284 



NA TURE 



[Feb. 12, 1874 



circumstance interfere with the employment of prismatic 

 analysis. 



If the thickness of the plate be such that the difference 

 of rotation of the planes of vibration of the rays corre- 

 sponding to the two ends of the visible spectrum (or, as it 

 is sometimes termed, the "arc of dispersion") be less 

 than 180°, there will be one dark band in the spectrum ; 

 because there can then be only one plane of vibration at 

 a time at right angles to that of the analyser. If the arc 

 of dispersion is greater than 1 80' and less than 360°, 

 there will be two bands. And so on for every 180° of 

 dispersion. 



This mode of examination by means cf prismatic 

 analysis is the mo=t accurate yet devised for measuring 

 the angle of rotation produced by circular polarisation ; 

 especially if solar light be employed, and the fixed lines 

 used to form a scale of measurement. 



The property of circular polarisation is, however, not 

 confined to quartz. Among solids, chloride of sodium is 

 the only other known instance, but among fluids and fluid 

 solutions there arc not a few. 



The following list is given by Verdet. The angles 

 have reference to the red rays given by a plate of glass 

 coloured with oxide of copper, and are affected with the 

 sign + in the case of right-handed, and with - in the 

 case of left-handed rotation. The length of the column 

 of the solution is in every case one decimetre. 



Essence of turpentine . . . — 29^'6 

 ,, lemon . . • +55°'3 



,, bergamot . . . -Hi9°'oS 



,, bigavade . . . +7*'"'94 



,, aniseed . . . — o°-7o 



„ fennel . . . "^■3°'i6 



,, carroway . . • +(^S°"i'-) 



,, lavender . . . -t- 2° 02 



,. peppermint. . . -l-i6''i.|. 



,, rosemary . . . + 2°'29 



,, mavjorum . . • -l-ii"'S; 



., sassafras . . • + 3 '^9 



■ Silii'inn of sugar 50 per cent. . ■I3 5"'64 

 ., ijuinine 6 per cent, in ) ,q". 



alcobn] . \ '' 



It will li; noticed that the rotary power of all these 

 substances is much less than that of quartz. 



A mixture of liquids, one or both of »hlch is active, 

 generally exhibits a rotatory action represented by the sum 

 or difference of their separate powers (a neutral liquid 

 being considered to have a power represented by c) ; but 

 this law is true only when no chemical action takes place 

 between the elements of the mixture. Saccharine solu- 

 tions vary not only in the amount but also in the character 

 of their power of rotation ; thus cane sugar is right-handed, 

 but grape sugar left-handed. 



The property in question has been turned to practical 

 use by employing the rotatory power of a saccharine 

 solution as a measure of the strength of the solution. For 

 this purpose a tube containing the solution to be examined 

 is placed between two Nicol's prisms. The simple fact of 

 circular polarisation is proved by a feeble exhibition of the 

 phenomena shown by a plate of quariz cut perpendicularly 

 to the axis. But for accurate measurement various 

 expedients have been adopted. If a biquartz be inserted 

 behind the analyser (the end of the apparatus next the eye 

 being considered the front), then for a certain position of 

 the analyser the two halves will appear of the same colour. 

 When the tube ior examination is inserted the similarity 

 of colour will be disturlied ; and the angle through which, 

 right or left, the analyser must be turned in order to 

 restore it will be a mtasure of the rotary power of the 

 fluid. 



Another method is as follows :^Use a single quartz 

 instead of a biquartz ; in front of it place a pair of quartz 

 wedges, with the thin end of one opposite the thick end 

 of the other ; the outer surfaces having been cut perpen- 

 dicularly to the axis. If the plate be right-handed, the 



wedges must be left-handed, and z'ke '•crsa. The wedges 

 must be made to slide one over another so as together to 

 form a plate of any required thickness, and a scale con- 

 nected with the sliding gear registers the thickness of the 

 plate produced. When the tube is removed the wedges 

 are adjusted so as to compensate the quartz plate, and 

 their position is considered as the zero point of the scale. 

 When the tube is replaced, the wedges are again adjusted 

 so as to compensate the action of the fluid in the tube, 

 and the difference of the readings gives the thickness of 

 quartz necessary for the compensation. The rotatory 

 effect of a given thickness of quartz being supposed known 

 we know at once the effect of a thickness of the fluid under 

 e.xamination equal to the length of the tube. 



Another method has been based upon the principle of 

 Savarts bands ; but sufficient has perhaps here been said 

 to illustrate the principle of the saccharometer. 



Circular polarisation may, however, be also produced 

 by other means, namely, by total reflexion, and by trans- 

 mission through doubly-refracting plates of suitable 

 thickness. 



It will perhaps be best to begin with the last. And in 

 order the better to understand the process we must con- 

 sider briefly the result of compounding two rectilinear 

 vibrations under different circumstances. 



.Suppose a particle of ether to be disturbed from its 

 point of rest O in a direction O A. The attraction of the 

 particles in its neighbourhood would tend to draw it back 

 to O ; and let O A be the extreme distance to whi.?h 

 under these attractions it would move. Having reached 

 A it would return to O, and passing through O with a 

 velocity equal to that with which it started under the dis- 

 turbing force, it would move to a point B equidistant from 

 O with A, but in the opposite direction. And if, as is 

 generally supposed, the ether is perfectly elastic, or that 

 there are no internal frictions or other conditions whereby 

 the energy of motion is converted into other forms of 

 energy, the oscillations or vibrations of the particle be- 

 tween the points A and B will continue indefinitely. Now 

 suppose that while these vib'ations are going on, a second 

 disturbing impulse, equal in intensity, but in a direction at 

 right angles to the first, be communic.ited to the particle, 

 it is clear that the effect on the motion of the particle will 

 be different according as it takes place at the point of 

 greatest velocity O, or at that of no velocity A or B, or at 

 some intermediate point. Our object is to consider the 

 effects under these various circumstances. 



A complete vibration consists in the motion from O to A, 

 thence to B, and finally back to O ; so that if O be the 

 starting point the pas-age through A will be removed one- 

 fourth, the passage through O from A towards B will be 

 one-half, the passage through B will be three-fourths, and 

 the passage through O from B to A a complete vibration 

 from the commencement. This being so, suppose that 

 the second impulse be communicated while the particle is 

 at O on its way towards A, then the impulses may be 

 considered as simultaneous and the vibrations to which 

 they give rise will commence together, and the waves of 



