151 I89G m-' r ist. ---5 ''■■—> ) .'7 •■ A ' ■'■- IV.;, ,.^ u '( • ■?' P r-. ■ J- ■■.;::•■ BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF Slenirg W. Sage 1891 A44IJ4.. /..b^/././..P:. ENGINEERING LIBRARY Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004590737 6^ vw(l«>> <-^ 63(0 /<.// BASEMEf^T STOFJS.GE «« ^^^ Cornell University Library QC 151.B361896 Experiments upon the contraction of the 3 1924 004 590 737 EXPERIMENTS UPON THE CONTRACTION OF THE LIQUID VEIN ISSUING FROM AN ORIFICE, AND UPON THE DISTRIBUTION OF THE VELOCITIES WITHIN IT. BY H. BAZIN, Inspecteur Gin^ral des Fonts et Ckaussies, TRANSLATED From M£moires PRfisENTfis par divers savants a L'AcAcfiMiE DES Sciences DK l'Institut de France, Tome XXXII. JOHN C. TRAUTWINE, Jr., Civil Engineer, FIRST EDITION. FIRST THOUSAND. NEW YORK ! JOHN WILEY & SONS. London: CHAPMAN & HALL, Limited. i8g6. Copyright, 1896, BY JOHN C. TRAUTWINE, Jr. JIOBERT DRUMMOND, ELKCTROTYPER AND PRINTER, NEW YORK, EXTRACTS FROM A REPORT OF MESSRS. RESAL, MAURICE L^VY, SAR- RAU, AND BOUSSINESQ {Rapporteur), COMMITTEE OF THE ACADEMIE DES SCIENCES, INSTITUT DE FRANCE. Comptes^ rendus, vol. CXVIII. Notwithstanding the numerous experiments made since the seventeenth century upon the flow of liquid veins through orifices, there are important matters connected with this phe- nomenon which still remain undetermined, or so imperfectly known as to give rise to most inexact hypotheses. Until now we have had no experimental results respecting the pressures exerted in the interior of the vein, or upon the velocities of the separate filaments. It was therefore highly desirable that delicate observations upon a large scale should be undertaken for the measurement of the pressures and velocities within the issuing vein under considerable heads and with both vertical and horizontal orifices of diverse forms. M. Bazin's memoir contains an account of a large number of just such observations, made at Dijon since 1890, and concluded within the last few months. The memoir contains an elaborate study of the flow through a vertical rectangular orifice, of the same width as the reser- voir itself, and furnished externally with two flat cheek-pieces for preventing the lateral dilation of the vein. These are, so far as we know, the first precise observations made in such IV EXTRA CTS. a case, the most important of all from a theoretical point of view, since it is the most elementary, and that to which mathe- matical analysis can be the most completely applied. We see, then, that the memoir of M. Bazin realizes in many respects a very marked advance in our knowledge of the im- portant and difficult question of the liquid vein. Your com- mittee has therefore unanimously approved the memoir, and asks of you its insertion in the Recueil des Savants Strangers. In this publication have already appeared, during the present century, the memorable experiments of Poncelet and Lesbros upon the flow through vertical orifices ; of Poiseuille upon the flow through capillary tubes ; of Darcy, upon the uniform flow in larger pipes ; of Darcy and of M. Bazin himself, upon the flow in open channels : a most valuable collection of original documents of the first order in the study of hydrodynamics, and one which will in no wise disparage the new work of M. Bazin. The conclusions of the report were put to vote and adopted. TRANSLATOR'S PREFACE. M. Bazin is perhaps best known to the English-reading pub- lic through his investigations of the flow of water in open chan- nels ; in which he was associated with M. Darcy, and which formed so important a part of the material employed by Gan- guillet and Kutter in the construction of their now world- famous formula. A few years ago, however, M. Bazin made another im- portant contribution to the literature of hydraulics in the shape of his experiments upon the flow over weirs, the results of which, rendered into English by Mr. Marichal and the present translator, were published in part in the Proceedings of the Engineers' Club of Philadelphia, Volumes VII., IX., and X. In these investigations M. Bazin not only carefully determined the coefficients of discharge under widely varying conditions, but also carried out very delicate measurements for the pur- pose of determining the shape of the sheet of water, or "nappe," falling over the weir and (by means of the Pitot tube) the velocities and pressures within the sheet itself. The investigations here presented proceeded upon nearly the same lines as those concerned with flow over weirs, and it is believed that they will be found to constitute an equally im- portant addition to our knowledge of hydraulics. J. C. T., Jr. Philadelphia, May, 1896. AUTHOR'S INTRODUCTION. Paris, 15 avril, 1896. Monsieur : — J'ai lu attentivement la traduction, que vous avez bien voulu me communiquer, de mon m^moire sur la con- traction des veines liquides et la distribution des vitesses dans leur int^rieur. Cette traduction me parait bien rendre le sens de I'original, et je vous autorise tr^s volontiers a presenter sous cette forme mon travail aux ingdnieurs am^ricains. Votre bien devoud, H. Bazin. Monsieur Trautwine, Engineer, Philadelphia. Dear Sir : — I have read attentively the translation, which you have sent me, of my paper on the contraction of the liquid vein and the distribution of the velocities in its interior. This translation appears to me to liender correctly the sense of the original, and I very willingly authorize you to present my work in this form to American engineers. EXPERIMENTS UPON THE CONTRACTION OF THE LIQUID VEIN. In their admirable experiments upon the flow through orifices, Messrs. Poncelet and Lesbros have established a fact which appears at first view to contradict the fundamental prin- ciples of hydraulics. In studying the liquid vein issuing from an orifice 0.20 m. square, in thin partition, they found, in 1828, that the mean velocity in the contracted section of the vein was a little greater than the velocity V2gh corresponding to the head h upon the center of that section. Surprised by this anomaly, M. Lesbros considered it necessary to repeat the experiment with the greatest care. This was done in 1834, with but little difference in the results.* He says : " We must admit that the minimum area of the sections of the vein in planes parallel to that of the orifice is 230.62 square centimeters, so that the coefficient of contrac- tion is 230.62 -e- 400, or, say, 0.577. Now the coefficient deduced from the comparison of the effective and theoretical discharge is 0.602, whence it results that the mean velocity in the contracted section is f^f of that due to the head of the liquid upon the center of the orifice." From this it appears that the actual velocity is -^^ greater * Exp6riences hydrauliques sur les lois de I'Scoulement de I'eau. Recueil des savants Strangers, vol. ill., 1832, and vol. xni., 1851. 2 EXPERIMENTS UPON THE than the theoretical, or -^ greater, if account be taken of the fact that the center of the contracted section is slightly lower than the center of the orifice. We have repeated the experiments of M. Lesbros with rectangular and circular orifices in vertical and horizontal walls, and, like him, we have found an excess of velocity in the con- tracted vein when the orifice is in a vertical plane. This, how- ever, we do not find the case with orifices in a horizontal plane. The orifices with which we have experimented are the following : 1. Orifices in a vertical plane : Square orifice, 0.20 m. square (contraction complete) ; circular orifice, 0.20 m. in diameter (contraction complete) ; rectangular orifice, 0.80 m. wide by 0.20 m. high (lateral contraction suppressed), 2. Orifices in a horizontal plane : Circular orifice, 0.20 m. in diameter (contraction complete); circular orifice, o. 10 m. in diameter (contraction complete.) Having determined the coefficients of discharge by filling a vessel of known capacity, we proceeded to determine the geometrical figure of the vein in order to be able to deduce from the discharge the mean velocity in transverse sections at different distances from the orifice. We have endeavored also to ascertain directly by the use of an instrument analogous to the Darcy tube, the distribution of the velocities through each of the several sections of the issuing vein. DETERMINATION OF THE COEFFICIENT OF DISCHARGE. The three vertical orifices were installed successively at the •origin of the channel employed in our experiments upon weirs.* Their center was placed 0.60 m. above the bottom of the chan- * Annales des Fonts et Chaussfees, October, 1888. CONTRACTION OF THE LIQUID VEIN. 3 nel. For the square and circular orifices, the channel retained its width of 2 meters. The sides of the orifices were therefore 0.90 m., from each of the two side walls of the channel. For the rectangular orifice, in order to suppress the lateral contraction, the width of the channel was reduced to 0.80 m. up-stream from the orifice, which thus occupied its entire width. Two cheek-pieces, A,B, prolonged the walls, for a distance of 0.50 m. down-stream, from the orifice, in order to guide the vein, while preventing its lateral expansion. As to the horizontal circular orifices, their center was placed at I m. from the lateral and terminal walls of the channel, and at 0.70 m. above the ground upon which the vein fell. The calibration of these orifices was accomplished by fol- lowing the process employed in calibrating our weirs, that is to say, by filling a part of the channel and noting exactly the time occupied in the filling.* The table on pp. 4, 5 presents a resume of the results obtained : The orifices were formed in iron plates 7 mm. in thickness. The edges, carefully finished in a machine, presented a very true, sharp edge. Let us now compare the values of m given by the foregoing table with those obtained by other experimenters. Square orifices 0.20 m. on the side. The mean of five experiments made under heads between 0.90 m. and i m., is m = 0.6066, a result corresponding very closely with the value 0.605, adopted by M. Lesbros.f for the same heads. Rectangular orifice 0.20 m. high, 0.80 m. wide. Dividing * This very simple operation nevertheless requires great care and precautions if we wish to eliminate all causes of error. For a detailed description of the processes employed, we refer the reader to our first Memoir upon Weirs. f See the table of coefficients for square orifices given by M. Lesbros, Recueil des savants Strangers, vol. xni, 185 1. EXPERIMENTS UFON TjHE Ex- periment No. Head on Centre of Orifice. h Contents of Channel. Time. Discharge per Second. 9 Coefficient of Discharge. Depth. Volume. SV^ Meters. Meters. Cu. Meters. Cu. Meters. Vertical Orifice 0.20 m.* Square. Area S = 0.04012 sq. meter. October, 1890. Mean temperature of water, g** C. 0.9016 0.9220 0.9518 0.9745 0.9945 0.4416 0.4332 0.4676 0.4505 0.4592 177-977 174-59' 188.455 181.564 185.070 29 00 28 04 29 52 28 25 28 45 0.10229 0.10368 o. 10516 o. 10649 0.10729 0.6062 0.6076 o. 6066 0.6071 0.6054 Vertical Rectangular Orifice 0.20 m. High, 0.80 m. WiDE.f without Lateral Contraction. Area S= 0.1592 square meter. October, 1890. Mean temperature of water, 13.5° C. 217.472 191.695 211. 717 185.289 201.130 223.503 204.507 209 . 461 210.005 200.192 188.066 201 .803 194.390 183,516 183.244 224 109 209.011 210.987 202.237 193-541 0.03132 square meter. Mean temperature of water, 11° 1 0.8000 0.5400 2 0.8074 0.4760 .3 U.8I70 0.5257 4 0.8205 . 4600 5 0.8260 0.4994 6 0.8347 0.5535 7 0.8468 0.5078 8 0.8567 0.5201 9 0.8658 0.5215 10 0.8799 0.4970 II 0.8880 0.4670 12 0.8971 0.5010 13 0.9II3 0.4827 14 0.9188 0.4556 15 0.9233 0.4550 16 0.9281 0.5550 17 0.9305 0.5190 18 U.9427 0.5238 iq 0.9508 0.5022 20 0.9594 Verti April 0.4807 CAL CiRCU Area.? and May, 18 9' oq" 0.39612 0.6280 8 04 0.39606 0.6251 8 53 0.39722 0.6233 7 46 0.39762 0.6225 8 23 0.39986 0.6240 9 II 0.40563 0.6296 8 26 0.40416 0.6228 8 35 0.40672 0.6231 8 30 0.41177 0.6276 8 03 0.41448 0.6266 7 30 0.41792 0.6289 8 02 0.41868 0.6270 7 38 0.42443 0.6306 7 14 0.42285 0.6255 7 12 0.42418 0.6260 8 49 0.42365 6237 8 12 0.42482 0.6246 8 14 0.42710 0.6239 7 49 0.43121 0.6271 7 24 0.43590 0.631a I 0.9536 0.4680 188.617 38' 47" 0.8106 0.5984 2 0.9619 0.4222 170.158 34 51 0.8138 0.5981 3 0.9722 0.4478 180.475 36 47 0.8177 0.5978 4 0.9799 0.3905 157-382 31 59 0.8201 0.5972 5 0.9883 0.4401 177-372 35 53 0.8238 0-5973 6 0.9966 0.4298 173-221 34 54 0.8272 0.5972 * Exactly 0.2003 ™- f Exactly 0.797 m. X 0.1997 m. X Exact mean diameter o. 1997 m. CONTRACTION^ OF THE LIQUID VEIN. Ex- periment Head on Centre of Orifice. h Contents of Channel. Time. Discharge per Second. Coefficient of Discharge. No Depth. Volume. m ^ Si^^gh Meters. Meters. Cu. Meters. Cu. Meters. Horizontal Circular Orifice 0.20 m. Diameter.* Area S = 0.03132 square meter. May, 1892. Mean temperature of water 13° C. I 0.9384 2 0.9481 3 0.9594 4 0.9680 5 0.9736 6 0.9923 7 1.0005 8 1.0094 9 0.9552 10 0.9636 n 0.9797 12 0.9888 13 1.0053 0.4487 0.4272 0.4390 0.4054 0.461 I 0.4383 0.4192 0.4400 0.4722 0.4588 0.4393 0.4665 0.4609 88.309 84.093 86.388 79- 799 90.727 86.280 82.497 86.620 92.963 90.324 86.482 91.841 90.737 18' 17 17 16 18 17 16 17 18 18 17 18 18 04- 07 35 II 17 16 27 II 53 16 26 23 05 0.08147 0.08188 0.08188 0.08218 0.08270 0.08328 0.08358 0.08402 0.08205 0.08241 0.08268 0.08326 0.08363 0.6062 0.6062 0.6025 0.6021 0.6041 0.6026 0.6023 0.6028 0.6051 0.6052 0.6021 o. 6036 0.6012 Quite frequently, with the horizontal circular orifice, 0.20 m. diameter, an ■eddy was formed, extending from the orifice to the free surface of the liquid in the channel of approach. It was found possible to prevent the formation of this eddy by allowing a plank to float above the orifice. As a matter of fact, the eddy did not appear to modify sensibly the discharge, for experiments Nos. i to 8 of May, 1892, in which no precaution was taken for its prevention, give the same mean value of m as the five experiments, Nos. g to 13, in which, on the contrary, the formation of the eddy was prevented by means of the floating plank. These eddies caused the formation of a long, narrow tube, drawing in air at ■the surface of the water and carrying it into the vein, which thus discharged, at the same time, water and air, and lost something of the regularity of its characteristic form. Horizontal Circular Orifice o.io m. Diameter.j Area S = 0.007886 square meter. June and July, 1892. Mean temperature of water 22.5*' C. I 0.9069 0.4850 30.285 25' 06" 0.02011 0.6046 2 0.9112 0.4849 30.279 25 02 0.020X6 0.6047 3 0.9236 0.4932 30.797 25 12 0.02037 0.6068 4 0.9421 0.4922 30.734 25 06 0.02041 0.6021 5 0.9493 0.4750 29.660 23 59 0.02061 0.6056 6 0.9564 0.4784 29.873 24 04 o.o2o6g 0.6057 7 0.9733 0.4939 30.841 24 27 0.02102 0.6100 8 0.9930 0.4928 30.772 24 12 o.02iig 0.6087 9 1.0023 0.4911 30.666 24 01 0.02128 0.6085 * Exact mean diameter 0.1997 m. \ Exact mean diameter 0.1002 m. 6 EXPERIMENTS UPON THE the series into three groups, following the increase of the heads, we obtain : Heads between 0.80 m. and 0.85 m. (7 experiments), m = 0.6250 " " 085 m. " 0.90 m. (5 " ), wz = 0.6266 " " 0.90 m. " 0.96 m. (8 " ), '« = 0.6266 In order to study the influence of variation of the head upon the value of ?«, we carried out another series of experi- ments in which the water discharged by the orifice was made to pass over a weir 0.35 m. in height, the coefficient M ol which was exactly known.* This weir having a length of 1.999 r"-- i^^ discharge under a head H was Q = 1.999 m. X MHV2gH ; that of the rectangular orifices being, on the other hand, ■ Q = 0.1592 X »2 V2gh. The comparison of these two experiments gives immediately 0.1592 k Examining the last column of the table, where the values of the coefficients are arranged by groups of heads, we see that m first diminishes slightly as the head h increases, but becomes sensibly constant when h exceeds 0.50 m. Its value, for heads between 0.85 m. and 0.96 m., is 0.6307. Direct gaug- ing had given, for the same heads, 0.6266, or Y3-0 less. But the two processes are not exactly comparable, and the method by the actual measurement of the volume discharged affords a greater guaranty of exactitude for the determination of an absolute value of m. Our sole object in comparing the discharge of the orifice with that of the weir, the head upon which is always more * For the table of values of this coefficient, see the Memoir already quoted, Annales des Fonts et Chauss6es, October, i888. CONTRACTION OF THE LIQUID VEIN. Calibration of the Rectangular Orifice 0.20 m. High X 0.80 m. Wide, BY Means of a Weir with Free Nappe.* Height of weir, 0.359 ™-; Length of weir, i.ggg m. October, 1890. Mean temperature of the water, 13° C. Head. Coefficients of Discharge Means by Groups. Experiment No. On the Centre of the Orifice. h On the Weir. H Weir. Orifice. m h = itt = Meters. Meters. Meters. I 2 3 0.1504 0.1761 0.1955 0.1268 0.1332 0.1373 0.4401 0.4406 0.4410 0.6434 ) 0.6409 )■ 0.6371 ) 0.15100.20 0.640s 4 5 0.2306 0.2424 0.1443 0.1472 0.4418 0.4421 0.6333 0.6368 0.20 to 0.25 0.6350 6 7 0.2738 0.2986 0.1531 0.1563 0.4428 0.4432 0.6366 0.6293 ■ 0.25 to 0.30 0.6330 8 9 10 II 0.3232 0.3492 0.3778 0.3984 O.1610 0.1652 0. 1692 0.1716 0.4438 0.4444 0.4449 0.4452 0.6332" 0.6340 0.6326 0.6296 0.30100.40 0.6324 12 13 14 15 0.4331 0.4423 0.4748 0.4919 0.1769 0.1776 O.1815 0.1853 0.4459 0.4460 0.4465 0.4470 0.6330" 0.6302 0.6292 o.6384_ 0.40100.50 0.6327 16 17 18 19 0.5249 0.5507 0.5779 0.5990 0.1887 0.1896 0.1940 0.1951 0.4475 0.4476 0.4483 0.4485 0.6358' 0.6253 0.6327 0.6270 0.50 to 0.60 0.6302 20 21 22 23 O.6311 0.6436 0.6766 0.6924 0.1985 0.1999 0.2032 0.2056 0.4490 0.4492 0.4496 0.4500 0.6276 ~| 0.6283 I 0.6286 0.6330 0.60100.70 0.6394 24 25 26 27 0.7254 0.7513 0.7796 0.7959 0.2083 0.2097 0.2129 O.2141 0.4504 0.4506 0.4510 0.4512 0.6313" 0.6268 0.6301 0.6292 0.70100.80 0.6294. 28 29 30 0.8245 0.8563 0.8784 0.2167 0.2196 0.2215 0.4515 0.4519 0.4522 0.6298 0.631 1 • 0.6316 ) 0.80100.90 0.630a 31 32 33 34 35 0.9028 0.9300 0.9575 0.9783 1.0059 0.2231 0.2253 0.2273 0.2297 0.2303 0.4525 0.4528 0.4531 0.4535 0.4535 0.6301" 0.6306 0.6301 • 0.6339 0.6274 0.90 to 1. 00 0.6304 * The " nappe" is the sheet of water falling over the weir. It is called ■ free" when it falls freely through the air without touching the face of the weir. 8 EXPERIMENTS UPON THE difficult to determine with precision, was to place in evidence the variation of m relatively to those of the head. In order to study these more thoroughly, it was, however, necessary to take account of the velocity of approach, which, owing to the large dimensions of the orifice,* was by no means negligible. We adopt, therefore, in the following calculations, the value m = 0.6266. One of the numerous arrangements employed by M. Lesbros is nearly comparable with our rectangular orifice. In that arrangement the square orifice 0.20 m. was placed at the ter- mination of a channel of the same width and the lateral con- traction was thus suppressed. The escaping vein was not, as in our experiments, guided by cheek-pieces preventing its lateral expansion, and that expansion, mentioned by M. Les- bros, resulted in a slight increase of the discharge of the orifice. It is this which explains why the coefficient m = 0.638, ob- tained by this skillful experimenter, exceeded byo.oii that which we have determined. Circular Orifices. — The coefficient of discharge of circular orifices is nearly constant. We find : For the vertical orifice 0.20 m. in diameter (mean of 6 ex- periments), in = 0.5977. For the horizontal orifice 0.20 m. in diameter (mean of 13 experiments), vi = 0.6035. For the horizontal orifice o.io m. in diameter (mean of 9 experiments), ;« = 0.6063. We know that this coefficient, varying but slightly from 0.6, does not sensibly increase except in the case of very small orifices or of low heads. Mr. Hamilton Smith, Jr., discussing numerous experiments * The influence of this element upon the value of m is never of great im- portance, since the height — , which corresponds to the velocity u of approach does not exceed a few mm. Diameter of Orifice. m. 0.05 m 0.600 o. lo m o. 599 o. 20 m 0.598 o. 30 m o. 597 CONTRACTION OF THE LIQUID VEIN. 9 made by several observers, including himself, has recently pub- lished * a table of coefficients applicable to vertical circular •orifices. This table gives, for a head of one meter, the follow- ing values of m : Diameter of Orifice. m. 0.006 m 0.627 -0.009 ni 0.617 0.012 m 0.61 1 -0.015 m 0.606 0.03 ra 0.603 The value 0.598 is precisely that which we ourselves have obtained for the vertical orifice 0.20 m. in diameter. As to horizontal orifices, the experimental results are much less numerous. In 1874, Mr. Ellis experimented with orifices 0.30 m. in diameter,f but unfortunately the discharges were determined not by direct measurement of the volume dis- charged, but by comparison with a weir. The mean of a large number of experiments with heads varying between 0.80 m. and 5.70 m. gives m = 0.600. The orifice was submerged. Plac- ing the same orifice vertically and allowing it to discharge into the air, Mr. Ellis obtained, with the same range of heads, m = 0.592. Our experiments also give, for a vertical orifice, a value of m slightlv less than that corresponding to a horizontal orifice. GEOMETRICAL FIGURE OF THE VEIN. Profile of the Jet. — We first observed the profile described \ty the vein issuing from vertical orifices, referring the center of its cross-section at each point to horizontal and vertical axes, the origin of co-ordinates being taken at the center of the orifice. This profile is comparable to the parabola de- scribed by a projectile subjected to the action of gravity and * The Flow of Water through Orifices and over Weirs, and through Open Conduits and Pipes, by Hamilton Smith, Jr.; London and New York, 1886. f Transactions American Society of Civil Engineers, February, 1876. lO EXPERIMENTS UPON THE passing the center of the orifice with a horizontal velocity, V = \'2.gh. Designating by x the horizontal distance of the projectile from the orifice, and byj/ its corresponding vertical distance below the center, it is easy to see that the equation of the parabola is^ = — . The curve passing through the centers of the successive sections of the vein differs but little from this parabola, and lies below it, departing from it progressively as the distance from the orifice increases.- Its co-ordinates for square and circular orifices are indicated in the following table : Square Orifice (A = o 953 m-). Circular Orifice (h = 990 m.). Ordinate of the Ordinate of the Parabola. Parabola. X y ''^b. X y ^'-'i 0.063 O.OOI O.OOIO 0.08 0.002 0.0016 0.082 0.002 0.0018 0.13 0.006 0.0043 0.104 0.004 0.0028 0.17 O.OIO 0.0073 0.128 0.006 0.0043 0.235 0.018 0.0139 O.151 0.009 0.0060 0.335 0.035 0.0283 0.175 0.012 0.0080 0.515 0.080 0,0670 0.210 0.017 0.0II6 0.248 0.024 0.0I6I 0.302 0.035 0.0239 The ordinates of the two curves are not proportional, and their ratio approaches unity simultaneously with the increase of their absolute difference. The following figures show the progressive modifications of liquid veins issuing from a vertical orifice. That issuing from a circular orifice remains regular. Its transverse section, at first exactly circular, is gradually flattened vertically, as is in- dicated in the successive cross-sections, ab, cd, and ef. As to the vein issuing from the square orifice, it undergoes a very remarkable change of form, frequently quoted as an ex- CONTRACTION OF THE LIQUID VEIN. ir ample of the inversion of the vein. The sections gh, ij, and kl show this gradual transformation, which finally gives to the vein a star-shaped figure, the points of which correspond to the sides of the orifice. This peculiarity explains the singular figure of the longitudinal section of the vein in a vertical plane, following the axis of the channel. Let us now consider the rectangular orifice. Instead of being circumscribed on all sides, as in the case of the orifices- already considered, the vein is of indefinite horizontal extent, and is limited by two surfaces nearly cylindrical, between which we may conceive a mean surface dividing the nappe into two sensibly equal parts. The intersection of this surface with the vertical plane passing through the axis of the channel corre- sponds to the central curve of the jet determined for square and circular orifices. The upper and lower surfaces of the nappe were observed for the 5 heads k, 0.790 m., 0.836 m., 0.887 "^v 0.950 m., and 1.005 "f^-* Deducing graphically the ordinate _y of the mean surface, we recognize that the product hy is sensibly constant for a given horizontal distance x from x' the orifice, and greater than the quantity — corresponding to 4 x^ the same product in the parabola^ = —. We have, in fact. Distance from Plane of Orifice, X. Ordjnates y of the Central Curve for Heads. k = Products hy for Heads. h = Mean Prod- ucts Ay for the Five Heads. Value of 0.790 0.836 0.887 0.950 1.005 0.790 0.836 0.887 0.950 1.005 4 ' O.IO 0.20 0.30 0.40 0.50 0.60 0.0078 0.01153 0.0377 0.0628 0.0929 0.1262 0.0073 0.0184 0.0356 0.0583 0.086B 0.1204 0,0078 0.0193 0.0354 0.0571 0.0848 0.1169 0.0072 0.0187 0.0332 0.0529 0.0774 0.1061 0.0062 0.0164 0.0300 0.0493 0.0733 0.1014 0.0062 o.oi5'.j 0.0298 . 0496 0.0734 0.0997 0.0061 0.0154 0.02q8 0.0487 0.0726 0.1007 0.0069 0.0I7I 0.0314 0.0506 0.0752 0.1037 0.0068 0,0169 0.0315 . 0503 0-0735 0,1008 0.0062 0.0165 0.0302 0.0495 0.0737 O.IOI9 0,0064 0.0162 0.0305 0.0497 0.0737 0.1014 0.0025 0.0100 0.0225 0.0400 0.0625 0.0900 * The elements of these profiles are given in a special table at the end of the present memoir. 12 EXPERIMENTS UPON THE Transverse Section of the Vein. — In order to obtain and reproduce the transverse sections of the veins issuing from square and circular orifices, we surrounded them with an oc- tagonal iron frame placed normally to their axes, and having its perimeter pierced by 24 screws projecting toward its center. These screws were moved little by little until their points touched the surface of the vein. The frame was then placed upon a sheet of paper and the transverse sections were traced and their area measured with great precision. This process is not applicable to the rectangular orifice, since the section of the vein was represented only by its thick- ness embraced between the upper and lower surfaces of the nappe. The profiles of these two surfaces were similarly de- termined by contact with a movable point. This operation, owing to the continual fluctuation of the nappe, was a very delicate one, the nappe being less stable than the contracted veins throughout the entire extent of their perimeter. We shall first discuss the results of the experiments rela- tive to the orifices with complete contraction, neglecting for the present the rectangular orifice. The quotient — , which appears in the last column of the table on p. 13, is simply the ratio of the velocity Um the sec- tion under consideration, to the velocity V'zgh, due to the head h upon the center. We have, in fact, jT _ 1 _ fnS V2gk 00 a? , 5' I and, dividing by V2gh and remarking that rr= 7^> U m V2gh M This ratio, at first less than unity, exceeds this and increases CONTRACTION OF THE LIQUID VEIN. 13 Distance of Section from Plane of Orifice. Ratio of Distance jt: to Width L of Orifice. Area of Section. CoeiBcient of Contraction. Ratio of Coeffi- cient of Discliaree to Coefficient of Contraction. X u Mt ta It =: — L '^ .y »■ Square Orifice. »» = o.6o56. 5' = 0.04012 sq. m. ,5 = 0.953 m. 0.063 0.31 0.02586 0.6446 0.941 0.082 0.41 0.02 5 II 0.6259 0.969 0.104 0.52 0.02497 0.6224 0.975 0.128 0.64 0.02467 0.6149 0.986 0.151 0.75 0.02428 0.6052 1.002 0.175 0.87 0.02419 0.6029 1.006 0.210 1.05 0.02395 0.5970 1. 016 0.248 1.24 0.02379 0.5930 1.023 0.302 I. 51 0.02326 0.5798 1.046 0.350 1-75 0.02320* 0.5783 1.049 Vertical Circular Orifice. »» = 0.5977. .y = 0.03132 sq. m. ^ = 0.990 m. 0.08 0.40 0.01904 0.6079 0.983 0.13 0.65 0.01870 0.5971 1. 001 0.17 0.85 0.01864 0.5951 1.004 0.235 1. 17 0.01849 0.5904 1. 012 0.335 1.67 0.01826 0.5830 1.025 0.515 2-57 0.01782 0.5690 1.050 Horizontal Circular Orifice 0.20 m. Diameter. »; = 0.6035. ^ = 0.975 m. .y = 0.03132 sq. m. 0.075 0.37 0.01880 0.6003 1.005 0.093 0.46 0.01860 0.5939 1. 016 O.IIO 0.55 0.01824 0.5824 1.036 0.128 0.64 0.01796 0.5734 1-053 O.I45 0.72 0.01772 0.5658 1.067 0.163 0.81 0.01753 0.5597 1.078 Horizontal Circular Orifice o.io m. Diameter. m = 0.6063. 1° h = \va. S = 0.007886 sq. m. 0.058 0.58 0.004717 0.5981 1. 014 0.088 0.88 0.004632 0.5874 1.032 0.138 1.38 0.004536 0.5752 1.054 0.188 1.88 0.004418 0.5602 1.082 0.288 2.88 0.004231 0.5365 1. 130 0.388 3.88 0.004094 0.5191 1. 168 0.488 4.88 0.003970 0.5034 1.204 0.588 5.88 0.003870 0.4907 1.236 2° A = 0.780 m. 0.058 0.58 0.004705 0.5966 1. 016 0.088 0.88 0.004584 0.5813 1.043 0.138 1.38 0.004453 0.5647 1.074 0.188 1.88 0.004359 0.5528 1.097 * Mean of 0.0226 and 0.0238 H EXPERIMENTS UPON THE gradually with the distance from the orifice. With this in view, it becomes necessary to make here a distinction between the axes of vertical and of horizontal orifices. In the first case the two coefficients m and /< become equal when the horizontal distance x from the orifice is about -^ of its width. In the second one that distance is one half less. In order to compare the velocity Urn. the section oo with its theoretical value, we must take account of the vertical distance y of the centre of gravity of that section below the centre of the orifice. The ratio which we must consider is therefore not Z7 , . ., U but rather may be written \/2giJi+y) U _ m Vzgh Hence the foregoing equation fn / h V2g {k -\-y) ^ ^2g{h -\-y) 'i^-^l h +7 We have already given the values of y. We may therefore calculate the coefficient of correction U 4: h +>' and then '^2g{h + y") We shall confine ourselves to those sections in which — ex- fX ceeds unity. Vertical and horizontal orifices will be considered separately. VERTICAL ORIFICES. Distance of Distance of Center of Section i^'i+y Below Center of m of V=«CA +y) Orifice. Orifice. X y Square Orific E. h = 0.953 m. 0.151 0.009 1.002 0.9953 0.997 0.175 0.012 1.006 0-9937 1. 000 0.210 0.017 1. 016 0.9912 1.007 0.248 0.024 1.023 0.9876 1. 010 0.302 0.035 1.046 0.9821 1.027 0.350 0.047 1.049 0.9762 1.024 CONTRACTION OF THE LIQUID VEIN. Circular Orifice. h = o.ggo m. 15 0.13 0.006 1. 001 0.9970 0.998 0.17 O.OIO 1.004 0.9950 0.999 0.235 0.018 1. 012 0.9910 1.003 0.335 0.035 1.025 U.9828 1.007 0.515 0.080 1.050 0.9619 1. 010 From the foregoing table it follows that with vertical ori- fices the velocity within the vein, when once contracted, slightly exceeds that due to the head A -\- j/. Messrs. Poncelet and Lesbros have already remarked this fact in connection with the square orifice 0.20 m. But the horizontal circular orifices lead to a totally different result. HORIZONTAL ORIFICES. Distance of Distance of Section from Center of Section |/.-T7 U Plane Below Center of Orifice. of Orifice. V^e{k+y) X y He )RIZONTAL CiRC ULAR Orifice 3. 20 M. DiAMET ER. /4 = 0.975- 0.075 0.075 1.005 0.9636 0.968 0.093 0.093 1 .016 0.9555 0.971 O.IIO O.IIO 1.036 0.9480 0.982 0.128 0.128 I.053 u . 9402 0.990 0.145 0.145 1.067 0.9330 0.996 0.163 0.163 1.078 0.9256 0.998 H< 3RIZ0NTAL CIRCULAR ORIFICE O.IO M. DlAMEl ER. h = 0.990. 0.058 0.058 1. 014 0.9720 0.986 0.088 0.088 1.032 0.9583 0.989 0.138 0.138 1.054 0.9369 0.987 0.188 0.188 1.082 0.9168 0.992 0.288 0.288 1. 130 0.8802 0.995 0.388 0.388 1.168 0.8476 0.990 0.488 0.488 1.204 0.8185 0.985 0.S88 0.588 1.236 0.7921 0.979 A = 0.790. 0.058 o.dBS 0.058 1.016 0.9652 0.981 0.088 1.043 . 9486 0.989 0.138 U.138 1.074 0.9227 0.991 0.188 0.188 1.097 0.8988 0.986 i6 EXPERIMENTS UPON THE We thus see that the velocity U does not exceed V 2g{h -\-yy when the orifice is horizontal, that is to say, when the head re- mains uniform over the entire surface of the orifice, and it is- in the inequality of the heads upon the different portions of the orifice that we must seek for an explanation of the anomaly^ mentioned. Returning finally to the rectangular orifice without lateral contraction, and performing the same calculations, we have Distance of Section from Plane of Orifice. Ratio of Distance X to Width L of Orifice. Area of Section per Linear Meter. Coefficient of Con- traction. Ratio of Coefficient of Dis- cliarge to Coefficient of Con- traction. Distance of Center of Section below Cen- ter of Orifice. /: h V^Sii +>) m = 0.6266 s = 0.1997 A = I 000 meters 0.15 0.75 0.1229 0.6154 1. 018 O.OIO 0.9950 1. 013 0.20 1. 00 0.1204 0.6029 I 039 0.016 0.9921 1. 031 0.25 1.25 0.1194 0.5979 1.048 0.023 0.9887 1.036 0.30 1.50 0.1187 0.5944 . 1.054 0.030 0.9853 1.039 0.3s 1-75 0.1185 O.S934 1.056 0.040 0.9806 1.036 The values of — and of = M V2g{h + y) are greater than those obtained with square and circular orifices. It is necessary^ however, to bear constantly in mind that they must undergo a slight reduction. We have admitted that the nappe was per- fectly cylindrical, and that in order to estimate w we must con- tent ourselves with measuring the thickness of the central part of the nappe ; but a closer observation has shown that this thickness is not rigorously uniform, and that the vein pre- sents, at a distance of about 0.20 m. on each side of its axis, a slight swelling. We must therefore increase slightly the value of w, reducing correspondingly the two ratios under considera- tion. The determination of the correction is rendered very difificult by the motion of the vein. In order to obtain aa CONTRACTION OF THE LIQUID VEIN. \J approximation of it, we measured, at distances of 0.15 m., 0.16 m., 0.17 m., 0.33 m., 0.34 m., and 0.35 m. from the orifice,. the thicknesses of the nappe, first in the axis itself, and second at o.io m., 0.20 m., and 0.30 m. on each side of that axis. This- operation was twice repeated on each side and four times in the axis itself, under a head of i meter. Taking the mean of 21 thicknesses thus measured from centimeter to centimeter between the limits ;ir =: o. 15 m. and .r = 0.35 m., we obtain the following results : Mean Thicknesses of Vein Measured on the Vertical between the Limits j; = 0.15 m. and x = 0.35 m. (Each of the following figures is the mean of 84 results.) Meters. On the axis o. 1200 0.10 m. to the right and left of the axis 0.1207 0.20 m. " " " " " " " " 0.1226 0.30 m. " " " " " " " " O.I2I2 The increase of the thickness at 0.20 m. from the axis is therefore 0.0026 m., or -^^. The vein rises a little near the wall of the channel. (See sketch on plate.) The swelling at 0.20 m. appeared in connection with the eddies which sometimes form in the up-stream angles, and was affected also by change.'; in the head. However this may be, it did not appear that the correction in question exceeded ybtt, and, even after this reduc- tion, the two ratios, — and--z= , are still greater than F V2g{k + y) with orifices where the contraction takes place throughout their entire perimeter. MEASUREMENT OF THE VELOCITIES IN THE INTERIOR OF THE VEINS. We have endeavored to measure directly the velocities in the interior of the vein by making use of the instrument em- ployed for a similar study in the interior of the nappes in the case of weirs. This instrument, which is simply a particular 1 8 EXPERIMENTS UPON THE form of the Pitot tube, consists of a copper plate 48 mm. wide by 3 mm. thick (Fig. a), sharpened at its upper edge and having two brass tubes 2 mm. in interior diameter soldered in a chan- nel formed in its lower edge. These two small tubes have no communication with each other. One of them has its opening at a in the up-stream extremity of the plate, and the other at b in the lateral face of the plate (Figs, e and /). The small orifices in which they terminate are 1.5 mm. in diameter and i cm. apart. The plate, introduced into the interior of the vein, does not sensibly modify the flow. It is so placed that its vertical plane is parallel to the axis of the vein, and is held between two iron guides, which enable it to resist the pressure of the fluid. Figs, a and b show the general arrangement of the apparatus. In Fig. a, which refers to the flow from vertical orifices, the plate is horizontal, while in Fig. b, which refers to horizontal orifices, it is necessary to turn the plate upward at a right angle so as to present its upper extremity normally to the orifice. The small tube A, which we shall call the velocity- tube, opens directly up-stream, and thus receives directly the shock of the liquid vein, while the pressure-tube B opens flush with the lateral face of the plate, which is parallel with the direction of flow. It is therefore subject only to the interior pressure of the filament of water passing before its terminal opening. The pressures exerted upon the two orifices A and B were transmitted by means of the tubes under the plate, and by flexible tubes of lead and caoutchouc, to two vertical glass tubes 8.5 mm. in diameter, open at their upper extremi- ties and placed side by side upon a graduated scale (Fig. c). The variations of the level of the water in these tubes thus per- mits us to observe every modification of the velocities and of the pressures in the different parts of the vein. CONTRACTION OF THE LIQUID VEIN. I9 We have made 37 experiments with the plate placed in the axis of the vein. They are as follows : Square orifice. — 8 experiments : in the plane of the orifice and at 0.04 m., 0.08 m., 0.12 m., 0.16 m., 0.20 m., 0.25 m., and 0.30 m. down-stream. Circular vertical orifice. — 7 experiments : in the plane of the orifice (under two different heads) and at 0.05 m., 0.09 m., 0.12 m., 0.13 m., and 0.15 m. down-stream. Rectangular orifice. — 6 experiments : in the plane of the orifice and at 0.05 m., o.io m., 0.15 m., 0.20 m., and 0.25 m. down-stream. Circular horizontal orifice^ 0.20 m. in diameter. — 9 experi- ments in the plane of the orifice and at 0.015 "!•> 0.035 !"•> 0.059 r"-. 0.085 m., 0.112 m., 0.135 m., 0.165 m., and 0.195 m. below the orifice. Circular horizontal orifice, o.io m. in diameter. — 7 experi- ments: in the plane of the orifice and at 0.26 m., 0.055 m- (2 experiments), 0.083 "^v 0.113 m., and 0.143 i"- below it. The heads varied between 0.95 and 0.99 m., except in the case of one of the two experiments at 0.05 5 m. from the circular horizontal orifice of o.io m. diameter, in which the head was reduced to 0.807 '^■ When the instrument just described is placed in the vein, we at once perceive, if the orifice on the velocity-tube is placed normally to the direction of flow, that the water rises in the tube to a level remaining perfectly constant. This level is v^ that of the water up-stream, plus a small head, — -, due to the 2.S velocity v of approach, if such velocity exists.* ^This velocity of approach was perceptible only in the case of the angular orifice, where — atta the other cases it was negligible. v' rectangular orifice, where — attained a value of 0.006 m. or 0.007 ™- I" 20 EXPERIMENTS UPON THE Designating by A the constant reading in the velocity- tube, we have therefore, for any point whatever in the vein, where z is the ordinate of that point, u the velocity, and P the pressure. But when the orifice of the velocity-tube is not normal to the direction of flow, as is the case on the circumference of the vein in the plane of the orifice and in the neighboring sec- tions down-stream, the level A' indicated by the tube becomes less than A* At the end of the present memoir will be found detailed tables giving the elements of these experiments. The first column shows the position of the point considered ; the second * From this result we might deduce, if not the exact measure, at least an approximate indication of the inclination cc of the axis to the direction of the flow by admitting that the level A' shown by the velocity-tube cor- responds to the action of the component « cos a parallel to the axis, which gives «* cos" a A' = Z + P- 2^ or — cos' a = A' — (z + P). If we could turn the instrument so as to present the orifice of the velocity- tube normally to the direction of flow, we should have, neglecting the velocity of approach, ' A=z+P+— 2^ or ~ ^=A-(z + P); from which, dividing the first expression by the second, "V^. {^ + ^) We thus find that the filament situated 20 mm. to one side of the circu- lar orifice would make an angle of about 30° with the axis. CONTRACTION OF THE LIQUID VEIN. 21 the head h upon the center ; the third and the fourth the heads A and B indicated by the two tubes of the instrument. The difference A — B and the value of the pressure P are ■given in the fifth and sixth columns. The ordinates, z, have been referred to the horizontal plane passing through the center of the orifice, so that the constant elevation A indicated by the velocity-tube is simply the head h upon the center. Examining the tables we find negative pressures in the sections furthest removed from the orifice, that is to say, pres- sures inferior to those of the atmosphere. This appears inad- missible, at least in so far as concerns the veins issuing from horizontal orifices where all the filaments converge, describing curves, the convexity of which is turned toward the vertical axis of the vein. These negative pressures cannot in general exist under normal conditions, but must result from the pres- ence of the instrument itself in the vein. If will be readily understood that notwithstanding the thinness of the plate car- rying the two tubes the liquid filaments must undergo a certain ■deviation and describe about the lateral orifice of the pressure- tube a curve whose concavity is turned toward that orifice. From this results a negative pressure, or suction, which reduces the level in the corresponding tube. This effect, which was not observable with the velocities measured by aid of the same instrument in our study of weirs, is rapidly accentuated with the increase of the velocity, which, in the veins issuing from our orifices, exceeded 4 m. per second. The negative pressures appeared first upon the sides of the vein. A little further from the orifice they were found in all parts of the section, but did not exceed a mean of 0.03 m. for vertical orifices and 0.06 m. for horizontal orifices, where the velocity is greater. When we calculate, by means of the velocities measured at 22 EXPERIMENTS UPON THE each point of the vein, the mean velocity for the entire section, and compare it with the value deduced from the discharge obtained in the experiments for calibration, we readily recog- nize that these negative pressures are really due to the presence of the instrument. If, in fact, we multiply each element of the surface doo by the corresponding velocity u, and then divide the sum ^udw by the total surface, £1, the mean velocity U' =^ — -;- — tnus obtained should coincide with the value U =^ ^ deduced in calibration ; but if, owing to the presence of the instrument, the pressure P becomes negative instead of remaining o or positive and very small, the velocities u deduced from the equation — = A — {s -{- P), and, consequently, their mean value U' will be somewhat too great. We obtain, therefore, by this process, mean velocities greater than those deduced from the discharge, and recognize accordingly the impossibility of attributing negative values to P. We shall first perform this calculation for the circular orifices only. The calculated velocity U' is therefore too great by about 3.5^, owing to the suction exerted upon the lateral orifice of the instrument, the presence of which causes a slight perturba- tion of the flow. The error is otherwise not explicable, for * This calculation is practicable only in the case of circular horizontal orifices, or of vertical rectangular orifices, these being the only ones where the distribu- tion of the velocities is regular. For the rectangular orifice, the elements dm are horizontal rectangles of thickness de. For the circular orifice they are circles of radius r and thickness dr. The mean velocities resulting from this method 2ude ^lurdr of calculation are -^- and — -j^ , where E is the thickness of the rectangular vein and R the radius of the circular vein. CONTRACTION OF THE LIQUID VEIN. Horizontal Circular Orifice 0.20 m. Diameter. 23 Head. Meters. 0.975 0.976 0.975 0.975 0.980 0.969 Discharge per Second. Cubic Meters. 0.08266 0.08270 0.08266 0.08266 0.08288 0.08241 Distance of Section from Plane of Orifice. Meters. 0.059 0.085 O. 112 0.135 0.165 0.195 Area of Section. Square Meters. 0.01936 0.01869 O.O1819 0.01786 0.01750 0.01723 Mean Velocity De^ duced from the Discharge. Meters per second. 4 270 4 425 4 544 4 628 4 736 4 783 Mean Velocity De- duced from Direct Meas- urements. U' Meters per second. 4.414 4.621 4.750 4.S20 4.852 4.897 Ratio. U' u I 034 X.044 1.045 1. 041 1.024 1.024 Horizontal Circular Orifice o.io m. Diameter. Re- marks A B C D E F 807 0.01902 0.055 0.004718 4.031 4.174 I 035 • G 0.970 0.02094 0.055 0.004729 4.428 4-578 1.034 H 0.974 0.02090 0.083 . 004646 4.499 4-659 1.036 1 0.976 0.02092 O.II3 0.004584 4.564 4-741 1.039 1 0.981 0.02097 0.143 0.004528 4.631 4.805 1.038 K A. Slight negative pressures at the edges. Mean = — 0.017 i"- Maximum pressure, P = -|- 0.158 m. B. Slight positive pressures in the central region ; ma.ximum, P.^ 0.035 '"I mean of negative pressures = — 0.035 •"- C. Negative pressures throughout the section. Mean — — 0.055 "i- D. " " " " " " = — 0.067 " E. " " " " " " = — 0.052 " F. " " " " " " = — 0.055 " G. Slight positive pressures at the center. Mean of negative pressures = — 0.022 m. H. Negative pressures throughout the section. Mean = — 0.033 m- I. " " " " " " = — 0.043 " J << 8i O.lR.... 0.638 0.634 0.726 0.731 0.853 0.843 0.643 0.652 0.887 0.887 0.2R.... 0.648 0.642 0.724 0.737 0.864 0.848 0.650 0.651 0.88S 0.901 0.3 A'... 0.650 0.654 0.734 0.745 0.863 0.859 651 0.660 0.904 0.894 0.4^".... 0.667 0.652 0.743 0.759 0.904 0.876 0.659 0.658 0.921 0.927 0.5A'.... 0.671 0.668 760 0.783 0.900 0.908 0.663 0.675 0.935 0.940 0.6/1'.... 0.682 0.677 0.798 0.820 0.948 929 0.689 0.688 0.964 0.974 0.7 A' 0.702 0.704 0.828 0.855 o.q8l 0.958 .... .... 0.984 0.994 0.8/t'.... 0.691 0.713 0.898 0.914 1. 000 1. 000 1,000 1. 000 CONTRACTION OF THE LIQUID VEIN. 2J Examination of the foregoing table shows with what ra- pidity the velocities vary with the distance from the orifice. For the orifice 0.20 m. diameter the ratio ^=r at the center V 2,gh of the vein is 0.84 at a distance of 0.35 m. from the orifice, while in the plane of the orifice itself it is but 0.64. For the orifice o. 10 m. in diameter, a distance O.026 m. from the orifice,, which, relatively to the diameter of the orifice, is greater than in the foregoing case, raised the same ratio from 0.64 to 0.88. At a distance'^ from the orifice we no longer find a trace of a minimum in the central region, and the velocities are com- pletely equalized throughout the entire cross-section. The velocities and the pressures vary no less rapidly up- stream from the orifice. We may take account of this by plung- into the basin up-stream, as Lagerjelm did, a vertical tube open at both ends, in such a manner that its lower end is near the plane of the orifice. Lagerjelm's experiment, often quoted, is. described in the following terms by Messrs Poacejet and Lesbros ; "M. Rudberg, the learned professor at the University of Stockholm, informed us at the time of his visit to Metz, in 1826, of the result of certain special experiments by M. Lager- jelm which seem to establish this fact,* and which he had occasion to repeat at Paris, in the presence of several members of the Royal Academy of Sciences, notably of M. Ampere. A tube, open at both ends, was plunged vertically above a circu- lar orifice formed in the plane horizontal face of a relatively very large reservoir, in such a manner that its lower extremity * The fact that the excess of the interior pressure over that of the atmos- phere appeared to differ but little from the pressure corresponding to the entire head of the liquid for all the points in the reservoir in the immediate vicinity of the orifice. 28 EXPERIMENTS UPON THE was at a little distance on one side or the other of the center of the orifice. Thereupon the liquid was seen to rise vertically in the tube nearly to the upper level of the reservoir, and to maintain practically that level so long as the lower extremity in question was not placed perceptibly below the inner edge ■of the orifice." If this fact were exact, that is to say, if the pressure P on the •center of the orifice were precisely equal to the head h, the velocity at that point would be zero, and this would be a con- tradiction of the results which we have just obtained. Desiring to ascertain the reason for this discrepancy, we repeated and completed the experiment of Lagerjelm upon our two orifices 0.20 m. and O.io m. in diameter, respectively. For this purpose we placed in the vertical line passing through the center of the orifice a glass tube opened at both ends and moved it up and down in that vertical so as to obtain the pressure not only on the plane of the orifice, but above it, up to the point where there is no longer an appreciable velocity. It was possible even to allow the tube to penetrate a little below the orifice and into the interior of the vein. The fact announced by Lager- jelm was not verified, and a material reduction of the level took place within the tube. A graduated scale attached to the tube and having its divisions visible through the liquid permitted an exact measurement of this reduction. At first we employed a tube 13 mm. in exterior diameter. When its lower extremity A touched the plane of the orifice, the re- duction BC of the level, slightly surpassed one half of the head h, hence the pressure yiC was less than h; in other words, sensibly less than the pressure obtained in our previous experi- ments. This difference is easily explained, inasmuch as the mean pressure in the dead space AD, about which the liquid filaments, separated by the tube, are in motion, previous to CONTRACTION OF THE LIQUID VEIN. 2<) their being reunited at D, is less than the pressure upon A. In order to eliminate this source of error, we substituted for the large tube AB a tube EF, tapered at the lower end, and ter- minating there in a very small orifice, i mm. in diameter. The deviation to which the filaments were subjected was thus ren- dered much less sensible, and in this way we again obtained the value of P already obtained by another process.* We moved the two tubes vertically away from the plane of the orifice until the reduction of the level became inappre- ciable. This took place when the elevation of their lower ex- tremity above the orifice was about equal to their diameter. The results are grouped in the two tables on pp. 30, 31. The first of these contains the immediate results of the experiment, that is to say, the pressure P measured in each point defined by p its ordinate z above the orifice, and the ratios of each Ii — z pressure to the corresponding head. The second table con- tains a resume of the figures given in the first, grouping to- p gether those values of which correspond, for the two orifices, to homologous points, that is to say, to points whose ordinate z has the same ratio to the diameter 2R of the orifice. An examination of the second table shows in the first place that the results are perfectly in accord for the two orifices, the P z values of -7 being equal for a given value of —^, and this is the case also with the large tube as well as with the tapering one. The discrepancy between their indications increases as the tube is plunged deeper into the liquid ; in other words, as the velocities increase. * The reduction of the level in the vertical tube increased notably when one of the eddies which we have mentioned was produced. 30 EXPERIMENTS UPON THE Height of Lower End of Tapered Tube. Cylindrical Tube. Tube above Plane of Orifice. Head. Pressure in the Tube. Ratio. p Head. Pressure in ^^°- the Tube. ^ z k P h - z' h P 1 k-z- Millimeters. Millimeters. Millimeters. Millimeters. Millimeters 1 i) Orifice 0.20 m. Diameter. + 200 1009 809 1. 000 957 75 5 0.999 + 160 1006 840 0.993 1020 85 3 0.988 + 140 995 845 0.988 997 84 3 0.984 + 120 1005 866 0.979 1005 86 t 0.973 -j- 100 lOOI 871 0.967 998 86 I 0.959 + 80 1005 868 0.938 1003 8"; \ 0.925 + 70 1000 863 0.928 lOOI 84. J o.go6 -f 60 995 838 0.896 997 82 [ 0.876 + 50 999 828 0.872 998 79 2 0.836 + 45 lOOI 814 0.851 1000 78 0.818 + 40 990 Boo 0.842 997 75 7 0.791 + 35 1008 787 0.809 lOOI 74. ! 0.769 + 30 1007 769 0.787 1000 7it ) 0.741 + 25 996 740 0.762 999 68^ ^ 0. 702 + 20 995 718 0.736 lOOI 65; 0.667 4- 15 1000 686 0.696 1000 6k ) 0.619 + 10 990 653 0.666 1003 57: 0.577 + 5 98a 619 0.635 996 52f i 0.533 999 587 0.588 1006 47c ) 0.476 - 5 998 551 0.549 1002 45c > 0.447 — 10 1000 503 0.498 998 39: i 0.390 - 15 1002 481 0.473 lOOI 35. 0.349 — 20 1002 430 0.421 1000 30; 0.299 - 25 1008 403 0.390 .... - 30 995 340 0.332 .... - 35 985 316 0.310 .... - 40 1002 280 0.269 ■ ■ > ■ - 45 955 250 0.250 • • . * - 50 1005 210 0.199 • . > - 55 998 197 0.187 — 60 1003 155 0.146 > . . . - 65 1003 "5 0.108 ( 2) Orifici ; o.io M. Di AMETER. + 100 1022 922 1. 000 1034 93: ! 0.999 + 90 1040 948 0.998 1037 94: i 0.996 + 80 1026 938 0.992 1034 94' 7 0.993 + 70 1040 957 0.987 1036 95; 0.989 + 60 1030 947 0.976 1033 95c > 0.976 -- 50 1038 954 0.966 1036 94' 1 0.960 -- 40 1032 935 0.943 1033 92C > 0.933 -- 30 1035 907 0.902 1033 83c ) 0.877 -- 20 1031 849 0.840 1035 80] 0.789 - 15 1032 802 0.789 1034 74: 0.729 -- 10 1031 750 0.735 1034 68c ) 0.664 -- 5 1031 690 0.673 1035 6o! 0.584 + 2 1032 631 0.613 1036 52; i 0.506 1032 608 0.589 1037 49f > 0.478 — 2 1032 568 0.549 CONTRACTION- OF THE LIQUID VEIN. RAsume for the Two Orifices. 31 Ratio of Value of j^. Height z to Diameter nR of Orifice. z ' Tapered Tube. Cylindrical Tube. 2^?' Diam. = 0.20 m. Diam. = o.i m. Diam. = 0.20 m. Diam. = o.io m. -- 1. 000 1. 000 1. 000 0.999 0.999 -- 0.900 .... 0.998 0.996 -- 0.800 0.993 0.992 0.988 0.993 - - 0. 700 0.988 0.987 0.984 0.989 -- 0.600 0.979 0.976 0.973 0.976 -- 0.500 0.967 0.966 0.959 0.960 - - 0.400 0.938 0.943 0.925 0.933 -- 0.350 0.928 . . . . 0.906 - - 0. 300 0.8g6 0.903 0.876 0.877 -- 0.250 0.872 0.836 -- 0.225 0.851 0.818 .... -- 0,200 0.842 0.84c 0.791 0.789 -- 0.175 0.809 . . . . 0.769 .... — 0.150 0.787 0.789 0.741 0.729 + 0.125 0.762 0.702 .... -j- O.IOO 0.736 0.735 0.667 0.664 -- 0.075 o.6g6 . . . . o.6ig -- 0.050 0.666 0.673 0.577 0.584 - - 0.025 0.635 0.533 + 0.020 .... 0.61 ' 0.506 0.588 0.58c 0.476 0.478 — 0.020 0.54c — 0.025 0.549 0.447 — 0.050 0.498 0.390 - 0.075 0.473 0.349 — O.IOO 0.421 0.299 — 0.125 0.390 — 0.150 0.332 — 0.175 0.310 — 0. 200 0.269 — 0.225 0.250 — 0.250 0.199 — 0.275 0.187 — 0.300 0.146 ' * - 0.325 0.108 ' ' * . ■ • * Considering in particular the very center of the orifice, -where z equals o, we have p Values of -7. h Tapered Tube. Large Tube. Orifice 0.20 m. in diameter 0.588 0.476 " 0.10 m." " ....0.589 0.478 32 EXPERIMENTS UPON THE When measuring the pressures we found: P Orifice 0.20 m. in diameter -r = O.59S P " o.io m. " " ^ = 0.585 The pressures indicated by the large tube are too small, as- P we have already indicated. The four other values of j are perfectly in accord, and give to that ratio the mean value 0.59. We thus have, for the corresponding velocity, zi =^ 0.64 ^2gh. The experiment was repeated with a tapering tube upon two smaller orifices 0.07 m. and 0.05 m. diameter. The reduc- tion of level, as in the case of the two orifices 0.20 m. and o.io m. diameter, first became perceptible after rising to a height nearly equal to the diameter. When the head was made to R vary between 0.50 m. and 0.90 m., we found that the ratio j was constant. Its value was 0.575 for the orifice of 0.07 m^ and 0.558 for that of 0.05 m. It thus appeared to diminish slightly with the diameter. It is not impossible that this diminution may be explained, in part at least, by the presence of the tube, the effect of which becomes more sensible with a small orifice. The experiment was, however, extremely delicate. The least displacement of the extremity of the tube caused a . P notable variatfon of the ratio -j. h The tapering tube having penetrated a little below the plane of the orifice of 0.20 m. diameter, we have, for that region, certain values comparable to those obtained by a direct meas- urement of pressures. The accord between the two methods of experimentation, is as satisfactory as could be wished. CONTRACTION OF THE LIQUID VEIN. 35 iS* o. . . . 0.025, • 0.050 ■ 0.075 • O.IOO ■ 0.175, ■ 0.275 • 0.295 ■ 0.300 - 0.325 - 0.425 Values of ; obtained. h ~ z With the Tapering Tube. 0.588 0,549 1.498 0.473 0.421 0.310 0.187 0,146 0.108 At the Time of Measuring the Velocities. 0.595 0.475 0.297 0.153- 0.029 Passing to the vertical orifices, the head being no longer constant throughout the surface of the orifice, the discussion of the results obtained with the Pitot tube leads to sensibly dif- ferent results. u Let us, in the first place, perform the calculation of ~77^^ for the two orifices with complete contraction, giving to z the values ± O.iA, ± 0.2A ... in which A denotes half the height of the opening, say o.io m. The sign -(-corresponds to points situated above the center, and the sign — to those situated below it. (See table on next page.) There is still, in the plane of the orifice, a minimum velocity u ^2gh , the value of which is approximately u = 0.64 V2gk for a square orifice, and u = 0.62 V2gk for a circular orifice. This minimum is no longer at the center, but a little above it. It disappears rapidly as the distance from the plane of the orifice increases. At 0.08 m. or 0.09 m. from that plane it is hardly perceptible. At o. lom. and 0.12 m. it disappears, and the 34 EXPERIMENTS UPON THE I s < a M 6 o> a 6 y II [I. is 5 ao ? 6 8 1 O f O^ O^ (?» odd CQ»OSO^O^O^CT»^0^ * 660666666 0-U CO 8 d cn « O o o d d <0 M M odd "^ ^ r~- '^ C" d d d d d d d is ao V d H Is ■ O CO IT) o d 1^ d en CO CT* i-i CO r-^ O^ CO CO d d d ^oO'Oor^coc^en'^ COCOOOCOOOOOOO ^ ^ 666666666 tt,!-* '. s- o C4 l-H e» IT) PI CO o TT T^ N M O O o O o o o 6666666666 1 «i. oo O 6 1 & d 1 d 1 O d 1 o o o odd 1 1 1 OOOOt-.Mh-M kH HHWen-^inor-.oo 00000000 6066666666 1 ++++++++ M K ■< D O" "a U It 11 s§ s H > 1 is a§ d a l^ V en cn o H r4 O 8 CO d m en CT" r^ vo -* 0^ O^ 0» d d d CO tHcooooo cnenco mw TrTl-enenen-*Tj--^\nin d d d d d d d d d d R,l-« o d en O d OO d CO O d g- 2 S odd MvO mJ^oo Ococo Tfr^ M HH n ooor-'UicniH WMt-iOOOOOOO 666666666-6 5 ao d a ll CO o ejo d •I- d O O es N 00 in O oo CO odd r^cnw N cnrj-inoo >-t '^ oooooococooococo c^ a^ 6666666666 a,|-« o o r^ ^ 2 r^ u^ ■^ r^ in CTi m o^ ^ N C4 Nco o^co enr-i-H eni-. >-. o^^-■^^lHO o^N cnencnwwCTWMOO o o o O O O O 0000000000 Is So a V CO o o lO m Tt lO O vO -t-M i~t wcoco TfO o*n en-1-'^Tenen^\OcO M O O o o o o o 0000000000 a.l-« in in CO « en Tt- lO VO lO o^co r^ioM encnw rf OcO t-^vOO menO^O O \n\n\rtxn\n\n-rT'^rt- o O O o o o 6666666666 '5 '^i'^ d 1 en O d 1 en o d 1 O d 1 M M M Tt en CI o o O 6 6 6 1 1 1 OMMMwenen-^ M l-^C^cn^u^^O^^00 00000000 6066666666 1 ++++++++ C o tfl d 1 d 1 d 1 m d 1 X X ^ ■d- en w d d d 1 1 1 ^ S ^' ^' ^" ^' ^" ^' \ ^' Mc:*-'"en^inior^oo d Ii 6 6 6 6 6 6 6 1 ++++++++ CONTRACTION OF THE LIQUID VEIN. 35 velocities increase continuously in crossing the vein from above to below. It now remains only to study the distribution of the veloci- ties of the rectangular orifice without lateral contraction. Ratio. z T Vertical Rectangular Orifice 0.20 m. High without Lateral Contraction. Mean Head, h = 0.949 m. Ordinate. In the Plane of the Orifice. 0.05 m. from the Orifice. o.io m. from the Orifice. P h U P h u P h w V^gh V^ V^ — 0.8.4 — 0.7.4 — 0.6.4 — 0.5.4 — 0.4.4 — 0.3.4 — 0.2.4 — 0.1.4 (center).. . . -- 0.1.4 -- 0.2/4 -0.3.4 + 0.4.4 + 0.5.4 + 0.6.4 + 0.7.4 + 0.8.4 — 0.084 — 0.074 — 0.063 — 0.053 — 042 — 0.032 — 0.021 — O.OII + O.OII + 0.021 + 0.032 + 0.042 + 0.053 + 0.063 + 0.074 + 0.084 o.2go 0.368 0.466 0.491 0.514 0.528 0.528 0.528 0.528 0.518 0.514 0.499 0.470 0.431 0.381 0.309 0.895 0.844 0.778 0.754 0.731 0.714 0.707 0.699 0.692 0.690 0.687 0.689 0.703 0.723 0.750 0.791 0.036 0.090 0.148 0.185 0.219 0.243 0.244 0.246 0.240 0.224 0.191 0.144 .0.092 0.040 1.022 0.990 0.954 0.929 0.905 0.885 0.879 0.872 0.870 0.873 0.885 906 0.928 0.951 0.965 0.013 0.048 0.042 0.050 0.041 0.033 0.021 1.038 1.033 1.028 1. 018 0.995 0.993 0.984 0.982 0.982 0.982 0.986 0.985 0.980 0.978 The minimum of the velocities, which, in the orifices with complete contraction, was only from 0.62 to 0.64 V2gk, here increases to 0.69 V2gk, owing to the suppression of the lateral contraction. It is still perceptible at 0.05 m. from the plane of the orifice, but it disappears at o.io m. r^sum:^ of the discussion of the experiments. We shall now endeavor to review in a few words the various results thus far obtained. In the first place, we remark that in our experiments we 36 EXPERIMENTS UPON THE have not observed the generally admitted existence of a con- tracted vein, if that expression is to be understood in the sense of a minimum section. In reality, the vein, after being rapidly contracted upon passing the orifice always continues to contract, much more slowly but constantly, as its distance from the orifice increases. There is no doubt as to the absence of the minimum of section for the veins issuing from our circular and rectangular orifices. As to the square orifice of 0.20 m. there may be some doubt. Messrs. Poncelet and Lesbros obtained in 1828, for the successive sections of the vein, the following figures : Distance of Section Area of Coefficient from the Orifice. the Section. of Contraction. X. O) >" = — s 0.064 m. 0.025205 m.' 0.630 0.1 10 " 0.024512 " 0.613 0.150 " 0.023746 " 0.594 0.200 " 0.023301 " 0583 0.250 " 0.023204 " 0.580 0.300 " 0.022506 " 0.563 0.350 " 6.023948 " 0.599 0.400 " 0.0^4362 " 0.609 0.500 " 0.024427 " 0.611 The value 0.022506 m.' at a distance of 0.30 m., is evidently not exact. M. Lesbros has substituted for it, in consequence of his verifications of 1834, the figure 0.023062 m.° A mini- mum exists, indeed, in the series, and corresponds to the dis- tance X = 0.30 m. Between the orifice and this minimum sec- tion, all the values of go are a little less than that which we ourselves have obtained. The two series are not entirely com- parable and the sections do not exactly correspond. The head being about 1.70 m. in the experiments of Messrs. Poncelet and Lesbros, the vein was more elongated than in ours, where the head was only 0.95. CONTRACTION OF THE LIQUID VEIN. 37 At distances greater than 0.30 m. the section becomes very difficult to measure. The vein, it is true, appears to expand, but, at the same time, it becomes hollow, forming four very sharp edges, and it is indeed uncertain whether the area of the section is really increased. Operating very carefully with our extreme section at 0.35 m. we arrived at two somewhat different values, 0.0226 m.°, and 0.0238 m.^ both less than those of the foregoing table. However this may be, the complex form of the vein and its instability render it ill adapted to a theoretical research such as that wil^h which we are occupied. Examining the distribution of the velocities in the plane of the orifice itself, we find t.hat there exists a minimum. For ■circular orifices in a horizontal plane this minimum is, of course, at the center. In the case of vertical orifices it is found a little above the center of gravity of the section. We have ■obtained as the value of this minimum 0.62 to 0.64 */2gli for orifices with complete contraction and 0.69 '^2gh for the rec- tangular orifice with the lateral contraction suppressed. As we increase the distance from the plane of the orifice, the velocities are rapidly equalized in the vein issuing from a circular orifice, and soon become uniform throughout the entire extent of the transverse section. This is not the case, however, with orifices in a vertical plane. The minimum existing in the central region soon dis- appears, but the velocities in the lower part of the vein remain greater than those in the upper part. The vein diminishes in cross-section as the distance from the orifice increases ; the section diminishing and the velocity C/" increasing by reason of the acceleration due to the fall. If we put U ^= K V2g{h -\-y), y representing the fall of the cen- ter of the section below that of the orifice, the coefficient K 38 EXPERIMENTS UPON THE is slightly less than unity in the case of the horizontal orifice. On the contrary, it exceeds unity for the vertical orifice. In both cases it appears to increase up to a certain distance from the orifice, where it attains a maximum and then diminishes progressively. This maximum would be only a few thou- sandths less than unity for horizontal circular orifices, but it might attain to 1.03 or 1.04 for vertical orifices, varying with their form and with the head. The determination of K is very delicate, since it depends upon the measurement of the transverse section, an operation which is rendered difficult by the continual movement in the liquid vein. With a circular orifice 0.20 m. in diameter, we must, in order to obtain the area of the section within o.oi of its value, be able to measure its mean diameter with an error not exceeding f of a millimeter. The great regularity of the vein permits this degree of approximation, and by measuring it by means of 24 convergent points, we obtain the maximum value oi K= i.oii. This measurement is much more difficult when the orifice is square, owing to the singularly complex form of that sec- tion. In 1828 M. Lesbros had obtained K=^ 1.064, ^n exagger- ated value, which he expected, after discussing all of the results, to be able to reduce to 1.024. Verification afterward made in 1834 gave 1.038 under a head of 1.71 m., and we our- selves obtained the value K ^^ 1.027 with a head of 0.95 m. These differences result from the causes of error inherent in the operation. The rectangular orifice without lateral contraction appeared at first very favorable to the determination of K, the measure- ment of the section being reduced to that of the thickness of the nappe. Unfortunately, however, that 'nappe oscillates in- CONTRACTION OF THE LIQUID VEIN. 39 cessantly in a manner even more pronounced than that of veins in complete contraction. We have already obtained K — 1.039 ^^ 0.30 m. from the orifice, a value probably a little too great. But, however great the difficulty of an exact determination of K, it is incontestable that that coefificient is greater than unity, with vertical orifices. This conclusion appears at first in contradiction with the fundamental principles of hydraulics. Concerning a single filament, or a pencil of filaments hav- ing equal velocities, we find indeed for K values a little less than unity owing to the internal friction of the liquid. This case is nearly realized in the circular horizontal orifice. The difference, i — K, is always very small, the effect of friction being scarcely appreciable. It would probably be the same for a vertical orifice if the head were very great relatively to its dimensions, so as to equalize the initial velocities, but the question is much more complex when the head is not very great. The velocities in the different filaments are then un- equal. Their directions depend upon the configuration of the contour of the orifice, and the formula V ^ V 2£^{A -{- f) is no longer rigorously exact from a theoretical point of view. In certain portions of the liquid vein the instrument em- ployed gives pressures less than that of the atmosphere. The comparison of these results with the discharges resulting from the direct calibration have shown that the negative pressures were due, at least so far as concerns the circular horizontal orifices, to the suction exerted by the water in motion over the small lateral orifice of the instrument. It is almost impossible, when the velocities are considerable, to eliminate this cause of error. We saw, in repeating the experiment of Lagerjelm, at what point it affected the indications of the vertical tube 13 mm. in external diameter lowered to the center of the 40 EXPERIMENTS UPON THE orifice. Although much reduced, it is certainly not com- pletely eliminated by the tapering of the tube. It is not impossible that, for certain special veins, subjected, like that of the square orifice, to considerable deformation, the divergence of certain filaments gives rise to pressures slightly less than that of the atmosphere; but, as we have just said, the experi- mental demonstration of this fact is very difficult, since we cannot completely protect the instrument used against the perturbing action exerted by neighboring filaments, when these are moving with great velocity. The experiments which we have described were made, under our direction, by M. H6gly, conducteur des Fonts et Chauss^es, whose services were placed at our disposal for the study of the flow over weirs, which we have followed for sev- eral years with the assistance of the Minister of Public Works. The knowledge and intelligence of this devoted collaborator have been of the greatest service to us in these delicate re- searches, which required a high degree of care and precision. CONTRACTION OF THE LIQUID VEIN. 41 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VEINS. The millimeter is taken as unity. The figure inscribed in the column a (position of the points taken) indicates: i. For vertical orifices, the ordinate z of the point under consideration referred to a horizontal plane passing through the center of the orifice; 2, for horizontal orifices, the distance measured hori- zontally from the point under consideration to the up-stream edge of the orifice. The indication placed at the head of each experiment, and showing the distance of the section from the plane of the orifice, refers to the position of the orifice of the pressure-tube, that of the velocity-tube being o.oi m. further up- stream. Position of Point. Head on Center of Orifice. Level in tiie Tube. Of Velocities. A Of Pressures. B Pressure. Value of A - B. Vertical Square Orifice 0.20 m. October and November, i8go. Mean Temperature of the Water, 10.5** C. (i) In the Plane of the Orifice. Mean Head, h = 0.953 m. - 81 -78 - 75 - 70 -65 - 60 - 55 - 50 - 45 - 40 - 35 - 30 - 25 - 20 - 15 - 10 - 5 o + 5 + 10 + 15 -|- 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 -f 60 + 65 + 70 + 75 + 80 + 81 952 800 302 383 498 952 820 320 398 500 952 855 390 465 465 956 865 420 490 445 953 895 460 525 435 954 905 475 535 430 950 922 510 565 412 956 929 520 570 409 952 937 525 570 412 952 940 534 574 406 955 942 538 573 404 953 945 545 575 400 952 947 554 579 393 952 948 556 576 392 951 950 558 573 392 953 953 570 580 383 951 951 561 566 390 952 952 560 560 392 952 952 563 558 389 952 952 560 550 392 953 951 562 547 389 953 951 558 538 393 954 949 562 537 387 954 950 565 535 385 953 947 562 527 385 953 946 564 524 382 952 940 558 513 382 953 938 558 508 380 952 930 547 492 383 953 922 530 470 392 953 903 515 450 388 950 898 510 440 388 950 870 482 407 388 952 830 465 385 365 953 825 460 379 365 42 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID Y-EXHS.— Continued. Position of Head on Center of Orifice. Level in the Tube. Pressure. Valiip nf Point. V aiue 01 A — 3. Of Velocities Of Pressures. a h A B P=£~z. (2) 0.04 m. below the Orifice. Mean Heac , /4 = 0.953 m. - 80 953 951 - 65 15 1016 - 75 951 947 - 50 25 997 - 70 953 950 - 25 45 975 - 65 950 945 -- 10 75 935 - 60 952 948 -- 40 100 908 - 55 953 949 + 85 140 864 - 50 952 948 + 100 150 848 - 45 954 951 -- 140 185 811 — 40 952 949 -- 145 185 804 - 35 950 948 + 185 220 763 — 30 953 953 --2I5 245 738 - 25 953 952 -- 242 267 710 — 20 953 953 + 261 281 692 — 15 952 952 + 270 285 682 — 10 953 953 + 278 288 675 - 5 953 953 + 290 295 663 952 952 + 294 294 658 + 5 953 953 + 298 293 655 -- 10 954 954 + 305 295 649 -- 15 953 953 ' + 300 285 653 + 20 955 955 --305 285 650 + 25 953 952 — 295 270 657 + 30 953 952 + 295 265 657 + 35 955 952 --295 260 657 + 40 953 950 -- 272 232 678 + 45 955 951 -- 259 214 692 + 50 952 946 --257 207 689 + 55 952 943 — 217 162 726 + 60 954 943 + 213 153 730 + 65 953 941 + 170 105 771 + 70 953 935 + 159 89 776 + 75 952 940 -j- 121 46 819 + 80 953 950 + 100 20 850 + 82 953 870 + 90 8 780 (3 1 0.08 m. below the Orifice. Mean Head, h = 0.95^ [■ - 82 953 - 71 11 - 81 953 940 - 65 16 1005 -78 955 945 - 65 13 lOIO - 74 954 950 - 40 34 990 - 70 955 945 - 40 30 9S5 - 66 952 950 - 18 48 968 - 59 955 942 — 13 46 955 - 51 952 950 + 28 79 922 - 44 955 943 + 30 74 913 -36 953 950 + 65 lOI 885 - 29 955 955 + 70 99 885 CONTRACTION OF THE LIQUID VEIN. 4J DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID NY-l^S— Continued. Position of Head on Center Level in he Tube. Pressure. Value of Point, of Orifice. Of Velocities. Of Pressures. A - B. a h A B P= B - z. — 21 953 950 -1- 94 115 856 - 14 955 955 -f- 95 109 860 - 6 955 951 + 99 105 852 + I 956 956 -1- 113 112 843 - 9 956 951 -1- 116 107 835 -- 16 950 950 + 114 98 836 --24 956 951 -|- 112 88 839 -- 31 950 950 + 114 83 836 -38 956 951 -I- 107 69 844 --45 955 958 -- 108 63 850 — 53 953 951 — 104 51 847 — 60 954 957 + 96 36 861 -1-64 955 950 + 94 30 856 + 68 952 950 - 78 10 872 + 72 954 944 -- 88 16 856- + 76 955 936 — 90 14 846 + 78 952 — 88 10 (4) 0.12 m. below the Orifice. Mean Head, /« = 0.951. - 88 950 -85 952 — 81 950 - 78 950 - 74 952 - 70 951 - 66 950 -59 952 - 51 950 - 44 954 -36 950 - 29 951 — 21 952 — 14 950 - 6 950 -F I 949 + 9 952 + 16 950 -t-24 953 + 31 950 -F38 952 + 45 950 + 53 950 + 60 950 + 64 950 + 68 951 + 72 950 -76 953 + 77 950 850 930 940 946 946 949 949 952 950 954 950 951 952 950 950 949 952 950 953 949 952 950 '949 948 946 943 935 933 - 91 - 79 -78 - 76 -63 - 56 - 40 - 25 - 10 - 2 + 11 + 16 + 28 + 34 + 40 + 45 + 52 + 60 -j- 60 + 66 + 62 + 70 + 67 + 65 + 67 + 68 + 68 + 4 + 3 - 10 - I - 4 - 6 + 3 + 3 + 11 + 19 + 26 + 27 + 32 + 30 + 34 + 33 + 31 + 29 + 28 -I- 29 + 22 + 21 + 9 + 10 + 3 - 3 - 5 - 8 - 9 934 1012 103 1 1025 1024 1025 1012 1008 990 979 960 953 941 934 922 915- 912 905. goi 887 878 879 865 44 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VY.YH'Si.—Continued. Position of Head on Center Level in the Tube, Pressure. Point. of Orifice. Value of A - B. Of Velocities. Of Pressures. a. h A B P = B ~ z (5 1 0.16 m. below the Orifice Mean Head, A = 0.952 - 97 952 , . . - 97 -96 952 800 - 92 + 4 892 — 93 952 929 - 85 + 8 IO14 -89 952 932 - 90 — I 1022 -85 950 941 -87 — 2 1028 - 8i 951 945 -84 - 3 1029 - 74 951 950 - 70 + 4 1020 -66 954 952 - 70 - 4 1022 - 59 952 952 - 55 + 4 1007 - 51 952 952 - 51 1003 -44 953 952 - 35 + 9 987 -36 950 951 - 30 + 6 981 - 29 952 952 — II + 18 963 — 21 952 952 — 9 + 12 g6i - 14 953 953 — 2 + 12 955 - 6 953 953 + 2 + 8 951 ■+ I 950 950 + 13 + 12 937 + 9 950 950 + 18 + 9 932 + 16 951 951 + 25 + 9 926 + 24 950 950 + 35 + " 915 + 31 952 952 + 43 + 12 909 + 38 952 952 + 46 + 8 906 + 45 952 950 + 55 + 10 S95 + 53 952 950 + 55 + 2 895 --60 950 947 + 64 + 4 883 -64 952 948 + 70 + 6 878 — 68 952 942 + 65 - 3 877 -72 952 937 + 71 — I 866 -75 950 900 + 62 - 13 838 -76 954 840 + 71 - 5 769 + 77 953 + 68 - 9 (6) 0.20 m. below the Orifice Mean Hea d, h =0.953 - 108 953 — no — 2 — 107 953 760 — 100 + 7 860 - 105 955 820 - 94 + 11 914 — 103 953 900 - 90 + 13 990 — 100 952 908 - 85 + 15 993 - 95 950 925 - 92 + 3 1017 - 88 951 941 - 85 + 3 1026 - 81 953 948 - 91 — 10 1039 - 73 953 950 - 86 - 13 1036 — 66 952 951 - 85 - 19 1036 - 58 953 952 - 65 - 7 1017 - 51 954 954 - 55 - 4 1009 — 43 952 952 - 40 + 3 992 - 36 953 953 - 38 — 2 991 CONTRACTION OF THE LIQUID VEIN. 45 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID NY-Y^S— Continued. Position of Head on Center of Orifice. Level in he Tube. Pressure. Value of Point. Of Velocities. Of Pressures. A - B. (* h A B P= B-z. - 28 953 953 - 28 981 — 21 953 953 — 22 — [ 975 - 13 953 953 — 12 + I 965 - 6 953 953 - 9 - 3 962 + 2 951 951 + 2 949 -- 9 953 953 -V 5 - 4 948 -- 17. 953 953 -)- 16 - I 937 -- 24 954 954 + 18 - 6 936 + 31 953 952 + 22 - 9 930 + 39 952 951 + 26 - 13 925 + 46 953 951 + 38 - 8 913 + 54 953 949 + 40 - 14 909 + 61 952 947 + 52 - 9 895 + 69 ■ 952 943 + 55 - 14 888 + 72 953 925 + 62 — 10 863 + 75 953 910 + 63 - 12 847 + 76 953 780 + 65 — II 715 + 77 953 + 65 — 12 (7) 0.25 m. below the Orifice. Mean Head, h = 0.953 m. — 126 953 — 132 - 6 - 125 952 740 - 134 - 9 874 - 118 953 855 - 136 - 18 991 — Ill 953 900 - 136 - 25 1036 - 103 952 935 -132 - 29. 1067 - 95 953 942 - 124 - 29 1066 - 88 952 947 - 124 -36 1071 - 81 955 947 - 125 - 44 1072 - 73 953 950 — no - 37 1060 - 66 952 646 - 103 - 37 1049 - 58 955 951 - 85 - 27 1036 - 51 953 951 - 80 - 29 1031 - 43 953 951 - 70 - 27 1021 - 36 952 952 - 68 - 32 1020 - 28 952 952 - 56 - 28 1008 — 21 953 953 - 50 - 29 1003 - 13 953 953 - 42 - 29 995 - 6 953 953 - 38 - 32 991 + 2 954 954 - 26 - 28 gSo -- 9 954 954 - 18 - 27 972 -- 17 952 952 — 12 - 29 964 -- 24 955 955 - 9 - 33 964 -- 31 952 952 + 3 - 28 949 -- 39 954 953 + 12 - 27 941 -- 46 953 950 + 20 — 26 930 -- 54 954 952 + 33 — 21 919 -- 61 952 947 + 41 — 20 906 46 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID Y^EVA?,.— Continued. Position of Point. Head on Center of Orifice. h Level in the Tube. Pressure. P=B-z Value of A - B. Of Velocities. A Of Pressures, B + 69 -- 75 -- 77 + 78 953 954 953 953 946 920 880 + 56 + 62 + 65 + 70 - 13 - 13 - 12 - 8 890 858 815 + + + + + (S) 0.30 m. below the Orifice. Mean Head, h = 0.953 160 953 — IdO + 20 156 953 650 - 160 — + 810 148 951 732 - 160 — 12 892 141 953 815 - 153 — 12 968 133 954 859 - 158 - 25 1017 126 953 900 - 156 - 30 1056 118 952 918 - 158 - 40 1076 III 953 935 - 152 - 41 1087 105 953 937 - 150 - 47 1087 95 953 944 - 135 - 40 1079 88 953 947 - 133 - 45 1080 81 955 949 — 120 - 39 1069 73 953 950 — 112 - 39 1062 66 954 948 - 98 - 32 1046 58 950 948 - 91 - 33 1039 51 954 952 - 90 - 39 1042 44 954 954 - 77 - 33 1031 36 952 952 - 68 - 32 1020 29 953 953 - 60 - 31 1013 21 952 952 - 48 - 27 1000 14 953 953 - 40 - 26 993 6 952 952 - 38 - 32 990 2 950 950 - 27 - 29 977 9 954 954 - 26 - 35 980 17 953 953 — 20 - 37 973 24 952 952 - 13 - 37 965 31 953 952 - 8 - 39 960 39 952 952 — I - 40 953 46 952 952 + 4 - 42 948 54 954 950 + 17 - 37 933 61 954 950 + 22 - 39 928 69 952 942 + 42 - 27 900 75 953 930 + 50 - 25 "880 78 953 780 + 66 — 12 714 80 953 + 66 - 14 Vertical Circular Orifice 0.20 m. Diameter. June, iSgo. Mean Temperature of the Water, 17*" C. (l) In the Plane of the Orifice. Mean Head, h ~ 0.952 m. - 76 952 831 340 416 491 - 71 952 856 387 458 469 - 66 953 885 435 501 450 - 61 954 895 458 519 437 CONTRACTION OF THE LIQUID VEIN. 47 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VKm?,.— Continued. Position of Point. Head on Center of Orifice. Level in he Tube. Pressure. Value of Of Velocities. Of Pressures. A - B. a h A B P= B - z - 56 952 913 484 540 429 - 51 950 921 494 545 427 -46 950 932 507 553 425 -41 952 939 517 558 422 -36 952 946 531 567 415 - 31 952 946 534 565 412 - 26 951 950 538 564 412 — 21 953 952 551 572 401 - 16 950 951 557 573 394 — II 952 952 567 578. 385 - 6 952 952 561 567 391 — I 954 954 573 574 381 - 4 952 952 573 569 379 " 9 952 953 578 569 375 - -14 951 951 576 562 375 _ -19 954 953 578 559 375 ~ -24 951 950 573 549 377 _ - 29 953 951 571 542 380 - -34 951 949 570 536 379 - -39 952 948 566 527 382 - -44 952 941 563 519 378 - -49 951 936 557 508 379 - -54 952 928 550 496 378 - -59 954 926 543 484 383 - -64 952 910 526 <62 384 H [-69 950 898 502 433 396 ^ " 74 . 951 878 491 417 387 H h79 952 848 481 402 367 (2) In the Plane of the Orifice. Mean Head, h = 0.990 m. - 81 990 828 238 319 590 -76 990 876 348 424 528 - 71 990 903 443 514 460 - 66 990 919 428 494 491 - 61 992 937 482 543 455 - 56 992 953 494 550 459 - 51 989 958 532 583 426 -46 992 966 542 588 424 - 41 991 974 541 582 433 -36 990 978 547 583 431 - 31 990 983 574 605 409 - 26 987 983 562 588 421 — 21 989 987 583 604 404 - 16 988 987 592 608 395 — II 990 989 601 612 388 - 6 992 992 595 601 397 — I 989 988 594 595 394 + 4 991 991 603 599 388 -f 9 990 989 607 598 382 48 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID N'EY^^.— Continued. Position of Head on Center Level in he Tube. Pressure. of Orifice. Value of Point. Of Velocities. Of Pressures. A - B. a h A B P= B - z ^ hl4 992 993 604 590 389 - -19 990 989 604 585 385 - -24 990 990 604 580 386 -29 989 987 605 576 382 h34 990 9B8 610 576 378 -39 991 984 607 568 377 - h44 990 974 592 548 382 - -49 989 969 592 543 377 - r 54 990 973 595 541 378 - h59 990 962 592 533 370 -64 990 940 553 489 387 -69 991 938 558 489 380 + 74 992 905 539 465 366 H r 79 990 903 532 453 371 (3) 0.05 m. below the Orifice. Mean Head h = 0.990 m. - 79 990 989 - 60 19 1049 -76 987 987 — 12 64 999 - 68 992 992 + 12 80 980 - 61 990 990 + 79 140 911 - 53 989 989 + 98 151 891 -46 9= B-z + 79 + 80 + 67 + 60 + 51 + 49 + 37 + 27 o - 13 - 16 - 17 Value of A - B. (5) 0.12 m. below the Orifice. Mean Head, h = 0.951 m. -78 - 71 -63 -56 -48 - 41 - 33 - 26 - 18 - II V' + 12 + 19 + 27 + 34 + 42 + 49 + 57 + 64 + 72 950 950 951 952 950 950 951 950 951 951 950 952 952 952 953 952 955 952 952 950 953 949 950 951 952 950 950 951 950 951 950 950 950 953 953 953 953 955 952 953 948 930 - 96 - 105 - lOI - 87 - 89 - 65 - 66 - 46 - 41 - 30 - 29 - 10 + 17 2 o + 8 + 17 + 17 + 17 + 26 + 49 - 18 - 34 -38 - 31 - 41 - 24 - 33 - 20 - 23 - 19 - 26 - 14 - 29 - 17 - 27 - 26 - 25 - 32 - 40 - 38 - 23 (6) 0.13 m. below the Orifice. Mean Head, h = 0.990 m. 918 911 917 917 917 912- 916 918- 937 944 941 932 1045- 1055 1052 1039 1039 1015 1017 996 992 986 979 960 970 951 953 945 938 935 936 922 881 -84 989 989 - 99 - 15 1088 -83 990 990 - 91 - 8 108 1 - 75 989 989 - 103 - 28 1092 - 68 990 990 - 91 — 23 108 1 - 60 990 990 - 91 - 31 1081 — 53 990 990 - 76 - 23 1066 -45 990 990 - 71 - 26 1061 -38 990 990 - 55 - 17 1045 - 30 990 990 - 43 - 13 1033 - 23 990 990 - 43 — 20 1033 - 15 989 989 - 23 — 8 1012 - 8 990 990 - 33 - 25 1023 so EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID \'£.V&S.— Continued. Position of Head on Center Level in he Tube. Pressure. Value of Point. of Orifice. Of Velocities. Of Pressures. A - B. a h A B P=B-z. 989 989 — 12 — 12 lOOI + 7 990 990 - 16 - 23 1006 + 15 989 989 - 8 - 23 997 + 22 990 990 + 4 - 18 986 H- 30 990 990 + 18 — 12 972 --37 990 990 + 4 — 33 986 --45 989 . 989 + 18 - 27 971 --52 991 991 + 11 - 41 980 --6o 990 990 + 27 — 33 963 + 67 991 991 + 49 - 18 942 (7) 0.15 m. below the Orifice. Mean Head, A = 0.951. - 86 - 78 - 71 -63 -56 -48 - 41 - 33 - 26 - 18 - II - 3 + 4 + 12 + 19 + 27 + 34 + 42 4-49 + 57 + 64 + 72 952 953 949 953 950 953 949 950 951 950 951 951 951 949 951 949 951 951 951 950 951 950 952 954 949 954 950 953 949 950 951 950 951 951 951 948 951 949 952 951 951 950 951 950 — 91 — 106 — 107 — 98 — 8b — 82 — 74 — 63 — 50 — 43 — 32 — 33 — 19 — 17 — 6 — 12 + 9 + 6 + 13 -1- 28 40 -- 68 5 1043 28 1060 36 1056 35 1052 30 1036 34 1035 33 1023 30 1013 24 lOOI 25 993 21 983 30 984 23 970 29 965 25 957 39 961 25 943 36 945 36 938 29 922 24 911 4 882 Vertical Rectangular Orifice 0.20 m. High by o. October, 1890. Mean Temperature of the Water, 13.5** (i) In the Plane of the Orifice. Mean Head, 80 M. Wide. C. -84 949 724 163 247 561 - 81 949 729 177 258 552 -76 048 792 269 345 523 - 71 950 795 260 331 535 - 66 950 860 355 421 505 - 61 948 880 375 436 505 -56 949 898 410 466 488 - 51 950 905 410 461 495 -46 949 925 439 485 486 - 41 948 930 445 486 485 -36 950 941 459 495 482 CONTRACTION OF THE LIQUID VEIN. 51 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VSXiiS— Continued. position of Head on Center Level in the Tube. Point. of Orifipf^* Pressure. Value of \J^ V^llllW-B Of Velocities. Of Pressures. A- B. a h A B P = B - z. - 31 949 945 469 500 476 - 26 949 950 480 506 470 — 21 949 952 477 498 475 - I6 949 955 495 511 460 — II 949 955 488 499 467 - 6 948 954 503 509 451 — I 949 954 500 501 454 -- 4 948 953 503 499 450 -- 9 948 952 501 492 451 --14 949 950 507 493 443 --19 949 949 509 490 440 -- 24 950 941 502 478 439 --29 948 938 508 479 430 --34 949 920 490 456 430 -f 39 949 921 488 449 433 - -44 950 900 480 436 420 - -49 949 895 465 416 430 - -54 949 870 435 381 435 - -59 950 858 430 371 428 - h64 948 825 392 328 433 -69 950 795 370 301 425 -74 950 749 335 261 414 h78 948 720 310 232 410 (2)0.05 m- below the Orifice. Mean Head, .4 = 0.949 i"- -78 949 - 75 950 - 71 950 — 68 948 -64 949 - 60 949 -56 950 — 49 949 - 41 950 - 34 947 - 26 949 - 19 948 — II 949 - 4 949 -- 4 949 -- n • 950 -- 19 950 --26 947 --33 949 --40 949 --47 949 --55 950 + 59 949 + 62 950 --66 950 + 70 949 - - 75 -h 3 943 '- 72 + 3 1015 919 - 42 -|- 29 961 915 - 25 4- 43 940 920 - 5 -f 69 915 925 - - 25 -f- 85 900 930 - - 45 -j- lOI S85 936 - L 98 + 147 838 943 - - 130 + 171 813 944 - - 169 -|- 203 775 - 950 - - 188 + 214 762 955 - -215 -f 234 740 955 - - 220 + 231 735 956 - - 232 -f-236 724 955 - - 235 + 231 720 957 - - 238 -|- 227 719 957 - -235 -1- 216 722 953 - - 220 + 194 733 955 - - 205 -1- 172 750 955 - [-177 -1- 137 778 953 - r 150 + 103 803 954 -117 -1- 62 837 951 L 102 -f 43 849 952 - h 91 + 29 861 953 - - 68 -\- 2 885 + 72 + 2 52 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID YY.l'ii?,.— Continued. Position of Point. Head on Center of Orifice. Level in the Tube. Pressure. Value of i Of Velocities. Of Pressures. A-B. " h \ A 1 B P=B-z. 1 1 (3) o.io below the Orifice. Mean Head, h = 0.949 ™ - 71 949 - 74 - 3 -67 950 956 76 - 9 1032 — 60 949 956 -69 - 9 1025 - 52 949 956 - -48 + 4 1004 - 45 949 956 - 52 - 7 1008 - 37 950 957 - 14 + 23 971 - 30 949 956 + 16 + 46 940 — 22 950 957 + 16 + 38 941 - 15 949 957 + 31 + 46 926 - 7 950 958 + 41 + 48 917 949 958 + 39 + 39 919 -- 8 950 959 + 41 + 33 918 --15 949 957 + 41 + 26 916 --23 949 958 + 39 + 16 919 + 30 950 958 + 33 + 3 925 + 37 949 958 + 35 — 2 923 + 44 948 957 + 37 - 7 920 + 52 949 957 + 45 — 7 912 + 58 950 + 48 — 10 (4 ) 0.15 below the Orifice. Mean Head, / 5 = 0.949 ™- - 75 949 - 80 - 5 - 71 949 950 — 82 — II 1032 — 68 949 — 81 — 13 .... -64 949 956 — 86 — 22 1042 — 60 949 - 85 - 25 - 56 948 954 77 — 21 1031 - 49 950 957 - 77 - 28 1034 — 41 948 956 - 47 - 6 1003 - 34 947 954 - 42 - 8 996 — 26 949 956 - 30 - 4 986 - 19 949 956 — 21 — 2 977 — II 949 956 - 7 -- 4 963 — 4 949 955 - 3 -- I 958 + 4 952 959 + I — 3 958 + 11 948 955 + 8 — 3 947 + 19 948 954 + 10 — 9 944 + 25 949 954 + 13 — 12 941 -- 33 953 960 + 18 — 15 942 --36 949 + 16 — 20 --40 947 953 + 21 — 19 932 --44 950 + 23 — 21 -48 951 957 + 29 — 19 928 + 51 948 --25 - 26 + 55 950 --33 — 22 CONTRACTION OF THE LIQUID VEIN. S3 DETERMINATION OF THE VELOCITIES AND OF THE PRESS. URES IN THE INTERIOR OF THE LIQUID N^X^S.— Continued. Position of Head oa Center Level in the Tube. Pressure. Value of Point. of Orifice. Of Velocities. Of Pressures. A — S. «. h A B P=B-!l. 1 1 (5) 0.20 m. below the Orifice. Mean Head, h = 0.949 m. - 77 950 - 95 - 18 .... - 74 950 950 - 98 - 24 1048 - 71 949 951 — no - 39 106 1 - 68 949 955 — Ill - 43 1066 -65 952 956 — 102 - 37 1058 - 61 949 956 — 100 - 39 1056 - 57 950 958 - 98 - 41 1056 - 53 943 956 - 80 - 27 1036 -46 946 954 - 65 - 19 1019 -38 949 956 - 40 — 2 996 - 31 949 957 - 40 - 9 997 - 23 949 958 - 25 — 2 983 - 16 948 956 — 20 - 4 976 - 8 949 956 - 16 - 8 972 — I 948 955 - 15 - 14 970 -- 7 948 955 - 7 955 -- 14 947 955 - 14 955 + 22 948 955 -- TO — 12 945 + 25 949 958 2 - 23 956 + 28 950 958 -- 10 - 18 948 + 32 948 956 -- 5 - 27 951 + 36 950 957 - 18 — 18 939 + 39 947 952 -(- 20 - 19 932 + 43 948 945 + 20 - 23 925 + 45 949 + 22 - 23 (6) 0.25 m. below the Orifice. Mean Heat A = 0.949 1 Tl. - 83 949 — 88 - 5 - 80 949 950 - 88 — 8 1038 -76 948 951 - 97 — 21 1048 - 72 949 955 — 100 - 28 1055 - 68 947 955 — 102 — 34 1057 -65 949 956 — 100 - 35 1056 - 6r 947 955 - 90 - 29 1045 -56 949 957 - 82 - 26 1039 - 53 947 954 — 72 - 19 1026 -46 950 958 - 62 — 16 1020 — 39 946 953 - 54 - 15 1007 - 31 950 958 — 50 - 19 1008 - 24 951 960 - 30 — 6 990 - 16 948 958 - 35 - 19 993 - 9 951 959 - 16 - 7 975 — I 949 958 - 16 - 15 974 + 6 948 958 - 8 - 14 966 + 9 949 957 — 2 — II 959 + 14 948 956 — 2 — 16 958 + 17 948 956 - 17 956 54 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VEAnS.— Continued. Position of Head on Center Level in tlie Tube. Pressure. Point. of Orifice. Value of Of Velocities. Of Pressures. A - B. a h A B P=B - z. ^ h2I 949 957 — I — 22 958 - -24 948 956 + 5 - 19 951 -28 950 958 + 8 — 20 950 -31 947 953 + 10 — 21 943 -35 949 950 + 8 - 27 942 19 20 23 28 33 38 48 53 58 69 74 79 89 94 99 104 109 114 119 129 135 140 150 155 160 171 176 179 181 Horizontal C June, 1892. (l) In the Plane 970 975 982 982 973 960 975 973 975 985 975 965 975 975 968 975 975 972 975 968 975 975 975 980 975 975 972 975 978 iRCULAR Orifice 0.20 Mean Temperatnre of the of the Orifice. Mean 835 850 860 875 895 890 942 935 955 970 965 965 975 975 968 975 975 972 975 968 975 975 975 967 958 943 goo 880 900 450 509 468 486 510 509 539 530 535 570 562 558 578 578 575 584 585 578 575 550 572 560 540 553 528 488 502 490 470 (2) 0.15 m. below the Orifice. Mean Head 15 976 775 120 18 975 820 143 23 975 855 225 28 974 885 270 33 975 900 330 38 973 908 340 44 975 925 355 49 970 940 395 54 975 940 430 M. Diameter. Water, ig". Head, h = 0.974. 450 509 468 486 510 509 539 530 535 570 562 558 578 578 575 584 585 578 575 550 572 560 540 553 528 502 490 470 , ;4 = 0.975 m. 135 158 240 285 345 355 370 410 445 385 341 392 389 385 381 403 405 420 400 403 407 397 397 393 391 390 394 400 418 403 415 435 414 430 455 398 390 430 655 677 630 615 570 568 570 545 510 CONTRACTION OF THE LIQUID VEIN. 55 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID V?A'^%.— Continued. Position of Point. Head on Center of Orifice. Level in he Tube. Pressure. Value of Of Velocities. Of Pressures. A — B. a h A B P=B - z. 64 975 965 426 441 539 74 978 974 452 467 522 84 971 968 455 470 513 94 980 980 453 468 527 105 975 975 458 473 517 115 980 980 435 450 545 125 974 974 440 455 534 135 980 980 409 424 571 145 975 968 404 419 564 150 975 968 368 383 600 155 976 965 380 395 585 160 975 950 310 325 640 165 975 942 310 325 632 170 967 gio 250 265 660 176 979 880 182 197 698 179 975 885 170 185 715 181 970 865 126 141 739 183 970 850 103 118 747- (3) 0.035 m. below the Orifice. Mean Head, h = 0.975 m. 14 17 20 25 30 40 50 60 70 80 90 100 no 120 130 140 150 160 170 175 180 183 975 976 974 974 977 972 977 975 977 974 978 971 975 971 974 972 982 974 974 979 977 974 969 959 949 947 950 v72 969 975 974 974 978 971 977 972 974 972 982 967 968 965 969 971 + 44 44 34 4 4 68 + 158 + 149 220 221 241 + 264 + 259 + 248 + 229 + 199 + 144 + 103 + 49 - 19 - 43 - 40 + + 9 9 I 31 39 + 103 + 193 + 184 + 255 + 256 + 276 + 299 + 294 + 283 + 264 + 234 + 179 + 138 + 84 + 16 1013 1003. 983 951 946 904- 811 826- 754 753- 737 707 718 724 745 773' 838- 864 919. 984- 1012 ion 18 20 21 23 28 (4) 0.059 "I- below the Orifice. 977 977 977 977 977 981 981 973 973 Mean Head, h = 0.975 m. -65 - 71 - 75 - 83 - 49 - 6 . . < . — 12 104S - 16 1052 - 24 1064 + 10 1022 56 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VYXik?,.— Continued. Position of Head on Center Level in he Tube. Pressure. Value of Point. of Orifice. A — B, Of Velocities. Of Pressures. a k A B P= B-z. 33 971 971 - 44 + 15 1015 43 977 974 — 21 + 38 995 48 974 974 + 24 + 83 950 53 974 974 + 7 + 66 967 63 972 973 + 44 + 103 929 68 974 974 + 57 + n6 917 73 969 969 + 31 + 90 938 83 979 979 + 77 + 136 902 88 976 976 + 84 + 143 892 93 974 974 + 106 + 165 868 99 971 971 + 99 + 158 872 103 974 978 + 93 + 152 885 108 974 974 + 61 + 120 913 113 969 972 + 57 + 116 915 123 979 979 + 59 + 118 920 128 974 974 + 24 + 83 950 133 974 974 + 29 + 88 945 143 977 977 — 16 + 43 993 148 974 974 — I + 58 975 153 974 974 — II + 48 985 163 974 974 - 93 - 34 1067 168 974 974 - 39 + 20 1013 173 974 974 - 93 - 34 1067 176 978 978 - 82 - 23 1060 178 974 974 - 76 - 17 1050 179 974 974 - 63 - 4 1037 181 974 971 - 63 - 4 1034 (5)0. 385 m. below the Orifice. Mean Head, h- 0.976 m. 22 974 974 - 94 - 9 1068 <27 974 974 - 133 - 48 1 107 .32 978 979 - 141 - 56 1 1 20 42 984 984 - 151 — 66 1135 52 984 984 - 119 - 34 1 103 62 979 979 — 106 — 21 1085 ■72 974 974 - 80 + 5 1054 ■82 977 977 - 64 + 21 1041 92 974 975 - 49 - h 36 1024 lOO 974 974 - 54 - - 31 1028 102 975 975 - 44 - - 41 1019 112 975 977 - 61 - - 24 1038 122 975 975 - 62 h 23 1037 1^2 979 982 - 63 + 22 1045 142 972 972 - 99 - 14 1071 152 983 983 - 93 - 8 1076 162 974 974 — 146 - 61 1120 172 - 959 964 — 136 - 51 1 100 177 975 975 - "7 - 32 1092 179 976 — lOI — 16 CONTRACTION OF THE LIQUID VEIN. 57 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID WEmS.— Continued. Position of Point. Head on Center of Orifice. Level in the Tube. Of Velocities. A Of Pressures. B ■B-z Value of A - B. (6)c .112 m. below the Orifice. Mean Head , h = 0.975 m. 24 982 - 137 - 25 .... 26 979 977 - 144 - 32 1121 31 974 974 - 171 - 59 1145 41 979 979 -178 - 66 1157 46 972 972 - 177 -65 1 149 51 973 973 — 184 - 72 1157 61 979 979 -178 - 66 II 5 7 71 969 969 - 167 - 55 1136 81 977 977 — 164 - 52 1 141 91 970 970 - 143 - 31 1113 96 974 974 - 166 - 54 1 140 101 974 974 — 169 - 57 "43 106 975 975 - 151 - 39 1126 III 973 973 - 163 - 51 1136 121 974 974 — 162 - 50 1136 131 971 971 - 172 - 60 1 143 141 971 971 - 174 -62 1145 151 974 974 — 203 -91 1177 156 974 974 — 200 - 88 1174 161 971 971 — 184 - 72 "55 171 975 975 - 183 - 71 1158 174 977 977 - 157 - 45 "34 176 976 976 - i6r - 49 "37 178 977 977 - 131 - 19 1 108 (7)c ).I35 m. beloT If the Orifice. Mean Heac I, h = 0.975 m. ^4 974 - 151 ' - 16 25 974 959 — 164 - 29 1123 ■27 979 979 — 169 - 34 1148 32 978 978 — 206 - 71 1 184 42 981 981 — 207 - 72 1188 47 969 969 - 217 - 82 1 186 52 979 979 — 221 - 86 1200 62 979 979 — 201 - 66 1180 72 972 972 — 228 - 93 1200 82 971 971 — 196 - 61 1167 92 969 969 - 191 - 56 1160 97 974 974 - 191 - 56 "65 100 974 974 - 197 - 62 1171 102 977 977 — 221 - 86 1 198 112 975 975 — 224 - 89 "99 122 979 979 - 236 — lOI 1215 132 975 975 — 228 - 93 1203 142 969 969 - 233 - 98 1202 147 969 969 - 243 — 108 I2I2 58 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID M'El^S.— Continued. Position of Head on Center Level in the Tube. Point. of Orifice. Of Velocities. Of Pressures. A - B. a h A B P=B-z 152 976 976 - 239 — 104 1215 162 971 971 — 198 - 63 1169 172 976 976 - 191 - 56 I167 175 977 977 - 151 - 16 II28 177 974 - 151 - 16 (8) 0.165 m. below the Orifice. Mean Head, h = 0.980 m. 25 27 30 35 40 50 55 60 70 75 80 90 95 100 lOI 105 no 115 125 130 135 145 150 155 165 175 177 970 980 968 980 970 979 978 986 980 978 976 982 985 980 975 985 975 987 988 975 978 985 985 980 985 980 968 980 970 979 978 986 980 978 976 982 985 980 975 985 975 987 988 975 978 985 985 970 - 175 ■ 178 ■ 203 • 185 ■ 225 ■ 225 • 228 ■ 230 230 253 222 208 235 190 193 240 250 222 232 240 210 220 230 235 220 200 178 - 10 • 13 -38 - 20 ■ 60 ■ 60 ■63 •65 •65 • 88 ■ 57 ■ 43 ■ 70 ■ 25 ■ 28. 75 85 57 67 75 45 55 65 70 55 35 13 1158 1171 1165 1195 1204 1206 1216 1210 1231 1198 iigo 1220 1 1 70 1168 1225 1225 1209 1220 1215 iigS 1208 1208 1220 1205 1170 (9) 0.195 m. below the Orifice. Mean Head, h = 0.969 m. 24 965 965 — 205 29 965 965 — 248 34 950 950 - 273 39 960 960 — 286 44 960 960 — 302 44 962 962 - 247 49 960 960 -285 54 972 972 -283 59 982 982 - 273 64 945 945 — 261 64 961 961 — 265 69 963 963 — 271 74 968 968 - 255 7ti 91 107 52 90 88 78 66 70 76 60 1170 1213 1223 1246 1262 1209. 1245 1255 1255 1206 1226 1234 1223 CONTRACTION OF THE LIQUID VEIN. 59 DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID V-S-mS.— Continued. Position of Head on Center Level in the Tube. Point. of Orifice. Pressure. Value of Of Velocities. Of Pressures. A-B. a h A B P^B-z 79 960 960 - 254 - 59 1214 84 987 987 — 252 - 57 1239 89 978 978 — 269 - 74 1247 94 960 960 — 222 - 27 II82 99 973 975 — 271 -76 1-246 104 990 990 — 200 - 5 1 190 109 975 975 — 256 - 6i 1231 114 950 950 — 220 - 25 H70 119 965 965 - 266 — 71 1231 124 975 975 — 220 - 25 1195 129 975 975 - 261 - 66 1236 134 995 995 — 222 - 27 1217 139 966 966 — 248 - 53 1214 139 970 970 — 240 - 45 1210 144 950 950 — 230 - 35 I180 149 963 963 — 228 - 33 II91 154 988 988 — 248 - 53 1236 154 965 965 — 220 - 25 1185 159 968 968 — 210 - 15 I178 164 996 996 - 257 - 62 1253 i5g 965 965 - 255 - 60 1220 174 995 - 215 — 20 .... Horizontal Circular Orifice; o.io m. Diameter. July, 1892. Mean temperature of Water, 24° C, except for the Experiments made in the Plane of the Orifice which were made in April, 1894; Temperature of Water, 14" C. (I) I n the Plane of the Orifice. Mean Head, h = 0.963 na. 20 965 923 508 508 415 25 955 930 535 535 395 30 963 950 545 545 405 35 990 982 570 570 412 40 953 950 550 550 400 45 968 967 568 568 399 50 968 967 565 565 402 50 943 943 553 553 390 50 940 938 550 550 388 50 970 970 566 566 404 55 982 984 565 565 419 60 966 961 556 556 405 65 972 973 548 548 425 70 967 958 548 548 410 75 941 935 512 512 423 80 972 933 512 512 421 (2) 0.026 m. below the Orifice. Mean Head, A =i: 0.970 m. 6 975 - 28 — 2 7 965 955 - 30 - 4 985 II 970 955 - 28 — 2 983 16 987 963 + ^4 + 40 949 6o EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID NY.1^%.— Continued. Position of Head on Center of Orifice. Level in he Tube. Pressure. Value of Point. Of Velocities. Of Pressures. A - B. a h A B P=B-z 21 960 940 + 52 + 78 888 26 990 980 + 113 + 139 867 31 970 965 + 129 + 155 836 36 981 979 + 165 + 191 814 41 988 988 + 195 + 221 793 46 978 978 + 187 + 213 791 50 945 945 + 185 + 211 760 51 976 976 + 205 + 231 771 51 974 974 + 200 + 226 774 56 975 975 + 184 + 210 791 61 960 957 + 155 + 181 802 66 974 970 + 180 + 206 790 71 972 967 -|- 100 + 126 867 75 975 968 + 90 + 116 878 76 958 948 + 51 + 77 897 81 955 943 + 20 + 46 923 86 955 935 - 23 + 3 958 89 960 950 — 27 — I 977 91 960 950 - 30 — 4 980 94 975 - 30 - 4 (3) 0.055 ™- below the Orifice. Mean Head, h = 0.807 m. 10 12 15 20 25 30 35 40 45 SO 50 50 55 60 65 70 75 80 85 88 90 806 812 803 812 800 810 806 812 800 808 812 815 800 818 797 815 798 809 810 800 775 812 803 812 800 810 806 812 800 808 812 815 800 818 797 8i5 798 809 807 700 70 68 84 95 82 68 58 60 30 42 58 45 50 82 58 90 85 92 98 92 75 - 15 - 13 - 29 - 40 - 27 - 13 - 3 - 5 + 25 + 13 + 5 27 3 35 30 37 43 37 20 (4) 0.055 P- below the Orifice 10 965 11 970 940 16 975 975 21 982 982 Mean Head, h = 0.978 m. - 58 - 70 - 93 - 108 843 896 868 868 866 842 842 866 857 865 882 876 887 900 890 907 899 775 - 3 .... - 15 lOIO - 38 1068 - 53 1090 CONTRACTION OP THE LIQUID VEIN. 6r DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URES IN THE INTERIOR OF THE LIQUID VY.Y&'S,.— Continued. Position of Head on Center Level in the Tube. Pressure. Point. of Orifice. Value of Of Velocities. Of Pressures. A-B. » h A B P=B-z 26 970 970 — 102 - 47 1072 31 978 978 — 102 - 47 1080 36 965 965 - 114 - 59 1079 41 990 990 — 102 - 47 1092 46 952 952 — 100 - 45 1052 46 992 992 - 105 - 50 1097 50 975 975 - 68 r 13 1043 50 982 982 - 58 - 3 1040 51 1000 1000 — 100 -45 1 100 56 965 965 — 108 - 53 1073 61 1000 1000 - 85 - 30 1085 66 970 970 — 80 - 25 1050 71 995 995 - 92 - 37 1087 76 972 972 - 75 — 20 1047 81 980 980 - 85 -30 1065 85 980 980 - 85 - 30 1065 88 975 975 - 79 - 24 1054 90 980 980 - 65 — 10 1045 (5)c .083 m. below the Orifice. Mean Head , h = 0.974 m. II 990 - 95 — 12 .... 12 980 950 - 95 — 12 1045 14 965 962 - 105 — 22 1067 16 965 965 - 125 - 42 1090 18 995 995 — 132 - 49 1127 21 960 960 - 142 - 59 1 102 26 955 955 — 140 - 57 1095 31 950 950 — 130 - 47 1080 36 960 960 — 122 - 39 1082 41 975 975 - 115 - 32 logo 46 980 980 — 112 — 29 1092 50 982 982 - 135 - 52 1117 51 962 962 — 120 - 37 1082 51 965 965 — 130 - 47 1095 56 972 972 - 89 - 6 io6i 61 975 975 - 130 - 47 1105 66 990 990 - 118 - 35 1108- 71 973 973 — 155 - 72 1128 76 967 967 — 148 - 65 1115 76 990 990 - 150 -67 1 140 81 975 975 - 150 -67 1125 81 990 990 - 170 -87 1 160 86 995 995 - 125 - 42 II20 89 975 - 90 - 7 .... (6) D.113 m. below the Orifice. Mean Heac \, h = 0.976 m. 12 976 — 130 - 17 13 975 900 -138 - 25 1038 16 976 976 - 155 - 42 1131 62 EXPERIMENTS UPON THE DETERMINATION OF THE VELOCITIES AND OF THE PRESS- URE IN THE INTERIOR OF THE LIQUID \Y.Y^^.— Concluded. Position of He&d on Center Level in he Tube. Point. of Orifice. Pressure. Value of Of Velocities. Of Pressures. A—B. "• h A B P=B-z 21 978 978 - 175 - 62 II53 26 971 971 - 185 - 72 I156 31 977 977 — 180 -67 II57 36 972 972 - 178 -65 I150 41 976 976 - 156 - 43 II32 46 972 972 - 175 - 62 1 147 50 970 970 - 165 - 52 II35 51 978 978 - 170 - 57 1 148 56 975 975 — 163 - 50 II38 61 976 976 - 185 - 72 I161 66 978 978 - 165 - 52 1 143 75 976 975 — 200 -87 I175 76 980 980 - 190 - 77 I170 Si 977 975 — 180 -67 1155 86 976 976 - 150 - 37 I126 «8 978 800 - 128 - 15 928 «9 977 — 125 — 12 (7) 0.143 m- below the Orifice. Mean Heac , A = 0.981 m. 11 996 800 — 160 - 17 960 12 973 973 - 173 - 30 1 146 12 1000 980 - 170 -27 1150 l6 990 990 — 190 - 47 1180 21 973 973 — 192 - 49 1165 26 986 986 — 212 -69 1198 31 968 968 - 185 - 42 1153 36 1000 1000 — 205 - 62 1205 36 974 974 — 212 -69 1186 41 980 980 - 195 - 52 1175 46 986 986 - 215 - 72 1201 50 973 973 — 210 -67 1183 50 980 980 — 220 - 77 1200 50 990 990 — 211 - 68 1201 II 972 972 — 190 - 47 1162 56 1000 1000 ~ 209 - 66 1209 56 973 973 — 210 -67 1183 61 975 975 ~ 210 -67 1185 66 985 985 — 206 - 63 1191 71 976 975 - 218 - 75 1 193 76 980 980 — 210 -67 1190 81 972 972 — 208 -65 1180 84 972 972 - 185 -42 "57 86 980 930 - 170 - 27 1 100 88 972 900 - 170 - 27 1070 89 972 - 150 - 7 CONTRACTION OF THE LIQUID VEIN. 63 PROFILES OF THE VEIN FOR THE RECTANGULAR ORIFICE. 0.20 m. high by 0.80 m. wide. Measurements in Millimeters. (i) Lower Surface. 'The point o is zg millimeters from the orifice for the heads 7S7 and I the heads 836, 950, and 1006. , and 23 millimeters for Abscissas or Ordinates. Distances from the Point 0. h = 787. h = 836. h = 888. h = 950. h = 1006. 20.3 19.9 20.0 20.4 20.1 10 22.7 21. 8 21.8 23-5 23.5 20 24.5 25-3 24.4 25.2 25.3 30 25.7 26.8 2S.5 26.6 27.8 40 27.3 28.3 28.0 28.2 28.8 50 27.9 29.3 27-5 29.5 28.8 60 28.6 2B.3 29.0 29-3 29.5 70 27.5 29.1 29.3 29.3 29.9 80 27.8 29-3 28.9 29-3 30.8 90 26.9 27.0 28.5 29.0 3*1 100 27.6 27-5 27.8 27.9 30.0 no 26.5 26.8 27.5 27.2 29.1 120 25 2 27-3 27.4 26.8 29.9 130 26.0 26.0 26.3 26.2 27-3 140 23.2 26.0 24.4 25.1 25-9 150 23-5 23.8 24.4 25.1 25-5 160 20.5 23.0 24.3 23.5 23.4 170 19-5 23.0 23.0 21.8 22.3 180 19.0 19-5 21,5 21.3 21.5 190 19.0 18.3 21.5 20.1 21.5 200 .... 18.3 18.3 .... 210 14.5 17-5 17-5 19.1 19.8 230 12.0 13-3 14.9 16.3 16.8 :250 9-3 9.8 II. 10.8 13-3 270 3-5 2.8 8.0 7.4 10.8 290 0.5 0.8 4.0 6.0 7-1 310 — I.O 1.8 5-3 320 - ' 8".3 .... — 2.0 330 - 4-7 - 3-0 0.8 350 -16.5 - ■ 8'.9 - 3.7 360 - 11-7 .... - 11-7 370 .... -■8'.4 390 -25.5 - 22.7 - 18.5 -17.9 - 13.8 420 .... - 23.9 — 20.5 430 - 34-7 — 25.2 .... 450 — 31-7 — 24.7 490 .... — 48.0 - 33-7 530 .... - 54-6 -48.7 64 EXPERIMENTS UPON CONTRACTION OF LIQUID VEIN. PROFILES OF VEIN FOR RECTANGULAR 0-&X?lCY..— Concluded. (2) Upper Surface. The point o is ig millimeters from tlie Orifice for tlie lieads 792 and 836, and 23 millimeters for the heads 885, 949, and 1004. Abscissas or Ordinates. from Point 0. h = 792. A = 836. k = 885. A = 949. A = 1004. 179.6 178.3 178.0 178.6 179-7 10 175.1 17I-9 172.4 174.0 172.5 20 170.3 167-9 168. 1 168.2 168.9 30 165.8 166.4 166.4 165.8 166.9 40 162.9 162.8 162.5 163.7 164. 1 50 162.2 161. 8 161. 3 160.2 162.9 60 160.6 159-7 157.9 159-4 161. 7 70 158.I 158.7 157-7 157-7 158.2 80 157.I 155-5 156.2 156.0 156.8 90 155.0 I53-I 153-1 156.6 156.4 100 154-6 153-1 151. 6 152.5 154-6 no 152.5 151-4 150.6 150.6 152.4 120 149-3 150.4 .149.6 150. 1 152.4- 130 148.8 148.6 149.9 151-0 151. 1 140 148.0 147.3 147.6 T48.6 149.8 150 146.5 146.5 145.6 148.4 148.4. 160 144.2 145. 1 1 44- 1 146.0 145-3 170 142.6 143.6 143.6 141. 6 142.8 180 140.7 142.5 138.6 141.4 142.6 I go 140.5 138.8 138.1 139.6 142.8 200 137-3 139- 1 139-I 210 136.5 137.6 136.0 139.6 141.1, 230 132.3 133.6 132.0 139.6 135-6 250 130.5 127.6 131. 1 133.3 135-2 270 127.4 126.5 126.4 127.8 131. 8 2go 122.6 123.8 123. 1 126.6 126.7 310 113. 6 120.3 124.2 320 II5.I 115.3 330 112.7 116. 7 123.4 350 103.7 109.6 118.2 360 106.2 113. 6 370 111.9 390 93-7 95-7 98.6 106.8 106.3 420 102.3 102.8 430 87.8 89.2 440 82.8 450 92.8 94.9, 470 76.8 490 67-8 68.9 80.9 81.9 510 65-3 530 68.9 73-2 540 48.2 55-9 550 52-9 590 31.4 34.0 38.1 52.7 56-0 630 32.0 640 17.0 36-9 690 - 16. 1 - 8.0 — I.O 135 19.5 790 - 55.5 - 50.9 - 43.9 - 25.9 — 26.2 890 — 113. - 97-8 - 95.9 - 71.9 — 61.9 990 - 176.9 - 158.6 - 157-0 - 132.7 — no. 7 1090 - 219.7 - 190.7 - 166.6 1^ ._ -2,-20- -OjOT f Elevation of Down-strenm Face. Section. Barbibk containing Square or C^ircular Orifice. Scale 0.03 = 1. ¥ ;D -ZfiO- a c e y i ! i bi (li f ^ Flan of Vein Elevation of Down-Btream Face. 8eotlon. Barrier containing Rectangular Orifice. Scale 0.03 = 1. r- s 1 n fD in — 1M;6->| t<-161,2^ Vm,i^' Section ab. O.SO m. l>om Orlflee. 0.80 Section ed. m. from Orlflee. l.SO Section ef. m. from Orl Vein issuing from Vertical Circular Orifice. Scale 0.05 = 1. Blan of Yeiu Section on Axis of Channel. Transverse Section throncb Center of Orlflee. Areangembnt of Horizontal Circular Orifice, Scale 0.03 = 1. Section sh. 0.10 m. fi-om Orifice, Section IJ. O.SO m. from Orlflee. Section kl. 0.86 m. iVom Orlfloe. Vein issuing from Vertical Square Orifice. Scale 0.05 = 1. Plate containing Circular Orifice. Section on Axis of Jet. Vein issuing from Vertical Rectangular Orifice. Scale 0.05 = 1. Apparatus for obtaining Transverse Sections of Veins. Cross-section of Vein from Rectangular Orifice. (Variations exaggerated.) Fig. a Fig. b Fig.e For Vertical Orifices. A sag.f / %-is.A V - 1 For Horizontal Orlflcea. Up-stream ends of Blade, Apparatus for measuring Velocities and Pressures in Veins issuing from Vertical and Horizontal Orifices. TJp-«itream yj vatoi le\el E ^ r^ Apparatus for Asckktaining Pressures within and aiiove a Vein issuing from a Horizontal Orifice. SHORT-TITLE CATALOGUE OF THE PUBLICATIONS OF JOHN WILEY & SONS, New York. London: CHAPMAJST & HALL, Limited. ARRANGED UNDER SUBJECTS, Descriptive circulars sent on application. Books marked with an asterisk are sold at net prices only. All books are bound in cloth unless otherwise stated. AGRICULTURE. Cattle Feeding— Dibeasbs of Animals — Gakdbning, Etc. Armsby's Manual of Cattle Feeding 12mo, $1 75 Downlng's Fruit and Fruit Trees 8vo, 5 00 Kemp's Landscape Gardening 13mo, 3 50 Stockbridge's Rocks and Soils 8vo, 3 50 Lloyd's Science of Agriculture 8vo, 4 00 Loudon's Gardening for Ladies. (Downing.) 13mo, 1 50 Steel's Treatise on the Diseases of the Ox 8vo, 6 00 Treatise on the Diseases of the Dog Svo, 3 50 Grotenfelt's The Principles of Modern Dairy Practice., (Woll.) 13mo, 3 00 ARCHITECTURE. Building — Carpentry — Stairs, Etc. Berg's Buildings and Structures of American Railroads 4to, 7 50" Birkmire's Ai cliitectural Iron and Steel Svo, 3 50 " Skeleton Construction in Buildings Svo, 3 00 ;2 00 3 00 3 00 2 50 4 00 5 00 5 00 4 00 1 00 3 00 2 50 75 1 35 2 50 Birkmire's Compound Riveted Girders 8vo, American Theatres —Planning and Construction . 8to, •CaTpenter's Heating and Ventilating of Buildmgs.'. . .....'. .8vo, Treitag's Architectural Engineering Svo, Kidder's Architect and Builder's Pocket-book Morocco flap, Hatfield's American House Carpenter Svo, " Transverse Strains Svo, Monckton's Stair Building — Wood, Iron, and Stone 4to, Gerhard's Sanitary House Inspection 16mo, Downing and Wightvfick's Hints to Architects Svo, Cottages Svo, Holly's Carpenter and Joiner ISmo, Worcester's Small Hospitals- -Establishment and Maintenance, including Atkinson's Suggestions for Hospital Archi- tecture 13mo, The World's Columbian Exposition of 1893 4to, ARMY, NAVY, Etc. Military Enginebring — Ordnance — Port Charges, Etc. ■Cooke's Naval Ordnance Svo, f 12 50 Metcalfe's Ordnance and Gunnery 13mo, with Atlas, 5 00 Ingalls's Handbook of Problems in Direct Eire Svo, 4 00 " Ballistic Tables Svo, 1 50 Bucknill's Submarine Mines and Torpedoes Svo, 4 00 Todd and Whall's Practical Seamanship Svo, 7 50 3Iahau's Advanced Guard ISmo, 1 50 " Permanent Fortifications. (Mercur.).Svo, half morocco, 7 50 Wheeler's Siege Operations Svo, 3 00 WoodhuU's Notes 'on Militarj' Hygiene 12mo, morocco, 2 50 Dietz's Soldier's First Aid 12mo, morocco, 1 35 Young's Simple Elements of Navigation.. ISroo, morocco flaps, 3 50 Reed's Signal Service 50 Phelps's Practical Marine Surveying Svo, 3 50 Very's Navies of the World Svo, half morocco, 3 50 Bourne's Screw Propellers 4to, 5 00 Hunter's Port Charges .8vo, half morocco, $13 00 "* Dredge's Modern French Artillery. .;..*.. .4to, half morocco, 30 00 " Record of the Transportation Exhibits Building, World's Columbian Exposition of 1893.. 4to, half morocco, 15 00 Mercur's Elements of the Art of War 8vo, 4 00 " Attack of Porlifled Places. 13mo, 3 00 Chase's Screw Propellers Svo, 3 00 Winthrop's Abridgment of Military Law 13mo, 3 50 De Brack's Cavalry Outpost Duties. (Carr.). .. .18mo, morocco, 3 00 Cronkhite's Gunnery for Non-com. Officers 18nio, morocco, 3 00 Dyer's Light Artillery 12mo, 3 00 Sharpe's Subsisting Armies 18mo, 1 35 " " " 18mo, morocco, 1 50 Powell's Army Officer's Examiner ISmo, 4 00 Hoffs Naval Tactics Svo, 150 BrufE's Ordnance and Gunnery Svo, 6 00 ASSAYING. Smelting — Obk Drbssing— Alloys, Etc. Turman's Practical Assaying Svo, 3 00 Wilson's Cyanide Processes 13mo, 1 50 Pletcher's Quant. Assaying with the Blowpipe.. 13mo, morocco, 1 50 Bicketts's Assaying and Assay Schemes ; Svo, 3 00 * Mitchell's Practical Assaying. (Crookes.) Svo, 10 00 Thurston's Alloys, Brasses, and Bronzes Svo; 2 50 Hunhardt's Ore Dressing i Svo, 1 50 -O'Driscoll's Treatment of Gold Ores Svo, 3 00 ASTRONOMY. Pbactical, Theoretical, and Descriptive. Michie and Harlow's Practical Astronomy Svo, 3 00 White's Theoretical and Descriptive Astronomy 12mo, 2 00 Doolittle's Practical Astronomy Svo, 4 00 iCraig's Azimuth .4to, 3 50 vGore's Elements of Geodesy Svn. 2 50 BOTANY. Gardening fok Ladies, Etc. Westermaier's General Botany. (Schneider.) 8vo, f 3 OO Thomg's Structural Botany 18mo, 2 35- Baldwin's Orchids of New England 8vo, 1 50 Loudon's GJardening for Ladies. (Downing.) 13mo, 1 50' BRIDGES, ROOFS, Etc. Cantilever — Highway — Suspension. Boiler's Highway Bridges 8vo, 3 00 * " The Thames River Bridge 4to, paper, 5 00 Burr's Stresses in Bridges 8vo, 3 51) Merriman & Jacoby's Text-book of Roofs and Bridges. Part L, Stresses 8vo, 3 50 Merriman & Jacoby's Text-book of Roofs and Bridges. Part IL, Graphic Statics 8vo, 3 50 Merriman & Jacoby's Text-book of Roofs aud Bridges. Part III., Bridge Design 8yo, 5 00' Merriman & Jacoby's Text-book of Roofs and Bridges. Part IV., Continuous, Draw, Cantilever, Suspension, and Arched Bridges (In preparation). Crehore's Mechanics of the Girder 8vo, 5 OO Du Bois's Strains in Framed Structures 4to, 10 OO Greene's Roof Trusses 8vo, 1 35 " Bridge Trusses 8vo, 2 50' " Arches ill Wood, etc 8vo, 2 50 Waddell's Iron Highway Bridges 8vo, 4 00 Wood's Construction of Bridges aud Roofs 8vo, 3 OO Foster's Wooden Trestle Bridges 4to, 5 00 *Morison's The Memphis Bridge Oblong 4to, 10 00 Johnson's Modern Framed Structures 4to, 10 OO CHEMISTRY. Qualitative — Quantitative — Organic— Inorganic, Etc. Fresenius's Qualitative Chemical Analysis. (Johngon.) 8vo, 4 00 " Quantitative Chemical Analysis. (Allen.) 8vo, 6 00 (Bolton.) 8vo, 1 50 Cvafts's Qualitative Analysis. (SchaefEer.) 12mo, Perkins's Qualitative Analysis 12mo, Thorpe's Quantitative Chemical Analysis 18mo, Classen's Analysis by Electrolysis. (Herrick.) 8vo, Stockbridge's Rocks and Soils 8vo, O'Brine's Laboratory Guide to Chemical Analysis 8vo, IVIixter's Elementary Text-book of Chemistry 13mo, "Wulling's Inorganic Phar. and Med. Chemistry 12mo, 3Iandel's Bio-chemical Laboratory 12mo, Austen's Notes for Chemical Students 12mo, Schimpf's Volumetric Analysis 12mo, Bammarsten's Physiological Chemistry (Maudel.) 8vo, Miller's Chemical Physics 8vo, Pinner's Organic Chemistry. (Austen.) 12mo, Kolbe's Inorganic Chemistry 12mo, Eicketts and Eussell's Kotes on Inorganic Chemistry (Non- metallic) Oblong 8vo, morocco, Drechsel's Chemical Reactions. (Merrill.) 12mo, Adriance's Laboratory Calculations 1 2mo, Troilius's Chemistry of Iron , 8vo, Allen's Tables for Iron Analysis .8vo, Nichols's Water Supply (Chemical and Sanitary) 8vo, Mason's " " " " " 8vo, Spencer's Sugar Manufacturer's Handbook . 12mo, morocco flaps, "Wiechmann's Sugar Analysis 8vo, " Chemical Lecture Notes 12rao, DRAWING. Elbmentakt — Gkometeical — Topographical. Hill's Shades and Shadows and Perspective. . . .(In preparation) Mahan's Industrial Drawing. (Thompson.) 3 vols., 8vo, 3 50 MacCord's Kinematics 8vo, 5 00 " Mechanical Drawing 8vo, 4 00 " Descriptive Geometry 8vo, 3 00 Reed's Topographical Drawing. (II. A.) 4to, 5 00 Smith's Topographical Drawing. (Macmillan.) 8vo, 2 50 Warren's Free-hand Drawing 12mo, 1 00 5 $1 50 1 00 1 50 3 00 2 50 2 00 1 50 2 00 1 50 3 50 4 00 2 00 1 50 1 50 75 1 25 1 25 2 00 2 50 5 00 2 00 3 50 3 00 Warren's Drafting Instrumeuts 13mo, $1 25 " Projection Drawing 12mo, 150 " Linear Perspective., 12mo, 100 Plane Problems , 12mo, 135 " Primary Geometry 13mo, 75 " Descriptive Oeometry 2vols.,8vo,. 3 50 " Problems and Theorems 8vo, 2 50 " Machine Construction. ., 2 vols., 8vo, 7 50 " Stereotomy— Stone Cutting 8vo, 3 50 " Higher Linear Perspective 8vo, 3 50 Shades and Shadows 8vo, 3 00 Whelpley's Letter Engraving 12mo, 2 00 ELECTRICITY AND MAGNETISM. Illumination — Battbkies — Physics. * Dredge's Electric Illuminations. . . .3 vols. , 4to, half morocco, Vol.11 4to, Niaudet's Electric Batteries. (Fishback.) 12mo, Anthony and Brackett's Text-book of Physics 8vo, Cosmic Law of Thermal Repulsion 18mo, Thurston's Stationary Steam Engines for Electric Lighting Pur- poses 13mo, Michie's Wave Motion Relating to Sound and Light 8vo, Barker's Deep-sea Soundings 8vo, Holman's Precision of Measurements 8vo, Tillman's Heat 8vo, Gilbert's De-magnete. (Mottelay.) 8vo, Benjamin's Voltaic Cell 8vo, Reagan's Steam and Electrical Locomotives 12mo ENQINEERINQ. Civil — Mechanical— Sanitary, Etc. * Trautwine's Cross-section Sheet, 25 * " Civil Engineer's Pocket-book. ..12mo, nior. flaps, 5 00 * " Excavations and Embankments 8vo, 2 00 * " Laying Out Curves 12mo, morocco, 3 50 Hudson's Excavation Tables. Vol. II 8vo, 1 00 6 25 00 7 50 2 50 4 00 75 1 50 4 00 2 00 2 00 1 50 2 50 8 00 3 00 Searles's Field Eugineering. 12mo, morocco flaps, $3 Off " Railroad Spiral 12iiio, morocco flaps, 1 50 Godwin's Railroad Engineer's Field-book. 13mo,pocket-bk. form, 2 50 Butts's Engineer's Field-book 12mo, morocco, 2 50 Gore's Elements of Goodesy ..8vo, 2 50 Wellington's Location of Railways .8vo, 5 00' * Dredge's Penn. Railroad Construction, etc. . . Polio, half mor., 20 00' Smith's Gable Tramways. .......' 4to, 2 50' " Wire Manufacture and Uses 4to, 3 00 Mahan's Civil Engineering. (Wood.) 8vo, 5 00' Wheeler's Civil Eugineering 8vo, 4 00 Mosely's Mechanical Engineering. (Mahan.) Svo, 5 00 Johnson's Theory and Practice of Surveying Svo, 4 00- " Stadia Reduction Diagram. .Sheet, 22 J x 28i inches, 50 * Drinker's Tunnelling .4to, half morocco, 25 00- Eissler's Explosives— Nitroglycerine and Eiynamite Svo, 4 00 Foster's Wooden Trestle Bridges. 4to, 5 OO' RuSner's Non-tidal Rivers Svo, 1 25- Greene's Roof Trusses Svo, 1 25 " Bridge Trusses Svo, 2 50 Arches in Wood, etc. .Svo, 3 50 Church's Mechanics of Engineering— Solids and Fluids Svo, 6 00 ' ' Notes and Examples in Mechanics Svo, 3 00 Howe's Retaining Walls (New Edition.) ."l2mo, 1 25 Wegmann's Construction of Masonry Dams 4to, 5 00 Thurston's Materials of Construction, Svo, 5 00 Baker's Masonry Construction Svo, 5 00 Surveying Instruments.. ... .: 12mo, 3 00 Warren's Stereotomy— Stone Cutting Svo, 2 50' Nichols's Water Supply (Chemical and Sanitary) Svo, 2 50 Mason's " " " " " Svo, 5 00 Gerhard's Sanitary House Inspection 16mo, 1 00' Kirkwood's Lend Pipe for Service Pipe Svo, 1 50 Wol£['s Windmill as a Prime Mover Svo, 8 00' Howard's Transition Curve Field-book 12mo, morocco flap, 1 50' Crandali's The Transition Curve ....12mo, morocco, 1 50' 7 Crandall's Earthwork Tables 8vo, f 1 50 Patton'a Civil Engineering 8vo, 7 50 " Foundations 8vo, 5 00 Carpenter's Experimental Engineering 8vo, 6 00 Webb's Engineering Instruments 12mo, morocco, 1 00 Black's U. S. Public Works 4to, 5 00 Merriman and Brook's Handbook for Surveyors. . . .12mo, mor., 2 00 Merriman's Betaining Walls and Masonry Dams 8vo, 2 00 " Geodetic Surveying 8vo, 2 00 Kiersted's Sewage Disposal ISmo, 1 25 Siebert and Biggin's Modern Stone Cutting and Masonry. . .8vo, 1 50 Kent's Mechanical Engineer's Pocket-book 12mo, morocco, 5 00 HYDRAULICS. Wateh-whbkls — Windmills — Service Pipe — Dkainagb, Etc. Weisbach's Hydraulics. (Du Bois.) 8vo, 5 00 Merriman's Treatise on Hydraulics. . , 8vo, 4 00 Oanguillet&Kutter'sFlowof Water. (Hering&Trautwine.).8vo, 4 00 J!Tichols's Water Supply (Chemical and Sanitary) 8vo, 2 50 Wolff's Windmill as a Prime Mover 8vo, 3 00 Perrel's Treatise on the Winds, Cyclones, and Tornadoes. . .8vo, 4 00 Kirkwood's Lead Pipe for Service Pipe 8vo, 1 50 IRuffner's Improvement for Non-tidal Rivers 8vo, 1 25 "Wilson's Irrigation Engineering 8vo, 4 00 Uovey 's Treatise on Hydraulics .8vo, 4 00 Wegmann's Water Supply of the City of New York . . . .. ..4to, 10 00 Hazen's Filtration of Public Water Supply 8vo, 2 00 JIason's Water Supply— Chemical and Sanitary 8vo, 5 00 Wood's Theory of Turbines , 8vo, 2 50 MANUFACTURES. Aniline — Boilers—Explosives — Ibon— Sugar — Watches- Woollens, Etc. IVEetcalfe's Cost of Manufactures 8vo, 5 ■ 00 Jttetcalf 's Steel (Manual for Steel Users). 12mo, 2 00 Allen's Tables for Iron Analysis 8vo, 8 "West's American Foundry Practice ISmo, |2 50 " Moulder's Text-book 12mo, 2 50 Spencer's Sugar Manufacturer's Handbook 12mo, mor. flap, 2 00 Wiechmann's Sugar Analysis. ' 8vo, 2 50 ■Beaumont's Woollen and Worsted Manufacture 13mo, 1 50 *Reislg's Guide to Piece Dyeing 8to, 35 00 Dissler's Explosives, Nitroglycerine and Dynamite 8vo, 4 00 Jleimann's Aniline Colors. (Crookes.). 8vo, 2 50 Ford's Boiler Making for Boiler Makers 18mo, 1 00 Tliurston's Manual of Steam Boilers 8vo, 5 00 Booth's Clock and Watch Maker's Manual 13mo, 2 00 Holly's Saw Filing 18mo, 75 .■Svedelius's Handbook for Charcoal Burners 12mo, 1 50 The Lathe and Its Uses 8vo, 6 00 W^oodbury's Fire Protection of Mills 8vo, 2 50 IBolland's The Iron Founder 13mo, 3 50 Supplement .12mo, 3 50 " Encyclopaedia of Founding Terms 13aio, 3 00 JBoavier's Handbook on Oil Painting 13mo, 3 00 •Steven's House Painting 18mo, 75 MATERIALS OF ENQINEERINQ. Stkkngth — Elasticity — Resistance, Etc. Thurston's Materials of Engineering 3 vols., 8vo, 8 00 Vol. I., Non-metallic 8vo, 2 00 "Vol. II., Iron and Steel 8vo, 3 50 Vol. III., Alloys, Brasses, and Bronzes 8vo, 3 50 Thurston's Materials of Construction ' 8vo, 5 00 JBaker's Masonry Construction 8vo, 5 00 Xanza's Applied Mechanics ;....'.; 8vo, 7 50 " Strength of Wooden Columns 8vo, paper, 50 Wood's Resistance of Materials 8vo, 3 00 Weyrauch's Strength of Iron and Steel. (Du Bois.) 8vo, 1 50 Burr's Elasticity and Resistance of Materials 8vo, 5 00 Merriman's Mechanics of Materials , 8vo, 4 00 "Church's Mechanic's of Engineering — Solids and Fluids 8vo, 6 00 9 Beardslee and Kent's Strength of Wrought Iron. ........ . .8to, $1 50 Hatfield's Transverse Strains .8vo, 5 00 Du Bois's Strains in Framed Structures. 4to, 10 00 Merrill's Stones for Building and Decoration 8vo, 5 00 Bovey's Strength of Materials 8vo, 7 50 Spalding's Roads and Pavements , 12mo, 3 00 Rockwell's Roads and Pavements in France 12mo, 1 25 Byrne's Highway Construction .8vo, 5 00 Pattou's Treatise on Foundations 8vo , 5 00' MATHEMATICS. Calculus — Gkometkt — Trigonombtky, Etc. Rice and Johnson's Difierential Calculus 8vo, " Abridgment of Differential Calculus 8vo, " Differential and Integral Calculus, 2 vols, in 1, 12mo, Johnson's Integral Calculus 12mo, " Curve Tracing 12mo, " Differential Equations — Ordinary and Partial 8vo, " Least Squares 12mo, Craig's Linear Differential Equations 8vo, Merriman and Woodward's Higher Mathematics. 8vo, Bass's Differential Calculus 12rao, Halsted's Synthetic Geometry 8vo, " Elements of Geometry c..8vo, Chapman's Theory of Equations 12mo, Merriman's Method of Least £ juares 8vo, Comptou's Logarithmic Computations .12mo, Davis's Introduction to the Logic of Algebra 8vo, Warren's Primary Geometry 12mo, " Plane Problems 12mo, ' ' Descriptive Geometry ^ .!..... 2 vols. , 8 vo, " Problems and Theorems 8vo, " Higher Linear Perspective 8v6, " Free-hand Drawing 12mo, " Drafting Instruments 12nio, 10 3 50- 1 50 2 50 1 50 1 00- 3 50 1 50- 5 00- 1 50- 1 75 1 50 2 00- 1 50' 1 50- 75. 1 25. 3 50- 2 50 3 50 1 OO 1 25. Warren's Projection Drawing ,.., 12mo, $1 50> Linear Perspective ISmo, 1 OO " Plane Problems 12mo, 125- Searles's Elements of Geometry 8vo, 1 50- Brigg's Plane Analytical Geometry 12mo, 1 00' "Wood's Co-ordinate Geometry 8vo, 2 00' Trigonometry ■ 12rao, 100 Mahan's Descriptive Geometry (Stone Cutting) 8vo, 1 50' Woolf s Descriptive Geometry Royal Svo, 3 00' Ludlow's Trigonometry with Tables. (Bass.) Svo, 3 00' " Logarithmic and Other Tables. (Bass.) ..Svo, 2 00' Baker's Elliptic Functions Svo, 1 50' Parlier's Quadrature of the Circle Svo, 2 50 Totten's Metrology Svo, 2 50- Ballard's Pyramid Problem , Svo, 1 50 Barnard's Pyramid Problem Svo, 1 50" MECHANICS-MACHINERY. Text-books and Practical Works. Dana's Elementary Mechanics 12mo, 1 50' Wood's " " 12mo, 125 " " " Supplement and Key 1 25 " Analytical Mechanics Svo, BOO Michie's Analytical Mechanics Svo, 4 00 Merriman's Mechanics of Materials Svo, 4 00 Church's Mechanics of Engineering Svo, 6 00 " Notes and Examples in Mechanics Svo, 2 00 Mosely's Mechanical Engineering. (Mahan.) Svo, 5 00 Weisbach's Mechanics of Engineering. Vol. III., Part I., Sec. L (Klein.) Svo, 5 00 Weisbach's Mechanics of Engineering. Vol. III., Part I. Sec.n. (Klein.) Svo, 5 00 Weisbach's Hydraulics and Hydraulic Motors. (Du Bois.)..8vo, 5 00 " Steam Engines. (Du Bois.) Svo, 5 00 Lanza's Applied Mechanics Svo, 7 50 11 Orehore's Mechanics of the Girder 8vo, $5 00 MacCord's Kinematics 8vo, 5 GO Thurston's Friction and Lost Work 8vo, 3 00 " The Animal as a Machine 13mo, 1 00 Hall's Car Lubrication 12mo, 1 00 "Warren's Machine Construction 2 vols., Svo, 7 50 Chordal's Letters to Mechanics 12mo, 2 00 The Lathe and Its Uses Svo, 6 00 Cromwell's Toothed Gearing 12mo, 1 50 Belts and Pulleys 12mo, 150 Du Bois's Mechanics. Vol. I., Kinematics Svo, 3 50 Vol. IL, Statics Svo, 4 00 Vol. IIL, Kinetics Svo, 3 50 Dredge's Trans. Exhibits Building, World Exposition, 4to, half morocco, 15 00 Elather's Dynamometers 12mo, 2 00 Rope Driving 12mo, 2 00 Richards's Compressed Air 12mo, 1 50 Smith's Press-working of Metals Svo, 3 00 Holly's Saw Filing ISmo, 75 Fitzgerald's Boston Machinist ISmo, 100 ^Baldwin's Steam Heating for Buildings 12mo, 2 50 Metcalfe's Cost of Manufactures Svo, 5 00 JBenjarain's Wrinkles and Recipes 12mo, 2 00 JDingey's Machinery Pattern Making 12mo, 2 00 METALLURQV. Iron— Gold— Silver — Allots, Etc. Egleston's Metallurgy of Silver Svo, 7 50 " Gold and Mercury Svo, 7 50 " Weights and Measures, Tables ISmo, 75 " Catalogue of Minerals Svo, 2 50 O'Driscoll's Treatment of Gold Ores Svo, 2 00 * Kerl's Metallurgy — Copper and Iron Svo, 15 00 * " " Steel, Fuel, etc Svo, 15 00 13 Thurston's Il-on and Steel 8vo, $3 50 Alloys 8vo, 3 50 Troilius's Chemistry of Iron. .8vo, 2 00 Kunbardt's Ore Dressing in Europe 8vo, 1 50 Weyrauch's Strength of Iron and Steel. (Du Bois.) 8vo, 1 50 Beardslee and Kent's Strength of Wrought Iron 8vo, 1 50 Compton's First Lessons in Metal Working 13mo, 1 50 West's American Foundry Practice 12mo, 3 50 " Moulder's Text-book ISmo, 3 50 MINERALOGY AND MININQ. Mine Accidents — Ventilation— Orb Dbbssing, Etc. Dana's Descriptive Mineralogy. (E. S.) 8vo, half morocco, " Mineralogy and Petrography. (J. D.) 13mo, ' ' Text-book of Mineralogy. (E. S. ) 8vo, " Minerals and How to Study Them. (E. S.) 13mo, " American Localities of Minerals 8vo, Brush and Dana's Determinative Mineralogy 8vo, Rosenbusch's Microscopical Physiography of Minerals aud Rocks. (Iddings.) 8vo, Hussak's Rock-forming Minerals. (Smith.) 8vo, Williams's Lithology 8vo, Chester's Catalogue of Minerals 8vo, " Dictionary of the Names of Minerals 8vo, Egleston's Catalogue of Minerals and Synonyms 8vo, Goodyear's Coal Mines of the Western Coast 13mo, Kunhardt's Ore Dressing in Europe 8vo, Sawyer's Accidents in Mines 8vo, Wilson's Mine Ventilation 16mo, Boyd's Resources of South Western Virginia 8vo, " Map of South Western Virginia Pocket-book form, Stockbridge's Rocks and Soils 8vo, Eissler's Explosives — Nitroglycerine and Dynamite. ..... .iSvo, 13 13 50 3 GO 3 50 1 50 1 GO 3 50 5 CO 2 GO 3 GO 1 35 3 00 3 50 2 50 1 50 7 GO 1 35 3 GO 2 00 3 50 4 GO "^Drinker's Tunnellicig, Explosives, Compounds, and Rock Drills. ;4to, half morocco, $25 00 Beard's Ventilation of Mines 13mo, 2 50 Ihlseng's Manual of Mining 8vo, 4 00 STEAM AND ELECTRICAL ENGINES, BOILERS, Etc. Stationaky — Marine— Locomotive — Gas Engines, Etc. Weisbach's Steam Engine. (Du Bois.) , 8vo, 5 00 Tliurston's Engine and Boiler Trials 8vo, 5 00 " Philosophy of the Steam Engine 12mo, 75 " Stationary Steam Engines 12mo, 1 50 " Boiler Explosion 12mo, 150 " Steam-boiler Construction and Operation 8vo, " Reflection on the Motive Power of Heat. (Carnot.) 12mo, 3 00 Thurston's Manual of the Steam Engine. Part I., Structure and Theoiy 8vo, 7 50 Thurston's Manual of the Steam Engine. Part II., Design, Construction, and Operation Svo, 7 50 2 parts, 12 00 ^5ntgen's Thermodynamics. (Du Bois.) 8vo, 5 00 Teabody's Thermodynamics of the Steam Engine Svo, 5 00 " Valve Gears for the Steam-Engine Svo, 2 50 Tables of Saturated Steam Svo, 100 Wood's Thermodynamics, Heat Motors, etc Svo, 4 00 Pupin and Osterberg's Thermodynamics 12mo, 1 25 Kneass's Practice and Theory of the Injector Svo, 1 50 Reagan's Steam and Electrical Locomotives 12mo, 2 00 Jleyer's Modern Locomotive Construction 4to, 10 00 Whitham's Steam-engine Design Svo, 6 00 " Constructive Steam Engineering Svo, 10 00 Hemen way's Indicator Practice 12mo, 2 00 Pray's Twenty Years with the Indicator Royal Svo, 2 50 Spangler'B Valve Gears Svo, 2 50 * Maw's Marine Engines Polio, half morocco, IS 00 Trowbridge's Stationary Steam Engines 4to, boards, 2 50 14 XPord's Boiler Haking for Boiler Makers 18ino, $1 00 Wilson's Steam Boilers. (Plather.). '. 12mo, 3 50 •Baldwia's Steam Heating for Buildings 13mo, 3 50 Hoadley's Warm-blast Furnace 8vo, 1 50 Sinclair's Locomotive Running 12mo, 3 00 'Clerk's Gas Engine 13mo, TABLES, WEIGHTS,. AND MEASURES. Tor Engineers, Mechanics, Actuaries— Metric Tables, Etc. Crandall's Railway and Earthwork Tables 8vo, 1 50 Johnson's Stadia and Earthwork Tables 8vo, 1 25 IBixby's Graphical Computing Tables Sheet, 35 fCompton's Logarithms 12mo, 1 50 Ludlow's Logarithmic and Other Tables. (Bass.) 18mo, 3 00> Thurston's Conyersion Tables 8vo, 1 00 lEgleston's Weights and Measures 18mo, 75 Totten's Metrology 8vo, 3 50 Tisher's Table of Cubic Yards Cardboard, 35 ^Hudson's Excavation Tables. Vol. II 8vo, 1 00 VENTILATION. Steam Heating — House Inspection — Mine Ventilation. 3eard's Ventilation of Miues 13mo, 3 50 Baldwin's Steam Heating 12mo, 3 50 Reid's Ventilation of American Dwellings .13mo, 1 50 Mott's The Air We Breathe, and Ventilation 16mo, 1 00 Gerhard's Sanitary House Inspection Square 16mo, 1 00 Wilson's Mine Ventilation 16mo, 1 35 ■Carpenter's Heating and Ventilating of Buildings 8vd, 3 00 niSCELLANEOUS PUBLICATIONSo Alcott's Gems, Sentiment Language Gilt edges, 5 00 Bailey's The New Tale of a Tub 8vo, 75 Ballard's Solution of the Pyramid Problem 8vo, 1 50 Barnard's The Metrological System of the Great Pyramid. .8vq, 1 50 15 * Wiley's Yosemite, Alaska, and Yellowstone 4to, $3 OO Emmon's Geological Guide-book of the Rocky Mountains. .8vo, 1 50 Fenel's Treatise on the Winds 8vo, 4 Oft Perkins's Cornell University Oblong 4to, 1 50 Ricketls's History of Rensselaer Polytechnic Institute 8vo, 3 OO Mott's The Fallacy of the Present Theory of Sound. .Sq. 16mo, 1 0* Rothcrham's The New Testament Critically Emphathized. 12mo, 1 50 Totteu's An Important Question in Metrology .Svo, 2 50 Whitehouse's Lake Moeris Paper, 25 HEBREW AND CHALDEE TEXT-BOOKS. For Schools and Theoloqioal Seminakies. Gesenius's Hebrew and Chaldee Lexicon to Old Testament. (Tregelles.) Small 4to, half morocco, 5 OO Green's Grammar of the Hebrew Language (New Edition). Svo, 3 OO " Elementary Hebrew Grammar 12mo, 1 25 " Hebrew Chrestomathy Svo, 2 OO Letteris's Hebrew Bible (Massoretic Notes in English). Svo, arabesque, 2 25- Luzzato's Grammar of the Biblical Chaldaic Language and the Talmud Babli Idioms 12mo, 1 50 MEDICAL. Bull's Maternal Management in Health and Disease 12mo, 1 OO Mott's Composition, Digestibility, and Nutritive Value of Food. Large mounted chart, 1 25- Steel's Treatise on the Diseases of the Ox Svo, 6 OO " Treatise on the Diseases of the Dog Svo, 3 50 Worcester's Small Hospitals — Establishment and Maintenance, including Atkinson's Suggestions for Hospital Archi- tecture 12mo, 1 25 Hammarsten's Physiological Chemistry. (Mandel.) Svo, 4 OO 16 jmSmaammiL I- :'■'/*• •.•.•^■»ii--r . ♦ ; » M, ■ 1 ,th".V3^ L^fsy.i