178 



Journal of Agricultural Research 



Vol. XII, No. 4 



observed in figure 21 that - = tan 6 where d has gradually increased values 



from O at 2=0 to 90° at z = L Further, ^ = ?. radians where 7 represents 



the lengths of arcs 11', 22', etc.; then | = tan QY From figure 20 the 

 equation of the circle with its center at O, taking p^ as the origin is 



In figure 20 



F=2nb cos <l> 



(y-Fy+(z+Gy = 4n^b^ 



<t>+ 7= 90°; 

 B+B'= 90°; 

 a + B'+ 7=180°; 

 <l) = a-B; 



(96) 

 (97) 



G=2nb sin ^ 



= zzzzz — +" 



(98) 



I 



2n6* 



(99) 



Substituting the values for F from equation (98) and for G from equation 

 (99) gives 



| = tan[/(2)], . (100) 



which is the equation of the surface. 



rahm's plow bottom ^ 



In 1846 Rev. W. L. Rham, an Englishman, brought forward the 

 theory that the lines of the moldboard running in the longitudinal 



direction should be 

 T— jL..^^^^ y straight, but that the 



section of the mold- 

 board formed by any 

 plane z = c (fig. 22) 

 should be a straight 

 line or a curve, ac- 

 cording to the phys- 

 ical characteristics of the soil to be worked. Mr. Rham agreed that 

 for medium, mellow soils the surface of the moldboard should be 



' Gould, J. S., et al. Op. cit., p. 442. 



^<J 



From Report of N. Y. State Agric. Soc. 1S67. 

 Fig. 22. 



