Earnest T. Child.

In our last talk we described the instruments which are necessary for the mechanical draftsman. Having secured the complete set or, if needs be, a partial set, the student should accustom himself to handle them properly. To learn to use dividers correctly will require some little practice, and the execution of a few conventional problems will be found the most satisfactory way in which to familiarize one's self with them. The following geometric problems have been selected from a large number, being the most important, as they cover the principles which apply to all.

Problem 1.

To draw parallel lines. Draw the line AB. At A, with radius R, draw an arc xx, and at B, with the same radius, draw arc yy. Draw line CD which shall be tangent to both arcs, just touching them. Line CD will be parallel to AB.

Problem 2.

To erect a perpendicular, bisecting a given line. On the line AB with center A and any radius, more than one-half AB, strike arcs xx and yy. With center B, and same radius, cut arcs xx and yy at 1 and 2. Draw CD through points 1 and 2. This line will be perpendicular to AB, and midway between points A and B.

Problem. 3. To erect a perpendicular at the end of a line. On line AB with A as a center and any radius construct arc xy. With center y and same radius cut xy at 1. With 1 as a center and same radius draw arc zz. Draw line from Y through intersection 1, and cut zz at 2. Draw lines AC through point 2. This line will be perpendicular to line AB.

Problem 4.

To construct a square. Proceed as in problem 3 to erect a perpendicular at A. With radius equal to AB cut vertical line at C. With center C and same radius strike arc xx. With center B, a nd same radius cut arc xx at D. Draw lines BD and CD. Fig. ACDB is a square.

Problem 5.

To construct an equilateral triangle. Draw line AB of the proper length for one side of the triangle. With radius AB and center A strike arc xx. With same radius and center B cut xx at C. Draw AC and BC, making triangle ABC, which is equilateral and also equiangular. By taking radii of the proper length, any triangle may be constructed in a similar manner. For instance, if AB = 6 inches, AC =4 inches and BC=5 inches, radius for arc xx will be 4 inches, and radius for arc to cut it at C will be 5 inches.

Problem 6.

To construct a circle on any three points, given the points ABC. Draw lines AB and BC. Erect perpendiculars at centers of these lines as per problem 2. Construct these perpendiculars until they meet at point O. With O as a center and radius OA, draw a circle, and it will be found to pass through points B and C.

Problem 7. To construct a trefoil. Draw an equilateral triangle as per problem 5, and bisect each side as per problem 2. Then with the apex of the angles as centers and radius equal to one-half the sides draw arcs xy, yz and zx. In a similar manner a quarterfoil may be drawn about a square.

Problem 8. To divide a straight line into a number of equal parts. Draw AB, and set off AC as an acute angle. Lay off on AC a number of equal lengths equal to the number into which the line is to be divided, say six. Draw B 6, and then draw lines 5-5, 4-4, 3-3, 2-2 and 1-1 all parallel to B 6, as in problem 1. These lines will divide AB as required.

Problem 9.

Problem No. 1.

Problem No. 2

Problem No. 3.

Problem No. 4.

Problem No. 5.

Problem No. 6.

Problem No. 8.

Problem No. 7

Problem No. 9.

To inscribe a polygon of any number of sides within a circle. On center E draw a circle, and draw diameter AB. Through center E erect the perpendicular EC, cutting the circle at F. Divide radius EF into four equal parts, and lay off FC equal to three of them. Divide diameter AB into as many equal parts as the polygon has sides, and draw line CD through the second point from A, cutting the circle at D. Then AD is equal to one side of the polygon, and by stepping with the dividers around the circumference with the length AD, the polygon may be completed.

The student should work out the above problems carefully, drawing with pencil first, and then tracing his work in ink on tracing-cloth, preferably using the dull side of the cloth. It is a common mistake in schools to have the pupil ink in his work on paper ; and while a very neat drawing is almost always the result, the pupil does not get the practice which he should have in the use of tracing-cloth. The use of paper for finished drawings has been practically abandoned in most drawing-rooms, and the cloth tracing stands as the record drawing. Thus the student is handicapped, as his work as a beginner in a drafting-room is invariably tracing on tracing-cloth from a pencil paper drawing, and unless he has had previous experience in using it he will surely find great difficulty in so doing. The writer's experience with beginners has been that they know absolutely nothing of the use of tracing-cloth, and blots, erasures, and even holes through the cloth are the not infrequent trials of the beginner, and his employer. It should be impressed on the student's mind that a thorough knowledge of the use of tracing-cloth is very essential to his' success as a draftsman.