LESSONS IN LAND-SURVEY 



line A i I.UH-I-, in the above example, tlio areas of the 



trapi . 



1.1 n 

 86 16 



J LS 



and 



2b 10 



So 28 



8)44 



13x38 807 22x37-814, 



and BO on. Those several areas must then bo added together, 

 nti'l ulsn the areas of the two triangles Ala and B 11 I, 

 tho whole together being added to the area of the triangle 



EXERCISE 6. Lay down the plan of a field, and eompute the 

 area from tho following notes : 



If it U intended to make a very finished plan of an estate, 

 containing, as it would, many fields, probably plantation*, and 

 perhaps buildings, it U necessary carefully to note all these 

 matters in the field-book in such a manner M that, with no 

 other help, they may all be subsequently correctly delineated. 



If the scale on which tle plan U required be large, the di- 

 mensions of ovary building, as well as its relative situation, 

 must be taken and shown. All these are mere matters of detail, 

 involving time, but the method of proceeding is simple, indeed 

 self-evident For instance, a bouse stands, it may be, to the 

 right of the line we are measuring; if it be within, say, 80 

 links, estimate a perpendicular point upon the line to on* of 

 the anglei of the bonne, and measure the distance with the 

 off-set staff, noting iu the field- jook thus 



4320 



L 



. ;.; i-.:'^ 

 corner of boas*. 



If necessary, describe the character of the building, and make 

 a marginal sketch of it, measuring the other walls with the 

 staff or a tape. Then, in crossing boundaries, note whether it 

 be a ditch, wall, hedge, etc., and the character of the ground 

 on either side. A good draughtsman will pride himself upon 

 correctly planning the nature of the country he passes orer, 

 showing where the ground rises, where it falls, water-courses, 

 etc. etc. 



Of course difficulties will frequently arise necessitating a 

 deviation from ordinary rules. Many of them, indeed most of 

 them, will be met by following out the rules laid down in our 

 Lessons in Mensuration, but all may be overcome by employing 

 a certain amount of common sense in conjunction with these 

 rules. As we are at present supposing we have only the use 

 of a chain and cross-staff, we will give an example of how a 

 difficulty may be met by their use, without calling in the aid 

 of an instrument for measuring other than right angles. 



Suppose it is necessary to continue the measurement of a 

 line D c across a river A B (Fig. 8), which is too wide and deep 



*C 



D 



to drag tho chain across. Fix a mark at c, close to the margin 

 of the river, upon the opposite side to that on which you are 

 standing, and upon the line you are measuring. From any 

 point E in this line erect with the cross-staff the perpendicular 

 E E' ; measure a convenient distance along it to r, and from r, 

 along the same perpendicular, measure v o = F E. From the 

 point o lay off the perpendicular a o', then the length along 

 this perpendicular from o to the point o', where it intersects 

 the line of sight F c, will equal the length from E to C. The 

 reason is obvious. In the two triangles F E c, r o o', F E = r o, 

 the opposite angles at F are equal, and the angles at E and at 

 o being right angles, are also equal : therefore the other homo- 

 logous aides are equal each to each (Euc. I. 26). 



We have now to consider that most useful instrument for 

 ensuring accuracy in large surveys, the theodolite ; and first we 

 shall give a brief description of it. The theodolite is an in- 

 strument consisting mainly of a telescope of greater or leu 

 power, according to its size and requirements, securely fixed 

 upon a semicircle of brass, arranged so as to admit of both the 

 telescope and the brass circle moving in a vertical plane upon 

 a horizontal pivot, the pivot being placed in the centre of the 

 circle of which the brass arc forms a portion. The edge of the 

 arc is accurately divided into degrees, and parts of a degree, 

 and can be clamped rigidly in any position required. Connected 

 with tho telescope, and underneath it, is a spirit-level, by which 

 the optical axis of the telescope can be brought to the horizontal, 



