In Fig. 662 arc shown two views of a boss such as is used for fastening a faucet into the side of a large can; the curvature of the body of the can being represented by the line A D B. For convenience in demonstration, what would be properly considered the front view of the article is here called the top view, the other view being considered as the side. Let H L and K N represent its desired length and width of base or part to fit against the body of the can, and PRO the circle of the top to fit around the neck of the faucet. Also let D E be its required projection from the can. Through E draw Y Z parallel to H L, the long diameter of the base. From P and 0 drop lines at right angles to H L, catting Y Z in the points
Y ami Z, also from H and L drop lines catting A D B, and connect the points thus obtained with Y and Z. as shown, thus completing the side view.
Commence by dividing one-quarter of the plan of the base K H into any convenient number of spaces. as shown by points 1, 2, 3, etc. For greater accuracy these spaces may be made shorter as they approach the ends of the base, where the line has more curve than near the middle. Having established the points 0, 1, 2, 3, etc., in K H, draw a line from each of them to the center of the plan M. By this means the quarter of the circle representing the top of the article, and shown in the diagram by P R, will be divided in the same mariner or proportionately to the plan of the base, all as shown by points 11, 21, 31, etc. It will be seen that these lines divide the surface of the boss into a number of four-sided figures, each of which must now be redivided diagonally so as to form triangles. Therefore connect 0 with 1', 1 with 21, etc., by means of dotted lines, as shown. These solid and dotted lines drawn across the top view represent the horizontal distances between the points given, while the vertical distances between the same can be measured on lines parallel to C E; hence it will be necessary to construct a series of triangles from these measurements, as shown at the right of C E, the hypothenuses of which will represent the real distances between the required points.
Fig. 662. - Top and Side View of Boss, Showing System of Triangulation.
Therefore from the points established in H K drop lines vertically cutting the section line A D B, as indicated, then carry lines from the points on A D horizontally till they cut the line C F and continue them indefinitely to the right. The points at which these lines cross the center line E C will represent the hights of the several triangles. On these horizontal lines, measuring from the center line C E, which is assumed as the common perpendicular for all the triangles, set off the liases of the several triangles, transferring the distances from the plan. From the points thus established draw lines to F. which will give the hypothenuses of the several triangles. For example, on the line drawn from the point 52, in A D B, measuring from C, set off a distance equal to 5' 5 and also a distance equal to 6' 5 in the top view. The difference between these two is so small as to be imperceptible in a drawing to so small a scale as this. In like manner, on the line drawn from 42 set off a distance equal to the length of the diagonal lines 4 51 and 4 41 in the top view, and in the same manner on the line drawn through 34 set off the distance equal to 3 41 in the top view and also 3 31. Then, as before remarked, lines drawn from the points thus established in the horizontal lines toward E will be the hypoth-enuses of the several triangles corresponding to sections represented by the diagonal lines in the top view.
In view of the fact that the base of the boss is carved as shown by A D it will be noticed that the measurements from K to H in the top view do not represent the real distances, because the distance H M is less than the distance A D. In case extreme accuracy is required it will therefore be necessary to develop an extended section on the base line A D, which may be done as follows: Extend the line M H of the top view, as shown at the left, upon which place a correct stretchout of A D; that is, make D1 11 equal to D 12. I3 21 equal to 12 22, etc., and through each of the points thus obtained draw measuring lines at right angles to D1 M. Place the T-square parallel to H M, and, bringing it successively against the points in the line K H, drop lines into the measuring lines of corresponding number, as shown by 04, l4, 24, etc. Then will the distances 04 l4, l4 24, etc., be the correct distances to be used in developing the pattern instead of the distances 0 1, 1 2, etc.
Fig. 663. - Pattern for Boss.
The pattern may now be developed as shown in Fig. 663. Lav off the line S T, in length equal to the required width of the pattern on one end, as shown by Y 62 in Fig. 662. With these two points established proceed to obtain other points in both lines of the pattern by striking arcs with radii equal to the spaces established in the plan of both base and top of the article and to the hypothenuses of the triangles already described. Thus, from S as center, with radius equal to the distance 62 54 of the stretchout of the base, describe a short arc, as shown at 5 in the pattern. Then from T as center, with radius equal to E 6' of the triangles, intersect it by a second arc, as shown. From T as center, with radius equal to 61 51 of the plan of the top of the article, describe a small arc, as shown, and from 5 of pattern as center, and radius equal to E 5' of the triangles, intersect it by another arc, thus determining the second point in the top. Proceed in this manner, adding one triangle after another in the order in which they occur in the top view, using the spaces of the plan of top and of the stretchout of the bottom and the hypotheneuses of the triangles as above described. Lines traced through the points thus obtained, as shown from S to N and from T to M, will give the pattern of one-quarter. This can be duplicated as often as is necessary to make the entire pattern in one piece, or to produce it in halves, as shown.