364 



NA TURE 



[May 26, 1910 



viduals are recognised to be functions of each other, 

 at death they are supposed to shrivel into isolated 

 and alien units." 



The only future that is possible is an immortality 

 of function. An organism is nothing but a centre 

 or focus through which the world-energy operates. 

 When the organism is lost in what we call death, the 

 function may well enough go on in terms of more 

 subtle forms of energetic activity (c/. Prof. James's 

 little book, "Human Immortality"). 



Perhaps, if a criticism may be ventured, modern 

 *' psychology-without-a-soul " has become too much 

 afraid of being metaphysical. A function must be a 

 function of something. If there is an act, there must 

 be an actor who is, in a way, greater and more real 

 than the act. A soul-entity, then, is justified. It is 

 as reasonable to posit it as to posit a surviving 

 " function." 



But the volume is full of deep and careful thinking, 

 and is suggestive and stimulating even in its more 

 questionable doctrines. The analysis of conscious- 

 ness, and the chapters on the test of truth and on 

 mind and matter, are particularly good. 



SOME GERMAN MATHEMATICAL TREATISES. 

 (i) Einfilhrung in die Vektoranalysis, mit Anwend- 



ungen auf die mathematische Physik. By Prof. 



Richard Gans. Zweite Auflage, Pp. x+126. 



(Leipzig : B. G. Teubner, 1909.) Price 3.60 marks. 



(2) Die Vektoranalysis und ihre Anwendung in der 

 theoretischen Physik. By Dr. W. v. Ignatowsky. 

 Teil I. Die Vektoranalysis, pp. vii+112. Teil II. 

 Anwendung der Vektoranalysis in der theoretischen 

 Physik. Pp. iv+123. (Leipzig: B. G. Teubner, 

 1909-10.) Price 6 marks. 



(3) Vorlesungen zur Einfiihrung in die Mechanik 

 raumerfiillender Massen. By Prof. Alexander Brill. 

 Pp. x+236. (Leipzig: B. G. Teubner, 1909.) 

 Price 8 marks. 



(4) Funktionentafeln mit Formeln und Kurven. By 

 Prof. Eugen Jahnke and Fritz Emde. Pp. xii + 176. 

 (Leipzig : B. G. Teubner, 1909.) Price 6 marks. 



(5) Die Zentrifugalkraft. By Prof. Friedrich Poske. 

 Pp. 80. (Berlin : Julius Springer, 1909.) Price 

 3 marks. 



(6) Interpolationsrechnung. By Prof. T. N. Thiele. 

 Pp. xiii+173. (Leipzig: B. G. Teubner, 1909.) 

 Price 10 marks. 



(i) ' I "HE simplified system of vector analysis pro- 

 J- moted by Gibbs and Heaviside has met with 

 such general acceptance in Germany that treatises 

 and memoirs on subjects of mathematical physics are 

 now often hardly intelligible to readers who do not 

 possess some familiarity with the notations and pro- 

 cesses of the calculus in question. A demand has 

 thus arisen for elementary expositions limited to what 

 is absolutely necessary for physical purposes. The 

 first book on our list, now in its second edition, is 

 written mainly with a view to the electrical applica- 

 tions. It deals in a clear and simple fashion with 

 the fundamental operations, and then passes on to' 

 the discussion of vector-fields' An interesting chapter 

 on " tensors," which have a bearing on the theories 

 NO. 21 17, VOL. 83] 



of stress and of quadratic moments, is added. The 

 work closes with a few elementary applications to 

 hydrodynamics and electromagnetism. It may be 

 commended as giving in a very brief compass almost 

 all that is of importance to the physical student. 



(2) This work consists of two parts. In the first of 

 these vector analysis is developed from its foundations 

 as an independent discipline, without any reference to 

 Cartesian or other special geometrical coordinates. 

 The author claims some degree of novelty for his 

 methods of exposition, we think with justice. In 

 particular the intrinsic nature of Hamilton's operator 

 V, whether as applied to a scalar quantity, or by 

 scalar multiplication to a vector, or by vector multi- 

 plication to a vector, is here explained with great 

 insight and (we believe) originality. The passages in 

 question may be recommended to the notice of those 

 who have felt the inadequacy of the usual Cartesian 

 treatment of the matter. The theorems of Green and 

 Gauss naturally present themselves for discussion, 

 and, as in the preceding work, a chapter is added on 

 tensors. The second volume contains a number of 

 applications to elasticity, hydrodynamics, electricity, 

 and crystalline reflection. 



(3) This is a course of lectures on the dynamics of 

 continuous systems, written from a special point of 

 view. The inspiration is derived from Hertz, but the 

 author prefers to employ Gauss's principle of least 

 constraint rather than the Hertzian law of the 

 " straightest path." The treatment is somewhat 

 academic, in the sense that stress is laid on unity of 

 method rather than on the specific interest of the 

 various topics discussed, but it is marked by clearness 

 and great mathematical elegance. The subjects con- 

 sidered include the kinetics of rigid bodies and of 

 fluid and elastic media, and, finally, the electro- 

 magnetic theory of light. On one point a protest 

 should, in the opinion of the present writer, be 

 entered. The notion that the apparent potential 

 energy of a dynamical system may be accounted for 

 as the kinetic energy of latent internal motions is 

 here, as in many recent Continental writings, attri- 

 buted too absolutely to Hertz. -If nowhere stated 

 so explicitly, perhaps, it must have been present to 

 the mind, not only of Lord Kelvin, but of all students 

 of his various expositions of the theory of gyrostatic 

 sjstems, to say nothing of the well-known "kinetic 

 theory " of elasticity. 



(4) This is intended as a supplement to the 

 ordinary tables of mathematical functions. Of 

 recent years a great deal of work has been jr 

 done, especially in this country, in tabulating the l| 

 functions which occur in various important problems 

 of mathematical physics, but the results are scattered 



in the proceedings of societies and in scientific 

 journals, and are often unavailable, and even unknown, 

 to those who have most need of them. The authors 

 of the present treatise have collected a number of such 

 tables, and have appended explanations of the nota- 

 tions, and lists of the important formulae. The whole 

 is brought within a moderate compass by restricting 

 the entries to four significant figures; this is, of 

 course, ample for most physical purposes, and more ; 

 than sufficient for graphical representation. We are j 



