lyo Journal of Agricultural Research voi. xit. No. 4 



To determine the values of the constants in 



ax^ + by'^ + lx + my+d=0, (45) 



the origin is moved to, x = 7. 65, y = o. 2. This changes the form of the 

 equation to 



a{x'f + h{y'f^l^x'-\-my^O. (67) 



Taking a=i, three constants remain to be evaluated. From the trace 

 of Path V upon the surface of the plow bottom, 



x' y' 



I 3.1 



4 5.45 



7 6.68 



Substituting these values of x' and y' in equation (67) gives 



a= I 

 6= 4.29 

 /i=-3o.85 

 Wi=- 3.67 



(x')' + 4.29(/)'-3o.85%'-3.67/ = 0. (68) 



The axes are translated back to the original origin by substituting 



x = x'-7.6s 

 y = y'—o. 2 



in equation (68), which gives 



ac2 + 4. 29^-46. 15a;- 5. 397+ 295. 45 = 0. (69) 



Numerical Example 

 The surface of a plow bottom is represented by the equation 



o.54x:2— 1.527^+ 1. 123^—3.6972;— 1.62x2 i- 2. o^xy 

 + 53.63X+ ii^-goy- 46.42+ 49.4 = 0. 



The motion of a soil particle which passes upon this bottom at the point 

 x=6.g, y=o.2, 2 = 9.5 is described by the following equations: 



2 = 0.00001622(^2 — 45. 55'+ 342)2 + 5' (70) 



— 0.II922— 1.126^2+ 20.78:^+ 10.032;— 201.63 = (71) 



x^ + 1. Sy^ - 42. 4XX- 1. 5y+ 245.25 = (72) 



s = vt. (47) 



