Jan. 28, 1918 



Study of Plow Bottoms 



177 



As this line is always parallel to the plane 2; = O, it follows that c = 2 and 



f(c)=nz). 



From equations (92) and (94) then, 



(x - &)[ J (e^iz /3ba + g-2iz /3ba) _ ^1 _ y ?^^ -b\ = 0, (95) 



which is the equation of Small's moldboard. 



STEPHEN'S PLOW BOTTOM * 



About the same time that Small brought out his moldboard another 

 Scotchman named Stephens developed a method for forming the surface 



f/x>m Report ofNYSfoHAgric SoC- 1867 

 Fig. 19. 



From Report of N Y Star-^ Aqric Soe /36T 

 Fig. 21. 



V^A 



Fig. 20. 



of a moldboard the general plan of which is shown in figure 19. The 

 generator for this surface is a straightedge laid upon op (fig. 19) and moves 

 backward parallel to the plane z=0 with the line on and the curve ph as 

 directrices. Stephen designed his surface by taking a quarter cylinder 

 opmnhg and laying out p^vti (fig. 20) equal in length to pm (fig. 19). 

 Perpendicular to line pj^m^^ draw mjii equal to the length of arc mh (fig. 

 19). Through points p, h^ (fig. 20) pass a circle of radius 2nb. The plane 

 figure p^m^hyh^ (fig. 20) is then laid upon the quarter cylinder (fig. 19) 

 so that /?! falls upon p, m^ upon m, and h^ upon h. This will locate the 

 curve ph (fig. 19), leaving a figure as shown in figure 21. It will be 



'GoutD. J. S., ct al. Op. cit., p. 431. 



