Book V. 



DIVIDING AND LAYING OUT LANDS. 



537 



3 r. 20 p. which is less than 5 ac. 2 r. 14 p. the true quantity, by ac. 2 r. 34 p. or 

 71,250 square links. Then measure a b, which suppose = 1,234 links, and divide 

 71,250 by 617, the half of it ; and the quotient, 115 links, will be the altitude of the 

 triangle to be added, and whose base is a, b. Therefore, if upon the centre b, with the 

 radius 115, an arc be described> and a line be drawn parallel to a, b, touching the arc, 

 and cutting b, d in d; and if a, d be drawn, it will be the line cutting oft" the required 

 quantity a, d, c, a. On the other hand, if the first piece had been too much, then d 

 must have been set below b. In this manner, the several shares of commons to be 

 divided, may be laid down upon the plan, and transferred thence to the ground itself. 



3313. The simplest mode of dividing lands, and that by which the agriculturist will make 

 fewest errors, is by trial and correction. Thus, supposing a piece of unenclosed land of 

 irregular shape to contain thirty-eight acres and a half, and it is desired to lay it out in 

 three fields, each of the same extent. Take a plan of the field, and lay it down on paper ; 

 divide it into three parts as near as possible by the eye : then ascertain the contents of 

 one of the outside divisions, wliich will be either somewhat too little or too much. Sup- 

 pose it too little by half a rood ; then, as the length of the straight line of the division is 

 1000 links, and 1000 links in length and 100 in breadth make an acre, and as half a 

 rood is the eighth of an acre, it follows that by extending the line the eighth part of 100 

 links, or 12*4 links at both ends, or 24-8 links at one end, the requisite quantity will be 

 added. Then go through the same operation with the projected field on the other 

 extreme of the plot ; and this being corrected, the middle field must necessarily be of the 

 exact contents of each of the two others : but to prove the whole, this field also may be 

 tried in the same manner. 



3314. In dividing a field with a view to sowing different crops in certain proportions : 

 say, for example, one acre and a half of common turnips, one acre of Swedish turnips, 

 three quarters of an acre of potatoes, and five acres of peas. Suppose the field a 

 parallelogram or nearly so; then first ascertain the length of the ridges, and next state the 

 question thus: — Such a length being given, required the breadth to give a fourth of an 

 acre — that being the smallest fraction in the proportions to be laid out ; then, if the 

 length of the ridges be ten chains, the breadth requisite to give a quarter of an acre will 

 be 25 links; consequently, a breadth of five times that space will be required for the 

 common turnips ; four times for the Swedish turnips ; three times for the potatoes ; and 

 twenty times for the peas. 



3315. In all more intricate cases, first lay down the plan of the space to be divided on 

 paper, to a large scale, say a chain to an inch ; then cover the paper with lines, drawn 

 so as to form squares, each square containing a certain number of feet and yards, or say 

 a pole each ; then on these squares adjust the figure, whatever it may be : thus, sup- 

 posing it desired to lay out a thicket of trees on the face of a hill, the outline of which 

 shall resemble the outline of the profile of a horse, dog, or say a human head, and yet 

 shall contain only one acre : lay down the outline of the horse or head on a large scale, 

 and divide it into squares ; then by trial and correction ascertain what each square must 

 necessarily contain. Say that there are 130 entire squares and 40 parts of squares, 

 making up in all 160 squares ; each of these squares must of course contain exactly one 

 pole, or 625 links, and their sides the square root of that number, or 25 links. From 

 these data it is easy to lay down the figure with perfect accuracy. 



3316. The layiiig out lines on lands, for the purposes of roads, fences, &c. requires to 

 be well understood by the agriculturist. On a plain surface, the business of tracing 

 straight lines is effected by a series of poles, so placed that the one nearest the eye con- 

 ceals all the rest. Where a straight line is to be indicated among objects or inequalities 

 not more than fifteen or twenty feet high, its plan or track on the earth («, b,fig. 523.) 



523 



£9 " 



