March 21, 1902.] 



SCIENCE. 



465 



is calculated and the regular polygons treated, 

 in particular those of five and of seventeen 

 sides. 



Congruence, symmetry, similarity, concur- 

 rence and collinearity are taken up in the 

 next section, and Desargues's, Pascal's, Ponce- 

 let's and other famous theorems presented for 

 demonstration. 



The remaining chapters treat of conies and 

 other plane curves, with historical notes and 

 references to certain applications, completing 

 in an attractive way a valuable addition to 

 the literature of elementary geometry — a ser- 

 viceable condensation of matheroatioal prop- 

 erties, theorems, puzzles and problems. We 

 may be permitted to doubt, however, whether 

 the average student who has attained to that 

 acquaintance with radicals, logarithms and 

 positional geotaetry which is evidently 

 assumed in Chapters XI.-XIV., will often 

 stop to obtain his actual results- by folding. 

 In fact the frequent use of the word 'draw' 

 implies the author's permission of a short- 

 cut; but it would probably be an encourage- 

 ment to the pupil actually to bring his folding 

 into the higher problems if in connection 

 with it the use of the compass, dividers and 

 straight-edge were frankly sanctioned. Sim- 

 ply in the interest of accuracy in folding, a 

 thin rule, preferably of nickel-plated steel, 

 beveled, would be desirable. 



Where the claim of the author is so modest 

 and his aim in so high degree attained, the 

 task of criticism is a light one. It is singular 

 that the expression 'equal halves,' if in the 

 original, should have passed two revisers unno- 

 ticed; and one could wish that pericycloids, 

 the involute and the cartesian ovals had not 

 been omitted, and that the relative impor- 

 tance of the curves treated were better indi- 

 cated by the space -allotted to them. 



The editors have performed a genuine ser- 

 vice in bringing this work before an American 

 audience and in such neat and attractive form. 

 The twenty-six exquisite half-tone illus- 

 trations with which they have replaced the 

 line drawings of the original, are a decided 

 enrichment of the volume. The practically 

 equal number of footnote references to their 

 own series, in one case duplicated, compels the 



question how far permission to edit carries 

 with it advertising privileges. 



F. ]Sr. WiLLSON. 



Princeton, N. J., 

 February, 1902. 



Pleuronectes (the Plaice). By F. J. Cole and 

 James Johnstone. Liverpool Marine Biol- 

 ogy Committee Memoirs, No. 8. London, 

 Williams & Norgate. Dec, 1901. Pp. 260, 

 11 plates. Price, la. 



In these L. M. B. C. Memoirs a single animal 

 or plant type is described by a specialist in 

 such a way as to serve primarily the interests 

 of college and private students of biology and 

 young amateurs. They are, however, far more 

 than mere laboratory guides, being authorita- 

 tive sources of information based on original 

 work upon species which for the most part are 

 not elsewhere adequately described. 



This, the latest memoir of the series, is de- 

 voted to an important food fish, the plaice, 

 containing descriptions with excellent figures 

 of the skeleton, abdominal viscera, blood vas- 

 cular system, nervous system and sense organs, 

 together with appendixes on life history, habits 

 and practical fishery matters. Its chief inter- 

 est for biologists in general lies in the discus- 

 sion of the asymmetry of the Heterosomata, 

 or flat fishes, of which the plaice is probably 

 the best known British representative. 



In explaining this asymmetry the authors 

 follow Traquair, disposing first of the mis- 

 chievous assumptions that the left eye has 

 passed either through the substance of the 

 head or over the top of the head to reach its 

 definitive position on the right side of the 

 body. "The fact is," they remark, "that the 

 left eye is not on the right side at all. Its 

 presence there is purely illusory. What has 

 happened is that the whole of the cranium in 

 the region of the orhit has rotated on its longi- 

 tudinal axis to the right side, until the two 

 eyes, instead of occupying a horizontal plane, 

 have assumed a vertical one, and the left eye is 

 dorsal to the right." 



The part of the work next in importance to 

 the discussion of the asymmetry is the section 

 devoted to the cranial nerves, which are given 

 a thorough critical treatment. The key to the 



