FORMATION OF THE FRUIT AND KITCHEN GARDEN. 



15 



above line, 300 feet, may be perfectly level; 

 and if three stakes, one at each end, and one 

 exactly in the middle, are driven in till their 

 tops are level with the ground, as where the 

 lines intersect the rod D, the ground may be 

 laid sloping, by lowering one end below the 

 level, and raising the other as much above it, 

 so that the top of the stake at one end shall 

 then be, say, 1 foot above the ground, and 

 the other 1 foot below it; still the top of the 

 middle stake will be, as formerly, level with 

 the surface, just as a plank supported at its 

 middle between two fixed points may be placed 

 horizontally, or more or less sloping, but the 

 point at the centre will always retain the same 

 position. 



3. To find the direction of a line according to 

 which the surface will form a regularly inclined 

 plane or uniform shape, with the least possible 

 movement of soil. — Instead of the ground being 

 made perfectly level by the line h I (fig. 797), 

 let it be laid sloping with its own soil by a 

 line ip. Place a rod at each extremity, A G, 

 and one exactly in the middle, at D. Find a 

 line that will correspond with the horizontal 

 level of the ground between A and D, and 

 another for the space between D and G. These 

 lines may be found in a similar manner to that 

 by which the line h I was found. Here the 

 total area of the spaces between A and D is 

 200 + 337-5 + 425 = 962-5 square feet. This, 

 divided by the length of base between A and 

 D, 150 feet, gives about 6 feet 5 inches to be 

 measured down from the datum line A G for 

 the horizontal level of the upper half of the 

 ground. The areas of the spaces between D 

 and G are 387*5, 362-5, 450; and their sum, 

 1200, divided by 150, gives 8, the number of 

 feet to be measured down from the line A G 

 for the horizontal level of the lower half of the 

 ground. This is 1 foot 7 inches below the 

 level of the other half. The mean between 

 these levels gives the position of the horizontal 

 line h I of the whole piece. 



Now, whether the surface is reduced to a 

 horizontal level, or whether it is laid sloping, 

 the point in the middle of the horizontal ground 

 line always retains the same position, the same 

 distance from the datum line A g, and it is 

 always at the surface of the ground, whether 

 this be level or formed with a uniform slope. 

 The mean level of both the upper and the lower 

 half of the ground having been ascertained, also 

 the general level of the ground h I, the central 

 point at the intersection of the rod D must 

 always be in the surface plane, whatever the 



inclination of this may be. On this point as a 

 centre the line h I may have one end elevated to 

 any required extent, whilst the other is equally 

 depressed; and still the ground will suffice to 

 level itself to that slope. 



But the question is, how to determine the 

 amount of slope so as to have the least pos- 

 sible quantity of soil to move. This can be 

 done by a line drawn through the centre of 

 the mean higher and lower levels, and such 

 line will also pass through the centre of the 

 general level. The same will be effected by 

 setting up the difference of height between the 

 higher and lower levels from I and down from 

 h, marking the points i p, a straight line be- 

 tween which will give the direction of an 

 inclined plane, requiring less moving of soil 

 to form it than would be the case with any 

 other; and at the same time the ground will 

 not have to be moved to so great a depth in 

 certain places as if a horizontal plane were 

 formed. These are important objects; for, 

 with reference to fig. 797, supposing the 

 ground were to be reduced to a level, and that 

 the portion of bank between A and B extended 

 200 feet, in that case 2670 cubic yards would 

 have to be moved, partly into the adjoining 

 hollow, and partly to the distance of upwards 

 of 200 feet to the hollow between F and G. 

 But by the slope ascertained to be best, the 

 removal of as much as 487 cubic yards is 

 saved, as well as the distant carriage. If the 

 ground were required to be taken down to the 

 level, the depth to be cut down from the sur- 

 face to I would be 4 feet 2\ inches. At that 

 depth solid rock might be met with; but by 

 adopting a slope, the cutting would be reduced 

 to 2 feet 7^ inches. 



Where the subsoil is as easily penetrated in 

 one place as another, and where the surface has 

 to be made of one uniform slope at the least 

 expense, proceed in the following manner: — 



Fie. 70S —Levelling. 



Find the mean levels of the upper and lower 

 halves, as a b and c d (fig. 798), and the difier- 

 ence of their heights, a d, say 4 feet. Half 

 the difference marks the position of h I, indi- 

 cating the mean level of the whole piece. 



