PREPARATION OF THE DESIGN 87 



3,200 cub. ft. There are six blocks over which this 

 amount has to be distributed which gives an aver- 

 age of 3-^- cub. ft = 533^ cub. ft. Dividing by 



10 for the breadth, and 10 for the distance be- 

 tween the levels gives 5j for the height of the 

 horizontal line to which the whole surface can be 

 worked. 



An examination of the foregoing method shows 

 that every figure has been taken twice except the 

 first and last, and a shorter method may accord- 

 ingly be followed. Add half the sum of the first and 

 last perpendiculars to the sum of all the rest, and 

 divide the result by the sum of their number minus 

 one. Thus from the same example we have 



^tJ: + 8+5+6 + 4 +2)- 7-1. 



==(7 + 8 +5 +6 +4 +2) -6 = 32 -6 = 5* ft. 



Unless the levels were taken at uniform dis- 

 tances this last method is unworkable, as difference 

 in the space between the perpendiculars is ignored 

 by it. Therefore if levels have been taken irregu- 

 larly the first method must be used, each block 

 being reckoned by itself. 



Supposing that the aforesaid strip of land is not 

 to be levelled but to be laid in a uniform slope, 

 moving as little soil as possible proceed in the 

 following manner. 



Divide the strip into two equal portions and 

 reckon each half separately for its mean level. 



