Dec. 9, I 



NATURE 



119 



7 HE ENCYCLOPAEDIA BRITANNICA 



The Encyclopadia Britannica. Ninth Edition. Vols. x. 



and xi. (Edinburgh: A. and C. Black.) 



THESE two volumes of the Encyclopadia Britannica 

 fully sustain the high character of the earlier 

 volumes. The articles dealing with branches of physical 

 and natural science are conspicuous by their high quality 

 and number. In geographical science this volume is 

 particularly strong. Dr. Rae contributes an article on 

 "Greece," several specialists contribute the article on 

 " Germany," and General Strachey of the Indian Civil 

 Sen'ice has produced a very striking and valuable essay 

 on the "Himalayas." Besides these there are shorter 

 articles on "Greenland," " Grisons," "Guiana," the 

 "Hawaiian Islands," and "Heligoland," all worthy of 

 attention and replete with information. In medical 

 science we note particularly the articles on " Gout," con- 

 tributed by Dr. Affleck, and on " Heart Diseases" by Dr. 

 G. W. Balfour. In the department of natural history the 

 articles are almost exclusively on subjects of a specific or 

 technical character ; Prof Newton writes on " Grouse," 

 and Mr. John Gibson on the " Hare " and the " Hippo- 

 potamus." Prof. Church contributes brief articles on 

 " Hemp " and " Guano," and Dr. Trimen has a good 

 descriptive paper on "Grasses." The article "Her- 

 barium," contributed by Mr. E. M. Holmes, is a remark- 

 ably useful and practical handling of a subject on which 

 most botanical writers have usually very little to say ; 

 and the summary of information as to the character of 

 the principal herbaria in existence will be found acceptable 

 for reference. The contributions to the physical sciences 

 arc numerous and of great interest. Dr. Ball's article on 

 " Gravitation " is at once simple and masterly. The article 

 on " Harmonic Analysis " by the late Prof. Clerk Maxwell is 

 all too short, but admirable in its way. Amongst technical 

 subjects we may single out the articles on " Gunpowder" 

 and " Gun-cotton " by Major Wardell and Prof. Abel 

 respectively, on " Heating " by Capt. D. Galton, two long 

 and very fully illustrated papers by Col. Maitland on 

 " Gunmaking " and " Gunnery," and one on " Harbours " 

 by Mr. T. Stevenson, which is accompanied by several 

 capital plates. Mr. J. BIyth contributes two valuable 

 articles on the "Gyroscope" and on "Graduation." 

 From the latter we miss one or two points that might well 

 have been added. There is no account of the dividing- 

 machine employed by Messrs. Cooke and Sons of York 

 in graduating the circles of the great Newall telescope ; 

 nor of the still more recent dividing engine constructed 

 by the Waltham Watch Company. The biographical 

 articles are numerous and excellent. Those on the two 

 " Herschels" are from the pen of Prof. Pritchard. That 

 on "Sir W. Hamilton "is contributed by MissE. Hamilton. 

 The biographical notice of " Sir W. Rowan Hamilton " 

 is by Prof. Tait, than whom no one is more competent 

 to write of the great mathematician ; though somehow 

 we miss in this thoughtful and appreciative article the 

 peculiar characteristics of Prof. Tait's trenchant style. 

 We propose to notice at greater length the important 

 articles on " Geometry," " Geology," and " Heat." 



The editor did well, we think, when he intrusted the 

 compilation of the article upon such an important sub- 

 ject as " Pure Geometry" to so accomplished a geometer 



as Prof. Hcnrici. We can fancy what such an article 

 would have been in the hands of the generality of English 

 mathematicians trained at our conservative Universities, 

 meek followers, for the most part, of one master : "There 

 is but one Geometry, and Euclid is its exponent." We 

 ourselves entertain a very high regard for Euclid : indeed 

 our indebtedness to him for what ability we may have in 

 geometrical science is as great as that of Cicero to 

 Archias for eloquence ; but we cannot help feeling that 

 we might have had a far greater mastery over modern 

 methods had our masters been acquainted with these 

 methods themselves. " This book," says one who has 

 recently left us, a consummate master of modern methods, 

 " has been for nearly twenty-two centuries the encourage- 

 ment and guide of scientific thought. . . . The encourage- 

 ment, for it contained a body of knowledge that was 

 really known and could be relied on, and that, moreover, 

 was growing in extent and application. . . . the guide, 

 for the aim of every scientific student of every subject 

 was to bring his knowledge of that subject into a form 

 as perfect as that which geometry had attained." In 

 our author we have one who, 



" NuUius addictus jurare in verba magistri, ' 



can ungrudgingly acknowledge the many good points of 

 the old-world geometer, whilst, with keen-cutting scalpel, 

 he boldly lays bare his numerous defects. The present 

 generation, perhaps, will not see Euclid superseded in 

 our schools ; but when his warmest defender makes 

 him admit that his proofs might be abridged and im- 

 proved, that alternative proofs may with advantage be 

 appended to his, and that new problems and theorems 

 might be interpolated, we may expect that a time will 

 come, quickly if only the Universities would not handicap 

 their favourite so heavily, when his order and numbering 

 of propositions may be abolished, and his treatment 

 of parallels shelved. In the meanwhile we must work in 

 hope, and the article under notice will possibly pave the 

 way for an improved mode of studying the science. As 

 is well known, Prof. Henrici has long been engaged 

 in writing a Geometry : to this work we must refer 

 readers for his views on the subject. In the book we see 

 him as the teacher, laying his foundations deep and 

 strong and broad enough for the vast superstructure — 

 all pure geometry — they have to bear : in the article, he 

 treats his subject at fiist rather as the historian and 

 critic, though subsequently he takes up the role of teacher 

 again ("use doth.breed such a habit in a man"), and 

 rapidly but most deftly sketches a beautiful outline — in 

 parts filled in— of the "higher" geometry. In a long, 

 but far from tedious, sketch of si.xty-four columns he 

 treats pure geometry in two sections : the first, in 

 twenty-five and a half columns, gives an account of 

 the Elementary, or Euclidian, Geometry : the second 

 is devoted to the Higher, or Projective, Geometry. In 

 section I we have a running commentary on Euclid's 

 text, which does at greater length, though somewhat in 

 the same style, what De Morgan did some years since in 

 the "Companion to the British Almanac" (1849). The 

 axioms which lie at the basis of the subject are well dis- 

 cussed, and their foundation upon experience established : 

 it is pointed out that the connection between these axioms 

 has only been shown "within the last twenty years 



