The leader then puts

chain in the direction of this mark. down one of his arrows, and proceeds a second chain's length towards the end of the line, while the follower comes up to the arrow first put down. A second arrow being now put down by the leader, the first is taken up by the follower, and the same operation is repeated till the leader has expended all his arrows. Ten chains, or 1000 links, have now been measured, and, this measurement having been noted in the field book, the follower returns the ten arrows to the leader, and the same operations are repeated. When the leader arrives at the end of the line, the number of arrows in the fol lower's hand shows the number of chains measured since the last exchange of arrows, noted in the field book, and the number of links extending from the last arrow to the mark, or staff, at the end of the line being also added, gives the entire measurement of the line. Thus, if the arrows have been exchanged 9 times, and if the follower have 4 arrows, and from the arrow last laid down to the end of the line measure 63 links, the whole measurement 9463 will be 9463 links.

9000

400

63

To assist in preserving the line straight, as well as to serve for a check upon the number of chains measured, it is a good method to set up a staff at each ten chains, when the arrows are exchanged.

In using the chain care must be taken to stretch it always with the same tension, and, as it will give when much used, it must occasionally be examined, and shortened if necessary

When the ground over which the measurement is taken rises or falls, or both alternately, the horizontal distances are what we require for plotting the survey, and not the actual distances measured along the line of the ground.

For many ordinary purposes the horizontal measurement may be obtained by holding one end of the chain up, so as to keep it, as nearly as can be judged, horizontal, the arrow being placed vertically under the end so held up; but, when a more accurate survey is required, the distances must be measured along the line of ground, and, the angles of elevation and depression of the several inclined parts of the line being afterwards taken with the theodolite, or the vertical risings and fallings being taken by the process of levelling with the spirit level and staves, the correct horizontal distances must thence be computed. The following table shows the number of links to be subtracted from every chain, or 100 links, for the angles there set down, being in fact the versed sines of those angles

to a radius of 100. The correction for each 100 links, for any angle whatever, may at once be taken from a table of natural versed sines, by considering the first two figures as integers. The correction may also be taken from a table of natural cosines, by subtracting each of the first four figures from 9, and reckoning the first two figures as integers, and the last two as decimals: thus, to find the correction for an inclination of 8° 19′, take the first four figures of the cosine of 8° 19′, which will be 9894, and, subtracting each of these four figures from 9, we obtain 0105: then, considering the first two figures of this result as integers, and the last two as decimals, we have 1.05 for the correction due to the inclination 8° 19′ for every 100 links. If the last figure in the correction thus found be increased by 1, whenever the fifth figure of the cosine is less than 5, the result will be more accurate.

TABLE showing the Reduction in Links and Decimals of a Link upon 100 Links for every half Degree of Inclination from 3° to 20° 30'.

The advantage of Gunter's chain is its adaptation to the superficial measure of land in acres, &c.; but, when a survey is to be made for the purpose of linear measurements only, or when it may be more convenient to compute the area in square feet, a chain 100 feet long, divided into links of a foot long, is to be preferred. Such a chain is best adapted to military surveying.

Offsets, perpendicular to the main line, to hedges and remarkable objects on either side of it, are measured from the chain as it lies stretched upon the ground, by means of an offsetting staff. This staff should be 10 links in length, and

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 capital 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 a capital instrument, being used in that department of surveying, termed levelling, which consists in measuring the vertical distances between various stations.

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 stood upon, cylindrical pivots. When, however, the level forms a permanent part of any instrument, the manner of attaching 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 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

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 raise or lowered by the screw B.

Beneath the compass box, which is generally in one piece with the bar, is a conical axis passing 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 mo tion 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 7 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