82 Rules and Tables adapted 
The tabular multipliers corresponding to angles of eleva- 
tion for cuttings, and depression for embankments, are taken 
from Table No. I.; and those corresponding to angles of 
depression for cuttings, and elevation tor embankments, are 
taken from Table No. II. Whenever the product of the 
horizontal half width (in column 6), by a tabular number, is 
less than the half base, it is an indication that there will 
be both cutting and embankment on the same side of the cen- 
tre stake. This is the case on the left side of stake No. 49 
of the given example; and the required side distance, in this 
instance, is obtained by deducting from the half base, or 15, 
the product of the height 1:2 by the slope of embankment 
14, and then multiplying this difference by the corresponding 
tabular number 1:175, taken from Table II., in accordance 
with the Formula No. III. 
Formula for occasional use in computing the volume of a por- 
tion of a Cutting or Embankment between two consecutive 
centre pegs, when the sidelong inclination differs considerably 
at each peg. 
I VENTURE to submit the following investigation of the 
volume of earthwork having rapidly changing profiles; as 
any rule that would tend to the attainment of greater ac- 
curacy in the computation of cubic contents in such cases, 
might be sometimes applicable in this colony, where the 
great cost of earthworks renders precision in the estimated 
contents thereof a matter of very great importance. 
The French have made long and complicated investigations 
in connexion with the subject of deblais and remblais, but 
their formule are too abstruse for any practical application, 
and their tables for facilitating ordinary computation of 
earthwork, are less convenient than Bidder’s improved tables 
and some others in use by British engineers. 
I am indebted to the French for the hypothesis of the 
mode in which the surface of the ground may be conceived 
to be generated in the following investigation ; but the in- 
vestigation itself, and comparatively simple formula obtained, 
are my own. 
Let ABCDEFGH(Fig. V.) represent a portion of railway 
cutting between consecutive stakes, and let the sidelong angle 
of inclination H G H’ be not equal to the sidelong angle of in- 
clination D Cc D! at the other end of this earthwork. In the first 
place it is evident that the surface D C G H is not a plane 
surface, but a contorted surface, and it may be conceived to 
