362.—A Horizontal Scale of Tangents was placed upon the surveying theodolites by Ramsden. This was divided upon a scale carried by the vernier plate, which read to the zero line (0°) of the limb. It is found in practice more accurate to take the tangent to any curve from a scale of tangents, as, for instance, that in Molesworth's pocket-book, and set this off upon the limb by means of the vernier.
363.—Gradient Scale.—Civil engineers engaged on railway work occasionally have a scale of gradients upon the back of the vertical arc 1 to 100, 150, 200, etc. These are better read from the circle with vernier from a table of gradient arcs.
CHAPTER VII.
THEODOLITES—CONSTRUCTIVE DETAILS OF 5-INCH AND 6-INCH TRANSITS—SPECIAL ADDITIONAL PARTS—PLUMMETS WITH SCREW ADJUSTMENTS OF IMPROVED FORM—STRIDING LEVEL—LAMP—ADJUSTMENT OF AXIS OVER A POINT—SOLAR ATTACHMENT—PHOTOGRAPHIC ATTACHMENT.
364.—The Theodolite is the most perfect instrument for measuring both horizontal and vertical angles by the aid of a telescope and graduated circles. For the purpose of surveying, the theodolite is mostly employed to take a system of triangles upon the horizontal plane of the surface of the land, and of objects at any position in which they may be placed. When altitude angles are taken separately these are generally applied to give corrections to chain or other actual measurements upon the surface by calculation of the difference of hypotenuse and base.
365.—The theodolite in all its essential features, as differentiated from sighted compasses for taking angles, mentioned by Digges,[15] was the invention of Jonathan Sisson, a celebrated mathematical instrument maker of the beginning of the 18th century.[16] Great improvements were afterwards made in this instrument by Ramsden, who brought it up nearly to its modern efficiency by the introduction of the transit principle.[17] Later improvements in portable instruments consist in the application of the transit principle to the telescope, which was formerly applied to astronomical and the larger geodetic instruments only. Other improvements have been made more recently in constructive details.
366.—Theodolites were commonly made of two distinct types, which were originally distinguished as plain theodolites and transit theodolites. In the plain theodolite the telescope moves through an arc of about 45° upwards or downwards from the horizontal plane, but very few of these are now made compared with the number of transit theodolites in which the telescope may take a complete revolution upon its horizontal axis, so that a back and fore sight may be taken by a half revolution. This difference of construction entails a difference in the manner of mounting the telescope to correct its adjustments. In the transit the accuracy of centring and reading is easily discovered by taking a back and fore sight at a distance as equivalent to an arc of 180°, which may be read on any part of the limb by transitting the telescope, wherein the correspondence of this arc to the reading of the limb to right and left hands will detect error. With the plain theodolite the equivalent method of examination is effected by placing the telescope in Y's, as previously discussed for the Y-level, and turning it end for end on its bearings, a process liable to disturb the direction of the telescope unless special care be taken. In the following description of the details of construction of a theodolite it will be convenient to take the transit form of instrument, as this is more comprehensive, the original pattern being selected, as this may be constructed with the limited amount of tools generally found in a surveying instrument workshop.
