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upon the level line the exact distance from the second stake b, to the third c; then let fall a perpendicular from c, and set off thereon 6: 8:0 pointed out by the cross hairs on the staff, which determines the depth of the hollow, as may be seen by the section.

With respect to the ground between each stake, as the distances are now very short, it will be easily expressed by the operator, whose judgment will settle the small inequalities by a comparison with those already ascertained.

Proceed thus with the other stations, until you arrive at the last, and you will obtain an accurate section in detail of your work; by such a section, it is easy to form a just estimation of the land to be dug away, in order to form the canal, by adding thereto the depth to be given to the canal.

Another example of compound levelling. In the levelling exhibited in plate 25, we have an example taken where the situation was so steep and mountainous, that it was impossible to place the staves at equal distances from the instrument, or ever. to make a reciprocal levelling from one station to another.

Such is the case between the first point A, taken from the surface of a piece of water, which falls from the mountains, and the last point K, at the bottom of a bason, where it is proposed to make a fountain, and the height is required, at which a jet d'eau will play by conducting the water from the reservoir A, to the point K, of the bason, by tubes or pipes properly made, and disposed with all the usual precaution.

From the manner in which the operator must proceed in this instance, it is evident, that the instrument should be adjusted with more than ordinary. care, as the true distance from one mountain to the other cannot be attained without much trouble.

The height is here so great, that it will be neces

sary to go by small ascents from A to D, and it will probably be commodious in some part of this work to use a smaller instrument; underneath is a table of the different level points as ascertained, which, with the profile and plan, render this part of the work sufficiently clear, without further explica

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Only two levellings are made here between A and D, though it is evident from the plan, that more would have been necessary; but as our design is only to shew the manner of proceeding in this particular case, and as more would have confused the plan and section, they are here neglected.

In the fourth, the height found was 16. 8; but as the distance E, 350 yards, was considerable, it was necessary to reduce the apparent level to the true one; the same was also done in all other cases where it was necessary; at the last limit we first get the height from no, then from o to I, then from I K, which added together, and then corrected for the curvature, gives 47. 3. 0. Now, by adding each column together, and then subtracting one from the other, we obtain 51 feet nine inches for the height, which the point A is above the bottom of the bason,

and which will cause the jet d'eau to rise about 45 feet.

The general section of this operation is delineated under the plan at fig. 2. and is sufficiently plain from what has been already said in the preceding instances. But an exact profile of the mountain is not so easy, as it would require many operations, as may be seen in the section; some of these might however be obtained, by measuring from the level line already mentioned, without moving the instrument, as at fig. 3.

Example 3, fig. 1, plate 26. Mr. Le Febere gives us in that of a river, being one part of the river Haynor, from Lignebruk to Villebourg, and the mode he observed in taking this level.

The first operation was that of having stakes driven at several parts of the river, even with the water's edge; the first stake A, a little above the mills at Lignebruk, shews the upper water mark when the water is highest, and is our first limit; the stake b, shews the low water mark at the same mills, the stake B, is the second limit.

The stakes C, and D, above and below the mills of Mazurance, shew the height of the waters when at the highest and lowest, and their difference; these stakes form our third and fourth limits. Lastly, the stakes at E and F, above and below the mills at Villebourg, mark as before the difference between the highest and lowest stations of the water, and are also the last limits of the operation.

Particular care was taken, that the marks should all be made exactly even with the edge of the water, and they were all made at their different parts of the river, as nearly as possible at the same instant of time.

The principal limits of the levelling being now determined and fixed, it only remains to find the level between the limits, according to the methods already pointed out, using every advantage that may

contribute to the success of the work, and at the same time avoiding all obstacles and difficulties that might retard, or injure the operations.

The first rule is always to take the shortest possible way from one limit to the other.

However, this rule must not be followed if there are considerable obstacles in the way, as hills, woods, marshy ground, &c. or, if by going aside, any advantage can be obtained; thus, in the present instance, it was found most convenient to go from A 2, to B, by the dotted line Acdefehik B, which, although it appears the longest, was in effect the shortest, as you have only to level from one pond to the other, at Ac, de, fe, hi, k B, (at the top of the plate,) the distances cd, ef, g h, ik, the surfaces, of the several ponds being assumed as level lines, thereby abridging the work without rendering it less exact; more so, as it was not the length of the river that was required, but only the declivity.

Having levelled from A to B, proceed from B to C, following the dotted line B1 m no C, whence we obtain the difference in height between the surface of the water at A, and that at C.

The next step was to level between C and D, above and below the mills, to find the difference between the water when at its highest and lowest situations. From D, levels were taken across the country to P, leaving P on account of the pond or lake which was assumed as level, we began at q, from thence to r, where we left off; beginning again at s, then levelling from thence to t, and so on to E, above the mills at Villebourg, and finished at F, below them.

By these operations we obtained the knowledge of how much the waters above and below the mills of Lignebruk are higher than those of Manzurance, and these, than those of Villebourg, with all the necessary consequences. From this example, the importance of a thorough knowledge of the ground

in order to carry on such a work is evident; very this piece of levelling was near five German miles in length, in a straight line, and nine or ten with the bendings of the river. For the profile or section of the foregoing operation, fig. 2, plate 26, first draw the dotted line A G, on which let fall perpen diculars from the principal limits, ABCE, produced; then beginning at the highest water mark at Lignebruk, set off three feet to six, for the difference between high and low water; from b draw the dotted line b c, parallel to A G. From the point set off on the perpendicular four feet to B, the difference found between band B; from B draw B d, parallel also to AG; then set off three feet from d to C downwards, for the difference found between B and C, and 4+ feet from C to D, for the difference in height of the mills at Mazurance. From D draw the line De parallel to AG, and from the point e to E, set off three feet for the difference of the level between D and E. And lastly, from E to F, set off one foot six inches for the difference between the higher and lower waters at the mills of Villebourg, shewing that there are 19 feet difference which the upper waters at Lignebruk are higher than the lower waters of Villebourg.

The pocket measuring tape of 100 feet in length, with the centesimals of a yard, is found to be an useful article in the practice of levelling.

ASTRONOMICAL OBSERVATIONS AT LAND, WITH
HADLEY'S OCTANT AND SEXTANT.

The portability of the sextant, its cheapness compared with other instruments, the ease with which it is used, the accuracy of the observations made with it, strongly recommend it to the attention of surveyors, &c. the only addition necessary to employ it advantageously in astronomical observations at land, is an artificial or reflecting horizon.

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