Atigust 23, 1877] 



NATURE 



343 



Glaisher, Mr. J. — Luminous Meteors 10 



Joule, Dr.— Determination of the Mechanical Equivalent 



of Heat (renewed) 65 



Thomson, Sir W. — Aleasurement of the Lunar Disturb- 

 ance of Gravity (renewed) 50 



Chemistry. 



Brown, Prof. Crum. — Quantitative Estimation of Atmo- 

 spheric Ozone 10 



Roberts, Mr. Chandler. — Chemical Composition and 



vSiructure of some of the less-known Alkaloids ... 25 



Geology. 



Evans, Mr. L — Kent's Cavern Exploration 50 



Evans, Mr. J. — Kecord of the Progress of Geology ... 100 



Godwin Austen, Mr. — Kertish Boring Exploration ico 



Harkness, Prof. — North-West Highlands Fossils 10 



HaugViton, Rev. Dr. — Fermanagh Caves Exploration ... 30 



Herschel, Prof. A. — Thermal Conductiviiy of Rocks ... 10 



Hull, Prof. — Circulation of Underground Waters 15 



I.ubbock, Sir J., Bait. — Victoria Cave, Settle, Exploration 100 



Biology. 



Dew Smith, Mr. — Table at the Zoological Station, 



Naples 75 



Fox, Col. Lane. — Exploration of Ancient Earthworks ... 25 

 McKendrick, Dr. — Investigation of Pulse Phenomena by 



Thomson's Siphon Recorder 10 



Rolleston, Prof. — Examination of two Caves and Tu- 

 muli near Tenby 25 



Stainton, Mr. — Record of Zoological Literature ico 



Thomson, Dr. Allen. — Transmission of Electrical Im- 

 pulses through Nerve Structure 30 



Statistics and Economic Science, 

 Farr, Dr. — Anthropometric Committee (renewed) 66 



mechanics. 

 Froude, Mr. \V. — Instruments for Measuring the Speed 



of Ships (renewed) 50 



Thomson, Sir W. — Datum Level of the Ordnance 



Survey 10 



^£■1,081 

 SECTION A. — M.vrHE.MATiCAL and Physical. 



On the Rate of Progression of Groups of Waves and the Kate 

 at which Energy is 7'ransmitfed by Heaves, by Prof. Osboine 

 Reyrolds, F.R. S. — When several waves forming a discontinuous 

 group travel over the surface of deep water, the rate of pro- 

 gress on of the group is always much less than the rate at which 

 the individual waves which compose the group are propagated. 

 As the waves approach the front of the group they gradually 

 dwindle down and die out, while fresh waves are continually 

 arising in the rear of the others. This, which is a well-known 

 phenomenon, presents itself to our notice in various ways. 



When a stune is thrown on 10 the surface of a pond, the series 

 of rings which it causes gradually expands so as finally to embrace 

 the entire suiface of the water ; but if carelul notice be taken it 

 is seen that the waves travel outwards at a considerably greater 

 rale than that at which the disturbance spreads. 



Or, when \newmg a rough sea, if we endeavour to follow with 

 the eye any wave wtiich is larger than its neighbours, we find, 

 after following it in its course for a short distance, that it has 

 lost its extra size, while on looking back we see that this has 

 been acquired by the succeeding wave. 



But perhaps the most striking manifestation of the phenomenon 

 is in the waves which spring from the bows of a rapid boat, and 

 attend it on its course. A wove from either bow extends liack- 

 wards in a slanting direction for some distance and then dis- 

 appears ; but immediately behind it has come into existence 

 another wave parallel to the first, beyond which it extends for 

 some distance when it also dies ou', but not before it is followed 

 by a third which extends still farther, and so on, each wave over- 

 lapping the others rather more than its predecessor. AlthoU(,h 

 not obvious, very little consiJeration serves to show that the 

 stepped form of these columns of w.aves is a result of the continual 

 dying out of the waves in front of the group, and the formation 



of fresh waves behind. For as each wave cuts slantwise through 

 the column formed by the group, one end is on the advancing 

 side or front of the group, and this is continually dying while the 

 other is in the rear and is always growing. 



So far as I am aware, no general explanation of these pheno- 

 mena has as yet been given It has been shown, and I believe 

 first by Prof Stokes, that if two series of parallel waves of equal 

 magnitude, but differing slightly in length, move simultaneously 

 in the same direciion over the same water so as to form a series 

 of groups of waves separated by bands of interference, that these 

 groups will advance with half the velocity of the indivicual 

 waves. This is doubtless an example of the same phen'imcnon, 

 and shows that the the iry of wave motion is capable of explain- 

 ing the phenomena ; but it aiipears to leave something to be 

 desired, — for in>tance, why should the bands of interference only 

 progress with half the velocity of propigaiion in a deep sea. 

 whereas in sound the corresponding bands of interference which 

 constitute the beats move at the sa'iie velocity as the waves. 



My object in this paper is to point out a fact in connection 

 with wave transmission which appears to have hitherto passed 

 unnoticed at all events in connection with the phenomena de- 

 scribed above, of which it affords a clear and complete explana- 

 tion. One of the several functions performed by waves progressing 

 through a medium is the transmission of energy. Thus the 

 energy which we receive from the sun is brought to us in the 

 waves of light and heat ; so in the case of sound the work done 

 by the arm of the drummer is transmitted to our ears by the 

 waves of sound. It is possible however to have waves which 

 travel through a medium without conveying energy; such are 

 the waves caused by the wind on a field of corn. This kind of 

 wave may be well understood by suspending a series of small 

 balls by threads, so that the balls all hang in a row, and the 

 threads are all of the same length. If we then run the finger 

 along, so as to set the balls oscillating in succession, the mo'ion 

 will be such as to give the idea of a .series of waves propagated 

 from one end to the other ; but in reality there is no propagation, 

 each pendulum swings independently of its neighbours, there is 

 no communication of tnergy, the waves being merely the result 

 of the general arrangement of the motion. 



In this case there is no communication of energy, neither is 

 there any propagation of disturbance. Any one ball may be set 

 swinging without in the least disturbing the others ; and what is 

 indicated here is a general law that wherever a disturbance is 

 transmitted through a medium by waves there must always be 

 communication of energy. The rate at which energy is trans- 

 mitted in different media, or by different systems of waves, is 

 very different. This may be illustrated at once by experiment. 

 If the balls just described are all connected by an elastic thread, 

 then they can no longer swing independently. If one be set in 

 motion then, by virtue of the connecting thread, it will communi- 

 cate its motion to its neighhouis until they swini; with it, so that 

 now waves wou'd he propagated through the balls. The rate at 

 which a ball would imp.irt its motion, i.e. its energy, to its 

 neighbours would clearly depend on the tension of the con- 

 necting thread. If this was very slight compared with the weight 

 of the balls it would stretch, and the ball might accomplish 

 several swings before it had set its neighbours in full motion, so 

 that of the initial energy of disturbance a very small portion is 

 communicated at each swing. But if the tension of the thread 

 be great compared with the weight of the bills, one ball cannot 

 be disturbed without causing a similar di.sturbance in its neigh- 

 bours, and then the whole energy will be communicated. 

 This is simply illustrated by laying a rope or chain on the ground, 

 and fas'ening down one end ; if then the luo^e end be shaken up 

 and down the wriggle caused will travel 10 the other end, leaving 

 the rope perfectly straight and quiet on the ground behind it, so 

 that in this case it is at once seen that the wave carries forward 

 with it the whole energy of disturbance. 



The straight cord and the pendulous balls represent media in 

 which the waves are at the opposite limits — in one case none of 

 the energy of disturbance is transmitted, and in the other case 

 the whole is transmitted. Between these two limits we may 

 have waves of infinite variety, in which any degree of energy 

 from all to nothing is transmitted. Now the waves of sound 

 belong to the class of the cord in which all the energy is trans- 

 mitted ; but what I want particularly to make clear is that the 

 waves on water are between the limits ihey are analogous to the 

 waves in the balls suspended when connected by an elastic string 

 And I have so to show that according to the accepted theory of 

 wave motion the waves on deep water only carry forward half 

 the energy of disturbance. 



