December 16, 1922] 



NA TURE 



others, have not, however, followed Dana — a crystal 

 right-hand crystallographically, is also right-hand 

 optically with them. F. Cheshire. 



Imperial College of Science, 

 South Kensington, 

 October 27. 



I am much indebted to Prof. Cheshire for stating 

 so clearly the historic incidence of the confusion 

 which has arisen in regard to the designation of the 

 two types of optical rotation, as to which shall be 

 called right-handed and which left-handed, due 

 .largely to the reversal of Biot's convention by Sir 

 John Herschel, and to the similar reversion in the 

 second edition of Dr. Pereira's book. Other in- 

 vestigators and experimenters have also adopted 

 the reversal, for instance, Sir William Spottiswoode 

 at the time he was president of the Royal Society, 

 for on pp. 47-48 of his book, " Polarisation of 

 Light," we read : "A right-handed ray is one in 

 which, to a person looking in the direction in which 

 the light is moving, the plane of vibration appears 

 turned in the same sense as the hands of a watch." 

 Moreover, if instead of using the polariscope as a 

 table instrument one projects the phenomena on the 

 screen, the picture there displayed is reversed exactly 

 like a lantern slide, which has to be inverted in the 

 lantern (the two spots in front at the top being 

 brought to the bottom at the back), in order to get 

 an upright picture on the screen. Thus, for example, 

 in the mica-sector experiment of the late Prof. S. P. 

 Thompson (pp. 1103-1104 of the second edition of 

 my " Crystallography and Practical Crystal Measure- 

 ment "), the black cross moves on the screen one 

 sector to the left for a right-handed quartz crystal 

 and to the right for a left-handed one ; whereas on 

 looking through the same instrument used as a table 

 polariscope the movement is to the right for a right- 

 handed crystal, in accordance with the Biot con- 

 vention. 



It is thus important to know the exact condi- 

 tions of the experiment whenever the question of 

 the correct discrimination of right- or left-handed- 

 ness in the optical rotation of crystals is being dealt 

 with. Further, the safest course, in the case of 

 quartz, is to cut the section-plate to be used to 

 afford the definite decision from a crystal which is 

 clearly a single individual, and not a twin, showing 

 the little s and x faces unmistakably, and this 

 course was pursued by me in the preparation of my 

 " Crystallography." As most in accordance with 

 current practice (that of von Groth and Pockels, 

 for example), and in rightful deference to Biot, the 

 discoverer of the two optically active kinds of quartz, 

 Biot's convention was used, in both editions of the 

 book, a course which it is satisfactory to learn meets 

 with the approval of Prof. Cheshire. The apparent 

 opposite, on p. 1101, lines 7-8, is due to this being a 

 projection experiment, the observer looking towards 

 the screen along with the light rays ; the direction 

 here, however, really does not matter, as only the 

 colour of the centre of the field is being referred to ; 

 even here, perhaps, it would be better in any future 

 edition (they were not present in the first edition) 

 to omit the words " from the point of view of the 

 observer looking in the same direction as the light 

 is being propagated," the text then conforming 

 clearly with the Biot convention. On p. 1083, 

 where a table experiment is being referred to, and 

 the conditions are otherwise similar to those in the 

 centre of the field in the case just referred to, there 

 is no ambiguity, the Biot convention being clearly 

 followed. 



no. 2772, vol. i ro] 



It was felt desirable to direct attention to the 

 confusion which has so obviously arisen, and this 

 was done in the footnote to p. 1082. Emphasis was 

 attempted to be laid on the fact that, after all, the 

 phenomena are due to the passage of the ray through 

 the helical structure of the crj'Stal, now so happily 

 confirmed by Sir William Bragg's X-ray analysis of 

 quartz, and that the observer does well to imagine 

 himself travelling with the rays through the screw, 

 in order to appreciate the cause of the rotation of 

 the plane of polarisation or vibration of the light 

 rays. The particular screw type, right- or left- 

 handed, is the same, however, whether we regard 

 the screw from one end of it or the other, whether 

 we look along with or against the light stream ; 

 otherwise it would matter which side up the quartz 

 plate were arranged, that is, which side were placed 

 the nearer to any particular one of the nicols. But 

 the optical effect, the rotation of the plane of polarisa- 

 tion or of vibration of the light rays, is, of course, 

 what matters and what is so clearly different for 

 the two different types of quartz helices, and it was 

 my intention to retain and use the Biot convention 

 for its directional (right- or left-handed) designation. 

 The footnote in question is not sufficiently explicit, 

 and must be amended in any future edition. Prof. 

 Cheshire and the writer are, however, quite agreed 

 on the facts, and that this Biot convention shall be 

 the one employed, and I am grateful to Prof. Cheshire 

 and to the editor of Nature for affording me the 

 opportunity of stating this. A. E. H. Tutton. 



Space-Time Geodesies. 



In his letter in Nature of November 25, replying 

 to mine which appeared in Nature of October 28, 

 Prof. Piaggio points out that the equations of Space- 

 Time geodesies may be deduced by other methods 

 than those of the calculus of variations, and suggests 

 that, in some such way, it is possible to get over 

 the difficulties to which I directed attention. 



My criticism, however, was directed, not merely 

 against the definition of Space-Time geodesies as 

 minimum lines, but against all seeming definitions 

 of them which start from ideas of measurement as a 

 fundamental basis. 



I must, however, in passing, warn my readers 

 against what at first sight looks like a suggestion, 

 though I have no doubt that it was not so intended 

 bv Prof. Piaggio, that Space-Time geodesies might 

 be defined in terms of " the osculating plane." 



If there were any strict analogy with the case of 

 geodesies on surfaces in ordinary three-dimensional 

 geometry, such an " osculating plane " would (apart 

 from a line of intersection) have to lie in some 

 mysterious region outside our Space-Time continuum 

 altogether. Prof. Piaggio, however, I have no 

 doubt, wishes to lav stress upon the equations he 

 obtains. 



I was of course aware that the equations of Space- 

 Time geodesies could be arrived at by various 

 analytical devices ; but how much better off does this 

 leave us ? Consider, for example, the simple Space- 

 Time analysis as given by Minkowski and see what 

 it implies. 



In the first place, it implies a set of co-ordinate 

 axes x, y, z, and t, which are themselves geodesies. 



How are these particular geodesies to be defined ? 



They cannot be defined as minimum lines, for 

 they are not minimum lines ; and we cannot use 

 our co-ordinate system to define them, since we 

 are now contemplating how the co-ordinate system 

 can be set up. 



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