109 



TifE Mathematics of Haul. 



H. O. Gasman. 



Haul or the average distance earth is moved when taken from exca- 

 vation and placed in embanliment has heen the source of much discussion 

 at different times for many years. For a review of the literature on the 

 subject, "Overhaul," the writer will call attention to the "Proceedings of 

 tlie American Railway Engineering and Maintenance of Way Associa- 

 tion," for 1906, vol. 7, pages 357 to 428. Among the contributors to the 

 subject will be found Italians, French and Germans, but it seemed to 

 excite more interest among our American engineers. 



The methematics of liaul deals, of course, with the methods of com- 

 puting haul and overhaul, but it is the purpose here to discuss more par- 

 ticularly the means for locating the center of mass. These centers of mass 

 may be located by any one of four methods, two algebraic and two graph- 

 ical. All four methods for locating the center of mass fail completely 

 for the volumes adjoining the grade ]K)int unless several extra interme- 

 diate sections are taken. 



In all the calculations a close rapid approximation was used at the.se 

 points 



/ / 



When the ground was a plane surface, the volume next the grade point 

 was assumed at least a wedge, and the center of gravity then taken h 

 the length of the wedge from its base. When the ground was a parabola 

 in longitudinal section, the center of gravity was taken § of the length 

 between section and grade point from the section. 



The four methods of computation were carried on under the condi- 

 tions of the three general tyi)es of i)rofile, i. e. : 



