578 



NA TURE 



[April 23, 1908 



" essaitch " and " seeaitch " is too cumbersome. For 

 computation integrals ought to be evaluated, as the 

 author does, in the form of logarithms, as there are 

 lew students who, when they have obtained any result 

 involving a " sneeze minus one," could calculate its 

 numerical value. 



We must not forget to mention the collect ion^ of 

 examples, which are of the type approved by the most 

 enlightened examining boards in Great Britain. Thev 

 are for the most part based on practical applications, 

 and are of such a character as to test the student's 

 knowledge of the calculus itself, not his power of 

 covering sheets of foolscap with uncomprehended 

 formulae. 



To sum up, it had become necessary to introduce 

 considerable changes in the elementary treatment of 

 the calculus, not only in the interests of the students 

 of physics and engineering whose claims have been 

 most prominently put forward, but also for the 

 sounder and more rational instruction of mathematical 

 students. The present book admirably meets the re- 

 quirements of the case. We do not say that further 

 improvements are impossible, but we consider that a 

 stage has now been reached when any attempt to 

 make the treatment better in one particular is very 

 liable to render it worse in another. 



May not an analogy also be suggested between the 

 coincidence of the author's and reviewer's views, and 

 probably the views of other teachers, and the con- 

 ditions in the calculus for maximum value, as showing 

 that the methods adopted are the best possible, subject 

 to present existing conditions. 



PREHISTORIC EUROPE. 

 L'Europe prchisloriqite. Principes d'Arch^ologie pre- 

 historique par Sophus Miiller, traduit du danois 

 avec la collaboration de I'auteur par Emmanuel 

 Philipot. Pp. 21J. (Paris: J. Lamarrc, n.d.) 

 Price 10 francs. 

 '"PHE prehistoric period in Europe is so extended, 

 *■ the conditions during the period so varied 

 according to .place and time, our knowledge of 

 the conditions so meagre and broken, that the task 

 of putting the events of the period into the form 

 of a connected narrative is not to be lightly estimated 

 or easily fulfilled. 



Dr. Muller decides at the outset to confine himself 

 to the consideration of matters which have received 

 general acceptance ; from this resolution he, however, 

 soon departs, or there would have been little to tell. 



The work is not so complete as the title implies; 

 llie long and important palaeolithic phase is sum- 

 marily dismissed at the foot of the fifteenth page. 

 The author, moreover, has drawn his facts from one 

 source only — that of archaeology ; the evidence of 

 craniology and philology is ignored. Nor has all the 

 liicrature been consulted. In a book which deals so 

 much with the prehistoric age of Greece it is strange 

 to find no mention of Prof. Ridgeway and his work. 

 Drspite^ these defects, however, the book forms an 

 interesting and suggestive study; it displays much 

 thought and judgment. 



NO. 200S, VOL. ::l 



The general argument, which is simple, can be 

 expressed in a few words ; it is that in prehistoric 

 time, as in early historic time, Europe was indebted 

 for her culture to Greece and Asia Minor ; that the 

 culture extended from the /Egean as a centre, under- 

 going more and niDre change as it neared the peri- 

 phery. Dr. Miiller likens south-east Europe, in its 

 relation to the rest of Europe, to a town in its 

 relation to the surrounding country. Just as the 

 habits and culture of a town slowly spread to the 

 rural districts, where they persist and not infrequently 

 attain a greater development than was known in the 

 town, so did the culture of Greece gradually extend 

 over the whole of Europe. While on this analogy it 

 may be well to refer to another feature — sometimes the 

 country misses a step in the development of culture ; 

 for instance, in many districts the lamp has been 

 directly superseded by electricity without the inter- 

 mediate use of gas ; so in the nortii of Europe the 

 Bronze age followed on the heels of the Neolithic, 

 whereas in the south of Europe a Copper age inter- 

 vened. It will be seen that to establish his argument 

 the author must prove that the different phases of 

 culture appeared earlier in the south than in the north. 

 The higher development of any phase in the north 

 is not against the general trend of his argument. 

 The evidence upon which he grounds his theory is 

 obtained from art objects, polished stone weapons, 

 articles of bronze and copper, pottery, particularly 

 that exhibiting decorative designs, grain, domesti- 

 cated animals, and the architecture of the graves. 



As is well known, culture alone can prove a very 

 misleading guide in correlating people, for where the 

 same environment obtains, there will a similar culture 

 tend to develop. The evidence which is at times 

 admitted cannot be allowed to pass unchallenged. It 

 is gravely argued, for instance, that a correlation 

 existed between the people who lived in Spain and the 

 Pyrenees during the Solutre period and the Iron-age 

 inhabitants of Greece, since statuettes of similar form 

 are forthcoming from both regions. No account is 

 taken of the great difference in the age of the statu- 

 ettes, a difference to be expressed in thousands of 

 years. 



To choose another illustration, the author finds that 

 the polished stone celts are bigger and more numerous 

 in the north than in the south, due to the Stone age 

 enduring longer and attaining a higher development 

 in the north. Moreover, in the north the stone celts 

 are of flint, whereas in the south they are of nephrite, 

 jadeite and chloromelanite, stones rare in Europe but 

 more common in Asia. He thereupon argues thai 

 when Man began to polish his stone tools he would 

 use such a soft stone as nephrite or jadeite, and would 

 not begin to polisli a stone so hard as flint until the 

 art of polishing had made considerable advance. He 

 therefore concludes that the nephrite celts are earlier 

 than those of flint, and that the art of polishing 

 extended from the south to the north. It may, how- 

 ever, well have been that it was the distribution of 

 the various stones which governed the materia! of 

 which the celts were made. 



He takes again the spiral motif — in mid-Europe he 



