RECENT ADVANCES IN SCIENCE 205 



discussing by his method the distribution in space of these 

 special type stars and finding the positions of the solar vertex 

 and apex relative to them. 



Dyson, F. W., A Statistical Discussion of the Proper Motions 

 of the Stars in the Greenwich Catalogue for 19 10, M.N., R.A.S. 

 77, 212, 191 7. 



Stellar Photometry, Seares, F. H., Photographic Magnitudes 

 of Stars in the Selected Areas of Kapteyn, Proc. Nat. Acad. 

 Sci. 3, 188, 191 7. Preliminary Note on Distribution of Stars 

 with respect to the Galactic Plane. Proc. Nat. Acad. Sci., 

 3, 217, 1917. 



The first paper describes the method of determining and 

 standardising the magnitudes. The second gives the result of 

 the determination from counts of these magnitudes of the 

 galactic condensation. A value much higher than the recent 

 determination of Chapman and Melotte is obtained, and it is 

 concluded that their counts omitted many of the fainter stars 

 in the richer fields. 



PHYSICS. By James Rice, M.A., University, Liverpool. 



For some time past a considerable body of mathematicians 

 have been engaged on a careful scrutiny of the concepts and 

 axioms on which rests the whole body of mathematics, and 

 in the March number of the Physical Review Dr. R. C. Tolman 

 suggests that the time is ripe for a similar investigation in 

 physics. As any branch of science develops, its considerations 

 become more and more deductive, the ideal form of exposition 

 being one in which all the important relations are derived 

 from a small number of independent general principles and 

 all the terms used are defined with the help of a small number 

 of indefinables, which are certain entities not defined in the 

 particular discussion undertaken, but assumed to be matters 

 upon which for the purposes at hand there is general agree- 

 ment. Dr. Tolman proceeds to discuss the nature of the 

 quantities which occur in the equations of mathematical physics 

 and to consider a set of indefinables for their definition in the 

 hope that he may thereby help in the preparation for that 

 more complete systematisation of mathematical physics which 

 is undoubtedly coming. 



Following Bertrand Russell, the author considers magni- 

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