points 1, 4, and 7, and also points U, R, and Z. Sections are thus formed on cutting planes DM and CK, and while these are not absolutely true sections, as defined by the laws of projection, they are near enough for all practical purposes and can be constructed in much less time.
The arcs of these sections are divided into equal spaces and the divisions given numbers or letters as shown in Fig. 310. Perpendicular lines are dropped from each division until they intersect lines DM and CK.
The order of sections is now decided upon as shown by the order given upon the drawing. The base lines for the sections may or may not be drawn in Fig. 310, according to the amount of dependence to be placed on their guidance.
The diagram of sections, Fig. 311, shows the condensed form in which the experienced draftsman usually develops this feature of the problem. All of the altitudes of points in the profile of one end of the transition are placed upon a vertical line. From the intersection of this vertical line with a horizontal base line all of the base lines from Fig. 310 are measured. Above this horizontal line, other horizontal lines are drawn at distances representing the altitudes of the points in profile of the other end of the transition.
From Fig. 310 base lines are laid down upon the horizontal line of Fig. 311, and perpendicular lines are erected to the proper altitude. The upper base of the section can be measured with the dividers and used in developing the pattern.
Supposing the true length of the upper base of Section R to 5 is desired. Starting at the short line labeled R–5, the vertical line is followed upwards until it meets the horizontal line labeled Alt. of R. The distance between this point and point 5 on the vertical line at the left of the diagram is the required distance.
It sometimes happens that two base lines have the same lengths as is the case with C–1 and 1–U. To find the true lengths, starting at C–1, the vertical line is followed upwards until it meets the base line of the diagram (points C and K having no altitude) and from this point the distance to point 1 on the vertical line at the left of the diagram is measured. Again starting at 1–U the same vertical line is followed upwards until it meets the horizontal line representing the altitude of U. The distance from this point to point 1 at the left of the diagram is the true length sought.
Starting with a vertical line. Fig, 312, upon which the length
