IS47.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



203 



cuttiiig at tlie two ends measured from the formation level; c the 

 breadth of the formation level; and r the slope: — then 



2r 



+ h 



a; 



_ + A' = 6. 

 2r^ 



But the quantity of parlhwork is equ.il to the volume of the above 

 frustum (if a pyramid, minus lliat portion which lies below the forma- 

 tion level; and tliis litter portion is a prism, bounded by two triangles 

 at the ends, the areas of which are, for a slope 1, (A — «)■; conse- 

 quently, if L were the length in chains of such a prism, its cubic con- 



22 22 r 



tents would be -^ . L (A — a)" ; and for a slope r -j- • L (n — A)' : 



.'. the quantity of earthwork taken for L distances, a chain apart, 

 and a slope r would be 



r.:S. J (a' + ab + b') — ^ L(a-A)=. 



22 

 In Mr. Bashforth's tables, — (a- -j- a6 + b-) is tabulated for all inte- 

 ger values of a and b, from a ^ to a = G5, and 6 = to 6 ^ (35 ; 

 and a scale of proportional parts is added, to extend the calculation 

 to decimal parts of a foot. 



Example for Equal Distances. 



To show how to use the tables, we wiU take out the following ex- 

 ample, working it first by Mr. Bashforth's, and then by Mr. Bidder's, 

 method : — 



Heights from formation level at distances a chain apart, 30, 40, 

 25,35; breadth of formation level, 30 feet; slope, IJ in 1. 



Mr. Bashforth's Method. 



To find the quantity to be added to each of the heights, divide Italf 

 the base by tlie slope: tlien 14 -;- \% ^8. Adding this quantity to 

 the heights, and taking the corresponding figures from Mr. tJashforth's 

 table, we have the following scheme : — 



Heights. Tabular Numbers. 



38, 48 4540 



48, 33 4055 



33, 43 3550 



12145 

 Subtract "^ X length (3 ch.) X square 



of the additional height (8) 469 



11676 



13 (the slope) 

 20433 cubic yards, (Ans.) 



Mr. Bidder's Method. 



238-4 

 28 (base) 



7863 



1| slope 



6675' 



13760 

 6675 



20435 cub. yds. (Ans.) 



Example for Unequal Distances. 



In the last example the sections were supposed to be taken at every 

 chain. If, however, we take the sections at unequal distances, the 

 difference betiveen Mr. Bashforth's method and Mr. Bidder's is more 

 npparent. In both, the tabular numbers have to be multiplied by the 

 distances; but as there are /»o tabular numbers in Bidder's table for 

 every distance, the number of multiplications is doubled. 



Let the sections be taken at distances 3, 2-3, 2, 1, chains, respec- 

 tively. Let the heights be 40, 30, 20, 15, and 10. The slope li to 1 ; 

 the base 25 feet. 



Mr. Bashforth's method. 

 The addition to the heights is half 25 -^ li = 10. Making the 



addition, taking the numbers from the table, and multiplying by tho 

 corresponding distances, vte have 



Subtract ''i X (10)= x 8^ 



Mr. Bidder's Method. 



27398 

 2077 



25321 



U (slope) 



31651 (Ans.) 



525-7 14810 



25 (base) li (slope) 



13142 



18512 

 13142 



Tot.il cub. yds. 31654 {Ans.) 

 Maciieill's method does not, like the above, give a general table for 

 all slopes and bases and any combination of them, but a number of 

 special tables of particular slopes combined with particular bases. 

 This method not being general, it would require not a volume, but a 

 library, to contain tables of all combinations of slopes and bases which 

 occur in railway practice. The cases above taken (for example) are 

 altogelher omitted in Macneih's tables. But wherever these tables 

 do apply, the arithmftical operations are nearly the same as Mr. 

 Bashforth's: and consist in multiplying the tabular numbers by the 

 distances, and adding the results. 



The great value of Mr. Bashforth's tables is the scale of proportional 

 parts; for the mode of using this, and likewise for the calculation of 

 earthwork in sidelong cuttings, we refer the reader to the next number 

 of the Journal : we cannot, however, dismiss the subject even tempo- 

 rarily, without expressing our conviction that Mr. Bashforth's tables 

 are by far the most simple and generally useful of any that have yet 

 appeared; — such we know is the opinion entertained by m^n who 

 have for years past been engaged in the computation of eartinvorks, 

 and, consequently, are best qualified to appreciate the value of 

 tabular modes of shortening the labour of calculation. 



The Hand-look of tlie "Sounder;" or Tkorelical and Practical 

 Treatise uf the Sounder (or Borer). — Guide da Suudeur, 4'c. By 

 J. Legoussee, civil engineer. Paris: 8vo. ; with maps. 1817. 



The work of M. Legoussee treats of every subject relating to 

 borings for underground works, and although there lias been no lack 

 of detached papers on this head, the work before us comprehends 

 the whole of the facts and reasoning hitherto known. After having 

 briefly sketched the history of the subject, the author proceeds to the 

 geological portion of the doctrine, and first defines what is to be 

 called a geological basin. He describes, then, the aspect of secondary 

 and tertiary basins in different countries, and examines the most 

 favourable localities for the boring of artesian wells, the strata of 

 fossil fuel, rock salt, mineral waters, &c. 



After these preliminaries, our author enters on the description of 

 the different systems, and the different applications of sounding ; the 

 explanatory apparatus for the study of the ground; the driving of piles, 

 and placing of poles (or tilegraphic lines; mooring stones, and foun- 

 dations for suspension bridg'-s; submarine boring for the removal of 

 shoals and reefs, and the improvement of bridges; horizontal be ring, 

 and other inin ng operations — ventilation, and absorbing pits for the 

 draining or absorption of fetid waters; in fine, on artesian wells and 

 the search for underground water. 



