Rule. Multiply the height of the segment by the whole circumference of the sphere, the product is the curve surface. To find the solidity, add the square of the height to three times the square of the radius of the base; multiply that sum by the height and by .5236, the product will be the solid content.

The diameter A B of the sphere A B C D=35.813 inches; what is the convex surface of that segment whose height E D = 13 inches.

3.1416 × 35.813 = 112.5101 × 13 1462.63 square inches144 = 10.1572

superficial feet nearly

The base F G of the segment F D G = 34.5 inches, and perpendicular E D 13 inches, what is the solid content?

=

34.52 17.252 × 3 = 892.6875 + 132 = 1061.6874 × 13 = 13801.937 × .5236 = 7226.69421728 = 4.182 cubic feet

Problem 109.

Required the number of ale gallons the segment A B C D contains; the base A B = 34.5 inches, and perpendicular height CD=13 inches, Fig. 12, Plate 5.

17.25 x 3 = 892.689 × 132 = 1061.689 × 13 = 13801.967 x .5236 = 7226.71÷ 282 25.63 gallons

75

PART II.

ON LAND SURVEYING.

GENERAL OBSERVATIONS.

PREVIOUS to the commencement of a survey, it is requisite to have a knowledge of the country, either by observation, taken on some eminence, or from a well authenticated map; from which may be determined the most suitable position to fix the principal or base lines, so as to avoid obstructions that may prevent a continuation in measuring these lines to the extent desired or intended, also to select the most favourable and level part of the country for chaining. Sometimes it is advantageous to run these lines through or into part of the adjoining property, by which a better diagram is formed and many difficulties surmounted; as all these lines forming the diagram are the basis of succeeding operations, see Plate 14.

Having determined the position of the base lines, and observed particular objects that may be seen from different parts of the survey, proceed to pole or range out these lines very carefully in straight lines, which in many instances is a work of difficulty and labour, and of the greatest importance to the whole survey.

Provide a number of straight deal rods about ten or twelve feet long, spiked at the bottom, and white and red flags at the

top, by which they are easily distinguished at a distance and over the fences, which are frequently an obstruction, and require to be cut away to give a clear sight; this should always be done cautiously, so as not to injure the fence or make gaps.

It frequently happens that a prominent elevated object presents itself in the distance as a favourable point to direct a line, and poling become unnecessary. Flags or marks must be left at all the intended stations, and fixed with great care in the direct line. Provided the distant object can only be seen at intervals, then the head surveyor should remain at the commencement, or any determined point on the line, to direct the assistants, who have proceeded forward, in fixing the flags; when several of these flags are truly fixed, the assistants may then continue poling out the line without signals, and the process of chaining commenced, the surveyor at the same time observing the flags are correct with the distant object, and that they are truly perpendicular, as it is the foot of the poles that forms the lines.

During the operation of chaining the surveyor will have an opportunity of observing the most favourable points to construct other lines intersecting those in operation.

It is impossible to make a correct survey if any one of the principal lines are in the least crooked; the same applies also to the plotting, as the lines drawn on the plan represent the chain lines; if they are drawn the least curved, it has the same effect in disturbing the accuracy of the whole.

To impress on the mind how important it is that the lines in chaining, and the lines in plotting, should be perfectly straight, and a proper allowance made for the undulation of the ground, it is recommended to plot all the principal lines from a wellknown accurate survey, and make only one of these lines a little curved, it will at once show the consequences that will occur to all the rest of the survey, therefore it requires as much attention in examining the straightness of the rule, and the correctness of the scale, as it does in poling the lines straight and the adjustment of the chain.

When the ground is hilly or thickly timbered, and no distant object visible, the best method of proceeding then is to plant the theodolite on rising ground about midway, so that, if possible, both ends of the line may be seen. Adjust the instrument perfectly level, and clamp the lower limb, loosen the clips that fix the telescope in the Y's, the upper limb being free, direct the telescope to the first station and clamp the upper limb; then reverse the telescope on the Y's; if the vertical wire in the telescope cuts the point required, let the instrument remain in that position until the whole line has been poled out, which is done by looking through the telescope and directing the assistants on both sides by signals as before.

The flag-poles, being few in number, should be fixed as far apart as may be clearly seen, and the intervening spaces filled up with straight sticks about a yard high, having a slit at top in which is fixed a piece of white paper; these will be found more generally useful for intervening stations, &c., the flagpoles being intended more for distant objects and particular stations.

Having shown the importance of straight lines, the next matter for consideration will be the form of the diagram or basis to the whole survey; this must be guided chiefly by the contour of the estate to be surveyed, and the nature of the ground as regards hills, woods, and water.

The two first principal lines should, if possible, intersect each other nearly in the middle at an angle as near 45 degrees as possible; these lines, also, should be the longest or bases of the two largest triangles; and when the connecting lines are added, the whole diagram will then consist of four large triangles. (See Plate 14.)

If the estate should be of a triangular form, the three prin

cipal lines may then be correctly proved, by having a line joining the two opposite sides, as Fig. 1, Plate 10.

When all the base lines of a survey are measured or chained they should be plotted before proceeding any further. First,

top, by which they are easily distinguished at a distance and over the fences, which are frequently an obstruction, and require to be cut away to give a clear sight; this should always be done cautiously, so as not to injure the fence or make gaps.

It frequently happens that a prominent elevated object presents itself in the distance as a favourable point to direct a line, and poling become unnecessary. Flags or marks must be left at all the intended stations, and fixed with great care in the direct line. Provided the distant object can only be seen at intervals, then the head surveyor should remain at the commencement, or any determined point on the line, to direct the assistants, who have proceeded forward, in fixing the flags; when several of these flags are truly fixed, the assistants may then continue. poling out the line without signals, and the process of chaining commenced, the surveyor at the same time observing the flags are correct with the distant object, and that they are truly perpendicular, as it is the foot of the poles that forms the lines.

During the operation of chaining the surveyor will have an opportunity of observing the most favourable points to construct other lines intersecting those in operation.

It is impossible to make a correct survey if any one of the principal lines are in the least crooked; the same applies also to the plotting, as the lines drawn on the plan represent the chain lines; if they are drawn the least curved, it has the same effect in disturbing the accuracy of the whole.

To impress on the mind how important it is that the lines in chaining, and the lines in plotting, should be perfectly straight, and a proper allowance made for the undulation of the ground, it is recommended to plot all the principal lines from a wellknown accurate survey, and make only one of these lines a little curved, it will at once show the consequences that will occur to all the rest of the survey, therefore it requires as much attention in examining the straightness of the rule, and the correctness of the scale, as it does in poling the lines straight and the adjustment of the chain.