I50 



Journal of Agricultural Research 



Vol. XII, No. 4 



to meet certain field conditions; but no well-developed theory is avail- 

 able to serve as a guide in this work. 



This paper is an attempt to begin a fundamental analysis of the plow 

 bottom and its work, in the hope that some light may be thrown upon the 

 theory of this humble but perplexing machine, and other attempts stimu- 

 lated to delve further into the secrets which are still to be revealed 

 regarding the theory of this important implement. Empirical methods 

 have given the world plow bottoms which work well. It is still to be 

 hoped that scientific investigation can refine and further perfect, supple- 

 ment as it were, the productions of experience. 



The work undertaken by the writer can be naturally divided into three 

 parts: (i) A study of the forms of plow bottoms; (2) an attempt to 



Pig. I. — Diagram giving the generatrices, directrices, and equations of surfaces of historical plow bottoms . 



analyze the motion of the soil particles as they pass over the surface, 

 and (3) a mathematical analysis of the surfaces of the most important 

 historical plow bottoms which were designed to be geometrically exact. 

 It was, and still is, hoped that a knowledge of just what the plow bottom 

 is and how it performs its work will be of material assistance in developing 

 a theory which will furnish a very definite basis for the proper design of 

 this fundamental implement of tillage. 



FORMS OF THE PLOW BOTTOM 



A study of modern American-manufactured plow bottoms reveals 

 the fact that a large number of these are so constructed that their surfaces 

 contain sets of straight lines, each set consisting of an infinite number of 

 straight lines, so related that an equation or equations satisfied by the 

 coordinates of points on the surface can be found. 



