being required, objects are seen more clearly. Practice quickly renders the inversion of the image immaterial to the observer. However, a second eye-piece is usually provided, which shows objects in their natural position, and may be substituted at the eye-end of the telescope.

THE SPIRIT-LEVEL.

The knowledge of the principal parts of the theodolite and its adjustments, will enable the student to understand by a simple inspection the use and adjustments of the Spirit-Level.

Description of the Spirit Level.

The instrument consists of a telescope precisely similar to that of the theodolite, and requiring analogous correction for parallax and adjustment of the line of collimation. To the telescope is attached a spirit-level, the longitudinal axis of which should be likewise, and for the same reason as in the theodolite, parallel to the line of collimation. Finally, the object of the instrument being to obtain a constantly horizontal axis of vision, the telescope or line of collimation is brought into a horizontal plane by means of the parallel-plate screws.

Parallax. The correction for parallax is made by bringing the tube carrying the eye-glass into such a position that the point of intersection of a distant object shall not be altered by a slight vertical or lateral movement of the eye.

Collimation. In the construction of the instrument known as the Y spirit-level, the telescope rests on supports similar to those which retain the telescope of the theodolite-for this construction, the line of collimation is rectified, as in the theodolite, by turning the telescope half round

in its Y's after the first observation has been made, and noting whether the horizontal cross wire then intersects the same point. The cross wires in the diaphragm of the level are arranged as shown in the diagram; the horizontal wire marks the intersection of the horizontal visual ray with the staff; the two vertical wires serve to direct the telescope so that the staff shall be seen between them, and thus be in the axis of the lenses, and likewise in a vertical direction.

In the Y level, the spirit-level is suspended beneath the telescope, as in the theodolite, and requires a similar adjustment to bring its longitudinal axis parallel to the line of collimation, which is performed by reversing the telescope end for end in its Y's, and altering the screws as described in the adjustments for the theodolite.

But in those modifications of the instrument known as "Troughton's Improved Level," and "Gravatt's Level," and which, from superior compactness, greater stability of the adjustments, and increased optical power, are more generally used, the adjustments of the line of collimation and of the spirit level are made in a different manner.

By a reference to the annexed diagram, which represents "Troughton's Improved Level," it will be seen that

the telescope is attached to the bearing-frame, and the spirit-level firmly fixed to the tube of the telescope. The spirit-level is adjusted perpendicularly to the vertical axis

of the instrument by correcting half of the observed deviation by the screws d, and the other half by the parallelplate screws e, until the telescope can be moved round in any direction without any material change taking place in the position of the bubble.

The spirit-bubble being thus adjusted, the instrument will fulfil the object of giving a line in any direction parallel to the plane of the horizon, provided that the line of collimation be itself parallel to the longitudinal axis of the spirit-level. This is examined and corrected as follows:

Let two staves be held upright at a distance of 400 or 500 feet from each other, and the instrument set up exactly midway between them. The line of collimation (whether it be correct or not, as appears from the figure,) will intersect the two staves on the same level; the difference of reading on the staves being noted, the instrument

is removed to a point near one of the staves, and if in this new position the difference of reading on the staves be the same as before, the line of collimation is correct; if not, the error is corrected by raising or depressing the diaphragm (as the case may be,) until the difference of reading

on the staves shall be, in this second position of the instrument, the same as it was in the first.

The application and mode of action of the parallel-plate screws needs no explanation.

LEVELLING STAVES.

The levelling staff simply consists of a rectangular rod or rods divided into feet and hundreds of a foot, by black lines appearing on a white ground. The hundredth part of a foot can be distinctly read at a distance of 400 or 500 feet with "Troughton's Improved" or "Gravatt's " Level. Two levelling staves are required with each instrument.

In certain operations of levelling, (as explained under that head,) it is required to determine the intersection of the horizontal axis of vision on the staff at very great distances. For this purpose, a sliding vane with a rhombus, marked by thick black lines on a white ground, is attached to the staff, on which it forms a conspicuous object. The angular points of the rhombus can be intersected with great precision by the horizontal wire, at a considerable distance. By means of signs, the staff-holder is directed to raise or lower the vane until the horizontal wire bisects the rhombus; and the reading, as shown by the index a, is noted

and registered by the assistant. When this index is placed, as in the figure (which is the usual construction), below the centre of the rhombus, the divisions, instead of commencing with zero at the bottom of the staff, are graduated at a distance above zero, equal to the distance from the index to the centre of the rhombus.

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CHAPTER III.

TRIGONOMETRICAL SURVEYING.

THE characteristic difference between a trigonometrical survey and a survey as described in the first chapter, consists in this:-that, whereas in the latter, the relative positions of the principal and secondary stations are ascertained by direct linear measurement; in the former they are ascertained by trigonometrical calculations based upon the direct linear measurement of a single line only, (called therefore a base line,) combined with the observation of angles as hereafter described. This trigonometrical operation is indispensable to obtain accuracy in the performance of any extensive survey. The first step con

sists in the measurement of the base line.

MEASUREMENT OF BASE LINE.

The measurement of a base line, from which the sides of the triangles of an extensive series are to be calculated, is a most difficult operation*, and one in which every refinement which mechanical ingenuity can devise has been of late adopted, with a view to obtain almost mathematical accuracy.

The length of the base is made to depend in general on the proposed length of the sides of the triangles which are to be deduced from it; but circumstances seldom allow it to exceed from seven to eight miles in extent, as its position has to be selected on an even plain, as nearly as possible horizontal, and otherwise conveniently adapted for purposes of measurement.

* SIR J. F. W. HERSCHEL'S Astronomy; Trigonometrical Survey of England and Wales; DELAMBRE, Base du Système Métrique.