April 8, 1922] 



NA TURE 



447 



Optical Rotatory Dispersion.^ 



By Prof. T. M. Lowry, F.R.S., and Dr. P. C. Austin. 



I . — Introduction. 



''I^HE discovery of optical rotatory dispersion may 

 A be said to have preceded rather than followed 

 the discovery of optical rotatory power, since it was 

 the unequal rotation of the plane of polarisation of 

 lights of different wave-lengths which gave rise to 

 the sequence of beautiful colours which Arago described 

 in 181 1 as being produced by the interposition of 

 quartz plates between a polariser and analyser set 

 to extinction. These colours were shown by Biot 

 in 181 2 to be due to a rotation of the plane of polarisa- 

 tion which increased with the thickness of the quartz 

 plate and with change of colour from red to violet. 

 When, therefore, a beam of polarised light had passed 

 through a quartz plate it was impossible any longer 

 to extinguish all the colours simultaneously with any 

 one setting of the analyser. 



Two features of Biot's work deserve special atten- 

 tion. In the first place, all his measurements oi 

 optical rotatory power included observations of 

 rotatory dispersion ; the custom of observing the 

 rotatory power of a substance for light of only one 

 wave-length and thus recording a single point on a 

 curve of unknown form is of comparatively recent 

 origin, and marks a distinct retrogression from the 

 more thorough methods of the earlier workers. The 

 second characteristic was the exact quantitative char- 

 acter of the work. Although he had no source of 

 inonochromatic light except a ruby glass which gave 

 a red light of average wave-length about 6530, Biot 

 made a quantitative study of the influence of wave- 

 length and of other physical conditions on rotatory 

 power, expressing his results, whenever this was 

 possible, by means of mathematical equations and 

 diagrams. 



Two of Biot's diagrams retain their interest even 

 at the present time. The first shows, by means of 

 a series of straight lines, the influence of dilution 

 with water on the rotatory power of tartaric acid. 

 This diagram enabled Biot to predict that dextro- 

 tartaric acid when in the anhydrous glassy form 

 would actually become laevorotatory at the red end 

 of the spectrum at all temperatures below 23° C, a 

 bold prediction that was verified experimentally ten 

 years later. 



The second of these diagrams was used by Biot 

 to illustrate his discovery that the rotation of the 

 plane of polarisation of light in quartz was inversely 

 proportional to the square of the wave-lengths, using 

 the figures determined by Newton for corresponding 

 regions of the spectrum. In this diagram the thick- 

 ness of quartz required to produce a given rotation 

 was plotted against the square of the wave-length, 

 and the result was a series of straight lines. Biot 

 recognised that some of the readings differed from 

 the calculated rotations by 2 or 3 per cent., but he 

 was not in a position to decide whether these deviations 

 were due to experimental errors or to some inaccuracy 

 in his formula. Our own measurements have shown 

 that Biot's diagram represents almost exactly the 



' Abridged from the Dakerian Lecture delivered before the Royal Society 

 11 June 2, 1921. 



rotatory dispersion in quartz if the lines are drawn 

 through a point a little to the right of the origin, and 

 there can be little doubt that if more accurate methods 

 of measurements had been available Biot's line of 

 thought and method of representation would have 

 led him almost inevitably to the simple formula for 

 rotatory dispersion which has come into general use 

 in recent years after the lapse of nearly a century. 



2. — Simple Rotatory Dispersion. 



As the accuracy of polarimetric work increased, 

 the deviations from Biot's law of inverse squares 

 became too important to be overlooked. The result 

 was unfortunate, since those who destroyed the 

 original formula had not got the skill to replace it 

 by one that was more exact. For half a century, 

 therefore, work on rotatory dispersion was limited 

 to the occasional plotting of a curve of unknown 

 form to represent the relationship between rotatory 

 power and wave-length. As a natural result interest 

 in the study of rotatory dispersion diminished, and 

 (following the discovery of the Bunsen burner in 1866) 

 the D line of the sodium flame acquired almost a 

 monopoly as a source of light for the investigation 

 of optical rotatory power. 



During this period corrected formulae were put 

 forward by Boltzmann, who wrote a = A/A2 + B/A.*, 

 and by Stefan, who wrote a = A-f-B/A2; but these 

 proved to be of little value, since they could not 

 readily be made to fit the curves, and, being obviously 

 empirical in character, could be used only as a means 

 of interpolation between the experimental values. 



This period of retrogression came to an end with 

 Drude's application to optics of the electronic theory 

 at the close of the nineteenth century. His theo- 

 retical investigations led to the enunciation of a 

 somewhat elaborate formula for optical rotatory dis- 

 persion which (when approximate results only were 

 required) could be used in the simplified form shown 

 in the equation, 



. V K 



where the dispersion-constants k^, \^ . . . X^^, could, 

 be deduced from the refractive power of the medium, 

 while ^„ represented a series of arbitrary constants 

 depending on the rotatory power of the medium. A 

 similar formula, which actually included the refractive 

 index, was put forward to express the influence of 

 wave-length on magnetic rotatory power. Drude 

 tested his formula for optical rotatory dispersion in 

 the case of quartz, whilst that for magnetic rotatory 

 dispersion was tested in the case of carbon disulphide 

 and of creosote ; but for some years both formulae 

 remained almost barren so far as practical applications 

 to measurements of rotatory dispersion were concerned. 

 In particular, it may be noted (i) that a complete 

 knowledge of the curve of refractive dispersion was 

 required before either formula could be applied to 

 measurements of rotatory dispersion, and (ii) that 

 even the approximate formula for optical rotatory 

 dispersion contained an indefinite number of arbitrary 



NO. 2736, VOL. 109] 



