Jan. 25. 1918 Study of Plow Bottoms 151 



Plate 6, A, represents a bottom with two sets of straight lines. The 

 few lines shown in the illustration indicate that through every point of 

 the surface two straight lines can be drawn which lie wholly on the surface 

 until they pass off the edges of the bottom. These straight Unes furnish 

 the basis for the proof that such a surface is a portion of an hyperboloid 

 of one sheet (for the form of this surface see fig. 3 to 7) whose equation 

 can be developed and studied with mathematical exactness. The 

 method of developing this equation will be given later, but at present we 

 are mainly interested in the fact that there is a classs of plow bottoms on 

 whose surfaces lie sets of straight lines, and, further, that one equation can 

 be developed which Vv'ill approximately represent the working surface of 

 such a bottom. 



Further study shows that the surfaces of other plow bottoms contain 

 sets of straight lines, but that one equation will not completely describe 

 such a surface. In Plate 6, B, a bottom is shown whose surface is com- 

 posed of a portion of each of two surfaces. Plate 6, C, shows a similar 

 bottom, but in this case the two surfaces merge into each other farther 

 back upon the moldboard. 



In Plate 6, D, a class of bottoms is represented whose entire surfaces 

 do not contain an inlinite set of straight lines. It is true that the share 

 and back end of the moldboard exhibit the same characteristics that the 

 first two classes have shown, but the lines do not continue to the fore part 

 of the moldboard. 



Plate 7, A, shows a plow bottom with a convex surface which has two 

 sets of straight lines. 



The American-manufactured plow bottoms studied can thus be 

 divided into three general classes: (i) A portion of one quadric surface; 

 (2) a portion of each of tv/o quadric surfaces, and (3) nonquadric sur- 

 faces. Nearly all forged bottoms belong to classes i and 2 with the 

 majority falling into class 2, while most of the cast bottoms belong to 

 class 3. It should be noted, however, that some recently designed cast 

 bottoms depart from the general characteristics of class 3 and show 

 clearly the two quadric surfaces of class 2. The lines running in the 

 general direction, front to rear, marked "/," (PI. 6, A) will be called 

 longitudinal lines, and those running in the general direction, top to 

 bottom, marked "t" (PI. 6, A) will be called transverse lines. 



For the purpose of studying the forms of the various surfaces under 

 consideration, a machine, illustrated in Plate 7, B, was designed and built 

 for measuring the space coordinates of any desired point. ^ By means 

 of slots and a system of pulleys attached to the drafting board the cross- 

 bar can be kept horizontal and be moved both laterally and vertically, 

 while the drafting board is attached to a frame which can be moved 



' Similar machines are described in the following publications: Gould, J. S., et al. report on trials 

 OP PLOWS. /» Trans. N. Y. state Agr. Soc, V. 27, pt. I, 1867, p. 426. 1868. 

 Giordano, Fedetigo. le ricerche sperimentali di meccanica agrarl\. p. no. Milanu, 1906. 



