This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 edition. Excerpt: ... CHAPTER V MISCELLANEOUS PRACTICAL EXERCISES 157. A shaft of a mine follows approximately the line between the points a ( -- 3, --, -- 1 ) and b ( -- 1, --1J, -- J). A tunnel is to be made from a point c (--2{, --1, -- j) on the side of a mountain to intersect the shaft. Find the shortest length of the tunnel, and the angle between the center line of the shaft and the center line of the tunnel. 158. In Fig. 48 a channel and an I-beam are shown as they intersect in a roof. Take the following coordinates for the points marked in the figure: a ( + 1, --1, -3, b ( + 3i, -4, -1TV), c( + 54, -4, -i), d{ + 2, -h -3}), e ( + 24, -2, -H), / (+2, -2*, -1*), (0 + 34, -2, 0), A ( + 3, -2, 0). Draw the projections of a bent plate connection and in a section drawing show the true angle between its sides. 159. A cylindrical pipe, 2 feet in diameter, passes through the roofs shown in Fig. 14 at a point in the intersection of the roofs. The axis of the pipe is perpendicular to the line of intersection and is inclined 45 from the vertical. Find the true size of the hole cut out of the roofs for the pipe. 160. Obtain by development the true size and shape of the covering needed for a symmetrical dome with eight sides. 161. In Fig. 49 a portion of a locomotive boiler is shown. Make the top element of the slope sheet at an inclina'tion of 30 to the horizontal, and show the true size of a steel plate to be used in making the slope sheet. 162. The sand-box on a locomotive stands partly on the slope sheet and partly on the cylindrical portion. Find the shape of the bottom of the sand-box to fit the boiler drawn for Ex. 161. 163. Make the pattern for the conical portion of the eavetrough outlet shown in the...