Jan. 28, 1918 Study of Plow Bottoms 1 69 



EVALUATING THE CONSTANTS IN EQUATIONS (48), (46), AND (45) 



The methods of evaluating the constants in equations (48), (46), and 

 (45) for a given soil path will now be considered. For this purpose 

 Path V (PI. 9, A) will be taken. The general form of equation (48) is 



z-s = a(s^ + bs + cy. (48) 



From the assumptions that have already been made (p. 164 to 168) the 

 following data for this curve are obtained : 



On substituting the above values for s and z in equation (48), three 

 equations are obtained from which it is found that 



a = o.ooooiii4 

 &=-5i-6 

 = 464 

 giving 



z— s = 0.00001 II 4{s^— ^i. 6s +4.64)^ (63) 



To determine the values of the constants in 



ax^ + bz^ + lxz + mx+nz + d^O, (46) 



the origin is moved to ^=7.65, 2=11.6. For this point as origin an 

 equation of the following form describes the curve ; 



a(x'y + b(zy + l^x'z' + m,x'^0. (64) 



Taking a=i, only three constants, b, l^, and m^, remain to be evaluated. 

 From the trace of Path V on the surface of the plow bottom the following 



gives 



rt^- 0.0192^-0.453x2- I. 4501+3. 912-49. 92 = 0. (66) 



