generally found to be more open and level, and therefore better adapted to sketching, as is here shown.

In either example, where wood or plantation interferes, then the use of the instrument is necessary, and even then it is difficult to obtain a clear sight for any distance without cutting a way purposely. For small surveys like these the box-sextant will be found the most convenient.

From the clearness of the field-book, there can be no difficulty in plotting both the examples to a larger scale.

Problem 13.

To continue a base line when obstructed by a piece of water, building, &c., Fig. 2, Plate 14.

This is one of the greatest calamities that can happen in chaining the principal line of a large survey. From the undulation of ground it is impossible for the surveyor in every instance to avoid such unexpected interruptions, although previously prepared for crossing a river, as shown in the next example.

It must be borne in mind that a base line is of such importance to a survey that it must not be abandoned; beyond this obstacle referred to, which is supposed to lay in a valley, the line has been accurately poled out to the extent on the opposite rising ground, therefore the intervening space has to be obtained to make the length complete.

On the base line, A B, raise two perpendiculars, either by the box-sextant or by the chain, as a b and c d; extend these lines to b and d equal to 400 links, then measure the distance from b to d, equal to 450 links, add this sum to the length of the main line up to a, say 1000, then will the line to c be equal to 1450 links; entering it into the field-book precisely as it occurred, then proceed with the chaining as before.

If the water should extend to the right, set out lines according to the nature of the figure, and sketch them in the fieldbook; this may be surveyed before proceeding on with the

main line.

H

Problem 14.

To erect a perpendicular by the chain, Fig. 2, Plate 14.

Set off on the main line A B 40 links from B to a; fix one end of the chain firmly at B, and take the chain at 80 links, hold that firm at a, then take the chain at 50 links, pulling it tight both ways until they are quite straight, and put down a peg at e, which will be the point of the perpendicular; so that Ba is 40, a e 30, and Be 50 links.

Another method :

At 40 links from a fix one end of the chain by the offset staff at B; let the assistant hold the chain at 80 links at a ; then take the middle of the chain 50 links, stretch the chain firmly on the ground, and a mark or peg put in at e will be the perpendicular to B a.

THEODOLITE SURVEYING.

Problem 15.

To continue a base line over an inaccessible river, Fig. 3, Plate 14.

When the base line crosses nearly at right angles.

From c measure back 400 links to a, and fix flags at both points; raise a perpendicular at c, and set off 300 links at d and fix a flag; at a raise another perpendicular and set off 600 links at b, and fix a flag; now measure from a to d, which should be exactly 500 links, otherwise it must be corrected; then from d to b 500 links; this point also must be minutely correct, as the distance across the river depends entirely on the accuracy of the points d b. These points being truly settled, send the assistant over the river to fix a flag at e correctly in a line with the flags at c a and the flags at db; then the distance across the river from e to c will be equal from c to a.

Another method, Fig. 4:

When the base line crosses the river obliquely.

First set out the line D BE as part of the survey to take up

the river; at any part of the line as E, with the box-sextant set at 90 degrees, having a flag previously fixed at C in a direct line with AB; keep moving on the line E B till you have brought the two flags together on the mirror, which will be the point perpendicular to E B; measure the distance from E to B equal to 400 links; measure the same distance from B to D; at D raise a perpendicular as before; directing the assistant to move till he is at the point of intersection at A, measure the distance from A to B equal to 475 links, which will be the distance across the river from B to C.

SURVEYING HILLY GROUND.

Chaining over hilly ground is not attended to by surveyors in general with that caution the subject deserves.

There are few countries where an extensive survey has to be made without a portion of hill and vale. A moderate gentle slope is by no means objectionable, as it enables the surveyor to have a better view of the country and to lay out the principal lines, in setting out which endeavour to command the sidelong ground for the chief lines, the hypothenusal angle will then be much reduced.

It must be remembered that when a survey is plotted it represents a perfect plane, and in chaining the lines they should be so conducted that every length should be a point exactly equal to the base of a right angled triangle.

For instance, by way of exemplifying the subject, suppose a flight of 20 steps, each step in width 1 foot, equal to 20 feet on the level, and the whole height 12 feet, the length of the ascent or hypothenusal line will be 23 feet 4 inches nearly in that short length (the difference is considerable, for as the angle of acclivity or declivity increases, so also will the difference increase); consequently, if a proper allowance in the length of the line measured up an incline is not made it is utterly impossible to plot a survey correctly.

It is the practice of many surveyors in chaining hilly ground

to hold up one-half the chain and drop a stone or one of the arrows to the ground, intending to make that a perpendicular point; it is perfectly ridiculous and imperfect.

The only true method is first to ascertain the angle, and make the allowance when plotting the survey, or by making the allowance on each chain at the time of measuring the line.

When surveying in a hilly country the surveyor should be provided with the table for reducing the hypothenuse (see Table, No. 12); take the angle by the box-sextant, or by a very simple and portable instrument for that purpose invented by the author. (See Quadrant, Fig. 1, Plate 38.)

The chief argument on hilly ground is the difference between the base and hypothenuse. (See Problem 19.)

In taking the angle of inclination or declination, be careful the forward object is equal exactly to the height of the eye when taking the sight, so that the imaginary line be parallel to the surface.

When an angle is measured by the theodolite, the allowance to each chain is engraved on the vertical arc according to the angle.

As a further elucidation on the subject of hilly ground, a pale fence or growing timber on the acclivity of a hill will not occupy more space than it will on level ground; but the rails to which they are fixed, having the same slope as the hill, must therefore be longer in proportion to its angle.

So also might be said in planting trees. This approaches very near to the first argument, that of the steps; the root of each tree must have a sufficient base for the nourishment of its root, having a certain width round it like so many steps; consequently there could not be more trees, and in some cases, according to the nature of the ground, there may be less than on the level ground.

It is rather questionable whether there be more corn or grass; at all events, it is well known the quality will be in

ferior.

The subject of quantity is already decided, as it is estimated from a perfect plane.

The only thing that can be reasonably admitted is the work of the labourer, consisting wholly of superficial and lineal measure, as mowing, reaping, hedging, ditching, &c.

When a hill approaches a semi-globular form it can only be an approximation, and the method of obtaining the difference is by fixing a number of poles round the hill, and observing the angles from the top; in practice the surveyor should avoid these difficulties as much as possible.

Those who are desirous of entering more minutely into the subject are referred to the calculations made by Dr. Hutton, and Dr. Maskelyne's observations in Scotland in the years 1775 and 1778. (See the Philosophical Transactions.)

TO SURVEY AN ESTATE OR PARISH BY THE CHAIN ONLY.

Problem 16.

Plates 15, 16. The chief point now is to draw the attention of the student to former observations on a more extensive survey; and he is strongly recommended to plot the whole of this survey from the field-book, to a scale of 3 chains to the inch, and compute the same by the several examples previously shown.

By this practice the knowledge gained will more than compensate for the trouble; merely reading over the field-book and referring to the plan will not impress the subject so firmly on the mind.

Agreeable to the instructions given in the General Observations, and referring to the plan, the lines 1 2 and (3 constitute the largest triangle. In poling out line 1 a tree on an eminence in the distance assists greatly; in like manner, at the same station, the steeple in the distance was another excellent object; in poling out line (12) these two lines will at once show the importance of their position in relation to the