July 31, 1884] 



NA TURE 



;i 1 



principal points, we can find geometrically the position of 

 the image of any point after refraction through the surface. 

 This we may describe as the geometrical treatment of the 

 subject. 



By the aid of analysis we can show that there is, to the 

 degree of approximation to which we go, a point image of 

 any point, and we can find in terms of known quantities 

 the positions of the cardinal points of the system and the 

 relation between a point and its conjugate focus. Mr. 

 Pendlebury adopts both methods indiscriminately ; it 

 seems to us that it would have been better to have kept 

 the two somewhat more distinct. 



A short account of the paper of Maxwell to which 

 reference has been made, " On the General Laws of Optical 

 Instruments," would form a valuable addition to the book, 

 and may, perhaps, be included when the author extends 

 it, as he hopes to do, so as to cover a wider area in the 

 field of geometrical optics. At present the field is open 

 to him, and a book on the whole subject as good and 

 interesting as " Lenses and Systems of Lenses " is greatly 

 needed. r. t. G. 



OUR BOOK SHELF 



Fuel and Water. Translated from the German of Franz 

 Schwackhofer, by Walter R. Browne, M.A. (London : 

 Charles Griffin and Co., 1884.) 

 Mr. Walter R. Browne has made a very good trans- 

 lation of a book written for the German students of agri- 

 culture in Vienna. He has added a clever sketch of the 

 mechanical theory of heat as an introduction. The 

 English of the translation is remarkably good and clear, 

 and the original treatise has been written by a competent 

 man. The translator in his preface appeals to manu- 

 facturers and users of steam on a large scale ; but the 

 work is much too scientific for them, dealing not with the 

 various forms of boiler now in the market, but rather with 

 the general principles on which boilers should be con- 

 structed. On the other hand I fear that the information 

 given is in many parts not full enough for the engineer, 

 and we frequently find data given such as will be of more 

 value to the German than to the English reader. The 

 chief physical formulae relating to heat and applicable to 

 practical questions connected with engineering are clearly 

 stated, but the comparison of results deduced from these 

 formulae with the results derived from actual experience 

 is rather sparingly made. The third chapter, which is 

 headed " Heating Apparatus," treats of the furnace and its 

 management. The author gives the results of some 

 actual experiments as to the loss of heat in the chimney, 

 in the ash-pits, in priming water, and by conduction and 

 radiation. He also gives an experiment with what is called 

 an economiser. This chapter seems to me one of the best in 

 the book. Altogether, I think the work is one which may 

 in many parts be profitably consulted by those engineers 

 who desire to compare theory with practice. 



Fleeming Jenkin 

 The Elements of Euclid. Books I. to VI. With Deduc- 

 tions, Appendices, and Historical Notes. By J S 

 Mackay, M.A. (London : W. and R. Chambers, 1884.) 

 This text-book has been compiled at the request of the 

 publishers, and the event shows that it was by a "happy 

 thought" their choice of an editor fell upon Mr. Mackay, 

 the Mathematical Master of the Edinburgh Academy! 

 Of it we have nothing to say but what is good. This 

 praise is not so much for the text, for others have done 

 well in this direction. Still even here Mr. Mackay has 

 shown great judgment and skill in his selection of proofs. 

 The text is in the main that of R. Simson's well-known 



editions, and no change has been made in Euclid's 

 sequence of propositions, and no violent change in his 

 modes of proof. 



But what we particularly like are the carefully prepared 

 historical notes, which take the form of footnotes or of 

 fuller paragraphs in the six appendices. Mr. Mackay 

 remarks, " It would perhaps be well if such notes were 

 more frequently to be found in mathematical text-books : 

 the names of those who have extended the boundaries, or 

 successfully cultivated any part of the domain, of science, 

 should not be unknown to those who inherit the results of 

 their labour." 



We regret that though authors have before expressed 

 themselves to similar effect, yet few have had the inclina- 

 tion or leisure to act as our present author. He has had 

 to curtail his material, but what he gives us shows that he 

 is well qualified by the extent of his reading to satisfv this 

 want. 



We note here that recent French mathematicians are 

 in the habit of attributing the first use of the word 

 " orthocentre " (which Mr. Mackay ascribes to Dr. W. H. 

 Besant) to Dr. Booth ; in so doing they are certainly in 

 error, as Dr. Booth himself, in the second volume of his 

 "New Geometrical Methods" (p. 261), says "the point 

 has been called by some geometers the orthocentre." 

 What he may lay claim to is his calling what is now 

 often called the pedal triangle the orthocentric triangle. 



The figures are admirably drawn and are quite a feature 

 of the book ; they deserve the editor's commendation 

 when he thanks Mr. Pairman for the " excellence of the 

 diagrams." 



This edition is well suited for the geometrical student, 

 and, at the same time, its cheapness puts it within the 

 reach of all who wish to study " Euclid." 



Traite Pratique d' Analyses chiiniques et d'Essais in- 

 dustries. Par Raoul Jagnaux. (Paris : Octave Doin, 

 1884.) 

 The purpose and character of this little book is best 

 indicated by the saying of Berzelius which heads the 

 author's preface : " Le meilleur mode d'analyse est celui 

 qui exige le moins d'habitude chez l'ope"rateur." The book 

 is mainly intended for the use of the chemical engineer 

 and the metallurgist, and the methods of analysis de- 

 scribed are essentially " works-methods," in which rapidity 

 of execution is a very important consideration. Many of 

 these methods are new, and have been devised partly by 

 M. Hautefeuille, and partly by the author. We would espe- 

 cially note those depending upon the precipitation of such 

 metals as zinc, copper, nickel, and bismuth as oxalates, 

 whereby the formation of gelatinous precipitates, difficult 

 to wash, is avoided. The book contains a large number 

 of analytical results as evidence of the validity of the 

 methods employed ; many of these analyses, such as those 

 of aventurine glass, garnierite, sylverine, are valuable 

 as illustrating the composition of substances which are 

 not frequently examined. T. 



LETTERS TO THE EDITOR 



[The Editor Joes not hold himself responsible for opinions expressed 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications . 



[The Editor urgently requests correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 of communications containing interesting and novel facts. ~\ 



The Relation between the B.A. Unit and the Legal 



Ohm of the Paris Congress 



At a meeting of the Electrical Standards Committee of the 



British Association held on Saturday, June 28, the following 



resolution was carried : — 



"That for the purpose of issuing practical standards of elec- 



