March 3, 1910] 



NATURE 



5 



accorded to each set of changes must necessarily de- 

 pend on the view that is taken of the purpose of a 

 mathematical training- in our educational system. It 

 is not easy to form a combination of what is useful 

 with what is interesting; and still less is it a simple 

 matter to determine how far it is judicious to discuss 

 at an early stage the fundamental ideas which under- 

 lie each branch of mathematics. But at the present 

 time we believe that there is a dangerous tendency 

 to pass over all considerations of mathematical philo- 

 sophy as too difficult or uninteresting. We therefore 

 welcome the present volume, which is a real attempt 

 to build up an elementary course of algebra on the 

 fundamental concepts of number and the operations 

 to which it is subject. 



The book is divided into four parts ; the first deals 

 with positive numbers, the second with zero and 

 negative numbers, the third with irrationals, and the 

 last with the more advanced applications, such as 

 simultaneous quadratics, proportion, progressions, and 

 the variation of simple functions. Each new idea 

 that occurs is explained at considerable length in the 

 text with admirable clearness, and is usually illus- 

 trated by graphical examples. In practice, no doubt, 

 this will be used as the substance of an oral treatment, 

 for few pupils will be sufficiently mature to be able 

 to read and assimilate it unaided. There are abundant 

 examples, a useful number of test papers, and an 

 index which should prove of great practical value. 

 We hope that this book will be widely used, for its 

 principles are sound, and it introduces the student to 

 a number of ideas that are both stimulating and 

 instructive. 



(2) This volume is intended to be used for a revision 

 course. Stress is therefore laid on such features of 

 the subject as are apt to be dealt with rathei cursorily, 

 or even omitted during the first reading. At the same 

 time, however, the plan of the book is not designed 

 to meet the wants of the professional mathematician, 

 but to suit those who need a reasonably complete 

 knowledge of the elementary principles of algebra. 

 The remainder- theorem and the principle of undeter- 

 mined coefficients are placed in an early chapter ; the 

 section on linear equations contains also the funda- 

 mental properties relating to the roots of equations 

 of any degree ; and the theory of simultaneous equa- 

 tions is expanded to include an elementary account 

 of the use of determinants. By such means as these, 

 the author has provided a course which is admirably 

 adapted for a second reading. The treatment is fresh 

 and vigorous, the explanations are clearly put, and 

 great care has been taken to ensure that the student 

 really understands the nature of the various operations 

 which he is called upon to perform. 



OUR BOOK SHELF. 



Les Tr emblements de Terre. By I'Abbe Moreux. 



Pp. vii + 378. (Paris : Henri Jouve, 1909.) Price 



4 francs. 

 On June 11, 1909, towns in south-eastern France, and 

 particularly those in the district of Provence, were 

 shattered by an earthquake. The places which 

 suffered most were Salon, Lambesc, Saint-Cannat, 

 NO. 2105, VOL. 83] 



Rognes, and Le Puy-Sainte-R^parade. Roughly 

 speaking, the damage done to structures was esti- 

 mated at 16,000.000 francs, which means something 

 more than half a million sterling. From a monetary 

 point of view this is a large sum, and it no doubt repre- 

 sents the effects of an unusually large earthquake. 

 Had a similar rock adjustment taken place beneath 

 a large city this sum would have been greatly mag- 

 nified. The damage at San Francisco has been esti- 

 mated at 70,000,000/. sterling. Naturally, the disaster 

 excited the imagination, and survivors have speculated 

 on the cause of earthquakes. One outcome of the 

 thoughts which were so rudely created is the book by 

 the Abbe Moreux. 



The author has read much about earthquakes. At 

 the outset, although he tells us that his writings are 

 not addressed to specialists, he has taken pains to 

 popularise speculations about which specialists have 

 but slight knowledge. He gives us a series of pic- 

 tures of the ruins, tells us about the heartrending 

 cries of the people, the arrival of the doctors, the 

 erection of huts, and the generosity of the Pope. 

 Next we read about possible premonitory signs. We 

 are told that before the earthquake people suffered 

 from vertigo, clocks struck wrongl}', whilst pigeons 

 flew about rather than going to rest. One interest- 

 ing picture, which is not unlike the Cullinan diamond, 

 is that of our pyramidal earth, the fourth corner of 

 which was found by Sir Ernest Shackleton. 



Reference is made to recent investigations relating 

 to seismology, from which we learn that our world 

 has a rigidity double that of steel. Volcanic and 

 seismic effects are not directly connected, but earth- 

 quakes are in part the result of tectonic adjustments. 

 They hold a relationship to the wobbling of the pole, 

 fluctuations in barometric pressure, the change of 

 seasons, lunar and solar attractions, and to internal 

 convection currents. Earthquakes explain certain 

 perturbations of magnetic needles and earth currents, 

 whilst thev are closely associated with solar radiation. 

 The periodicity of earthquakes and their prediction 

 are subjects which are not overlooked, whilst many 

 pages are devoted to construction in earthquake coun- 

 tries, and to the mitigation of disasters. The rela- 

 tionship of pressure to temperature as we descend in 

 the earth, and the fact that bodies may during 

 crystallisation, or when they pass from the fluid to 

 the solid state, suddenly expand, are phenomena which 

 the Abbe discusses at considerable length. In fact, 

 we are told that the shock accompanying such expan- 

 sions mav be the principal cause of many earthquakes. 



It is an interesting little book, and will furnish 

 many with subjects for speculation which have never 

 crossed their minds before. J. Milne. 



The Methods of Textile Chemistry, being the Syllabus 

 of a Lecture Course adapted for use in Textile 

 Laboratories. By Dr. F. Dannerth. Pp. viii + 164. 

 (New York : John Wiley and Sons ; London : Chap- 

 man and Hall, Ltd., 1908.) Price 8s. 6d. net. 



If the author had employed the title " Some Methods 

 of Textile Chemistry " in place of the one he has 

 chosen he would have erred on the right side. But 

 to attempt to deal with the whole subject of textile 

 chemistry — one of the most difficult and involved 

 branches of analytical chemistr}- — in 120 small octavo 

 pages of large type can scarcely result in anything 

 of real value, even if the work is done as well as it is 

 possible to do it. But when, as in the present case, 

 the information is badly arranged, containing much 

 that is superfluous if not useless, while omitting many 

 matters of fundamental importance, and is not without 

 a liberal sprinkling of mistakes and inaccuracies, the 



