44 



♦ KNOWLEDGE ♦ 



[December 1, 1887. 



aspect to the tender mercies of competent Hebrew scholars, 

 let us turn for a few moments to his chapter on " The 

 Number Seven in Nature." Now, to begin with, he here 

 alles;es that there are seven constituent colours in white 

 light, which everyone possessing the merest smattering of 

 science knows to be false. So, again, with our arbitrary 

 arrangement of seven musical tones. But it is when our 

 author arrives at our absolutely artificial systems of classifi- 

 cation in the animal, vegetable, and mineral kingdoms that he 

 shines the most. That they are purely conventional and in- 

 vented to facilitate the study of the objects included in the 

 various categories never seems to have occurred to him ; and 

 the way in which he gets seven out of Cuvier's classification is 

 delightful. A page or two further on he is driven to sepa- 

 rate the aquatic mammalia (as a class) from the terrestrial 

 ones to eke out one of his " sevens," and, later still, to adopt 

 a kind of table from Mr. Ralph Tate to show that there 

 were seven geological epochs I He is very great, too, in 

 chemistry, and it will, we think, rather astonish Professors 

 Eoscoe and Schorlemnier to see how ingeniously details in 

 their classical book are twisted to fit Mr. Samuell's craze. 

 We almost wonder that, in this connection, he did not give 

 the seven bodies in alchemy. What we have said about 

 zoological classification may be repeated, mutatis mutandis, 

 with reference to our absolutely artificial arrangement of 

 clouds ; while, on cognate pi-inciples, he finds seven conti- 

 nents and seven oceans in the globe. The human body 

 bothers him rather more, and here he flounders considerably 

 in his efforts to show indications of some heptadic arrange- 

 ment. Even the exploded delusion of phrenology hiis to be 

 invoked to drag in thirty-five primitive faculties and seven 

 rules ! Then there are seven races of men, seven sciences 

 (Heaven save the mark !), and we sulisequently are treated 

 to some of the arithmetical properties of the number seven. 

 As our author obviously knows nothing whatever of the 

 theory of numbers, he may be surprised to learn that the 

 properties which so astonish him have their origin in our 

 decimal system of notation, and would pertain to another 

 number in, say, a duodecimal one. But we have already 

 devoted very much moi'e space than it deserves to a book 

 which would be merely ridiculous but for the pity we must 

 perforce feel for its author. Wrapped up^ in an overwhelm- 

 ing sense of his own almost superhuman wisdom and acumen, 

 he is calmly thankful that to him has been revealed, in these 

 latter days, that hidden meaning of the Bible, and, incident- 

 ally, of creation generally, which has hitherto been concealed 

 from the best and wisest of mankind. To any one who 

 cares to peruse a perfect example of what we have previously 

 spoken of as the most absolutely perverse literary ingenuity 

 we commend the study of " Seven the Sacred Number." 

 But he ought to be a good-tempered man, of large and 

 charitable views, or he may finish by speaking very dis- 

 respectfully indeed even of the author's common sense. 



A Treatise on Geometrical Optics. By R. S. Heath, 

 M.A. D.Sc. (Cambridge University Press. 1887.) — Dr. 

 Heath's volume may be described, with but scant exaggera- 

 tion indeed, as the very model of what a work on 

 geometrical optics should be. He has availed himself cf 

 the researches of Abbe, Gauss, Helmholtz, Listing, and 

 Maxwell, to say nothing of those of Cayley, Lloyd, 

 Rayleigh, and Tait, with the result that he has succeeded 

 in producing a text-book of great excellence. In the case 

 of Gauss's theory of lenses. Dr. Heath works it out by 

 elementary geometrical methods in accordance with the 

 general plan of his work ; but subsequently supplements 

 this by Gauss's own beautiful analysis ; which we a little 

 fear will have to be skipped by many who will otherwise 

 make good use of the book. The examples appended to 

 each chapter seem remarkably well chosen. The chapters 



on recent improvements in the microscope, and on meteoro- 

 logical optics, contain much that is at once novel and 

 interesting. 



Philip's Flanisphere, showing the principal Fixed Stars 

 visible for every Hoiir in the Year from Lat. 35° South. 

 (London ; G. Philip & Son.) — This planisphere is identical 

 in form with that of the Northern Sky, issued by the same 

 publishers, of which we were enabled to speak so favourably 

 on page 21 of our tenth volume, and will be found corre- 

 sponding!)' useful by dwellers in South Australia, New 

 Zealand, South Afiica, and part of South America. 



Elementary C'heuiistri/. By M. M. Pattison ^Iuir, M.A., 

 and Charles Slater, M.A., M.B. Practical Chemistry. 

 By M. M. Pattison Muir, M.A., and Douglas Carnegie, 

 B.A. (London : C. J. Clay & Sons ; Cambridge : Deighton, 

 Bell, & Co.) — Conscientiously written and brought carefully 

 up to the present stage of our knowledge, the two volumes 

 whose titles head this notice form an admirable and 

 thoroughly trustworthy introduction to the study of 

 chemistry ; and the beginner who will lead them attentively 

 through and perform the experiments described in the second 

 of them with his own hands will have acquired a sound 

 knowledge of the fundamental principles of the science, and 

 laid a solid foundation for future study. The experiments 

 seem particularly well chosen. We have, of course, made 

 no attempt to check the figures which abound in the book, 

 but, opening " Practical Chemistry " almost at random at 

 page 20G, we find the logarithm of 0'3937 given as 

 9 5951742; the real log. of 03937 being 9 (or, strict!)', 

 1) -5951654. 



Moffatt's Deductions from Euclid. (London : Moffatt & 

 Paige.) — These are series of riders, corollaries, itc, to the 

 familiar propositions of the first sis books of Euclid, some 

 of them original and others derived from various sources. 

 Their great use lies in the means they afford the student of 

 finding out how far he has understood the various pro- 

 blems and theorems which they illustrate;, and for this pur- 

 pose they seem remarkably well adapted. 



An Elementary Treatise on Light and Heat. By Rev. 

 F. WiLKiNS Aveling, M.A., B.Sc. (Loudon : Relfe 

 Brothers.) — Elementary Chemistry. By J. C. Buckmaster. 

 Revised and Corrected by C. A. Bickmastek, M.A., F.C.S. 

 (London : Moffatt & Paige.) — A Pupil Teacher's Handbook 

 of Alijebra. By Rev. A. D. Capel, M.A. (London : Joseph 

 Hughes. 1887.) — Innumeral)le additions have been made 

 to our textbooks of science since the craze for examination 

 set in, and " the cry is still. They come." Many of the 

 more recent ones have been leally too good for merely 

 cramming purposes, and Mr. Aveling's work is among them. 

 Both Mr. Buckmaster 's and Mr. Capel's books too at least 

 fulfil the purpose for which they were written. 



A Treatise on the Ititegral Calculus. Part I. By Ralph 

 A. Roberts, M.A. (Dublin : Hodges, Figgis, & Co. Lon- 

 don : Longmans, Green, tt Co. 1887.) — We have a solitary 

 fixnlt to find with Mr. Roberts's valuable addition to our 

 mathematical text-books. It is this : that his own ac- 

 quaintance with his subject is so intimate and profound 

 that he occasionally loses sight of the fact that the student 

 must, ex necessitate, approach its con.sideration from a dif- 

 ferent standpoint, or lower level altogether, than he does. 

 But having said this, we have little but praise for his book. 

 His explanation of elliptic integrals is remarkably good, 

 and throughout the work the numerous and well-chosen 

 examples leave nothing to be desired. 



The Peal History of the Posicrucians. By Arthur 

 Edward Waite. (London : George Red way. 1887.) — 

 We would recommend Mr. Waite's very painstaking 

 volume to all who may be desirous to get to the back of the 



