February 3. 192 1] 



NATURE 



725 



Letters to the Editor. 



yrht Editor docs not hold himself responsible for opinions 

 expressed >y his correspondents. Neither can he undertake to 

 return, or to correspond with «h« writers of. refected manu- 

 scripts intended for this or any other part of Nature. So 

 notice is taken of anonymous communications. \ 



The Arrangement of Atoms in Crystals. 



In Nature for January b, p. 609, was published a 

 note in which some figures given in my paper on 

 "The Arrangement of Atoms in Crystals" (Phil. 

 Mag., vol. xl., .\ugust, 1920) were contrasted with 

 similar figures given by Wyckoff {Amer. Journ. Sci., 

 [iv], vol. 1., pp. 317-60, November, 1920). The.se 

 figures were estimates of the distances between atoms 

 of metal, carbon, and oxygen in the crystals calcite, 

 CaCO,, rhodochrosite, MnCO,, and siderile, FeCO,. 

 In this note it is stated that our data differ consider- 

 ably, " the deviations rising to 06 A. in the distance 

 from carbon to metal." 



There are no discrepancies of this magnitude 

 between Wyckoff's results and mine. The large 

 differences to which the note directs attention are 

 due to errors in quoting the results given in my 

 paper, owing, I tfiink, to a misconception of the 

 structure which WyckoH and I agree in assigning to 

 these crystals. 



I give the correct figures, the distances being 

 expressed in Angstrom units : 



Wyckoff. Bragg. 



1. II. Experimental Sum of radii 



Ca-O ... 230 242 230 235 



C -O ... I-2I 1-28 1-42 1-47 



Ca-C ... 304 s'"'^ S'iod 



Mn-O ... 1-96 2-13 2-IO 2-II 



C -O ... I 22 1-32 I '42 1-47 



Mn-C ... 2-83 3-072 3'o7» 



If I understand Wyckoff's results rightly, we are 

 in agreement as to the type of structure in the case 

 of these carbonates, and the symmetry of the crystal 

 alone suffices to fix the positions of the calcium and 

 carbon atoms. The distance between them can be 

 calculated from the molecular volume of calcite, 

 .Vvqgadro's number N, and the crystal axial ratios. 

 The dimensions of the calcite structure have been 

 made the subject of careful investigation (Uhler, Phys. 

 Rev., July, 1918), as it has been used for standard 

 X-ray wave-length determinations. Taking the value 

 ''(■••) = 3'028 A. given by I'hler, it follows that this 

 distance from calcium to carbon atoms is 3206 A. 

 Wyckoff give.s the value 304 A., and so ascribes to 

 the whole structure a smaller scale. If, as I believe, 

 his scale is too .small, all his figures should be in- 

 creased in the ratio 3206 to 304. .\ similar 

 increase of scale holds for rhodochrosite. Under I. 

 are given Wyckoff's values, and under II. those values 

 increased in what 1 believe to Ix- the correct ratio. 



Wyckoff gives figures which differ from mine for 

 the distance between carbon and oxygen atoms. He 

 has made a very careful determination of a certain 

 parameter (denoted by "u " in his paper), and I 

 believe his value for it, 025, to be much more truRt- 

 worthy than my approximate value 0-30. VV'vckoff's 

 value confirms n determination o-2S-o-27 by W. H. 

 Bragg (Trans. Rov. Soc., .A, vol. ccxv.. pp. 253-74) 

 in iQis — a determin.Ttion which I did not know when 

 I publisfied mv figures. If the figures in column II. 

 are accepted, this would mean that mv estimate of the 

 "diameter" of carbon in compounds is too high. an<l 

 that a f«"tfer value would be nearer that of fluorine, 

 I-3/; A. This is the only serious discrepancy between 

 our results, and it does not seem to me that it affects 

 in any way the general conrlu.sion« which I drew in 

 tnv oaper. 

 The figure 247 A., quoted as being given by me 

 NO. 2675, VOL. 106] 



for the distance Ca-C, has presumably been arrived 

 at by the author of the note by adding the radii for 

 these atoms. .\s they are partially separated by the 

 oxygen atoms which surround the calcium atom, there 

 is no direct connection between the sum of the radii 

 and^the distance between them. 1 used in my cal- 

 culations the theoretical value obtained as above. 



Mav 1 take this opportunity to corri-ct another error 

 in the note? The figures given for the "diameters " 

 of the electro-negative elements are quoted correctly 

 from my paper, but those given for the metals are 

 one-half the value which 1 gave under this head. 



VV. L. Bragg. 



.Manchester University, January .22. . 



A Case of Coloured Thinking with Thought-forms 

 and Linked Sensations. 



Coloured thinking is such a peculiar condition 

 that those interested in it will welcome the details 

 of a well-marked case of it. It must be distinguished 

 from linked sensations such as coloured hearing — one 

 of the synaesthesiae— in which heard sounds call up 

 colours, as when the low notes of the organ suggest 

 violet or the high notes white or yellow, etc. 



Coloured thinking or chromatic mentation (psycho- 

 chromaesthesia) is the visualising of concepts as 

 coloured, the ability to think of a letter of the 

 alphabet, a number, a date, a month, or a name as 

 .issociated with some colour or other — white, black, 

 red, green, etc. To those who have never experi- 

 enced this sort of thing it is unintelligible. 



One coloured thinker thus expressed himself : 

 "When I think at all definitely about the word 

 Januarv the name appears to me reddish, whereas 

 .April is white and May yellow; the vowel 'i' is 

 always black, the letter ' o ' white, and ' w ' indigo- 

 blue. Only by a determined effort can I think of 

 ' b ' as green or blue, for to me it has always been 

 and must be black ; to imagine August as anything 

 but white seems to me an impossibility, an altering 

 of the inherent nature of things." 



Of course, the same person who has coloured 

 hearing — the commonest of the linked sensations — 

 mav likewise have coloured thinking, although most 

 coloured thinkers do not also have linked sensations. 

 The ca.se the interest of which I think sufficiently 

 great to report on now is one both of linked sensa- 

 tions and of coloured thinking. But there is also a 

 third element of interest in it, namely, that of thought- 

 forms. .\ thought-form or psychogram is the 

 visualising of, say, the numerals or letters of the 

 alphabet or months of the vear in such a way that 

 they seem to form some definite figure in .space — for 

 instance, an arc of a circle or a ladder sloping up 

 to the right or left, and .so forth. .\ psychogram is 

 the uncoloured form of a concept or a series of 

 them : the psychochrome is the concept itself ex- 

 teriorised in colour. 



The case the coloured thoughts, linked sensations, and 

 thouuht-forms of w^hich f subjoin is that of a student 

 of this I'niversitv (Miss .\. M.), who has alt the 

 features charnrteristic of these cases. .She has been 

 a coloured thinker ever since she can remember; 

 the colours have pot altered with laose of time, they 

 are exceedingly definite, thev do not agree with the 

 colours seen bv other thinkers for any one piven 

 concept, and, finally, the "seer" cannot account for 

 them in any way. 



The onlv feature in the present rase not quite 

 I typical is that it is not so clearlv hereditary a* i^ 

 usually observed. Miss .\ M. snvs that neither of 

 her parents is a coloured thinker, though her 

 "mother associates colours with the characters of 

 people." This has been called "individuation," and 

 is not so uncommon as might be imagined. 



