542 SCIENCE PROGRESS 



Rome and Palermo and the Atii of Padua on the new mathe- 

 matical physics of Einstein and Minkowski were noticed and 

 commented upon by G. B. Mathews in Nature (191 7, 100, 155). 

 R. I. Pocock (Journ. Indian Math. Soc. 191 7, 9, 202-3) gives 

 a short and useful account of astronomy and the theory of 

 relativity, with references to work by de Sitter, Silberstein, 

 Eddington, and Wilson. C. E. Weatherburn (Proc. Camb. 

 Phil. Soc. 191 7, 19, 72-85) works out much of the theory of 

 hydrodynamics from the point of view of the theory of rela- 

 tivity. 



A paper of importance in connection with the foundations of 

 the theory of errors is that by L. Becker (Proc. Roy. Soc. Edin- 

 burgh, 191 7, 37, 210-14). The author shows that, in a certain 

 case, we do not find to be borne out by observation the usual 

 assumption that the arithmetical mean of similar meteorological 

 observations is to be regarded as their representative value. 



Arithmetic and Theory of Numbers. — F. Robbins (Trans. 

 Roy. Soc. Edinburgh, 191 7, 52, 167-74) gives some tables of 

 factorials and allied products together with their logarithms . The 

 logarithms are given with eighteen decimal places, and " when 

 any one of the . . . tables has been given in the past to an 

 extent useful at the present time, it will be found by the 

 computer that the necessary volume is only with difficulty 

 accessible and hardly ever to be purchased." 



H. C. Pocklington (Proc. Camb. Phil. Soc. 191 7, 19, 57-9) 

 develops the direct method of solving quadratic and cubic 

 binomial congruences with prime moduli. 



H. Todd (ibid. 1 1 1-16) gives a new and elementary proof of 

 a particular case of the famous theorem of Dirichlet on the 

 unities of an algebraic corpus. A short introduction is given 

 by H. T. J. Norton explaining the relation of Todd's argument 

 to the theory of algebraic numbers. 



L. J. Mordell (ibid. 117-24) finds that the expansions of S. 

 Ramanujan (Trans. Camb. Phil. Soc. 191 6, 22) are simple conse- 

 quences of the properties of modular functions. 



H. T. J. Norton (Proc. Lond. Math. Soc. 191 7, 16, 294-300) 

 obtains a result in Diophantine approximation which completes 

 a theorem in G. H. Hardy and J. E. Littlewood's paper on the 

 subject published recently in Acta Mathematica. 



G. H. Hardy and J. E. Littlewood (Acta. Math. 191 7, 41, 

 119-96) give a full account of contributions, principally of 1914 



