December 7, 191 1] 



NATURE 



of groups. Oddly enough, on the other hand, group- 

 theory assumes less preliminary knowledge than any- 

 thing else except arithmetic, so that beginners, in a 

 sense, start level, and have equal chances for a prize. 

 Many of Prof. Burnside's examples, and, in parti- 

 cular, the notes at the end of the volume, are intended 

 to suggest various lines of research. 



It has already been observed that some of the matter 

 of the first edition has been rearranged. The general 

 effect has been to put more of the abstract theory in 

 the earlier chapters ; this will probably commend itself 

 to experts, but will not make the book easier for 

 beginners. They will probably find it convenient to 

 !)ick and choose, and pay special attention to examples ; 

 they might begin by reading chaps, i.-v., vii.-ix., 

 wiii.-xx., passing lightly over the more difficult parts ; 

 they must, in any case, become quite familiar with 

 transformation, conjugate and self-conjugate operations 

 and sub-groups, and the meaning of Holder's symbol 

 G/H. The great landmarks in the less advanced part 

 of the theory are the properties of composition-series 

 and their allies, together with Sylow's theorem and 

 its consequences; these, at any rate, must be fully 

 mastered before trying to advance. 



The English student of group-theorv is now for- 

 tunate in having at his disposal three excellent text- 

 ibooks in his own language: Mr, Hilton's "Finite 

 Groups," which is a capital introduction to the subject, 

 with plenty of easy examples ; the present volume ; and 

 Prof. Dickson's "Linear Groups," which is parti- 

 cularly valuable for its completeness of detail, and its 

 analysis of Galois fields. Our younger mathematicians 

 are now fairly free from the shackles of ancient 

 tradition, and we may confidently hope that some of 

 them will add to our knowledge of this fascinating 

 theory. G. B. M. 



A GUIDE-BOOK FOR INDIA. 



A Handbook for Travellers in India, Burma, and Cey- 

 lon, including the Provinces of Bengal, Bombay, 

 Madras, the United Provinces of Agra and Luck' 

 now, the Panjab, Eastern Bengal and Assam, the 

 North-West Frontier Province, Baluchistan, and 

 the Central Provinces, and the Native States of 

 Rajputana, Central India, Kashmir, Hyderabad, 

 Mysore, <27-c. Eighth edition, with 80 maps and 

 plans. Pp. cxvi + 530. (London: J. Murray; Cal- 

 cutta: Thacker, Spink, and Co., 191 1.) Price 20s. 

 net. 



'T'HE handbook to India, Burma, and Ceylon issued 

 ■■- by Mr. John Murray, which now appears in its 

 eighth edition, has reached its present form after a 

 long series of revisions. It was first published be- 

 tween 1859 and 1883 in four volumes, and was the 

 work of a well-known Oriental scholar, the late Cap- 

 tain E. B. Eastwick, who collected the material during 

 several journeys to India. When we remember that 

 in tlie period immediately following the Mutiny of 

 fl 1857 communications throughout the Empire were 

 imperfect, and that the present vast library of Indian 

 books of reference, such as the imperial and provin- 

 No. 2197, VOL. 88] 



cial gazetteers, the census, archaeological, and other 

 departmental reports were not available for reference, 

 Captain Eastwick's work was, in its way, admirable. 

 Since the book appeared in its original form it has 

 been subjected to constant revision by competent 

 scholars, and has now been practically rewritten by 

 Mr. H. C. Fanshawe, late secretary to the Govern- 

 ment of the Panjab, and author of an excellent 

 account of the imperial city of Delhi. The arrange- 

 ment has been recast in accordance with the most 

 recent railway developments, and the accounts of the 

 most important places have been revised in the light 

 of modern research. 



The handbook in its present form thus furnishes a 

 compendium of the most trustworthy information re- 

 garding the topography, races, antiquities, and modem 

 history of the Empire. As might have been expected, 

 there are in some places signs that the new material 

 has been imperfectly assimilated with the old, and 

 some errors, misprints, and omissions have escaped 

 the attention of the latest editor. Thus, Sir Colin 

 Campbell's force at the final relief of Lucknow, which 

 consisted of seventeen battalions of infantry, twenty- 

 nine squadrons of cavalry, and 134 guns, certainly 

 aggregated more than 2000 men ; the venerable error 

 that the River Gumti, really the Gomati, "rich in 

 cows," means " serpentine," should not have been 

 repeated; the sportsman might have been warned 

 that rifles carrying the army cartridges are rigidly 

 excluded, and he should have been advised to supple- 

 ment his Express rifle by a smaller bore, high-velocity 

 weapon. 



These, however, are trifling matters, and the intro- 

 ductory chapter which gives advice on expenses, cloth- 

 ing, food, sanitation, and camping represents the accu- 

 mulated experience of many competent authorities, 

 while the accounts of the great cities, their architec- 

 ture and industries, the campaigns and battles, leave 

 little to be desired. The maps and plans are 

 numerous, and, as a rule, excellent. The present 

 edition, while it will be indispensable to the tourist, 

 will find a wider circle of readers among officers on 

 Indian service and their friends at home who are 

 interested in the country and its people. For ordinary 

 people it will be a useful substitute for a collection 

 of the more bulky books of reference, such as the 

 imperial and provincial gazetteers and the depart- 

 mental reports, which must be consulted by all serious 

 students of the Indian Empire, its races, and their 

 history. 



ENGINEERING GEOLOGY. 

 Geology for Engineers. By Lieut.-Colonel R. F. 

 Sorsbie, R.E. Pp. xxvii + 423. (London : C. 

 Griflfin and Co., Ltd., 191 1.) Price 10^. 6d. net. 



ONE important engineering lesson from this book 

 is the danger of working with unknown mate« 

 rials and of using unfamiliar terms. The book is a 

 compilation, mainly from second-hand sources of in- 

 formation, half of which are out of date. The author 

 has seldom discovered the recent original authorities. 

 The work consists of two parts; the first 238 pages 



