Ex. 2. Required the folidity of a parabolic fpindle, whose length is 40, and middle diameter 10. Anf. 1675.52. Ex. 3. Required the folidity of a parabolic fpindle, whofe length is 100, and middle diameter 10.

PROBLEM XXVII.

Anf. 16755.2.

To find the folidity of the middle fruftum of a parabolic spindle.

RULE.

Add into one fum 8 times the fquare of the greatest diameter, 3 times the square of the leaft diameter, and 4 times the product of the two diameters; multiply the fum by the length of the fruftum, and the product again by .05236 for the folidity.

EXAMPLE I.

Required the folidity of the middle fruftum of a parabolic spindle, the length being 20, the greatest diameter 16, and the

least 12.

162=256×8=2048
12'=144X3= 432

16X 12 =192X4= 768

3248

20

64960

.05236

389760

194880

129920

324800

3401.3056c Ans.

Ex. 2. Required the folidity of the fruftum of a parabolic spindle, whofe length is 10, the diameters being 8 and 6. Anf. 425.1632. Ex. 3. Required the folidity of the middle fruftum of a parabolic fpindle, whose length is 30 feet, and diameter 16 and Anf. 8243-5584.

20.

SURVEYING,

SURVEYING of Land is confidered to have been the primitive

part of Geometry, and confifts of three principal parts, viz, The taking of the dimenfions, and making the neceffary obfervations on the ground;-the laying down the fame in a map or drawing on paper or vellum ;--and the finding the content or area thereof.

The inftruments commonly used in furveying of land, are, the gunter's chain, a case of instruments, a set of plotting scales, the theodolite, and plain table.

The gunter's chain, whether Scots or English, is divided into 100 links. The English chain is 66 feet, and the Scots 74; confequently a link of the English chain is 7.92 inches, and that of the Scots 8.88 inches: likewife the English chain is divided into 4 poles or perches, each 16 feet, and the Scots chain into 4 falls, each 184 feet. 10 fquare chains are 1 acre, either Scots or English; and 4 Scots acres are nearly equal to 5 English miles.

A

The Scots elwand is the foundation of all land-furveying in Scotland, the length of which is 37 inches, when compared with the English yard. It was first established by King David I.; the standard of which is kept in the Council Chamber of Edinburgh.

Writers on this fubject are generally very prolix in defcribing the method in which furveyors take dimenfions, use their inftruments, &c. But it must be confeffed, that the practice of a few hours in the field is preferable to all the description that can be given. We shall therefore be very brief as to this particular, and shall only point out a method or two by which an irregular field may be measured, its plan delineated on paper, and its contents found.

Let the figure ABCDEF Fig. 1. represent a field, whose plan and area is required.

First, walk over the field, and make the neceffary remarks on the ground, and draw an eye-draught, or a representation of the field, as exact as can be done by the fight of the eye.

Divide this draught into triangles, rectangles, or trapezias, as the figure of the field directs. Erect poles at the different

corners.

Choose any of the corners A for your firft ftation; provide yourself with a perfon to lead the chain, and let him have to arrows or iron pins in one hand, and the end of the chain in the other. You take your station at A, while he advances the length of the chain towards B. Direct him, by waving your hand, to the right or left, till you find him in so straight a line as to intercept the view of the pole B: Then ftretch the chain at full length, and let him leave one of the arrows at the far end, as a mark for you to go to. In the mean time let him advance another chain-length towards B, directed to keep in a ftraight line as above. At the end of the fecond chain-length let him stick another arrow, and you take up the first and proceed to the next, where you are to ftand till the chain is again ftretched in the direction AB, and he put down another as a mark; which done, you take up the fecond, and proceed to the third; and so on, till you come to B. The number of arrows taken up by you is the number of chain-lengths; and the dif

tance