Mechanical Conditions of the Plow. 187 



in area and periphery. Suppose, again, a slice whose sides, a I, 

 is less than the corresponding side, a c, and let it be six inches; 

 from I through the point ^, as before, draw I m, and construct the 

 parallelogram, aim n, we- shall have a transverse section of a 

 third slice of ten by six inches, whose exposed faces, a I, lb, 

 occupy the same horizontal breadth as before. Here the triangle 

 alb lies between the parallels a b and i' k', consequently to afb, 

 and less than a c b. 



This simple geometrical demonstration as applicable to the slice 

 may be corroborated by the usual formula of the triangle. Thus 

 the altitude of the triangle acbis'^-^ = ^ inches == c c', and the side 

 a c or c b is = ^a c^-{-g c^; or a c and c c being each equal to five 

 inches, a c or cb will = V 25 + 25 = 7 • 071 inches, which is the 

 depth due to a slice of ten inches in breadth, and the sum of the 

 two exposed faces will be 7 • 071 + 2 = 14 • 142 inches. 



In the triangle a f b, a b = 10 inches, and a f = S inches, 

 then ab^ — af =fb'^, and the V/^^ = ^ inches. The three 

 sides, therefore, of this triangle are ten, eight and six inches, 

 and the altitude,//', is easily found by the principles of similar 

 triangles. Thus, in the similar triangles, a //',/ bf', a b : a f 

 • • / ^ • //'• The perpendicular//' is therefore = 4-8 inches, 

 hence the exposed surfaces are as 14 • 141 : 14, and the altitudes 

 as 5 to 4 • 8. 



Since it turns out that a I is equal to f b, and a 5 is common to 

 both, it follows that I b is equal to a / and the periphery and 

 altitude is also equal and less in all respects than the triangle 

 a c b, and so of any other position or dimension. 



By recurring to Fig. 94, it will be seen that when the furrow 

 slices are laid at an angle of 45 degrees, a triangular drain, g d h, 

 is left under each furrow. This not only drains off the surface 

 water, but allows the air to enter freely beneath the surface, 

 which, in conformity with what has been said in the preceding 

 section, is of very great advantage, and strongly recommends the 

 adoption of this mode of plowing in stiff and retentive soils. 



It will follow, from what has been stated, that the proportion 

 of the depth to the width must always be in the ratio of 2 to 3. 

 Six inches deep and nine inches broad, or seven inches by ten, 

 are the most usual proportions. 



Fig. 96 illustrates the action of the plow in this style of plow- 

 ing; a b is the exterior edge of the slice which is being turned; 

 e f is the edsje along which the land side of the plow has just 



