28o SCIENCE PROGRESS 



theorem of Pythagoras was in constant use in Japanese mathe- 

 matics, but many of the demonstrations had no logical force 

 owing to the lack of systematic establishment of geometry. 

 On this point reference may be made to Smith and Mikami's 

 History of Japanese Mathematics, pp. 10, 13, 180. 



A. J. Rahilly (Proc. Roy. Ir. Acad. 191 5) very simply shows 

 that relations between geometrical determinants of the type 

 considered in a theorem of Frobenius exist between many sets 

 of geometrical entities ; in fact, a large part of the metrical 

 geometry of the point, line, circle, plane, and sphere may be 

 reduced to such determinant-equations. 



Lastly, in 191 5 Gaston Darboux has presented to the Paris 

 Academy of Sciences papers on the representation on a plane 

 of the surface of the fourth order with double conic ; and a 

 new edition of Salmon's Geometry of Three Dimensions will 

 be reviewed in the January number of this Quarterly. 



Notes on Applied Mathematics. — Prof. Louis T. More, in his 

 book on The Limitations of Science (New York : Henry Holt & 

 Co., 191 5) has practically taken the same attitude towards 

 modern physical science, with its theories of electrons and 

 relativity, that Stallo did towards the modern physics of his day. 

 It requires a degree of ignorance which is not so frequently met 

 with among men of science nowadays as it was formerly to 

 maintain that neither theory of knowledge or metaphysics enters 

 into physical theory or even method in general. Dr. H. 

 Wildon Carr discusses {Proc. Aristot. Soc. 19 14, 14, 407) the 

 relations to metaphysical theory of the new kinematics resulting 

 from the principle of relativity. It appeared to H. S. Shelton 

 (ibid. 100), in working out a thesis that the co-ordination of 

 the facts and theories of science is a branch of philosophy and 

 that this co-ordination should not be a shadow but a solid 

 reality, that the principles of the interrelation between mathe- 

 matics, considered as a pure science, and its application to 

 physical problems required investigation. For a lack of a clear 

 understanding of the methodology of mathematics, the whole 

 of the work of Lord Kelvin and Tait on the secular cooling of 

 the earth and allied subjects was absolutely invalid, not merely 

 on account of discovery in radioactivity, but inherently and 

 theoretically invalid. This is to prove the claim as to the 

 solid reality of the philosophy of co-ordination above referred 

 to — what Shelton calls " objective philosophy " — and the 



