March 13, 1902] 



NA TURE 



of s(;ale. In the pass itself the mound and the Phocian wall 

 are the only debatable points, and they might have been 

 relegated (if necessary) to a little inset plan. (It is 

 ridiculous, by the way, to treat the pretty story of the 

 Spartans combing their hair as serious evidence for 

 topography or " autopsy " — the other Greeks had to be 

 invisible and the wall was a good excuse for hiding them, 

 that is all !) But the real problems are concerned with the 

 valley of theAsopus,the road into Doris, the site of Trachis 

 and the path Anop^'ea, about the identification of which 

 we have sometimes felt doubts. There must be a railway 

 survey of the valley somewhere, which would give a base 

 to work from, but Mr. Grundy is here less helpful than 

 M. Hauvette, and does not even elucidate his own text — 

 where, for example, is the Great Gable (p. 302) ? Why is not 

 Trachis the same as Heraclea, or its acropolis ? What is 

 the point of the polemic against Leake, who seems to 

 have accomplished the not unprecedented feat of riding 

 at six miles an hour? There is a useful note on p. 262 to 

 show that "it seems to have been a recognised principle 

 in later times that an effective defence of Oeta included 

 the occupation of Heraklea as well as of Thermopylae." 

 But why not in earlier times too.' Surely, if topography is 

 worth anything as a test of the narrative of Herodotus, 

 it points here to a serious omission. 



Mr. Grundy has perhaps scarcely sufificiently guarded 

 himself against the natural tendency to fix sites and 

 positions on the authority of Herodotus and then trium- 

 phantly claim that the evidence of the topography con- 

 firms the story. We believe that he is right in his theory 

 as to the " Island " at Platsa, but where the identifica- 

 tion of so many points is so uncertain we cannot avoid an 

 uncomfortable notion that a turn of the spade may any day 

 undermine his whole construction of the campaign, not to 

 say the narrative of Herodotus itself. 



On the other battles of the war Mr. Grundy has little 

 that is new to contribute and scarcely anything of a 

 geographical character. His theory of the campaign 

 of Marathon is essentially Busolt's early view, recently 

 revived by Mr. Munro, of the battle of Salamis 

 a development of Prof. Goodwin's. He scarcely seems 

 to appreciate the full significance of the position at 

 Artemisium, which covers all the landing-places between 

 Tempe and Attica. Apheta: is a dubious point. It is 

 hard to reconcile Mr. Grundy's situation with the remark 

 of Herodotus, that the wreckage of the first sea-fight 

 drifted out to .\phetfe, which is badly misrendered in the 

 words " was thrust in upon the Persian fleet." Mr. 

 Grundy is much put about to find a reason for the Greeks 

 taking the offensive in 479. He concludes that they 

 feared the establishment of a Persian frontier at Cith;eron 

 Obviously the Persians would keep all they could conquer, 

 but why should they stop at Cithitron ? and is not the 

 real difficulty the Gieek delay in taking the offensive 

 after the victory of Salamis had entirely changed the 

 situation .' 



Where Mr. Grundy has seen with his own eyes he 

 generally has something useful to say, but where he has 

 not seen he cannot always be trusted. It is an absurd 

 exaggeration to call the Taurus an " all but blank im- 

 passable wall " ; and other references to it would certainly 

 suggest that it runs north and south ! The theory of the 

 weak strategic situation of the Asiatic Greeks will not 

 NO. 1689, VOL. 65] 



hold where any communication by sea is so much better 

 than any by land as in western Asia Minor. Was it 

 either land or sea that divided, e.g.^ Samos and Miletus ? 

 For downright geographical nonsense it would be hard to 

 beat the description of Pteria as "a town whose position 

 renders it the chief strategic point in the Halys region, 

 commanding, as it does, the middle portion of the cleft- 

 like valley through which the river flows" (p. 15). Mr. 

 Grundy does not appear conscious of all the difficulties 

 which beset Xerxes' march through Thrace as conceived 

 by Herodotus. They do not harmonise well with his 

 doctrine that the historian had himself traversed the 

 road. 



In the early chapters, the author makes great play with 

 the idea of the " Ethnic frontier." As applied to the Persian 

 attacks on Greece this is no novelty; but will it explain the 

 conquest of Thrace ? Are Phrygians and Bithynians 

 still to be called Thracians in the days of Darius .'' 



The book is sumptuously got up. It is a pity that so 

 many misprints have been overlooked. Some of these 

 are very unfortunate, e.g. banaustic (p. 94), St. Demetrion 

 (three times), Elataea (four times), Oeroe with initial 

 diphthong (always). Xerxes on p. 69 ought to be 

 Darius. On the map of Marathon, Kynossema ought 

 to be Kynosoura. On p. 350, Mr. Grundy has inter- 

 changed east and ivest — did he "alter his point of 

 view"? On p. 378, a whole paragraph is based on a 

 childish mistranslation of Herodotus. 



In conclusion, we must heartilyjthank Mr. Grundy for 

 publishing the many exquisite sketches by Edward Lear. 

 They are as accurate as they are beautiful, and even had 

 this book no solid merits of its own to recomm end it, they 

 would suffice to make it valuable. 



GEOMETRY ON THE SPHERE. 

 Spherical Trigonometry. By the late I. Todhunter, M.A., 

 F.R.S. Revised by J. G. Leathem, M.A., D.Sc. 

 Pp. xii -t- 275. (London : Macmillan and Co., Ltd., 

 1901.) Price ys. bd. 



THIS volume gives a systematic treatment of the 

 subject of spherical trigonometry, based on the 

 sound foundation of Todhunter rearranged and amplified. 

 While the merit of the original work] is sufficiently indi- 

 cated by its vitality, the preface bearing the date 1859, it 

 is natural that a text-book designed for the use of students 

 forty years ago should to some extent fail to satisfy the 

 requirements of the present day. 



The subject falls naturally under two heads, (i) 

 Formuke connected with the Spherical Triangle and the 

 Solution of Triangles, (2) Spherical Geometry. In both 

 departments the reviser has used skill and judgment in 

 grafting fresh shoots on the old stock, and has produced 

 a homogeneous and well-balanced volume, double the 

 size of the original and worthy to take its place among 

 the best of our modern text-books. In trigonometry 

 proper, Todhunter's treatment has been rendered very full 

 and thorough. The theory is illustrated by well-selected 

 numerical exercises, fully worked out and presented in 

 the most concise form with due attention to labour-saving 

 devices. Critical and ambiguous cases are carefully con- 

 sidered, discussed and illustrated diagrammatically, while 



