Fig. 402.Pntterns of Cold Air Box. - Second Solution.

PROBLEM 100. The Patterns for the Inclined Portion of a Cold Air Box to Meet the Horizontal Portion Obliquely in Plan.

This problem is here introduced on account of the similarity of its conditions with those of the one immediately preceding, although, as its patterns are obtained entirely without the use of profiles, it does not properly belong in this connection. Its solution will serve to show what widely different means may be employed to obtain the same ends. In the preceding case the miter cut was obtained without reference to the miter at the upper end of the oblique arm. In this case the oblique portion is required to join, at its upper end, with another arm like and exactly parallel with the arm joining its lower termination.

Under such conditions it follows that the planes of the upper and lower miters must be parallel, and, therefore, that miter cut at the upper end of either of the faces of the oblique portion must be parallel with that at the lower end of the same. Advantage may be taken of these conditions to obtain a very simple solution of the problem, as will be seen below.

The first requisite is, of course, a correctly drawn elevation and plan in which all the points in each are duly projected from corresponding points in the other view. In Fig. 403 is shown a plan and elevation of the box, with the lines of projection connecting corresponding points in each, all of which may be constructed very much as described in the preceding problem.' The inclined arm is required to have a rise equal to a of the elevation and a forward projection equal to b of the plan. Corresponding points in the two views are lettered alike. Thus the elevation shows clearly that it is an elevation of the front A B F E of the plan, with the back C D H G dotted behind, while the plan shows clearly A B D C of the elevation with the bottom E F H G dotted below.

Fig. 403. - Patterns for the Inclined Portion of a Cold Air Box to Meet the Level Portion Obliquely in Plan.

The first important information to be derived from the correctly drawn views is that the front and back are the same, likewise the top and bottom are alike. The patterns of the top and front are given separately. upon the supposition that joints will be made at all of

Pattern Problem. 215 the angles; should they be wanted in one piece they could readily be connected. As all the surfaees of the inclined portion of the pipe are oblique to the given new, only some of their dimensions will be correct as they appear on the paper. An inspection of both elevation and plan will show that the lines A C and B D are both horizontal and parallel, and, therefore, correct as they appear in the plan, and may be used as given in the construction of a pattern of the top piece. The shortest distance between these two lines will be represented by a line at right angles to both, as M N. Since the point N in the line B D is higher than the point M of the line A G, by the distance a of the elevation, it will be necessary to construct the diagram J L K in order to get the correct distance between the points M and N. J K is made equal to the distance M X, as indicated by the dotted lines. K L is equal to the rise given in the elevation; hence the distance J L represents the true distance between the points M and N. Upon the continuation of the line M N of the plan set off the distance J L, as shown at J' L'. Through each of these points lines are drawn parallel to A C and B D of the plan. The line A' C' is made equal to A C, and B' D' is made equal to B D by means of the dotted lines drawn parallel to M N. This pattern is completed by connecting the point A' with B' and C' with D'.

In developing the pattern of the side A B F E the same course might be pursued, beginning with the lines A E and B F, whose lengths are correctly given in the elevation, but for the sake of diversity another method has been employed. Beginning with the known fact that the point B is higher than the point A, as shown by a in the elevation, construct a diagram, O P R, making O P equal to and parallel with A B of the plan, and O R equal to a, thus giving B P as the correct length of the line represented by A B of the plan. From the points E and F draw, at right angles to E F, the lines E S and F T indefinitely. Since the distances A E and B F are the same and are correctly given in the elevation, take that distance between the feet of the dividers, and placing one foot at the point B describe a small arc, cutting the line E S in the point S. By repeating this operation from the point P, the point T is established in the line F and T. Lines connecting the points B S, S T and T P will complete the pattern of the front and back.