Junk 3, 1922] 



NATURE 



711 



Letters to the Editor. 



i The Editor does not hold himself responsible Jar 

 pinions expressed by his correspondents. Neither 

 in he undertake to return, or to correspond with 

 Ihe writers of, rejected manuscripts intended for 

 this or any other part of NATURE. No notice is 

 taken or anonymous co7nmunicaiions^ 



The SmaU Haloes of Ytterby. 



The following letter, received from Mr. Svein 

 Rosseland, of the Institute of Theoretical Physics, 

 University of Copenhagen, contains an interesting 

 suggestion. I publish it with the writer's consent. 



" . . . In connection with your letter to Nature 

 of April 22 on radioactive haloes in Ytterby mica I 

 venture to comment upon the probable location of 

 the hypothetical element in the periodic table. You 

 make in your letter the interesting remark that the 

 element cannot belong to the radioactive disintegra- 

 tion series previously known, since the life period, 

 according to the Geiger-Nuttall relation, would have 

 to be so immensely large, and the intensity of the 

 radiation correspondingly feeble, that it is difficult 

 to believe that the radioactivity of the element could 

 be detected. This remark raises the question of the 

 origin of the energy of the a-particles and the meaning 

 of the above-mentioned relation. 



Now it is known that the a-particles are strongly 

 repelled by the nuclear electrostatic field of the 

 parent atom, and it is clear that this repulsion must 

 contribute appreciably to the energy of the particle. 

 Without further knowledge of the exact dimensions 

 of the nucleus and the character of the field close to 

 it we cannot of course calculate the relative import- 

 ance of this energy in the resulting energy of the 

 particle, but we can calculate inversely a minimal 

 radius for the nucleus of the transformation product 

 by supposing the whole energy to be due to the 

 nuclear electrostatic repulsion. 



In this way we obtain a series of minimal radii 

 for the elements consecutive to the a-radiating 

 elements. The longer the life period the larger is this 

 radius. The largest radius is afforded by uranium-Xi, 

 where, corresponding to a range of 2-53 cm. N.P.T., 

 it comes out as 6-5 x lo"^'^ cm. This value is so 

 large that in view of the experiments on single 

 scattering it seems improbable that the real radius 

 will be much greater. But then we are led to the 

 assumption that the main part of the energy of the 

 a-particle from uranium- 1 comes from the nuclear 

 repulsion. As it seems iinlikely that variations in the 

 nuclear dimensions will be so large as to account for 

 the energy of the swifter a-particles, there must be an 

 energy term of expulsion from the nucleus, resembling 

 in some respects the energy difference between two 

 stationary states of an atom. If we assume the 

 term due to electrostatic repulsion to be only slightly 

 variable, as is the case if the nuclear dimensions 

 vary but slightly, the variability of the ranges of the 

 a-particles will be due mainly to variations in this 

 energy of expulsion, and it is this which is linked to 

 the life period of the elements according to the 

 Geiger-Nuttall relation. It seems not wholly im- 

 probable that the difference between the constants 

 in this relation corresponding to the different series 

 may ultimately be due to differences in the nuclear 

 dimensions. 



If the Ytterby haloes were due to an element of 

 an atomic number of the order found in the families 

 of the known radioactive elements, the nuclear 

 dimensions of its transformation product would be 

 nearly i-8 as large as that calculated for uranium-Xj. 



NO. 2744, VOL. 109] 



If, on the other hand, we reject such a size for the 

 nucleus as improbable, we can calculate the atomic 

 number of the element in question by assuming a 

 law for the large scale variation of the nuclear radii, 

 assuming at the same time the energy of expulsion 

 of the transformation to be small. As the volume 

 of the protons included in the nucleus on the basis 

 of current opinion is negligibly small, it seems natural 

 to assume as a rough approximation that the volume 

 of the nucleus is simply the sum of the volumes of 

 the individual electrons contained in the nucleus, 

 where, however, this electronic volume is not 

 necessarily equal to that calculated from the mass 

 of the electron. This assumption is equivalent to 

 assuming the nuclear radii to be proportional to the 

 third root of the number of electrons in the nucleus, 

 A - N, where A is the atomic weight and N the atomic 

 number. 



Calculating in this way the radius of the trans- 

 formation product of the element in question corre- 

 spon-ding to a range of i cm. in air we finally arrive 

 at an atomic number in the neighbourhood of 40. 

 Since the /3-radiating element rubidium is number 

 37 this calculation immediately suggests that hibern- 

 ium is identical with yttrium, which is related to 

 rubidium just in the right way to account for the 

 i3-radioactivity of the latter. 



This calculation of course is to be regarded 

 meiJ'ely as a suggestion, but I should be interested 

 to know if yttrium were ever found to be associated 

 with Ytterby mica." 



The conclusion arrived at by Mr. Rosseland seems 

 not improbable. In a paper by Ivar Nordenskjold 

 (Bull, of the Geol. Inst, of Upsala, vol. ix.) two 

 analyses of the black mica of Ytterby are given, 

 one referring to a much altered variety and the other 

 to a less altered mica. The former contains yttrium, 

 the latter contains none. This suggests that the 

 yttrium has been introduced in the process of 

 alteration. The mica containing the reversed or 

 bleached haloes has, to all appearance, been con- 

 siderably altered. It is therefore probable that it 

 contains yttrium. On the other hand, according to 

 Mr. Rosseland's theory, rubidium should be present, 

 or — derived from it by loss of a /3-ray — strontium. 

 Neither of these elements appears in the analyses. 

 Nor am I aware of any mineral analysis in which 

 there is an association of any two of the elements 

 in question. But it is, of course, quite possible 

 that spectroscopic examination of yttrium minerals 

 would reveal such traces of rubidium and strontium 

 as would support Mr. Rosseland's deductions. 



J. JOLY. 



Trinity College, Dublin. 



Muscular Efficiency. 



In Nature, April 15, 1920 (vol. 105, p. 197). there 

 is a letter of mine on this subject, and the proposition 

 there given relating to maximum efficiency is in the 

 following applied to the case of the most efficient 

 speed for a bicycle. The values chosen for the 

 constants are merely guesswork, but the result is 

 more or less in accordance with the facts. 



The assumptions made are : 



(i) The total power developed remains constant. 



(2) All the power used in the acceleration of the 

 limbs is lost. 



(3) There is a perpetual leakage of power when a 

 muscle is exerting any force. 



I do not suppose that (i) is strictly true, but 

 the tendency is in that direction. 



