September io, 1908] 



NA TURE 



443 



of this kind, but a select list would be useful to the 

 beginner. 



In writing on group-theory clearness is essential, 

 and in this respect Mr. Hilton appears to be successful. 

 Group-theory is so important that every advanced 

 mathematical student ought to know something about 

 its principles and methods. University teachers will 

 now have a text-book which ought to help them in 

 making the subject attractive and popular. A good 

 many years ago Cayley foretold the development of 

 group-theory, and his prophecy has been fully justified. 

 The fact is that all analysis may be brought into con- 

 nection with group-theory; and not only so, but in 

 making this connection clear, we are submitting the 

 particular subject (theory of numbers, algebraic func- 

 tions, or what not) to its ultimate logical test, and 

 disclosing its real and most fundamental basis. 



It should be added that, with the help of Prof. 

 Burnside, Mr. Hilton has given, by way of appendix, 

 a list of twelve problems in group-theory which have 

 not yet been solved. The best known of these is " Can 

 a group of odd order be both non-cyclic and simple? " 

 A definite answer to this question would give great 

 satisfaction to students of group-theory, and as in the 

 case of problems in higher arithmetic, a novice with a 

 natural gift for these researches may succeed where 

 the veterans have failed. G. B. M. 



A Short History of Philosophy. By A. B. D. Alex- 

 ander. Pp. xxii + 601. (Glasgow: MacLehose and 

 Sons, 1907.) Piice Si. 6d. net. 



The author offers this work as a substitute for G. H. 

 Lewes's well-known " Biographical History of 

 Philosophy," which, if for no other reason than that 

 it was written expressly to discredit philosophy, has 

 too long enjoyed its position as the one British attempt 

 to exhibit the entire course of European speculation. 

 Mr. Alexander does not emulate Lewes's literary 

 brilliance, but he writes for a generation of readers 

 who are willing to take the philosophic view even of 

 philosophy, and to regard it not as a noxious counter- 

 feit of knowledge, but as a necessary complement of 

 positive thought at each epoch of man's history — an 

 indispensable and highly significant part of the form 

 and pressure of the time ; such readers will welcome 

 him as a competent and trustworthy guide to the 

 salient features in the evolution of speculative thought. 



The accounts which Mr. Alexander gives of the 

 various systems of philosophy are clear and sound, 

 and in all important cases have the vital quality that 

 comes from first-hand acquaintance with the classics 

 of his subject. He has dealt more fully with modern 

 than with ancient philosophy, devoting nearly three- 

 quarters of his book to post-Renaissance thinkers and 

 more than half to writers since Hume. It is, 

 perhaps, to be regretted that so much of the space 

 rendered available by the author's restraint in the 

 earlier stages of his enterprise has been given to 

 German philosophers whose importance is national 

 rather than European. It must be admitted, on the 

 other hand, that the great names have received their 

 due, and that, in particular, the chapters on Hegel 

 will give renewed hope to many an honest student 

 who has found the master himself only a shade more 

 perplexing than some of his English interpreters. 



The pages which we grudge to the lesser Teutonic 

 lights might well have been used to make more 

 adequate the author's picture of recent philosophical 

 discussion in this country. The writer of a handbook 

 for students must, of course, be reserved in his treat- 

 ment of current controversies, but, in the case of a 

 subject like the history of philosophy, he will give 

 point to his whole work by a conclusion in which the 

 NO. 2028, VOL. 78] 



questions of vital contemporary interest are at least 

 indicated and set in their relations to the classical 

 speculative movements. It is to be hoped that Mr. 

 Alexander will find in a second edition of his useful 

 work an opportunity of supplementing it in a manner 

 which would render it still more acceptable to many 

 others besides his scientific readers. 



LETTER TO THE EDITOR. 

 [The Editor does not hold himself resl>onsible for opinions 

 expressed by his correspondents. Neitlier can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part 0/ Nature. 

 No notice is taken of anonyynous communications.] 



The Size of the Mammoth. 



Several references have recently been made in Nature 

 to the size of the mammoth, and I venture to present 

 some notes on the subject, the result of several years' 

 observation and measurements, principally of North 

 American species. 



Three good species of true elephant occur in North 

 America — the northern mammoth, E. primigenius ; the 

 southern, or Columbian, mammoth, E. colombi ; and the 

 Imperial mammoth, E. imperator. The first of these is 

 the one commonly known as the mammoth, and is the 

 species found in northern Siberia and Europe. This 

 attains a height of about 9 feet or 9 feet 6 inches, though 

 an occasional specimen may exceed this, just as now and 

 then an Indian elephant exceeds the average size of the 

 species. The Columbian mammoth reached a height of 

 II feet, and the Imperial mammoth 13 feet to 13 feet 

 6 inches, being, so far as I l^now, the tallest species of 

 elephant on record. Unfortunately, the Columbian and 

 Imperial mammoths are mainly known from scattered 

 teeth and odd bones, so that their exact proportions cannot 

 be definitely given, even in the case of the Columbian 

 mammoth, the most complete specimen of which lacks 

 the lower limb bones. It may, furthermore, be said that 

 it is occasionally difficult, if not impossible, to say whether 

 a given tooth belongs to the Columbian or Imperial 

 mammoth, but the typical or full-sized specimen may 

 readily be distinguished. 



The three species noted above occupied fairly definite 

 ranges in North America, although there was a great 

 overlapping of their boundaries, particularly between the 

 I wo southern species. The southern boundary of the 

 northern mammoth roughly follows that assigned to the 

 great North American ice-sheet, and the Columbian 

 slightly overlaps this on the east and west, and in the 

 interior of the continent runs far northwards. The 

 Imperial mammoth is not positively known to have 

 reached the Mississippi River, but extended south into 

 Mexico and west to the Pacific coast. This is a west- 

 ward extension of the range assigned to the species in 

 the report of the Maryland Geological Survey, and is based 

 on material examined since that report was published. 



Referring to the mammoth in the museum of the 

 Chicago Academy of Science, it should be said that this 

 specimen has been restored, all the long bones being 

 lengthened, and that the specimen stands certainly 2 feet 

 higher than it should. It has been painted over, so that 

 it is very difficult to tell where the original bones leave 

 off and the restoration commences. The animal is prob- 

 ably the Columbian mammoth, and it is said that the 

 skull is that of a recent Indian elephant. 



Finally, a word might be said in regard to the American 

 mastodon, the size and proportions of which are definitely 

 known. This species rarely reached a height of 9 feet 

 6 inches, the majority of specimens runningabout 9 feet; 

 but it was a much more heavily built animal than the 

 mammoth or the Indian elephant, so that a specimen 

 q feet 6 inches high would weigh from one-third to one- 

 half more than an Indian elephant of the same height — 

 that is, it would weigh from eight to nine tons. 



Brooklvn Institute Museum. F. A. Lucas. 



