Apparent reading error

A summary of the results shows the average apparent reading error for a standardtype alidade to be about 1.1 minutes per pointing, and in the best series of readings, about 0.7 minute. With the pendulum alidade, the average is less than 0.5 minute, and in the best series, about 0.3 minute. The average time required for each reading with the standard-type alidade was 54 seconds; with the pendulum alidade, 27 seconds.

These test readings were limited in number, and were made under good conditions.

tative, but do indicate great promise for good field results.

From the data recorded during these tests, the time required to complete a reading with the pendulum alidade was compared with that required to make the same reading with two other standard-type alidades. In general, the time required for the pendulum alidade was about half that for the other two. With the pendulum alidade, an average time of about 20 seconds was needed for stadia and elevation readings compared with over 50 seconds with the other instruments. During a day of field

work with 100 setups, or 200 readings, the time saved would amount to more than an hour. The speedier operation is due in part to the pendulum, in part to the optical reading system, and also to the more convenient tangent screw arrangement.

APPARENT ADVANTAGES

The advantages expected from the use of the pendulum principle are not entirely those of speed and convenience of operation, however. It also has some inherent advantages over a bubble, not completely proven at this time, but strongly suggested. A bubble, particularly a sensitive and ac

curate bubble, is fragile and must be handled very carefully and guarded against shocks and vibration. It is hoped that the pendulum will prove to be more rugged and reliable. Also, a bubble, as is well known, is subject to inaccuracies due to temperature changes, especially when it is exposed to direct sunlight. The pendulum, it seems fairly certain, will not be affected in this way.

The four shop models will be given extensive field use tests this coming summer, on regular field mapping work. When the results of these tests are available, it will be possible to evaluate the experimental work described here with more assurance.

the free surface of a pool of liquid, and a bubble in a confined liquid have indicated the direction of gravity for astronomer, geographer, and surveyor.

The limitations of each method have determined the extent of its use and, judged in this manner, it is obvious that the limitations of the bubble in a confined liquid, or the spirit level, have been the easiest to eliminate or accommodate. However, anyone who has used a spirit level knows that all of its limitations have not been overcome, and experience shows that to a great extent a leveling instrument is good or bad depending on the designer's awareness of these limitations and his success in allowing for them. And, finally, this awareness must be shared by the instrument user to insure a successful survey.

These opening remarks are not meant to convey that the problem of designing a good leveling instrument has received too little attention. The contrary is probably nearer the truth. It is likely that these very facts are the cause for the complete break with tradition which the Zeiss Opton level certainly is. Indeed it is with difficulty that some, long associated with levels and astrolabes, are made to understand that nothing. in the Zeiss level remains level or plumb.

The Ni-2 level was introduced in this country in June of 1951 at the Eleventh Annual Meeting of the American Congress on Surveying and Mapping in Washington, D. C. The Zeiss Company exhibited two instruments and sold both from the exhibit floor, one to the U. S. Coast and Geodetic Survey, and the other to the U. S. Geological Survey. The Geological Survey took

Presented at the first annual fall conference of the Land Surveyor's Division of the New Jersey Society of Professional Engineers, November 7, 1953, Princeton University, Princeton, N. J.

in the field, then in the Instrument Design Section where it was dismantled for study. The reports resulting from the tests and the study, as well as an article by Dr. M. Drodofsky,1 the inventor of the automatic feature, have been used in preparing this paper.

from a distant target imaged at the center cross of the reticle. Figure 1b shows the telescope tilted upward an angle a with the distant target now imaged a distance ƒ sin a above the center cross. The problem is to shift the image back to the center. Figure 1c shows schematically how this is done. A mirror placed at A, a distance s from the reticle, turns the rays though angle ẞ to fall at the center. The conditions which must be satisfied are: to control the rotation of the mirror about A in such a manner that s sin ẞf sin a; and to make the telescope truly anallactic, and to consider the tilt axis to be coincident with the anallactic point. The second condition results from variations in the value of ƒ with changes in focus.

=

Figure 2 shows a diagram of the Ni-2 optical system. Elements 1 and 2 are the telescope objective, 3 is the focusing lens, 4 and 6 are mirrors fixed to the telescope, 5 is the compensating mirror, 7 is the reticle, and 8 the two lenses of the eyepiece. AC and BD are wires attached to the telescope at A and B and to the compensating mirror at C and D, the weight of the compensating mirror acting as a pendulum supported by the wires. From the relation s sin ẞ = ƒ sin a it will be seen that the compensating mirror must tilt through an angle greater than the tilt angle of the telescope. In the Ni-2 level this ratio is about 2: 1.

Part of the angular magnification required is obtained through the difference in the lengths of AB and CD, figure 3, the re

maining magnification being obtained by a shifting of the center of gravity, S.

THE SOLUTION

The swinging system CDS, figure 3, is in balance when the vector of gravity originating in the center of gravity, S, passes through the point of intersection, P, of the extension of lines AC and BD. With a disturbance of CDS (AB remaining fixed) it will be seen that both S and P move in the same direction, with P moving a greater distance than S, the difference being r. With the disturbing force removed the system will swing back until the vertical force vector through S again passes through P.

Now consider the telescope, AB, tilted, with AC being momentarily fixed, figure 4. In this case S will move the greater distance and, when AC is released, CDS will continue to swing until point P has caught up with S, thus adding to the tilt magnification caused by the shorter length of CD. If the center of gravity is moved upward (S above CD), P will travel farther giving greater magnification, with less magnification resulting from a lowering of the center of gravity. Referring back to figure 3 it will be seen that there is a limit to such magnification control, for, as S is raised, r becomes smaller until, with r = 0, neutral equilibrium is reached and, with continued raising, the pendulum will topple over.

To be sensitive to the few seconds of arc required for precise leveling it is necessary

the instrument. The operators of today's fast, precise, optical-reading surveying instruments should not be expected nor allowed to repair them any more than such permission is granted the operator of a modern precision automatic machine tool.

A three-quarter view of the level mounted on its tripod is shown in figure 5. Figure 6 shows the telescope removed from the upper plate with the eyepiece and objective end caps removed. The compensator is nested jections from the main telescope body castbetween and supported by two heavy pro

ing and the reticle assembly is fastened to the ends of the projections. The end cap standing at the right both supports the eyepiece and protects the compensator and reticle.

THE COMPENSATOR

In figure 7 the compensator is shown removed from the telescope and resting on the base of the pendulum. In this position the weight of the compensator body and prism assembly is being borne by the damp

FIGURE 3.-Swinging system.

moval of the circular level adjusting screw cap is the only dismantling that can be done without removing the telescope from the upper plate. And this cannot be done without removing the proper screws and parts From the lower plate. It is not intended that this paper enable the reader to take the instrument apart but rather to so satisfy his curiosity that he will not want to. I know of no case in the Tennessee Valley Authority or the U. S. Geological Survey the field of my experience) where a field nan tried to finish the day's work by making ■ repair inside an optical reading instrunent, but what the only thing finished was

FIGURE 4. Swinging system with tilted tele

scope.