ON THE DISCHARGE OF WATER THROUGH SLUICES By K. R. BORNEMANN. Foreign Abstracts of Institution of Civil Engineers. THE first part of the paper treats of The effective head (h,—h,+k) varied the flow of water through submerged from 21 millimeters to 231 millimeters sluices, and the author gives the results (0.83 to 9.09 inches). of an extensive series of observations The author endeavors to find an made by himself with a view of determ- empirical formula from which u can be ining the coefficients of discharge for calculated so as to agree with the exsuch cases. The experimental sluices periments. He tried successively eleven were made by placing a flat board across different formulæ, and determines the a parallel trough, the board resting coefficients in each case from the experiagainst a strip on each side, the bottom ments by the method of least squares. of the opening being formed by and The two formula which give the most flush with the bottom of the trough. satisfactory results for submerged disThe height of the opening was varied charge are by raising or lowering the sluice board, and three different widths of troughs u=a+ß· and sluices were used. In experiments 1 to 16 the trough was 1.135 meter wide (44.7 inches), and the clear opening 1.006 meter (39.6 inches) wide; in experi- u=a+B 2 0.520 meter (20.47 inches) wide; and in With the experimental sluices he finds as the final series 45 to 63 the trough the most probable values of the coeffimeasured 0.802 meter (31.75 inches) cients for the whole sixty-three observawide, and the opening 0.774 meter (30.47 tions: inches) wide. In the above experiments weir boards were inserted in the trough about 11 feet 4 inches below the sluice, so as to pond up the tail water sufficiently to submerge the issuing stream. For the first formula a=0.54138; p=0.14965 For the second formula a=0.43479; B=0.25666; y=0.031212. The author also gives some experiments on submerged discharge communicated to him long ago by Weisbach. In these the trough was 0.363 meter (14.29 inches) wide, and the opening the same, there being no side strips. The bottom edge of the sluice was also beveled off on the tail water side. The conditions of experiments vary too much, and their number is too few to deduce reliable formulæ from them. This part of the paper also contains a critical examination of some formulæ proposed by Linnenbrügge, and published in 1879 in the Civilingenieur. These formula the author considers unsatisfactory. The second section of the paper deals in similar manner with the best extant The rectangular orifices 0.200 meter observations on free discharge from (7.87 inches) wide, and with contraction sluices; the data used being the experi- all round; for heads up to 1.800 meter ments by Weisbach, by Boileau, and by (5 feet 11 inches) Lesbros. The empirical formulæ for the coeffi- u=0.5951+0.01360 √/a cient of discharge are as follows: the а +0.0008844 -0.000 (-1). head to the center of the opening being And for similar orifices 0.020 meter h, and the clear height and width a and (0.787 inch) wide b as before, all in meters. For sluices built across a trough 0.9 μ=0.6262 +0.003291 meter (35.4 inches) wide, the opening reaching the whole width, and the bottom being flush, along the top of opening only, for heads to 0.580 meter (22.8 inches) √a h For openings 0.200 meter (8 inches) μ=0.5074+0.02126/ b +0.3958 2(a+b) h For orifices 0.200 meter wide, with contraction along the top and bottom, but not at the sides μ=0.6550+0.036111/a α 11/-0.07884 -0.07884 (a+b). For orifices fitted with a trough-shaped mouthpiece in front, and contraction at the top and sides, but not at the bottom For sluices 0.6 meter (23.62 inches) wide, μ=0.5732+0.01355+0.02109/ 1 a For sluices similar to the last, but with guide strips ail round the opening, 5 For similar orifices, with contraction at the top and the bottom, but not at the sides centimeters (2 inches) from the edge, for μ-0.6967-0.10331/ heads to 1.800 meter AN INSTRUMENT FOR THE DETERMINATION OF LATITUDE. By S. C. CHANDLER, Jr. From Proceedings of the Society of Arts. Ir requires a great deal of temerity to claim anything novel in the determination of time and latitude, and even more to claim an improvement in this respect. Nevertheless, I believe that the principle involved in the instrument I have devised is novel, for, after a careful investigation, I have not been able to discover any instance where it has been used in the same way. the telescope turns cannot be made perfectly circular, and are not of absolutely the same size; and this deviation from the perfectly circular form, and from absolute equality in size, causes irregularity in the motion of the telescope. 2. Error in collimation. This error is due to the telescope not being perpendicular to the axis on which it turns; and causes the telescope to describe a The nearest approach to it, in previous small circle of the heavens to one side of constructions, is to be found, I believe, the meridian. The correction for this in the floating collameter which Captain is determined by observing some slowly Cater invented in 1805, for obtaining the moving star, and then, before it has zero point of a vertical graduated circle; crossed the field, reversing the telescope but no one seems to have had the idea in the Y's and observing again. of floating a telescope on mercury. Thus 3. Error in level. The deviation of the far the astronomical transit instrument instrument, on account of the axis on has been the universally acknowledged which it turns not being horizontal, is means for the accurate determination of ascertained by means of a level supported time. Astronomical transits vary in size, on the two pivots, the errors of the from those which are as small as the level itself being eliminated by reversordinary surveyor's transit to those of ing it. eight inches aperture and ten feet focal length, and two or three thousand pounds weight. These instruments are placed in the plane of the meridian, and it is intended that, as the telescope turns in the Y's, its axis shall remain always in the plane of the meridian. The measurement of time means merely the measurement of the angle which a point in the celestial sphere has described. In order to determine the error of a time-piece, therefore, by means of the transit instrument moving in the plane of the meridian, it is only necessary to observe by means of this time-piece the time at which a certain star crosses the meridian, and then, knowing the time at which it should cross the meridian, we have in the difference the error of the clock. Certain difficulties are met with, on account of the inaccuracy of the construction, and of these the following four are the principal ones, viz. ; 1. Error in pivots. The axles on which 4. The error in azimuth has to be determined by astronomical observations. We thus have in the transit four errors to be allowed for, viz.: error in pivots, in level, in collimation, and in azimuth. In the instrument which I have devised three of these errors are eliminated, and there only remains one error, which is analogous to the error in collimation of the transit. This instrument, made by Mr. Clacey, of this city, consists of a base of walnut with approximate leveling screws at the four corners. From the middle of this base rises a pillar of black walnut, firmly bolted to the base, and surrounded by collars of hard brass. An outside sleeve of hard brass, which turns on these collars, supports the remainder of the instrument-this sleeve being rotated in azimuth by a rack and pinion movement, and provided at its base with a graduated setting circle. On top of this sleeve is a wooden cross head which supports a wooden trough in the form of a hollow rectangle, and in this trough is placed mercury to a depth of one-eighth of an in the case of the transit, but by observinch. The trough is constructed of wood ation of the stars, in a similar way to instead of brass, because the mercury that by which the azimuth error of the would attack brass. Whether it would transit is found. As to the disturbance be better to use cast iron is an open of the instrument by oscillations, the question. In this trough, on the mercury, there floats a wooden float, also in the form of a hollow rectangle, and nearly as large as the inside of the trough, this float being held in position at the middle of the two sides by two cast iron pins which move in vertical slots in the sides of the float, and which are sufficiently loose not to interfere with its floating freely, but which serve to prevent any violent or sudden motion. The above-mentioned float has attached to it two brass arms which support the telescope, the latter projecting through the hollows of the hollow rectangles of the float and trough. The trough is not supported in the middle, but nearer one end, in order to allow of zenith observation; and on this account a counterpoise is attached at the other end of the trough. The attempt has also been made to so proportion the parts as to bring the center of gravity of the floating part as near the axis of oscillation of the telescope as possible, in order to reduce oscillations due to jars, etc. The illumination is effected by a series of reflectors, and comes from the side. The cross hairs are horizontal, and not vertical as in the transit. The reason for this will be explained later. In using the instrument the telescope is set at a certain inclination to the vertical, and, as the instrument is rotated in azimuth, the line of sight sweeps out a horizontal, small circle of the heavens, i. e., a circle of which the zenith is the pole. most violent oscillations I have been able to produce have required thirty seconds to have their effect dissipated, and after this time had elapsed the instrument is as quiescent as though it were mounted on stone. It is, of course, specially adapted for observing equal altitudes, and can also be used to observe the transit of stars across any desired small circle having the zenith for a pole, and hence the reason why the cross hairs are horizontal instead of vertical. All observations are influenced by refraction, but refraction operates to elevate all the stars equally at the same time. Hence, we can disregard the error of refraction in a series of observations, taken so, near each other that there is no probability that the coefficient of refraction of the air has changed, and we can simply account it as part of the instrumental error; it having the same coefficient, hence, when the observations are reduced to middle time, this error is almost wholly eliminated. Next, as to the results that can be obtained by this instrument, I have not yet been able to make a great many observations, but those that I have made encourage me to believe that when as good mounting is given to it as is given to an astronomical transit, better results can be obtained with it than with the latter. I have used it very roughly, making observations from the roof of my house, which was subjected to a constant jarring from the teaming in the street below, and where the instrument was exposed to the wind. All the observations that I have made are the following: For the determination of the zenith, the free, upper surface of a liquid is used, and we have dispensed with the Showing the determination of clock error of pivots, the error of level and correction on various dates, by combinthe error of azimuth, and have left only ing stars in pairs, east and west, after what is, in a certain sense, analogous to latitude correction had been introduced. the error of collimation in a transit in- It should be noted that the instrument strument, the characteristic of both is of one and three-quarters inches apererrors being that the telescope describes a small circle parallel but very close to the circle in which it is intended to revolve. The amount of this deviation in this instrument is not, however, determined by reversals of the telescope, as ture, and twenty-five inches focal length, provided with but five threads, whose intervals have, as yet, been only imperfectly determined, and that it was mounted in the open air, over a box of sand, and was entirely unprotected from the wind. The observations of the 5th of January were made from the middle of the roof of a four-story dwelling. January 25, 1880. The above are all the observations taken thus far, and form an exceedingly good set of results. I have not at present access to any results obtained with portable transits of the same size, with which to compare them, but do not be-24.93 seconds of time. lieve that as good results can be obtained with the latter instruments. I have, however, compared my results with those of larger coast-survey transits, and mine are the best. -25.12 -25.06 66 -25.08 66 66 66 -25.06 -25.14 64 2d 3d 4th " 5th 6th " 7th -6.62 -6.44 Next, as to latitude. The transit instrument, when placed in the meridian, -6.34 seconds of time. is used only for time; it can be used for the determination of latitude if placed in the prime vertical. The Coast Survey have introduced for this purpose the zenith telescope, and have obtained with it the very best results. To compare my instrument with this is a very severe test; but it will be seen that, although I have had only three evenings on which I could make observations for latitude, the results obtained are remarkably good. The claims, therefore, that I make for my instrument are the following, viz. : Probable Errors. Of Chron. Single 1. The ability to use any part of the heavens that are not obscured by clouds. In using the transit it is often impossible to obtain observations when clouds hang in the meridian, even though there may be any amount of clear sky on either side. With my instrument we can use any region of clear sky in the heavens, as we can use any horizontal circle whatever; although the use of the same circle all the time renders the computations easier. 2. There is only one instrumental error to determine inatead of four. 3. This instrument is unaffected by errors in mounting. 4. Simplicity in use; requiring no Probable readings of level nor reversals. In the Error. use of the transit about one-half the time ±0.90 is taken up by these processes, which are ±0."85 ±0.′′84 unnecessary with instrument. my |