136 



KNOWLEDGE 



[June 1, 1896. 



SHORT NOTIOES. 



Principles of MetaUiirgi/. B_v Arthur H. Iliorns. (Miiemillan.) 

 lUiistrotod. (is. Tlio author's " KU'iiientnry Motiillurpv " is alreiicU 

 well known to students ol" tlio subjci't. and tlu' prt'st'iit woyV forms an 

 admirabli- soiiuel to it. Besides exphiiniu'j tlu- i)rini'ipli's of metal- 

 lurgy, ami giving other valuable infornuition, il expounds the views 

 of modern nietallurgiats, and the methods of exlnioling various 

 metals from their ores. 



Firxt Stai/e Mechanics. By F. Rosenberg, M . A . (Olive.) 2s. This 

 work has been designed, we ai-e told in the preface, to eover tlic 

 requirements of the elcnu-ntarv stage of the Science and Art Depart- 

 ment in the theoretical mechanics of solids. To this end the work 

 is cminentlv successful. 



Practical Inorganic Chemistri/. By d. S. Turpiu, M.A., D.Sc. 

 (Macniillau.) Illustrated. 28. 6d. This is a clear and practical 

 guide lo ehMuentary chemistry. 



Submarine Telegraphii. By" James Bell and S. Wilson. {Elect ricifi/.) 

 Illustrated. Is. (id. This book is composed of reprints of ])apers 

 which were )iublished under the heading of "Technical Telegraphy 

 Papers" in Kleclricity. It should prove useful to telegrajihists. 



Messrs. Wesley & Son send us a very full catalogue of valuable 

 books wliich should be seen by every zoologist. 



I * I 



BOOKS RECEIVED. 



Artistic and Scicntijic Taxidermi/ and Modelling. By Montagu 

 Browne, F.G.S., F.Z.S. (A. & C. Black.) lUustrated. 2l3. 



Introduction to the Stiidi/ of Fiiur/i. For the Use of Collectors. 

 By M. C. Cooke, M.A., LL.D." (A. & C. Black.) Illustrated, lis. 



A Dictionari/ of Chemical Solubilities — Inorganic. By A. M. 

 Corney, Ph.D. " (Macmillan.) 15s. 



A Compendium of General Botany. By Dr. Max Wcstermaier. 

 Translated by Dr. Albert Schneider. (New York : Wilev. London : 

 Chapman & Hall.) Illustrated. 8s. 6d. 



The Elements of Physics. By E. L. Nichols and W. S. Franklin. 

 Vol. I. — " Mechanics and Heat." (Macmillan.) Illustrated. 6s. 



A Handbook- of the Order Lepidoptera. By W. F. Kirby, F.L.S., 

 F.E.S. Part I.—" Butterflies." Vol. II. AUen's Naturalist Library. 

 (Allen.) Illustrated. 6s. 



Handbook- for the Bio-Chemical Laloratory. By J. A. Maudel. 

 (New York : Wiley. London : Chapman & Uall.) 6s. 6d. 



Milk : its Nature and Composition. By C. M. Aikman, M.A., 

 D.Sc. (A & C. Black.) Illustrated. 3s. (id. 



Meteors and Sunsets observed at Lick- Observatory in 1S93, 1S94, 

 and 1895. (Sacramento; A.T.Johnston.) Illustrated. 



Biological Experimentation. By Sir B. W. Richardson, M.D., 

 F.R.S. (Bell & Sons.) 23. 6d. 



Notes on the Revised Latin Primer. By A. A. Ogle, B.A. 

 (Relfe.) Is. 



WAVES.-VI. 



STANDING WAVES IN FLOWING WATER. 



By Vaughan CoENisH, M.Sc. 



WAVES of flowing water are the familiar surface 

 corrugation of babbling brooks, rippling 

 streams, mountain burns, the rapids of 

 rivers, and the tide races of the sea. There 

 are also most beautiful varieties of these 

 waves to be seen where water cuts a channel through a 

 sandy bed in making its way across the beach to the sea, 

 as shown in Fig. 1. 



If a stone too heavy for the current to move be thrown 

 into a shallow, rapid, brook, the water rises in a heap over 

 the obstacle, the forward motion of the water being checked, 

 and an upward slope being given to the current, whilst on 

 the lee side of the obstacle the water gathers speed 

 as it slides along the downward slope of the billow, and 

 falls below the proper level of the stream. If we watch 

 attentively the course of events, we find that a second 

 billow is quickly formed to leeward of the first, and then a 

 third and a fourth, and so on ; until the lengthening 

 group of diminishing waves extends to a considerable 

 distance down stream. Each wave crest maintains its 

 position relatively to the stone, and from this comes the 

 term standing wave, for there is apparently no bobbing 

 up and down as in the stationary {i.e., non-progressive) sea 



waves which may be seen near a vertical breakwater, 

 or in harbours, or in docks. Sometimes, however, they 

 are called stationary waves of flowing water, but standing 

 waves is a more descriptive term. It is further to be 

 noticed that although the wave crests are stationary rela- 

 tively to the stono wliich produced them, yet they travel 

 relatively to the water. The stone and the water are in 

 relative motion, just as when a boat is tugged along a 

 canal the boat and the water are in relative motion. A 

 canal boat, if moving sufliciently quickly, is followed by a 

 group of waves, each crest keeping its position relatively 

 to the boat as long as the \elocity of the boat remains the 

 same. Most of the facts which are known about canal- 

 boat waves may be applied directly to standing waves in 

 shallow streams. If the stone which we used to form the 

 group of standing waves be slowly rolled down stream by 

 the force of the current, the group of waves moves with it. 

 If, on the other hand, we attach a cord to the stone and drag 

 it up stream, the group of waves travels up stream with the 

 stone. If the velocity of the stream should sliicken, the 

 length from crest to crest of the waves to leeward of our 

 stationary stone is diminished ; if, on the other hand, the 

 stream should swell, and flow more quickly, the wave- 

 length is increased. The relation of wave-length to 

 velocity is the same as in the case of canal-boat waves. 



The diii'erences of level in the standing waves are such 

 as to balance the diflerences of horizontal pressure, the free 

 surface of the water being a surface of uniform pressure. 

 Thus the height of the first hillock of water depends upon 

 the pressure of the stream upon the stone. It will be 

 noticed in looking at the waves of rapid streams that their 

 steepness is often much greater than that which is attained 

 by wind-formed waves, and is comparable to the steepness 

 of " steamboat waves." When a particle of water has been 

 forced by the current to the summit of the heap which 

 surmounts the stone, gravity pulls it down, and the inertia 

 of the motion thus imparted carries it below its proper 

 level, from which the hydrostatic pressure of the neigh- 

 bouring water again raises it ; and so the oscillation goes 

 on, the amphtude diminishing at each swing. The particle, 

 however, has a forward motion given by the current, as 

 well as the pendular oscillation, so that at the end of the 

 oscillation the particle is not in the same position as that 

 from which it started. The pull of gravity causes the 

 particle to occupy successively positions above and below 

 the proper stream level. There is also an alternate back- 

 ward and forward motion relatively to the current, as the 

 current would be if the stream were allowed to flow 

 uniformly without the interruption caused by the stone. 

 The forward motion of the surface particle is retarded when 

 it is above the mean level of the stream and accelerated 

 when it is below the mean level. On the whole, therefore, 

 the (rave motion of the particle is the repeated description 

 of a closed curve about the positions which it would 

 successively occupy if flowing in the undisturbed stream. 

 The actual motion compounded of current and wave motion 

 of a particle on the corrugated surface of a stream is similar 

 to the motion of the car of the switchback railway : slow, 

 horizontal, on the top of the hill, gaining velocity on the 

 downward slope, flying up the lower portion of the next 

 hillock with the aid of the momentum gained in its fall, 

 but with slackening speed as it rises ; its velocity less than 

 that proper to the stream at all points above the nodal line 

 of the undisturbed level of the stream, greater than this at 

 all points below the nodal line. That the general velocity 

 of the stream under the troughs is greater than that under 

 the crests, is sufficiently obvious from the fact that when 

 a group of standing waves has been formed the current 

 which flows is constant in quantity. Therefore the same 



