530 



NATURE 



[April 6, 189; 



of phase is the interesting subject of inquiry, as showing 

 to what extent the "equilibrium theory" of the bodily 

 tides of the earth, considered in the preceding chapter, 

 can be adopted as a working theory. 



Lord Kelvin has shown how the inertia of a pendulum 

 appears reversed in sign if the point of support is actuated 

 by a vertical vibration, when the forced and free periods 

 are as two to one ; but when the periods are made in the 

 ratio of three or four to one, the equilibrium theory can be 

 adopted. This principle has been employed recently by 

 Sarrau and Vieille in the measurement of powder pres- 

 sures by means of spring gauges ; the free period of the 

 spring is so adjusted in comparison with the period of the 

 applied pressure, so that the vibrations of the spring do 

 not make their appearance, and the indications of the 

 gauge are the same as those for an equal statical pres- 

 sure, steadily applied. 



Valuable work in the discussion of particular 

 problems of a somewhat general nature has been 

 carried out by the late Prof. Belti, of Pisa, and con- 

 tinued by his disciple Cerruti ; particularly also by M. 

 Boussinesq, in his theory of "local perturbations " in an 

 elastic solid bounded by a plane, as illustrated, for in- 

 stance, in the deflection produced in a sheet of ice by a 

 man standing on it ; these questions occupy Chapters 

 Vin. and IX. 



The applications of conjugate functions in Chapter 

 Xn. introduce some interesting problems. The book 

 concludes with the consideration of an elliptic cylinder, 

 turned through a small angle. Something appears want- 

 ing here, as the balancing couples on the interior and 

 exterior confocal ellipses are not brought into evidence. 

 When the exterior ellipse becomes indefinitely large the 

 stresses over it are evanescent, but their resultant is a 

 finite couple. So, too, when the inner ellipse becomes 

 the line joining the foci ; in this case the Jacobian h 

 becomes infinite at the centre, and the displacements u 

 and V at this point require closer investigation. 



It is unfortunate, as Maxwell remarked, that we have 

 no space functions corresponding to the conjugate 

 functions of a plane. But by the rotation of these con- 

 jugate plane curves about an axis, Waugerin has obtained 

 a system of space co-ordinates, suitable for application 

 to certain surfaces of revolution, and he, Mr. Hicks, 

 and Mr. W. D. Niven, have worked out the analysis 

 completely for certain quadric surfaces, cones, and tores. 



In the questions considered m this first volume the 

 forces which produce the elastic displacements are of 

 moderate amount, so that the proportionality of stress to 

 strain may be taken as true, and they act as distributed 

 forces throughout the solid, such as gravity and the 

 forces of inertia introduced by vibrations. 



Mr. Love measures these forces per unit mass, and not 

 per unit volume, as in Thomson and Tait's " Natural 

 Philosophy," so that the component forces appear as 

 pX, pY, pZ, quaHfied by p, the density as a factor. 



Cases might arise, however, say in a dynamo, where 

 some of the forces, the forces of inertia and gravity, would 

 be measured per unit mass, and the others, the electro- 

 magnetic forces, per unit volume ; for this reason the 

 Thomson and Tait method of measurement appears 

 preferable, as the factor p can be inserted where required. 



The difficulties of constructing a rational theory will 

 NO. 1223, VOL. 47] 



turn up in the second volume, when the question of the 

 elastic equilibrium of a lamina has to be considered, 

 in which the stresses are due to an applied finite pressure 

 on one side of the lamina. Mr. Basset has performed a 

 valuable service in pointing out the insufficiency of pre- 

 ceding methods for constructing a theory of such an 

 important practical question as the collapse of boiler 

 flues {Phil. Mag., September, 1892), and he might have 

 added of the Bourdon gauge. We await with interest 

 Mr. Love's contribution to this delicate and baffling part 

 of the Theory of Elasticity. 



In the preface of the " Treatise on Solid Geometry,"^ 

 by Frost and Wolstenholme, the authors, after thanking 

 the proof-readers for their trouble, conclude by " express- 

 ing their regret that they have not escaped a large number 

 of errors, which it will be punishment enough to them to 

 see tabulated in an adjoining page." 



Where the critic has also been a proof-reader he lays 

 himself open to this ambiguous acknowledgment, if he 

 points out any misprints ; but we are pleased to find that 

 the present volume, on careful re-examination, appears 

 to be very clearly and correctly printed. 



A. G. Greenhill. 



BIOLOGY AND THE MEDICAL STUDENT. 

 Text-book of Elementary Biology. Introductory Science 

 Text-book Series. By H.J. Campbell, M.D. (London : 

 Swan Sonnenschein and Co. New York : Macmillan 

 and Co., 1893.) 



THIS volume of 266 pages octavo is an ultra-ele- 

 mentary one, subdivided into a first part of 155 

 pages, which deals with generalities of plant and animal 

 morphology and physiology, together with the principles 

 of classification, and into a second of 1 1 1 pages devoted 

 to the consideration of certain type organisms. With 

 the exception of the dog-fish, which the author dismisses 

 in four short pages, the said types are those of the ex- 

 amination syllabus of the Conjoint Board of the Royal 

 Colleges of Physicians and Surgeons ; and the fact that 

 the book is the first one which has been written up to 

 that standard invests it with a special interest. It is 

 illustrated by 136 borrowed woodcuts, some of which 

 are very poor and antiquated, while others are de- 

 fective. Its author shows himself to be possessed of a 

 considerable power of discretion, and his book is clear 

 and attractive in style. It is, however, a pure compila- 

 tion, for the most part from well-known text-books, as is 

 only too apparent in certain gross errors transcribed, for 

 example, that of the assertion that the Monotreme 

 brains are " not convoluted " ; its only novelty lies in the 

 judicious introduction of concise and useful historical 

 resumes, giving the dates, names, and achievements of 

 epoch-making investigators. Trivial errors abound, and 

 controversial matters of the moment are here and there 

 dogmatically introduced, as though finally established ; to 

 wit (a) the allusion (pp. 39 and 145) to the ectoblastic 

 origin of the segmental duct, which, so far as it may be 

 to-day regarded as an undisputed fact, rests upon Van 

 Wijhe's discovery of a dividing nucleus connecting it 

 with the parent epiderma, and (/3) the assumed conjuga- 

 tive reproduction of Amoeba (p. 160). Conversely 



