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. 1. 3 and those corresponding to angles of 

 depression for cuttings, and elevation for embankments, are 

 talicn from Table 5Jo. 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 cvitting 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 

 \\, 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 Avould 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 formulte 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 ABODEFGH (Fig. V.) represent a portion of railway 

 cutting between consecutive stakes, and let the sidelong angle 

 of inclination H G be not equal to the sidelong angle of in- 

 clination D C at the other end of this earthwork. In the first 

 place it is evident that the surface r» c o H is not a plane 

 surface, but a contorted surface, and it may be conceived to 



