I V* 
 
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 Serial 502 
 
 (Rev. 1935) 
 
 U. S. DEPARTMENT OF COMM 
 
 DANIEL C. ROPER, Secretary 
 
 COAST AND GEODETIC SURVEY 
 
 R. S. PATTON, Director 
 
 FIRST-ORDER LEVELING 
 
 Leveling is the operation of determining differences of elevation between 
 any two points on the surface of the earth. There are few surveying or 
 civil-engineering operations in which leveling does not occur in some form. 
 While for many purposes only the relative elevations of points are required, 
 it is desirable for the proper coordination and comparison of leveling results 
 that all elevations be referred to a common datum or surface of reference. In 
 the network of leveling which covers the United States, the elevations are 
 expressed in meters and feet above the mean level of the sea. The mean 
 
 PiGUliE 1.—FISCHER FIRST-ORDER LEVEL. 
 
 This instrument has an extremely sensitive level bubble and is so constructed that the 
 observer may see the bubble with one eye and read the rod with the other without 
 moving about the instrument. 
 
 level of the sea is assumed to be at the same elevation on the open coasts 
 of the Atlantic and Pacific Oceans and the Gulf of Mexico, and it provides 
 a, datum easily established and accessible at many widely separated points. 
 
 The principal method now in use in the Coast and Geodetic Survey for 
 the determination of elevations is first-order leveling. This is the most 
 accurate method known and differs from ordinary leveling only in the sensi¬ 
 tiveness of the instruments used, the care with which the observations are 
 made, and the refinement of the computations. 
 
 INSTRUMENTS 
 
 The instrument used in first-order leveling (see fig. 1) consists, essentially, 
 of a telescope carrying a delicate spirit level mounted in such a manner on a 
 portable tripod that it may be quickly and readily placed in a horizontal 
 position. 
 
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 Various types of instruments have been used for first-order leveling, some 
 
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 Figure 2.— FIRST-ORDER LEVEL 
 RODS. 
 
 Both the face and back of the rods 
 are shown. Three wires are read 
 on the face of the rod and the 
 middle one of the three is read 
 on the back as a rough check. 
 
 Y level used extensively by engineers on con¬ 
 struction work, and others differing widely from 
 it. The principal characteristics which distin¬ 
 guish the form of first-order level now in use 
 in the Coast and Geodetic Survey are the irre¬ 
 versibility of the telescope and level; the ab¬ 
 sence of wyes; the rigid fastening of the level 
 vial to the telescope, and its juxtaposition to 
 the latter, in the barrel of which it is counter¬ 
 sunk ; the use in the construction of the tele¬ 
 scope and adjacent parts of a metal known as 
 invar which has a very small coefficient of 
 expansion,; the protection of the level vial and 
 the middle part of telescope from sudden and 
 unequal changes of temperature by incasing 
 them in an outer tube; and an arrangement 
 by which, without any change of the observer’s 
 position, the level bubble can be clearly seen 
 by his left eye at nearly the same instant in 
 which the distant rod is observed through the 
 telescope by his right eye. 
 
 RODS 
 
 The readings are made upon a graduated 
 metal strip of invar. The strip, which is about 
 1 inch wide, fits loosely in a groove of a flat 
 wooden rod about 10 feet long, and it is free 
 to move upward for temperature changes, being 
 fastened rigidly only at the bottom of the rod. 
 The bottom of the rod is made of metal and 
 terminates in a flat base of hardened steel 
 about 1 inch in diameter. When leveling along 
 a railroad, the top of a spike, which serves 
 to hold the rail in place, is used as the rod 
 support; off the railroad the rod is supported 
 on the top of a steel pin driven in the ground. 
 
 For a complete description of the instrument, 
 the rods, and the method of graduating the 
 rods, see Coast and Geodetic Survey Special 
 Publication No. 129, Geodetic Level and Rod, 
 revised (1935) edition. 
 
 FIELD PROCEDURE 
 
 The first-order leveling of the Coast and Geo¬ 
 detic Survey is run along railroads and im¬ 
 proved highways. Automobile trucks are used 
 for transporting the leveling party to and from 
 
 during the actual 
 
 about 
 
 tions. 
 
 a mile in 
 In case 
 
 length, and each 
 of disagreement 
 
 the working grounds, but 
 leveling the party walks. 
 
 Graduated rods are held at two points, the 
 instrument being placed midway between them. 
 The telescope is sighted first on one rod and 
 then on the other. The difference of the read¬ 
 ings of the rods is the difference of height be¬ 
 tween the two points. The length of sight is 
 usually short and should not exceed 165 yards, 
 under most favorable conditions. By repeat¬ 
 ing the operation at successive stations the 
 difference of elevation of widely separated 
 points is determined. 
 
 A line of levels is broken up into sections 
 section is always run twice in opposite direc- 
 of the results beyond prescribed limits, one 
 
3 
 
 Figure 8— A FIRST-ORDER LEVEL PARTY IN ACTION. 
 
 The umbrella is to protect the instrument from the heat of the sun rather than for the 
 comfort of the observer. One of the two rodmen does not appear in the picture. 
 
 Figure 4.—A STANDARD BENCH MARK TABLET. 
 
 This tablet is set solidly in masonry structures, rock outcrops, boulders, or concrete 
 
 posts so that only the inscribed disk is visible, 
 
4 
 
 or more additional runnings are made. Permanent points called bench marks 
 (see tig. 4) are established at short intervals for the use of surveyors and 
 engineers. 
 
 ACCURACY 
 
 For the leveling done since 1890 the maximum discrepancy allowed between 
 two measurements on a section 1.6 kilometers (1 mile) long is 5 millimeters, 
 or one-fifth of an inch. For sections of other lengths the discrepancy allowed 
 is proportional to the square root of the length. 
 
 A much more severe test of the accuracy of the leveling is obtained from 
 the closures of large circuits, 50, 100, or 1,000 miles in circumference. When 
 elevations are carried from one point continuously in one direction around the 
 circuit, the computed elevation for the starting point on closing the circuit 
 should agree with that assumed for it at the start if there are no errors in the 
 leveling. 
 
 In the network of first-order leveling which now covers the United States 
 there are approximately 500 such circuits. The lines are so interlaced that each 
 line usually forms a part of two circuits. The greatest error indicated by the 
 circuit closures in any line of the whole system, involving about 100,000 miles of 
 leveling executed by the Coast and Geodetic Survey, the Corps of Engineers 
 (U. S. Army), and other organizations, is 2 millimeters per kilometer, or about 
 one-eighth of an inch per mile, while the average error is 0.3 millimeter per 
 kilometer, or about one-fiftieth of an inch per mile. The leveling done in recent 
 years by the Coast and Geodetic Survey has an average closing error about 
 0.2 millimeter per kilometer. 
 
 EXTENT 
 
 Since the adoption of the present instrument and methods the Coast and 
 Geodetic Survey has completed over 85,000 miles of first-order leveling. The 
 average rate of progress of this leveling lias been about 75 miles per month 
 per party of six men, each mile being leveled at least twice, once in a forward 
 and once in a backward direction. During the month in which the most rapid 
 leveling was done, 165 miles of line were completed by a single party. The cost 
 of this recent leveling has been from $7 to $16.50 per mile of progress, leveled in 
 both directions. 
 
 First-order leveling will eventually cover the whole United States with a 
 network of lines spaced at intervals of approximately 100 miles. Within the 
 areas formed by these lines of first-order leveling, second-order levels will 
 be run at intervals of 50 and 25 miles, approximately. At present there is very 
 little first-order leveling left to complete the above program and the second- 
 order leveling will be finished by the summer of 1935 insofar as available 
 routes can be found along which the line of levels can be run economically. 
 In some of the high mountain regions it is impossible at the present time to 
 complete the net to the 50- and 25-mile spacings for lack of railroads or 
 highways along which the lines of levels can be extended. 
 
 Second-order leveling is run with the same instrumental equipment and 
 under the same general instructions as first-order leveling, the only difference, 
 being that the second-order leveling is run once and not leveled in both 
 directions as is the case with first-order leveling. By the middle of the 
 summer of 1935, approximately one-quarter of a million miles of first- and 
 second-order leveling will have been run and included in the fundamental 
 leveling net of the United States. 
 
 As the first- and second-order leveling to reduce the fundamental net to the 
 25-mile spacing is practically completed, the work of further subdividing the 
 net is now in progress and will require probably more than a quarter million 
 miles of additional lines of levels, to furnish the vertical control for the 
 topographic mapping of the country. 
 
 
 3 0112 110789176 
 
 U.S.GOVERNMENT PRINTING OFFICE: 1935