July 19, 1883] 



NATURE 



275 



At present you see nothing in the tube; it still continues 

 to be, as before the admission of the vapours optically 

 transparent ; but gradually you will see an exquisite blue 

 cloud. That is Tyndall's "blue sky." You see it now. I 

 take a Nicol's prism, and by looking through it I find the 

 azure light, coming from the vapours in any direction 

 perpendicular to the exciting beam of light, to be very 

 completely polarised in the plane through my eye and the 

 exciting beam. It consists of light-vibrations in one 

 definite direction, and that, as finally demonstrated by 

 Professor Stokes, it seems to me beyond all doubt, through 

 reasoning on this phenomenon of polarisation, 1 which he 

 had observed in various experimental arrangements 

 giving minute solid or liquid particles scattered through a 

 transparent medium, must be the direction perpendicular 

 to the plane of polarisation. 



What you are now about to see, and what I tell you I 

 have seen through the Nicol's prism, is due to what I 

 may call secondary or derived waves of light diverging 

 from very minute liquid spherules, condensed in conse- 

 quence of the chemical decomposing influence exerted by 

 the beam of light on the matter in the tube, which was 

 all gaseous when the light was first admitted. 



To understand these derived waves, first you must 

 regard them as due to motion of the ether round each 

 spherule ; the spherule being almost absolutely fixed, 

 because its density is enormously greater than that of the 

 ether surrounding it. The motion that the ether had in 

 virtue of the exciting beam of light alone, before the 

 spherules came into existence, may be regarded as being 

 compounded with the motion of the ether relatively to 

 each spherule, to produce the whole resultant motion 

 experienced by the ether when the beam of light passes 

 along the tube, and azure light is seen proceeding from 

 it laterally. Now this second component motion, is 

 clearly the same as the whole motion of the ether would 

 be, if the exciting light were annulled and each spherule 

 kept vibrating in the opposite direction, to and fro through 

 the same range as that which the ether in its place had, 

 in virtue of the exciting light, when the spherule was not 

 there. 



Supposing now, for a moment, that without any exciting 

 beam at all, a large number of minute spherules are all 

 kept vibrating through very small ranges = parallel to one 



1 Extract from Professor Stokes' paper, ''On the Change of Refran- 

 gibilily of Light," read before the Royal Society, May 27th. 1852. and 

 published in the Transactions for that date : — 



" § 183. Now this result appears to me to lave ni remote bearing on the 

 'question of the direction of the vibrations in polarised light. So long as 

 " the suspended particles are large compared with the waves of light, reflection 

 " takes place as it would from a portion of the surface of a large solid immersed 

 " in the fluid, and no conclusion can be drawn either way. But if the diameters 

 ' ' of the particles be small compared with the length of a wave of light, it 

 " seems plain that the vibrations in a reflected ray cannot be perpendicular 

 " to the vibrations in the incident ray. Let us supp ose for the present, that 

 " in the case of the beams actually observed, the suspended p.trlicles were 

 " small compared with the length of a wave of light. Observation showed 

 " that the reflected ray was polarised. Now all the appearances presented 

 "by a plane polarised ray are symmetrical with respect to the plane of 

 "polarisation. Hence we have two directions to choose between for the 

 " direction of the vibrations in the reflected ray, namely, that of the incident 

 " ray, and a direction perpendicular to both the incident and the reflected 

 " r.iys. The former would be necessarily perpendicular to the directions of 

 11 vibration in the incident ray. and therefore we are obliged to choose the 

 " latter, and consequently to suppose that the vibrations of plane polarised 

 "light are perpendicular to the plane of polarisation, since experiment shows 

 "that the plane of polarisation of the reflected ray is the plane of reflection. 

 " According to this theory, if we resolve the vibrati'ns in the [horizontal] 

 " iocid nt ray horizontally and vertically, the resolved parts will correspond 

 " to the two rays, polarised respectively in and perpendicularly to the plane of 

 " reflection, into which the incident ray may be conceived to be divided, and 



"of these the former alone is capable of furnishing a ray reflected 



" vertically upwards [to be seen by an eye above the line of the incident ray, 

 "and looking vertically downwards]. And, in fact, observation shows that, 

 " in order to quench the dispersed beam, it is sufficient, instead of analysing 

 "the reflected light, to polarise the incident light in a plane perpendicular to 

 " the plane of reflection." 



2 In the following question of the recent Smith's Prize Examination at 

 Cambridge (paper of Tuesday, Jan. 30. 1883), the dynamics of the subject, 

 and particularly the motion of the ether produced by keepinga single spherule 

 embedded in it vibrating to and fro in a straight line, are illustrated in parts 

 (n) and (//): — 



" 8. (a) From the known phenomenon that the light of a cloudless blue 

 "sky, viewed in any direction perpendicular to the sun's direction, is almost 

 " wholly polarised in the plane through the sun, assuming that this light is 



line. If you place your eye in the plane through the 

 length of the tube and perpendicular to that line, you will 

 see light from all parts of the tube, and this light 

 which you see will consist of vibrations parallel 

 to that line. But if you place your eye in the line of 

 the vibration of a spherule, situated about the middle of 

 the tube, you will see no light in that direction ; but keep- 

 ing your eye in the same position, if you look obliquely 

 towards either end of the tube, you will see light fading 

 into darkness, as you turn your eye from either end 

 towards the middle. Hence, if the exciting beam be of 

 plane polarised light— that is to say, light of which all 

 the vibrations are parallel to one line — and if you look at 

 the tube in the direction perpendicular to this line and to 

 the length of the tube, you will see light of which the 

 vibrations will be parallel to that same line. But if you 

 look at the tube in any direction parallel to this line, you 

 will see no light ; and the line along which you see no 

 light is the direction of the vibrations in the exciting 

 beam ; and this direction, as we now see, is the direction 

 perpendicular to what is technically called the plane of 

 polarisation of the light. Here, then, you have Stokes's 

 experimentum cruets by which he has answered, as seems to 

 me beyond all doubt, the old vexed quest ion — Whether is the 

 vibration perpendicular to, ax in the plane of polarisation? 

 To show you this experiment, instead of using unpolarisei 

 light for the exciting beam, as in the previous experiment, 

 and holding a small Nicol's prism in my hand and telling 

 you what I sav when I looked through it, I place, as is 

 now done, this great Nicol's prism in the course of the 

 beam of light before it enters the tube. I now turn the 

 Nicol's prism into different directions and turn the appa- 

 ratus round, so that, sitting in all parts of the theatre, 

 you may all see the tube in the proper direction for the 

 successive pheno.nena of "light," and "no light." You 

 see them now exactly fulfilling the description which I 

 gave you in anlicipation. If each of you had a Nicol's 



" due to particles of matter of diameters small in comparison with the wave- 

 " lciigih of light, pr_.ve that the direction of the vibrations of plane polarised 

 " light is perpendicular to the plane of polarisation. 



(/>) Show that the equations of motion of a homogeneous isotropic elastic 

 "solid of unit density, are 



V- =<*+*«> 



di 



+ "V=1, 



" where k den>tes the modulus of resistance to compression ; n the rigidity- 

 " modulus ; a, (3, 7 the components of displacement at (.r, y, z, t) ; and 



J = p + f + *, 



dx dy dz 



dx 2 dy 3 



d2? 



" (t"} Show that every p jssible solution is included in the f -Mowing ; 



a = ** + u. 13 = £* + V, 1 = d ± + W, 

 dx dy dz 



' where u, v, ~.u are such that 



du , dv , dw 



— -+■ — -J- — 5= o. 



dx dy dz 



" Find differential equations for the determination of 0, «. v, w. Find 

 'the respective wave-velocities for the <p-s Iution, and for the (//, -', u<)- 

 ' solution. 



"(//) Prove the following to be solutions, and interpret each for values o 

 ' r W C* 3 + y~ + 3= )J verv £ reat in comparison with -\ (the wave-length). 

 d<& „ d<p dtp 



« 



(2) 



\ where <p = - sin — [r ■ 

 { r X 



' dz 



■ tV(k + 1 "1 



d± 

 dz ' 



_d<l, 

 "~dy 



(3) 



la = o. /} 



1 where <fr = - sin £S-|r - l\'n]. 

 \ r 



* r 



d'i 



,/x dy ' 



d 2 -j, 

 dx dz 



