368 



NATURE 



[November i8, 1920 



Royal Institution in 1854 : " I am not bound to 

 explain how a table tilts any more than to indicate 

 how, under the conjurer's hands, a pudding 

 appears in a hat." Baron von Schrenck-Notzing 

 and Dr. Fournier d'Albe have a clear course 

 before them. Let them bring "Eva C." to 

 London to exhibit her "materialisations" 

 before a committee of which Sir Ray Lankester, 

 Sir Bryan Donkin, and Mr. Nevil Maskelyne 

 should be members. Then the matter would 

 be put beyond doubt whether the so-called 

 evidence, thus judicially sifted, is or is not based 

 upon the collusive action of mediums and upon 

 the bad, because prejudiced, observation of the 

 sitters. The need to keep in mind what Hume 

 says about occult phenomena was never more 

 urgent than it is to-day. "As finite added to 

 finite never approaches a hair's breadth nearer to 

 infinite, so a fact [statement?] incredible in itself 

 acquires not the smallest accession of probability 

 by the accumulation of testimony." 



Boltzmann's Lectures. 



Ludwig Boltztnanns Vorlesungen iiber die Prinzipe 

 der Mechanik. Dritter Teil. Elastisitatstheorie 

 und Hydromechanik. Edited by Prof. Hugo 

 Buchholz. Pp. xiii + 608-820. (Leipzig: Johann 

 Ambrosius Barth, 1920.) Price 21.60 marks. 



THE name of Ludwig Boltzmann will live on 

 account of his great creative work, the 

 study of which has happily been facilitated by the 

 publication of his collected " Wissenschaftliche 

 Abhandlungen " (3 vols., 1909, Barth), through 

 the co-operation of the Academies of Berlin, Got- 

 tingen, Leipzig, Munich, and Vienna. But he was 

 distinguished also as a teacher, and his power of 

 exposition is shown in several volumes of lectures 

 which have appeared in print. Perhaps the best 

 of these are his "Vorlesungen iiber Gastheorie " 

 (2 vols., 1895), based chiefly on Maxwell's and 

 his own fundamental researches on the subject. 

 Less well known are his lectures on Maxwell's 

 theory of electricity and light, and those on the 

 principles of mechanics, each occupying two 

 volumes. 



The book now under review comes from the 

 same Leipzig press, and forms a third and final 

 volume of the lectures on mechanics. Unlike the 

 preceding volumes, it does not come direct from 

 Boltzmann himself; it is written, on the basis of 

 his lectures, by one of his pupils, Buchholz, to 

 whom Boltzmann, and afterwards his widow, 

 allotted the work of editorship. It first appeared 

 in 1916 as an appendix to a larger volume of 

 Boltzmann's lectures, also edited by Buchholz, 

 NO. 2664, VOL. 106] 



entitled " Applied Mathematics : the Mechanical 

 Potential and its Application to the Determination 

 of the Figure of the Earth (Higher Geodesy)." It 

 contains the theory of elasticity and hydrO' 

 dynamics which was a necessary adjunct to the 

 geodetic part of that treatise ; but its separate 

 publication as a third volume of the principles of 

 mechanics fulfils Boltzmann's intentions regarding 

 the latter course of lectures, and renders it readily 

 available to those who do not wish to study the 

 larger work from which it is reprinted. 



Boltzmann's lectures on mathematical physics 

 formed a "cycle" unified by his use of the con- 

 ception of the potential — the mechanical, electrical, 

 and electrodynamic potentials, as in the lectures 

 previously published, and, in the present volume, 

 the elastic and hydrodynamic potentials. One 

 further set of lectures remains unpublished — 

 namely, that on the general mechanical theory of 

 heat; in this course the thermodynamic potential 

 is introduced and illustrated by three important 

 examples of its application, of which Gibbs's 

 theory of chemical equilibrium is the chief. This 

 final instalment is at present held up owing to 

 financial difficulties ; it is much to be hoped that 

 these may be overcome, in order to complete 

 Boltzmann's representation of mathematical 

 physics and in view especially of the close relation 

 of these lectures to his work on gas theory. 



Although beyond a certain point the theories of 

 elasticity and hydrodynamics diverge widely, their 

 kinematical foundations are almost identical, while 

 the theory of the stress ellipsoid is as necessary to 

 hydrodynamics as it is to elasticity when the vis- 

 cosity of liquids is taken into account (though in 

 the present volume the latter is not done). It is 

 therefore illuminating to consider the two subjects 

 together, and their treatment in these lectures is 

 admirable.- The explanations of the kinematical 

 and mechanical principles are simple and detailed, 

 and the elastic potential is then Introduced and 

 applied to a few important general problems — in 

 particular, to the proof of the Hamiltonian prin- 

 ciple for elastic potential energy, to the deter- 

 mination of the potential for various forms of 

 crystal, and to the propagation of waves of com- 

 pression and distortion in an elastic solid. This is 

 all done in comparatively little compass — a 

 hundred pages — and a general grasp of the subject 

 is rendered easy by the avoidance of individual 

 problems, such as the theory of bending in beams, 

 or the vibrations of rods, strings, and membranes^ 

 in which the potential plays no prominent part. 



The second hundred pages are devoted, oa 

 similar lines, to the general equations of hydro- 

 dynamics, the velocity potential, and the theory 



