June lo, 1922J 



NATURE 



111 



distinguishing symbol and name for each of the 

 nstituent isotopes of chlorine or bromine, e.g. as 

 ■-. Aston has suggested, Cl^s, CP', Br'», BrSi, etc. 

 rhis subject was discussed at the recent meeting 

 the Solvay Institute in Brussels, and the latter 

 alternative appeared to find favour among the 

 iiajority of the chemists who were present. In this 

 imexion it is of interest to notice that the last 

 casion on which it became necessary to reconsider 

 the traditional definition of an element arose from the 

 promulgation of Dalton's atomic theory. In his 

 "New System of Chemical Philosophy" (Part I., 

 p. 143) published in 1808, Dalton puts forward the 

 conclusion that " the ultimate particles of all homo- 

 geneous bodies are perfectly alike in weight, figure, 

 etc." If this statement be applied to the nucleus 

 atom of Rutherford, it would appear that the atoms 

 of a homogeneous element must be alike both in 

 weight and in the configuration of the protons and 

 electrons of which the atom is composed. Modern 

 investigations have shown that it is possible to find, 

 on one hand, isotopes composed of atoms which 

 possess a like configuration of the planetary electrons 

 in the outer domain of the atoms, but which differ in the 

 weight of the nucleus ; on the other hand, isobares are 

 known {e.g. Ne*** and Ca^°) the atoms of which are alike 

 in weight but differ in configuration. It is of course 

 possible that, in the future, atoms may be discovered 

 which are alike both in weight and in the configuration 

 of their planetary electrons, but differ in their radio- 

 active properties as the result of a different arrangement 

 of the protons and electrons in the nucleus, giving rise 

 to a sort of nuclear isomerism. One such case has 

 been suspected amongst radioactive elements ; but 

 Prof. Piccard, of Brussels, has suggested that this 

 assumption need not be made if the actinium series of 

 radioactive bodies be assumed to have its origin in 

 an isotope of uranium, instead of in the element which 

 gives rise to the radium series. 



On this hypothesis odd atomic weights may be 

 assigned to the radio-elements of the actinium series, 

 while retaining even atomic weights for those of the 

 radium and thorium series ; under these conditions iso- 

 topic members of the actinium and radium series would 

 always differ in atomic weight and the occurrence of 

 isobaric isotopes would be impossible. Prof. Piccard 

 states that this conclusion is supported by recent 

 measurements made to test the application to actinium 

 of the Geiger-Nuttall relationship between the pene- 

 trating power of the rays and the life of the atoms 

 emitting them. There is therefore at the present time 

 no valid objection in regarding as the criterion of a 

 homogeneous element the fact that its atoms must 

 be alike both in " weight " and in " figure " (as 

 NO. 2745, VOL. 109] 



indicated by identical atomic weights and atomic 

 numbers) and using this as a basis in constructing a 

 working definition of the element. 



Elementary Pure Mathematics. 



(i) An Introduction to Projective Geometry. By Prof. 

 L. N. G. Filon. Third edition. Pp. viii + 253. 

 (London : Edward Arnold and Co., n.d.) 75. 6i. 



(2) Elementary Analysis. By Prof. C. M. Jessop. 

 Pp. viii +175. (Cambridge : At the University 

 Press, 192 1.) 6s. 6d. net. 



(3) The School Algebra (Matriculation Edition). By 

 A. G. Cracknell. Sixth impression (second edition). 

 Pp. viii + 456 + Ixviii. (London : W. B. Clive : 

 University Tutorial Press, Ltd., 1921.) 6s. 6d. 



(4) A First Book in Algebra. By Dr. F. Durell and 

 E. E. Arnold. Pp. v + 339 + xli. (New York and 

 Chicago : C. E. Merrill Co., n.d.) n.p. 



(5) A Second Book in Algebra. By Dr. F. Durell and 

 E. E. Arnold. Pp. v + 330-l-xliii. (New York and 

 Chicago : C. E. Merrill Co., n.d.) n.p. 



(6) Plane and Solid Geometry. By Dr. F. Durell and 

 E. E. Arnold. Pp. 503. (New York and Chicago : 

 C. E. Merrill Co., n.d.) n.p. 



(7) Plane Geometry : Practical and Theoretical, Pari 

 Passu. By V. Le Neve Foster. (Bell's Mathematical 

 Series for Schools and Colleges.) Vol. i . Pp. xi -h 229 

 + xi. Vol. 2, Pp. xii + 230-423 + xi. (London : 

 G. Bell and Sons, Ltd., 1921.) 35. each. 



(8) Plane Geometry for Schools. By T. A. Beckett 

 and F. E. Robinson. Part i. Pp. viii -H 239 + v. 

 (London : Rivingtons, 1921.) 55. 



(9) Wightman's Secondary School Mathematical Tables. 

 Edited by F. Sandon. Pp. 96. (London : Wight- 

 man and Co., Ltd., 1921.) 6d. 



T 



of Prof. Filon's book on projective geo- 

 metry is a sufficient indication of its usefulness and 

 merit. There is little to record as regards changes 

 or innovations. One would only like to say that while 

 from chapter 2 onwards the book reads fairly plainly, 

 the first chapter is not at all easy reading. Why need 

 the student be frightened off by such an introduction 

 to a subject full of fascination ? If a further edition 

 is called for, perhaps the author could see his way to 

 simplify this chapter and improving the illustrations 

 so as to make it more palatable. 



(2) A text-book should avoid two extremes : the 

 tendency, on one hand, to include all possible cases 

 that are likely to arise, and all kinds of questions 

 that an examiner is likely to set ; and the danger, on 

 the other hand, of presenting the subject-matter of 

 the book in the form of an almost " bald and uncon- 



2B I 



