164 



Journal of Agricultural Research 



Vol. XII, No. 4 



Fig. h. 



These observations reveal, first, that when a cross section of the furrow 

 slice is considered (fig. 12) the portion marked "A" is compressed in 

 plowing and the portion marked "B" is stretched, while the soil in the 

 position of line /; is neither compressed nor stretched; and, second, that 

 there is a definite relation between the z coordinate of a soil particle and 



the distance the plow has moved for- 

 ward. This relation is developed on 

 pages 164 to 167. 



The next step was to analyze in detail 

 the motion of the soil particles. This 

 study was limited to the soil particles 

 upon the bottom of the furrow slice, but 

 the methods developed are applicable to 

 other portions. The paths of the soil particles upon the bottom of the 

 furrow slice can be very accurately traced from the scratches which 

 they make upon the moldboard. Plate 9, B, shows the paths of five soil 

 particles. By taking the axes as shown in figure 8, a projection of these 

 paths upon the plane z-0 showed a very uniform set of curves. Each 

 of these curves (fig. 13) can be very accurately described by equations 

 of the general form 



aoc^ + b'f + lx + 'my + d = 0. (45) 



When these same paths are projected upon the plane y = 0,Q. set of curves 

 resulted (fig. 14), each of which could be very accurately described by 

 equations having the following general form : 



ax'^-\-hz'' + lxz + inx + nz + d = 0, (46) 



From equation (45) 



-~- and -jZ the veloc- 

 dt df 



ity and acceleration, 

 respectively, of a soil 

 particle in the y direc- 

 tion can be found if 



dx d^x 



-jr and -j^ are known. 



dt df 



dx 



The values of —r, 



dt 



(Px 

 df 



and 



- I I I I I r+y t-'r 



/S I* 13 12 // 10 



can be found from 



dz 

 equation (46) if -7- and 



d^z 



-Ta are known. Thus, 



to analyse the velocity and acceleration of any soil particle whose path 

 upon the surface of the plow bottom is known, an equation must be 

 found between z and time (/). 



Fig. 



-Projectiou of tlie paths shown in Plate 9, A, upon plane 



2 = 0. 



