January 19, 191 1] 



NATURE 



369 



is also classed by the authors as "approximate in- 

 tegration"; this is a view which does not seem alto- 

 gether satisfactor\\ At any rate, the nature of the 

 approximation involved in using an infinite series is 

 certainly different from that associated with the use 

 of Simpson's rules. Incidentally, at least one 

 example (p. 379), in which the integration is effected 



by a series \\\yl{y-\-c)\d?> integrated over a circle), is 



easily reduced to finite terms in the form, 



Some of the integrals proposed for evaluation by the 

 aid of series are not very easy to evaluate directly ; for 

 instance (p. 380), the elliptic integrals, 



r /" and r ''■^ .. 



Both of these can be expressed in various forms, but 

 the series which are more immediately suggested are 

 not ven,- suitable for ordinary calculations; in par- 

 ticular the second of them suggests the binomial ex- 

 pansion of {i — x*)-i, but the resulting series is quite 

 hopeless for numerical work. Of course, there are 

 several ways of transforming the integrals before con- 

 version to series ; but such transformations might well 

 be suggested in the questions, or the reader may not 

 succeed in guessing what to do first. 



In reading the chapters on applications to plane 

 curves one cannot help regretting some of the old- 

 fashioned geometrical types of proof; no doubt the 

 older books contain much that is not only unsound, 

 but incapable of being made sound. But in spite of 

 this, a geometrical treatment is more attractive to 

 the ordinary reader, and in many cases the proofs can 

 be made reasonably accurate by the aid of very little 

 additional analvsis. 



T. J. I'A. B. 



BOOKS ON NATURE-STUDY. 



(i) Der Natiirfreund am Strande der Adria und des 

 Mittelmeergebietes. By Prof. Carl I. Cori. 

 Pp. viii+ 148 + 22 plates. (Leipzig: Verlag von Dr. 

 Werner Klinkhardt, 1910.) Price 3.50 marks. 

 (2) The Aims and Methods of Nature-Study. A Guide 

 for Teachers. By Dr. John Rennie. With an in- 

 troduction by Prof. J. Arthur Thomson. Pp. xvi + 

 352. (London : \\'. B. Clive, University Tutorial 

 Press, Ltd., 1910.) Price 3^. 6d. 

 ' "pROF. CORPS volume is not intended to give 

 -L descriptions of the systematic characters and 

 organisation of marine creatures, but rather to be a 

 companion to direct the attention of the nature-student 

 to the more commonly occurring marine organisms 

 and to the chief phenomena associated with 

 them. After a brief account of the past history 

 of the Mediterranean and Adriatic, the author 

 passes to the consideration of the animals 

 of the beach — Arenicola, Sipunculus, Solen, Venus, 

 Echinocardium, Synapta, Carcinus, &c. — the chief 

 Teatures and theoretical points of interest associated 

 ^vith many of which are indicated. While dealing 

 ith Annelids, the author directs attention to their 

 lationship to the Crustacea and to the theory of the 

 Annelid ancestry of vertebrates. Modifications of 

 NO. 2 15 I, VOL. 85] 



structure correlated with certain habitats, as illus- 

 trated, for example, by sessile molluscs, and the 

 habits of animals, e.g. the shamming death and auto- 

 tomy of crabs, are dealt with in an interesting manner. 

 The description of the abundance of life on the beach 

 leads up to remarks on the origin of life in shallow 

 water, '"die Geburtsstiitte alles Seins." The lagoons 

 and their flora and fauna — Mysidae, Carcinus, Car- 

 dium, Labrax, Anguilla, &c. — and the Zostera 

 meadows, with their e-xtensive and characteristic 

 fauna — Virbius, Spadella, Turbellaria, Cerianthu-., 

 Sepia, pipe-fish, sea-horses, &c. — are the subjects of 

 two chapters. 



The account of Sepia contains interesting references 

 to the antiquity and former greater abundance of 

 species of Cephalopods in the period when the Ammon- 

 ites flourished, and to the power of colour change, 

 owing to which "spiegelt sich sozusagen die Seele der 

 Sepia auf ihrer Haut ab." Throughout the volunvi 

 the author brings before the reader observations on 

 the mode of life, the food and special points in the 

 physiology of the animals under description ; for in- 

 stance, he points out that in Trachinus, the weever- 

 fish, the spreading of the spines and the assumption 

 of the defensive attitude are dependent chiefly on 

 stimulation of the tail. The organisms of the rocks 

 and rock-pools are then considered, attention being 

 given to boring animals, e.g. Pholas, Paracentrotus, 

 the former boring by chemical, the latter by mechan- 

 ical means. 



The concluding chapters give accounts of the larger 

 organisms obtained by dredging, and in the plankton 

 (Rhizostoma, some Siphonophores, Ctenophores, and 

 Salps) and on the high sea (fishes, dolphins, &c.;. 

 The figures are for the most part excellent, but a 

 few, for instance, those of Aphrodite, Arenicola, and 

 Balanoglossus on Taf. vi., are capable of improve- 

 ment. A few errors of spelling occur in the names 

 of the animals figured, e.g. pilleata (for pileata), 

 forscalea, Litorina, and Echineis. But these are only 

 slight blemishes, and do not seriously detract from the 

 value of this excellent work, which cannot fail to 

 stimulate the interest and imagination of the nature- 

 lovers for whom it is intended. 



(2) Dr. Rennie aims at imparting a definite con- 

 tinuity of principle to the teaching of the subject of 

 nature-study and to this end he outlines series of care- 

 fully graded courses. He holds rightly that the facts 

 need to be carefully grouped or arranged in sequence, 

 according to principle, in the mind of the teacher 

 (although the principle need not always be enunciated 

 to the pupils), for only in this way can the teaching 

 be effective. Four school courses are suggested, 

 namely, for pupils of seven or eight years, eight or 

 nine years, n«ne to twelve years, and seniors, all of 

 which are arranged on a seasonal plan and deal in 

 turn with plants, animals, weather studies, calendars, 

 and general considerations. Several chapters are 

 devoted to excellent object-lessons on common living 

 things, e.g. frogs and toads, birds and their eggs and 

 feathers, the mole, shells, the snail, caterpillars and 

 moths, earthworms, gnats, buttercups, common fruitP 

 and seeds, trees, ferns, &-c. Then follow elementarv 

 studies of some common rocks, suggestions for a 



