divided into links. With Gunter's chain the staff, then, will be 6.6 feet, or 6 feet 7.2 inches long, while with the 100 feet chain it will be 10 feet in length.

THE SPIRIT LEVEL.

Certain parts of the principal instruments used in surveying, and in astronomical observations, require to be adjusted in truly horizontal positions; and, to arrive at this adjustment, one or more subsidiary instruments, called spirit levels, are attached to such principal instruments. The spirit level attached to a good telescope, furnished with a compass, and such means of correct adjustment as we shall presently describe, becomes also itself an important instrument, being used in that department of surveying termed levelling, which consists in measuring the vertical distances between various stations.

b

The spirit level consists of a glass tube, differing from the cylindrical form by having its diameter largest in the middle, and decreasing slightly and with great regularity from the middle to the ends. The tube is nearly but not quite filled with spirits of wine, thus leaving in it a bubble of air, b b, which rises to the highest part of the tube, so as to have its two ends equally distant from the middle, when the instrument is in adjustment, as represented in the annexed figure. The tube is generally fitted into another tube of metal, and attached to a frame terminating in angular bearings, by which the level can either be suspended. from, or else be supported on, cylindrical pivots. When, however, the level forms a permanent part of any instrument, the manner of attacning it is modified to suit the particular form of the instrument to which it is attached. A small and accurately-divided scale is attached to the best instruments, or otherwise a scale is scratched upon the glass tube itself, as represented in the figure given above.

The annexed figure

is a representation of such a level as is used for levelling the axis of the best astronomical instruments. It is provided with a fixed

scale, seen in the figure, and is suspended by means of accurately constructed angular bearings.

The following criteria of a good level are extracted from

Dr. Pearson's valuable work on Practical Astronomy, before referred to

"Firstly, the bubble must be long enough, compared with the whole tube to admit of quick displacement, and yet not too long to admit of its proper elongation by low temperature.

"Secondly, the curve must be such, that the sensibility and uniform run of the bubble will indicate quantities sufficiently minute, while those quantities correspond exactly to the changes of inclination, as read on the graduated limb of the instrument of which it forms a part.

"Thirdly, the bubble must keep its station when the angles are moved a little round the pivots of suspension.

"Fourthly, the opposite ends of the bubble must vary alike in all changes of temperature, or, in other words, the ends of the bubble must elongate or contract alike in opposite directions, so that the middle point may always be stationary.

"Fifthly, the angles of the metallic end-pieces must be so nicely adjusted that reversion on horizontal pivots that are equal will not alter the place of the bubble.

"Sixthly, the distance between the two zeros of a fixed scale, when such a graduated scale is used, should be equal to the length of the bubble at the temperature of 60° of Fahrenheit's scale, and should be marked at equal distances from the visible ends of the glass tube. Then, as the bubble lengthens by cold, or shortens by heat, its extreme ends may always be referred to these fixed marks, 00, on the scale, and will fall either within, upon, or beyond them, according to the existing temperature. The number of subdivisions of the scale that each end of the bubble is standing at, counted from the fixed zero marks, at the instant of finishing an observation, must always be noted, that an allowance may be made for the value of the deviation in seconds, or as the case may require.

"Seventhly, when the two ends of the bubble are not alike affected by a change of temperature, the scale should be detached, and adjustable to the new zero points, by an inversion of the level.

Eighthly, when the scale has only one zero at its center, which is a mode of dividing the least liable to misapprehension, the positions must be reversed at each observation, and both ends of the bubble read in each position; for in this case, if any change has taken place in the true position of this zero, the resulting error will merge in the reduction of the observation. This mode of graduating is generally practised on the continent."

We proceed now to the description of the most accurate instruments for measuring the differences of level, or vertical distances, between different stations.

Of spirit levels for this purpose there are now three in use, namely, the Y level, Troughton's improved level, and Gravatt's level.

THE Y LEVEL.

The following figure represents this instrument. A is an achromatic telescope, resting upon two supporters, which in shape resemble the letter Y, and are consequently called the Ys. The lower ends of these supporters are let perpendicu

F

larly into a strong bar, which carries a compass box c. This compass box is convenient for taking bearings, and has

a contrivance for throwing the needle off its center, when not in use. One of the Y supporters is fitted into a socket, and can be raised or lowered by the screw B. Beneath the compass box,

which is gene

rally in one piece

with the bar, is a

conical axis pass

WMR.QUICK.

ing through the upper of two parallel plates, and terminating in a

ball supported in a socket. Immediately above this upper parallel plate is a collar, which can be made to embrace the conical axis tightly by turning the clamping screw E, and a slow horizontal motion may then be given to the instrument by means of the tangent screw D. The two parallel plates are connected together by the ball and socket already mentioned, and are set firm by four milled-headed screws, which turn in sockets fixed to the lower plate, while their heads press against the under side of the upper plate, and thus serve the purpose of setting the instrument up truly level.

Beneath the lower parallel plate is a female screw, adapted to the staff-head, which is connected by brass joints with three mahogany legs, so constructed as, when shut together, to form one round staff, a very convenient form for portability, and, when opened out, to make a very firm stand, be the ground

ever so uneven.

The spirit level 77 is fixed to the telescope by a joint at one end, and a capstan-headed screw at the other, to raise or depress it for adjustment.

In looking through a telescope a considerable field of view is embraced; but the measurements indicated by any instru

ment, of which the telescope may form a part, will only have reference to one particular point in this field of view, which particular point is considered as the center of this field of view. We must therefore place, some fixed point in the field.. of view, and in the focus of the eye-piece, and the point to which the measurement will have reference will be that point of the object viewed, which appears to be coincident with this fixed point, or which, as the technical phrase is, is bisected by the fixed point.

The intersection of two fixed lines will furnish us with such a fixed point, and consequently two lines of spider's thread are fixed at right angles to each other in the focus of the eye-piece. They are attached by a little gum to a brass ring of smaller dimensions than the tube of the telescope, and which is fixed to the tube by four small screws, a, b, c, d. If the screw d be eased, while at the same time c is tightened, the ring will be moved to the right; but, if c be eased and d tightened, the ring. will be moved to the left; and in a like manner it may be moved up or down by means of the screws a and b.

When the instrument is in adjustment, the axis of the tube of the telescope is set truly horizontal by means of the level beneath it, and the line of observation ought consequently to be parallel to this axis. Let A represent the proper position of the intersection of the cross

wires, and o A, the direction of the axis of a pencil of light passing through the object

glass and coming to its focus at A. Then, the axis of the tube of the telescope being set truly horizontal, the line a o is also truly horizontal, and every point bisected by the intersection of the cross wires will be situated on the prolongation of the horizontal line A o.

Suppose now the position of the diaphragm carrying the cross wires to have become deranged. so that the point of intersection is moved to B, then every point bisected by the intersection of the cross wires will be on the prolongation of the line B Oo, and will consequently be below the true level point on the line a 0.

Let now the telescope be turned half round in the Ys, and

let the annexed figure represent it in its new position; then, in this new position of the telescope, the prolongation of the line в O will rise above the prolongation of the level

line Ao, and, at the same distance from the telescope, the point now bisected by the intersection of the cross wires will be as much above the true level point on the line A o as the point before bisected by them was below it. The true level point is therefore midway between the two points observed in the two positions of the telescope, and the diaphragm carrying the cross wires is to be moved by means of the screws a, b, c, d, till their point of intersection coincides with that true level point. The telescope is then to be again turned round upon the Ys, and, if the same point be still bisected by the intersection of the cross wires, they are in their proper position; but, if not, the same method of adjustment must be repeated till the same point is bisected by the intersection of the cross wires in every position of the telescope.

This error of derangement has a technical denomination. The line o A, or o B, from o to the point of intersection of the cross wires, is called the line of collimation, and the error arising from their derangement, which we have shown the method of detecting and correcting, is called the error of collimation.

When the image of the object viewed, formed by the objectglass, either falls short of, or beyond the place of the cross wires, the error arising from this cause is called parallax. The existence of parallax is determined by moving the eye about when looking through the telescope, observing whether the cross wires change their position, and are flittering and undefined.

To correct this error, first adjust the eye-piece, by means of the moveable eye-piece tube, till you can perceive the cross wire clearly defined, and sharply marked against any white object.

Then by moving the milled-headed screw A, at the side of the telescope, the internal tube a is thrust outwards or drawn inwards, until you obtain the proper focus, according to the distance of the object, and you are enabled at once to see clearly the object, and the intersection of the wires, clearly and sharply defined, before it. The existence of parallax is very inconvenient, and, where disregarded, has frequently been productive of serious error. It will not always be found sufficient to set