Book V. 



TAKING THE LEVELS OF SURFACES. 



479 



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 witli notes, the country examined would be firmly 

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

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



SuBSECT. 2. Of taking the Levels of Surfaces. 



3059. 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 that of 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 countiy, every where on the 

 same level. 



3060. Two or more jilaces 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 parallel to it, or concentrical with it. 



3061. 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 levels the difference of which is always equal to the excess of tlie secant of the 

 arch of distance above the radius of the earth. 



3062. 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, Avhich 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 a2>parent above the true level at the distance of one 

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

 distances, tables shewing 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 con- 

 structed. (See Dr. Huttons Mathematical Dictionary, art. Level.) 



3063. The ojyeration of levelling is performed by placing poles or staves at diff'erent parts 

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

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

 adjusted. In describing the more common levels used in agriculture, (2421.) 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 are 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 imple- 

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

 person not accustomed to their frequent use. 



3064. Levelling to produce an even line (fg> 420.), 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 di- 



420 



rections, and so transferring the points by horizontal levels to the proper line. Straight 

 rods are the ready means of measuring down, and the points must be marked by hil- 



