deflection from P. C. at Sta. 3 + 20 to the intermediate transit point at Sta. 4+ 50 is 2° 36′. The total angle is double this deflection, or 5° 12′, which is recorded on the same line in the third column. The record of total angles at once indicates the stations at which transit poínts are placed. The total angle at the P. T. will be the same as the angle of intersection, if the work is correct. When the curve is finished, the transit is set up at the P. T., and the bearing at the forward tangent taken, which affords an additional check upon the previous calculations. The magnetic bearing is recorded in the fourth column, and the deduced or calculated bearing is recorded in the fifth column. LEVELING. Examples in Direct Leveling.-The principles of direct leveling are illustrated in the figure. = Let A be the starting point, which has a known elevation of 20 ft. The instrument is set at B, leveled up and sighted to a rod held at A. The target being set, the reading, 8.42 ft., called a backsight, is the distance that the point where the line of sight cuts the rod is above the point 4, and is to be added to the elevation of the point A. 20.00 + 8.42 28.42 is called the height of instrument and is designated by H. I. The instrument being turned in the opposite direction, a point C is chosen, which must be below the line of sight. This point is called a turning point, and is designated by the abbreviation T. P. Drive a peg at C, or take for a turning point a point of rock or some other permanent object upon which the rod is held. The reading at this point is a foresight, and is to be subtracted from the height of the instrument at B to find the elevation of the point at C. Let the rod reading be 1.20 ft. As this reading is a foresight, it must be subtracted from 28.42, the height of instrument at B; 28.42 1.20 27.22 ft., the elevation of the point C. The leveler carries the instrument to D, which should be of such a height above C that, when leveled up, the line of sight will cut the rod near the top. The backsight to C gives a reading of 11.56 ft., which, added to 27.22 ft., the elevation of C, gives 38.78 ft., the height of the instrument at D. The rodman then goes to E, a point where a foresight reading is 1.35, which, subtracted from 38.78, the H. I. at D, gives 37.43 ft., the elevation of E. The level is then set up at F, being careful that line of sight shall clear the hill at L. The backsight, 6.15 ft., added to 37.43 ft., the elevation of E, gives 43.58 ft., the H. I. at F. The rod held at G gives a foresight of 10.90 ft., which, subtracted from 43.58 ft., the H. I. at F, gives 32.68 ft., the elevation at G. Again moving the level to H, the backsight to G of 4.39 ft. added to 32.68 ft., the elevation of G, gives 37.07 ft., the H. I. at H. Holding the rod at K, a foresight of 5.94, subtracted from 37.07, gives 31.13, the elevation of the point K. The elevation of the starting point A is 20.00 ft.; the elevation of the point K is found by direct leveling to be 31.13 ft., and the difference in the elevations of A and K is 31.13-20.00 = 11.13 ft.; that is, the point K is 11.13 ft. higher than the point A. Turning points previously mentioned are the points where backsights and fore sights are taken. The backsights are plus (+) readings, and are to be added; the foresights are minus (-) readings, and are to be subtracted. A point for a foresight having been determined, the rodman drives a peg firmly in the ground and holds the rod upon it. After the instrument is moved, set up, and a backsight taken, the peg is pulled up and carried in the pocket until another turning point is called for. Turning points should be taken at about equal distances from the instrument, in order to equalize any small errors in adjustment. In smooth country an ordinary level will permit of sights of from 300 to 500 ft. To Keep Level Notes.-Many forms are used. The distinguishing feature of one of the best (see page 295) is a single column for all rod readings. The backsights being additive and the foresights subtractive readings, they are distinguished from other rod readings by the characteristic signs + (plus) and- (minus). The turning points, whose foresight readings are, are further abbreviated T. P. To Check Level Notes.-A well-known method of checking level notes provides for checking the elevations of turning points and heights of instrument only, which is sufficient, as all other elevations are deduced from them. The method depends on the fact that all backsights are additive (i. e. +) quantities, and all foresights are subtractive (i.e.-) quantities. The notes given on page 295 are checked as follows: The elevation of the bench mark at station 0 is 100.00 ft., to which all backsights, or + readings, are to be added and from this sum all foresights, or - readings, are to be subtracted. The sum of the backsights, with elevation of bench mark at 0, is 122.59. Sum of foresights is 24.27, and difference is 98.32 ft., the elevation of the turning point last taken. As soon as a page of level notes is filled, the notes should be checked and a check mark placed at the last height of instrument or elevation checked. When the work of staking out or crosssectioning is being done, the levels should be checked at each bench mark on the line. After each day's + Thus, 100.00 5.61 5.41 11.57 122.59 24.27 98.32 10.22 2.52 11.53 24.27 work, the leveler must check on the nearest bench mark. Profiles. A profile represents a longitudinal projection of the line of survey. In it all abrupt changes in elevation are clearly outlined. Vertical and horizontal measurements are usually represented by different scales, to render irregularities of surface more distinct through exaggeration. For railroad work, profiles are commonly made to the following scales, viz., horizontal, 400 ft. = 1 in.; vertical, 20 ft. 1 in. A section of profile paper is shown in the following diagram. Every fifth horizontal line and every tenth vertical line is heavy. By the aid of these heavy lines, distances and elevations are quickly and correctly estimated and the work of platting greatly facilitated. The level notes Grade 0.8 ft. per hundred fo 0 10 given in the preceding diagram are platted in the accompanying section. The elevation of some horizontal line is assumed. This elevation is, of course, referred to the datum plane, and is the base from which the other elevations are estimated. Every tenth station number is written at the bottom of the sheet under the heavy vertical lines. The profile is first platted in pencil and then inked in in black. Grade Lines. The principal use of a profile is to enable the engineer to establish a grade line, i. e., a line showing the slope of the road on which the amounts of excavation and embankment depend. The rate of a grade line is measured by the vertical rise or fall in each hundred feet of its length, |