54 Report on Trials of Flows. 



each division of the length, while the degree of flexure in the 

 curve or line of transit remains uniform by the same, from any 

 one point to any other equidistant points. 



To convert the prism thus prepared and lined off" into that of 

 the twisted wedge, we have only to cut away that portion of it 

 contained within the boundaries abed x, preserving the terminal 

 edges ab, ax and dx, and the prism will thus be resolved into a 

 form represented by a joortion, a b d x e, of Fig. 125, also in 

 isometrical perspective. Of this figure, ab d x is the true theo- 

 retical surface of the mould-board, from the edge, a b, of the share 

 to the zero line, dx; ab ex is the sole; the curve, b p n m /, etc., 

 is the Ihie of transit of the slice, and the triangles, lyi, 2'(7 2, 

 oil 3, 4V4, etc., are vertical planes, supposed to cut the solid thus 

 reduced in the divisions 1, 2, 3, 4, etc., to the height of the line 

 of transit, as in the analytical sections of the mould-boards. 



The surface, now completed, can only raise the slice to the per- 

 pendicular position; and, to complete the operation, we have to 

 carry the twisted wedge back till it shall place the slice at the 

 angle of 45 deg. To do this we have to extend the original 

 prism, or suppose it to have been at first sufiiciently elongated 

 toward d d', Fig. 125, Plate IV., and to superimpose upon its flat 

 side the portion d d' ux, or a du of Fig. 126. The part d d' u x is 

 now to be worked off into a part of a new cylindrical surface, 

 whose radius is yd or y u, Fig. 126, and upon this surface the line 

 du, Fig. 125, is to be drawn tangent to the curve b d at d. A 

 continuation of the divisions of three inches is to be made upon 

 the line d d\ and the parallels a' q', b' r' and u d' continued on 

 the cylindrical surfaces. Whatever portion of the superimposed 

 piece, a d' u, may be found to fall within the small arc, a t, Fig. 

 126, is to be cut away, forming a small portion of an interior 

 cylinder concentric to the point y, which, being done, the remain- 

 ing portions of the superimposed piece are to be cut away to the 

 (lotted lines d x, a y, b z, u ii' of Fig. 125, or, what is the same 

 thing, to the lines d a, a' a, b' t and u t of Fig. 126, forming tan- 

 gents to the curves at a t, and which will complete the surface 

 of the tAvisted wedge through its entire length, and to the height 

 of the line of transit, producing what I conceive to be the tvae 

 theoretical surface of the mould-board. 



Fig. 126, Plate IV, exhibits distinctly in the quadrants o b d, 

 the inequality of the angles of ascent for the slice, where the 

 radii a ]>', a n', a rii\ k(;. repi'cscnt the ascents to the correspond- 



