LESSONS IN LAND.8URVEY 



EXERCISE 1. A triangular field measures 5,720 links along 

 Its base, and the length of tho perpendicular U 2,170 link* ; 

 what in its area 'f 



<>ur next step is to suppose a field in the form of a trapezium, 

 as shown in Fig. 2. 



We have here a figure which 

 is formed of two triangles standing 

 upon opposite sides of the same 

 base A B. By means of the cross- 

 staff ascertain the points D and r 

 along that base, and measure 

 r. Them the area = A B x 



K V 



-f A B X-j , which formula wo can reduce to 2 A B x 



c D 



Pig. 2. 



:;.Mi'ars CD, 



C D -f E F 



= AB X 



c D + 



that is, the area of a trapezium 



I 2 



is the diagonal multiplied by half the Bum of the perpendiculars. 



1!\ \MPLE 1. The diagonal A B = 725 links, and the two 



liculars = respectively 432 links and 328 links. What 



is the area of the trapezium P 



JQO _i_ 300 



=275,500 links, or 2 acres 3 roods 8 poles. 

 Ans. 



i :CISE 2. What is the area of a trapezium whose diagonal 

 measures 825 links, and the two perpendiculars 320 and 540 links ? 



It is possible to have a trapezium of such a shape as A B c D 

 c E 3 (Fig. 3), in which upon one or both 



of the diagonals the perpendiculars 

 will fall outside the triangle : for 

 instance, if A B be taken as the 

 diagonal, the perpendicular c o from 

 c would fall outside the lino c A ; 



.1- 

 ' a 



Fig. 3. 



nd if c D bo the diagonal, the perpendicular B H from B would 

 fall outside B D. In such cases it may bo necessary to make one 

 of the sides the base, as, for instance, c B in the triangle CAB, 

 making E the point whence to measure the perpendicular E A, 

 whilst the diagonal A B will furnish the base for the vertical lino 

 F D. A little consideration will always show the surveyor what 

 lines to select as his base, so as to facilitate his calculations 

 as much as possible. The fact is that in these remarks we are 

 doing little more than repeating the problems explained in our 

 lessons upon the mensuration of superficies, our object being to 

 show how readily they can be applied to practice in surveying. 

 We have yet to explain the method of taking notes of mea- 

 surements upon the field, that is, of compiling a " Field Book," 

 and also to show how afterwords to reduce the Field Book 

 to a plan, that is, to lay down a fac-simile of the ground upon 

 paper. We shall speak of this shortly. 



Let ns now see how the area of more irregularly-shaped fields 

 may be ascertained. Imagine a field ABCDEFOH shaped as 



in Fig. 4. Having judiciously 

 divided it into the fewest 

 number of imaginary tri- 

 angles, measure all those 

 sides which will form the 

 bases upon which to erect 

 perpendiculars. In this case 

 these bases will be A c, ED, 

 and o H ; and the perpen- 

 diculars to be measured will 

 be a B, H b, and c F, and by 



the help of these six lines the area of the figure ABCDEFOH 

 can bo ascertained. We should, however, decidedly recom- 

 mend that check measurements be made, as, for instance, the 

 length of H D, forming a side of the triangle H B D ; also 

 H F, a side of the triangle F o n. By the use of these, 

 as applied by previous problems, the surveyor will ascertain 

 if his measurements are correct. For instance, if he has cor- 

 rectly measured the base E D, the perpendicular H 6, and 

 distance b D, he can find if -/n I" + 60* equals the length 

 of H D by actual measurement ; or if <v/c H 1 + c F 1 = H F as 

 actually measured, and so on. Then, having proved the correct- 

 ness of the measurements, the area of the whole will be the sum 

 of the areas of the three triangles A B c, E H D, and F H. 



Another method of ascertaining the area of irregular pieces of 

 ground as, for instance, that shown in Fig. 5 is to divide it 



Klf . 5. 



by the diagonal A B, and along that & Mi of perpendfeolani 

 at 1, 2, 8, ete., right and left to the several angls*. By this 

 airangmumt the fiekJbeooin** divided into a series of trapeaoids 

 and rigb^angbd triangle, the areas of which can b* readily 

 found by previous roles, and 

 their sum will give the area of 

 the field. 



We will now explain the 

 met hod of taking mesjaresBsat* 

 on the ground, and transferring 

 them in snob a way to a book as 

 that a representation of the grand can be correctly laid down 

 on paper. The bettor plan is to take a preliminary walk over 

 the ground, having a book which opens lengthways ruled with 

 a single column down the middle, the space between the line* of 

 the column being sufficiently wide to put in four fignrw tide b/ 

 (ride. This column represents the line being walked over, and the 

 margins right and left are for measurements taken by the ey- 

 perpendicularly to this line, and also for any notes with respect 

 to thorn. The surveyor will, by a little practice, be able to pace 

 thirty-six inches at a stride so correctly as to err on an average 

 only a few inches upon several hundred yard*. 



Keeping the ruled book before him, and oonuneneinf alwayv 

 at the bottom of the page, let him pace from any given point OB 

 the border of tho ground to some other point also on the out- 

 skirts of the ground, but at an opposite side, being careful as h 

 paces to keep his oyo upon that point, so as to ensure the line of 

 march being straiyht. Should he cross a road, a hedge, or a 

 ditch, or any other distinctive mark, let it be noted in toe book 

 by a line drawn across too page, but avoiding the ruled column. 

 the number of paces where the hedge, etc., intersects it being in* 

 sorted in tho column, and so on to the end ; tho total will then 

 stand at the top part of the column, that i, above all the other 

 figures. For the sake of distinction, call tho starting and termi- 

 nating points letters, as A, B, etc. 



This lino (which, if judiciously selected, will become a base for 

 further operations) having been thus approximately recorded, 

 let tho surveyor start from one or the other extremes to some 

 other point on the borders of the property, which may become the 

 apex of a triangle, having the first measured line for a base, 

 observing tho same method as before, and so on until the whole 

 property has been walked over. On a distinct page of the book 

 let a rough plan of the lines walked over bo laid out, and let their 

 relative positions as to anglo or inclination bo marked down 

 thus ; keeping tho ruled columns as nearly in a lino as possible 

 with that paced, and let the eye form an estimate of the direction 

 of any intended lino from it, and mark that direction down. If 

 these rules are carefully attended to, a very fair plan of the pro- 

 perty may bo obtained without the help of the chain or noes 

 staff, and a subsequent examination of this plan will very greatly 

 assist the surveyor in his actual measurements, which will form 

 his next operation. 



The mode of measuring with the chain is accomplished thu. 



The chain leader starts with the front end of the chain and ten 



iron arrows. When ho has extended tho chain he keeps bis eye 



directed upon the surveyor, who stands at its back end, and who 



directs his movements right or left, so as to keep the chain in the 



correct line. This being done, he with one of the arrow* marks 



;he exact spot in the ground at which tho chain terminated. 



eaving the arrow sticking in the ground. The pro QMS is then 



repeated, but after the first chain length has been measured 



he chain follower picks up the arrow left in the ground, *nd 



carries it forward with him. If the line being measured is longer 



;han ten chains, the tenth ch un U allowed to rest on the ground, 



vhilst the follower carries the ten arrows forward to the leader, 



he fact being noted in the Field Book by the surveyor. When 



he end of tho line is reached, the number of tens added to the 



number of arrows in the follower's hand, and the number of links 



n the last chain up to the exact point, gives the total length of 



.he line. For instance, suppose the follower has carried forward 



he ten arrows five times to the leader, this will imply 5 X 10 



= 50 chains, or 5,000 links ; and suppose he finds he has six 



arrows in his hand at last, this will make nix chains, or 600 links 



additional ; and suppose the end point of the line touches the 



orty-sevonth link, the whole length of the line would then be 



5,647 links, and for the convenience of computation a itoflimiO 



>oint would bo put before the two last figures, making the length 



"6 '47 chains. 



