August ii, 1910] 



NATURE 



169 



lingly inaccurate assertion that "Prof. Grassi, of 

 Rome, discovered the breeding grounds (of the eel) 

 to be out in the Atlantic Ocean from Norway, Den- 

 mark, France, and Spain in some parts looo miles 

 from shore." 



With salmon and trout the case is different; any 

 work upon this subject by a fisherman and fishery 

 manager of Mr. Malloch's experience cannot fail to 

 be of interest. Some readers will doubtless not be 

 prepared to accept in their entirety all the views ad- 

 vanced, but all will be grateful to the author for 

 recording the conclusions which he has drawn from 

 a very wide personal experience. 



The most interesting feature of the book is the 

 really excellent series of illustrations, reproduced from 

 photographs of Tay salmon of all ages and conditions, 

 and of sea-trout and brown trout from various rivers 

 and lochs. Illustrations such as these give a far 

 better impression of the changes due to growth and 

 condition and the variations caused by environment 

 than any letterpress. The investigations of the Scot- 

 tish Fishery Board and the Department of Agriculture 

 in Ireland have familiarised us with the great indi- 

 vidual difference in the period spent by salmon in the 

 sea, and Mr. Malloch figures salmon which were 

 marked as smolts and subsequently re-captured on 

 their return to the river after a longer or shorter 

 sojourn in the sea, and discusses the probable length 

 of such sojourn. He e.xpresses himself as "fully con- 

 vinced that many (Tay) fish from 40 lb. and upwards 

 are on their first return from the sea when they are 

 captured in fresh water"; we could wish that some- 

 definite evidence were forthcoming in support of this 

 conviction, for a 40-lb. salmon is presumably eight, or 

 at least seven, years old, and Calderwood has stated 

 that " it appears to be somewhat unusual for a fish to 

 remain till its fourth sea year" (i.e. its sixth year) 

 " without spawning." 



In the Tay, salmon run at all seasons of the year, 

 and Mr. Malloch is of opinion that the clean winter 

 fish which run in October remain thirteen months in 

 fresh water before spawning. We must confess to 

 feeling sceptical on this point, more particularly as 

 there seems to be nothing to show that such fish may 

 not drop back again to the sea after a short sojourn 

 in fresh water without spawning. In the case of the 

 Blackwater (mentioned in this context as a spring 

 river) there is some positive evidence that clean early- 

 spring fish do drop back into the sea. 



The opinion now generally held that the "bull- 

 trout " of the Tay is a salmon is confirmed by an 

 illustration of such a fish side by side with a salmon 

 of the same size and weight ; we understand Mr. 

 Malloch to regard "bull-trout" as salmon which have 

 spawned and again ascended the river as mended fish, 

 a view which seems hardly consonant with that held 

 by Calderwood, though not inconsistent with the re- 

 sults of some of the marking experiments conducted 

 by the Scottish Fisherv Board. It cannot, of course, 

 be seriously suggested that all salmon, after once 

 spawning, become "bull-trout." 



Some space is, very properly, given to a considera- 

 tion of the deductions to be drawn from an e.xamina- 

 NO. 2128, VOL. 84] 



tion of the scales of salmon. While the figures given 

 by Mr. Malloch are excellent, we find his explanations 

 in the text rather difficult to follow ; the generalisation 

 that a salmon adds sixteen rings to its scale in e? 

 year of its life, so long as it feeds and grows, is not 

 borne out by the scales figured or by the observations 

 of other persons ; the two years spent as a parr and 

 smolt would, in fact, seem to account for a number of 

 rings, varying from about twenty to twenty-seven, 

 while from twenty to thirty rings may be added in 

 any subsequent year spent wholly in the sea. 



Such matters as the spawning and feeding of sal- 

 mon in fresh water and their movements in tidal 

 rivers are briefly discussed, and interesting figures are 

 given of land-locked salmon up to three-quarters of a 

 pound in weight. 



Did space permit we would willingly quote freely 

 from the chapters dealing with sea-trout and brown 

 trout, and in particular from a most interesting dis- 

 cussion of the effect of environment on the latter fish, 

 and the lessons to be drawn therefrom in the stocking 

 and management of fisheries. 



In conclusion we must deplore the entire absence 

 of either inde.x or detailed table of contents. 



L. W. B. 



NON-EUCLIDEAN GEOMETRY. 

 Theories of Parallelism : an Historical Critique. By 

 W. B. Frankland. Pp. xviii + 70. (Cambridge: 

 University Press, 1910.) Price 3^. net. 



THE appearaiice of this tract is a welcome sign 

 of the growing interest in the foundations of 

 geometry. Those who, greatly daring, first disputed 

 or denied Euclid's fifth postulate were treated, if not 

 as charlatans, at least as idle speculators, whose 

 theories, even if sound in the abstract, had no relation 

 to actual space. It may be added that the earlier 

 works on the non-Euclidean geometries were not very 

 attractive to the average mathematician, because they 

 were either so analytical that the reader was inclined 

 to regard their geometrical interpretation as a mere 

 fa(on de pnrler, or so vague and intuitive as to raise 

 a suspicion of want of rigour. 



Things have altered so much, not in substance, but 

 in mode of presentation, that it may fairly be said that 

 anyone with a knowledge of spherical trigonometry 

 and elementary calculus may satisfy himself of the 

 validity and coordinate rank of the elliptic, hyperbolic, 

 and parabolic (or Euclidean) geometries ; and he could 

 hardly wish for a better introduction to the subject 

 than that which Mr. Frankland has provided. 



The tract falls naturally into three parts. The first, 

 with remarkable brevity and clearness, gives the prin- 

 cipal formulae derived from the assumptions that the 

 area of a polygon of n sides is proportional to the 

 difference between the sum of its interior angles and 

 (i!-2)ir, and that Euclidean geometry holds for in- 

 finitesimal figures. The second part gives, in separate 

 paragraphs, short accounts of forty contributors to 

 the theory, ranging from Euclid to Dodgson. This 

 list seems fairly complete, with one noteworthy excep- 

 tion — Sophus Lie. In the third volume of his "Theorie 

 der Transformationsgruppen " (section v.) Lie gives a 



