Problems. 



127 



Art. XI. — Problems; by D. C. Lapham, Civil Engineer. 

 Problem I. 



To find the area of a cross section of a canal, when the surface is 

 inclined. 



Given BC, At, Dm, (Fig. 1,) and the ratio of the side slopes, {Cm 

 to Dm,) to find the area. 



A Fig. 1. 



k\ 



Area of EBCD=BC + CwxDot. Area of AED=EDx JAA;. 

 Area of ABCD=AED + EBCD. 



Ppoblem II. 



To find the cubic content of a portion of canal excavation, when 

 ihe surface inclines both in the direction and across the line of the 

 canal. 



Let ABCD, abed, (Fig. 2,) be a portion of canal, of a given length; 

 the perpendicular depth also being given at A, a, d, D, and the ratio 

 of the side slopes, to find the cubic content. 



Fig. 2. 



Rule. — Find, by Prob. I, the area of the cross sections ABCD, 



abed ; also the area of the middle cross section cfgh, (which is dedu- 

 ced from the given depths thus, A+ff-^2= depth at e, D+t/-^2 = 

 depth at h.) 



