The angles at these trigono metrical points of whatever order, are invariably observed with a theodolite, and as this is without doubt the most important of all surveying instruments, it is desirable to give a description of it.
The Theodolite.—The theodolite is a surveying instrument consisting of two graduated circles placed at right angles to each other, for the measurement of horizontal and vertical angles, a telescope, which turns on axes mounted centrically to the circles, and an alidade for each circle, which carries two or more verniers or micrometer microscopes. The whole is supported by a pedestal resting on footscrews, which are also employed to level the in strument. The size has varied from a minimum with circles 24 in. in diameter to a maximum with a 36-in. horizontal and an i8-in. vertical circle, but these very large circles are now obsolete owing to improvements in dividing machines. The largest now in use is 12 in. in diameter.
As an example of a modern theodolite suitable for use in topographical or exploratory surveying, we may take a 5-inch transit theodolite, fitted with micrometer microscopes. The accompanying fig. (3) shows such an instrument by Messrs. Cooke, Troughton and Simms. The instrument rests on a tripod stand, which is not shown in the figure. The levelling base has
three screws. The horizontal and vertical reading circles are 5 in. in diameter, and are each read, by two microscopes, by estima tion to single seconds. The telescope, which can be completely rotated in its horizontal bearings, has a magnification of 25. The instrument packs up in two boxes for transport. Excellent work has been done with such a theodolite all over the world. It does not appear desirable to give a more elaborate description, for the use of such an instrument can only be acquired by practice.
Triangulation.—This may be carried out either in the form of chain or of a net-work (fig. 4). In a small country even the first-order triangulation might cover the land with a net-work, with sides about 3o miles long; and this was done in the case of the British Isles. But in large countries such as India or the United States a very considerable saving of time and money is effected by running chains of triangles, generally north and south, or east and west. Second order work may also be either in the form of chains or of a net-work ; it would be dependent on the first order work, if that existed. Third order work, which is re , quired by the detail surveyors, would usually cover the ground completely.
At each station of the triangu