﻿of Light by small Particles. 453 



ing further; but I have not arrived at any results of interest. 

 Without calculation, we may anticipate that, as the diameter of 

 the particles approaches in magnitude the quarter wave-length, 

 the amplitude of the diffracted vibration will begin to increase 

 less rapidly than T, and that about the time the half wave-length 

 is passed an absolute diminution will set in. Of course, when 

 the incident light is compound, the more refrangible elements 

 will be the first to show a sensible deviation from the more 

 simple law. 



In his interesting experiments with precipitated vapours, 

 Professor Tyndall* found that when the particles of the cloud 

 illuminated by unpolarized light from the electric lamp had 

 attained such a size that the light discharged normally had lost 

 most of its power of affecting the naked eye with the sensation 

 of colour, even then by analyzing the light with a Nicol placed 

 in its position of minimum transmission the azure could be re- 

 vived in increased splendour. Professor Tyndall calls this the 

 " residual blue." Experimentally it is doubtless more conve- 

 nient to analyze the light after diffraction from the cloud ; but in 

 theoretical explanation and deduction it is simpler, and comes to 

 the same thing in the end, to consider the original beam as po- 

 larized before it falls on the cloud. The residual blue is then 

 the light discharged from the cloud in a direction parallel to that 

 in which the incident light swings. The complete explanation 

 of this and other allied phenomena is yet to be made out ; but 

 one thing we learn from our theory, if indeed it is at all to 

 be depended on. However large the particles may be, the light 

 scattered or reflectedf parallel to the primary vibrations depends 



on the square and higher powers of — =r — , or, in experimental 



language, of 2 . It is easy to see, too, that the first term in 



the expression of the amplitude must contain a much higher in- 

 verse power of \ than X, -2 , and that if it stood alone it would cor- 

 respond to a compound light of a much richer colour than that due 

 to very small particles acting in the ordinary way. Still I cannot 

 honestly say that the residual blue is predicted by theory : before 

 the light discharged in this unfavourable direction could become at 

 all sensible, the particles must have grown to such a size that their 

 diameter would bear no inconsiderable proportion to the waves of 

 light ; and then we have no right to suppose that the first term in 

 the expansion proceeding by powers of the diameter may be taken 



* Phil. Mag. vol. xxxviii. p. 156. Phil. Trans. 1870. 



t This may be verified with Fresnel's expression for the intensity of the 

 light regularly reflected when the plane of polarization and plane of inci- 

 dence include a right angle. 



Phil. Mag. S. 4. Vol. 41. No. 275. June 1871. 2 H 



