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lines of penetration of the two solids seen in elevation. To find the plans of these lines, let fall projectors from points 2, 5 and 1, 4, in No. 5, to cut the corresponding edges of the prism B in No. 6, and they will give points 1, 2, 4, 5 ; join these as before by straight lines as shown, and they will be the plans of the two lines of penetration 1, 2, 4, 5 previously found in No. 5. On looking upon the two pyramids, in the direction of the arrow shown in No. 5, two pairs of lines of penetration will be seen. These are the two front ones 1, 2; 4, 5 ; and the two, 1, 2'; 4, 5', imme- diately behind them, shown in No. 6. To show the position of the four lines of penetration made by the two lower inclined sides of pyramid B, let fall projectors from points 3, 6 in No. 5, to cut the corresponding edge of the same pyramid in 3, 6 in No. 6 ; join these points by dotted lines to 2, 2' ; 5, 5' respectively, and they will be the plans of the lower, or return lines of penetration of the two solids. Should the two prisms have such a relative position that their axes are inclined to each other at some angle other than a right angle, in a plane common to both, the procedure for finding their lines of penetra- tion woul,d still be the same. As a test of its application, let the two pyramids in the last problem penetrate each other in such a way that the axis of the penetrating one is inclined at an angle of 30 to the horizontal, while that of the penetrated remains vertical, and let it be required to find their projection and lines of penetration when the axial plane of the solids is parallel to the VP, and also when that plane is inclined to the VP at a given angle. As the solids in the first-named position have their axial plane parallel to the YP, and the axis of one of them is inclined to the HP,