536 



SCIENCE OF AGRICULTURE. 



Part II. 



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 hillocks or hol- 

 lows (b), or by smooth-headed stakes driven into the surface, and protruding above, or 

 sunk under it, according to the obstructions. 



3306. Lines of uniform declivity or acclivity {fig. 521. e, e, e) are readily formed on the 

 same principle. In this and the former case, the common level and the horning pieces 

 (a and d), with measuring-rods and stakes, are all the instruments required. 



SuBSECT. 3. Division and laying out of Lands. 



3307. The division of lands is one of the most important and not the least difficult 

 parts of the land surveyor's art. In intricate cases, as in the subdivision of large estates 

 or commons, the professional surveyor will generally be resorted to ; but it is essen- 

 tial for the land-steward and proprietor, and even for the farmer, or professional 

 cultivator, to know the general principles on which this business is founded. We 

 shall therefore shortly develope these principles from Dr, Hutton's valuable Dictionary, 

 and next olFer some general rules of our own for ordinary cases of dividing and laying 

 out lines. 



3308. In the division of commons, after the whole is surveyed and cast up, and the 

 proper quantities to be allowed for roads, &c. deducted, divide the net quantity remain- 

 ing among the several proprietors, by the rule of fellowship, in proportion to the real 

 value of their estates, and you will thereby obtain their proportional quantities of the 

 land. But as this division supposes the land, which is to be divided, to be all of an 

 equal goodness, you must observe, that if the part in which any one's share is to be 

 marked off be better or worse than the general mean quality of the land, then you must 

 diminish or augment the quantity of his share in the same proportion. 



3309. Or divide the ground among the claimants in the direct ratio of the value of 

 their claims, and the inverse ratio of the quality of the ground allotted to each : that 

 is, in proportion to the quotients arising from the division of the value of each person's 

 estate, by the number which expresses the quality of the ground in his share. 



3310. But these regular methods cannot always be put in practice; so that, in the 

 division of commons, the usual way is to measure separately all the land that is of 

 different values, and add into two sums the contents and the values; then the value 

 of every claimant's share is found by dividing the whole value among them in pro- 

 portion to their estates ; and lastly, a quantity is laid out for each person, that shall be 

 of the value of his share before found. 



3311. It is required to divide any given quantity of ground, or its value, into any given 

 number of parts, and in proportion to any given number. Rule. Divide the given 

 piece, or its value, as in the rule of fellowship, by dividing the whole content or value 

 by the sum of the numbers expressing the proportions of the several shares, and mul- 

 tiplying the quotient severally by the said proportional numbers for the respective shares 

 required, when the land is all of the same quality. But if the shares be of different 

 qualities, then divide the numbers expressing the proportions or values of the shares, by 

 the numbers which express the qualities of the land in each share ; and use the quotients 

 instead of the former proportional numbers. 



Ex. 1. If the total value of a common be 2500Z. it is required to deter, 

 mine the values of the shares of the three claimants A, B, C, whose 

 estates are of these values, 10,000/., 15,000/., and 25,000/. The estates 

 being in proportion as the numbers 2, 3, 5, whose sum is 10, we shall have 

 2,500-^ 10=250; which being severally multiplied by 2, 3, 5, the products 

 500, 750, 1250, are the values of the shares required. 



Ex. 2. It is required to divide 300 acres of land among A, B, C, D, E, 



F, G, and H, whose claims upon it are respectively in proportion as the 



numbers 1, 2, 3, 5, 8, 10, 15, 20. The sum of these proportional numbers 



is 64 ; by which dividing 300, the quotient is 4 ac. 2 r. 30 p. ; which being 



multiplied by each of the numbers, 1, 2, 3, 5, &c. we obtain for the several 



shares as annexed. 



3. It is required to divide 780 acres among A, B, and C, whose estates are 1,000/., 3,000/., and 



522 4,000/. a year; the ground in their shares being worth 5, 8, and 10 



" shillings the acre respectively. Here their claims are as 1, 3, 4 : and 



the qualities of their land are as 5, 8, 10 ; therefore their quantities 



must be as one fifth, three eighths, two fifths; or by reduction, as 



8, 15, 16. Now the sum of these numbers is 39 ; by which dividing the 



780 acres, the quotient is 20 ; which being multiplied severally by the 



three numbers 8, 15, IH, the three products are 160, 300, 320, for the 



shares of A, B, C, respectively, 



3312. To cut off from a plan a given number of acreSj 

 c. by a line drawn from any point in the side of it. - 

 Rule. Let a {fig. 522.) be the given point in the 

 plan, from which a line is to be drawn cutting off suppose 

 5 ac. 2 r. 14 p. Draw a b cutting off the part a 6 c as near 

 as can be judged equal to the quantity proposed ; and let 

 the true qiiantity of a h r, when calculated, be only 4 ac. 



Ex. 



