37G 



THE FARMER'S MAGAZINE. 



. . 45.0 degrees 

 . . 40.0 „ 

 .. 39.6 „ 

 .. 37 „ 

 35.0 to 36.0 ,, 



the area of such figure being divided by the sum of the 

 Bides and bottom. 



The slopes for the sides of open water-courses, when 

 not siipported by walls of masonry, or by piling, should 

 never be less than the natural angle of reiwse at which 

 the earth in which they are made will stand, and which 

 may be stated to be as follows, viz : 



Clay or strong earth.. 

 Dry sand .. . . 



Sand less dry ., 



Commoa mould 

 Wet gravel . . 



But in most cases the sides should have much more 

 slope than stated in the table above ; and abrupt 

 bends or changes of direction should be avoided as 

 much as possible, as such deviations from a straight 

 direction not only retards the velocity of the current, 

 but renders the sides and bottom of the water-course 

 liable to be destroyed by the eddies in the angles of the 

 bends. 



The most perfect form for the section of a watercourse 

 is a semi-circle, as in tuch the greatest body of water is 

 enclosed by the smallest bounding surface; and, there- 

 fore, the surface offers the least resistance by friction to 

 the velocity of the stream. But such form would ne- 

 cessitate the watercourse being lined with masonry, 

 and, on account of the expense, can only be applied 

 to watercourses of very small size, and where it is im- 

 portant to assist the motion of the water to the greatest 

 extent under circumstances of small declivities. For 

 channels bounded by straight lines the best form is for 

 the sides and bottom being tangents of a circle, of which 

 the radius is equal to the depth of the channel or course, 

 as such form, under the circumstances, offers the least 

 resistance to the motion ol the water, and consequently 

 gives the greatest degree of permanence to the sides and 

 bottom. Under circumstances in which the expense 

 may not be an object, and either a very great declivity 

 rendering the bottom liable to destruction by the action 

 of too rapid a current, or too small a declivity rendering 

 every aid to the motion of water important, the section of 

 the bottom may be an inverted arch of a segment of a 

 circle to which the sides are tangents. Such arch will 

 behest formed of glazed earthenware segments, which? 

 for lightness, may be hollow, andmade with the drain-tile 

 machine, now in general use, at a very moderate cost. 

 The number of segments to form the inverted arch may 

 be any uneven number that the size of the channel, the 

 extent of it to be protected, and avoidance of too great 

 weight of the segments for being conveniently handled 

 may render necessary. Whatever may be the number 

 of such segments that may be required, their sweep 

 should be with a radius of a circle equal to the depth of 

 watercourse. The following diagram is that of a section 

 of a watercourse having the bottom protected by an in- 

 verted arch formed of the glazed earthenware segments 

 recommended and described, and the sides lined with 

 brickwork, in which the first course above the arch are 

 bricks on bed laid as headers, the second course are 

 stretchers, and the subsequent courses bricks on edge as 

 stretchers, with every sixth brick a header. Where 

 sttch a lining may be required to be carried to a con- 



siderable height, then at every eighth or tenth course 

 the first two courses described above may be repeated ; 

 and for any height the last two courses of the brickwork 

 should be the same as the first two reversed, i. e., the 

 course of stretchers should be under, instead of above, 

 the course of headers of bricks laid on bed. 



The length of the sloping side of a watercourse form- 

 ing a tangent to the circular arc of the inverted arch of 

 the bottom is found by the following rule, viz., to twice 

 the depth multiplied by the difference between half the 

 breadth at top and the depth, add the square of the 

 difference between half the breadth at top and the depth, 

 and the square root of the sum is the length of the side 

 required. 



To find the length of the circular arc forming the in- 

 verted arch of the bottom of a watercourse, divide the 

 depth by half the breadth at top, and the quotient is the 

 natural sine of the angle of the slope of the side with the 

 horizon, which is also half the angle subtended by 

 the arc forming the inverted arch, the number of de- 

 grees and decimals of a degree of which multiplied by 

 •01745, which is the length of one degree of a circle of 

 which the radius is unity, and the product of which 

 again multiplied by the depth gives the length of the arc 

 required. 



S. concise, and at the same time sufficiently accurate 

 rule for practical purposes, to find the velocity of water 

 running in open courses of given dimensions and decli- 

 vity, is to multiply the hydraulic depth or radius of the 

 section by the declivity per mile, both in feet, and ex- 

 tract the square root of the product, and the result 

 multiplied by 82i gives the velocity in feet per minute, 

 and which result divided by 5 gives the velocity in inches 

 per second. 



The last rule only applies strictly to a straight course. 

 When there are bends, a correction of the result of the 

 ■formula is required for the effect of friction or obstruc- 

 tion caused by the bends ; which correction consists in 

 reducing the actual height by a head or height that will 

 overcome the obstruction spoken of, and which may be 

 found as follows, viz. : divide the continued product of 

 the square of the velocity in inches per second as found 

 by the last previous rule, the square of the natural sine 

 of the bend, or the sum of the squares of the natural 

 sines of the angles of the bends or deviations from a 

 straightforward direction, and '0003 by the square root 

 of the hydraulic depth in feet, and the quotient is the 

 required correction in inches. It will then be necessary 

 to repeat the operation of finding the velocity from the 

 given declivity reduced by the correction. It should, 

 however, be remarked that, unless the declivity is very 

 considerable, or the bends numerous or very abrupt, the 

 decrease of velocity from deviations from a straight- 



