difference presents itself, it may be further examined by taking fresh levels from the nearest bench mark; sometimes an error may be confined, but very rarely, as if once an error occurs it is generally carried through and affects the whole section; this shows the importance of check levelling.

If the same person checks his former levels, it is better to commence where he finished. Any number of persons may also be engaged at the same time, by giving to each a certain portion between two bench marks.

In passing over streams both banks should be taken, and, where possible, the middle of the stream; the same observation also applies to roads, as frequently they are considerably above or below the adjoining ground.

In levelling through a town it is necessary to mark out distinctly the point where the line crosses from a fixed point; the lengths also will be obtained in like manner. This part is tedious, as the levels would have to be continued round from one street to another, making only an addition of heights in the book which are not required in the plotting for the section.

In the same manner, where the levels are obstructed by bogs or any other impediment, the levels must be continued until an opportunity arrives to get into the line marked out.

It is to be remembered that it is not absolutely necessary to plant the instrument on the direct line; it should be placed in the best position that can be chosen to take advantage of the lowest point of one staff and the highest of the other, that is where the ground is suddenly undulating.

When the instrument in the first instance is carefully adjusted it requires but little alteration during the day, particularly the eye-piece, but the object-glass may occasionally require to be moved by the milled screw as the distances vary; there should be only the parallel plate-screws to adjust on each move of the instrument.

A great deal of labour is saved, and time gained, in having a good staff-holder, who may be very soon drilled to hold the staff perpendicular, and to understand the motions when to move.

When commencing a course of levels, if there be no datum height given, always assume one, say 100 feet, more if the country is very hilly, so as to avoid having any of the levels below datum; when that is the case it is subject to errors in casting or reducing the levels; if any particular datum line is afterwards required it can be easily adjusted.

The datum line is the horizontal line upon which all the lengths are pointed off, and from which the heights are marked off perpendicular to it.

When the line is staked out for constructing, stakes are driven into the ground nearly close to the surface at every chain's length, and the heights taken off each stake; where a change takes place for the curves, two or three stumps are then driven to note the tangent point corresponding with the working plan and section.

The horizontal scale, or the scale to the datum line, is always the same as the plan, 3, 4, or 5 chains to the inch, according to circumstances; and the vertical scale, that is the scale used for marking the heights from the datum line to the ground surface, also varies from 20 to 100 feet to the inch. A section is never plotted with the heights to the same scale as the horizontal line; sometimes the same scale is used by taking the horizontal at 3 chains to the inch, and the vertical scale at 30 feet to the inch. Therefore when a section is drawn it does not present the natural surface of the ground, but a deformed figure, otherwise it would not be possible to calculate the cuttings and embankments, and other engineering matters.

The leveller should have nothing to do beyond attending to his levels and the staves; a tracing of the ground to be levelled, having the line carefully drawn on it, is given to the assistants deputed to measure the lengths, and report to him from time to time as required, and to mark out the line by putting up marks at the fences as the work proceeds.

Having endeavoured to explain the several matters requiring attention in taking the longitudinal levels, it will be necessary to make a few remarks on cross or transverse levels.

These levels are chiefly, as before noticed, principally roads, both public and private, as well as where the ground is very side-laying; they are generally taken about 5 chains each side the line; on tolerably level ground they can be taken at the same time the other levels are being taken, and entered into the book the same way as the intermediates are, noting in the remarks the distance from the line on each side they are taken; but when it is hilly it will be necessary to take them distinctly, beginning from the bench mark as before noted, and taking a height in the middle of the road where the line crosses. When there are many cross sections required, it is better to take them separately. The scales used for plotting cross sections are usually larger than those for the general section. (See Plate 30.)

LEVEL BOOK.

The greatest attention is required in keeping the level book; the more simple it is constructed, the less liability will there be in making errors. There are a variety of forms, some complicated with numerous unnecessary columns.

The two forms here introduced, No. 1 and No. 2, are selected for conciseness and legibility, and most generally used in practice.

Problem 6.

Fig. 2, Plate 29. This example is purposely introduced to show the difficulties and liability to errors in casting out the levels arising from the datum line A C, crossing the section at D and E, thereby changing the regular system of adding and subtracting the back and fore sights, and in reducing those heights, whereby it becomes necessary to mark the changes by the algebraic symbols of plus and minus.

The surface line is shown by the line A D E B.

The strong black vertical lines denote the points where the level staves are held, which are figured with feet, tenths, and hundredths.

The spirit level is shown between them, and the dotted line represents the line of vision as taken by the telescope when the

instrument has been perfectly adjusted, and is parallel to the datum line.

This example should be carefully studied, and compared with the following example, Fig. 3, Plate 29.

When taking levels in the field, all that is entered into the book are the back, intermediate, and fore sights, with the distances at each point, where a height is taken and the remarks required.

The levels that have been taken during the day should always be cast up and proved every night before proceeding further with the levels.

The level may be taken as an intermediate, by measuring the height to the centre of the eye-glass, as is shown in this example, and noted in the book.

In all cases, when the height in the column of back sights exceeds the heights in the fore sights' column, the latter is subtracted from the former, and the difference entered in the column marked RISE, as at 7.00 marked A a on the section and 1.55 at b, leaves 5.45 rise.

And when the back sight is less than the fore sight, it is subtracted and carried to the fall column, as 0.80 at b and 9.20 at d, leaves 8.40 fall.

This is the general rule on every principle of keeping the book. When all the heights of the back and fore sights are reduced and carried to their respective columns, then proceed to reduce them to the column called reduced levels.

The first reduced level (see Level Book, No. 1) is 5.45 plus, or above datum; the next number is 8.40 difference in the fall column, which is greater than the last reduced number 5.45, and shows at once it is below datum; consequently the order is changed, and instead of adding to 5.45, that number must be taken from 8.40, carrying the difference 2.95 to the reduced column as minus or below datum.

Now proceed to the next move of the instrument. The back sight is. 1.65 as at d, and the fore sight 1.00 as at e, both of which are below datum, the difference being 0.65 rise; this

number is subtracted from the last reduced 2.95, bringing the reduced level to 2.30.

At this last point it must be remarked that, when the datum crosses the section, the heights in the rise column are subtracted and the fore column added, being quite the reverse when the datum line continues below. It is at these points of crossing where the great liability of error exists.

The instrument being again removed, the back sight is 12.00 at e, and the fore sight at ƒ 1.85; now the line crosses again at E, between the back sight and the intermediates, the last reduced level is subtracted from 10.15 and carried to the reduced column 7.85, plus or above datum, and the preceding intermediates in the same manner, all being plus or above datum.

The next change of the instrument alters the calculation; the height in the rise column 3.40 is now added to the last reduced number 7.85; the total height B C = 11.25 above the point of commencement at A.

When all the back and fore sights are reduced, then, before reducing the intermediates, prove the whole by casting up the back and fore sights, and subtract the one from the other, as shown by the book; if the remainder is the same as at the last reduced number 11.25, the levels are correct.

The same proof can be made by casting up the columns of rise and fall.

Then proceed in like manner with the intermediates, observing the changes in crossing the datum line.

This example shows distinctly the trouble and difficulties that arise through not providing a number to prevent the datum line running through the section.

Problem 7.

Fig. 3, Plate 29. In the last example is shown how to reduce the levels when the datum crosses the section.

In this example the same dimensions are adopted, and an assumed number given to avoid the difficulties before described, producing the same section.