;40 



NATURE 



[February io, 1^98 



As every student of astronomy now knows, the satel- 

 lites were not discovered^ until 1877, and one of them 

 actually does revolve round Mars three times while the 

 planet makes a rotation. The coincidence is remarkable ; 

 but it is to be hoped, for the sake of the peace of mind of 

 terrestrial inhabitants, that Mr. Wells does not possess 

 the prophetic insight vouchsafed to Swift. 



In conclusion, it is worth remark that scientific 

 romances are not without a value in furthering scientific 

 interests ; they attract attention to work that is being 

 done in the realm of natural knowledge, and so create 

 sympathy with the aims and observations of men of 

 science. R. A. G. 



OUR BOOK SHELF. 



Introductory Course in Differential Equations. By D. 



A. Murray, B.A., Ph.D. Crown 8vo. Pp. xv + 234. 



(New York and London : Longmans, Green, and Co., 



1897-) 

 Ordinary Differential Equations ; with an Introduction 



io Lie's Theory of the Group of One Parameter. By 



James Morris Page. Crown 8vo. Pp. 226 -I- xviii. 



(London : Macmillan and Co., 1897.) 



Mr Murray's book is adapted to provide for students that 

 knowledge of the subject of differential equations which 

 they are likely to want in applications of mathematics to 

 physics, and in the general courses in arts and science 

 in "classical" colleges. The author is chiefly occupied 

 with giving expositions of the devices usually c.nployed 

 in the solution of the simple differential equations which 

 such students meet with, and he will be found a safe 

 guide in these matters. He follows the plan, which 

 most recommends itself to teachers, of omitting theo- 

 retical considerations, or postponing them until the 

 student has had practice in carrying out the processes 

 with which he must be acquainted before the theory 

 can be understood. But he does not leave the reader 

 altogether in the dark as to the underlying theory and 

 the modern developments. These are considered near 

 the end of the book in a series of notes, which ought to 

 prove very useful to those who wish to know more about 

 the subject than can be learned from the text. In one 

 case, that of the integration of linear equations in series, 

 the author has departed from his general practice of 

 giving an account of the simple and particular rather 

 than of the difficult and general. It seems unfortunate 

 that he did not choose for discussion the forms of the 

 series which satisfy such equations in the neighbourhood 

 of ordinary points. When a second edition is called for 

 he will do well to alter this, and to avoid such ex- 

 pressions as "concentric cylinders" and "consecutive 

 curves." The book is well printed, and is adequately 

 supplied with well-chosen examples, some of them 

 relating. to physical subjects; and it ought to prove of 

 service both to those for whom it is primarily intended, 

 and also to British students who have not time to master 

 Forsyth's treatise, but wish to learn rather more about 

 the subject than is to be found in Lamb's " Infinitesimal 

 Calculus." 



In several important respects Mr. Page's book differs 

 considerably from most existing text-books on differential 

 equations. It is not sufficiently elementary for students 

 reading the subject for the first time, since it makes no 

 attempt to supply that thorough drilling in the solution 

 of linear equations with constant coefficients and other 

 simple forms, which our Universities insist on as a pre- 

 liminary test of proficiency. Those, however, who have 

 passed beyond the threshold of the subject, and who 

 wish to study the general machinery underlying the 

 methods they have learnt, will find in Mr. Page's work 



NO. 1476, VOL. 57] 



the fii-st attempt to present to English readers a concise 

 account of some of Prof. Lie's important developments 

 of the theory of transformation groups, by which he has 

 shown that the usual methods are only applicable to 

 such differential equations as admit of known infini- 

 tesimal transformations. A great many of the methods 

 here described are due exclusively to Prof. Lie ; the 

 examples at the end of each chapter are, however, 

 largely taken from existing text-books. A feature which 

 strikes us as distinctly good, is the treatment together 

 of simultaneous systems and the equivalent linear partial 

 equation. 



The two books before us are thus, to a great extent, 

 complementary in scope. Starting with no knowledge of 

 differential equations, a course of study first under Mr. 

 Murray's and then under Mr. Page's guidance will lead 

 the student by easy stages up to an insight into the 

 Theory of Groups. 



Nature Study in Elementary Schools j a Manual for 



Teachers. By Mrs. L. L. W. Wilson. Pp. xix -f 262. 



Woodcuts. (New York : The Macmillan Company. 



London : Macmillan and Co., Ltd., 1897.) 

 There is a notion in this book— a sensible, practicable 

 notion ; and this is enough to distinguish Mrs. Wilson's 

 lessons from the common run of school natural histories. 

 Her aim is to stimulate the children to work for them- 

 selves ; and now and then she succeeds in laying out 

 really interesting work for them, as in the lessons on 

 seedlings and on some common American trees. We 

 recommend the book to the notice of enterprising 

 teachers. In spite of very obvious defects, it may be a 

 guide to better methods than those which prevail at this 

 time. The great fault of the book is the feeble execution 

 of an excellent idea. Many of the lessons do no sort of 

 justice to the objects, and pass over without remark fea- 

 tures which ought to arouse the curiosity of the children. 

 We can hardly understand how any teacher could work 

 through the thorn-apple with a class, and then write 

 down so poor a description as that on p. 19. Many of 

 the drawings, particularly those of insects, are too crude 

 and hasty to be produced as e.xamples even of what can 

 be done m school. In the present writer's opinion the 

 mythology and the poetical pieces are overdone. These 

 things may be allowed to come in as extempore illustra- 

 tions ; but when they are laboured, they simply distract 

 the attention and prevent the children from focussing 

 their minds upon the objects. 



A word as to the use of printed lessons. On no account 

 should the book be produced in class ; that would be to 

 give the solution of the problems in advance. Nor should 

 the teacher reproduce the very lessons given in the book, 

 but devise lessons of his own upon the same lines. In 

 this way the book now before us can be turned to 

 excellent account. L. C. M. 



Botanical Microtechnique : a Handbook of Methods of 

 Preparation^ .Staining, and of Microscopical Investiga- 

 tion of Vegetable Structures. By Dr. A. Zimmermann, 

 Privat-docent in the University at Tiibingen. Trans- 

 lated from the German by James Ellis Humphrey, S.D. 

 Pp. xii -I- 296. (Westminster : Archibald Constable 

 and Co., 1896.) 

 Modern advanced work in vegetable, as in animal, 

 histology requires the aid of a refined and often com- 

 plicated technique in order to render apparent the more 

 difficult details of structure. The zoologist possesses at 

 least one good treatise on methods ; but until the ap- 

 pearance, in its English form, at the hands of Dr. 

 Humphrey, of Zimmermann's excellent work, there was 

 no advanced handbook available to a student un- 

 acquainted with German. The scope of the book is suffi- 

 ciently indicated by the title, and under its new form 

 can be confidently recommended to English-speaking 

 students. 



