. It is very similar to the three previous problems on the rectangular blocks. The first step in the construction of the perspective projec- tion is to make a diagram (§ 53) which shall show the horizontal projections of all the features that are to appear in the drawing. The diagram should be placed at the top of the sheet, and turned so that the sides of the house make the desired angles with the picture plane. In Fig. 22 the diagram is shown with the long side making an angle of 30° with the picture plane. The roof lines, the chimney, and the positions of all windows, doors, etc., that are to be visible in the perspective projection, will be seen marked on the diagram. The nearest vertical edge of the house is to lie in the picture plane. This is indicated by drawing HPP through the corner of the diagram which represents this nearest edge. VH may be chosen at any convenient distance below HPP. The position of the station point is shown in the figure by its two projections SP V and SP H . SP V must always be in VH. The* distance between SP H and HPP shows the distance of the observer’s eye in front of the picture plane (§ 43). •y ab and v ad may be found as in the preceding problems. The position of the plane on which the object is to rest should next be established by drawing VH L , the distance between VH and VHj showing the height of the observer’s eye above the ground (§ 44). In addition to the plane of the ground represented by VH lv a second ground plane, represented by VH 2 , has been chosen some distance below VHj. In the figure, two perspective projections have been found, one resting on each of these two ground planes. The perspective which rests upon the plane represented by VIIj shows the house as though seen by a man standing with his eyes 285 34 PERSPECTIVE DRAWING. nearly on a level with the tops of the windows (§ 29). The view which rests on the plane represented by VH 2 shows a bird’s-eye view of the house, in which the eye of the observer (always in VH) is at a distance above the plane on which the view rests, equal to about two and one-half times the height of the ridge of the house above the ground. The&3 two perspective projections illustrate the effect of changing the distance between VH and the vertical trace (§ 34, note) of the plane on which the perspective projection is supposed to rest. The construction of both views is exactly the same. The following explanation applies to both equally well, and the student may consider either in s-tudying the problem. 61. We will first neglect the roof of the house, and of the porch. The remaining portion of the house will be seen to con- sist of two rectangular blocks, one representing the main body of the house, and the other representing the porch. The block representing the main part of the house occupies a position exactly similar to that of the block shown in Fig. 19. First consider this block irrespective of the remainder of the house. A vertical line dropped from the corner of the diagram that lies in HPP will be a measure line for the block, and will establish, by its intersection with VH 1 (or VH 2 ), the position of the point e F , in exactly the same way that the point e F in Fig. 19 was established. e F a F shows the true height of the part of the house under consideration, and should be made" equal to the cor- responding height a v e Y , as shown by the elevations. The rec- tangular block representing the main part of the house may now be drawn exactly as was the block in Fig. 19, Problem IV. 62. Having found the perspective of the main part of the house, the porch (without its roof) may be considered as a second rectangular block, no vertical edge of which lies in the picture plane. It may be treated in a manner exactly similar to that of the block shown in Fig. 21, § 59. We may consider that the rear vertical face of the block, which forms the porch of the house (y, y), has been extended until it intersects the picture plane in the line ae , giving a line of measures for this face, just as in Fig. 21 the nearest vertical face of the block was extended until it intersected the picture plane in the line of measures mn. 5386 PERSPECTIVE DRAWING. On e T a v , make e p e p equal to the true height of the vertical wall of the porch, as given by the elevation. A line through r p , vanishing at v ab , will be the perspective of the upper horizontal edge of the rear face of the block which forms the porch. The line through e p , vanishing at y ab , which forms the lower edge of the front face of the main body of the house, also forms the lower edge of the rear face of the porch. Through the point h in the diagram, draw a visual ray, and through the intersection of this visual ray with HPP drop a vertical line. Where this vertical line crosses the upper and lower horizontal edges of the rear face of the porch, will establish the points oints for systems of oblique lines in the object, in addi- tion to the vanishing points for the horizontal systems. Take, for example, the lines g T y v and x^z v in Fig. 22. The perspective projections of these two lines were obtained by first finding the points ad , and v fd (§ 24 d). Jf all three of these vanishing points do not lie in a straight line, it shows some inaccuracy, either in draughting or in the method used in finding some of the vanishing points. The student should not be content until the accuracy of his work is proved by draw- ing the vanishing trace of each plane in the object through the vanishing points of all lines that lie in that plane. The plane M contains the lines fd, gc, and do. The last line belongs to the system ab, and hence its vanishing point is v' Ah . The vanishing trace (TM) of the plane M must pass through v {d , v gc , and v ab . Similarly, the vanishing trace (TP) of the plane P must pass through v gc , t> bg , and v Rd . TN must pass through v ab , v af , and v hg . TQ must pass through v hk and t; ad . TR must pass through v kl and v Ad . 73. The vanishing trace of a vertical plane will always be a vertical line passing through the vanishing points of all lines which lie in the plane. Therefore, the vanishing trace of the vertical planes in the house that vanish towards the left will be represented by a vertical line (TS) passing through v Ad . The vanishing trace of the vertical planes of the house that vanish towards the right will be represented by a vertical line (TT) passing through y ab . As the vertical plane which forms the face of the porch belongs to this system, and as this plane also contains the lines hk and Id , TT will be found to pass through v hk and v kl as well as v ab . 74. It will be noticed that the vanishing points for the lines mn and on have not been found. These vanishing points might have been found in a manner exactly similar to that in which the other vanishing points were found, or they may be determined now, directly from the vanishing traces already drawn, in the following manner : — The line mn is seen to be the line of intersection of the two planes N and Q. Therefore (§ 24 e) v mn must lie at the inter- section of TN and TQ. For a similar reason, v on must lie at the intersection of TN 299 44 PERSPECTIVE DRAWING. and TR. TN and TR do not intersect within the limits of the plate, but they are seen to converge as they pass to the ieft, and, if produced in that direction, would meet at the vanishing point for the line on. T5. Having found v ab , v ad , v bg , and v m , TN could have been drawn through v ab and v bg ; and TO could have been drawn through v ad and v fd . As af is the intersection of the two planes N and O, v af could have been found at the intersection of TN and TO without actually constructing this vanishing point. Similarly, v gG could have been determined by the intersec- tion of TM and TP. By an examination of the plate, the student will notice that the vanishing point for each line in the object is formed at the intersection of the vanishing traces of the two planes of which the line forms the intersection. Thus, the line ad forms the inter- section between the plane O and the left hand vertical face of the house. v ad is found at the intersection of TO and TS. The line fg , which forms the ridge of the roof, is the inter- section of the planes M and N. The vanishing point for fg is v ab , and TM and TN will be found to intersect at v* h . v bk is found at the intersection of TQ and TT, r kl is found at the inter- section of TR and TT, etc. It will be noticed also that the two lines hk and kl lie in the same vertical plane, and make the same angle with the horizontal, one vanishing upward, and one vanishing downward. Since both lines lie in the same vertical plane, both of their vanishing points will be found in the vertical line which represents the vanishing trace of that plane. Also, since both lines make equal angles with the horizontal, the vanishing point of the line vanishing upward will be found as far above VH as the vanishing point of the line vanishing downward is below VH. In a similar way, the line bg vanishes upward, and the line fd vanishes downward ; each making the same angle with the horizontal (as shown by the given plan and elevation). These two lines do not lie in the same plane, but may be said to lie in two imaginary vertical planes which are parallel to one another. Their vanishing points will be seen to lie in the same vertical line, v hg being as far above VH as ^ fd is below it. 300 PERSPECTIVE DRAWING 45 As a general statement, it may be said that if two lines lie in the same or parallel vertical planes, and make equal angles with the horizontal, one vanishing upward and the other van- ishing downward, the vanishing points for both lines will be found vertically in line with one another, one as far above VH as the other is below it. This principle is often of use in constructing the vanishing point diagram. Thus, having found F lk , v kl could have been determined immediately by making it lie in a vertical line with F lk , and as far below VH as F lk is above it. VANISHING POINT DIAGRAM. 76. The somewhat symmetrical figure formed by the vanish- ing traces of all the planes in the object, together with all vanishing points, HPP, and the vertical and horizontal projec- tions of the station point, is called the Vanishing Point Diagram of the object. 77. Having found the complete vanishing point diagram of the house, the perspective projection may be drawn. VH t may be chosen in accordance with the kind of a perspective projection it is desired to produce (§ 29). In order that all the roof lines may be visible, VHj has been chosen far below VH. The result- ing perspective is a somewhat exaggerated bird’s-eye view. The point e p will be found on VIR, vertically under the point e in the diagram. a p e p lies in the picture plane, and shows the true height of the vertical wall of the house. From a v and e p , the horizontal edges of the walls of the main house vanish to v' Ah and v ad . The points d p , b p , m p , and o p are found on the upper hori- zontal edges of the main walls, vertically under the points where HPP is crossed by visual rays drawn through the points c?, b, m , and o in the diagram. Vertical lines from d p and b p complete the visible vertical edges of the main house. In a similar manner the perspective of the vertical walls of the porch is obtained. Each roof line vanishes to its respective vanishing point. a p f p vanishes at v at . f p d p vanishes at v fd . These two lines inter- 301 46 PERSPECTIVE DRAWING. sect in the point / p . The ridge of the main house passes through f p , vanishing at ^ ab . g p c p vanishes at v gc , passing through the point c p , which has already been determined by the intersection of the two upper rear horizontal edges of the main walls. b p g p vanishes at v hs , completing the perspective of the main roof. In the porch, h p k p vanishes at F lk , passing through the point A p , already determined by the vertical walls of the porch. k p l p passes through l p , and vanishes at v kl . From k? the ridge of the porch roof vanishes at v ad . From m p , a line vanishing at v mn will intersect the ridge in the point w p , and represent the intersec- tion of the roof planes Q and N. The vanishing point for o p n p falls outside the limits of the plate. o p m p may be connected with a line which, if the drawing is accurate, will converge towards both TN and TR, and, if produced, would meet them at their intersection. 78. While constructing the vanishing point diagram of an object, the student should constantly keep in mind the general statements made in the note under § 69. Plate IV. should now be solved. PARALLEL OR ONE=POINT PERSPECTIVE. 79. When the diagram of an object is placed with one of its principal systems of horizontal lines parallel to the picture plane, it is said to be in Parallel Perspective. This is illustrated in Fig. 24, by the rectangular block there shown. One system of horizontal lines in the block being parallel to the picture plane, the other system of horizontal lines must be perpendicular to the picture plane. The vanishing point for the latter system will be coincident with SP V (§ 52). The horizontal system that is parallel to the picture plane will have no vanishing point within finite limits (§ 54, with note ; also last paragraph of note under § 69). The third system of lines in the object is a vertical one, and will have no vanishing point within finite limits (§ 54). Thus, of the three systems of lines that form the edges of the block, only one will have a vanishing point within finite limits. This fact has led to the term One-Point Perspective, which is often applied to an object in the position shown in Fig. 24. As will be seen, this 302 47 PERSPECTIVE DRAWING. is only a special case of the problems already studied, and the construction of the perspective of an object in parallel perspective is usually simpler than when the diagram is turned at an angle with HPP. 80. The vertical face ( abfe ) of the block lies in the picture plane. It will thus show in its true size and shape (§ 24 A). The points e p and / p will be found on VHj vertically below the points e and /in the diagram. 81. Both the edges e T a v and f l b v are lines of measures, and will show the true height of the block, as given by the elevation. 82. The two lines a v b p and p , e F , and / p , the horizontal edges, which are perpendicu- lar to the picture plane, will vanish at v ad (coincident with SP V ). The rear vertical edges of the block may be found in the usual manner. 84. The lines a p b F , d F c p , e p f F , and h F g F , which form the hori- zontal edges parallel to the picture plane, will all be drawn paral- lel to one another (§ 54, note) ; and since the lines in space which they represent are horizontal, a p 6 p , d F c p , e r f p , and h F g F will all be horizontal (see last paragraph of note under § 69). All of the principles that have been stated in connection with the other problems will apply equally well to an object in parallel perspective. 85. Interior views are often shown in parallel perspective. One wall of the interior is usually assumed coincident with the picture plane, and is not shown in the drawing. For illustration, the rectangular block in Fig. 24 may be considered to represent a hollow box, the interior of which is to be shown in perspective. Assume the face ( a v b v f v e v ) that lies in the picture plane to be removed. The resulting perspective projection would show the interior of the box. In making a parallel perspective of an interior, however, VH is usually drawn lower than is indicated in Fig. 24, in order to show the inside of the upper face, or ceiling, of the interior. With such an arrangement, three walls, the ceiling, and the floor of the interior, may all be shown in the perspective projection. 86. Fig. 25 shows an example of interior parallel perspective. The plan of the room is shown at the top of the plate. This has been placed so that it may be used for the diagram, and save the necessity of making a separate drawing. The elevation of the room is shown at the left of the plate, and for convenience it has been placed with its lower horizontal edge in line with VHj. In this position all vertical dimensions in the object may be carried by horizontal construction lines directly from the elevation to the vertical line of measures (a F e p or b p f F> ) in the perspective projection. 87. The front face of the room ( 'a v b v f*e F ) f which is coinci- dent with the picture plane, may first be established. Each point 304 PERSPECTIVE DRAWING. 49 in the perspective of this front face will he found to lie vertically under the corresponding point in plan, and horizontally in line with the corresponding point in elevation. Thus, a F is vertically under a n , and horizontally in line with a y . All lines in the room which are perpendicular to the picture plane vanish at v ad (coincident with SP V ). Drawing visual rays from every point in the diagram, the corresponding points in the perspective projection will be verti- cally under the points where these visual rays intersect HPP. The construction of the walls of the room should give the student no difficulty. 88. In finding the perspective of the steps, the vertical heights should first be projected by horizontal construction lines from the elevation to the line of measures (a p e p ), as indicated by the divisions between e F and m. These divisions can then be carried along the left hand wall of the room by imaginary hori- zontal lines vanishing at v ad . The perspective of the vertical edge where each step intersects the left hand wall may now be determined from the plan. Thus, the edge s ? r p of the first step is vertically below the intersection of HPP with a visual ray drawn through the point s H in plan, and is between the two hori- zontal lines projected from the elevation that show the height of the lower step. The corresponding vertical edge of the second step will be projected from the plan in a similar manner, and will lie between the two horizontal lines projected from the elevation that show the height of the second step, etc. From s F the line which forms the intersection of the wall with the horizontal surface of the first step will vanish to t ,ad , etc. From r F the intersection of the first step with the floor of the room will be a line belonging to the same system as a F b F , and will therefore show as a true horizontal line. The point t F may be projected from the diagram by a visual ray, as usual. From t F the vertical edge of the step may be drawm till it intersects a horizon- tal line through s r , and so on, until the steps that rest against the side wall are determined. 89. The three upper steps in the flight rest against the rear wall. The three upper divisions on the line e ? m may be carried along the left hand wall of the room, as indicated, till they inter- 305 50 PERSPECTIVE DRAWING. sect the rear vertical edge of the wall, represented by the line d T h F . From these intersections the lines may he carried along the rear wall of the room, showing the heights of the three upper steps where they rest against the rear wall. The three upper divisions on the line e v m have also been projected across to the line f r b v , and from this line carried by imaginary horizontal lines along the right hand wall of the room to the plane N, across the plane N to the plane O, and from the plane O to the plane M. Thus, for illustration, the upper division, representing the height of the upper step, has been carried from rn toe; from c to g along the right hand face of the wall; from g to j along the plane N ; from j to k on the plane O, and from k to p v on the plane M. The jDoint p v is where the line which represents the height of the upper step meets a vertical dropped from the intersection of HPP with a visual ray through the point p H in the diagram. p v is one corner in the perspective of the upper step, the visible edges of the step being represented by a horizontal line, p v k , a line (y> p o p ) vanishing at v' Ad , and a vertical line drawn from p T between the two horizontal lines on the plane 11, which represent the height of the upper step. The point o T is at the intersection of the line drawn through y> p , vanishing through v ad , with the hori- zontal line on the rear wall drawn through the point n , and representing the upper step where it rests against the rear wall. The remaining steps may be found in a similar manner. The student should have no difficulty in following out the construction, which is all shown on the plate. 90. The position of the point t v on the line r v t v was deter- mined by projecting in the usual manner from the diagram. The position of t v might have been found in the following manner : In the figure the line e F f F is a line of measures (§ 81), and divisions on this line will show in their true size. Thus, if we imagine a horizontal line to be drawn through £ p , parallel to the wall of the room, it will intersect e T f T in the point u. Since e T u is on a line of measures, it will show in its true length. Thus, t F might have been determined by laying off e v u equal to the distance e H ?q taken from the plan, and then drawing through the point u a line van- 306 * PERSPECTI VE DRAWING. isliing at v ad . The intersection of this line with the horizontal line drawn through r v will determine t v . In a similar manner the vertical edges of the steps, where they intersect the plane M, might have been found by laying off from u, on e v f v , the divisions uv and vw taken from the plan. These divisions could have been carried along the floor by hori- zontal lines parallel to the sides of the room (vanishing at v ad ), to the plane M, and then projected vertically upward on the plane M, as indicated in the figure. Solve Plate Y. METHOD OF PERSPECTIVE PLAN. 91. In the foregoing problems the perspective projection has been found from a diagram of the object. Another way of con- structing a perspective projection is by the method of Perspective Plan. In this method no diagram is used, but a perspective plan of the object is first made, and from this perspective plan the per- spective projection of the object is determined. The perspective plan is usually supposed to lie in an auxiliary horizontal plane below the plane of the ground. The principles upon which its construction is based will now be explained. 92. In Fig. 26, suppose the rectangle a H b H c H d H to represent the horizontal projection of a rectangular card resting upon a horizontal plane. The diagram of the card is shown at the upper part of the figure. It will be used only to explain the construc- tion of the perspective plan of the card. First consider the line ad , which forms one side of the card. On HPP lay off from a , to the left, a distance ( ae ) equal to the length of the line ad. Connect the points e and d. ead is by construction an isosceles triangle lying in the plane of the card, with one of its equal sides ( ae ) in the picture plane. Now, if this triangle be put into perspective, the side ad, being behind the pic- ture plane, will appear shorter than it really is ; while the side ae, which lies in the picture plane, will show in its true length. Let VHj be the vertical trace of the plane on which the card and triangle are supposed to rest. The position of the station point is shown by its two projections SP H and SPY The vanish- 309 52 PERSPECTIVE DRAWING. ing point for the line ad will be found at v ad in the usual man- ner. In a similar way, the Vanishing point for the line ed , which forms the base of the isosceles triangle, will be found at v ed , as indicated. a v will be found on YHj vertically under the point a, which forms the apex of the isosceles triangle ead. The line a v d F will vanish at v ad . The point e F will be found vertically below the point e. e p d p will vanish at v etl , and determine by its intersection with a v d p the length of that line. e p a p d p is the perspective of the isosceles triangle ead. If the line ad in the diagram is divided in any manner by the points t, s, and r, the perspectives of these points may be found on the line a p d p in the following way. If lines are drawn 310 PERSPECTIVE DRAWING. through the points t, s, and r in the diagram parallel to the base de of the isosceles triangle ( ead ), these lines will divide the line ae in a manner exactly similar to that in which the line ad is di- vided. Thus, aw will equal at , wv will equal ts, etc. Now, in the perspective projection of the isosceles triangle, a p e p lies in the picture plane. It will show in its true length, and all divisions on it will show in their true size. Thus, on a p e p lay off a p w p , iv p v p , and v p u p equal to the corresponding distances at , ts, and $>% given in the diagram. Lines drawn through the points iv p , v p , and u p , vanishing at v ed , will be the perspective of the lines wt , vs , and ur in the isosceles triangle, and will determine the positions of t p , s p , and r p , by their intersections with a p d p . 93. It will be seen that after having found r ad and v ed , the perspective of the isosceles triangle can be found without any reference to the diagram. Assuming the position of a p at any desired point on VHj, the divisions a p , w p , v p , u p , e p may be laid off from a p directly, making them equal to the corresponding divisions « H , t H , s 11 , r H , d n , given in the plan of the card. A line through a p vanishing at v ad will represent the perspective side of the isosceles triangle. The length of this side will be determined by a line drawn through e p , vanishing at v ed . The positions of t p , s p , and r F may be determined by lines drawn through w p , v p , and u p , van- ishing at v ed . 94. It will be seen that the lines drawn to r ed serve to measure the perspective distances a p t p , t p s p , s p r p , and r p d F , on the line a p d p , from the true lengths of these distances as laid off on the line a p e p . Hence the lines vanishing at v ed are called Measure Lines for the line a p d p , and the vanishing point v ed is called a Measure Point for a p d p . 95. Every line in perspective has a measure point, which may be found by constructing an isosceles triangle on the line in a manner similar to that just explained. Note. - — The vanishing point for the base of the isosceles triangle always becomes the measure point for the side of the isosceles triangle which does not lie in HPP. 96. All lines belonging to the same system will have the same measure point. Thus, if the line be , which is parallel to ad, be continued to meet HPP, and an isosceles triangle Qcku) con 311 64 PERSPECTIVE DRAWING. structed on it, as indicated by the dotted lines in the figure, the base ( uc ) of this isosceles triangle will be parallel to de, and its vanishing point will be coincident with v de . 97. There is a constant relation between the vanishing point of a system of lines and the measure point for that system. Therefore, if the vanishing point of a system of lines is known, its measure point may be found without reference to a diagram, as will be explained. In constructing the vanishing points v ad and v ed ,fh was drawn parallel to ad,fg was drawn parallel to ed, and since hg is coinci- dent with HPP, the two triangles ead and fhg must be similar. As ae was made equal to ad in the small triangle, hf must be equal to lig in the large triangle ; and consequently v ed , which is as far from v ad as g is from h, must be as far from ^ ad as the point/ is from the point h. If the student will refer back to Figs. 8, 9, and 9a, he will see that the point li bears a similar relation in Fig. 26 to that of the point m H in Figs. 8, 9, and 9a, and that the point li in Fig. 26 is really the horizontal projection of the vanishing point v ad . (See also § 32.) Therefore, as v ed is as far from v ad as the point h is from the point/, we may make the following statement, which will hold for all systems of horizontal lines. 98. The measure point for any system of horizontal lines will be found on VII as far from the vanishing point of the system as the horizontal projection of that vanishing point is distant from the hori- zontal proj ection of the station point. Note. — In accordance with the construction shown in Fig. 26, SP V will always lie between the vanishing point of a system and its measure point. 99. The measure point of any system of lines is usually de- noted by a small letter m with an index corresponding to its re- lated vanishing point. Thus, m ab signifies the measure point for the system of lines vanishing at v ah . 100. The vanishing point for ab in Fig. 26 has been found at ^ ab . The point n , in HPP, is the horizontal projection of this vanishing point. The measure point (m ab ) for all lines vanishing at v ah will be found on VH, at a distance from v ah equal to the distance from n to SP H (98). In accordance with this statement, 312 PERSPECTIVE DRAWING. ra ab has been found by drawing an arc with n as center, and with a radius equal to the distance from n to SI )ir , and dropping from the intersection of this arc with IIPP a vertical line. m &h is found at the intersection of this vertical line with VII. 101. The perspective of ab has been drawn from a v , vanishing at v ab . a v b l on VI^ is made equal to the length of a n b 11 given in the plan of the card. A measure line through vanishing at m ab , will determine the length of a?b v . A line from b v vanishing at v ad , and one from cF vanishing at v* h , will intersect at u < J Q □ ■ i 1=1 1 \ □ Id I < z r > PERSPECTIVE DRAWING, 71 PLATE VI. PROBLEM XVIII. Construct, by the method of perspective plan, a perspective projection of the object shown in the given plan and elevations. HPP and VH are to be taken coincident (§ 107), as in- dicated on the plate. The vanishing points (v ab and v ad ) for the two systems of horizontal lines in the object are given. The line ab is to make an angle of 60° with the picture plane. VH 2 is the vertical trace of the horizontal plane on which the perspective plan is to be drawn. The corner (« p ) of this plan is given. The perspective projection of the object is to rest on the horizontal plane determined by VH!. An oblique projection of the object is given to assist in read- ing the plan and elevations. The student may use his discretion in lettering this plate. No letters are required except those indicating the positions of the station point and the measure points. 337 plate: vi date: RENAISSANCE CAPITA!.. An example of charcoal drawing. FREEHAND DRAWING, 1. The Value cf Freehand Drawing to an Architect. Out- side of its general educational value freehand drawing is as abso- lutely essential to the trained architect as it is to the professional painter. It is obviously necessary for the representation of all except the most geometric forms of ornament, and it is equally important in making any kind of a rapid sketch, either of a whole building or a detail, whether from nature or in the study of plans and elevations. It is perhaps not so generally understood that the training it gives in seeing and recording forms accurately, culti- vates not only the feeling for relative proportions and shapes, but, also, that very important architectural faculty — the sense of the third dimension. The essential problem of most drawing is to express length, breadth, and thickness on a surface which has only length and breadth. As the architect works out on paper, which has only length and breadth, his designs for buildings which are to have length, breadth, and thickness, he is obliged to visual- ize; to see with the mind’s eye the thickness of his forms. lie must always keep in mind what the actual appearance will be. The study of freehand drawing from solid forms in teaching the representation on paper of their appearance, stimulates in the draughtsman his power of creating a mental vision of any solid. That is, drawing from solids educates that faculty by means of which an architect is able to imagine, before it is erected, the appearance of his building. 2. Definition of Drawing. A drawing is a statement of cer- tain facts or truths by means of lines and tones. It is nothing more or less than an explanation. The best drawings are those in which the statement is most direct and simple; those in which the explanation is the clearest and the least confused by the introduc- tion of irrelevant details. A drawing never attempts to tell all the facts about the form depicted, and each person who makes a drawing selects not only the leading truths, but also includes those characteristics which 341 0 FREEHAND DRAWING appeal to him as an individual. The result is that no two people make drawings of the same subject exactly alike. 3. The Eye and the Camera. The question immediately arises: Why should we not draw all that we see; tell all that we know about our subject ? Since the photograph does represent, with the exception of color, all that we see and even more, another question is raised: AVliat is the essential difference between a photograph of an object and a drawing of an object ? These are questions which bring us dangerously near the endless region of the philosophy of fine arts. Stated simply and broadly, art is a refuge invented by man as an escape from the innumerable and bewildering details of nature which weary the eye and mind when we attempt to grasp and comprehend them. Without going into an explanation of the differences in struct- ure between the lens of a camera and the lens of the eye, it may be accepted as a general statement that in spite of apparent errors of distortion the photograph gives us an exact reproduction of nature. Every minutest detail, every shadow of a shade, is pre- sented as being of equal importance and interest, and it is easy to demonstrate that the camera sees much more detail than the human eye. In any good photograph of an interior the patterns on the walls and hangings, the carving and even the grain and texture of woods are all presented with equal clearness. In order to perceive any one of those details as clearly with the eye it would be neces- sary to focus the eye on that particular point, and while so focused all the other details of the room would appear blurred. The camera, on the contrary, while focused at one point sees all the others with almost equal clearness. This fact alone is enough to demonstrate tlie danger of assuming that the photograph is true to the facts of vision. Again, a photograph of an antique statue will exaggerate the im- portance of the weather stains and disfigurements at the expense of the subtle modelling of the muscular parts which the eye would instinctively perceive first. Nature, then, and the photograph from nature, is a bewilder- ing mass of detail. The artist is the man of trained perceptions who, by eliminating superfluous detail and grasping and present- ing only the essential characteristics, produces a drawing in which we see the object in a simplified but nevertheless beautiful form. 342 FREEHAND DRAWING 3 In looking at the drawing we become conscious of the subject and its principal attributes; we comprehend and realize these with far less effort of the mind and eye than we should expend in taking in and comprehending the real object or a photograph of it. Com- pared to nature it is more restful and more easily understood, and the ease with which it is comprehended constitutes, the psycholo- gists say, a large part of the pleasure we take in art; it certainly explains why we enjoy a drawing of an. object when we may take no pleasure in the object itself, or a photograph of it. 4. Restraint in Drawing. The practical application of the preceding broad definition is neither difficult nor abstruse. The beginner in drawing usually finds his work swamped in a mass of detail, because his desire is to be absolutely truthful and accurate, and the more he has read Ruskin* and writers of his school the more does he feel that art and nature are one, and that the best drawing is that which most successfully reproduces nature with photographic fidelity. It maybe taken for granted that a drawing must be true; true to nature. But truth is at best a relative term, and while it may be said that every normal eye sees prac- tically the same, yet, after all, the eye sees only what it is trained to see. It is the purpose of all teaching of drawing to train the eye to see and the hand to put down the biggest and most impor- tant truths and to sacrifice small and unimportant details for the sake of giving greater emphasis or accent to the statement of the larger ones. “Art lives by sacrifices” is the expression of the French, the most artistic nation of modern times. The experience of the beginner is very practical testimony to the truth of the expression, for he very soon realizes that he lias not the ability, even if it were best, to draw all he sees, and he has to face the question of what to leave out, what to sacrifice. Sense will tell him that he must at all costs retain those elements which have the most meaning or significance, or else his drawing will not be in- telligible. So he is gradually taught to select the vital facta and make sure of them at least. It is true that the more accomplished the draughtsman becomes the greater will be his ability to suc- cessfully represent the lesser truths, the smaller details he sees, * Note.— A mple corroboration for all that is stated above may be found in Ruskin, but it is embedded in a mass of confusing and contradictory assertions. Ruskin is a very dangerous author for the beginner. 343 4 FREEHAND DRAWING because having trained his perception to the importance of grasping the big truths he has also attained the knowledge and ability to express the smaller facts without obscuring the greater ones. Nevertheless the question of what to sacrifice remains one of the most important in all forms of representation. One of the com- monest criticisms pronounced by artists on the work of their col- leagues is that “ he has not known when to stop”; the picture is overloaded and obscured with distracting detail. 5. Learning to See. It is very important that the student of drawing shall understand in the beginning that a very large part of his education consists in learning to see correctly. The power to see correctly and the manual skill to put down with accuracy what he sees — these he must acquire simultaneously. It is usually difficult at first to convince people that they do not naturally and without training see correctly. It is true that there is formed in every normal eye the same image of an object if it is seen from the same position, but as minds differ in capacity and training, so will they perceive differently whatever is thrown upon the retiqa or mirror of the eye. It is a matter of common observation that no two people agree in their description of an object, and where events are taking place rapidly in front of the eyes, as in a football game, one person with what we call quick perceptions, will see much more than another whose mind works more slowly; yet the same images were formed in the eyes of each. The person who understands the game sees infinitely more of its workings than one who does not, because he knows what to look for; and to draw with skill one must also know what to look for. Many people who have not studied draw- ing say they see the top of a circular table as a perfect circle in whatever position the eye may be in regard to the table. Others see a white water lily as pure white in color, whether it is in the subdued light of an interior or in full sunlight out of doors. I11 questions of color it is a matter of much study, even with persons of artistic gifts and training, to see that objects of one color appear under certain conditions to be quite a different color. 6. OutSineo The untrained eye usually sees objects in out- line filled in with their local color, that is, the color they appear to be when examined near the eye without strong light or shade 344 FREEHAND DRAWING 5 thrown upon them. One of the first things the student has to learn is that there are no outlines in nature. Objects are distin- guished from each other not by outlines but by planes of light and dark and color. Occasionally a plane of dark will be so narrow that it can only be represented by a line, but that does not refute the statement that outlines do not exist in nature. Very often only one part of an object will be detached from its surroundings. Some of its masses of light may fuse with the light parts of other forms or its shadows with surrounding shadows. If enough of the form is revealed to identify it, the eye unconsciously supplies the shapes which are not seen, and is satisfied. The beginner in drawing is usually not satisfied to represent it so, but draws definitely forms which he does not see simply because he knows they are there. Obviously then it is necessary to learn what we do not see as well as what we do. 7. Although there are no outlines in nature, most planes of light and shade have definite shapes which serve to explain the •form of objects and these shapes all have contours, edges or bound- aries where one tone stops and another begins. As the history of drawing shows, it has always been a convention of early and primi- tive races to represent these contours of objects by lines, omitting effects of iight and shade. To most people to-day the outline of an object is its most important element — that by which it is most easily identified — and for a large class of explanatory drawings outlines without light and shade are sufficient. By varying the width and the tone of the outline it is even possible to suggest the solidity of forms and something of the play of light and shade and of texture. 8. Since, in order to represent light and shade, it is neces- sary to set off definite boundaries or areas and give them their proper size and contour, it follows that the study of outline may very well be considered a simple way of learning to draw, and a drawing in outline as one step in the production of the fully devel- oped work in light and shade. An outline drawing is the simplest one which can be made, and by eliminating all questions of light and shade the student can concentrate all his effort on representing contours and proportions correctly. But he should always bear in mind that his drawing is a convention, that it is not as he actually 345 6 FREEHAND DRAWING sees nature, and that it can but imperfectly convey impressions of the surfaces, quality and textures of objects. 9. It is often asserted that whoever can learn to write can learn to draw, but one may go further and assert that writing is drawing. Every letter in a written word is a drawing from mem- ory of that letter. So that it may be assumed that every one who can write already knows something of drawing in outline, which is one reason why instruction in drawing may logically begin with the study of outline. Some good teachers advocate the immediate study of light and shade, arguing that since objects in nature are not bounded by lines to represent them so it is not only false but teaches the student to see in lines instead of thinking of the solidity of objects. But these arguments are not sufficient to overbalance those in favor of beginning with outline, especially in a course planned for architectural students to whom expression in outline is of the first importance. nATERIALS. 10. Pencils. Drawings may be made in “ black and white” or in color. A black and white drawing is one in which there is no color and is made by using pencil, charcoal, crayon or paint which produces different tones of gray ranging from black to white. The pencil is the natural medium of the architect and the materials for pencil drawing are very inexpensive and require little time for their preparation and care. Drawings in pencil are very easily changed and corrected if necessary. All the required plates for this course are to be executed in pencil. The pencil will make a drawing with any degree of finish ranging from a rough outline sketch to the representation of all the light and shade of a complicated subject. In addition it is the easiest of all mediums to handle. Students are sometimes led to think that it is more artistic to draw in charcoal crayon or pen and ink. It may be that an additional interest is aroused in some students by working in these materials, but the beginner must assure himself at once that artistic merit lies wholly in the result and not at all in the material in which the work is executed. Pencils are made in varying degrees of hardness. The softest 346 FREEHAND DRAWING 7 is marked BBBBBB or OB; 5B is slightly less soft and they increase in- hardness through the following grades: 4B, 3B, 2B, B, IIB, F, H, 211, 311, 411, 5 II, OH. A pencil should mark smoothly and be entirely free from grit. The presence of grit is easily recog- nized by the scratching of the pencil on the paper and by the unevenness in the width and tone of the line. The leads of the softer pencils are the weaker and are more easily broken. They give off their color the most freely and produce blackest lines. What hardness of pencils one should use depends upon a number of considerations, one of the most important being the quality of paper upon which the drawing is made. Quick effects of light and shade can be best produced by the use of soft pencils because they give off the color so freely and the strokes blend so easily into flat tones. A medium or hard pencil is necessary when a drawing is to be small in size and is intended to express details of form and con- struction rather than masses of light and shade. This is because o the lines made by hard pencils are liner, and more clean and crisp than can be obtained by using soft grades. The smaller the draw- ing, the more expression of detail desired, the harder the pencil should be; a good general rule for all quick studies of effects of light and shade is to use as soft a pencil as is consistent with the size of the drawing and the surface of the paper. Beginners, how- ever, are obliged to make many trial lines to obtain correct propor- tions, and in that way produce construction lines so heavy that the eraser required to remove them leaves the paper in a damaged condition. Until the student can draw fairly well he should begin every piece of work with a medium pencil and take care to make very light lines and especially to avoid indenting the paper. It should be understood that pencil drawings ought never to be very large. There should always be a proportional relation between the size of a drawing and the medium which produces it. The point of a pencil is so small that to make a large drawing with it consumes a disproportionate amount of time. For large drawings, especially such showing light and shade, crayon or char- coal are the proper materials for they can be made to cover a large surface in a very short time. The larger the area to be covered the larger should be the point and the line producing it. 347 8 FREEHAND DRAWING Special pencils with large leads can be obtained for making large pencil drawings. 11. Paper. In general the firmer the surface of the paper the harder the pencil one can use on it. For a medium or hard pencil the paper should be tough and rather smooth but never glazed. Many very cheap grades of paper, for example that on which newspapers are printed, take the pencil very well but have not a sufficiently tough surface to allow the use of the eraser. They are excellent for rapid sketches made very directly without altera- tions. Paper for effects of light and shade should be soft and smooth. For this work the cheaper grades of paper are often more suitable than the expensive sorts. Paper with a rough surface should always be avoided in pencil drawings, as it gives a disagreeable “ wooly ” texture to the lines. 12. Holding the Pencil. Any hard and fast rules for the proper use of the pencil would be out of place, but until the stu- dent has worked out for himself the ways which are the easiest and best for him he cannot do better than adoot the following; sugges- tions, which will certainly aid him in using the pencil with effect and dexterity. The most important points in drawing are to be accurate and at the same time direct and free. Of course, accuracy — the ability to set down things in their right proportions — is indispensable; but the abilty to do this in the most straightforward way without constraint, fumbling, and erasures is also necessary. Art has been defined as the doing of any one thing supremely well. The pencil should be held lightly between the thumb and forefinger three or four inches from the point, supported by the middle finger, with hand turned somewhat on its side. There are three ways in which it is possible to move the pen- cil; with the fingers, the wrist, or the arm. Most people find it convenient to use the finger movement for drawing short, vertical lines. In order to produce a long line by this movement it is only necessary to make a succession of short lines with the ends touch- ing each other but not overlapping, or by leaving the smallest pos- sible space between the end of one line and the beginning of the next. The wrist movement produces a longer line and is used 348 FREEHAND DRAWING 9 naturally to make horizontal lines. For a very long sweep of line the movement of the arm from the shoulder is necessary. This is, perhaps, the most difficult way of drawing for the beginner, but it affords the greatest freedom and sweep, and many teachers con- sider it the only proper method. 13. Position. The draughtsman should sit upright and not bend over his drawing, as that cramps the work and leads him to look, while working, at only a small portion of his drawing instead of comprehending the whole at a glance. The surface to receive the drawing must be held at right angles to the direction in which it is seen, otherwise the drawing will be distorted by the foreshortening of the surface. A rectan- gular surface such as a sheet of paper is at right angles to the direction in wdiich it is seen when all four corners are equally distant from the eye. A fairly accurate test may be made in the following manner: Locate the center of the paper by drawing the diagonals. Flat against this point place the unsharpened end of a pencil. Tip the surface until the length of the pencil disappears and only the point and sharpened end are visible, then the surface will be at right angles to a line drawm from the eye to its center. The pencil represents this line for a part of the distance because if properly held it is at right angles to the surface. FIRST EXERCISES. Before trying to draw any definite forms the student should practice diligently drawdng straight lines in horizontal, vertical, and • _ oblique positions, and also circles and • — — *— — ' ellipses. 14. Straight Lines. In drawing the ~~ | A straight line exercises points should first be placed lightly and the line drawn to connect them as in Fio*. 1. Draw 7 a series of ten or fif- O v / / / ./ teen lines in each position, placing the points to be connected by the lines one inch apart / / and leaving a space of one quarter of an inch betw T een each line. Next draw 7 a series Points. placing the points two inches apart, then a group with the points four inches apart, and finally a set which ! 1 i! i / 349 10 FREEHAND DRAWING will give lines eight inches long. Start to draw vertical lines from the top, horizontal lines from the left to right, oblique lines which slant upward toward the right, from the lower point, and those slanting upward toward the left, from the upper point. Use all three pencils, 3H, F and a solid ink pencil for these exercises, and take the greatest care not to press too strongly on the paper with the harder grades. They are intended to make rather light gray lines. Where dark lines are desired always use the solid ink pencil. Try also making the exercises with different widths of line regulated by the bluntness of the point, and do at least one set using the solid ink pencil and making very wide lines as near together as is possible without fusing one line with another. In all of these exercises the lines should each be drawn with one pen- cil stroke without lifting the pencil from the paper and absolutely no corrections of the line should be made. 15. Circles and Ellipses. In practicing drawing circles start from a point at the left and move around toward the right as in Fig. 2. Draw a series of ten cir- cles half an inch in diameter, forming o each with a single pencil stroke. Next draw a group of ten with a one-inch pencil stroke. Follow these with a set, each being two inches in diameter and another set with a three-incli diameter. In drawing these larger circles the free arm movement will be found necessary and the lines may be swept about a number of times for the purpose of correcting the first outline and giving practice in the arm movement. As the circles increase in diameter the difficulty of drawing them with accuracy by a single stroke increases also, but instead of erasing the faulty positions and laboriously patching the line, it is better to make the correc- tions as directed, by sweeping other lines about until a mass of lines is formed which gives the shape correctly. The single outline desired will be found somewhere within the mass of lines and may be accented with a darker line and the other trial lines erased. Draw a series of ten ellipses, Fig. 3, with a long diameter of diameter, still keeping to the single 350 11 FREEHAND DRAWING half an inch, forming each with a single pencil stroke. Follow with a group of ten, having the long diameter one inch in length, joining each outline with a single pencil stroke. Proceed with a set having’ a long diameter of two inches and a set with a long o o o diameter of three inches. Follow the same instructions for these last two groups as were laid down for drawing the larger circles, that is, sweep the lines about several times with the free arm movement. In drawing horizontal straight lines the elbow should be held close to the body. For vertical lines and for all curved lines the elbow should be held as Fig. 3. Ellipses. far from the body as possible. These exercises and similar ones of his own invention should be practiced by the student for a long period, even after he is studying more advanced work. Any piece of waste paper and any spare moments may be utilized for them. As in acquiring any form of manual skill, to learn to draw requires incessant practice, and these exercises correspond to the live-finger exercises which are such an important part of the training in instrumental music. While they are not very interesting in themselves the training they give to the muscles of the hand and arm is what enables the draughtsman to execute his work with rapidity, ease, and assurance. The student should bear in mind that a straight freehand line ought not to look like a ruled line. A part of the attraction of freehand drawing, even of the simplest description, is the sensi- tive, live quality of the line. A straight line is defined in geom- etry as one whose direction is the same throughout, but slight deviations in a freehand straight line, which recover themselves and do not interfere with the general direction are legitimate, as the hand, even when highly trained, is not a machine, and logically should not attempt to do what can be performed with more mechanical perfection by instruments. Where freehand straight lines are used to indicate the boundaries of forms, the slight in- evitable variations in the line are really more true to the facts of vision than a ruled line would be, inasmuch as the edges even of geometric solids appear softened and less rigid because they are affected by the play of light and by the intervening atmosphere. 351 12 FREEHAND DRAWING This the beginner will not be able to see at first, for in this case as in so many others, his sight is biased by his knowledge of what the object is and how it feels. 16. Freehand Perspective. One of the chief difficulties in learning to draw is, as before stated, in learning to see correctly, because the appearance of objects so often contradicts what we know to be true of them. More than one beginner has drawn a handle on a mug because he knew it? was there, regardless of the fact that the mug was turned in such a way that the handle was not visible. The changes which take place in the appearance of forms through changes in the position from which they are seen, are governed by the principles of perspective. Although students of this course are supposed to be familiar with the science of per- spective, it is necessary to restate certain general principles of perspective with which the freehand draughtsman must be so familiar that he can apply them almost unconsciously as he draws. The most important of these are demonstrated in the following paragraphs, and their application should be so thoroughly under- stood that they become a part of the student’s mental equipment. In theory the draughtsman draws what he sees, but practically he is guided by his knowledge as to how he sees. The principles can be most clearly demonstrated through the study of certain typical geometric forms which are purposely stripped of all intellectual or sentimental interest, so that nothing shall divert the attention from the principles involved in their representation. The student will readily recognize the great variety of subjects to which the principles apply and the impor- tance of working out the exercises and mastering them for the sake of the knowledge they impart. These principles can be explained very clearly by the use of the glass slate, which is a part of the required outfit for this course. All drawings should be made from the models in outline and in freehand on the glass, using the Cross pencil. The drawing should be tested and corrected according to the instructions for testing. 17. Tracing on the Slate. In beginning to study model drawing the model may be traced upon the slate held between the model and the eye and at right angles to the direction in which the object is seen. (See section 13.) In order to do this with 352 FREEHAND DRAWING 13 accuracy it is absolutely necessary that the slate shall not move and it is equally necessary that the position of the eye shall not change. As neither of these conditions can be fulfilled exactly without mechanical contrivances for holding both the slate and the head fixed, it follows that the best tracing one' can make will be only approximately correct and even that only if the object is of a very simple character. The more complicated the object the less satisfactory will be the tracing from it. Perhaps the best method is to mark the important angles and changes of direction in the contour with points and then rapidly connect the points with lines following the contours. Although the result may not be very correct, if carefully made the tracing will at least demonstrate the principal points wherein the appearance of an object differs from and contradicts the facts, and that is the sole object of the tracing. It awakens in the student the power of seeing accurately as it teaches the mind to accept the image in the eye as the true appear- ance of an object even if that image differs from the actual shape and proportion of the object as we know it by the sense of touch. Except as it helps us to leccrn to see , the tracing gives no train- ing in freehand drawing other than the slight manual exercise involved in drawing the line. 18. Testing with the Slate. The great value of the slate for the beginner in freehand drawing is the ease with which the accuracy of a drawing may be tested. To obtain satisfactory re- sults the models should be placed about a foot and a half in front of the spectator and the drawings made rather large. The draw- ing should be made freehand, in outline, and the greatest care taken to make it as accurate as possible before testing it because the object in making the drawing is to exercise the hand and eye. Drawing exercises should not be confounded with the preliminary exercises in tracing whose only object is to emphasize the fact that forms appear different as the position of the eye changes. In order to test a drawing place the slate at right angles to a line from the eye to the model according to the directions in sec- tion 13. Holding the slate at this angle and keeping one eye closed move it backward and forward until the lines of the draw- ing cover the lines of the model. Any difference in the general direction of the lines or proportions can be readily observed. Cor- 353 14 FREEHAND DRAWING rections should not be made by tracing, but errors should be care- fully noted and the alterations made freehand from a -re-study of the models. If the drawing is too large to cover the lines of the model, errors may be discovered by testing the different angles of the drawing with those of the model. If all the angles coincide the drawing must be correct. In making the tests the slate should be held firmly with both hands, and it cannot be emphasized too strongly that the test is of no value unless the slate is at right angles to the direction in which the model is seen. When groups of models or other complicated subjects are being tested only the directions of important lines and proportions of leading masses can be compared. It must be clearly understood that it takes some practice and much care to test the drawing of a simple form, and that the slate is' not to be used as a means of tracing. The student will soon discover that it is impossible to trace any form or group having much detail or multiplication of parts owing to the impossibility of holding the slate and the eye for long in the same position at the same time. Do not expect too much of the slate. Even the first exercises in tracing simple forms will show the student that unless he has acquired some facility in making lines freehand he cannot trace lines. Indeed it has often been observed that no one can trace who cannot draw. Another difficulty in using the slate at first is the resistance which the pencil encounters on the glass. It calls for a different pressure and touch from that used with a pencil on paper, so that the beginner is often discouraged unnecessarily and becomes impatient with the slate, partly because he expects too much from it and partly because he has not learned how to use it. Do not try to make perfect lines on the slate. Be satisfied at first to indicate the general direction of lines. Understand also that the slate is only to be used in beginning to draw. The student should as soon as possible emancipate himself from the use of the tests and depend upon the eye alone for judging the relations of proportions and lines. From the beginning a drawing should be corrected by the eye as far as possible before applying any tests. 354 FREEHAND DRAWING 15 FREEHAND PERSPECTIVE.* 19. The Horizon Line or Eye Level. This, as the name implies, is an imaginary horizontal line on a level with the eye. It is of great importance in representation, as all objects appear to change their shape as they are seen above or below the horizon line. The following 1 expe riments should be made before beginning" to draw any of the exercises in freehand perspective. Fasten two square tablets together at right angles to each other so that the adjacent corners exactly coincide, giving two sides of a cube. Hold it at arm’s length with the edge where the two planes touch, parallel to the eyes and the upper plane level. Lower it as far as the arms allow, then raise it gradually to the height of the eyes, and above as far as possible, holding it as far out as possible. Observe that the level tablet appears to become narrower as it approaches the eye level, and when it is opposite the eye it becomes only a line showing the thickness of the cardboard. Observe that this line or front edge of the tablet always appears its actual length while the side edges have been gradually appearing to become shorter. As the tablet is lifted above the horizon the lower side begins to appear very narrow at first, but widening gradually the higher the tablet is lifted. It will be seen also that when the tablet is below the horizon line the side edges appear to run up- ward, and when the tablet is above the eye its side edges appear to run downward, toward the horizon. That they and similar lines appear to con - JevA o|_V . r / \A 1 JlliV....... ui Fig. 4. Book with Strings. verge and vanish in the horizon line is proved by the following experiment: Place a book on a table about two feet away with its bound edge toward the spec- tator and exactly horizontal to the eye, that is, with either end equally distant from the eye. Between the cover and the first page b and as near the back as possible place a string, leaving about two feet of it on either side. Hold the left end of the *Note.— 1 Thrcmgta. the courtesy of its author and publishers, these exercises in free- hand perspective have been adopted from the text-book on “ Freehand Drawing,” by Anson K. Cross. Ginn & Co., Boston. 355 16 FREEHAND DRAWING string in the right hand and move it until it coincides with or Hold the right end of the string covers the left edge of the book. O in the left hand and move it until it covers the right edge of the O O two strings will O two converging or O O be seen to form at a point on the level of the eye, book. The vanishing lines which meet that is, in the horizon line. This and the preceding experiment illustrate the following rule; Hide 1. Horizontal retreating lines above the eye appear to descend or vanish downward , and horizontal retreating lines below the eye appear to ascend or vanish upward. The vanishing point of any set of parallel , retreating , horizontal lines is at the level of the eye. It is necessary to remember that the horizon line is changed when the specta- tor’s position is changed. This is very noticeable when one stands on a high hill and observes that the roof lines of houses which one is accustomed to see vanishing downward to the level of the eye, now vanish upward, since the eyes have been raised above the roofs. Retreating lines are those which have one end nearer the eye than the other. Exercise i. Foreshortened Planes and Lines. Cut from paper a tracing of the square tablet, which is a part of the set of drawing models, and leave a pro- jecting flap as at A, Fig. 5. Paste the flap on the under side of the slate, with the edges of the square parallel to the edges of the slate, and trace the actual o Holding the slate vertical and so that half the squave is above and half below the level of the eye, turn the square somewhat away from the slate and trace the appearance. Turn it still farther and trace. Turn it so that the surface disap- pears and becomes a line. 356 FREEHAND DRAWING 17 Trace a circular tablet and cut it out of paper, leaving a flap as at B, Fig. 5. Paste tlie flap on the back of the slate, as with the square, and trace its real appearance. Turn the circle .away at a moderate angle and trace its appearance. Trace it as it appears at a greater angle and finally place it so that it appears as a line. Try similar experiments with the triangle, the pentagon, and the hexagon and observe that these exercises all show that lines and surfaces under certain conditions appear less than their true dimensions, and that this diminution takes place as soon as the surfaces are turned away from the glass slate. When the square rests against the slate, with the centers of the square and slate coinciding, and the slate held so that half is above and half below the horizon line, all four corners of the square will be at equal distances from the eye so that a line from the eye to the center of the slate and of the square is at right angles to the surface of the slate, the latter represents in these experiments what in scientific perspective is called the picture plane. Thus a sur- face or plane appears its true relative dimensions only when it is at right angles to the direction in which it is seen. It is for this reason that it is always necessary to arrange the surface on which a drawing is made, at right angles to the eye, otherwise the surface and drawing upon it become foreshortened; that is, they appear less than their true dimensions. It is easy to see from the drawing of the foreshortened square in Fig. 4, that of the two equal and parallel lines a b and c d the nearer appears the longer, although neither of the lines are fore- shortened as the respective ends of each are equally distant from the eye. This illustrates the following rule : Rule 2. Of t wo equal and parallel lines , th e nearer appears tlie longer. Exercise 2. The Horizontal Circle. Hold the circular tablet horizontally and at the level of the eye. Observe that it appears a straight line. Place the tablet horizontally on a pile of books about half way between the level of the eye and the level of the table. Trace the appear- , ance upon the slate. circles. Place the tablet on the table and trace its appearance. 357 is FREEHAND DRAWING While making both tracings the distance between the eye and the object, and the eye and the slate should be the same. Hold the tablet at different heights above the level of the eye and observe that the ellipse widens as the height above the eye increases. These exercises illustrate the following rules: Rule 3. A horizontal circle appears a horizontal straight line when it is at a level of the eye. When below or above this level the horizontal circle always appears an ellipse whose long axis is a horizontal line. Rule 4. As the distance above or below the level of the eye increases the ellipse appears to widen. The short axis of any ellipse which represents a horizontal circle changes its length as the circle is raised or lowered. The long axis is always repre- sented by practically the same length at whatever level the circle is seen. Place the tablet on the table almost directly below the eye and trace its appearance. Move it back to the farther edge of the table and trace it. It will be seen that where the level of the circle remains the same, its apparent width changes with the distance from the eye to the circle. Exercise 3. Parallel Lines. Place the square tablet on the table 1^ feet from the front, so that its nearest edge appears hori- zontal; that is, so that it is at right angles to the direction in which it is seen. By tracing the appearance the following rules are illus- Fig. 7. Parallel Lines. t rated: Rule 5. Parallel retreating edges appear to vanish , that is , to converge toward a point. Rule 6. Parallel edges which are parallel to the slate, that is, at right angles to the direction at which they are seen, do not appear to co nverge , and any parallel edges whose ends are equally distant from the eye appear actually parallel. Exercise 4. The Square. Place the square tablet as in Exercise 3, and it will be seen that two of the edges are not fore- shortened but are represented by parallel horizontal lines. The others vanish at a point over the tablet on a level with the eye. How place the tablet so that its edges are not parallel to those 358 FREEHAND DRAWING 13 of the desk and trace its appearance on the slate. None of its edges appear horizontal, and when the lines of the tracing are con- tinued as far as the slate will allow, the fact that they all converge will be readily seen; the drawing illustrates the following rule : Rule 7. When one line of a right angle vanishes toward the right , the other line vanishes tovmrd the left. The drawing also shows that the edges appear of unequal length and make unequal angles with a horizontal line and illus- trates the following rule : Rule 8. When two sides of a square retreat at unequal angles , the one which is more nearly parallel to the picture plane {the slate) appears the longer and more nearly horizontal. Exercise 5. The Appearance of Equal Spaces on Any Line. Cut from paper a square of three inches and draw its diagonals. Place this square horizontally in the middle of the back of the table, with its edges parallel to those of the table, and then trace its appear- ance and its diagonals upon the slate. (Fig. 8.) Note — The diagonals of a square bisect each other and give the center of the square. Compare the distance from the nearer end, 1, of either diagonal to the centerof the square, 2, with thatfrom the centerof the square to the farther end of the diagonal, 3, for an illustration of the following rule: Rule 9. Equal distances on any retreating line appear unequal, the nearer of any two appearing the longer. Exercise 6. The Triangle. Draw upon an equilateral tri- angular tablet a line from an angle to the center of the opposite side. (This line is called an altitude.) Connect the triangular tablet with the o square tablet, and. place them on the table so that the base of the triangle is foreshortened, and its altitude is vertical. Trace the triangle and its altitude upon the slate. The tracing illustrates the fact that the nearer half of a re- ceding line appears longer than the farther Fig 9 The Triangle, half (see Pule 9), and also the following rule: Ride 10. The upper angle of a vertical isosceles or equilateral triangle , whose base is horizontal, appears Fig. 8. Equal Space on any Line. 359 20 FREEHAND DRAWING in a vertical line erected at the- perspective center of the base. Exercise 7. The Prism. Connect two square tablets by a rod to represent a cube, and bold the object so that one tablet only is visible, and discover that it must appear its real shape, A, Fig. 10. This illustrates the following; rule: Rule 11. When one face only of a prism is visible, it appears its * eal shape. Place the cube represented by tablets (Fig. 10) in the middle of the back of the desk, and trace its appearance. First, when two Fig. 10. The Prism. faces only of the solid would be visible (B); and, second, when three faces would be seen (C). These tracings illustrate the fol- lowing rule: Rule 12. When two or more faces of a cube are seen , none of them can appear their real shapes. Place the cubical form on the desk, with the tablets vertical, and one of them seen edgewise (D) and discover that the other tablet does not appear a straight line. This illustrates the follow- ing rule: o Rule 13. Only one end of a prism can appear a straight line at any one time. Exercise 8. The Cylinder. Connect two circular tablets by a 2A-inch stick, to represent the cylinder. Hold the object so that one end only is visible, and see that it appears a circle (Fig. 11). Place the object on the table, so that its axis is horizontal but appears a vertical line, and trace its appearance. The tracing illustrates the following rule: Rule 14. When an end and the curved surface of a cylin- der are seen at the same time , the end must appear an ellipse (Fig. 12). 360 FREEHAND DRAWING 21 Place the object horizontally, and so that one end appears a vertical line, and trace to illustrate the following rule: Rule 15. When one end of a cylinder appears a straight line , the other appears an ellipse. ( Fig . 13.) Place the object upright on the table, and trace its ends and axis. Draw the long diameters of the ellipse, and discover that they are at right angles to the axis of the cylinder. This illustrates the following rule: Ride 16. The bases of a vertical cylinder appear horizontal ellipses. The nearer base always appears the narrower ellipse. {Fig. 14.) Place the object with its axis horizontal and at an angle, so that the surfaces of both tablets are visible. Trace the tablets and the rod, and then draw the long diameters of the ellipses, and discover that they are at right angles to the axis of the cylindrical form. The axes of the ellipses are inclined, and the drawing; illus- o trates the following rules: Rule 17. The bases of a tode'r-uprigh?' F 1 £ilis T HOTifin“ a a! r oyVmder appear ellipses, whose and at an Angie. i on g diameters are at right angles to the axis of the cylinder , the nearer base appearing the nar- rower ellipse. Note.— The farther end may appear narrower than the nearer, but must always appear proportionally a wider ellipse than the nearer end. 361 22 FREEHAND DRAWING Rule 18. Vertical foreshortened circles below or above the level of the eye appear ellipses whose axes are not vertical lines. Ride 19. The long axis of an ellipse representing a ver- tical circle below or above the level of the eye is at right angles to the axis of a cylinder of which the circle is an end. Rule 20. The .< elements of the cylinder appear to converge in the direction of the invisible end. This convergence is not represented when the cylinder is vertical. Note i. — Less than half the curved surface of the cylinder is visible at any one time. Note 2 — The elements of the cylinder appear tangent to the bases and must always be represented by straight lines tangent to the ellipses which represent • the bases. When the elements con- verge, the tangent points are not in the long axes of the ellipses. See Fig. 12, in which if a straight line tangent to the ellipse be drawn, the tangent points will be found above the long axes of the ellipses. Exercise 9. The Cone. Hold the cone so that its axis is directed toward the eye, and the cone appears a circle. Hold the cone so that its base appears a straight line, and it appears a triangle. (Fig- 16.) Place a circular tablet, Fig. 17, having a rod attached, to represent the axis of the cone, so that the axis is first vertical and second inclined. Trace both positions of the object, and discover that the appear- ance of the circle is the same as in the case of the cylinder. The tracings illustrate the following rule: Rule 21. When the base of the cone appears an ellipse , the long axis of the ellipse is p>erpen- dicular to the axis of the cone. Note 1 — More than half the curved surface of the cone will be seen when the vertex is nearer the eye than the base, and less than half will be seen when the base is nearer the eye than the vertex. The visible curved surface of the cone may range from all to none. Note 2 The contour elements of the cone are represented by straight lines tangent to the ellipse which represents the base, and on 1 r the points of tangency are not in the long axis of this ellipse. Fig. 17. The Cone—Tablet with Rod. Fig. 16. The Cone. 30 « FREEHAND DRAWING 23 Exercise 10. The Regular Hexagon. In Fig. 18 the opposite sides are parallel and equal. The long diagonal A D is parallel to the sides B C and E F, and it is divided into four eijual parts by the short diagonals B F and C E, and by the long diagonals B E or C F. The perspective drawing of this figure will be corrected by giving the proper vanishing to the different sets of parallel lines, and by making the divisions on the diagonal A 1) perspectively equal. Draw the long and short diagonals upon a large hexagonal o o I o o tablet. Place this tablet in a horizontal or vertical position, Fig. 19, and then trace upon the slate its appearance and the lines upon it. The tracing illustrates the following rule: Rule 22. In a correct drawing of the regular hexagon , any long diagonal when intersected by a long diagonal and two short diagonals, will be divided into four equal parts. Exercise ii. The Center of the Ellipse Does Not Represent the Center of the Circle. Cut from paper a square of three inches, after having inscribed a circle in the square. Draw the diameters of the square and then place the square horizontally at the middle Fig. 20. Center of Circle not Fig. 21. Concentric Circles. Center of Ellipse. of the back of the table, with its edges parallel to those of the table. Trace the square, its diameters, and the inscribed circle, upon the slate. The circle appears an ellipse, and as the long axis of an ellipse bisects the short, it is evident that it must come below the 363 24 FREEHAND DRAWING center of the square, and we discover that the center of the ellipse does not represent the center of the circle, and that the diameter of the circle appears shorter than a chord of the circle. Exercise 12. Concentric Circles. Cut a 4-inch square from practice paper, and draw the diagonals. With the center of the square as center draw two concentric circles, 4 inches and 2 inches in diameter. Place the card horizontally upon the table, as illustrated, and trace its appearance upon the slate, together with all the lines drawn upon it. Draw the vertical line which is the short axis of both ellipses. Bisect the short axis of the outer ellipse, and draw the long axis of this ellipse. Bisect the short axis of the inner ellipse, and draw its long axis. It will be seen that the long axes are parallel but do not coincide, and that both are in front of the point which rep- resents the center of the circles. Each diameter of the larger circle is divided into four equal parts. The four equal spaces on the diameter which forms the short axis appear unequal, according to Rule 9. The diameter which is parallel to the long axes of the ellipses has four equal spaces upon it, and they appear equal. This diameter is behind the long axes, but generally a very short distance; and in practice, if the distance 1 2 between the ellipses measured on the long axis is one-fourth of the entire long axis, then the distance between the ellipses measured on the short axis must be a perspective fourth of the entire short axis. This illustrates the following rule: Rule 23. Foreshortened concentric circles appear ellipses whose short axes coincide. The distance between the ellipses on the short axis is perspectively the same proportion of the entire short axis , as the distance between the ellipses measured on the long axis , is aeometrically the same p>roportion of the entire long axis. Exercise 13. Frames. In the frames are found regular con- centric polygons with parallel sides, the angles of the inner poly- gons being in straight lines connecting the angles of the outer polygon with its center. In polygons having an even number of sides, the lines containing the angles of the polygons form diagon- als of the figure, as in the square. 364 FREEHAND DRAWING 25 In polygons having an odd number of sides, the lines con- taining the angles of the polygon are perpendicular to the sides opposite the angles, as in the triangle. Di ’aw upon large triangular and square tablets the lines shown in Fig. 22. Place the tablets horizontally on the table, or support them vertically, and trace upon the slate the appearance of the edges and all the lines drawn upon them. The tracings illustrate the following; rule: Rule 24. In representing the regular frames , the angles of the inner figure must he in straight lines passing from the angles of the outer figure to the center. These lines are alti- tudes or diagonals of the polygons. 20. After making the tracings described in the foregoing exercises, draw (not trace) freehand on the slate the various tab- lets, arranged to illustrate each one of the exercises. This is really drawing from objects, and where the rods are used to connect the tablets the figures are equivalent to geometric solids. After the proportions of the surfaces are correctly indicated, lines connect- ing the corresponding corners of the tablets should be drawn to complete the representation of solid figures. The lines indicating the rods and those lines which in a solid form would naturally be invisible, maybe erased. By the use of the three rods of different lengths, three figures of similar character but different proportions may be obtained. These should each be drawn, but each in a dif- ferent position. The following directions, which are based on general prin- ciples, apply to all drawing whether from objects or from the flat, for work in pencil or in any other medium; drawing from another drawing, a photograph or a print, whether at the same size or larger, is called working from the fiat. 365 26 FREEHAND DRAWING 21. General Directions for Drawing Objects. First observe carefully the whole mass of the object, its general proportions and the direction of lines as well as the width of the angles. Then sketch the outlines rapidly with very light lines, and take care that all corrections are made, not by erasing but by lightly drawing new lines as in Fig. 23. By working in this manner much time is saved and the drawing gains in freedom. Where the drawing is kept down to only one line which is corrected by erasure, the line becomes hard and wiry, and there is a tendency to be satisfied with something inaccurate rather than erase a line which has taken much time to produce. There is always a difficulty at first in draw- ing lines light enough, and it is well for the beginner to make the first trial lines with a rather hard pencil. Practice until the habit of sketching lines lightly is fixed. The ideal is to be able to set down exact proportions at the first touch. This, however, is attained by com- paratively few artists, and only after long study, but the student will soon find himself able to ob- tain correct proportions with only a few corrections. 22. It cannot be too strongly emphasized that the student must teach himself to regard the subject he is depicting, as a whole, and to put down at once lines that suggest 'the outline of the whole. This he will find contrary to his inclination, which with the beginner is always to work out carefully one part of the draw- ing before suggesting the whole. There are two objections to this ; in the first place, much time having been spent on one part, it is almost inevitable that the addi- tion of other portions reveals faults in the completed part, and un- necessary time is consumed in correcting. The second objection is that a drawing made piecemeal is sure to have a disjointed look, even if the details are fairly accurate in their relative proportions. 366 FREEHAND DRAWING 27 The idea of unity is lost and some one detail is apt to assume un- due importance, instead of all details being subordinated to the general effect of the whole. It is always most important to state the general truths about the subject rather than small particular truths, which impair the general statement. This applies particu- larly to small variations in the outline which should be omitted until the big general direction or shape has been established. 23. Where an outline drawing is desired, after the correct lines have been found, they should be made stronger than the others and then all trial lines erased. In doing this the eraser will o usually remove much of the sharpness of the correct lines so that only a faint indication of the desired result remains. These should be strengthened again with a softer pbncil and each line produced, as far as possible, directly with one touch ; in the case of curves and very long lines, breaking the line and beginning a new one as near as possible to the end of the previous line, but taking care that the lines do not lap. As soon as the student has acquired some proficiency in draw- ing the single figures made from the tablets, groups of two or three objects should be attempted. Combinations of books or boxes with simple shapes, or vases, tumblers, bowls and bottles will illus- trate most of the principles involved in freehand perspective. Outline sketches may be made on the slate first and tested in the usual way, and afterward the same group may be drawn larger on paper. The chief difficulty in drawing a group is to obtain the rela- tive proportions of the different objects. There is the same objec- tion to completing one object and* then another as there is to drawing a single object in parts. The whole group must be sug- gested at once. This can best be done by what is called blocking in, by lines which pass only through the principal points of the group. The block drawing gives hardly more than the relative height and width of the entire group and the general direction of its most important lines. But if these are correct, the subdivision of the area within into correct proportions is not difficult. The longer and more important lines of the parts are indicated and short lines and details lost. 24. Testing Drawings by Measurement. In drawings which are not made on the slate the following method of testing propor- 367 28 FREEHAND DRAWING . tions is usual. WMh the arm stretched forward to its greatest length, hold the pencil upright so that its unsharpened end is at the top. Move it until this end coincides with the uppermost point of the object. Holding it fixed and resting the thumb against the pencil, move the thumb up and down until the thumb nail marks the lowest point of the object. The distance measured off on the pencil represents the upright dimension. Holding the pencil at exactly the same distance from the eye, turn it until it is horizon- tal and the end of the pencil covers the extreme left point of the object. Should the height and width be equal, the thumb nail would cover the extreme right edge of the object. If the width is greater than the height, use the height as a unit of measurement and discover the number of times it is contained in the width. Always use the shorter dimension as the unit of measurement. The accuracy of the test demands that the pencil should be at ex- actly the same distance from the eye while comparing the width and height. In order to insure this, the arm must not be bent at the elbow and must be stretched as far as possible without turning the body, which must not move during the operation. The dis- tance from the eye to the object must not change during the test, and the position of the eye and body is first fixed by leaning the shoulders firmly against the back of the chair and keeping them in that position while the test is taking place. It is equally impor- tant in both the upright and horizontal measurement that the pen- cil be held exactly at right angles to the direction in which the object is seen ; i.e., at right angles to an imaginary line from the eye to the center of the object. In either position the two ends of the pencil will be equally distant from the eye. The test should be made several times in order to insure accuracy, as there is sure to be some slight variation in the distances each time. Avoid tak- ing measurements of minor dimensions, as the shorter the distances measured the more inaccurate the test becomes. At the best meas- urements obtained in this way are only approximately correct, and too much care cannot be taken in order to render the test of use. Applied carelessly, the test is not only valueless, but thoroughly misleading. W r hen there is any great conflict between the appear- ance of the object and the drawing after it has been corrected by the test, it is often safe to assume some mistake in applying the 368 FREEHAND DRAWING 29 test and to trust the eye. In such a case the test may be tested by the use of the slate. A few lines and points will be sufficient to indicate the width and height on the slate, and the relative propor- tions can then be calculated. The plumb-line affords another method of testing. A thread or a string with any small object for a weight attached to one end, is sufficient. Hold the string so that it hangs vertical and motion- less, and at the same time covers some important point in the ob- ject. By looking up and down the line the points directly over and under the given point can be determined and the relative distances of other important points to the right and left can be calculated. The plumb-line will also determine all the vertical lines in the object and help to determine divergence of lines from the vertical. A ruler, a long rod, or pencil held in a perfectly horizontal position is also of assistance in determining the width of angles and divergences of lines from the horizontal. 25. Misuse of Tests. The use of tests may easily be per- verted and become mischievous. Since the object of all draw- ing is to train the hand and eye, it follows naturally that the more the student relies upon tests the less will he depend upon his per- ceptions to set him right, and the less education will he be giving to his perceptions. There is no greater mistake for a student than to use the measuring test before making a drawing. Spend any amount of time in calculating relative proportions by the eye, but put these down and correct them by the eye, not once but many times before resorting; to tests. All the real education in drawing takes place before the tests are made. Let the student remember that the tests may help him to make an accurate drawing, but they will never make him an accurate draftsman in the true sense. Nothing but training the eye to see and the hand to execute what the eye sees, will do that. When the student has reached the end of his knowledge, has corrected by the eye as far as he can, then by applying tests he is enabled to see how far his percep- tions have been incorrect. That is the only educational value of the test. Merely to make an accurate drawing with as little men- tal effort as possible, relying upon test measurements, requires considerable practice and skill in making the tests, but gives very little practice or training in drawing. 369 30 FREEHAND DRAWING 26. Light and Shade. Objects in nature, as before explained, detach themselves from each other by their differences in color and in light and shade. In drawing without color, artists have always allowed themselves a very wide range in the amount of light and shade employed, extending from drawing in pure outline up to the representation of exact light and shade, or of true values, as it is called. Drawings which contain light and shade may be divided into two classes: Form drawing, which is from the point of view of the draftsman, and value drawing, which is from the point of view of the painter. 27. Form Drawing. In form drawing the chief aim, as the name implies, is to express form and not color and texture. In order to do this, shadows and cast shadows are indicated only as far ^s they help to express the sl^ape. This is the kind of drawing practiced by most of the early Italian masters, and it has been called the Florentine method. It is often a matter of careful out- line with just enough shadow included to give a correct general impression of the object. There is usually little variety in the shadow and no subtle graduations of tone, but the shadows are indicated with sufficient exactness of shape to describe the form clearly. Form drawing is a method of recording the principal facts of form with rapidity and ease and of necessity deals only with large general truths. Perhaps its most distinguishing feature is that it does not attempt to suggest the color of the form. 28. Value Drawing. The word value as it is used in draw- ing is a translation from the French word valeur , and as used by artists it refers to the relations of light and dark. Value drawing represents objects exactly as we see them in nature; that is, not as outline, but as masses of lights and darks. In value drawing the artist reproduces with absolute truth the dif- ferent degrees of light and shade. While form drawing suggests relief, value drawing represents it, and it also represents by trans- lating them into their corresponding tones of gray, the values of color. In form drawing, a draftsman representing a red object and a yellow one, would be satisfied to give correct proportions and outlines with one or two principal shadows, while a value 370 FREEHAND DRAWING 31 drawing of the same objects would show not only the relation of the shadows as they are in nature, but also the further truth that the red object was as a whole darker than the yellow one. The light side of the red object might even be found to be darker in value or tone than the shadow side of the yellow form. 29 . Values. Drawing has been called the science of art, but artists have rarely approved the introduction of scientific methods in the study of drawing, fearing lest the use of formulas should lead to dull mechanical results. Students are left to discover methods and formulas of their own. It is true that every success- ful draftsman or artist has a method which he has worked out for himself, but he usually feels it to be so much a matter of his own individuality, that he is reluctant to impose it on students, who are likely to confound what is a vital principle with a personal man- nerism, and by imitation of the latter injure the quality of personal expression which is so important in. all creative work. So there is an inclination among drawing teachers to distrust anything which tends even to formulate the principles of drawing. Recently there has been, however, a distinct advance in the study of these prin- ciples, under the leadership of Dr. Denman AV. Ross, of Harvard University, who has made it possible for the first time to speak with exactness of colors and values. As Dr. Ross has permitted the use of his valuable scale in this text book, it will greatly assist in making tangible and clear, what would otherwise be obscure and difficult to explain. The word values as used in the text book refers entirely to relations of light and dark. For instance, the value of a given col- or, is represented by a tone of gray which has the same density or degree of light and dark that the color has. The value of a spot of red paint on a white ground is expressed by a spot of gray paint which appears as dark on the white ground as does the red paint, but from which the color principle has been omitted. A good pho- tograph of a colored picture gives the values of the picture. A poor photograph, on the contrary, distorts the values and blues are often found too light, while reds and' yellows will be too dark to truth- fully express the values of the original color. 30. The Value Scale. All possible values which can be rep- resented in drawing, lie between the pure whites of paper or pig- 371 32 FREEHAND DRAWING merits and the pure black of pen- cil, ink, or other pigments. In order to think or speak precisely of the great range of values be- tween black and white, it is necessary that they shall be clas- sified in some way. It is not sufficient to say that a given shadow is light, or medium, or dark in value. Dr. Ross has overcome the difficulty by ar- ranging a value scale of nine equal intervals, which covers the whole range from pure white to pure black. Each interval has its appropriate designation and a convenient abbreviation. This scale affords a practical working basis for the study of values. It is evident that while the indi- vidual scale does not include all possible values, it can readily be enlarged indefinitely by intro- ducing values between those of O the scale as described. As a matter of fact, any differences in value that might come between any two intervals of the scale would rarely be represented, as it is the practice in drawing to simplify values as much as pos- sible; that is to consider the general value of a mass, rather than to cut it up into a number of slightly varying tones which are not necessary for expressing anything of importance in the object. 372 FREEHAND DRAWING 33 31. How to Make a Value Scale. Fig. 24 shows a value scale with the names of the intervals and their abbreviations. In making a value scale the student should work in pencil, confining each interval within a circle three-quarters of an inch in diameter. White will be represented by the white paper with a circle penciled about it. Black (B) and white (W) should be established first, then the middle value (M), light (L) and dark (D) ; afterward the remaining values, low light (LL), high light (HL), low dark (LD) and high dark (HD). 32. How to Use a Value Scale. When the objects to be drawn are neutral in color, that is, are black, white, or gray, the relative values are perceived without special difficulty. When the objects are in color, the draftsman is obliged to translate the color element into terms of light and dark. I*n order to determine the value of any surface, it is a help to compare the surface with a piece of white paper held in such a way that it receives the greatest amount of light. It not infrequently happens that two surfaces quite different in color will be of exactly the same value. The student should make a practice of observing the relative values of things about him, even when he is not engaged in drawing. Place a sheet of white paper in the sunlight as it falls through a window and compare its value with that of white paper further in the room and outside of the sunlight. Try a similar experiment with black. These merely show what everyone may suppose that he knows already — that the less light a surface receives the darker value it appears to have. As a matter of fact, beginners are more ready to accept this truth with regard to color than they are when it relates to black and white. An instructive way of studying values is to look through a closed window and compare the values of forms outside to the value of the window sash. Even when the sash is painted white, it will often be observed to appear darker than any shadow out of doors. 33. General Directions for Drawing the Examination Plates. The examination plates are planned to give as great a variety to the style of drawing as possible. The architect is called upon to use freehand drawing in two general ways; to make work- ing drawings of ornament, either painted or carved, and to make, 373 FREEHAND DRAWING 34 for reference, sketches or notes, more or less elaborate, from orna- ment already in existence, or from buildings either entire or in part, as well as from their landscape setting. This course will not include drawing of architecture and landscape. In making a working drawing of ornament every shape and curve should be drawn to perfection, with clean, careful lines, in order that there shall be no opportunity for the craftsman who executes the work to interpret it differently from the designer’s intention. Light and shade are used sparingly as the exact amount of relief is indicated by sections. In making sketches or notes, while proportions must be accu- rately studied, form may be suggested by a much freer quality of line. In a working drawing light and shade maybe merely indi- cated or may be carried to any degree of elaboration. The natural way of teaching this kind of drawing is to work from the objects themselves or from casts. This is not possible in a correspondence course, but all the principles of sketching may be very well taught by drawing from photographs of ornament, and this method has some decided advantages of its own for a beginner. The light and shade in the photograph are fixed, while in sketching objects out of doors it changes constantly, and even indoors is subject to some fluctuation; and then, in the photograph the object is more isolated from its surroundings and so is less confusing to perceive. In order to train the sense of proportion as thoroughly as pos- sible, the plates are to be executed on a much larger scale than the examples, but at no fixed scale. Plan each drawing to be as large as possible, where no dimensions are given, but do not allow any point in the drawing to approach nearer than one inch to the border line. 34. Varieties of Shading. In drawing in pen and ink, all effects of shadow are made by lines, and different values are ob- tained by varying the width of lines, or of the spaces between the lines, or by both. In any case the integrity of each line must be preserved and there can be very little crossing or touching of shade lines, as that causes a black spot in the tone unless lines cross each other systematically and produce cross hatching. With the pen- cil, however, owing to its granular character one may produce a tone without any lines; a tone made tip of lines which by touching or overlapping produce a soft, blended effect, in which the general 374 FREEHAND DRAWING 35 direction of the strokes is still visible, or a tone made up of pure lines as in pen work. In general it does not matter so much, as in pen drawing, if lines touch or overlap. Indeed, the natural character of the pencil line leads to a treatment which includes both pure lines and more or less blended effects. 35. Directions of Shade Lines. It is always a very impor- tant matter to decide what direction shade lines shall take. While it is impossible to give rules for it, a good general principle is to make the direction of the lines follow the contours of the form. The easiest and simplest method is to make all the lines upright. This method is a very popular one with architects. The objec- tions to it are monotony and a lack of expression, but it is certainly a very safe method and far preferable to one where desire for variety has been carried too far and lines lead the eye in a great number of different directions which contradict the general lines of the surface or form. A natural treatment is to adapt the direc- tion of lines to the character of the surface represented; that is, to treat curved surfaces with curving lines and flat planes with straight lines, and in general, lines may very well follow either the contours or the surfaces of the form. I 11 that way variety is obtained and the direction of the shading helps to express the char- acter of the thing represented. This principle must, however, be modified when it leads to the introduction of violently opposing sets of lines. Abrupt transitions must be avoided and the change from one direction to another must be accomplished gradually. Where a large surface is to receive a tone, the tone can best be made by a series of rather short lines side by side with succeed- ing series juxtaposed. The lengths of the lines in each of the series must vary considerably in order that the breaks in the lines may not occur in even rows, producing lines of white through the tone. (See Fig. 25.) The crossing of one system of parallel lines by another system is called cross hatching. This method probably originated in copperplate engraving, to which it is very well adapted, especially as a means of modifying and deepening Fig. 25. Method of Breaking Lines Covering a Large Surface. 375 36 FREEHAND DRAWING tones. It also changes and breaks up the rather stringy texture produced by a succession of long parallel lines. It has now become somewhat obsolete as a general method for pen or pencil drawing, largely because the result looks labored, for it is always desirable to produce effects more simply and directly, that is, with one set of lines instead of two or more. If the tone made by one set of lines needs darkening, it is now more usual to go over the first tone with another set of lines in the same direction. A great many drawings have been made with shade lines all in a diagonal direction, but this is open to serious objection and should be avoided. A diagonal line is always opposed to the prin- ciple of gravitation, and tends to render objects unstable and give them the appearance of tilting. It is often desirable to begin a tone with diagonal lines which, however, should gradually be made to swing into either an upright or horizontal direction. 376 EXAMINATION PAPER FREEHAND DRAWING Materials Required. One Wollff’s solid ink black pencil; one F pencil; one HU pencil; two dozen sheets of paper (same as practice paper of other courses, but to be used for examination sheets in this) ; one red soft rubber; one medhim rubber— green or red. with wedge ends ; one drawing board ; six thumb tacks ; one box natural drawing models ; one Cross slate; one Cross pencil; one-half dozen sheets of tracing paper. After the preliminary practice with straight lines and curves the student may pro- ceed to execute Plates I and II. PLATE I. The principal dimensions in inches are indicated on the model plate. All dimensions and proportions should however be determined by the eye alone. Measurements may be used as a test after the squares are laid in. The figures on the left should be executed first, in order to avoid rubbing by the hand and sleeve. Figs. 1, 2, 3, 4, 5 are motives from Egyptian painted decoration. Figs. 1, 2, 4 and 5 are all derived from or suggested by patterns pro- duced by plaiting or wearing. The borders of Fig. 3 are derived from bundles of reeds bound together. As all the figures are large and simple, they should be executed with a rather wide line drawn with the F pencil. Draw the construc- tion lines on this and on all other plates where they are necessary, so lightly that they can be perfectly erased without leaving any indenta- tion in the paper. After the construction lines are drawn out in Figs. 4 and 5, strengthen the lines of the pattern. In erasing, much of the pattern will be removed. This time go over each line with a single stroke of the solid ink pencil. Do not turn the paper in drawing diagonal and vertical lines. They are given especially to train the hand to execute such lines. By turning the paper the exercise be- comes one of drawing horizontal lines, which are the least difficult. Fig. 6 is the skeleton of a very common type of ornament con- sisting of curved lines radiating from a point at the base, on either side of a central axis. 379 3 '5tJ' I PLATE I. Motives of Common Types of Ornament. FREEHAND DRAWING 89 PLATE II. Fig. 1 is the basis of a large class of ornament founded on the lines of organic growth, called scrolls or meanders. Fig. 2 is an Egyptian border consisting of alternate flower and bud forms of the lotus, the most typical and universal of all the Egyp- tian decorative units. The outline of the flower displays the Egyp- tian feeling for subtlety and refinement of curve. Observe how the short rounded curve of the base passes into a long subtle curve which becomes almost straight and terminates in a short full turn at the end. Fig. 3 is a simple form of the guilloche (pronounced gheeyoche), a motive which first becomes common in Assyrian decoration and is afterward incorporated into all the succeeding styles. Fig. 4 is the skeleton of a border motive where the units are dis- posed on either side of the long axis of the border. Figs. 5 and 7 are varieties of the Greek anthemeum or honey- suckle pattern, one of the most subtle and perfect of all ornamental forms. Observe in Fig. 5 the quality of the curves — the contrast of full rounded parts with long curves almost straight which characterize the Egyptian lotus. Note in both examples that there is a regular ratio of increase both in the size of the lobes and in the spaces between each, from the lowest one up to the center. It is invariably the ride that each lobe shall be continued to the base without touching its neighbor. Fig. G is an Egyptian “ all-over” or repeating pattern painted on wall surfaces. It is made up of continuous circles filled with lotus forms and the intervening spaces with buds. PLATE III. This plate is to contain nine outline drawings illustrating Rules 8, 12, 13, 14, 15, 17, 18, 19, 20. The drawings may be made and cor- rected on the slate and then copied on to the paper or they may be drawn directly on the paper. They may be from the models or from simple geometric objects such as boxes, blocks, cups, pans, plates, spools, flower pots, bottles, etc. PLATE IV.* These are characteristic forms of Greek vases. Fig;. 1. the Lechv- Note. This plate and all succeeding ones are to be surrounded by a border line, drawn freehand one inch from the edge of the paper. 381 PlyATE II. Typical Egyptian, Assyrian and Greek Motives. 382 FREEHAND DRAWING 41 tlios, was used to hold oil, Fig. 2, the Kantheros, is one form of the drinking cup, and Fig. 3, the Ilydria, for pouring water. The drawing of these vases includes a great variety of beautiful curves. They are to be executed entirely in outline, and both con- tours and bands of ornament and the relative sizes of each are to be preserved. Calculate the heights so that the bases shall each be one inch from above the border line and the upper point of Fig. 3 about one inch below the border line. In sketching them in, first place a con- struction line to represent the central axis. Across this, sketch the outlines of the horizontal bands and then sketch the contours, follow- ing the general directions given in Sections 21 and 25. Remember that lines are to be drawn lightly and corrections made by new lines and not by erasures. Use the arm movement as much as possible in drawing the curves. Before executing the examination paper, prac- tice drawing each vase entirely without corrections of the lines. PLATE V. Fig. 1 is from the pavement in the Baptistery at Florence and is in the style called Tuscan Romanesque. The pointed acanthus leaves in the small border to the left, are identical in character with the Byzantine acanthus. This drawing is to be treated like a sketch made from the object. After sketching in the pattern and correcting in the usual way by drawing new lines, erase superfluous lines and strengthen the outlines by lines made with one stroke. The final outline should, however, be loose and free in character and express the somewhat roughened edges of the pattern in white. This does not mean that the direction of the line must vary enough to distort any shapes. Observe that most of the shapes appear to be perfectly symmetrical only their edges seem slightly softened and broken. Fill in the background with a tone equal to the dark (D) of the value scale. Make this tone by upright lines nearly touching each other and if the value is too light at first, go over them again by lines in the same direction. If a back- ground line occasionally runs over the outline, it will help to produce the effect of the original. Figs. 2, 3, 4 and 5 comprise typical forms of Greek decorated mouldings. The examples have much the character of a working 383 PLATE IV. FIG. 1. The Ivechythos. Typical Greek Vase Used to Hold Oil. PLATE IV. FIG. 2. The Kantheros. Typical Greek Vase Used for a Drinking Cup. PLATE IV. FIG. 3. The Hydria. Typical Greek Vase Used far Pourintr Water. PIRATE) V. PIG. 1. Pavement from the Baptistery, Florence. FIG. 4 PI.ATE V. FIG> 5 ; Typical Forms of Greek Decorated Mouldings. 48 FREEHAND DRAWING drawing and the plates are to be enlarged copies, but instead of fol- lowing the character of the light and shade of the original, the shadows are to be executed by upright lines. (See Section 37.) The darker shadows are to be the value of dark (D) of the scale, the lighter ones the value of middle (M). PLATE VI. Place these drawings so that there will be at least an inch be- tween them and about half an inch between the border line and the top and bottom. Fig. 1 is from a drawing of a wrought iron grille in a church in Prague. Some idea of the shape of the pieces of iron is conveyed by the occasional lines of shading. The pattern will be seen to be dis- posed on radii dividing the circle into sixths. Construct the skeleton of the pattern shown, establishing first an ecjuilateral triangle and the lines which subdivide its angles and sides. About this draw the inner line of the circle and extend the lines which subdivide the angles of the triangles, to form the six radii of the circle. Complete the outlines of the pattern before drawing the shading lines. This drawing with its lines and curves all carefully perfected represents the kind of working drawing which an architect might give to an iron- smith to work with, although in a working drawing, a section of the iron would be given and each motive of the design would propably be drawn out only once and then as it was repeated it would be merely indicated by a line or two sketched in. Fig. 2 is from a photograph of a wrought iron grille at Lucca in the style of the Italian Renaissance. The drawing to be made from this, the student must consider to be a sketch, the sort of note or memorandum he might make were he before the original. The accompanying detail gives a suggestion of the proper treat- ment. The general shape of the whole outline should be indicated and the larger geometric subdivisions; the details of two of the compartments suggested by light lines and those of the remainder either omitted or very slightly suggested. Try to make the drawing suggest the “hammered” quality of the iron. Although the curves are all beautifully felt, there are slight variations in them produced by the hammer, or they are bent out of shape by time, and the thick- ness of the iron varies sometimes by intention and sometimes by acci- PI, ATE VI. FIG. 1. Wrought Iron Grille, Prague. PIRATE VI. FIG. 2. Wroug-ht Iron Grille, Lucca. FREEHAND DRAWING 51 dent. Take care, however, not to exaggerate the freedom of the lines and do not carry the variation so far that curves are distorted. Make the drawing in outline first with a line which breaks occasion- ally, with portions of the line omitted. This helps to indicate the texture of the iron and suggests its free hand-made character. That part of the background which in the photograph appears black behind the iron, should be filled in with a tone equal to the dark (D) of the value scale. It should only be placed behind the two compartments which are most carefully drawn, with perhaps an irregular patch of it in the adjoining compartment. In making the background use single pencil strokes, side by side, w T ith the solid ink pencil, very near together or occasion- ally touching. Give a slight curve to each stroke. The direction of the lines may be either upright, or they may keep the leading direction of the general lines of the pattern, but they should not be stiff or mechanical. If the value is not dark enough another set of lines may be made over the first ones, keeping the same direction. The only parts of the ironwork itself which require shading are those twisted pieces which mark the subdivision, the outer edge, and the clasp. For this use a tone equal to the middle (M) of the value scale. Avoid explaining too carefully the twists and use the shading only in the dark side. Use a few broken outlines on the right side, just enough to suggest it and do not darken the flat piece of iron behind the twists except on the shadow side. Do not count the number of twists but indicate them in their proper size and the effect will be near enough for this kind of a drawing. Shade only those twists which are nearest the compartments which are detailed; from them let the detail gradually die away. PLATE VII. This figure is a rosette made up of the Roman or soft acanthus, 392 52 FREEHAND DRAWING and the drawing has the general character of a working drawing. Every part is very clearly expressed in outline, slightly shadowed, and a section explains the exact contours. In drawing the outline of the leaflets, observe that one edge, usually the upper is generally ex- pressed by a simple curve and the other edge by a compound curve, the variation in which, however, is slight. Draw a circle first to con- tain the outer edge of the rosette and sketch in lightly the main rib or central axis of each leaf. Then block in the general form of the leaves, not showing the subdivisions at edges. Next place the eyes — the small elliptical spots which separate one lobe from another — and draw the main ribs of each lobe, finally detailing the leaflets in each lobe. In shading use the value dark (D) for the darkest values and the middle value (M) for the others, and instead of producing a perfectly blended tone as in the original, let the tone retain some suggestion of lines, the general direction of which should follow that of the main ribs in the leaves. In the shadow of the rosette on the background, let the lines be upright. Lines naturally show less in very dark values than in lighter tones, for it is difficult to produce the darker values without going over the lines with another set and that has a tendency to blend all the lines into a general tone. PLATE VIII. Plate VIII is a sculptured frieze ornament introducing various forms of the Roman or soft acanthus. In this as in all scroll drawing, the skeleton of the pattern should be carefully drawn, then the leaves and rosettes disposed upon it. Always draw the big general form of the acanthus, and proceed gradually to the details as described in the directions for Plate VII. This like Plate VII, has the general charac- ter of a working drawing, only in this case there is no section. Use the same values and same suggestions for directions of line as in Plate VII. PLATE IX. This plate is an example of the Byzantine acanthus on a fragment in the Capitoline Museum. In drawing this, place the central axis or main rib of the leaf first, then establish the position of the eyes — the egg-shaped cuts which separate the lobes. The general contour of the lobes and their main ribs should next be blocked in before the final disposition of the points or leaflets is determined. 394 Section Througii Center. PLATE VII. Acanthus Rosette. PLATE IX. This is also to be drawn as Fig-. 1, Plate X. Byzantine Acanthus, from a fragment in the Capitoline Museum. 56 FREEHAND DRAWING The drawing of this plate is to be enlarged to about ten inches in height and well placed on the sheet with the center of the drawing coinciding with the center of the plate. This drawing is to be made by the use of two values only, with white, and the student may select his own values. The object is to select the most important features and to omit as much as possible. It would be well for the student to first try to see how much he can express with one value and white. The values are to be obtained by upright lines. Outlines are to be omitted as far as possible in the finished sketch and forms are to be expressed by the shapes of the masses of shadow. Where only two values and white are to be used, it is desirable to leave as much white as possible and not allow the shadow values to run too near to black as that produces too harsh a contrast with the white. On the other hand, if the shadow values are too high in the scale, that is too near white, the drawing becomes weak and washed out in effect. As this drawing is to be large in scale, it should be made with the solid ink pencil and with wide pencil strokes. After the outline has been sketched in, the shading or “ rendering” may be studied, first on tracing paper over the drawing. There should be no attempt at rendering the background in this drawing. PLATE X. Figs. 1 and 2 are to be placed on this plate, but Fig. 1 is to be rendered this time as near to the true values as it is possible to go by using four values and white in shading. The pencil lines should be blended together somewhat, but the general direction of the shad- ing should follow the central axis of the lobe§. Only the leaf itself is to be drawn and the background value should be allowed to break in an irregular line about the leaf. It shoukl not be carried out to an edge which would represent the shape of the entire fragment of stone on which the leaf is carved. In studying the shapes of the different shadows it is well at first to exaggerate somewhat and give each value a clean, definite shape even if the edges appear somewhat indefinite in the original. At the last those edges which are blurred may be blended together. Fig. 2 is a Byzantine capital from the church of San Vitale, at Ravenna. This is to be drawn so that the lines of the column shall fade off gradually into nothing and end in a broken edge instead of FREEHAND DRAWING 57 stopping on a horizontal line as in the original. The top of the draw- ing above the great cushion which rests on the capital proper should also fade off into nothing and with a broken line instead of the hori- zontal straight line. A small broken area of the background value should be placed either side of the capital. In drawing an object like this which is full of small detail there is danger of losing the larger qualities of solidity and roundness by insisting too much upon the small parts and there is also danger of making the drawing too spotty. It is a good principle to decide at first that the detail is to be expressed either in the shadow or in the light, but not equally in both. This principle is based on one of the facts of vision, for in looking at an object one sees only a comparatively small amount of detail; what falls on either side of the spot on which the eye is focused appears blurred and indistinct. In an object of this kind whose section is circular, one can best express the shape by concentrating the study of detail at the point where the light leaves off and shadow begins, representing less and less detail as the object turns away from the spectator. In this drawing, however, there may be more detail ex- pressed in the shadow than in the light, but remember that outlines of objects in shadow lose their sharpness and become softened. Do not attempt to show all the grooves in the parts in shadow; indicate one or two principal ones and indicate more and more detail as the leaves approach the point where the light begins. There the richness of detail may be fully represented, but as the forms pass into the light, omit more and more detail. Again observe that any small plane of shadow surrounded by intense light, if examined in detail, appears darker by contrast, but if represented as dark as it appears it becomes spotty and cut of value. If observed in relation to the whole object its real value will be seen to be lighter than it appears when examined by itself. Use whit3 and four values to be determined by the student. Guard against too strong contrasts of values within the shadow as it cuts it up and destroys its unity, and in every drawing made, show clearly just which is the shadow side and which is the light. That is, do not place so many shadow values within the light that it destroys it, and do not invade shadows with too many lights and reflected lights. Note that it is characteristic of the Byzantine acanthus to have the points of every tine or lobe touch something; no points are left free, but observe also that the points have some sub- 309 58 FREEHAND DRAWING stance and width at the place they touch and must not be represented by a mere thread of light. It would be a mistake to introduce much variety of direction in the lines in this drawing, especially in the shadows, as it would “ break it up ” too much. The concave line of the contour of the capital may well determine the dominant direction of the lines which should not be very distinct as lines, but should blend considerably into general tones. W herever a plane of shadow stops with a clean sharp edge the drawing must correspond, for its interest and expressiveness depend upon its power to suggest differences in surface — those surfaces which flow gradually into one another as well as those in which the transitions are sharp and abrupt. The student should be very scrupulous about using only the values of the scale, and in the lower left corner of each sheet he should place within half-inch squares examples of each value used on the drawing with its name and symbol indicated. PLATE XI. This capital, of the Roman Corinthian order, is in the Museum of the Baths of Diocletian in Rome. The foliated portions consist of olive acanthus, and the student should carefully study the differences between this and the soft acan- thus. It will be noted that the greatest difference is in the subdivi- sion of the edges into leaflets. In the soft acanthus there is always a strong contrast of large and small leaflets and the lobes overlap each other, producing a full rich effect and the general appearance is more like that of a natural leaf. In the olive acanthus the leaflets in one lobe differ slightly from each other in size, are narrower, and bounded by simple curves on either side, where the leaflet of the soft acanthus has the compound curve on one side. The student may use as many values as he thinks necessary, but he should be conscientious in keeping his values in their scale relations and should place an example of each value used, with its name in one corner of the drawing. To make a satisfactory drawing of a form so full of intricate detail as this is difficult, as there is a great temptation to put in all one sees. The general instructions for drawing Plate VII are equally applicable here. The student should remember that a drawing is an explanation, but an explanation which can take much for granted, 400 PLATE X. FIG. 2. Byzantine Capital, from the Church of San Vitale Ravenna. PLATE XI. Roman Corinthian Capital, from the Baths of Diocletian. PLATE XII. Italian Renaissance Pilaster. 62 FREEHAND DRAWING For instance, if the carved ornament on the mouldings or at the top of the capital are expressed where they receive full light, they must become more and more vague suggestions and finally disappear in the strong shadows; so the division line between the two mouldings of the abacus may be omitted in shadow and the mind will fill in what the eye does not see. One could go farther and express the detail only for a short space, letting it gradually die away into light or be merely indicated by a line or two, and still the explanation would be sufficient and far less fatiguing to the eye than literal insistence on every detail for the entire length. It is an excellent plan to look at the original, whether a photograph or the real object, with half closed eyes. This helps decidedly to separate the light masses from the darks and shows how much that is in shadow may be omitted. The smaller lobes on the olive acanthus have no main ribs and lines are carried from the intersection of each leaf toward the base, the section of the leaflet being concave. The section of the leaflets on the soft acanthus is more V-shaped. PLATE XII. This is a portion of a pilaster decoration in the Italian Renais- sance style. The acanthus is of the soft Roman type, but much more thin and delicate with the eyes cut back almost to the main ribs and a space cut out between each lobe so there is rarely any overlapping of lobes. Lay out construction lines for the scrolls, block in all forms correctly / detailing little by little, so carrying the whole drawing along to the same degree of finish 404 .Me-in. BvildirvR ARM°VR INSTITVTE op TECHNOLOGY A STUDY IN PEN AND INK RENDERING. (F° r a different treatment of the same building , see page 248.) RENDERING IN PEN AND INK, learn engraving on wood in a f< ink- rendering difficulties are to To render in pen and ink a large and important drawing is no small accomplishment. Usu- ally years of experience are nec- essary before one can sucess- fully undertake such drawings. Now and then a student is to be found having talent to the ex- tent that the attainment of this skill seems a very easy matter, but in general this talent is com- paratively rare. N inety-five out of every hundred have a long task ahead before success is pos- sible. This difficulty of attain- ment, however, makes the ac- complishment all the more val- uable. No one would expect to brief lessons, and yet in pen and met not unlike those connected with engraving. But there are many things concerning pen and ink work which can be readily learned ; they are worth the trouble and the labor expended, and may prove useful. A consideration of these will, in any case, introduce the art and serve also as a good founda- tion for further pursuit of the subject if desired. It is the purpose of this paper to seek the most modest of results, which may be set forth thus, — the rendering of a small building at a small scale in the very simplest manner, with few or no accessories. Kind of Drawing. There are three ways in which a sketch may be rendered, viz: with pen, pencil, or brush. Pen rendering will be considered first, and later additional notes will be made as to pencil work. Rendering with the brush is another line of work, 407 4 RENDERING but much that may be advised in regard to pen rendering would also apply to brush work. MATERIALS. Pens. The tendency of beginners is to use too fine a pen. It must be remembered that many pen drawings are reproductions much smaller than the originals, and consequently the lines appear much finer than in the drawing itself. There are two pens that can be recommended, shown herewith. Years of experience prove them to be perfectly satisfactory. Occasionally a finer pen is needed, such as Gillott No. 303. The Esterbrook No. 14, a larger pen, is necessary in making the blacker portions of a drawing. The Gillott 404 is to be used for general work in the same drawing. Ink is not of as ESTERBROOK BANK . . pen, no. 14. much importance as pens. The va- gillott no. 404. rious prepared India inks put up in bottles are all that can be desired. They are more convenient than ink that must be rubbed up, and they have the advantage of always being properly black. Some ordinary writing inks • serve the purpose very well if reproduction is not an object, but if reproduction is desired, India ink, being black, is preferred. Paper. The very best surface is a hard Bristol board. The softer kinds of Bristol boards should be avoided, as they will not stand erasure. Most of the drawing papers do very well. What- man’s hot pressed paper is very satisfactory. An excellent draw- ing surface is obtained by mounting a smooth paper on cardboard, thus obtaining a level surface that will not spring up with each pressure of the pen. This is equivalent to a Bristol board. However, the size of Bristol board is limited and frequently draw- ings must be much larger, in which case the mounted paper is a necessity. LINE WORK. Quality of Line. Too much stress cannot be laid on the im- portance of a good line, however insignificant it may seem. Care in each individual line is absolutely necessary for good work. A line 408 RENDERING 5 GOOD QUALITY OF LINE. that is stiff and Laid, feeble, scratchy or broken, will not do. Such work will ruin a drawing that in other respects may be excel- lent. The accompanying illustration by one of the students of the Massachusetts Institute of Technology is an example of excellent quality of line. Each line, even to the very smallest, has grace and beauty. By a very few, the ability to make such lines is speedily ac- quired — but by a few only — others may attain it by careful practice. Every line of a drawing-^the outline of the building and each line of the rendering, even to the very shortest must be done feelingly, gracefully, positively. Usually a WMtott «" Pin# lit (ii! Ilk miu/ju slight curve is advisable and if long lines are I end. used, a quaver or tremble adds much to the result. Each line of a shadow should have a slight pressure of the pen at the lower This produces a dark edge in the group of lines that 409 6 RENDERING make the shadows, giving definiteness to the shadow and contrast to the white light below it. Method. The combination of individual lines produces what we may term a method. The individual line may be good but the combining may be unfortunate. In making a wash drawing no thought is necessary concerning the direction of the wash, but in using lines at once the query arises as to what direction they shall take. A method is something one must grow into from a small, simple beginning. The accompanying illustration, the work of another Massachusetts Institute of Technology student, is an example of rare skill in method quickly acquired. There is an utter absence of anything rigid or mechanical in the w T hole. Ob- serve how softly the edges of the drawing merge in-to the white of the paper. The vigor of the drawing is gathered in the dormer itself. 410 RENDERING 7 Vertical Lines. The simplest method is ob- tained by the use of the vertical line. Some draw- ings can be made entirely by this means. See Fig. 3, every line of which is vertical. This illustrates the value of a good indi- vidual line. It will be d* observed that although ver- o tical, these lines are not severely straight and stiff, they tremble a little, or have a slight suggestion o oo of a curve. In the sliad- i* Ate, \ Fig. 4. FREE LINE METHOD. Fig. 3. VERTICAL LINE METHOD. ow at the bottom of the drawing each line is em- phasized at the top by a slight pressure, and made thin at the lower end in ' “ sA . * order to soften off the edges of the drawing as a whole. Free Lines. Eig. 4 shows another method. The vertical line is dis- carded and the freest pos- sible line is used. No one direction is followed, but the lines go in any or all directions. Which 411 8 BEN DERING is the better method ? The answer doubtless must be that the free method is the least conspicuous. It is better adapted for general use, in the showing of various surfaces and textures. VARIOUS EXAMPLES OF METHODS. Short, broken line, resulting in a spotty effect; a fault common with beginners. The white spaces between the ends of the lines are very conspicuous. Short lines, individually they may be very good, as they curve freely, but the combination is fussy and finnicky. The opposite in character to A. Long, unbroken lines, but so se- verely straight as to be hard and dry in general appearance. Direction of line not bad, but is rather too coarse to be agreeable. Wide spacing of lines on light por- tions add to the coarse result. These illustrate four bad methods. A has the least merit, the others approach to a fair quality. In E an effort is made to avoid all the faults shown in the others — the short or severely straight line, the over labor combination of C, and the coarse line of D. LIGHT AND SHADE. Values. If several lines are drawn parallel and quite close together, but not touching, a gray, or half-tone value is the result. 412 RENDERING 9 Lines drawn so close together that the ink of one runs into that of the other, with little or no white space between, give a black value. The white of the paper untouched by the pen gives a white value. Fig. 5 shows only two values — black and white; Fig. 6 also has two, — gray and white; Fig. 7 has the three, — black, gray and white. The first is harsh, the second is pale, and the third seems most satisfactory. This is a safe rule to follow — get into every pen drawing, black, gray and white. Usu- ally, in early attempts, there is a tendency to omit the black. Look for the place in the Fig. 6. GRAY AND WHITE. Fig. 5. BLACK AND WHITE. Fig. 7. BLACK, GRAY AND WHITE. 413 10 RENDERING drawing where you can locate this black; you are not likely to get too much of it. Let the half tone or gray be rather light, mid- way in strength between white and black. A heavy half tone is Fig. 8, ONE SIDE IN SHADE. a dangerous value. The black may often grade off into the gray, or there may be distinct fields or areas of each value. Lighting. The first thing to consider in the rendering of an architectural subject is the choosing of the direction of light. Sometimes when the building is turned well to the front, showing O ' o Fig. 9. ALL IN LIGHT. a sharp return of the end, it may be best to put that side in shade, Fig. 8, but it is not necessary. Values may be obtained by other means such as by shadows, or color of material. It is not wise to attempt a heavy rendering in pen work. Usually it is safer RENDERING 11 to keep both sides of the building in light as shown in two of these sketches, Figs. 9 and 10. Fig. 10. ALL IN LIGHT WITH HALF-TONE VALUE TO ROOF. Color of riaterial. One of the means by w T hich values may be introduced into a rendering, is by considering the color of the ma- terial of which the building is constructed. O Fig. 11. HALF-TONE WALLS. In this example, Fig. 11, we may first use the brick walls as a place to locate a gray value. In the second example, Fig. 12, the roof is used for the same value. For the very dark or black value we must depend on the shadows. Neither one of these draw- 415 12 RENDERING ings is wholly satisfactory.- In the first, the roof, and in the other, the walls, seem too glaringly white. For that reason it is not always best to use the material color so broadly. To give color to HALF-TONE ROOF. both walls and roof would destroy the white value, and the white value must not be lost. Fig. 13 shows an attempt at a compro- mise. Shadows Only. The simplest means for obtaining values is 416 RENDERING 13 by the use of shadows. Sometimes the shadows alone will com- plete a drawing in a very satisfactory manner, as in Fig. 14. Some of the shadows may be made gray, and others black or nearly so, in order to get the needed variety in values. A building like that shown in Fig. 15, The Alden House, is not favorable to shadows only. It has no porch or other projection sufficiently large to cast a strong shadow. In such a case a little accessory helps one out of the difficulty, and a little rendering of the material gives needed half tone. Otherwise the draw- ing would be too white. Principality or Accent. 4\ r e now enter into a matter of composition. One sim- ple rule will be given and there is none more useful. Let there be one place in the drawing where a strong accent of black shall exist. It may be one black, or it may be a group of them. This accent will be found in nearly every illustration in this paper. It is usually best to get the accent in the building itself, by the aid of some large shad- ow perhaps, but when there is no chance for this it may be neces- sary to get it in an accessory such as foliage. This is shown in Fig. 16, a drawing of a barn. In connection with this black accent let there be a large white area if possible. A princi- SHADOWS ONLY. 417 Por-t-EvJ £>e//i/N, a o B'/^aaioy RENDERING 15 pal white, as well as a principal black is thus obtained. Most drawings permit the dark accent and the light area also. Fig. 17 is rendered to a greater extent than should be at- tempted by the student in this course, but it may be helpful to call attention to some things in its composition. The location of the dark accent is apparent in the trees at the left. The other blacks, the trees in front of the building and those down at the extreme right, simply repeat in diminishing force and size, this first dark accent. The light area of the draw- ing is as distinctly shown as the dark accent; in fact this large light is the feature of this rendering. The light brick rendering of the gable is necessary to confine the light a little more surely to the important portion of the wall. Also, if this light rendering were omitted the building would appear unpleasantly white. The half tone of the roof is necessary to give a soft contrast to the light wall surface. The sky has its use. Cover it up, and see how the whole subject slumps downward. Last, but not least, observe that the corners of the drawing are kept free from rendering. This is usually safe. Let the rendering of every sort gather about the central object. The cor- ners of a drawing may then be left to take care of themselves. PENCIL WORK. A pencil is a quicker medium for the rendering of a sketch than a pen. A pencil sketch may be made directly on a sheet of drawing paper, and completed on that same sheet. But it is neater to first draw the perspective on smooth white paper, then place Alba tracing paper over this outline, and trace and render. By this means all construction lines in the layout can be omitted, 419 16 RENDERING and the sunny edge of projections can be left out, thus adding greatly to the brightness of the drawing. Use a soft pencil for rendering, a BB or softer. If the draw- ing is to be much handled, spray it with fixatif. Trim the sketch, lightly gum the corners, and lay on white card with good margin. SUMMARY. The following summary of advice for the rendering of work generally, with pen or pencil may be found helpful. 1. Consider the direction of the light. 2. Discover in the outline before you. the opportunity for a leading; dark accent. 3. Look out also for the location of a large light area. 4. Put in shadows. 5. Get at least three distinct values; black, gray and white. 6. Consider the color of roof or the wall, and if necessary use one of them or portions of each for a gray value. 7. Use a very free method. 8. Keep rendering out of the corners of the drawing. 1 AN APPLICATION OF PEN AND INK RENDERING TO THE CONVENTIONAL METHOD OF INDICATING PATHS, SHRUBBERY, TREES, TERRACES, ETC., IN PLAN. This is usually done in washes. ( See also t>ages 1 8 and 45 3 ) . EXAMINATION PAPER EXA'lf NATION PLATES. With this Instruction Paper are sent three sets of outline plates; one set for practice with pencil, one set for practice with ink and the third set (on better paper) to be rendered in ink and sent to the School for correc- tion and criticism. The practice work need not be sent to the School. Should the ink not flow well, rub the whole plate lightly with a soft eraser, or rub over it a little powdered chalk. Before beginning to render the drawing, dust off any loose chalk remaining on the paper. Plates I to VI inclusive constitute the examination for this instruction paper. The student’s name should be lettered in the lower right-hand corner in a manner similar to that shown in the illustrations of the Instruc- tion Paper. RENDERING 19 EXAMINATION PLATES. Before attempting to render the drawings in ink, the student is advised to practice both with pencil and ink, using the practice plates provided for the purpose. PLATE I. In order to get quickly into the practice, the student will he asked to make a copy of this rendering, Fig. A. Do not try to copy too exactly, but use the same freedom. Observe that the dark accent is obtained by the large shadow and the end of the long shadow just over it. The dark rendering in the window is brought into the group also. Having thus formed the accent, it is best that the shadow under the hood in the roof should be made rather light, lest it come into competition with the porch shadow. If the student prefers he may make it a trifle darker than here shown. A little clapboard rendering is put in on the left, to make still more evident the large light, which occurs mainly on the roof but at the same time takes in other white spaces at that end of the drawing. PLATE II. Tliis subject introduces a roof rendering, also a simple treat- ment of windows and blinds. Here the roof serves as a half-tone value. The shadow of the eaves and some of the blinds are the black values. To get the dark accent, the nearest blinds and the near portion of the shadow on the eaves are made very dark. The shadow under the porch shows how safely much of the detail of the door itself may be omitted and not be missed. A broad treatment is better than a fussy one. Observe that the roof lines are made as free as possible, avoiding a straight, wiry line. After copying this plate original work may be attempted. PLATES III AND IV. Make the shadows only for the first rendering, Plate III, just as shown in this value scheme, Fig. C. Then make a second drawing of the same, Plate IV, and give a half tone to the front area of the roof, and to the end of the roof a darker value, as shown in suggestion in upper corner. Finally on this second 425 PLATE OUTLINE DRAWING READY FOR RENDERING. All lines should be very light so as not to show through rendering. finished drawing. PLATE < Fig. B. (For Plate II.) ^LATE 3 TWO DIFFERENT TREATMENTS OF SAME SUBJECT, (See opposite page.) \3 3XV1J EENDEPJNG 21 drawing, put a small amount of rendering on the wall at the distant right, in the same manner as on Plate II. This will give a large white light on the walls nearest the observer. The long shadows under the eaves should be darkest at the corner nearest the observer and gradually lighten up as it approaches either end. PLATE V. Put in the shadows first. Get the nearest shadows very dark; then give a half-tone rendering to the whole of the brick-wall sur- face. Do not ink in the lines at the edges of the brick walls. Let O Fig. D. (For Plate V.) your rendering make the edge as shown in Fig. 18. An outline in such a place produces a mechanical looking rendering, as is seen in the illustration. Outlining is absolutely necessary where there 433 REN DEEDS G 99 is no rendering, but in connection with it, omit the outline, if PLATE VI. The doorway shadow selects for itself the honor of being the leading accent; the shadows at left and right simply repeat it in a small way. The roof affords an opportunity for half-tone. The Fig. E. (For Plate VI.) grass, which may be rendered as illustrated in the two preceding examples, gives also an additional half-tone value. To retain or produce a large light area, the stone jointing should be omitted on the upper portion of the wall, as indicated in the scheme. The roof may be rendered in a free line method, as shown in the sketch. With a good quality of line, and a free, vigorous method, this draw- ing will be a brilliant one, as its composition of values is favorable. 434 PLATE fl' 24 RENDERING This ends the practice. Only a beginning has been made in the work — a foundation laid, but it is a safe one. What has been taught will be a help to a further pursuit of the subject should the student feel that he has developed sufficient talent to encourage further study. Suggestion for treatment of house showing roof in light with half-tone value to walls. 436 CORINTHIAN CAPITAL, AND BASE. Showing conventional shadows and rendering. Original drawing by Emanuel Brune. Reproduced by permission of Massachusetts Institute of Technology. RENDERING IN WASH. All studies and completed exhibition drawings in the archi- tectural schools are tinted in India ink or water-color. This is done to show the shadows, and to indicate the relative position of the different planes, and is the method of representation in com- mon use in architects 5 offices, especially in the presentation of com- petition drawings. MATERIALS. Chinese, Japanese or India inks are used for rendering, on account of their clear quality and rich neutral tone. The ink comes in sticks, Fig. 1, and it is ground in a slate slab provided with a piece of glass for a cover. See Fig. 2. Fig. 1. India Ink. There are various kinds of brushes. Camel’s hair brushes are the cheapest and are useful for rough work. Sable brushes, Fig. 3, are two to three times as expensive as the camel’s hair ones on Fig. 2. Ink Slab account of the material, but are also very much better. The sable brushes have a spring to them not to be found in the camel’s hair brush, and they come to a finer, firmer point. Chinese and 441 2 RENDERING IN WASH Japanese brushes are used a good deal of late, as they are cheaper than the sable brushes and have some spring to them. A stip- pling brush is one with a square end, used mostly in china paint- ing. A bristle brush is a stiff brush used in oil painting ; on account of its stiffness it is used for taking out hard edges, as described later on. Fig. 4 shows a nest of porcelain cabinet saucers. Fig. 3. Sable Brush. Besides these materials the student should provide himself with a large and a small soft sponge, and large blotters, which will sop up water readily. Whatman’s “ cold pressed ” paper is the best paper to use for rendering in India ink. nETHOD OF PROCEDURE. Stretching Paper. All drawings on which washes are to be laid should be stretched, as described in the Mechanical Drawing, Part 1. Fig. 4. Nest of Saucers. Inking the Drawing. The lines should be drawn witli ground India ink, the ink being as black as possible without being too thick to flow. Ornament should be inked in with lighter lines than the vertical and horizontal lines. This accents the struc- tural lines. Very often the outline of the ornament is drawn in a heavier line than the remainder. The width of the line 442 RENDERING IN IV ASH n O should vary with the scale of the drawing, the larger and bolder the drawing the wider the line. India ink evaporates very rapidly. It should be kept covered and changed several times a day, especially in summer. After the drawing is inked it should be washed to remove the surplus ink, otherwise when the tint is applied the ink will spread. This is best done by placing it under a faucet and rubbino- it very dightly with a soft sponge. If the inking has been properly done the lines will now have the appearance of a firm pencil line of a soft neutral color forming a harmonious background for the tint. T1 le shadows should then be cast and drawn in with a hard pencil in faint lines. Preparing the Tint. For large washes India ink should be freshly ground in a clean saucer each time it is required. In no case use the prepared India ink which comes in bottles, as this is full of sediment which settles out in streaks on the drawiner. Always use the stick ink. Rub the ink in the saucer until it is very black; then let it stand, keeping the saucer covered. This allows the sediment, which is so fatal to a clear wash, to settle. After it has set- tled take the ink from the top with a brush without disturbing the bottom. Put this ink into another saucer and dilute it with the necessary amount of water. Never use the ink in the saucer in which it was originally ground. In dipping the brush into the second saucer it is well to take this ink also from the surface and thus avoid stirring any sediment wdiich may still remain in the ink. In other words, the sediment which is found in even the. most carefully ground ink should never be used for washes, otherwise streaks and spots may show in the washes. Where only a small surface is to be rendered the tint can be mixed- on a piece of paper in the same manner in which it is mixed in the saucer. Thus various shades can be obtained more quickly and experiments made more easily. Skill in laying washes is only acquired by practice. However, some instruction is neces- sary. If, after all possible care* has been taken during the draw- ing, such as placing paper under the hand to keep the paper from getting greasy and keeping the drawing covered to protect it from the dust, the paper has nevertheless become soiled, it should be 443 4 RENDERING IN WASH cleaned by giving it a light sponging with a very soft sponge and perfectly clean water. Touch the surface lightly, sop on the water liberally, and dry it off immediately with a sponge or blotter with- out rubbing. Before washing, the paper should be cleaned by rubbing it very lightly with a soft rubber. Especial care must be taken not to injure the surface of the paper by rubbing too hard. It may seem that all this care is unnecessary, but it is only by observing this extreme care that the skilled draftsman obtains the transparent wash and the beautiful, even, clear tints free from all streaks, which give so much charm to an India ink rendering. Handling the Brush. Skill in handling the brush is acquired only by constant practice. The brush demands great lightness of hand. The right arm should never support the body. The arm should not rest on the drawing; only the little finger of the right hand should come in contact with the paper. The brush should be held somewhat like a pencil between the thumb and index finger, and the little finger should be very free in its movements. Touch the paper only with the point of the brush. The brush should be well filled with the tint and care should be taken that there is practically the same amount of tint in the brush at all times. If this is not done, for example, if the brush is allowed to get too dry, one part of the wash will dry faster than the other and streaks will result. If the brush should be too wet, the surplus moisture can be removed by touching it to blotting paper. If the paper is too wet the surplus tint can be removed by drying the brush on blotting paper and applying it to the surplus tint which will then be rapidly absorbed by the brush. Great care must be taken not to remove too much of the tint; otherwise it will dry too fast and leave a streak. Laying Washes. There are two kinds of washes; the clear washes used in rendering shadows, window openings, etc., and the washes in which the color is allowed to settle, the latter being used to render the grounds surrounding a building. When laying clear washes it is better to tip the board slightly so that the washes may flow slowly in the direction in which they are being carried. If the board is placed flat there is danger of the wash running back over the part that is already dry and thus forming a streak. 444 r DORIC DOORWAY FROM ROMAN TEMPLE AT CORI, ITALY. An example of classic lettering - , conventional shadows and rendering, Reproduced by permission of Massachusetts Institute of Technology . RENDERING IN WASH 5 The edge of the wash should always be kept wet, for if it begins to dry a streak will surely follow. The tint should be carried down evenly across the board, moving the brush rapidly from side to side so that one side does not advance faster than the other. Carry the tint down about an inch at a time, the amount depending upon the size of the brush and of the surface rendered. Always go over the previous half inch at every new advance, taking care not to touch any part that has already dried. In this way the tint will dry gradually, parallel to the work. Carry the sides of the tint forward a little more slowly than the center. This will make the tint run towards the center and help to avoid the lines or streaks due to uneven drying. The tint should be carried forward in such a way that the paper will be thoroughly and evenly wet. In fact, it is a very good plan to dampen the entire drawing with a soft sponge before beginning to lay a wash This dampening should be carried well beyond the edges of the drawing so as to prevent the color from spreading to the drier and more absorbent parts of the paper. Always remove the pool of tint which remains at the bottom of a wash in the manner described under “ Handling the Brush.” If allowed to remain it will dry more slowly than the rest of the drawing and a streak will show. The drawing board should be left inclined until the wash is dry. Never lay one wash over another before the previous one is absolutely dry. In laying washes which grade gradually, either from dark to light or light to dark, grade the tint by the addition of water or color each time that an advance is made, and be careful that these additions are such that the change in color is made evenly. It is very difficult to lay an evenly graded dark tint with one wash only. It is usually better to lay a light flat wash or a light graded wash to serve for a background on which to lay the dark graded wash. By a flat wash is meant a wash which is the same tone or color throughout; that is, a wash that is not graded. See opening in Doric Doorway, Roman Temple, Cori, opposite page. Water has to be added constantly in grading. Where there is a series of graded washes, as in successive window openings, it is better to have two or three saucers containing tints of different 447 6 RENDERING IN WASH strength and carry each tint for the same distance in each window so that the gradation of color may be the same. In grading in this way it is necessary to carry each new wash well back over the old one so the point where one tint ends and another begins may not show. Sometimes gradations are obtained by laying successive flat washes, each wash beginning a little lower than the previous one. In this way the rendered surface will begin with one flat tint and end with a number of tints, one on top of the other. This is called the French method and is done by drawing very faint parallel lines at close intervals to mark the limit of each wash. A very light wash is then put over the whole surface, and this is followed with successive washes, each starting from the next lower line. This method is especially good for rendering narrow, long, hori- zontal graded washes. See rendering of mouldings in classical cor- nice, Fig. 5. Note particularly the application of this method on the crown moulding, and practically all the curved mouldings. Avoid laying too many washes in the same place, as the con- tinuous wetting and rubbing which the paper gets from the brush is liable to injure the surface. If the tints are too dark, a soft sponge can be used to lighten them or to take out hard or dark border lines ; but a large brush about two inches wide is still better for this purpose. If it is necessary to use a sponge, use it with a great deal of water, rub very lightly and very patiently. The water should be kept very clean, and the surrounding parts should be thoroughly wet before wetting the tinted part, otherwise the tint may spread over the other parts of the drawing. After using the sponge, dry the paper carefully with a clean blotter. Another and better way is to place the whole drawincr under the faucet, turn on the water and use the sponge or brush, as already described, on the parts to be lightened. To make light places darker, use the point of a brush, apply- ing the tint in small dots. Be careful not to begin with too dark a tint. This process is called stippling, and it must be done very gradually and very carefully. Do not forget that the first quality of a wash is crispness. It is necessary to draw with the same precision with a brush as with a pencil. When the drawing is finished it should be allowed to dry thoroughly before it is cut from the drawing board. 448 Fig. 5. Showing Lights and Shadows on Classical Cornice, and French Method of Rendering. 8 RENDERING IN WASH Rendering Elevations. The object of rendering a drawing is to explain the building. Those parts of the building nearest to the spectator should show the greatest contrast in light and dark, for in nature, as an object recedes from the eye, the contrast be- comes feebler and feebler and finally vanishes in a monotone. Every elevation shows the horizontal and vertical dimensions of a building, or details of a building, but in a line drawing the pro- jections of the different parts when in direct front elevation are not shown ; and it is to indicate these projections that the shadows are cast and the drawing is rendered. The appearance of a building or any details of a building will be clearly shown by the shadows in their different values of light and dark. (See plates, pages 172 and 440.) The windows and other openings of a building should be colored dark, but not black — although this is sometimes re- quired in competition drawings — and varying lighter tints should be used to indicate the color of the material in the roof and walls, the difference in the color intensity indicating the varying dis- tances from the spectator. Note in plate on page 189, the com- parative values of rendering in roof and shadows on roof ; also portions of order in light, portions in shadow, and background of column. This method of drawing is frequently carried to an elab- orate extent by showing high lights, reflected shadows, etc., and an elevation can thus be made to show almost as much of the character of the proposed building as would be shown by a perspective view or by a photograph of the completed structure. See frontispiece, “ Fragments from Roman Temple at Cori.” Study the different tone values of the various objects in the foreground and in the background, and note the perspective effect of the background. It is a good plan, before starting to render a drawing, to make a small pencil sketch to determine the tone values which the vari- ous surfaces should have, so that they will assume their proper relative positions in the picture. Drawings of this kind are much superior to any others as a means of studying the probable effect of the building to be con- structed, as they show the character of the building and, at the same time, dimensions can be figured directly on the drawing. It is difficult and unusual to give measurements on a perspective drawing. 450 10 RENDERING IN WASH Rendering Sections and Plans. Sections are frequently ren- dered in the same manner as elevations to show the interior of buildings. The shadows are cast in such a way that they show the dimensions and shapes of the rooms. The parts actually in section are outlined with a somewhat heavier line and tinted with a lio-ht o tint. The surfaces are modeled just as they are in the elevations. See Fig. 6. Plans are rendered to show the character of the different rooms by tinting the mosaic, furniture, surrounding grounds, trees, walks, etc. The shadows of walls, statuary, columns and furniture are often cast, so that the completed rendered plan is an architec- tural composition which tells more than any other drawing the character of the finished building. The interior of the building and all covered porticoes are left much lighter than the surrounding grounds because the buildincr is the most important portion of a drawing and should, therefore, receive the first attention of the. spectator. The sharp contrast of the black and white of the plan to the surroundings brings about the desired effect. The mosaic, furniture, etc., should be put in in very light tints in order to avoid giving the plan a spotty look. The walls in the plan should be tinted dark or blacked in so that they will stand out clearly. See Fig. 7. Graded Tints. One rule in laying all tints should be strictly followed : Grade every wash. A careful study of the actual shadows on buildings will show that each shadow varies slightly in degree of darkness ; that is, shows a gradation. The lower parts of window openings are, as a rule, lighter than the upper parts. Therefore, the washes or tints should grade from dark at the top of the door or window openings to light at the bottom. Further- more, it will be found that the reflection from the ground lights up shadows cast on the building, so that shadows which are dark at the top become almost as light as the rest of the building at its base. Windows and doors are voids in the facade of a building, and they have a greater value in the composition of a design than shadows or ornaments in general. This character should be care- fully shown in the rendering ; and to that end the grading should never show such violent contrasts as to distract the eye from the design as a whole, and thus destroy the unity of the design and 462 RENDERING IN WASH 11 the true mass of the openings. Many good designs are greatly injured in the rendering by the violent contrast in the grading of the openings from dark to light. In the shadow itself it will be found that detail is accented or Fig. 7. Conventional Method of Rendering Plan. (See also page 1 8 .) 458 12 RENDERING IN WASH brought out by reflected shadows. These shadows are in a direc- tion opposite to the shadows cast by the sun. If the light is assumed to come in the conventional way, namely at an angle of forty -five degrees from the upper front left corner to the lower back right corner, the reflected light may be assumed to be at an angle of forty-five degrees from the lower right front corner to the upper left rear corner, and the reflected shadows will accordingly be cast in this direction. See detail of Greek Doric Order, page 189. If these are worked up in their correct relation to one another the character of the details will be well expressed. Distinction Between Different Planes. The different planes of a building which project one in front of the other are distin- guished from each other in the following manner: The parts toward the front have a warm color, the portions receiving direct light have a tone over them indicating the mate- rial, the shadows are strong and bold, and the reflected shadows are more or less pronounced. The parts toward the rear, on the other hand, have no such strong contrasts of light and dark. The light parts are often left very light and the shadows put in even tones. The further the object is from the spectator the less pro- nounced will be the reflected lights and shadows. Note the grad- ing on the steps in plate, page 172, and study the frontispiece as an illustration of this point. In rendering, a difference should be made for different mate- rials. Note the difference between the stone and the metal work in Fig. 8. O A FEW WATER COLOR HINTS FOR DRAFTSMEN. Many draftsmen who are strong in drawing, are very weak in color work. The reason for this is, in most cases, that the colors are not fresh, that the brush is too dry, and that the color values are not correct. Fresh crisp color is most important. To get this it is necessary to start with a clean color box, clean brushes, and clean paints. The colors should be moist and not dry and hard. Tube and Pan Colors. After having acquired some facility in the use of colors, tube colors are the best to use, although they are somewhat more wasteful than pan colors. They are less likely to harden and dry up and are not more expensive. The 454 Fig. 8, Showing Difference in Rendering Stone and JNIetal. 14 RENDERING IN WASH colors in the tubes can be squeezed out on the palette as needed, and if this is done fresh bright effects are obtained. For the be- Fig. 9. Box for Pan Colors. ginner, however, pan colors are recommeded, as they are more easy to handle. Fig. 9 shows a japanned tin box for pan colors. Fig. 10 shows a pan color, and Fig. 11 a tube color. List of Colors: The following; list of colors will make a very good palette: Cadmium Indian Yelloiv Lemon Yellow Gallstone Yellow Ochre Orange Vermilion Carmine Light Red Burnt Sienna Warm Sepia Cobalt Blue New Blue Prussian Blue I aine's Gray Emerald Green Hooker's Green Chinese White The colors printed in italics are clear colors which will give clear even washes. The others will settle out, the color settling Fig. 10. Pan Color. WINS OR & NEWTON i ^ i W If TJatHbene Place. LTD,, tj] 1) j LONDON. ENGLAND I; ' -1 - MOIST COLOUR. li ■HE ^COBALT BLUF. S 01 Fig. 11. Tube Color. into the pores of the paper producing many small spots. This effect is often desirable, giving a texture which cannot be obtained with the clear colors. 456 RENDERING IN WASH 15 For use in the offices, India ink, Chinese white, gallstone, carmine and indigo will be found very convenient. The latter three are convenient forms of the three primary colors to use with India ink in rendering. Many draftsmen use these alone. manipulation. The washed-out look of many of the color sketches seen in architectural exhibitions is very noticeable. The sketches lack strength and crispness. Color properly applied should be put on boldly in broad simple washes without fear of too much color. Remember that colors when dry are much lighter than when in a moist state. Use plenty of clear water in the brush. Do not go over one wash with another before the first is entirely dry. This is particularly true where a deeper tone is to be put over a lighter one. In broad sky washes where there is a great deal of paper to be covered, dampen the surface well first with a small sponge, then with a large brush and bold yet light quick strokes put in the sky. Brushes and Paper. A small brush with a good point is necessary for “ drawing in ” and for detail. A bristle brush is very useful to remove color and to soften hard lines. Chinese brushes are very good, as they hold a great deal of color and at the same time have a good point. If an edge shows a hard line, this can be softened by dipping the bristle brush into clean water and rubbing the point lightly over the edge that is too hard, sopping up the water at frequent intervals with a clean blotter. It is important that plenty of clean water should be used and that the water be taken up with a blotter very often AYhen a “high light” is lost, and a bristle brush does not take out enough color, the “high light” may be put in with Chinese white, mixing it with a little of the color of the material. Look at your subject broadly and do not try to put in too many details. Whatman’s hot pressed 70- or 90-lb. paper is good to use. The hot pressed paper, which has a smooth surface, takes the color better than the rough surfaced or cold pressed paper, but the cold pressed has more texture and gives better atmospheric effects. Combination of Color. For the inexperienced a few hints as to what combinations of color to use may be helpful. It must 457 16 RENDERING IN WASH always be remembered that the colors must be clean to get fresh bright effects. O A simple blue sky: Prussian Blue, Antwerp Blue or Cobalt Blue. Clouds: Light Bed. For the distance use lighter tones with the addition of a little Emerald Green or Carmine. Dark part of clouds: Light Bed and New Blue. Boads and pathways in sunlight : Yellow Ochre and Light Bed with a little New Blue to gray it. Cast shadows: Cobalt and Light Bed or Carmine with a little green added. Grass in sunlight: Lemon Yellow and Emerald or Hooker’s Green; or Indian Yellow and Emerald Green. Grass in shadow: Prussian Blue and Indian Bed; or Prussian Blue and Burnt Sienna. Aurora Yellow and Prussian Blue gives a green color similar to Emerald. For gray roofs in sunlight: Light Bed and New Blue. Primary, Secondary and Complementary Colors. The com- bination of colors maybe learned by means of the diagram, Fig. 12, which will assist the student greatly in his water color work. The three primary colors are yellow, red and blue. The combination of any two of these will give a sec- ondary color — orange, purple or green. Two colors are called com- o plementary colors if the one is com- posed of two of the primary colors and the other one is the third pri- mary color. Thus, green, composed of the primary colors blue and yel- low, has as complementary color the third primary color; i.e., red. Con- sulting the diagram it will be found that opposite colors are complemen- tary colors; i.e , blue and orange, red and green, yellow and purple. If two complementary colors are put alongside of one another, each color will look brighter along- side the other than if plaeed by itself; this is due to the law of contrasts. Thus, the same green if placed alongside red, will look greener than when by itself, and the same holds good for the 458 RENDERING IN WASH 17 red. If complementary colors are mixed together you get a softer color, a gray and sometimes muddy effect. If blue, red and yel- low are mixed together in the right proportion a soft gray is obtained Water Color Rendering. Where colors are used for architec- tural drawings they should be mixed fresh, if clear tints are wanted, but in places where it is desired to have certain effects obtained by allowing color to settle, tints that have stood some time may be used. Especially is this true for plans, where the color is allowed to settle in putting in grass, trees, statues, etc. When it is desired to let the color settle it is better to leave the board flat and carry the color along with the brush, leaving it until it is dry. Some draftsmen keep the board level for all their work. Sketch elevations in pencil may be inked in or may be ren- dered directly in water color, the shadows being cast and various colored tints laid on to show the different materials, shadows, win- dow openings, etc. Sketches rendered in sepia only are very effective, putting in the lines with the pen, and rendering with light sepia washes. Elevations are usually most effective when the shadows are put in by washes that grade quickly from dark to light, brilliancy is thus obtained. It is astonishing what effects can be obtained with very faint washes. This applies especially to small scale drawings. The larger the scale of the building or detail, the stronger should be the coloring and values of light and dark. © © When sections are colored the parts actually in section are outlined with a strong red line and tinted a very light pink. The colors on the wall are merely suggested. On the plans the mosaic, furniture, etc., is often shown in a light pink. Where a statue has a prominent place it is put in in strong vermilion. Attention is called here to the fact that letter- ing on a plan counts as mosaic, and should be done in such a way that it will help the effect sought for, a very important point to remember in competition drawings. The important thing to remember in rendering is to get the correct relative value of lights and darks. To do this it is neces- sary to have clearly in mind what the important features to be brought out are and what is the most direct way of accomplishing 459 18 RENDERING IN WASH this ; in other words, the aim should be to make as harmonious a composition as taste, talent and thought can produce. Water Color Sketching. Nothing is more useful to an archi- tectural draftsman than out-of-door sketching in colors. A water color block should be his constant companion on his Saturday half holidays, and if possible, he should join some sketching class. The sketches in water color may be taken from natural scenery, but the student should also make studies and color sketches from color decorations of exterior and interior of buildings. Do not indicate too much in water color sketching, search for the big masses in shape and color values and put them in direct and simple. A draftsman who gives his leisure time to water color sketch- ing in summer, and to evening classes in drawing from the antique and from life in winter, will have as good a training as could be wished for in this part of his architectural career. 460 EXAMINATION PAPER PLATE A RENDERING IN WASH. General Remarks. Whatman’s cold pressed paper is the best for these examination plates. The Imperial size is 22 in. X 30 in., and one of these sheets will cut into two sheets 15 in. X 22 in., which will be large enough for all of the examination plates. The lines are to be inked with India ink, after which the drawing is to be washed before rendering. The lines must be drawn very neatly and carefully. Before starting to render, small pencil sketches should be made to study the relations of the lights and shadows and to deter- mine their values. The student will find that with the aid of such pencil sketches, he can render with greater accuracy, and will obtain quicker and better results. The shadows in plates C to E are indicated by dotted lines. In the finished drawings, these should be shown in fine light full pencil lines. In fastening the paper to the board, care must be taken not to allow the paste to extend more than half an inch back from the edge of the paper. Be sure to write your name and address legibly on the back of each drawing. PLATE I. This plate is to be three times the size of plate A and the different rectangles are to be rendered as follows: Rectangle A, with a light even wash similar in tone to “ High Light” in the value scale: Rectangle B, with a medium even wash similar to “ Middle”: Rectangle C, with a very dark even wash similar in tone to ‘‘Dark”: Rectangle D has various compartments which are to be rendered with an even wash having the same tone in each compartment similar to “ Low Light”: Rectangle E, with a medium even wash similar to ** Middle”, leav- ing the four enclosed spaces “ White”: 493 m - jO L v ' d ■ liffl L > /TV/?] Or /~&\ PLATE B RENDERING IN WASH Rectangle F, with alternating dark and medium stripes, the first, third, fifth and seventh stripe to be dark, similar to “ High Dark”, the others light sim- ilar to u Low Light”: Rectangle G has various strips which are to he graded evenly, the top strip be- ing the darkest, the next one a little lighter and so on until the last strip is very light in tone. The successive values of the strips should be “ Dark”, “High Dark”, “Middle”, “Low Light”, “Light” and “High Light”: Rectangle H, with a graded wash varying from dark at the top to light at the bottom. Care should be taken to have the wash evenly graded. The dark should be similar in value to “ High Dark” and the light similar to “ Low Light”: Rectangle I, with a graded wash varying from light at the top to dark at the bottom. In rendering this rectangle the board should not be turned around and the wash put on by grading from light to dark, but the board should be left in the same position and the wash graded by the admixture of color in- stead of water. The light should be similar to “ Light” and the dark sim- ilar to “Middle”: Rectangle J, with a graded wash varying from dark to light, the spaces between the two halves of the rectangle being left “ White”. The dark is similar to “ Middle” and the light similar to “ Light”. ■■■•/J Light VALUE SCALE. 465 PLATE C RENDERING IN WASH 25 The Value Scale is given merely to show the relative degrees of dark- ness, not to show the actual appearance of the wash. The wash itself must be perfectly clear and transparent Note. The various values should not be made in one wash. Better effects are obtained by superimposing several light washes and thus obtain- ing a dark wash, than by putting on a dark wash in one operation. PLATE II. This plate is to be drawn three times the size of plate B. The section of the mouldings is to be drawn first, then lines drawn at an angle of 45° from the different corners of the mouldings. The vertical surfaces are to be rendered darker than the horizontal ones as shown in the top moulding in the first column. The mould- ings in the second and fourth columns are to be rendered by the French method, drawing^*? light parallel pencil lines and render- ing by successive washes, as shown in the rendered illustrations. The mouldings in the third and fifth columns are to be rendered by grading directly, by the addition of water if the tone changes from dark to light or by the addition of tint if the tone chancres from light to dark. The letters and the border lines are to be rendered as indicated. A margin of half an inch of white paper is to be left outside of the border lines. PLATE III. Rendering of Doric Order. This plate is to be three times the size of plate C. The order is the same size as the order on plate VII, in the Roman Orders. For rendering the order, the plate on page 189, “ Detail of Greek Doric Order”, will serve as a guide. The background A should be graded from dark at the top to light at the bottom similar to the wash between the column and pilaster in the plate mentioned above. The mouldings may be put in by the French method as shown in Fig. 5. The background B should be a light evenly graded wash similar to the upper part of the background in the frontispiece, “ Fragments from Roman Temple”, having the wash somewhat darker at the top and grading it out to very light at the bottom. No trees, etc., are to be shown in the background. The steps will have a very light wash, that on step C being hardly noticeable, the step D a slightly more pronounced wash, and the step E a little darker still, but very light in tone. Study the value scale to determine these gradations. The tablet with letters may be rendered similar to the tablet at the bottom of 467 RENDERING IN WASH 26 the plate mentioned above. Reflected shadows are to be put in and care should be taken to show the reflected lights in the shade. o PLATE IV T1 lis plate is to be drawn double the size of plate D. A mar- gin one and one-half inches is to be left as a white border outside the border line. The “ Doric Doorway from Roman Temple at Cori”, page 446, will serve as a guide for rendering this plate. The window opening is to be rendered with an even dark wash, and the wall surface is to have a light tone. The shadows are indicated by a faint wash and are to be modeled and graded m such a way that they all have proper relative values. \ PLATE V. This plate is to be drawn double the size of plate E, and a margin of an inch and a half of white is to be left outside of the border line. Plate XXXI II, in the Roman Orders, can be used as a guide, the Temple drawn there being of the same size required for this problem. If the flutes on the columns are put in, they should be drawn with watered ink so that they are not too pronounced. The shadows and the parts in shade are shown by a faint flat wash outlined by dotted lines. All the lights and shadows are to be carefully modeled in their proper relations to one another. The wall Aj and A 2 is on a line with the rear wall of the Temple; hence the portion of the wall, A 2 , on the right of the Temple will be in shade, and the portion, A . on the left will have a light tone over it to show that it is in the background. For the rendering of the spaces between the columns ana the doorway, the plate 14 Detail from Temple of Mars Vengeur”, page 172, will be help- ful as well as for the rendering of the steps. The shadows on the steps will be similar in grading to the shadow of the altar on the steps. The bronze candelabra is to be rendered dark, care being taken to leave high lights of u White” on the round surfaces receiving the most direct light. For suggestions for rendering the bronze see Fig. 8. In rendering background, the frontispiece, 44 Fragments from Roman Temple at Cori”, will prove helpful. 468 PLATE D PLATE E Fig. 21. Study for Lettering on Granite Frieze of Boston Public Library, McKim, Mead & White, Architects. ARCHITECTURAL LETTERING Architectural lettering may be divided into two general classes. The first is for titling and naming drawings, as well as for such notes and explanations as it is usual or necessary to put upon them; this may well be called “Office Lettering.” The second includes the use of letters for architectural inscriptions to be carved in wood or stone, or cast in metal: for this quite a different character of letter is required, and one that is always to be considered in its relation to the material in which it is to be executed, and designed in regard to its adaptability to its method of execution. This may be arbitrarily termed “Inscrip- tion Lettering,” and as a more subtle and less exact subject than office lettering it may better be taken up last. OFFICE LETTERING. Architectural office lettering has nothing in common with the usual Engineering letter, or rather, to be more exact, the re- verse is true : Engineering lettering has nothing in common with anything else. Its terminology is wrong and needlessly confusing inasmuch as it clashes with well and widely accepted definitions. Therefore it will be necessary to start entirely anew, and if the student has already studied any engineering book on the subject, to warn him that in this instruction paper such terms as Gothic, etc., will be used in their well-understood Architectural meaning and must not be misinterpreted to include the style of letter arbitrarily so called by Engineers. The first purpose of the lettering on an architectural plan or elevation is to identify the sheet with its name and general descriptive title, and further, to give the names of the owner and architect. The lettering for this purpose should always be rather important and large in size, and its location, weight and 473 4 ARCHITECTURAL LETTERING height must be exactly determined by the size, shape and weight of the plan or elevation itself, as well as its location upon and relation to the paper on which it is drawn, in order to give a pleasing effect and to best finish or set off the drawing itself. The style of letter used may be suggested, or even demanded, by the design of the building represented. Thus Gothic lettering might be appropriate on a drawing of a Gothic church, just as Italian Renaissance lettering would be for a building of that style, or as Classic lettering would seem most suitable on the drawings for a purely Classic design; while each letter or legend would look equally out of place on any one of the other drawings. LETTER FORHS. It may be said that practically all the lettering now used in architectural • offices in this country is derived, however re- motely it may seem in some cases, from the old Roman capitals as developed and defined during the period of the Italian Renais- sance. These Renaissance forms may be best studied first at a large size in order to appreciate properly the beauty and the subtlety of their individual proportions. For this purpose it is Avell to draw out at rather a large scale, about four or four and one-half inches in height, a set of these letters of some recognized standard form, and in order to insure an approximately correct result some such method of construction as that shown in Figs. 1 and 2 should be followed. This alphabet, a product of the Renaissance, though of German origin, is one adapted from the well-known letters devised by Albrecht Diirer about 1525, and is here merely redrawn to a simpler constructive method and ar- ranged in a more condensed fashion. This may be accepted as a good general form of Roman capital letter in outline, although it lacks a little of the Italian delicacy of feeling and thus be- trays its German origin. The letter is here shown in a complete alphabet, including those letters usually omitted from the Classic or Italian inscrip- tions: the J, U (the V in its modern form) and two alternative W’s, which are separately drawn out in Fig. 1. These three do not properly form part of the Classic alpha- bet and have come into use only within comparatively modern 474 ARCHITECTURAL LETTERING 5 times. For this reason in any strictly Classic inscription the letter I should be used in place of the J, and the V in place of the U. It is sometimes necessary to use the W in our modern spelling, when the one composed of the double V should always be employed. The system of construction shown in this alphabet is not exactly the one that Diirer himself devised. The main forms of the letters as well as their proportions are very closeiy copied from the original alphabet, but the construction has been some- what simplified and some few minor changes made in the letters themselves, tending more towards a modern and more uniform character. The two W’s, one showing the construction with the use of the two overlapping letter V’s, and one showing the W incorporated upon the same square unit which carries the other Fig. 1. Two Alternative Forms of the Letter W, to accompany the Alphabet shown in Fig. 2. letters (the latter form being the one used by Diirer himself), are shown separately in Fig. 1. It should be noticed that every letter in the alphabet, except one or two that of necessity lack the requisite width — such as the I and J — is based upon and fills up the outline of a square, or in the case of the round letters, a circle which is itself contained within the square. This alpha- bet should be compared with the alphabet in Fig. 4, attributed to Sebastian Serlio, an Italian architect of the sixteenth century. By means of this comparison a very good idea may be obtained of the differences and characteristics which distinguish the Italian and German traits in practically contemporaneous lettering. After once drawing out these letters at a large size, the be- ginner may find that he has unconsciously acquired a better con- structive feeling for the general proportions of the individual let- 475 6 ARCHITECTURAL LETTERING ters and should thereafter form the letters free-hand without the aid of any such scheme of construction, merely referring occa- sionally to the large chart as a sort of guide or check upon the Fig. 2. Alphabet of Classic Renaissance Letters according to Albrecht Diirer, adapted and reconstructed by F. C. Brown. (See Fig. 1.) eye. For this purpose it should be placed conveniently, so that it may be referred to when in doubt as to the outline of any in- dividual letter. By following this course and practicing thor- 476 ARCHITECTURAL LETTERING ( oughlv the use of the letters in word combinations, a ready com- mand over this important style of letter will eventually be acquired. Fig. 2. (Continued) In practice it will soon be discovered that a letter in outline and of a small size is more difficult to draw than one solidly blacked-in, because the defining outline must be even upon both 477 8 ARCHITECTURAL LETTERING its edges ; and that as the eye follows more the inner side of this line than it does the outer, both in drawing and afterwards in recognizing the letter form, the inaccuracies of the outer side of the line are likely to show up against the neighboring letters, and produce an irregularity of effect that it is difficult to overcome, especially for the beginner; while in a solidly blacked-in letter, it is' the outline and proportions alone with which the draftsman must concern himself. Therefore, a letter in the same style is more easily and rapidly drawn when solidly blacked-in than as an “open” or outline letter. In many cases where it is desired to give a more or less formal and still sketchy effect, a letter of the same construction but with certain differences in its charac- teristics may be used. It should not be so difficult to draw, and much of the same character may still be retained in a form that TAVNTON'PVBLIC' LIBRA R V TAVNTON ' M A A A A C H V >5 E T T 5 ALBERT RANDOLPH RO.S.5 ARCHITECT ONE HUNDRED AND FIFTY SIX FIFTH AVENUE NEW YORK CITY Fig. 3. Title from Competitive Drawings for the Taunton Public Library, Albert Randolph Ross, Architect. is much easier to execute. Some such letter as is shown at the top of Fig. 10, or any other personal variation of a similar form such as may be better adapted to the pen of the individual drafts- man would answer this purpose. The titles shown in Figs. 3 and 5 include letters of this same general type, but of essentially different character. In drawing a letter that is to he incised in stone it is cus- tomary to show in addition to the outline, a third line about in the center of the space between the outside lines. This addi- tional line represents the internal angle that occurs at the meeting of the two sloping faces used to define the letter. An example is shown in Figs. 24 and 25, while in Fig. 7, taken from drawings for a building by McKim, Mead & White, the -same convention is frankly employed to emphasize the principal lettering of a pen-drawn title. 478 ARCHITECTURAL LETTERING 9 Fig. 4. Italian Renaissance Alphabet, according to Sebastian Serlio. 479 10 ARCHITECTURAL LETTERING For the purpose of devising a letter that may be drawn with one stroke of the pen and at the same time retain the general character of the larger, more Classic alphabet, in order that it may be consistently used for less important lettering on the same drawing, it is interesting to try the experiment of making a skeleton of the letters in Figs. 1 and 2. This consists in running a single heavy line around in the middle of the strokes that form JERSEY- GTY • FREE ’ PVBLIC * LIBRARY -SCALE - QNE’JNCH - Ej3V\LS - KM - FEET • BRJTL * AND - BACON * ARCHITECTS * IlIFlFlE ^AVENVE* NEW ^ YORK* QIY- Fig. 5. Title from Drawings for the Jersey City Public Library, Brite & Bacon, Architects. the outline of these letters. This “skeleton” letter, with a few modifications, will be found to make the best possible capital letter for rapid use on working drawings, etc., and in a larger size it may be used to advantage for titling details (Fig. 9). It will also prove to be singularly effective for principal lettering on plans, to give names of rooms, etc. (Fig. 13), while in a still smaller size it may sometimes be used for notes, although a minuscule or lower case letter will be found more generally useful for this purpose. In Fig. 6 are shown four letters where the skeleton has been drawn within the outline of the more Classic form. It is un- 480 ARCHITECTURAL LETTERING 11 o e < tU o & Ols 2 necessary to continue this experi- ment at a greater length, as it is believed the idea is sufficiently de- veloped in these four letters. In addition it is merely the theoreti- cal part of the experiment that it is desirable to impress upon the draftsman. In practice it will be found advisable to make certain further variations from this “skel- eton” in order to obtain the most pleasing effect possible with a single-line letter. But the basic relationship of these two forms will amply indicate the propriety of using them in combination or upon the same drawing. It will be found that the letter more fully shown in Fig. 10 is almost the same as the letter pro- duced by this “skeleton” method, except that it is more condensed. That is, the letters are narrower for their height and a little freer or easier in treatment. This means that they can be lettered more rapidly and occupy less space, and also that they will pro- duce a more felicitous effect. In actual practice, the free cap- itals shown in Fig. 10 will be found to be of the shape that can be made most rapidly and easily, and this style or some similar let- ter should be studied and practiced very carefully. Other examples of similar one-line capitals will be found 481 12 ARCHITECTURAL LETTERING used with classic outline or blacked-in capitals on drawings, Figs. 3, 5 and 7. In Figs. 8, 9 and 13 these one-line letters are used for principal titles as well, and with good effect. In Fig. 10 is shown a complete alphabet of this single-line blLl OF INDIANA LIMESTONE QENESEE VALLEY TRJ/ST COS bVILDINAi Fig. 8. Title from Architectural Drawing, Claude Fayette Bragdon, Architect. letter, and the adaptability of this character for use on details is indicated by the title taken from one and reproduced in Fig. 9. In the same plate, Fig. 10, is also shown an excellent form of small letter that may he used with any of these capitals. It is o. 22) OF Frejtonf Jhelt C 405 ■ COAmONWEALTtt Avl v_/e pCember - <2> ® ^ * Frank - Chouteau - brown -Architect- N ° \3 * PoLrko -cjtreet- Maair • Fig. 9. Title from Detail. quite as plain as any Engineer’s letter, and is easier to make, and at the same time when correctly placed upon the drawing it is much more decorative. This entire plate is reproduced at a slight reduction from the size at which it was drawn, so that it may he studied and followed closely. 482 ARCHITECTURAL LETTERING 13 - LETTERS FOR- - PRINCIPAL- TITLES- • SCALE THREE • QUAKERS • • OF AN INCH EQVALS ONE - • FOOT • Small Letters aabcd c&hyklmnopqnstuv • • wxyz • for rapid, -work CAPITALS ABGDEG FHIJKLMNOPQEJT UVXWYZ FEEE- HAND Fig. 10. Letters for Architectural Office use. 483 14 ARCHITECTURAL LETTERING Fig. 10 should be most carefully studied and copied, as it represents such actual letter shapes as are used continually on AN ALPHABET £r ARCHITECTS abcdefabi/klmnopg rsiuvwxuz 12J4567 Plan of Second Floor ABCPEFCHIJKLM NOPQkfTUVWYZ A gooS alphabet (or lettering plans &>tc Fig. 11. Single-line Italic Letters, by Claude Fayette Bragdon. architectural drawings, and such as would, therefore, be of the most use to the draftsman. He should so perfect himself in these alphabets that he will have them always at hand for instant use. 484 ARCHITECTURAL LETTERING 15 The alphabets of capital and minuscule one-line letters shown in Fig. 11 are similar in general type to those we have just been discussing, except that they are sloped or inclined letters and therefore come under the heading of “Italics.” The Italic letter is ordinarily used to emphasize a word or phrase in a sentence where the major portion of the letters are upright; B T P f CORINTHIAN CAP FROM HADRIAN BUILDINGS. ATHDNS. ROSE TTL FROM TEMPLE* OF MARS. ROME CAULICULUSI OF CORINTHIAN CAP BALUSTER) 3Y SAN GALLO Fig. 12. Drawing, by Claude Fayette Bragdon. but where the entire legend is lettered in Italics this effect of emphasis is not noticeable, and a pleasing and somewhat more unusual drawing is likely to result. If it is deemed advisable to emphasize any portion of the lettering on such a drawing, it is necessary only to revert to the upright form of letter for that portion. The single-line capitals and small letters on the usual archi- tectural plan or working drawing are illustrated in Fig. 13, where such a plan is reproduced. This drawing was not one made spe- 485 16 ARCHITECTURAL LETTERING cially to show this point, but was selected from among several as best illustrating the use of the letter forms themselves, as well as good- placing and composition of the titles, both in regard to the general outline of the plan and their spacing and location in the various rooms. It is apparent that it is not exactly accurate in the centering in one or two places. For instance, in the general title, the two lower lines are run too far to the right of the center line, and this should be corrected in any practice work where these principles will be utilized. It may be well to say that the actual length of this plan in the original drawing was thirteen Inches, and the rest of it large in proportion. The student should not attempt to redraw any such example as this at the size of the illustration. lie must always allow for the re- duction from the original drawing, and endeavor to reconstruct the example at the original size, so that it would have the same effect when reduced as the model that he follows. The letters for notes and more detailed information should be much simpler and smaller than and yet may he made to accord with the larger characters. Such a rapid letter as that shown in Fig. 10, for instance, may he used effectively with a severely clas;- sical title. Of course, no one with a due regard for propriety or for economy of time would think of using the Gothic small letter for this purpose. The portion of a drawing shown in Fig. 14 illustrates an- other instance of the use of lettering on an architectural working drawing. The lettering defined by double lines is in this case a portion of the architectural design, the two letters on the pend- ant banners being sewn on to the cloth while those on the lower portion of the drawing are square-raised from the background and gilded. Single-line capitals are used in this example for the notes and information necessary to understand the meaning of the drawing. A drawing of distinction should have a principal title of equal beauty, such as that shown in Fig. 5 or Fig. 7. The ex- cellent lettering reproduced in Fig. 12, from a drawing by Mr. Claude Fayette Bragdon, is a strongly characteristic and in- dividual form, although based on the same “skeleton” idea as the other types of single-line lettering already referred to. 486 Jicond - Floor,' Plan * • One, - G jv.g yt>e-r JncK vSccrle. Fig. 13. ARCHITECTURAL LETTERING 19 The ‘"skeleton” letter, formed on the classic Roman letter, displays quite as clearly as does the constructive system of Al- brecht Diirer, the distinctively square effect of the Roman capi- tal. The entire Roman alphabet is built upon this square and its units. The letters shown in Figs. 22 and 23 are redrawn from rubbings of old marble inscriptions in the Roman Forum, and may be taken as representative of the best kind of classic letter •ysamr BIGELOW KENNARD2CO GOLDSMITHS SILVERSMITHS JEWELERS IMPORTERS MAKERS OF FINE WATCHES AND CLOCKS 5ir WASHINGTON ST CORNER OF WEST ST Fig. 15. Advertising Design, by Addison B. Le Boutillier. for incision in stone. The Diirer letter, while a product of a later period, is fundamentally the same, and differs only in minor, if characteristic, details. However, for purposes of comparison it will serve to show the difference between a letter incised in mar- ble, or in any other material, and one designed for use in letter- ing in black ink against a white background. COMPOSITION. After acquiring a sufficient knowledge of letter forms, the student is ready to begin the study of “lettering.” W hile a knowledge of architectural beauty of form is the first essential, it 4S9 20 ARCHITECTURAL LETTERING BIGELOW, KENNARD AND CO. WILL HOLD, IN THE®. ART RO OMS, MARCH Sj TO APRIL 6 INCLUSIVE, A SPECIAL EXHIBI- TION AND SALE OF GRUEBY POTTERY INCLUDING THE COLLECTION SELECTED FOR THE BUFFALO EXPOSITION MDCCCCS WASHINGTON STREET COR- NER OF WEST STREET BOSTON Fig. 16. Cover Announcement, by Addison B. Le Boutillier. ARCHITECTURAL LETTERING 21 is not the vital part in lettering, for the composition of these sep- arate characters is by far the most important part of the problem. Composition in lettering is almost too intangible to define by any rule. All the suggestions that may be given are of necessity laid out on merely mathematical formulae, and as such are in- capable of equaling the result that may be obtained by spacing and producing the effect solely from artistic experience and intui- tion. The final result should always be judged by its effect upon the eye, which must be trained until it is susceptible to the slight- est deviation from the perfect whole. It is more difficult to define what good composition is in lettering than in painting or any other of the more generally accepted arts, and it resolves itself back to the same problem. The eye must be trained by constant study of good and pleasing forms and proportions, until it appre- ciates instinctively almost intangible mistakes in spacing and ar- rangement. This point of “composition” is so important that a legend of most beautiful individual letter forms, badly placed, will not produce as pleasing an effect as an arrangement of more awkward letters when their composition is good. This quality has been so much disregarded in the consideration of lettering, that it is important the student’s attention should be directed to it with additional force, in order that he may begin with the right feel- ing for his work. An excellent example of composition and spacing is shown in Fig. 16, from a drawing by Mr. Addison B. Le Boutillier. The relation between the two panels of lettering and the vase form, and the placing of the whole on the paper with regard to its margins, etc., are exceptionally good, and the rendered shape of the vase is. just the proper weight and color in reference to the weight and color of the lettered panels. In this reproduction the border line represents the edge of the paper upon which the design itself was printed, and not a border line enclosing the panel. The real effect of the original composition can be obtained only by eliminating the paper out- side of this margin and by studying the placing and mass of tin- design in relation to the remaining “spot” and proportions of the paper. Perhaps the simplest and most certain way to realize the 491 22 ARCHITECTURAL LETTERING effect of tlie original is to cut out a rectangle tlie size of this panel from a differently colored piece of paper, and place it over the page as a “mask,” so that only the outline of the original design will show through. The other example by the same designer, shown in Fig. 15, is equally good. The use of the letter with the architectural ornament, and the form, proportion, spacing and composition of the lettering are all admirable. The title page, by Mr. Claude Fayette Bragdon, shown in Fig. 17, is a composition in- cluding the use of many differ- ent types of letters ; yet all be- long to the same period and style, so that an effect of sim- plicity is still retained. In composition, this page is not unlike its possible composition in type, but in that case no such variety of form for the letters would be feasible, while the en- tire design has an effect of coherence and fusion which the use of a pen letter alone makes possible, and which could not be obtained at all in typograph- ical examples. The treatment of the ornament incorporated in Fig. 17 . Title Page, by Claude this design should be noticed for Fayette Bragdon. its weight and rendering, which bear an exact relation to the “color” of the letter employed. In Fig. 18 is a lettered panel that will well repay careful study. The composition is admirable, the letter forms of great distinction — especially the small letters — and yet this example has not the innate refinement of the others. The decorative panel at the top is too heavy, and the ornament employed has no special beauty of form, fitness, or charm of rendering (com- pare Figs. 15 and 10), while the weight of the panel requires STORIES from the <=^D Chap-Book Being a MISCELLANY op Curious and interefting Tale* Hiftories, &c; newly com- pofed by Many Celb- b rated Writers and very delight- ful to read. CHICAGO: Printed for Herbert S. Stone tj Company. and are to be fold by them at The CaatonBu.ild.iTVi in Dearborn Street ibyC 492 ARCHITECTURAL LETTERING 23 some such over-heavy border treatment as has been used. Here, again, in the slight Gothic cusping at the angles a lack of restraint or judgment on the part of the designer is indicated, this Gothic touch being entirely out of keeping with the lettering itself, and only partially demanded by the decorative panel. Of course, it Our First Exhibit of ROOKWQOD POTTERY comprising several hundred pieces of the best creations of this celebrated pottery will open Monday March 9th, 1903 in, th e,Roo£woocl ‘Room Third Floor, Annex MARSHALL FIELD COMPANY Fig. 18 . Advertising Announcement. is easy to see that these faults are all to be attributed to an attempt to attract and hold the eye and thus add to the value of the design as an advertisement ; but a surer taste could have obtained this result and yet not at the expense of the composition as a whole. It is nevertheless an admirable piece of work. In Fig. 19 is shown an example of the use of lettering in 493 24 ARCHITECTURAL LETTERING composition, in connection with a bolder design, in this case for a book cover, by Mr. H. Van Buren Magonigle. Note the nice sense of relation between the style of lettering employed and the design itself, as well as the subject of the work. The letter form is a most excellent modernization of the classic Roman letter shape (compare Figs. 22 and 23). Fig. 19 . Book Cover, by H. Van Buren Magonigle. The student must he ever appreciative of all examples of the good and bad uses of lettering that he sees, until he can distin- guish the niceties of their composition and appreciate to the utmost such examples as the first of these here shown. It is only by constant analysis of varied examples that he can be able to distinguish the points that make for good or bad lettering. 494 ARCHITECTURAL LETTERING 25 SPACING. There is a workable general rule that may be given for obtaining an even color over a panel of black lettering; that is, if the individual letters are so spaced as to have an equal area of white between them this evenness of effect may be attained. But when put to its use, even this rule will be found to be surrounded by pitfalls for the unwary. Ibis rule for spacing must not be understood to mean that it applies as well to composition. It does not: it is, at the best, but a makeshift to prevent one from eroinir far wrong in the general tone of a panel of lettering, and must therefore fully apply only to a legend employing one single type of letter form. One with sufficient authority and experience to give up de- pendence upon merely arbitrary rules, and to rely upon his own judgment and taste may, by varying sizes and styles of letters, length of word lines, etc., obtain a finer and much more subtle effect. To acquire this authority in modern lettering it is necessary to observe and study the work turned out today by the best de- signers and draftsmen, such as the drawings of Edward Penfield, Maxfield Parrish, A. B. Le Boutillier and several others. The architectural journals, also, publish from month to month beauti- fully composed and lettered scale drawings by such draftsmen as Albert R. Ross, II. Van Buren Magonigle, Claude Fayette Brag- don, Will S. Aldrich and others, who have had precisely the same problem to solve as is presented to the draftsman in every new office drawing that he begins. Of course, the freer and the further removed from a purely Classic capital form is the letter shape employed by the drafts- man, the less obliged is he to follow Classic precedent ; but at the same time he will find that his drawing at once tends more toward the bizarre and eccentric, and the chances are that it will lose in effectiveness, quietness, legibility and strength. The student will soon find that he unconsciously varies and individualizes the letters that he constantly employs, until they become most natural and easy for him to form. This insures his developing a characteristic letter of his own, even when at the start he bases it upon the same models as have been used by many other draftsmen. 495 26 ARCHITECTURAL LETTERING niNUSCULE OR SHALL LETTERS. In taking up the use of the small or minuscule letter, a word of warning may be required. While typographical work may furnish very valuable models for composition and for the individ- ual shapes of minuscule letters, they should never be studied for the spacing of letters, as such spacing in type is necessarily arbi- trary, restricted and often unfortunate. Among the lower case types will be found our best models of individual minuscule letter forms, and the Caslon old style is especially to be com- mended in this respect; but in following these models the aim must be to get at and express the essential characteristics of each letter form, to reduce it to a “skeleton” after much the same fashion as has already been done with the capital letter, rather than to strive to copy the inherent faults and characteristics of a type-minuscule letter. The letter must become a “pen form” before it will be appropriate or logical for pen use; in other words, the necessary limitations of the instrument and material must be yielded to before the letter will be amenable to use for lettering architectural drawings. The small letters shown in Figs. 17, 18 and 20 are all adapted from the Caslon or some similar type form, and all ex- hibit their superiority of spacing over the possible use of any type letter. Fig. 20 is a particularly free and beautiful example indicating the latent possibilities of the minuscule form that are as yet almost universally disregarded. An instance of the use of the small letter shown in a complete alphabet in Fig. 10, may be seen in Figs. 9 and 13. In lettering plans for working drawings, the small letter is used a great deal. All the minor notes, instructions for the builders or contractors, and memoranda of a generally unimpor- tant character, are inscribed upon the drawing in these letters. Referring again to Fig. 10, the letters at the top of the page would be those used for the principal title, the name of the drawing, the name of the building or its owner, while the outline capitals would be used in the small size beneath the general title, to indicate the scale and the architect, together with his address. Tn a small building, or one for domestic use, these same letters would be employed in naming the various rooms, etc., although in an 496 ARCHITECTURAL LETTERING 27 elaborate ornamental or public building, letters similar to those in the principal title might be better used, while the minuscule letter would be utilized for all minor notes, memoranda, direc- tions, etc. By referring to Figs. 3, 5, 7, 8, 9, 13 and 14, examples from actual working drawings and plans are shown, which should sufficiently indicate the application of this principle. It must again be emphasized that practice in the use of these forms combined together in words, as well as in more diffi- cultly composed titles and inscriptions where various sizes and kinds of letters are employed, is the only method by which the draftsman can become proficient in the art of lettering; and even then he must intelligently study and criticise their effect INTERAVDES benoath tho Linens of SIR. R.ICHAR.D LOVELAGE POEM called — '"To Luoafta on going to the_> wars " which saith : Fig. 20. Pen-drawn Heading, by Harry Everett Townsend. after they are finished, as well as study continually the many good drawings carrying lettering reproduced in the architectural jour- nals. For this purpose, in order to keep abreast of the modern advance in this requirement, he must early learn to distinguish between the instances of good and bad composition and lettering. ARCHITECTURAL INSCRIPTION LETTERING. The use of a regular Classic letter for any purpose neces- sitates the reversion to and the study of actual Classic examples for spacing and composition. In using this letter in a pen- drawn design, certain changes must be made in adapting it from the incised stone-cut form — which variations are, of course, prac- tically the reverse of those required in first adapting the letter for use in stone. The same letter for stone incision requires, in addition, a careful consideration of the nature of the material, and the spacing and letter section that it allows. Also the effect 497 ABCDEFGHIJKLMN Architectural Capitals. ARCHITECTURAL LETTERING 29 of a letter in the inscription in place must be carefully studied, its height above or below and relation to the eye of the observer, f he fact is that the letter form must in this case be determined solely by the light and shadow cast by the sun on a clear, bright day, or diffused more evenly on a cloudy one. If in an interior location its position in regard to light and view-point is even more -important, as the conditions are less variable. CLASSIC ROMAN LETTERS. In any letter cut in stone, or cast in metal, it is not the out- line of the letter that is seen by the eye of the observer, but the shadow cast by the section used to define the letter. This at once changes the entire problem and makes it much more complicated. In incising or cutting a letter into an easily carved material, such as stone or marble, we have the examples left us by the inventors, or at least the adapters, of the Roman alphabet. They have gen- erally used it with a V-sunk section, and in architectural and monumental work this is still the safest method and the one most generally followed. One improvement has been made in adapt- ing it to our modern conditions. The old examples were most often carved in a very fine marble which allowed a deep sinkage at a very sharp angle, thus obtaining a well-defined edge and a deep shadow. In most modern work the letters are cut in sandstone or even in such coarse material as granite, where sharp angles and deep sinkage of the letter-section is either impossible, or for com- mercial reasons influencing both contractors and stonecutters, very hard to obtain. To counterbalance this fault a direct sinkage at right angles to the surface of the stone before beginning the V section has been tried, and is found to answer the purpose very well, as it at once defines the edge of the letter with a sharp shadow. See the two large sections shown in the upper part of Fig. 31. This section requires a letter of pretty good size and width of section, and, therefore, may be used only on work far removed from the eye, as is indeed alone advisable. An inscription that is to be seen close at hand must rely upon the more correct section and be cut as deeply as possible. For lettering placed at a great height, an even stronger effect may be obtained by making the incised section square, and sinking it directly into the stone. 499 so ARCHITECTURAL LETTERING Such pleasant grading of shadows as may be attained by the other method is then impossible, and there are no subtle cross Fig. 22. Classic Roman Alphabet. From Marble Inscriptions in the Roman Forum. lights on the rounding letters to add interest and variety, but the letter certainly carries farther and has more strength. 500 ARCHITECTURAL LETTERING 31 In Fig. 21 is shown a photograph from a model of the incised V-sunk letters cut in granite on the frieze of the Boston Fig. 23. Fragments of Classic Roman Inscriptions. Public Library. This photograph indicates the shadow effect that defines the incised form of the letter, and will assist the student 32 ARCHITECTURAL LETTERING somewhat in determining the section required for the best effect It will be observed that this letter is different in character from the one used by the same architects in a different material, sand- stone, shown in Fig. 24. In Fig. 22 is shown an alphabet redrawn from a rubbing of Roman lettering, and in Fig. 23 are shown portions of Classic inscriptions where letters of various characters are indicated. These letters were very sharply incised with a Y-sunk section in marble, and were possibly cut by Greek workmen in Rome. It is on some such alphabet as this that we must form any modern letter to be used in a Classic inscription or upon a Classic build- ing. These forms should be compared with the letters shown in Fig. 24, on the Architectural Building at Harvard, by McKirn, Mead & White, architects, where they were employed with a full understanding of the differences in use and material. The Roman letter was cut in marble ; the modern letter in sandstone. Both were incised in the V-sunk section, but the differences in material will at once indicate that the modern letter could not have been cut as clearly nor as deeply as the old one. The modern letter was done a little more than twice the original size of the old one, which explains certain subtleties in its outline as here drawn. The sandstone being a darker material than the marble, the letter should of necessity be heavier and larger in the same location, in order to “carry” or be distinguishable at the same distance; while the Classic example, being sharply and deeply cut in a beautiful white material which even when wet retains much of its purity of color, would be defined by a sharper and blacker outline, and therefore be more easily legible, other conditions being the same, even for a longer distance. In both these figures, the composition of the letters may be seen to advantage, as in even the Classic example, where they are alphabetically arranged, they are placed in the same relation to each other as they held in the original inscription. A complete alphabet of the letter shown in word use in Fig. 24, is shown at larger size in Fig. 25. Although the lettering of the Italian Renaissance period was modeled closely after the Classic Roman form, it was influenced by many different considerations, styles and peoples. 502 Lettering from Harvard Architectural Building. McKim. Mead & White, Architects. 34 ARCHITECTURAL LETTERING Fig. 25. Complete Alphabet. Redrawn from Inscription on Architectural Building (See Fig. 24). 504 ARCHITECTURAL LETTERING. 35 505 36 ARCHITECTURAL LETTERING Fig. 26. Fragment of Italian Renaissance Inscription. From the Marsuppini Tomb in Florence. 506 ARCHITECT!.' 1! AL LETTERI XG 37 ITALIAN RE- NAISSANCE LETTERING ABCDEFG H1JK.LMNE OPQRSTU VXWYZ Fig. 27. Italian Renaissance Lettering. Adapted from Inscription shown in Fig. 26. 507 38 ARCHITECTURAL LETTERING In Fig. 26 is shown a fragment of the inscription on the Marsuppini tomb at Florence. This outline letter was traced from a rubbing, and shows very nearly the exact character of the original, a marble incised letter. Fig. 27 is an alphabet devised TOpaeunx^sf-prpp FlTOeffpoMppCfl-wBi Fig. 28. Italian Renaissance Inscription at Bologna. from this incised letter for use as a pen-drawn form and redrawn at the same size. It will be noticed that in the letters shown in the four lower lines a quite different serif* treatment has been adopted, and certain of the letters, such as the F/s, have been fRKPR-9-Olfl QOB1-D0 RFHH RISD0R6609I PSOFlOCRXLai Fig. 29. Italian Renaissance Inscription, Chiaravelle Abbey in Milan. “extended” or made wider in proportion. These variations are such as modern taste would generally advocate, but in the first three lines of this plate the feeling, serif treatment and letter width of the original have been retained ; the only change has *Note. The “serif” is the short spur or cross stroke used to define and end the main upright and horizontal lines of the letter. 508 ARCHITECTURAL LETTERING 39 H0GO Gfi0E iann CD D O Q QG06 avcnis Z3ZW Fig. 30 . Alphabet of Uncial Gothic Capital Letters, 16 th Century. 509 40 ARCHITECTURAL LETTERING been to narrow up the thin lines in relation to the thick lines to the proportions that they should have in a solidly black and inked-in letter form. The two small panels, one from a monument in Bologna, and one from the Cliiaravelle Abbey in Milan, Figs. 28 and 29, show a letter which was incised in stone and follows the so-called uncial or round form, with characteristics showing the probable influence of the Byzantine art and period. These two inscriptions may be compared with another alphabet showing the uncial character when used in black against' a white page, as in Fig. 30. This same style of letter was often used in metal, and may be seen in many of the mortuary slabs of this and succeeding periods. Fig. 31. Inscription Letter Sections. In many of the Renaissance wall monuments the V-sunk letter sections have been filled with a black putty to make the letter very clear, and when this falls out, as it often does, the V-cut section may still be seen behind it. Also in many Italian floor slabs the letters are either V-sunk or shallow, square sinkages filled with mastic, or sometimes they are of inlaid marble of a color different from the ground. Again a V-sunk letter section sometimes carries an additional effect because it is smoothly cut 510 ARCHITECTURAL LETTERING ABCDEFG I HljKLMNM NPPQQRK SVTWXYZ Fig. 32. English 17th Century Letters, from Tombstones. 511 42 AECHITECTUEAL LETTEEING and finished and the surface of the stone is left rough, thus obtaining a different texture and color effect; or, though more rarely, the opposite treatment may be used. Then, again, the sides of the letter sinkage may be painted or gilded. Often even the shadow is painted into the section, but this is generally done on interior cutting where there is no direct light from the sun, because if direct sunlight does fall upon a letter so treated, a very amusing effect occurs when the shadow is in any other position than that occupied by the painted representation. For still further effects, raised lettering may be cut on stone surfaces. This is more expensive, as it necessitates the more labor in cutting back the entire ground of the panel, but for certain purposes it is very appropriate. In such a letter the section may be a raised V-shape, or it may be rounded over to make a half circle in section, as drawn in Fig. 31. This latter form is especially effective in marble, but it is, of course, very delicate and does not carry to any great distance. Its use should be restricted to small monu- mental headstones or to lettering to be read close to, and below the level of, the eye. A raised letter is more generally appropriate for cast copper and bronze tablets, when its section may be a half round, a raised V-form, or square-raised with sharp corners ; or, better still, a combination of square and V-raised with a hollow face. See Fig. 31. Experience has proved that this last-named section produces the most telling letter for an ordinary cast-metal panel. Fig. 32 shows an alphabet of a letter derived from English tombstones. This letter was cut in slate or an equally friable material, and was comparatively shallow. A certain tendency toward easing the acute angles may be observed in this alphabet, evidently on account of the nature of the material in which it was carved rendering it easily chipped or broken. In wood carving, a letter exactly reversing the V-sunk sec- tion with direct sinkage, gives the best effect for a raised letter. Every material, from its nature and limitations, requires special consideration. A letter with many angles is not adapted to slate, as that material is liable to chip and sliver; hence an 512 A RCII ITECTU RA L LETTE KING Fig. 33. German Black Letters, from a Brass. 513 44 ARCHITECTURAL LETTERING uncial form with rounded angles suggests itself (as in Fig. 29), and is, indeed, frequently used. It would be quite impossible to take up in detail the entire list of available materials and consider their limitations at length, as the task would be endless. For the same reason, it is not possible to take up each letter style and consider its use in stone and other materials. Of course, a Homan letter or any other similar form when drawn for stone-incised use must have its narrow lines at least twice as wide as when drawn in ink, black against a white background. (Compare Figs. 26 and 27.) Experience and intuition combined with common sense will go farther than all the theory in the world to teach the limitations Fig. 34. Black-Letter Alphabet. required by letter form and material. The student, however, should bear in mind that it is not necessary that he himself should make a number of mistakes in order to learn what not to do. lie may get just as valuable information at a less cost by observing the mistakes and successes of others in actually executed work, and avail himself of their experience by applying it with intelli- gence to his own problems and requirements. GOTHIC LETTERING. Gothic lettering is extremely difficult, and has little practical use for the architectural designer or draftsman. It is often appropriate, but it is quite possible to get along without employing this form at all. However, in case he should require a letter of this style, it would be better to refer him to some book where he may study its characteristics more particularly, remembering it is just as important he should know something of the history, 514 ARCHITECTURAL LETTERING 45 uses and materials from which this letter has been taken, as in any instance of the use of the Roman form. Indeed, it might be Fig. 35. Italian Black Letters, after Bergomensis. said, it is even more important, as the Gothic letter is more uni- versally misunderstood and misapplied than the simpler Iloman letter. 515 46 ARCHITECTURAL LETTERING Fig. 36. English Gothic Text. 516 ARCHITECTURAL LETTERING 47 The alphabet of German black letters shown in Fig. 35 is taken from a very beautiful example of Gothic black letter devised bj Jacopus Pbillipus Foresti (Bergomensis) and used bv him in the title page of “De Claris Mulieribus,” etc., published* in Fer- rara in 149 i . Although Italian, this letter is as German in character as any of the examples from the pen of Albrecht Diirer. A German black letter redrawn from a brass is shown in Fig. 33, while an English form of Gothic letter is shown in Fig. 30. In Fig. 34 is another example of a black-letter alphabet. The entire effect of a black-letter page depends upon the literal interpretation of the title “black letter.” That is, the space of white between and among the letters should be overbalanced by the amount of black used in defining the letter form itself. Inasmuch as this letter is likely to be used but little by architectural draftsmen, and as it is a much more difficult form to compose than even the Roman type, it seems better to refer the student to some treatise where its characteristics are taken up more thoroughly and at greater length. Any draftsman having occasion to use lettering to any extent should have some fairly elaborate textbook always at hand for reference. EXAMINATION PLATES. In addition to the following Examination Plates the student is expected to make careful reproductions of the lettering in this Instruction Paper. These plates need not be sent to the School. PLATES I, II, III. Draw the alphabet, using the same construction as given in Figs. 1 and 2, and making each letter two inches high. Put ten letters on each of the first two plates, and on the third arrange the remainder, including the two forms of W given in Fig. 2. 517 48 ARCHITECTURAL LETTERING PLATE IV. Make a careful reproduction of Fig. 10 on the left-hand side of the plate. The letters should be of the same size as in Fig. 10. On the right-hand side of the plate use the letter forms shown in Fig. 10 and of the same size, and letter the following title, arrang-. ing the legend to look well on the plate: Front Elevation, Coun- try House at Glen Ridge, New Jersey, Aug. 24, 1903. David Carlson Mead, Architect, No. 5925 State St., Chicago, 111. PLATE V. Reproduce on this plate Figs. 27 and 32 of the Instruction Paper, using letters of the same size. PLATE VI. On the left-hand side of this plate, copy the lettering shown in Fig. 9, making the letters at least as large as those in the illus- tration. On the right-hand side, following the same style and size, letter the following title: Detail of Entrance Porch, Coun- try House at Glen Ridge, New Jersey, Sept. 10, 1903. David Carlson Mead, Architect, No. 5925 State St., Chicago, 111. This plate to be done in pencil only. PLATE VII. Using individual letter forms like those shown in Figs. 24 and 25, letter the following title: Museum of Architecture, Erected in Memory of John Howard Shepard, First President Technology, Bangor, Me. The letters should be of a size suited to the title; the title should occupy five lines. All plates except Plate VI should be inked in. The student should first lay out his lettering in pencil in order to obtain the proper spacing of the center line on his page or panel. He should also place guide lines in pencil at the top and bottom of his lettering for both capitals and small letters. The plates should be drawn on a smooth drawing paper 11 inches by 15 inches in size. The panel inside dhe border lines should be 10 inches by 14 inches. For best work Strathmore (smooth finish) or Whatman’s hot-pressed drawing paper is recommended. The date, the student’s name and address, and the plate number should be lettered on each plate in one- line letters such as are shown in Fig. 10. 518 GENERAL INDEX irsuDEzx: The Cyclopedia of Drawing is inn.de up of the regular instruction papers from courses in the American School of Correspondence at Armour Institute of Technology. The titles and page numbers of these instruction papers are given as running headings at the top of the pages. The page numbers referred to in the Index will be found at the bottom of the pages. Page Adjustable T-square 12 Angles, measurement of 5G Apparent distortion 324 Architectural lettering 473-513 classic letters 474 classic renaissance letters 476 classic Roman letters 499 composition 489 Diirer letter 489 early English letters 511 English Gothic 516 Gothic lettering 514 inscription lettering 497 Italian Renaissance lettering 507 Italic letters 485 office lettering 473 plates 517-518 “skeleton” letter ■ 489 small letters 496 spacing 495 uncial Gothic capital 509 Assembly drawing 154 Auxiliary line of measures 279 Auxiliary planes 198 Beam compasses 25 Black print solution 155 Blue print solution 155 Blue printing 153 Bow pen 20 Bow pencil 20 Brushes and paper for rendering 457 Note.— For page numbers see foot of pages Camera and eye Page 342 Color combination 457 Colors 458 Combination of color 457 Compasses 16 beam 25 Composition in lettering 489 Cross hatching 374 Curves in perspective drawing 319 Definitions drawing 341 geometrical .51-64 ray of light 174 shade 173 shade line 174 shadow 173 Umbra 174 Developments 112 , 163 cone 111 cylinder 116 intersection of pyramid 120 rectangular prism 113 right prism 113 Directions of shade lines 375 Dividers 19 Drawing definition of 341 restraint in 343 Drawing board, mechanical drawing 9 Drawing paper, mechanical drawing 7 523 2 INDEX Drawing pen Page 20 Geometrical definitions Page Drawing plates, general directions for 373 polygons 54 Elementary problems in perspective 271 pyramids 58 Ellipse, actual size of 111 quadrilaterals 53 English Gothic text letters 516 solids 57 English letters, early 511 spheres 60 Erasers 10 surfaces 52 Eye and camera 342 triangles 52 Five axioms of perspective 255 Geometrical problems, mechanical Forms of letters, derivation of 475 drawing 65-89 Free-hand drawing 341 -404 Gothic lettering 143 first exercises 349 -354 Holding the pencil 348 circles and ellipses 350 Horizon 255 free-hand perspective 352 Incised letters 478 learning to see 344 Ink 22 straight lines 349 Inking 37, 42, 47 testing with the slate 353 Inscription lettering 497 tracing on the slate 352 Instruments in mechanical drawing 7 materials 346 beam compasses 25 plates 379 -404 bow pen 20 value of to an architect 341 bow pencil 20 Free-hand lettering 168 compasses 16 Free-hand perspective 355' -376 dividers 19 appearance of equal spaces 359 drawing board 9 center of ellipse 363 drawing pen 20 concentric circles 364 erasers 10 cone 362 irregular curve 24 cylinder 360 pencils 10 foreshortened planes and lines 356 protractor 23 frames 364 scales ’ 23 horizon line or eye level 355 thumb tacks 9 horizontal circle 357 triangles 13 parallel lines 358 T-square 11 prism 360 Intersection 107 regular hexagon 363 Intersection of plane with solids 108 square 358 Irregular curve 24 triangle 359 Isometric axes 127 General directions' for drawing objects 366 Isometric and oblique projection 164 Geometrical definitions Isometric projection 125 angles 52 bench 137 circles 55 box 132 cones 59 cube 125 conic sections 61 Italic letters 485 cylinders 59 Kind of drawing 407 lines 51 Learning to see 344 odontoidal curves 63 Letter forms 474 Note.— For page numbers see foot of pages. 524 INDEX Lettering 25-29, Page 142, 16S Mechanical drawing Page architectural 473 -518 lettering 142 on arc of a circle 148 line shading 140 capital letters 28 materials 7 free-hand 168 oblique projections 137 Gothic 143 orthographic projections 91 Gothic capitals 26 pencilling 31 lower-case letters 28, 145 plates 29-48 mechanical 25 shade lines 103 Roman 143 tracing 150 Roman capitals 26 Minuscule 496 spacing in 147 Misuse of tests 369 Light and shade 370, 412 Notation, perspective drawing 269 color of material 415 Oblique lines, vanishing points of 289 form drawing 370 Oblique projection 137 lighting 414 cube 138 principality or accent 417 line shading 140 shadows only 416 Office lettering 473 value drawing 370 One-point perspective 302 values 412 Orthographic projection 91 Line shading 140 Outline 344 Line work in rendering 408 Parallel perspective 302 free lines 411 Pen and ink, rendering in 407-437 method 410 Pencil work 419 quality of line 408 Pencilling 31, 32, 41, 43 vertical lines 411 Pencil rendering 419 Lines of measures 279 Pencils 10 Lower-case letters 145 Perspective drawing 249-337 Materials for free-hand drawing 346 axioms 257 paper 348 curves 319 pencils 346 definitions 249 Materials in mechanical drawing 7 lines of measures 279 Materials for pen rendering 408 notation 269 Measure lines in perspective 279, 311 parallel perspective 302 Measure point in perspective 311 perspective plan method 309 Measurement of angles 56 planes of projection 259 Mechanical drawing 7- -168 plates 329-337 conic sections 61 problems in perspective development 112 point 271 drawing paper 7 line 272 geometrical definitions 51 L-64 vanishing point 273 geometrical problems 65-89 revolved plan method 274 ink 22 vanishing point diagram 301 instruments 7 vanishing point of oblique line 289 intersections 107 Perspective free-hand 355 isometric projection 125 Perspective of a house 285 Note.— Fop page numbers see foot of pages. 525 4 INDEX Perspective of interior Page 304 Restraint in drawing Page 343 Perspective plan, method of 309 Revolved plan, method of 274 Perspective of a point 261 Roman lettering 143 Perspective projection 259 Scales 23 Perspective of steps 305 Shade lines 103, 140 Picture plane 250 directions of 375 Plane of the horizon 255 orthographic projection 103 Planes of light 203 sphere 204 Planes of projection 259 Shades and shadows 173-248 Plates, mechanical drawing 25-48, 156-168 auxiliary planes 19S Point of sight 250 chimney on a sloping roof 187 Position 349 cone 194 Projection planes 259 construction 20S Projections, mechanical drawing 91 definitions 173 developments 112 hand rail 191 intersection 107 notation 175 isometric 125 object 184 oblique 137 oblique cylinder 196 orthographic 91 pedestal 187 profile plane 97 planes of light 203 shade lines 103 polyhedron 182 Ray of light 175 prism 183 Rendering in pen and ink 407-437 problems 176-217 accent 417 right cylinder 19£ brushes and paper 457 short method construction 208-211 kinds of drawing 407 cylinder 212 light and shade 412 intrados 214 line work 408 line 209 manipulation 457 point 208 materials 40S right cylinder 213 pencil work ’ 419 sphere 215 plates for practice 425-437 spherical hollow 215 Rendering in wash 441-470 torus 216 materials 441 vertical line 214 method of procedure 442 in spherical hollow 198 distinction between planes 454 Shading, varieties of 374 graded tints 452 Shadow of handling the brush 444 given line 178 inking the drawing 442 given plane 181 laying washes 444 lines 178 preparing the tint 443 pediment mouldings 204 rendering elevations 450 planes 181 rendering sections and plans 452 points 176 stretching paper 442 scotia 200 plates 463-470 solids 18? water color hints 454-460 Skeleton letters 480 Note.- For page numbers see foot of pages. 526 INDEX Page Small letters 490 Spacing in lettering 495 Station point 250 T-square 11 Testing drawing by measurement 367 Thumb tacks, mechanical drawing 9 Tracing 150 Triangles 13 Tube and pan colors 454 Value of free-hand drawing to an architect 341 Values of light and dark 371 Value scale 371 how to make 373 Page Value scale how to use 373 Vanishing point diagram 301 Vanishing point of lines 252 Vanishing point of oblique lines 289 Vanishing trace 251 Varieties of shading 374 Visual element 253 Visual plane 253 Visual rays of light 249 Water color hints 451 Water color rendering 459 Water color sketching 460 Note.— For page numbers see foot of pages. 5 2Ti OFFICES, AMERICAN SCHOOL OF CORRESPONDENCE. THE FOLLOWING PAGES ARE TAKEN FROM THE BULLETIN OF THE AMERICAN SCHOOL OF CORRESPONDENCE AT ARMOUR INSTITUTE OF TECHNOLOGY, CHICAGO. OTHER COURSES OFFERED ARE! HEATING, VENTILATING AND PLUMBING; CIVIL, ELECTRI- CAL, MECHANICAL, STATIONARY, LOCOMOTIVE, AND MARINE ENGINEERING; ELECTRIC WIRING; REFRIGERATION; TELEPHONY; TELEGRAPHY, TEX- TILES, INCLUDING KNITTING; THE MAUFACTURE OF COTTON AND WOOLEN CLOTH , TEXTI LE CHEM- ISTRY, DYEING, FINISHING, AND DESIGN; ALSO COLLEGE PREPARATORY, FITTING STUDENTS FOR ENTRANCE TO ENGINEERING COLLEGES. THE COLLEGE PREPARATORY COURSE PRAC- TICALLY COVERS THE WORK OF THE SCIENTIFIC ACADEMY OF ARMOUR INSTITUTE OF TECH- NOLOGY, AND IS ACCEPTED AS FULFILLING THE REQUIREMENTS FOR ENTRANCE TO THE COL- LEGE OF ENGINEERING OF THAT INSTITUTION- THE BULLETIN OF THE SCHOOL, GIVING COMPLETE SYNOPSIS OF THE ABOVE COURSES, MAY BE HAD ON REQUEST • GREEJGDORIC-AND ‘ I ON I C AH, TO BUILD, TO BUILD! THAT IS THE NOBLEST ART OF ALL THE ARTS. PAINTING AND SCULPTURE ARE BUT IMAGES, ARE MERELY SHADOWS CAST BY OUTWARD THINGS ON STONE OR CANVAS, HAVING IN THEMSELVES NO SEPARATE EXISTENCE. ARCHITECTURE, EXISTING IN ITSELF, AND NOT IN SEEMING A SOMETHING IT IS NOT, SURPASSES THEM AS SUBSTANCE SHADOW. Henry Wadsworth Longfellow . ' CRESTS SPECIMEN PAGE FROM INSTRUCTION PAPER ON THE ORDERS. DEPARTMENT OF ARCHITECTURE COURSES COMPLETE ARCHITECTURE ARCHITECTURAL ENGINEERING CONTRACTORS’ AND BUILDERS’ ARCHITECTURAL DRAWING CARPENTERS’ ARCHITECTURE HE courses in Architecture are planned to cover the actual problems arising in daily work. They offer young men in the architect’s office or in the con- tractor’s employ an opportunity to obtain practical information which ordinarily could be acquired only : after long apprenticeship. The instruction is of im- mediate value to carpenters, contractors and others engaged in build- ing, as great stress is laid on the practical as well as the artistic side of the work. The courses offer experienced draftsmen and practicing architects an opportunity to make up deficiencies in their early pro- fessional training. The instruction in Heating, Ventilating, Plumb- ing, Gas Lighting, Wiring, — Electricity and Steam as applied to power and light— is such as to enable an architect to obtain an intelligent knowledge of subjects which are of growing importance in the plan- ning of large buildings. The instruction comprises Mechanical Drawing, Descriptive Geometry as used in framing, Isometric and Perspective Drawing, Shades and Shadows, Free-hand Drawing, Pen and Ink Rendering, and the conventional methods of making, figuring, lettering and ren- dering plans, elevations, sections and details. -The student is taught the theory of the design of columns, beams, girders and trusses. Building Materials, Building Construction . and Details, including framing” sheet-metal work, fireproofing, wiring, piping, heating and ventilating systems, Building Superintendence, Specifications and Contracts, Building Laws and Permits, and general office practice are also discussed. . , , • • In connection with Architectural History, instruction is given in History of Ornament, Ornamental Design, followed by . a car ® fll ^ s ^ lldy of the fundamental principles of design beginning with the Orders. These principles are impressed upon the student by a sen< - of interest- ing problems in architectural design. 533 COMPLETE ARCHITECTURE Prepared for Draftsmen, Designers, Architects, Architectural En- gineers, Landscape Architects, Building Superintendents, Quantity Sur- veyors, Clerks of Building Works, Inspectors, Contractors and Builders, Masons, Plasterers, Carpenters and Joiners, Heating and Ventilating En- gineers, Steam Fitters, Salesmen of Building Materials, Real Estate Agents, Instructors, Students and others. INSTRUCTION PAPERS IN THE COURSE Arithmetic Part I. Arithmetic Part II. Arithmetic Part III. Elementary Algebra and Men- suration. Algebra Part I. ♦Algebra Part II. Geometry. ♦Trigonometry and Logarithms. Mechanical Drawing Part I. Mechanical Drawing Part II. Freehand Drawing. Mechanical Drawing Part III. Mechanical Drawing Part IV. Architectural Lettering. Shades and Shadows. Perspective Drawing. Architectural Drawing. Rendering. Study of the Orders Part I. Study of the Orders Part II. Study of the Orders Part III. History of Architecture. Practical Problems in Design. Building Superintendence Part I. Building Superintendence Part II. Working Drawings. Building Materials. Strength of Materials Part I. Strength of Materials Part II. Foundations. Masonry. Carpentry and Joinery Part I. Carpentry and Joinery Part II. Stair Building. Statics. Steel Construction Part I. Steel Construction Part II. Steel Construction Part III. Fireproofing. Contracts and Specifications. Legal Relations. Heating and Ventilation Part I. Heating and Ventilation Part II. Heating and Ventilation Part III Plumbing Part I. Plumbing Part II. ♦Optional. 534 ISP SPECIMEN PAGE FROM INSTRUCTION PAPER ON TUE ORDERS. SPECIMEN PAGE FROM INSTRUCTION PAPER ON WORKING DRAWINGS. SYNOPSIS OF COURSE MATHEMATICS ARITHMETIC: Units: Numbers; N dj. vision; Factoring; Cancellation; Fractions: Decimals: Symbols of Aggregation; per- centage; Denominate Numbers; Tables of Linear and Square Measure: Tables of Weights; Involution; Evolution; Square Root; Cube Root; Roots of Fractious; Ratio; Proportion. ELEMENTARY ALGEBRA: Use of Letters; Addition; Sub- traction; Multiplication; Division; Cancellation; Equations; Transportation Finding Value of Unknown Quantities. MENSURATION: Lines; Angles: Polygons; Circles: Sectors and Segments. Measurement of Angles; Triangles; Rect- angles; Trapezoids; Hexagons: Circles; Volumes and Sur- faces of Prisms; Cylinders; Pyramids; Cones: Frustums; Sphere. Practical Problem: Measurement of Steam Space in a Horizontal Multitubular Boiler. ALGEBRA EXPRESSIONS: Symbols: Coefficients and Exponents: Symbols of Relation; Symbols of Abbreviation: Positive and Negative Terms: Monomial; Binomial; Trinomial: Poly- nomials; Similar Terms. Finding Numerical Value by Substitution. Finding Values of Unknown Quantities. FUNDAMENTAL PROCESSES: Addition; Subtra< Multiplica- tion; Division; Formulae; Factoring; Highest Common Factor; Lowest Common Multiple. FRACTIONS: Fractions and Integers; Reduction of Fractions t<> Lowest Terms; Reduc- tion of Fractions to Entire or Mixed Quantities; Reduction of Mixed Quantities to Fractions: Reduction of Fractions to Lowest Common Denominator: Addition and Sub- traction of Fractions; Multiplication and Division of Fractions; Complex Fractions. SIMPLE EQUATIONS: Transposition; Solution of Simple Equations; S lntl tions Containing Fractions: Literal Equations; Equations Involving Decimals; Equa- tions Containing Two Unknown Quantities: Elimiuation by Addition, Subtraction, Substitution and Comparison. INVOLUTION AND EVOLUTION: Monomials and Polynomials; Squares. Cubes and Higher Powers. The Radical Sign; Theory of Exponents: Radicals; Reduction of Radicals to Simplest Form; Addition, Subtraction, Multiplication and Division of Radi- cals. Involution and Evolution of Radicals. Irra- tional Denominators; Approximate Values. IMAGINARY QUANTITIES: Multiplication and Division of Imaginary Quantities. Quad- ratic Surds. EQUATIONS: Solution of Equations Containing Radicals. Pure and Affected Quadratic Equations; Simultaneous Equations Involving Quadratics. RATIO AND PROPORTION: Alternation; Inversion; Composition; Divi PROGRESSION: Arithmetical and Geometrical. BINOMIAL THEOREM: Formulae; Positive Integers; Finding Terms in an Expansion. GEOMETRY DEFINITIONS: Principles; Axioms: Abbreviations. Angles: Acute; Obtuse; Comple- mentary; Supplementary; etc. Parallel Lines; Axioms. FUNDAMENTAL THEOREMS: Plane Figures: Polygons: Equilat- , eral and Equiangular. Quadrilaterals; Circles; Measurements “f Angles; Similar Figures; Trapezium; Trapezoid; gram: Rectangle; Square; Rhomboid; Rhombus. Proportion. Division. SIMILAR POLYGONS: Definitions. Theorems. Areas of Miscel- laneous Figures; Equivalent Polygons: Rectangles, Parallelo- grams. Twenty-nine Problems in Construction of Plane Figures. C K Terms; Alternation; The Circle: Theorems; Parallelo- Ratio and Inversion; Composition and Area; Circumference, etc. PROBLEMS OF CONSTRUCTION: 537 TRIGONOMETRY AND LOGARITHMS TRIGONOMETRY: Definitions; Functions of Acute Angles; Measurement of Angles; Complementary Functions. Theorems Connecting the Different Functions of an Angle. FUNCTIONS: From One Function of an Angle to Find the Other Functions. Functions of 45 degrees, 30 degrees and 60 degrees. Trigonometric Functions of Any Angle. Positive and Negative Angles; The Four Quadrants. Functions of 0 degrees, 90 de- grees, 180 degrees and 270 degrees. Angles and Triangles. LOGARITHMS: Nature and Use of Logarithms; Logarithms of a Product, a Fraction, a Power, a Root. Solutions of Arith- metical Problems by Logarithms. TRIANGLES: Right Triangles: Solution by Natural Functions; Solutions by Logarithms; Areas. Oblique Triangles: Solu- tion by Breaking up into Right Triangles; Areas. EXERCISES: Length of Belt over two Pulleys; Stress in Rods forming an Acute Angle. DRAWING INSTRUMENTS AND MATERIALS: Drawing Paper; Board; Pencils; T-Squares; Tri angles; Compasses; Line Pens; Scales; Irregular Curves; Lettering Plates; Exercises GEOMETRICAL DRAWING: Lines; Angles; Triangles; Parallelograms; Pentagon; Hexa gon; Circles; Measurement of Angles. Prisms Pyramids; Cylinders; Cones; Spheres. Ellipse; Parabola; Hyperbola; Twenty-eight Problems in Geometrical Drawing. PROJECTIONS: Orthographic: Plan and Elevation; Projection of Points, Lines, Surfaces and Solids.« Third Plane of Projection; True Length; Inter- section of Planes with Cones and Cylinders; De- velopment of Prisms, Cylinders, Cones, etc. De- velopment of Elbow. Isometric: Isometric Axes; Cube; Cylinder; Directions of Rays of Light. Oblique Projections: Shade Lines; Co-ordinates. Isometric of House, etc. WORKING DRAWINGS: Lines. Location of Views; Cross-Sections; Crosshatching; Dimensions; Finished Surfaces; Material; Conventional Representations of Screw Threads. Bolts and Nuts. Threads in Sectional Pieces; Broken Shafts, Columns, etc. Tables of Standard Screw Threads, Bolts and Nuts. Scale Drawing; Assembly Drawing; Blue Printing; Formulas for Solutions for Blue-Print Paper. PERSPECTIVE DRAWING: Station Point; Picture Plane; Ground Line; Horizon; Line of Measures; Axis; Vertical Trace; Horizontal Trace; Bird’s-eye View; Worm’s-eye View; Vanishing Points. Projections: Planes; Notation. Problems Involving Perspective of Points, Lines and Planes. Revolved Plan; Lines of Measure; Diagrams; Revolved Plan and Elevation; Systems of Lines and Planes; Visual Ray; Perspective Diagram; Method of Perspective Plan; Curves; Apparent Distortion; Choice of Position of Station Point. Plates. SHADES AND SHADOWS: Principles and Notation; Shadows of Points, Lines and Planes. Co-ordinate Planes; Lines on More Than One Surface. Choosing Ground Line Problems: Shadows of Prism; Pedestal; Chimney on Roof; Rail on Steps; Cone: Cylinder. Auxiliary Planes; Shadow of Spherical Hollow; Shadow of Scotia. Planes of Light; Shadow of a Sphere; Shadow on Pediment Moulding. Short Methods: Shadows of Points; Lines Parallel and Perpendicular to Co-ordinate Planes. Shadows on Inclined Planes; on Planes Parallel and Perpendicular to Co-ordinate Planes. Shade and Shadow of Cylinder; of Line Moulding; on Intrados of Circular Arch; of Spherical Hollow and Niche; of Sphere; of Torus. RENDERING: Pen and Ink: Materials Used, Examples Showing Common Faults, Values, Lighting, Rendering by Shadows Only, Accent, Pencil Work, Suggestions and Cautions, Examples of Drawings with Criticisms. WASH DRAWINGS: Inking the Drawing; Preparing the Tint; Handling the Brush; Laying on the Washes; Tinting Eleva- tions, Sections and Plans; Graded Tints; Distinction between different Planes; French Method. WATER-COLOR HINTS FOR DRAFTSMEN: List of Colors; Manipulation; Brushes and Paper; Combinations of Color; Primary, Secondary and Complementary Colors; Water-color Rendering; Water-color Sketching. FREE HAND DRAWING: Paper; Pencils; Drawing Board. Difference between a Drawing and a Photograph. Lines and Surfaces. Flat Ornament: Anthemia; Frets; Mosaics; Stained Glass; All Over Patterns. Light and Shade: Value Scale; Form Drawing; Point of View; Value Drawing. Geo- Working Drawings. metric Solids. Carved Ornament: Rosettes; Greek, Roman and Byzantine Acanthus; Ionic; Corinthian and Gothic Capitals; Renaissance Pilaster. ARCHITECTURAL LETTERING: Office Lettering; Purpose; Relative Sizes and Shapes of Letters for Titles; Forms and Proportions of Various Alphabets. Skeleton Letters. Composition and Spacing: Title Page; Lettering Plans and Working Drawings. In- scription Lettering. Letters for Stone; Shadows; Cast Letters; Raised Letters; Examples of Lettering; Gothic; Roman. Examination Plates. fife 538 SPECIMEN PAGE FROM INSTRUCTION PAPER ON THE ORDERS. W' o, " or " -1«V»V d -d FRONT" FLE.VAT10JV ARCHITECTURE HISTORY OF ARCHITECTURE: Ancient Architecture; Egyptian; Mzyrtan; G. Done, Ionic and Corinthian Orders. Greek Tombs and Theatres; The Acropolis; Roman Architecture: Temples; Theatres; Tombs; Triumphal Arches; Medieval Arehl- teeture: Romanesque; Gothic; English Gothic; Early French Styles; Renaissance; Italian; French; Spanish; German; English. Classic. European Architecture. American Ar- chitecture: Colonial; Residences; Public Buildings; Churches: Commercial Architecture. STUDY OF THE ORDERS: The Five Orders: Tuscan; Doric; Ionic; Corinthian; Composite: Character; Proportions; Uses; Typical Examples; Parallel of the Orders; Columns; Pilasters; Base; Shaft; Capital; Architrave; Frieze; Cor- nice; Arris; Entecis; Triglyphs; Metopes; Volutes; Modules. Proportion of Arches; Doorways; Pediments; Windows; Bal- ustrades; Colonnades and Arches. WORKING DRAWINGS: Details of Window Frames for Brick and Wooden Buildings; Details of Framing: Floors; Par- titions; Joists and Girders; Sills and Posts; Rafters; Attic Floor; Roof. Dormer Construction. Tenon and Tusk Joint. - Hanger. Details: Bulkhead; Fireplace. Details of Finish; Sliding Doors; Ironwork in Connection with Framing. Details of Gutters. ARCHITECTURAL DESIGN: Utility; Effect; Unity; Grouping: Interiors; Exteriors; Orders; Moldings; Greek and Roman Moldings; Pedestals; Arcades; Columns; Pilas- ters; Imposts; Balusters; Doors and Windows; Piers; Capitals; Spires; Form and Color. Ornament: Greek; Egyptian; Roman: Byzantine; Gothic; Italian; French; English. Plans: Rooms; Stairways. Entrance. City and Country Houses; Office Buildings: Light; Heating; Ventilation. Churches and Public Buildings. BUILDING MATERIALS AND SUPERINTENDENCE: Limes; Cements and Mortars: Strength; Proportions; Data for Estimating Cost. Stone; Granite; Limestone; Marble; Slate; Testing Building Stone. Brick: Paving Brick: Fire Brick; Glazed and Enameled Brick; Building Brick. Size; Mortar; Construction of Walls; Hollow Walls; Brick Arches; Brick Veneer; Fireplaces. Terra Cotta: Composition and Manufacture. Durability; Inspection. Setting and Pointing. Examples of Construc- tion. Iron and Steel: Girders and Lintels; Supports; Bear- ing Plates; Chimney Caps. etc. Laths and Plastering. Metal Laths; Stucco. Concrete. Superintendence: Necessity for Superintendence. Visits; Setting out the Building; Inspecting Material; Inspecting Construction; Costs; Contracts. STRENGTH OF MATERIALS: Stresses and Deformations: Ten- sion; Compression; Shear; Factors of Safety; Working Stresses. Beams: Simple Beams; Cantilever Beams; Re- actions; Bending Moments; Moment of Inertia; Center of Gravity; Safe Loads; I-Beams; Deflection; Beams of Uni- form Strength; Continuous Beams. Columns: Cross-sections; Radius of Gyration; Designing. Torsion: Shafts for Trans- mitting Power: Combined Stresses. Testing Timber, Brick, Cement, Wrought Iron. Cast Iron and Steel. Resilience: Sudden Loads and Impact: Elastic Resilience of Beams. Tension, Compression, Shear and Torsion. FOUNDATIONS: Staking Out. Excavation; Loads; Artificial Foundations; Timber; Piles; Bearing Power; Cofferdam; Wrought Iron; Cast Iron; Blast Furnace Slag; Retaining Walls; Concrete; Mixing; Laying; Compressive Strength; Period of Repose; Variations of Proportions. Shoring; Needling; Bracing. ■ KTAIL • OT- CCNttAL • v/mcw fXAH»J MASONRY: Classes of Masonry; Culverts; Wing Walls; Pointing; Grouting; Freezing; Brick Masonry. Cement: Hydraulic; Natural; Portland; Characteristics of Portland Cement; Testing; Effect of Age; Quick and Slow Set; Specifications ; Mortar; Pro- portions; Sand; Water; Strength of Mortar ; Shearing, Compressive and Tensile Strength; Effect of Frost; Permanency; Data; Specifications. CARPENTRY AND JOINERY: Timber; Shake: Knots; Quarter Sawing; Seasoning; Kinds of Wood; Uses. Framed Structures: Joints; Sills; Posts; Studs; Bridging; Flooring: Par- titions; Lathing; Trussed Partitions Roofs; Jack Rafters; Hip and Valley; Mansard; Gables; Construction of Roofs: Shingles; Flashing. Balloon Framing. Siding; Verandas; Arches; Ceiling. Joinery: Joints; Tongue and Groove; Dove- tail; Dowel; Mortise and Tenon; Keys. Interior Work; Wain- scots; Paneling; Door Making; Sliding arid Folding Doors; Windows Sashes; Glass. Splayed Work. Bending Wood: Veneering. Blinds; Hinges; Interior Finish. STAIR BUILDING: Materials; Terms; Classification. Construction: Treads; Risers; Stringers; Steps and Platform; Molding; Balustrades: Hand Rails. Straight Stair- ways; Winding Treads; Winders. Open and Closed Stringers; Curved Stringers. Quarter-Turn Winding; Half-Turn Platform. Winding Stairways; Circular Stuirwuya- 541 GRAPHIC STATICS: Force Triangle; Polygon; Conditions of Equilibrium; Stresses in Truss, in Polygonal Frame; Reactions of Beams; Concentrated Loads; Uniform Loads; Overhanging Beams. Roof Trusses: Dead and Snow Loads; Stresses; Wind Loads; Fixed Ends; Truss with One End Free. Abbreviated Methods for Wind Stress; Com- plete Stresses for a Triangular Truss; Ambiguous Cases. Unsymmetrical Loads and Trusses. Stresses; Design Plate Girders. STEEL CONSTRUCTION : Elements and Functions of Frame- work; Use of Handbooks; Rolled Shapes; Tables. Beams: Loads; Effect of Openings; Commercial and Practical Con- siderations in Design. Columns: Connections; Shapes; Se- lection; Calculation of Section; Tables; Use of Concrete Steel Columns. Trusses. Types; Determination of Loads; Shipping and Erection. Details of Framing: Connections of Beams to Girders and Columns; Plate and Box Girder Con- nections; Column Caps and Bases; Roof Details. Shop Drawings: Processes of Manufacture; Conventions; Mill and Shop Invoices; Checking; Details of Work. High Build- ing Construction: Steel Skeleton; Limiting Heights; Laws; Effect of Wind. Portal, Knee and Diagonal Bracing. Vibra- tion; Column Loads. Mill Construction: Requirements of Underwriters; Slow Burning Construction; Steel; Details of Connections. Types of Construction. FIREPROOFING: Material; Parts to be Protected; Choice of Material; Use of Material; Floor and Roof Arches; Comparison of Terra Cotta and Concrete Steel: Expanded Metal; Tests; Suspended Ceilings; Furring; Partitions; Column Coverings; Fire- Resisting Wood; Paint; Metal Coverings; Relation of Construction to Architect’s Design. Relation of Construction to Strength of Steel Frame. CONTRACTS AND SPECIFICATIONS: Classes; Drawing Up; Seals; Clauses; Subletting; Assignment. Failure to Complete Work; Insolvency; Insurance; Appliances; Disputes; Condemned Material. Penalties; Cost; Monthly Estimate; Final Acceptance; Defi- nition of “Engineer” and “Contractor.” Specifications: Forms; Clauses; Material; Workmanship; Performance; Specifications for Stone Work; Building; Lumber; Cement; Mortar; etc. HEATING AND VENTILATION HEATERS: Stoves; Furnaces; Steam; Hot Water; Electricity. Furnaces: Location; Parts; Direct and Indirect Draft; Pipes and Ducts. Care and Management. Ventila- tion: Carbonic Acid; Location of Inlets and Outlets; General Considerations. Heat Loss from Buildings. B. T. U. Calculations and Tables. STEAM HEATING: Radiators; Systems of Piping; Wet and Dry Returns; Valves; Pipe Sizes; Indi- rect Steam Heating: Heaters; Stacks; Ducts; Wall Box; Care of Systems. Exhaust Steam Heating: Reducing Valves; Grease Extractor; Ex- haust Plead; Pumps and Traps; Paul System; Plenum Method; Efficiency of Heaters; Fans; Factory Heating; Temperature Regulators. HOT WATER HEATING: Radiating Surface; Piping; Expansion Tank; Distribution; Valves and Pipes; Location of Radiators. Indirect Hot Water Heating Sizes; Care of Hot Water Heaters. VENTILATION OF BUILDINGS: Choice of Systems; Calculations, and Hints for Heating and Ventilating Schoolhouses, Theatres, Apartment Houses, Greenhouses, Factories, etc. © ° A bolts spaced 2.'o *, ° ° 1 COMPOUND -BEAM 1 Cast. Iron •Separators o *»■ D I BEAMS '"A C l SEPARATOR n 1 Top and bottom plates I riveted 1 BEAM BOX GKDER. PLUMBING FIXTURES: Bath Tubs; Water Closets; Lavatories; Vents; Connections; Bowls; Sinks; Traps; Pipes; Sewers and Cesspools. Plumb- ing: Connections for Bath Room. Kitchen Sink Connections. Plumbing Dwelling Houses, Apartment Houses, Railroad Stations, Schoolhouses, and Fac- tories. Testing and Inspection. DOMESTIC WATER SUPPLY: Friction in Pipes; Pipe Lining; Pumps; Hydraulic Ram; Kitchen Boiler; Coils; Water-Back Connections; Circulation Pipes; Laundry Boilers; Boilers with Steam Coils; Tem- perature Regulators. SEWAGE: Systems; Considerations Governing Choice. Design and Construction: Topography; Manholes; Grades; Flushing; House Connections; Ventilation; Catch Basins; Pumping Stations. Purification; Sedimentation; Chemical Precipitation; Irrigation; Intermittent Filtration. GAS FITTING: Pipes; Meters; Fittings; Joints; Risers; Location of Pipes; Testing Gas Pipes. Gas Fixtures: Burners: Batswing; Fishtail; Bunsen; Argand; etc. Chandeliers. Shades. Heating and Cooking by Gas. Automatic Hot-Water Heaters. Position; Dials; Reading. Gas Machines. Globes and Gas Meters' 542 uu/n/oj cr/ow Roof G/rcfer Defa/Z of Cannae f/on of flnee Braces fo Columns ancZ G/rders. / \ \ / / \ / / Diagram of one Column Bay Braced by Knee P/ates and Angles to resist Wind Pressure. TYPES OF WIND BRACING Diagram of one Column Boy Braced by Porta/s of P/ates and Anp/es to res/sf Wine/ Pressure. SPECIMEN PAGE FROM INSTRUCTION PAPER ON STEEL CONSTRUCTION. ARCHITECTURAL ENGINEERING INSTRUCTION PAPERS IN THE COURSE Arithmetic (3 parts). Elementary Algebra and Men- suration. Geometry. Mechanical Drawing (4 parts). Freehand Drawing. Algebra (2 parts). Perspective Drawing. Mechanics (2 parts). Building Materials. Trigonometry and Logarithms. Strength of Materials (2 parts). Foundations. Masonry. Statics. Steel Construction (3 parts). Fireproofing. CONTRACTORS’ AND BUILDERS’ COURSE INSTRUCTION PAPERS IN THE COURSE Arithmetic (3 parts). Elementary Algebra and Men- suration. Geometry. Mechanical Drawing (4 parts). Working Drawings. Building Superintendence (2 parts). Strength of Materials (2 parts). Masonry. Carpentry and Joinery (2 parts). Sheet Metal Work (2 parts). Metal Roofing. Cornice Work. Electric Wiring. Electric Lighting. Heating a n d Ventilation (3 parts). Plumbing (2 parts). Contracts and Specifications. Legal Relations. CARPENTERS’ COURSE INSTRUCTION PAPERS IN THE COURSE Arithmetic (3 parts). Elementary Algebra and Men- suration. Geometry. Mechanical Drawing (4 parts). Freehand Drawing. Architectural Drawing. Perspective Drawing. Building Materials. Working Drawings. Strength of Materials (2 parts). Carpentry and Joinery (2 parts). Stair Building. ARCHITECTURAL DRAWING INSTRUCTION PAPERS IN THE COURSE Arithmetic (3 parts). Elementary Algebra and Men- suration. Geometry. Mechanical Drawing (4 parts). Freehand Drawing. Architectural Lettering. Shades and Shadows. Architectural Drawing. Perspective Drawing. Rendering. Study of the Orders (3 parts). Practical Problems in Design. 544 PARTIAL LIST OF TEXTBOOK WRITERS, INSTRUCTORS, AND EDITORS, IN THE DEPARTMENT OF ARCHITECTURE WILLIAM H. LAWRENCE, S. B. Professor Department of Architecture, Massachusetts Institute of Technology. FRANK A. BOURNE, M. S. Architect, Boston, Fellow, Massachusetts Institute of Technology. DAVID A. GREGG, Teacher and Lecturer, Pen and Ink Drawing. Massachusetts Institute of Technology. H. W. GARDNER, S. B. Professor Department of Architecture, Massachusetts Institute of Technology. EDWARD A. TUCKER, S. B. Architectural Engineer, Boston. FRANK CHOUTEAU BROWN, Architect, Boston, Author of “Letters and Lettering.” HERBERT E. EVERETT, Professor Department of Architecture, University of Pennsylvania. CHARLES L. HUBBARD, S. B., M. E. Heating and Ventilating Expert, Boston. EDWARD NICHOLS, Architect, Boston. GILBERT TOWNSEND, S. B. With Post and McCord, New York City A. E. ZAPF, S. B. American School of Correspondence. HERMAN V. VON HOLST, A. B., S. B. Architect, Chicago ROBERT V. PERRY, B. S., M. E Armour Institute of Technology. EDWARD R. MAURER, B. C. E. Professor Department of Mechanics, University of Wisconsin. J. R. COOLIDGE, JR Architect, BostoD 545 SPECIMEN PAGE FROM INSTRUCTION PAPER ON THE ORDERS, Man}) young men have a wishbone instead of a backbone. " TO PURCHASERS OF THE “CYCLOPEDIA OF DRAWING” struction papers. Our object, therefore, in publishing the “Cyclopedia of Drawing” is to enable you to examine, at your leisure, the character we make you the following special offer : If you enroll within thirty days from receipt of the books, we will include with your course a set of our new twelve-volume reference library “Modern Engineering Practice,” FREE OF ALL COST, as an additional help in your studies. For description and contents of this valuable set of books see the next four pages. It is the most simple, complete, practical and up-to-date technical reference work yet published, and is alone worth more than the entire cost of the course. We employ no agents to secure new students, preferring to spend the large sums necessary to pay canvassers in building up that part of our school in which you, as a student, would be most interested, namely, in main- taining the very highest standard of instruction that it is possible to give by correspondence, at the lowest possible tuition fees. Thirty minutes of study each day for eighteen months should enable you to qualify for a position which commands at the start $ i , 200 and upwards per year. If you are already earning this without a technical education, it is be- cause you have special ability which, with proper training, would enable you to double or treble your present pay. It will cost you about ten cents a day to get the necessary education. Is not this an investment well worth making? If you are in a rut and discouraged, there is .all the more reason for start- ing today to fit yourself for more congenial work. All that is needed is the backbone to begin and to stick to it. Thirty minutes of study a day will prove an investment from which you will draw interest the rest of your life. Can you afford to pass this opportunity by ? AMERICAN SCHOOL OF CORRESPONDENCE HE “CYCLOPEDIA OF DRAWING” is compiled from the regular instruction papers of the American School of Correspondence. These papers are not for sale to the public. Experience, however, has shown that no better recommendation for our school can be placed in the hands of interested persons than these in- of the instruction offered, in the confident expectation that you will de- cide to take a course. As a special inducement for deciding promptly. at Armour Institute of Technology, Chicago, Illinois “ Today is your opportunity; tomorrow some other fellow’s. ’* P?47 ' A machine doesn't need brains. A man does. You must be a machine or a man. REFERENCE LIBRARY MODERN ENGINEERING PRACTICE IN TWELVE VOLUMES A Reliable Guide for Engineers, Mechanics, Machinists and Students; Illustrating and Explaining the Theory, Design, Construction and Operation of all kinds of Machinery; Containing over Six Thousand Pages, Illustrated with more than Four Thousand Diagrams, Working Drawings, full-page Plates and Engravings of Machines and Tools PARTIAL TABLE OF CONTENTS Volume One Elements of Electricity — Current — Measurements — Electric Wiring- Telegraphy — Including Wireless and Telautograph— Insulators— Electric Welding. Volume Two Direct Current Dynamos and Motors — Types of Dynamos — Motor Driven Shops — Storage Batteries. Volume Three Electric Lighting — Electric Railways — Management of Dynamos and Motors — Power Stations. Volume Four Alternating Current Generators — Transformers— Rotary Converters— Synchronous Motors — Induction Motors — Power Transmission — Mer cury Vapor Converter. Volume Five Telephone Instruments — Lines — Operation — Maintenance — Common Battery System — Automatic and Wireless Telephone. Volume Six Chemistry — Heat — Combustion— Construction and Types of Boilers — Boiler Accessories — Steam Pumps. Volume Seven Steam Engines — Indicators — Valves. Gears and Setting — Details — Steam Turbine— Refrigeration— Gas Engines. Volume Eight Marine Engines and Boilers — Navigation — Locomotive Boilers and Engines — Air Brake. Volume Nine Pattern Making— Moulding— Casting— Blast Furnace— Metallurgy- Metals — Machine Design. Volume Ten Machine Shop Tools — Lathes — Screw Cutting — Planers -Milling Machines— Tool Making— Forging. Volume Eleven Mechanical Drawing— Perspective Drawing-Pen and Ink Rendering — Architectural Lettering. Volume Twelve Systems— Heaters— Direct and Indirect Steam and Hot Water Heating — Temperature Regulators — Exhaust Steam Heating Plumbing Installing and Testing— Water Supply— Ventilation— Carpentry ‘Next to knowing a thing, is knowing where to look for it. 549 “In science, read the newest books; in literature, the oldest. ” V is the man who has learned through long experience and careful study who knows best. Years of experience in teaching thousands of students living in every portion of the globe, and careful study of existing conditions, have enabled the American School of Correspondence con- stantly to enlarge and revise its work so as to make it best adapted to meet the needs of the correspondence student. The text books of the American School of Correspondence have been pre- pared by the leading college professors, engineers and experts in this country. In their preparation careful study has been given to actual shop needs. Sim- plicity, brevity, clearness and thoroughness are marked features. It may be said in this connection that the United States government has secured the right to use these instruction papers as text books in some of its schools. “Storage Batteries,” by Professor Crocker, is used in the senior class work in Columbia University. The Westinghouse Electric and Manufacturing Company have secured a large number of papers to be used in their educa- tional classes, and the only gold medal for superior excellence in Engineering Education and Technical Publications awarded at the St. Louis Exposition was given to the American School of Correspondence. There has been on the part of the school’s large student body a great need of a practical, concise and thorough reference work — a reference work which would supplement their studies and also assist them in the solution of such problems as daily confront every practical man. To meet this need the school has compiled its twelve-volume reference library of ‘‘Modern En- gineering Practice.” The “Library” is edited by Dr. F. W. Gunsaulus, assisted by a corps of able specialists and experts. It covers a broad field of engineering work and includes, in addition to the school’s regular work, many special articles on such subjects as Wireless Telegraphy, Automobiles, Gas Engines, etc., thus forming a complete reference work on the latest and best practice in the Machine Shop, Engine Room, Power House, Electric Light Station, Drafting Room, Boiler Shop, Foundry, Pattern Shop, Black- smith Shop, Round House, Plumbing Shop and Factory. The “Library” contains 6000 pages, 8x10 inches in size, is well indexed, profusely illus- trated, and substantially bound in three-quarters red morocco. IT FREE SPECIAL OFFER TO PURCHASERS OF THIS BOOK If you enroll within 30 days from receipt of this book, in any of the courses listed on the opposite page, we will include, free of all cost, a set of the 12-volume reference library, “Modern Engineering Practice.” “Books, like friends, should be few and well chosen. ” 550 The world pays a salary for what you know, wages for what you do. ” COURSES AND TUITION FEES DEPARTMENT OF ELECTRICAL ENGINEERING Paid in Advance 1 $5.00 a Month $3.00 a Month Electrical Engineering Reference Library (12 vols.) $52 00 $65 00 $72 00 Central Station Work Reference Library (12 vols.) 48 00 60 00 66 00 Electric Lighting Reference Library (12 vols.) 40 00 50 00 55 00 Electric Railways Reference Library (12 vols.) 40 00 50 00 65 00 Telephone Practice Reference Library (12 vols.) 40 00 50 00 55 00 DEPARTMENT OF MECHANICAL ENGINEERING Mechanical Engineering Reference Library (12 vols ) 52 00 65 00 72 00 Mechanical-Electrical Engineering. . Ref erence Library (12 vols.) 52 00 65 00 72 00 Sheet Metal Pattern Drafting Reference Library (12 vols.) 44 00 55 00 60 00 Shop Practice Reference Library (12 vols.) 40 00 50 00 55 00 Heating, Ventilation and Plumbing.. Reference Library (12 vols.) 40 00 50 00 65 00 Mechanical Drawing Reference Library (12 vols.) 40 00 50 00 55 00 DEPARTMENT OF STEAM ENGINEERING Stationary Engineering Reference Library (12 vols.) 40 00 50 00 55 00 Marine Engineering Reference Library (12 vols.) 40 00 50 00 55 00 Locomotive Engineering Reference Library (12 vols.) 40 00 50 00 55 00 DEPARTMENT OF CIVIL ENGINEERING Structural Engineering Reference Library (12 vols.) 60 00 75 00 85 00 Municipal Engineering Reference Library (12 vols.) 60 00 75 00 85 00 Railroad Engineering Reference Library (12 vols.) 60 00 75 00 85 00 Surveying Reference Library (12 vols.) 40 00 60 00 55 00 Hydraulics Reference Library (12 vols.) 40 00 50 00 55 00 Structural Drafting Reference Library (12 vols.) 40 00 50 00 55 00 DEPARTMENT OF ARCHITECTURE Complete Architecture Reference Library (12 vols.) 60 00 75 00 85 00 Architectural Engineering Reference Library (12 vols.) 45 00 55 00 60 00 Contractors’ and Builders’ Course. . .Reference Library (12 vols.) 40 00 50 00 55 00 DEPARTMENT OF TEXTILE MANUFACTURING Cotton Course Reference Library (12 vols. ) 40 00 50 00 55 00 Woolen and Worsted Goods Course.. Ref erence Library (12 vols.) 40 00 50 00 55 00 Knit Goods Course Reference Library (12 vols.) 40 00 50 00 55 00 200-page Bulletin giving full description of the above and 50 short courses on request will be s ent fret AMERICAN SCHOOL OF CORRESPONDENCE at Armour Institute of Technology, Chicago, U. S. A. “A man’s brains can do more work than both his hands. ” 551 Practical Lessons IN Electricity Compiled from the instruction papers of the American School of Correspondence and pub- lished to show the standard and scope of the instruction offered Storage Batteries (prepared especially for home studies by Prof. F. B. Crocker, Columbia University) Electric Wiring (prepared by H. C. Cushing, jr., author of “Standard Wiring”) Electric Current (by L. K. Sager, S. B.) Elements of Electricity (by L. K. Sager, S. B.) The Scientific American in reviewing the book says: “Practical Les- sons in Electricity is distinguished by a common-sense treatment of a subject which is apt to confuse the student not a little. Prof. Crocker’s wide experience as a teacher is apparent in the division on storage batteries. That portion of the work is charac- terized by the lucidity of treatment which is unfortunately not often found in books on this subject. The division on electrical wiring is a simple, condensed account of what a practical man ought to know. A valuable part of the book is a series of prac- tical test questions pertaining to the subject treated.” American School of Correspondence f“ih c No°is 552 / ===== CYCLOPEDIA OF — APPLIED ELECTRICITY Five Volumes— 2,500 Pages-Fully Indexed -Size of Pace. 8x10 inches. Bound in Red Morocco. Over ^.000 Full Page Plates. Diagrams, Tables. Formula . etc. Ahkri can ^srican rJS American American ^choo yof 15 nqpi ! # * — — • , ^ | CTCLOPEDIA CYOjOPBHA CYCLOPEDIA CYCLOPEDIA CYOjOPEDIA °s tf # •/ •y APPLIED applied APPLIED APPLIED APPLIED I^HfljrRicn^SffiTRicrn^ HicnacrrY BKTwcrn Eacrwcrnf 1 current DYNAMOS UQHTINO ALTERNATING W MEASUREMENTS MOTORS RAILWAY9 CURRENTS TELEPHONY 1* WIRING STORAGE POWER POWER INDEX g TELEGRAPH batteries STATIONS transmission , PRICE UPON REQUEST Some of the Writers Prof. F. B. Crocker, Head of Department of Electrical Engineering, Columbia University. Prof. William Estey, Head of the Department of Electrical Engineering, Lehigh University. H. C. Cushing, Jr., Wiring Expert and Con- sulting Engineer. Prof. Geo. C. Shaad, University of Wisconsin. J. R. Cravalh, Western Editor of the Street Railway Journal. William Boyrer, Division Engineer, N. Y. and N. J. Telephone Company. Chas. Thom, Chief of Qundruplex Department Western Union Telegraph Co. Prof. Louis Derr, Massachusetts Institute of Technology. Percy H. Thomas, Chief Electrician, Cooper- Hewit Co., New York City. A. Frederick Collins, Author of "Wireless Telegraphy.” Partial Table of Contents Parti. Magnetism — Electric Cur- rent — Measurements — Wiring — Telegraph, including Wireless and Telautograph. Part II. Di rect-Current Dynamos and Motors, including Types — Motor Drives — Westinghouse Three -wire System — Storage Batteries. Part III. Electric Lighting— R til- ways— Management of Dynamos and Motors — Power Stations. Part IV. Alternating-Current Ma- chinery — Power Transmission — Testing of Insulators. Part V. Telephony, including Common Battery System and Automatic Telephone. AMERICAN SCHOOL OF CORRESPONDENCE CHICAGO 553 Cyclopedia of Drawing New Enlarged Edition 5,000 Sets Already Sold TWO VOLUMES 1,200 Pages, 1,500 Illustrations PRICE .oo By Express Prepaid Payable in Small Monthly Payments. Money Refunded if not Satisfactory “Comment and Appreciation** H. W. Le S0URD, Instructor, Milton Academy, says: “ * * have decided to put the books into our drawing room as reference books, so you will find check enclosed for another set. ” BERT P. FAWNS, Philadelphia, Pa., says: “I have attended an art institute for four years, but from all my studying there I have not received as much knowledge as from the “Cyclopedia of Drawing.” It brings the student in touch with all kinds of drawings and plans, and teaches him the little things necessary that an instructor would not take time to explain. I consider it the best work of the kind I have ever seen.” “ AMERICAN MACHINIST,” New YorK, says : “Without making invidious comparisons, for all the parts are good, we may mention as especially good and thoroughly practical the chap- ters on Machine Design and on Sheet Metal Pattern Drafting.” American School of Correspondence : Chicago, Illinois ~ nr 554 555 | FOREIGN STUDENTS