186 



Report on Trials of Plows. 



equal a b, the breadth of the slice, which must always be equal 

 to the distance between the apices of two contiguous furrows. 



Complete the parallelogram, a c cl e, which will represent the 

 transverse section of a rectangular slice, whose breadth is ten 

 inches, and whose two exposed faces, a c and c b, lie at angles of 

 45 degrees, and their breadth, as well as the area of the triangle, 

 a b c, will be a maximum. In order to prove this, let a section 

 of another slice be formed, whose exposed side, a f, shall be 

 greater than the corresponding side, a c, of the former, and let 

 this be taken at eight inches. Fromy, through the point 6, draw 



f g; then will af b be a right angle as before; f g, being also made 

 equal to ten inches, complete the parallelogram, afgr h, which 

 will represent the transverse section of a rectangular slice ten 

 inches by eight inches, occupying the same horizontal breadth as 

 before, and whose exposed faces will be a / and / b. Draw the 

 line i c k parallel to a b, and passing through the apex, c, of the 

 triangle, a c b; and the line i k, also parallel to the line, a b, 

 passing through the apex, /, of the triangle, a f b. Here the 

 triangles, a c b and afb, stand on equal bases, a b; but the first 

 lies between the parallels a b and i c k, and the second between 

 those of a 6 and i' k'; the altitude,//', therefore, of the triangle 

 a f b is less than the altitude, c c', of the triangle, a c b. And 

 triangles on equal bases being proportioned to their altitudes, it 

 follows that the triangle afb is less than the triangle a c b, both 



