NATURE 



[June 13. 1907 



gesting methods of presentment of new mathematical 

 ideas by means of concrete illustrations which will 

 bring them home more vividly and interestingly to 

 the pupil, the method of question and answer being 

 often used to make the pupil think for himself — 

 though, indeed, this is generally done now by good 

 teachers as occasion serves — and, secondly, by the 

 teacher taking the class from time to time through 

 a selected set of the examples when they have assimil- 

 ated the underlying book-work. 



There is one thing which the author has touched 

 on, though apparently only in an example (No. 7, 

 p. 293), which one would have liked to see brought 

 into much greater prominence, viz. the graphic solu- 

 tion of a quadratic equation x- — 'bx + ac = a by draw- 

 ing lines OA = a, BC = f, perpendicular to a line 

 OB = fc, and drawing a circle on AC as diameter, 

 cutting OB in P, Q : the roots being OP and OQ. 

 This method gives the clue to the geometrical solu- 

 tion of many problems some of which would other- 

 wise be difficult; for example, the construction of a 

 triangle of given area when two sides are given in 

 position, and a point in the plane through which 

 the third side is to pass; also the construction of a 

 right-angled triangle from the data given in the 

 book on p. 261 ; also the division of a line in extreme 

 and mean ratio; and, indeed, any problem the solu- 

 tion of which depends on a quadratic. It is a most 

 valuable link between algebra and geometry. 

 Another method which is applicable to the case of 

 .'V'- + b.r = a-, and is perhaps better than the first 

 for this particular case (though really only a 

 modification of the above general method), is given on 

 p. 264. The book is, in fact, bristling with ideas and 

 suggestions, and we wish it the great success it 

 undoubtedly deserves. A. L. 



EGY?TIA}^ ANTIQUITIES. 

 Egyptian Antiquities in the Pier Collection. Part i. 

 By G. C. Pier. Pp. 27 + xxi plates. (Chicago: 

 University of Chicago Press, 1906.) Price I'js. 



MR. GARRETT CHATFIELD PIER, of New- 

 York, is an amateur of Egyptian antiquities, 

 and has begun to publish a catalogue of his collec- 

 tion, of which the first part has reached us. The 

 book is produced by the Academical Press of the 

 University of Chicago, which, at the instigation of 

 its Egyptological specialist. Prof. Breasted, is 

 beginning to take an important part in Egyptian 

 archaeological work. 



We find various traces of Prof. Breasted in Mr. 

 Pier's book. The learned professor's " particular 

 wanities " in the way of transliteration of Egyptian 

 names, such as " Ikhnaton " for Akhenaten, or 

 " Harmhab " for Haremheb, either stamp Mr. Pier 

 as a faithful follower of Prof. Breasted or show that 

 the professor revised Mr. Pier's Egyptology. Mr. 

 Pier's use of the Berlinish algebraic transliteration 

 {e.g. "s;-r' Nb-m;'-t-r'-nb-t;wj " for what might 

 just as well be written sa-ra Neb-maat-Ra neb-tatii, 

 p. 5) points the same way. But Mr. Pier should be 

 careful, if he uses this highly learned transliteration, 

 NO. 1963, VOL. 76] 



to use it consistently, and not write sometimes " Nub- 

 khprw-r' " (p. 19), sometimes " ','-hprw-r' " (p. 22), 

 sometimes " Mn-hpr'," sometimes " Men-khepr-r' " 

 (p. 21), or " Ishrw " (p. 6) for " Jsrw," or 

 "Thy" (p. 13) for "Tjj," in such a sentence as 

 " Stn-hmt-wr-mrj-f-Thy (surely, surely, Tjj ! j 'nh-ty, " 

 which also exhibits confusion between the orthodox 

 Teutonic " j " and the slightly heretical English 

 "y." Thy is the queen whose tomb has just been 

 discovered at Thebes; if the German transliteration; 

 is used for her name at all, it must appear as " Tjj," 

 but in realitv there is no need whatever to use pcdan 

 licallv, in a guide to a collection of objects of purely 

 anthropological interest, a transliteration of ancient 

 Egyptian which is utilised only by a few German or 

 germanised philologists for pu^-ely philological pur- 

 poses. 



Mr. Pier's collection does not, so far as published, 

 appear to contain anything of extreme interest, com- 

 pared, that is, with such important private collec- 

 tions as those of Mr. Hilton Price or Mr. Macgregor. 

 He seems to be chiefly interested in objects of "the 

 prehistoric period and scarabs of the XVIIIth 

 Dynasty, of which he possesses some fine specimens. 

 Of later scarabs he does not appear to own many, 

 which may account for the inaccurate statement on 

 p. 15 : — " with the Twenty-sixth Dynasty richer 

 materials are used for scarab .seals and plaques, such 

 as carnelian, amethyst, serpentine, &c. , rarely, if 

 ever, inscribed." We italicise the erroneous state- 

 ment, which may well seem odd to those who know 

 how constantly the little stone scaraboid plaques of 

 the Saite period were inscribed with all manner of 

 sentences, wishing a good new year, invoking 

 Khonsu as a protection, and so forth. But probably 

 Mr. Pier has not yet devoted much attention to these 

 later objects. He is thinking of the fact that the 

 Xllth Dynasty amethyst and other stone scarabs 

 were but rarely inscribed : this is so. 



Mr. Pier draws his scarabs extremely well, much 

 better than his fiint implements, of which he pub- 

 lishes some scratchv pen-and-ink representations 

 [Plates v.-ix. : Plate ix. (of a slate) is especially bad]. 

 The mirror on Plate x. is also very badly drawn, 

 and the two dishes on Plate xi. are not much better. 

 Mr. Pier would be well advised to reproduce these 

 things by means of photography in future, and to 

 confine his artistic efforts to scarabs and hieroglyphs, 

 which he knows how to draw. 



His coloured plates of ceramics are very successful, 

 though not so successful as Mr. Henry Wallis's in 

 his "Egyptian Ceramic .\rt." Mr. Pier's blues, 

 yellows, and violets do not so perfectly reproduce their 

 originals, and Mr. Wallis's do. But it would be in- 

 deed difficult to rival Mr. Wallis's drawings or Mr. 

 Carter's in the publication of the " Tomb of Thout- 

 mosis IV." 



-So far as the literarv part of the book is concerned, 

 quite apart from the usual aberrations of American 

 spelling, Mr. Pier has one or two specialities of his 

 own. One is " faun-colored " (for " fawn-coloured "), 

 which occurs two or three times, and so cannot be 

 a misprint. Presumnblv Mr. Pier has forgotten what 



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