Jrxi: 3, 1922] 



NATURE 



T^Z 



Half Quanta. 



The Wilson-Sommerfeld principle when applied 

 to the case of a rotating molecule, supposed rigid, 

 leads to the expression mhl^ir {m integral, h Planck's 

 constant) for the angular momentum of the molecule, 

 and on this basis, with the help of several other 

 assumptions, it has been found possible to account 

 very satisfactorily for the main features of the struc- 

 ture of band-series. The theory is found to apply 

 not only to ordinary bands in the region of the visible 

 spectrum but also to absorption bands of very 

 different appearance, such as those due to the halogen 

 acids which occur in the infra-red. In the latter 

 case, however, a discrepancy exists which has given 

 rise to a good deal of discussion. The observed 

 bands consist of a number of lines distributed, to a 

 first approximation, according to the formula 



y = vo± WW, 

 where m takes successive positive integral values 

 and w is a constant. The line of wave-number 

 I'o {i.e. m-o) is invariably absent. 



The theoretical expression, on the other hand, is 

 of the form 



" = "0+ (W— l/2)w, 



which, it will be noted, represents a similar set of 

 lines displaced through a distance w/2. The reality 

 of the discrepancy is therefore dependent upon the 

 correct identification of vg, and as this is not entirely 

 beyond question some workers have preferred to 

 take the value indicated by the theory, although 

 by doing so fresh difficulties in the interpretation of 

 the results arise. Einstein, however, pointed out 

 (quoted by Reiche, Zeitschr. f. Phys., 1920, p. 283) 

 that theory and observation would agree if instead 

 of the usual value mh/2ir for the angular momentum 

 one assumed it to be given by {m +i/2)h/2ir. The 

 evidence from the infra-red absorption bands seems 

 scarcely strong enough to warrant such a revolu- 

 tionary change, but other data bearing on the 

 question have recently become available. In the 

 band spectrum of helium, for example, series exist 

 which show this same peculiarity, and here its 

 existence is indubitable, for the normal (i.e. theo- 

 retical) series are in this case also present, and a trust- 

 worthy value for v^ can be determined from them. 



Following up Einstein's suggestion, I have found 

 that the abnormal series may in all cases be very 

 simply derived from the normal group by displacing 

 the quantum number by one-half. As an illustration 

 of the sort of agreement which is obtained I may 

 cite the case of the X5730 band (see Curtis, Roy. Soc. 

 Proc, loi, 1922, p, 38), which consists of six series, 

 only three of which satisfy completely the theoretical 

 requirements. The " half-quantum series " calcu- 

 lated from these three are as follows : — 



17436-6 -3I-5W +o-95m* 



17436-6 +3i-5m +o-95m* 



17436-6 +0-95W -f-o-95w* 



The remaining three observed series are represented by 

 the formulae : — . 



I7437'3 -30-om +o-87w'' 



17436-8 +29-5m +i-09m'' 



17437-3 +I-I5W +0-87W* 



The correspondence is very close, having regard to 

 the approximate character of the formulae upon 

 which the calculation is based. It is certainly good 

 enough to justify the proceeding as an empirical 

 method of expressing the relationship between the 

 two groups and to encourage theoretical inquiry 

 into its physical significance. 



As the matter stands at present, the inference — 



NO. 2744, VOL. 109] 



illusory though it may be — is that the molecules fall 

 into two classes, according to whether their angular 

 momenta are given by mhj^iv or by (m + i/2)A/27r. 

 Transitions between the two classes do not occur 

 (or, if they do, give rise to no radiation), since there 

 are no lines corresponding to changes of one-half 

 in the quantum number. That is to say, whether 

 or no the half-quantum may be involved in the 

 determination of the possible states of a molecule, 

 it does not appear to play any direct part in the 

 radiation process. W. E. Curtis. 



Wheatstone Laboratory, King's College, W.C.2. 



Fossils in Burmese Amber. 



Amber mines have long been known in Upper 

 Burma, or rather in the adjacent " unadministered 

 tracts." In 1916 Mr. R. C. J. Swinhoe, of Mandalay, 

 began to send me specimens of Burmese amber 

 (Burmite) containing insects. As opportunity has 

 offered, he has continued to obtain such material, all 

 of which has been transmitted, after investigation, to 

 the British Museum (Natural History). Up to the 

 present time I have been able to describe 38 species 

 of insects, three arachnids and one diplopod. Many 

 other species, which I did not feel competent to deal 

 with, or which could not be seen properly, exist in 

 the amber, and will, I hope, eventually be described by 

 others. On the whole, the fauna is very remarkable, 

 containing a large preponderance of types which are 

 usually considered primitive. The amber was said 

 to come from Miocene clay, in which, however, it was 

 presumably of secondary origin. Judging from the 

 fossils, I suggested as early as 191 7 that the amber 

 might be actually very much older than Miocene, 

 conceivably even Upper Cretaceous {Amer. Journ. 

 Sci., Nov. 1917, p. 360). 



Recently, information has been received which 

 tends to confirm the suspicion that the amber is much 

 older than Miocene. Dr. F. A. Bather of the British 

 Museum has kindly transmitted a letter from Dr. 

 E. H. Pascoe, Director of the Geological Survey of 

 India, dated July 20, 1921. Dr. Pascoe states that 

 Dr. M. Stuart, in his recent journey down the Hukong 

 Valley, saw something of the amber mines, and 

 reported that the shafts were sunk in beds which 

 appeared to be identical with the Tipam sandstone or 

 the Irrawaddy series. Whether they passed through 

 into underlying rocks could not be determined, but 

 from the evidence obtained by Noetling and others it 

 seemed probable that they frequently did. The 

 Tipam sandstone is unconformable on the underlying 

 beds, and frequently contains fragments of them in 

 its lowest horizons. Such fragments may very well 

 include lumps of amber derived from the underlying 

 clays. Dr. Pascoe continues : " Among the debris 

 of spme pits sunk into these clays, which are the true 

 home of the amber. Dr. Stuart found a fragment of 

 chalky nummulitic limestone. The pits had been 

 sunk into the clays, not to obtain amber, but flint 

 from the chalky limestone lying in them. Dr. Stuart 

 describes the clay^ as totally unlike any Disang beds 

 that he had seen, and he is inclined to accept the view 

 that they are Eocene in age. If it is possible to deter- 

 mine the species of the nummulite, I wiU let you 

 know ; but it is, of course, not certain that this 

 nummulitic limestone occurs in situ within the clays." • 



On August I, 192 1, Dr. Pascoe wrote that Dr. 

 Stuart thinks the nummulite is Nummulites biaritz- 

 ensis d'Arch., characteristic of the uppermost zone 

 of the Lower Khirthar. The Khirthars correspond 

 approximately, according to Mr, E. Vredenburg, to 

 the Lutetian. The Lutetian represents the earlier 

 part of the Middle Eocene, below the Bartonian. 



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