526 



NA TURE 



[September 26, 1901 



this time !), an irresistible group of nestlings of the 

 Canada jay, and a trio of manatees depicting three 

 leading attitudes, make up a selection which is alto- 

 gether admirable, and if for only these the book deserves 

 support. On the contrary, however, illustrations such as 

 those which do duty for a transverse section of a Hydra, 

 for a tactile papilla and that of the calf's tongue, are 

 beneath criticism ; and doubtful to a degree are the 

 incorporation in such a book as this, as all-typical, of 

 such forms as Gonium, Calcolynthus, and Prophysema, 

 about the latter two of which the less that is put before 

 the elementary student the better. Old friends are with 

 us, as, for example, the puss moth larva, with its 

 " intensely exaggerated caricature of a vertebrate face." 

 Anthropomorphic truly ; but is this science ? 



We assume the authors would have the beginner read 

 this book while prosecuting- a more detailed study of 

 individual forms, as with the now universal type-system. 

 Its appearance within a year of Davenport's " Introduc- 

 tion to Zoology," a book of somewhat kindred aims, 

 betokens a desire on the part of those responsible for the 

 elementary scientific education of young America for a 

 liberalising and humanising influence. The experiment 

 is an interesting one, and it in some respects meets the 

 ever-recurring question of the teacher, "What best can I 

 give the student to read ?" The lines on which the book 

 is written appear to us risky in their great breadth and 

 cursoriness ; but while we await the result of experience 

 before pronouncing further upon the book we admit that 

 salient truths are expressed in a refreshingly familiar 

 way, and that it is pleasant reading. The authors have 

 fallen into the common error of according uneven recog- 

 nition to authority, as, for example, in attributing the 

 well-known series of drawings of Amccba to Schulze on 

 p. S, but not on p. 53, where at least a cross reference 

 should have been inserted. 



OUR BOOK SHELF. 

 Giis/av Thcodor Fcclincr. By W. Wundt. Pp. 92 



(Leipzig : Engelmann, igoi.) Price zs. net. 

 G. T. Fechner, at once a distinguished and industrious 

 devotee of exact research, and a poetic and religious 

 enthusiast, is a most attractive figure in the history of 

 German thought in the nineteenth centuiy ; and in the 

 lecture delivered by Prof. Wundt before the Royal 

 Society of Saxony in commemoration of the hundredth 

 anniversary of his birth (April 19), the general reader 

 will find a readable account of him which is composed 

 with the double authority of a personal friend and 

 colleague and of a successor. 



The chief interest of the lecture itself lies in the proof 

 that Fechner was first led to the psychophysical work by 

 which he will be best remembered from a desire to find 

 experimental confirmation for his poetico-philosophical 

 theory of the universal animation and intelligence of 

 physical nature. 



Many readers will perhaps turn with most interest to 

 the section of the appendix which contains the author's 

 personal reminiscences of his famous predecessor. It is 

 curious to learn from Prof Wundt that Fechner's interest 

 in the experimental psychology of which he was the 

 originator was entirely confined to the problem of the 

 so-called "logarithmic law" of psychophysical action, 

 and that he could not be brought to read exact researches 

 into other psychological questions. A. E. T. 



NO. 1665, VOL. 64] 



LETTERS TO THE EDITOR. 

 YThe Edilor docs not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to coi respond with the writers of, rejeciei 

 Manuscripts intended for this or any other part of Natuke. 

 No notice is taken of anonvmoiis comntunications.'i 



Two Problems of Geometry. 

 L\ your issue of August 22, Mr. A. B. Basset .'isks for solu- 

 tions of the two problems, the trisection of an angle by means 

 of the cissoid, and the duplication of the cube by the conchoid. 

 I happened to come across a solution of the latter in an old 

 book, Leslie's "Geometrical Analysis" (1821), where the 

 problem is solved also in several other ways — by means of the 

 cissoid, two parabolas, a rectangular hyperbola and circle, and 

 the logarithmic curve. The problem of the trisection of an 

 angle is also solved in several ways — by means of the conchoid 

 (two ways), an hyperbola (e = 2) and intersecting circle, a rect- 

 angular hyperbola and circle, the quadratrix, the companion to 

 the cycloid, and the Archimedean spiral, but nothy the cissoid. 

 The problem cf the duplication of the cube is- solved in the 

 following way by the conchoid. 



Let AB, AC be the two given lines placed' at right angles; 

 Complete the rectangle AD and circumsewbe a circle about it. 

 Then if through C a line ECG be drawn cutting, BD(, BA. pro- 



duced in E and G and the circle again in H, and making EC= 

 HG, it is known that AG and DE are the two mean propor- 

 tionals between AC and AB. (Philo's construction.) Bisect 

 BD at F, and on AB describe an isosceles triangle having BK = 

 AK=BF. Join KG. 



Then ED . EB^EC . EH = GH . GC=GA . GB, 



,-. GA. GB-fBF-' = ED . EBi-Br^=EF2; 



and GK'- = AK--t-GA . GB = EF2, .-. GK = EF. 



Join CF meeting AB produced in L, join LK and draw 

 AM II LK. 



Then LA = 2AB, and ED : BA = CA : AG 

 .-. 2DE : AC = 2AB : AG = AL: AG 

 ... AL : AG = DE : DF, .-. EF: DF=LG: AG 

 = GK : GM ; but EF^GK, .-. GM = DF = iAC. 



