126 OPERATIONS OF TILLAGE. 



the position G H I K, corresponding with that of fig. 16. 

 In this manner the side D C, which was formerly un- 

 derneath, will be above, namely, in the position H I ; 

 and if successive shoes be thus reversed, they will rest 

 upon each other in the manner shown by the section of 

 the slices P Q R S, O L M N, and G H IK. 



" The angle of inchnation at which these different 

 shoes will naturally rest upon each other in the manner 

 shown in the figure, will depend upon the proportion which 

 the width of the slices bears to their depth ; and that the 

 greatest extent of surface may be exposed to the air, the 

 angle of their inchnation will be 45°. In order, there- 

 fore, that the slices may be at this angle, the proportion 

 which the width of the shoes bears to their depth is to be 

 determined ; and this can be done by simple calculation ; 

 for it can be shown that, the width of the slice A B being 

 the hypotenuse of an isosceles right-angled triangle, the 

 depth of the slice B C will be one of the sides. Sup- 

 posing, therefore, the width of the sod A B to be ten 

 inches, the depth B C will, by calculation, be 7.071 

 inches. 



'' If, then, beginning at one side of a field, we shall cut 

 off a shoe of earth, the entire length of this field, and place 

 it in the position P Q R S, fig. 17, and then cut off a 

 second slice, and place it in the position of O L M N, 

 and then a third shoe, and place it in the position 

 G H I K, and so on, the various slices will rest upon 

 each other at a given angle, in the manner represented. 



" A similar operation is to be performed by the plough. 

 Beginning at the right-hand side of the field or ridge to 

 be ploughed, a sod, which we shall now call a furrow- 

 shce, is to be cut from the firm ground, raised up and 

 turned over, and so on. In this manner, an entire new 



5^ A' t> / ^^ i.<^- ^-^^i^'' r 



