384 Notices respecting New Books. 



marvellous power and extreme generality of analytical methods. 

 The particular nature of the physical entities dealt with vanishes 

 into thin air by the time we have established our differential 

 equations, and w T e are then left simply to deal with a number o£ 

 variables connected by certain relations. A system of "general 

 dynamics " founded on the consideration of the nature of the 

 relationships existing among, the variables is. the subject-matter 

 of the little volume under review, Avhieh forms No. 27 of the 

 " Scientia " series. After a brief introduction arid some preliminary 

 considerations regarding the use of analogies, the author outlines 

 a system of general dynamics, and then studies various important 

 groups of problems. In the concluding chapter the possible 

 applications of the system are briefly discussed. The book is a 

 suggestive one, and should prove interesting reading to the 

 mathematical physicist. 



Quadratic Forms and their Classification by means of Invariant 

 Factors. By T. J. I'A. Bromwich. Cambridge University 

 Press. 1906. 



This is the third of the Cambridge Tracts in Mathematics and 

 Physics now being published under the editorship of J. Gr. Leathern 

 and E. T. Whittaker ; and both in purpose and method it carries 

 out in an interesting way the object aimed at in these tracts. 

 Rapidly and yet step by step the student is led from simpler to 

 more complex cases. The treatment is arranged in five chapters. 

 In Chapter III., "A Family of Quadratic Forms," the reduction 

 is completely worked out both for three and for four variables, and 

 is used to classify the contacts of conies and quadric surfaces 

 respectively. The last chapter gives further geometrical illus- 

 trations, and also the important dynamical case of reduction to 

 normal coordinates. Full references are given to original memoirs 

 on the subject from the early and pioneer work of Sylvester in the 

 middle of last century down to recent times. The reader is also 

 referred to papers dealing with developments which could not be 

 discussed in the limited space of a tract of 100 pages. It is indeed 

 surprising how much Professor Bromwich has managed to pack 

 into the space at his disposal, and how in spite of the conciseness 

 demanded he has presented a clear and logical statement complete 

 so far as it goes. The real student of algebraic form will find the 

 pamphlet of the greatest service to him in many ways. 



Annuaire pour V An 1907. Publie par le Bureau des Longitudes. 

 Avec des Notices scientinques. Paris: Gauthier-Villars. 1907. 

 Pp. vi+682 + 8+20 + 146 + 45. 



This well-known annual contains, besides the usual tables, the 

 following special articles : — " Diametre de Venus," by Bouquet de 

 la Grye; and "Histoire des idees et des recherches sur le Soleil. 

 Revelation recente de Tatmosphere entiere de l'astre," by H. Des- 

 landres. It is published at the moderate price of 1 fr. 50 c. 



