July 14, 1923] 



NATURE 



53 



Letters to the Editor. 



The Editor does not hold himself responsible for 

 opitiions expressed by his correspondents. Neither 

 can he undertake to return^ nor to correspond with 

 the wi iters of rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous cotnmunications^ 



The Crossed-Orbit Model of Helium. 



The spectrum formula 



. = N[3-^^F(sm-^)], 



{a) 



proposed for helium in my letter of March i (Nature 

 of April 28, p. 567), was shown to yield, for - cos i = \, 

 the correct ionisation potential and, for +, 'i, f, %, the 

 four Lyman lines ; with that corresponding to the 

 former as the limit. The deduction of this formula 

 (on lines by no means classical) and the attitude to 

 be taken with regard to the " negative " results ob- 

 tained in the meantime by Dr. Kramers by means of 

 classical mechanics {Zeits. f. Physik, 13, 312) have 

 been fully explained in a paper appearing in the June 

 issue of the Astrophys. Journal, and need not be 

 repeated here. The purpose of this letter is to point 

 out some further peculiarities of the formula (a) as 

 such, which will be seen to bring order into the 

 apparently queer correlation given before. 



If the simple rational values of - cos i are ordered 

 in descending magnitude, namely, 



M^) I (t) * (f) *. ... (6) 



every second, bracketed one, covers no observed 

 line, while the others represent orderly the first four 

 members, m=i, etc., of the Lyman series oS - mP. 

 Extrapolating the regular sequence of the last three 

 fractions by 



(t'V) and iV, 

 one would expect the former to cover no line and the 

 latter to represent the line oS - 5P, which, though 

 hitherto not observed, can be expected with confid- 

 ence. Now, with Lyman's oS and the usual 5P, this 

 line should lie at X5 = 512-1, while formula (a) gives, 

 for cos z= - 7/13, X = 512-3. Again, turning to the left- 

 hand end of the sequence (&), the next fraction t 

 naturally suggested itself as worth trying. For this 

 value of - cos i (z/2 = 73-221°, F = 2-6642) formula (a) 

 gives X = 6oi-2, which is very close indeed to the 

 "single line at 600-5 + 0-3," repeatedly obtained by 

 Lyman. As I understand from Prof. Lyman him- 

 self, he feels reasonably certain that it is genuine and 

 that it belongs to the spectrum of helium. More- 

 over, from the semi-empirical point of vie-vv, the " com- 

 bination " line oS - iS = 198,300- 32,033 would lie at 

 X = 6oi-3, which is still closer to our result. 



Thus, gathering the scattered items, we have, as 

 an extension of (b), the following correlation (in which 

 the bracketed numbers cover no observed lines) : 



* i Mi) iv (§) * (f) g (A) A 



0S-lS|A, Aj A3 A, A5 



i. 



(0) 



Notice that, according to Prof. Lyman, the arc 

 spectrum of He contains no lines in addition to those 

 here covered. The regular intermittency of (c), so 

 far as the members oS - mP are concerned, is manifest. 

 The position of oS - iS — the " queer " line, as Dr. 

 Compton of Princeton called it — is correspondingly 

 queer. Yet even this, though only a combina- 

 tion line, fits into the further remarkable regularity 

 of the whole sequence (c), to wit, that the differences 

 between the successive fractions are all of the form 

 ilnp, thus 5-5 -4-6=1, 4-4 -3-5 = 1, 3-3-4-2=1, and 

 so on. This curious feature was first noticed by my 



NO. 2802, VOL. I 12] 



friend Prof. A. S. Eve of Montreal only after the whole 

 array (c) was spread over the black-board in a recent 

 lecture at the Bureau of Standards. It may thus be 

 said to have grown out spontaneously, and certainly 

 did not influence the writer in constructing the pro- 

 posed formula. 



So long as intra-atomic dynamics is awaiting its 

 final shaping from modern groping attempts at a 

 suitable modification of ordinary mechanics, every 

 such regularity of correlation, no matter how 

 " magical " in appearance, seems worthy of noticing, 

 as a possibly helpful hint how to alter the old laws 

 for intra-atomic purposes. Ludwik Silberstein. 



129 Seneca Parkway, 



Rochester, N.Y., May 15. 



Symmetry of Calcium Thiosulphate Hexahydrate. 



Calcium thiosulphate hexahydrate, CaSjOg . 6H2O, 

 is usually quoted in works on crystallography as an 

 example of the triclinic asymmetric class, C^^ — 

 perhaps as the only known crystal which definitely 

 represents this type of structure. It is described in 

 Tutton's " Crystallography " (new edition, p. 280, 

 old edition, p. 285), and, in more detail, in Groth's 

 " Chemische Krystallographie, " vol. 2, p. 676. In 

 the latter we read 



CaSjOa . 6H2O. Asymmetric. Sp. gr. 1-872. 



a : b : c =0-7828 : i : 1-5170. 



a = 72° 30', ,3=98° 34', 7=92° 45r. 



The process by which symmetrical crystals are 

 built up from less symmetrical material has been 

 recently described by Sir William Bragg (" The 

 Significance of Crystal Structure," Trans. Chem. 

 Soc, 1922, vol. 121) and G. Shearer (" The Relation 

 between Molecular and Crystal Symmetry as shown 

 by X-ray Crystal Analysis," Proc. Phys. Soc, 

 February, 1923). In the latter paper the author 

 suggests that Nature never uses more molecules 

 than are absolutely necessary for the purpose ; that 

 is, no more than N asymmetrical molecules will be 

 used in the construction of a crystal of " symmetry- 

 number " N, or, if the symmetry of the molecules 

 be that of some class n, then no more than N/« will 

 be used. Up to the present this hypothesis seems 

 to be justified. In all organic crystals that have 

 been examined in Sir William Bragg's laboratory 

 not one has yet been found to contradict it. In all 

 cases there has been no evidence to show that 

 polymers of chemical molecules have been used, but, 

 on the contrary, abundant evidence to show that the 

 ultimate structural bodies correspond to the simple 

 chemical molecules. Furthermore, it has been shown 

 that, in general, the symmetry of a crystal is of a 

 higher type than that of the molecules from which 

 it is built — a rule which seems to be almost universally 

 true. Especially with complex molecules does Nature 

 resort to the device of combining a molecule with 

 its digonal or its enantiomorph before using them to 

 construct a Bravais lattice. 



In view of these considerations it seemed very 

 probable that, should a truly asymmetric crystal be 

 obtained, its space-lattice would be found to be 

 constructed of asymmetric groups of atoms corre- 

 sponding to single chemical molecules ; that is, it 

 would be found to contain only one molecule per 

 fundamental cell. Such a case seemed to be pre- 

 sented by CaSgOs . 6H0O, and, indeed, it was expected 

 that X-rays would show it to be a simple triclinic 

 lattice of single asyinmetrical molecules, obeying, of 

 course, the law of rational indices, but exhibiting 

 no symmetry operation beyond that of identity. 



