82 



JOURNAL OF THE 



TO SET SLOPE STAKES WHEN THE SURFACE 

 IS STEEP RUT SLOPES UNIFORMLY. 



BY J. M. BANDY. 



Let mn represent the surface of the ground. Let C repre- 

 sent the position of the centre peg, and let CD (=<?, the 



value of which is 

 found from the level 

 notes) represent the 

 centre cut. The 

 width of the road, 

 BA, is b. 



It is proposed to 

 find what engineers 

 designate as cuts at P, P\ S, and T. 



In the direction of P, and in connection with C, one 

 setting of the rod determines the slope of the ground mn. 

 Call this slope in. Now, since the cds. of C are (^;, a), the 

 equation of the surface, ;;/;/, is 



y = mx -T a^ (i). 



The quality of the soil determines the slopes of PA P^B. 

 Call this slope ;;/\ 

 equation of PA is 



Then since the cds. of A are (^, o), the 



m'b 



y 



(2). 



Combining (i) and (2),. the cds. of P are known. Hence 

 the cut at this point is known. 



Designating the cds. of P, just found, by (.1-", y^) and 

 the cds. of C by {x\ y^) \_=[o, a\\ 



CP = ^(.r^^ - x^)' + (j" -yj, (3). 



Then measure this distance, CP, and fix stake at P. 



