April 6, 191 1] 



NATURE 



^11 



one boundary and only one face, and that this pro- 

 perty remains if the surface is "deformed" in the 

 usual sense of that word. But it would be very 

 troublesome to prove these facts analytically, and an 

 ordinary person finds it hard to think of such a proof 

 as being anything more than a superfluous tour de 

 force. 



Before leaving this chapter, attention may be 

 directed to the use which is made of cuts (coupures) in 

 the plane of reference. For certain purposes, as shown 

 for instance by Hermite and Heine, it is more simple 

 to use a plane with cuts in it than to construct a 

 Riemann surface ; and the beginner in function-theory 

 may be recommended to master this method before 

 proceeding to Riemann 's. 



The remaining chapters may be more briefly sum- 

 marised. There is one on definite integrals introduc- 

 ing the indispensable notions of integrals by excess 

 and defect, and functions of limited variation ; one on 

 development in series ; two on complex variables and 

 their functions; and one on the difi'erentiation and 

 integration of such functions. Very properly, the 

 author has confined himself to well-known and com- 

 paratively simple functions as examples, and he has 

 given figures to illustrate the conformal transforma- 

 tions efi"ected by C = e^, C = s'm-^z, and so on. As 

 incidental examples, we may mention the Eulerian 

 functions, and Weierstrass's factorial formula for a 

 function the zeros of which are given. 



Mathematical teachers will doubtless find this work 

 of great value, because it helps to suggest what is 

 really practicable in a course of lectures on this sub- 

 ject. The fact is that the theory of aggregates, and 

 the classification of functions, have become such an 

 essential part of all analysis that they cannot be 

 ignored. A serious mathematical student must under- 

 stand what is meant by such terms as closed and open 

 agg''egates, limiting points, uniform convergence, &c.. 

 and know something of the conditions for differentia- 

 tion and integration. But if, with excess of zeal, the 

 lecturer tries to bring out every point, and to be 

 impeccably logical, he runs a serious risk of boring 

 his audience. G. B. M, 



PHYSIOLOGY OF REPRODUCTION. 

 The Physiolofiy of Reproduction. Bv Dr. F. H. A. 

 Marshall. Preface by Prof. E. A. Schafer, F.R.S., 

 and contributions by Dr. W. Cramer and Dr. J. ■ 

 Lochhead. Pp. xviii + 706. (London : Longmans, 

 Green, and Co., 1910.) Price 21s. net. 



THE progress of science is very haphazard. For 

 centuries the problems of breeding and heredity 

 ave engaged the attention of intelligent men, but it 

 k only within the last five decades that any accurate 

 Bientific knowledge on the subject of breeding has 

 n reached. Even now almost all our knowledge 

 this subject has been derived chiefly from a study 

 I the results of the mating of two germ-cells. This 

 tie-sidedness is due to the processes which take place 

 Wring reproduction being so little known. 



This unequal advancement of the sciences is seen 



gain in physiology. Here the physiology of diges- 



k»n, of muscular contraction, of the nervous system, 



NO. 2162. VOL. 86] 



has been extensively studied, but that of reproduction 

 has been largely neglected. Dr. Marshall has set 

 himself to remedy this defect, and has collected all 

 the available information on the subject. Reproduc- 

 tion incidentally concerns many difi'erent categories of 

 people, and they have recorded their observations in 

 numerous and varied periodicals and books. It must 

 have been a task of considerable magnitude for the 

 author to have collated all his sources of information ; 

 a glance at the references to quoted literature will con- 

 vince us of this. The bibliography is in consequence 

 not the least valuable part of the book. 



But Dr. Marshall's volume is not merely a digested 

 abstract of scattered papers taken from a great many 

 journals ; the author's own extensive work has given 

 him an insight into his subject which enables him to 

 impart information to his readers in a clear and lucid 

 way. He has compiled a treatise which will remain 

 a standard work for some time to come. 



The work is to a great extent morphological, but, 

 as everyone knows, it is absolutely necessary to have 

 a sound knowledge of the structure of any organ before 

 physiology is investigated. In studying such a process 

 as the oestrus cycle, the exact niorphological changes 

 which take place in the uterus must first be known. 

 This knowledge we owe to Heape, to whom we are 

 glad to see the volume is dedicated, and it is the 

 foundation of all our knowledge of the physiology of 

 the oestrus cycle. 



The author commences with a chapter on the breed- 

 ing season of animals, examples being taken from 

 invertebrates as well as vertebrates, but in subsequent 

 chapters the higher mammalia are, with few excep- 

 tions, alone referred to. He then deals with the 

 oestrus cycle and the changes which take place in 

 both sexes both before and during reproduction. After 

 this we have detailed all the evidence bearing on the 

 changes in the maternal organs during pregnancy. 

 The chapter on the biochemistry of the sexual organs 

 seems only to show us how little we know, the 

 information in it is so sparse and disconnected, and 

 surely here is a valuable field for research. The last 

 three chapters are on general questions of breeding, 

 such problems as fertility and the determination of 

 sex being dealt with. 



Interspersed with the subject-matter we find the 

 author's views on many theories as seen in the light 

 of his own research. Thus, in the chapter on fer- 

 tilisation, he gives a criticism of Mendelism. Close 

 study of the actual physiology of reproduction does 

 not lead the author to believe in the conception of 

 unit characters, which the Mendelians have put for- 

 ward. He speaks of the idea of attempting to^ 

 locate latent characters of organisms in difi'erent 

 parts of the germ-cell, as a survival from the times 

 when all qualities, abstract or otherwise, were sup- 

 posed to reside in different portions of the body. 

 Whatever be the merits of this particular criticism, it 

 seems that when further work has been done on the 

 physiology of reproduction, a new mechanism may 

 have to be supposed which will account for Mendelian 

 facts, and fit in , as well willi (he teachings of 

 physiology. 



Dr. Marshall has produced a masterly treatise 



