Jan. 28, 1918 



Study of Plow Bottoms 



175 



a helacoid generated as follows : Lay out a rectangle opan (fig. 1 6) twice 

 the desired width of the furrow and of an empirically determined length. 

 Take the point m midway between points and p and draw the line mm 

 parallel to pq. A straightedge laid upon mo and moved backward along 

 the line mm,^ being kept 

 parallel to the plane 

 z = 0, and with an 

 angular rotation pro- 

 portional to the move- 

 ment toward m^, gen- 

 erates the surface of 

 the Lambruschini bot- 

 tom. The point of the straightedge which was at will describe the 

 helix 00i7 (fig. 1 6) . The equation of this surface is 



-=tane, 



X ' 



where 9 has uniformly increasing values as 2 increases. 

 Then d=f (z), when = 90°=— radians, 



Fig. 16. 



/ = length of line mnii 



^ = 2' 



2 2 



n 



Hence, 



f=Kr> 



(90) 



small's plow bottom ^ 



About 1760, a Scotchman, James Small, established a factory in 

 Scotland for the manufacture of plows. The surface of Small's mold- 

 board is obtained by 

 laying a straightedge 

 upon op (fig. 17) and 

 moving it backward 

 parallel to the plane 

 2=0, with the line pvi 

 and the curve oh as 

 directrices. The equa- 

 tion of the curve, a half 

 catenary, is obtained by 

 drawing a line og (fig. 18) the length of line og (fig. 17). At o erect a line 

 ooj perpendicular to line og and equal in length to line gh (fig. 17). 



' Gould, J. S., et al. Op. at., p. 415. 



rrom Report of N.Y.Sfote Agric50C. I3S7 



Fig. 17. 



