Preparation of Diagram

CHAPTER VII.

Quantities of Materials (Cont'd).

II. Volumes from Original Contours.

2. Grading Over Extended Areas.

Preparation of Diagram.

In the diagram let the elevation marked Grade be the final height to which the surface of the lot is to be brought, and let the lines marked 2.0, 4.0, 6.0, etc., be counter lines of the original surface or lines of intersection of the original surface of the ground with equidistant, parallel, horizontal planes— the cutting planes being two feet apart vertically— and the numbers at the end of each contour being the number of feet that the given plane is above the Zero or Grade plane to which the surface of the lot is to be brought by excavating.

It is evident that by passing these parallel, horizontal planes in the manner described we have divided the total volume of material necessary to be excavated to bring the surface of the lot down to the desired surface into ten continuous prismoids, having for their respective bases the areas included within the contour lines and the intercepted portions of the two sides of the lot, and for their lengths the vertical distance between the horizontal cutting planes, which in this case has been taken as two feet.

As we have assumed the excavation to be vertical at the sides of the lot, we have as the upper base of our first prismoid the area included between the Contour line 20.0 and the intercepted portions AB and AC of the sides of the lot, while the lower base of the prismoid is the Area included within the Contour line 18.0 and the intercepted lengths AD and AE of the sides.

The second prismoid has the area ADE for its upper base and the area AFG for the lower base, and so on to the last prismoid, whose upper base is evidently the area AMNV and whose lower base is the area ARSTV: the length of each prismoid being equal to the vertical distance between the cutting planes, is of course two feet.

Since these prismoids are continuous, the lower base of one prismoid being also the upper base of the one below it, it is evident that we can apply to it the same method of measurement as explained in our previous discussion of Railroad excavation under the head of “Continuous Prismoids.” To do this in this case, two adjoining prismoids, each having a length of two feet, are considered as a single prismoid having a length of four feet. The upper base of one prismoid and the lower base of the other prismoid are thus taken as the even A's of Eq., 14 and 15 Pg. 66 while the intermediate A's are evidently the odd A's of the same Equation.

In the particular example we are discussing, since there are 10 prismoids each 2 ft. in length, the total volume would be considered as the volume of 5 prismoids each having a length of 4 ft., and the demonstration would be exactly the same as in the previous case, and hence does not require further repetition here.

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