,transcriber's ,note ,in what follows1 italic text is denoted by underscores while bold text is denoted by equal signs4 ,small capitals in the original text have been transcribed as ,,all ,,capitals4 ,superscripted text is prefixed by the #8' symbol4 ,braces #8' may enclose the text when necessary to avoid ambiguity4 ,subscripted text is always enclosed in braces #8' but will not be preceded by a #8'4 ---------- ,see the end of this document for details of corrections and other changes4 ---------------------------------- ,start of ,book ---------------------------------- ,illustration3 ,a ,,christmas ,,lecture ,,at ,,the ,,royal ,,institution3 8,,waves ,,and ,,ripples ,,in ,,the ,,air40 ,,fig4 #df 7see p4 #aji74 ,drawn by ,f4 ,c4 ,dickinson4 ,from the 8,graphic40 ,,waves ,,and ,,ripples ,,in ,,water1 ,,air1 ,,and ,,ther ,,being ,a ,,course ,,of ,,christmas ,,lectures ,,delivered ,,at ,,the ,,royal ,,institution ,,of ,,great ,,britain ,,by ,j4 ,a4 ,,fleming1 ,m4,a41 ,d4,sc41 ,f4,r4,s4 ,m4 ,,inst4 ,e4,e41 ,m4,r4,i41 ,,etc41 ,,etc4 ,,professor ,,of ,,electrical ,,engineering ,,in ,,university ,,college1 ,,london ,,second ,,issue1 ,,revised ,,london ,,society ,,for ,,promoting ,,christian ,,knowledge ,,northumberland ,,avenue1 ,w4,c4 #dc1 ,,queen ,,victoria ,,street1 ,e4,c4 ,,brighton3 #abi1 ,,north ,,street ,,new ,,york3 ,e4 ,s4 ,,gorham #aiab ,,published ,,under ,,the ,,direction ,,of ,,the ,,general ,,literature ,,committee ,,printed ,,by ,,william ,,clowes ,,and ,,sons1 ,,limited1 ,,london ,,and ,,beccles4 ,,preface4 ,the ,christmas ,lectures at the ,royal ,institution are1 by a time-honoured custom1 invariably addressed to a 8juvenile audience40 ,this term1 however1 has always been held to be an elastic one1 and to include those who are young in spirit as well as those who are young in years4 ,the conditions1 therefore1 necessarily impose on the ,lecturer the duty of treating some subject in such a manner that1 whilst not beyond the reach of youthful minds1 it may yet possess some elements of interest for those of maturer years4 ,a subject which admits of abundant experimental illustrations is accordingly1 on these occasions1 a popular one1 particularly if it has a bearing upon topics then attracting public attention4 ,the progress of practical invention or discovery often removes at one stroke some fact or principle out of the region of purely scientific investigation1 and places it within the purview of the popular mind4 ,a demand then arises for explanations which shall dovetail it on to the ordinary experiences of life4 ,the practical use of ther waves in wireless telegraphy has thus made the subject of waves in general an interesting one4 ,hence1 when permitted the privilege1 for a second time1 of addressing ,christmas audiences in the ,royal ,institution1 the author ventured to indulge the hope that an experimental treatment of the subject of ,waves and ,ripples in various media would not be wanting in interest4 ,although such lectures1 when reproduced in print1 are destitute of the attractions furnished by successful experiments1 yet1 in response to the wish of many correspondents1 they have been committed to writing1 in the hope that the explanations given may still be useful to a circle of readers4 ,the author trusts that the attempt to make the operations of visible waves a key to a comprehension of some of the effects produced by waves of an invisible kind may not be altogether without success1 and that those who find some of the imperfect expositions in this little book in any degree helpful may thereby be impelled to study the facts more closely from that 8open page of ,nature0 which lies ever unfolded for the instruction of those who have the patience and power to read it aright4 ,j4 ,a4 ,f4 ,,university ,,college1 ,,london1 #aijb4 ,,contents4 ---- ,,chapter ,i4 ,,water ,,waves ,,and ,,water ,,ripples4 ,,page ,a visit to the seaside--,what is a wave8--,wave-motion on water--,definition of a wave--,sea waves--,various forms of wave-motion--,wave length1 velocity1 and frequency--,atlantic waves--,rules for speed of sea waves--,illustrations of wave-motion--,a stone falling on water--,production of a wave-train--,wave-energy--,conditions for the production of wave-motion--,distinction between wave-velocity and wave-train velocity--,why a wave breaks--,waves in canals--,rule for speed of a canal wave--,falling bodies--,a 8bore0--,tidal waves--,ripples--,distinction between waves and ripples--,surface tension on liquids--,a needle floating on water--,experimental production of ripples--,reflection and refraction of ripples and waves--,interference of waves and ripples--,photography of waves and ripples #a ,,chapter ,,ii4 ,,waves ,,and ,,ripples ,,made ,,by ,,ships4 ,ship-waves--,the viscosity of liquids--,how it is demonstrated--,rotational and irrotational motion in fluids--,eddies and whirls--,smoke rings--,vortex motion--,professor ,hele-,shaw's experiments--,irrotational or stream-line motion in water--,the motion of water round a ship--,the motion of water along a pipe--,flow in uniform pipes and non-uniform pipes--,relation between fluid velocity and pressure--,skin resistance and wave-making resistance--,the movement of a fish--,motion through a perfect fluid--,the waves made by moving objects--,waves made by ducks and swans--,echelon waves--,ship bow waves--,the form of ship-waves--,mr4 ,froude's experiments--,ship-models and experimental tanks--,how a ship is designed--,froude's laws--,testing ship-models--,the design of a racing-yacht--,comparison of ,british and ,american yachts--,the ,cup race--,scott ,russell's experiments on canal-boats #eg ,,chapter ,,iii4 ,,waves ,,and ,,ripples ,,in ,,the ,,air4 ,air necessary for the production of sound--,a sounding body is in vibration--,harmonic motion--,the difference between noise and music--,the nature of an air wave--,the physical qualities of air--,longitudinal or compressional waves--,wave-models to illustrate the nature of sound waves--,quality of a sound--,velocity of an air wave--,an illustration on a gigantic scale--,the voice of a volcano heard round the world--,the effect of temperature on air-wave velocity--,comparison of theory and experiment--,circumstances affecting distance at which sounds can be heard--,funeral guns--,fog-signals and sirens--,effect of wind and density--,sensitive flames as sound-detectors--,inaudible sounds--,the reflection and refraction of sound waves--,a sound-lens and sound-prism--,the interference of sounds--,two sounds producing silence--,the phonograph--,a soap-bubble film set in vibration by air waves #ajc ,,chapter ,,iv4 ,,sound ,,and ,,music4 ,the difference between sounds and musical tones--,the natural period of vibration of an elastic body--,the effect of accumulated impulses--,free and forced vibrations--,breaking down a bridge with a pea-shooter--,the vibration of a stretched string--,stationary waves--,a string vibrating in segments--,acoustic resonance--,nodes and anti-nodes--,the musical scale or gamut--,musical intervals--,the natural gamuts and the scale of equal temperament--,concords and discords--,musical beats--,helmholtz's theory of discords--,musical instruments--,pipes--,strings and plates--,a pan-pipe--,an organ-pipe--,open and closed organ-pipes--,the distribution of air pressure and velocity in a sounding organ-pipe--,singing flames--,stringed instruments--,the violin--,the ,stroh violin--,the structure of the ear--,the ear a wonderful air-wave detector and analyzer #adg ,,chapter ,v4 ,,electric ,,oscillations ,,and ,,electric ,,waves4 ,the conception of an ther--,the phenomena of light require the assumption of an ther--,the velocity of light--,interference of light--,two rays of light can produce darkness--,an electric current--,the phenomena of electricity require the assumption of an electro-magnetic medium--,properties and powers of an electric current--,alternating and continuous electric currents--,electromotive force and electric strain--,a ,leyden jar--,the oscillatory discharge of a condenser--,oscillatory sparks--,transformation of electric oscillations--,hertz oscillator--,production of a wave of electric displacement--,detection of electric waves--,metallic filings detectors--,the coherer--,inductance and capacity of circuits--,electro-static and electro-magnetic energy--,an induction coil--,electric oscillations give rise to electric waves--,the electron theory of electricity #ahe ,,chapter ,,vi4 ,,waves ,,and ,,ripples ,,in ,,the ,,ther4 ,the experiments of ,heinrich ,hertz--,electric radiation--,lecture apparatus for producing and detecting electric radiation--,electric transparency and opacity--,why this difference--,the reflection of electric radiation--,the refraction of electric rays--,an electric prism and an electric lens--,the electric refractive index--,interference of electric rays--,the velocity of electric radiations identical with that of light--,dark heat rays--,actinic or photographic rays--,the cause of colour--,the frequency of light waves--,the classification of electric or ther waves--,the gamut of ther waves--,the eye an ther-wave detector of limited power--,the electro-magnetic theory of light--,artificial production of light--,use of ,hertz waves in wireless telegraphy--,marconi's methods--,marconi's aerial and wave-detector--,the ,morse alphabet--,how a wireless message is sent--,the tuning of wireless stations--,communication between ships and shore--,the velocity of wireless waves--,conclusion #bcb ,,appendix #bhg ,,index #bic ,,useful ,,memoranda4 ,one statute mile is #ebhj feet4 ,one nautical mile is #fjhf feet #a statute mile4 ,a knot is a speed of #a nautical mile per hour4 ,hence the following rules3-- ,to convert ,knots to miles per hour--multiply by #a4 ,miles per hour to knots--multiply by 4 ,feet per second to miles per hour--multiply by 4 ,feet per second to knots--multiply by 4 ,knots to feet per minute--multiply by #ajj4 ,,waves ,,and ,,ripples ,,in ,,water1 ,,air1 ,,and ,,ther4 ---- ,,chapter ,i4 ,,water ,,waves ,,and ,,water ,,ripples4 ,we have all stood many times by the seashore1 watching the waves1 crested with white foam1 roll in and break upon the rocks or beach4 ,every one has more than once cast a stone upon still water in a lake or pond1 and noticed the expanding rings of ripples2 and some have voyaged over stormy seas1 whereon great ships are tossed by mighty billows with no more seeming effort than the rocking of a cradle4 ,in all these things we have been spectators of a wave-motion1 as it is called1 taking place upon a water surface4 ,perhaps it did not occur to us at the time that the sound of the splash or thunder of these breaking waves was conveyed to our ears as a wave-motion of another sort in the air we breathe1 nay1 even that the light by which we see these beautiful objects is also a wave-motion of a more recondite description1 produced in a medium called the ther1 which fills all space4 ,a progressive study of ,nature has shown us that we are surrounded on all sides by wave-motions of various descriptions--waves in water1 waves in air1 and waves in ther--and that our most precious senses1 our eyes and ears1 are really wave-detectors of a very special form4 ,the examination of these waves and their properties and powers has led us to see that waves in water1 air1 and ther1 though differing greatly in detail1 have much in common2 and many things about them that are difficult to understand become more intelligible when we compare these various wave-motions together4 ,in these lectures1 therefore1 ,i shall make use of your familiar experiences concerning sea and water waves to assist you to understand some of the properties of air waves to which we owe our sensations of sound and music2 and1 as far as possible1 attempt an explanation of the nature of ther waves1 created in the all-pervading ther1 to which are due not only light and sight1 but also many electrical effects1 including such modern wonders as wireless telegraphy4 ,in all departments of natural science we find ourselves confronted by the phenomena of wave-motion4 ,in the study of earthquakes and tides1 telegraphs and telephones1 as well as terrestrial temperature1 no less than in the examination of water waves and ripples1 sound1 music1 or light and heat1 we are bound to consider waves of some particular kind4 ,fastening our attention for the moment on surface water waves1 the first question we shall ask ourselves is--,what is a wave8 ,if we take our station on a high cliff looking down on the sea1 on some clear day1 when the wind is fresh1 we see the waves on its surface like green rounded ridges racing forward1 and it appears at first sight as if these elevations were themselves moving masses of water4 ,if1 however1 we look instead at some patch of seaweed1 or floating cork1 or seagull1 as each wave passes over it1 we shall notice that this object is merely lifted up and let down again1 or1 at most1 has a small movement to and fro4 ,we are led1 therefore1 to infer that1 even when agitated by waves1 each particle of water never moves far from its position when at rest1 and that the real movement of the water is something very different from its apparent motion4 ,if we place on the surface of water a number of corks or pieces of paper1 and then watch them as a wave passes over them1 we shall notice that the corks or bits of paper rise and fall successively1 that is1 one after the other1 and not all together4 ,a little more careful scrutiny will show us that1 in the case of sea waves in deep water1 the motion of the floating object as the wave passes over it is a circular one1 that is to say1 it is first lifted up1 then pushed forward1 next let down1 and1 lastly1 pulled back2 and so it repeats a round-and-round motion1 with the plane of the circle in the direction in which the wave is progressing4 ,this may be illustrated by the diagram in ,fig4 #a1 where the circular dotted lines represent the paths described by corks floating on the sea-surface when waves are travelling over it4 ,illustration3 ,,fig4 #a4 ,accordingly1 we conclude that we have to distinguish clearly between the actual individual motion of each water particle and that general motion called the wave-motion4 ,we may define the latter by saying that to produce a wave-motion1 each separate particle of a medium1 be it water1 or air1 or any other fluid1 must execute a movement which is repeated again and again1 and the several particles along any line must perform this same motion one after the other1 that is1 lagging behind each other1 and not simultaneously4 ,we might illustrate this performance by supposing a row of fifty boys to stand in a line in a play-ground1 and each boy in turn to lift up his arm and let it down again1 and to continue to perform this action4 ,if all the boys lifted up their arms together1 that would not produce a wave-motion2 but if each boy did it one after the other in order1 along the rank1 it would constitute a wave-motion travelling along the line of boys4 ,in more learned language1 we may define a wave-motion by saying that a wave-motion exists in any medium when the separate portions of it along any line execute in order any kind of cyclical or repeated motion1 the particles along this line performing the movement one after the other1 and with a certain assigned delay between each adjacent particle as regards their stage in the movement4 ,it will be evident1 therefore1 that there can be many different kinds of waves1 depending upon the sort of repeated motion the several parts perform4 ,some of the numerous forms of wave-motion can be illustrated by mechanical models as follows3-- ,a board has fastened to it a series of wooden wheels1 and on the edge of each wheel is fixed a white knob4 ,the wheels are connected together by endless bands1 so that on turning one wheel round they all revolve in the same direction4 ,if the knobs are so arranged to begin with1 that each one is a little in advance of its neighbour on the way round the wheel1 then when the wheels are standing still the knobs will be arranged along a wavy line 7see ,fig4 #b74 ,on turning round the first wheel1 each knob will move in a circle1 but every knob will be lagging a little behind its neighbour on one side1 and a little in advance of its neighbour on the other side4 ,the result will be to produce a wave-motion1 and1 looking at the general effect of the moving knobs1 we shall see that it resembles a hump moving along1 just as in the case of a water wave4 ,illustration3 ,,fig4 #b4 ,illustration3 ,,fig4 #c4 ,the motion of the particles of the water in a deep-sea wave resembles that of the white knobs in the model described4 ,those who swim will recall to mind their sensations as a sea wave surges over them4 ,the wave lifts up the swimmer1 then pushes him a little forward1 then lets him down1 and1 lastly1 drags him back4 ,it is this dragging-back action which is so dangerous to persons who cannot swim1 when they are bathing on a steep coast where strong waves are rolling in towards the shore4 ,two other kinds of wave-motion may be illustrated by the model shown in ,fig4 #c4 ,in this appliance there are a number of eccentric wheels fixed to a shaft4 ,each wheel is embraced by a band carrying a long rod which ends in a white ball4 ,the wheels are so placed on the shaft that1 when at rest1 the balls are arranged in a wavy line4 ,then1 on turning round the shaft1 each ball rises and falls in a vertical line1 and executes a periodic motion1 lagging behind that of its neighbour on one side4 ,the result is to produce a wave-motion along the line of balls4 ,by slightly altering the model1 each ball can be made to describe a circle in a direction at right angles to the line of the balls1 and then we have a sort of corkscrew wave-motion propagated along the line of balls4 ,illustration3 ,,fig4 #d4 ,again1 another form of wave-motion may be illustrated by the model shown in ,fig4 #d4 ,in this case a number of golf-balls are hung up by strings1 and spiral brass springs are interposed between each ball4 ,on giving a slight tap to the end ball1 we notice that its to-and-fro motion is handed on from ball to ball1 and we have a wave-motion in which the individual movement of the balls is in the direction of the wave-movement1 and not across it4 ,the kind of wave illustrated by the model in ,fig4 #c is called a transverse wave1 and that shown in ,fig4 #d is called a longitudinal wave4 ,at this stage it may be well to define the meaning of some other expressions which will be much used in these lectures4 ,we have seen that in a wave-motion each part of the medium makes some kind of movement over and over again2 and of its neighbours on either side1 one is a little ahead of it in its performance1 and the other a little in arrear4 ,if we look along the line1 we shall see that we can select portions of it which are exactly in the same stage of movement--that is1 are moving in the same way at the same time4 ,the distance between these portions is called one wave-length4 ,thus1 in the case of sea waves1 the distance between two adjacent crests1 or humps1 is one wave-length4 ,when we use the expression1 a long wave1 we do not mean a wave which is of great length in the direction of the ridge1 but waves in which the crests1 or humps1 are separated far apart1 measuring from crest to crest across the ridges4 ,strictly speaking1 the wave-length may be defined as the shortest distance from crest to crest1 or hollow to hollow1 or from one particle to the next one which is in the same stage of its movement at the same time4 ,another way of illustrating the same thing would be to pleat or pucker a sheet of paper into parallel ridges4 ,if we make these pleats very narrow1 they would represent what we call short waves2 but if we make these pleats very far apart1 they would represent long waves4 ,another phrase much used is the term wave-velocity4 ,suppose that a seagull were to fly along over a set of sea waves so as to keep always above one particular hump1 or wave-crest2 the speed of the gull1 reckoned in miles per hour or feet per minute1 would be called the speed of the waves4 ,this is something very different from the actual speed of each particle of water4 ,a third and constantly used expression is the term wave-frequency4 ,if we watch a cork floating on a wave-tossed sea1 we observe that it bobs up and down so many times in a minute4 ,the number of times per second or per minute that each particle of the medium performs its cycle of motion is called the wave-frequency1 or simply the frequency4 ,again1 we employ the term amplitude to denote the extreme distance that each individual particle of the medium moves from its mean position1 or position of rest4 ,in speaking of sea waves1 we generally call the vertical distance between the crest and the hollow the height of the wave1 and this is twice the amplitude4 ,with regard to the height of sea waves1 there is generally much exaggeration4 ,voyagers are in the habit of speaking of 8waves running mountains high10 yet a sea wave which exceeds #dj feet in height is a rare sight4 ,waves have been measured on the ,southern ,indian ,ocean1 between the ,cape of ,good ,hope and the ,island of ,st4 ,paul1 and of thirty waves observed the average height was found to be just under #cj feet4 ,the highest was only #cg feet in height4 ,on the other hand1 waves of #af to #bj feet are not uncommon4 ,travellers who have crossed the ,atlantic ,ocean in stormy weather will often recount experiences of waves said to be #ajj feet high2 but these are exceedingly rare1 if even ever met with1 and unless wave-heights are obtained by some accurate method of measurement1 the eye of the inexperienced voyager is apt to be deceived4 ,in all cases of wave-motion there is a very close connection between the wave-velocity1 or speed1 the wave-length1 and the wave-frequency4 ,this connection is expressed by the numerical law that the velocity is equal to the product of the length and the frequency4 ,thus1 supposing we consider the case of ,atlantic waves #cjj feet from crest to crest1 which are travelling at the rate of #bg miles an hour1 it is required to calculate the frequency or number of times per minute or per second that any floating object1 say a boat1 will be lifted up as these waves pass over it4 ,we must first transform a speed of #bg miles per hour into its equivalent in feet per second4 ,since one mile is #ebhj feet1 #bg miles per hour is equal to #bcgf feet per minute4 ,accordingly1 it is easy to see that the wave-frequency must be #gib1 or nearly #h1 because #gib times #cjj is #bcgf4 ,the answer to the question is1 then1 that the floating object will rise and fall eight times a minute4 ,this rule may be embodied in a compact form1 which it is desirable to hold firmly in the memory1 viz4-- ,wave-velocity wave-length wave-frequency4 ,this relation1 which we shall have frequent occasion to recall1 may be stated in another manner4 ,we call the period of a wave the time taken to make one complete movement4 ,the periodic time is therefore inversely proportional to the frequency4 ,hence we can say that the wave-length1 divided by the periodic time1 gives us the wave-velocity4 ,in the case of water waves and ripples1 the wave-velocity is determined by the wave-length4 ,this is not the case1 as we shall see1 with waves in air or waves in ther4 ,in these latter cases1 as far as we know1 waves of all wave-lengths travel at the same rate4 ,long sea waves1 however1 on deep water travel faster than short ones4 ,a formal and exact proof of the law connecting speed and wave-length for deep-sea waves requires mathematical reasoning of an advanced character2 but its results may be expressed in a very simple statement1 by saying that1 in the case of waves on deep water1 the speed with which the waves travel1 reckoned in miles per hour1 is equal to the square root of #b times the wave-length measured in feet4 ,thus1 for instance1 if we notice waves on a deep sea which are #ajj feet from crest to crest1 then the speed with which those waves are travelling1 reckoned in miles per hour1 is a number obtained by taking the square root of #b times #ajj1 viz4 #bbe4 ,since #ae is the square root of #bbe 7because #ae times #ae is #bbe71 the speed of these waves is therefore #ae miles an hour4 ,in the same way it can be found that ,atlantic waves #cjj feet long would travel at the rate of #bf miles an hour1 or as fast as a slow railway train1 and much faster than any ordinary ship4#a ,the above rule for the speed of deep-sea waves1 viz4 wave-velocity square root of #b times the wave-length1 combined with the general rule1 wave-velocity wave-length multiplied by frequency1 provides us with a useful practical method of finding the speed of deep-sea waves which are passing any fixed point4 ,suppose that a good way out at sea there is a fixed buoy or rock1 and we notice waves racing past it1 and desire to know their speed1 we may do it as follows3 ,count the number of waves which pass the fixed point per minute1 and divide the number into #aih2 the quotient is the speed of the waves in miles per hour4 ,thus1 if ten waves per minute race past a fixed buoy1 their velocity is very nearly #bj miles an hour4#b ,waves have been observed by the ,challenger #dbj to #dhj feet long1 with a period of #i seconds4 ,these waves were #ah to #bb feet high4 ,their speed was therefore #ej feet per second1 or nearly #cj knots4 ,atlantic storm waves are very often #ejj to #fjj feet long1 and have a period of #aj to #aa seconds4 ,waves have been observed by officers in the ,french ,navy half a mile in length1 and with a period of #bc seconds4 ,it has already been explained that in the case of deep-sea waves the individual particles of water move in circular paths4 ,it can be shown that the diameter of these circular paths decreases very rapidly with the depth of the particle below the surface1 so that at a distance below the surface equal only to one wave-length1 the diameter of the circle which is described by each water-particle is only of that at the surface4#c ,hence storm waves on the sea are a purely surface effect4 ,at a few hundred feet down--a distance small compared with the depth of the ocean--the water is quite still1 even when the surface is tossed by fearful storms1 except in so far as there may be a steady movement due to ocean currents4 ,by a more elaborate examination of the propagation of wave-motion on a fluid1 ,sir ,george ,stokes showed1 many years ago1 that in addition to the circular motion of the water-particles constituting the wave1 there is also a transfer of water in the direction in which the wave is moving1 the speed of this transfer depending on the depth1 and decreasing rapidly as the depth increases4 ,this effect1 which is known to sailors as the 8heave of the sea10 can clearly be seen on watching waves on not very deep water4 ,for the crest of the wave will be seen to advance more rapidly than the hollow until the wave falls over and breaks2 and then a fresh wave is formed behind it1 and the process is repeated4 ,hence waves break if the depth of water under them diminishes2 and we know by the presence of breakers at any place that some shallow or sandbank is located there4 ,it is necessary1 in the next place1 to point out the difference between a mere wave-motion and a true wave4 ,it has been explained that in a wave-motion each one of a series of contiguous objects executes some identical movement in turn4 ,we have all seen the wind blowing on a breezy day across a cornfield1 and producing a sort of dark shadow which sweeps along the field4 ,this is clearly caused by the wind bending down1 in turn1 each row of cornstalks1 and as row after row bows itself and springs up again1 we are presented with the appearance of a wave-motion in the form of a rift rushing across the field4 ,illustration3 ,,fig4 #e4 ,illustration3 ,,fig4 #f4 ,illustration3 ,,fig4 #g4 ,a very similar effect can be produced1 and another illustration given of a wave-motion1 as follows3 ,coil a piece of brass wire into an open spiral like a corkscrew1 and affix to it a small fragment of sealing-wax 7see ,fig4 #e74 ,hold this in the sun1 and let the shadow of it fall upon paper4 ,then turn it round like a screw4 ,we shall see that the shadow of the spiral is a wavy line1 and that1 as it is turned round1 the humps appear to move along just as do the crests of sea waves1 but that the shadow of the little bit of sealing-wax simply moves up and down4 ,another wave-motion model may be made as follows3 ,procure a painter's comb4 ,this is a thin steel plate1 cut into long narrow teeth4 ,provide also a slip of glass about #c inches wide and #ab inches long4 ,paint one side of this glass with black enamel varnish1 and when it is quite dry scratch a wavy line upon it 7see ,fig4 #f74 ,place the glass slip close in front of the comb before the light1 and1 holding the comb still1 move the glass slip to and fro1 lengthways4 ,the observer will see a row of dots of light lying in a wavy line1 and these1 as the glass moves1 will rise and fall4 ,if the movement is rapid enough1 the appearance of a wave moving along will be seen4#d ,in all these exhibitions of wave-motion the movement of the particles is due to a common cause1 but the moving particles do not control each other's motion4 ,there is no connection or tie between them4 ,suppose1 however1 that we suspend a series of heavy balls like pendulums1 and interconnect them by elastic threads 7see ,fig4 #g71 then we have an arrangement along which we can propagate a true wave4 ,draw the end ball to one side1 and notice what takes place when it is released4 ,the first ball1 being displaced1 pulls the second one through a less distance1 and that the third one1 and the third the fourth1 and so on4 ,this happens because the balls are tied together by elastic threads1 which resist stretching4 ,when the first ball is released1 it is pulled back by the tension of the thread connecting it to its neighbours1 and it begins to return to its old position4 ,the ball possesses1 however1 a quality called inertia1 and accordingly1 when once set in motion1 its motion persists until an opposing force brings it to rest4 ,hence the returning ball overshoots the mark1 and passes to the opposite side of its original position of rest4 ,then1 again1 this displacement stretches the elastic threads connecting it to its fellows1 and a controlling or retarding force is thus created1 which brings it to rest1 and forces it again to return on its steps4 ,we see1 therefore1 that each ball must oscillate1 or swing to and fro1 and that its movement is gradually communicated to its neighbours4 ,a wave-motion is thus started1 and a true wave is propagated along the line of balls1 in consequence of the presence of elasticity and inertia4 ,the necessary conditions for the production of a true wave in a medium of any kind are therefore3 7#a7 that the medium must elastically resist some sort of deformation2 and 7#b7 when it is deformed at any place1 and returns to its original state1 it must overshoot the mark or persist in movement1 in consequence of inertia1 or something equivalent to it4 ,briefly speaking1 any material or medium in or on which a true self-propagating wave-motion can be made must resist and persist4 ,it must have an elastic resistance to some change or deformation1 and it must have an inertia which causes it to persist in movement when once set in motion4 ,these two qualities1 or others equivalent to them1 must invariably be present if we are to have a true wave produced in a medium4 ,these things may be best understood by considering1 for example1 the production of surface waves on water4 ,let us ask ourselves1 in the first place1 what alteration or change it is that a water-surface resists4 ,the answer is1 that1 for one thing1 it resists being made unlevel4 ,a still water surface is everywhere a level surface4 ,if we attempt to make it unlevel by pouring water on to it at one point1 or by heaping it up1 the water surface would resist this process4 ,we can dig a hole in sand1 or heap up sand to form a hillock1 but we know full well we cannot do the same thing with water4 ,if1 for instance1 some water is placed in a glass tube shaped like the letter 1 then it stands at the same level in both limbs4 ,again1 if water is set in motion1 being a heavy substance1 it cannot be brought to rest instantly4 ,like every other body1 it possesses inertia4 ,accordingly1 if we do succeed by any means in making a depression in a water-surface for an instant1 the water would immediately press in to fill up the hole2 but more1 it would1 so to speak1 overshoot the mark1 and1 in consequence of its inertia1 it would create a momentary hump1 or elevation1 in the place on the surface where an instant ago there was a depression4 ,this elevation would again subside into a hollow1 and the process would be continued until the water-motion was brought to rest by friction1 or by the gradual dispersion of the original energy4 ,the process by which a wave is started on the surface of water1 as a consequence of these two qualities of resistance to being made unlevel and persistence in motion1 is beautifully shown by the study of waves made by throwing stones into a pond4 ,the events which give rise to the expanding wave are1 however1 over so quickly that they can only be studied by the aid of instantaneous photography4 ,the most interesting work on this subject is that of ,professor ,a4 ,m4 ,worthington1 who has photographed1 by the exceedingly brief light of an electric spark1 the various stages of the events which happen when a drop of water or a stone falls into water4#e ,these photographs show us all that happens when the falling object touches the water1 and the manner in which it gives rise to the wave or ripple which results4 ,some of ,professor ,worthington's results for a drop of water falling into milk are reproduced in the appended diagrams4 ,in the first place 7,fig4 #h7 the drop is seen just entering the water4 ,as it plunges down1 it leaves behind it a cavity1 or1 as it may be called1 a hole in the water 7see ,fig4 #i74 ,illustration3 ,time after contact #jbfb sec4 ,,fig4 #h4 ,this hole1 at a certain stage1 begins to fill up4 ,the water rushes in on all sides1 and the impetus carries up the inrushing water so that it builds up a tall pillar of water in the place where an instant ago there was a hole 7see ,fig4 #aj74 ,no one could anticipate such an extraordinary effect2 but the instantaneous photographs1 taken by the light of an electric spark1 which reveal it1 cannot but be truthful4 ,the next stage is that this pillar of water breaks up1 and falls back again on the surface4 ,hence the water1 at the place where the drop plunges into it1 is subjected to two violent impulses--a downward1 succeeded by an up-lifting1 force4 ,the effect of this is exactly analogous to that of giving a blow to the interconnected string of balls in the model shown in ,fig4 #g--;it propagates a wave4 ,in ,fig4 #aj is illustrated the next stage1 in which this outward-moving initial wave-crest is shown4 ,illustration3 ,time after contact #jcia sec4 ,,fig4 #i4 ,illustration3 ,time after contact #aja sec4 ,,fig4 #aj4 ,so much for the events revealed by the flash-light of an electric spark2 but succeeding these there is a long train of interesting wave-making performance which can be watched with the eye1 or the stages photographed with a hand camera4 ,this wave production is best seen when a large stone is thrown into calm water in a lake or pond4 ,a story is recorded of the great artist ,turner1 that he once spent a morning throwing stones into a pond4 ,a friend reproved him for his idleness4 8,no10 said the painter1 8,i have not been idle2 ,i have learnt how to paint a ripple40 ,if the artist's eye has to be carefully trained to notice all that there is to see when a stone is hurled into a pond1 it is not strange that a careless observer cannot grasp at once what really happens to the water in this ordinary occurrence4 ,illustration3 ,,fig4 #aa4--,ripples on a lake 7,sierre71 produced by throwing in a stone4 ,the photograph in ,fig4 #aa will1 however1 show one stage in the event4 ,as soon as the first wave-crest1 the origin of which we have already explained1 is formed1 it begins to move outwards in a circular form1 and as it moves it gives rise to a wave-train1 that is1 it multiplies itself into a series of concentric ripples1 or waves1 which move outwards1 multiplying in number1 but getting smaller as they move4 ,thus if a large stone is thrown far out into a deep1 still lake1 after the first splash we shall see a circular wave spreading out from the place where the commotion was made in the water4 ,as we look at this wave we shall see it growing in size and multiplying itself4 ,at first there is but a single wave1 then two1 four1 seven1 ten1 or more concentric ripples are seen1 each circular wave expanding and getting feebler1 but seeming to give birth to others as it moves4 ,moreover1 a very careful examination will show us that the whole group of waves1 or the wave-train1 has an outward motion with a less speed than any individual wave4 ,this observation will serve to initiate the conceptions of a wave-train and of a wave-group velocity4 ,at first it is difficult to understand that a group of waves may move more slowly than the individual waves which compose it4 ,if1 however1 we cast a stone into a pond1 and look very carefully at what takes place1 we shall see that the circular expanding band of ripples has an ill-defined but visible inner and outer edge1 and that wavelets or ripples which compose it are being continually brought into existence on its inner edge1 and dying away on its outer edge4 ,waves1 so to speak1 pass through the ripple band with a greater speed than that at which the whole band of waves moves forward4 ,this rather difficult1 but important1 idea of the distinction between the velocity of a group of waves and that of an individual wave was first suggested by ,sir ,george ,stokes1 who set a question in a ,cambridge ,examination on the subject in #ahgf1 and subsequently it was elucidated by ,professor ,osborne ,reynolds#f and ,lord ,rayleigh4 ,it can be further explained as follows3 ,let us consider a wave-motion model such as that represented in ,fig4 #g1 in which a number of suspended heavy balls are connected to one another by elastic threads4 ,let one ball in the centre be drawn on one side and then released4 ,it will swing to and fro1 and will start a wave outwards in both directions4 ,if the row of balls is sufficiently long1 it will be seen that the ball by which the wave was started soon comes to rest1 and that the wave-motion is confined to a certain group of balls on either side4 ,as time goes on1 the wave-motion in each group dies away on the side nearest the origin1 and extends on the side furthest away4 ,hence the particular group of balls which are the seat of the visible wave-motion is continually being shifted along4 ,the rate at which the centre of this active group of vibrating balls is displaced may be called the velocity of the wave-train4 ,the velocity of the wave is1 however1 something greater1 since the waves are all the time moving through the group4 ,this wave-velocity is numerically estimated by taking the product of the wave-length and frequency of the motion4 ,at this stage it is necessary to explain that waves are not merely a mode of motion2 they are a means of conveying energy4 ,it is difficult to give in a compact form any simple definition of what is meant in modern scientific writings by the word ,energy4 ,briefly speaking1 we may say that there are two fundamental agencies or things in ,nature with which we are in contact1 manifesting themselves in many different forms1 but of which the total quantity is unchangeable by human operations4 ,one of these is called ,matter4 ,this term is the collective name given to all the substance or stuff we can see or touch1 and which can be weighed or has weight4 ,all known solids1 liquids1 or gases1 such things as ice1 water1 steam1 iron1 oil1 or air1 are called material substances1 and they have in common the two qualities of occupying space or taking up room1 and of having weight4 ,experiment has shown that there are some eighty different kinds of simple matter which cannot be transformed into each other1 and these forms are called the ,elements4 ,any other material substance is made up of mixtures or combinations of these elements4 ,the elementary substances are therefore like the letters of the alphabet1 which1 taken in groups1 make up words1 these last corresponding to compound chemical bodies4 ,exact research has shown that no chemical changes taking place in a closed space can alter the total weight or amount of gravitating matter in it4 ,if a chemist and numerous chemicals were enclosed in a great glass ball1 and the ball balanced on a gigantic but very sensitive pair of scales1 no operations which the chemist could conduct in the interior of his crystal laboratory would alter1 by the ten-thousandth part of a grain1 the total weight of it all4 ,he might analyze or combine his chemicals1 burn or mix them as he pleased1 but as long as nothing entered or escaped from the ball1 the total gravitating mass would remain precisely the same4 ,this great fact is called the ,law of ,conservation of ,matter1 and it teaches us that although a scuttle of coal may seem to disappear when burnt1 yet the weight of the ashes and of all the gaseous products of combustion are together equal to the weight of the original coal and the air required to burn it4 ,in addition to various material substances we find that we have to recognize different forms of something called ,energy1 associated with ,matter4 ,thus an iron ball may be more or less hot1 more or less electrified or magnetized1 or moving with more or less speed4 ,the production of these states of heat1 electrification1 magnetization1 or movement1 involves the transfer to the iron of ,energy1 and they are themselves forms of ,energy4 ,this ,energy in all its various forms can be evaluated or measured in terms of ,energy of movement4 ,thus the ,energy required to heat a ball of iron weighing one imperial pound from a temperature of the melting point of ice to that of boiling water1 is nearly equal to the ,energy required to impart to it a speed of #ajjj feet a second4 ,in the same way1 every definite state of electrification or magnetization can be expressed in its mechanical equivalent1 as it is called4 ,moreover1 it is found that we can never create any amount of heat or mechanical motion or other form of energy without putting out of existence an equivalent of energy in some other form4 ,we are therefore compelled to consider that ,energy stands on the same footing as ,matter in regard to our inability to create or destroy it1 and its constancy in total amount1 as far as we can ascertain1 gives it the same character of permanence4 ,the difference1 however1 is that we cannot1 so to speak1 ear-mark any given quantity of energy and follow it through all its transformations in the same manner in which we can mark and identify a certain portion of ,matter4 ,the moment1 however1 that we pass beyond these merely quantitative ideas and proceed to ask further questions about the nature of ,energy and ,matter1 we find ourselves in the presence of inscrutable mysteries4 ,we are not able as yet to analyze into anything simpler this 8something0 we call ,energy which presents itself in the guise of heat or light1 electricity or magnetism1 movement or chemical action4 ,it is protean in form1 intangible1 yet measurable in magnitude1 and all its changes are by definite equivalent amount and value4 ,there is a most rigid system of book-keeping in the transactions of the physical universe4 ,you may have anything you like in the way of ,energy served out to you1 but the amount of it is debited to your account immediately1 and the bill has to be discharged by paying an equivalent in some other form of ,energy before you can remove the goods from the counter4 ,matter in its various forms serves as the vehicle of ,energy4 ,we have no experience of ,energy apart from ,matter of some kind1 nor of ,matter altogether devoid of ,energy4 ,we do not even know whether these two things can exist separately1 and we can give no definition of the one which does not in some way presuppose the existence of the other4 ,returning1 then1 to the subject of waves1 we may say that a true wave can only exist when ,energy is capable of being associated with a medium in two forms1 and the wave is a means by which that ,energy is transferred from place to place4 ,it has already been explained that a true wave can only be created in a medium which elastically resists some kind of deformation1 and persists in motion in virtue of inertia4 ,when any material possesses such a quality of resistance to some kind of strain or deformation of such a character that the deformation disappears when the force creating it is withdrawn1 it is called an elastic material4 ,this elasticity may arise from various causes4 ,thus air resists being compressed1 and if the compressing force is removed the air expands again4 ,it possesses so-called elasticity of bulk4 ,in the case of water having a free surface there is1 as we have seen1 a resistance to any change of level in the surface4 ,this may be called an elasticity of surface form4 ,whenever an elastic material is strained or deformed1 energy has to be expended on it to create the deformation4 ,thus to wind up a watch-spring1 stretch a piece of indiarubber1 compress some air1 or bend a bow1 requires an energy expenditure4 ,as long as the material is kept strained1 it is said to have potential energy associated with it4 ,this term is not a very expressive one1 and it would be better to call it ,energy of strain1 or deformation4 ,if1 however1 we relax the bent bow or release the compressed air1 the ,energy of ,strain disappears1 and we have it replaced by ,energy of ,motion4 ,the arrow which flies from a bow carries with it1 as energy of motion1 some part of the energy of strain associated with the bent bow4 ,a little examination of wave-motion shows us1 therefore1 that we always have at any instant associated with the material in which the wave is being propagated1 both ,energy of ,strain and ,energy of ,motion4 ,it can be shown that in a true wave of permanent type1 the whole energy at any one moment is half energy of strain and half energy of motion1 or1 as it is called1 half potential and half kinetic4 ,thus if we consider a wave being propagated along a line of balls elastically connected1 at any one moment some of the balls are moving with their greatest velocity1 and some are at the extremity of their swing4 ,the former have energy of motion1 and the latter energy of strain4 ,or1 look at a train of sea waves4 ,some parts of the water are at any moment lifted high above the average level of the sea1 or are much below it1 but are otherwise nearly at rest4 ,these portions possess what is called potential energy1 or energy of position4 ,other parts of the water are at the average level of the sea1 but are moving with considerable velocity1 and these portions possess energy of motion4 ,every other part of the wave has in some degree both energy of motion and energy of position1 and it can be shown that the energy of the whole wave is half of one kind and half of the other4 ,as a wave progresses over the surface1 wave-energy is continually being imparted to portions of the water in front1 and it is transferred away from others in the rear4 ,in the very act of setting a fresh particle of water in oscillation1 the portions already vibrating must diminish their own motion4 ,they may hand on the whole of their energy or only a part of it to their neighbours4 ,this distinction is a very important one1 and it determines whether a single act of disturbance shall create a solitary wave or wave-train in a medium4 ,illustration3 ,,fig4 #ab4 ,the difference may be illustrated as follows3 ,consider a row of glass or steel balls suspended by threads so hung as to be quite close to each other 7see ,fig4 #ab74 ,withdraw the first ball1 and let it fall against the second one4 ,the result is that the last ball of the row flies off with a jerk4 ,in this case the whole energy imparted to the first ball is transmitted along the row of balls4 ,the first ball1 on falling against the second one1 exerts on it a pressure which slightly squeezes both out of shape4 ,this pressure is just sufficient to bring the first ball to rest4 ,the second ball1 in turn1 expands after the blow and squeezes the third1 and so on4 ,hence1 in virtue of ,newton's ,third ,law of ,motion1 that 8action and reaction are equal and opposite10 it follows that the pressure produced by the blow of the first ball is handed on from ball to ball1 and finally causes the last ball to fly off4 ,in this case1 owing to the rigid connection between the elastic balls1 each one hands on to its neighbour the whole of the energy it receives4 ,supposing1 however1 that we separate the balls slightly1 and give the first ball a transverse1 or side-to-side swing4 ,then1 owing to the fact that there is no connection between the balls1 the energy imparted to the first ball would not be handed on at all1 and no wave would be propagated4 ,between these two extremes of the whole energy transferred and a solitary wave produced1 and no energy transferred and no wave produced1 we have a condition in which an initial disturbance of one ball gives rise to a wave-train and part of the energy is transferred4 ,for if we interconnect the balls by loose elastic threads1 and then give1 as before1 a transverse or sideways impulse to the first ball1 this will pull the second one and set it swinging1 but it will be pulled back itself1 and will be to some extent deprived of its motion4 ,the same sharing or division of energy will take place between the second and third1 and third and fourth balls1 and so on4 ,hence the initial solitary vibration of the first ball draws out into a wave-train1 and the originally imparted energy is spread out over a number of balls1 and not concentrated in one of them4 ,accordingly1 as time goes on1 the wave-train is ever extending in length and the oscillatory motion of each ball is dying away1 and the original energy gets spread over a wider and wider area or number of balls1 but is propagated with less speed than the wave-velocity for that medium4 ,there need be no difficulty in distinguishing between the notion of a wave-velocity and a wave-train velocity1 if we remember that the wave travels a distance equal to a wave-length in the time taken by one oscillation4 ,hence the wave-velocity is measured by taking the quotient of the wave-length by the time of one complete vibration4 ,if1 for example1 the wave-length of a water wave is #d inches1 and we observe that twelve waves pass any given point in #c seconds1 we can at once infer that the wave-velocity is #af inches per second4 ,the transference of energy may1 however1 take place so that the whole group of waves moves forward much more slowly4 ,they move forward because the waves are dying out in the rear of the group and being created in the front1 and the rate of movement of the group is1 in the case of deep-water waves1 equal to half that of the single-wave velocity4 ,a very rough illustration of this difference between a group velocity and an individual velocity may be given by supposing a barge to be slowly towed along a river4 ,let a group of boys run along the barge1 dive over the bows1 and reappear at the stern and climb in again4 ,then the velocity of the group of boys on the barge is the same as the speed of the barge1 but the speed of each individual boy in space is equal to the speed of the barge added to the speed of each boy relatively to the barge4 ,if the barge is being towed at #c miles an hour1 and the boys run along the boat also at #c miles an hour1 then the velocity of the group of boys is only half that of the individual boy1 because the former is #c miles an hour and the latter is #f miles an hour4 ,before leaving the subject of sea waves there are two or three interesting matters which must be considered4 ,in the first place1 the breaking of a wave on the shore or on shallow water calls for an explanation4 ,if we watch a sea wave rolling in towards the beach1 we shall notice that1 as it nears the shore1 it gets steeper on the shore side1 and gradually curls over until it falls and breaks into spray4 ,the reason is because1 as the wave gets into the shallow water1 the top part of the wave advances more rapidly than the bottom portion4 ,it has already been explained that the path of the water-particle is a circle1 with its plane vertical and perpendicular to the wave-front or line4 ,accordingly1 if the wave is moving in shallow water1 the friction of the water against the bottom retards the backward movement at the lowest position of the water1 but no such obstacle exists to the forward movement of the water at its highest position4 ,an additional reason for the deformation of the wave on a gently sloping shore may be found in the fact that the front part of the wave is then in shallower water1 and hence moves more slowly than the rearward portion in deeper water4 ,from both causes1 however1 the wave continually gets steeper and steeper on its landward side until it curls over and tumbles down like a house which leans too much on one side4 ,the act of curling over in a breaking wave is a beautiful thing to watch1 and one which attracts the eye of every artist who paints seascapes and storm waves1 or of any lover of ,nature who lingers by the shore4 ,another matter of interest is the origin of sea waves4 ,undoubtedly they are due originally to the action of the wind upon the water4 ,whenever two layers of fluid lie in contact with each other1 and one moves faster than the other1 the faster-moving layer will throw the other into waves4 ,this is seen1 not only in the action of moving air or wind upon water1 but even in the action of air upon air or water upon water4 ,from the tops of high mountains we may sometimes look down upon a flat surface of cloud beneath4 ,on one occasion the author enjoyed a curious spectacle from the summit of an ,alpine peak4 ,the climb up had been through damp and misty air1 but on reaching the summit the clouds were left behind1 and a canopy of blue sky and glorious sunshine were found overhead4 ,beneath the clouds lay closely packed like a sea of white vapour1 and through this ocean of cloud the peaks of many high mountains projected and stood up like islands4 ,the surface of this sea of white cloud1 brilliantly illuminated by the sunshine1 was not1 however1 perfectly smooth4 ,it was tossed into cloud waves and billows by the action of currents of air blowing over its upper surface1 and it had a striking resemblance to the surface of a rough sea4 ,when such a cloud layer is not too thick1 the ruffling of its upper or under surface into cloud waves may thin it away into regular cloud rolls1 and these cloud rollers may then be cut up again by cross air-currents into patches1 and we have the appearance known as a 8mackerel sky40 ,another familiar phenomenon is that known as the 8ripple-mark0 on wet sand4 ,as the tide ebbs out over a smooth bank of sea-sand1 it leaves the surface ploughed into regular rounded ridges and furrows1 which are stationary waves on the sand4 ,this is called the ripple-mark4 ,it is due to the fact that the sand1 when covered by the water1 forms a surface which in a certain sense is fluid1 being saturated and filled with water1 but the movement of this bottom sand-logged water is hindered by the sand1 and hence the layer of overlying water moves over it at a different speed in ebbing out1 and carves it into what are virtually sand waves4 ,even a dry sand or snow surface may in this manner be moulded into a wave-form by the wind1 and very curious effects of this kind have been noticed and described by ,dr4 ,vaughan ,cornish1 who has made a great study of the science of waves4#g ,the production of waves on water by means of a current of air blowing over it is easily exhibited on a small scale by blowing through an indiarubber pipe1 the end of which is held near the surface of the water in a tub or tank4 ,the exact manner in which the moving air gets a grip of the water is not quite plain1 but it is clear that1 if once an inequality of level is set up1 the moving air has then an oblique surface against which it can press1 and so increase the inequality by heaping up the water in some places1 and hollowing it out in others4 ,hence oscillations of the water-surface are set up1 which go on accumulating4 ,these waves then travel away with a speed depending upon their wave-length1 and we may have great disturbances of the sea-surface at places where there is no actual storm-wind4 ,these 8echoes of a far-off storm0 are known as a 8ground swell40 ,in some localities the inhabitants are able to apprise themselves of the coming of a storm by noticing movements of the sea which indicate the arrival of waves which have travelled more quickly than the storm-centre itself4 ,every visitor to the seaside will have noticed occasions on which the sea is violently disturbed by waves1 and yet the air in the locality is tolerably calm4 ,in this case the waves have been propagated from some point of disturbance at a distance4 ,a study of breaking waves shows us that the cause of their great power to effect damage to coast structures1 such as piers1 harbour works1 and shipping in harbours1 is really due to the forward motion of the water as the wave is breaking4 ,every cubic foot of water weighs #fc lbs41 so that a cubic yard of water weighs about three-quarters of a ton4 ,if this water is moving with a speed of many feet per second in a forward direction1 the energy of motion stored up in it is tremendous1 and fully sufficient to account for the destructive power of storm waves on a coast4 ,the total volume of water which is comprised in the space occupied by even one sea-storm wave of moderate dimensions may have a mass of many hundreds of tons1 and its energy of motion may easily amount to that of an express train in motion4 ,hence when1 in the last stage of its career1 this mass of water is hurled forward on the shore1 its destructive effects are not a matter for surprise4 ,we must now leave the subject of waves in the open sea on a large level surface1 and consider that of waves in narrow channels1 such as canals or rivers4 ,the laws which govern water-wave production in a canal can best be studied by placing some water in a long tank with glass sides4 ,if at one end we insert a flat piece of wood and give it a push forward1 we shall start what is called a long wave in the tank4 ,the characteristic of this kind of wave is that the oscillatory motion is chiefly to-and-fro1 and not up-and-down4 ,this may be very easily seen by placing some bran in the water1 or floating in it some glass balls which have been adjusted so as to just float anywhere in the water4 ,when this is done1 and a wave started in the tank1 it runs up and down1 being reflected at each end 7see ,fig4 #ac74 ,illustration3 ,,fig4 #ac4--,water-wave produced in a tank4 ,from the motion of the bran we can see that the water swings backwards and forwards in a horizontal line with a pendulum-like motion1 but its up-and-down or vertical motion is much more restricted4 ,a wave of this kind travels along a canal with a speed which depends upon the depth of the canal4 ,if waves of this kind are started in a very long trough1 the wave-length being large compared with the depth of the trough1#h it can be shown that the speed of the wave is equal to the velocity which would be gained by a stone or other heavy body in falling through half the depth of the canal4 ,hence1 the deeper the water1 the quicker the wave travels4 ,this can be shown as an experimental fact as follows3 ,let two galvanized iron tanks be provided1 each about #f feet long and #a foot wide and deep4 ,at one end of each tank a hollow cylinder1 such as a coffee-canister or ball made water-tight1 is floated1 and it may be prevented from moving from its place by being attached to a hinged rod like the ball-cock of a cistern4 ,the two tanks are placed side by side1 and one is filled to a depth of #f inches1 and the other to a depth of #c inches1 with water4 ,two pieces of wood are then provided and joined together as in ,fig4 #ad1 so as to form a double paddle4 ,by pushing this through the water simultaneously in both tanks at the end opposite to that at which the floating cylinders are placed1 it is possible to start two solitary waves1 one in each tank1 at the same instant4 ,these waves rush up to the other end and cause the floats to bob up4 ,it will easily be seen that the float on the deeper water bobs up first1 thus showing that the wave on the deeper water has travelled along the tank more quickly than the wave on the shallower water4 ,illustration3 ,,fig4 #ad4 ,in order to calculate the speed of the waves1 we must call to mind the law governing the speed of falling bodies4 ,if a stone falls from a height its speed increases as it falls4 ,it can be shown that the speed in feet per second after falling from any height is obtained by multiplying together the number #h and a number which is the square root of the height in feet4 ,thus1 for instance1 if we desire to know the speed attained by falling from a height of #be feet above the earth's surface1 we multiply #h by #e1 this last number being the square root of #be4 ,accordingly1 we find the velocity to be #dj feet per second1 or about #bf miles an hour4 ,the force of the blow which a body administers and suffers on striking the ground depends on the energy of motion it has acquired during the fall1 and as this varies as the square of the speed1 it varies also as the height fallen through4 ,let us apply these rules to calculate the speed of a long wave in a canal having water #h feet deep in it4 ,the half-depth of the canal is therefore #d feet4 ,the square root of #d is #b2 hence the speed of the wave is that of a body which has fallen from a height of #d feet1 and is therefore #af feet per second1 or nearly #aa miles an hour4 ,when we come to consider the question of waves made by ships1 in the next chapter1 a story will be related of a scientific discovery made by a horse employed in dragging canal-boats1 which depended on the fact that the speed of long waves in this canal was nearly the same as the trotting speed of the horse4 ,illustration3 ,,fig4 #ae4 ,it may be well1 as a little digression1 to point out how the law connecting height fallen through and velocity acquired by the falling body may be experimentally illustrated for teaching purposes4 ,the apparatus is shown in ,fig4 #ae4 ,it consists of a long board placed in a horizontal position and held with the face vertical4 ,this board is about #af feet long4 ,attached to this board is a grooved railway1 part of which is on a slope and part is horizontal4 ,a smooth iron ball1 ,a1 about #b inches in diameter1 can run down this railway1 and is stopped by a movable buffer or bell1 ,b1 which can be clamped at various positions on the horizontal rail4 ,at the bottom of the inclined plane is a light lever1 ,t1 which is touched by the ball on reaching the bottom of the hill4 ,the trigger releases a pendulum1 ,p1 which is held engaged on one side1 and1 when released1 it takes one swing and strikes a bell1 ,g4 ,the pendulum occupies half a second in making its swing4 ,an experiment is then performed in the following manner3 ,the iron ball is placed at a distance1 say1 of #a foot up the hill and released4 ,it rolls down1 detaches the pendulum at the moment it arrives at the bottom of the hill1 and then expends its momentum in running along the flat part of the railway4 ,the buffer must be so placed by trial that the iron ball hits it at the instant when the pendulum strikes the bell4 ,the distance which the buffer has to be placed from the bottom of the hill is a measure of the velocity acquired by the iron ball in falling down the set distance along the hill4 ,the experiment is then repeated with the iron ball placed respectively four times and nine times higher up the hill1 and it will be found that the distances which the ball runs along the flat part in one half-second are in the ratio of #a1 #b1 and #c1 when the heights fallen through down the hill are in the ratio of #a1 #d1 and #i4 ,the inference we make from this experiment is that the velocity acquired by a body in falling through any distance is proportional to the square root of the height4 ,the same law holds good1 no matter how steep the hill1 and therefore it holds good when the body1 such as a stone or ball1 falls freely through the air4 ,the experiment with the ball rolling down a slope is an instructive one to make1 because it brings clearly before the mind what is meant by saying1 in scientific language1 that one thing 8varies as the square root0 of another4 ,we meet with so many instances of this mode of variation in the study of physics1 that the reader1 especially the young reader1 should not be content until the idea conveyed by these words has become quite clear to him or her4 ,thus1 for instance1 the time of vibration of a simple clock pendulum 8varies as the square root of the length20 the velocity of a canal wave 8varies as the square root of the depth of the canal20 and the velocity or speed acquired by a falling ball 8varies as the square root of the distance fallen through40 ,these phrases mean that if we have pendulums whose lengths are in the ratio of #a to #d to #i1 then the respective times of their vibration are in the ratio of #a to #b to #c4 ,also a similar relation connects the canal-depth and wave-velocity1 or the ball-velocity and height of fall4 ,returning again to canal waves1 it should be pointed out that the real path of a particle of water in the canal1 when long waves are passing along it1 is a very flat oval curve called an ellipse4 ,in the extreme cases1 when the canal is very wide and deep1 this ellipse will become nearly a circle2 and1 on the other hand1 when narrow and shallow1 it will be nearly a straight line4 ,hence1 if long waves are created in a canal which is shallow compared with the length of the wave1 the water-particles simply oscillate to and fro in a horizontal line4 ,there is1 however1 one important fact connected with wave-propagation in a canal1 which has a great bearing on the mode of formation of what is called a 8bore40 ,as a wave travels along a canal1 it can be shown1 both experimentally and theoretically1 that the crest of the wave travels faster than the hollow1 and as a consequence the wave tends to become steeper on its front side1 and its shape then resembles a saw-tooth4 ,a very well known and striking natural phenomenon is the so-called 8bore0 in certain tidal rivers or estuaries4 ,it is well seen on the ,severn in certain states of the tide and wind4 ,the tidal wave returning along the ,severn channel1 which narrows rapidly as it leaves the coast1 becomes converted into a 8canal wave10 and travels with great rapidity up the channel4 ,the front side of this great wave takes an almost vertical position1 resembling an advancing wall of water1 and works great havoc with boats and shipping which have had the misfortune to be left in its path4 ,to understand more completely how a 8bore0 is formed1 the reader must be reminded of the cause of all tidal phenomena4 ,any one who lives by the sea or an estuary knows well that the sea-level rises and falls twice every #bd hours1 and that the average interval of time between high water and high water is nearly #ab hours4 ,the cause of this change of level in the water-surface is the attraction exerted by the sun and moon upon the ocean4 ,the earth is1 so to speak1 clothed with a flexible garment of water1 and this garment is pulled out of shape by the attractive force of our luminaries2 very roughly speaking1 we may say that the ocean-surface is distorted into a shape called an ellipsoid1 and that there are therefore two elevations of water which march across the sea-covered regions of the earth as it revolves on its axis4 ,these elevations are called the tidal waves4 ,the effects1 however1 are much complicated by the fact that the ocean does not cover all parts of the earth4 ,there is no difficulty in showing that1 as the tidal wave progresses round the earth across each great ocean1 it produces an elevation of the sea-surface which is not simultaneous at all places4 ,the time when the crest of the tidal wave reaches any place is called the 8time of high tide40 ,thus if we consider an estuary1 such as that of the ,thames1 there is a marked difference between the time of high tide as we ascend the estuary4 ,taking three places1 ,margate1 ,gravesend1 and ,london ,bridge1 we find that if the time of high tide at ,margate is at noon on any day1 then it is high tide at ,gravesend at #b4ae p4m41 and at ,london ,bridge a little before three o'clock4 ,this difference is due to the time required for the tidal wave to travel up the estuary of the ,thames4 ,when an estuary contracts considerably as it proceeds1 as is the case with the ,bristol ,channel1 then the range of the tide or the height of the tidal wave becomes greatly increased as it travels up the gradually narrowing channel1 because the wave is squeezed into a smaller space4 ,for example1 the range of spring tides at the entrance of the ,bristol ,channel is about #ah feet1 but at ,chepstow it is about #ej feet4#i ,at oceanic ports in open sea the range of the tide is generally only #b or #c feet4 ,if we look at the map of ,england1 we shall see how rapidly the ,bristol ,channel contracts1 and hence1 as the tidal wave advances from the ,atlantic ,ocean1 it gets jambed up in this rapidly contracting channel1 and as the depth of the channel in which it moves rapidly shallows1 the rear portion of this tidal wave1 being in deeper water1 travels faster than the front part and overtakes it1 producing thus a flat or straight-fronted wave which goes forward with tremendous speed4#aj ,we must1 in the next place1 turn our attention to the study of water ripples4 ,the term 8ripple0 is generally used to signify a very small and short wave1 and in ordinary language it is not distinguished from what might be called a wavelet1 or little wave4 ,there is1 however1 a scientific distinction between a wave and a ripple1 of a very fundamental character4 ,it has already been stated that a wave can only exist1 or be created1 in or on a medium which resists in an elastic manner some displacement4 ,the ordinary water-surface wave is termed a gravitation wave1 and it exists because the water-surface resists being made unlevel4 ,there is1 however1 another thing which a water-surface resists4 ,it offers an opposition to small stretching1 in virtue of what is called its surface tension4 ,in a popular manner the matter may thus be stated3 ,the surface of every liquid is covered with a sort of skin which1 like a sheet of indiarubber1 resists stretching1 and in fact contracts under existing conditions so as to become as small as possible4 ,we can see an illustration of this in the case of a soap-bubble4 ,if a bubble is blown on a rather wide glass tube1 on removing the mouth the bubble rapidly shrinks up1 and the contained air is squeezed out of the tube with sufficient force to blow out a candle held near the end of the tube4 ,again1 if a dry steel sewing-needle is laid gently in a horizontal position on clean water1 it will float1 although the metal itself is heavier than water4 ,it floats because the weight of the needle is not sufficient to break through the surface film4 ,it is for this reason that very small and light insects can run freely over the surface of water in a pond4 ,this surface tension is1 however1 destroyed or diminished by placing various substances on the water4 ,thus if a small disc of writing-paper the size of a wafer is placed on the surface of clean water in a saucer1 it will rest in the middle4 ,the surface film of the water on which it rests is1 however1 strained or pulled equally in different directions4 ,if a wire is dipped in strong spirits of wine or whisky1 and one side of the wafer touched with the drop of spirit1 the paper shoots away with great speed in the opposite direction4 ,the surface tension on one side has been diminished by the spirit1 and the equality of tension destroyed4 ,these experiments and many others show us that we must regard the surface of a liquid as covered with an invisible film1 which is in a state of stretch1 or which resists stretching4 ,if we imagine a jam-pot closed with a cover of thin sheet indiarubber pulled tightly over it1 it is clear that any attempt to make puckers1 pleats1 or wrinkles in it would involve stretching the indiarubber4 ,it is exactly the same with water4 ,if very small wrinkles or pleats1 as waves1 are made on its surface1 the resistance which is brought into play is that due to the surface tension1 and not merely the resistance of the surface to being made unlevel4 ,wavelets so made1 or due to the above cause1 are called ripples4 ,it can be shown by mathematical reasoning#aa that on the free surface of a liquid1 like water1 what are called capillary ripples can be made by agitations or movements of a certain kind1 and the characteristic of these surface-tension waves or capillary ripples1 as compared with gravitation waves1 is that the velocity of propagation of the capillary ripple is less the greater the wave-length1 whereas the velocity of gravitation on ordinary surface waves is greater the greater the wave-length4 ,it follows from this that for any liquid1 such as water1 there is a certain length of wave which travels most slowly4 ,this slowest wave is the dividing line between what are properly called ripples1 and those that are properly called waves4 ,in the case of water this slowest wave has a wave-length of about two-thirds of an inch 7#jfh inch71 and a speed of travel approximately of #i inches 7#jgh foot7 per second4 ,more strictly speaking1 the matter should be explained as follows3 ,sir ,george ,stokes showed1 as far back as #ahdh1 that the surface tension of a liquid should be taken into account in finding the pressure at the free surface of a liquid4 ,it was not1 however1 until #ahga that ,lord ,kelvin discussed the bearing of this fact on the formation of waves1 and gave a mathematical expression for the velocity of a wave of oscillatory type on a liquid surface1 in which the wave-length1 surface tension1 density1 and the acceleration of gravity were taken into account4 ,the result was to show that when waves are very short1 viz4 a small fraction of an inch1 they are principally due to surface tension1 and when long are entirely due to gravity4 ,it can easily be seen that ripples run faster the smaller their wave-length4 ,if we take a thin wire and hold it perpendicularly in water1 and then move it quickly parallel to itself1 we shall see a stationary pattern of ripples round the wire which moves with it4 ,these ripples are smaller and closer together the faster the wire is moved4 ,ripples on water are formed in circular expanding rings when rain-drops fall upon the still surface of a lake or pond1 or when drops of water formed in any other way fall in the same manner4 ,on the other hand1 a stone flung into quiet and deep water will1 in general1 create waves of wave-length greater than two-thirds of an inch1 so that they are no longer within the limits entitling them to be called ripples4 ,hence we have a perfectly scientific distinction between a ripple and a wave1 and a simple measurement of the wave-length will decide whether disturbances of oscillatory type on a liquid surface should be called ripples or waves in the proper sense of the words4 ,the production of water ripples and their properties1 and a beautiful illustration of wave properties in general1 can be made by allowing a steady stream of water from a very small jet to fall on the surface of still water in a tank4 ,in order to see the ripples so formed1 it is necessary to illuminate them in a particular manner4 ,the following is a description of an apparatus1 designed by the author for exhibiting all these effects to a large audience3-- ,the instrument consists essentially of an electric lantern4 ,a hand-regulated or self-regulating arc lamp is employed to produce a powerful beam of light4 ,this is collected by a suitable condensing-lens1 and it then falls upon a mirror placed at an angle of #de1 which throws it vertically upwards4 ,the light is then concentrated by a plain convex lens placed horizontally1 and passes through a trough of metal having a plane glass bottom4 ,this trough is filled to a depth of half an inch with water1 and it has an overflow pipe to remove waste water4 ,above the tank1 at the proper distance1 is placed a focussing-lens1 and another mirror at an angle of #de to throw an image of the water-surface upon a screen4 ,the last lens is so arranged that ripples on the surface of the water appear like dark lines flitting across the bright disc of light which appears upon the screen4 ,two small brass jets are also arranged to drop water into the tank1 and these jets must be supplied with water from a cistern elevated about #d feet above the trough4 ,the jets must be controlled by screw-taps which permit of very accurate adjustment4 ,these jets should work on swivels1 so that they may be turned about to drop the water at any point in the tank4 ,the capillary ripples which are produced on the water-surface by allowing water to drop on it from a jet1 flit across the surface so rapidly that they cannot be followed by the eye4 ,they may1 however1 be rendered visible as follows3 ,a zinc disc1 having holes in it1 is arranged in front of the focussing-lens1 and turned by hand or by means of a small electric motor4 ,this disc is called a stroboscopic disc4 ,when turned round it eclipses the light at intervals1 so that the image on the screen is intermittent4 ,if1 now1 one of the water-jets is adjusted so as to originate at the centre of the tank a set of diverging circular ripples1 they can be projected as shadows upon the screen4 ,these ripples move at the rate of #a or #b feet per second1 and their shadows move so rapidly across the field of view that we cannot well observe their behaviour4 ,if1 however1 the metal disc with holes in it is made to revolve and to intermittently obscure the view1 it is possible to adjust its speed so that the interval of time between two eclipses is just equal to that required by the ripples to move forward through one wave-length4 ,when this exact speed is obtained1 the image of the ripples on the screen becomes stationary1 and we see a series of concentric dark circles with intermediate bright spaces 7see ,fig4 #af71 which are the shadows of the ripples4 ,in this manner we can study many of their effects4 ,if1 for instance1 the jet of water is made to fall1 not in the centre of the trough1 but nearer one side1 we shall notice that there are two sets of ripples which intersect--one of these is the direct or original set1 and the other is a set produced by the reflection of the original ripples from the side of the trough4 ,these direct and reflected ripple-shadows intersect and produce a cross-hatched pattern4 ,if a slip of metal or glass is inserted into the trough1 it is very easy to show that when a circular ripple meets a plane hard surface it is reflected1 and that the reflected ripple is also a circular one which proceeds as if it came from a point1 ,q1 on the opposite side of the boundary1 just as far behind that boundary as the real centre of disturbance or origin of the ripple ,p is in front of it 7see ,fig4 #ag74 ,in the diagram the dotted curves represent the reflected ripple-crests4 ,illustration3 ,,fig4 #af4 ,if we make two sets of ripples from origins ,p and ,q 7see ,fig4 #ah71 at different distances from a flat reflecting boundary1 it is not difficult to trace out that each set of ripples is reflected independently1 and according to the above-mentioned rule4 ,we here obtain a glimpse of a principle which will come before us again in speaking of ther waves1 and furnishes an explanation of the familiar optical fact that when we view our own reflection in a looking-glass1 the image appears to be as far behind the glass as we are in front of it4 ,illustration3 ,,fig4 #ag4--,reflection of circular ripples4 ,illustration3 ,,fig4 #ah4 ,a very pretty experiment can be shown by fitting into the trough an oval band of metal bent into the form of an ellipse4 ,if two pins are stuck into a sheet of card1 and a loop of thread fitted loosely round them1 and a pencil employed to trace out a curve by using it to strain the loop of thread tight and moving it round the pin1 we obtain a closed curve called an ellipse 7see ,fig4 #ai74 ,the positions of the two pins ,a and ,b are called the foci4 ,it is a property of the ellipse that the two lines ,,ap and ,,bp1 called radii vectores1 drawn from the foci to any point ,p on the curve1 make equal angles with a line ,,tt called a tangent1 drawn to touch the selected point on the ellipse4 ,if we draw the tangent ,,tt to the ellipse at ,p1 then it needs only a small knowledge of geometry to see that the line ,,pb is in the same position and direction as if it were drawn through ,p from a false focus ,a1 which is as far behind the tangent ,,tt as the real focus ,a is in front of it4 ,accordingly1 it follows that circular ripples diverging from one focus ,a of an ellipse must1 after reflection at the elliptical boundary1 be converged to the other focus ,b4 ,this can be shown by the use of the above described apparatus in a pretty manner4 ,illustration3 ,,fig4 #ai4 ,a strip of thin metal is bent into an elliptical band and placed in the lantern trough4 ,the band is so wide that the water in the trough is about halfway up it4 ,at a point corresponding to one focus of the ellipse1 drops of water are then allowed to fall on the water-surface and start a series of divergent ripples4 ,when the stroboscopic disc is set in revolution and its speed properly adjusted1 we see that the divergent ripples proceeding from one focus of the ellipse are all converged or concentrated to the other focus4 ,in fact1 the ripples seem to set out from one focus1 and to be1 as it were1 swallowed up at the other4 ,when1 in a later chapter1 we are discussing the production and reflection of sound waves in the air1 you will be able to bring this statement to mind1 and it will be clear to you that if1 instead of dealing with waves on water1 we were to create waves in air in the interior of a similar elliptically shaped room1 the waves being created at one focus1 they would all be collected at the other focus1 and the tick of a watch or a whisper would be heard at the point corresponding to the other focus1 though it might not be heard elsewhere in the room4 ,with the appliances here described many beautiful effects can be shown1 illustrating the independence of different wave-trains and their interference4 ,if we hurl two stones into a lake a little way apart1 and thus create two sets of circular ripples 7see ,fig4 #bj71 we shall notice that these two ripple-trains pass freely through each other1 and each behave as if the other did not exist4 ,a careful examination will1 however1 show that at some places the water-surface is not elevated or disturbed at all1 and at others that the disturbance is increased4 ,illustration3 ,,fig4 #bj4--;,intersecting ripples produced on a lake by throwing in simultaneously two stones4 ,if two sets of waves set out from different origins and arrive simultaneously at the same spot1 then it is clear that if the crests or hollows of both waves reach that point at the same instant1 the agitation of the water will be increased4 ,if1 however1 the crest of a wave from one source reaches it at the same time as the hollow of another equal wave from the other origin1 then it is not difficult to see that the two waves will obliterate each other4 ,this mutual destruction of wave by wave is called interference1 and it is a very important fact in connection with wave-motion4 ,it is not too much to say that whenever we can prove the existence of interference1 that alone is an almost crucial proof that we are dealing with wave-motion4 ,the conditions under which interference can take place must be examined a little more closely4 ,let us suppose that two wave-trains1 having equal velocity1 equal wave-length1 and equal amplitude or wave-height1 are started from two points1 ,a and ,b 7see ,fig4 #ba74 ,consider any point1 ,p4 ,what is the condition that the waves from the two sources shall destroy each other at that point8 ,obviously it is that the difference of the distances ,,ap and ,,bp shall be an odd number of half wave-lengths4 ,for if in the length ,,ap there are #ajj waves1 and in the distance ,,bp there are #ajj waves1 or #aja or #ajc1 etc41 waves1 then the crest of a wave from ,a will reach ,p at the same time as the hollow of a wave from ,b1 and there will be no wave at all at the point ,p4 ,this is true for all such positions of ,p that the difference of its distances from ,a and ,b are constant4 ,illustration3 ,,fig4 #ba4 ,but again1 we may choose a point1 ,q1 such that the difference of its distances from ,a and ,b is equal to an even number of half wave-lengths1 so that whilst in the length ,,aq there are1 say1 #ajj waves1 in the distance ,,bq there are #aja1 #ajb1 #ajc1 etc41 waves4 ,when this is the case1 the wave-effects will conspire or assist each other at ,q1 and the wave-height will be doubled4 ,if1 then1 we have any two points1 ,a and ,b1 which are origins of equal waves1 we can mark out curved lines such that the difference of the distances of all points on these lines from these origins is constant4 ,these curves are called hyperbolas 7see ,fig4 #bb74 ,illustration3 ,,fig4 #bb4 ,illustration3 ,,fig4 #bc4--;,interfering ripples on a mercury surface1 showing interference along hyperbolic lines 7,vincent74 ,all along each hyperbola the disturbance due to the combined effect of the waves is either doubled or annulled when compared with that due to each wave-train separately4 ,with the apparatus described1 we can arrange to create and adjust two sets of similar water ripples from origins not far apart1 and on looking at the complicated shadow-pattern due to the interference of the waves1 we shall be able to trace out certain white lines along which the waves are annulled1 these lines being hyperbolic curves 7see ,fig4 #bc74 ,with the same appliances another characteristic of wave-motion1 which is equally important1 can be well shown4 ,illustration3 ,,fig4 #bd4 ,we make one half of the circular tank in which the ripples are generated much more shallow than the other half1 by placing in it a thick semicircular plate of glass4 ,it has already been explained that the speed with which long waves travel in a canal increases with the depth of the water in the canal4 ,the same is true1 with certain restrictions1 of ripples produced in a confined space or tank1 one part of which is much shallower than the rest4 ,if waves are made by dropping water on to the water-surface in the deeper part of the tank1 they will travel more quickly in this deeper part than in the shallower portion4 ,we can then adjust the water-dropping jet in such a position that it creates circular ripples which originate in deep water1 but at certain places pass over a boundary into a region of shallower water 7see ,fig4 #bd74 ,the left-hand side of the circular tank represented in the diagram is more shallow than the right-hand side4 ,when this is done1 we notice two interesting facts1 viz4 that the wave-lines are bent1 or refracted1 where they pass over the boundary1 and that the waves are shorter or nearer together in the shallower region4 ,this bending1 or refraction1 of a wave-front in passing the boundary line between two districts in which the wave has different velocities is an exceedingly important characteristic of wave-motion1 and we shall have brought before us the analogous facts in speaking of waves in air and waves in ther4 ,illustration3 ,,fig4 #be4 ,it is necessary to explain a little more in detail how it comes to pass that the wave-line is thus bent4 ,imagine a row of soldiers1 ab1 marching over smooth grass1 but going towards a very rough field1 the line of separation ,,ss between the smooth and the rough field being oblique to the line of the soldiers 7see ,fig4 #be74 ,furthermore1 suppose the soldiers can march #d miles an hour over the smooth grass1 but only #c miles an hour over the rough field4 ,then let the man on the extreme left of the line be the first to step over the boundary4 ,immediately he passes into a region where his speed of marching is diminished1 but his comrade on the extreme right of the row is still going easily on smooth grass4 ,it is accordingly clear that the direction of the line of soldiers will be swung round because1 whilst the soldier on the extreme left marches1 say1 #cjj feet1 the one on the extreme right will have gone #djj feet forward2 and hence by the time all the men have stepped over the boundary1 the row of soldiers will no longer be going in the same direction as before--it will have become bent1 or refracted4 ,this same action takes place with waves4 ,if a wave meets obliquely a boundary separating two regions1 in one of which it moves slower than in the other1 then1 for the same reason that the direction of the row of soldiers in the above illustration is bent by reason of the retardation of velocity experienced by each man in turn as he steps over the dividing line1 so the wave-line or wave-front is bent by passing from a place where it moves quickly to a place where it moves more slowly4 ,the ratio of the velocities or speeds of the wave in the two regions is called the index of refraction4 ,we can1 by arranging suitably curved reflecting surfaces or properly shaped shallow places in a tank of water1 illustrate all the facts connected with the change in wave-fronts produced by reflection and refraction4 ,we can generate circular waves or ripples diverging from a point1 and convert them1 by reflection from a parabolic reflector1 into plane waves2 and again1 by means of refraction at a curved or lens-shaped shallow1 converge these waves to a focus4 ,interesting experiments of this kind have been made by means of capillary ripples on a mercury surface by ,mr4 ,j4 ,h4 ,vincent1 and he has photographed the ripples so formed1 and given examples of their reflection and refraction1 which are well worth study4#ab ,we do not need1 however1 elaborate apparatus to see these effects when we know what to look for4 ,a stone thrown into a lake will create a ripple or wave-train1 which moves outwards at the rate of a few feet a second4 ,if it should happen that the pond or lake has an immersed wall as part of its boundary1 this may form an effective reflecting surface1 and as each circular wave meets the wall it will be turned back upon itself as a reflected wave4 ,at the edge of an absolutely calm sea1 at low tide1 the author once observed little parallel plane waves advancing obliquely to the coast2 the edge of the water was by chance just against a rather steep ledge of hard sand1 and each wavelet1 as it met this reflecting surface1 was turned back and reflected at an angle of reflection equal to that of incidence4 ,it is well to notice that a plane wave1 or one in which the wave front or line is a straight line1 may be considered as made up out of a number of circular waves diverging from points arranged closely together along a straight line4 ,thus1 if we suppose that a1 b1 c1 d1 etc4 7see ,fig4 #bf71 are source-points1 or origins1 of independent sets of circular waves1 represented by the firm semicircular lines1 if they send out simultaneous waves equal in all directions1 the effect will be nearly equivalent to a plane wave1 represented by the straight thick black line1 provided that the source-points are very numerous and close together4 ,supposing1 then1 we have a boundary against which this plane wave impinges obliquely1 it will be reflected and its subsequent course will be exactly as if it had proceeded from a series of closely adjacent source-points1 a1 b1 c1 d1 etc41 lying behind the boundary1 each of which is the image of the corresponding real source-points1 and lies as far behind the boundary as the real point lies in front of it4 ,illustration3 ,,fig4 #bf4 ,an immediate consequence of this is that the plane reflected wave-front makes the same angle with the plane reflecting surface as does the incident or arriving wave1 and we thus establish the law1 so familiar in optics1 that the angle of incidence is equal to the angle of reflection when a plane wave meets a plane reflecting surface4 ,at the seaside1 when the tide is low and the sea calm or ruffled only by wavelets due to a slight wind1 one may often notice trains of small waves1 which are reflected at sharp edges of sand1 or refracted on passing into sudden shallows1 or interfering after passing round the two sides of a rock4 ,a careful observer can in this school of ,nature instruct himself in all the laws of wave-motion1 and gather a fund of knowledge on this subject during an hour's dalliance at low tide on some sandy coast1 or in the quiet study of seaside pools1 the surface of which is corrugated with trains of ripples by the breeze4 ,,chapter ,,ii4 ,,waves ,,and ,,ripples ,,made ,,by ,,ships4 ,it is impossible for the most careless spectator to look at a steam-vessel making her way along a lake1 a boy's boat skimming across a pond1 or even a duck paddling on a stream1 without noticing that the moving body is accompanied in all cases by a trail of waves or ripples1 which diverge from it and extend behind4 ,in the case of a steamer there is an additional irregular wave-motion of the water caused by the paddle-wheels or screw1 which churn it up1 and leave a line of rough water in the steamer's wake4 ,this1 however1 is not included in the true ship-wave effect now to be discussed4 ,we can best observe the proper ship-wave disturbance of the water in the case of a yacht running freely before the wind when the sea is fairly smooth4 ,the study of these ship-waves has led to most important and practical improvements in the art of ship-designing and shipbuilding1 and no treatment of the subject of waves and ripples on water would be complete in which all mention of ship-waves was omitted4 ,in order that we may explain the manner in which these waves are formed1 and their effect upon the motion of the ship1 and the power required to move it forward1 we must begin by a little discussion of some fundamental facts concerning liquids in motion4 ,every one is aware that certain liquids are1 as we say sticky1 or1 to use the scientific term1 viscous4 ,a request to mention sticky liquids would call up the names of such fluids as tar1 treacle1 gum-water1 glycerine1 and honey4 ,very few people would think of including pure water1 far less spirits of wine1 in a list of sticky1 or viscous liquids2 and yet it is quite easy to show by experiment that even these fluids possess some degree of stickiness1 or viscosity4 ,an illustration may be afforded as follows3 ,we provide several very large glass tubes1 nearly filled respectively with quicksilver1 water1 alcohol1 glycerine1 and oil4 ,a small space is left in each tube containing a little air1 and the tubes are closed by corks4 ,if we suddenly turn all the tubes upside down1 these bubbles of air begin to climb up from the bottom of the tube to the top4 ,we notice that in the quicksilver tube it arrives at the top in a second or two1 in the water tube it takes a little longer1 in the oil tube longer still1 and in the tube filled with glycerine it is quite a minute or more before the bubble of air has completed its journey up the tube4 ,this experiment1 properly interpreted1 shows us that water possesses in some degree the quality of viscosity4 ,it can1 however1 be more forcibly proved by another experiment4 ,to a whirling-table is fixed a glass vessel half full of water4 ,on this water a round disc of wood1 to which is attached a long wire carrying a paper flag1 is made to float4 ,if we set the basin of water slowly in rotation1 at first the paper flag does not move4 ,the basin rotates without setting the contained water in rotation1 and so to speak slips round it4 ,presently1 however1 the flag begins to turn slowly1 and this shows us that the water has been gradually set in rotation4 ,this happens because the water sticks slightly to the inner surface of the basin1 and the layers of water likewise stick to one another4 ,hence1 as the glass vessel slides round the water it gradually forces the outer layer of water to move with it1 and this again the inner layers of water one by one1 until at last the floating block of wood partakes of the motion1 and the basin and its contents turn round as one mass4 ,this effect could not take place unless the water possessed some degree of viscosity1 and also unless so-called skin friction existed between the inside of a glass vessel and the water it contains4 ,we may say1 however1 at once that no real liquid with which we are acquainted is entirely destitute of stickiness1 or viscosity4 ,we can nevertheless imagine a liquid absolutely free from any trace of this property1 and this hypothetical substance is called a perfect fluid4 ,it is clear that this ideal perfect liquid must necessarily differ in several important respects from any real fluid1 such as water1 and some of these differences we proceed to examine4 ,we must point out that in any liquid there may be two kinds of motion1 one called irrotational motion1 and the other called rotational or vortex motion4 ,consider any mass of water1 such as a river1 in motion in any way2 we may in imagination fix our attention upon some small portion of it1 which at any instant we will consider to be of a spherical shape4 ,if1 as this sphere of liquid moves along embedded in the rest of the liquid1 it is turning round an axis in any direction as well as being distorted in shape1 the motion of that part of the fluid is called rotational4 ,if1 however1 our little sphere of liquid is merely being stretched or pulled into an ovoid or ellipsoidal shape without any rotation or spinning motion1 then the motion of the liquid is said to be irrotational4 ,we might compare these small portions of the liquid to a crowd of people moving along a street4 ,if each person moves in such a way as always to keep his face in the same direction1 that movement would be an irrotational movement4 ,if1 however1 they were to move like couples dancing in a ball-room1 not only moving along but turning round1 their motion would be called rotational4 ,examples of rotational1 or vortex motion are seen whenever we empty a wash-basin by pulling up the plug4 ,we see the water swirl round1 or rotate1 forming what is called an eddy1 or whirlpool4 ,also eddies are seen near the margin of a swiftly flowing river1 since the water is set in rotation by friction against objects on the banks4 ,eddies are likewise created when two streams of water flow over each other with different speeds4 ,a beautiful instance of this may be viewed at an interesting place a mile or two out of the city of ,geneva4 ,the ,rhone1 a rapid river1 emerges as a clear blue stream from the ,lake of ,geneva4 ,at a point called ,junction d'eaux it meets the river ,arve1 a more sluggish and turbid glacier stream1 and the two then run together in the same channel4 ,the waters of the ,rhone and ,arve do not at once mix1 but the line of separation is marked by a series of whirlpools or eddies set up by the flow of the rapid ,rhone water against the slower ,arve water in contact with it4 ,again1 it is impossible to move a solid body through a liquid without setting up eddy-motion4 ,the movement of an oar through the water1 or even of a teaspoon through tea1 is seen to be accompanied by little whirls which detach themselves from the oar or spoon1 and are really the ends of vortices set up in the liquid4 ,the two facts to notice particularly are that the production of eddies in liquids always involves the expenditure of energy1 or1 in mechanical language1 it necessitates doing work4 ,to set in rotation a mass of any liquid requires the delivery to it of energy1 just as is the case when a heavy wheel is made to rotate or a heavy train set in movement4 ,this energy must be supplied by or absorbed from the moving solid or liquid which creates the eddies4 ,in the next place1 we must note that eddies or vortices set up in an imperfect fluid1 such as water1 are ultimately destroyed by fluid friction4 ,their energy is frittered down into heat1 and a mass of water in which eddies have been created by moving through it a paddle1 is warmer after the eddies have subsided than before4 ,it is obvious1 from what has been said1 that if a really perfect fluid did exist1 it would be impossible by mechanical means to make eddies in it2 but if they were created1 they would continue for ever1 and have something of the permanence of material substances4 ,illustration3 ,,fig4 #bg4--,the production of a vortex ring in air4 ,a vortex motion in water may be either a terminated vortex1 in which case its ends are on the surface1 and are seen as eddies1 or whirls2 or it may be an endless vortex1 in which case it is called a vortex ring4 ,such a ring is very easily made in the air as follows3 ,a cubical wooden box about #ah inches in the side has a hole #f inches in diameter made in the bottom 7see ,fig4 #bg74 ,the open top of the box is covered tightly with elastic cloth4 ,the box is then filled with the white vapour of ammonium chloride1 by leading into it at the same time dry hydrochloric acid gas and dry ammonia gas4 ,when quite full of dense white fumes1 we give the cloth cover of the box a sharp blow with the fist1 and from the round hole a white smoke ring leaps out and slides through the air4 ,the experiment may be made on a smaller scale by using a cardboard box and filling it with the smoke of brown paper or tobacco4#ac ,if we look closely at the smoke ring as it glides through the air1 we shall see that the motion of the air or smoke particles composing the ring is like that of an indiarubber umbrella-ring fitted tightly on a round ruler and pushed along4 ,the ring turns itself continually over and over1 the rotation being round the circular ring axis line4 ,this rotatory motion is set up by the friction of the smoky air against the edge of the hole in the box1 as the puff of air emerges from it when the back of the box is thumped4 ,a simple but striking experiment may be made without filling the box with smoke4 ,place a lighted candle at a few feet away from the opening of the above-described box1 and strike the back4 ,an invisible vortex ring of air is formed and blows out the candle as it passes over it4 ,although it is quite easy to make a rotational motion in an imperfect fluid1 and in fact difficult not to do it1 yet of late years a very interesting and valuable discovery has been made by ,professor ,hele-,shaw1 of a method of creating and rendering visible a motion in an imperfect liquid like water1 which is irrotational4 ,this discovery was that1 if water is made to flow in a thin sheet between two plates1 say of flat glass1 not more than a fiftieth of an inch or so apart1 the motion of the water is exactly that of a perfect fluid1 and is irrotational4 ,no matter what objects may be placed in the path of the water1 it then flows round them just as if all fluid friction or viscosity was absent4 ,this interesting fact can be shown by means of an apparatus designed by ,professor ,hele-,shaw4#ad ,two glass plates are held in a frame1 and separated by a very small distance4 ,by means of an inlet-pipe water is caused to flow between the plates4 ,a metal block pierced with small holes is attached to the end of one plate1 and this serves to introduce several small jets of coloured water into the main sheet4 ,in constructing the apparatus great care has to be exercised to make the holes in the above-mentioned block very small 7not more than inch in diameter7 and placed exactly at the right slope4 ,the main water inlet-pipe is connected by a rubber tube with a cistern of water placed about #d feet above the level of the apparatus4 ,the frame and glass plates are held vertically in the field of an optical lantern so as to project an image of the plates upon the screen4 ,the side inlet-pipe leading to the pierced metal block is connected to another reservoir of water1 coloured purple with permanganate of potash 7,condy's fluid71 and the flow of both streams of water controlled by taps4 ,the clear water is first allowed to flow down between the plates1 so as to exclude all air-bubbles1 and create a thin film of flowing water between two glass plates4 ,the jets of coloured water are then introduced1 and1 after a little adjustment1 we shall see that the coloured water flows down in narrow1 parallel streams1 not mixing with the clear water1 and not showing any trace of eddies4 ,the regularity of these streams of coloured water1 and their sharp definition1 shows that the liquid flow between the plates is altogether irrotational4 ,the lines marked out by the coloured water are called stream-lines1 and they cut up the whole space into uniform tubes of flow4 ,the characteristic of this flow of liquid is that the clear water in the space between two coloured streams of water never passes over into an adjacent tube4 ,hence we can divide up the whole sheet of liquid into tubular spaces called tubes of flow1 by lines called stream-lines4 ,if now we dismount the apparatus and place between the glass a thin piece of indiarubber sheet--cut1 say1 into the shape of a ship1 and of such thickness that it fills up the space between the glass plates--we shall be able to observe how the water flows round such an obstacle4 ,if the air is first driven out by the flow of the clear water1 and then if the jets of coloured water are introduced1 we see that the lines of liquid flow are delineated by coloured streams or narrow bands1 and that these stream-lines bend round and enclose the obstructing object4 ,the space all round the ship-shaped solid body is thus cut up into tubes of flow by stream-lines1 but these tubes of flow are now no longer straight1 and no longer of equal width at all points4 ,they are narrower opposite the middle part of the obstruction than near either end4 ,illustration3 ,,fig4 #bh4 ,at this point we must make a digression to explain a fundamental law concerning fluid flow in tubes4 ,suppose we have a uniform horizontal metal tube1 through which water is flowing 7see ,fig4 #bh74 ,at various points along the tube let vertical glass pipes be inserted to act as gauge or pressure-tubes4 ,then when the fluid flows along the horizontal pipe it will stand up a certain height in each pressure-tube1 and this height will be a measure of the pressure in the horizontal pipe at the point where the pressure-tube is inserted4 ,we shall notice that when the water flows in the horizontal pipe1 the water in the gauge-pipes stands at different heights1 indicating a fall in pressure along the horizontal pipe4 ,we also notice that a line joining the tops of all the liquid columns in the pressure-pipes is a straight1 sloping line1 which is called the hydraulic gradient4 ,this experiment proves to us that when fluid flows along a uniform-sectioned pipe there is a uniform fall or decrease in pressure along the pipe4 ,the force which is driving the liquid along the horizontal pipe is measured by the difference between the pressures at its extreme ends1 and the same is true of any selected length of the horizontal pipe4 ,it will also be clear that1 since water is not compressible to any but the very slightest extent1 the quantity of water1 reckoned1 say in gallons1 which passes per minute across any section of the pipe must be the same4 ,illustration3 ,,fig4 #bi4 ,in the next place1 suppose we cause water to flow through a tube which is narrower in some places than in others 7see ,fig4 #bi74 ,it will be readily admitted that in this tube also the same quantity of water will flow across every section1 wide or narrow1 of the tube4 ,if1 however1 we ask--,where1 in this case1 will there be the greatest pressure8 it is certain that most persons would reply--,in the narrow portions of the tube4 ,they would think that the water-particles passing through the tube resemble a crowd of people passing along a street which is constricted in some places like the ,strand4 ,the crowd would be most tightly squeezed together1 and the pressure of people would therefore be greater1 in the narrow portions of the street4 ,in the case of the water flowing through the tube of variable section this1 however1 is not the case4 ,so far from the pressure being greatest in the narrow portions of the tube1 it can be shown experimentally that it is precisely at those places it is least4 ,this can be demonstrated by the tube shown in ,fig4 #bi4 ,if water is allowed to flow through a tube constricted in some places1 and provided with glass gauge-pipes at various points to indicate the pressure in the pipe at those places1 it is found that the pressure1 as indicated by the height of the water in the gauge-glasses at the narrow parts of the tube1 is less than that which it would have at those places if the tube were of uniform section and length1 and passed the same quantity of water4 ,we can formulate this fact under a general law which controls fluid motion also in other cases1 viz4 that where the velocity of the liquid is greatest1 there the pressure is least4 ,it is evident1 since the tube is wider in some places than in others1 and as a practically incompressible liquid is being passed through it1 that the speed of the liquid must be greater in the narrow portions of the tube than in the wider ones4 ,but experiment shows that after allowing for what may be called the proper hydraulic gradient of the tube1 the pressure is least in those places1 viz4 the constricted portions1 where the velocity of the liquid is greatest4 ,this general principle is of wide application in the science of hydraulics1 and it serves to enable us to interpret aright many perplexing facts met with in physics4 ,we can1 in the next place1 gather together the various facts concerning fluid flow which have been explained above1 and apply them to elucidate the problems raised by the passage through water of a ship or a fish4 ,let us consider1 in the first place1 a body totally submerged1 such as a fish1 a torpedo or a submarine boat1 and discuss the question why a resistance is experienced when an attempt is made to drag or push such a body through water4 ,the old-fashioned notion was that the water has to be pushed out of the way to make room for the fish to move forward1 and also has to be sucked in to fill up the cavity left behind4 ,most persons who have not been instructed in the subject1 perhaps even now have the idea that this so-called 8head resistance0 is the chief cause of the resistance experienced when we make a body of any shape move through water4 ,a common assumption is also that the object of making a ship's bows sharp is that they may cut into the water like a wedge1 and more easily push it out of the way4 ,scientific investigation has1 however1 shown that both of these notions are erroneous4 ,the resistance felt in pulling or pushing a boat through the water is not due to resistance offered by the water in virtue of its inertia4 ,no part of this resistance arises from the exertion required to displace the water or push it out of the way4 ,the ,schoolmen of the ,middle ,ages used to discuss the question how it was that a fish could move through the water4 ,they said the fish could not move until the water got out of the way1 and the water could not get out of the way until the fish moved4 ,this and similar perplexities were not removed until the true theory of the motion of a solid through a liquid had been developed4 ,briefly it may be said that there are three causes1 and only three1 for the resistance which we feel and have to overcome when we attempt to drag a boat or ship through the water4 ,these are3 ,first1 skin friction1 due to the friction between the ship-surface and the water2 secondly1 eddy-resistance1 due to the energy lost or taken up in making water eddies2 and thirdly1 wave-resistance1 due to energy taken up in making surface-waves4 ,the skin friction and the eddy-resistance both arise from the fact that water is not a perfect fluid4 ,the wave-resistance arises1 as we shall show1 from the unavoidable formation of waves by the motion of the boat through the water4 ,in the case of a wholly submerged body1 like a fish1 the only resistance it has to overcome is due to the first two causes4 ,the fish1 progressing through the water wholly under the surface1 makes no waves1 but the water adheres to its skin1 and there is friction between them as he moves4 ,also he creates eddies in the water1 which require energy to produce them1 and whenever mechanical work has to be done1 as energy drawn off from a moving body1 this implies the existence of a resistance to its motion which has to be overcome4 ,accordingly ,nature1 economical on all occasions in energy expenditure1 has fashioned the fish so as to reduce the power it has to expend in moving through water as much as possible4 ,the fish has a smooth slippery skin4 7,we say 8as slippery as an eel407 ,it is not covered either with fur or feathers1 but with shiny scales1 so as to reduce to a minimum the skin friction4 ,the fish also is regular and smooth in outline4 ,it has no long ears1 square shoulders1 or projecting limbs or organs1 which by giving it an irregular outline1 would tend to produce eddies in the water as it moves along4 ,hence1 when we wish to design a body to move quickly under the water1 we must imitate in these respects the structure of a fish4 ,accordingly1 a ,whitehead torpedo1 that deadly instrument employed in naval warfare1 is made smooth and fish-shaped1 and a submarine boat is made cigar-shaped and as smooth as possible1 for the same reason4 ,if the floating object is partly above the surface1 yet nevertheless1 as far as concerns the portion submerged1 there is skin friction1 and the production of eddy-resistance4 ,hence1 in the construction of a racing-yacht1 the greatest care has to be taken to make its surface below water of polished metal or varnished wood1 or other very smooth material1 to diminish as far as possible the skin friction4 ,in the case of bodies as regular in outline as a ship or fish1 the proportion of the driving power taken up in making eddies in the water is not large1 and we may1 without sensible error1 say that in their case the whole resistance to motion is comprised under the two heads of skin friction and wave-making resistance4 ,the proportion which these two causes bear to each other will depend upon the nature of the surface of the body which moves over the water1 and its shape and speed4 ,at this point we may pause to notice that1 if we could obtain a perfect fluid in practice1 it would be found that an object of any shape wholly submerged in the fluid could be moved about in any way without experiencing the least resistance4 ,this theoretical deduction is1 at first sight1 so opposed to ordinary preconceived notions on the subject1 that it deserves a little attention4 ,it is difficult1 as already remarked1 for most people who have not carefully studied the subject1 to rid their minds of the idea that there is a resistance to the motion of a solid through a liquid arising from the effort required to push the liquid out of the way4 ,but this notion is1 as already explained1 entirely erroneous4 ,in the light of the stream-line theory of liquid motion1 it is easy to prove1 however1 the truth of the above statement4 ,let us begin by supposing that a solid body of regular and symmetrical shape1 say of an oval form 7see ,fig4 #cj71 is moved through a fluid destitute of all stickiness or viscosity1 which therefore does not adhere to the solid4 ,then1 if the solid is wholly submerged in this fluid1 the mutual action of the liquid and the solid will be the same1 whether we suppose the liquid to be at rest and the solid to move through it1 or the solid body to be at rest and the liquid to flow past it4 ,illustration3 ,,fig4 #cj4--,stream-lines round an ovoid4 ,illustration3 ,,fig4 #ca4--,tube of flow in a liquid4 ,if1 then1 we suppose the perfect fluid to flow round the obstacle1 it will distribute itself in a certain manner1 and its motion can be delineated by stream-lines4 ,there will be no eddies or rotations1 because the liquid is by assumption perfect4 ,consider now any two adjacent stream-lines 7see ,fig4 #ca74 ,these define a tube of flow1 represented by the shaded portion1 which is narrower in the middle than at the ends4 ,hence the liquid1 which we shall suppose also to be incompressible1 must flow faster when going past the middle of the obstacle where the stream-tubes are narrow1 than at the ends where the stream-tubes are wider4 ,by the principle already explained1 it will be clear that the pressure of the fluid will therefore be less in the narrow portion of the stream-tube1 and from the perfect symmetry of the stream-lines it is evident there will be greater and equal pressures at the two ends of the immersed solid4 ,the flow of the liquid past the solid subjects it1 in fact1 to a number of equal and balanced pressures at the two ends which exactly equilibrate each other4 ,it is not quite so easy to see at once that if the solid body is not symmetrical in shape the same thing is true1 but it can be established by a strict line of reasoning4 ,the result is to show that when a solid of any shape is immersed in a perfect liquid1 it cannot be moved by the liquid flowing past it1 and correspondingly would not require any force to move it against and through the liquid4 ,in short1 there is no resistance to the motion of a solid of any shape when pulled through a perfect or frictionless liquid4 ,when dealing with real liquids not entirely free from viscosity1 such resistance as does exist is due1 as already mentioned1 to skin friction and eddy formation4 ,in the next place1 leaving the consideration of the movement of wholly submerged bodies through liquids whether perfect or imperfect1 we shall proceed to discuss the important question of the resistance offered by water to the motion through it of a floating object1 such as a ship or swan4 ,we have in this case to take into consideration the wave-making properties of the floating solid4 ,we have already pointed out that to make a wave on water requires an expenditure of energy or the performance of mechanical work4 ,if a wave is made and travels away over water1 it carries with it energy1 and hence it can only be created if we have a store of energy to draw upon4 ,if we suppose that skin friction is absent1 and that the ship floats upon a perfect fluid1 it would nevertheless be true that1 if the moving object creates waves1 it will thereby reduce its own movement and require the application of force to it to keep it going4 ,we may say therefore that if any floating object creates waves on a liquid over which it moves1 these waves rob the floating body of some of its energy of motion4 ,the creation of the waves will bring it to rest in time1 unless it is continually urged forward by some external and impressed force1 and wave-generation is a reason for a part at least of the resistance we experience when we attempt to push it along4 ,accordingly1 one element in the problem of designing a ship is that of finding a form which will make as little wave-disturbance as possible in moving over the liquid4 ,it is comparatively easy to find a shape for a floating solid which shall make a considerable wave-disturbance on the water when it is pulled over it1 but it is not quite so easy to design a shape which will not make waves1 or make but very small ones4 ,if we look carefully at a yacht gliding along before a fresh breeze on a sea or lake surface which is not much ruffled by other waves1 it is possible to discover that a ship1 when going through the water1 creates four distinct systems of waves4 ,two of these are very easy to see1 and two are more difficult to identify4 ,these wave-systems are called respectively the oblique bow and stern waves1 and the transverse and rear waves4 ,we shall examine each system in turn4 ,the most important and easily observed of the four sets of waves is the oblique bow wave4 ,it is most easily seen when a boy's boat skims over the surface of a pond1 and readily observed whenever we see a duck paddling along on the water4 ,let any one look1 for instance1 at a duck swimming on a pond4 ,he will see two trains of little waves or ripples1 which are inclined at an angle to the direction of the duck's line of motion4 ,both trains are made up of a number of short waves1 each of which extends beyond or overlaps its neighbour 7see ,fig4 #cb74 ,illustration3 ,,fig4 #cb4--;,echelon waves made by a duck4 ,hence1 from a common ,french word1 these waves have been called echelon waves1#ae and we shall so speak of them4 ,illustration3 ,,fig4 #cc4--;,echelon waves made by a model yacht4 ,on looking at a boy's model yacht in motion on the water1 the same system of waves will be seen2 and on looking at any real yacht or steamer in motion on smooth water1 they are quite easily identified 7see ,fig4 #cc74 ,the complete explanation of the formation of these bow or echelon waves is difficult to follow1 but in a general way their formation can be thus explained3 ,suppose we have a flat piece of wood1 which is held upright in water1 and to which we give a sudden push4 ,we shall notice that1 in consequence of the inertia of the liquid1 it starts a wave which travels away at a certain speed over the surface of the water4 ,the sudden movement of the wood elevates the water just in front of it1 and this displacement forms the crest of a wave which is then handed on or propagated along the surrounding water-surface4 ,if two pieces of wood are fastened together obliquely1 as in ,fig4 #cd1 and held in water partly submerged1 we shall find that when this wood is suddenly thrust forward like a wedge1 it starts two oblique waves which move off parallel to the inclined wooden sides4 ,the bows of a ship1 roughly speaking1 form such a wedge4 ,illustration3 ,,fig4 #cd4 ,hence1 if we consider this wedge or the bows of a ship to be placed in still water and then pushed suddenly forward1 they will start two inclined waves1 which will move off parallel to themselves4 ,if we then consider the wedge to leap forward and repeat the process1 two more inclined waves will be formed in front of the first2 and again we may suppose the process repeated1 and a third pair of waves formed4 ,the different positions of the ship's bows are shown in the diagram at #a1 #b1 and #c in ,fig4 #ce2 and c1 e1 and f are the three corresponding sets of echeloned waves4 ,for the sake of simplicity1 the waves are shown on one side only4 ,if1 then1 we imagine the ship to move uniformly forwards1 its bows are always producing new inclined waves1 which move with it1 and it is always1 so to speak1 leaving the old ones behind4 ,all these echelon waves produced by the bow of the ship are included within two sloping lines which each make with the direction of the ship's line of movement1 an angle of #ai #bh4af ,this angle can be thus set off3 ,draw a circle 7see ,fig4 #cf71 and produce the diameter ,,bc of this circle for a distance1 ,,ca1 equal to its own length4 ,from the end ,a of the produced diameter draw a pair of lines1 ,,ad1 ,,ad1 called tangents1 to touch the circle4 ,then each of these lines will make an angle of #ai #bh with the diameter4 ,if we suppose a ship-to be placed at the point marked ,a in the diagram 7see ,fig4 #cf71 all the echelon waves it makes will be included within these lines ,,ad1 ,,ad4 ,illustration3 ,,fig4 #ce4 ,moreover1 the angle of the lines will not alter1 whether the ship goes fast or slow4 ,this is easily seen in the case of a duck swimming on a lake4 ,throw bits of bread to a duck so as to induce it to swim faster or slower1 and notice the system of inclined or echelon ripples made by the duck's body as it swims4 ,it will be seen that the angle at which the two lines1 including both the trains of echelon ripples meet each other is not altered as the duck changes its speed4 ,illustration3 ,,fig4 #cf4 ,this echelon system of inclined waves is really only a part of a system of waves which is completed by a transverse group in the rear of the vessel4 ,a drawing has been given by ,lord ,kelvin1 in his lecture on 8,ship ,waves10 of the complete system of these waves1 part of which is as represented by the firm lines in ,fig4 #cg4 ,this complete system is difficult to see in the case of a real ship moving over the water4 ,the inclined rear system of waves can sometimes be well seen from the deck of a lake steamer1 such as those on the large ,swiss or ,italian lakes1 and may sometimes be photographed in a snap-shot taken of a boy's yacht skimming along on a pond4 ,illustration3 ,,fig4 #cg4 ,in addition to the inclined bow waves1 there is a similar system produced by the stern of a vessel1 which is1 however1 much more difficult to detect4 ,the other two wave-systems produced by a ship are generally called the transverse waves4 ,there is a system of waves whose crest-lines are at right angles to the ship1 and they may be seen in profile against the side of any ship or yacht as it moves along4 ,these transverse waves are really due to the unequal pressures resulting from the distribution of the stream-lines delineating the movement of the water past the ship4 ,if we return again to the consideration of the flow of a perfect fluid round an ovoid body1 it will be remembered that it was shown that1 in consequence of the fact that the stream-lines are wider apart near the bow and stern than they are opposite the middle part of the body1 the pressure in the fluid was greater near the bow and stern than at the middle4 ,when a body is not wholly submerged1 but floats on the surface as does a ship1 these excess pressures at the bow and stern reveal themselves by forcing up the water-surface opposite the ends of the vessel and lowering it opposite the middle4 ,this may be seen on looking at any yacht in profile as it sails4 ,the yacht appears to rest on two cross-waves1 one at the bow and one at the stern1 and midships the water is depressed 7see ,fig4 #ch74 ,illustration3 ,,fig4 #ch4 ,these waves move with the yacht4 ,if the ship is a long one1 then each of these waves gives rise to a wave-train2 and on looking at a long ship in motion1 it will be seen that1 in addition to the inclined bow wave-system1 there is a series of waves which are seen in profile against the hull4 ,illustration3 ,,fig4 #ci4 ,when a ship goes at a very high speed1 as in the case of torpedo-boat destroyers1 the bow of the vessel is generally forced right up on to the top of the front transverse waves1 and the boat moves along with its nose entirely out of water 7see ,fig4 #ci74 ,in fact1 the boat is1 so to speak1 always going uphill1 with its bows resting on the side of a wave which advances with it1 and its stern followed by another wave1 whilst behind it is left a continually lengthening trail of waves1 which are produced by those which move with the boat4 ,the best way to see all these different groups of ship-waves is to tow a rather large model ship without masts or sails--in fact1 a mere hulk--over smooth water in a canal or lake4 ,let one person carry a rather long pole1 to the end of which a string is tied2 and by means of the string let the model ship be pulled through the water4 ,let this person run along the banks of the canal or lake1 and tow the ship steadily through the water as far as possible at a constant speed4 ,let another person1 provided with a hand camera1 be rowed in a boat after the model1 and keep a few yards behind4 ,the second observer will be able to photograph the system of ship-waves made by the model1 and secure various photographs when the model ship is towed at different rates4 ,the echelon and transverse waves should then be clearly visible1 and if the water is smooth and the light good1 it is not difficult to secure many useful photographs4 ,by throwing bits of bread to ducks and swans disporting themselves on still water1 they also may be induced to take active exercise in the right direction1 and expose themselves and the waves or ripples that they make to the lens of a hand camera or pocket kodak4 ,from a collection of snap-shot photographs of these objects the young investigator will learn much about the form of the waves made by ships1 and will see that they are a necessary accompaniment of the movement of every floating object on water4 ,by conducting experiments of the above kind under such conditions as will enable the exact speed of the model to be determined1 and the resistance it experiences in moving through the water1 information has been accumulated of the utmost value to shipbuilders4 ,our scientific knowledge of the laws of ship-resistance we owe chiefly to the labours of two great engineers1 ,mr4 ,scott ,russell and ,mr4 ,william ,froude4 ,mr4 ,froude's work was begun privately at ,torquay about the year #ahgj1 and was subsequently continued by him for the ,british ,admiralty4 ,mr4 ,froude was the first to show the value and utility of experiments made with model ships dragged through the water4 ,he constructed at ,torquay an experiment tank about #bjj feet in length1 which was a sort of covered swimming-bath1 and he employed for his experiments model ships made of wood or paraffin wax1 the latter being chosen because the model could be so easily cut to the desired shape1 and all the chips and the model itself could be melted up and used over again for subsequent experiments4 ,without detailing in historic order his discoveries1 suffice it to say that1 as the outcome of his work1 ,mr4 ,froude was able to state two very important laws which relate to the relative resistance experienced when two models of different sizes are dragged through the water at different speeds4 ,the first of these relates to what is called the 8corresponding speeds40 ,suppose we have a real ship #bej feet long1 and we make an exact model of this ship #aj feet long1 then the ship is twenty-five times longer than the model4 ,mr4 ,froude's law of corresponding speeds is as follows3-- ,if the above model and the ship are both made to move over still water1 the ship going five times as fast as the model1 the system of waves made by the model will exactly reproduce on a smaller scale the system of waves made by the ship4 ,in other words1 if we were to take a couple of photographs1 one of the ship going at #bj miles an hour1 and one of the model one twenty-fifth of its size going at #d miles an hour1 and reduce the two photographs to the same size1 they would be exactly alike in every detail4 ,expressed in more precise language1 the first law of ,froude is as follows3 ,when a ship and a model of it move through smooth water at such speeds that the speed of the ship is to the speed of the model as the square root of the length of the ship is to the square root of the length of the model1 then these speeds are called 8corresponding speeds40 ,at corresponding speeds the wave-making power of the model resembles that of the ship on a reduced scale4 ,if we call ,l and l the lengths of the ship and the model1 and ,s and s the speeds of the ship and the model1 then we have-- ,s_/s 7,l_/l7 where ,s and s are called corresponding speeds4 ,mr4 ,froude then established a second law of equal importance1 relating to that part of the whole resistance due to wave-making experienced by a ship and a model1 or by two models when moving at corresponding speeds4 ,mr4 ,froude's second law is as follows3 ,if a ship and a model are moving at 8corresponding speeds10 then the resistances to motion due to wave-making are proportional to the cube of their lengths4 ,to employ the example given above1 let the ship be #bej feet long and the model #aj feet long1 then1 as we have seen1 the corresponding speeds are as #e to #a1 since the lengths are as #be to #a4 ,if1 therefore1 the ship is made to move at #bj miles an hour1 and the model at #d miles an hour1 the resistance experienced by the ship due to wave-making is to that experienced by the model as the cube of #be is to the cube of #a1 or in ratio of #ae1fbe to #a4 ,in symbols the second law may be expressed thus3 ,let ,r be the resistance due to wave-making experienced by the ship1 and r that of the model when moving at corresponding speeds1 and let ,l and l be their lengths as before2 then-- ,r_/r ,l#c_/l#c ,before these laws could be applied in the design of real ships1 it was necessary to make experiments to ascertain the skin friction of different kinds of surfaces when moving through water at various speeds4 ,mr4 ,froude's experiments on this point were very extensive4 ,for example1 he showed that the skin friction of a clean copper surface such as forms the sheathing of a ship may be taken to be about one quarter of a pound per square foot of wetted surface when moving at #fjj feet a minute4 ,this is equivalent to saying that a surface of #d square feet of copper moved through water at the rate of #aj feet a second experiences a resisting force equal to the weight of #a lb4 due entirely to skin friction4 ,very roughly speaking1 this skin resistance increases as the square of the speed4#ag ,thus at #bj feet per second the skin friction of a surface of #d square feet of copper would be #d lbs41 and at #cj feet per second it would be #i lbs4 ,any roughness of the copper surface1 however1 greatly increases the skin friction1 and in the case of a ship the accumulation of barnacles on the copper sheathing has an immense effect in lowering the speed of the vessel by increasing the skin friction4 ,hence the necessity for periodically cleaning the ship's bottom by scraping off these clinging growths of seaweed and barnacles4 ,mr4 ,froude also made many experiments on surfaces of paraffin wax1 because of this material his ship models were made4 ,it may suffice to say that the skin friction in this case1 in fresh water1 is such that a surface of #f square feet of paraffin wax1 moving at a speed of #djj feet per minute1 would experience resistance equal to the weight of #a lb4 ,there are1 however1 certain corrections which have to be applied in practice to these rules1 depending upon the length of the immersed surface4 ,the mean speed of the water past the model or ship-surface depends on the form of the stream-lines next to it1 and it has already been shown that the velocity of the water next to the ship is not the same at all points of the ship-surface4 ,it is greater near the centre than at the ends4 ,hence the longer the model1 the less is the mean resistance per square foot of wetted surface due to skin friction when the model is moved at some constant speed through the water4 ,the above explanations will1 however1 be sufficient to enable the reader to understand in a general way the problem to be solved in designing a ship1 especially one intended to be moved by steam-power4 ,if a shipbuilder accepts a contract to build a steamer--say a passenger-steamer for cross-,channel services--he is put under obligation to provide a ship capable of travelling at a stated speed4 ,thus1 for instance1 he may undertake to guarantee that the steamer shall be able to do #bj knots in smooth water4 ,in order to fulfil this contract he must be able to ascertain beforehand what engine-power to provide4 ,for1 if the engine-power is insufficient1 he may fail to carry out his contract1 and the ship may be returned on his hands4 ,or if he goes to the opposite extreme and supplies too large a margin of power1 he may lose money on the job1 or else he may again violate his contract by providing an engine and boiler too extravagant in fuel4 ,it is in solving the above kind of practical problem that ,mr4 ,froude's methods of experimenting with models in a tank are of such immense value4 ,the first thing that the naval architect does in designing a ship is to prepare a series of drawings1 showing the form of the hull of the vessel4 ,from these drawings a model is constructed exactly to scale4 ,in ,england1 following ,mr4 ,froude's practice1 these models are usually made of paraffin wax1 about #ab or #ad feet long and #a inch in thickness4 ,in the ,united ,states wood is used4 ,these models are constructed with elaborate care and by the aid of special machinery1 and are generally #aj or #ab feet in length1 and some proper fraction of the length of the real vessel they represent4 ,the models are then placed in a tank and experiments are made1 the object of which is to ascertain the force or 8pull0 required to drag the model through the water at various speeds4 ,the tank belonging to the ,british ,admiralty is at ,haslar1 ,gosport1 near ,portsmouth1 and the experiments are now conducted there by ,mr4 ,e4 ,edmund ,froude1 who continues the scientific work and investigations of his distinguished father1 ,mr4 ,william ,froude4 ,this ,admiralty tank at ,haslar is #djj feet in length4 ,the well-known firm of shipbuilders1 ,messrs4 ,denny ,bros41 of ,dumbarton1 ,scotland1 have also a private experimental tank of the same kind4 ,the ,government of the ,united ,states of ,america have a similar tank at ,washington1 the ,italian ,government have one at ,spezzia1 and the ,russian ,admiralty has also made one4 ,these tanks resemble large swimming-baths1 which are roofed over 7see ,fig4 #dj74 ,illustration3 ,,fig4 #dj4--;,an experimental tank for testing ship models 7,washington74#ah ,over the water-surface is arranged a pair of rails1 on which runs a light carriage or platform4 ,this carriage is drawn along by a rope attached to a steam-engine1 which moves at a very uniform rate1 and its speed can be exactly ascertained and automatically recorded4 ,this moving carriage has a rod or lever depending from it1 to which the model ship is attached4 ,the pull on this rod is exactly registered on a moving strip of paper by very delicate recording mechanism4 ,the experiment is conducted by placing the model at one end of the tank1 and taking a run at known and constant speed to the other end4 ,the experimentalist is thus able to discover the total resistance which it is necessary to overcome in pushing the model ship at a certain known speed through the water4 ,the immersed surface of the model being measured and the necessary calculations made1 he can then deduct from the total resistance the resistance due to skin friction1 and the residue gives the resistance due to wave-making4 ,suppose1 then1 that the experiment has been performed with a model of a ship yet to be built1 the run being taken at a 8corresponding speed40 ,the observations will give the wave-making resistance of the model1 and from ,mr4 ,froude's second law the wave-making resistance of the real ship is predicted4 ,adding to this the calculated skin-friction resistance of the real ship1 we have the predetermined actual total ship-resistance at the stated speed4 ,for the sake of giving precision to these ideas1 it may be well to give an outline of the calculations for a real ship1 as given in a pamphlet by ,mr4 ,archibald ,denny4#ai ,the tank at the ,leven shipyard1 constructed by ,messrs4 ,denny ,bros4 for their own experiments1 is #cjj feet long1 #bb feet wide1 and #aj feet deep1 and contains #aejj tons of fresh water4 ,at each end are two shallower parts which serve as docks for ballasting and trimming models4 ,as an example of the use of the tank in predicting the power required to drive a ship of certain design through the water1 ,mr4 ,a4 ,denny gives the following figures3 ,the ship to be built was #bdj feet in length1 and from the drawings a model was constructed #ab feet in length1 or one-twentieth the size4 ,it was then required to predetermine the power required to drive the ship through the water at a speed of #ac knots4 ,a knot1 be it remarked1 is a speed or velocity of #a nautical mile an hour1 or #fjhj feet per hour4 ,it will be seen that this is not far from #ajj feet per minute4 ,by ,froude's first law1 the corresponding speed for the #ab-;foot model is therefore-- #ac #fjhj_/fj 7#ab_/bdj7 #cjf feet per minute ,the model was accordingly dragged through the tank at a speed of nearly #e feet per second1 and1 after deducting from the total observed pull the resistance due to the calculated skin friction of the model1 it was found that the resistance to the motion of the model at this speed due to wave-making was #ajh lb4 ,hence1 by ,froude's second law1 the wave-making resistance of the ship was predetermined to be-- #ajh 7#bdj_/ab7c #dj_/ci #hhej lbs4 ,the last fraction #dj_/ci is a correcting factor in passing from fresh water to salt water4 ,the surface of the proposed ship was #aj1bhj square feet1 and the skin friction was known to be #aja lb4 per square foot at a speed of #ace knots4 ,hence the total skin resistance of the ship would be-- #aj1bhj #aja #dj_/ci #aj1fbj lbs4 ,adding to this1 the #hhej lbs4 for wave-making resistance1 we have a total resistance of #ai1dgj lbs4 predetermined as the total pressure required to be overcome in moving the ship at a speed of #ace knots4 ,hence1 since #a horse-power is defined to be a power which overcomes a resistance of #cc1jjj lbs4 moved #a foot per minute1 it is easy to see that #ai1dgj lbs4 overcome at a rate of #ace knots represents a power of-- 7#ai1dgj #ace #fjhj7_/7cc1jjj #fj7 #haj horse-power ,but now1 in the case of a screw-driven steamer1 a part of the power is lost in merely churning up the water1 and a part in internal frictional losses in the engine and screw-shaft4 ,it is not far from the truth to say that #ej per cent4 of the applied engine-power is lost in useless water-churning4 ,hence1 for the above steamer1 an actual power of at least #afjj ,h4,p4 would have to be applied to the screw-shaft4 ,to allow1 however1 for the loss of power in friction1 and to allow a margin for emergencies1 it would be usual to provide for such a steamer engines of at least #cjjj indicated horse-power4 ,each shipbuilder has1 however1 at call a mass of data which enable him1 from actual measured mile trials1 to determine the rates between the calculated driving horse-power and the indicated horse-power of the engines1 and so enable him1 in the light of experience1 to provide in any new ship the exact amount of steam-power necessary to produce the required speed4 ,as an instance of how accurately this can be done by the aid of the tank experiments1 ,mr4 ,a4 ,denny gives an example drawn from experience in building the well-known paddle-steamers ,princess ,josephine and ,princess ,henriette for the ,belgian ,government ,dover to ,ostend fast mail-steamer service4 ,the speed guaranteed before the boats were built was #bj knots4 ,the estimate was made for #ba knots1 and the actual results of trials on the measured mile1 when the ships were built1 showed that each did #baa knots on prolonged and severe test4 ,the reader1 therefore1 cannot fail to see how important are these methods1 laws1 and researches of ,mr4 ,froude4 ,the above-described process for testing models is being continually conducted in the case of all new battleships and cruisers for the ,british ,navy1 and also is pursued by the naval constructors of other nations4 ,in connection with the extensive programme of battleship construction which has been carried out of late years1 ,sir ,william ,white1 the late eminent ,chief ,director of ,naval ,construction1 states that it is not too much to say that these methods of investigation and experiment have placed in the hands of the naval architect an instrument of immense power for guiding him safely and preventing costly mistakes4 ,sir ,william ,white has declared that it would have been impossible to proceed with the same certainty in battleship design1 were it not for the aid afforded by these methods4 ,mr4 ,froude was not content1 however1 with experiments made with models4 ,he ascertained by actual trials the total force required to drive an actual ship through the water at various speeds1 and obtained from other experiments valuable data which showed the proportion in which the total resistance offered to the ship was divided between the skin friction and the wave-making resistance4 ,then he made experiments on a ship of #aaeg tons1 viz4 ,h4,m4,s4 ,greyhound4 ,this vessel was towed by another vessel of #cjgh tons1 viz4 ,h4,m4,s4 ,active1 by means of a tow-rope and a dynamometer1 which enabled the exact 8pull0 on this hawser to be ascertained when the ,greyhound was towed at certain speeds4 ,the following are some of the results obtained3-- ,speed in knots ,strain in tons of ,h4,m4,s4 ,greyhound4 on towing-rope4 #d knots #jf tons #f 0 #ad 0 #h 0 #be 0 #aj 0 #dg 0 #ab 0 #ij 0 ,it will be seen that the total resistance increases very rapidly with the speed1 varying in a higher ratio than the square of the speed4 ,in addition1 the indicated horse-power of the engine of the ,greyhound was taken when being self-driven at the above speeds1 and it was found that only #de per cent4 of the indicated horse-power of the engines was used in propelling the ship1 the remaining #ee per cent4 being wasted in engine and shaft friction and in useless churning of the water by the screw4 ,it is an important thing to know how this total resistance is divided between skin friction and wave-making resistance4 ,mr4 ,r4 ,e4 ,froude has kindly furnished the author1 through the intermediation of ,sir ,william ,white1 with some figures obtained from experiments at ,haslar1 showing the proportion of the whole ship-resistance which is due to skin friction for various classes of ships going at certain speeds4 ,at full speed4 ,at #aj knots4 ,battleships #ee per cent4 #gi per cent4 ,cruisers #ee 0 #hd 0 ,torpedo-boat destroyers #dc 0 #hj 0 ,the above table gives the percentage which the skin friction forms of the total resistance1 and the remainder is1 of course1 wave-making and eddy-resistance4 ,the curves shown in ,fig4 #da 7taken1 by kind permission of the editor1 from an article by ,mr4 ,e4 ,h4 ,tennyson-,d',eyncourt1 in ,cassier's ,magazine for ,november1 #aija7 give1 in a diagrammatic form1 an idea of the manner in which the two principal sources of ship-resistance vary with the speed4 ,illustration3 ,,fig4 #da4--7,reproduced1 by permission1 from ,cassier's ,magazine47 ,it will be seen that when a ship is going at a relatively slow speed1 the greater portion of the whole resistance is due to skin friction1 but when going at a high speed1 the greater portion of the resistance is due to wave-making4 ,hence the moral is that ships and boats intended to move at a high speed must be so fashioned as to reduce to a minimum the wave-making power4 ,in general1 the naval architect has to consider many other matters besides speed4 ,in battleship design he has to consider stability1 power of carrying guns and armour1 and various other qualities4 ,in passenger-steamers he has to take into consideration capacity for passengers and freight1 also steadiness and sea-going qualities2 and all these things limit and control the design4 ,there is one class of vessel1 however1 in which everything is sacrificed to speed1 and that is in racing-yachts4 ,hence1 in the design of a racing-yacht1 the architect has most scope for considerations which bear chiefly upon the removal of all limitations to speed4 ,a little examination1 therefore1 of the evolution of the modern racing-yacht shows how the principles we have endeavoured to explain have had full sway in determining the present form of such boats4 ,attention has chiefly been directed to this matter in connection with the international yacht race for the possession of the ,america ,cup4 ,in #ahea a yacht named the ,america crossed the ,atlantic and made her appearance at ,cowes to compete for a cup given by the ,royal ,yacht ,squadron4 ,up to that time ,british yachts had been designed with full bluff bows and a tapering run aft4 ,these boats were good sea-boats1 but their wave and eddy making powers were considerable4 ,the ,america was constructed with very fine lines and a sharp bow1 and was a great advance on existing types of yacht4 ,in the race which ensued the ,america won the cup1 and carried it off to the ,united ,states4 ,since that date there has been an intermittent but steady effort on the part of ,british yachtsmen to recover the trophy1 so far1 however1 without success4 ,illustration3 ,,america1 #ahea4 ,,vigilant1 #ahic4 ,,puritan1 #ahhe4 ,,defender1 #ahie4 ,,volunteer1 #ahhg4 ,,columbia1 #ahii4 ,united ,states yachts entered for the ,america ,cup race1 #ahea-ahii4 7,,fig4 #db47 ,illustration3 ,,genesta1 #ahhe4 ,,valkyrie ,,iii41 #ahie4 ,,thistle1 #ahhg4 ,,shamrock1 #ahii4 ,,valkyrie ,,ii41 #ahic4 ,,shamrock ,,ii41 #aija4 ,,fig4 #db4--;,british yachts entered for the ,america ,cup race1 #ahhe-aija4 ,in a very interesting article in ,harmsworth's ,magazine1 in #aija1 ,mr4 ,e4 ,goodwin has traced the gradual evolution of the modern yacht1 such as ,shamrock ,,ii4 or the ,columbia1 from the ,america4 ,no doubt the methods of 8measurement0 in force at the time1 or the dimensions which determine whether the boat can enter for the ,cup race or not1 have had some influence in settling the shape4 ,the reader1 however1 will see1 on comparing the outlines of some of the competing yachts as shown in ,fig4 #db1bj that there has been a gradual tendency to reduce the underwater surface as much as possible1 and also to remove the wave-making tendency by overhanging the bows4 ,the only rule now in force restricting the yacht size for the ,cup race is that it must not be more than #ij feet in length when measured on the water-line4 ,in order that the yacht may have stability1 and be able to carry a large sail-surface1 it must have a certain depth of immersed hull4 ,this is essential also to prevent the boat from making leeway when sailing with the wind abeam4 ,but consistently with this object1 the two great aims of the yacht-builder are1 first1 to reduce as much as possible the skin friction by making the yacht-surface smooth and highly polished4 ,thus modern racing-yachts are not always built of wood1 but very often of some metal1 such as bronze1 steel1 or aluminium alloys1 which admit of a very high polish4 ,this hull-surface is burnished as much as possible before the race1 to reduce to a minimum the skin friction4 ,then in the second place1 the designer aims at fashioning the form of the bow of the yacht so as to reduce as much as possible its wave-making qualities4 ,a fine type of modern yacht glides through the water with hardly any perceptible bow wave at moderate speeds4 ,thus the following extract from the ,chicago ,recorder of ,september #d1 #aija1 respecting ,sir ,thomas ,lipton's yacht1 ,shamrock ,,ii41 during her trials for the ,cup race1 shows how marked a feature this is in the case of a yacht of the best modern type3-- 8,with her owner1 designer1 builder1 manager1 and sailmaker on board1 the yacht ,shamrock ,,ii4 sailed her seventh trial race to-day off ,sandy ,hook4 ,although at times there was not more than a three-knot air1 at no time did the yacht act sluggishly4 8,she slipped through the water at an amazingly good rate under the influence of her great mainsail and light sails4 ,the water was smooth1 but even when pressed to a speed of #i knots the yacht made a very small wave at the bow1 and left an absolutely clean wake40 ,we may say1 therefore1 that the ideal form of yacht is one which would travel through the water without making any wave at all at bow or stern4 ,this condition can1 however1 only be reached approximately1 but the clear recognition of the principle has enabled yachts to be designed with vastly greater speed powers than in the old days of bluff bows and tapering bodies4 ,before passing away from the subject of waves made by ships1 it is desirable to refer a little more in detail to the complicated wave-system made by a ship in motion4 ,this has been most carefully elucidated by ,lord ,kelvin1 who1 in this as in so many other matters1 is our great teacher4 ,lord ,kelvin has shown that if a small floating body is towed through the water at a uniform speed1 it originates a system of waves1 each one of which is of the form shown in ,fig4 #dc4 ,the whole system of waves formed is represented in ,fig4 #cg1 where the position of the ship or moving object is at the point marked ,a4 ,the key to a correct comprehension of this ship wave-system is to be found in the fact explained in ,chapter ,i41 that a group of water waves on an indefinitely extended water surface advances at half the speed of a single wave4 ,it has already been shown that when a single wave-disturbance is made upon water it gradually develops itself into a group of waves4 ,the single wave when created causes a disturbance on water which extends both forwards and backwards4 ,as the wave moves forward the wave-disturbance is always growing in front and dying away behind1 and the wave-group therefore moves forward1 but the centre or limits of the group move with only half the velocity of a single wave4 ,illustration3 ,,fig4 #dc4 ,now consider the ship originally at ,b 7see ,fig4 #cf71 and let us suppose the ship to make a small jerk forward4 ,this operation is like plunging a stone into the water1 and it starts a wave-system4 ,but if the ship moves forward with a uniform speed1 by the time the ship has reached the point ,a1 the end of the wave-group will have reached a point ,c1 such that ,c is halfway between ,b and ,a4 ,the movement of the ship1 however1 originates a group of waves1 and the velocity of a wave on water is dependent upon its wave-length1 as already explained1 so that the greater the wave-length the greater the velocity4 ,hence the conditions that determine the form of the wave-system round the ship are3 7#a7 that the head of the procession goes forward with the speed of the ship2 7#b7 that there is an end or limit to the transverse system of waves behind1 which moves forward with half the speed of the ship2 7#c7 the inclination of the wave at any point to the direction of motion of the ship must be such that its velocity1 in its own direction1 is consistent with the wave-length at that place4 ,these general conditions determine the form of the wave-group as shown in ,fig4 #cg2 but the detailed predetermination of the exact form of the oblique and rear wave cannot be made without the employment of mathematical reasoning of a somewhat advanced character4 ,for the purposes of the general reader it will be sufficient to note that this procession of ever-extending waves1 which lengthens backwards behind a ship1 requires energy to produce it4 ,this energy must be supplied from the ship1 and the wave-production constitutes therefore a cause of resistance to motion which is felt and has to be overcome in keeping the speed of the ship constant4 ,in close connection with this subject is the fine investigation made about the year #ahcd by another eminent engineer1 ,mr4 ,scott ,russell1 on the motion of canal-boats4 ,his researches were communicated to the ,royal ,society of ,edinburgh4 ,it has already been explained that when a wave is started in a canal1 the wave-length being large compared with the depth of the canal1 then the velocity of the long wave is the same as that attained by a stone in falling through air a distance equal to half the depth of the canal4 ,scott ,russell made the interesting discovery that it is only when the speed of a canal-boat is less than that of a long wave in the canal that the boat leaves behind it a procession of waves4 ,the position of the boat is then on the rearward side of the first wave4 ,as already mentioned1 the boat leaves behind it a trail of waves1 and the rear of this procession travels forward at half the speed of the boat4 ,if the speed of the boat is greater than that of the longest free wave in that canal1 it cannot make any procession of waves1 and then there would be no system of ever-lengthening waves behind it1 but only one wave or hummock travelling along under the boat4 ,lord ,kelvin describes1 in his lecture on 8,ship ,waves10#ba how this important discovery was in fact made by a horse4 ,the horse belonged to one ,william ,houston1 and its daily duty was to drag a canal-boat on the ,glasgow and ,ardrossan ,canal4 ,on one occasion the horse took fright and galloped off1 and ,houston1 being an observant man1 noticed that when once the horse had attained a certain speed the tractive resistance evidently became lessened1 and the boat was dragged along more easily and without wash behind it4 ,accordingly1 he started a system of light canal-boats--or fly-boats1 as they were called--each #fj feet long1 and drawn by two horses at #g1 #h1 or #i miles an hour4 ,the horses were whipped up and made to gallop1 and soon dragged the boat up on to the top of its own wave1 whereupon it went along much more easily1 and without a system of stern waves4 ,mr4 ,scott ,russell instituted a searching investigation into this effect in #ahcg at the bridge of ,hermiston1 on the ,forth and ,clyde ,canal1 at a place where there was a straight run of #aejj feet4 ,the depth of the canal water was #d to #e feet1 and the speed of the long wave was accordingly #ab feet per second1 or #h miles an hour4 ,experiments were made1 amongst others1 with a boat called ,raith1 the weight of which was #aj1bci lbs41 or #e tons4 ,this boat was towed along the canal1 and the 8pull0 on the tow-rope measured by means of an instrument called a dynamometer4 ,it was found by ,mr4 ,scott ,russell that the pull or force required to drag the boat did not increase with the speed regularly1 but fell off in a marked manner when the speed of the boat reached #i miles per hour4 ,this is shown by the following table3-- ,,scott ,,russell',s ,,experiments ,,on ,,canal-,,boats4 ,tractive force in pounds ,speed of boat in miles applied to boat4 per hour4 #aab #dgb #bfa #eib #bge #fai #bej #ijd #bfi #ajdh ,for another boat-weighing #ab1egi lbs41 or #f tons1 the results obtained in the same manner were as follows3-- ,tractive force in pounds4 ,speed in miles per hour4 #bej #fai #ejj #geg #djj #heb #bhj #ijd ,this last experiment shows1 in a very remarkable manner1 the way in which the force required to drag the boat falls off as the critical speed of #i miles an hour is reached4 ,here1 then1 we have the outlines of the proof first given by ,mr4 ,scott ,russell1 that the tractive force undergoes a sudden diminution when the speed of the boat in a canal approximates to or just exceeds that of the long wave in that particular depth of water4 ,if passenger traffic on canals had not been destroyed by the advent of railways1 we should1 no doubt1 have seen extensive applications of the principle discovered so curiously by the aid of an alarmed horse1 and so skilfully investigated by a celebrated engineer4 ,the whole theory of the trail of waves made by a canal-boat is only comprehensible if it is clearly seen that a water-surface wave has a certain velocity determined by its wave-length4 ,if the wave-speed is small1 the waves are short4 ,as the speed increases the waves get longer4 ,or the matter may be put in another way4 ,we may say that just as a pendulum has a certain rate of vibration depending on its length1 so a water wave has a certain frequency1 and therefore1 a certain speed of propagation dependent upon the wave-length1 or shortest distance from one wave-crest to the next4 ,when a boat moves along a canal the waves it makes move with it1 and the first wave of all moves with the speed of the boat4 ,hence the wave-length must accommodate itself to that speed4 ,as the speed of the boat increases towards that of the free 8long wave10 the wave-length gets greater and greater1 and when the boat-speed is equal to that acquired by a heavy body1 say a stone in falling through half the depth of the canal1 then there is only one wave1 and the boat rides up on that one4 ,the next wave is practically so far behind that it is non-existent1 and the boat ceases to be followed by any trail of waves1 or 8wash40 ,,chapter ,,iii4 ,,waves ,,and ,,ripples ,,in ,,the ,,air4 ,leaving the consideration of waves and ripples on a water-surface1 we pass on to discuss the subject of waves and ripples in the air4 ,nearly every one is aware1 in a general way1 that sound is due to a disturbance created in the atmosphere4 ,few1 however1 are fully acquainted with the nature of the movements in the air which excite our sense of hearing1 and to which we owe1 not only the pleasures of conversation and the enjoyment of all the sounds in nature1 but those delights of music which are amongst the purest forms of pleasure we possess4 ,in the first place1 it is necessary to demonstrate the fact that in a place where there is no air there can be no sound4 ,before you on the table is a brass plate covered with a glass dome4 ,under the dome is a piece of clockwork1 which1 when set in action1 strikes a gong4 ,this clockwork is suspended by silk strings from a frame to keep it out of contact with the plate4 ,the plate is in connection1 by a pipe1 with an air-pump downstairs1 and from the space under the dome we can at pleasure remove the air4 ,before so doing1 however1 the clockwork shall be set in motion1 so that you will then see the hammer striking the gong1 and you also hear the sound4 ,if now we exhaust the air1 the sound rapidly dies away1 and when a fairly perfect vacuum has been made1 whilst you see the hammer continuing to pound the bell1 you notice that no sound at all reaches your ears4 ,turning a tap1 ,i let in the air1 and once more the ring of the bell peals forth4 ,the experiment shows conclusively that sound is conveyed to us through the air1 and that if we isolate a sounding body by removing the air around it1 all transmission of sound is stopped4 ,even rarefying the air greatly weakens the sound1 for it is noticed that an exploding pistol or cracker does not create the same intensity of sensation in the ear at the top of a very high mountain as it does in the valley below4 ,we have then to show1 in the next place1 that a substance which is emitting sound is in a rapid state of vibration1 or to-and-fro movement4 ,taking a tuning-fork in my hand1 ,i strike its prongs against the table1 and you hear it faintly sounding4 ,your unassisted vision will not1 however1 enable you to see that the prongs are in rapid motion4 ,if1 however1 ,i hold it against a pith-ball suspended by a silk fibre1 you see by the violent bouncing of the ball that the prongs must be in energetic vibration4 ,another experiment of the same kind1 which you can yourselves repeat1 is to elicit a sound from a small table-gong by striking it with the hammer4 ,then hold near the surface of the metal a small ball of wood or cork1 to which a suspending thread has been tied4 ,the ball will keep jumping from the gong-surface in a manner which will convince you that the latter is in a state of violent agitation4 ,the mode and extent of this movement in a sound-emitting body must next be more thoroughly examined4 ,let me explain the means by which ,i shall make this analysis4 ,on the prong of a tuning-fork1 ,t 7see ,fig4 #dd71 is fixed a small mirror1 ,m1 and a ray of light is reflected from an electric lantern on to this mirror4 ,the ray is then reflected back again on to a sort of cubical box1 ,c1 the sides of which are covered with looking-glass1 and finally it falls upon the screen4 ,the mirrors are so arranged that if the cubical mirror is at rest and the fork also1 a bright spot of light is seen upon the screen4 ,if the fork is set in vibration1 then the spot of light moves up and down so rapidly that it forms a vertical bar or line of light upon the screen4 ,the cubical mirror is carried upon an axis1 and can be set in rotation4 ,if the fork is at rest and the cubical mirror revolves1 then the spot of light marches horizontally across the screen1 and when the motion of the mirror is sufficiently rapid it forms a horizontal and brilliant band of light4 ,if1 then1 these two motions are performed at the same time1 the tuning-fork being set in vibration and the cubical mirror in rotation1 we find that the spot of light on the screen executes a wavy motion1 and we see in consequence a sinuous bright line upon the wall4 ,illustration3 ,,fig4 #dd4 ,we have here two principles involved1 which it may be better to explain a little more in detail4 ,an impression made upon the eye lasts for about the tenth part of a second4 ,hence1 if a luminous point or bright object moves sufficiently rapidly1 we cease to be able to follow its movement1 and we receive on our eyes merely the effect of a luminous line of light4 ,every boy sees this when he whirls round a lighted squib or stick with a flaming end4 ,in the next place1 notice that two independent movements at right angles combine into what is called a resultant motion4 ,thus the vertical up-and-down motion of the spot of light in our experiment1 combined with its uniform horizontal movement1 results in the production of a wavy motion4 ,for the sake of those who wish to repeat the experiment1 a few little hints may be given4 ,the revolving cubical mirror is a somewhat expensive piece of apparatus1 but found in every well-appointed physical laboratory4 ,a cheap substitute1 however1 may be made by firmly sticking on to the sides of a wooden box pieces of thin looking-glass4 ,the box is then to be suspended by a string4 ,if the string is twisted1 the box may be set spinning like a joint of meat roasting before the fire4 ,an ordinary magic lantern may be used to provide a parallel beam of light4 ,in lecture demonstrations it is necessary to employ the electric arc lamp1 and to make use of an arrangement of lenses to create the required powerful parallel beam of light4 ,then as regards the fork4 ,we are employing here a rather elaborate contrivance called an electrically driven tuning-fork1 but for home demonstration it is sufficient to make use of a single piece of stout steel clock-spring1 or any other flexible and highly tempered piece of steel4 ,this must be fixed to a block of wood as a support1 and to its end must be fastened with care a small piece of lead1 to which is attached a fragment of thin silvered glass of the kind called a galvanometer mirror1 which may be procured of any scientific instrument maker4 ,the position of this vibrating spring must be such that1 if the spring vibrates alone1 it will reflect the ray of light on to one face of the cubical mirror1 and thence on to a white wall1 and create a vertical bar of light1 which becomes a spot of light when the spring is at rest4 ,it is possible to purchase very small concave mirrors about half an inch in diameter1 made of glass silvered at the back4 ,if one of these can be procured1 then there is no need to employ an optical lantern2 with an ordinary table-lamp1 or even a candle as a source of light1 it is easy to focus a bright spot of light upon the screen1 which effects the desired purpose of making evident the motion of the spring4 ,before we dismiss the experiment1 let me say one or two more words about it4 ,you notice when it is proceeding that the luminous wavy line is a regular and symmetrical one4 ,this shows us that the motion of the prong of the fork is similarly regular4 ,this kind of backwards-and-forwards motion is called an harmonic motion1 or a simple periodic motion4 ,it is very similar to the kind of movement executed by the piston of a steam-engine as it oscillates to and fro4 ,the exact nature of the wavy line of light you see upon the screen can be delineated by a line drawn as follows3 ,on a sheet of paper describe a circle1 and divide its circumference into twelve equal parts 7see ,fig4 #de74 ,through the centre and through each of these points on the circumference draw parallel lines4 ,divide up a length of the line drawn through the centre into twelve equal parts1 and number these divisions #a to #ab4 ,number also the points on the circumference of the circle4 ,through the twelve points on the horizontal line erect perpendiculars4 ,make a dot at the intersection of the perpendicular1 or ordinate1 as it is called1 drawn through point #a on the horizontal line1 and the horizontal through point #a on the circumference of the circle4 ,do this for all the twelve intersections1 and then carefully draw a smooth curve through all these points4 ,we obtain a wavy curve1 which is called a sine curve1 or simple harmonic curve1 and is the same form of curve as that exhibited on the screen in the experiment with the tuning-fork and spot of light4 ,the piece of the curve drawn as above is called one wave-length of the harmonic curve4 ,illustration3 ,,fig4 #de4--;,a simple harmonic curve4 ,in our case the tuning-fork is making one hundred complete vibrations 7to and fro7 per second4 ,hence the periodic time1 or time occupied by one complete wave1 is the hundredth part of a second4 ,to realize what this small interval of time means1 it is sufficient to remember that the hundredth part of a second is to one second as the duration of this lecture 7one hour7 is to four days and nights4 ,the prongs of a sounding tuning-fork or the surface of a gong or a bell1 when struck1 are therefore in rapid motion4 ,we can then proceed to an experiment fitted to indicate the difference between those motions in sounding bodies which create musical tones1 and those which create mere noises or vocal sounds4 ,i have on the table before me a bent brass tube provided with a mouthpiece at one end1 and the other end of the tube is covered over with a very thin piece of sheet indiarubber tied on like the cover of a jam-pot4 ,to the outer surface of this indiarubber is cemented a very small1 light silvered-glass mirror4 ,the same arrangements are made as in the case of the previous experiment1 and the ray of light from a lantern is reflected from the little mirror on to the revolving cubical mirror1 and thence on to the screen4 ,setting the cubical mirror in rotation1 we have a line of bright light upon the screen4 ,if1 then1 my assistant sings or speaks into the mouthpiece1 the motion of the indiarubber sets in vibration the little attached mirror4 ,this mirror is not attached to the centre of the membrane1 but a little to one side4 ,hence you can easily understand that when the indiarubber is bulged in or out1 the attached mirror is more or less tilted1 and the spot of light is displaced up or down on the screen4 ,in this manner the movements of the spot imitate those of the diaphragm4 ,hence the form of the bright line on the screen is an indication of the kind of movement the diaphragm is making4 ,let us then1 in the first place1 sing into the tube whilst the cubical mirror is uniformly rotated4 ,if my assistant sounds a full pure note1 you will see that the straight line of light instantly casts itself into a wavy form1 which is not1 however1 quite of the same shape as in the case of the tuning-fork4 ,here the zigzag line resembles the outline of saw-teeth 7see ,frontispiece74 ,if he varies the loudness of his sound1 you see the height of the teeth alter1 being greater the louder his note4 ,if he changes the tone1 singing a bass or a treble note1 you observe that1 corresponding to a high or treble note1 the waves are short1 and corresponding to a deep or bass note1 the waves are long4 ,accordingly1 the shape of the line of light upon the screen gives us exact information as to the nature of the movement of the indiarubber diaphragm1 viz4 whether it is moving in and out1 slowly or quickly1 much or little4 ,again1 suppose1 instead of singing into the tube1 my assistant speaks a few words4 ,if1 for instance1 he repeats in a loud tone the simple but familiar narrative of 8,old ,mother ,hubbard10 you will see that1 corresponding to each word of the sentence1 the line of light upon the screen bends itself into a peculiar irregular form1 and each particular word is as it were written in lines of fire upon the wall4 ,notice how certain sounds1 such as b and p and also t are represented by very high notches or teeth in this line of light4 ,these sounds are called explosive consonants1 and if you examine the manner in which they are made by your mouth1 you will notice that it consists in closing the mouth by the lips or tongue placed between the teeth1 and then suddenly withdrawing the obstruction so as to allow the air from the lungs to rush forcibly out4 ,hence the air outside1 and in this case the diaphragm1 receives a sudden blow1 which is represented by this tall tooth or notch in the luminous band4 ,the experiment teaches us that whereas musical tones are caused by certain very regular and uniform vibrations of the sounding body1 vocal sounds and noises are caused by very irregular movements4 ,also that loud sounds are created by large motions1 and feeble ones by small motions4 ,again1 that the difference between tones in music is a difference in the rate of vibration of the sounding body4 ,we may infer also that the difference between the quality of sounds is connected with the form of the wave-motion made by them4 ,having established these facts1 we must1 in the next place1 proceed to notice a little more closely the nature of an air wave4 ,it will be necessary to remind you of certain qualities possessed not only by the air we breathe1 but by all gases as well4 ,here is a cylinder with a closely fitting piston1 and a tap at the bottom of the tube4 ,if ,i close the tap and try to force down the piston1 ,i feel some resistance1 which increases as the piston is pushed forward4 ,if the pressure is removed1 the piston flies back to its old position1 as if there were a spring underneath it4 ,the air in the tube is an elastic substance1 and it resists compression4 ,at constant temperature the volume into which the air is squeezed is inversely as the pressure applied4 ,the air1 therefore1 possesses elasticity of bulk1 as it is called1 and it resists being made to occupy a smaller volume4 ,again1 the air possesses inertia1 and when it is set in motion it continues to move like any other heavy body1 after the moving force is withdrawn4 ,we have1 therefore1 present in it the two essential qualities for the production of a wave-motion1 as explained in the first lecture4 ,the air resists compression in virtue of elasticity1 and when it is allowed to expand again back1 it persists in motion in virtue of inertia4 ,let us consider next the process of production of a very simple sound1 such as an explosion4 ,suppose a small quantity of gun-cotton to be detonated4 ,it causes a sound1 and therefore an air wave4 ,the process by which this wave is made is as follows3 ,the explosion of the gun-cotton suddenly creates a large quantity of gas1 which administers to the air a very violent outward push or blow4 ,in consequence of the inertia of the air1 it cannot respond everywhere instantly to this force4 ,hence a certain spherical layer of air is compressed into a smaller volume4 ,this layer1 however1 almost immediately expands again1 and in so doing it compresses the next outer layer of air and rarefies itself4 ,then1 again1 the second layer in expanding compresses a third1 and so on4 ,accordingly1 a state of compression is handed on from layer to layer1 and each state of compression is followed by one of rarefaction4 ,the individual air-particles are caused to move to and fro in the direction of the radii of the sphere of which the source of explosion is the centre4 ,hence we have what is called a spherical longitudinal wave produced4 ,each air-particle swings backwards and forwards in the line of propagation of the wave4 ,the actual motion of each air-particle is exceedingly small4 ,the speed with which this zone of compression travels outwards1 is called the velocity of the sound wave1 and the extent to which each air-particle moves backwards and forwards is called the amplitude of the wave4 ,suppose1 in the next place1 that instead of a merely transitory sound like an explosion1 we have a continuous musical sound1 we have to inquire what then will be the description of air-movement executed4 ,the experiments shown already will have convinced you that1 in the case of a musical sound1 each air-particle must repeat the same kind of motion again and again4 ,the precise nature of the displacement can be best illustrated by the use of two models4 ,before you is placed a frame to which are slung a series of golf-balls suspended by threads 7see ,fig4 #d1 ,chapter ,i474 ,between each pair of balls there is a spiral brass spring1 which elastically resists both compression and extension4 ,you will see that the row of balls and springs1 therefore1 has similar properties to the air4 ,in virtue of the springs it resists compression and expansion1 and in virtue of the mass or inertia of the balls any ball1 if displaced and allowed to move back1 overshoots its position of equilibrium because it persists in motion4 ,the row of balls1 therefore1 resists extension and compression in consequence of the elasticity of the springs1 and each ball persists in movement in consequence of the inertia of the ball4 ,if we then administer a little pat to the first ball1 you will see a wave-motion run along the line of balls4 ,each ball in turn moves to and fro a little way1 and its movement is handed on to its neighbours4 ,we have here an example of a longitudinal wave-motion which resembles that of the air when it is traversed by a sound wave4 ,another model which is of a more elaborate character shows us the sort of motion made in a tube when a sound wave due to a continuous musical sound is passing along it4 ,it consists of a glass disc which is blackened1 and has the paint removed along certain excentric circular lines4 ,this disc is made to revolve in front of a wide slit in a piece of metal4 ,by means of an optical lantern we project on to the screen an image of the slit1 which you see is crossed by certain bright bars of light1 crowded together at some places and more spaced apart at others4 ,when the disc revolves1 these bars of light each move to and fro successively1 and the result is that the crowded place moves along1 or is displaced4 ,a wave of compression is propagated along the slit1 and the localities where the bars of light are compressed or expanded continually change their place4 ,if we imagine the air in a tube to be divided into slices1 represented by these bars of light1 the motion of the model exactly represents the motion of the air in the tube when it is traversed by a series of sound waves4 ,the distance from one place of greatest compression to the next is called the wave-length of the sound wave4 ,hence1 although a sound such as that of an explosion may consist in the propagation of a single layer of compression1 the production of a continuous musical note involves the transference of a series of equidistant compressional zones1 or waves4 ,these models will have assisted you1 ,i trust1 to form a clear idea of the nature of a sound wave in air4 ,it is something very different1 in fact1 from a wave on the surface of water1 but it is characterized by the same general qualities of wave-motion4 ,it is a state of longitudinal periodic motion in a row of particles1 which is handed on from one to another4 ,each particle of air oscillates in the line of propagation of the wave1 and moves a little way backwards and forwards on either side of its undisturbed position4 ,it will be seen1 therefore1 that a solitary sound wave is a state of air-compression which travels along in the otherwise stationary air4 ,the air is squeezed more tightly together in a certain region1 and successive layers of air take up this condition4 ,in the case of water-surface waves the wave is a region of elevation at which the water is raised above the general or average level1 and this elevated region is transferred from place to place on otherwise stationary water4 ,in the case of an air-wave train we have similar regions of compression following each other at distances1 it may be1 of a fraction of an inch or of several feet4 ,thus in the case of ordinary speech or song1 the waves are from #b to #h feet in length1 that is1 from one compressed region to the next4 ,in the case of a whistle1 the wave-length may be #a or #b inches1 whilst the deepest note of an organ produces a sound of which the wave-length is about #cb feet4 ,as in every other instance of wave-motion1 air waves may differ from each other in three respects4 ,first1 in wave-length2 secondly1 in amplitude2 and thirdly1 in wave-form4 ,the first determines what we call the tone1 i4e4 whether the sound is high or low1 treble or bass2 the second determines the intensity of the sound1 whether faint or loud2 and the third determines its quality1 or1 as the ,germans expressively call it1 the sound-colour 7,klangfarbe74 ,we recognize at once a difference between the sound of a vowel1 say ah1 sung by different persons to the same note of the piano and with the same loudness4 ,there is a personal element1 an individuality1 about voices which at once arrests our attention1 apart altogether from the tone or loudness4 ,this sound-quality is determined by the form of the wave-motion1 that is1 by the nature of the movement of the air-particle during its little excursion to and fro in which it takes part in producing a zone of compression or rarefaction in the air and so forms a sound wave4 ,we have next to discuss the speed with which this air-compression is propagated through the air4 ,every one knows that it is not instantaneous4 ,we see the flash of a gun at a distance1 and a second or so afterwards we hear the bang4 ,we notice that the thunder is heard often long after the lightning flash is seen4 ,it would take too long to describe the experiments which have been made to determine precisely the speed of sound waves4 ,suffice it to say that all the best experiments show that the velocity of a sound wave in air1 at the temperature of melting ice1 or at #j ,c4 #cb ,fahr41 is very nearly #ajhg feet per second1 or #cc1acf centimetres per second4 ,this is equivalent to #gda miles per hour1 or more than ten times the speed of an express train4 ,at this rate a sound wave would take #d hours to cross the ,atlantic ,ocean1 #af hours to go half round the world or to the antipodes1 and some #b minutes to cross from ,dover to ,calais4 ,an opportunity of observing this speed of sound waves on a gigantic scale occurred about #bj years ago on the occasion of a great volcanic eruption near ,java4 ,if you open the map of ,asia and look for ,java and ,sumatra in the ,asiatic ,archipelago1 you will easily find the ,sunda ,strait1 and on a good map you will see a small island marked called ,krakatoa4 ,this island possesses1 or rather did possess1 a volcano which1 until the year #ahhc1 had not been known to be in eruption4 ,in that year1 however1 it again burst into activity1 and after preliminary warnings a final stupendous outburst occurred on ,august #bg1 #ahhc4 ,the roar of this volcanic explosion was probably the loudest noise ever heard upon this earth4 ,the pent-up volcanic gases and vapours burst forth from some subterranean prison with such appalling power that they created an air wave which not only encircled the earth1 but reverberated to and fro seven times before it finally faded away4 ,the zone of compressed air forming the mighty air wave as it passed from point to point on the earth's surface1 caused an increase of atmospheric pressure which left its record on all the self-registering barometers1 and thus enabled its steps to be traced4 ,a diligent examination of these records1 as collected in a celebrated ,report of the ,royal ,society upon the ,eruption of ,krakatoa1 showed exactly the manner in which this great air wave expanded4 ,starting from ,krakatoa at #aj a4m4 on the #bgth of ,august1 #ahhc1 the air wave sped outwards in a circle of ever-increasing diameter until1 by #g p4m4 on the same day1 or #i hours later1 it formed a girdle embracing the whole world4 ,this stupendous circular air wave1 #bd1jjj miles in circumference1 then contracted again1 and in #i hours more had condensed itself at a point in the northern region of ,south ,america1 which is the antipodes of ,krakatoa4 ,it then rebounded1 and1 expanding once more1 just like a water wave reflected from the side of a circular trough1 returned on its own steps1 so that #cf hours afterwards it had again reached the point from whence it set out4 ,again and again it performed the same double journey1 but each time weaker than before1 until1 after seven times1 the echoes of this mighty air wave had completely died away4 ,this is no fancy picture1 but a sober record of fact obtained from the infallible records of self-registering air-pressure-measuring instruments4 ,but we have evidence that the actual sound of the explosion was heard1 #d hours after it happened1 on the other side of the ,indian ,ocean1 by human ears1 and we have in this an instance of the measurement of the velocity of sound on the largest scale on which it was ever made4 ,there are many curious and interesting facts connected with the transmission of a sound wave through air1 affecting the distance at which sounds can be heard4 ,the speed of sound in air is much influenced by the temperature of the air and by wind4 ,the speed of sound increases with the temperature4 ,for every degree ,fahrenheit above the melting-point of ice 7#cb ,fahr47 the speed is increased by one foot per second4 ,a more accurate rule is as follows3 ,take the temperature of the air in degrees ,centigrade1 and add to this number #bgc4 ,in other words1 obtain the value of #bgc t where t is the temperature of the air4 ,then the velocity of sound in feet per second at this temperature is equal to the value of the expression-- #ajij77bgc t7_/#bgc7 ,there is one point in connection with the velocity of propagation of a sound wave which should not be left without elucidation4 ,it has been explained that the velocity of a wave in any medium is numerically given by the number obtained by dividing the square root of the elasticity of the medium by the square root of its density4 ,the number representing the elasticity of a gas is numerically the same as that representing its absolute pressure per square unit of surface4 ,the volume elasticity of the air may therefore be measured by the absolute pressure it exerts on a unit of area such as #a square foot4 ,at the earth's surface the pressure of the air at #j ,c4 is equal to about #baafd lbs4 per square foot4 ,the absolute unit of force in mechanics is that force which communicates a velocity of #a foot per second to a mass of #a lb4 after acting upon it for #a second4 ,if we allow a mass of #a lb4 to fall from rest under the action of gravity at the earth's surface1 it acquires after #a second a velocity of #cbb feet per second4 ,hence the force usually called 8a pressure of #a lb40 is equal to #cbb absolute units of force4 ,accordingly1 the atmospheric pressure at the earth's surface is #baafd #cbb #fh1adh absolute units of force in that system of measurement in which the foot1 pound1 and second are the fundamental units4 ,the absolute density of the air is the mass of #a cubic foot3 #ac cubic feet of air at the freezing-point1 and when the barometer stands at #cj inches1 weigh nearly #a lb4 ,more exactly1 #a cubic foot of air under these conditions weighs #jjhjgbh lb4 avoirdupois4 ,if1 then1 we divide the number representing the absolute pressure of the air by the number representing the absolute density of air1 we obtain the quotient #hdd1afh2 and if we take the square root of this1 we obtain the number #iabf4 ,the above calculation was made first by ,newton2 and he was unable to explain how it was that the velocity of the air wave1 calculated in the above manner from the general formula for wave-speed1 gave a value for the velocity1 viz4 #iabf1 which was so much less than the observed velocity of sound1 viz4 #ajij feet per second at #j ,c4 ,the true explanation of this difference was first given by the celebrated ,french mathematician ,laplace4 ,he pointed out that in air1 as in all other gases1 the elasticity1 when it is compressed slowly1 is less than that when it is compressed quickly4 ,a gas1 when compressed1 is heated1 and if we give this heat time to escape1 the gas resists the compression less than if the heat stays in it4 ,hence air is a little more resilient to a very sudden compression than to a slow one4 ,laplace showed that the ratio of the elasticity under sudden compression was to that under slow compression in the same ratio as the quantities of heat required to raise a unit mass of air #a ,c4 under constant pressure and under constant volume4 ,this ratio is called 8the ratio of the two specific heats10 and is a number close to #ada4 ,hence the velocity1 as calculated above1 must be corrected by multiplying the number #hdd1afh by the number #ada1 and then taking the square root of the product4 ,when this calculation is made1 we obtain1 as a result1 the number #ajia1 which is exactly the observed value of the velocity of sound in feet per second at #j ,c4 and under atmospheric pressure4 ,the velocity of sound is much affected by wind or movement of the air4 ,sound travels faster with the wind than against it4 ,hence the presence of wind distorts the shape of the sound wave by making portions of it travel faster or slower than the rest4 ,these two facts explain how it happens that loud sounds are sometimes heard at great distances from the source1 but not heard at places close by4 ,illustration3 ,,fig4 #dg 7reproduced by permission of proprietors of ,knowledge74--,map of ,south of ,england1 showing places 7black dots7 at which sound of funeral guns was heard1 ,february #a1 #aija4 ,consider the case of a loud sound made near the surface of the earth4 ,if the air were all at rest1 and everywhere at the same temperature1 the sound waves should spread out in hemispherical form4 ,but if1 as is generally the case1 the temperature near the ground is higher than it is up above1 then the part of the wave near the earth travels more quickly than that in the higher regions of the air4 ,it follows that the sound wave will have its direction altered1 and instead of proceeding near the earth in a direction parallel to the ground1 it will be elevated1 so as to strike in an upward direction4 ,again1 it may be brought down by meeting with a current of air which blows against the lower portion and so retards that to a greater extent than it does the upper part4 ,so it comes to pass that a sound wave may1 as it were1 8play leap-frog0 over a certain district1 being lifted up and then let down again2 and persons in that region will not hear the sound1 although others further off will do so4 ,a very striking instance of this occurred on the occasion of the funeral procession of our late beloved ,queen ,victoria of blessed memory4 ,the body was conveyed across the ,solent on ,february #a1 #aija1 between lines of battleships which fired salutes with big guns4 ,arrangements were made to determine the greatest distance the sound of these guns was heard4 ,in a very interesting article in ,knowledge for ,june1 #aija1 ,dr4 ,c4 ,davison has collected the results of observation from eighty-four places1 some of which are indicated in the map 7see ,fig4 #dg71 taken1 by kind permission of the editor of ,knowledge1 from that journal4 ,observations were received from places as far distant as ,alderton 7,suffolk71 #aci miles from the ,solent4 ,at several places the sound of the guns was loud enough to make windows shake4 ,this occurred at ,longfield 7#ef miles71 ,sutton 7#eh miles71 and ,richmond ,hill 7#fa miles74 ,but whilst there is clear evidence that the sound of the guns was heard even at ,peterborough 7#abe miles71 most curious to say1 the sound was hardly heard at all in the neighbourhood of the ,solent4 ,the nearest place from which any record was received was ,horley1 in ,surrey 7#ej miles74 ,hence it appears evident that the sound was lifted up soon after leaving the ,solent1 and passed right over the heads of observers near1 travelling in the higher air for a considerable distance1 probably #dj or #ej miles1 and was then deflected down again1 and reached observers on the earth's surface at much greater distances4 ,an examination of the wind-charts for that day makes it tolerably clear that this was due to the manner in which the wind was blowing at the time4 ,dr4 ,davison1 loc4 cit41 says-- 8,now1 on ,february #a1 the wind at places to the west of ,spithead was generally light1 and from the west or nearly so1 though near ,lyndhurst there was a fresh breeze from about ,w4,n4,w4 or ,n4,w4 ,at ,portsmouth1 again1 the wind is described as from the shore4 ,on the other hand1 many of my correspondents at great distances from ,spithead state that the wind1 when sensible1 was southerly in direction4 ,thus the sound-rays were first of all refracted by contrary winds over the heads of observers between #aj and #de miles1 and were afterwards brought down again by favourable upper currents1 so that the reports were clearly audible beyond #ej miles and up to #adj miles from ,spithead1 and were so loud at a distance of #hd miles that labourers in the fields put down their spades and listened40 ,the same explanation has been given of the extraordinary differences that are found at various times in the distance at which lighthouse fog-horns are heard by ships at sea4 ,there is in this case1 however1 another possible explanation1 due to what is called interference of sound waves1 the explanation of which will be given presently4 ,the late ,professor ,tyndall1 who was an authority on this subject1 was of opinion that in some states of the atmosphere there existed what he called 8acoustic opacity10 the air being non-uniform in temperature and moisture2 and through this very irregular medium1 sound waves1 when passing1 lost a great deal of their intensity by internal reflection1 or eclipses1 just as light is stopped when passing through a non-homogeneous medium like crushed ice or glass4 ,at each surface a little of the light is wasted by irregular reflection1 and so the medium1 though composed of fragments of a transparent substance1 is more or less opaque in the mass4 ,on the subject of sound-signals as coast-warnings1 some exceedingly interesting information has recently been supplied by ,mr4 ,e4 ,price-,edwards 7see ,journal of the ,society of ,arts1 vol4 #ej1 p4 #cae1 #aijb74 ,the ,lighthouse ,boards of different countries provide the means for making loud warning sounds at various lighthouses1 as a substitute for the light when fog comes on4 ,the distance at which these sounds can be heard1 and the distance-traversing power of various kinds of sounds1 have been the subject of elaborate investigations4 ,the instrument which has been found to be the most effective in producing very powerful sound waves is called a siren4 ,it consists of a tube or horn1 having at the bottom a fixed disc with slits in it4 ,outside this disc is another movable one which revolves against the first1 and which also has slits in it4 ,when the second disc revolves1 the passage way into the horn is opened and closed intermittently and suddenly1 as the slits in the discs coincide or not4 ,air or steam under a pressure of #aj to #dj lbs4 on the square inch is blown into the horn1 and the rapid interruption of this blast by the revolving slits causes it to be cut up into puffs which1 when sufficiently frequent1 give rise to a very loud sound4 ,the air under pressure is admitted to a back chamber and awaits an opportunity to escape1 and this is given to it when the revolving disc moves into such a position that the slits in the fixed and moving disc come opposite each other4 ,in comparative trials of different sound-producing instruments1 nothing has yet been found to surpass this siren as a producer of penetrating sounds4 ,it has been found very important that the frequency of the note given by the siren should coincide with the fundamental tone of the trumpet or horn4 ,as will be explained in the next lecture1 every column of air in a tube has a particular natural time-period of oscillation4 ,suppose1 for instance1 that for a certain length of trumpet-tube this is second4 ,then the siren with that trumpet will be most effective if the interruptions of the air-blast are #ajj per second4 ,lord ,rayleigh has also shown that the shape of the mouth of the trumpet is important1 and that this should not be circular as usual1 but elliptical or oval1 the shortest diameter of the ellipse being one quarter of the longest one4 ,also that the mouth should occupy such a position that the longer axis is vertical4 ,moreover1 he considers that the short axis of the oval should not exceed half the wave-length of the sound being emitted4 ,with a trumpet-mouth of such a shape1 the sound is prevented to some extent from being projected up and down1 but diffused better laterally--a result which is desired in coast sound-signals4 ,the information accumulated as regards the distances at which sounds can be heard is very briefly as follows3-- ,first as regards wind4 ,the direction of the wind has a most remarkable influence on the distance at which a given loud sound can be heard4 ,in one instance1 the noise of a siren was heard #bj miles in calm weather2 whereas1 with an opposing wind1 it was not heard more than #a mile away4 ,it has been found that for calm weather a low-pitched note is better in carrying power than a high note1 but in rough weather the opposite is the case4 ,one thing that has been noticed by all who have experimented with this subject is the curious occurrence of 8areas of silence40 ,that is to say1 a certain siren will be well heard close to its position4 ,then a little farther off the sound will be lost1 but on going farther away still it is heard again4 ,many theories have been advanced to account for this1 but none are completely satisfactory4 ,it is1 however1 a well-established effect1 and one with which it behoves all mariners to be acquainted4 ,one curious fact is the very great power that can be absorbed in creating a loud siren note4 ,thus in one case1 a siren giving a high note was found to absorb as much as #fjj horse-power when the note was sounded continuously4 ,the most striking and in one sense the most disappointing thing about these loud sounds is the small distance which they travel in certain states of the wind4 ,as a general result1 it has been found that the most effective sound for coast-warnings is one having a frequency of #ajj1 or a wave-length of about #aj feet4 ,when dealing with the subject of waves in general1 it was pointed out that the velocity of a wave depended upon the elasticity and the density of the medium in which it was being propagated4 ,in the case of a sound wave in air or any other gas1 the speed of wave-transmission is proportional to the square root of the elasticity of the gas1 and inversely proportional to the square root of the density4 ,at the same temperature the elasticity of a gas may be taken to be the same as its pressure4 ,hence1 at the same pressure1 the speed of sound-wave transmission through different gases varies inversely as the square root of their densities4 ,an example will make this clear4 ,if we take the density of hydrogen gas to be unity 7 #a71 then the density of oxygen is #af4 ,the ratio of the densities is therefore #a to #af1 and the square roots of the densities are as 7#a7 to 7#af71 or as #a to #d4 ,accordingly1 the velocity of sound waves in hydrogen gas is to that in oxygen gas as #a is to 4 ,in other words1 sound travels four times faster in hydrogen than it does in oxygen at the same temperature and pressure4 ,the following table shows the velocity of sound in different gases at the melting-point of ice 7 #j ,c47 and atmospheric pressure 7 #gfj mm4 barometer74 ,gas4 ,velocity4 ,hydrogen #dafc feet per second ,carbonic oxide #aajf 0 0 ,air #ajij 0 0 ,oxygen #ajda 0 0 ,carbonic acid #hef 0 0 ,accordingly1 we see that the lighter the gas the faster sound travels in it1 pressure and temperature being the same4 ,if the atmosphere we breathe consisted of hydrogen instead of a mixture of oxygen1 nitrogen1 and many other gases1 a clap of thunder would follow a flash of lightning much more quickly than it does in our present air1 supposing the storms to be at the same distance4 ,under present circumstances1 if #bj seconds elapse between the flash and the peal1 it indicates that the storm is about #d miles away1 but if the atmosphere were of hydrogen1 for a storm at the same distance the thunder would follow the lightning in about #e seconds4 ,furnished with these facts about the propagation of air waves1 it is now possible to point out some interesting consequences4 ,it will be in your recollection that in the first chapter it was pointed out that a wave on water could be reflected by a hard surface1 and that it could be refracted1 or bent1 when it passed from a region where it was moving quickly to one where it was moving more slowly4 ,it will be necessary now to prove experimentally that the same things can be done with sound1 in order that a body of proof may be built up in your minds convincing you that the external cause of sound-sensation must be a wave-motion in the air4 ,in the first place1 ,i must describe to you1 somewhat in detail1 the nature of the arrangements we shall employ for producing and detecting the sound waves which will be used in these experiments4 ,it would not do to rely upon the ear as a detector because you cannot all be so placed as to hear the sounds which will be produced1 and we shall1 therefore1 employ a peculiar kind of flame1 called a sensitive flame1 to act as a detector4 ,if ordinary coal-gas stored in a gasometer is burnt at a small jet under considerable pressure1 we are able to produce a tall flame about #ah to #bd inches in height4 ,the jet used is one with a steatite top and small pin-hole gas exit about inch in diameter4 ,the pressure of gas must be equal to about #aj inches of water1 and it cannot be drawn straight off the house gas-pipes1 but must be supplied from a special gasometer or gasbag under a pressure sufficient to make a flame #ah inches or so in height4 ,if the pressure is too great1 the flame roars2 if the pressure is slightly reduced1 the flame can be made to burn quietly and form a tall reed-like flame 7,a1 ,fig4 #dh74 ,this flame1 when properly adjusted1 is curiously sensitive to shrill1 chirping sounds4 ,you may shout or talk loudly near it1 and it takes no notice of your voice1 but if you chirrup or whistle in a shrill tone1 or clink your keys or a few coins in your hand1 the flame at once shortens itself to about #f or #g inches in height1 and becomes possessed of a peculiarly ragged edge1 whilst at the same time it roars 7,b1 ,fig4 #dh74 ,when in adjustment1 the clink of a couple of coins in the hand will affect this sensitive flame on the other side of the room4#bb ,the flame is also very sensitive to a shrill whistle or bird-call4 ,it will be clear to you1 from previous explanations1 that the flame responds1 therefore1 to very short air waves forming high notes4 ,the particular flame ,i shall now use responds with great readiness to air waves of #a inch to inch in length4 ,illustration3 ,,fig4 #dh4--;,a sensitive flame3 ,a1 quiescent2 ,b1 roaring4 ,it may be well to explain that the sensitive portion of the flame is the root1 just where it emerges from the burner1 and it is the action of the sound wave in throwing this portion of the flame into vibration which is the cause of its curious behaviour4 ,if you think what the action must be1 you will easily see that the operation of the sound wave is to throw the particles of the gas1 just as they escape from the hole in the jet1 into vibration in a direction transverse or at right angles to the direction of their movement in the flame4 ,the gas molecules are1 when unacted upon by the sound wave1 rushing out of the jet1 in an upward direction4 ,when the sound wave impinges on them they are1 so to speak1 caught1 and caused to rock to and fro in a direction across the flame4 ,the combination of these two motions results in a spreading action on the flame1 so that instead of being a thin lance-like shape1 it becomes more blunt1 stumpy1 and ragged at the sides4 ,the flame acts1 therefore1 as a detector of certain sounds4 ,it is a very sensitive kind of ear which listens and responds to the slightest whisper if only uttered in certain tones1 but is deaf to all other sounds4 ,its great use to us is that it acknowledges the presence of air waves of short wave-length1 and shows at once when it is immersed in a stream of air waves or ripples of very short wave-length4 ,in addition to this1 ,i am provided with a whistle giving a very shrill or high note1 which is blown steadily by a current of air supplied under constant pressure from a reservoir4 ,if the whistle is set in action1 you will at once see the sensitive flame dip down and acknowledge the presence of the air-waves sent out by the whistle4 ,the air waves sent out by this whistle proceed1 of course1 in all directions1 but for our present purpose we require to create what ,i may call a beam of sound4 ,you all know the action of a magnifying-glass1 or lens1 upon a ray of light4 ,what boy is there who has not1 at some time or other1 amused himself by concentrating the rays of the sun by a burning-glass1 and by bringing them to a focus set light to a piece of paper1 or burnt his own or companion's hand8 ,in this case we use a piece of glass called a lens1 which is thicker in the middle than at the edges1 to converge parallel rays of light to a point or focus4 ,we also use such a lens in our optical lantern to render the diverging rays from an electric lamp parallel1 and so make a parallel beam of light4 ,i shall defer for a moment an explanation of this action1 and simply say here that it is possible to construct a sound-lens1 which operates in the same manner on rays of sound4 ,i have had such a sound-lens constructed for our present experiments1 and it is made as follows3-- ,it is possible to buy small balloons made of very thin material called collodion1 this latter consisting of gun-cotton dissolved in ether and alcohol1 and then poured out on a glass plate and allowed to dry4 ,if one of these balloons is purchased1 it is possible with great dexterity to cut from it two spherical segments or saucer-shaped pieces4 ,these have then to be cemented with siccotine to a wooden ring having two small pipes opening into it 7see ,fig4 #di74 ,by means of these pipes we can inflate the lens-shaped bag so formed with a heavy gas called carbonic acid gas1 made by pouring strong acid upon marble or chalk4 ,the result of these operations1 all of which require considerable skill of hand1 is to furnish us with a sound-lens consisting of a collodion film in the shape of a magnifying-glass1 or double convex lens1 filled with carbonic acid gas heavier than the air4 ,the sound-lens so made is fixed up against a hole in a glass screen of the same size as the lens1 and on one side of the lens is placed the whistle1 and on the other side the sensitive flame4 ,these have to be adjusted so that the whistle ,w1 the centre of the lens ,l1 and the jet of the flame ,f are in one straight horizontal line perpendicular to the glass plate4 ,illustration3 ,,fig4 #di4--;,a sound-lens focussing a divergent beam of air waves4 ,the distance of the whistle from the lens has then to be adjusted so as to produce on the other side a nearly parallel beam of sound4 ,in other words1 the whistle must be placed in the focus of the lens4 ,a rule for doing this is as follows3 ,if the balloon from which the segments of collodion were cut was nearly spherical1 and had a diameter of #h inches1 then the whistle must be placed at slightly less than #h inches from the side of the lens next to it4#bc ,the exact distance1 however1 will have to be found by trial1 but it is somewhere near the point so determined4 ,the sensitive flame should be about #d or #e feet away from the lens on the other side of the screen4 ,these arrangements having been made and the whistle set in action1 it will be found that the flame responds vigorously when it is placed on the axis-line of the lens1 but if moved a few inches to right or left of this line1 it will cease to flare4 ,this shows us that we have formed a beam of sound1 and with some little care it is possible to make this a nearly parallel beam1 so that when plunged in this stream of air waves the flame dips1 but by removing it just outside the stream of sound it no longer flares4 ,i have found it not difficult1 when using a sound-lens #f or #g inches in diameter1 to make a beam of sound from a whistle some #aj inches wide at about #d feet from the lens4 ,supposing the sound-lens and sensitive flame so adjusted1 it is then necessary for our purpose to provide a sound-prism1 made in the following manner3 ,a zinc box is made in wedge form1 and the two inclined sides are cut out1 and these windows are covered with thin collodion film4 ,the box has two pipes connected with it1 by means of which it can be filled with carbonic acid gas4 ,provided with this apparatus1 it is now possible to show you a series of experiments which will leave no doubt in your minds that the external agency which creates in us the sensation of sound is a wave-motion in the air we breathe4 ,let me1 in the first place1 show you that a sound-beam can be reflected4 ,we adjust our sensitive flame and set the whistle in action1 and create1 as described1 by the lens1 a beam of sound4 ,at a little distance1 say a couple of feet1 outside the parallel beam we place the sensitive flame1 and1 being sheltered from the direct action of the whistle1 it remains perfectly quiescent4 ,taking a sheet of glass in my hand1 ,i hold it at an angle of #de in the sound-beam1 and you see the flame at once roars4 ,the beam has been reflected on to the flame1 but a very small angular movement of the glass is sufficient to reflect the sound-ray past the flame without touching it1 and the flame then exhibits no agitation4 ,a few experiments of this kind with the flame in various positions are sufficient to show that the sound-beam is reflected by the glass in accordance with the law of reflection of wave-motion1 viz4 that the angle of incidence is equal to the angle of reflection4 ,we can in the same way reflect the sound-beam by a wooden board1 a piece of cardboard1 a looking-glass1 or a sheet of metal4 ,we can reflect it from a wet duster1 but not very well from a dry handkerchief4 ,if we place the flame in the direct beam1 it is easy to show that all the above good reflectors of sound are opaque to a sound-ray1 and cast an acoustic shadow4 ,in fact1 ,i can prevent the flame from roaring by merely interposing my hand in front of it4 ,a wet duster is found to be opaque to these sound waves1 but a dry linen handkerchief is fairly transparent4 ,the collodion film used in making the lens and prism is also exceedingly transparent to these short air waves4 ,we may then go one step further1 and show that these air waves are capable of refraction4 ,it will be in your remembrance that1 in speaking of water ripples1 it was shown by experiment that1 when water ripples passed over a boundary between two regions1 in one of which they travelled more quickly than in the other1 a bending of the direction of ripple-motion took place4 ,we can show precisely the same thing with these air waves4 ,the collodion prism has been filled with a heavy gas called carbonic acid4 ,this gas is about half as heavy again as air1 and it is this heavy and poisonous gas which1 by accumulating in old wells or brewers' vats or in coal-mines after an explosion1 causes the death of any man or living animal immersed in it4 ,it has already been explained that the velocity of sound waves in different gases varies inversely as the square root of their density4 ,hence the speed of a sound wave in carbonic acid gas will be less than that in air in the ratio of the square roots of the densities of these gases4 ,the density of carbonic acid gas is to that of air as #aeeb is to #a4 ,the square root of #aeeb is #abdf1 or nearly #a4 ,accordingly1 the speed of a sound wave in carbonic acid gas is to the speed in air as #d is to #e4 ,a sound wave in air will therefore travel #e feet or #e inches in the same time that it travels #d feet or #d inches in carbonic acid gas4 ,let us now consider what must happen if a sound wave falls obliquely upon the face of our carbonic acid prism4 ,illustration3 ,,fig4 #ej4--,the refraction of a wave by a prism4 ,let ,,abc be the prism 7see ,fig4 #ej7 represented in plan1 and let ab1 ab1 ab1 be a train of sound waves advancing against the face ,,ac4 ,as soon as the left end b of the wave ab touches the face ,,ac1 and enters the carbonic acid gas1 its speed will begin to be retarded1 and in the time taken by the right end a to move in air from a to c1 the left end will have moved in carbonic acid gas1 by a less distance1 bd1 the distances ca and db1 being in the ratio of #e to #d4 ,hence it is clear that the wave-front ab will be swung round1 and when the wave has wholly entered the prism1 its direction of motion will have been bent round to the left4 ,the same thing will happen at emergence4 ,the right end1 e1 of the wave ef gets out into the air whilst the left end1 f1 is still in carbonic acid4 ,accordingly1 in the time taken for the end f to move to h1 the end e will have moved a greater distance1 in the ratio of #e to #d1 to g1 and therefore we have again a bending round of the wave-direction4 ,it is evident1 therefore1 that this unequal retarding of the two sides of the wave will result in a refraction1 or bending1 of the wave-direction1 and that whereas the sound-ray was proceeding1 before entering the prism1 in the direction of the arrow on the right hand1 it is altered1 after passing through the prism1 so as to be travelling in the direction of the arrow on the left-hand side4 ,the double bending of the sound-ray is therefore caused by1 and is evidence of the fact that1 the sound wave travels more slowly in carbonic acid gas than it does in air4#bd ,let us1 then1 bring these statements to the test of experiment4 ,we again start in action the whistle ,w1 and place the sensitive flame in the line of the lens-axis1 and notice how violently the flame flares 7see ,fig4 #ea74 ,the flame is now at a distance of #d feet from the lens4 ,i move the flame #a foot to the left hand1 and it is now outside the beam of sound1 and remains quiescent4 ,the prism ,p1 previously filled with carbonic acid gas1 is then inserted between the sound-lens and the flame1 and close to the former4 ,when properly placed1 the sensitive flame ,f immediately dips and roars4 ,it will be abundantly evident to you that this can only arise because the prism has bent round the sound-beam1 and deflected it on to the flame4 ,but if the beam is bent round1 then it follows that if the flame is now moved back to the central position ,f1 the prism remaining in front of the lens1 that the flame will not now roar1 and this we find to be the case4 ,if1 however1 the prism is then removed1 the flame at once bursts into a roar4 ,illustration3 ,,fig4 #ea4--,the refraction of a sound-ray4 ,this experiment proves to demonstration that we can refract waves of sound just as we can refract ripples on water4 ,having regard to what we have now seen1 ,i do not think you will have any difficulty in seeing how it is that the biconvex sound-lens1 filled with carbonic acid gas1 is able to render divergent sound-rays parallel2 in other words1 can convert a spherical sound wave into a plane sound wave4 ,consider what the effect really must be4 ,let the sound-lens be represented in section by ,,ab 7see ,fig4 #di71 and let ,w be the whistle sending out spherical sound waves1 represented by the dotted lines4 ,when the spherical wave meets the lens1 the central portion of the wave passes into a retarding medium1 whilst the right and left wings of the wave are still in air4 ,hence1 as before1 the wings gain on the centre4 ,again1 at emergence the wings emerge before the centre of the wave1 and hence again the wings gain on the centre4 ,after complete emergence the spherical wave-surface has been flattened out and made into a plane wave4 ,hence the sound-rays diverging from the whistle are rendered parallel or even convergent1 provided that the whistle is properly placed with regard to the lens4 ,you will see1 therefore1 that we can use a gas denser than the air1 contained in a transparent bag or vessel of collodion1 as the means of changing the form and direction of sound waves4 ,we can make lenses and prisms of carbonic acid gas which act on rays of sound just as do lenses and prisms of glass on rays of light4 ,there is1 however1 one great difference between the operation of a carbonic acid prism on rays of sound1 and that of a glass or other prism on rays of light4 ,in the lectures on ther waves it will be made clear to you that what we call light really consists in waves in a medium known as the ther4 ,but when such light waves are propagated through a transparent material like glass1 the speed of transmission depends on the wave-length1 just as in the case of water waves4 ,but as regards sound waves there is no difference between the velocity of propagation or speed with which waves of different wave-lengths move4 ,hence a bass note travels just as fast as a treble note1 and the sound waves from a flute have a speed of the same value as that from a trumpet or bassoon4 ,if it were not so1 it would be impossible for us to hear music or song at a distance1 because the notes would arrive all in the wrong order1 and the most familiar melody would be unrecognizable4 ,it follows from this that air waves1 no matter what their wave-length1 are equally refracted on passing from one medium to another of different density4 ,we shall see later on that this is not the case with waves of light and ther waves generally4 ,in the case of most transparent substances the ther waves which constitute light are transmitted with different velocities1 the longer waves moving faster than the shorter ones4 ,hence we have the familiar result of the decomposition of a ray of white light into its different constituents by a glass prism4 ,we cannot1 however1 perform a similar experiment on a complex series of waves of sound by means of a carbonic acid prism4 ,in other words1 a sound-prism refracts1 but does not disperse sound waves of various wave-lengths4 ,one thing1 however1 should be pointed out before dismissing this experiment1 and that is that to show successfully the experiment with the prism1 the length of the sound waves used must be small compared with the dimensions of the prism4 ,the reason for this is that otherwise there would be too much bending of the waves round the obstacle4 ,when a train of waves1 no matter whether waves in air or waves in water1 meets with an impervious body1 there is always a certain bending of the waves round it1 which is technically called diffraction4 ,we may see this effect on a large scale when sea waves1 rolling in1 pass by some large rock standing up like an island out of the water4 ,the waves meet it1 pass round it1 and1 so to speak1 embrace it and continue on the other side4 ,if there is to be any calm water on the leeward side1 the island must be large compared with the length of the waves4 ,the same thing holds good with regard to air waves4 ,in order that an object may form an acoustic or sound-shadow1 it is necessary that the construction shall be large compared with the length of the wave4 ,thus the hand held in front of the mouth does not much obstruct the waves of the speaking voice1 because these waves are about #b to #d feet long4 ,but as you have seen when using sound waves only #a inch long1 the hand will form a very well-marked sound-shadow1 as shown by its effect when held between a whistle and a sensitive flame4 ,in order to complete our proof that the agency which affects our ears as sound is really due to air waves1 it is necessary to be able to show that we can produce interference with air waves1 as in the case of waves on water4 ,the nature of the effect called interference by which one wave is made to annihilate another has been already fully explained4 ,i will now endeavour to exhibit to you the interference of two sound-wave trains in an experiment due to ,lord ,rayleigh1 the apparatus for which he has kindly lent to me4 ,it consists1 as you see1 of a stand1 to which is fixed a jet1 from which we form a tall sensitive flame4 ,behind the flame is placed a sheet of glass1 which is held vertically1 but can be slid towards or from the flame4 ,at a little distance we place a bird-call1 or sort of whistle1 which produces1 when blown with air1 a note so shrill as to be inaudible to human ears4 ,the air-vibrations so generated are at the rate of #cc1jjj per second1 which is beyond the limit of audition4 ,hence1 even when blown strongly1 you hear no sound from this appliance4 ,it produces1 however1 as you can see1 a very violent effect upon the sensitive flame4 ,hence this flame hears a note which we cannot hear1 and it suggests that perhaps some animals or insects may have a range of hearing quite beyond the limits fixed for our human ears4 ,such being the case1 you will see that if the glass plate is placed behind the flame at a certain distance1 the flame at once stops flaring and becomes quiescent4 ,if1 however1 the plate is moved to or from the flame by a very small distance equal to about the one-twelfth part of an inch1 the tall flame at once drops in height and begins to flare4 ,if we move the plate steadily backwards by equal small distances1 we find the flame alternately quiescent and waving4 ,the explanation of this effect is that it is due to the interference between the direct and reflected sound-rays4 ,the waves of air are turned back when they meet the glass in such a manner that the crests of the arriving waves are made to coincide with the hollows of the reflected waves1 or1 to speak more correctly1 the zones of condensation of one are coincident with the places of rarefaction of the other4 ,when the glass is adjusted so that this happens1 all air-wave motion just in front of it is destroyed1 and hence the sensitive detecting flame remains quiescent4 ,if1 however1 the glass is moved nearer to or further from the flame1 then the condensations of the reflected wave may be made to fall in the same places as the condensations of the arriving wave1 and in that case the disturbance is doubled1 and not destroyed4 ,illustration3 ,,fig4 #eb4 ,a little model may be made which will help the reader to grasp this point4 ,cut out a piece of paper in the form shown in ,fig4 #eb to represent a wave4 ,bend back the paper on itself at the dotted line ab1 and let one half represent the arriving wave1 and the other the reflecting wave4 ,it will be seen that in this case the crests of the incoming wave are obliterated by the hollows of the returning wave4 ,if1 however1 the paper is bent back at cd1 then the crests of the reflected and incident waves conspire1 and there is no interference4 ,whenever we can produce interference in this manner between two sets of sound-rays1 or light-rays1 or rays of any other kind1 we have the strongest possible proof that we are concerned with a wave-motion2 because in no other way that we can understand is it possible that a destruction of sound by sound can take place by1 so to speak1 superimposing two sound-rays1 or a destruction of light by bringing together two rays of light4 ,we may1 then1 conclude our discussion of this part of our subject by examining the manner in which vibrating bodies communicate a different form of wave to the air4 ,as already explained1 we are by our ears enabled to appreciate the fact that the air is thrown into a wave-motion1 and that this wave-motion may consist of waves of great or small wave-length1 and great or small amplitude4 ,but we are able to do something more--we are able to detect a difference between the form of two waves1 so that if represented by a wavy line of light1 as you have seen1 the nature of the outline of that line impresses itself upon our consciousness4 ,nothing is more remarkable than the extraordinary delicacy of the ear in this respect4 ,amongst all our scores of friends and acquaintances we recognize each by a quality of voice which we speak of as harsh1 melodious1 sympathetic1 rasping1 penetrating1 or clear4 ,this is not altogether a matter of enunciation or vocalization1 for if different persons pronounce correctly the same vowel-sound1 we can detect a great difference between their voices4 ,we have1 then1 to ask wherein this difference consists when considered with respect simply to what goes on outside of us in the air4 ,great light was thrown on this by the invention and perfection of the phonograph and telephone1 and also a more recent and wonderful invention1 variously called the micro-phonograph or telegraphone4 ,you have all heard a phonograph speak1 or sing1 or reproduce music4 ,in its original form the ,edison phonograph consisted of a cylinder covered with tinfoil1 against which pressed lightly a steel point attached to the centre of a metal disc4 ,in its modern form1 as improved by ,edison1 ,bell1 ,tainter1 and others1 it is a far more perfect instrument for recording and reproducing sound4 ,it now consists of a cylinder covered with a composition similar to very hard soap4 ,this cylinder is carried on a metal drum1 and caused to revolve by clockwork slowly and very uniformly4 ,a metal arm carries an elastic metal disc called a receiving diaphragm1 and to the back of this is attached a very delicate cutting-tool like a small chisel4 ,by means of a screw the chisel and diaphragm are made to travel along the cylinder1 and if no vibration is given to the disc the tool cuts a spiral on the recording cylinder1 which is a clean groove with smooth bottom ploughed out of the soft composition4 ,if1 however1 we speak or sing to the diaphragm1 the air waves cause it to vibrate1 and this makes the tool cut a furrow1 the bottom of which is irregular1 the undulations corresponding exactly to the movements of the diaphragm4 ,thus1 if we could look at the section of the furrow1 we should see it undulating like a miniature switchback railway1 each up-and-down corresponding with one vibration of the diaphragm4 ,in this manner we store up a record of air waves on the hard-soap cylinder4 ,in the next place1 to reproduce the sound1 another diaphragm with a trumpet mouthpiece has at its back a little pointed lever or set of levers1 one extremity resting upon the bottom of the irregular furrow4 ,then1 if the cylinder is so set that this reproducing diaphragm travels over the record cut by the receiving diaphragm1 we have a motion communicated to it which is the exact facsimile of that which produced the furrow4 ,accordingly1 the reproducing diaphragm gives back to the air impulses which reproduce the same wave-trains1 and therefore the same speech or song1 as that which created the record4 ,we may in this manner record any human utterance and receive it again1 word-perfect1 months or years after it was made4#be ,the action of the phonograph leads us to inquire how a disc of metal or other elastic material responds to aerial vibrations which fall upon it1 and ,i shall conclude this lecture by showing you one experiment of a kind to illustrate this point1 which1 though not very easy to perform1 is certainly one of the most attractive that can be shown4 ,there is on the table a brass tube1 of a shape somewhat like a square-shouldered funnel1 and over the smaller end is loosely slipped a wide indiarubber tube with a mouthpiece4 ,it is essential that the indiarubber tube shall not fit tightly1 but shall be supported so that an air space exists all round between it and the brass funnel tube4 ,the latter may be carried on a wooden stand4 ,the wider end of the funnel must have a diameter of about #b inches1 and the lip must be quite smooth4 ,the interior of the funnel should be blackened4 ,a soap solution has then to be prepared as for blowing soap-bubbles4 ,a good formula for making this solution is given by ,professor ,vernon ,boys1 in his book1 8,soap ,bubbles and the ,forces which mould them10 and is as follows3 ,fill a clean stoppered bottle three-quarters full of soft water4 ,add one-fortieth part of its weight of oleate of soda1 which will probably float on the water4 ,leave it until it is dissolved4 ,then nearly fill up the bottle with ,price's glycerine1 and shake well4 ,leave the bottle stoppered for a week in a dark place4 ,then syphon off the clear liquid from the scum at the top4 ,add one or two drops of strong ammonia to every pint of the liquid4 ,do not warm or filter the liquid1 and keep it carefully from exposure to the air4 ,do not expose the liquid to the air more than necessary2 but in blowing a bubble pour out a little of the liquid into a saucer4 ,in default of this good solution a substitute may be found by dissolving bits of clear yellow soap in soft water2 but this soapy water does not yield films which last so long as those made with the ,plateau solution above described4 ,by dipping the wide end of the funnel tube into some of the soap solution placed in a saucer1 it is easy to cover the end with a flat soap film which will last a considerable time4 ,this tube has then to be fixed in front of an electric arc or lime-light lantern1 so that a powerful parallel beam of light can be directed on to the film by a small flat mirror or looking-glass4 ,a lens is also placed so as to focus an image of the film on to a screen4 ,in finding the right position for the lens1 it is a great help to place a piece of white card with some bold black letters upon it over the brass funnel in the place which will be occupied with the soapy film1 and to focus this so as to obtain a sharp image of the letters on the screen4 ,when the soap film is then substituted for the card1 we should have on the screen a reflection of the film surface1 which at first will appear as a patch of white light upon the screen4 ,if we allow the film to stand for a few seconds1 it begins to get thinner at the upper part than at the bottom1 and the image on the screen will exhibit gorgeous bands of red and green1 called interference colours1 which are due1 like the colours on a soap-bubble1 to the interference of the rays of light reflected from the inner and outer surfaces of the film4 ,if the experiment is skilfully performed1 the appearance on the screen will then be very beautiful4 ,we shall have a patch of light which exhibits bands of colours1 becoming more intense the longer the film stands1 and towards the end having somewhat the appearance of an unusually lovely sunset4 ,just before this condition of the film is reached1 if we sing gently into the mouthpiece of the indiarubber tube1 the soap film will be thrown into vibration4 ,the image on the screen will exhibit a set of regularly arranged concentric stationary ripples1 which will alter in appearance with every change in the note sung4 ,the experiment requires some care and practice to perform it properly1 and should not be attempted in public without many rehearsals2 but when well shown it is a most effective and interesting experiment4 ,we see1 therefore1 that so delicate an object as a stretched soap-film can take up the vibrations of the air and be itself thrown into vibration4 ,the reason is that the soap-film1 as already explained in the first lecture1 resists stretching1 and behaves like a sheet of elastic indiarubber4 ,hence1 as each air wave falls upon it1 the film is alternately pushed out and pulled in1 but being held at the edges1 it can only accommodate itself by stretching4 ,we have1 therefore1 set up in the film a set of stationary waves similar to those set up on a rope fixed at one end when the loose end is regularly jerked up and down by the hand4 ,the experiment shows us clearly the way in which an elastic disc is set in vibration when compressional waves fall upon it1 and in the next lecture we shall proceed to discuss the vibrations of this kind which give rise to musical effects4 ,,chapter ,,iv4 ,,sound ,,and ,,music4 ,our discussion of waves and ripples in the air would be very incomplete if we left it without any further reference to the difference between those motions in the air which constitute noise or sound1 and those to which we owe the pleasure-producing effects of musical tones4 ,i propose1 therefore1 to devote our time to-day to a brief exposition of the properties and modes of production of those air-vibrations which give rise to the class of sensations we call music4 ,sufficient has already been said to make it clear to you that one essential difference between sound or noise and music1 as far as regards the events taking place outside of our own organism1 is that1 in the first case1 we have a more or less irregular motion in the air1 and1 in the second1 a rhythmical movement1 constituting a train of air waves4 ,the greater pleasure we experience from the latter is1 no doubt1 partly due to their rhythmic character4 ,we derive satisfaction from all regularly repeated muscular movements1 such as those involved in dancing1 skating1 and rowing1 and the agreeable sensation we enjoy in their performance is partly due to their periodic or cyclical character4 ,in the same way1 our ears are satisfied by the uniformly repeated and sustained vibrations proceeding from an organ-pipe or tuning-fork in action1 but we are irritated and annoyed by the sensations set up when irregular vibrations of the air due to the bray of a donkey or the screech of a parrot fall upon them4 ,before1 however1 we can advance further in an analysis of the nature of musical sounds1 two things must be clearly explained4 ,the first of these is the meaning of the term natural period of vibration1 and the second is the nature of the effect called resonance4 ,you see before you three small brass balls suspended by strings4 ,one string is #a foot long1 the second #d feet1 and the third #i feet4 ,these suspended balls are called simple pendulums4 ,taking in my hands the balls attached to the #a-;foot and the #d-;foot strings1 ,i withdraw them a little way from their positions of rest and let them go4 ,they vibrate like pendulums1 but1 as you see1 the #a-;foot pendulum makes two swings in the time that the #d-;foot makes one swing4 ,repeating the experiment with the #a-;foot and the #i-;foot pendulum1 we find that the short one now makes three swings in the time the long one makes one swing4 ,the inference immediately follows that these pendulums1 whose respective lengths are #a1 #d1 and #i feet1 make their swings from side to side in times which are respectively in the ratio of #a1 #b1 and #c4 ,again1 if we withdraw any of the pendulums from its position of rest and let it swing1 we shall find that in any stated period of time1 say #a minute1 it executes a certain definite number of oscillations which is peculiar to itself4 ,you might imagine that1 by withdrawing it more or less from its position of rest1 and making it swing over a larger or smaller distance1 you could make these swings per minute more or less as you please4 ,but you would find1 on trying the experiment1 that this is not the case1 and that1 provided the arc of vibration is not too great1 the time of one complete swing to and fro is the same whether the swing be large or small4 ,in scientific language this is called the isochronism of the pendulum1 and is said to have been discovered by ,galileo in the ,cathedral at ,pisa1 when watching the swings of a chandelier die away1 whilst counting their number by the beats of his pulse4 ,this periodic time of vibration1 which is independent of the amplitude of vibration1 provided the latter is small1 is called the natural time of vibration of the pendulum1 or its free periodic time4 ,in the case of the simple pendulum the free periodic time is proportional to the square root of the length of the pendulum4 ,accordingly1 a short pendulum makes more swings per minute than a long one1 and this rate of swinging is quite independent of the weight of the bob4 ,we can1 of course1 take hold of the bob with our hand and force it to vibrate in any period we please1 and thus produce a forced vibration2 but a free vibration1 or one which is unforced1 has a natural time-period of its own4 ,in order that any body may vibrate when displaced and then set free1 two conditions must exist4 ,in the first place1 there must be a controlling force tending to make the substance return to its original position when displaced4 ,in the second place1 the thing moved must have mass or inertia1 and when displaced and allowed to return it must in consequence overshoot the mark1 and acquire a displacement in an opposite direction4 ,in the case of the pendulum the elastic control or restoring force is the weight of the bob1 which makes it always try to occupy the lowest position4 ,we can1 however1 make a pendulum of another kind4 ,here1 for instance1 is a heavy ball suspended by a spiral spring 7see ,fig4 #ec74 ,if ,i pull the ball down a little1 and then let it go1 it jumps up and down1 and executes vertical vibrations4 ,the elastic control here is the spring which resists extension4 ,in this instance1 also1 there is a natural free time of vibration1 independent of the extent of the motion1 but dependent upon the weight of the ball and the stiffness of the spring4 ,illustration3 ,,fig4 #ec4 ,a good illustration of the above principles may be found in the construction of a clock or a watch4 ,a clock contains a pendulum which vibrates in a certain fixed time4 ,the arrangements we call the 8works0 of a clock are only a contrivance for counting the swings1 and recording them by the 8hands0 of the clock4 ,owing1 however1 to the friction of the 8works10 the pendulum would soon come to rest1 and hence we have a mainspring or 8weights0 which apply a little push to the pendulum at each swing1 and keep it going4 ,in a watch there is no pendulum1 but there is a 8balance-wheel and hair-spring10 or a wheel which has a spiral spring attached to it1 so that it can swing backwards and forwards through a small angle4 ,the so-called 8escapement0 is a means by which the swings are counted1 and a little impulse given to the wheel to keep it swinging4 ,the watch 8keeps time0 if this hair-spring is of the right degree of stiffness1 and the balance-wheel of the right weight and size4 ,thus a clock can be made to go faster or slower by slightly altering the length of its pendulum1 and the watch by slightly changing the stiffness of its hair-spring4 ,it may be noted in passing that our legs1 in walking1 swing like pendulums1 and every particular length of leg has its own natural time of vibration1 so that there is a certain speed at which each person can walk which causes him or her the least amount of fatigue1 because it corresponds with the natural free or unforced period of vibration of the leg considered as a pendulum4 ,we now pass on to notice another very important matter4 ,if we have any pendulum1 or mass suspended by a spring1 having therefore a certain natural period of vibration1 we can set it in motion by administering to it small repeated blows or pushes4 ,if the interval between these impulses corresponds with the natural time-period of oscillation1 it will be found that quickly a very large swing is accumulated or produced4 ,if1 on the other hand1 the interval between the blows does not correspond with the natural time of vibration1 then their effect in producing vibration is comparatively small4 ,this may be illustrated with great ease by means of the ball suspended by a spring4 ,suppose that by means of an indiarubber puff-ball ,i make a little puff of air against the suspended ball4 ,the small impulse produces hardly any visible effect4 ,let this puff be repeated at intervals of time equal to that of the natural free period of vibration of the suspended ball4 ,then we find that1 in the course of a very few puffs1 we have caused a very considerable vibration or swing to take place in the heavy ball4 ,if1 however1 the puffs of air come irregularly1 they produce very little effect in setting the ball in motion4 ,in the same manner a pendulum1 consisting of a heavy block of wood1 may be set swinging over a considerable range by a very few properly timed taps of the finger4 ,we may notice another instance of the effect of accumulated impulses when walking over a plank laid across a ditch4 ,if we tread in time with the natural vibration-period of the flexible plank1 we shall find that very soon we produce oscillations of a dangerously large extent4 ,whereas1 if we are careful to make the time of our steps or movement disagree with that of the plank1 this will not be the case4 ,it is for this reason that soldiers crossing a suspension bridge are often made to break step1 lest the steady tramp of armed men should happen to set up a perilous state of vibration in the bridge4 ,it is not untruthful to say that a boy with a pea-shooter could in time break down ,charing ,cross ,railway ,bridge over the ,thames4 ,if we suppose a pea shot against one of the sections of this iron bridge1 there is no doubt that it would produce an infinitesimal displacement of the bridge4 ,also there is no question that the bridge1 being an elastic and heavy structure1 has a natural free time of vibration4 ,hence1 if pea after pea were shot at the same place at intervals of time exactly agreeing with the free time-period of vibration of the bridge1 the effects would be cumulative1 and would in time increase to an amount which would endanger the structure4 ,impracticable and undesirable as it might be to carry out the experiment1 it is nevertheless certainly true1 that a boy with a pea-shooter1 given sufficient patience and sufficient peas1 could in time break down an iron girder bridge by the accumulation of properly timed but infinitely small blows4 ,the author had an instance of this before him not long ago4 ,he was at a place where very large masts were being erected4 ,one of these masts1 about #ej feet long1 was resting on two great blocks of wood placed under each end4 ,this mast was a fine beam of timber1 square in section1 and each side about #b feet wide4 ,the mast1 therefore1 lay like a bridge on its terminal supports4 ,standing or jumping on the middle of this great beam produced hardly any visible deflection4 ,the writer1 however1 placed his hand on the centre of the log and pressed it gently4 ,repeating this pressure at intervals1 discovery was soon made of the natural time-period of vibration1 and by repeating the pressures at the right moment it was found that large oscillations could be accumulated4 ,if he had ventured to proceed far with this operation1 it is certain that1 with properly timed impulses1 it would have been possible1 by merely applying the pressure of one hand1 to break in half this great wooden mast4 ,we have constant occasion in mechanical work to notice that whereas one pull or push of great vigour will not create some desired displacement of an object1 a number of very small hits1 or properly timed pushes or pulls1 will achieve the requisite result4 ,we might summarize the foregoing facts by saying that it is a maxim in dealing with bodies capable of any kind of free vibration that impulses1 however small1 will create oscillations of any required magnitude1 if only applied at intervals equal to the natural free period of vibration of the body in question4 ,we can illustrate these principles by a few experiments which have special reference to musical instruments4 ,if we fasten one end of a rope to a fixed support1 we find we can produce a wave or pulse in the rope by jerking the free end up and down with the hand4 ,the speed with which a pulse or wave travels along a rope depends upon its weight per unit of length1 or1 say1 on the number of pounds it weighs per yard1 and on the tension or pull on the rope4 ,the tighter the rope1 the quicker it travels2 and for the same tension the heavier the rope1 the slower it travels4 ,it is not difficult to show that the speed with which the pulse travels is measured by the square root of the quotient of the tension of the rope by its weight per unit of length1 or1 as it may be called1 the density of the rope4 ,we have already explained that1 in a medium such as air1 a wave of compression is propagated at a speed which is measured by the square root of the quotient of the air-pressure1 or elasticity1 by its density4 ,in exactly the same way the hump that is formed on a rope by giving one end of it a jerk1 runs along at a speed which is measured by the square root of the quotient of the stretching force1 or tension1 by the density4 ,the propagation of a pulse or wave along a string is most easily shown for lecture purposes by filling a long indiarubber tube with sand1 and then hanging it up by one end4 ,the tube so loaded has a large weight per unit of length1 and accordingly1 if we give one end a jerk a hump is created which travels along rather slowly1 and of which the movement can easily be watched4 ,we may sometimes see a canal-boat driver give a jerk of this kind to the end of his horse-rope1 to make it clear some obstacle such as a post or bush4 ,if we do this with a rope fixed at one end1 we shall notice that when the hump reaches the end it is reflected and returns upon itself4 ,if we represent by the letter l the length of the rope1 and by t the time required to travel the double distance there and back from the free end1 then the quotient of #bl by t is obviously the velocity of the wave4 ,but we have stated that this velocity is equal to the square root of the tension of the rope 7call it e7 by the weight per unit of length1 say m4 ,hence clearly-- #bl_/t 7e_/m72 or t #bl 7m_/e7 ,supposing1 then1 that the jerks of the free end are given at intervals of time equal to t1 or to the time required for the pulse to run along and back again1 we shall find the rope thrown into so-called stationary waves4 ,if1 however1 the jerks come twice as quickly1 then the rope can accommodate itself to them by dividing itself into two sections1 each of which is in separate vibration2 and similarly it can divide itself into three1 four1 five1 or six1 or more sections in stationary vibration4 ,the rope1 therefore1 has not only one1 but many natural free periods of vibration1 and it can adapt itself to many different frequencies of jerking1 provided these are integer multiples of its fundamental frequency4 ,the above statements may be very easily verified by the use of a large tuning-fork and a string4 ,let a light cord or silk string be attached to one prong of a large tuning-fork which is maintained in motion electrically as presently to be explained4 ,the other end of the cord passes over a pulley1 and has a little weight attached to it4 ,let the tuning-fork be set in vibration1 and various weights attached to the opposite end of the cord4 ,it is possible to find a weight which applies such a tension to the cord that its time of free vibration1 as a whole1 agrees with that of the fork4 ,the cord is then thrown into stationary vibration4 ,this is best seen by throwing the shadow of the cord upon a white screen1 when it will appear as a grey spindle-shaped shadow4 ,the central point ,a of the spindle is called a ventral point1 or anti-node1 and the stationary points ,n are called the nodes 7see ,fig4 #ed74 ,next let the tension of the string be reduced by removing some of the weight attached to the end4 ,when the proper adjustment is made1 the cord will vibrate in two segments1 and have a node at the centre4 ,each segment vibrates in time with the tuning-fork1 but the time of vibration of the whole cord is double that of the fork4 ,similarly1 by adjusting the tension1 we may make the cord vibrate in three1 four1 or more sections1 constituting what are called the harmonics of the string4 ,the string1 therefore1 in any particular state as regards tension and length1 has a fundamental period in which it vibrates as a whole1 but it can also divide itself into sections1 each of which makes two1 three1 four1 or more times as many vibrations per second4 ,illustration3 ,,fig4 #ed4 ,in the case of a violin or piano string1 we have an example of the same action4 ,in playing the violin1 the effective length of the string is altered by placing the finger upon it at a certain point1 and then setting the string in vibration by passing along it a bow of horsehair covered with rosin4 ,the string is set in vibration as a whole1 and also in sections1 and it therefore yields the so-called fundamental tone1 accompanied by the harmonics or overtones4 ,every violinist knows how much the tone is affected by the point at which the bow is placed across the string1 and the reason is that the point where the bow touches the string must always be a ventral point1 or anti-node1 and it therefore determines the harmonics which shall occur4 ,another good illustration of the action of properly intermittent small impulses in creating vibrations may be found in the following experiment with two electrically controlled tuning-forks3 ,a large tuning-fork1 ,f 7see ,fig4 #ed71 has fixed between its prongs an electro-magnet1 ,e1 or piece of iron surrounded with silk-covered wire4 ,when an electric current from a battery1 ,b1 traverses the wire it causes the iron to be magnetized1 and it then attracts the prongs and pulls them together4 ,the circuit of the battery is completed through a little springy piece of metal attached to one of the prongs which makes contact with a fixed screw4 ,the arrangement is such that when the prongs fly apart the circuit is completed and the current flows1 and then the current magnetizes the iron1 and this in turn pulls the prongs together1 and breaks the circuit4 ,the fork1 therefore1 maintains itself in vibration when once it has been started4 ,it is called an electrically driven tuning-fork4 ,here are two such forks1 in every way identical4 ,one of the forks is self-driven1 but the current through its own electro-magnet is made to pass also through the electro-magnet of the other fork1 which is1 therefore1 not self-driven1 but controlled by the first4 ,if1 then1 the first fork is started1 the electro-magnet of the second fork is traversed by intermittent electric currents having the same frequency as the first fork1 and the electro-magnet of the second fork administers1 therefore1 small pulls to the prongs of the second fork1 these pulls corresponding to the periodic time of the first fork4 ,if1 as at present1 the forks are identical1 and ,i start the first one1 or the driving fork1 in action it will1 in a few seconds1 cause the second fork to begin to sound4 ,let me1 however1 affix a small piece of wax to the second fork4 ,i have now altered its proper period of vibration by slightly weighting the prongs4 ,you now see that the first fork is unable to set the second fork in action4 ,the electro-magnet is operating as before1 but its impulses do not come at the right time1 and hence the second fork does not begin to move4 ,if we weight the two forks equally with wax1 we can again tune them in sympathy1 and then once again they will control each other4 ,illustration3 ,,fig4 #ee4--;,an experiment on resonance4 ,all these cases1 in which one set of small impulses at proper intervals of time create a large vibration in the body on which they act1 are said to be instances of resonance4 ,a more perfect illustration of acoustic resonance may be brought before you now4 ,before me1 on the table1 is a tall glass cylindrical jar1 and ,i have in my hand a tuning-fork1 the prongs of which make #bef vibrations per second when struck 7see ,fig4 #ee74 ,if the fork is started in action1 you at a distance will hear but little sound4 ,the prongs of the fork move through the air1 but they do not set it in very great oscillatory movement4 ,let us calculate1 however1 the wave-length of the waves given out by the fork4 ,from the fundamental formula1 wave-velocity wave-length frequency2 and knowing that the velocity of sound at the present temperature of the air is about #aabf feet per second1 we see at once that the length of the air wave produced by this fork must be nearly #dd feet1 because #dd #bef #aabfd4 ,hence the quarter wave-length is nearly #aa foot1 or1 say1 #a foot #a inch4 ,i hold the fork over this tall jar1 and pour water into the jar until the space between the water-surface and the top of the jar is a little over #a foot1 and at that moment the sound of the fork becomes much louder4 ,the column of air in the jar is #aa foot in length and this resounds to the fork4 ,you will have no difficulty in seeing the reason for this in the light of previous explanations4 ,the air column has a certain natural rate of vibration1 which is such that its fundamental note has a wave-length four times the length of the column of air4 ,in the case of the rope fixed at one end and jerked up and down at the other so as to make stationary vibrations1 the length of the rope is one quarter of the wave-length of its stationary wave4 ,this is easily seen if we remember that the fixed end must be a node1 and the end moved up and down must be an anti-node1 or ventral segment1 and the distance between a node and an anti-node is one quarter of a wave-length4 ,accordingly the vibrating column of air in the jar also has a fundamental mode of vibration1 such that the length of the column is one quarter of a wave-length4 ,hence the vibrating prongs of the #bef-period tuning-fork1 when held over the #aa foot long column of air1 are able to set the air in great vibratory movement1 for the impulses from the prongs come at exactly the right time4 ,accordingly1 the loud sound you hear when the fork is held over the jar proceeds1 not so much from the fork as from the column of air in the jar4 ,the prongs of the fork give little blows to the column of air1 and these being at intervals equal to the natural time-period of vibration of the air in the jar1 the latter is soon set in violent vibration4 ,we can1 in the next place1 pass on now to discuss some matters connected with the theory of music4 ,when regular air-vibrations or wave-trains fall upon the ear they produce the sensation of a musical tone1 provided that their frequency lies between about #dj per second and about #djjj4 ,the lowest note in an organ usually is one having #cb vibrations per second1 and the highest note in the orchestra is that of a piccolo flute1 giving #dgeb vibrations per second4 ,we can appreciate as sound vibrations lying between #af and #cb1jjj1 but the greater portion of these high frequencies have no musical character1 and would be described as whistles or squeaks4 ,when one note has twice the frequency of another it is called the octave of the first4 ,thus our range of musical tones is comprised within about seven octaves1 or within the limits of the notes whose frequencies are #dj1 #hj1 #afj1 #cbj1 #fdj1 #abhj1 #befj1 and #eabj4 ,these musical notes are distinguished1 as every one knows1 by certain letters or signs on a clef4 ,thus the note called the middle ,c of a piano has a frequency of #bdh1 and is denoted by the sign ,illustration ,the octave is divided into certain musical intervals by notes1 the frequencies of which have a certain ratio to that of the fundamental note4 ,this ratio is determined by what is called the scale1 or gamut4 ,thus1 in the major diatonic natural scale1 if we denote the fundamental note by ,c1 called do or ut in singing1 and its frequency by n1 then the other notes in the natural scale are denoted by the letters1 and have frequencies as below4 do re mi fa sol la si do ,c ,d ,e ,f ,g ,a ,b ,c#a n n n n n n n #bn ,hence if the note ,c has #bdh vibrations per second1 then the note ,d will have #i #bdh #h #bgi vibrations per second4 ,on looking at the above scale of the eight notes forming an octave1 it will be seen that there are three kinds of ratios of frequencies of the various notes4 7#a7 ,the ratio of ,c to ,d1 or ,f to ,g1 or ,a to ,b1 which is that of #h to #i4 7#b7 ,the ratio of ,d to ,e1 and ,g to ,a1 which is that of #i to #aj4 7#c7 ,the ratio of ,e to ,f1 or ,b to ,c#a1 which is that of #ae to #af4 ,the first two of these intervals or ratios are both called a tone1 and the third is called a semitone4 ,the two tones1 however1 are not exactly the same1 but their ratio to one another is that of to or of #hj to #ha4 ,this interval is called a comma1 and can be distinguished by a good musical ear4 ,several of these intervals or ratios of frequencies have received names4 ,thus the interval ,c to ,e1 #d3e1 is called a major third1 and the interval ,e to ,g1 #e3f1 is called a minor third2 the interval ,c to ,g1 #b3c1 is called a fifth1 and that of ,c to ,c#a1 #a3b1 is called an octave4 ,for the purposes of music it has been found necessary to introduce other notes between the seven notes of the octave4 ,if a note is introduced which has a frequency greater than any one of the seven in the ratio of #be to #bd1 that is called a sharpened note2 thus the note of which the frequency is n would be called ,g sharp1 and written ,g4 ,in the same way1 if the frequency of any note is lowered in the ratio of #bd to #be1 it is said to be flattened4 ,then the note whose frequency is n would be called ,g flat1 and written ,g4 ,it is obvious that if we were to introduce flats and sharps to all the eight notes we should have twenty-four notes in the octave1 and the various intervals would become too numerous and confusing for memory or performance4 ,hence in keyed instruments the difficulty has been overcome by employing a scale of equal temperament1 made as follows3 ,the interval of an octave is divided into twelve parts by introducing eleven notes1 the ratio of the frequency of each note to its neighbours on either side being the same1 and equal to the ratio #a to #ajeidf4 ,the scale thus formed is called the chromatic scale1 and by this means a number of the flats and sharps become identical2 thus1 for instance1 ,c and ,d become the same note4 ,the octave has therefore twelve notes1 which are the seven white keys1 and the five black ones of the octave of the keyboard of a piano or organ4 ,every one not entirely destitute of a musical ear is aware that certain of these musical intervals1 such as the fifth1 the octave1 or the major third1 produce an agreeable impression on the ear when the notes forming them are sounded together4 ,on the other hand1 some intervals1 such as the seventh1 are not pleasant4 ,the former we call concords1 and the latter discords4 ,the question then arises--,what is the reason for this difference in the effect of the air-vibrations on the ear8 ,this leads us to consider the nature of simple and complex air vibrations or waves4 ,let us consider1 in the first place1 the effect of sending out into the air two sets of air waves of slightly different wave lengths4 ,these waves both travel at the same rate1 hence we shall not affect the combined effects of the waves upon the air if we consider both sets of waves to stand still4 ,for the sake of simplicity1 we will consider that the wave-length of one train is #bj inches1 and that of the other is #ba4 ,moreover1 let the two wave-trains be so placed relatively to one another that they both start from one point in the same phase of movement2 that is1 let their zero points1 or their humps or hollows1 coincide4 ,then if we draw two wavy lines 7see ,fig4 #ef7 to represent these two trains1 it will be evident that1 since the wave-length of one is #a inch longer than that of the other--that is1 a distance equal to twenty wave-lengths--one wave-train will have gained a whole wave-length upon the other1 and in a distance equal to ten wave-lengths1 one wave train will have gained half a wave-length upon the other4 ,if we therefore imagine the two wave-trains superimposed1 we shall find1 on looking along the line of propagation1 an alternate doubling or destruction of wave-effect at regular intervals4 ,in other words1 the effect of superimposing two trains of waves of slightly different wave-lengths is to produce a resultant wave-train in which the wave-amplitude increases up to a certain point1 and then dies away again nearly to nothing1 as shown in the lowest of the three wave-lines in ,fig4 #ef4 ,illustration3 ,,fig4 #ef4--,the formation of beats by two wave-trains4 ,we must1 then1 determine how far apart these points of maximum wave-amplitude or points of no wave effect lie4 ,if the wave-length of one train is1 as stated1 #bj inches1 then a length of ten wave-lengths is #bjj inches1 and this must be1 therefore1 the distance from a place of maximum combined wave-effect to a place of zero wave-effect4 ,accordingly1 the distance between two places where the two wave trains help one another must be #djj inches1 and this must also be the distance between two adjacent places of wave-destruction4 ,if1 therefore1 we look along the wavy line representing the resultant wave1 every #djj inches we shall find a maximum wave-amplitude1 and every #djj inches a place where the waves have destroyed each other4 ,we may call this distance a wave-train length1 and it is obviously equal to the product of the constituent wave-lengths divided by the difference of the two constituent wave-lengths4 ,it follows from this that if we suppose the two wave-trains to move forward with equal speed1 the number of maximum points or zero points which will pass any place in the unit of time will be equal to the difference between the frequencies of the constituents4 ,let us now reduce this to an experiment4 ,here are two organ-pipes exactly tuned to unison1 and when both are sounded together we have two identical wave-trains sent out into the air4 ,we can1 however1 slightly lengthen one of the pipes1 and so put them out of tune4 ,when this is done you can no longer hear the smooth sound1 but a sort of waxing and waning in the sound1 and this alternate increase and diminution in loudness is called a beat4 ,we can easily take count of the number of beats per second1 and by the reasoning given above we see that the number of beats per second must be equal to the difference between the frequencies of the two sets of waves4 ,thus if one organ-pipe is giving #ajj vibrations per second to the air1 and the other #ajb1 we hear two beats per second4 ,now1 up to a certain point we can count these beats1 but when they come quicker than about #aj per second1 we cease to be able to hear them separately4 ,when they come at the rate of about #cj per second they communicate to the combined sound a peculiar rasping and unpleasant effect which we call a discord4 ,if they come much more quickly than #gj per second we cease to be conscious of their presence by any discordant effect in the sound4 ,the theory was first put forward by the famous physicist1 ,von ,helmholtz1 that the reason certain musical intervals are not agreeable to the trained ear is because the difference between the frequencies of the constituent fundamental tones or the harmonics present in them give rise to beats1 approximately of #cj to #dj per second4 ,in order to simplify our explanations we will deal with two cases only1 viz4 that of the octave interval and that of the seventh4 ,the first is a perfect concord1 and the second1 at least on stringed instruments1 is a discord4 ,it has already been explained that when a string vibrates it does so not only as a whole1 but also in sections1 giving out a fundamental note with superposed harmonics4 ,suppose we consider the octave of notes lying between the frequencies #bfd and #ebh1 which correspond to the notes ,c and ,c#a forming the middle octave on a piano4 ,the frequencies and differences of the eight tones in this octave are as follows3-- ,,frequencies ,,of ,,the ,,notes ,,of ,,the ,,middle ,,octave ,,of ,a ,,piano4 ,notes4 ,frequency4 ,difference4 ,c #bfd #cc ,d #big #cc ,e #ccj #bb ,f #ceb #dd ,g #cif #dd ,a #ddj #ee ,b #die #cc ,c#a #ebh ,it will thus be seen that the differences between the frequencies of adjacent notes are such as to make beats between them which have a number per second so near to the limits of #cj to #dj that adjacent notes sounded together are discords4 ,suppose1 however1 we sound the seventh1 viz4 ,c and ,b1 together4 ,the frequencies are #bfd and #die1 and the difference is #bca4 ,since1 then1 the difference between the frequencies lies far beyond the limit of #cj to #dj per second1 how comes it that in this case we have a discord8 ,to answer this question we must consider the harmonics present with the fundamentals4 ,write down each frequency multiplied respectively by the numbers #a1 #b1 #c1 #d1 etc4-- ,c4 ,b4 ,fundamental #bfd #die ,first harmonic #ebh #iij ,second 0 #gib #adge ,third 0 #ajef #aihj ,fourth 0 #acbj #bdge ,fifth 0 #aehd #bigj ,on looking at these numbers we see that although the difference between the frequencies of the two fundamentals is too great to produce the disagreeable number of beats1 yet the difference between the frequencies of the fundamental of note ,b 7#die7 and the first harmonic of note ,c 7#ebh7 is exactly #cc1 which is1 therefore1 the required number4 ,accordingly1 the discordant character of the seventh interval played on a piano is not due to the beats between the primary tones1 but to beats arising between the first harmonic of one and the fundamental of the other4 ,it will be a useful exercise to the reader to select any other interval1 and write down the primary frequencies and the overtone frequencies1 or harmonics1 and then determine whether between any pairs disagreeable beats can occur4 ,the presence of harmonics or overtones is1 therefore1 a source of discord in some cases1 but nevertheless these overtones communicate a certain character to the sound4 ,helmholtz's chief conclusions as regards the cause of concord and discord in musical tones were as follows3-- 7#a7 ,musical sounds which are pure1 that is1 have no harmonics mixed up with them1 are soft and agreeable1 but without brilliancy4 ,of this kind are the tones emitted by tuning-forks gently struck or open organ-pipes not blown violently4 7#b7 ,the presence of harmonics up to the sixth communicates force and brilliancy and character to the tone4 ,of this kind are the notes of the piano and organ-pipes more strongly blown4 7#c7 ,if only the uneven harmonics1 viz4 the first1 third1 fifth1 etc41 are present1 the sound acquires a certain nasal character4 7#d7 ,if the higher harmonics are strong1 then the sound acquires great penetrating force1 as in the case of brass instruments1 trumpet1 trombone1 clarionet1 etc4 7#e7 ,the causes of discord are beats having a frequency of #cj to #dj or so1 taking place between the two primary tones or the harmonics of either note4 ,the pleasure derived from the sound of a musical instrument is dependent1 to a large extent1 on the existence of the desirable harmonics in each tone1 or on the exclusion of undesirable ones4 ,in the next place1 let us consider a little the means at our disposal for creating and enforcing the class of air-waves which give rise to the sensations of musical tones4 ,broadly speaking1 there are three chief forms of musical air-wave-making appliance1 viz4 those which depend on the vibrations of columns of air1 on strings1 and on plates respectively4 ,one of the oldest and simplest forms of musical instrument is that represented by the pan-pipes1 still used as an orchestral accompaniment in the case of the ever-popular peripatetic theatrical display called ,punch and ,judy4 ,if we take a metal or wooden pipe closed at the bottom1 and blow gently across the open end1 we obtain a musical note4 ,the air in the pipe is set in vibration1 and the tone we obtain depends on the length of the column of air1 which is the same as the length of the pipe4 ,the manner in which this air-vibration is started is as follows3 ,on blowing across the open end of the pipe closed at the bottom a partial vacuum is made in it4 ,that this is so1 can be seen in any scent spray-producer1 in which two glass tubes are fixed at right angles to each other4 ,one tube dips into the scent1 and through the other a puff of air is sent across the open mouth of the first4 ,the liquid is sucked up the vertical tube by reason of the partial vacuum made above it4 ,if we employ a pipe closed at the bottom and blow across the open end1 the first effect of the exhaustion is that the jet of air is partly sucked down into the closed tube1 and thus compresses the air in it4 ,this air then rebounds1 and again a partial vacuum is made in the tube4 ,so the result is an alternate compression and expansion of the air in the closed tube4 ,the column of air is alternately stretched and squeezed1 and a state of stationary vibration is set up in the air in the tube2 just as in the case of a rope fixed at one end and jerked up and down at the other end4 ,the natural time-period of vibration of the column of air in the tube controls the behaviour of the jet of air blown across its mouth1 the energy of the jet of air being drawn upon to keep the column of air in the tube in a state of oscillation4 ,thus a flutter is excited in the air in the tube1 which is maintained as long as there is a blast of air across its mouth1 and this communicates to the air outside a wave-motion4 ,we have1 therefore1 a musical note produced1 the wave-length of which is four times the length of the closed tube across the mouth of which we are blowing4 ,accordingly1 a very simple musical instrument such as the pan-pipes consists of a row of tubes closed at the bottom1 the tubes being of different lengths4 ,a current of air from the mouth is blown across the tubes taken in a certain order1 and we can obtain a simple melody by that process of selection4 ,illustration3 ,,fig4 #eg4--;,a closed organ-pipe4 ,an organ-pipe is only a more perfect means for doing the same thing4 ,organ-pipes may be either open or closed pipes4 ,also they have either a reed or a flute at one end for the purpose of establishing air-vibrations when a current of air is blown into the pipe4 ,the form of organ-pipe most easy to understand is the closed flute pipe4 ,this consists of a wooden tube closed at the upper end1 and at the lower end having a foot-tube and mouthpiece as shown in section in ,fig4 #eg4 ,when a gentle current of air is blown in at the foot-tube1 it impinges on the sharp edge or chamfer of the mouthpiece1 and it acts just as when blown across the open end of a simple closed pipe4 ,that is to say1 it sets up a state of alternate compression and expansion of the air in the pipe4 ,at the closed end1 period-changes in density in the air are established1 but no great movement takes place4 ,at the open end or mouth there are no great changes of density1 but the air is alternately moving in and out at the mouthpiece4 ,the steady blast of air against the chamfer1 therefore1 sets up a state of steady oscillation of the air in the pipe1 the air being squeezed up and extended alternately so that there is first a state of compression1 and then a state of partial rarefaction in the air at the closed end of the pipe4 ,in this case1 also1 the wave-motion communicated to the surrounding air has a wave-length equal to four times the length of the pipe4 ,if we open the upper end of the pipe1 it at once emits a note which has a wave-length equal to double the length of the pipe4 ,hence the note emitted by an open-ended organ-pipe is an octave higher than that given out by a closed organ-pipe of the same length4 ,the action of an open organ-pipe is not quite so easy to comprehend as that of a closed pipe4 ,the difficulty is to see how stationary air waves can be set up in a pipe which is open at both ends4 ,the easiest way to comprehend the matter is as follows3 ,when the blast of air against the lip of the pipe begins to partially exhaust the air in it1 the rarefaction so begun does not commence everywhere in the pipe at once4 ,it starts from the mouthpiece end1 and is propagated along the pipe at a rate equal to the velocity of sound4 ,the air at the open ends of the pipe moves in to supply this reduced pressure1 and1 in so doing1 overshoots the mark1 and the result is a region of compression is formed in the central portions of the pipe 7see ,fig4 #eh74 ,the next instant this compressed air expands again1 and moves out at the two open ends of the pipe4 ,we have thus established in the pipe an oscillatory state which1 at the central region of the pipe1 consists in an alternate compression and expansion or rarefaction of the air1 whilst at the open end and mouthpiece end there is an alternate rushing in and rushing out of the air4 ,hence in the centre of the pipe we have little or no movement of the air1 but rapid alternations of pressure1 or1 which is the same thing1 density2 and at the two ends little or no change in density1 but rapid movement of the air in and out of the pipe4 ,illustration3 ,,fig4 #eh4--;,an open organ-pipe4 ,an analogy between the vibration of the air in a closed and open organ-pipe might be found in considering the vibration of an elastic rod--first1 when clamped at one end1 and secondly1 when clamped at the two ends4 ,the deflection of the rod at any point may be considered to represent change of air-pressure1 and the fixed point or points the open end of the pipe at which there can be no change of density1 because there it is in close communication with the open air outside the pipe4 ,it is at once evident that the length of the open organ-pipe1 when sounding its fundamental tone1 is one-half of the length of the air wave it produces4 ,accordingly1 from the formula1 wave-velocity frequency wave-length1 we see that1 since the velocity of sound at ordinary temperature is about #aabj feet per second1 an approximate rule for obtaining the frequency of the vibrations given out by an open organ-pipe is as follows3-- ,frequency #aabj divided by twice the length of pipe4 ,we say approximate1 because1 as a matter of fact1 for a reason rather too complicated to explain here1 the wave-length of the air-vibrations is equal to rather more than double the length of the pipe4 ,in fact1 what we may call the effective length of the pipe is equal to its real end-to-end length increased by a fraction of its diameter1 which is very nearly four-fifths4 ,illustration3 ,,fig4 #ei4 ,we can confirm by experiments the statements made as to the condition of the air in a sounding organ-pipe4 ,here is a pipe with three little holes bored in it at the top1 middle1 and bottom 7see ,fig4 #ei74 ,each of these is covered with a thin indiarubber membrane1 and this1 again1 by a little box which has a gas-pipe leading to it and a gas-jet connected with it4 ,if we lead gas into the box and light the jet1 we have a little flame1 as you see4 ,if1 then1 the indiarubber membrane is pressed in and out1 it will cause the gas-flame to flicker4 ,such an arrangement is called a manometric flame1 because it serves to detect or measure changes of pressure in the pipe4 ,the flicker of the flame when the organ-pipe is sounded is1 however1 so rapid that we cannot follow it unless we look at the image in a cubical revolving mirror of the kind already used4 ,when so regarded1 if the flame is steady1 we see a broad band of light4 ,if we sound the organ-pipe gently and look at the bands of light corresponding to the three flames1 we see that the flames at the top and bottom of the pipe are nearly steady1 but that the one at the middle of the pipe is flickering rapidly1 the band of light being changed to a saw-tooth-like form 7see ,fig4 #fj74 ,this shows us that rapid changes of pressure are taking place at the centre of the pipe4 ,again1 if we prepare a little tambourine 7by stretching parchment-paper over a wooden ring71 and lower it by a string into the sounding organ-pipe1 we shall find that grains of sand scattered over this tambourine jump about rapidly when the membrane is held near the top or the bottom of the pipe1 but are quiescent when it is at the middle4 ,illustration3 ,,fig4 #fj4 ,this shows us that there is violent movement of the air at the ends1 but not in the centre1 thus confirming the deductions of theory4 ,it should be noted that if the pipe is over-blown or sounded too strongly1 harmonics will make their appearance1 and the simple state of affairs will no longer exist4 ,the celebrated mathematician1 ,daniel ,bernoulli1 discovered that an organ-pipe can be made to yield a succession of musical notes by properly varying the pressure of the current of air blown into it4 ,if the pipe is an open one1 then1 if we call the frequency of the primary note #a1 obtained when the pipe is gently blown1 if we blow more strongly1 the pipe yields notes which are the harmonics of the fundamental one1 that is to say1 have frequencies represented by #b1 #c1 #d1 #e1 etc41 as the blast of air increases in force4 ,thus1 if the pipe is one about #b feet in length1 it will yield a note near to the middle ,c on a piano4 ,if more strongly blown1 it gives a note1 ,c#a1 an octave higher1 having double the frequency4 ,if more strongly blown still1 it yields a note which is the fifth1 ,g#a1 above the last1 and has three times the frequency of the primary tone2 and so on4 ,if the pipe is closed at the top1 then over-blowing the pipe makes it yield the odd harmonics1 or the tones which are related in frequency to the primary tone in the ratio of #a1 #c1 #e1 etc4 ,hence1 if a stopped pipe gives a note1 ,c1 its first overtone is the fifth above the octave1 or ,g#a4 ,it is usual1 in adjusting the air-pressure of an organ-bellows1 to allow such a pressure as that some of the overtones1 or harmonics1 shall exist4 ,the presence of these harmonics in a note gives brilliancy to it1 whereas an absolutely pure or simple musical tone1 though not disagreeable to the ear1 is not fully satisfying4 ,any one with a good ear can detect these harmonics or overtones in a single note sounded on a piano or organ due to the subdivision of the vibrating string or air-column into sections separated by nodes4 ,it will be seen that the acoustic action of the organ-pipe depends essentially upon some operation tending at the commencement to make an expansion of the air in the pipe at one end1 and subsequently to cause an increase of air-pressure in it4 ,this can be effected not only by blowing into the pipe1 but in another way1 by introducing a hot body into a pipe open at both ends4 ,we can show here as an illustration of this an interesting experiment due to ,lord ,rayleigh4 ,a long cast-iron water-pipe about #d inches in diameter and #h feet long is suspended from the ceiling4 ,about #a foot up the tube from the lower end a piece of iron-wire gauze is fixed 7see ,fig4 #fa74 ,by means of a gas-burner introduced into the tube1 we heat the gauze red hot1 and on withdrawing the lamp the tube suddenly emits a deep organ-like note for a few moments4 ,the heated metal creates an up-draught in the tube at the lower end1 and1 as in the case of the open organ-pipe1 causes also an in-suction of air at the upper end4 ,the column of air is thus set vibrating with a point of alternate condensation and rarefaction in the centre1 and in-draughts and out-rushes of air at the ends4 ,indeed1 this rush of air into and out of the pipe at the lower end during the time it is sounding its note is so violent that if the hands are placed just below the bottom end of the tube they will feel chilled1 as if placed near an electric fan1 by the blast of air4 ,closing the bottom end of the pipe with a sheet of metal at once stops the air-movement1 and with it the musical note4 ,illustration3 ,,fig4 #fa4 ,illustration3 ,,fig4 #fb4--,singing flame4 ,in another form the experiment has long been known under the name of a singing flame4 ,a small jet of burning hydrogen gas is introduced into a glass tube about #c feet in length4 ,the jet must consist of a long narrow brass tube1 and the proper position for the jet must be found by trial 7see ,fig4 #fb74 ,when this is done1 however1 the tube emits a clear musical note1 due to the tube acting as an open organ-pipe4 ,if the flame is examined in a revolving mirror when the tube is singing1 it will be found to be in vibration in sympathy with the movement of air in the tube4 ,the tube often refuses to start singing1 but may be made to do it by giving it a little tap4 ,the actions taking place in the tube are something as follows3 ,when the flame is introduced1 it heats and rarefies the air around it4 ,this causes an in-rush of air both at the top and bottom of the tube4 ,a state of steady oscillation is then established1 in which the air at the centre undergoes periodical expansions and compressions1 and the pressure of the air round the flame changes in the same manner4 ,the flame is therefore alternately expanded and contracted4 ,when it expands1 it heats the air more4 ,when it is compressed1 it heats it less4 ,this variation of the flame causes air to be sucked in or expelled from both open ends of the tube1 and establishes the state of steady vibration in accordance with the length of the tube4 ,the flame and the air-column act and react on each other1 and establish a state of stationary aerial oscillation in accordance with the natural time-period of the column of air4 ,the tube can be made to give out not only its fundamental note1 but a series of harmonics1 or overtones1 with frequencies #b1 #c1 #d1 #e1 etc41 times the fundamental note1 by varying the position of the flame1 which must always be just under the place where a node1 or place of alternate condensation and rarefaction1 occurs4 ,we may1 in the next place1 with advantage briefly examine the principles of construction of one musical instrument1 and allude to some recent improvements4 ,one of the most interesting of all the musical appliances devised by human ingenuity is the violin1 comprising as it does in its construction an art1 a science1 and a tradition4 ,in principle the violin is nothing but a wooden box1 along the top of which are stretched four strings1 which are strained over a piece of wood called a bridge4 ,these strings have their effective length altered in playing by placing the finger of the performer at some place on them1 and they are set in vibration by drawing over them a well-rosined bow made of horsehair4 ,the vibrating string communicates its vibrations to the surface of the box or body by means of the bridge1 and this again to the air in the interior4 ,the body thus serves two purposes4 ,it acts as a resonating-chamber1 and also it affords a large surface of contact with the surrounding air1 whereby a greater mass of air is set simultaneously in wave-motion4 ,the four strings are normally tuned in fifths1 so that the fundamental note of each is an interval of a fifth above the next4 ,the performer varies the note given by each string by shortening its vibrating length by pressing the finger upon it4 ,the skilled violinist has also great control over the tone1 and can determine the harmonics1 or overtones1 which shall accompany the fundamental by altering the point on the string at which the bow is applied1 and lightly touching it at some other point4 ,the great art in the construction of the violin rests in the manufacture of the wooden body4 ,its form1 materials1 and minute details of construction have been the subject of countless experiments in past ages1 and until quite recently no essential improvement was made in the instrument as completed by the masters of violin construction three centuries ago4 ,in classical form the violin consists of a wooden box of characteristic shape1 composed of a back1 belly1 and six ribs4 ,these are shaped out of thin wood1 the belly being made of pine1 and maple used for the rest4 ,a neck or handle is affixed to one end1 and a tail-piece1 to which the gut-strings are fastened1 to the other4 ,the strings are strained over a thin piece of wood which rests on two feet on the belly4 ,one of these feet rests over a block of wood in the interior of the box called the sound-post1 and this forms a rigid centre2 the other foot stands on the resonant part of the belly4 ,the belly is strengthened in addition by a bar of wood1 which is glued to it just under the place where the active foot of the bridge rests4 ,the ribs or sides of the box are bent inwards at the centre to enable the playing-bow to get at the strings more easily4 ,the selection of the wood and its varnishing is the most important part of the construction4 ,the wood must be elastic1 and its elasticity has to be preserved by the use of an appropriate hard varnish1 or else it will not take up the vibrations imparted by the strings4 ,the old makers used wood which was only just sufficiently seasoned1 and applied their varnish at once4 ,an essential adjunct is a good bow1 which is of more importance than generally supposed4 ,something may be got out of a poor violin by a good player1 but no one can play with a bad bow4 ,the process of eliciting a musical tone from the violin is as follows3 ,the player1 holding the instrument in the left hand1 and with its tail end pressed against the left shoulder1 places a finger of the left hand lightly on some point on a string1 and sweeps the bow gently across the string so as to set it in vibration1 yielding its fundamental note1 accompanied by the lower harmonics4 ,the purity and strength of the note depend essentially upon the skill with which this touch of the bow is made1 creating and sustaining the same kind of vibration on the string throughout its sweep4 ,the string then presses intermittently on the bridge1 and this again turns1 so to speak1 round one foot as round a pivot1 and presses intermittently on the elastic wooden belly4 ,the belly takes up these vibrations1 and the air in the interior is thrown into sympathetic vibration by resonance4 ,the sound escapes by the -holes in the belly4 ,the extraordinary thing about the violin is that the shape of the box permits it to take up vibrations lying between all the range of musical tones4 ,the air-cavity does not merely resonate to one note1 but to hundreds of different rates of vibration4 ,the peculiar charm of the violin is the quality of the sound which a skilled player can elicit from it4 ,that wonderful pleading1 sympathetic1 voice-like tone1 which conveys so much emotional meaning to the trained musical ear1 is due to the proper admixture of the harmonics1 or overtones1 with the fundamental notes4 ,the string vibrates not merely as a whole1 but in sections4 ,hence the place at which the bow touches must always be an anti-node1 or ventral point1 and the smallest change in this position greatly affects the quality of the tone4 ,quite recently an entirely new departure has been made in violin construction by ,mr4 ,augustus ,stroh1 a well-known inventor4 ,he has abolished the wooden body and bridge1 and substituted for them an aluminium trumpet-shaped tube as the resonant chamber1 ending in a circular corrugated aluminium disc1 on the centre of which rests an aluminium lever pivoted at one point4 ,the strings are strained over this lever1 and held on a light tube1 which does duty as a point of attachment of all parts of the instrument4 ,the strings are the same1 and the manipulation of the instrument identical with that of the ordinary violin4 ,the vibrations of the strings are communicated by the pivoted lever over which they pass to the corrugated aluminium disc1 and by this to the air lying in the trumpet-tube4 ,this tube points straight away from the player1 and directs the air waves to the audience in front4 ,the tone of the new violin is declared by connoisseurs to be remarkably full1 mellow1 and resonant4 ,the notes have a richness and power which satisfies the ear1 and is generally only to be found in the handiwork of the classical constructors of the ordinary form of violin4 ,one great advantage in the ,stroh violin is that every one can be made perfectly of the same excellence4 ,the aluminium discs are stamped out by a steel die1 and are therefore all identical4 ,the element of chance or personal skill in making has been eliminated by a scientific and mechanical construction4 ,thus the musician becomes possessed of an instrument in which scientific construction predominates over individual art or tradition in manufacture1 yet at the same time the musical effects which skill in playing can produce are not at all diminished4 ,whilst our attention has so far been fixed on the external operations in the air which constitute a train of music-making waves1 it seems only appropriate to make1 in conclusion1 a brief reference to the apparatus which we possess in our ears for appreciating these subtle changes in air-pressure with certainty and pleasure4 ,the ear itself is a marvellous appliance for detecting the existence of waves and ripples in the air1 and it embodies in itself many of the principles which have been explained to-day4 ,illustration3 ,,fig4 #fc4--;,diagram of the human ear4 ,the organ of hearing is a sort of house with three chambers in it1 or1 rather1 two rooms and an entrance hall1 with the front door always open4 ,this entrance passage of the ear is a short tube which communicates at one end with the open air1 being there provided with a sound-deflecting screen in the shape of an external ornamental shell1 commonly called the ear4 ,in many animals this external appendage is capable of being turned into different positions1 to assist in determining the direction in which the sound wave is coming4 ,the entrance tube of the ear is closed at the bottom by a delicate membrane called the tympanum1 or drum4 ,against this drum-head the air waves impinge1 and it is pressed in and out by the changes of air-pressure4 ,this drum separates the outer end from a chamber called the middle ear1 and the middle ear communicates1 by a sort of back staircase1 or tube called the ,eustachian tube1 with the cavity at the back of the mouth 7see ,fig4 #fc74 ,behind the middle ear1 and buried in the bony structure of the skull1 is a third1 more secret chamber1 called the inner ear4 ,this is separated from the middle ear by two little windows1 which are also covered with delicate membranes4 ,in the middle ear there is a chain of three small bones linked with one another1 which are connected at one end with the tympanum1 or drum1 and at the other end with the so-called oval window of the inner ear4 ,helmholtz has shown that this little chain of bones forms a system of levers1 by means of which the movements of the tympanum are diminished in extent1 but increased in force in the ratio of #b to #c4 ,the internal ear is the real seat of audition1 and it comprises the parts called the labyrinth1 the semicircular canals1 and the cochlea4 ,these are cavities lined with delicate membranes and filled with fluid4 ,in the cochlea there is an organ called ,corti's organ1 which is a veritable harp of ten thousand strings4 ,this consists of innumerable nerve-fibres1 which are an extension of the auditory nerve4 ,the details of the organic structure are far too complicated for description here4 ,suffice it to say that air waves1 beating against the tympanum1 propagate vibrations along the chain of bones into the fluids in the inner ear1 and finally expend themselves on these nerve-fibres1 which are the real organs of sound-sensation4 ,helmholtz put forward the ingenious hypothesis that each fibre in the organ of ,corti was tuned1 so to speak1 to a different note1 and that a composite sound falling upon the ear was analyzed or disentangled by this organ into its constituents4 ,although this theory1 as ,helmholtz originally stated it1 has not altogether been upheld by subsequent observation1 it is certain that the ear possesses this wonderful power of analysis4 ,it can be shown by mathematical reasoning of an advanced kind that any musical sound1 no matter what its quality1 can be resolved into the sum of a number of selected pure sounds such as those given by a tuning-fork4 ,consider now for one moment the physical state of the air in a concert-room in which a large orchestra is performing4 ,the air is traversed by a chaos of waves of various wave-lengths4 ,the deep notes of the violincello1 organ1 and trumpets are producing waves #aj to #bj feet in wave-length1 which may be best described as billows in the air4 ,the violin-strings and middle notes of the piano1 harp1 or flute are yielding air waves from #f or #h feet to a few inches long1 whilst the higher notes of violins and flutes are air ripples some #c or #d inches in length4 ,if we could see the particles of the air in the concert-room1 and fasten our attention upon any one of them1 we should see it executing a most complicated motion under the combined action of these air-wave-producing instruments4 ,we should be fascinated by the amazing dance of molecules to and fro and from side to side1 as the medley of waves of compression or rarefaction embraced them and drove them hither and thither in their resistless grasp4 ,the tympana of our ears are therefore undergoing motions of a like complicated kind1 and this complex movement is transmitted through the chain of bones in the middle ear to the inner ear1 or true organ of sensation4 ,but there1 by some wondrous mechanism not at all yet fully understood1 an analysis takes place of these entangled motions4 ,the well-trained ear separates between the effect due to each kind of musical instrument1 and even detects a want of tuning in any one of them4 ,it resolves each sound into its harmonics1 appreciates their relative intensity1 is satisfied or dissatisfied with the admixture4 ,in the inner chamber of the ear physical movements are in some wholly inscrutable manner translated into sensations of sound1 and the confused aggregation of waves and ripples in the air1 beating against the tympanic membrane there1 takes effect in producing impulses which travel up the auditory nerve and expend their energy finally in the creation of sensations of melody and tune1 which arouse emotions1 revive memories1 and stir sometimes the deepest feelings of our minds4 ,,chapter ,v4 ,,electric ,,oscillations ,,and ,,electric ,,waves4 ,in the previous chapters your attention has been directed to the subject of waves on water and waves in air1 and we shall now proceed to discuss some of the more difficult matters connected with the production of waves in the ther4 ,we shall find that this portion of our subject makes more demands upon our powers of comprehension1 since much that we have to consider is not directly the object of sense perception1 and the inferences which we have to make from observed facts are less simple and easy to follow4 ,nevertheless1 ,i trust that if you have been able to grasp clearly the nature of a surface-wave on water and of a compressional wave in air1 you will not readily allow yourselves to be discouraged from encountering a new class of ideas1 but will be able to advance still further1 and gain a more or less clear conception of the nature of an electric wave in the ther4 ,in the first place1 we must consider the medium in which these waves are created4 ,we can see with our eyes a water-surface1 and we are able to understand without much difficulty that the surface can be thrown into humps and hollows1 or become wrinkled1 and also that these elevations and depressions can change their position1 thus creating a surface wave which moves forward4 ,the movement of the water wave is1 therefore1 only the result of a local elevation of the surface which travels along or takes place progressively at different places on the surface4 ,then1 again1 in the case of an air wave1 although we cannot see the air1 we are able1 with some little assistance from experiments1 to present to ourselves a clear mental picture of a progressive movement through the air of a region of compression1 that is to say1 a certain slice1 layer1 or zone of the air is more compressed than the neighbouring portions1 and this region of compression changes its place progressively4 ,it has been carefully explained that the production of a wave of any kind implies1 therefore1 two things--first1 a medium or material in which the wave exists2 and1 secondly1 some kind of periodic change or movement which is experienced by the various portions of this medium at different places successively4 ,if1 therefore1 we are given any medium1 say water or air1 and asked to explain the production of a wave in it1 we have first to consider what kind of changes can take place in it1 or on it1 which can appear progressively at different parts4 ,in the case of the water-surface1 some parts may be heaped up higher than the rest1 and the heaping up may occur at successive places in such fashion that when it disappears at one place it reappears at a contiguous or neighbouring place4 ,in the case of air1 some portion may be compressed more than the rest1 and the place of compression may move forward1 so that as the compression is released in one place it makes its appearance in an adjacent one4 ,in the first case1 we have a wave of elevation on water2 in the second case1 a wave of compression in the air4 ,in the next place1 let me carry you with me one step more4 ,here is a glass bulb from which the greater part of the air has been removed4 ,we say1 therefore1 that there is a vacuum in the bulb4 ,it is impossible for us to remove absolutely every trace of air from the bulb1 and so produce what would be called a perfect vacuum2 but we can imagine it to be accomplished1 and we can picture to ourselves the glass bulb absolutely deprived of every trace of air or other material substance4 ,the question then arises--,is the bulb really empty1 or is there still something in its interior8 ,the same inquiry may be put in another way4 ,the air we breathe forms an atmosphere which surrounds our earth as a garment1 but it decreases rapidly in density as we ascend4 ,at a height of about #ej miles above the earth there is reason to believe the air is exceedingly rarefied and1 except for the presence of meteoric dust1 the space between the sun and the earth1 and between the stars and the earth1 is in all probability a highly perfect vacuum1 in the sense that it is empty of generally diffused matter4 ,the question then arises--,is interstellar space absolutely and completely empty8 ,we know perfectly well that rays of light come to us from the sun and stars through this empty space1 and a fact of capital importance is1 that these rays of light1 swift-footed though they are1 take time to travel4 ,it was long ago suspected that this was the case1 and the celebrated ,galileo made the first experimental attempt to determine the velocity of light4 ,no real knowledge on the subject was gained1 however1 until after he had made his discovery that the planet ,jupiter is accompanied by four moons 7a fifth moon has been discovered since71 and that these rotate round the planet in definite periods of time1 constituting1 therefore1 the 8hands0 of a perfect celestial clock4 ,the sunlight1 falling on the great globe which forms the body of the planet ,jupiter1 casts behind it a conical shadow2 and the little moons1 in their rotation1 are plunged into this shadow cone at intervals1 and then for a time become invisible1 or eclipsed4 ,as soon1 however1 as these eclipses of ,jupiter's moons began to be regularly observed1 it was found that the intervals of time between two eclipses of any one moon were not equal1 but exhibited a progressive variation in magnitude1 and were longer by about #af minutes and #bf seconds at one time of the year than at the other4 ,the astronomer ,roemer1 in the year #afge1 correctly concluded that this difference must be due to the fact that rays of light take time to traverse the earth's orbit1 and not to any want of regularity in the operation of this celestial timepiece4 ,hence1 although the eclipses do happen at equal intervals of time1 our information about them is delayed by the time taken for the ray of light to travel over the variable distance between ,jupiter and our earth4 ,these observations1 critically considered1 led1 therefore1 to the conclusion that the speed of light rays is about #ahf1ejj miles a second4 ,by means which it would take too long to describe here1 experimental measurements of the velocity of light have been made many times since by various investigators by methods which do not involve astronomical observations1 and the result has been to confirm the above value1 and to give us a very exact knowledge of the speed with which rays of light travel through space4 ,it is as shown in the table below3-- ,,the ,,velocity ,,of ,,light4 ,miles per second4 ,from observations on ,jupiter's satellites 7,roemer7 #ahf1ejj 0 experimental measurements by ,foucault 7#ahfb7 #ahe1agg 0 0 0 0 ,cornu 7#ahgd7 #ahe1dhg 0 0 0 0 0 7#ahgh7 #ahf1dac 0 0 0 0 ,michelson 7#ahgi7 #ahf1cfd 0 0 0 0 0 7#ahhb7 #ahf1cbh 0 0 0 0 ,newcomb 7#ahhb7 #ahf1ccc ,when anything takes time to travel from one place to another1 it can only be one of two things4 ,it must either be an actual object which is transferred bodily from place to place1 like a letter sent by post or a bullet fired from a gun1 or else it must be a wave-motion created in a medium of some kind which fills all space4 ,the illustrious ,newton suggested an hypothesis or supposition as to the nature of light1 viz4 that it consists of small corpuscles shot out violently from every luminous body4 ,it is a wonderful testimony to ,newton's exalted powers of thought1 that the most recent investigations show that hot and luminous bodies1 such as the sun and a lamp1 are in fact projecting small bodies called corpuscles into space1 but there is abundant proof that these are not the cause of light4 ,subsequently to the date of ,newton's speculations on the nature of light1 the alternative hypothesis was developed1 viz4 that it consists in a wave-motion in a universally diffused medium called the ther4 ,a great gulf1 however1 separates mere conjecture and speculation from that accumulation of rigid proof which scientific investigation demands1 and hence1 although this conception of an ther had arisen as an hypothesis in the minds of ,huyghens1 ,descartes1 and many other philosophers1 it was not accepted by ,newton1 and the general assent of scientific investigators to the hypothesis of a universal ther was long deferred4 ,the philosopher to whom we owe the crucial demonstration of the validity of1 and indeed necessity for1 this assumption was ,dr4 ,thomas ,young1 the first ,professor of ,natural ,philosophy in the ,royal ,institution of ,london4 ,young was a man whose exalted intellectual powers were not properly appreciated by the world until after his decease4 ,his researches in physical optics alone are1 however1 epoch-making in character4 ,he it was who first gave a proof that under some circumstances it is possible for two rays of light to destroy each other1 and thus produce darkness4 ,briefly described1 the experiment is as follows3 ,if a beam of light of one colour1 say red1 proceeding from a single source of light1 falls upon a screen in which are two small holes very near together1 we shall obtain from these holes two streams of light originating1 as it were1 from closely contiguous sources4 ,if we then hold a white screen not far from these holes1 and receive on it the light proceeding from them1 we shall find that the screen is marked with alternate bands of red light and black bands4 ,if we cover up one of the small holes1 the black bands vanish and the screen is uniformly illuminated4 ,young pointed out that this effect was due to interference1 and that the difference of the distances from any black band to the two holes was an exact odd multiple of a certain small distance called the wave-length of the light4 ,if light is a substance1 no possible explanation can be given which will enable us to account for the combination of two rays of light producing darkness at their meeting-point4 ,if1 on the other hand1 rays of light consist of waves of some kind in a medium1 then1 as we have seen in the case of water ripples and air waves1 it is quite possible for two wave-trains to annihilate each other's effect at a certain point1 if a hollow of one wave-train reaches that place coincidently with a hump belonging to the other4 ,accordingly1 the experiment of producing interference between two sets of light rays so that they destroy each other is a strong argument in favour of the view that light must consist in some kind of wave-motion existing in a medium susceptible of supporting it1 filling all space1 and existing in all transparent bodies4 ,this medium we call the luminiferous ther4 ,the term 8ther10 or 8ether10 has been in use for many centuries to express the idea of something more rare1 tenuous1 or refined than ordinary matter4 ,the classical writers employed it to describe the space above the higher regions of the atmosphere1 which was1 as they2 supposed1 occupied by a medium less palpable or material than even air itself4 ,thus ,milton1 speaking of the downfall of the enemy of mankind 78,paradise ,lost10 ,book ,i4 line #dd71 says-- 8444 ,him the ,almighty ,power ,hurled headlong1 flaming1 from the thereal sky ,with hideous ruin and combustion down40 ,but although poets and philosophers had made free use of the notion of an ther1 or even assumed the existence of several thers1 the conception did not become a serious scientific hypothesis until it was experimentally shown by ,young that the phenomena of optics imperatively demand the assumption of such a medium in space which is not ordinary matter1 but possesses qualities of a special kind1 enabling it to have created in it waves which are propagated with the enormous velocity of nearly one thousand million feet a second4 ,the proofs which have accumulated as to the validity of this hypothesis to explain optical effects show that this medium or ther must exist1 not only in free space1 but also in the interior of every solid1 liquid1 or gaseous body1 although its properties in the interior of transparent bodies are certainly very different from those which it possesses taken by itself4 ,this ther fills every so-called vacuum1 and we cannot pump it out from any vessel as we can the air4 ,it occupies1 likewise1 all celestial space1 and suns and stars float1 so to speak1 in an illimitable ocean of ther4 ,we cannot remove it from any enclosed place1 because it passes quite easily through all material solid bodies1 and it is for the same reason intangible1 and it is not possessed of weight4 ,hence we cannot touch it1 see it1 smell it1 taste it1 or in any way directly appreciate it by our senses1 except in so far as that waves in it of a certain kind affect our eyes as light4 ,the fact that there is such a space-filling ther is1 therefore1 only to be deduced by reasoning from experiments and observations1 but it is not directly the object of our sense-perceptions in the same way that water or air can be4 ,nevertheless1 there is abundant proof that it is not merely a convenient scientific fiction1 but is as much an actuality as ordinary gross1 tangible1 and ponderable substances4 ,it is1 so to speak1 matter of a higher order1 and occupies a rank in the hierarchy of created things which places it above the materials we can see and touch4 ,the question we have next to discuss is--,what are the fundamental properties of this ther8 and what are the terms in which we must describe its qualities8 ,in order to answer these questions1 we must direct attention to some electrical effects1 since it has been shown that most of the electrical phenomena1 like those of optics1 point to the necessity for the assumption of a similar universal medium1 different from ordinary matter4 ,abundant proof has been gathered in1 that the electro-magnetic medium and the luminiferous ther are one and the same4 ,we are met at the very outset of our electrical studies by the term electric current4 ,most of us know that the operation of electric telegraphs and telephones1 electric lamps and electric railways1 depend upon this employment of an agency called an electric current4 ,the question then arises--,what is an electric current8 and the answer to this question is not easy to give in a few words4 ,we can1 however1 begin by explaining what an electric current can do1 and how its presence can be recognized4 ,before me on the table is a spiral of copper wire1 and in this wire1 by special means1 ,i can create what we call an electric current4 ,i shall ask you to notice that when this is done two effects are immediately produced4 ,in the first place1 the wire becomes hot1 and1 secondly1 it becomes magnetic4 ,the fact that it is hot is evident1 because it is now nearly red hot1 and is visibly incandescent in the dark4 ,if we dip the wire in iron filings1 you will see that these cling to the wire and are taken up by it1 just as when an ordinary steel magnet is substituted for the wire4 ,the copper wire1 when traversed by the current1 also attracts a compass needle1 and we thus demonstrate in another way its magnetic quality4 ,whenever1 therefore1 we find these two states of heat and magnetism present together in and round a wire1 we may take it as an indication that it forms part of a circuit through which an electric current is flowing4 ,an electric current is a physical state or condition which can only exist in or all along a closed path which is called an electric circuit4 ,this electric circuit may consist of a metallic wire1 or1 as we generally call it1 a conductor1 or1 as we shall see1 it may also in part consist of what is usually called a non-conductor4 ,it is necessary1 in the next place1 to point out that an electric current has a directive quality4 ,it belongs to that category of things like forces and movements1 which have direction as well as magnitude4 ,it is not completely defined by the answer to the question--,how much8 ,we must also ask--,in what direction8 ,the direction of an electric current is settled by holding a small compass needle near to the conductor or wire in which the current exists4 ,the little magnet will set itself with its north pole in one direction or in the opposite1 across the wire4 ,that is to say1 the axis of the compass needle places itself at right angles to that of the wire4 ,the direction of the electric current is decided in accordance with the following conventional rule3 ,imagine yourself placed with your arms extended straight out like a cross1 and that the wire conveying the current is placed before your face in a vertical position4 ,imagine1 also1 that the position in which the compass needle naturally sets when held between you and the wire is such that its ,north pole is on your right-hand side4 ,then the current would be said to move upwards in the wire4 ,a current which is always in one and the same direction in a wire is called a continuous1 direct1 or one-way current4 ,a current which periodically changes its direction so that it is first in one direction and then in the other is called an alternating or two-way current4 ,i can now show you two experiments1 the employment of which will enable us always to decide whether a current in a wire is a one-way or a two-way current4 ,in the first experiment you see a copper wire stretched between the poles of a powerful horseshoe magnet4 ,when a one-way current is sent through the wire1 it is pulled either up or down1 like a fiddle or harp string being plucked by the finger4 ,if1 however1 we send a two-way current through the wire1 it moves alternately up and down1 and vibrates just like a harp-string when plucked and left to itself4 ,the next experiment gives us1 however1 a more convenient method of ascertaining the presence in a wire of an alternating or two-way electric current4 ,if two wire circuits are laid parallel to each other1 and we send through one of these an electric current1 then1 in accordance with ,faraday's most notable discovery1 we find that the beginning or the ending of the one-way current in the first wire gives rise at the moment to a transitory current in the second wire4 ,if1 however1 we pass through the first wire1 which we call the primary circuit1 a two-way current1 then1 since this is1 so to speak1 continually beginning and ending1 we have a similar alternating or two-way electric current produced in the secondary circuit4 ,this fact may be most neatly and forcibly illustrated by the employment of the following pieces of apparatus3 ,an insulated wire is wound many times round a great bundle of iron wire1 thus forming what is called an electro-magnet4 ,through this wire is passed a strong alternating electric current which reverses its direction #afj times a second4 ,over the top of the electro-magnet we hold another coil of insulated wire1 the ends of which are connected to a small electric glow lamp 7see ,fig4 #fd74 ,when held near to the pole of the electro-magnet1 we find the little lamp in the secondary coil lights up brilliantly1 because there is created in that circuit a secondary or induced alternating electric current by the action of the other current in the primary or electro-magnet circuit4 ,thus we see that one alternating electric current can1 so to speak1 give birth to another in a second circuit held parallel to the first4 ,in like manner this secondary current can give rise to a third or tertiary current1 and the third to a fourth1 and so on indefinitely4 ,illustration3 ,,fig4 #fd4 ,we can always make use of this test to ascertain and prove the existence of an alternating current in any electric circuit4 ,if we provide a coil of insulated wire1 having its ends connected to a small incandescent lamp1 and hold this lamp coil or secondary circuit near to and parallel with any other circuit in which we suspect the existence of an alternating electric current1 and if the lamp in the secondary circuit lights up1 then we can say with certainty that there is an alternating or two-way electric current in the first circuit4 ,having1 then1 indicated briefly the effects which are produced by an electric current when it exists in a conducting circuit1 and the way in which we can determine its presence and direction1 we must pass on to discuss some other facts connected with its production4 ,it is a maxim in philosophy that every effect must have a cause2 hence we must assign a name to the cause of the effect we call electric current4 ,this cause we call electromotive force4 ,electromotive force may be created in many ways1 and time will not permit us to refer to these in detail1 but it must be taken that electrical machines1 batteries1 and dynamos are all of them appliances for creating electromotive force1 or1 as it is sometimes called1 electric pressure1 just as various kinds of force-pumps are contrivances for creating pressure in fluids4 ,we find that electromotive force acts differently on various substances when they are subjected to its operation4 ,in some substances electromotive force produces a continuous electric current1 and in these cases the material is called a conductor4 ,in other cases electromotive force creates what is called electric strain1 or electric displacement1 and these substances are generally called non-conductors4 ,the difference between conductors and non-conductors can be illustrated by a mechanical analogy4 ,consider1 for instance1 a force-pump consisting of a cylinder with a tightly fitted piston2 suppose the bottom of the pump-tube to be closed by a pipe having in it a tap4 ,if we open the tap and apply pressure to the piston1 we can force out of the pipe a current of air which continues to flow as long as the piston is being pressed down4 ,in this case the pressure on the piston corresponds to an electromotive force1 and the current of air flowing out corresponds with the electric current in the electrical circuit4 ,supposing1 however1 that we shut the tap and then attempt to force down the piston1 we find at once an elastic resistance to motion4 ,the piston can be pressed down a little way1 compressing the air and thus creating a strain2 but if the pressure is removed the piston flies up again1 on account of the compressional elasticity of the air4 ,in this operation we have a mechanical illustration of the action of electromotive force on a material such as glass or air1 which is called a non-conductor1 or sometimes a dielectric4 ,in these bodies electromotive force produces an electric strain1 just as the mechanical force produces in the air enclosed in the cylinder a mechanical strain4 ,when the tap at the bottom of the cylinder is closed1 we can1 by applying pressure1 force down the piston a little way1 but that movement cannot be continued1 because we are building up an opposing pressure due to the elasticity of the air4 ,it is possible to show you an electrical experiment which has a close analogy with the above simple mechanical experiment4 ,here is a glass tube which has platinum wires sealed into the two ends1 and the tube is partly exhausted of its air4 ,such a tube is called a vacuum tube1 and when an electrical current is passed through this rarefied air1 it causes it to become luminous1 and1 as you see when the room is darkened1 the tube is filled with a reddish light4 ,a tube1 therefore1 of this kind is very convenient in some experiments1 because we can1 in effect1 see the electric current passing through it4 ,if ,i connect one end of this tube with the earth1 and the other with the terminal of an electrical machine1 and if then the handle of the electrical machine is turned1 the tube will continue to glow as long as the electrical machine is rotated4 ,the electrical machine must be regarded as a pump which is forcing something called electricity through the vacuum tube1 and as long as the pressure is continued the current flows4 ,this corresponds with the case in which the tap at the bottom of the force pump was open and a continuous current of air could be forced out of it by pressing down the piston4 ,supposing1 however1 that ,i insert between the vacuum tube and the electrical machine a plate of glass1 which is covered over with tinfoil on the two sides such an arrangement constitutes what is called a condenser1 or ,leyden pane4 ,we now repeat the experiment1 and begin to turn the handle of the electrical machine4 ,you will notice that the vacuum tube glows as before1 and is filled with a reddish light for a short time1 but as we continue to turn the handle this dies away1 and after a few moments there is no further evidence of an electric current passing through the vacuum tube4 ,you will understand1 therefore1 that an electric current cannot be caused to flow for an indefinite time in one direction through a glass plate1 although1 by the application of electromotive force1 it does evidently1 as you see1 pass through it for a short time4 ,this is analogous to the operation of the force-pump when the tap at the bottom is closed4 ,we then find that we can move the piston down a little way1 compressing or straining the enclosed air1 but that its motion is soon stopped by an opposing resistance4 ,we therefore say that in the glass plate we have created an electric strain by the action of the electromotive force1 just as we describe the effect of the mechanical pressure on the air by saying that we have created a compression in it4 ,but there is an additional resemblance between the electrically strained glass and the mechanically compressed air4 ,when any elastic object has been strained1 and is suddenly released1 it regains its position of equilibrium by a series of oscillations or vibrations4 ,thus1 for instance1 if we take a strip of steel and fix one end of it in a vice1 and pull the other end on one side and then release it1 the steel regains its position of equilibrium only after having executed a series of diminishing swings to and fro4 ,in the same way1 if we place some mercury or water in a glass tube bent in the shape of the letter 1 and displace the liquid by blowing into the tube1 then1 on releasing the pressure suddenly1 the liquid will regain its position of equilibrium by a series of oscillations which die gradually away4 ,you will not have any difficulty in seeing that this is really due to the inertia of the material1 whether it be steel or mercury or water which is displaced4 ,in an exactly similar manner1 we find that when we have produced an electric strain in a sheet of glass by the application of electromotive force1 and if we then remove the electromotive force and connect the two tinfoil or metal surfaces by means of a piece of wire1 the electric strain in the glass disappears with a series of electric oscillations2 that is to say1 the electric strain in the glass does not disappear or die away gradually1 but it is alternately reversed1 at each reversal the strain becoming less and less in magnitude4 ,the result of this oscillatory strain in the glass is to produce in the connecting wire an alternating electric current4 ,illustration3 ,,fig4 #fe4 ,a very familiar and simple piece of electric apparatus is that known as a ,leyden jar 7see ,fig4 #fe74 ,a ,leyden jar consists of a glass vessel1 the outside and inside surfaces of which are respectively covered with tinfoil4 ,if we apply to these two surfaces an electromotive force1 we produce what is called an electric charge in the jar1 which in reality consists in a state of electric strain in the walls of the vessel4 ,when the jar is charged1 if we connect together1 by means of a thick wire1 the outside and the inside tinfoil surfaces1 we have a bright spark produced at the moment of making contact1 and we have a rapidly alternating electric current produced in the connecting wire4 ,if this connecting wire has a low resistance--in other words1 is a very good conductor--then this electric spark consists1 not in a discharge of electricity uniformly in one direction1 but of a series of rapidly succeeding sparks which are really discharges of electricity or electric currents passing through the air alternately in opposite directions4 ,this can be demonstrated by taking a photograph of the electric spark on a rapidly revolving photographic plate or strip4 ,you are probably all familiar with the sensitive photographic film which is employed in hand cameras1 such as the kodak4 ,if a strip of this sensitive film is bound round the edge of a wheel1 and if the wheel is set in very rapid rotation1 and if we throw on the film1 by means of a lens1 an image of an oscillatory electric spark1 it will be clear to you that1 if the spark is continuous1 it will produce upon the moving photographic film an image which will be of the nature of a broad band4 ,if1 however1 the electric spark is intermittent1 then this photographic image will be cut up into a series of bars or patches1 each one of which will correspond to a separate image of one constituent of the oscillatory spark4 ,photographs of oscillatory electric sparks have in this way been taken by many observers1 and have afforded a demonstration that the electric discharge of a ,leyden jar1 when taken through a wire of low resistance1 is not a continuous movement of electricity in one direction1 but a rapidly alternating electric current through the wire1 forming the oscillatory spark1 and corresponding with an equally rapid alternating electric strain in the glass1 both strain and current dying gradually away4 ,although this operation takes a long time to describe1 yet1 nevertheless1 an oscillatory spark consisting of #bj or #cj electric oscillations may all be over in the or even second4 ,in the photograph now thrown upon the screen 7see ,fig4 #ff7 you see the image of an oscillatory electric spark1 each oscillation of which lasted second4 ,we can1 however1 give a still further proof that the discharge of a ,leyden jar or electric condenser is1 under some circumstances1 oscillatory1 in the following manner3-- ,illustration3 ,,fig4 #ff4--;,a photograph of an oscillatory electric spark 7,hemsalech74 ,you have already seen that an alternating or two-way electric current existing in one circuit can produce another alternating or two-way electric current in a neighbouring circuit4 ,before me1 on the table1 is an arrangement by which a battery of six ,leyden jars1 ,l1 is continually being charged and discharged through a thick wire which is wound a dozen times round a square wooden frame1 ,p 7see ,fig4 #fg74 ,in proximity to this wooden frame there is another wooden frame1 ,s1 also having on it a dozen or two turns of insulated wire2 the circuit of this last conductor is completed by a small incandescent lamp1 ,g4 ,you will notice that when the ,leyden jars are charged and discharged rapidly through the primary conductor1 the little glow-lamp of the secondary circuit lights up brilliantly1 and1 in virtue of what has already been explained1 you will see that this experiment is a proof that the discharge of the ,leyden jars through the primary circuit must consist in an alternating or two-way current2 in other words1 it must be oscillatory4 ,illustration3 ,,fig4 #fg4 ,a still further proof may be given that the discharge of a ,leyden jar or condenser1 when taking place through a low-resistance circuit1 is oscillatory in the following manner3-- ,we employ the vacuum tube that we brought to your notice a few moments ago4 ,when an electric current is sent always in the same direction through such a tube1 it is well known that the two ends of the tube are not alike in appearance4 ,the tube1 as you have seen1 is filled with a luminous glow2 but this glow is interrupted1 forming what is called a dark space near one terminal of the tube1 this terminal being that which is termed the negative pole4 ,accordingly1 this unsymmetrical appearance in the light in the tube is a proof that the electric current is passing through it always in one direction4 ,we can1 however1 vary the experiment1 and instead of illuminating the tube by means of a direct-discharge or induction coil1 which is always in one direction1 we are able to illuminate it by means of a rapid series of discharges from a ,leyden jar4 ,you will then see that the glow-light in the tube is symmetrical--the tube1 in other words1 is alike at both ends2 and this shows us that the discharge from the tube under these circumstances must be alternating--that is1 first in one direction and then in the other4 ,whilst this apparatus is in use1 we can show you with it two other very pretty experiments dependent upon the fact that the discharge of a ,leyden jar through a low-resistance circuit is alternating or oscillatory4 ,a moment ago we employed this oscillatory discharge in one circuit to induce a secondary oscillatory discharge in another metallic circuit1 and this secondary oscillatory or alternating current was made manifest by its power to illuminate a little incandescent lamp4 ,if1 however1 we place a large glass bulb1 ,p1 which has been partly exhausted of its air1 in the interior of the primary discharge coil1 you will see that this primary oscillatory discharge of the ,leyden jar is able to create in the glass bulb a brilliant luminous ring of light 7see ,fig4 #fh74 ,this is called an electrodeless discharge1 and it is due to the fact that the rapidly oscillatory current existing in the wire wrapped round the bulb creates a similar oscillatory discharge in the rarefied air in the interior of the bulb1 this being a conductor1 and thus renders it luminous along a certain line4 ,the production of these electrodeless discharges in rarefied gases has been particularly studied by ,professor ,j4 ,j4 ,thomson4 ,another experiment illustrating what is called the inductive transformation of electrical oscillations is in the arrangement commonly called a ,tesla coil4 ,such a coil is now before you4 ,it consists of a long coil of insulated wire which is placed in the interior of a tall glass vessel1 and on the outside of this glass vessel is wound another insulated and much longer wire4 ,if the alternating or oscillatory discharge of a ,leyden jar is allowed to take place through the thicker wire in the interior of the glass cylinder1 it generates in the outer or secondary wire a very powerful alternating or oscillatory electromotive force1 and we see that this is the case by connecting the ends of this secondary circuit to two insulated brass balls1 between which a torrent of sparks now passes4 ,we may vary the experiment by connecting the ends of the secondary circuit of the ,tesla coil to two insulated concentric rings of thin1 bare1 brass wire1 and then1 when the room is darkened1 we see the space between these rings filled with a brilliant purple light1 which is due to the discharge taking place through the air under the action of the rapidly oscillatory electromotive force generated in the secondary circuit4 ,illustration3 ,,fig4 #fh4--;,an electrodeless discharge in an exhausted bulb4 ,i trust that these experiments will have produced a conviction in your minds that the release of the electric strain in the glass dielectric of a ,leyden jar results in the production of electric oscillations or rapidly alternating electric currents in the metallic circuit connecting the two surfaces1 just as the sudden release of a compressed spring results in a series of mechanical oscillations4 ,we may here remark that any arrangement of two metallic plates with a sheet of insulator or non-conductor between them is called a condenser4 ,thus1 a condenser can be built up by coating a sheeting of glass on its two sides with tinfoil1 or in place of glass we may use mica1 paraffin paper1 or any other good non-conductor4 ,we may even use air at ordinary pressures2 and thus1 if two metal plates are placed near to one another in air1 the plates being both insulated--that is1 supported on non-conductors1--this arrangement constitutes what is called an air condenser4 ,an air condenser1 therefore1 is virtually only a kind of ,leyden jar in which the glass is replaced by air1 and the tinfoil by two stout metal plates4 ,illustration3 ,,fig4 #fi4--;,hertz oscillator4 ,i must now proceed to describe and show you a particular kind of air condenser which was invented by the late ,professor ,hertz1 and1 in consequence1 is called a ,hertz oscillator 7see ,fig4 #fi74 ,it consists of two square or round metal plates which are carried on glass or ebonite legs1 and these plates have short1 stout wires attached to them1 ending in brass knobs4 ,if these plates are placed in line with one another1 they constitute an air condenser of a very peculiar kind1 the two brass plates correspond with the tinfoil surfaces of a ,leyden jar1 and the air all round them corresponds with the glass of the jar4 ,supposing the plates are so arranged that the brass knobs are about inch apart1 or rather less1 if then we connect these two brass plates to the secondary terminals of an induction coil or electrical machine capable of giving long sparks in air1 we shall find1 when the electrical machine or induction coil is set in action1 that a very bright crackling spark passes between these little knobs1 and with proper experience it is easy to adjust the distance from the knobs so that this spark is an oscillatory spark4 ,under these circumstances1 what is taking place is as follows3 ,in the first place1 an electromotive force is acting between the two plates1 and creating an electric strain in the air all round them along certain lines1 and also between the two knobs4 ,the air1 and all other gases like it1 possess this peculiar property1 that whilst at ordinary pressures they are nearly perfect non-conductors1 yet1 nevertheless1 if they are subjected to more than a certain electric pressure1 they pass instantly into a condition in which they become very good conductors4 ,accordingly1 if we progressively increase the electromotive force acting between the plates1 up to a certain point the whole arrangement acts like a ,leyden jar2 but there comes a moment when the air between the knobs breaks down and passes from a non-conductive to a conductive condition4 ,the two plates then resemble at that moment the surfaces of a charged ,leyden jar which are connected together by a good conductor1 and1 as we have already seen1 under those circumstances the discharge is oscillatory1 and the electric strain in the non-conductor1 or dielectric1 viz4 the air around the plates1 dies away by a series of rapidly alternating electric strains in opposite directions4 ,now1 at this point ,i must recall to your recollection that1 in speaking about the production of air waves1 ,i pointed out that one condition essential to the production of an air wave was that there must be a very sudden application or release of the air-pressure1 such as is caused by an explosion or escape of compressed air4 ,we cannot produce an air wave by moving any object such as a fan slowly to and fro through the air4 ,in order to produce an air wave we must strike the air a very sudden blow1 or1 which comes to the same thing1 we must apply and remove a very sudden pressure to the air2 and under these circumstances we start into existence an air wave1 which travels away from the vibrating or rapidly moving body1 and continues its journey out into surrounding space4 ,i want to show you that1 in the case of the ,hertz oscillator1 these very sudden reversals of electric strain in the air or space round about it1 which take place at the moment when the oscillatory spark passes between the knobs1 creates in a similar manner what is called an electric wave1 which travels out into the space around4 ,the point you must appreciate is1 that just as an air wave conveys away to distant places a rapidly alternating compression made in the air by a vibrating body at a particular place1 so an electric wave conveys away to distant places an alternating electric strain1 which is originated at some point in the medium by the oscillatory discharge of some form of condenser4 ,before1 however1 we can demonstrate this fact1 we must have some means for detecting the influence of what we call an electric wave4 ,you will remember that1 in the case of experiments with air waves1 ,i used a sensitive flame in order to make evident to you the presence of waves in the air which you could not see1 so here ,i must use an appropriate detector for electric waves1 the operation of which will render evident to us the existence in the space round our electric oscillator of the electric waves we cannot see4 ,time will not permit me to discuss all the different forms of electric-wave detector which have been invented4 ,for our present purposes we must limit ourselves to the description of one plan1 which depends on the remarkable fact that finely powdered dry metal or metallic filings are non-conductors of the electric current until they are subjected to an electromotive force exceeding a certain value1 when the metallic filings at once pass into a conductive condition4 ,if you recall the remarks made just now in connection with the special electrical properties of air and other gases1 you will notice that there is a remarkable similarity between the electrical behaviour of air at ordinary pressures to electromotive force1 and that of a loose mass of metallic filings4 ,both the air and the metallic filings are non-conductors as long as the electromotive force acting on them does not exceed a certain value1 but if it exceeds this critical value1 they pass at once into a conductive condition4 ,the fact that pieces of metal in loose contact with one another behave in a similar manner was discovered more than twenty years ago by the late ,professor ,d4 ,e4 ,hughes1 who1 as you may perhaps know1 was the inventor of a printing telegraph1 the microphone1 and many other most important electrical instruments4 ,professor ,hughes was a great genius1 and in many respects in advance of his age4 ,he it was who undoubtedly discovered that an electric spark has the power of affecting at a distance the electric conductivity of a metallic junction consisting of two metals in loose contact4 ,the peculiar behaviour of metallic filings under electromotive force1 and under the influence of electric sparks at a distance1 was subsequently rediscovered by ,professor ,branly2 and the effect of an electric oscillatory spark in changing the conductivity of a light metal contact was also rediscovered by ,sir ,oliver ,lodge1 and the phenomena investigated by many other observers4 ,i can show you the experiment on a large scale in the following manner3-- ,illustration3 ,,fig4 #gj4--;,a metal disc-coherer4 ,i have here a number of aluminium discs1 the size of sixpences1 stamped out of thin metal1 and these are arranged in a sort of semi-cylindrical trough between two terminal screws1 so that the discs are very lightly pressed together4 ,under these circumstances the pile of metal discs is not a conductor1 and it will not pass the electric current from a battery which is joined up in series with an electric bell and the pile of discs 7see ,fig4 #gj74 ,supposing1 however1 that ,i make an oscillatory spark in proximity to this pile of metal discs1 as ,i can do by taking the discharge from a large ,leyden jar near it2 the pile of discs at once becomes a conductor2 the electric current from the battery can then pass through it1 and the bell rings4 ,such an arrangement has been named by ,sir ,oliver ,lodge a coherer1 because1 under the action of the oscillatory spark1 the discs cohere or stick together4 ,we can separate the discs by giving them a sharp rap1 and then the operation can be again repeated4 ,a much more sensitive arrangement can be made by taking a small box of wood through the bottom of which pass two nickel wires which are parallel to one another1 but not in contact4 ,in this box is placed a small quantity of very finely powdered metallic nickel or nickel filings1 and if the quantity of these filings is properly adjusted1 it is possible to make an arrangement which possesses the property that there is no conductivity between the two nickel wires under ordinary circumstances1 but that they become conductively connected to one another the moment an oscillatory electric spark is made in the neighbourhood4 ,we shall speak of this contrivance as an electric wave indicator1 and we shall employ it in subsequent experiments to enable us to detect the presence of an electric wave4 ,we must then return for a moment to the consideration of the production of electrical oscillations in circuits of various kinds4 ,i trust it has been made plain to you that if two metallic surfaces1 separated by a non-conductor such as air or glass1 are acted upon by an electromotive force1 the non-conductor becomes electrically strained4 ,another way of stating this is to say that a positive charge of electricity exists on one metal surface1 and a negative charge on the other4 ,the only objection which can be raised to expressing the facts in this manner is that it fastens attention rather upon the conductors than upon the insulator1 which is the real storehouse of the energy4 ,if these two metal surfaces are then connected together by a conductor of low resistance1 the charges disappear by a series of oscillations1 and the result is an electric current in the conducting circuit connecting the plates1 which rushes backwards and forwards in the circuit1 but gradually diminishes in strength until it completely dies away4 ,you may picture to yourselves the electrical effect as analogous to the following experiment with two air-vessels3 ,supposing we have two strong steel bottles1 into one of which we compress a quantity of air1 and in the other we make a vacuum by pumping out nearly all the air4 ,these vessels would correspond with two conductors1 one charged with positive electricity and the other with negative4 ,imagine these vessels connected by a wide pipe in which is placed a tap or valve1 which can be opened suddenly so as to permit the air to rush over from the full vessel to the empty one4 ,if this is done1 it is a matter of experience that the equality of pressure between the two vessels is not at once established1 but in virtue of the inertia quality of the air1 it only takes place after a series of oscillations of air in the pipe4 ,in rushing over from the full vessel to the empty one the air1 so to speak1 overshoots the mark1 and the state of the vessels as regards air-pressure is exactly interchanged4 ,the air then rushes back again1 and it is only after a series of to-and-fro movements of the air in the pipe that an exact equality of pressure in the two vessels is attained4 ,the electrical actions which take place in connection with an electric discharge between two conductors1 one of which is charged positively and the other negatively1 are exactly analogous to the above-described experiment with two air-vessels1 one of which has air in it under compression1 and the other has had the air removed from it4 ,you will notice1 however1 that the oscillations of the air in the pipe in the air-vessel experiment depend essentially upon the fact that air is a substance which has inertia1 or mass1 and you will naturally ask what is it which has inertia1 or its equivalent1 in the electrical experiment8 ,the answer to this question is as follows3 ,every electric circuit has a quality which is called inductance1 in virtue of which an electric current cannot be started in it instantly1 even under any electromotive force1 and conversely when the current is started it cannot be immediately brought to rest4 ,from the similarity of this quality of the circuit to the inertia of ordinary material substances1 it has been sometimes called the electric inertia of the circuit4 ,the word 8inertia0 really means inactivity1 or laziness1 but the term as used in mechanics implies something more than mere inactivity4 ,it involves the notion of a persistence in motion when once the body is set moving4 ,when a material substance is in motion it possesses energy1 and has the power of overcoming up to a certain point resistance to its motion4 ,this energy-holding power1 or capacity for storing up energy of motion1 which is characteristic of all material substances1 is a consequence of their inertia4 ,the fact is otherwise expressed by stating that the mass of a material substance is one element in the production of energy of motion4 ,an electric current in one sense resembles a moving substance1 for it is an exhibition of energy in association with matter4 ,the current-energy is measured by the product of two factors3 one is half the square of the current-strength1 and the other is the inductance of the circuit4 ,the analogy between the two cases may be more exactly brought out by pointing out that the energy of motion of a moving body is measured by the product of its mass and half the square of its velocity4 ,hence it follows that the power of overcoming resistance1 or1 in other words1 of doing useful work or mischief1 which is possessed by a heavy body in motion is proportional1 not simply to its speed1 but to the square of its speed4 ,if a bullet1 moving with a certain speed1 can just pass through one plank #a inch thick1 then1 when moving with twice the speed1 it will pass through four such planks1 and if moving with three times the speed1 through nine planks of equal thickness4 ,the energy of an electric current is similarly measured by the product of the inductance of the circuit and half the square of the current-strength4 ,in the same or equal circuits two currents1 the strengths of which are in the ratio of #a to #b1 have energies in the ratio of #a to #d4 ,the greater1 therefore1 the inductance of an electric circuit1 the greater is the tendency of an electric current set flowing in it to run on after the electromotive force is withdrawn4 ,the inductance of a circuit is increased by coiling it into a coil of many turns1 and decreased by stretching it out in a straight line4 ,the important idea to grasp in connection with this part of the subject is that1 just as there are two forms of mechanical energy1 viz4 energy of mechanical strain and energy of motion1 so also there are two forms of electrical energy1 viz4 energy of electro-static strain and electric-current energy4 ,if1 for instance1 we bend a bow or extend a spring1 this action involves the expenditure of mechanical energy1 or work1 and the energy so spent is stored up as energy of strain1 or1 as it is called1 distorsional energy in the distorted bow or spring4 ,when1 however1 the bow communicates its energy to the arrow or the spring to a ball1 and so sets these in motion1 we have in the flying arrow or ball a store of energy of motion4 ,if a slip of steel spring is fixed at one end1 and then set in vibration1 we have a continual transformation of energy from the motional to the distorsional form4 ,at one moment the spring is moving violently1 and at the next it is bent to its utmost extent2 and these states succeed each other4 ,the store of energy in the vibrating spring is1 however1 gradually frittered away1 partly because the continual bending of the steel heats it1 and this heat dissipates some of the energy2 but also because the spring1 if vibrating quickly enough1 imparts its energy to the surrounding air1 and creates air waves1 which travel away1 and rapidly rob the vibrating spring of its stock of energy4 ,in a precisely similar manner all electrical oscillation effects depend upon the fact that electric energy can exhibit itself in two forms4 ,in one form it is electro-static energy1 or energy of electric strain4 ,in this form we have it when we charge a ,leyden jar4 ,the glass is then1 as explained1 in a state of electrical strain1 and its condition is analogous to that of a stretched spring4 ,the same holds good when we have two conductors insulated from each other in air4 ,we have then an electrical strain in the air4 ,it is important1 however1 to notice that1 since a perfect vacuum can support electric strain1 it follows that1 in the cases where air or glass constitute this non-conductor1 or dielectric1 of a condenser1 the whole of the energy cannot be stored in the material substance1 the glass or the air4 ,the real storehouse of the energy is the ther1 as modified by the presence of the ordinary matter in the same place4 ,when we discharge the ,leyden jar or condenser1 the electro-static energy in the dielectric disappears1 and we obtain in its place an electric current in the connecting conductor2 and this1 as described1 is an exhibition of energy in another form4 ,if the resistance of the connecting conductor is small1 then we have electrical oscillations established which consist in an alternate transformation of the energy from an electro-static form to the electric-current form4 ,at each oscillation some energy is frittered away into heat in the conductor1 and if the conductor and condenser have a special form1 energy may be rapidly removed from the system by the electric waves which are formed in the surrounding ther or dielectric4 ,these waves consist in the propagation through the medium of lines of electric strain1 just as an air wave consists in the propagation through the air of regions of air-compression1 or a water wave consists in the propagation of an elevation on the surface4 ,returning again to the discussion of the production of electrical oscillations1 it is necessary to consider a little more in detail the manner in which we can create an electrical oscillation in what we have called an open electric circuit4 ,let me begin with an experiment1 and it will then be easier for you to understand the particular points to be explained4 ,illustration3 ,,fig4 #ga4 ,before me are two long brass rods1 each of them about #e feet in length1 and the ends of these rods are provided with polished brass balls 7see ,fig4 #ga74 ,the rods are placed in one line and supported on pieces of ebonite1 and are so fixed that the two balls are separated from one another by a space of about inch4 ,the two rods constitute1 therefore1 two insulated conductors4 ,these rods are connected by coils of wire with the terminals of an instrument called an induction coil1 which ,i shall not stop to describe1 but which you may regard as a kind of electrical machine for producing electromotive force4 ,if we set the induction coil in action1 it creates between its terminals an intermittent but very powerful electromotive force1 which gradually increases up to a certain value1 at which it breaks down the conductivity of the air-gap between the two balls4 ,let us think carefully what happens as the electromotive force of the induction coil is increasing4 ,one of the rods is in effect being electrified with positive1 and the other with negative1 electricity1 and these charges are increasing in magnitude4 ,the two rods constitute1 as it were1 the two coated surfaces of a kind of ,leyden jar1 or condenser1 of which the surrounding air is the non-conductor4 ,accordingly1 by all that has been previously explained1 you will easily understand that there is an electric strain in the air which exists along certain lines1 called lines of electro-static strain1 and this state in the air is exactly similar to the condition in which the glass of a ,leyden jar finds itself when the jar is charged4 ,if we were to delineate the direction of this electric strain by lines drawn through the space around the rods1 we should have to draw them somewhat in the fashion represented by the dotted lines in ,fig4 #ga4 ,as the electrical state of the rods gradually increases in intensity1 a point is reached at which the air between the balls can no longer maintain this strain1 and it breaks down and passes into a conductive condition4 ,the state of affairs round the rods is then similar to that of a ,leyden jar being discharged4 ,an electric current is produced across the air-gap1 moving from one rod to the other1 and the intensely heated air in between the balls is visible to us as an electric spark4 ,this spark1 if photographed1 would be found to be an oscillatory spark4 ,the electric current in the rods cannot continue indefinitely3 it gradually falls off in strength1 but as it flows it creates in the space around the rods an electric strain which is in the opposite direction to that which produced it1 although taking place along the same lines4 ,after a very short time1 therefore1 the electrical conditions which existed at the moment before the air broke down are exactly reproduced1 only the direction of the strain is reversed4 ,in other words1 the rod which was positively electrified is now negatively1 and vice vers4 ,then this state of strain again begins to disappear1 producing in the rod an electric current1 again in the reverse direction2 and so the energy1 which was originally communicated to the space round the rods in the form of an electric strain1 continually changes its form1 existing at one moment as energy of the electric current passing across the spark gap1 and the next moment as energy of electric strain4 ,we may ask why this state of things does not continue indefinitely1 and the answer to that question is twofold4 ,first because the rods possess a property called electrical resistance1 and this acts towards the electric current just as friction acts towards the motion of material substances2 in other words1 it fritters away the energy into heat4 ,so at each reversal of the electric current in the rod a certain quantity of the original store of energy has disappeared1 due to the resistance4 ,there is1 however1 a further and more important source of dissipation of energy1 and this is due to the fact that an electrical oscillation of this kind taking place in a finite straight circuit1 or1 as it is called1 an open electric circuit1 creates in the space around an electric wave4 ,the rapid reversal of the electric strain in the air results in the production of an electric wave1 just as in the case of an explosion made in air1 the rapid compression of the air results in the production of an air wave4 ,it is not easy for those who come to the subject for the first time to fully grasp the notion of what is implied by the term 8an electric wave40 ,in the first lecture1 you will perhaps remember1 ,i pointed out that the production of a wave in a medium of any kind can take place if the medium possesses two properties4 ,in the first place1 it must elastically resist some change or distortion1 and1 in the second place1 when that distortion is made it must tend to disappear if the medium is left to itself1 and in so doing the displacement of the medium must overshoot the mark and be reproduced in the opposite direction1 owing to some inertia-like quality or power of persistence in the medium4 ,it would lead us into matters beyond the scope of elementary lectures if we were to attempt to summarize all the evidence which exists tending to show that the phenomena of electricity and magnetism must depend upon actions taking place in some medium called the electro-magnetic medium4 ,all the great investigators at the beginning of the last century1 when electrical and magnetic phenomena were beginning to be explored1 came to this conclusion1 and in the writings of ,joseph ,henry1 of ,ampre1 and of ,faraday we find references again and again to their conviction that the phenomena of electricity imply the existence of a medium exactly in the same way as do the phenomena of optics4 ,it is only1 however1 in recent years that we have had evidence before us1 some of which will be reviewed in the next lecture1 which affords convincing proof that the luminiferous ther and the electro-magnetic medium must be the same4 ,the consideration of the simplest electrical effects is sufficient to show that1 if this medium exists1 it possesses at least two properties1 one of which is that it offers an elastic resistance to the production of electric strain in it by means of electromotive force4 ,a question which is sure to arise in the minds of those who consider this subject carefully is1 ,what is the nature of an electric strain8 ,and the only answer which we can give at the present moment is that we must be content to leave the question unanswered4 ,we do not know enough yet about the mechanical structure of the electro-magnetic medium1 or ther1 to be able to pronounce in detail on the nature of the change we call an electric strain4 ,it may be a motion of some kind1 it may be a compression or a twist1 or it may be something totally different and at present unthinkable by us1 but1 whatever it is1 it is some kind of change which is produced under the action of electromotive force1 and which disappears when the electromotive force is removed4 ,clerk-,maxwell1 to whom we owe some of our most suggestive conceptions of modern electricity1 coined the phrase electric displacement to describe the change which we are here calling an electric strain4 ,one essential element in ,maxwell's theory of electricity is that an electric strain or displacement1 whilst it is being made or whilst it is disappearing1 is in effect an electric current1 and it is for that reason sometimes spoken of as a displacement current4 ,we have seen that every electric circuit possesses a quality analogous to inertia1 that is to say1 when a current is produced in it it tends to persist1 and it cannot be created at its full value instantly by any electromotive force4 ,just as we cannot1 at the present moment1 pronounce in detail on the real nature of electric strain1 so we cannot say whether that quality which we call inductance of a circuit is dependent upon a true inertia of the electro-magnetic medium or on some entirely different quality more fundamental4 ,it may be remarked1 in passing1 that there is a strong tendency in the human mind to seek for and be satisfied with what we called mechanical explanations4 ,this probably arises from the fact that the only things which we can picture to ourselves in our minds very clearly are movements or changes in relative positions4 ,if we can in imagination reduce any physical operation to some kind of movement or displacement taking place in some kind of material1 we seem to arrive at a kind of terminus of thought which is more or less satisfactory4 ,we invariably aim at being able to visualize an operation concerning which we are thinking1 and it requires some mental self-control to be able to content ourselves with a general expression which does not lend itself readily to visualization4 ,there are plenty of indications1 however1 that this mental method of procedure1 and this endeavour to reduce all physical operations to simple mechanics and to movements of some kind1 may in the end be found to be unjustifiable2 and the time may arrive when we may be more satisfied to explain mechanical operations in terms of electrical phraseology rather than aim at dissecting electrical effects into mechanical operations4 ,thus1 for instance1 instead of speaking of electric inertia1 it may be really more justifiable to speak of the inductance of ordinary matter4 ,the final terms in which we endeavour to offer ourselves an explanation of physical events are in all probability very much a matter of convenience and custom4 ,we may1 however1 for present purposes rest content by thinking of the electro-magnetic medium as in some sense like a heavy elastic substance which is capable of undergoing some kind of strain or distortion1 the said strain relieving itself as soon as the distorting force is withdrawn2 but1 in addition1 we must think of the medium as possessing a quality analogous to inertia1 so that as distortion vanishes it overshoots the mark1 and the medium only regains its state of equilibrium at the particular point considered1 by a series of oscillations or alternate distortions1 gradually decreasing in amount4 ,any medium which possesses these two qualities has1 in virtue of explanations already given1 the property of having waves created in it1 and what we mean by an electric wave is a state of electric strain which is propagated through the ther with a velocity equal to that of light1 just as an air wave consists of a state of compression which is propagated through the air with a velocity of #aajj feet a second4 ,illustration3 ,,fig4 #gb4--;,electric-radiation detector 7,fleming74 ,to sum up1 we may then say that whenever rapid electrical oscillations are created in open circuit1 such as the two rods above described1 the arrangement constitutes a device for creating an impulse or effect in the surrounding space called an electric wave in the ther or electro-magnetic medium2 just as an organ-pipe or piano-string or other musical instrument constitutes a device for creating waves in the air by means of mechanical oscillations4 ,the existence of these electric waves1 and their transference to distant places1 can be rendered evident by their action as already described upon finely powdered metals4 ,an apparatus which shows this effect very well is now arranged before you4 ,at one end of the table ,i have a pair of rods connected to an induction coil1 constituting a ,hertz radiator1 the action of which has just been described4 ,at the other end of the table are two similar long rods1 but their inner ends are connected to two small plates of silver1 which form the sides of a very narrow box1 and between these plates is placed a very small quantity of metallic powder4 ,the construction of this little box is as follows3 ,a thin slip of ivory has a little gap cut out of it 7see ,fig4 #gb71 and on the two sides of this slip of ivory are bound two silver plates bent in the shape of the letter ,l1 forming1 therefore1 a very narrow box with silver sides4 ,the two silver plates are connected to the two long rods4 ,as already explained1 the metallic filings or finely powdered metal are not in their ordinary condition an electric conductor4 ,accordingly1 if we connect to one of the silver plates one terminal of a battery joined in series with an electric bell1 the other end of the bell being connected to the second silver plate1 this battery cannot send a current through the bell1 because the circuit is interrupted by the non-conductive metallic powder in the little box4 ,supposing1 then1 that we cause a spark to pass between the balls of the radiator1 and start an electric wave4 ,when this electric wave reaches the long rods connected to the receiving arrangement1 it sets up in these rods a sudden electromotive force1 and this electromotive force1 as already explained1 if of sufficient magnitude1 causes the loose mass of metallic filings to pass from a non-conductive to a conductive condition4 ,at that moment1 therefore1 the battery is able to send an electric current through the bell1 and to cause it to ring4 ,we can1 however1 stop the ringing by giving the little box containing the metallic filings a tap1 which separates them from one another and interrupts the electric conductivity4 ,the function of the two rods connected with the receiver is not quite the same as the function of the two rods connected to the radiator4 ,in order to create a vigorous electric wave1 we must have a radiator which possesses what is called considerable electric capacity1 and also considerable inductance1 and we can only do this in general by using long rods4 ,on the other hand1 at the receiving end the efficacy of the rods is due to the fact that they1 so to speak1 add together the electric strain taking place over a considerable distance2 in other words1 the electromotive force which is set up in the receiving circuit is dependent on the length of the rods4 ,the longer1 therefore1 these rods1 the greater is the distance at which we can obtain the effect which is shown to you with a given spark-length4 ,one point it is important to notice1 and that is1 that the rods of the receiver must be parallel to the rods of the radiator if we are to obtain any effect at a distance4 ,if we turn the rods of the radiator round so that they are at right angles to those of the receiver1 you see that no sparks produced at the radiator balls cause the bell in connection with the receiver to ring4 ,the reason for this is because the electric strain1 which is propagated out into the space1 exists in a direction parallel to the radiator rods all along a line drawn perpendicular to the rods through the spark-gap4 ,the receiver rods will not have electromotive force produced in them by this travelling line of electric strain unless they are parallel to its direction4 ,it is to be hoped that the above explanations have afforded indications of what is meant by an electric wave4 ,on the other hand1 there may be many who find it exceedingly difficult to derive clear ideas when the subject is presented to them clothed in such general terms as we have been obliged to use4 ,it may assist matters1 therefore1 if1 before concluding this chapter1 a word or two is said on the subject of recent investigation into the inner mechanism of an electric current and an electric strain4 ,it is impossible to do this1 however1 without making mention1 in the briefest possible way1 of modern researches into the constitution of matter4 ,if you can imagine yourselves furnished with a little crystal of ordinary table salt1 chemically called chloride of sodium1 and the means of cutting it up under an immensely powerful microscope1 you might go on dividing it up into smaller and smaller pieces4 ,if this process could be continued sufficiently far1 we should ultimately obtain a very small fragment of salt1 which1 if still further divided1 would yield two portions of matter not alike and not salt4 ,this smallest possible portion of salt is called a molecule of sodium chloride4 ,chemical facts teach us that this molecule is made up of two still smaller portions of matter1 which are called respectively atoms of chlorine and sodium4 ,we have good reason to believe that all solids1 liquids1 and gases are composed of molecules1 and these are built up of atoms1 few or many4 ,in the case of some substances1 such as salt1 the molecule is very simple and composed of two atoms4 ,in other substances1 such as albumen or white of egg1 the molecules are very complicated and composed of hundreds of atoms4 ,the word atom means something which 8cannot be cut10 and until comparatively recent time the opinion was held that atoms of matter were the smallest indivisible portions of matter which could exist4 ,more than twenty-five years ago1 ,sir ,william ,crookes showed1 by numerous beautiful experiments1 that in a vacuum tube1 such as you have seen used to-day1 a torrent of small particles is projected from the negative terminal when an electric current is passed through the tube4 ,this stream of particles is called the cathode stream1 or the cathode radiator4 ,within recent times1 ,sir ,joseph ,thomson has furnished a proof that this cathode stream consists of particles very much smaller than chemical atoms1 each particle being charged with negative electricity4 ,these particles are now called corpuscles1 or electrons4 ,it has been shown that these electrons are constituents of chemical atoms1 and when we remove an electron from an atom we leave the remainder positively electrified4 ,an atom can1 therefore1 by various means be divided into two portions of unequal size4 ,first1 a very small part which is charged with negative electricity1 and1 secondly1 a remaining larger portion charged with positive electricity4 ,these two parts taken together are called ions1 i4e4 wanderers4 ,the negative ions1 or electrons1 or corpuscles1 taken together constitute what we call negative electricity1 and up to the present no one has been able to show that the corpuscle can be unelectrified4 ,hence the view has been expressed that what we call electricity is a kind of matter1 atomic in structure1 and that these negative ions or corpuscles collectively are1 in fact1 the atoms of the electric fluid4 ,these corpuscles can move freely in the interior of some solids1 moving between the molecules of the solid just as little dogs can run about in and amongst a crowd of people in a street4 ,in these cases the substance is called a conductor of electricity4 ,in other substances the movement of the corpuscles is more restricted1 and these constitute the various kinds of so-called non-conductors4 ,the corpuscle1 being a small charge of negative electricity1 creates in all surrounding space a state called electric force4 ,it is impossible to expound this action more in detail without the use of mathematical reasoning of a difficult character4 ,suffice it to say that this electric force must be a particular condition of strain or motion in the ther4 ,if the corpuscle is in rapid motion1 it creates in addition another kind of strain or motion called magnetic force4 ,the electric force and the magnetic force are related to each other in free space in such a manner that if we know the difference between the values of the electric force at two very near points in space1 we are able to tell the rate at which the magnetic force is changing with time in a direction at right angles to the line joining these near points in space4 ,we cannot specify in greater detail the exact nature of these states or conditions which constitute magnetic force and electric force1 until we know much more than we do at present about the real nature of the ther4 ,the two fundamental qualities of the ther are1 however1 its capacity to sustain these states we call the magnetic force and the electric force4 ,the electrons of which we have spoken not only give rise to electric and magnetic force when in movement1 but they are themselves set in motion by these forces4 ,thus electric force at any point moves electrons placed at that spot1 and an electron in motion is affected and has its direction of motion changed when magnetic force acts on it4 ,leaving further remarks on the relations of atoms1 electricity1 and ther until the end of the last lecture1 we may conclude the present one by explaining the manner in which the observed facts connected with a ,hertz oscillator are interpreted in terms of this electron hypothesis of electricity4 ,take the simple case of two long insulated metal rods separated by a spark-gap4 ,the process of charging one rod positively and the other negatively consists in forcing more corpuscles1 or negative ions or electrons1 into one conductor and removing some from the other4 ,any source of electromotive force1 such as a dynamo or induction coil1 is1 on this hypothesis1 a sort of electron-pump1 which pumps electrons from one conductor and puts them into another4 ,one conductor1 therefore1 gains in electron-pressure1 and the other loses4 ,the excess of electrons in one conductor endeavour to escape1 and a strain is produced on the electrons or atoms in the surrounding dielectric or air1 which may be looked upon as the effort of the electrons1 more or less tethered to the atoms1 to escape4 ,the air in the spark-gap is subjected to the most intense strain1 and when this reaches a certain intensity some of the electrons are torn away from their atoms1 and the air in the gap then becomes a conductor4 ,the excess of electrons in one conductor rush through the channel thus prepared1 and this constitutes an electric current4 ,the first rush carries over too many electrons to equilibrate the electron-pressure1 and hence the first torrent of migrating electrons in one direction is followed by a back-rush in the opposite one1 this again in turn by another in the original direction1 and so the equality in the number of electrons in each conductor is only established after a gradually diminishing series of to-and-fro rushes of electrons across the air-gap4 ,this action constitutes a train of electrical oscillations4 ,at the same time that these operations are going on in and between the conductors1 the electrons attached to the atoms of the air or other dielectric all around are being violently oscillated4 ,these oscillations may not proceed to such an extent as to detach electrons from their atoms1 but they are sufficient to create rapidly reversed electric and magnetic forces4 ,it appears that the very rapid movement to and fro of an electron causes a wave in the ther1 just as the rapid movement of the hand through water causes a wave in water1 or the vibration of the prong of a tuning-fork creates a wave in the air4 ,the electron has some grip on the ther1 such that the sudden starting or stopping of the electron makes a disturbance which we may popularly describe as a splash in the ther4 ,hence1 if a large number of electrons are suddenly started into motion in the same direction1 the effect on the ther is something like casting a multitude of stones on the surface of still water1 or the simultaneous action of a number of small explosions in the air4 ,anything1 therefore1 which1 so to speak1 lets the electrons go gradually1 or softens the first rush1 is inimical to the production of a vigorous electric wave4 ,on the other hand1 anything which causes the first rush of electrons from one conductor to another across the air-gap to be very sudden is advantageous1 and results in a powerful wave4 ,experience shows that the nature of the metal surfaces1 whether polished or rough1 has a great influence on the wave-making power of the radiator4 ,if the spark-balls or surfaces are rough and not polished1 it seems to tone down the violence of the first electron rush1 and the wave-making power of the oscillator is not so great as if the balls are polished4 ,at this point1 however1 it will be best to withhold further discussion on points of theory until we have considered the facts to be brought before you in the next lecture1 showing that the electric radiation manufactured by means of electric oscillations is only one variety of a vast range of ther waves1 some forms of which are recognizable by us as light and radiant heat4 ,,chapter ,,vi4 ,,waves ,,and ,,ripples ,,in ,,the ,,ther4 ,having in the last chapter explained the nature and mode of production of electric oscillations1 and shown that when these take place in an open electric circuit or long straight rod they give rise to certain actions at a distance1 rendered evident by the changes taking place in the conductivity of metallic powders1 we have now to present the outlines of a proof that these actions are really due to a wave-motion of some description set up in the ther1 which in nature is essentially the same as that which constitutes the agency we call light4 ,we shall begin by studying a few of the epoch-making discoveries we owe to the celebrated ,heinrich ,hertz1 announced in a series of famous researches with which he surprised and delighted the scientific world in the years #ahhg and #ahhh4 ,these investigations opened a new and remarkable field of experimental work4 ,the precise form of apparatus used by ,hertz in these researches is1 however1 unsuited for lecture demonstration1 and ,i shall use on this occasion some arrangements of my own1 which are only convenient modifications of appliances previously employed by other experimentalists4 ,the devices here shown are1 however1 very convenient for public demonstrations4 ,this apparatus consists of two parts1 a part for generating electric waves1 which we shall call the radiator1 and a part for detecting them1 which is called the receiver4 ,the radiator consists of a zinc box1 ,a 7see ,fig4 #gc71 which is provided with hollow trunnions1 and can be fixed to a suitable stand and turned in any direction4 ,the box has an open end to it1 and in its interior there are two brass rods about #d inches long1 each terminating in brass balls1 ,s1 #a inch in diameter4 ,these rods are thrust through corks fixed in the end of two ebonite tubes1 which pass through the hollow trunnions of the box4 ,the rods have their ends attached to very closely wound spirals of gutta-percha-covered wire contained in the ebonite tubes4 ,these spirals are called choking coils4 ,when the balls are arranged in the interior of the box in their proper position1 they are about inch apart1 and the rods to which they are attached are in line with each other4 ,illustration3 ,,fig4 #gc4--;,electric wave radiator 7,a7 and receiver 7,b74 ,the outer ends of the choking coils are connected to an induction coil or electrical machine1 say a small ,wimshurst machine1 suitable for producing electric sparks about #b or #c inches in length4 ,if then sparks are taken between the balls1 we have an arrangement which is1 in fact1 a small ,hertz oscillator or radiator4 ,it has been fully explained in the last chapter that the action of the induction coil or electrical machine is first to create a difference in the electric condition of the balls1 such that one is positively electrified and the other negatively4 ,the balls and rods and the surrounding air1 as already explained1 then form a sort of ,leyden jar or condenser1 and in virtue of the electromotive force the air is electrically strained around the balls4 ,when this strain reaches a particular value1 the air between the balls passes at once into a conductive condition1 and we have a discharge which is oscillatory in nature produced between the conductors4 ,we may consider that the electrical charges on the two rods rush backwards and forwards1 setting up on the rods an oscillatory surface electric current1 and that this is accompanied by a very rapid reversal of the strain in the surrounding non-conductor or dielectric4 ,this state of affairs results in sending out into space an effect called an electric wave4 ,illustration3 ,,fig4 #gd4--;,electric radiation detector 7,miller74 ,turning1 then1 to the receiver ,b 7,fig4 #gc71 we notice that this consists of a similarly shaped metal box1 having in it a board to which are fixed two short nickel wires4 ,these are crossed without touching in the interior of a small ebonite box 7see ,fig4 #gd74 ,the wires are just covered inside the box with a very small quantity of fine nickel filings4 ,to the end of the zinc receiver-box is fixed a long lead pipe1 in the interior of which are two insulated wires1 c1 d4 ,these wires are joined to the extremities of the nickel wires in the receiver-box and then1 passing through the lead pipe1 they enter another metal box which contains a battery and electric bell4 ,the pinch of nickel filings in the small ebonite box is not an electric conductor in its ordinary condition1 and hence the electric circuit1 including the battery and bell1 is not complete4 ,if1 however1 an electric oscillation is set up in the nickel receiver-wires1 the mass of metal particles connecting them at once becomes a conductor1 because little metallic granules stick or cohere together4 ,the battery is thus able to send an electric current through the circuit1 which includes the coherer1 and the electric bell is caused to ring4 ,it may be mentioned that in the actual apparatus employed the arrangement is not quite so simple4 ,the coherer would be permanently injured if we were to attempt to send through it an electric current strong enough to ring an electric bell4 ,hence we associate with the coherer a contrivance called a relay4 ,a single voltaic cell1 ,e 7a dry cell7 7see ,fig4 #ge71 is joined up in series with the coherer ,c and this relay ,r4 ,the latter is a sort of switch or circuit-closer of such kind that when a very feeble current passes through it it closes a second circuit through which a much stronger current can pass4 ,the transition of the nickel filings from a non-conductive to a conductive condition is1 therefore1 only the means by which a very small current of electricity is allowed to pass through the circuit of an electro-magnet which forms the circuit of the relay4 ,this action causes a piece of iron to be attracted1 and this again in turn closes another circuit1 and so enables the current from a second battery1 ,f1 of five or six cells to actuate the electric bell ,g4 ,the arrangement of the two batteries1 the relay coherer1 and bell will be understood by studying the diagram of connections in ,fig4 #ge4 ,the really important condition in securing success in the performance of the experiments made with this apparatus is that the long wires which connect the receiver-box with the metal box containing the bell1 battery1 and relay shall be entirely enclosed in a lead pipe without joint1 which is soldered at one end into the receiver-box and at the other into the battery-box4 ,another practical point is that these wires1 where they enter the battery-box1 must have included in their circuit two little coils of insulated wire of a good many turns1 which are called 8choking coils40 ,a third element of success is that the coherer or sensitive conductor shall be sensitive enough1 but not too sensitive4 ,this condition can only be obtained by a process of trial and failure4 ,being provided with these two pieces of apparatus1 we can now proceed to exhibit a series of experiments of great interest4 ,illustration3 ,,fig4 #ge4 ,in the first place1 let the radiator-box and receiver-box be placed a few feet apart with their open mouths facing each other1 like two guns arranged to fire down each other's throats4 ,then1 if all is in order when we make an electric spark between the two balls of the radiator1 the electric bell in connection with the receiver will begin to ring1 showing that the coherer in the receiver-box has been affected and made conductive by the electric wave sent out from the radiator-box4 ,if a smart rap is then given to the receiver-box the clinging metallic filings in the ebonite box will be separated again and1 the circuit being interrupted1 the bell will stop ringing4 ,this being done1 the radiator-box is then turned a little on one side by rotating it round its hollow trunnions like a gun until the open mouths of the two boxes no longer face each other4 ,it will then be found1 on repeating the former experiment1 that the bell will not ring when a spark is made between the balls4 ,a little experimenting will show that the action which affects the coherer is propagated out from the radiator-box in straight lines like the light from a lamp1 and that we are here dealing with something which has all the character of radiation4 ,in the next place1 let the receiver- and radiator-boxes be again arranged with their open mouths facing each other4 ,we make a spark and again secure the responsive action of the bell4 ,we shall now proceed to prove that this effect1 which is called electric radiation1 passes quite freely through certain substances1 but is more or less completely stopped by others4 ,for instance1 if we hold a sheet of iron1 tinfoil1 or even paper covered with silver leaf between the open mouths of the radiator and receiver1 we find that the bell of the receiver will not ring even when a rapid series of oscillatory sparks are made in the radiator4 ,these sheets of metal1 thick or thin1 are quite opaque to the electric radiation proceeding from the spark-balls4 ,on the other hand1 we find a sheet of paper or card1 a wooden board1 a sheet of glass1 a slab of wax or bitumen1 sulphur1 marble1 or slate1 are all quite pervious or transparent1 and when held between the radiator and receiver do not hinder at all perceptibly the action of the former on the latter4 ,we conclude1 therefore1 that some bodies are opaque and some transparent to the electric radiation4 ,but the classification does not agree with the classification as regards opacity or transparency for light4 ,wood1 marble1 and pitch are optically opaque1 but electrically transparent4 ,the general law1 however1 which decides the question of opacity or transparency for electric radiation1 is as follows3 ,all good electrical conductors are opaque to electric radiation1 and all good insulators or non-conductors are transparent4 ,hence we see at once why metal sheets are opaque1 and wood1 wax1 or glass transparent1 to the electric radiation from the spark-balls4 ,we may go one step further4 ,if we take some sheets of perforated zinc or wire gauze1 or even a large packet of pins1 or paper bag full of iron filings1 we shall find that all these bodies are practically opaque to the electric rays4 ,moreover1 we can show that not only is the above law true for solids1 but it holds good for liquids as well4 ,i have provided here a number of flat glass bottles which are filled with various liquids1 salt water1 fresh water1 solution of soda1 paraffin oil1 olive oil1 turpentine and methylated spirits4 ,if we test an empty glass bottle between the radiator and receiver1 we can assure ourselves that the bottle itself is transparent to the electric radiation4 ,if1 then1 we take the bottles containing the various liquids and test them one by one between the radiator and the receiver1 we find that the bottles containing the paraffin oil1 the olive oil1 and the turpentine are transparent to the electric radiation1 but that the bottles containing the salt water1 the fresh water1 the solution of soda1 and the methylated spirits are all opaque4 ,the oils and liquids similar to them are all good non-conductors1 whereas water and various aqueous solutions are fairly good conductors of electricity1 and hence these liquids1 although they are all about equally transparent to light1 behave very differently to electric radiation4 ,as regards the electric ray1 a bottle full of pure water is as opaque to the electric radiation we are here using as it would be to light if it were filled with black ink4 ,experiment shows that every object containing water1 or which is wet1 is exceedingly opaque to the electric radiation we are employing4 ,thus1 for instance1 if ,i take a dry duster folded in four1 and hold it in the path of the electric ray1 you see that it is quite transparent1 and that the bell attached to the receiver rings as easily as if there were no duster there at all4 ,if1 however1 we dip the duster in water1 and then hold it between the radiator and receiver1 we find that the wet duster is perfectly opaque4 ,the human body consists largely of water which exists in the tissues1 and hence it is not surprising to find that the hand or any part of the body placed between the radiator and receiver intercepts the electric ray4 ,you see1 if ,i hold my hand in front of the radiator1 that nothing is able to escape from it1 when sparks are made between the balls1 which can affect the receiver4 ,in the same way it can be shown by experiment that the human head is perfectly opaque--in fact1 much more opaque than an equally thick block of wood2 and this opacity to the electric ray is due in a veritable sense to the water in the brain4 ,all dry animal tissues1 such as leather1 bone1 gelatine1 and flesh1 if dry1 are very transparent to electric radiation of the kind we are now using1 but if these objects are made thoroughly wet1 then they become intensely opaque4 ,illustration3 ,,fig4 #gf4--,the reflection of an electric ray4 ,we can1 then1 proceed to show that this electric radiation can be reflected1 just like light or sound1 by metal or other conducting surfaces1 and that the law of reflection of the electric ray is the same as the law of reflection for rays of light or sound4 ,if we place the radiator ,a with its mouth upwards1 still preserving the receiver ,b in a horizontal position1 it is possible to adjust the two very near to one another1 but yet so that the radiation from the radiator does not affect the receiver4 ,if ,i now hold a metal plate1 ,p1 at an angle of #de above the mouth of the radiator1 you will notice that the bell at once rings1 thus showing that the electric radiation has been reflected into the receiver-box 7see ,fig4 #gf74 ,also we find that a very small deviation from the angle of #de is sufficient to prevent the effect4 ,careful experiments in the laboratory show that the electric ray is reflected according to the optical law1 viz4 that the angle of reflection is equal to the angle of incidence4 ,we find that any good conducting surface will1 in this manner1 affect the electric radiation4 ,thus ,i can reflect it from a sheet of tinfoil or even from my hand1 and the fact that ,i can1 so to speak1 take hold of this electric radiation1 and deflect it in different directions by the palm of my hand1 produces in the mind a very strong conviction that we are dealing with something of a very real nature in experimenting with this electric radiation4 ,it will be in your remembrance that1 in the chapter in which we were dealing with waves in the air1 ,i showed you a very interesting experiment illustrating the refraction of rays of sound by means of a carbonic acid prism1 and ,i have now to bring before you an exactly analogous experiment performed with electric radiation4 ,here1 for instance1 is a prism made of paraffin wax1 a substance which you have already seen is transparent to the electric ray4 ,if we arrange the radiator- and receiver-boxes at an angle to one another1 it is possible so to adjust them that the electric radiation projected from the radiator-box ,a just escapes the receiver-box ,b1 and does not therefore cause the bell to ring 7see ,fig4 #gg74 ,when this adjustment has been made we introduce the paraffin prism ,p into the path of the electric ray1 and if the adjustments are properly made1 we find that the electric ray is bent round or refracted1 and that it then enters the receiver-box and causes the bell to ring4 ,this experiment was first performed by ,hertz with a very large pitch prism1 but his apparatus was too cumbersome for lecture purposes1 and the smaller and more compact arrangement you see before you is therefore preferable for present purposes4 ,illustration3 ,,fig4 #gg4--,the refraction of an electric ray4 ,i have it in my power to show you a still more remarkable experiment in electric refraction4 ,it is found that dry ice is very transparent to these electric rays1 but if the ice is wetted on the surface1 then1 as you have already learnt1 the film of moisture is opaque4 ,we have had constructed for the purposes of this lecture a prism of ice by freezing water in a properly shaped zinc box4 ,this prism is now being arranged between the radiator and the receiver1 and its surfaces must next be dried carefully with dusters and white blotting paper to remove every trace of moisture4 ,when this is done we find we can repeat with the ice prism the same experiment performed just now with the paraffin prism1 and we can refract the electric ray4 ,if you will recall to your memory the statements which were made in connection with the refraction of rays of sound and waves of water1 you will remember that it was pointed out that the refraction of a ray of sound and the bending of a train of water waves was due to the passage of the waves in the air or in the water from a region where they were moving quickly to a region in which they were compelled to move more slowly2 and it was furthermore shown that this bending must take place whenever a plain wave of any kind passes in an oblique direction from one region to another region where it undergoes an alteration in velocity4 ,in other words1 it was shown that the bending or refraction of the direction of motion of a wave1 whether in air or water1 is a proof that there is a difference in its velocity in the two places bounded by the surface at which the refraction takes place4 ,if this bending takes place in such fashion that the ray is bent towards the perpendicular line drawn to the bounding surface1 which is the same thing as saying if the line of the wave is bent so as to make a less angle with the bounding surface after it has passed from one region to the other1 then it shows that the wave-motion travels more slowly after it has passed the bounding surface than before4 ,if we now return to the consideration of the electric experiment with the prism of paraffin or ice1 we shall find that this1 properly interpreted1 gives us a proof that the electric radiation travels more slowly in paraffin wax or ice than it does in air1 and the ratio between its velocity in air or in empty space and its velocity in any non-conductor is called the electric index of refraction for that non-conductor4 ,this index can be determined by making two measurements4 ,first1 that of the refracting angle of the prism2 and secondly1 that of the deviation of the ray4#bf ,i have made these two experiments for the prisms of paraffin and ice in my laboratory1 and ,i find the electric refractive index of paraffin to be #afd1 and the electric refractive index of ice to be #ahc4 ,in connection with the refraction of rays of sound1 it was pointed out that a curved surface has the power to diverge or converge rays of sound1 and you will remember that we employed a sound-lens for converging the rays of sound diverging from a whistle1 just as an ordinary burning-glass1 or double convex lens1 can be employed to bring the rays of sunlight to a focus4 ,we shall now attempt a similar experiment with the electric ray4 ,a block of paraffin is fashioned into the shape of a semi-cylinder1 flat on one side and convex on the other1 and this plano-convex paraffin lens has a convex surface having a radius of #f inches4 ,if ,i place the radiator ,a and receiver ,b about #d feet apart1 then by making a few little adjustments it is possible to so arrange matters that the radiation which proceeds from the radiator is not powerful enough at a distance of #d feet to sensibly affect the coherer and make the bell ring 7see ,fig4 #gh74 ,if1 however1 ,i adjust the paraffin lens ,l halfway between1 ,i shall converge this electric radiation to a focus just about the place where the coherer is situated1 and the consequence is that on making sparks between the balls of the radiator1 we find that the bell attached to the receiver at once rings4 ,illustration3 ,,fig4 #gh4--;,converging a beam of electric radiation4 ,we have1 therefore1 here brought to a focus1 by means of a paraffin lens1 the electrical radiation just in the same manner that an ordinary burning-glass focuses the rays of light and heat of the sun1 and enables us to light with it some paper or a cigar4 ,we have1 therefore1 indubitable proof in all these experiments that we have something proceeding from the radiator which is capable of being reflected or refracted just like the rays of sound or ripples on the surface of water2 and1 moreover1 we find that this electric radiation passes through some substances but not through others4 ,there is1 therefore1 a strong presumption that we are here dealing with something which is similar in nature to light1 although it cannot affect the eye4 ,in order that we may complete the proof we must show that this radiation is susceptible of interference4 ,this proof may be partly obtained from the consideration of the following facts connected with the opacity or transparency of wire grating to the electric radiation3-- ,i have here a wooden frame across which are strained some wires about a quarter of an inch apart 7see ,fig4 #gi74 ,if we hold this frame or grid in front of the radiator so that the direction of these wires is at right angles to the direction of the radiator rods which carry the balls1 we find that the grid is quite transparent to the electric radiation1 but if we turn the grid round so that the wires of the grid are parallel to the radiator rods1 we find at once that the grid becomes perfectly opaque4 ,the same experiment can be prettily shown by means of a paper of pins4 ,here are some large carpet pins arranged in rows in paper1 and if ,i hold this paper of pins in between the radiator and receiver with the pins parallel to the radiator1 it is perfectly opaque to the electric ray1 but if ,i turn it so that the pins are at right angles1 it is quite transparent4 ,the same experiment succeeds with a paper of ordinary pins1 but not so well with a paper of midget pins4 ,illustration3 ,,fig4 #gi4 ,the explanation of this action of a grid is as follows3 ,you have already seen that an alternating current in one electric circuit can produce another alternating current in a secondary circuit placed parallel with the first4 ,it is not difficult to show1 either experimentally or from theory1 that when the primary current is an electrical oscillation--that is1 a very rapid alternating current--the current in the secondary circuit is also an electrical oscillation of the same frequency or rapidity1 but that the currents in the two circuits1 primary and secondary1 are always moving in opposite directions at the same moment4 ,accordingly1 if we hold a grid in front of the radiator1 the wires of the grid have what are called induced oscillations set up in them1 and these induced oscillations themselves create electric radiation4 ,accordingly1 it is clear that if a grid of this kind is held near to a radiator with the wires of the grid parallel to the radiator rods1 we have two sets of radiations produced which1 at any point on the side of the grid furthest from the radiator rods1 must neutralize one another1 and therefore destroy each other's effect4 ,hence it is possible to cause the electric radiations proceeding from two electric circuits parallel with each other to destroy one another at a distant point2 and we may1 therefore1 make use of the same arguments as in the case of a similar experiment with light to prove that this electric radiation must be a wave-motion4 ,it would occupy too much of our time1 and it would involve the discussion of matters which are rather beyond the scope of elementary lectures1 if we were to enter into a complete analysis of all the arguments proving that this electric radiation1 which proceeds from an electric oscillator1 is really a wave-motion4 ,i may1 however1 mention one fact1 which has been the outcome of an enormous amount of experimental research1 and that is1 that the velocity of this electric radiation through space is identical with that of light4 ,it has already been mentioned that a ray of light flits through space at the rate of #a1jjj1jjj1jjj feet1 or nearly #ahf1ejj miles a second4 ,by suitable and very ingenious arrangements1 physicists have been able to measure the velocity of electric radiation1 and have found in every case that its velocity of propagation is precisely the same as a ray of light4 ,let us1 then1 summarize briefly what we have learnt4 ,we find that when we set up an electrical oscillation in an open circuit consisting of two metallic rods placed in one straight line1 we have proceeding from this circuit an electrical radiation which is capable of being propagated through space1 which moves in straight lines1 can be reflected and refracted1 can exhibit the phenomena of interference1 and moreover which is propagated with exactly the same velocity as light4 ,is it possible to resist the conclusion that this effect which we call electric radiation1 and the similarly behaving physical agency which we call light1 must both be affections of the same medium8 ,it is hardly necessary to occupy time with experiments in showing that a ray of light can be reflected and refracted by mirrors and prisms1 and converged or diverged by transparent lenses4 ,these are simple optical facts1 and if you are not familiar with them it will be easy for you to make their acquaintance by studying any simple book upon optics2 but ,i should like to draw your attention to the fact that1 in addition to rays of light and electric radiation1 we are acquainted with another kind of radiation1 which is also susceptible of being refracted1 and that is commonly called dark heat4 ,supposing that we take an iron ball and make it red hot in a furnace1 then1 in a perfectly dark room1 we see the ball glowing brilliantly1 and we are conscious by our sensations that it is throwing off heat4 ,let us imagine that the ball is allowed to cool down to a temperature of about #ejj ,c42 it will then just cease to be visible in a perfectly dark room1 but yet if we hold our hand or a thermometer near to it1 we can detect its presence by the dark radiant heat it sends out4 ,experiments show that even when the ball is brilliantly incandescent1 nearly #ih or #ii per cent4 of all the radiation it sends out is dark heat1 and only #a or #b per cent4 is radiation which can affect the eye as light4 ,it is quite easy to show that this dark heat can be reflected just like light4 ,if ,i fix this red-hot ball in the focus of a metallic mirror and lift up ball and mirror nearly to the ceiling and then place upon the table another convex1 polished1 metallic mirror1 the top mirror will gather up and project downwards the radiation from the iron ball and the bottom mirror will converge that to a focus4 ,if then we fix a red-hot ball in the focus of the upper mirror and allow it to cool until it is just not visible in the dark1 we shall find that we can still ignite a piece of phosphorus or some other inflammable substance by holding it in the focus of the bottom mirror1 thus showing that the dark radiation from the iron ball is susceptible of reflection just as are rays of light or electric rays4 ,in fact1 if time permitted1 it would be possible to show a whole series of experiments with dark radiant heat which would prove that this radiation possesses similar properties of luminous or electric radiation in its behaviour as regards reflection1 refraction1 and interference4 ,a vast body of proof has been accumulated that all these forms of radiation are merely varieties of one and the same thing1 and that the only thing in which they really differ from one another is in what is called their wave-length4 ,at this point ,i will remind you once more of that general law which connects together the velocity of propagation of a wave-motion1 the wave-length and the frequency4 ,it is expressed in the formula3 wave-velocity 7,v7 equals frequency 7n7 multiplied by wave-length 771 or in symbolical language-- ,v n ,accordingly1 if the velocity of propagation can be determined1 and if the frequency or periodicity of the wave-motion is known1 then the wave-length can be found from the above simple rule2 or conversely1 if the velocity of propagation and the wave-length are known1 the frequency is determined4 ,the wave-length of various kinds of monochromatic 7one-colour7 light can be easily determined by means of ,young's experiment on interference4 ,if the distance between the two small holes from which the two streams of light emerge is measured1 and if the distance from them to the screen and also the distance of the first dark band from the central line is determined1 it is then very easy to calculate the difference in the distances from the two holes to the dark band4 ,this difference1 however1 must1 as already explained1 be equal to one-half wave-length of the light employed4 ,experiments made in various ways have shown that the wave-length of yellow light is not far from the fifty thousandth part of an inch4 ,hence as the velocity of visible light is #ahf1ejj miles per second1 or #ajjj million feet1 or #ab1jjj million inches per second1 whilst the wave-length is something like inch1 it is clear that the frequency1 or number of light waves which enter the eye per second1 must be reckoned in millions of millions4 ,in fact1 it ranges from #djj to #gjj billions4 ,there is a certain difference of opinion as to what is meant by a billion4 ,we here use the word to signify a million times a million1 a million being a thousand times a thousand4 ,the following table shows us the frequency or number of waves per second1 corresponding to light rays producing colour-sensations of various kinds3-- ,,vibration ,,rates ,,of ,,ther ,,waves ,,affecting ,,the ,,eye ,,as ,,light4 ,colour sensation4 ,vibrations per second4 ,deep red #djj billions4 ,red-orange #dcg 0 ,yellow-orange #deg 0 ,yellow #eji 0 ,green #egj 0 ,blue-green #fag 0 ,blue-violet #fif 0 ,violet #gej 0 ,investigation has shown that the quality in a light ray which causes it to affect our eye with a particular colour-sensation is its wave-length1 whereas the quality which affects our eyes as brightness or brilliancy is due to the amplitude of the waves4 ,it is somewhat difficult to realize at first that1 outside of ourselves1 there is no such thing as colour4 ,colour is a sensation produced when ther waves of a certain wave-length enter the eye and fall on the retina4 ,if the retina is stimulated #djj billions of times per second1 we experience a sensation of redness1 and if it is stimulated #gjj billion times per second1 we experience a sensation of blueness2 but externally1 there is no such thing as red and blue1 there is only a difference in wave-frequency4 ,it is astonishing when we learn for the first time that #djj millions of millions of times per second something in the back of our eyes is moved or stimulated whenever we look at a lady's red dress1 a surgeon's red lamp1 or the red petal of a geranium flower4 ,you will notice1 on referring to the above table of frequencies1 that the range of sensibility of the human eye is very much smaller than that of the ear4 ,our eyes are wonderful instruments for detecting wave-motion in the ther1 and our ears are appliances for detecting wave-motion in the air4 ,the ear1 however1 is1 as explained in a previous chapter1 sensitive to air-vibration forming musical tones which lie between #cj and #cj1jjj per second1 and these numbers are in the ratio of #ajjj to #a1 and cover a range of about ten octaves4 ,the eye1 however1 is only sensitive to ther-vibrations which lie in frequency between #djj and #gjj billions per second1 and these numbers are in the ratio of nearly #b to #a1 or comprise only one octave4 ,the question1 of course1 immediately arises--,what are the properties of ther waves the frequency of which lies outside the above limits8 ,scientific investigation has made us acquainted with a vast range or gamut of ther-vibrations1 and we are able to summarize our present knowledge as follows3-- ,the physical effect we call light1 and that which we have up to the present moment merely called electric radiation1 are really identical in nature1 and both consist in waves propagated through the space-filling ther1 the only difference between them is in wave-length and wave-amplitude4 ,in between these two classes of radiation comes a third1 which is called the dark-heat radiation1 and beyond the limits of visible radiation we are acquainted with another group of ther waves which cannot affect the eye as light1 but which from their power to affect a photographic plate1 is called actinic radiation4 ,hence1 briefly speaking1 four great groups of ther waves are known to us1 called respectively-- #a4 ,actinic1 or photographic rays4 #b4 ,luminous1 or light rays4 #c4 ,ultra-red1 or dark-heat rays4 #d4 ,electric1 or ,hertz rays4 ,convincing proof has been afforded that these various rays are essentially the same in nature1 and that they consist in periodic disturbances or waves propagated through the ther in every case with the velocity of #ahf1ejj miles1 or #ajjj million feet1 or #cj1jjj million centimetres per second4 ,we may1 therefore1 say that these classes of ther waves differ from each other only in the same sense in which a bass note in music differs from a treble one2 that is1 the difference is a difference in frequency4 ,just1 therefore1 as we have a gamut1 or scale of musical tones1 or air-vibrations of increasing frequency1 so we may arrange a gamut or scale of ther waves progressively placed according to their vibration-rates4 ,our present knowledge concerning ther waves can best be exhibited by arranging in a chart a series of numbers showing the wave-lengths of the waves with which we are so far acquainted4 ,as a limit of length we shall take the one-thousandth part of a millimetre4 ,most persons know that a millimetre is a thousandth part of a metre1 and is a short length nearly equal to one twenty-fifth of an inch4 ,the thousandth part of a millimetre is called a micron1 and is denoted by the symbol #a4 ,this last is therefore an exceedingly short length1 nearly equal to one twenty-five thousandth part of an inch4 ,following1 also1 the musical nomenclature1 we shall speak of all those waves included between two wave-lengths1 one of which is double or half the other1 as an octave4 ,thus all the various waves whose wave-lengths lie between #a and #b in length are said to be an octave of radiation4 ,as a preliminary to further discussion let us consider1 in the first place1 the simple facts about the radiation which affects our eyes as light4 ,the light which comes to us from the sun is not a simple thing4 ,it consists of ther waves of many different wave-lengths mingled together4 ,sir ,isaac ,newton first revealed to us the compound nature of white light by his celebrated experiment with a glass prism1 and his optical discoveries were the starting-point for our information on this subject4 ,if a beam of sunlight is allowed to fall on a glass prism1 the rays of light of different wave-lengths which compose it are each bent or refracted to a different degree4 ,in free space ther waves of various wave-lengths all travel1 as far as we know1 at the same rate4 ,this equality in speed is1 however1 disturbed the moment the waves enter a transparent material substance such as glass4 ,the velocity of propagation is then reduced in all cases1 but it is generally more reduced for the shorter waves than for the longer ones2 and as a consequence the rays of shorter-wave lengths are more bent or refracted than the rays of longer wave-length4 ,we have1 therefore1 a dispersion of the component rays1 or a sorting out or analysis of the mixture of rays of various wave-lengths1 and if we receive the light on a screen after passing through the prism we have a band of coloured light called a spectrum1 which consists of a series of patches of light each of a different wave-length4 ,the component rays of the original beam of light are spread out fan-fashion by the prism4 ,we may note1 in passing1 that it is not every transparent body when fashioned into a prism which thus analyzes the light into a fan-shaped beam with rays of various wave-lengths arranged in the order of their wave-lengths4 ,the substances which behave as does glass or water when made into prisms are said to exhibit normal dispersive power4 ,there are1 however1 some bodies1 such as iodine or an alcoholic solution of fuschine1 which exhibit anomalous dispersion and refract some longer waves of light more than some shorter ones4 ,the arrangements for forming a normal spectrum are as follows3 ,we pass a beam of light from the electric lamp through a lens1 and place in front of this lens a metal plate with a narrow vertical slit-shaped opening in it4 ,at a proper distance in front of the slit we place another lens1 and project upon the screen a sharp image of the slit in the shape of a bar of white light4 ,placing a hollow glass prism filled with bisulphide of carbon in front of the last lens1 we find that the various rays in the white light are dispersed1 and we produce on the screen a band of rainbow-coloured light1 called the spectrum4 ,this spectrum is in reality a series of differently coloured images of the slit placed side by side4 ,by making use of the principle of interference as disclosed by ,young1 it is possible to make a measurement of the wave-length of the rays of light which produce the sensation of various colours when they fall upon the eye4 ,thus the wave-length of those ther waves which produce the sensation of deep red is #jge1 and that of the waves producing the sensation of violet when they fall upon the retina of the eye is #jdc4 ,the whole of the visible spectrum is therefore included within a single octave of ther radiation4 ,within these limits any change in the wave-lengths makes itself felt in our eyes as a change of colour4 ,it is commonly said that there are seven colours in the spectrum--red1 orange1 yellow1 green1 blue1 indigo1 and violet4 ,as a matter of fact1 a highly trained eye can discover about a thousand different tints in the spectrum of white light4 ,time will not allow us to enter into any discussion of what is called colour-vision and the theory of sensations of colour4 ,the fact ,i wish to impress upon you here is that1 outside of ourselves1 there is no such thing as colour4 ,the rays of light which produce these sensations of colour when they enter the eye differ from one another only in wave-length and wave-amplitude4 ,hence there is a complete analogy between light of different colours and sounds of different pitches or tone4 ,red light differs from blue light only as a bass note in music differs from a treble note4 ,hence you must distinguish very carefully between a ray of light in itself1 and the sensation it produces when it falls upon the retina of the eye4 ,our eyes are gifted with a marvellous power of detecting slight differences between the wave-length and the amplitude of the rays which may stimulate two adjacent portions of the retina of our eyes4 ,that range of sensibility is1 however1 very limited4 ,supposing we allow a ray having a wave-length greater than #jge or less than #jdc to enter the human eye4 ,it produces no sensation of light at all4 ,accordingly1 if we form a spectrum with sunlight1 we find a tolerably sharp limit to the visible spectrum4 ,supposing1 however1 we allow the spectrum to fall upon a sensitive photographic plate1 we find that the plate will be chemically acted upon far beyond the limits of the visible violet end of the spectrum4 ,hence we learn that beyond the violet there is radiation of a kind which is invisible to the eye1 yet can affect a photographic plate4 ,this is called the ultra-violet1 or actinic radiation4 ,schumann1 in #ahic1 measured waves in actinic radiation of a wave-length as short as #ja1 or one two hundred and fifty thousandth part of an inch1 and hence we may say that we are acquainted with at least two octaves of invisible ultra-violet or actinic radiation1 or ther waves have wave-lengths lying between the limits #ja and #jd4 ,in a similar manner very delicate heat-detecting instruments or thermometers called bolometers1 or thermopiles1 show us that beyond the visible-red end of the normal spectrum there is radiation called the ultra-red radiation1 or dark-heat1 which cannot affect the eye4 ,the wave-length of dark-heat radiation has been measured up to a limit of #fg by ,professor ,rubens and ,professor ,nichols in #ahig and #ahih4 ,accordingly1 we can assert that beyond the red end of the spectrum we are acquainted with six octaves or more of ultra-red radiation1 viz4 that lying in wave-length between #jge and #fg4 ,we may represent the above facts in another way as follows3 ,in most pianos the keyboard extends over a range of seven or eight octaves4 ,imagine a piano having a keyboard with nine octaves1 and that each key was labelled to correspond with a light wave of a particular length4 ,at the extreme treble end let the first key be labelled #ja1 and at the extreme base end let the last key be labelled #eab4 ,then the various octaves will be comprised between the keys marked #ja1 #jb1 #jd1 #jh1 #af1 #cb1 #fd1 #abh1 #bef1 and #eab 7see ,fig4 #gg74 ,suppose that each key when struck caused some kind of electric radiator to emit an ther wave whose wave-length reckoned in microns or thousandths of a millimetre1 is indicated by the number on the key4 ,of all this great gamut of ther waves only the notes of one octave1 viz4 the third from the treble end1 the wave-lengths of which lie between #jd and #jh1 affect the retina of the human eye as light4 ,those waves in the two octaves higher up1 that is1 of wave-length less than #jd1 are able powerfully to affect a photographic plate1 and so1 indeed1 do some of the waves in the visible octave4 ,we may1 in fact1 say that all the ther waves with which we are acquainted1 the wave-length of which is less than about #je1 are able to make an impression upon a photographic plate4 ,these rays1 whatever their wave-lengths1 are called the actinic rays4 ,on the other hand1 all the ther waves with wave-length greater than about #jh1 and for six octaves further down1 can only be recognized by their ability to heat a delicate thermopile or other heat-measuring instrument4 ,they cannot affect the eye1 and they have little or no effect in decomposing silver salts and impressing a sensitive photographic surface4 ,illustration3 ,,gamut ,,of ,,ther ,,waves4 ,wave-lengths in microns4 of a millimetre4 #ja ,shortest ultra-violet wave-length measured by ,schumann1 #ahic4 #jb ,two octaves of ultra-violet waves4 #jd 4444444444444 #jdc violet light ,v ,i ,b ,g ,y ,o ,r one octave of light waves4 4444444444444 #jge red light #jh #af #cb #fd #abh ,seven octaves of dark-heat waves4 #bef #eab 4444444444444 ,longest dark-heat wave-length #fg1 measured #ajbd by ,nichols in #ahih4 #bjdh #djif #haib ,five octaves of unknown radiation4 #afchd #cbgfh ,shortest ,hertz wave made by ,lampa #d mm4 7#ahig74 4444444444444 #feecf #ac mm4 #bf #eb #ajd #bjh ,hertz radiation1 #ab octaves of most frequently #daf used ,hertz waves4 #hcb #affd #ccbh #ffef #accab 4444444444444 ,longer waves still up to #ajjj feet or more in wave-length are used in wireless telegraphy4 ,,fig4 #hj4 ,it should be noted1 however1 that whilst there are more or less definite limits to the wave-lengths of the eye-affecting radiation1 and probably also to the actinic1 or photographic radiation 7radiation of some wave-lengths being both visible and actinic71 rays of every wave-length are in some degree thermal1 or heat-producing4 ,the term dark-heat radiation is1 however1 generally restricted to radiation of that wave-length which is non-visible and non-actinic4 ,this mode of presenting the facts will call your attention again to the narrow limits of sensibility of the human eye as compared with those of the ear4 ,the above-mentioned range of wave-lengths does not1 however1 exhaust our powers of ther-wave production4 ,if we skip over six octaves lying below the limits of the longest dark-heat wave with which we are acquainted1 we should arrive at a wave whose wave-length is about #djjj1 or #d millimetres4 ,at this point we encounter the shortest ther waves which have yet been made by means of electrical oscillations in the fashion first discovered by ,hertz4 ,it is not possible to define exactly the wave-length limits of radiation as yet made by means of electrical oscillations4 ,lampa has experimented with ther waves made by the ,hertz method1 the wave-length of which was not more than #d millimetres4 ,professors ,lodge1 ,rhigi1 ,bose1 ,trouton1 the author1 and many others1 have carried out quasi-optical experiments with electrically made ther waves1 the wave-length of which ranged from a few millimetres to several inches4 ,hertz's own work was chiefly done with ther waves from #a or #b feet to #cj or #dj feet in wave-length4 ,more recently1 ther waves of #hjj to #ajjj feet in wave-length have been employed in wireless telegraphy4 ,perhaps we shall not be wrong in saying that we are acquainted with sixteen or seventeen octaves of ther-wave radiation which is made electrically1 and is usually called the ,hertz radiation4 ,between the radiation of greatest wave-length which proceeds from hot or incandescent bodies such as the sun1 the electric arc1 or a hot ball1 and that of the shortest wave-length which has been created by means of electrical oscillations set up in some form of ,hertz oscillator1 there is a range of six octaves of ther waves which1 so far as we know1 have not yet been manufactured or detected4 ,herein lies an opportunity for much future scientific work4 ,we have to discover how to create and recognize these interconnecting wave-lengths4 ,from the fact that all ,hertz waves travel with the same speed as light1 and from our ability to imitate1 as you have seen1 the well-known optical phenomena with ,hertz radiation of short wave-length1 the great induction has been made that all ther waves have the same essential nature1 and that invisible actinic rays1 light rays1 dark-heat rays1 and ,hertz rays are all of them ther waves of various wave-lengths and amplitudes4 ,thus we see1 as ,maxwell long ago predicted1 that light in all probability is an electro-magnetic phenomenon1 and therefore all optical effects must be capable of receiving an electro-magnetic explanation4 ,the inclusion thus made of the whole science of ,optics within the domain of ,electricity and ,magnetism is one of the grandest achievements of ,physical ,science4 ,it stands second only to ,newton's great discovery of universal gravitation1 which reduced all ,physical ,astronomy to pure ,dynamics1 and showed that the force concerned in the falling of a stone is identical with that which holds the planets in their orbits1 and controls the motions of galaxies of suns4 ,at the end of the last chapter it was explained that these ,hertz radiations are created in the ther by the suddenly starting1 stopping1 or reversing the motion of crowds of electrons1 which are1 as it were1 instantly released from a state of pressure or tension1 and set moving inside a straight insulated conductor1 which forms an open electric circuit4 ,the radiations we call light and dark heat are probably1 therefore1 started in a similar manner by vibrations of the electrons which form parts of1 or which build up1 atoms4 ,there are many physical phenomena which seem to show that the electrons which we can detach from atoms in a high vacuum tube are capable of vibrating freely in definite periods when in connection with their atom4 ,if the atoms are able to move freely1 and if each is practically independent1 as is the case in a gas1 and if they are then caused to radiate by any means1 the radiation emitted by the vibration of these electrons consists of certain definite wave-lengths4 ,hence1 when we form the spectrum of an incandescent gas1 we find it to consist of several detached bright lines1 each corresponding to one particular wave-length1 and we do not obtain a uniformly graduated band of coloured light4 ,if an atom is struck by colliding with another1 and then left to itself1 it appears as if the electrons which compose it and form part of it are set in vibration1 and each executes its oscillation in some definite period of time4 ,an atom has1 therefore1 been compared to a 8collection of small tuning-forks10 which1 if rudely struck1 would result in the emission of a set of air-wave trains1 each one corresponding in wave-length to one particular tuning-fork which emitted it4 ,hence1 if we could administer a blow to such a congeries of tuning-forks1 and then analyze the compound sound1 we should obtain a sound spectrum consisting of separated tones--in other words1 a bright line spectrum of the complex sound4 ,supposing1 however1 that we have a mass of atoms much more closely in contact1 as in the case of a solid body1 the continual collisions between the atoms and the closer contact between them cause the vibrations of the electrons to be 8forced10 and not 8free40 ,hence the electrons are compelled to execute all varieties of irregular motion1 and these predominate over their regular free natural vibrations4 ,accordingly1 the waves emitted are of a large variety of wave-length1 and when the radiation is analyzed by a prism1 we obtain a continuous spectrum1 or band of many-coloured light1 as the result of the separation of the rays of different wave-lengths present in it4 ,it is this fact which renders our present method of creating artificial light so excessively uneconomical4 ,all our practical methods for making light consist in heating a solid body in one way or another4 ,in the case of the electric light we heat electrically a carbon rod or filament1 or else1 as in the ,nernst lamp1 a rod composed of magnesia and the rare earths4 ,in the case of the lime-light we heat a cylinder of lime4 ,in an ordinary gas or candle flame we heat small particles of carbon1 and the same is the case even in the sun itself4 ,but this process manufactures not only the single octave of radiation which can affect our eyes as light1 but a dozen other octaves of radiation to which they are insensible4 ,hence it follows that of the whole radiation from a gas flame1 only about #c per cent4 is eye-affecting light1 the remainder is dark heat4 ,in the case of an incandescent electric lamp1 this luminous efficiency may amount to #e per cent41 and in the electric arc to #aj or #ae per cent4 ,there is1 however1 always a great dilution of the useful light by useless dark heat4 ,the proportion of the light or eye-affecting radiation to the dark heat in the total radiation from any source of light increases with the temperature1 but it is not always merely a question of temperature4 ,thus the electric arc is hotter than a candle flame1 and the sun is hotter than the electric arc4 ,hence1 whilst the luminous rays only form #c parts out of #ajj1 or #c per cent4 of the radiation of a candle1 they constitute #aj to #ae per cent4 of those of the electric arc1 and more than #cj per cent4 of those of the sun4 ,on the other hand1 the glow-worm and the fire-fly seem to have possession of a knowledge and an art which is as yet denied to man4 ,it has been shown by ,professor ,langley and ,mr4 ,very that nearly the whole of the radiation from the natural torch of the fire-fly is useful light1 and none of it is useless dark heat4 ,hence these photogenic 7light-producing7 insects have the art1 which we have not1 of creating cold light1 or unadulterated luminous radiation4 ,at the present moment in ordinary incandescent or glow-lamp electric lighting we require to expend an amount of power1 called one horse-power1 to produce illumination equal to that of #fjj candles4 ,supposing1 however1 that all our power could be utilized in generating merely the rays useful for vision1 or which can impress our eyes1 we might be able to create by the expenditure of one horse-power more than twenty times as much illumination1 that is1 a light equal to #ab1jjj candles4 ,these figures show us what rewards await the inventor who can discover a means of generating ther waves having wave-lengths strictly limited to the range lying between the limits #jd and #jg without1 at the same time1 being obliged to create radiation comprising longer waves which are not useful for the purpose of rendering objects visible to us4 ,for the purposes of artificial illumination we require only the ther waves in this one particular octave1 and nothing else4 ,this increase in the efficiency of our sources of artificial illumination is only likely to be brought about when we abandon the process of heating a solid substance to make it give out light1 and adopt some other means of setting the electrons in vibration4 ,it is almost impossible to discuss the subject of ther waves without some reference to the most modern utilization of them in the so-called wireless telegraphy4 ,without entering upon the vexed questions of priority1 or on the historical development of the art1 we shall simply confine our attention here to a consideration of the methods employed by ,mr4 ,marconi1 who has accomplished such wonderful feats in this department of invention4 ,we have already seen that when two insulated conductors are placed with their ends very near together1 and are then electrified1 one positively and the other negatively1 and then allowed to be suddenly connected by an electric spark1 they constitute an arrangement called an electrical oscillator4 ,if the conductors take the form of two long rods placed in one line1 and if their contiguous ends are provided with spark-balls separated by a small gap1 we have seen that we have shown that1 under the above-mentioned conditions1 electric currents of very high frequency are set up in these rods4 ,for creating these oscillations1 an instrument called an induction coil or spark-coil is generally employed4 ,you will understand the arrangements better if a brief description is given first of the spark-coil itself as used in wireless telegraphy4 ,illustration3 ,,fig4 #ha4--;,a #aj-;inch induction coil for wireless telegraphy 7,newton74 ,the appliance consists of a large bundle of fine iron wires1 which are wound over with a long coil of insulated wire4 ,this forms the primary coil4 ,it is enclosed entirely in a tube of ebonite4 ,one end of this coil is a contact-breaker1 which automatically interrupts an electric current flowing from a battery through the primary coil 7see ,fig4 #ha74 ,a hand-key is also placed in the circuit to stop and start the primary current as desired4 ,over the primary coil is a very long coil of much finer silk-covered copper wire1 called the secondary coil4 ,the length of this coil is very considerable1 and may amount to many miles4 ,the secondary coil is divided into sections all carefully insulated from each other4 ,another important part is the condenser4 ,this consists of sheets of tinfoil laid between sheets of waxed paper1 alternate tinfoil sheets being connected4 ,the arrangement forms virtually a ,leyden jar1 and one set of tinfoils is connected to one side of the automatic break1 and the other to the adjacent side4 ,when1 therefore1 the primary circuit is interrupted by the break1 the condenser is at that moment thrown into series with the primary coil4 ,the rapid interruption of the primary current causes a secondary current in the fine-wire coil4 ,the automatic contact-breaker makes from ten to fifty such interruptions per second4 ,at every 8break0 of the primary a very high electromotive force is generated in the secondary circuit1 which may amount to many hundreds of thousands of volts4 ,this very high secondary electromotive force is able to cause an electric discharge in the form of a spark between brass balls connected to the secondary circuit terminals4 ,coils are generally rated by the length 7in inches7 of the spark they can produce between brass balls about inch in diameter4 ,the coil most commonly used in wireless telegraphy is thus technically termed a 8#aj-;inch induction coil10 from the length of the spark this particular type of coil can produce4 ,if the insulated brass balls1 called the spark-balls1 connected to the secondary terminals1 are placed an inch or so apart1 and the hand-key in the primary circuit is closed1 a battery connected to the primary circuit will send a rapidly interrupted current through the primary coil1 and a torrent of sparks will pass between the spark-balls4 ,the primary current of the #aj-;inch coil is usually a current of #aj ampres1 supplied at a pressure of #aj volts4 ,if the hand-key is raised or pressed1 it is possible to make long or short torrents of secondary sparks4 ,suppose1 then1 that we connect to the secondary spark-balls two long insulated rods1 and place the spark-balls about inch apart4 ,on pressing the hand-key1 we obtain a peculiarly bright crackling spark between the balls1 which is an oscillatory spark1 and at the same time1 as already described1 electrical oscillations are set up in the rods and electric waves given off4 ,we may represent to ourselves these electrical oscillations in the rods as similar to the mechanical vibrations which would be set up in a long elastic wooden rod1 clamped at the middle and set in vibration at the ends4 ,or we may consider them similar to the fundamental vibrations of an open organ-pipe1 the middle of the pipe corresponding with the middle of the rod4 ,in comparing the mechanical vibrations of the rod or the acoustic vibration of the air in the organ-pipe with the electrical oscillations in the long rods1 we must bear in mind that the displacement of the rod or the air in the organ-pipe at any point corresponds with electrical pressure1 or potential1 as it is called1 at any point in the long oscillator4 ,hence1 bearing in mind the remarks in the fourth lecture1 it will be evident to you that just as the length of the air wave emitted by the open organ-pipe is double the length of the pipe1 so the length of the electric wave thrown off from the pair of long rods is double their total length4 ,instead of using a pair of rods for the electrical oscillator1 it was found by ,mr4 ,marconi to be an improvement to employ only one insulated rod1 held vertically1 and to connect it to one spark-ball of the coil1 and to connect the opposite spark-ball to a metal plate buried in the earth4 ,then1 when the spark-balls are placed a little apart and the hand-key pressed1 we have a torrent of oscillatory sparks between the 8earthed ball0 and the insulated rod ball4 ,this sets up in the rod electrical oscillations1 which run up and down the rod4 ,it is easy to show that there is a strong electric current passing into and out of the rod by connecting it to the spark-ball by means of a piece of fine wire4 ,when the sparks are taken1 we find this wire will become hot1 it may be red hot1 or sometimes it may be melted4 ,by applying the principles already explained1 it is not difficult to demonstrate that in the case of an oscillator consisting of a single rod connected to one spark-ball the electric waves thrown off are in wave-length four times the length of the rod4 ,the electrical actions taking place1 therefore1 are as follows3 ,at each interruption of the primary current of the spark-coil there is an electromotive force created in the secondary circuit1 which gradually charges up the insulated rod until it attains a state in which it is said to be at a potential or electrical pressure of several thousand volts4 ,the spark then happens between the balls1 and the rod begins to discharge4 ,this process consists1 so to speak1 in draining the electric charge out of the rod1 and it takes the form of an electric current in the rod1 which has a zero value at the top insulated end1 and has its maximum value at the spark-ball end4 ,also1 when the oscillations take place1 we have variations of electric pressure1 or potential1 which are at a maximum at the upper or insulated end1 and have a zero value at the spark-ball end4 ,from the rod we have a hemispherical electric wave radiated4 ,in the language of wireless telegraphists1 such a simple insulated rod is called an insulated aerial1 or an insulated antenna4 ,a simple insulated aerial has1 however1 a very small electrical capacity1 and it can store up so little electric energy that the whole of it is radiated in the first oscillation4 ,hence1 strictly speaking1 we have no train of electric waves radiated1 but merely a solitary wave or electric impulse4 ,the effect on the ther thus produced corresponds to the effect on the air caused by the crack of a whip or an explosion1 and not to a musical note or tone as produced by an organ-pipe4 ,we can1 however1 make an arrangement which is superior in electric wave-making power1 as follows3-- ,illustration3 ,,fig4 #hb4--,transmitter for wireless telegraphy4 ,the vertical rod1 or antenna1 ,a1 is not insulated1 but is connected by its lower end with one end of a coil of insulated wire1 ,s1 wound on a wooden frame 7see ,fig4 #hb74 ,the other end of this last coil is connected to a metal plate1 e1 buried in the earth4 ,around the wooden frame is wound a second insulated wire1 ,p1 one end of which is connected to one spark-ball of the induction coil1 and the other end to the outside of a ,leyden jar1 ,l1 or collection of jars4 ,this double coil on a frame is called an oscillation transformer4 ,the inside of this condenser is connected to the second spark-ball of the induction coil ,i4 ,when these spark-balls ,s are placed a short distance apart1 and the coil set in action1 we have a torrent of oscillatory electric sparks between these balls1 and powerful oscillations set up in one circuit of the oscillation-transformer4 ,these oscillations induce other oscillations in the second circuit of the oscillation-transformer1 viz4 in the one connected to the aerial4 ,the oscillations produced in the air-wire1 or aerial1 are therefore induced1 or secondary oscillations4 ,the aerial wire1 or antenna1 has therefore a much larger store of electric energy to draw upon1 viz4 that stored up in the ,leyden jars1 than if it was itself directly charged by the coil4 ,in order1 however1 to obtain the best results certain adjustments have to be made4 ,it has already been explained that every open electrical circuit has a certain natural time-period for the electrical oscillations which can be set up in it4 ,this is technically called its tune4 ,if we administer a blow to a suspended pendulum we have seen that1 if left to itself1 it vibrates in a definite period of time1 called its natural period4 ,in the same manner1 if we have a condenser or ,leyden jar having electrical capacity which is joined in series with a coil of wire having electrical inertia or inductance1 and apply to the circuit so formed a sudden electromotive force or impulse1 and then leave the circuit to itself1 the electric charge in it vibrates in a certain definite period1 called its natural electrical periodic time4 ,the aerial1 or antenna1 is simply a rod connected to the earth1 but it has a certain inductance1 and also a certain electrical capacity1 and hence any metal rod merely stuck at one end in the earth has a perfectly definite periodic time for the electrical oscillations which can be produced in it4 ,we may compare the rod in this respect with a piece of steel spring held at one end in a vice4 ,if we pull the spring on one side1 and let it vibrate1 it does so in accordance with its natural time-period for mechanical vibrations4 ,the sound waves given out by it have a wave-length equal to four times the length of the spring4 ,in the same manner the fundamental wave-length of the electric waves emitted by an 8earthed aerial10 or rod stuck in the earth1 when an electric impulse is applied to its lower end1 and electrical oscillations are set up in it1 have a wave-length equal to four times that of the rod4 ,hence to obtain the best result the circuit1 including the aerial ,a1 must be 8tuned0 electrically to the circuit including the ,leyden jar ,l4#bg ,a consideration of these arrangements will show you that if the hand-key in the primary circuit of the induction coil is pressed for a long or short time1 we have long or short torrents of sparks produced between the secondary balls1 and long or short trains of electric waves emitted from the aerial1 or earthed vertical wire4 ,whenever we have any two different signals1 we can always make an alphabet with them by suitable combinations of the two4 ,in the well-known ,morse alphabet1 with which every telegraphist is as familiar as we all are with the printed alphabet1 the sign for each of the letters of the alphabet is composed of groups of long and short symbols1 called dots and dashes1 as follows3 ,each letter is made by selecting some arrangements of dots or dashes1 these being the technical names for the two signs4 ,the ,morse code1 as used all over the world1 is given in the table below-- ,illustration3 ,,the ,,morse ,,alphabet4 ,a -- ------ ,b ------ -- -- -- ,c ------ -- ------ -- ,d ------ -- -- ,e -- ,f -- -- ------ -- ,g ------ ------ -- ,h -- -- -- -- ,i -- -- ,j -- ------ ------ ------ ,k ------ -- ------ ,l -- ------ -- -- ,m ------ ------ ,n ------ -- ,o ------ ------ ------ ,p -- ------ ------ -- ,q ------ ------ -- ------ ,r -- ------ -- ,s -- -- -- ,t ------ ,u -- -- ------ ,v -- -- -- ------ ,w -- ------ ------ ,x ------ -- -- ------ ,y ------ -- ------ ------ ,z ------ ------ -- -- ,illustration3 ,,the ,,morse ,,numerals4 #a -- ------ ------ ------ ------ #b -- -- ------ ------ ------ #c -- -- -- ------ ------ #d -- -- -- -- ------ #e -- -- -- -- -- #f ------ -- -- -- -- #g ------ ------ -- -- -- #h ------ ------ ------ -- -- #i ------ ------ ------ ------ -- #j ------ ------ ------ ------ ------ ,full ,stop -- ------ -- ------ -- ------ ,signal for calling up -- -- -- ------ -- -- -- ------ ,the process of sending a wireless message consists in so manipulating the key in the primary circuit of the induction coils that a rapid stream of sparks passes between the secondary balls for a shorter or for a longer time4 ,this gives rise to a corresponding series of electric waves1 radiated from the aerial4 ,the dash is equal in duration to about three dots1 and a space equal to three dots is left between each letter1 and one equal to five dots between each word4 ,thus1 in ,morse alphabet the sentence 8,how are you80 is written-- ,illustration3 -- -- -- -- ------ ------ ------ -- ------ ------ -- ------ -- ------ -- -- ,h ,o ,w ,a ,r ,e ------ -- ------ ------ ------ ------ ------ -- -- ------ ,y ,o ,u ,we have1 in the next place1 to explain how the signals sent out are recorded4 ,illustration3 ,,fig4 #hc4--,marconi receiving arrangement for wireless telegraphy4 ,at the receiving station is erected a second insulated aerial1 antenna1 or long vertical rod1 ,a 7see ,fig4 #hc71 and the lower end is connected to the earth through a coil of fine insulated wire1 ,p1 which forms one circuit of an oscillation-transformer4 ,the secondary circuit1 ,s1 of this oscillation-transformer1 which is called a jigger1 is cut in the middle and has a small condenser1 ,c#a1 inserted1 consisting of two sheets of tinfoil separated by waxed paper 7see ,fig4 #hc71 and to the ends of this circuit is connected the coherer1 or metallic filings tube1 ,t1 which acts as a sensitive receiver4 ,the ,marconi sensitive tube 7see ,fig4 #hd7 is made as follows4 ,a glass tube about inch in diameter and #b inches long has two silver plugs put in it1 and these are soldered to two platinum wires which are sealed into the closed ends of the tube4 ,the ends of the plugs are cut in a slanting fashion and made very smooth4 ,these ends very nearly touch each other4 ,a very small quantity of very fine metallic powder consisting of nineteen parts nickel and one part silver is then placed between the plugs4 ,the quantity of this powder is scarcely more than could be taken up on the head of a large pin4 ,the glass tube is then exhausted of its air and sealed4 ,the tube is attached to a bone rod by means of which it is held in a clip4 ,illustration3 ,,fig4 #hd4--,marconi coherer4 ,to the two sides of the above-mentioned condenser are connected two wires which lead to a circuit including a single voltaic cell1 ,v1 and a relay1 ,e4 ,the relay is connected to another circuit which includes a battery1 ,b1 and a piece of apparatus called a ,morse printer1 ,m1 for marking dots and dashes on a strip of paper4 ,the working details of the above rather complicated system of apparatus devised by ,mr4 ,marconi would require for its full elucidation a large amount of explanation of a technical character4 ,the general reader may1 however1 form a sufficiently clear idea of its performance as follows3-- ,when the electrical waves from the distant transmitting station reach the aerial at the receiving station1 they set up in it sympathetic electrical oscillations4 ,the most favourable conditions are when the two aerials at the distant stations are exactly similar4 ,these electrical oscillations1 or rapid electric currents1 set up an electromotive force in the secondary circuit of the oscillation-transformer1 and this acts1 as already explained1 upon the metallic filings in the coherer-tube and causes it to become an electrical conductor4 ,the cell attached to the relay then sends a current through the conductive circuit so formed and operates the relay4 ,this last contrivance is merely a very delicate switch or circuit-closer which is set in action by a small current sent through one of its circuits1 and it then closes a second circuit and so enables another much larger battery to send a current through the ,morse printer4 ,the printer then prints a dot upon a moving strip of paper and records a signal4 ,one other element in this rather complicated arrangement remains to be noticed1 and that is the tapper4 ,underneath the coherer-tube is a little hammer worked by an electro-magnet like an electric bell4 ,this tapper is set vibrating by the same current which passes through the ,morse printer1 and hence almost as soon as the latter has begun to print1 the sensitive tube receives a little tap which causes the metallic filings to become again a non-conductor1 and so arrests the whole of the electric currency4 ,if it were not for this tapper1 the arrival of the electric wave would cause the printer to begin printing a line which would continue4 ,the dot is1 so to speak1 an arrested line4 ,if1 however1 trains of electric waves continue to arrive1 then dots continue to be printed in close order1 and form a dash on the paper strip4 ,it will thus be seen that the whole arrangements constitute an exceedingly ingenious device of such a nature that a single touch on the hand-key at one station causing a spark or two to take place between the spark-balls makes a dot appear upon a band of paper at the distant station2 whilst1 if the hand-key is held down so that a stream of sparks takes place at the transmitting station1 a dash is recorded at the receiving station4 ,the means by which this distant effect is produced is the train of electric waves moving over the earth's surface setting out from one aerial and arriving at the other4 ,illustration3 ,,fig4 #he4 ,the reader who has difficulty in following the above explanations may perhaps gather a sufficiently clear notion of the processes at work by considering a reduced1 or simplified1 arrangement4 ,imagine two long insulated rods1 ,a1 ,a 7see ,fig4 #he71 like lightning-conductors set up at distant places4 ,suppose each rod cut near the bottom1 and let a pair of spark-balls1 ,s1 be inserted in one gap and a coherer or sensitive tube1 ,c1 in the other4 ,at one station let an electrical machine have its positive and negative terminals connected to the two spark-balls1 and at the other let a battery and electric bell be connected to the ends of the coherer4 ,then1 as long as the coherer remains in a non-conductive condition1 the electric bell does not ring4 ,if1 however1 a spark is made between the balls1 in virtue of all that has been explained1 the reader will understand that the coherer-tube becomes at once conductive by the action of the electric wave sent out from the transmitter-rod4 ,the battery at the receiver-rod then sends a current through the coherer1 and rings the bell4 ,all the other complicated details of the receiver are for making the process of stopping the bell and beginning over again self-acting1 and also for the production of two kinds of signals1 a long and a short1 by means of which an alphabet is made4 ,in order that we may have telegraphy in any proper sense of the word1 we must be able to transmit any intelligence at pleasure1 and not merely one single arbitrary signal4 ,this transmission of intelligence involves the command of an alphabet1 and that in turn requires the power of production of two kinds of signals4 ,it remains to notice a few of the special details which characterize ,mr4 ,marconi's system of wireless telegraphy4 ,in establishing wireless communication between two places1 the first thing to be done is to equip them both with aerials4 ,if one station is on land1 it is usual to erect a strong mast about #aej feet high1 and to the top of this is attached a sprit4 ,from this sprit a stranded copper wire is suspended by means of an insulator of ebonite1 so that the upper end of the wire is insulated4 ,the lower end of the wire is led into a little hut or into some room near the foot of the mast in which is the receiving and transmitting apparatus4 ,if the apparatus is to be installed on board ship1 then a similar insulated wire is suspended from a yardarm or from a sprit attached to a mast4 ,each station is provided with the transmitting apparatus and the receiving apparatus1 and the attendant changes over the aerial from one connection to the other so as to receive or send at pleasure4 ,in the case of long-distance wireless telegraphy1 the aerial is not a single wire1 but a collection of wires1 suspended so as to space them a little from each other4 ,thus in the case of the first experiments made by ,m4 ,marconi across the ,atlantic1 the aerial erected on the coast of ,cornwall consisted of fifty stranded copper wires each #aej feet in length suspended in a fan-shaped fashion from a long transverse stay upheld between two masts4 ,the wires were spaced out at the top and gathered in together at the bottom4 ,the question which almost immediately occurs to most people to ask is how far it is possible to prevent the electric waves emanating from one station affecting all receiving instruments alike within a certain radius4 ,the answer to this is that considerable progress has been made in effecting what is called 8tuning0 the various stations4 ,in speaking of acoustic resonance it has been pointed out that a train of air waves can set up vibration in other bodies which have the same natural period of vibration4 ,thus1 if we open a piano so as to expose the strings1 and if a singer with a strong voice sings a loud true note and then stops suddenly1 it will be found that one particular string of the piano is vibrating1 viz4 that which would give out if struck the note which was sung1 but all the rest of the strings are silent4 ,it has been pointed out that every open electric circuit has a natural electrical time-period of vibration in which its electric charge oscillates if it is disturbed by a sudden electromotive force and then left to itself4 ,if the two aerials at two stations are exactly alike1 and if the various circuits constituting the oscillation-transformers in the transmitting and receiving appliances are all adjusted to have the same electrical period1 then it is found that the stations so tuned are sympathetic at distances vastly greater than they would be if not so tuned4 ,hence it is possible to arrange wireless telegraph apparatus so that it is not affected by any electric waves arriving from a distance which have not a particular time-period4 ,mr4 ,marconi has also proved that it is possible to receive on the same aerial1 at the same time1 two different messages on separate receiving instruments from two distant but properly tuned transmitting stations4 ,since the date of these pioneer inventions many different forms of wave detector have been discovered1 and wireless telegraphy has shown itself to be of the greatest utility in effecting communication between ship and ship1 and ship and shore4 ,its value in enabling intelligence to be transmitted from lightships or lighthouses to coast stations cannot be over estimated4 ,one very remarkable feature of the apparatus as arranged by ,mr4 ,marconi is the small space it occupies4 ,it is in this respect most admirably adapted for use on board ship4 ,it only requires a long1 insulated1 vertical wire which can easily be suspended from a mast1 and the whole receiving and transmitting apparatus can be placed on board ship in a small cabin4 ,employing the sensitive tube and ,marconi receiving arrangements1 messages can easily be sent #aej miles over the sea-surface by means of an aerial #aej feet high and a #aj-;inch induction coil4 ,it is a curious fact that better results are obtained over a water-surface than over land4 ,two similar stations with the same appliances can communicate at two or three times greater distance if they are separated by sea than if they are on land and have no water between4 ,this is connected with the fact that electric waves are not able to pass through sea-water1 but can diffuse through dry earth4 ,the sea-surface acts somewhat like an optical reflector or mirror1 and the electric waves glide along its surface4 ,the rotundity of the earth within certain limits hardly makes any perceptible effect upon the ease of communication4 ,the waves sent out by the transmitter of a long-distance wireless station are from #cjjj to #bj1jjj feet in length1 and there is1 therefore1 a considerable amount of bending or diffraction4 ,it is a familiar fact1 as already explained1 that a wave-motion1 whether on water or in air1 spreads round an obstacle to a certain extent4 ,thus an interposing rock or wall does not form a sharply marked sound-shadow1 but there is some deflection of the air waves by the edge of the obstacle4 ,the amount of bending which takes place depends on the length of the wave4 ,if we take two places on the sea-surface #bjj miles apart1 the surface of the sea at the halfway distance is just #a miles above the straight line joining the places4 ,in other words1 the rotundity of the earth interposes a mountain of water #a miles high between the places4 ,the electric waves used in wireless telegraphy have a wave-length of about #fjj to #ajjj feet1 or say five or six to the mile4 ,hence the interposition of an object1 the height of which is one-fortieth of the distance1 is not sufficient to make a complete electric shadow4 ,if we were1 for instance1 blowing a trumpet creating air waves #e feet long1 the interposition of a cliff between two places a mile apart1 but so situated that the cliff protruded to the extent of #dj yards across the line joining them1 would not cut off all sound4 ,there would be diffraction or diffusion enough of the air waves to enable the sound to be heard round the corner4 ,in the same manner the electric waves are1 so to speak1 propagated round the corner of the earth4 ,more remarkable still1 they have been detected1 when sufficiently powerful1 at a distance of #fjjj miles from the generating station1 and in this case they must have travelled a quarter of the way round the earth4 ,a good conception of the relative speeds of water waves1 air waves1 and ther waves can be gained by considering the time each of these would take to cross the ,atlantic ,ocean1 travelling in its own medium4 ,suppose we could1 at the same moment1 create a splash in the sea near ,england sufficiently great to cause a wave which would travel over the surface of the ,atlantic at the speed of many ocean waves1 say at #cj miles an hour4 ,to cover a distance of #cjjj miles this water wave would then require #ajj hours4 ,imagine that we could1 at the same moment1 make a sound loud enough to be heard across the same ocean1 travelling at the rate of #aajj feet a second1 or about #gjj miles an hour1 the sound wave would cross from ,england to the coast of the ,united ,states in about four hours4 ,if1 however1 we were to make an ther wave it would flit across the same distance in about the sixtieth part of a second4 ,if you have been able to follow me in these descriptions1 you will see that the progress of scientific investigation has led us from simple beginnings to a wonderful conclusion4 ,it is that all space is filled with what we may call an ocean of ther1 which can be tossed into waves and ripples just as the air we breathe is traversed in all directions by aerial vibrations1 and the restless sea by waves and ripples on the water-surface4 ,we cannot feel or handle this imponderable ther1 but we have indubitable proof that we can create waves in it by suddenly applying or reversing something we call electric force1 just as we are able to produce air or water waves by the very sudden application of mechanical force or pressure4 ,these ther waves1 when started1 not only travel through the ocean of ther with astonishing speed1 but they are the means by which enormous quantities of energy are transferred through space4 ,from every square yard of the sun's surface energy is cast forth at a rate equal to that produced by the combustion of eleven tons of best ,welsh coal per hour1 and conveyed away into surrounding space by ther ripples1 to warm and light the sun's family of planets4 ,every plant that grows upon the earth's surface is nourished into maturity by the energy delivered to it in this way4 ,every animal that basks in the sunlight is kept warm by the impact of these ther waves upon the earth4 ,all the coal we possess buried in the earth's crust1 and in this age of steam forming the life-blood of the world1 has been manufactured originally by ther ripples beating in their millions1 in long-past ages1 upon the vegetation of the primeval world4 ,but in another way the ther serves as a vehicle of energy--in the form of an electric current4 ,every electric lamp that is lighted1 every electric tram-car that glides along1 is drawing its supply of energy through the ther4 ,the wire or conductor1 as we call it1 serves to guide and direct the path of the energy transferred2 but the energy is not in but around the wire4 ,we have lately learnt to make what we may best describe as billows in the ther1 and these are the long waves we employ in wireless telegraphy4 ,but in telegraphy1 whether with wires or without1 we are merely manipulating the ther as a medium of communication1 just as in speech or hearing we use the air4 ,we therefore find our physical investigations lead us to three great final inquiries1 when we ask--,what is the nature of electricity1 ther1 and energy8 ,already1 it seems possible1 we may obtain some clue to an answer to the first question1 and find it in a study of the electrons1 or tiny corpuscles which build up atoms4 ,concerning the structure of ther1 physical investigation1 which has revealed its existence1 may be able to analyze a little more deeply its operations4 ,but the question1 ,what is ,energy8 seems to take us to the very confines of physical inquiry1 where problems concerning the structure of the material universe seem to merge into questions concerning its origin and mystery4 ,in its ultimate essence1 energy may be incomprehensible by us1 except as an exhibition of the direct operation of that which we call ,mind and ,will4 ,in these final inquiries into the nature of things1 the wisest of us can merely speculate1 and the majority but dimly apprehend4 ,we must not1 however1 travel beyond the limits of thought proper for these elementary lectures4 ,their chief object has been to show you that the swiftly moving ocean waves1 which dash and roll unceasingly against the coast-lines of our island home1 are only instances of one form of wave-motion1 of which we find other varieties in other media1 giving rise to all the entrancing effects of sound and light4 ,in these expositions we have been able to do no more than touch the fringe of a great subject4 ,their object will have been fulfilled if they have stimulated in you a desire to know more about these interesting things4 ,every star and flower1 every wave or bird that hovers over it1 can tell us a marvellous story1 if only we have eyes to see1 and ears to hear4 ,we may find in the commonest of surrounding things a limitless opportunity for intelligent study and delight4 ,when1 therefore1 you next sail your boat upon a pond1 or watch ducks or swans swimming1 or throw stones into a pool1 or visit the seaside1 may ,i hope that some of the matters here discussed will recur to your minds1 and that you will find a fresh meaning and new interest in these everyday objects4 ,yon may thus1 perhaps1 receive an impulse attracting you to the study of some chapters in the 8,fairy ,tale of ,science10 more wonderful than any romance woven by the imaginations of men1 and open to yourselves a source of elevating pleasure1 which time will neither diminish nor destroy4 ,,appendix4 ---- ,,note ,a 7see p4 #ba74 ,the distinction between the individual wave-velocity and a wave-group velocity1 to which1 as stated in the text1 attention was first called by ,sir ,g4 ,g4 ,stokes in an ,examination question set at ,cambridge in #ahgf1 is closely connected with the phenomena of beats in music4 ,if two infinitely long sets of deep-sea waves1 having slightly different wave-lengths1 and therefore slightly different velocities1 are superimposed1 we obtain a resultant wave-train which exhibits a variation in wave-amplitude along its course periodically4 ,if we were to look along the train1 we should see the wave-amplitude at intervals waxing to a maximum and then waning again to nothing4 ,these points of maximum amplitude regularly arranged in space constitute1 as it were1 waves on waves4 ,they are spaced at equal distances1 and separated by intervals of more or less waveless or smooth water4 ,these maximum points move forward with a uniform velocity1 which we may call the velocity of the wave-train1 and the distance between maximum and maximum surface-disturbances may be called the wave-train length4 ,let v and v be the velocities1 and n and n the frequencies1 of the two constituent wave-motions4 ,let and be the corresponding wave-lengths4 ,let ,v be the wave-train velocity1 ,n the wave-train frequency1 and ,l the wave-train length4 ,then ,n is the number of times per second which a place of maximum wave-amplitude passes a given fixed point4 ,then we have the following obvious relations3-- v n1 v n1 ,n n - n v_/ - v_/ ,also a little consideration will show that-- ,l_/ _/7 - 7 since is nearly equal1 by assumption1 to 4 ,hence we have-- #a_/,l #a_/ - #a_/2 and also ,v ,,nl ,accordingly-- ,v ,n_/7#a_/,l7 7v_/ - v_/7_/7#a_/ - #a_/7 ,let us write #b_/k instead of 1 and #b_/k instead of 2 then we have-- ,v 7vk - vk7_/7k - k7 7i47 ,and since k and k1 v and v are nearly equal1 we may write the above expression as a differential coefficient2 thus-- ,v d7vk7_/d7k7 7ii47 ,suppose1 then1 that1 as in the case of deep-sea waves1 the wave-velocity varies as the square root of the wave-length4 ,then if ,c is a constant1 which in the case of gravitation waves is equal to g_/#b1 where g is the acceleration due to gravity1 we have-- v#b ,c1 or v#b 7g_/#b7 ,but #b_/k1 hence-- vk #b;,c_/v ,hence if we differentiate with respect to v1 we have-- d7vk7_/dv -#b;,c_/v#b ,again1 k #b_/ #b;,c_/v#b2 therefore-- d7k7_/dv -#b7b;,c_/v#c7 ,hence1 dividing the expression for d7vk7_/dv by that for d7k7_/dv1 we have-- ,v d7vk7_/d7k7 v_/#b ,in other words1 the wave-train velocity is equal to half the wave-velocity4 ,this is the case with deep-sea waves4 ,suppose1 however1 that1 as in the case of air waves1 the wave-velocity is independent of the wave-length4 ,then if two trains of waves of slightly different wave-length are superposed1 we have k and k different in value but nearly equal1 and v and v equal4 ,hence the equation 7i47 takes the form-- ,v v ,in other words1 the beats travel forward with the same speed as the constituent waves4 ,and in this case there is no difference between the velocity of the wave-train and the velocity of the individual wave4 ,the above proof may be generalized as follows3-- ,let the wave-velocity vary as the nth root of the wave-length1 or let vn ,c2 and let #b_/k as before4 ,then-- vn #b;,c_/k1 and vk #b;,c_/vn-#a #b;,cv-7n-#a7 also k #b_/ #b;,c_/vn #b;,cv-n ,hence d7vk7_/d7k7 7n-#av-7n-#a7-a7_/7nv-n-#a7 77n-#a7_/n7v or ,v 77n-#a7_/n7v ,that is1 the wave-train velocity is equal to 7n-#a7_/n times the wave-velocity4 ,in the case of sea waves n #b1 and in the case of air waves n infinity4 ,if n were #c1 then ,v 7#b_/c7v1 or the group-velocity would be two-thirds the wave-velocity4 ,,note ,b 7see p4 #bgc74 ,every electric circuit comprising a coil of wire and a condenser has a definite time-period in which an electric charge given to it will oscillate if a state of electric strain in it is suddenly released4 ,thus the ,leyden jar ,l and associated coil ,p shown in ,fig4 #hb1 p4 #bga1 constitutes an electric circuit1 having a certain capacity measured in units1 called a microfarad1 and a certain inductance1 or electric inertia measured in centimetres4 ,the capacity of the circuit is the quality of it in virtue of which an electric strain or displacement can be made by an electromotive force acting on it4 ,the inductance is the inertia quality of the circuit1 in virtue of which an electric current created in it tends to persist4 ,in the case of mechanical oscillations such as those made by vibrating a pendulum1 the time of one complete oscillation1 ,t1 is connected with the moment of inertia1 ,i1 and the mechanical force brought into play by a small displacement as follows3 ,suppose we give the pendulum a small angular displacement1 denoted by 4 ,then this displacement brings into existence a restoring force or torque which brings the pendulum back1 when released1 to its original position of rest4 ,in the case of a simple pendulum consisting of a small ball attached to a string1 the restoring torque created by displacing the pendulum through a small angle1 1 is equal to the product mgl1 where m is the mass of the bob1 g is the acceleration of gravity1 and l is the length of the string4 ,the ratio of displacement 77 to the restoring torque mgl is #a_/mgl4 ,this may be called the displacement per unit torque1 and may otherwise be called the pliability of the system1 and denoted generally by ,p4 ,let ,i denote the moment of inertia4 ,this quantity1 in the case of a simple pendulum1 is the product of the mass of the bob and the square of the length of the string1 or ,i ml#b4 ,in the case of a body of any shape which can vibrate round any centre or axis1 the moment of inertia round this axis of rotation is the sum of the products of each element of its mass and the square of their respective distances from this axis4 ,the periodic time ,t of any small vibration of this body is then obtained by the following rule3-- ,t #b77moment of inertia round the axis of rotation7 7displacement per unit of torque1 or pliability77 or ,t #b7;,,ip74 ,in the case of an electric circuit the inductance corresponds to the moment of inertia of a body in mechanical vibration2 and the capacity to its pliability as above defined4 ,hence the time of vibration1 or the electrical time-period of an electric circuit1 is given by the equation-- ,t #b7,,lc7 where ,l is the inductance1 and ,c is the capacity4 ,it can be shown easily that the frequency n1 or number of electrical vibrations per second1 is given by the rule-- n #ejjjjjj_/777;capacity in microfarads7 7inductance in centimetres777 ,for instance1 if we discharge a ,leyden jar having a capacity of of a microfarad through a stout piece of copper wire about #d feet in length and one-sixth of an inch in diameter1 having an inductance of about #abjj centimetres1 the electrical oscillations ensuing would be at the rate of #b millions per second4 ,any two electrical circuits which have the same time-period are said to be 8in tune0 with each other1 and the process of adjusting the inductance and capacity of the circuits to bring about this result is called electrical tuning4 ,in the case of a vertical aerial wire as used in wireless telegraphy1 in which the oscillations are created by the inductive action of an oscillation-transformer as shown in ,fig4 #hb1 page #bga1 the capacity of the ,leyden jar in the condenser circuit must be adjusted so that the time-period of the nearly closed or primary oscillation ,p agrees with that of the open or secondary circuit ,s4 ,when this is the case1 the electrical oscillations set up in the closed circuit have a far greater effect in producing others in the open circuit than if the two circuits were not in tune4 ,the length of the wave given off from the open circuit is approximately equal to four times the length of the aerial wire1 including the length of the coil forming the secondary circuit of the oscillation-transformer in series with it4 ,,footnotes #a ,the wave-velocity in the case of waves on deep water varies as 7g_/#b71 where is the wave-length4 ,the rule in the text is deduced from this formula4 #b ,if ,v is the velocity of the wave in feet per minute1 and ,v is the velocity in miles per hour1 then 7,v #ebhj7_/fj ,v4 ,but ,v 7#b71 and ,v n1 where is the wave-length in feet and n the frequency per minute2 from which we have ,v #aih_/n1 or the rule given in the text4 #c ,the amplitude of disturbance of a particle of water at a depth equal to one wave-length is equal to #a_/b of its amplitude at the surface4 7,see ,lamb's 8,hydrodynamics10 p4 #ahi47 #d ,this can easily be shown to an audience by projecting the apparatus on a screen by the aid of an optical lantern4 #e ,see 8,the ,splash of a ,drop10 by ,professor ,a4 ,m4 ,worthington1 ,f4,r4,s41 ,romance of ,science ,series1 published by the ,society for ,promoting ,christian ,knowledge4 #f ,see ,osborne ,reynolds1 ,nature1 vol4 #af1 #ahgg1 p4 #cdc1 a paper read before the ,british ,association at ,plymouth2 see also ,appendix1 ,note ,a4 #g ,a very interesting article on 8,kumatology1 or the ,science of ,waves10 appeared in a number of ,pearson's ,magazine for ,july1 #aija4 ,in this article1 by ,mr4 ,marcus ,tindal1 many interesting facts about1 and pictures of1 sea waves are given4 #h ,lord ,kelvin 7see lecture on 8,ship ,waves10 ,popular ,lectures1 vol4 iii4 p4 #dfh7 says the wave-length must be at least fifty times the depth of the canal4 #i ,see article 8,tides10 by ,g4 ,h4 ,darwin1 8,encyclopdia ,britannica10 #ith edit41 vol4 #bc1 p4 #cec4 #aj ,the progress of the ,severn 8bore0 has been photographed and reproduced by a kinematograph by ,dr4 ,vaughan ,cornish4 ,for a series of papers bearing on this sort of wave1 by ,lord ,kelvin1 see the ,philosophical ,magazine for #ahhf and #ahhg4 #aa ,see ,lord ,kelvin1 8,hydrokinetic ,solutions and ,observations10 ,philosophical ,magazine1 ,november1 #ahga4 #ab 8,on the ,photography of ,ripples10 by ,j4 ,h4 ,vincent1 ,philosophical ,magazine1 vol4 #dc1 #ahig1 p4 #daa1 and also vol4 #dh1 #ahii4 ,these photographs of ripples have been reproduced as lantern slides by ,messrs4 ,newton and ,co41 of ,fleet ,street1 ,london4 #ac ,some smokers can blow these smoke rings from their mouth1 and they may sometimes be seen when a gun is fired with black old-fashioned gunpowder1 or from engine-funnels4 #ad ,for details and illustrations of these researches1 the reader is referred to papers by ,professor ,h4 ,s4 ,hele-,shaw1 entitled1 8,investigation of the ,nature of ,surface-resistance of ,water1 and of ,stream-line ,motion under ,experimental ,conditions10 ,proceedings of the ,institution of ,naval ,architects1 ,july1 #ahig1 and ,march1 #ahih4 ,a convenient apparatus for exhibiting these experiments in lectures has been designed by ,professor ,hele-,shaw1 and is manufactured by the ,imperial ,engineering ,company1 ,pembroke ,place1 ,liverpool4 #ae ,the ,french word chelon means a step-ladder-like arrangement2 but it is usually applied to an arrangement of rows of objects when each row extends a little beyond its neighbour4 ,soldiers are said to march in echelon when the ranks of men are so ordered4 #af ,see ,lord ,kelvin on 8,ship ,waves10 ,popular ,lectures1 vol4 iii4 p4 #dhb4 #ag ,more accurately1 as the #ahc power of the speed4 #ah ,this figure is taken by permission from an article by ,mr4 ,r4 ,w4 ,dana1 which appeared in ,nature for ,june #e1 #aijb1 the diagram being borrowed from a paper by ,naval ,const4 ,d4 ,w4 ,taylor1 ,u4,s41 read before the 7,u4,s47 ,society of ,naval ,architects and ,marine ,engineers 7#aijj74 #ai 8,practical ,applications of ,model ,experiments to ,merchant ,ship ,design10 by ,mr4 ,archibald ,denny1 ,engineering ,conference1 ,institution of ,civil ,engineers1 ,may #be1 #ahig4 #bj ,reproduced here by the kind permission of the editor of ,harmsworth's ,magazine4 #ba ,see ,lord ,kelvin's ,popular ,lectures1 vol4 iii41 8,navigation10 ,lecture on 8,ship ,waves40 #bb ,see ,professor ,w4 ,f4 ,barrett1 ,nature1 #ahgg1 vol4 #af1 p4 #ab4 #bc ,this follows from the ordinary formula for the focal length f of a biconvex lens1 each surface having a radius of curvature equal to r4 ,for then it can be shown that f 7r_/#b7 7#a_/7 - #a77 where is the index of refracture of the lens material4 ,as shown later on1 the acoustic index of refraction of carbonic acid1 when that of air is taken as unity1 is #abgc4 ,hence1 - #a #jbgc1 and #a_/7 - #a7 #c4 ,hence1 f #br771 or f is slightly less than twice the radius of curvature of the spherical segment forming the sound-lens4 #bd ,we can1 in fact1 discover the ratio of the velocities from the amount of bending the ray experiences and the angle ,,bac of the prism1 called its refracting angle4 ,it can be shown that if we denote this refracting angle by the letter ,a1 and the deflection or total bending of the ray by the letter ,d1 then the ratio of the velocity of the wave in air to its velocity in carbonic acid gas 7called the acoustic refractive index71 being denoted by the ,greek letter 2 we have-- sin77,a ,d7_/#b7_/sin7,a_/#b7 #be ,on the occasion when this lecture was given at the ,royal ,institution1 a large phonograph1 kindly lent by the ,edison-,bell ,phonograph ,company1 ,ltd41 of ,charing ,cross ,road1 ,london1 was employed to reproduce a short address on ,natural ,history to the young people present which had been spoken to the instrument ten days previously by ,lord ,avebury1 at the request of the author4 ,the address was heard perfectly by the five or six hundred persons comprising the audience4 #bf ,in the case of the paraffin prism the refracting angle 7i7 was #fj1 and the deviation of the ray 7d7 was #ej4 ,hence1 by the known optical formula for the index of refraction 7r71 we have-- r sin77i d7_/#b7_/sin7i_/#b7 sin7#ee7_/sin7#cj7 #afd ,for the ice prism the refracting angle was #ej1 and the deviation #ej2 accordingly for ice we have-- r sin77#ej #ej7_/b7_/sin7#ej_/b7 sin7#ej7_/sin7#be7 #ahh ,see 8,cantor ,lectures10 ,society of ,arts1 ,december #ag1 #aijj4 ,j4 ,a ,fleming on 8,electric ,oscillations and ,electric ,waves40 #bg ,see ,appendix1 ,note ,b4 ,,index4 ,a ,actinic rays1 #bed ther1 the1 #aia ----1 properties of1 #aib ---- wave radiation1 range of1 #bfb ---- waves1 various kinds of1 #bcd ,air1 movement of1 in a concert-room1 #ahc ---- necessary for production of sound1 #ajc ---- particles1 mode of motion of1 in case of sound wave1 #aab ---- waves1 #ajc ---- ----1 interference of1 #aci ---- ----1 length of1 #aad ---- ----1 nature of1 #aad ---- ----1 speed of1 #aae ,alphabet used in telegraphy1 #bgd ,america ,cup race1 pictures of yachts entered for the1 #id1 #ie ,america yacht1 the1 #ic ,amplitude1 #h ,anti-node1 #aei ,apparatus for detecting electric waves1 #bcg ---- for exhibiting motion of air in case of sound wave1 #aji ---- for investigating the laws of falling bodies1 #ce ,atlantic waves1 height of1 #h ---- ----1 length of1 #i ,atomic theory1 #bbf ,b ,beam of sound focused by collodion lens1 #aca ,beats1 ,helmholtz's theory of1 #afe ----1 musical1 #afc ,billows1 #a ,bore1 #ch ,branly1 ,professor1 electric wave detector1 #baa ,breaking wave1 #bi ,c ,canal-boat waves1 #ajj ,canal wave1 #cb ---- ---- velocity1 #cd ,capillary ripples1 #dd ,chromatic scale1 #afb ,clef1 musical1 #afj ,closed organ-pipe1 #aga ,cloud waves1 #cj ,coherer1 ,lodge1 #bab ----1 ,marconi1 #bgf ,column of air set in vibration by tuning-fork1 #aeh ,conclusion1 #bhe ,concords and discords in music1 nature of difference between1 #afb ----1 musical1 #afb ,conditions necessary for production of true wave in a medium1 #ae ,conductor1 electric1 #aig ,conservation of energy1 law of1 #bc ,conservation of matter1 law of1 #bb ,convergence of an electric ray by a paraffin lens1 #bdc ,cornish1 ,dr4 ,vaughan1 #ca ,corresponding speeds1 ,froude's law of1 #ha ,cup ,races1 #ic ,current1 electric1 #aic ,d ,dark heat1 #bej ,deep-sea waves1 rule for determining speed of1 #aa ---- ----1 velocity of1 #aa ,definition of a ripple1 #db ---- of wave-frequency1 #h ---- of wave-length1 #g ,depth of water1 effect of1 on speed of canal wave1 #cd ,difference between electric conductors and non-conductors1 #aih ---- between velocity of a wave and of a wave-train1 #bj ,discords in music1 #afb ,dispersion of ther waves1 #bef ,distances at which sound can be heard1 #abj ,e ,ear1 power of1 to analyze sound1 #ahb1 #ahc ,echelon waves made by a duck1 #gd ,eddies in liquids1 #fj ,eddy1 #fj ---- motion1 #fj ---- resistance1 #fh ,edison phonograph1 #adb ,elasticity of the air1 #aaa ,electric circuit1 open1 #bag ---- conductor and non-conductor1 #aig ---- corpuscles1 #bbg ---- current1 #aic ---- ----1 alternating1 #aid ---- ----1 continuous1 #aid ---- ---- energy1 #bae ---- ----1 nature of1 #aic ---- displacement1 #bba ---- energy1 mechanical analogue of1 #baf ---- force1 #bbh ,electric index of refraction1 #bde ---- inductance1 #bad ---- inertia1 #bad ---- oscillations1 #ahe ---- ----1 apparatus for producing1 #bjc ---- ---- in open circuit1 #bag1 #bah ---- ---- produced by discharge of ,leyden jar1 #bjj ---- radiation1 #bch ---- ---- and light1 identity in nature of1 #bea ---- radiation-detector 7,fleming71 #bbd ---- ---- 7,miller71 #bce ---- radiation1 velocity of1 #bdi ---- ray1 reflection of1 #bda ---- ----1 refraction of1 #bdc ---- strain1 #aig ---- transparency and opacity1 #bci1 #bdj ---- wave and air wave compared1 #bbc ---- ---- detector1 #baj ---- ----1 nature of1 #bcj ---- ----1 production of1 #bji ---- waves1 #ahe ,electrical or ,hertz rays1 #bed ,electrodeless discharge1 #bje ---- ----1 apparatus for producing1 #bjf ,electro-magnet1 #aie ,electro-magnetic medium1 #bbj ---- theory of light1 #bfb ,electromotive force1 #aif ,electronic theory of electricity1 #bbi ,electrons1 #bbg ,energy1 #ba ----1 kinetic1 #be ---- of electro-static strain1 #bae ---- of motion1 #be ---- of moving water1 #cb ----1 potential1 #be ----1 two forms of electric1 #bae ,ether1 the1 #aia ,experimental tank1 uses of1 in ship-design1 #hf ---- tanks1 #he1 #hf ,experiments illustrating surface tension1 #dj1 #da ,explosion of guns heard at great distances1 #abj ,f ,falling bodies1 laws of1 #ce ,fish1 motion of a1 #fg ,flame1 sensitive1 #abg ,flow of liquid in non-uniform tubes1 #ff ---- ---- in tubes1 #fe ---- ---- in uniform tubes1 #fe ,fog-signals1 #abc ----1 influence of wind upon distance at which they are heard1 #abd ----1 power absorbed in making1 #abe ,free period of vibration1 influence upon force required to move a body1 #aea1 #aeb ,froude1 ,mr4 ,william1 #ha ,froude's experimental tank1 #ha ---- experiments at ,torquay1 #ha ,g ,gamut1 #afj ---- of ther waves1 #bfj ,gravitation wave1 #dj ,ground swell1 #ca ,h ,harmonic curve1 #ajh ---- motion1 #ajg ,harmonics1 #aef ,hele-,shaw1 ,professor1 #fb ---- ----1 discovery of means of producing irrotational motion in liquids1 #fc ---- ----1 investigations on liquid motion1 #fc ,helmholtz's investigation into nature of musical tones1 #afg ---- theory of discords and concords1 #afe ,hertz oscillation1 #bjg ,hertz's researches4 ,experiments with electric waves1 apparatus for1 #bcd ,hughes1 ,professor1 investigations on electric waves1 made by1 #baj ,human ear1 the1 #aha ,hydraulic gradient1 #fe ,i ,illustration of difference between wave-velocity and wave-group velocity1 #bh ,inaudible sound1 #adj ,index of refraction1 #ed ,inductance1 #bad ,induction coil for wireless telegraphy1 #bfg ,inefficiency of present methods of manufacturing light1 #bfe ,inertia of the air1 #aaa ,interference of air waves1 #aci ---- of electric rays1 #bdh ---- of ripples and waves1 #dh ,irrotational motion1 #ei ,k ,kelvin1 ,lord1 investigations on ship waves1 #gg ,kinetic energy1 #be ,krakatoa1 eruption of1 #aaf ----1 sound produced by the eruption of1 #aaf ,l ,laplace1 calculation of1 concerning sound-velocity1 #fi ,law connecting velocity and pressure in liquid motion1 #fg ,length of wave1 definition of the term1 #g ,light1 velocity of1 #ahg1 #ahi ,liquid flow in constricted tube1 #ff ,lodge1 ,sir ,oliver1 coherer invented by1 #baa ,long wave1 #g ,longitudinal waves1 #g ,luminous efficiency1 #bfd ---- rays1 #bed ,m ,magnetic force1 #bbh ,major third in music1 #afa ,marconi coherer1 #bgf ---- aerial wire1 #bff ----1 experiments with wireless telegraphy across the ,atlantic by1 #bhj ---- system of wireless telegraphy1 #bgf1 #bgi ,matter1 #bb ,maxwell's electro-magnetic theory of light1 #bfb ,mechanical explanations of electrical phenomena1 #bbb ,methods of manufacturing light1 #bfe ,minor third in music1 #afa ,model illustrating longitudinal wave1 #aad ---- ---- nature of an air wave1 #aac ,models1 illustrating wave-motion1 #e1 #f ,morse alphabet1 #bgd ,motion1 harmonic1 #ajg ----1 irrotational1 #ei ---- of water in sea waves1 #c ----1 periodic1 #ajg ----1 rotational1 #ei ----1 vortex1 #ei ,movement of the air in the case of a sound wave1 #aab ,music1 theory of1 #aei ,musical beats1 #afc ---- scale1 notes of the1 #afj ---- tones and noises contrasted1 #aaj ---- ----1 sharp and flat1 #afa ,n ,natural period of vibration of a body1 #adh1 #aej ,node1 #aei ,non-conductor1 electric1 #aig ,non-resistance to body moving through perfect fluid1 #gb ,o ,octave1 #afj ,open electric circuit1 #bag ---- organ-pipe1 #aga ,optical proof that a sounding body is in vibration1 #aje1 #ajf ,organ-pipes1 construction of1 #afi1 #aga ----1 distribution of air-pressure in1 #agb ----1 overtones of1 #agc ----1 relation between length of pipe and length of wave1 #agc1 #agd ,oscillations1 electric1 #ahe ---- of a stretched string1 #aed ,oscillator1 ,hertz1 #bjg ,oscillatory electric sparks1 photographs of1 #bjb ,overtones1 #aef ,p ,pendulum1 isochronism of the1 #adi ,perfect fluid1 #ei ,periodic motion1 #ajg ---- time1 #i ,phonograph1 action of the1 #adb ,photographic study of the production of waves1 #af ,photographs of ripples on a mercury surface1 #ea ,plane wave1 #ee ,potential energy1 #be ,power required to propel ships1 #ij1 #ia ,prism for refracting a beam of sound1 #acf ,production of a sound wave1 #aaa ,q ,quality of sound1 #aae ,r ,radiation1 electric1 #bch ----1 nature of1 #bfc ---- of energy from the sun1 #bhd ,rayleigh1 ,lord1 an acoustic experiment with an open pipe by1 #agd ,receiver for wireless telegraphy 7,marconi71 #bge ,reflection of a beam of sound1 #acb1 #acc ---- of an electric ray1 #bda ---- of a wave1 #ee ---- of ripples1 #df1 #dg ,refraction1 explanation of1 #ec1 #ed ---- of a beam of sound1 #acc1 #acd ---- of an electric ray1 #bdc ---- ---- by an ice prism1 #bdb ---- of ripples1 #eb ,refractive index1 #ed ,relation of wave-velocity and wave-length1 #i ,relay1 telegraphic1 #bcf ,resistance curves of ships1 #ib ---- to a body moving through a fluid1 causes of the1 #fh ,resonance1 #adh ----1 an experiment on1 #aeh ,ripple and wave1 distinction between1 #dj ---- mark1 #cj ----1 reflection of a1 #de1 #df ----1 scientific definition of a1 #db ,ripples1 #a ----1 apparatus for producing1 #dc ----1 interference of1 #dh ----1 intersecting1 #di ---- in the air1 #ajc ---- on a lake1 photographs of1 #ai ----1 photography of1 #ea ----1 by ,j4 ,h4 ,vincent1 #ed ---- produced by stone thrown into water1 #ai ----1 velocity of1 #da1 #db1 #dc ,rotational motion1 #ei ,russell1 ,scott1 ,mr41 #ha ---- experiments of1 on canal-boat waves1 #aja ,s ,scale1 musical1 notes of the1 #afj ---- of equal temperament1 #afb ,sea waves1 #b ---- ----1 motion of1 #c ---- ----1 relation of velocity and length in case of1 #aj ,semitone1 #afa ,sensitive flame1 influence of sound upon a1 #abi ,severn bore1 #ch ,shamrock ,,ii41 trials of1 #ig ,ship bow wave1 mode of production1 #ge1 #gf ---- design1 #hg1 #hh ---- ----1 the problem of1 #gc ---- models1 the testing of1 #he1 #hf ---- resistance1 ,froude's law of1 #hb1 #hc ---- waves1 #eg ---- ----1 complete system of1 #gh ---- ----1 various systems of1 #gc ,short wave1 #g ,sine curve1 mode of drawing a1 #ajh ,singing flame1 #age ,siren1 #abc ,skin friction1 #ei1 #fh ---- ---- for various classes of ships1 #ia ,soap film thrown into vibration by air waves1 #ade ---- solution for making bubbles1 #add ,solitary wave1 #bf ---- ---- and wave-train1 difference between1 #bf ,sound1 and music1 #adg ----1 causes in variation in quality of1 #adb ---- due to air waves1 #ajc1 #ajd ---- lens1 method of making a1 #acj ---- prism1 #acf ----1 quality of1 #aae ---- signals1 #abc ----1 velocity of1 in various cases1 #abf ,sounding body is in vibration1 #ajd1 #aje ,speed of a falling body1 #ce ---- of sound1 #aae ,stationary waves1 #aee1 #aef ,stone falling into water1 photographs of a1 #ag ,stream-lines1 #fd ---- ---- round an ovoid1 #ga ,stroh violin1 #agi ,structure of the human ear1 #aha ,surface tension of liquid1 #dj ,t ,temperature1 effect of1 on sound-velocity1 #aah ,tesla coil1 #bje ,tidal wave1 #ch ---- ----1 speed of1 #ci ,tides1 #ci ,time of vibration of a stretched string1 #aed ,tone1 #afa ,torpedo1 motion of1 in water1 #fg ,transference of wave-motion1 #bg ,transverse ship wave1 #gi ---- wave1 #g ,true wave1 conditions for producing a1 #ae ---- ----1 definition of a1 #ab ,tubes of flow1 #fd ---- ---- in a liquid1 #ga ,u ,utilization of the ther1 #bhd ,v ,various kinds of resistance to a body moving through a fluid1 #fh ,velocity of electric radiation1 #bdi ---- of light1 #ahi ---- of sea waves1 rule for calculating the1 #aj ---- of sound1 how affected by temperature1 #aag ---- ---- in different gases1 #abf ---- ----1 influence of specific heats upon the1 #aai ---- ----1 measurements of the1 #aaf ---- ----1 theoretical determination of the1 #aah ---- of sound wave1 #aae ---- of waves in water1 air1 and ther compared1 #bhc ,vernon ,boys1 ,professor1 instructions by1 for making soap solution1 #add ,vibration rates of musical tones1 #afj ---- ---- of various ther waves1 #beb ,vibrations1 forced1 #adi ----1 free1 #adi ---- giving rise to musical tones1 #afj ,vincent1 ,mr4 ,j4 ,h41 #ea ,violin1 improved by ,mr4 ,augustus ,stroh1 #agi ,violin1 structure of1 #agg1 #agh ,viscosity of liquids1 #eh ,vortex motion1 #ei ---- ring in air1 #fa ---- ----1 production of1 in air1 #fa ,w ,wave amplitude1 definition of1 #h ----1 causes of breaking1 #bi ----1 electric1 nature of an1 #ahe ---- frequency1 #h ----1 gravitation1 #dj ---- group1 velocity of a1 #bj ---- length1 #g ---- lengths of various kinds of ther waves1 #beg ----1 longitudinal1 #g ---- motion1 #b ---- ----1 definition of1 #d ---- ---- model1 #e ---- ----1 model for illustrating1 #ac1 #ad ---- ----1 various kinds of1 #d ---- produced in a canal1 #cc ----1 reflection of a1 #ee1 #ef ---- resistance1 #fh ,waves1 #a ---- and ripples in the ther1 #bcb ----1 conditions of1 for interference of1 #di1 #ej ----1 electric1 #ahe ----1 interference of1 #dh ---- in the air1 #ajc ---- made by canal-boats1 experiments on1 #aja1 #ajb ---- made by ships1 #eg1 #eh ---- on a snow surface1 #ca ---- on clouds1 #cj ---- produced by high-speed ships1 #gi ----1 refraction of1 #eb1 #ec ----1 sea1 #b ----1 stationary1 #aee ---- train1 #bj ---- ----1 velocity of1 #bj ----1 transverse1 #g ---- velocity1 a rule for determining1 #i ,wind1 influence of1 upon distances at which sounds are heard1 #abj1 #aba1 #abb ,wireless telegraphy across the ,atlantic1 #bhj ---- ----1 apparatus for1 #bfg ---- ----1 explanation of1 #bgc ---- ----1 ,marconi's system of1 #bfi ---- ----1 method of conducting1 #bgd ---- ----1 transmitter for1 #bga ---- ----1 utility of1 #bha ,worthington1 ,professor1 photographs of splash of drop1 #af1 #ag ,y ,yacht-design1 object of1 #if ,yachts entered for the ,america ,cup race1 pictures of1 #id1 #ie ,young1 ,dr4 ,thomas1 investigations of1 on interference of light1 #aij ,,the ,,end4 ,,printed ,,by ,,william ,,clowes ,,and ,,sons1 ,,limited1 ,,london ,,and ,,beccles4 ---------------------------------- ,end of ,book ---------------------------------- ,transcriber's ,note 7continued7 ,errors in punctuation and simple typos have been corrected without note4 ,variations in spelling1 hyphenation1 accents1 etc41 have been left as they appear in the original publication unless as stated in the following3 ,page #ef - 8sea-side0 changed to 8seaside0 7,at the seaside7 ,page #ef - 8sea-side0 changed to 8seaside0 7study of seaside pools7 ,page #acf - 8sound ray0 changed to 8sound-ray0 in ,fig4 #ea caption ,page #ade - 8limelight0 changed to 8lime-light0 7lime-light lantern7 ,page #aef - 8over-tones0 changed to 8overtones0 7accompanied by the harmonics or overtones7 ,page #afb - 8key-board0 changed to 8keyboard0 7keyboard of a piano7 ,page #agf - 8arial0 changed to 8aerial0 7stationary aerial oscillation7 ,page #agg - 8horse-hair0 changed to 8horsehair0 7bow made of horsehair7 ,page #bgd - 8,full ,stop -- -- -- -- -- --0 changed to 8,full ,stop -- ------ -- ------ -- ------0 -------- ,footnotes have been re-indexed using numbers and placed before the ,index4 -------- ,large bracketing is not available to surround built-up fractions in displayed equations and expressions so ordinary bracketing and the solidus 7_/7 is used to represent them instead4 ,thus the built-up x #a fraction ---------- is rendered in this text in the conventional manner #b as 7x #a7_/b4 ,if the sin of that expression is required it would be rendered unambiguously as sin77x #a7_/b74 ,for consistency this also means that a simple sin function that would normally be displayed as #8sin x' will instead be rendered as #8sin7x7'4 ,a large radical 77 symbol is not available either so in order to make the radicand expression unambiguous a similar approach to the above is used4 x #a ,thus the square root of the fraction ---------- is rendered in this text as #b 77x #a7_/b74 ,again this means that1 for consistency1 the simple square root of1 say1 the natural number #e1 which would normally be displayed as #8#e' will instead be rendered as #87#e7'4 ,in other expressions and equations some additional bracketing may have been added to make the meaning clear and unambiguous or consistent with bracketing as used in immediately surrounding equations and expressions4