object in the immediate vicinity, such as the rim of a
manhole cover, a rod, or the finish floor of an existing
structure. This object may be given its relative sea
level elevation (if it is known); or it may be given a
convenient, arbitrarily assumed elevation, usually a
whole number, such as 100.0 feet. An object of this
type, with a given, known, or assumed elevation,
which is to be used in determining the elevations of
other points, is called a bench mark.
PRINCIPLES OF DIFFERENTIAL
Figure 5-15 illustrates the principle of differential
The instrument shown in the center
represents an engineers level.
instrument provides a perfectly level line of sight
through a telescope, which can be trained in any
direction. Point A in the figure is a bench mark (it
could be a concrete monument, a wooden stake, a
sidewalk curb, or any other object) having a known
elevation of 365.01 feet. Point B is a ground surface
point whose elevation is desired.
The first step in finding the elevation point of
point B is to determine the elevation of the line of
sight of the instrument. This is known as the height of
instrument and is often written and referred to simply
as H.I. To determine the H.I., you take a backsight
on a level rod held vertically on the bench mark
(B.M.) by a rodman.
A backsight (B.S.) is always
taken after a new instrument position is set up by
sighting back to a known elevation to get the new H.I.
A leveling rod is graduated upward in feet, from 0 at
its base, with appropriate subdivisions in feet.
In figure 5-15, the backsight reading is 11.56 feet.
Thus, the elevation of the line of sight (that is, the
H.I.) must be 11.56 feet greater than the bench mark
elevation, point A. Therefore, the H.I. is 365.01 feet
plus 11.56 feet, or 376.57 feet as indicated.
Next, you train the instrument ahead on another
rod (or more likely, on the same rod carried ahead)
held vertically on B.
This is known as taking a
foresight. After reading a foresight (F.S.) of 1.42 feet
on the rod, it follows that the elevation at point B must
be 1.42 feet lower than the H.I. Therefore, the
elevation of point B is 376.57 feet minus 1,42 feet, or
The term grade is used in several different
senses in construction. In one sense, it refers to the
steepness of a slope; for example, a slope that rises 3
vertical feet for every 100 horizontal feet has a grade
of 3 percent. Although the term grade is commonly
used in this sense, the more accurate term for
indicating steepness of slope is gradient.
In another sense, the term grade simply means
surface. On a wall section, for example, the line that
Figure 5-15.Procedure for differential leveling.