stones that form the arch is sufficiently illustrated by the drawing itself. Fig. 41 is the drawing of a small building, and, according to the scale here given, it is only six by eight feet on the ground, with corner posts only three feet high, the ridge rising two feet above the level of the tops of the posts, and the chimney two feet above the ridge. Observe how the ridge runs centrally over the building, and how the chimney is placed centrally on the ridge, and also equidistant from the two extremes of the ridge. Fig. 42 represents a structure having a ground-plan in the form of a cross. The four roofs have sloping ends as well as sloping sides, and are what are called hip-roofed. Moreover, the slope of the ends is the same as the slope of the sides. Thus the point 3 is two feet above the level of the tops of the posts; and if the end 4 6, and the side 45, were extended upward, the horizontal distance to the side would be the same as the horizontal distance to the end, being three feet in both cases. Fig. 43 is a clustered column, formed of four pieces, each one foot square at the upper end, but each beveling outward below. The moulding around it is beveled also, to correspond to the sides of the column. With the aid of the foregoing illustrations and the isometrical drawing-paper, the student ought now to meet with little difficulty in applying the isometrical method of representation to all objects that are bounded by straight lines. or by regular curves. Irregular surface curves may also be represented isometrically without difficulty by first drawing them on the rectangular ruled paper, from which they may be easily transferred to the isometrical paper, as the spaces on both measure alike. The student would do well to represent, isometrically, all the figures and problems in Drawing-Books II., III., and IV.; and he will generally find the change quite easy from the cabinet to the isometrical drawing, if he understands the former. TABLE FOR DRAWING CIRCLES IN ISOMETRICAL PERSPECTIVE. The figures in the columns of Isometrical Diameters denote the lengths of isometric diameters (or sides of isometric squares); and the figures in the other two columns denote the corresponding lengths of the minor and major axes. Thus, if an ellipse is to be drawn in an isometric square of 10 spaces to a side, the isometric diameter will be 10 spaces in length, the minor axis will be 7.071 spaces in length, and the major axis 12.247 spaces in length. The Table gives the relative proportions of the isometric diameters, minor axes, and major axes for all isometric ellipses drawn in isometric squares of from 1 to 90 spaces in diameter. The principle holds good whatever measure of length the figures in the columns of Isometrical Diameters represent. 10 11 12 13 9.192 30.406 Isom. Minor Major Isom. Minor Major Isom. Minor Major Diam. Axis. Axis. Diam. Axis. Axis. Diam. Axis. .707 1.225 31 21.920 37.967 61 43.134 1.414 2.449 32 22.627 39.192 62 43.841 2.121 3.674 33 23.335 40.417 63 44.548 77.159 2.828 4.899 34 24.042 41.641 64 3.536 6.124 35 24.749 42.866 65 4.243 7.348 36 4.950 8.573 37 5.657 9.798 38 6.364 11.023 39 7.071 12.247 40 7.778 13.472 41 8.485 14.697 42 15.922 43 Axis. 74.709 75.934 45.255 78.384 45.962 79.608 50.215 71 50.205 25.456 44.091 66 46.669 80.833 47.376 82.058 84.507 85.732 86.957 50.912 88.182 51.619 89.406 17.146 44 10.607 18.371 45 16 11.314 19.596 46 32.527 56.338 76 17 12.021 20.821 47 33.234 18 12.728 22.045 48 33.941 58.783 78 55.154 19 13.435 23.270 49 34.648 60.012 79 20 14.142 24.495 50 35.355 61.237 80 56.569 14.849 25.720 51 36.062 15.556 26.944 52 36.770 63.687 82 57.983 23 16.263 28.169 53 37.477 64.911 83 58.690 101.654 24 16.971 29.394 54 38.181 66.136 81 59.397 102.879 25 17.678 30.619 55 38.891 67.361 85 60.104 104.103 26 18.385 31.843 56 39.598 68.586 86 60.811 105.328 19.092 33.068 57 40.305 69.810 87 61.518 106.553 19.799 34.293 58 41.012 71.035 88 62.225 107.778 41.719 72.260 89 62.933 109.002 30 21.213 36.742 60 42.426 73.485 90 63.640 110.227 31.820 55.114 75 |