1883.] on the Size of Atoms. 207 



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 j)erpendicular 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 jDarallel 

 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 experimerificm cruets by which he has answered, 

 as seems to me beyond all doubt, the old vexed question — Whether is 

 the vibration perpendicular to, or in the plane of polarisation ? To 

 show you this experiment, instead of using unpolarised 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 saw 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 apparatus round, 

 so that, sitting in all parts of the theatre, you may all see the tube in 

 the proper dii'ection for the successive phenomena of " light," and 

 " no light." You see them now exactly fulfilling the description 

 which I gave you in anticipation. If each of you had a Nicol's prism 

 in your hand, you would learn that when you see light at all, its plane 

 of polarisation is in the plane through your eye and the axis of the 

 tube ; and I hope you all now perfectly understand the proof that the 

 dii-ection of vibration is perpendicular to this plane. 



Now I want to bring before you something which was taught me 



where m, v, w are such that 



d u d V d 10 



— + — + T-=0. 

 ax ay dz 



"Find differential equations for the determination of <p, u, v, w. Find the 

 reispective wave-velocities for the (i)-S()lution, and for the (m, u, M)-solution. 



"(c/) Prove the following to be solutions, and interpret eacli for values of 

 >' [VC-^' + y"^ + -2^)] very great in comparison with A (the wave-length). 



(1) 



(2) 



dd) dd) dd) 



d X dy d z 



1 27r 



where ^ = -sin — [^ — ^ V (^^ + I w)]- 



d z d y 



1 2 TT 



where il' = - sin — \r — t J n\ 



(3) '-m^^'^, ^=,^., .= ''' 



\J c?x^ ' dxdy^ dxdz' 



Vol. X. (No. 76.) 



