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A new Method of Surveying Countries, or large Tracts of Land
HE common Method of perforining Tthis Problem, is by taking and protracting inacceffible Diffances, which has been treated of (in general) already; and therefore, fuppofing that the Ingenious Surveyor cannot be incapable of applying it to this particular, I fhall wholly omit this, and give you a few Method, invented by thofe Learned Mathematicians Mr Whiffon and Mr Ditton, in order to which, let us premise the following Lemmata.
I. All founds are propagated almoft evenly, and are obferved to move 8 measured Miles in 37 Seconds.
This is well known from the laft and most accurate Obfervations about wom
the Velocity of Sounds, which
II. An ordinary Mortar is eafily able to caft a Projectile about a Mile in Perpendi cular Heigth; and the Sound thereof may be heard near 20 Miles.
The truth of both thefe Propofitions have been fufficiently proved by divers Experi ments made by Mr Whiffon for that purpose.
III. A Projectile may be fill'd with Combustible Matters, to take Fire as foon as difcharg'd, and continue burning till it comes to the Ground."
This all that deal in Rockets, Bombs," and Mortars, do very well know, and is found to be true upon Tryal.
IV. Fire, or Light about a Mile high will be vifible in the Night time, when? the Air is tolerably clear about, 70 Miles. This alfo hath been made manifeft by many Experiments made on purpoft.
The Solution of the Problem.
Let a Shell that will take Fire as foon as difcharg'd, and continue Burning till it comes to the Ground, be hot perpendicularly about a Mile high out of a Mortar at any convenient place in a clear Night; and this Difcharge will by the Bearing, and Interval of the Flash and Sound, give the Diftance and Bearing of an Obferver within the Hearing and Sight thereof, according to the foregoing Lemmata.
Fig. 2. Let the Bearing of a Shell difcharg'd out of a Mortar at C, and alfo the Interval of the Flath and Sound thereof be obferv'd by Perfons fent to A. B. E. F. G.
H.I.D. places within 20 Miles round C, who muft be furnished with an Inftrument to meafure Angles, for taking the Bearing of the fhell; and a Thread 39.2 Inches long, with a Plummet faften'd to one end, which being fufpended by the other end to a Pin,or Nail, and made to fwing, will vibrate feconds by which the Interval between the Flash and Sound may be nicely measured, and let their Obfervations be as follows.
To protract which, through the point C, draw the Meridian N. S. and lay
off the Angles NCD. 3 ̊, NCA. 30°,NCG. 87° from the North towards the Weft. The AnglesNCE.40°,NCF 90',from the North towards the Eaft.The Angles SCI. 6° „SCH 50°, from the South towards the Weft. Lastly, Lay off the Angle SCB 60° from the South towards the Eaft. Then fet off their diflances from the Mortar at C. viz. DC= 14m. A C = 16 m. &c. according to the Obfervations. So will you have an exact Map of the place A.B.C.D.E.F.G.H.L, and the Scituation of the Villages about each Station may be easily taken by the Obferver thereof after the commen unethod of taking inacceffible Distances.
I. If each Obferver were to let off a Rocket at his own Station, and take the mutual Bearing, of each others it wou'd be a great Check to any Error that could poffibly happen.
II. If a great Gun were discharg'd near the Mortar, and the Sound thereof ufed inftead of that of theMortar; it would be beard nuch further, and confequently a muchlarger Tract of Land might be furveyed at
A ready way to find a true Meridian line by the Pole Star.
The right Afcenfion of the Pole Star for this Year (1716) is 37 Minutes of Time; and it increases one Minute 16 Seconds every ten Years: Therefore having at any time this Star's Right Afcenfion, and the Right. Afcenfion of the Sun both in Time, if you fubftract the latter from the former, adding 24 Hours to the Right Afcenfion of the Pole-Star, when it is lefs than the Sun's the Remainder will be the time of the Star's, coming to the Meridian; at which time hang up two Pendulums between your Eye and the Pole Sfar, and a Right-line drawn through them, will be a true Meridianline.
In the Survey juft now treated of, you may ufe the fights of a good Circumferentor, or any other Surveying Inftrument, ha ving one of the fights long enough to take in the Pole-Star.
If you wou'd know, what Angle the Pole-Star makes with the true Meridian at other times, the following Table will