Feb. 12, 1874] 



NA TURE 



285 



which they fonn part will be coincident. If the second 

 impulse take place when the particle is at A, the two sets 

 of vibrations or waves to which they belong will have a 

 difference of phase {i.e. the first will be in advance of the 

 ■ second) equal to one-fourth of a vibration or one-fourth of 

 a wave-kngth. If the second impulse take place when 

 the particle is at O on its way to B,the difference of phase 

 will be half ; if when it is at B the difference will be three- 

 fourths of a wave-length. 



The particle being at O, and subject to two simultaneous 

 impulses of equal strength, one in the direction of A, the 

 other in that of C, must move as much in the direction of 

 C as in that of A, that is, it must move in a straight line 

 equally inclined to both, namely O E in the same figure. 

 And inasmuch as the two impulses in no way impede one 

 another, ihe particle will move in each direction as far as 

 it would have done if the other had not taken place. In 

 other words, if we draw a square about O with its sides at 

 distance equal to O A or O B, the extent of the vibration 

 will be represented by O E where E is a corner of the 

 square. The complete vibration will then be represented 

 by the diagonal E F in the same way as it was by the 

 line A B in the first instance. If the impulse had been 

 communicated at the instant of passage through O on the 

 way to B, it is clear that a smnlar train of reasoning 

 would have shown that the vibration would have been in 

 the other diagonal G H. We conclude, therefore, that if 

 two sets of rectilinear vibrations, or plane waves, at right 

 angles to one another combine, then when they are coin- 

 cident they will produce a rectilinear vibration, or wave, 

 whose plane is equally inclined to the two, and lying in 

 the direction towards which the motions are simulta- 

 neously directed. In the figure this is represented by the 

 de.xter diagonal When the two sets of waves have a dif- 

 ference ol phase equal to half a wave length, their com- 

 bination gives rise to a wave represented in the figure by 

 the sinister diagonal. 



Suppose now that the second impulse is communicated 

 at the instant when the particle is at A ; in other words, 

 that the two sets of waves have a difference of phase 

 equal to one-fourih of a wave-length. At that instant the 

 particle will have no velocity in the direction of A B (for 

 convenience, say eas wards), and will consequently begin 

 to move in the directiun of the second impulse, say north- 

 wards. But as time goes on the paiticle will have an in- 

 creasing velocity westwards and a diminishing velocity 

 northwards, it will therefore move in a curve which gra- 

 dually and uniformly bends, until when it has reached its 

 greatest distance northwards it will be moving wholly 

 westwards. And as the motion not only will be the same 

 in each quadrant, but would be the same even if the di- 

 rections of the impulses were reversed, it is clear that the 

 curvature of the path will be the same throughout, that is 

 to say, if two sets of waves of the same magnitude in 

 planes perpendicular to one another, and with a difference 

 of phase equal to one-fourth of a wave-length combine, 

 they will produce a wave with circular vibrations. 



If the second impulse be given when the particle ar- 

 rives at B, that is, if the waves have a difference of phase 

 equal to three-fourths of a wave-length, similar considera- 

 tions will show that the motion will be circular, but in the 

 opposite direction. 



Suppose, therefore, that we allow plane-polarised light 

 to fall upon a plate of doubly refracting crystal cut per- 

 pendicularly to the axis in the case of a unia.xal crystal, 

 or in the case of a biaxal to the plane containing the two 

 axes, say a plate of mica which splits easily in that direc- 

 tion ; then the vibrations will, as before explained, be re 

 solved in two directions, at right angles to one another. 

 And further, if the original directions of vibration be 

 equally inclined to the new directions, i.e., if it be inclined 

 at 45'-' to them, the amount or extent of vibration resolved 

 in each direction will be equal. Further, if the thickness 

 of the plate be such as to produce retardation or differ- 



ence of phase equal to a quarter of a wave, or an odd 

 number of quarter wave-lengths, for the particular ray under 

 consideration ; then the two sets of vibrations on emerg- 

 ing from the mica plate will recombine, and. in accord- 

 ance with the reasoning given above, they will form a cir- 

 cular vibration, left-handed or right-handed according as 

 the retardation amounts to an integral number of three- 

 quarter wave-lengths or not. 



It thus appears that a plate of mica which retards one 

 of the sets of waves into which it divides an incident set 

 by an odd multiple of quarter-wave lengths, aftords a 

 means of producing circular from plane polarisation. It 

 remains to be shown that, with the same plate in different 

 positions, right or left handed circular polarisation may 

 be produced at pleasure. Suppose that the original vi- 

 brations are in the direction E F in the foregoing figure ; 

 the mica plate will resolve them into the two directions 

 A B, C D, one of the rays, say the first, will be trans- 

 mitted with greater velocity than the other, and the vi- 

 brations along C D will be one-fourth of a wave-length 

 behind those along A B. This will correspond to the 

 case discussed above, and will give rise to a circular 

 vibration in a direction opposite to that of the hands of 

 a clock. Suppose, however, that the plate be turned 

 round through a right angle, so that the vibrations which 

 are transmitted with greater velocity are placed parallel 

 to C D, and those which are transmitted with lesser along 

 A B. The ray whose vibrations aie along A B will then 

 be a quarter wave-length in advance, or, what comes to 

 the same thing, they are three-quarters of a wave-length 

 in rear of the others ; and this condition of things pio- 

 duces, as explained before, a circular vibration in a 

 direction the reverse of the former. It thus appears that 

 the plate placed in one direction will convert plane into 

 right-handed circular polarisation ; and ii turned round 

 through a right angle from that position will convert 

 plane into left-handed circular polarisation. A like 

 change from right-handed to left-handed circular pola- 

 risaiion, or vice-versa, may obviously be effected by 

 turning the orginal plane of polarisation through a right 

 angle ; so that it shall lie between lines of concurrent 

 instead of between lines of discordant motion. 



W. Spottiswoode 

 {To be conliiitied.) 



A COMPLETE SPECIMEN OF A PAL.EO- 

 THERIUM 



FROM La Nature we learn that the palseontological 

 collection of the IVluseum of Natural History of 

 Paris has just been enriched by the addition of a new 

 specimen of very great scientific interest, which is the 

 entire skeleton of Palaollieiiuin magnum, imbedded in a 

 large block of gypsum and marl, ttie whole being exhi- 

 bited in the anatomical department of the museum. 



The Palirolheriiim magnum, whose name alone indi- 

 cates its ancient existence, was first recorded by the great 

 French naturalist Cuvier, in his celebrated " Recherches 

 sur les Ossemens Fossiles." , It is an animal which is 

 entirely extinct, without any present representative. In- 

 dividuals of the species must have been extremely abun- 

 dant during the period that it existed. Modern zoologists 

 place it among the Perissodactylates, that is to say, with 

 the at present existing rhinoceros, tapir, and horse. It 

 forms part of the fauna which is found abundantly em- 

 bedded in the deposits of gypsum. All palreontological 

 collections, even the most humble, have for a long time 

 been provided with the remains, or more or less complete 

 portions of this fossil form, but none have yet had the 

 good fortune to obtain a complete skeleton. 



The principal result of the examination of the new 

 ■specimen which we are describing has been to show that 

 until now verv inexact rotions have been entertained as 



