As Radius; Sine 90 d.

Is to the Hypothenuse NR 380.
So is the S'ne of the Angle NRK 61. 32.

To the Sine of NK 335. Equal to the Height of the Object and the Hill together.

And so is the Cosine of NRK, viz. RNK 28, 28. To the Logar fide RK, 179. 4 Foot.

To which, if you add the measured dia stance PR 212. Their Sum will be 391.9, for the whole length PK. Then,

In the Triangle POK, you have given, PK 391.9 Foo', and the LOPK 22 25.

, by which you may find OK, by Cale 1/4, of Trigonometry BR, L, T. Thus,

As Radius, Tang.45 d.

Is to the S de PK 391.9
So is the Tangent of the LOPK 22.2;'.
To the Height of the Hill OK 160.19F00%.

Which subtracted from 335. The whole Height, there remains 174.81 Fuit for the Altitude of the Object NO.

Prob. 1.

Of Longimetria.

Hov (f.mnding upon an Obje& of a known Height,) to find the distance tion thence, to some other remote Object.

Fig. 69 Sippose CA to be the fide of a Fort or Bilwirk 22. 5 Foot high, and being upon the Platform at C, youfe a


D 3

Tree, or other Object at B, whose distance you would know from the Foot of the Wall at A.

The Lines AB and ACbeing drawn, and the he'g'rth of the Wall 22. 5 Foot, set from A to C, where by your luftrument directed to B, you find the Degrees cut to be 71'. 25, which Angle lay down; so have you the Righ-angled Triangle CAB, in which there is given, (1.) CA, the heighth of the Wall 22. 5 Foct (2.) the Angle observed at C, 77: 25' D g. by which you may find the díitance AB (by Cafe 2. of Right Angled

ly plane Triangles.) thus,

As Radius, Tangeot 45 Deg.

To CA, the heighth of the Wall 22. 5 Foot.

So is the Tangent of ACB, the Angle ola served, 71.25 Deg.

To the diftance AB, 66. 28 Foot. And if you would find the Length of the Line CB, you may (by Cale 3 of Right Argle Triangle) thus,

As the Sine of the Angle observed at C 712.2;' Deg.

Is to the distance BA, 66. 28 Foot.
So is the Radius, Sine 99 Dig.
To the Line CB, 69. 98 Foot.

Fig. 68. Is Supposed to be a piece of a River, and you measuring along one side of it, would as well know the Breadth of it, as also make a true Plot therea


of, putting down what remarkable things are seen on the other side.

Being at on. the first Station, cause one of your Affiftants to go to the next bend of the River, as 0 2. and there fet up a inark for you; then fee what Angle froin the Meridian 0 1 0 2 inaks, which let be N. W. 6 deg. also seeing several marks on the other side of the River, take their bea:ings, as the House A which stands upon the Bank, and is a Mark for the Breadth of the

a River bears N.W.52 digrees, the Wind-mill B up in the Land, bears N W. 40 dig the Tree C by the Water-side, bears N. W 17 drg: all this note down in your Field Book, and measure the distance from o I to © 2, 19 Chains, 20 Links. After this com g

IS to2, fee how the next bend of the River bears from you, viz. O 3; which let be N. E.15 deg. See also how the House A there bears trom you, viz. S. W. 20 deg. the Wind-Mill S. w. 50 deg the Trre, N. W. 77o. Also as you are going forward if you see any thirg more at this second Station take the Bearirg thereof, as ba noted Castle D upon the Land, bears NW. 28", as a Church E close by the River Brink NW,4o. measure the distance from 02, to 93. And pacing your Instrument al @ 3., he Church bears froin you N W.88 dg the Caftle up in the Land at D you cannot se: for the Church, therefore let it alone for

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the next Station. But here you may fee forward a little Village F, the first House thereof bears from you NW 32° deg. Measure the distance fromo 360 4,and Planting your luflruunent in 4, the first House of the Vil. lige F bears from you South West 32 d. and the Castle D, which you could vot see at the third Sation, S W. 24° Havirg put down all this in your Field-Bock, it will be as follows,

N. W. 6° 18 Chains 21 Links


A Tree up p the Bank of the

N. W. 17. Co
River bears
A Wind-Mill upon the Land

N. W. 40 00
A House on the River Bank

N. W.

52 00

2 N E, 15°. 18 Chains 20 Links. The Tree N. W. 77ooo? These look to Ob. 'The House S. W. 20 00

Tervation co o I. The Wind-Mills.W.50 00

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ACastl: far up in the LandN.W. 28,00 For

3 wardoba A Church upon che River N.W. 4 Bank


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03 N.W. 150.20 Ch. Solin.
The Church Bears N. W. 88 There look back-
The Castle cannot be seen ward to Obr. 2.
The end of the little Village

A forward Obf. O. N. W.32. i

The end of the little Village S W3:,

These rer
The Cafle respecting O 3 SW.2.
in the Land.

S. 24, S and O':

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To srotract this, draw the Line N. S toc a Meridian, and laying your Protiator upon it, the Center shereof to @ I; against NW. 6° make a Mark for the Line that goes to @ 2. Allo aguinst N. W. 17. make a Mark for the Tree, and against 40° and 52' for the Wind-Mill and Housi. Then froin

I, through these marks draw the Lines

A, B, C, 2. Secondly, Take froin your Scale 18 Chains and 20 Lin, and fer it off upon the Line ©2, which will reach to 2. There lay again the Center of your Protractor ; the Diameter thereof Parallel to the Line NS, and make marks as you see in the field. Book, againft N E 15° NW 77 SW 20°, SW 50, NW 28., NV 4°, and through these inasks draw Lines, the first Line directs to your third Station ; the second Line NW 77° directs you to the Tree Cupon the River Bank, for that Line cutting the Line Oi C, fhews you by the Intersection where the Tree food, and also the Breadth of the River. Also the Line SW 20° cuts the Line from the firft Station NW 52°, in the place where House A ftood upon the Bank of the River. If therefore you draw a Line from A to Cit will represent the farther Bank of the River, And so you may proceed on Plotting, according to the Notes in your Field-Book ; : and you will not only have a true Plot of the River, but also know how far the Wind



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