1844.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



36d 



0-02 



2*81 

 ■ 2-02Si; 



Refraction'^ 



, 26-02 seconds -7814 

 From 3° 47' 45'' 

 Trtke 26-02 



Angleofdepresiion = 3° 47' 18-98 

 When the anE;les of elevation or depression are small, the remainder, 

 after the hundreds are obtained, will be sufficient allowance for the 

 reduction of the right line, which joins the objects to one which mea- 

 sures the arc between the radii of the objects in the surface of the 

 earth. 



II. Having observed in a horizontal line, the top of Mr. Muspratt's 

 chimney at Newton, near Liverpool, (which is the highest edifice in 

 the world,) from a neighbouring hill, 3U miles distant : — taking M. 

 Delambre's allowance of j\ the arc of distance, what is the depression 

 of the object i 



30 miles == 15840U feet; 

 ^j of 158400 = 14400 



100" = 10143 from table. 



4257 

 40" — — 4057-2 ditto. 



199-8 

 1" := — 101-43 



0-9" = 



98-37 

 -91-289 



141"-9 7-081 &c. &c. 



Hence the angle of refracticin — Hl"9, or 2' 21"-9, which is also 

 tlir angle of depression, as the object appeared in the horizon. 



111. The angle of elevation uf an object 298 yards distant is 33- 

 41' 20", what is the true angle uhen tiirestrial refiaction is allowed 

 tor according to M. Legendie, who takes -^ the arc of distance ? 

 298 yards = 894 feet ; 

 ^ of 894 = 03-857 



0"-0 = 60-859 



Correct angle == 33° 44' 19-371" 



All Art, Invention — i. e. original art — is but the embodiment of 

 " spirit" in ionie form directly or indirectly useful to man. Art is but the 

 comliination or arrangement of natural principles to produce new results ; 

 and the organization of bodies of men or bodies of matter are, in all cases, 

 operations of the " spirit." The art by which Michael Angclo found the 

 statue in the marble block, and the art by which Oliver Cromwell found a 

 cavalry regiment in the rude mass of men and horses, were alike operations 

 of the " spirit." The spirit of Watt could discern the form of the steam- 

 engine in the metallic ore, with the dim vista of countless thousands of 

 human beings set free from drudgery in the hewiug of wood and the drawing 

 of water ; and the spirit of Arkwright beheld the forms of various kinds of 

 matter combining into a mill for grindiiig out clothing by miles. These men 

 put forth their " spirit" in actual forms to the cognizance of the world. 

 Other spirits, as Homer and Shakspeare, gave their creations to the world in 

 written descriptions ; their ideal embodied their actual. Michael Angelo, 

 Oliver Cromwell, Watt, and Arkwright, actualised their ideal. But there it 

 is, the self-same " spirit" in all, making itself obvious to mau's apprehension 

 in one or other of the various modes by which man holds converse with his 

 fellows, of greater or lesser significance. — Westmimier Review. 



AREAS OF CUTTINGS AND EMBANKMENTS. 



(From the American Journal of the Franklin Instiitiie. ) 



Short methods of calculating correctly the Sectional .Areas oj Excava- 

 tions, or Embankments. By Solomon W. Roberts, C. E., of Phi- 

 ladelphia. 



In the construction of most canals and railroads a large number of 

 calculations are required of the sectional areas of excavations and 

 embankments, many of which (called cross-sections of three cuttings) 

 liave the general form of the figure a b c g e; the depths of the cut- 

 ting, or filling, being taken at the points a, 6, and e. The point 6, is 

 in the centre line, and a and c, are the points where the side slopes 

 strike the surface of the ground. 



The three following methods, devised some years since, for accu- 

 rately and readily obtaining such areas, are well adapted to facilitate 

 the operation, and their correctness may be easily demonstrated: — 



No. I. Multiply the extreme width of the excavation, or embank- 

 ment, measured horizontally, by one-half of the depth at the centre ; 

 multiply the sum of the depths at thf sides, by one-fourth of the base 

 line, or bottom width (e g) — the sum of these products will be the 

 sectional area required. — Thus, in the following diagram the centre 

 stake standing at b .- 



(dhx^y'rCael+chX j) = Sectional Area of a 6 cgfe. 



The diagram in this posiiion represents an excavation, by inverting 

 it an embankment. 



No. II. The same result may be obtained with less calculation, by 

 the use of a table, as follows, the cuttings being taken in feet and 

 tenths, as usual : 



Prepare a table of three columns, the first containing the dejiths at 

 the centre, the second the sectional areas for each depth on level 

 ground, the third the horizontal distance from the centre stake to the 

 side slopes — such a table may be readily constructed. Then find the 

 difference between the centre depth, and the average of the side 

 depths, and multiply tliis difference into the number in the third 

 column of the table opposite the centre cutting. If the average of 

 the side depths is greater than the centre depth, add this product to 

 the number in the second column, if less, subtract it, and the result 

 will be the cross-section required. 



No. III. The following method, after making the table, is very con- 

 venient, on account of the substitution of addition and subtraction, for 

 multiplication and division: 



Prepare a table of twelve columns, the first containing the centre 

 cuttings for feet and tenths, and the second the sectional area for each 

 centre cutting, when the sum of the side cuttings is equal to that at 

 the centre. The remaining columns, numbered from 1 to lU, are to 

 be filled by inserting in the first, half the distance from each centre 

 stake to the side slope, measured horizontally ; in the second column 

 twice the amount in the first; in tlie third three times the amount in 

 the first ; and so on. 



To calculate a Sectional Ana by this Table. 



Subtract the centre cutting from the sum of the side cuttings— sup- 

 pose this difterence to be 4-70, for example — then from the column 

 numbered 4, take out the amount opposite the given centre cutting ; 

 and for the seven-tenths take the amount in the 7th column, and move 

 the decimal point one figure to the left; add these two amounts to the 

 number in the column of areas, and the sum mill be the sectional area re- 

 quired. 



If the number of feet in the difference between the centre cutting, 

 and the smn of the side cuttings exceeds ten, the amount for ten feet 

 must be taken from the table, and be added to that for the remaining 

 height taken from its corresponding column. 



In those rare cases in which the sum of the side cuttings is less than 

 the centre cutting, the amount caused by the difference must be de- 

 ducted from that taken from the column of areas. 



The demonstration of the foregoing rules depends upon simple tri- 

 gonometrical principles, and it does not require to be elucidated here. 



