October 3, 1895] 



NA TURE 



54: 



•course reassuring to know that the functions employed 

 in the physical applications, rest on a sound analytical 

 basis, and that the convergency of the scries has been 

 carefully examined. liut there is no compulsion to follow 

 these demonstrations, tedious to all but pure mathema- 

 ticians ; so we can pass on direct to Chapter x., where the 

 physical interest is resumed, under the head of " Vibra- 

 tions of Membranes," for instance the notes produced on 

 a circular drum-head. Lord Kelvin's oscillations of a 

 columnar vortex. Lord Rayleigh's waves in a circular 

 tank, and Sir George .Stokes's investigation of the drag 

 of the air in pendulum vibrations, make up an interest- 

 ing Chapter xi. on Hydrodynamics. 



Chapter xii. deals with the steady flow of electricity or 

 of heat, and Chapter xiii. with the fascinating and novel 

 phenomenon of Hertz's electromagnetic waves, when 

 propagated along wires, in which problem the Bessel 

 function assumes an essential importance. 



The Diffraction of Light, considered in Chapter xiv., 

 contains important applications of the Bessel functions ; 

 the hydrodynamical analogue would be the investigation 

 of the effect of a breakwater in smoothing the waves 

 which bend round behind into its shelter ; for instance, 

 the effect of the tjoodwin Sands on the safe anchorage in 

 the Downs. 



Newton rejected the Undulatory Theory of Light, 

 partly because he could not understand the existence of 

 shadows on this hypothesis, a curious effect of Newton's 

 early ideas as a countiy boy ; had he been brought up 

 on the sea coast, this apparent difficulty could not have 

 troubled him. 



It would be a needless complication to consider any 

 but straight waves in the case of the breakwater ; and 

 similarly in the Diffraction problem, the authors might 

 have made a simplification by parallelising the incident 

 light by passing it through a lens ; or at least this special 

 case, which is the one of practical importance in the 

 subsequent discussion of the resolving power of a tele- 

 scope, might receive separate treatment as the analysis 

 now becomes almost self-evident. This chapter concludes 

 with a discussion of Fresnel's integrals, required in the 

 diffraction through a narrow slit ; the integrals are ex- 

 pressed by a series of Bessel Functions of fractional 

 order, half an odd integer, and are represented graphi- 

 cally by Cornu's spirals. 



The problem of the stability of a vertical mast or tree, 

 considered under the head of Miscellaneous .-Vpplication 

 in the last chapter, may well be amplified by examining 

 the effect of centrifugal whirling on the stability, as in the 

 case of the chain on p. I ; for the number of revolutions 

 required to start instability is exactly equal to the number 

 of vibrations which the mast or tree will make when 

 swaying from side to side. A differential equation of the 

 fourth order, with a variable coefficient, now makes its 

 appearance, the solution of which will express the oscilla- 

 tions of the Ijullrushes in a stream, or the waving of corn- 

 stalks in a field. The curious appearance of permanence 

 in the waves on a cornfield gives an illustration, analogous 

 to Prof. Osborne Reynolds's disconnected pendulum, of a 

 case of zero group-velocity ; and by some intuitive deduc- 

 tions from the appearance of these waves the farmer can 

 judge the time suitable for harvest. 



The authors have been fortunate in securing an original 

 NO. 1353, VOL. 52] 



collection of numerical lablca, nicludlny those of Dr 

 Meissel, who did not live quite long enough to see his 

 valuable calculations published in this book. 



A collection of examples adds greatly to the interest 

 of the treatise, and will probably form the nucleus of a 

 still larger list in the future. 



.\ltogetherthe authors are to be congratulated in bring- 

 ing their task to such a successful conclusion; and they 

 deser\'e the gratitude of the mathematical and physical 

 student for their lucid and interesting mode of pre- 

 sentment. A. t:;. Grkenhii.i,. 



OUR BOOK SHELF. 



Proloplasmc ct Noyau. Par J. Perez, Professeur a la 

 Faculte des Sciences de Bordeaux. Bordeaux : 

 Imprimerie G. (jounouilhou, 1894.) 



EXPEKIMEXTAI, work in recent years has repeatedly 

 shown that in plants as well as in animals the physio- 

 logical role of the nucleus in the cell is one of great 

 importance. It has been demonstrated that non-nucleated 

 fragments of protoplasm, whether of a Spirogyra or an 

 Infusorian, are incapable of growth and reproduction ; 

 while, on the other hand, fragments containing a portion 

 of nuclear material are capable of complete recrescence. 

 Impressed by these facts the writer of the essay before 

 us has been led to doubt whether protoplasm can be 

 properly regarded as the " physical basis of life," since it 

 cannot retain its life when removed from the influence of 

 the nucleus. Consistently with this position the writer 

 throws doubt upon the existence of non-nucleate organ- 

 isms in geneial. The presence of nuclei has been 

 demonstrated in many forms once believed to be destitute 

 of them — e.g. Mushrooms, marine Rhizopods, and Plas- 

 modia. There remains only Haeckel's group of Monera 

 in which the presence of a nucleus may still be disputed. 

 M. Perez considers in turn each of Haeckel's subdivisions 

 of this most artificial group. In the Lobomonera {e.g. 

 Protama'ba) he believes that the nucleus has been oxer- 

 looked. In the Rhizomonera the nucleus has been observed 

 in various species of Vampyrella ; and it probably exists 

 also in Pro/o/iiyxu, since this form produces zoospores ; 

 the zoospores of those Myxomycetes which most resemble 

 Protomyxa have been shown by Zopf to be nucleated. 

 In the Tachymonera (Schizomycetes) the greater part of 

 the body seems to consist of nucleoplasm, while the 

 zoogloea may perhaps be compared with the undivided 

 protoplasm of a plasmodium. 



M. Perez concludes that non-nucleated organisms or 

 cytodes are creations of the imagination ; that protoplasm, 

 by which our author means cytoplasm, is not the primitive 

 living matter, but a product of nucleoplasm ; and that 

 nucleoplasm, and not protoplasm, is the most primitive 

 living substance known to us. 



Analytical Key to the Natural Orders of Flo^vering 

 Plants. By Franz Thonner. Small 8vo. pp. 151. 

 (London : Swan Sonnenschein and Co., 1895.) 



The authors apology for his little book is that few 

 "Exotic Floras" contain artificial keys to the natural 

 orders, even such as contain keys to the genera and 

 species. But we imagine few persons would attempt 

 working with a flora, exotic or native, without some pre- 

 liminary knowledge of botany, and especially of the 

 natural orders. Indeed a considerable acquaintance with 

 the subject would be necessary to enable a person to use 

 the present key to advantage. For example, the author 

 begins with "ovules naked," and "ovules enclosed in an 

 ovary," &c. Now, to be able to decide this point means 

 a great deal, for a person who could do it would most 

 likely know his gymnosperm without looking at the ovule 



