3 S8 



NA TURE 



[February 26, 1903 



number of finite segments at infinity; to enumerate 

 them we require transcendent integers, but there is 

 nothing illogical in the conception, provided that we 

 use it consistently. But we must not criticise one con- 

 ception by the results of another with which it is 

 radically incompatible. 



To show how weak the author's logic is, it is suffi- 

 cient to refer to his discussion of the old fallacy of 

 Achilles and the tortoise. Here it is established that 

 an indefinite number of successive intervals of time can 

 be found, for each of which the tortoise is ahead ; and 

 it is falsely concluded that the sum of these intervals 

 of time tends to an indefinitely long period. Instead 

 of pointing out this simple fact, Dr. Geissler argues 

 that the division of the initial interval between Achilles 

 and the tortoise is illegitimate! ("Man darf sich 

 nicht einbilden, es liege schon im Wesen einer Strecke 

 AB auf ihr in irgend einer Weise Strecken zu tragen.") 

 In fact, his hankering for infinitesimals, in the sense 

 of indivisibles, makes all his treatment of limits and 

 convergence quite unsatisfactory. 



It is a matter for real regret that Dr. Geissler has so 

 completely failed to contribute anything of value to the 

 discussion of his subject. The development of mathe- 

 matics since the time of Kant has surely provided some 

 new material for speculation ; how long must we wait 

 for a philosopher competent to deal with it? Even De 

 Morgan failed to appreciate Rowan Hamilton's con- 

 ception of algebra as the science of pure time ; the 

 truth of this idea (except, perhaps, for group-theory) 

 is becoming daily more evident. But while analysis 

 is thus practically reduced to a subjective construction, 

 there are elements in geometry which refuse to be so 

 assimilated. Not all mathematicians are geometers, 

 but those who are will sturdily maintain that, in some 

 sense or other, there are geometrical data which are 

 not expressible in terms of arithmetic. The present 

 tendency towards critical analysis may, we hope, be 

 succeeded by renewed interest in pure geometry. Then, 

 perhaps, something more may be done towards dis- 

 tinguishing its primary axioms. 



The analytical doctrine of the infinite has been 

 sketched in a very interesting manner by Dr. Hobson 

 in his recent presidential address to the London Mathe- 

 matical Society ; this deserves to be widely read, be- 

 cause it presents the main discoveries of Dedekind, 

 Cantor, &c. , in a form which does not assume any 

 advanced mathematical knowledge on the part of the 

 reader. G. B. M. 



PRACTICAL PHYSIOLOGY. 



Practical Physiology. By A. P. Beddard, J. S. 

 Edkins, Leonard Hill, J. J. R. Macleod and M. S. 

 Pembrey. Pp. xiv + 495 (London : Edward Arnold, 

 1902.) Price 155-. net. 

 " I 'HE aim of the authors of this text-book has been to 

 -*- provide medical students with a course of physi- 

 ology which shall not only give them sufficient mental 

 training — practical Chinese or Greek would do this — but 

 also ensure that this training shall be of substantial use 

 NO. 1739, VOL. 67] 



in their after medical career. In some respects, this aim 

 has been carried out in an admirable manner. Many of 

 the articles are clearly written and well illustrated, and 

 some of the sections — notably those on circulation, blood 

 gases and physiological optics — contain valuable inform- 

 ation not readily accessible to the student in any of the 

 existing text-books. Other parts hardly maintain this 

 high level, and the chapters on muscle and nerve in par- 

 ticular are noticeably deficient, even allowing for the 

 author's expressions of dissent in the preface, and it is 

 curious to see a text-book of 495 pages in which only 

 two are devoted to the description of the galvanometer 

 and capillary electrometer together, and where three 

 lines contain the major part of the information on the 

 electromotive phenomena of the heart ! 



The book is divided into four parts ; the first two of 

 these, comprising the more elementary exercises, are, 

 on the whole, very good. The labour involved in 

 preparing new illustrations and tracings must have 

 been considerable, and the authors are justly to be 

 congratulated on the result of their exertions. In 

 addition to the experimental exercises already noticed, 

 the section on physiological chemistry merits favourable 

 comment, and as a pleasing matter of detail, the draw- 

 ings of crystals are particularly accurate. 



There are certain places, however, which might be 

 subjected to a little revision in the next edition. While 

 the authors reject Von Fleischl's ha?moglobinometer on 

 the ground of inaccuracy, the directions given for the 

 use of the Thoma-Zeiss htemocytometer will in practice 

 lead all but the very careful student to far more serious 

 errors of estimation. With a little skill, the method for 

 the detection of albuminuria by heat could be carried out 

 so as to show no trace of albumin even when it was 

 present in considerable amount, as acid albuminate would 

 readily be formed under the conditions recommended. 

 " Ethylic acid," on p. 180, is a pretty obvious misprint for 

 "ethyl alcohol.'' We think that the information on 

 p. 72 is a little out of place, but perhaps this is a matter 

 of opinion. 



The "advanced" portion of the text-book is hardly so 

 well written as the "elementary," though the articles on 

 optics and on Haldane's methods for determining oxygen 

 capacity and mass of the blood could hardly be sur- 

 passed. Here, moreover, is to be found the largest part 

 of the " comedy of errors " which is inseparable from a 

 first edition. Constantine was an Emperor who reigned 

 at Constantinople ; the alloy of manganese and iron used 

 for theimoelectric work was not called after him. The 

 directions for preparing sarcolactic acid, on pp. 442-3, 

 would be improved by the substitution of the word 

 "phosphoric" for "sulphuric," and the method, on 

 p. 426, for decomposing proteids contains more than one 

 serious error, and should be re-written throughout. 



But besides these smaller matters, there is an authori- 

 tative method adopted of disposing summarily of con- 

 troversial points by ex cathedra, utterances ; we think 

 that a text-book writer might, in a fairly complete work 

 such as this, at least mention the possibility of different 

 views being held by other physiologists, absurd though 

 this may seem to him. 



It is a pity that an index was not included in the book ; 



