358 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



LNovembeb, 



EARTHWORK CALCULATIONS. 



Oil tliB Calculating of Earthinirlc. By James Henderson, C.E., 

 Glasfj;ow. 



In the calculating of earthwork, %vhere the base and slopes are 

 regular and uniform, as in the case of railways, roads, &c., the fol- 

 lowing short table I have found lioth useful and expeditious: 



Rule. To the quantity in column of Sides, corresponding to the 

 mean height in column of No.'s, add the quantity in column of 

 Difference corresponding to the difference of heights in column of 

 No.'s, and multiply the sum by the length of cut or bank in chains; 

 and that product by the slope of banks, for tlie cubic yards in sides 

 of said cut or bank. 



Again, multi])ly the quantity in column of Centre, corresponding 

 to the mean heigiit in column of No.'s, by the length of the cut or 

 bank, in chains; and that product by the breadth of base, in feet, 

 for the cubic yards in centre of said cut or bank. 



The sum of these two quantities gives the total cutting or bank- 

 ing, in cubic yards. 



Example. 



Transverse Section, 



Longitudinal Section. 



750-5 

 30 



22515 



182486 

 H 



18248 C 

 9124-3 



Sides . . 27372-9 

 Centre . 225150 



Total . . 49887 9 cubic yds. 



The principle on which this table is based is — That the differ- 

 ence between the true contents of the sides of a cut or bank and 

 the contents found by taking the mean section, varies as the square 

 of the difference of heights ; the true contents more or less ex- 

 ceeding the contents obtained by taking the mean section as the 

 difference of heights is more or less. In table, the quantities in 

 cdlumn of Sides are the contents of sides by taking the mean sec- 

 titin, and the <iuantities in column of Difference those required to be 

 added in order to obtain the true contents. In Bidder's table for 

 calculating earthwork, the true contents of sides are given for 

 every variation of mean and difference, which consequently causes 

 a very large number of different quantities in table ; so much so, 

 that if, instead of being carried out every foot in height to 50 feet, 

 it were carried out every tenth of a foot to 50 feet, it would occupy 

 a good-sized volume; while, by keeping the difference separate, as 

 in the above table, the same could be comprehended within a few 

 pages, and be less complicated. 



In this, as well as in Bidder's table, the contents are correct only 

 when the ground is uniformly level transversely; but, as the sur- 

 face is generally more or less sloped, it becomes important to 

 ascertain the additional quantity required to be added in order to 

 obtain the true contents. 



Take C = contents as found by the former table; B = ^ of 

 base in feet; L = length of cut or bank, in chains; S = slope of 

 banks; and T = tabular number corresponding to the slope of 

 banks and surface of ground, as given in the adjoining table. 

 .^^ / 22.B2.L\ 

 1 hen, ( C -1 — g — I X T = additional quantity required to be 



added to contents C, in order to obtain the true contents. 



Example. Suppose that in the former example the average slope 

 of the ground was 1 in 10. Then, 



/ 22.15-.13\ 



U9887^9 -\- — Q-JX—) X -023 = 1257 cubic yards, 



which, added to 49887-9, gives 5114-J-9 cubic yards for the true 

 contents of cutting. 



SYMMETRIC PROPORTION. 



On an Application of the Laws of Numerical Harmonic Ratio to 

 Forms yenerally, and particularly to that if the Human Figure. By 

 D. R. H.\Y, i;sq.— (Paper read at the Royal Society of Ed"inburgh.') 



The author stated in some prefatory remarks, that a belief in 

 the operation of the laws of numerical harmonic ratio in the con- 

 stitution of beautiful forms had long existed, although those laws 

 had not been systematised so as to render them apjdicable in the 

 formative arts. In proof of this, Mr. Hay quoted a correspond- 

 ence upon the subject of harmonic ratio, between Sir John Harring- 

 ton and Sir Isaac Newton, in which the latter expresses his beliel in 

 such laws in the following words: "I am inclined to believe some 

 general laws of the Creator prevailed with respect to the agree- 

 able or unpleasing affections of all our senses; at least, the sup- 

 position does not derogate from the power or wisdom of God, and 

 seems highly consonant to the simplicity of the macrocosm in 

 general." 1 he belief of this great philo.sopher, the author trusted, 

 would form some apology to men of science for the repeated at- 

 tempts he has made to establish the fact. These attempts he had 

 hitherto made with reference to architecture, to ornamental 

 design, and latterly to the human head and countenance; but on 

 the present occasion he intended to show the operation of these 

 laws in constituting the symmetrical beauty of the entire human 

 figure. 



He next proceeded to point out the remarkable similarity that 



