1841.] 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



417 



1. That taking averagp earth (yielding readily to the plough,) at 

 mean stages cf weather and seasons, a scoop load may be taken at one 

 tenth of a cubic i/ard mcnsurcd in excavation. 



2. That the time lost in loading, unloading, and all other ways per 

 load (except in turning,) is, at an average, two-thirds of a minute. 



3. That in every complete turn, or semicircle, described by the 

 horses, one-third of a minute is lost. 



4. That if tlie mean horizontal distance of transportation of the 

 earth in a right line, he added lo the extreme height scooped, measur- 

 ing vertically from the buttom of the excavation to the top of the 

 bank, then fur every 70 feet of this aggregate distance, one minute 

 will be consumed by the horses iu going out and returning back. 



5. That if the earth be all scooped io one side, as for instance, to the 

 tow-path bank alone, of a canal, two turns, or a complete circle, will be 

 made by the horses, for every load deposited in bank. 



C>. That if the earth be scooped to both s/des of a canal, but one turn, 

 or a semicircle onhj, will be described by the horses, for each load put 

 in bank. 



From the oth and 0th observations, it follows that clear of the time 

 needed to overcome the horizontal haul and vertical height, the con- 

 stant amount of time lost per load, will be : — In Double Scooping, 1 

 minute, and tn Side Scooping, l~ minute. Now if the sura of the mean 

 horizontal haul, and the extreme height scooped, both in feet, be put = 

 a; the number of hours wrought per day, zzz b; the number.of cubic 

 yards excavated and placed iu bank, per day, by each scoop, = .v. 

 Then the general formula to find .(,- in double scooping will be : 



(it) 



b 



Vyy-r 1 y 



. .f. 



10 



Transforming this equation by the rules of algebraic fractions, and 

 substituting for b the average number of hours commonly wrought per 

 day, = 10, we are able to reduce the formula to the following ; 



III Double Scooping, — ^_ = .!• 



And for side scooping the general formula will be : 



GO 



I. 



10 



Transforming which, by the rules of algebraic fractions, we have: 

 re,-. 4200 



In Side Scooping, — — -j = .r II. 



Now putting the cost per cubic yard of excavation put in bank clear 

 of aU profit, = y ; the daily wages of a scoop and driver, in cents, ^ 

 c ; the cost per cubic yard, in cents, of loosening the earth, = rf; the 

 formula to find y, the cost in pence* per yard, either in double or single 

 scooping, will be : 



.^i='J 



III. 



The actual number of cubic yards excavated and put in bank by 

 scoops, in several instances, having become accurately known to the 

 writer, the correctness of the formuls I. and II. will be tested by those 

 cases. 



E.vaniplt I. Double Scooping. 



In this case, 3o00 cubic yards of earth were excavated and put in 

 bank by 00 days work of scoops, or per scoop, per day, 40 cubic yards, 

 x; the mean horizontal haul was 2GA feet; and tlie extreme height 

 scooped, 8 feet; making the aggregate distance 34-i feet. Then by 



4200 



the formula (I.) we have .j-r;— .— ,=7; = 40-2 cubic yards = .r. 



o4;s -j- /O 



Here the calculated and actual day's work of the scoops is the same 

 within -nj of a cubic yard. 



Example II. Single or Side Scooping. 



In this case, 5000 cubic yards of earth were excavated and deposited 

 in bank by 17G days work of scoops, or per scoop per day, 2>)i cubic 

 yards, =: x ; the mean horizontal haul was 44 feet, and the extreme 

 height scooped, 11 feet; making the aggregate distance, 55 feet, ^= a. 



'' We have adopted the English pence fur calculation, instead of the dollar 

 and cents, as given m the original paper by the auihor, allowing 04 pence for 

 the dcllar. — Editor. 



Then by the formula (II.) we have 



4200 



2S'3 cubic yards =r .v. 



aa + 933^ 



Here the ditterence between the real and calculated days work of a 

 scoop is 5 of a yard. 



Conceiving it to be unnecessary to display at length anv more of 

 tlie examples, we will embody, in the following table, the results of 

 actual experiments, and compare them with tliose calculated by the 

 formula;. 



No. of Experiments. 



Kind of scooping iDouble 



Mean horizontal haul ! 26 o 



Extreme height scooped 



Value of « 



Number of cubic yards excavated 

 and put in bank 



Days work of scoops employed . . 



No. of cubic yards actually exca- 

 vated per day by each scoop . . 



No. of cubic yards excavated per 

 day per scoop ; calculated hy 

 formula I. and II 



Cost per cubic yard of the excava- 

 tion calculated by formula III. 



8 

 34-5 



5000 

 126 



39-: 



40-2 



4|-rf. 



Double 

 20-5 



8 

 31'5 



3000 

 90 



40 



40-2 

 4-}d. 



Side. 

 44 

 11 

 55 



5000 

 170 



28-.') 



28-3 

 off/. 



In calculating column 10 of the above table, the hire per day of a 

 scoop and drii'er, has been assumed to be 12s. 5!id., and the cost of 

 loosening, at 1 cent (•.34t/.) per cubic yard. 



The near coincidence of the results in columns 8 and 9, shows how 

 closely the calculated number of cubic yards, excavated per day, in 

 each of the kinds of scooping, agrees with the real day's work of each 

 scoop, as actually ascertained in excavating 20,062 cubic yards of 

 earth; consequently we may regard the formulee which we have de- 

 duced, as being sufficiently coii/iniwd to Justify a full reliance upon them 

 in practice. 



ON THE COMPRESSION OF EARTH, AND THE INCREASE Of ROCK IN EM- 

 BANKMENT, CO.MPARED WITH THE VOLUME IN EXCAVATION. 



I. On the Compression of Earth in Bank. 



It is well known to practical engineers, that when earlli is excavated 

 and formed into embankment, it occupies less space iu bank than in 

 the cut whence it came. 



Although experience has sulficiently established this fact, yet a 

 contrary opinion is often entertained by persons who have not bestow- 

 ed much attention upon such art'airs ; and this idea is encouraged by 

 inadvertent paragraphs, which are sometimes met with in works of 

 high professional authority.* 



Thus even in Professor JIahan's able treatise upon Civil Engineer- 

 ing, (page lis,) we find the following sentences: — "In determining 

 the relations between the volumes of the embankments, and the exca- 

 vations by which they are furnished, it must also be borne in mind that 

 earth, in its natural state, occupies less space than when broken up ; 

 and as the embankments, when first formed, are iu the state of earth 

 newly broken up, an allowance must be made according to the nature 

 of the soil. This allowance will generally vary between one-twelfth 

 and one-eighth ; that is, earth, when first broken up, will occupy from 

 one-twelfth to one-eighth more bulk than it does in its natural state." 



Now, so far from this being the case with embankments of earth, it 

 is directly the reverse, and the fact is in practice, that the compression, 

 and not the expansion, of earth, when formed into bank, is usually 

 found to be from «h eighth to a tmlfth part of its volume in the natural 

 state. 



Although it is evident that a subject of this nature does not admit 

 of a precise determination, because an almost endless variety exists in 

 the consistency, and hence in the compressibility of earths; still it is 

 quite possible to form an approximation which will not, in general, err 

 very far. 



- The must common error upon ihis subject, which we meet with in books, 

 is the supposition that a certain amount of earth excavation, will forni the 

 same quantity of emb: nkmcnt ; which, in practice, can never be the case in 

 banks ihat arc ma:ic with cans. 



Thus in ProTessor MiUington's excellent '• Elements of Civil Engineering," 

 we tinil it stateil (at jir.go 184.) ihat by a particular arrangement ol levels. 

 •' one-half of the canal will be in excavatiun, and the remaining half in em- 

 bankment, and the soil that is dug out of one end will serve to lorm the em- 

 bankment at the other.'' The same idea runs through other works, nhich 

 we might quote if it were necessary. 



3 K 



