Jan. 28, i9i8 Study of Plow Bottoms i8i 



Solve these equations for x^, y^ and put their values in 



A = [4^2 (x+ c) — 2cz^ — 2>xhr], 



B = {^kzly -\-d)- adz" - 8yk% 



C= [4R~k^-4k^(x^+y^) - 4kxz-4kzy- 4.kRh-hz^(c^ + d?)] 

 A ' = [2kz(x+d) — 2xk'^— 2az^], 

 B'=[2kz(y+b)-2yk^-2bz^], 



a = [R'k^ + k\x^ + f)-4kz(ax+by-R^)i-z\a^ + b^ + ^R^)]. 



_ B'C-BC' 

 ^'~AB'-A'B' 



_ C'A-CA' 

 ^' AB'-A'B' 

 hence {B'C-BCy+{C'A-CAy = R\AB'-A'B)\ (103) 



CYLINDRICAL PLOW BOTTOMS 



In 1854 an American, Joshua Gibbs/ patented a plow bottom the 

 surface of which is a portion of a circular cylinder. Taking a point upon 

 the axis of the cylinder as the origin, the equation of this surface is 



x^ y"^ 



-2 + p-I=C> (104) 



In some foreign countries, notably Germany, the hyperbolic cylinder has 

 been suggested as suitable for forming the surface of the moldboard. In 

 this cotmection it is interesting to note that any cylindrical surface can be 

 described by an equation of the general form. 



^,±^±.=0 (105)= 



mead's plow bottom ^ 



In 1863 a Mr. Mead, of New Haven, Conn., patented a plow bottom, 

 the surface of which conformed exactly to a portion of a frustrum of a 

 cone. The general equation of this surface is 



^ ,^2 ^2 



a' + p-3-« COS) 



holbrook's plow bottom 



The Report of the New York State Agricultural Society for 1867 con- 

 tains a very complete report of the plow trials held at Utica, N. Y., 

 in 1867, at which trials a line of plows designed by F. F. Holbrook, of 

 Boston, Mass., showed general superiority to all other makes. The 



»GouLD. J. S., etal. Op. cit, p. 502. » GotJiD. J. S., et al. Op. cit.. p. S05. 



* Snyder. Virgil, and Sisam, C. H. Op. dt., p. 82. 



27807°— 18 3 



