4 lo 



NA TV RE 



[March 3, 1898 



by an admirable extension of the method of exhaustion 

 are considered, and copiously illustrated ; and the intro- 

 duction concludes with a most useful account of the 

 mathematical terms and phraseology employed by 

 Archimedes. 



Dr. Heath's general treatment of the text is excellent, 

 biit there is one point on which we do not think that he 

 has exercised a sound judgment. This is the renumber- 

 ing of the propositions in three of the books, which renders 

 reference to them a matter of entire uncertainty. Thus 

 the celebrated Prop. 37 of Book I. on the Sphere and 

 Cylinder, which gives | as the ratio of the surfaces and of 

 the volumes of a sphere and the cylinder that just con- 

 tains it, appears in Dr. Heath's book as a corollary of 

 Prop. 36, which is numbered 34 ; he further puts Props. 33 

 43, 45, 46 as corollaries, and includes Prop, i in the 

 introductory letter, thus reducing to 44 the 50 proposi- 

 tions of the MSS. In Book II. he treats Prop, i simi- 

 larly, even though Archimedes himself, in the introductory 

 • letter to his work on Spirals (p. 152), mentions this pro- 

 position as the first of those which were proved in this 

 book. In the book on Conoids and Spheroids he further 

 puts as a Lemma what appears as Prop, i in all the 

 Greek and Latin texts, so that the famed Prop. 12 on 

 certain plane sections of these figures, the characters of 

 which are said by Archimedes to be (fyavepal, appears as 

 Prop. 1 1, and Prop. 18 is put as the third part of Prop. 17 

 (numbered 16) — without any reason, since it is not an 

 extension of, though deducible from, the other parts. 



Complete as the book is, there is one addition that 

 would be welcomed by all students, viz. a table of all the 

 writers named, and of the approximate dates at which 

 they flourished ; this, if of easy reference, would be of 

 great help when the relation of different geometers to 

 any problem was under consideration. A larger number 

 of references is also desirable in the interests of the 

 student who is stirred to go to the fountain-head by his 

 thirst for first-hand information. Thus the proofs on 

 pp. liv-lviii of the above-cited Prop. 12 on Conoids 

 and Spheroids are so introduced, especially in being 

 contrasted with Zeuthen's, as to appear to be quite 

 modern, while really being contained in Torelli's edition, 

 and practically also in the earlier editions of M.aurolycus 

 and Rivaltus. 



We feel much inclined to challenge Dr. Heath's 

 rendering of Euclid's definition of a straight line in his 

 note on p. 3, and to maintain the correctness of the 

 ordinary version of it. The special point seems to us to 

 lie in the word eVt, " on," the use of which seems to be 

 due to the thought in the writer's mind of points marked 

 by letters over the line ; thus Aristotle (" Ethics," v. 4, 12) 

 writes tcrai al [i.e. -ypa/x/iat] e0' hv AA, BB, IT dXXj/Xats 

 where the sentence can only mean " the lines AA, BB, CC 

 are equal to one another"; the words must therefore 

 mean "the lines are equal over the two ends of which 

 A and A, B and B, C and C are written," so that Euclid's 

 TO. e(j)' eavrrjs a-rffxela must mean " its Own extreme 

 points." 



Such slight blemishes, however, or what we deem to 

 be such, do not detract from the very great value of this 

 work, and Dr. Heath deserves our grateful thanks for the 

 labour he has expended upon it. It is a fitting addition 



NO. 1479. VOL. 57] 



to his former task y for as, to quote Charles, in Apollonius 

 work we find the origin of the geometry of Forms and 

 Situations as it is now developed, so in the present 

 book we are introduced to the basis of the geometry of 

 Measurement which has demanded a new calculus for 

 its perfection. R. E. B. 



A NEW TEXT-BOOK OF EXPERIMENTAL 



PHYSIOLOG V. 

 The Essentials of Experimental Physiology. For the 



use of Students. By T. G. Brodie, M.D., Lecturer 



on Physiology, St. Thomas's Hospital Medical School. 



Pp. xiv -f- 231. (London : Longmans, Green, and Co., 



1898.) 



THIS volume appears in the same series as two books 

 already well known to the medical student of this 

 country, viz. Schafer's "Essentials of Histology" and 

 Halliburton's " Essentials of Chemical Physiology." It 

 is bound uniformly with these two volumes, but on 

 opening the books all resemblance disappears. Instead 

 of being divided into a number of "lessons," each of 

 suitable length for one day's work of a practical class, 

 the new volume is divided into " chapters " the length of 

 which bears no proportion to the practical work of a 

 class-meeting. In the other two volumes of the series, 

 each lesson is commenced by a concise and definite 

 description for the student of how to perform a number 

 of experiments ; and this description is followed by a 

 few pages of theoretical teaching bearing on those 

 experiments. In the present volume this arrangement 

 is departed from, and the experiments are interpolated in 

 a discursive fashion through the text. 



An attempt is made to mark off by heavy type a 

 portion of the book as an elementary course, but it is 

 questionable whether this would not have been much 

 better done by dividing the volume into an elementary 

 and advanced course, as has been done by Prof 

 Halliburton in the "Essentials of Chemical Physiology." 

 Again, some of the experiments described in this ele- 

 mentary portion are quite beyond the reach of the junior 

 student — for example, the maximum work performed 

 during a muscular twitch ; while other simple and 

 important experiments, such as the effect of temperature 

 on muscular contraction, are excluded from this part. 



The book commences with a description of various 

 forms of galvanic cells and the chemical changes in- 

 volved in their action. Such a description is scarcely 

 necessary, for the student is supposed to be already 

 familiar with the commoner forms of galvanic cell before 

 commencing practical work in physiology ; but, if in- 

 serted, it would have been much better to have described 

 the action of the cells correctly. For example, the 

 student who has just attended a junior course of in- 

 struction in a physical laboratory will be somewhat 

 disturbed in his notions of electrolysis by being told 

 that when the Daniell's element is in action — 



"the chemical changes in the battery are, solution of 

 zinc and formation of ZnS04 at the zinc plate, and 

 decomposition of the CUSO4, by the hydrogen appearing 

 .at the copper plate to form H2SO4 and metallic Cu, 

 which latter is deiposited on the copper surface." 



