322 



NATURE 



[December 27, 1917 



mathematics, has much to say which will interest 

 the considerable public whose attention has been 

 arrested by the modern logistic school. His style 

 of writing- suffers from being- too ornate, and his 

 somewhat oveitloaded sentences are often a hin- 

 drance to a clear comprehension of his meaning. 



In their essays on the philosophy of mathe- 

 matics and on logic both the authors exhibit at 

 times a tendency, common in the school of 

 thought to which they belong, to attach too 

 much relative importance to deductive logic, and 

 even to represent it as being almost the sole 

 form in which rigorous thinking is embodied. 

 Inductive logic, a subject of perhaps greater 

 importance, as lying nearer to the actual modes 

 in which living thought moves, than deductive 

 logic, is apt to be ignored in an estimate of what 

 constitutes rigorous thinking. The reduction of 

 the whole or of parts of mathematics to a purely 

 deductive scheme in which everything flows by 

 chains of syllogisms from a certain body of postu- 

 lations consisting of existential assumptions and 

 axioms is no doubt of distinct philosophical and 

 aesthetic interest, but it is doubtful whether it 

 can do much to further the progress of mathe- 

 matics as a living and growing organism. 



Mathematical knowledge could not possibly have 

 been discovered by purely deductive processes. 

 The purely deductive form is one in which a mathe- 

 matical theory can be exhibited only after its 

 completion ; it operates as a gauge which tests the 

 exactitude and completeness of what has been 

 discovered by the operation of mental processes 

 of a higher and more subtle kind than those in- 

 volved in following a chain of syllogisms. Even 

 a purely, deductive scheme could not be constructed 

 without the factor of purposiveness in the con- 

 structer; in default of a perception of aim, a set^ 

 of given postulations, definitions, and axioms" 

 would be useless. The possession of them would 

 not of itself enable anyone to move a single step 

 in construction, any more than a fount of type 

 would enable a compositor to set up a book if no 

 copy were given to him. It would be unfair to 

 imply that Prof. Whitehead and Prof. Keyser are 

 unaware of these considerations, but at least 

 amongst their disciples of the modern logistic' 

 school they are by no means always adequately 

 recognised. E. W. H. 



THE FUNDUS OCULI OF BIRDS. 

 The Fundus Oculi of Birds, especially as viewed 

 by the Ophthalmoscope : A Study in Compara- 

 tive Anatomy and Physiology. By Casey A. 

 Wood. Pp. 180 + plates Ixi. (Chicago: The 

 Lakeside Press, 1917.) 

 T\R. CASEY WOOD is an ophthalmic surgeon 

 -*-^ with a large practice in one of the busiest 

 cities in America. He is a voluminous writer on 

 subjects connected directly with the science and 

 art of his speciality, and he is the editor of an 

 Encyclopaedia of Ophthalmology, of which several 

 volumes have already appeared. It would seem 

 NO. 2513, VOL. 100] 



that in this there was enough to provide labour 

 for more than the ordinary day of any man, yet 

 he has found time to devote himself to the ex- 

 ploration of what may almost be described as an 

 untrodden field of science. It is true that in this 

 country Dr. Lindsay Johnson has done work of a 

 similar kind, but he mainly concerned himself with 

 the ophthalmoscopic examination of the mam- 

 malian eye. Dr. Wood is the first to make a sys- 

 tematic examination of the fundus appearances in 

 the eyes of birds, and the present volume, with its 

 beautiful series of illustrations by Mr. A. W. 

 Head, is a sufficient proof that it has been a 

 labour of love. The present writer is not in a 

 position to judge whether the ophthalrrioscope 

 will prove to be the valuable aid to the classifica- 

 tion of birds and the identification of species that 

 Dr. Wood seems to think, but a strong case has 

 been made out for the use of the ophthalmoscope 

 by the ornithologist. For his benefit two chapters 

 are devoted to a description of the ophthalmo- 

 scope and its use ; but an hour or two with a 

 friendly oculist in the ophthalmic department of a 

 large hospital would do far more than many pages 

 of description to enable those interested in birds 

 to gain a glimpse of this new field. 



The most interesting chapters in the book deal 

 with the relationship between the macular arrange- 

 ments in the retina and the habits of the bird. 

 In these we have a description of all the variations 

 from the almost human-like owl family with simple 

 binocular vision, through the classes which seem 

 to be capable either of binocular or monocular 

 vision, to the purely monocular type with its 

 nasally placed macula. The author differentiates 

 six types of macular arrangement : (i) The 

 amacular fundus ; (2) the nasal monomacular fun- 

 dus, the commonest type in birds ; (3) the temporal 

 monomacular fundus, i.e. like the human eye and 

 found almost exclusively in owls ; (4) the bi- 

 macular fundus, with the nasal fovea usually more 

 deeply marked than the temporal fovea, the latter 

 being used in binocular vision and becoming 

 more deeply marked the more the power of 

 binocular stereoscopic single vision is called into 

 play ; (5) the infula-macular fundus, where the 

 area of clear vision takes a band-like form, with 

 a well-defined fovea placed nasally to the disc 

 in some part of the band ; (6) the infula-bimacular 

 fundus, in which there is a similar band-hke area 

 with two foveae, of which the nasal is invariably 

 in the band, while the temporal sometimes forms 

 an extremity of the band, but sometimes lies 

 above and apart from it. 



It would have added very greatly to the 

 scientific value of this work if Dr. Wood had con- 

 firmed his description of the macroscopic appear- 

 ances of these various types by microscopic 

 sections through the macular areas of the prin- 

 cipal types. It is obvious that he himself has 

 grave doubts as to the amacular type, and a 

 description of the histological appearances of one 

 specimen from each of the other types would have 

 more than compensated for the loss of several 



