Jan 28,1918 Study of Plow Bottoms 167 



particle passed upon the share at the point i^=ii.6, the point of 

 maximum stretching occurs at 5^ = 25.8 inches. 



40 — 11.6 = 28.4 inches. 

 28.4^2 =14.2 inches. 

 14.2+ 11.6 = 25.8 inches. 



The following is the simplest form of a function which meets the 

 requirements imposed by the above conditions and, when the constants 

 are determined, will describe the relations between 2 and ^ for a soil 

 particle on the bottom of the furrow slice as it passes over the surface of 

 the plow bottom: 



z — s = a{r + hs+cf (48) 



From equations (47) and (48) 



z-vt=a[{vtf + hvt+cY; (49) 



dz d^z 



From (49) -j7 and -^ , the velocity and acceleration, respectively, of a 



soil particle in the z direction can be obtained. 

 From equation (46) by differentiation we have 



dx dz 



{2ax+lz+fn)-^+ {2bz+lx+n)-j- = 0; (50) 



and 



+ (26^+/x+«)y,+(.6^ + /^j^-0. (51) 



Similarly from equation (45) we find 



and 



(2a^ + 0j+(26:v+m)^=O; (52) 



(2a. + //^+ -(!>+ (^^y+-)g^+ ^<|>= O. (53) 



. dx dy 



From equations (50), (51), (52), and (53) the velocities -j., ^-, and the 



d X d/^ 

 accelerations -yw, -r^- of a soil particle on the bottom of the furrow slice 



dz d/Z 



can be obtained when -n and -j^ are known. 

 at dr 



In this problem, however, we are interested in the accelerations in the 



directions of the normal to the surface, designated by "A^," the tangent 



to the soil path " T," and the perpendicular to the plane formed by the 



normal and the tangent "7?." 



