B .OK V. 



TAKING THE LEVELS OF SURFACES. 



535 



scenery nearest the house, may be taken down or remembered, and also the distant 

 scenery, or that exterior to the estate. In riding through a country which it is desired to 

 recollect, a sketch should be made in imagination of the road and the leading objects 

 adjoining ; another of what may be called the objects in the middle distance ; and, finally, 

 one of the farthest distance. If, instead of the imagination, a memorandum book were 

 used, and the sketches accompanied with notes, the country examined would be firmly 

 impressed on the memory. In this way temporary military maps are formed by the 

 engineers of the army in a few hours, and with astonishing accuracy. 



Subsect. 2. Taking the Levels of Surfaces. 



3300. Levelling, or the operation of taking the levels of surfaces, is of essential use in 

 agriculture, for ascertaining the practicability of bringing water to particular points in 

 order to drive machinery ; for irrigation ; for roads led along the sides of hills ; for 

 drainages, and various other purposes. There are few works on the earth's surface more 

 useful, grand, and agreeable, than a road ascending, passing over, and descending a 

 range of steep irregular mountains, but every where of the same and of a convenient 

 slope ; next to this is a canal passing through an irregular country, yet every where on 

 the same level. 



3301. Two or more places are said to be on a true level, when they are equally distant 

 from the centre of the earth. Also, one place is higher than another, or out of level with 

 it, when it is farther from the centre of the earth : and a line equally distant from that 

 centre in all its points, is called the line of true level. Hence, because the earth is round, 

 that line must be a curve, and make a part of the earth's circumference, or at least be 

 parallel to it, or concentrical with it. 



3302. The line of sight given by the operation of levelling is a tangent, or a right line 

 perpendicular to the semidiameter of the earth at the point of contact, rising always 

 higher above the true line of level, the farther the distance is, which is called the apparent 

 line of level, the difference of which is always equal to the excess of the secant of the arch 

 of distance above the radius of the earth. 



3303. The common methods of levelling are sufficient for conveying water to small dis- 

 tances, &c. ; but in more extensive operations, as in levelling for canals, which are to con- 

 vey water to the distance of many miles, and such like, the difference between the true 

 and the apparent level must be taken into the account, which is equal to the square of 

 the distance between the places, divided by the diameter of the earth, and consequently 

 it is always proportional to the square of the distance ; or from calculation almost eight 

 inches, for the height of the apparent above the true level at a distance of one mile. 

 Thus, by proportioning the excesses in altitude according to the squares of the distances, 

 tables showing the height of the apparent above the true level for every hundred yards 

 of distance on the one hand, and for every mile on the other, have been constructed. 

 (See Dr. Huttoris Mathematical Dictionary, art. Level.) 



3304. The operation of levelling is performed by placing poles or staves at different parts 

 or points from which the levels are to be taken, with persons to raise or lower them, 

 according to circumstances, when the levelling instrument is properly applied and 

 adjusted. In describing the more common levels used in agriculture (2497.), we have 

 also given some account of the mode of using them for common purposes. Their use, 

 as well as that of the different kinds of spirit levels, will be better acquired by a few 

 hours' practice with a surveyor than by any number of words : and indeed in practice, 

 whenever any very important point or series of levels is to be taken, it will commonly be 

 found better to call in the aid of a land surveyor than to be at the expense of implements 

 to be seldom used, and with which errors might easily be made by a very skilful person 

 not accustomed to their frequent use. 



3305. Levelling to produce an even line (Jig. 521.), as in road-making, whether that 



line be straight or curved in direction, can only be determined on an irregular surface by 

 measuring down from an elevated level line (a), or from level lines in parallel directions, 



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