488 REPORT OF COMMISSIONER OF FISH AND FISHERIES. [22] 



the s-xme space of dike and ditcli. In order to make it clearer we have 



aLX on ilUxstration a very «n.all pond and a con.paratnely large 



set" 1 to 120, which, however, wdl n.ake no difference as regards the 



correct solution of the problem. h.tprvds of 



We now place along the line of the proposed ditch, at intervals ot 



1 2Tneters fhe squads of laborers at points 1 to 10 (we count lour men 



rd "quad, ^^-, one man with a pickax to break the ground, one 

 shoveler who removes the earth from the ditch, one shoveler who throws 

 the etth to the next shoveler, and one man for leveling the earth on 



h Tetf the dike). Squad 1 along the line of the ditc^ .einoves Ui 

 earth to 1 on the line of the dike B A, 3 to 2, 5 to 3, 7 to 4, 9 to o, . to 1 

 on the line of the dike B A, 4 to 2, to 3, 8 to 4, and 10 to o of the same 



''It Ztli be an error if, instead of directing the ditch in a straight line 

 to^ls the center of tlu. dike and letting the laboring squads alternate 

 on the right and left of the ditch, one was to work a P-^ of the ^ ke 

 AC placed i,erpendicularly, or also at an angle at point B of the ditch, 

 tm/ilM>oints A or C, as in that case the work would go from points 



1 2 3 to 10 ak)ng the ditch towards the corresponding points 1, -., o, 

 J; 10 along the dUce. The earth would then have to be thrown one- 

 thir<l farther than is the case in the plan illustrated by our hgure 

 The case would be similar if one was to work from points 1 to 5 

 along the line of the ditch towards the corresponding points 1 to a 

 along the line BC of the dike, and from the points 6 to 1«/^0"S ^h^ 

 ditch towards the corresponding points 1 to 5 along the 1"^^ BA o 

 the dike. Moreover, the laboring squads would interfere with each 

 other. This also applies to illustration of method 2, given below. 



As will be seen from the figure, one-half of the dike and the ditch 

 form a rectangular triangle, and the lines on which the earth is to 

 be moved towards the dike divide the large triangles BCD -"'d 1>AJ) 

 into a number of smaller ones, whose hypotenuses are formed by the 

 lines on which the earth is removed. If theJwo_sides of the right 

 angle are a and b the hypotenuse will be Va^+b\ As will readb 

 be seen from the ligure, the distances along which the earth is to be 

 removed from the ditch, supposing that a is the space assigned to a 

 squad along the dike and h that assigned to a squad along the ditcii, 



will be as follows : 



No. 1 = V I^+TP ^'o. 2 = Vr^^T^iF 



No. 3= V2«2+3"^2 Xo. 4= V2«2+~T?/^ 



Xo. 5= V3a2+5l>^ ^"o. {\ = x/^id^'+^iih' 



No. 7 = Vlo^^+T?? ^^o- >^ = VT^M^-SP 



No. 9 = Vr,a^+9// ^'o. 10 = V5^?+10P 



As will be seen, these distances increase at a certain rate from squad 

 to squad, viz., if we always add 2 distances (1 + 2, 3 + 4, 5 + G, &c.) 



