THE PLANE TABLE A plane table consists of an alidade carrying a line of sight attached by a support to a ruler with a fiducial edge. The alidade is free to move on a drawing board mounted on a tripod and the table is leveled by means of plate levels. The alidade consists of a telescope provided with a level tube, a vertical circle and stadia wires. (Fig. 25.) To facilitate computations of horizontal and vertical dis tances an attachment known as the Beaman Stadia Arc hal been patented, and which may be attached to the vertical circle of transits as well as plane table instruments and by means of which stadia tables or slide rules may be eliminated, the vertical angles are not read and yet the results are obtained much quicker and with accuracy equal to that obtained by the other methods; and its simplicity tends to eliminate errors that might otherwise occur. The Beaman Stadia Arc patent is controlled and manu factured by W. & L. E. Gurley, (Troy, N. Y.) and their description of the- method of computations is as follows: (Fig.
Difference in Elevation between Instrument and Rod. The outer scale, marked "Vert.," indicates multiples of the interval, for determining differences in elevation between instru ment and rod. The zero point of this scale is marked 50, so that a direct scale reading will indicate whether the telescope is elevated or depressed.
A' unique feature of the use of the multiple scale is that only such inclinations of the telescope are used as will give a whole number scale reading, while the fractional part of the elevation is quickly and accurately determined by the reading of the middle wire on the rod.
To obtain the desired multiple, therefore, sight anywhere on the rod, it does not matter where, so that a whole number reading is obtained on the multiple scale.
Subtract 5o from this scale reading and use the algebraic remainder; e.g., if the Vert. scale reads 56, the multiple is 56-50= +6. If the scale reads 47, the multiple is 47-5o= 3.
Example: Suppose the observed subtended stadia reading on the rod to be 6.4o (640 ft.), and to obtain a whole number for the scale reading, the telescope is inclined so that the multiple scale reads 33, at which setting the middle wire reads 7.30 on the
rod.
Then the desired multiple equals 33 17 and 17X6.40= 108.8 Difference in elevation between instrument and base of rod is then, 7.30-108.8= ri6.1 ft.
The negative point indicates that the point where the rod was held is lower than the instrument.
To Reduce Observed Distance to True Horizontal Distance. The inner scale, marked "Hor.," gives at the same pointing a direct reading of the percentage of correction (always sub tractive) necessary to reduce the observed stadia reading (in feet subtended) to the true horizontal distance.
Example: At the above setting the reduction scale would read 3, or 3%.
3% of 64o ft. = 19.2 ft.
640-19.2=620.8 ft., the true horizontal distance.
To facilitate the slight computation necessary to determine differences in elevation, a special form of notes as devised by the United States Geological Survey for use with this attachment is as follows: The Beaman Arc reading is placed under the appropriate heading, B.S. or F.S., in the above table. All sights are to be regarded as foresights, except those taken to determine the H.I. Thus, after B.S. has been taken to determine the H.I., all intermediate rod stations, whether taken before the rod reaches the instrument or after the rod goes ahead, are to be entered as foresights.
The distance is recorded as 4.2, 6.3, etc., meaning 42o feet, 63o feet, etc.
The column headed "Product" is for the multiple times the distance, for example 4 x4.2 =16.8; 4 being the multiple for a stadia arc setting of 54.
The column headed "Rod Correction" is for the final reading of the middle wire on the rod.
The signs to be affixed to the "Product" and to the "Rod Correction" are determined according to'whether the observation is a B.S. or a F.S., by following a rule of universal application, namely: A stadia arc reading of 54 indicates +; therefore; here the sign of the "Product" is for a B.S., and + for a F.S.