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ofDefcents, draining of Moraffes, conducing of Waters, l£c. One Place is faid to be higher than another, or out of Level with it, when it is more remote from the Centre of the Earth j and a Line equally diilant from the Centre of it in all its Points, is called the Line of true Level : whence, becaufe the Earth is round, that Line mull be a Curve, and make a part of the Earth's Circumference, or an Arch concentrical with it, as the Line B C F G ; Plate Surveying, Fig. 9. all the Points whereof ate equally diflant from the Centre of the Earth A. But the Line of Sight which the Operations of Levels give, is a Tangent or a Right Line perpendicular to the Semi-diameter : One Extreme of which Tangent, being the Point of Con- tact, the other will be that of a Secant drawn from the Centre of the Earth 5 and the Point which determines it, will be above the Surface of the Earth, and of the true Level, as much as that Secant exceeds the Radius or Semi-diameter of the Earth.
This Extremity of the Tangent is faid to be in the ap- parent Level, as being that given by the Sight, but is eafily reduced to the true Level, becaufe we know by Trigonometry, how much each Secant exceeds the Ra- dius; and becaufe by meafuring we have difcovered the precife Length of that Radius. It was for want of the Knowledge of this, the Antients were not able to reduce the apparent Level to the true one ; and accordingly, to prevent falling into an Error, never levell'd above 20 Feet at once, where fuch Reduction was not neceffary. By the Tables fince made, it appears that at the Diftance of 100 Yards, the apparent Level is raifed above the true one about f of a Line: So that the Antients, in this |re- fpect, were more fcrupulous than needed. By means of this Reduction, we are now able to level DHlances of one or two Miles, at one Operation, which the Antients could not do in lefs than 300.
The Operation of Levelling is as follows: Suppofe the Height of the Point A (Plate Surveying, Pig. 10.) on the Top of a Mountain, above that of the Point B, and at the Foot thereof required; Place the Level about the middle Diilance, between the two Points, as in D, and Staffs in A and B, and let there be Perfons inftrucfed with Signals for railing and lowering on the faid Staffs little Marks of Pafteboard, or other Matter. The Level being placed horizontally by the Bubble, i£c. look towards the Staff A E, and caufe the Mark to be raifed or lowered, till the Middle, upper Edge, or other moft confpicuous Part appear in the vifual Ray. Then meafuring exaftly the perpendicular Height of the Point A above the Point E, which fuppofe 6 Feet 4 Inches, fet that down in your Book j then turn the Level horizontally about, that the Eye-Glafs of the Telefcope may be ftill next the Eye when you look the other way (if you have only plain Sights, the Infttument need not be turned) and caufe the Perfon at the Staff B to raife or lower his Mark, till fome confpicuous part of it fall in the vifual Ray, as at C. then meafure the perpendicular Height of C above B, which fuppofe itf Feet, iC Inches ; fet thisalfo down in the Book above the other Number of the firft Obferva- tion ; fubftract the one from the other, the Remainder willbeio Feet, 4 Inches, which is the Difference of Level between A and B, or the Height of the Point A above the Point B. Whete Note, that if the Point D, where the Inftrument is fixed, be in the middle between the two Points A and B, there will be no Neceffity for reducing the apparent Level to the true Level, the vi- fual Ray in that Cafe being raifed equally above the true
Level.
If it be further required to know whether there be a
fufficient Defcent for conveying Water from the Source A
to the Point B, Plate Surveying, Fig. 11. Here in regard the Diflance from A to B is confiderable, 'tis required that feveral Operations be made. Having then chofen a
proper Place for the firft Station, as at I, fet up a Staff 10 the Point A near the Source, with a proper Mark to Hide up and down the Staff as L, and meafure the Dif- tance from A to I, which fuppofe 2000 Yards. Then the Level being adjulled in the Point I, let the Mark L be raifed and lowered till fuch time as you fpy fome con- fpicuous Part of it thro' the Telefcope or Sights of the Level, and meafure the Height A L, which fuppofe 1 3 Foot 5 Inches. But in regard the Diftance Al is 2oco Yards you muft have recourfe to your Table for a Re- duction fubflracting 11 Inches, which will leave the Height AL 12 Foot 6 Inches; and this note down in your Book. Now turn the Level horizontally about, fo as the Eye-Glafs of the Telefcope may be towards the Staff at A ; and fixing up another Staff at H, caufe the Mark G to be moved up and down, till you fpy fome confpicuous Part thro the Telefcope or Sights. Meafure the Height H G, which fuppofe 6 Yards, 4 Feet, 2 In- ches. Meafure likewife the Diftance of the Points I H, which fuppofe 1 300 Yards 5 for which Diftance, according
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to the Table, 4. Inches, 8 Lines, muft be fuburacled from the Height H G, which confequenrly will but leave 6 "Yards, 3 Feet, o Inches, 4 Lines, to be taken down in your Book.
This done, remove the Level forwards to fome other Eminence, as E, whence the Staff H may be view'd, as alfo another Staff at D, the Place whither the Water is to be convey'd. The Level being again adjufted in the Point E, look back to the Staff H j and managing the Mark as before, the vifual Ray will give the Point F. Meafure the Height H F, which fuppofe 11 Feer, 6 In- ches. Meafure likewife the Diilance H E, which fuppofe ioco Yards ; for which Diilance the Table gives 2, Inches, 9 Lines of Abatement ; which being taken from the Height H F, there will remain 1 1 Feet, 3 Inches-, 3 Lines, which enter in your Book. Lzjily, turning the Level to look at the next Staff D, the vifual Ray will give the Point D. Meafure the Height of D from the Ground, which fuppofe 8 Feet, 3 Inches. Meafure alfo the Diilance from the Station H to B, which fuppofe pco Yards ; for which Diilance the Table gives 2 Inches, 3 Lines of Abatement 5 which being taken from the Height BD, there will remain 8 Feet, 9 Lines, which enter as before.
For the Manner of entering down Obfervations in your Book, obferve that when a proper Place or Station for the Level, between the two Points, has been pitched upon, you muft write down the two Heights obferved at that Station, in two different Columns, viz. under the firft Column, thofe obferved in looking thro 1 the Telefcope when the Eye was from the Source, or to- wards the Point, which we may call Back-Sights 5 and un- der the fecond Column thofe obferved, when the Eye was next the Source, which we call Fore-Sights, in the manner following :
Back-Sights. Fore-Sights.
Foot. Inc. Line, Foot. Inc. Lin.
Firft Height \ | Second Height 21 : 9:4.
Correfted 5" : 6 ' j Fourth Height S : o : 9
ThirdHeight 11 ; 3 : 3 |
29 : IO : I
- 9 : 3 I
Having fummed up the Heights of each Column fe- parately, fubftrafr the leffer from the greater, the Re- mainder will be the Difference of Level between the Points A and B 5 as in this Example,
Feet. Inch. Lin. 29 ; 10 : I
23 : 09 : 3 1
6 : 00 : 10 The Difference of Height or Le~ vet between the Points A and B.
If the Diftance of the two Points be required, add all the Diftances meafured, rogether, and dividing the Diffe- rence of Height by the Yards of the Diftances, for each 200 Yards you will have a Defcent of about z Inches, 9 Lines.
Levelling Staffs are Inftruments ufed in Levelling, ferving to carry the Marks to be obferv'd, and at the fame time to meafure the Height of thofe Marks from the Ground. They ufually coniift each of two long fquare Wooden Rulers, made to Aide over one another, and divided into Feet, Inches, £5?c.
For the common Occafions of Levelling to be perform'd without much Apparatus of Inftruments, Time, or Trou- ble, the following Method is recommended. Set a Pole upright in a Spring, Pond, River, or other Place whence Water is to be brought, and mark how many Feet and Inches of it are above Water. Then fet up another Pole, of equal length with the other, in the place to which the Water is to come. Place the Center of a Qua- drant on the top of this laft Pole, the Plummet hanging free -, fpy thro the Sights the Top of the Pole that is in the Water, and if the Thread cuts any Degree of the Quadrant, the Water may be convey'd by a Pipe laid in the Earth. If you can't fee from one Extreme to the other, the Operation may be repeated in the manner already directed.
Dr. Hattey fuggefts a new Method of Levelling, which has been put in practice by fome of ihe French Academy : This is performed wholly by means of the Barometer, in which the Mercury is found to be fufpended to fo much the lefs Height, as the Place is further remote from the Centre of the Earth. Hence it follows, that the diffe- rent Heights of the Mercury in two Places give the Dif ference of Level. Mr. T)crham, from fome Obfervations he made at the top and bottom of the Monument, found that the Mercury fell 7 *- of an Inch at every 82 Foot of
perpen-
