August 13, 1909] 



SCIENCE 



213 



work, his methods and his manner should or 

 should not be recommended for the guidance 

 of those who wish to aim at similar achieve- 

 ments. This at any rate is true with respect 

 to works like the one before us, their intrinsic 

 value not being open to question. In reading 

 such productions, especially in collected form, 

 one necessarily forms a picture, conscious or 

 otherwise, of the author's mind quite apart 

 from any personal acquaintance, and it may 

 be that no apology is needed for recording 

 such an impression and for pointing out some 

 features of the author's work and methods 

 which appear to the present reviewer to be of 

 high value in the study of applied mathe- 

 matics. 



The lines on which Sir George Darwin has 

 so far published memoirs have been mainly 

 laid in the subject of hydromechanics and its 

 mathematical associate, the theory of elastic 

 solids. These have been applied to masses in 

 bulk and subject to the Newtonian law of 

 gravitation with applications to present-day 

 astronomical and geophysical problems and 

 to theories of cosmogony on the basis of a 

 continuous evolution of planetary and satellite 

 systems. These problems, whether we consider 

 them from the mathematical or physical side, 

 are certainly the most' difficult of all the 

 studies in celestial mechanics which have 

 received attention in the past. It is true that 

 there are many ideal problems which admit of 

 moderately simple treatment, but the majority 

 of these can not be considered even as a first 

 approximation to the real problems presented 

 by the observed phenomena. One notices 

 throughout Professor Darwin's work that he 

 rarely takes up an ideal problem without hav- 

 ing in view the ultimate answer to some 

 physical question. Almost the single excep- 

 tion to this is his paper on periodic orbits, and 

 the possible complications of solar systems 

 other than that to which we belong makes this 

 exception a doubtful one. 



The difficulties are increased when it is de- 

 sired either to interpret the mathematical re- 

 sults in terms of simple and easily understood 

 phenomena or to put them into such forms 

 that numerical values may be substituted 

 directly for the symbols. These objects Pro- 



fessor Darwin appears to have continually in 

 view. He is rarely contented with the mathe- 

 matical solution of a set of differential equa- 

 tions, however intricate or interesting the so- 

 lution may be from the symbolic point of 

 view, but searches to find the physical expla- 

 nation or analogy which will enable him and 

 the reader to follow without great mental 

 effort the various sequences of events which 

 must result from the formulse obtained. 



One notices too the wide range between 

 what are popularly called " practical results " 

 and speculative theory. On the one hand, we 

 have his work on tidal prediction with all its 

 associated problems, solutions of which are 

 necessary or valuable in the concerns of daily 

 life, and on the other hand, the highly specu- 

 lative (I use his ovsTi term) investigations into 

 the past history of the satellites and planets 

 which form our solar system. In the former 

 case the object in view was chiefly the discov- 

 ery of methods for obtaining the times and 

 heights of the tides at any place without ex- 

 cessive labor, that is, in these days when nu- 

 merical computation is a recognized profes- 

 sion, at a cost which is within the means of 

 those who desire the results. In such work 

 the mathematical developments have generally 

 a minor interest : they are considered to be 

 merely tools for the fashioning of the ma- 

 chine under construction. At the other end 

 of the scale is the work of purely scientific in- 

 terest related to problems of cosmogony, 

 chiefly those of the past, in which the mathe- 

 matical developments frequently have an inter- 

 est of their own and give rise to problems in 

 pure mathematics which may be entirely 

 separated from any physical considerations. 



In using the term " highly speculative " it is 

 well to distinguish between work of the char- 

 acter of Darwin's theory of the lunar evolu- 

 tion based on known physical data clearly 

 stated, developed with rigid mathematical ac- 

 curacy and with careful attention to any fac- 

 tors which may modify the results, and the 

 ill-defined guesses developed, it may be, from 

 some isolated principle which not infrequently 

 appear as proofs of the correctness or falsity 

 of some new or old idea. In the matter of 

 cosmogony this has been especially obvious of 



