//>;-// 2, 1885] 



NA TURE 



509 



Calling P the lathe with forced vibrations (correspond- 

 ing to the external massless shell acted on by the ether), 

 and £ its displacement, m , m u &c, are the successive 

 masses, .r„, x it &c, are their displacements 



»., = - a* 



and measures the relative displacement of m 1 and »i-,. 

 < 1, t\„ &c, are the constants of successive spring connec- 

 tions. c 2 (jTj-.f.j) is the force of restitution in virtue of 

 the spring connection between .\\ and .1:,. t is the period 

 of forced vibration. 



We thus arrive at the equation 

 dn 



~, ' —7 IlliXi- + III 1 + 



+ 



+ >"j *j 



and since the right hand member is essentially negative, 

 it follows that all the it's diminish with increase of period. 

 The critical cases occur when the period of forced vibra- 

 tion agrees with the natural period of any of the shells or 

 lathes. When the forced vibration is very rapid, all 

 successive masses move in opposite directions. When 

 the forced period is slower, tt, becomes zero, and .r, is in- 

 finite — i.e. the vibration of the lowest mass is infinite 

 in comparison with the forced vibrator, and 50 with the 

 other vibrators. When the forced period is slower, //' 

 becomes negative, i.e. the lowest mass begins to vibrate 

 in the same direction, as the forced vibrator. Successive 

 critical cases occur as the forced period reaches the 

 natural periods of successive vibrators. At the critical 

 period for any one vibrator, all those below it are 

 vibrating in one direction, while the critical one and 

 those above it are executing very large vibrations in 

 opposite directions successively. 



These critical periods are admirably adapted for ex- 

 plaining absorption and also anomalous dispersion. In 

 highly absorbing media which cut off a band of light 

 from the spectrum, the refractive index for colours neigh- 

 bouring to the band is remarkable ; thus light of greater 

 wave-length than the band is refracted more, and light of 

 less wave-length than the band is refracted less than in 

 normal substances. Lord Rayleigh considered this to be 

 due to the mutual influence of the vibrating molecule and 

 ether. If the point of support of a pendulum is vibrated 

 in a different period, the period of the pendulum is 

 changed. Lommel seems to have been the first to make 

 dispersion depend upon associated matter. 



The influence of a large number of the spring and 

 shell molecules distributed through the ether upon the 

 velocity of light in that medium is examined and shovrn 

 to depend upon the wave-length or period. Finally at 

 p. io3 we obtain the following formula : — 



r If I t-.rV k,--A', k*R, 



Ri 



■•■>}} 



density and rigidity. 

 I nerga of ith shell 

 Energy of trie whole 

 = the /th critical per.od. 



" This is the expression for the square of the refractive 

 index, as it is affected by the presence of molecules 

 arranged in that way. It is too late to go into this for 

 interpretation just now, but I will tell you that if you 

 take r considerably less than k, and very much greater 

 than k.. you will get a formula with enough disposable 

 constants to represent the index of refraction by an em- 

 pirical formula, as it were, which from what we know, 

 and from what Sellmeier and Ketteler have shown, we 

 can accep; as ample for representing the refraction index 

 of most transparent substances. We have the means of 

 extruding its po.vers and introducing the effects of those 

 other terms, so that we have a formula which is more 

 than sufficient to give us a mathematical expression of 

 the refrangibility in the case of any transparent body 

 whose refrangibility is reliable." 



In fact the above formula is equivalent to the well- 

 known formula of Cauchy and others, viz. 



when we are not dealing with critical cases. Exa- 

 mining the formula for -,■ or p", we see that as t ap- 

 proaches k,, fi- becomes infinite, and for t a little 

 greater than «,, p- is negative, which is impossible, 

 and we can have no assignable velocity for such 

 a period — i.e. there is absorption for all values of 

 t > k,, which make p* negative. Moreover, owing 

 to the existence of a critical period, «,, the re- 

 fractive index is abnormally increased for values of r 

 which are just less than «,, and it is abnormally dimi- 

 nished just when /*'- becomes positive. This means that 

 the refrangibility of rays in a highly absorbent medium, 

 in the neighbourhood of the band of absorption, is 

 anomalous in the direction indicated by Kundt in his 

 researches on anomalous dispersion. Here is what we 

 find at p. 1 50 on critical values of t and the manner of 

 absorption : — 



" We shall try to see something more of the effect of 

 light propagated through a medium of a period exactly 

 equal K v I believe each sequence of vibrations will 

 throw in a little energy which will spread out among the 

 different possible motions of the molecule. The com- 

 bination of the sequences, forming what we call con- 

 tinuous light, is not a continuous phenomenon at all. I 

 believe that the first effect when light begins will be : each 

 sequence of waves of the exact period throws in some 

 energy into the molecule. That goes on until, somewhere 

 or other, the molecule gets uneasy. It takes in an 

 enormous amount of energy before it begins to get parti- 

 cularly uneasy. It then moves about, and begins to col- 

 lide with its neighbours perhaps, and will therefore give 

 you heat in the gas, if it be a gaseous molecule. It goes 

 on colliding with the other molecules, and in that way 

 imparting its energy to them. The energy will be simply 

 carried away, by convection if you please, or a part of it 

 perhaps. Each molecule set to vibrating in that way 

 becomes a source of light, and so we may explain the 

 radiation of heat from the molecule after it has been 

 got into the molecule by sequences of waves of light. I 

 believe we can so explain the augmented pressure of a 

 gas due to the absorption of heat in it. 



" We may consider, however, that the chiefest vibra- 

 tion of the molecule is that in which the nucleus goes in 

 one direction, and the shell in the opposite direction, but 

 with a great amount of energy in the interior vibrations 

 and very little in the shell, so that the shell may go on 

 giving out phosphorescent energy for two or three hours 

 or days, simply vibrating for ever, except in so far as the 

 energy is drawn off and allowed to give motion to other 

 bodies." 



A great deal more is said about the influence of critical 

 periods upon anomalous dispersion, but, as the author 

 says, "it is like fiddling when Rome is burning to discuss 

 anomalous dispersion when double refraction is waiting 

 to be explained," so I will pass from this subject. 



We have in the lectures some indications of the effect 

 ol introducing a gyrostat inside the shell molecule, 

 especially with relation to magnetic rotation of the plane 

 of polarisation. On this subject the author said sadly : 

 •' But alas ! my results give me another law, not more 

 effect with greater frequency, but less effect with greater 

 frequency, according to the inverse square of the wave- 

 length. I therefore lay it aside for the present, but with 

 perfect faith that the principle of explanation of the thing 

 is there " (p. 244). 



But, on returning to this country, a more complete 

 theory of the gyrostatic molecule was worked out, sent to 



