204 



NATURE 



{Jan. 15, 1874 



coloured red andgrecn respectively ; t'-cn one of the sha- 

 dows will be due to the shutting off of the red light, and the 

 other to that of the green. But in the first case the space 

 occupied by the shadow will be still illuminated by the 

 green light, and in the second by the red. In other 

 words, neither of the two shadows will be black, one will 

 be green, and the other red. If in any part of their 

 extent the two shadows overlap, the part common to the 

 two, being deprived of both red and green light, will be 

 black. 



But in order to explain how it comes to pass that colour 

 is produced at all, as well as to find a more strict proof 

 that the colours of the two images are complementary, we 

 must have recourse to some considerations based upon 

 the wave theory of light. And first as to the mode in 

 which waves may be produced. 



Consider a row of balls lying originally in a hori- 

 zontal straight line. Let the balls start one after another 

 and vibrate at a uniform rate up and down. At each 

 moment some will be at a higher, others at a lower level, 

 at regular intervals in a wave-like arrangement ; the 

 higher forming the crests, the lower the hollows of the 

 waves. The distance from crest to crest, or from hollow 

 to hollow, is called the wave length. The distance from 

 crest to hollow will consequently be half a wave-length. 

 This length will be uniform so long as the vibrations are 

 executed at a uniform rate. 



Each ball in turn will reach its highest point and form 

 a crest ; so that the crests will appear to advance from 

 each ball to the next. In other words, the waves will 

 advance horizontally, while the balls vibrate vertically. 



If the row of balls were originally arranged in a wave 

 form, and caused to vibrate in the same way as before, 

 those on the crests would vibrate wholly above, and those 

 in the hollows wholly below the middle line. When the 

 balls originally on the crests rise to their highest points, 

 those in the hollows will fall to their lowest positions, and 

 the height of the wave will consequently be doubled. 

 When the balls originally at the crests fall, those in the 

 hollows will rise, both to the middle line ; and the wave 

 will consequently be annihilated. The first of these 

 corresponds to a condition of things wherein the crests 

 of the new wave motion coincide with those of the old, 

 and the hollows with the hollows ; the second to that 

 wherein the crests of the new coincide with the hollows 

 of the old, and vice vcrsA. 



Hence, when two sets of waves are coincident, the 

 height of the wave or extent of vibration is doubled ; 

 when one set is in advance of the other by half a wave 

 length, the motion is annihilated. The latter phenomenon 

 is called interference. When one set of waves is in ad- 

 vance of the other by any other fraction of a wave-length, 

 the height of the wave, or extent of vibration, is dimi- 

 nished, but not wholly destroyed ; in other words, partial 

 interference takes place. The distance whereby one set 

 of waves is in advance of another is called the difference 

 of phase. 



The Wave Theory of Light consists in explaining opti- 

 cal phenomena by vibrations and waves of the kind above 

 described. And according to that theory the direction in 

 which the waves move is the direction of propagation of 

 the ray of light. 



The intensity of light depends upon the extent of the 

 vibrations or the height ol the waves ; the colour upon 

 the number of vibrations executed in a given interval of 

 time. And since throughout any uniform medium the 

 connection of the parts and the rate of propagation may 

 be considered to be uniform, it follows that the waves due 

 to the slower vibrations must be longer than those due to 

 the more rapid. Hence the colour of the light may be 

 regarded as depending upon the wave length. 



The substance to the vibrations of which hght is sup- 

 posed to be due, is an elastic fluid or medium pervading 

 all space, and even permeating the interior of all bodies. 



A full statement of the reasons which have led philoso- 

 phers to make this hypothesis would involve considera- 

 tions derived from other sciences besides optics, and 

 would be out of place here. But it may still be pointed 

 out that one strong argument is furnished by the fact of 

 the transmission of light from the sun and from the fixed 

 stars through space, where no atmosphere or known gases 

 can be conceived to exist. That the light so traversing 

 interstellar space must be transmitted by a material sub- 

 stance, is a fundamental proposition of mechanical philo- 

 sophy ; and the hypothesis of the ether simply consists in 

 attributing to the substance or medium the property of 

 elasticity (a property possessed in a greater or less de- 

 gree by all known bodies), without assuming anything 

 else whatever as to its nature or relation to other sub- 

 stances. 



In the illustrations of wave motions given above, the 

 balls would represent successive portions or molecules of 

 the ether ; and the means whereby the motion of one 

 molecule is transmitted to its neighbour, is the elastic co- 

 hesion attributed to the whole medium in the hypothesis 

 above mentioned. 



The difference between ordinary and polarised light has 

 been explained above ; and the mechanical contrivances 

 devised for representing wave motion always have refer- 

 ence only to polarised light. But as this is the subject 

 with which we are here concerned, the limitation in ques- 

 tion is not of consequence. A variety of instruments have 

 been constructed for showing the effects of compounding 

 vibrations or waves under different circumstances. The 

 best with which I am acquainted is that by Sir Charles 

 Wheatstone. 



In plane polarised light, such as is produced by tour- 

 malin plates, by double refraction in Iceland spar, &c., 

 the vibrations are rectilinear, and are executed in one 

 and the same plane throughout the entire length of the 

 ray. In circularly polarised light the vibrations are all 

 circular, and the motion is performed in the same direc- 

 tion. In cUiptically polarised light the vibrations are all 

 elliptical, the ellipses are all similarly placed, and the 

 motion is in the same direction for the entire ray. These 

 are the only known forms of polarisation, and indeed they 

 are the only forms compatible with the usual, simplest 

 assumption respecting the elasticity of the ether. 



These general considerations being premised, we are in 

 a position to trace the course and condition of a ray of 

 light issuing from the lamp or other source, and tra- 

 versing first the polarising Nicol's prism ; secondly, the 

 plate of doubly refracting crystal ; thirdly, the analysing 

 Nicol. 



The vibrations of the ray on leaving the polariser are 

 all restricted to a single plane. On entering the plate of 

 doubly refracting crystal, every ray is divided into two, 

 whose vibrations take place in planes perpendicular to 

 one another. The angular position of these planes about 

 the axis of the beam of light is dependent upon the 

 angular position of the crystal plate about its centre. 

 The two sets of rays traverse the crystal with different 

 velocities, and therefore emerge with a difference of 

 phase. The amount of this difierence is proportional to 

 the thickness of the plate. On entering the analyser the 

 vibrations of each pair of rays are resolved into one 

 plane ; and are then in a condition to exhibit the pheno- 

 mena of interference. If the plane of vibration of the 

 analyser be parallel to one of those of the plate, that ray 

 will be transmitted without change ; the other will be 

 suppressed. In any other position of the analyser those 

 monochromatic rays (spectral components of white light 

 whose difference of phase most nearly approaches to half 

 a wave-length, will be most nearly suppressed ; and those 

 in .which it approaches most nearly to a whole wave- 

 length will be most completely transmitted. The amount 

 of light suppressed increases very rapidly in the neigh- 

 bourhood of the ray whose difterence of phase is exactly 



