observing is completed, as to materially increase the speed, reduce the cost, and reduce the divergence.

144. Methods of Running.-In precise leveling a double line is invariably run for the purpose of check on every bench-mark. The U. S. Engineers adopt a method of sequence which is that already described for double rod for ordinary spirit-levels (Art. 130).

For peed they use two rod

men, and the levelman backsights on rodman A at a, (Fig. 104)

FIG. 104.-Single-roddING WITH Two RODMEN.

and foresights on rodman B at b,. Then the levelman and A move forward, and the former backsights on B at b, and foresights on A at a,. This is a single line of levels, and the party duplicate their own work by rerunning over the same line in an opposite direction.

In the U. S. Coast Survey the levelman backsights on rodman A (Fig. 105) at the turning-point a,, and then back

FIG. 105.-DUPLICATE RODDING, BOTH LINES DIRECT ONLY.

sights on rodman B at the turning-point b,. Both A and B then pass him, and he then foresights on rodman A at turning-point a, and on rodman B at b,, the rear turning-points a, and b, being left in the ground until the turning-points a, and b, are set.

145. Precise Rods. The Coast Survey rod is of thoroughly paraffined wood, and the bottom, which is hemispherical, is set in saucer-shaped turning-points, the curvature of which is greater than that of the rod foot. This rod is single and non-extensible, 12 feet long, and divided into fractions of a meter by large, easily legible markings. At

short intervals on its face are inserted in the pine wood metal plugs on each of which is engraved a fine line, and these are the zero marks on which the vernier is read; it being believed that these lines are finer than divisions can possibly be made upon wood. The rod can be read directly to thousandths of a meter, and by estimation to one ten-thousandth of a meter, by means of a target which is moved up and down by an endless chain passing over pulleys at either end of the rod, while the target can be clamped by means of another chain. which is convenient to the hand of the rodman.

The U. S. Engineers use a rod made of one piece of wood 12 feet in length. It has a T-shaped cross-section, a footplate, and a turning-point similar to the above. The rod is self-reading, that is, without targets, and graduated to centimeters. Closer records are made by estimation by the levelman, since there are three horizontal cross wires in the instrument, on each of which readings are made, and the mean of these is the value used.

The precise rods used by the U. S. Geological Survey are of two kinds, target-rods and speaking-rods. The doubletarget rods are made by Messrs. W. & L. E. Gurley of the best selected white pine, well seasoned and heated to a high temperature, when they are impregnated with boiling paraffine to a depth of one-eighth inch. The rods are a little over 10 feet long, and the graduations are commenced about a foot from the bottom of the rod to prevent readings being taken too near the bottom of the rod because of refraction. They are made of three pieces of wood bolted together, the cross-section forming a (Fig. 106). These rods are graduated on both sides, and each is supplied with two targets, which are, one oval and red, the other rectangular and black, with verniers on the edge of a square hole in the face. These verniers can be moved by means of a spring in a direction at right angles. to the line of sight, so as to bring them to a close bearing against the graduations and thus prevent parallax in reading.

One-third size.

The zero of the targets consists of a white stripe, wider at the outer edges than in the middle and of such width that at the nearest possible setting of the level the cross-hair of the latter will easily bisect the narrower part of the stripe, it being found preferable to bisect a stripe rather than cover a line with the cross-hair. The targets are handled by endless tapes running over pulleys at either end of the rods. The bottoms of the rods are protected by steel plates narrowed down to one half inch in area by giving them the shape of truncated pyramids. The rods are graduated in feet and hundredths, and read by vernier to thousandths.

These rods greatly increase the speed of leveling and reduce the amount of walking. The difference in shape and color of the two targets reduces to a minimum the possibility of error in the record of the two faces; much of the time expended in comparison of notes and check-reading of rod by instrumentman and rodmen is saved, because the instrumentman can set the target on the face of the rear rod and then on the corresponding face of the front rod and, without the necessity of reading or exchange of notes, both rodmen set on the next turning-points, clamping the targets on the other face.

The single-target rods used are similar in all essential respects to the double rods just described, but have only one face divided and one target. They lack, therefore, the advantages gained by speed in manipulation with the double rods. They are, however, superior in speed and accuracy to other forms of target-rods (Fig. 96).

The precise speaking-rods used by the U. S. Geological Survey are an adaptation of the non-extensible speaking-rods used in European geodetic surveys. They were designed by the author after suggestions received from Mr. Horace Andrews. They are a little over 10 feet in length and are graduated for 10 feet. The divisions of this rod are peculiar and are illustrated to half-scale in Fig. 107. They are SO arranged as to divide the spaces into five parts, on the theory

that the eye can estimate the position of the cross-hair on the rod to five parts more readily than by attempting to divide the same space by estimation into ten parts. In order to get the desired result, and as a foot is too small a space to be divided in the manner required, this rod is divided into units of 2 feet each. Accordingly, each actual foot is but a half of a unit, and so on for tenths and hundredths, the result being that the 10-foot rod is divided into five units and each of these into ten others and each of these again into. ten spaces. Thus one-fifth of the smallest unit space, the hundredths, can be easily estimated by eye with the aid of the crossFIG. 107.-U. S. GEO- hair at the greatest distance permitted in PRECISE SPEAKING- precise leveling whereas tenths could not be estimated. This space being .01 of a unit, One-half size. a fifth of it is .002 of a unit, actually equivalent to .004 of a foot. The portion of the rod hatched in the illustration is painted red and the remainder is painted black on white enamel, the ruling of the black lines being very fine, as shown.

LOGICAL SURVEY

ROD.

The mode of keeping the notes with this rod is unique. Whatever the initial elevation may be, say 100 feet, it is put in the column of elevations as being one half of this, or 50 feet. Then the backsights and foresights are recorded, and the computations made as with any other rod, the actual figures read being used. Whenever a bench-mark is reached and it is desired to know its elevation, that given in the book is doubled. This introduces no complications in note-keeping, simplifies the rod reading, and permits of the estimation of differences of heights on a speaking-rod to .001 of a foot.

146. Manipulation of Instrument. -In precise leveling several important details of manipulation, although apparently