474 



NATURE 



[September 17, 1908 



with another little girl, and shows plainly enough that 

 premature formal teaching must be injurious by 

 destroying independence of thought. Unfortunately, 

 the ages of the girls are not stated. 



The volume is very miscellaneous, and, indeed, 

 suffers from the fact that addresses, lectures, notes, 

 &c., have been gathered together without much atten- 

 tion to revision or general effect. There are notes on 

 lessons in geometry (often good), a long extract from 

 an address by Bidder to the Institution of Civil 

 Engineers, scraps of mathematical history, and a 

 certain amount of that twaddling " psychology," so- 

 called, and puerile classification, in which paedagogists 

 take such unaccountable delight. For instance, we 

 are solemnly told that " Geometry is the resultant of 

 Sense-Perception and Abstract Thought," a statement 

 equally true of all the sciences and most of the arts. 

 Then we have a strobic disc, supposed to indicate the 

 different proportions, at different ages, of perception 

 to abstraction, and a so-called chart, something like a 

 toy-trumpet or a church spire, to indicate the stages 

 of mathematical progress in the race and the in- 

 dividual. This last is distinctly misleading, because 

 it makes the advance linear, and it has been nothing 

 of the kind, so far as the race is concerned. 



The bibliography is neither discriminating nor up to 

 date. Montucla and Marie are mentioned without a 

 hint that, as works of reference, they have been made 

 obsolete by M. Cantor's history; and the latter is 

 described (without date) as in three volumes, whereas 

 five complete volumes have appeared, and vols. ii. 

 and iii. are in a second and revised edition. No 

 mention is made of Merz's " History of European 

 Thought," which has some very good sections on 

 mathematics, or of Heath's studies of the Greek 

 geometers. 



But in spite of these defects the book is worth 

 reading, and the author's views appear to be sound. 

 Thus he realises that one great practical problem is to 

 find out, if we can, how far the education of the race 

 should be imitated in that of the individual ; he has 

 a reasonable idea of the proportion of experiment to 

 theory in teaching geometry to boys and girls of 

 different ages; and he very properly recommends the 

 study of algebra, in its early stages, as a generalised 

 arithmetic. Few will dispute that mechanical algebra 

 does more than anything else to blunt a boy's mathe- 

 matical faculties. 



O" PP- 352-6 there are samples of old algebraic 

 notation, on pp. 356-60 a good collection of fallacies, 

 and there is an index of twelve pages. G. B. M. 



THE ORIGIN OF THE SOLAR SYSTEM. 

 Das Problem dcr Entwicklung unseres Planeten- 



systems, Aiifstellung einer neucn Theorie. By Dr. 



Friedrich Nolke. Pp. xli + 216. (Berlin: Julius 



Springer, 1908.) Price 6 marks. 

 'T^HOL'GH it is perfectly true, as the author reminds 

 -•- us, that the problem of the origin of the solar 

 system has attracted the attention and exercised the 

 ingenuity of the foremost minds in all ages, it is 

 easy to recognise decisive steps in the gradual develop- 

 XO. 2029, VOL. 78] 



ment, rendered possible by the acquisition of new and 

 epoch-marking facts. Such were the discovery of the 

 theory of gravitation, the modern views concerning 

 the conservation of forces, and it is not impossible but 

 that in theories yet to be broached, the recent concep- 

 tions as to the nature of matter may considerably 

 modify the views that have hitherto been regarded as 

 orthodox. Our theory of the cosmos is progressive, 

 and continued adjustment is necessary to accommo- 

 date our conceptions to observed facts. Dr. Nolke 

 reopens the graves of a long succession of these 

 theories which have undergone amendment, and 

 naturally finds them inadequate to explain phenomena 

 with which their authors were unacquainted. But in 

 any case, since Dr. Nolke is the author of a rival 

 theory, he could not be satisfied with the work of 

 his predecessors. To destroy is easier than to build, 

 and he has little difficulty in pointing to many short- 

 comings ; but though he confidently believes that he 

 has removed all the objections that disfigure the efforts 

 of earlier physicists, and is in possession of an abso- 

 lutely flawless conception, it is not impossible but 

 that his views will also pass into the limbo of dis- 

 credited statements when reviewed by critics as severe 

 as he has proved himself. 



As in the theory of Moulton, the author starts with 

 a spiral nebula resembling that in Canes, but with 

 more delicate convolutions and a smaller mass. In 

 that nebula an outlying portion is seen apparently 

 detaching itself, and Dr. Nolke regards the formation 

 of Neptune to have been accomplished in a similar 

 manner. He next supposes the connecting' link that 

 holds the newly-formed Neptune to the original nebula 

 to separate itself from the parent nebulous mass and 

 the detached Neptune to make a Uranus. Saturn 

 and Jupiter are formed by analogous processes. 

 Within the internal folds of the spiral there apparently 

 exists a mass of greater density, with four other 

 regions of condensation surrounded by flocculent 

 matter. This latter incoherent material formed the 

 asteroids, while the condensations towards the centre 

 gave rise to the four internal planets. Then, by the 

 action of molecular forces and the " resistance of the 

 aether," the slowly rotating sphere of gas forming the 

 innermost nebula contracted, and the sun was pro- 

 duced. To bring about the necessary contractions and 

 separations, the author has to introduce within the 

 nebulous mass the action of other forces than those of 

 gravitation, and to give to the aether a resistance which 

 we fail to understand. But it is permitted to hold 

 verv varied views of the constitution of the aether, and 

 possibly we have failed to grasp exactly the author's 

 contention. We are willing to give him every latitude 

 in this undecided question, but when he goes on to 

 explain the occurrence of the Ice age on the earth as 

 due to the passage of the sun through a nebulous 

 mass, and selects the Orion nebula as the most prob- 

 able, we feel that our guide becomes untrustworthy. 

 Moreover, to use such a hypothesis as affording the 

 means of determining the density of the Orion nebula 

 must be regarded as unwarranted and calculated to 

 bring into disrepute any points of merit the theory 

 may possess. 



