682 



NATURE 



[July 28, 192 1 



of some facts which appear to have escaoed the notice 

 of biologists ; for example, the truism I have men- 

 tioned, that, apart from variations, offspring tend to 

 recapitulate the development of their parents. 



G. Archdall Reid. 

 9 Victoria Road South, Southsea. 



Solar Eclipse Results and the Principle of Relativity. 



On a recent occasion I read a paper before the Man- 

 chester Literary and Philosophical Society on the 

 nature of dimensions, in which, admitting: the possi- 

 bility and even probability of space and time having 

 secondary characteristics, like those suggested by 

 Lorentz and Einstein, reasons were given for doubting 

 whether the methods employed for finding them could 

 be relied on, and experimental evidence, before it 

 could be accepted, would have to be subjected to 

 searching adverse criticism. Prof. Eddington's solar 

 eclipse results were therefore submitted to a process 

 essentially the reverse of his, which had for object 

 not the confirmation of a theory, but the discovery 

 of an empirical relation. During this process it soon 

 became evident that the astigmatism of the coelostat 

 mirrors, which had given much trouble during the 

 eclipse by distorting the star images, had also 

 affected the field and altered the star positions. The 

 stopping down of the objectives aggravated this evil 

 in a double sense : first, the reduction of the star- 

 image astigmatism makes it impossible to construct 

 a picture of what might be called the field astig- 

 matism of the mirrors ; and, secondly, the smaller 

 the diameter of the pencil of light rays for each star, 

 the further apart would be the regions on the mirror 

 from which these pencils were reflected. Therefore, 

 if the various regions of the mirror had semi- 

 independent tilts, the places of the stars on the plates 

 would be affected by these tilts. If for some of the 

 existing plates these pencils should be found to over- 

 lap, and if the star -image astigmatism is sufficiently 

 marked, then these plates might still be used for the 

 object for which they were taken. 



Wishing, first of all, to redetermine the positions 

 of the stars as they appeared before scale corrections 

 had been applied in order to trace the wandering of 

 the images, it was found that for the outermost stars 

 10 and II these negative corrections would amount to 

 0-45". This in itself was a most disconcerting dis- 

 covery, for the difference of displacement on which 

 the eclipse conclusions were based is only 0-75". It 

 is, of course, quite impossible for the telescope tube 

 to have altered sufficiently in four and a half minutes 

 to produce this result, and a change of focus 

 of the objective would have had no effect ; therefore 

 the mirror must have warped even during this short 

 time. At Principe the passage of clouds would pro- 

 duce an irregular warping effect, and this would 

 account for the unsatisfactory photographs obtained 

 there. In order to form some idea about the nature 

 of the field astigmatism it was now decided to esti- 

 mate the tangential displacements of the stars, for 

 these would not be influenced either by the scale 

 corrections or by the radial displacements, but only 

 by the mirror warpings. It was then found that 

 stars 3, 4, and 6, which lie almost in a straight line 

 between 5 and 10, had moved about 045" across the 

 connecting line of these outer stars. On averaging 

 the uncorrected radial displacements It was found that 

 a slight scale correction of about +0-0002" had to be 

 made, as was done by Prof. Eddlngton, in order to 

 harmonise them with the Einstein estimates, the 

 excuse In my case being that the mirror may have 

 acquired a slight temporary concavity. If, however, 

 there was a temporary convexity, necessitating a scale 



NO. 2700, VOL. 107] 



correction of, say, -oooos", the displacements would 

 appear to conform to the empirical formula 109" — 

 000022". It will thus be seen that the use of coelostat 

 mirrors is not advisable where, as under eclipse 

 conditions, rapid changes of temperature are unavoid- 

 able. C. E. Stromeyer. 

 "Lancefield," West Didsbury, July 21. 



Mr. C. E. Stromeyer greatly exaggerates the 

 possible feffects of astigmatism of the coelostat mirrors 

 on the positions of the star images. He appears to 

 consider that the. pencils forming the different images 

 are reflected from entirely different portions of the 

 coelostat surface. As a matter of fact, with the 4-in. 

 lens the pencil producing the extreme star image was 

 reflected from a portion of the mirror which had 

 85 per cent, of its area common to that producing 

 the central pencil, and with the 13-in. lens (stopped 

 down to 8 in.) the common portion was even greater. 



That there was a slight astigmatism of the mirrors 

 is not denied. Its presence was indicated by small 

 differences in the scale and orientation constants of 

 the plates determined in two different ways : from 

 the right ascensions or declinations. These differences 

 gave a measure of the amount of the astigmatism, 

 and showed it to be very small and of very slight 

 effect on the gravitational displacement. The ques- 

 tion has been fully discussed by Prof. H. N. Russell 

 (Monthly Notices, R.A.S., vol. Ixxxi., No, 2, Decem- 

 ber, 1920), with the result that the conclusions deduced 

 from the original reductions of the eclipse plates were 

 fully substantiated and the Einstein displacement con- 

 firmed. F. W. Dyson. 



The Atomic Radius and the lon^sation Potential. 



Prof. Eve's interesting contribution to Nature of 

 June 30, p. 552, on the relation between the ionisation 

 potential and the atomic radius Induces me to publish 

 certain similar ideas of mine on the same subject to 

 which I referred some time ago before the Royal 

 Society in some remarks on Prof. Ranklne's paper 

 " On the Proximity of Atoms in Gaseous Molecules " 

 (Proc. Roy. Soc., February, 192 1). I did not publish 

 the results, because I desired to wait for further data. 

 These ideas may be stated as follows : — 



According to the Rutherford-Bohr model of the 

 atom, by the radius of the atom is meant the distance 

 from the nucleus of the outermost electron, i.e. the 

 electron the quantum vibrations of which cause the 

 radiation of the arc lines of the atom. Sommerfeld 

 has shown that in the normal (unexclted) state the 

 orbit is characterised by the azimuthal quantum- 

 number unity and the radial quantum-number zero. 

 This orbit is circular, but to calculate its radius we 

 must know what is the field of force exerted by the 

 central nucleus and the remaining (n— i) electrons 

 upon the vibrating electron. This is at present an 

 insoluble problem, but Mr. S. N. Basu {Thil. Mag., 

 November, 1920) has shown that we can at least 

 arrive at a qualitative explanation of Rydberg's laws 

 of spectral regularity by assuming the attracting 

 system to be equivalent to a net central charge unity, 

 with a doublet of strength L. On the bases of this 

 theory, if a^ is the radius of the monoquantic orbit, 

 it Is easy to show that 



— = - energy of the vibrating electron. 



— hi'is) where (ij) = convergence frequency of the 

 principal series of the element in absolute 

 measure. 



= eVx, Va; = ionisation potential in e.s. units. 



For the H-atom we have, according to Bohr's 

 theory, 



