338 



NA TURE 



[January 21, 1909 



which the various systems of coordinates are con- 

 sidered is in some respects rather curious, e.g. tangen- 

 tial equations are not dealt with until the last chapter 

 but one, after discussions on cross-ratios and involu- 

 tion and a chapter on invariants, the succeeding 

 chapter being on covariants. After Miss Scott's brave 

 and able attempt to introduce tangential coordinates 

 to beginners, this seems rather a retrograde step. 



Then areal coordinates are introduced before tri- 

 linears, because in the majority of cases the resulting 

 equations are so much simpler than the corresponding 

 trilinear equations. In spite of one's sympathy with 

 the reasons, and one's pleasure in the author's treat- 

 ment of areals, it seems a pity to depart from the his- 

 torical order, .which introduced the student first to 

 abridged notation, which slid so naturally into tri- 

 linears, thus preparing the student for appreciating the 

 greater simplicity of areals. 



Indeed, in the present book the abridged notation 

 that was so charmingly put in Salmon's treatise is 

 to be found only in scattered places, with no great 

 emphasis placed on it, at any rate until the fifteenth 

 chapter. It is there, but it would need expert guidance 

 for a student to appreciate it at its full value. In 

 this respect, and in the treatment of reciprocation, 

 Salmon's book should still be read. In fact, it is 

 difficult to imagine a time when this incomparable 

 treatise will cease to be a source of inspiration and a 

 delight. 



The great interest of the present book lies in its 

 masterly treatment of innumerable problems, and the 

 use that is made of determinants at every turn. The 

 methods of the differential calculus are introduced as 

 altarnative to other methods, but are not made an es- 

 sential part of the development of the subject, as one 

 would rather have expected nowadays, when all 

 scholarship students learn the elementary methods of 

 the differential and integral calculus. Probably this 

 subordination or avoidance of calculus methods is due 

 to the requirements of the Cambridge course. 



For scholarship work in schools, the better students 

 could very profitably read a good deal of the earlier 

 part, after they have mastered some easier book. In 

 this respect it is somewhat like Dr. Hobson's invalu- 

 able treatise on trigonometry, only selected portions 

 of which are within the range of reading of the 

 majority of scholarship students. 



OUR BOOK SHELF. 



Fonncln uiid Hilfstafeln jilr geographische Ortshes- 

 iimmungen. By Prof. Th. Albrecht. Vierte 

 Auflage. Pp. viii + 348. (Leipzig : Wilhelm Engel- 

 mann, 1908.) Price 20 marks. 

 The object of this work, which has run through 

 four editions, is to supply within a convenient 

 compass the formute that are used most frequently 

 in the determination of time, and of terrestrial coordin- 

 ates, together with tables by which the application 

 of these formulae can facilitate the ordinary work 

 of an observatory. But the author has contrived that 

 the book should be more than the mere collection of 

 formute and tables. In an illuminating introduction 

 he considers the sources of error which are likely to 

 affect each class of observation, and uses his familiarity 



NO. 2047, VOL. 79] 



with different processes to sho\V how many of these 

 errors can be eliminated or rendered harmless by due 

 precaution in the manipulation of instruments or by 

 judicious selection of methods of observation. In this 

 way the treatise becomes a practical guide in those 

 matters of which it treats. These include the formulae 

 involved in the reduction of observations made for the 

 determination of time, latitude, longitude, and azi- 

 muth. The instruments may be used on the meridian, 

 on the prime vertical, or in the vertical of the Polar 

 Star ; they may be altazimuths or zenith telescopes ; 

 each finds its suitable application here ; similarly, the 

 particular methods which have been suggested to meet 

 practical difficulties are discussed with the thorough- 

 ness of the expert. 



The chapter on clocks contains much useful informa- 

 tion to which Prof. Wanach, of Potsdam, has contri- 

 buted. The tables of refraction have received special 

 attention, incorporating the Pulkowa results. The 

 numerical values, which very properly are not con- 

 tinued below 80° of zenith distance, may not differ 

 greatly from those of Bessel, but they are founded 

 on more modern theories, and with improved values 

 of the refraction constant. .As might have been ex- 

 pected from the author's long connection with geodetic 

 work, references connected with the problems of the 

 determination of longitude and the figure of the earth 

 are particularlv full. Indeed, in the latter section some 

 of the tables can hardly be brought under the heading 

 of " Ortsbestinmnungen " as usually understood, but 

 the tendencv of all such compilations is to increase by 

 the addition of tables and formulae which have only 

 a very limited application. Such tables have the ad- 

 vantage of being at hand if wanted. 



It seems less defensible to cumber the book by other 

 tables with which observatories are equipped quite as 

 convenientlv and with greater completeness in other 

 forms. Those tables which give the squares of 

 numbers up to 1000, or of the logs, of numbers up 

 to i960, or of trigonometrical functions of angles 

 with no great accuracy, seem to us to be hardly war- 

 ranted in a work of this character. But we hasten to 

 say that this superfluity is not gained at the expense of 

 material more immediately connected with astronomical 

 work, and so far as we have been able to test the care 

 and accuracy exhibited in the compilation, it is possible 

 to speak in the highest terms. 



Human Speech, a Study in the Purposive Action 0/ 

 Living Matter. By N. C. Macnamara. Pp. xiii + 

 284. "(London : Kegan Paul, Trench, Triibner and 

 Co., Ltd., 1908.) Price 5^. 

 Major Macnamara's object in writing this book is to 

 trace the gradual evolution of the living matter found 

 in the cerebral centres on which intelligent speech de- 

 pends. This is truly a herculean task, and one from 

 which most physiologists and psychologists would 

 shrink; and yet the author has succeeded in producing 

 a readable book, full of information, and in many 

 places both interesting and suggestive. There is not 

 much said about human speech, either as regards its 

 nervous or muscular mechanisms, but the author ap- 

 proaches the subject from the standpoint of general 

 biology. He traces the influence of stimuli on living 

 matter, the effects of the accumulation of stimuli, the 

 gradual evolution of the senses, the corresponding de- 

 velopment in greater complexity of the nerve centres, 

 more especially of those connected with the higher 

 centres of vision and hearing, and the changes that 

 coincide with the appearance of such psychic activity 

 as we associate with the brains of man and the higher 

 animals. Waves of sound, falling on the ear, " reach 

 the living matter forming his centre of hearing in such 

 a form that they become impressed on this matter." 

 The sensori-motor auditory centres become related 



