,,radiation ,,by ,p4 ,,phillips ,d4,sc4 7,b',,ham71 ,b4,sc4 7,,london71 ,b4,a4 7,,cantab47 ,,london3 ,t4 ,c4 ,e4 ,c4 ,,jack #fg ,,long ,,acre1 ,w4,c41 ,,and ,,edinburgh ,,new ,,york3 ,,dodge ,,publishing ,,co4 #aiab ,,contents ,,chap4 ,,introduction ,i4 ,,the ,,nature ,,of ,,radiant ,,heat ,,and ,,light ,,ii4 ,,graphic ,,representation ,,of ,,waves ,,iii4 ,,the ,,meaning ,,of ,,the ,,spectrum ,,iv4 ,,the ,,laws ,,of ,,radiation ,v4 ,,full ,,radiation ,,vi4 ,,the ,,transformation ,,of ,,absorbed ,,radiation ,,vii4 ,,pressure ,,of ,,radiation ,,viii4 ,,the ,,relation ,,between ,,radiant ,,heat ,,and ,,electric ,,waves ,,index vii ,,introduction ,we are so familiar with the restlessness of the sea1 and with the havoc which it works on our shipping and our coasts1 that we need no demonstration to convince us that waves can carry energy from one place to another4 ,few of us1 however1 realise that the energy in the sea is as nothing compared with that in the space around us1 yet such is the conclusion to which we are led by an enormous amount of experimental evidence4 ,the sea waves are only near the surface and the effect of the wildest storm penetrates but a few yards below the surface1 while the waves which carry light and heat to us from the sun fill the whole space about us and bring to the earth a continuous stream of energy year in year out equal to more than #cjj million million horsepower4 ,the most important part of the study of ,radiation of energy is the investigation of the characters of the waves which constitute heat and light1 but there is another method of transference of energy included in the term ,radiation2 the source of the energy behaves like a battery of guns pointing in all directions and pouring out a continuous hail of bullets1 which strike against obstacles and so give up the energy due to their motion4 ,this method is relatively unimportant1 and is usually treated of separately when considering the subject of ,radioactivity4 ,we shall therefore not consider it in this book4 #i ,,radiation ,,chapter ,i ,,the ,,nature ,,of ,,radiant ,,heat ,,and ,,light ,similarity of ,heat and ,light4--,that light and heat have essentially the same characters is very soon made evident4 ,both light and heat travel to us from the sun across the ninety odd millions of miles of space unoccupied by any material4 ,illustration3 ,figure #a ,both are reflected in the same way from reflecting surfaces4 ,thus if two parabolic mirrors be placed facing each other as in the diagram 7,fig4 #a71 with a source of light ,l at the focus of one of them1 an inverted image of the light will be formed at the focus ,i of the other one1 and may be received on a small screen placed there4 ,the paths of two of the rays are shown by the dotted lines4 ,if ,l be now replaced by a heated ball and a#a blackened thermometer bulb be placed at ,i1 the thermometer will indicate a sharp rise of temperature1 showing that the rays of heat are focussed there as well as the rays of light4 #a ,see page #cg4 #aj ,both heat and light behave in the same way in passing from one transparent substance to another1 e4g4 from air into glass4 ,this can be readily shown by forming images of sources of heat and of light by means of a convex lens1 as in the diagram 7,fig4 #b74 ,illustration3 ,,fig4 #b4 ,the source of light is represented as an electric light bulb1 and two of the rays going to form the image of the point of the bulb are represented by the dotted lines4 ,the image is also dotted and can be received on a screen placed in that position4 ,if now the electric light bulb be replaced by a heated ball or some other source of heat1 we find by using a blackened thermometer bulb again that the rays of heat are brought to a focus at almost the same position as the rays of light4 ,the points of similarity between radiant heat and light might be multiplied indefinitely1 but as a number of them will appear in the course of the book these few fundamental ones will suffice at this point4 ,the ,corpuscular ,theory4--,a little over a century ago everyone believed light to consist of almost inconceivably small particles or corpuscles shooting out at enormous speed from every luminous surface and causing the sensation of sight when impinging #aa on the retina4 ,this was the corpuscular theory4 ,it readily explains why light travels in straight lines in a homogeneous medium1 and it can be made to explain reflection and refraction4 ,reflection4--,to explain reflection1 it is supposed that the reflector repels the particles as they approach it1 and so the path of one particle would be like that indicated by the dotted line in the diagram 7,fig4 #c74 ,illustration3 ,,fig4 #c4 ,until reaching the point ,a we suppose that the particle does not feel appreciably the repulsion of the surface4 ,after ,a the repulsion bends the path of the particle round until ,b is reached1 and after ,b the repulsion becomes inappreciable again4 ,the effect is the same as a perfectly elastic ball bouncing on a perfectly smooth surface1 and consequently the angle to the surface at which the corpuscle comes up is equal to the angle at which it departs4 ,refraction4--,to explain refraction1 it is supposed that when the corpuscle comes very close to the surface of the transparent substance it is attracted by the denser substance1 e4g4 glass1 more than by the lighter substance1 e4g4 air4 ,thus a particle moving along the dotted line in air 7,fig4 #d7 would reach the #ab point ,a before the attraction becomes appreciable1 and therefore would be moving in a straight line4 ,between ,a and ,b the attraction of the glass will be felt and will therefore pull the particle round in the path indicated4 ,beyond ,b1 the attraction again becomes inappreciable1 because the glass will attract the particle equally in all directions1 and therefore the path will again become a straight line4 ,we notice that by this process the direction of the path has become more nearly normal to the surface1 and this is as it should be4 ,further1 by treating the angles between the two paths and the normal mathematically we may deduce the laws of refraction which have been obtained experimentally4 ,one other important point should be noticed4 ,since the surface has been attracting the particle between ,a and ,b the speed of the particle will be greater in the glass than in the air4 ,illustration3 ,,fig4 #d ,ejection and ,refraction at the same ,surface4--,a difficulty very soon arises from the fact that at nearly all transparent surfaces some light is reflected and some refracted4 ,how can the same surface sometimes repel and sometimes attract a corpuscle8 ,newton surmounted this difficulty by attributing a polarity to each particle1 so that one end was repelled and the other attracted by the reflecting and refracting #ac surface4 ,thus1 whether a particle was reflected or refracted depended simply upon which end happened to be foremost at the time4 ,by attributing suitable characteristics to the corpuscles1 ,newton with his superhuman ingenuity was able to account for all the known facts1 and as the corpuscles were so small that direct observation was impossible1 and as ,newton's authority was so great1 there was no one to say him nay4 ,wave ,theory4 ,rectilinear ,propagation4--,true1 ,huyghens in #afgh had propounded the theory that light consists of waves of some sort starting out from the luminous body1 and he had shown how readily it expressed a number of the observed facts2 but light travels in straight lines1 or appears to do so1 and waves bend round corners and no one at that time was able to explain the discrepancy4 ,thus for nearly a century the theory which was to be universally accepted remained lifeless and discredited4 ,the answer of the wave theory to the objection now is1 that light does bend round corners though only slightly and that the smallness of the bend is quite simply due to the extreme shortness of the light waves4 ,the longer waves are1 the more they bend round corners4 ,this can be noticed in any harbour with a tortuous entrance1 for the small choppy waves are practically all cut off whereas a considerable amount of the long swell manages to get into the harbour4 ,interference of ,light4 ,illustration by ,ripples4--,the revival of the wave theory dates from the discovery by ,dr4 ,young of the phenomenon of interference of light4 ,in order to understand this we will #ad consider the same effect in the ripples on the surface of mercury4 ,a tuning-fork1 ,t 7,fig4 #e71 has two small styles1 ,s ,s1 placed a little distance apart and dipping into the mercury contained in a large shallow trough4 ,when the tuning-fork is set into vibration1 the two styles will move up and down in the mercury at exactly the same time and each will start a system of ripples exactly similar to the other4 ,at any instant each system will be a series of concentric circles with its centre at the style1 and the crests of the ripples will be at equal distance from each other with the troughs half-way between the crests4 ,illustration3 ,,fig4 #e4 ,the ripples from one style will cross those from the other1 and a curious pattern1 something like that in ,fig4 #f1 will be formed on the mercury4 ,s ,s represents the position of the two styles1 while the plain circles denote the positions of the crests and the dotted circles the positions of the troughs at any instant4 ,where two plain circles cross it is evident that both systems of ripples are producing a crest1 and so the two produce an exaggerated crest4 ,similarly where two dotted circles cross an exaggerated trough is produced4 ,thus in the shaded portions of the diagram we get more violent ripples than those due to a single style4 ,where a plain circle cuts a dotted one1 however1 one system of ripples produces a #ae crest and the other a trough1 and between them the mercury is neither depressed below nor raised above its normal level4 ,at these points1 therefore1 the effect of one series of ripples is just neutralised by the effect of the other and no ripples are produced at all4 ,this occurs in the unshaded regions of the diagram4 ,the mutual destruction of the effects of the two sets of waves is ,interference4 ,illustration3 ,,fig4 #f4 ,now imagine a row of little floats placed along the line ,,edcbabcde4 ,at the lettered points the floats will be violently agitated1 but at the points midway between the letters they will be unmoved4 ,this exactly represents the effect of two interfering sources of light ,s1 ,s1 sending light which is received by a screen at the dotted line ,,edcbabcde4 ,the lettered points will be brightly illuminated while the intermediate points will be dark4 ,in practice it is found impossible to make two #af sources of light whose vibrations start at exactly the same time and are exactly similar1 but this difficulty is surmounted by using one source of light and splitting the waves from it into two portions which interfere4 ,young's ,experiment4--,dr4 ,young's arrangement is diagrammatically represented in ,fig4 #g4 ,light of a certain wave length is admitted at a narrow slit ,s1 and is intercepted by a screen in which there are two narrow slits ,a and ,b parallel to the first one4 ,illustration3 ,,fig4 #g4 ,a screen receives the light emerging from the two slits4 ,if the old corpuscular theory were true there would be two bright bands of light1 the one at ,p and the other at ,q1 but instead ,dr4 ,young observed a whole series of parallel bright bands with dark spaces in between them4 ,evidently the two small fractions of the original waves which pass through ,a and ,b spread out from ,a and ,b and interfere just as if they were independent sources like the two styles in the mercury ripples experiment4 #ag ,speed of ,light in ,rare and ,dense ,media4--,the discovery of interference again brought the wave theory into prominence1 and in #ahej the death-blow was given to the corpuscular theory by ,foucault1 who showed that light travels more slowly in a dense medium such as glass or water than in a light medium such as air4 ,this is what the wave theory anticipates1 while the reverse is anticipated by the corpuscular theory4 ,but if light and heat consist of waves1 what kind of waves are they and how are they produced8 ,elastic ,solid ,theory4--,in the earlier days of the wave theory it was supposed that the whole of space was filled with something which acted like an elastic solid material in which the vibrations of the atoms of a luminous body started waves in all directions1 just as the vibrations of a marble embedded in a jelly would send out waves through the jelly4 ,these waves are quite easily imagined in the following way4 ,if one end of an elastic string be made to oscillate to and fro a series of waves travels along the string4 ,if a large number of these strings are attached to an oscillating point and stretch out in all directions1 the waves will travel along each string1 and if the strings are all exactly alike will travel at the same speed along all of them4 ,any particular crest of a wave will thus at any instant lie on the surface of a sphere whose centre is the oscillating point4 ,if now we imagine that the strings are so numerous that they fill the whole of the space we have a conception of the transmission of waves by an elastic solid4 ,electromagnetic ,waves4--,since ,maxwell published #ah his electromagnetic theory in #ahgc it has been universally held that heat and light consist of electro-magnetic waves4 ,these are by no means so easy to imagine as the elastic waves1 as there is no actual movement of the medium2 an alternating condition of the medium is carried onward1 not an oscillation of position4 ,when a stick of sealing-wax or ebonite is rubbed with flannel it becomes possessed of certain properties which it did not have before4 ,it will attract light pieces of paper or pith that are brought near to it1 it will repel a similar rubbed piece of sealing-wax or ebonite and will attract a rod of quartz which has been rubbed with silk4 ,the quartz rod which has been rubbed with silk has the same property of attracting light bodies which the ebonite and sealing-wax rod has1 but it repels another rubbed quartz rod and attracts a rubbed ebonite or sealing-wax rod4 ,positive and ,negative ,electrification4--,the ebonite is said to be negatively electrified and the quartz positively electrified4 ,when the two rods1 one positively and the other negatively electrified1 are placed near to one another1 we may imagine the attraction to be due to their being joined by stretched strings filling up all the space around them4 ,if a very small positively electrified body be placed between the two it will tend to move from the quartz to the ebonite1 i4e4 in the direction of the arrows4 ,illustration3 ,,fig4 #h4 ,the ,electric ,field4 ,lines of ,force4--,the space #ai surrounding the electrified sticks in which the forces due to them are appreciable is called the electric field1 and the direction in which a small positively electrified particle tends to move is called the direction of the field4 ,the lines along which the small positive charge would move are called lines of force4 ,the conception of the electric field as made up of stretched elastic strings is1 of course1 a very crude one1 but there is evidently some change in the medium in the electric field which is somewhat analogous to it4 ,illustration3 ,,fig4 #i4 ,electric ,oscillations4--,if the position of the two rods is reversed1 then of course the direction of the field at a point between them is reversed1 and if this reversal is repeated rapidly1 we shall have the direction of the field alternating rapidly4 ,if these alternations become sufficiently rapid they are conveyed outwards in much the same way as the oscillations of position are conveyed in an ordinary ripple4 ,thus suppose the two rods are suddenly placed in the position in the diagram4 ,the field is not established instantaneously1 the lines of force taking a short time to establish themselves in their ultimate positions4 ,during this time the lines of force will be travelling outwards to ,a in the direction of the dotted arrow4 #bj ,before they reach ,a let us suppose that the position of the rods is reversed4 ,then the direction of the lines is reversed and these reversed lines will travel outwards towards ,a1 following in the track of the original lines4 ,thus a continuous procession of lines of force1 first in one direction and then in the opposite direction1 will be moving out perpendicular to themselves in the direction of the dotted arrow4 ,this constitutes an electric wave4 ,magnetic ,oscillation1 ,lines of ,force1 and ,field4--,almost exactly the same kind of description applies to a magnetic wave4 ,the space near to the ,north and ,south poles of a magnet is modified in somewhat the same way as that between the electrified rods1 and the magnetic lines of force are the lines along which a small ,north magnetic pole would move4 ,we may imagine a rapid alternation of the magnetic field by the rapid reversal of the positions of the ,north and ,south poles1 and we may imagine the transmission of the alternations by means of the procession of magnetic lines of force4 ,changes in ,magnetic ,field4--,but experiment shows that whenever the magnetic field at any place is changing an electric field is produced during the alteration1 and vice-versa4 ,electric and magnetic waves must therefore always accompany one another1 and the two sets of waves together constitute electro-magnetic waves4 ,these are the waves which a huge amount of experimental evidence leads us to believe constitute heat1 light1 the electric waves used in wireless telegraphy1 #ba and the invisible ultraviolet waves which are so active in inducing chemical action4 ,oscillation of ,electric ,charges within the ,atom4--,we have seen how these waves might be produced by the oscillation of two electrified rods1 and it is supposed that the light coming from luminous bodies is produced in a similar way4 ,there are many reasons for believing that there exist in the atoms of all substances1 minute negatively electrified particles which may rotate in small orbits or oscillate to and fro within the atom4 ,there also exists an equal positive charge within the atom4 ,as the negative particles rotate or oscillate in the atom1 it is evident that the field between them and the positively electrified part of the atom alternates1 and so electro-magnetic waves are sent out4 #bb ,,chapter ,,ii ,,graphic ,,representation ,,of ,,waves ,a system of ripples on the surface of water appears in vertical section at any instant somewhat as in ,fig4 #aj4 ,the dotted line ,,ab represents the undisturbed surface of the wafer1 and the solid line the actual surface4 ,if the disturbance which is causing the ripples is an oscillation of perfectly regular period the individual ripples will be all alike1 except they will get shallower as they become more remote from the disturbance4 ,illustration3 ,,fig4 #aj4 ,wave-length4--,the distance between two successive crests will be the same everywhere1 and this distance or the distance between any two corresponding points on two successive ripples is called the wave-length4 ,evidently1 the wave-length is the distance in which the whole wave repeats itself4 ,phase4--,the position of a point in the wave is called the phase of the point4 ,thus the difference of phase between the two points ,a and ,c is a quarter #bc of a wave-length4 ,as the waves move on along the surface it is evident that each drop of water executes an up and down oscillation1 and at the points ,c1 ,c the drop has reached its highest position and at the points ,t1 ,t its lowest4 ,amplitude4--,the largest displacement of the drop1 i4e4 the distance from the dotted line to ,c or to ,t1 is called the amplitude of the wave4 ,the time taken for a drop to complete one whole oscillation1 i4e4 the time taken for a wave to travel one whole wave-length forward1 is called the period of the wave4 ,the number of oscillations in one second1 i4e4 the number of wave-lengths travelled in one second1 is called the frequency4 ,illustration3 ,,fig4 #aa4 ,although there is no visible displacement in the waves of light and heat1 yet we may represent them in much the same way4 ,thus if ,,ab1 ,fig4 #aj1 represents the line along which a ray of light is travelling1 the length ,,np is drawn to scale to represent the value of the electric field at the point ,n1 and is drawn upwards from the line ,,ab when the field is in one direction and downwards when it is in the opposite direction4 ,thus the direction of the field at different points in the wave ,,xy1 ,fig4 #aa1 is shown by the dotted arrows as if due to electrified rods of quartz and ebonite placed above and below ,,xy4 ,in the case of the electromagnetic wave1 the #bd amplitude will be the maximum value to which the electric field attains in either direction1 and the other terms--wave-length1 phase1 period and frequency--will have the same meaning as for water ripples4 ,wave ,form4--,waves not only differ in amplitude1 wave-length1 and frequency1 but also in wave form4 ,waves may have any form1 e4g4 ,fig #ab4 ,or we may have a solitary irregular disturbance such as is caused by the splash of a stone in water4 ,illustration3 ,,fig4 #ab4 ,but there is one form of motion of a particle in a wave which is looked upon as the simplest and fundamental form4 ,it is that form which is executed by the bob of a pendulum1 the balance wheel of a watch1 the prong of a tuning-fork1 and most other vibrations where the controlling force is provided by a spring or by some other elastic solid4 ,it is called ,simple ,harmonic ,motion or ,simple ,periodic ,motion1 and the essential feature of it is that the force restoring the displaced particle to its undisturbed position is proportional to its displacement from the undisturbed position4 ,a wave in which all the particles execute simple harmonic motion has the form in ,fig4 #aj or ,fig4 #aa1 which is therefore looked upon as the fundamental wave form or simple wave form4 ,simple waves will vary only in amplitude1 wave-length1 and frequency1 and the energy in the wave will depend upon these quantities4 #be ,energy in a ,simple ,wave4--,if the velocity is the same for all wave-lengths1 then the frequency will evidently be inversely proportional to the wave-length and the energy will depend upon the amplitude and the wave-length4 ,the kinetic energy of any moving body1 i4e4 the energy due to its motion1 is proportional to the square of its velocity1 and we may apply this to the motion of the particles in a wave and to show how the energy depends upon the amplitude and wave-length4 ,since the distance travelled by a particle in a single period of the wave will be equal to four times the amplitude1 the velocity at any point in the wave must be proportional to the amplitude and therefore the kinetic energy is proportional to the square of the amplitude4 ,with the same amplitude but with different wave-lengths1 we see that the time in which the oscillation is completed is proportional to the wave-length and that the velocity is therefore inversely proportional to the wave-length4 ,the kinetic energy is therefore inversely proportional to the square of the wave-length4 ,addition of ,waves4--,the superposition of two waves so as to obtain the effect of both waves at the same place is carried out very simply4 ,the displacements at any point due to the two waves separately are algebraically added together1 and this sum is the actual displacement4 ,in ,fig4 #ac the dotted lines represent two simple waves1 one of which has double the wave-length of the other4 ,at any point ,p on the solid line1 the displacement ,,pn is equal to #bf the algebraic sum of the displacement ,,nq due to one of the waves and ,,nr due to the other4 ,the solid line1 therefore1 represents the resulting wave4 ,we may repeat this process for any number of simple waves1 and by suitably choosing the wave-length and amplitude of the simple waves we may build up any desired form of wave4 ,the mathematician ,fourier has shown that any form of wave1 even the single irregular disturbance1 can thus be expressed as the sum of a series of simple waves and that the wave-lengths of these simple waves are equal to the original wave-length1 one-half of it1 one-third1 one-quarter1 one-fifth1 and so on in an infinite series4 ,fourier has also shown that only one such series is possible for any particular form of wave4 ,illustration3 ,,fig4 #ac4 ,the importance of this mathematical expression lies in the fact that in a number of ways ,fourier's series of simple waves is manufactured from the original wave and the different members of the series become separated4 ,thus the most useful way in which we can represent any wave is1 not to draw the actual form of a wave1 but to represent what simple waves go to form it and to show how much energy there is in each particular simple wave4 #bg ,energy--,wave-length ,curve4--,this can be done quite simply as in ,fig4 #ad4 ,the distance ,,pn from the line ,,oa being drawn to scale to represent the energy in the simple wave whose length is represented by ,,on4 ,illustration3 ,,fig4 #ad4 ,thus the simple wave of length ,,ox has the greatest amount of energy in it4 ,illustration3 ,,fig4 #ae4 ,fig4 #ae wall represent a simple wave of wave-length ,,ox1 the energy in all the other waves being zero4 #bh ,the three curves given in ,fig4 #af give a comparison of the waves from the sun1 an arc lamp1 and an ordinary gas-burner4 ,illustration3 ,,fig4 #af4 #bi ,,chapter ,,iii ,,the ,,meaning ,,of ,,the ,,spectrum ,the ,spectrum4 ,dispersion4--,when a narrow beam of white light is transmitted through a prism of glass or of any other transparent substance1 it is deflected from its original direction and is at the same time spread out into a small fan of rays instead of remaining a single ray4 ,if a screen is placed in the path of these rays a coloured band is formed on it1 the least deflected part of the band being red and the colours ranging from red through orange1 yellow1 green1 blue1 and indigo1 to violet at the most deflected end of the band4 ,this band of colours is called the spectrum of the white light used1 and the spreading out of the rays is called dispersion4 ,newton's ,experiment4--,newton first discovered this fact with an arrangement like that in ,fig4 #ag4 ,illustration3 ,,fig4 #ag4 ,if by any means the fan of coloured rays be combined again into a single beam1 white light is reformed1 and ,newton therefore came to the conclusion that white light was a mixture of the various colours in the spectrum1 and that the only function of the prism was to separate the constituents4 ,of the nature of the constituents ,newton had little knowledge1 since he had rejected the wave theory1 which could alone give the clue4 #cj ,we now believe that white light is an irregular wave1 and that the prism manufactures from it the ,fourier's series of waves to which it is equivalent4 ,it is supposed that the manufacture is effected by means of the principle of resonance4 ,as an example of resonance let a small tap be given to a pendulum just as it commences each swing4 ,then because the taps are so timed that each of them increases the swing of the pendulum by a small amount1 they will very soon cause the pendulum to swing very violently even though the effect of a single tap can scarcely be detected at all4 ,thus when any body which has a free period of vibration is subject to periodic impulses of the same period as its own1 it will vibrate very vigorously and absorb nearly all the energy of the impulses4 ,electrons and their ,vibrations4--,there is conclusive evidence to show that in the atoms of all substances1 and therefore of the glass of which the prism is composed1 there are a number of minute negatively electrified particles which are called electrons4 ,these are held in position by a positive charge on the rest of the #ca atom1 and if they are displaced from their usual positions by any means they will vibrate about these positions4 ,the time of vibration of the electron will depend upon its position in the atom and upon the position of neighbouring atoms4 ,in solid or liquid bodies the neighbouring atoms are so near that they have a considerable influence in modifying the period of an electron or a system of electrons1 and consequently we may find almost any period of vibration in one or other of these electrons or systems4 ,as the wave of light with its alternating electric fields comes up to the prism1 the field will first displace the electrons in one direction and then in the other1 and so on4 ,if the period of one particular type of electron happens to coincide with the period of the wave1 that electron will vibrate violently and will in its turn send out a series of waves in the glass4 ,if the wave is an irregular one it will start all the electrons vibrating1 but those electrons will vibrate most violently whose periods are equal to the periods of the ,fourier's constituents which have the greatest energy4 ,thus we shall actually have the ,fourier's constituent waves separated into the vibrations of different electrons4 ,but the speed with which any simple wave travels in glass or in any transparent medium1 other than a vacuum1 is dependent upon its period4 ,the shorter the period1 i4e4 the shorter the wave-length1 the slower is the speed in most transparent substances4 ,but the slower the speed in the prism the more is the ray deviated1 and therefore we conclude that the violet end of the spectrum consists of the shortest waves while the red end consists of the #cb longest waves1 and that the different parts of the spectrum are simple waves of different period4 ,the ,whole ,spectrum4--,the visible spectrum is by no means the whole of the series of ,fourier's waves1 however4 ,the eye is sensitive only to a very small range of period1 while there exists in sunlight a range many times as great4 ,those waves of shorter period than the violet end of the visible spectrum will be deviated even more than the violet1 and will therefore be beyond the violet4 ,they are called the ultra violet rays1 and can easily be detected by means of their chemical activity4 ,they cause a number of substances to glow1 and therefore by coating the screen on which the spectrum is received with one of these substances1 the violet end of the spectrum is extended by this glow4 ,the waves of longer period than the red rays will be deviated less than the red1 and will therefore lie beyond the red end of the visible spectrum4 ,they are called the infra-red rays1 and are chiefly remarkable for their heating effect4 ,all the rays are absorbed when they fall on to a perfectly dull1 black surface1 and their energy is converted into heat4 ,this heating effect provides the best way of measuring the energy in the different parts of the spectrum1 and of thus constructing curves similar to those given in ,fig4 #af4 ,the instrument moat commonly used is called ,langley's bolometer4 ,it consists of a fine strip of blackened platinum1 which can be placed in any part of the spectrum at will and thus absorb the waves over a very small range of wave-length4 ,it is heated by #cc them1 and the rise in temperature is found by measuring the electrical resistance of the strip4 ,the electrical resistance of all conductors varies with the temperature1 and since resistance can be measured with extreme accuracy this forms a very sensitive and accurate method4 ,spectrum of an ,incandescent ,solid or ,liquid4--,the spectra given by different sources of light show certain marked differences4 ,an incandescent solid or liquid gives a continuous spectrum1 i4e4 all the different wave-lengths are represented1 but the part of the spectrum which has the greatest energy is different for different substances and for different temperatures3 cf4 arc and gas flame in ,fig4 #af4 ,this is quite in keeping with the idea already suggested that in solids and liquids there are electrons of almost every period of vibration4 ,when they are agitated by being heated1 a mixture of simple waves of all periods will be sent out giving a very irregular wave4 ,gases may also become incandescent4 ,thus when any compound of sodium is put into a colourless flame the flame becomes coloured an intense yellow4 ,this is due to the vapour of sodium1 and the agitation of the electrons in it is probably due to the chemical action in which the compound is split up into sodium and some other parts4 ,we may also make the gas incandescent by enclosing it at low pressure in a vacuum tube and passing an electrical discharge through it4 ,the glow in the tube gives the spectrum of the gas4 ,incandescent gases give a very characteristic kind of spectrum4 #cd ,it consists usually of a limited number of narrow lines1 the rest of the spectrum being almost perfectly dark4 ,the light therefore consists of a few simple waves of perfectly definite period4 ,this would suggest that in the atom of a gas there are only a few electrons which are concerned in the emission of the light waves4 ,thus the spectra of gases and of incandescent solids are represented in character by the curves in ,fig4 #ah4 ,illustration3 ,,fig4 #ah4 ,spectrum ,analysis4--,the lines in a gas spectrum are so sharply defined and are so definitely characteristic of the particular gas that they serve as a delicate method of detecting the presence of some elements4 ,these spectra which are emitted by incandescent bodies are called emission spectra4 ,but not only do different materials emit different kinds of light when raised to incandescence1 but they also absorb light differently when it passes through them4 ,when white light is passed through some transparent solids or liquids and then through a prism1 it is found that whole regions of the spectrum are absent4 ,thus a potassium permanganate solution #ce which is not too concentrated absorbs the whole of the middle part of the spectrum1 allowing the red and blue rays to pass through4 ,since with solids and liquids the absorbed regions are large and somewhat ill-defined1 the absorption spectra are not of any great use in the detection of substances4 ,the absorption spectra of gases show the same sharply defined characteristics as the emission spectra4 ,thus if white light from an arc lamp passes through a flame coloured yellow with sodium vapour1 the spectrum of the issuing light has two sharply defined narrow dark lines close together in the yellow part of the spectrum in exactly the same position as the two bright yellow lines which incandescent sodium vapour itself gives out4 ,the flame has therefore absorbed just those waves which it gives out4 ,this is perfectly general1 and applies to solids and liquids as well as to gases4 ,it is perfectly in keeping with our view of the refraction of light by the resonance of electrons to the ,fourier's constituents which have the same period4 ,for if the electrons have a certain period of vibration they will resound to waves of that period and therefore absorb their energy4 ,spectrum of the ,sun4--,one of the most interesting examples of the absorption by incandescent gases of their own characteristic lines is provided by the sun4 ,the spectrum of the sun is crossed by a large number of fine dark lines which were mapped out by ,fraunhfer and are therefore called ,fraunhfer lines4 ,these lines are found to be in the position of the characteristic lines of a number of known elements1 #cf and therefore we assume that these elements are present in the sun4 ,the interior of the sun is liquid or solid owing to the pressure of the mass round it4 ,it therefore emits a continuous spectrum4 ,but the light has to pass through the outer layers of incandescent vapour1 and these layers absorb from the light their characteristic waves and so produce the dark lines in the spectrum4 ,the spectra of stars show similar characters to those of the sun1 and therefore we assume them to be in the same condition as the sun4 ,the spectra of nebul consist only of bright lines1 and we therefore assume that nebul consist of incandescent masses of gas which have not yet cooled enough to have liquid or solid nuclei4 #cg ,,chapter ,,iv ,,the ,,laws ,,of ,,radiation ,absorbing ,power4--,a perfectly dull black surface is simply one which absorbs all the light which is falling on it and reflects or diffuses none of it back4 ,if the surface absorbs the heat as well as the light completely1 it is called a perfect or full absorber4 ,other surfaces merely absorb a fraction of the heat and light falling on them1 and this fraction1 expressed usually as a percentage1 is called the absorbing power of the surface4 ,the absorbing powers of different kinds of surfaces can be measured in a great many ways1 but the following may be taken as fairly typical4 ,a perfectly steady beam of heat and light is made to fall on a small metallic disc1 and the amount of heat which is absorbed per second is calculated from the mass of the metal and the rate at which its temperature rises4 ,the disc is first coated with lamp-black1 and the rate at which it then receives heat is taken as the rate at which a full absorber absorbs heat under these conditions4 ,the disc is then coated with the surface whose absorbing power is to be measured1 and the experiment is repeated4 ,then the rate at which heat is received in the second case divided by the rate at which it is received in the first is the absorbing power of the second surface4 #ch ,experiments with a large number of surfaces show that the lighter in colour and the more polished is the surface1 the smaller is its absorbing power4 ,radiating ,power4--,but the character of the surface affects not only the rate at which heat and light are absorbed1 but also the rate at which they are emitted4 ,for example1 if we heat a fragment of a willow pattern china plate in a blowpipe flame until it is bright red hot1 we shall notice that the dark pattern now stands out brighter than the rest4 ,thus the dark pattern1 which absorbs more of the light which falls on it when it is cold1 emits more light than the rest of the plate when it is hot4 ,this is one example of a general rule1 for it is found that the most perfect absorbers are the greatest radiators1 and vice-versa4 ,the perfectly black surface is therefore taken as a standard in measuring the heat and light emitted by surfaces1 in exactly the same way as for heat and light absorbed4 ,thus the emissive or radiating power of a surface is defined as the quantity of heat radiated per second by the surface divided by the amount radiated per second by a perfectly black surface under the same conditions4 ,as it is somewhat paradoxical to call a surface a perfectly black surface when it may even be white hot1 the term a full radiator has been suggested as an alternative and will be used in this book4 ,illustration3 ,,fig4 #ai ,relation between ,absorbing and ,radiating ,powers4--,the exact relation between the absorbing and radiating powers of a surface was first determined by ,ritchie by means of an ingenious experiment4 ,two equal air-tight metal chambers ,a and ,b were connected by a glass tube bent twice at right angles as #ci in ,fig4 #ai4 ,a drop of mercury in the horizontal part of this tube acted as an indicator4 ,when one of the vessels became hotter than the other1 the air in it expanded and the mercury index moved towards the colder side4 ,between the two metal chambers a third equal one was mounted which could be heated up by pouring boiling water into it and could thus act as a radiator to the other two4 ,one surface of this radiator was coated with lamp-black and the opposite one with the surface under investigation1 e4g4 cinnabar4 ,the inner surfaces of the other two vessels were coated in the same way1 the one with lamp-black1 the other with cinnabar4 ,the middle vessel was first placed so that the lamp-blacked surface was opposite to a cinnabar one1 and vice-versa4 ,in this position1 when hot water was poured into it no movement of the mercury drop was detected1 and therefore the amounts of heat received by the two outer vessels must have been exactly equal4 ,on the one side the heat given out by the cinnabar surface of the middle vessel is only a fraction1 equal to its radiating power1 of the heat given out by the black surface4 ,all the heat given out by the cinnabar surface to the black surface opposite to it is absorbed1 however1 while of the heat given out by the black surface to the cinnabar surface opposite it only a fraction is absorbed equal to the absorbing power of the cinnabar surface4 ,thus on the one side only a fraction is sent out but all of it is absorbed1 and on the other side all is sent out and only a fraction absorbed4 ,since #dj the quantities absorbed are exactly equal1 it is obvious that the two fractions must be exactly equal1 or the absorbing and radiating powers of any surface are exactly equal4 ,this result is known as ,kirchoff's law1 and it applies solely to radiation which is caused by temperature4 ,later experiments have shown that it applies to each individual wave-length1 i4e4 to any portion of the spectrum which we isolate1 as well as to the whole radiation4 ,thus at any particular temperature let the dotted line in ,fig4 #bj represent the wave-length--energy curve for a full radiator1 and let the solid line represent it for the surface under investigation4 ,then for any wave-length1 ,,on1 the radiating power of the surface would be equal to ,,qn divided by ,,pn4 ,illustration3 ,,fig4 #bj4 ,now a wave-length--energy curve may be as easily constructed for absorbed as for emitted radiation by means of a ,langley's bolometer4 ,the strip of the bolometer is first coated with lamp-black and the spectrum of the incident radiation is explored in exactly the same way as is described in ,chapter ,,iii4 #da ,the strip is then coated with the surface under investigation and the spectrum is again explored4 ,since the incident radiation is exactly the same in the two experiments1 the differences in the quantities of heat absorbed must be due solely to the difference in the absorbing powers of the two surfaces4 ,in ,fig4 #ba the dotted line represents the wave-length--energy curve for the radiation absorbed by the blackened bolometer strip1 and the solid line the curve for the strip coated with the surface under investigation4 ,illustration3 ,,fig4 #ba4 ,the actual form of the curves may and probably will be quite different from the form in ,fig4 #bj1 but it will be found for the same wave-length ,,on that ,,pn_/,,qn is exactly the same in the two figures4 ,it has already been mentioned that dull1 dark-coloured surfaces radiate the most heat1 and that polished surfaces radiate the least4 ,a radiator for heating a room should therefore have a dull1 dark surface1 while a vessel which is designed to keep its contents from losing heat should have a highly polished exterior4 ,a perfectly transparent substance would radiate no energy1 whatever the temperature to which it is #db raised1 for its absorbing power is zero and therefore its radiating power is also zero4 ,no perfectly transparent substances exist1 but some substances are a very near approach to it4 ,a fused bead of microcosmic salt heated in a small loop of platinum wire in a blowpipe flame may be raised to such a temperature that it is quite painful to look at the platinum wire1 yet the bead itself is scarcely visible at all4 ,any speck of metallic dust on the surface of the bead will at the same time shine out like a bright star4 ,gases as ,radiators4--,most gases are an even nearer approach to the perfectly transparent substance1 and consequently1 with one or two exceptions1 the simple heating of gases causes no appreciable radiation from them4 ,of course1 gases do radiate heat and light under some circumstances1 but the radiation seems to be produced either by chemical action1 as in the flames coloured by metallic vapours1 or by electric discharge1 as in vacuum tubes1 the arc or the electric spark4 ,the agitation of the electrons is thus produced in a different way in gases1 and we must not apply ,kirchoff's law to them1 although at first sight they appear to conform to it4 ,we have seen that the particular waves which an incandescent gas radiates are also absorbed by it4 ,this we should expect1 because the particular electron which has such a period of vibration that it sends out a certain wave-length will naturally be in tune to exactly similar waves which fall on it1 and will so resound to them1 and absorb their energy4 ,the quantitative law1 however1 that the absorbing power is exactly equal to the radiating power1 is not true for gases4 #dc ,emission of ,polarised ,light4--,one very interesting result of ,kirchoff's law is the emission of polarized light by glowing tourmaline and by one or two other crystal when they are heated to incandescence4 ,in ordinary light the vibrations are in all directions perpendicular to the line along winch the light travels1 that is1 the vibrations at any point are in a plane perpendicular to this line4 ,now any vibration in a plane may be expressed as the sum of two component vibrations1 one component in one direction and the other in a perpendicular direction4 ,if we divide up the vibrations all along the wave in this way we shall have two waves1 one of which has its vibrations all in one direction and the other in a perpendicular direction4 ,such waves1 in which the vibrations all lie in one plane1 are said to be plane polarised4 ,tourmaline is possessed of the curious property of absorbing vibrations in one direction of the crystal much more rapidly than it does those vibrations perpendicular to this direction1 and therefore light which passes through it emerges partially1 or in some cases wholly1 plane polarised4 ,since the absorbing power of tourmaline is different for the two components1 the emissive power should also be different1 and that component which was most absorbed should be radiated most strongly4 ,this was found to be true by ,kirchoff himself1 who detected and roughly measured the polarised light emitted4 ,subsequently in #aijb1 ,pflger carried out exact experiments which gave a beautiful confirmation of the law4 #dd ,,chapter ,v ,,full ,,radiation ,the ,full ,radiator4--,we have assumed that a lamp-blacked surface is a perfect absorber1 and consequently a full radiator1 but although it is a very near approach to the ideal it is not absolutely perfect4 ,no actual surface is a perfectly full radiator1 but the exact equivalent of one has been obtained by an ingenious device4 ,a hollow vessel which is blackened on the inside has a small aperture through which the radiation from the interior of the vessel can escape4 ,if the vessel is heated up1 therefore1 the small aperture may act as a radiator4 ,the radiation which emerges through the aperture from any small area on the interior of the vessel is made up of two parts1 one part which it radiates itself1 and the other part which it scatters back from the radiation which it receives from the other parts of the interior of the vessel4 ,these two together are equal to the energy sent out by a full radiator1 and therefore the small aperture acts as a full radiator3 e4g4 suppose the inner surface has an absorbing power of #ij per cent41 then it radiates #ij per cent4 of the full radiation and absorbs #ij per cent4 of the radiation coming up to it therefore scattering back #aj per cent4 ,we have therefore coming from the inner surface #ij per cent4 #de radiated and #aj per cent4 scattered1 and the radiated and scattered together make #ajj per cent4 ,illustration3 ,,fig4 #bb4 ,one form in which such radiators have been used is shown in section in ,fig4 #bb4 ,a double walled cylindrical vessel of brass has a small hole1 a1 in one end4 ,steam can be passed through the space between the double walls1 thus keeping the temperature of the inner surface at #ajj ,c4 ,a screen with a hole in it just opposite to the hole in the vessel1 or rather several such screens1 are placed in front of the vessel in order to shield any measuring instrument from any radiation except that emerging through the hole4 ,the ,full ,absorber4--,in an exactly similar way an aperture in a hollow vessel will act as a full absorber1 for the fraction of the incident radiation which is scattered on the inner surface again impinges on another portion of the surface and so all is ultimately absorbed except a minute fraction which is scattered out again through the aperture4 ,the variation in the heat radiated by a full radiator at different temperatures forms a very important part of the study of radiation1 and a very large number of experiments and theoretical investigations have been devoted to it4 ,these investigations may be divided into two sections3 those concerned with the total quantity of heat radiated at different temperatures and those concerned with the variation in the character of the spectrum with varying temperatures4 #df ,the experiments in the first section have been carried out mainly in two ways4 ,in the first1 the rate of cooling of the full radiator has been determined1 and from the rate of cooling at any temperature the rate at which heat was lost by radiation was immediately calculated4 ,newton was the first to investigate in this way by observing the rate at which a thermometer bulb cooled down when it was surrounded by an enclosure which was kept at a uniform temperature4 ,he found that the rate of cooling1 and therefore the rate at which heat was lost by the thermometer1 was proportional to the difference of temperature between the thermometer and its surroundings4 ,this rule is known as ,newton's ,law of ,cooling1 and is still used when it is desired to correct for the heat lost during an experiment where the temperature differences are small4 ,it is only true1 however1 for very small differences of temperature between the thermometer and its surroundings1 and as early as #agdj ,martine had found that it was only true for a very limited range of temperature4 ,prvost's ,theory of ,exchanges4--,in #agib1 ,prvost of ,geneva1 when endeavouring to explain the supposed radiation of cold1 introduced the line of thought1 that any body is not to be regarded as radiating heat only when its temperature is falling1 or absorbing heat only when its temperature is rising1 but that both processes are continually and simultaneously going on4 ,the amount of heat radiated will depend on the temperature and character of the body itself1 while the amount absorbed will depend upon the condition of the surroundings as well as upon the nature #dg of the body4 ,if the amount of heat radiated is greater than the amount absorbed the body will fall in temperature1 and vice-versa4 ,this view of ,prvost's is called the ,theory of ,exchanges1 and we can see that it is a necessary consequence of our ideas as to the production of heat and light waves by the agitation of electrons in the radiating body4 ,if the rate of cooling of a body at a certain temperature is measured when it is placed in an enclosure at a lower temperature1 it must be borne in mind that the rate of loss of heat is equal to the rate at which heat is radiated minus the rate at which it is absorbed from the enclosure4 ,a second way in which the heat lost by a body has been measured at different temperatures is by heating a conductor such as a thin platinum strip by means of an electric current1 and measuring the temperature to which the conductor has attained4 ,when its temperature is steady1 all the energy given to it by the current must be lost as heat1 and therefore the electrical energy1 which can very easily be calculated1 must be equal to the heat radiated by the body minus the heat received from the enclosure4 ,so many attempts have been made to establish1 by one or other of these two methods1 the relation between the quantity of heat radiated and the temperature1 that it is impossible to give even a passing reference to most of them4 ,unfortunately1 the results do not show the agreement with one another which we would like1 but probably the most correct result is that stated by ,stefan in #ahgh1 after a close inspection of the experimental results of ,dulong and #dh ,petit4 ,he stated that the quantity of heat radiated per second by a full radiator is proportional to the fourth power of its absolute temperature4#a ,thus the quantity of heat radiated by one square centimetre of the surface of a full radiator whose absolute temperature is ,t1 is equal to ,,et7sup7#d1 where ,e is some constant multiplier which must be determined by experiment and which is called the radiation constant4 ,if the absolute temperature of the enclosure in which the surface is placed is ,t1 then the rate at which the surface is losing heat will be ,e7,t7sup7#d-,t7sub7#a7sup7#d71 for it will receive heat at the rate ,,et7sub7#a7sup7#d and will radiate it at the rate ,,et7sup7#d4 #a ,see page #ef4 ,stefan's fourth power law has been verified by a number of good experiments1 notably those of ,lummer and ,pringsheim 7,congrs ,international de ,physique1 ,vol4 ,,ii4 p4 #gh71 so that although some experiments do not agree with it1 we are probably justified in taking it as correct4 ,in #ahhd ,boltzmann added still further evidence in support of this law by deriving it theoretically4 ,he applied to a space containing the waves of full radiation the two known laws which govern the transformation of energy1 by imagining the space to be taken through a cycle of compressions and expansions in just the same way as a gas is compressed and expanded in what is known as ,carnot's cycle4 ,variation of ,spectrum with ,temperature4--,the variation of the character of the spectrum of a full radiator has been determined mainly by the use of ,langley's bolometer1 but the general nature of the change may be readily observed by the eye4 #di ,as the temperature of a full radiator rises it first gives out only invisible heat waves2 as soon as its temperature exceeds about #ejj ,c4 it begins to emit some of the longest visible rays2 and as the temperature rises further1 more and more of the visible rays in the spectrum are emitted until1 when the radiator is white hot1 the whole of the visible spectrum4 is produced4 ,thus the higher the temperature of the radiator the more of the shorter waves are produced4 ,illustration3 ,,fig4 #bc4 ,by means of ,langley's bolometer the distribution of energy in the spectrum has been measured accurately1 with the results of confirming and amplifying the general results just stated4 ,the energy in the spectrum of even the hottest of terrestrial radiators is mostly in the longer waves of the infra-red1 but the position of the maximum of energy moves to shorter and shorter wave-lengths as the temperature rises1 and so more of the shorter waves make their appearance4 ,the sun is not a full radiator1 but is nearly so1 and its temperature is so high that the maximum of energy in its spectrum is in the visible part near to the red end4 #ej ,fig4 #bc shows the results obtained by ,lummer and ,pringsheim1 and brings out clearly the shift of the maximum with rising temperature and also the position of the greatest part of the energy in the infrared region4 ,wien's ,laws4--,examination of the results also shows that the wave-length at which the maximum energy occurs is inversely proportional to the absolute temperature and that the actual energy at the maximum point is proportional to the fifth power of the absolute temperature4 ,these two results have both been derived theoretically by ,wien#b in a similar way to that in which ,boltzmann derived ,stefan's fourth power law1 i4e4 by imagining a space filled with the radiation to be taken through a cycle of compressions and rarefactions4 #b ,wied4 ,ann41 #df1 p4 #fcc2 #eb1 p4 #acb4 ,wien derived an amplification of the last result by showing that if a wave-length in the spectrum of a full radiator at one temperature and another wave-length in the spectrum at another temperature are so related as to be inversely proportional to the two absolute temperatures1 they may be said to correspond to each other1 and the energy in corresponding wave-lengths at different temperatures is proportional to the fifth power of the absolute temperature4 ,we see therefore that if the distribution of energy in the spectrum of the full radiator be known at any one temperature it may be calculated for any other temperature by applying these two laws of corresponding wave-lengths and the energy in them4 ,neither of them give us any information1 however1 #ea about the actual distribution of energy at any one temperature from which we may calculate that at any other temperature4 ,for that1 some relation must be found between the energy and the wave-length4 ,planck1 by reasoning founded on the electromagnetic character of the waves1 derived such a relation1 but both his reasoning and his results are a little too complicated to be introduced here4 ,his results have been confirmed in the most striking manner by experiments carried out by ,rubens and ,kurlbaum 7,ann4 der ,physik1 #d1 p4 #fdi1 #aija74 ,they measured the energy in a particular wave-length 74#jjea cms41 i4e4 nearly #ajj times the wave-length of red light7 in the radiation of a full radiator from a temperature of #he up to #aggc absolute1 and their results are given in the following table3 ,absolute ,temperature4 ,observed ,energy4 ,energy calculated from ,planck's ,formula4 #he -#bj4f -#ba4i #aic -#aa4h -#ab #bic #j #j #ebc #ca #cj4d #ggc #fd4f #fc4h #ajbc #ih4a #ig4b #abgc #acb #acb #aebc #afd #afj #aggc #aif #bjj ,we have therefore the means of calculating both the total quantity and the kind of radiation given out by any full radiator at any temperature1 and a number of very interesting problems may be solved by means of the results4 #eb ,efficiency in ,lighting4--,one very simple problem is concerned with efficiency in lighting4 ,we see by reference to ,fig4 #af1 that in the radiation from the electric arc very little of the energy is in the visible part of the spectrum even though the temperature in the arc is the highest yet obtained on the earth1 whereas the energy in the visible part of the spectrum from a gas flame is almost wholly negligible4 ,the problem of efficient lighting is to get as big a proportion as possible of the energy into the visible part of the spectrum1 and therefore the higher the temperature the greater the efficiency4 ,this is the reason of the greater efficiency of the incandescent gas mantle over the ordinary gas burner1 for the introduction of the air into the gas allows the combustion to be much more complete1 and therefore the temperature of the mantle becomes very much higher than that of the carbon particles in the ordinary flame4 ,the modern metallic filament electric lamps have filaments made of metals whose melting point is extremely high1 and they may therefore be raised to a much higher temperature than the older carbon filaments4 ,the arc is even more efficient than the metallic filament lamps1 because its temperature is higher still2 and we must assume that the temperature of the sun is very much higher even than the arc1 since its maximum of energy lies in the visible spectrum4 ,temperature of the ,sun4--,the actual temperature of the sun may be calculated approximately by means of ,stefan's fourth power law4 ,we will first assume that the earth and the sun are both full radiators1 and #ec that the earth is a good conductor1 so that its temperature is the same all over4 ,the first assumption is very nearly true1 and we will make a correction for the small error it introduces2 and the second1 although far from true1 makes very little difference to the final result1 for it is found that the values obtained on the opposite assumption that the earth is an absolute non-conductor differ by less than #b per cent4 from those calculated on the first assumption4 ,we will further assume that the heat radiated out by the earth is exactly equal to the heat which it receives from the sun4 ,this is scarcely an assumption1 but rather an experimental fact1 for experiment shows that heat is conducted from the interior of the earth to the exterior1 and so is radiated1 but at such a small rate that it is perfectly negligible compared with the rate at which the earth is receiving heat from the sun4 ,the sun occupies just about one #id1jjjth part of the hemisphere of the heavens or one #ahh1jjjth part of the whole sphere4 ,if the whole sphere surrounding the earth were of sun brightness1 the earth would be in an enclosure at the temperature of the sun1 and would therefore be at that temperature itself4 ,the sphere would be sending heat at #ahh1jjj times the rate at which the sun is sending it1 and the earth would be radiating it at #ahh1jjj times its present rate4 ,but the rate at which it radiates is proportional to the fourth power of its absolute temperature1 and therefore its temperature would be the fourth root of #ahh1jjj times its present temperature1 i4e4 #bj4h times4 ,if the radiating or absorbing power of the earth's surface be taken as #i_/aj1 which is somewhere near the mark1 #ed the calculation gives the number #ba4e instead of #bj4h4 ,the average temperature of the earth's surface is probably about #ag ,c4 or #bij absolute1 and therefore the temperature of the sun is #bij x #ba4e1 i4e4 about #fbjj absolute4 ,it is easy to see that if we had known the temperature of the sun and not of the earth1 we could have calculated that of the earth by reversing the process4 ,by this means we can estimate the temperatures of the other planets1 at any rate of those for which we may make the same assumptions as for the earth4 ,probably those planets which are very much larger than the earth are still radiating a considerable amount of heat of their own1 and therefore to them the calculation will not apply2 but the smaller planets ,mercury1 ,venus and ,mars have probably already radiated nearly all their own heat and are now radiating only such heat as they receive from the sun4 ,the temperatures calculated in this way are-- ,average ,absolute ,temperature ,mercury 4 4 4 4 4 4 4 4 4 #dfg ,venus 4 4 4 4 4 4 4 4 4 4 #cdb ,earth 4 4 4 4 4 4 4 4 4 4 #bij ,mars 4 4 4 4 4 4 4 4 4 4 #bce ,since the freezing point of water is #bgc absolute1 we see that the average temperature of ,mars is #ch ,c4 below freezing1 and it is almost certain that no part of ,mars ever gets above freezing point4 ,in a very similar way we may find the temperature to which a non-conducting surface reaches when it is exposed to full sunlight by equating the heat absorbed to the heat radiated1 and the result comes #ee to #dab absolute1 i4e4 #aci ,c41 or considerably above boiling point4 ,this would be the upper limit to the temperature of the surface of the moon at a point where the sun is at its zenith4 ,on the surface of the earth the sunlight has had to pass through the atmosphere1 and in perfectly bright sunshine it is estimated that only three-fifths of the heat is transmitted4 ,any surface is also radiating out into surroundings which are at about #cjj absolute4 ,taking into account these two facts1 we find that the upper limit to a non-conducting surface in full sunshine on the earth is about #cfe absolute1 or only a few degrees less than the boiling point of water4 ,effective ,temperature of ,space4--,the last problem we will attack by means of the fourth power law is the estimation of the effective temperature of space1 i4e4 the temperature of a full absorber shielded from the sun and far away from any planet4 ,it is estimated by experiment that zenith sun radiation is five million times the radiation from the stars4 ,this estimate is only very rough1 as the radiation from the stars is so minute4 ,as the sun only occupies one #id1jjjth part of the heavens1 the radiation from a sunbright hemisphere would be five million times #id1jjj times starlight1 i4e4 #dgj1jjj1jjj1jjj times4 ,the temperature of the sun is therefore the fourth root of this quantity times the effective temperature of space1 i4e4 about #gjj times4 ,since the temperature of the sun is about #fbjj1 the temperature of space is a little under #aj absolute2 i4e4 lower than -#bfc ,c4 #ef ,note on ,absolute ,temperature4--,it is found that1 if a gas such as air has its temperature raised or lowered while its pressure is kept uniform1 for every one degree centigrade rise or fall its volume is increased or decreased by one two hundred and seventy-third of its volume at freezing point1 i4e4 at #j centigrade4 ,if therefore it continued in the same way right down to -#bgc centigrade1 its volume would be reduced to zero at this temperature4 ,this temperature is therefore called the absolute zero of temperature1 and temperatures reckoned from it are called absolute temperatures4 ,to get absolute temperatures from centigrade temperatures we evidently need to add #bgc4 #eg ,,chapter ,,vi ,,the ,,transformation ,,of ,,absorbed ,,radiation ,no account of radiation would be complete without mentioning what becomes of the radiation which bodies absorb1 but a good deal of the subject is in so uncertain a state that very little space will be devoted to it4 ,absorbed ,radiation converted into ,heat4--,the most common effect of absorbed radiation is to raise the temperature of the absorbing body1 and so cause it to re-emit long heat-waves4 ,as the usual arrangement is for the absorbing body to be at a lower temperature than the radiating one1 the waves given out by the absorber are longer than those given out by the radiator1 and so the net result is the transformation of shorter waves into longer ones4 ,but we have seen by ,prvost's theory of exchanges that radiator and absorber are interchangeable1 and therefore we see that those waves which are emitted by the absorber and absorbed by the radiator are re-emitted by the latter as shorter waves4 ,the mechanism by means of which the waves are converted into heat in the body is still a mystery4 ,that the waves should cause the electrons to vibrate is perfectly clear1 but how the vibrations of the electrons are converted into those vibrations of the atoms #eh and molecules which constitute heat is still unsolved1 and the reverse process is1 of course1 equally puzzling4 ,the heating of the body and the consequent re-emission of heat-waves is not1 however1 the only process which goes on4 ,in a large number of substances1 waves are given out under the stimulus of other waves without any heating of the body at all4 ,in most of these cases the emission stops as soon as the stimulating waves are withdrawn1 and in these cases the phenomenon has been called fluorescence4 ,the name has been derived from fluor spar1 the substance which was first observed to exhibit this peculiar emission of waves4 ,a familiar example of fluorescence is provided by paraffin-oil1 which glows with a blue light when it is illuminated with ordinary sunlight or daylight4 ,perhaps the easiest way to view it is to project a narrow beam of light through the paraffin-oil contained in a glass vessel and view the oil in a direction perpendicular to the beam4 ,the latter will then show up a brilliant blue4 ,a water solution of sulphate of quinine1 made acid by a few drops of sulphuric acid1 also exhibits a blue fluorescence1 while a water solution of sculin 7made by pouring hot water over some scraps of horse-chestnut bark7 shines with a brilliant blue light4 ,some lubricating oils fluoresce with a green light1 as does also a solution in water of fluorescene1 named thus because of its marked fluorescence4 ,a solution of chlorophyll in alcohol1 which can be readily prepared by soaking green leaves in alcohol1 shows a red fluorescence2 uranium glass--the canary glass of which small vases are very frequently #ei made--exhibits a brilliant green fluorescence1 as does also crystal uranium nitrate4 ,it is found1 on observing the spectrum of the fluorescent light1 that a fairly small range of waves is emitted showing a well-marked maximum of intensity at a wave-length which is characteristic of the particular fluorescing substance4 ,there also seems to be a limited range of waves which can induce this fluorescence1 and this range also depends upon the fluorescing substance4 ,as a rule1 the inducing waves are shorter in length than the induced fluorescence1 but this rule has some very marked exceptions4 ,the fact that only a limited range of waves produces fluorescence explains a noticeable characteristic of the phenomenon4 ,if the fluorescing solutions are at all strong the fluorescence is confined to the region close to where the light enters the solution1 thus showing that the rays which are responsible for inducing the glow become rapidly absorbed1 whereas the remainder of the light goes on practically unabsorbed4 ,phosphorescence4--,sometimes the emission of the induced light continues for some time after the inducing waves are withdrawn1 and then the phenomenon is termed phosphorescence1 since phosphorus emits a continuous glow without rise of temperature4 ,sometimes the glow will continue for several hours after the exciting rays have been cut off1 a good example of this being provided by ,balmain's luminous paint1 which is a sulphide of calcium4 ,with other substances the glow will only continue for a very small fraction of a second1 so that it is impossible to #fj say where fluorescence ends and where phosphorescence begins4 ,in order to determine the duration of the glow in the case of these small times1 an arrangement consisting of two rotating discs1 each of which have slits in them1 is set up4 ,through the slits in one of them the substance is illuminated1 and through the slits in the other the substance is observed while the light is cut off4 ,by adjusting the position of the discs with regard to each other the slits may be made to follow one another after greater or shorter intervals1 and so the time of observation can be made greater or smaller after the illumination is cut off4 ,all the bodies which have been observed to exhibit phosphorescence are solid4 ,theory of ,fluorescence4--,it is fairly simple to imagine a mechanism by which fluorescence might be brought about1 as we might assume a relation between the periods of oscillation of certain types of electron in the substance and the period of the stimulating waves4 ,thus resonance might occur1 and the consequent vibrations of the electrons would start a series of secondary waves4 ,if1 however1 we assume resonance1 it is difficult to see why there is a range of wave-lengths produced and another range of wave-lengths which may produce them4 ,we should have expected one definite wave-length or a few definite ones producing one or a few definite wave-lengths in the glow1 while if a whole range of waves will produce the effect it is difficult to see why all bodies do not exhibit the phenomenon4 ,but the phenomenon of phosphorescence finally #fa disposes of any such description1 for the two phenomena have no sharp distinction between them4 ,some substances are known in which the phosphorescence lasts for such an extremely small fraction of a second after the stimulating waves are withdrawn that it is difficult to know whether to call the effect fluorescence or phosphorescence4 ,it is probable1 therefore1 that both are due to the same action4 ,now a wave of orange light completes about five hundred million million vibrations in one second1 and therefore if an orange-coloured phosphoresence were to last for only one five-hundredth of a second it would mean that the electrons responsible for it vibrate one million million times after the stimulus is removed4 ,this is hardly credible1 and becomes more credible when we remember that in some phosphorescent substances the effect lasts for many hours4 ,chemical ,theory of ,phosphoresence4--,it is more probable that the stimulating rays produce an actual chemical change in the phosphorescent substance4 ,for instance1 it is possible that the vibrations of a certain type of electron in one kind of atom become so violent as to detach it from the atom and the temporarily free electron attaches itself immediately to another kind of atom4 ,the new arrangement may be quite stable2 it is so in the action of light on a photographic plate1 but it may only be stable when the electrons are being driven out of their original atoms1 and in this case the electrons will begin to return to their old allegiance as soon as the stimulus is withdrawn4 ,in the return #fb process the electrons will naturally be agitated1 and will therefore emit waves having their characteristic period4 ,the rate at which the return process takes place will evidently depend upon the stability of the new arrangement4 ,if it is extremely unstable1 the whole return may only occupy a fraction of a second1 but if it is nearly as stable as the original arrangement the return may be extremely slow4 ,on this view1 then1 those substances will phosphoresce which have an electron which is fairly easily detached from its atom and which will attach itself to another atom1 forming an arrangement which is less stable than the original4 ,temperature and ,phosphorescence4--,a confirmation of this chemical view is provided by the effect of temperature on phosphorescence4 ,the rate of a chemical change is usually very largely increased by rise of temperature1 and further1 at very low temperatures a large number of chemical changes which take place quite readily at ordinary temperatures do not take place at all4 ,similarly at very low temperatures the action of the light may be more or less stable4 ,for example1 ,dewar cooled a fragment of ammonium-platino-cyanide by means of liquid hydrogen1 and exposed it to a strong light4 ,after removing the light no phosphorescence was observed1 though at ordinary temperatures a brilliant green phosphorescence is exhibited1 but on allowing the fragment to warm up it presently glows very brightly4 ,a partial stability is shown by ,balmain's luminous paint1 for if it be kept in the dark until it becomes quite non-luminous it will begin to glow again for a #fc short time if warmed up in any way4 ,by means of this property the infra-red region of the spectrum may be made visible4 ,for this purpose a screen is coated with the paint1 exposed to strong sunlight1 and then placed so as to receive the spectrum4 ,the first effect of the invisible heat rays is to make the portions of the screen on which they fall brighter than their surroundings2 but this causes the phosphorescence to be emitted more rapidly1 and soon it is all emitted1 leaving a dark region where the heat has destroyed the phosphorescence4 ,on the whole1 then1 those substances which phosphoresce at ordinary temperatures do so more rapidly as the temperature rises4 ,but ,dewar has found a number of substances which phosphoresce only at low temperatures1 e4g4 gelatine1 celluloid1 paraffin1 ivory and horn4 ,this is not a fatal objection to the idea of chemical change1 as some chemical actions will only take place at low temperatures1 but it is an objection as quite a large number of substances only phosphoresce at low temperatures1 whereas there are not many chemical reactions which will only take place there4 ,as a matter of fact1 even if the idea of a chemical change be the true one1 it is not a very satisfactory one1 as chemical changes are undoubtedly very complicated ones1 and it would be too difficult to trace the change from the vibration of an electron to the chemical change1 and vice-versa4 ,no satisfactory theory therefore exists to account for the absorption and the remission of the waves1 whether accompanied or unaccompanied by a rise in temperature of the absorbing body4 #fd ,,chapter ,,vii ,,pressure ,,of ,,radiation ,prediction of ,pressure by ,maxwell4--,had the fact that light exerts a pressure been known in ,newton's time there is no doubt that it would have been hailed as conclusive proof of the superiority of the corpuscular theory over the wave theory4 ,yet1 ironically enough1 it was reserved for ,james ,clerk ,maxwell to predict its existence and calculate its value on the assumption of his electromagnetic wave theory2 and further1 the measurement of its value has given decisive evidence in favour of the wave theory1 for the value predicted by the latter is only one-half that predicted by the corpuscular theory1 and the measurements by ,nicholls and ,hull agree to within #a per cent4 with the wave theory value4 ,maxwell showed that all waves which come up to and are absorbed by a surface exert a pressure on every square centimetre of the surface equal to the amount of energy contained in one cubic centimetre of the beam4 ,if the surface is a perfect reflector1 the reflected waves produce an equal back pressure1 and therefore the pressure is doubled4 ,as the waves are reflected back along their original direction1 the energy in the beam will also be doubled1 and so #fe the pressure will still be equal to the energy per cubic centimetre of the beam4 ,as the energy which is received in one second from the sun on any area can be measured by measuring the heat absorbed1 and since the speed of light is known1 we can calculate the energy contained in one cubic centimetre of full sunlight1 and hence the pressure on one square centimetre of surface4 ,for the energy received on one square centimetre of surface in one second must have been spread originally over a length of beam equal to the distance which the light has travelled in one second1 i4e4 over a length equal to the speed of light4 ,if we divide that energy1 therefore1 by the speed of light1 we shall get the energy in a one-centimetre length of the beam1 and therefore in one cubic centimetre4 ,this turns out to be an extremely small pressure indeed1 being only a little more than the weight of half a milligram1 on a square metre of surface4 ,maxwell suggested that a much greater energy of radiation might be obtained by means of the concentrated rays of an electric lamp4 ,such rays falling on a thin1 metallic disc delicately suspended in a vacuum might perhaps produce an observable mechanical effect4 ,nearly thirty years after ,maxwell's suggestion it was successfully carried out by ,prof4 ,lebedew of ,moscow1 who used precisely the arrangement which ,maxwell had suggested4 ,measurement of the ,pressure4--,a beam of light from an arc lamp was concentrated on to a disc suspended very delicately in an exhausted glass #ff globe about #h inches across4 ,actually four discs were suspended1 as in ,fig4 #bd1 and arrangements were made to concentrate the beam on to either side of any of the four discs4 ,illustration3 ,,fig4 #bd4 ,the suspension was a very fine quartz fibre q4 ,the discs d1 d1 d1 d1 were half a centimetre in diameter and were fixed on two light arms1 so that their centres were one centimetre from the glass rod1 g1 which carried them4 ,a mirror1 m1 served to measure the angle through which the whole system was twisted owing to the pressure of the beam on one of the discs4 ,in order to measure the angle a telescope viewed the reflection of a scale in m1 and as m turned different divisions of the scale came into view4 ,the two discs on the left were polished and therefore the pressure on them should be about twice that on the blackened discs on the right4 ,having measured the angle through which a beam of light has turned the system1 it is a simple matter to measure the force which would cause this twist in the fibre q4 ,in order to test whether the pressure agrees with the calculated value1 we must find the energy in the beam of light4 ,this was done by receiving the beam on a blackened block of copper and measuring the rate at which its temperature rose4 ,from this rate and the weight of copper it is easy to calculate the amount of heat received per second1 and therefore the amount of energy received per second on one square #fg centimetre of the area4 ,knowing the speed of the light we can1 as suggested above1 calculate the energy in one cubic centimetre of the beam4 ,lebedew's result was in very fair accord with the calculated value4 ,the chief difficulty in the experiment is to eliminate the effects due to the small amount of gas which remains in the globe4 ,each disc is heated by the beam of light1 and the gas in contact with it becomes heated and causes convection currents in the gas4 ,at very low pressures a slightly different action of the gas becomes a disturbing factor4 ,this effect is due to the molecules which come up to the disc becoming heated and rebounding from the disc with a greater velocity than that with which they approached it4 ,the rebound of each molecule causes a backward kick on to the disc1 and the continual stream of molecules causes a steady pressure4 ,this would be the same on both sides of the disc if both sides were at the same temperature1 but since the beam of light comes up to one side1 that side becomes hotter than the other and there will be an excess of pressure on that side4 ,this action is called radiometer action1 because it was first made use of by ,crookes in detecting radiation4 ,between the ,scylla of convection currents at higher pressures and the ,charybdis of radiometer action at lower pressures1 there seems to be a channel at a pressure of about two or three centimetres of mercury4 ,for here the convection currents are small and the radiometer action has scarcely begun to be appreciable4 ,by working at this pressure and using one or two #fh other devices for eliminating and allowing for the gas action1 ,professors ,nicholls and ,hull also measured the pressure of light in an exceedingly careful and masterly way4 ,their results were extremely consistent among themselves1 and agreed with the calculated value to within one per cent4 ,those who know the difficulty of measuring such minute forces1 and the greatness of the disturbing factors1 must recognise in this result one of the finest experimental achievements of our time4 ,effect of ,light ,pressure in ,astronomy4--,forces due to light pressure are so small that we should not expect to be able to detect their effects on astronomical bodies1 and certainly we cannot hope to observe them in the large bodies of our system4 ,the pressure of the sunlight on the whole surface of the earth is about #ge1jjj tons weight4 ,this does not sound small until we compare it with the pull of the sun for the earth1 which is two hundred million million times as great4 ,when we consider very small bodies1 however1 we find that the pressure of the light may even exceed the gravitational pull1 and therefore these small particles will be driven right away from our system4 ,in order to show that the light pressure becomes more and more important1 let us imagine two spheres of the same material1 one of which has four times the radius of the other4 ,then the weight of the larger one1 that is its gravitational pull1 will be sixty-four times as great as that of the smaller one1 while the area1 and therefore the light pressure1 will be sixteen times as great4 #fi ,the light pressure is therefore four times as important in the sphere of one-quarter the radius4 ,for a sphere whose radius is one two hundred million millionth of the radius of the earth and of the same density1 the pressure of the light would equal the pull of the sun1 and therefore such a sphere would not be attracted to the sun at all4 ,this is an extremely small particle1 much smaller than the finest visible dust1 but even for much larger things the light pressure has an appreciable effect4 ,thus for a sphere of one centimetre radius and of the same density as the earth1 the pressure due to the sunlight is one seventy-four thousandth of the pull due to gravitation4 ,it therefore need not move in its orbit with quite such a high speed in order that it may not fall into the sun1 and its year is therefore lengthened by about three minutes4 ,the lengthening out of comets' tails as they approach the sun1 and the apparent repulsion of the tail by the sun1 has sometimes been attributed to pressure of sunlight1 but it is pretty certain that the forces called into play are very much greater than can be accounted for by the light4 ,doppler ,effect4--,the ,doppler effect also has some influence on the motion of astronomical bodies4 ,when a body which is receiving waves moves towards the source of the waves1 it receives the waves more rapidly than if it were still1 and therefore the pressure is greater4 ,when the body is moving away from the source it receives the waves less rapidly1 and hence the pressure of light on it is less than for a stationary body4 ,if a body is moving in an elliptical orbit1 it is moving towards the sun in one part of its orbit and #gj away in another part2 it will therefore be retarded in both parts1 and the ultimate result will be that the orbit will be circular4 ,the ,doppler effect can act in another way4 ,a body which is receiving waves from the sun on one side is thereby heated and emits waves in all directions4 ,as it is moving in its orbit it will crowd up the waves which it sends out in front of it and lengthen out those which it sends out behind it4 ,but the energy per cubic centimetre will be greater where the waves are crowded up than where they are drawn out1 and therefore the body will experience a retarding force in its orbit4 ,as the body tends to move more slowly it falls in a little towards the sun1 and so approaches the sun in a spiral path4 ,three ,effects of ,light ,pressure4--,we thus have three effects of light pressure on bodies describing an orbit round the sun4 ,the first effect is to lengthen their period of revolution1 the second is to make their orbits more circular1 and the third is to make them gradually approach the sun in a spiral path4 ,these effects are quite inappreciable for bodies anything like the size of the earth1 but for small bodies of the order of one centimetre diameter or less the effects would be quite large4 ,our system is full of such bodies1 as is evidenced by the number of them which penetrate our atmosphere and form shooting stars4 ,the existence of such bodies is somewhat of a problem1 as whatever estimate of the sun's age we accept as correct1 he is certainly of such an age that if these bodies had existed at his beginning they would all have been drawn in to him long ago4 ,we must therefore #ga suppose that they are continually renewed in some way1 and since we can see no sufficient source inside the ,solar system1 we must come to the conclusion that they are renewed from outside4 ,there is every reason to believe that some of them originate in comets which have become disintegrated and spread out along their orbits4 ,these form the meteoric showers4 ,thus the very finest dust is driven by the sun right out of our system1 and all the rest he is gradually drawing in to himself4 #gb ,,chapter ,,viii ,,the ,,relation ,,between ,,radiant ,,heat ,,and ,,electric ,,waves ,in this concluding chapter it is proposed to show how the wave-lengths of radiant heat have been determined and to state what range of wave-lengths has been experimentally observed4 ,it is then proposed to show how electromagnetic waves have been produced by straightforward electrical means and how their wave-lengths have been measured4 ,the similarity in properties of the radiant heat and of the electric waves will be noted1 leading to the conclusion that the difference between the two sets of waves is merely one of wave-length4 ,diffraction ,grating4--,the best method of measuring the wave-lengths of heat and light is by means of the ,diffraction ,grating4 ,this consists essentially of a large number of fine parallel equidistant slits placed very close to one another4 ,for the measurement of the wave-lengths of light and of the shorter heat waves1 it is usually produced by ruling a large number of very fine close equidistant lines on a piece of glass or on a polished mirror by means of a diamond point4 ,the ruled lines are opaque on the glass and do not reflect on the mirror1 and consequently the spaces in between act as slits4 #gc ,rowland's ,gratings4--,the ruling of these gratings is a very difficult and tedious business1 but the difficulties have been surmounted in a very remarkable manner by ,rowland1 so that the gratings ruled on his machine have become standard instruments throughout the world4 ,he succeeded in ruling gratings #f inches in diameter with #ad1jjj lines to the inch1 truly a remarkable performance when we remember that if the diamond point develops the slightest chip in the process1 the whole grating is spoilt4 ,illustration3 ,,fig4 #be4 ,the action of the grating can be made clear by means of ,fig4 #be4 ,let ,a1 ,b1 ,c1 ,d represent the #gd equidistant slits in a grating1 and let the straight lines to the left of the grating represent at any instant the crests of some simple plane waves coming up to the grating4 ,the small fractions of the original waves emerging from the slits ,a1 ,b1 ,c1 ,d will spread out from the slits so that the crests of the small wavelets may at any instant be represented by a series of concentric circles1 starting from each slit as centre4 ,the series of crests from each slit are represented in the figure4 ,now notice that a line ,,pq parallel to the original waves lies on one of the crests from each slit1 and therefore the wavelets will make up a plane wave parallel to the original wave4 ,this may therefore be brought to a focus by means of a convex lens just as if the grating were removed1 except that the intensity of the wave is less4 ,but a line1 ,,lm1 also lies on a series of crests1 the crest from ,a being one wave-length behind that from ,b1 the one from ,b a wave-length behind that from ,c1 and so on4 ,the wavelets will therefore form a plane wave ,,lm1 which will move in the direction perpendicular to itself 7i4e4 the direction ,,dk7 and may be brought to a focus in that direction by means of a lens4 ,draw ,,ch and ,,dk perpendicular to ,,lm1 and draw ,,ce perpendicular to ,,dk1 i4e4 parallel to ,,lm4 ,the difference between ,,ch and ,,dk is evidently one wave-length1 i4e4 ,,de is one wave-length4 ,if ,greek3 alpha is the angle between the direction of ,,pq and ,,lm1 ,,de is evidently equal to ,,cd sin ,greek3 alpha and therefore one wave-length,,cd sin ,greek3 alpha4 ,from the ruling of the grating we know the value #ge of ,,cd1 and therefore by measuring ,greek3 alpha we can calculate the wave-length4 ,we find that a third line ,,rs also lies on a series of crests1 and therefore a plane wave sets out in the direction perpendicular to ,,rs4 ,we notice here that the crest from ,a is two wave-lengths behind that from ,b1 and so on1 and therefore if ,greek3 beta is the angle between ,,rs and ,,pq1 ,,cd sin ,greek3 beta is equal to two wave-lengths4 ,similarly we get another plane wave for a three wave-lengths difference1 and so on4 ,the intensity of the wavelets falls off fairly rapidly as they become more oblique to their original direction1 and therefore the intensity of these plane waves also falls off rather rapidly as they become more oblique to the direction in which ,,pq goes4 ,we see that the essential condition for the plane wave to set out in any direction1 is that the difference in the distances of the plane wave from two successive slits shall be exactly a whole number of wave-lengths4 ,should it depart ever so little from this condition we should see1 on drawing the line1 that there lie on the line an equal number of crests and troughs1 and therefore1 if a lens focus waves in this direction1 the resulting effect is zero4 ,the directions of the waves ,,pq1 ,,lm1 ,,rs1 c41 will therefore be very sharply defined and will admit of very accurate determination4 ,dispersion by ,grating4--,evidently the deviations ,greek3 alpha1 ,greek3 beta will be greater the greater is ,,de1 i4e4 the greater the wave-length1 and therefore the light or heat will be dispersed into its different wave-lengths as in the prism2 but in this case the dispersion #gf is opposite to that in the normal prism1 the long waves being dispersed most and the short waves least4 ,evidently1 too1 the smaller the distance ,,cd the greater the angle1 and therefore for the extremely short wave-lengths of light and of ultraviolet rays we require the distance between successive slits to be extremely small4 ,illustration3 ,,fig4 #bf4 ,the ,spectrometer4--,the grating is usually used with a spectrometer1 as shown in plan diagrammatically in ,fig4 #bf4 ,the slit ,s from which the waves radiate is placed at the principal focus of the lens ,l1 and therefore the waves emerge from ,l as plane waves which come up to the grating ,g4 ,the telescope ,t is first turned until it views the slit directly1 i4e4 until the plane waves like ,,pq in ,fig4 #be are brought to a focus at the principal focus ,f of the objective of the telescope4 ,the eyepiece ,e views the image of the slit ,s which is formed at ,f4 ,the telescope is then turned through an angle1 ,greek3 alpha1 until it views the second image of the slit which will be formed by the plane waves similar to ,,lm in ,fig4 #be4 ,the angle ,greek3 alpha is carefully measured by the graduated circle on the spectrometer1 #gg and hence the wave-length of a particular kind of light1 or of a particular part of the spectrum1 is measured4 ,this spectrometer method is exactly the method used for measuring the wave-lengths in the visible part of the spectrum4 ,for the ultraviolet rays1 instead of viewing the image of the slit by means of the eyepiece of the telescope1 a photographic plate is placed at the principal focus ,f of the objective of the telescope1 and serves to detect the existence and position of these shorter waves4 ,for the heat rays a ,langley's bolometer strip is placed at ,f1 in fact the bolometer strip might be used throughout1 but it is not quite so sensitive for the visible and ultraviolet rays as the eye and the photographic plate4 ,absorption by ,glass and ,quartz4--,two main difficulties arise in these experiments4 ,the first one is that although glass1 or better still quartz1 is extremely transparent to ultraviolet1 visible1 and the shorter infra-red waves1 yet it absorbs some of the longer heat waves almost completely4 ,for these waves1 therefore1 some arrangement must be devised in which they are not transmitted through a glass diffraction grating or through glass or quartz lenses4 ,to effect this1 the convex lenses are replaced by concave mirrors and the ruled grating is replaced by one which is made of very fine wires1 which are stretched on a frame parallel to and equidistant from each other4 ,the wire grating cannot be constructed with such fine or close slits as the ruled grating1 but for the longer waves this is unnecessary4 #gh ,reflecting ,spectrometer4--,an arrangement used by ,rubens is represented roughly in plan in ,fig4 #bg4 ,l represents the source of heat1 the rays from which are reflected at the concave mirror ,m1 and brought to a focus on the slit ,s4 ,emerging from ,s the rays are reflected at ,m7sub7#b and are thereby rendered parallel before passing through the wire grating ,g4 ,after passing through the grating1 the rays are reflected at ,m7sub7#c and are thereby focussed on to a bolometer strip placed at ,b4 ,turning the mirror ,m7sub7#c in this arrangement is evidently equivalent to turning the telescope in the ordinary spectrometer arrangement4 ,illustration3 ,,fig4 #bg4 ,absorption of ,waves by ,air4--,by using a spectrometer in an exhausted vessel ,schumann discovered that waves existed in the ultraviolet region of much smaller wave-length than any previously found1 and that these waves were almost completely absorbed on passing through a few centimetres of air4 ,to all longer waves1 however1 air seems to be extremely transparent4 ,the second difficulty arises from the fact1 already explained1 that a diffraction grating produces not one1 but a number of spectra4 ,if only a small range of waves exists1 this will lead to no confusion1 but if a large range is being investigated1 we may get two or more of these spectra overlapping4 ,suppose1 for example1 we have some waves of wave-length ,,de 7in ,fig4 #be71 some of wave-length one-half #gi ,,de and some of one-third ,,de4 ,then in the direction ,,dk we shall get plane waves of each of these wave-lengths setting out and being brought to a focus in the same place4 ,this difficulty can be fairly simply surmounted where the measurement of wave-length alone is required1 by placing in the path of the rays from the source of light1 suitable absorbing screens1 which will only allow a very small range of wave-lengths to pass through them4 ,there will then be no overlapping and no confusion4 ,where the actual distribution of energy in the spectrum of any source of heat is to be determined the difficulty becomes more serious1 and probably there is some error in the determinations1 especially in the longest waves1 which are masked almost completely by the overlapping shorter waves4 ,rest-,strahlen or ,residual ,rays4--,a very beautiful method of isolating very long heat waves1 and so freeing them from the masking effect of the shorter waves1 was devised by ,rubens and ,nichols4 ,it is found that when a substance very strongly absorbs any waves that pass through it1 it also strongly reflects at its surface the same waves4 ,for example1 a sheet of glass used as a fire-screen will cut off most of the heat coming from the fire1 although it is perfectly transparent to the light4 ,if1 now1 it is placed so as to reflect the light and heat from the fire1 it is found to reflect very little light but a very large proportion of the heat4 ,some substances have a well-defined absorption band1 i4e4 they absorb a particular wave-length very strongly1 and these substances will therefore reflect #hj this same wave-length strongly4 ,if instead of a single reflection a number of successive reflections be arranged1 at each reflection the proportion of the strongly reflected wave-length is increased until ultimately there is practically only this one wave-length present4 ,it can therefore be very easily measured4 ,these waves resulting from a number of successive reflections1 rest-strahlen or residual rays as they have been named1 have been very largely used for investigating long waves4 ,quartz gives rest-strahlen of length 4#jjjhe centimetres and very feeble ones of 4#jjbj centimetres long4 ,sylvite gives the longest rays yet isolated1 the wave-length being 4#jjf centimetres4 ,range of the ,waves4--,the lengths of the waves thus far measured are3-- ,schumann waves 4 4 4 4 4 4 4 4 4#jjjja to 4#jjjjb cms4 ,ultraviolet 4 4 4 4 4 4 4 4 4 4#jjjjb to 4#jjjjd ,violet 4 4 4 4 4 4 4 4 4 4 4 4 4#jjjjd ,green 4 4 4 4 4 4 4 4 4 4 4 4 4#jjjje ,red 4 4 4 4 4 4 4 4 4 4 4 4 4 4#jjjjf to 4#jjjjge ,infra-red 4 4 4 4 4 4 4 4 4 4 4#jjjjge to about 4#jjja ,rest-strahlen from quartz 4 4 4#jjjhe and 4#jjbj ,rest-strahlen from ,sylvite 4 4 4#jjfj ,thus the longest waves are six hundred times the length of the shortest4 ,the corresponding range of wave-lengths of sound would be a little more than eight octaves1 of which the visible part of the spectrum is less than one4 ,electromagnetic ,induction4--,in the attempt to explain the nature of an electromagnetic wave 7pp4 #ag-ba7 it was stated that an electric wave must always be accompanied by a magnetic wave4 ,in order to #ha understand the production of these waves1 the relation between electric and magnetic lines of force must be stated in more detail4 ,a large number of quite simple experiments show that whenever the electric field at any point is changing1 i4e4 whenever the lines of force are moving perpendicular to themselves1 a magnetic field is produced at the point1 and this magnetic field lasts while the change is taking place4 ,an exactly similar result is observed when the magnetic field at a point is changing--an electric field is produced which lasts while the magnetic field is changing4 ,when the electric field changes1 therefore1 there is both an action and a reaction--a magnetic field is produced and this change in magnetic field produces a corresponding electric field4 ,this induced electric field is always of such a kind as to delay the change in the original electric field2 if the original field is becoming weaker the induced field is in the same direction1 thus delaying the weakening1 and if the original field is becoming stronger the induced field is in the opposite direction1 thus delaying the increase4 ,momentum of ,moving ,electric ,field4--,imagine now a small portion of an electric field moving at a steady speed2 it will produce1 owing to its motion1 a steady magnetic field4 ,if now the motion be stopped1 the magnetic field will be destroyed1 and the change in the magnetic field will produce an electric field so as to delay the change1 i4e4 so as to continue the original motion4 ,the moving electric field thus has momentum in exactly the same way as a moving mass has4 ,the parallel between the two #hb is strictly accurate4 ,the mass has energy due to its motion1 and in order to stop the mass this energy must be converted into some other form of energy and work must therefore be done4 ,the electric field has energy due to its motion--the energy of the magnetic field--and therefore to stop the motion of the electric field1 the energy of the magnetic field must be converted into some other form1 and work must therefore be done4 ,one consequence of the momentum of a moving mass is well illustrated by the pendulum4 ,the bob of the pendulum is in equilibrium when it is at its lowest point1 but when it is displaced from that point and allowed to swing1 it does not swing to its lowest point and stay there1 but is carried beyond that point by its momentum4 ,the work done in displacing the bob soon brings it to rest on the other side1 and it swings back again only to overshoot the mark again4 ,the friction in the support of the pendulum and the resistance of #hc the air to the motion makes each swing a little smaller than the one before it1 so that ultimately the swing will die down to zero and the pendulum will come to rest at its lowest point4 ,the graph of the displacement of the bob at different times will therefore be something like ,fig4 #bh4 ,should the pendulum be put to swing1 not in air1 but in some viscous medium like oil1 its vibrations would be damped down very much more rapidly1 and if the medium be viscous enough the vibrations may be suppressed1 altogether1 the pendulum merely sinking to its lowest position4 ,illustration3 ,,fig4 #bh4 ,electric ,oscillation4--,these conditions have their exact counterpart in the electric field4 ,to understand them1 three properties of lines of force must be borne in mind3 7i47 lines of force act as if in tension and therefore always tend to shorten as much as possible2 7ii47 the ends of lines of force can move freely on a conductor2 7iii47 lines of force in motion possess momentum4 ,now imagine two conducting plates ,a and ,b1 ,fig4 #bi1 charged positively and negatively1 and therefore connected by lines of force as indicated4 ,let the two plates be suddenly connected by the wire w1 so that the ends of the lines of force may freely slide from ,a to ,b or vice-versa1 and therefore all the lines will slide upwards along ,a and ,b1 and then towards each other along w1 until they shrink to zero #hd somewhere in w4 ,the condition of equilibrium will evidently be reached when all the lines have thus shrunk to zero1 but the lines which are travelling from ,a towards ,b will have momentum and will therefore overshoot the equilibrium condition and pass right on to ,b4 ,that is1 the positive ends of the lines will travel on to ,b1 and similarly the negative ends will pass on to ,a4 ,the lines of force between ,a and ,b will therefore be reversed4 ,the tension in the lines will soon bring them to rest1 and they will slide back again1 overshoot the mark again1 reach a limit in the original direction and still again slide back4 ,the field between ,a and ,b will therefore be continually reversed1 but each time its value will be a little less1 until ultimately the vibrations will die down to zero4 ,thus if we were to replace the displacement in ,fig4 #bi by the value of the field between ,a and ,b we should have an exactly similar graph4 ,illustration3 ,,fig4 #bi4 ,the amount by which the oscillations are damped down will depend upon the character of the wire w4 ,if it is a very poor conductor it will offer a large resistance to the sliding of the lines along it1 and the vibrations will be quickly damped down or1 if the resistance is great enough1 be suppressed altogether4 ,this rapid alternation of the electric field will send out electromagnetic waves which die down as the oscillations decrease4 ,the ,spark ,discharge4--,in practice the wire w is not actually used1 but the air itself suddenly becomes a conductor and makes the connection4 ,when the electric field at a point in the air exceeds a certain limiting strength1 the air seems to break down and #he suddenly become a conductor and remains one for a short time4 ,this breaking down is accompanied by light and heat1 and is known as the spark discharge or electric spark4 ,experiments of ,hertz4--,in the brilliant experiments carried out by ,hertz at ,karlsruhe between #ahhf and #ahia1 he not only demonstrated the existence of the waves produced in this way1 but he showed that they are reflected and refracted like ordinary light1 he measured their wave-length and roughly measured their speed1 this latter being equal to the speed of light within the errors of experiment4 ,illustration3 ,,fig4 #cj4 ,one arrangement used by ,hertz is shown in plan in ,fig4 #cj4 ,a ,ruhmkorff coil ,r serves to charge the two conductors ,a and ,b until the air breaks down at the gap ,g1 and a spark passes4 ,before the spark is #hf produced1 the lines of force on the lower side of ,,ab will in form be something like the dotted lines in the figure1 but as soon as the air becomes a conductor1 the positive ends of the lines will surge from ,a towards ,b and on to ,b1 and the negative ends will surge on to ,a4 ,these to and fro surgings will continue for a little while1 but will gradually die out4 ,as the surgings are all up and down ,,ab1 the electric vibrations in the electromagnetic waves sent out #hg will all be parallel to ,,ab1 and therefore they will be polarised4 ,illustration3 ,,fig4 #ca4 ,this is characteristic of all electric waves1 as no single sparking apparatus will produce anything but waves parallel to the spark gap4 ,the electric vibrations coming up to a conductor placed in the position of the wire rectangle1 ,m1 will cause surging of the lines along it1 and1 if these surgings are powerful enough1 will cause a spark to pass across the small gap ,s4 ,such a rectangle was therefore used by ,hertz as a detector of the waves1 but since that time many detectors of very much greater sensitiveness have been devised4 ,reflection4--,in order to show that these waves are reflected in the same way as light waves1 ,hertz placed the sparking knobs1 ,g1 at the focus of a large parabolic metallic reflector1 and his detector1 ,d1 at the focus of a similar reflector placed as in ,fig4 #ca1 but much farther away 7cf4 ,fig4 #a74 ,in this position sparking at ,g produced strong sparking in the detector1 although the distance was such that no sparking was produced without the reflectors4 ,refraction4--,the refraction of the waves was #hh shown by means of a large prism made of pitch4 ,this had an angle of #cj and was about #a4e metres high and #a4b metres broad4 ,illustration3 ,,fig4 #cb4 ,setting it up as shown in plan in ,fig4 #cb1 strong sparking was produced in the detector1 thus showing that the rays of electric waves were deflected by #bb on passing through the prism4 ,moving the mirror and detector in either direction from the line ,,lm1 made the sparks decrease rapidly in intensity1 so that the exact position of ,,lm can be determined with considerable definiteness4 ,wave-length1 by ,stationary ,waves4--,the wave-lengths of the oscillations were found by means of what are known as stationary waves4 ,when two exactly similar sets of waves are travelling in opposite directions over the same space1 they produce no effects at certain points called nodes4 ,these nodes are just half a wave-length apart4 ,their production can be understood by reference to ,fig4 #cc4 ,the dotted lines represent the two waves which are travelling in the direction indicated by the arrows4 ,in ,a the time is chosen when the waves are exactly superposed1 and the resultant displacement will be represented by the solid line4 ,the points marked with a cross will be points at which the displacement is zero4 ,illustration3 ,,fig4 #cc4 ,in ,b each wave has travelled a distance equal to a quarter of a wave-length1 and it will be seen that the two sets of waves cause equal and opposite displacements4 ,the resulting displacement is therefore zero1 as indicated by the solid line4 ,in ,c the waves have travelled another quarter of a wave-length and #hi are superposed again1 but in this case the displacements will be in the opposite directions from those in ,a4 ,in ,d1 still another quarter wave-length has been traversed by each wave1 and another quarter wave-length would bring back the position ,a4 ,in ,e1 we have the successive positions of the wave drawn in one diagram1 and we notice that the points indicated by a cross are always undisplaced and their distance apart is one-half a wave-length4 ,hertz produced these conditions by setting up his coil and sparking knobs at some distance from a reflecting wall1 ,fig4 #cd4 ,then the waves which are coming up to the wall and those which are reflected #ij from the wall will be travelling in opposite directions over the same space4 ,true1 the reflected waves will be rather weaker than the original ones1 so that there will be a little displacement even at the nodes1 but there will be a well-marked minimum4 ,thus when the detector is placed at ,a1 ,b1 ,c or ,d no sparking or very feeble sparking occurs1 while midway between these points the sparking is very vigorous1 and the distance between two successive minima is one-half a wave-length4 ,illustration3 ,,fig4 #cd4 ,the wave-length will depend upon the size1 form1 c41 of the conductors between which the sparking occurs1 for the time which the lines of force take to surge backwards and forwards in the conductors will depend upon these things4 ,other things being equal1 the smaller the conductors the smaller the time and therefore the shorter the wave-length4 ,the shortest wave which ,hertz succeeded in producing was #bd centimetres long1 but since then waves as little as #f millimetres long have been produced4 #ia ,the waves which are produced in a modern wireless telegraphy apparatus are miles in length4 ,we thus see that there is rather a large gap between the longest heat waves which have been isolated1 4#jjf cms41 and the shortest electric waves1 4#f cms4 ,the surprising fact1 however1 is that this gap is so small1 for the heat waves are produced by vibrations within a molecule1 or at most within a small group of molecules1 whereas the electric surgings1 even in the smallest conductors1 take place over many many millions of molecules4 ,in conclusion1 therefore1 we see that from the ,schumann waves up to the longest heat waves a little over eight octaves of electromagnetic waves have been detected1 then after a gap of between five and six octaves the ordinary electrically produced electromagnetic waves begin and extend on through an almost indefinite number of octaves4 #ib ,,books ,,for ,,further ,,reading ,j4 ,h4 ,poynting1 ,the ,pressure of ,light4 ,e4 ,edser1 ,heat for ,advanced ,students3 the chapters on ,radiation4 ,e4 ,edser1 ,light for ,advanced ,students3 the chapters on the ,spectrum4 ,b4 ,w4 ,wood1 ,physical ,optics3 the chapters on ,fluorescence and ,phosphorescence1 ,laws of ,radiation1 ,nature of ,white ,light1 and ,absorption of ,light4 #ic ,,index ,,absorbing power1 #cg -- and radiating power1 #ch ,absorption1 spectra1 #cd -- by glass and quartz1 #gg -- by air1 #gh ,addition of waves1 #be ,amplitude1 #bc ,,balmain1 luminous paint1 #ei ,boltzmann1 laws of radiation1 #dh ,,convection currents1 #fg ,corpuscular theory1 #aj -- reflection and refraction by1 #aa ,crookes' radiometer1 #fg ,,dewar1 temperature and phosphorescence1 #fb ,diffraction grating1 #gb -- dispersion by1 #ge -- wire grating1 #gg ,dispersion1 #bi1 #ge ,doppler effect1 #fi ,,efficiency in lighting1 #eb ,elastic solid theory1 #ag ,electric field1 #ah ,electric charges within the atom1 #ba ,electric oscillations1 #ai1 #hc ,electrification1 positive and negative1 #ah ,electromagnetic induction1 #hj ,electromagnetic waves1 #ag1 #hd ,electrons1 #cj ,energy in simple wave1 #be ,energy--wave-length curve1 #bg ,,fluorescence1 #eh -- theory of1 #fj ,foucault1 speed of light in different media1 #ag ,fourier's series of waves1 #bf1 #cj ,fraunhfer lines1 #ce ,full radiator and absorber1 #dd1 #de ,,gases as radiators1 #db ,,huyghens' wave theory1 #ac ,hertz1 experiments on electric waves1 #he -- reflection1 #hf -- refraction1 #hg -- wave-length by stationary waves1 #hh ,,infra-,,red rays1 #cb ,interference1 #ac ,,kirchoff',s law1 #dj ,,langley1 ,bolometer1 #cb1 #dh1 #di1 #gg ,lebedew1 pressure of light1 #fe ,lummer and ,pringsheim1 law of radiation1 #dh1 #ej ,,magnetic oscillations1 #bj ,maxwell1 electromagnetic theory1 #ag -- pressure of light1 #fd ,momentum of moving electric field1 #ha ,,newton1 dispersion1 #bi -- corpuscular theory1 #ab -- law of cooling1 #df ,nichols1 ,rubens and1 ,rest-strahlen1 #gi ,nicholls and ,hull1 pressure of light1 #fd1 #fh ,,pfl,,ger1 emission from tourmaline1 #dc ,phase1 #bb ,phosphorescence1 #ei -- chemical theory of1 #fa -- temperature and phosphorescence1 #fb ,planck1 energy and wave-length1 #ea ,polarised light1 emission from tourmaline1 #db ,pressure of light1 prediction of by ,maxwell1 #fd -- measurement by ,lebedew1 #fe -- measurement by ,nicholls and ,hull1 #fd1 #fh -- on the earth1 #fh -- on fine dust1 #fi -- on comets' tails1 #fi -- three effects of in astronomy1 #gj ,prvost1 ,theory of ,exchanges1 #df ,,radiating power1 #ch ,radiometer action1 #fg ,reflection1 corpuscular theory1 #aa -- of electric waves1 #hg ,refraction1 corpuscular theory1 #aa -- of electric waves1 #hg ,resonance1 #cj ,rest-strahlen or residual rays1 #gi ,ripples on mercury1 #ac ,ritchie1 radiating and absorbing powers1 #ch ,rowland1 gratings1 #gc ,rubens and ,kurlbaum1 proof of ,planck's law1 #ea ,rubens and ,nichols1 ,rest-strahlen1 #gi ,,schumann waves1 #gh ,simple harmonic motion1 simple periodic motion1 #bd ,spark discharge1 #hd ,spectrometer1 #gf -- reflecting1 #gh ,spectrum1 #bi -- the whole1 #cb -- incandescent solid or liquid1 #cc -- incandescent gas1 #cc -- analysis1 #cd -- emission and absorption1 #cd -- sun1 #ce -- stars and nebul1 #cf -- and temperature1 #dh ,stationary waves1 #hh ,stefan1 law of radiation1 #dg ,,temperature1 absolute1 #ef -- of planets1 #ed -- of space1 #ee -- of sun1 #ec ,,ultraviolet rays1 #cb1 #gg ,,wave form1 #bd ,wave-length1 #bb -- range of1 #hj -- of electric waves1 #ij ,wave theory1 rectilinear propagation1 #ac ,wien1 ,law of ,radiation1 #ej ,,young1 interference1 #af ,printed by ,,ballantyne1 ,,hanson ,,co4 ,edinburgh ,london _/tb ,,the ,,people',s ,,books ,a wonderful enterprise1 admirably planned1 and deserving the highest success4--,the ,nation4 ,,the ,,first ,,dozen ,,volumes #e4 ,,botany3 ,,the ,,modern ,,study ,,of ,,plants4 ,by ,m4 ,c4 ,,stopes1 ,d4,sc41 ,ph4,d41 ,f4,l4,s4 ,a wonderful 'multum in parvo1' and cannot fail1 by its lucidity and pleasant method of exposition1 to give the reader not only a clear conception of the science of botany as a whole1 but also a desire for fuller knowledge of plant life4--,notes and ,queries4 #aj4 ,,heredity4 ,by ,j4 ,a4 ,s4 ,,watson1 ,b4,sc4 ,accurate1 and written in a simple manner which will stimulate those who are interested to wider reading4--,athenum4 #ab4 ,,organic ,,chemistry4 ,by ,professor ,j4 ,b4 ,,cohen1 ,b4,sc41 ,f4,r4,s4 ,an excellently clear and efficient treatise on a subject not easily confined within a short or untechnical discourse4--,the ,manchester ,guardian4 #ac4 ,,the ,,principles ,,of ,,electricity4 ,by ,,norman ,r4 ,,campbell1 ,m4,a4 ,as for ,mr4 ,norman ,campbell's treatise 'in petto' ,i cannot but think it a model of its kind4 ,he takes next to nothing for granted4--,sunday ,times4 #ae4 ,,the ,,science ,,of ,,the ,,stars4 ,by ,e4 ,w4 ,,maunder1 ,f4,r4,a4,s41 of the ,royal ,observatory1 ,greenwich4 ,will convey to the attentive reader an enormous amount of information in a small space1 being clear and abreast of current knowledge4--,the ,athenum4 #bf4 ,,henri ,,bergson3 ,,the ,,philosophy ,,of ,,change4 ,by ,h4 ,,wildon ,,carr4 ,the fact that ,m4 ,bergson has read the proof-sheets of ,mr4 ,carr's admirable survey will give it a certain authoritativeness for the general reader4--,daily ,news4 #cb4 ,,roman ,,catholicism4 ,by ,h4 ,b4 ,,coxon4 ,preface1 ,mgr4 ,r4 ,h4 ,,benson4 ,this small book is one which cannot fail to be of use to those who desire to know what ,catholics do1 and do not1 believe4--,the ,catholic ,chronicle4 #ci4 ,,mary ,,queen ,,of ,,scots4 ,by ,e4 ,o',,neill1 ,m4,a4 ,mrs4 ,o',neill1 on ',mary ,queen of ,scots1' is splendid2 it is an attempt to give the very truth about a subject on which all feel interest and most lie freely4--,daily ,express4 #dg4 ,,women',s ,,suffrage4 ,by ,m4 ,g4 ,,fawcett1 ,,ll4,d4 ,mrs4 ,fawcett's admirably concise and fair-minded historical sketch of the women's suffrage movement4 ,we could hardly ask for a better summary of events and prospects4--,daily ,news4 #ea4 ,,shakespeare4 ,by ,professor ,c4 ,h4 ,,herford1 ,litt4,d4 ,well worth a place alongside ,professor ,raleigh's book in the ',english ,men of ,letters4' 444 ,sets a high note and retains it without effort4--,observer4 #ec4 ,,pure ,,gold--,a ,,choice ,,of ,,lyrics ,,and ,,sonnets4 ,by ,h4 ,c4 ,o',,neill4 ,an anthology of good poetry such as we might expect from a man of taste4--,daily ,news4 #eg4 ,,dante4 ,by ,a4 ,g4 ,,ferrers ,,howell4 ,it is a fine piece of scholarship1 and should be read by any one who is beginning the study of ,dante1 or indeed any one who is interested generally in the early process of ,european literature1 for the process is here admirably analysed4--,the ,manchester ,guardian4 ,,the ,,second ,,dozen ,,volumes 7,ready7 #a4 ,,the ,,foundations ,,of ,,science4 ,by ,w4 ,c4 ,d4 ,,whetham1 ,m4,a41 ,f4,r4,s4 #aa4 ,,inorganic ,,chemistry4 ,by ,professor ,k4 ,c4 ,c4 ,,baly1 ,f4,r4,s4 #ad4 ,,radiation4 ,by ,p4 ,,phillips1 ,d4,sc4 #bb4 ,,lord ,,kelvin4 ,by ,a4 ,,russell1 ,m4,a41 ,d4,sc41 ,m4,i4,e4,e4 #bc4 ,,huxley4 ,by ,professor ,g4 ,,leighton1 ,m4,d4 #cf4 ,,the ,,growth ,,of ,,freedom4 ,by ,h4 ,w4 ,,nevinson4 #da4 ,,julius ,,caesar3 ,,soldier1 ,,statesman1 ,,emperor4 ,by ,,hilary ,,hardinge4 #dc4 ,,england ,,in ,,the ,,middle ,,ages4 ,by ,mrs4 ,e4 ,o',,neill1 ,m4,a4 #ed4 ,,francis ,,bacon4 ,by ,professor ,a4 ,r4 ,,skemp1 ,m4,a4 #ee4 ,,the ,,bront,s4 ,by ,miss ,,flora ,,masson4 #fj4 ,a ,,dictionary ,,of ,,synonyms4 ,by ,,austin ,k4 ,,gray1 ,b4,a4 #fa4 ,,home ,,rule4 ,by ,l4 ,g4 ,,redmond ,,howard4 ,list of other ,volumes in ,preparation may be had4 ,,london ,,and ,,edinburgh3 ,t4 ,c4 ,e4 ,c4 ,,jack ,,new ,,york3 ,,dodge ,,publishing ,,co4