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Fig. fcrew it faft, and turn the Index about, till through the Sights, XVII. you fee the Angle at F, and there note what Degrees of the In
ftrument were cut by the Index, which we will fuppofe to be 300 Deg. for the Quantity of the Exterior Angle FA B, without the Field: Or, 60 Deg. for the Quantity of the Interior Angle within the Field: Then measure the Side A F, which fuppofe to be 41.00 Pole or Perches, and the Side A B 30.00 Perches. Thefe Distances, with the Quantity of the Angle before obferved 300, or 60 Deg. fet down in a Book or Paper, as you fee in the following Table.!...
bc2. Remove your Inftrument to B, and laying the Index upon the Diameter, turn the Inftrument abouf, till through the Sights you fee the Place where the Inftrument laft ftood at A, and there fcrew it faft; and turn the Index about, 'till, through the Sights, you -fee the Angle C, and note the Degrees which the Index cutteth; which are here 145 Deg. for the Exterior, or 215 Deg. for the Interior Angle ABC, and the Distance BC measured is 28.40 Perches: Both which, note down as before.
3. Remove your Inftrument to C, and placing the Index on the Diameter, look back to B, and there screw it fift, and turn the Index about, till you fee the Angle at D, where the Index cutteth 270.25 Deg. for the Exterior, or 89.75 Deg. for the Interior Angle BCD, and the measured Diftance CD is 23.40 Deg.
4. Remove the Inftrument to D, the Index on the Diameter, and look back to C, and then fcrew it faft; then turn the Index about till by the Sights you fee the Angle at E, the Index cutting 263 Deg. for the Exterior, or 97 Deg. for the Interior Angle Č DÉ, the Measured Distance DE being 28.00 Perches: Which note down as the other.
5. Place your Inftrument at E, the Index on the Diameter, look back to D, and then fcrew it faft, and turn the Index about till through the Sights you fee the Angle at F, the Index there cutting 220 Deg. for the Exterior, or 140 Deg. for the Interior Angle DEF; the Meafured Distance E F being 42.80 Perches.
6. Place the Inftrument at F, and the Index lying on the Dia meter, look back to E, and then fcrew it; and turn the Index a bout, till through the Sights you fee the Angle at A, (or the Place where you first placed your Inftrument) where the Index cuts 2 10 Deg. for the Exterior, or 150 Deg. for the Interior Angle EFA, the Meafured Distance F Á being 41.00 Perches, as before. All which being noted down according to thefe Obfervations, and Meafured, will ftand as in this Table..
A to B 30.co
C to D-23.40
D to E-28.00
E to F-42.80
F to A-41.00
The Angle at D 263.00
Thefe Obfervations of Sides and Angles, as they were taken in the Field, being noted down in a Book or Paper, as in this Table; a Plot of the Field may be drawn upon Paper or Parchment, by the following Directions.
To Protract the former Work.
1. Upon a Sheet of Paper or Parchment draw a Line A B, to contain 30.00 Perches, of any Scale: And upon the end thereof A, place the Centre of a Protracter, laying the Diameter of it upon the Line A B: Then, the Exterior Angle at A, being 300.00 Deg. make a Mark against 300.00 Deg. of your Protra tor; and through that Point, and the Point A, draw a Right Line, downwards, as A F, to contain 41.00 Perches, of the fame Scale.
2. Apply the Centre of the Protractor to the Point B, and the Diameter upon the Line A B; then against 145.00 Deg. (the Angle at B) make the Mark, and through that Mark, and B, draw a Right Line B C, to contain 28.40 Perches.
3. Lay the Centre of the Protractor upon C, and the Diameter upon B ̊C, and against 270.25 Deg, make a Mark; through which, and the Point C, draw the Line CD, to contain 23.40 Perches.
4. Apply the Centre of the Protractor to the Point D, and its Diameter to the Line CD; making a Mark againft 263.00 Deg. through which, and the Point D, draw the Line DE, to contain 28.00 Perches.
5. Lay the Center of the Protractor upon the Point E, and its Diameter upon DE, and against 220.00 Deg. make a Mark through which, and the Point E, draw a Right Line; which (if you have committed no former Error) will cut the Line, first drawn, in the Point F: And, by this Means, you will have upon your Paper, the exact Figure of your Piece of Ground: Which you may caft up, and find the Quantity thereof in Perches, (by the Directions of the Third Chapter hereof) which being divided by 160, will give the Content in Acres and odd Perches.
Fig. In this Example, we have wrought by the Exterior, (or Outward) XVII. Angles: But if you would Protract the fame by the Interior (or Inward) Angles; it is done, by fubftracting the Exterior Angle from 360 Deg. and the Remainder will be the Interior Angle: So, the Angle at A, being 300 Deg. that fubftracted from 360 Deg. leaves 60 Deg. for the Interior Angle at A And fo of all the reft, as they are fet down in the Table.
CHA P. V.
Menfuration of Solids.
I. Of the Cube ABCDEF, thofe Side is 5.20 Foot.
As : 5.20 :: 5.20 27.04: : 27.04 : 140.61 Foot.
Log. of 140.61
Equal to the Solidity of the Cube in Feet.
This might have been done more eafily, for the Logar. of the XIX. Side 5.20, which is 0.716003, multiplied by 3, would have produced 2.148009, the Logar. of 140.61, the Solidity.
H. Of a Long Cube or Parallelipipedon, GHI KL, whofe Side of the Square at the End, K I, is 1.27 Foot, and of its Length GH, 5.32 Foot.
1.27: L27; 1.61 :: 5.32 : 8.58 Foot.
III. Of an Oblong Parallelipipedon MNOPQR, whofe Breadth Fig. XX: at the End NO is 3.40 Foot, and Depth M N 6.50 Foot, and
the Length thereof MP, 16.25 Foot.
As 1 : 3:40: 6.50: 22.10:: 16.25: 159.12 Foot.
2.555245 The Solidity.
IV. Of a Pyramis S TV X N, whofe Side of its Bafe ST, &c. is Fig.XXI. 1.12 Foot, and Altitude NX 12.90 Foot.
As : 1.12: : 1.12: 1.25: NX 4.30: 5.39 the Sol. Con.
0.73.1904 the Solid Content.
V. Of a Cone A B CD, whofe Diameter BC is 6:12, and Alti- Fig.
tude AD 12.90 Foot.
Let ABCHGF be the Fruftum of a Square Pyramid, the XXIV. Side of the Square at the Lefer end A B, is 1.60 Foot; and there
fore the Area of that Square A B CD is 2.56 Foot: -The Side of the Square at the Greater End F G, is 2.30 Foot; and therefore the Area thereof is 5.29 Foot, and the Altitude DE 39.3 Foot.
The Log. of
Which is the Solidity of the Fruftum ABCDEFGH.
In the fame manner the Fruftum of a Cone of the fame Altitude, and the Area's of the Circles, at both Ends, the fame with the Area's of the Squares; the Solidity of fuch a Fruftum Cone, will be found to be the fame.
VIL. Of a Globe or Bullet, whofe Diameter is 1.75
The Logar. of the Diameter 1.75
Multiplied by 3
The Logar. of 355
Logar. of [678 always] Subftra&t
Refts the Logar. of 2.806 Foot
Which is the Solidity of the Bullet.