Book V. 



DIVIDING AND LAYING OUT LANDS. 



481 



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, h. Therefore if upon the cen- 

 tre by with the radius 1 15, an arc be described, and a line be drawn parallel to a, b, touch- 

 ing the arc, and cutting b,d in rf ; and if a, d be drawn, it will be the line cutting off the 

 required quantity a, f/, 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 di- 

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



3072. The simplest mode of dividing lands, and that by which the agriculturist will make 

 fewest errors is, by trial and correction. Thus, supposing apiece 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, which will be either somewhat too little or too much. Suppose 

 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. 



3073. In dividing a field with a view to sowing different crops in certain proportions : say, 

 for example, one acre and a half of common turnip, one acre of Swedish turnip, three 

 quarters of an acre of potatoes, and five acres of pease. Suppose the field a parallel- 

 ogram 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 



pase. 



3074. 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, drawr 

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

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

 desired to lay out a thicket of trees on the face of a hill, the outline of wluch shall resem-- 

 ble 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. 



3075. The laying 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 tract on the earth ( a, b,fig. 422.) 



422 



may be found by the use of poles, a few feet higher than the elevation of the obstructions, 

 tile director being placed on a step-ladder, or other elevation at one end. Where this method 



