i6o 



Journal of Agricultural Research 



Vol. XII, No. 4 



For the X-axis 



For the V-axis 



For the Z-axis 



7= T0.6136 

 H= =Fo.48 

 v= ±0.627. 



7= ±0.7515 

 M==Fo.i437 

 u= ±0.6445. 



T0.1415 



±0.828 



±0.5425- 



Figure 10 shows the axes after translation and rotation and the por- 

 tion of the hyperboloid of one sheet which is a close approximation 



to the surface of this plow 

 i^ bottom . 



SURFACES ONE PORTION FROM 

 EACH OF TWO QUADRIC 

 SURFACES 



Fig, 10. 



were obtained from the share 

 board. 



By the use of the method 

 which has just been em- 

 ployed to develop the equation 

 of the surface of the plow 

 bottom shown in Plate 6, 

 A, two equations can be 

 developed which will approx- 

 imately represent the surface 

 of the bottom shown in 

 Plate 6, B. By taking the 

 origin as at O, figure 8, the 

 data of Tables III and IV 

 and the front portion of the mold- 



Table III. — Values {in inches) developed for the surface of the share and front portion 

 of the moldboard of the plow bottom shown in Plate 6, B 



Xi= 3.92 



yi= 



2i = 



^4= 



3^4 = 



.8 

 8.0 



= 6.78 



= 1-75 

 = 16.0 



X2= 7-4 



y2= -75 

 £2=12.0 



.1:5= 2.36 



r5= 4-05 

 25=15-0 



••^3= 1-73 



)'3= 2.67 



23=12.0 



•1^6= 5-87 



}•&= 2.7 



0.25%' + 2.34^^ + 0.462^— 3.2572— o.77a!;2: + 2. 66:^^ 



+ 6.88a; + 32.3>/- 



5.812-4.4 = (43) 



