RECENT ADVANCES IN SCIENCE 9 



(Proc. Edinburgh Math. Soc. 191 5-16, 34; Research Paper, 

 1916, No. 2) discusses briefly a point in the method of Peano 

 (1888) and Baker (1902) of solving linear differential equations. 

 E. T. Whittaker (Proc. Roy. Soc. Edinburgh, 191 7, 37, 95-116 ; 

 Research Paper, 191 7, No. 3) obtains interesting results on the 

 " adelphic integral " of the differential equations of dynamics. 



A. S. Merrill (Amer. Journ. Math. 191 9, 41, 60-78) discusses 

 completely the conditions for an extreme in the case of isoperi- 

 metric problems with variable end-points. G. A. Bliss (Trans. 

 Amer. Math. Soc. 191 8, 19, 305-14) deals with the problem 

 of Mayer in the calculus of variations with variable end-points. 

 Eleanor Pirman (Proc. Edinburgh Math. Soc. 191 7-18, 36; 

 Research Paper, 191 8, No. 1) proves certain results on the 

 solutions of a modified Stirling's (1730) difference equation. 

 T. P. Ballantine (Amer. Math. Monthly, 1919, 26, 53-9) shows 

 that, by a suitable extension of the conception of the difference 

 quotient, the method of interpolation by means of algebraic 

 polynomials for the case when the ordinates are equally spaced 

 can be generalised for the case when the ordinates are spaced 

 according to any law. 



Whittaker (Proc. Roy. Soc. 191 8, A. 94, 367-83) obtains 

 solutions of integral equations of Abel's and of Poisson's type 

 in forms which can be made the basis of numerical calculation. 



Geometry. — G. Loria (Amer. Math. Monthly, 19 19, 26, 45- 

 53) gives, in a series of letters, some reflections, historical, edu- 

 cational, and scientific on certain constructions of descriptive 

 geometry. 



J. W. Clawson (ibid. 59-62) states a general theorem in the 

 geometry of the triangle of which the well-known theorem on 

 the Wallace (or Simson) line is a very special case, and gives 

 a further discussion and application of the theorem. D. F. 

 Barrow (ibid. 108-11) examines the envelope of the Wallace 

 lines of an inscribed quadrangle. N. Altshiller (ibid. 65-6) 

 remarks that some of his theorems given in this Monthly for 

 191 8 (242-6) were proved in 1906 by J. Neuberg. 



J. H. Grace (Proc. Lond. Math. Soc. 191 9, 17, 259-71) finds 

 the possible relations between the inscribed and circumscribed 

 spheres of a tetrahedron and also some general properties of 

 quadrics in relation to a tetrahedron. 



E. Ciani (Boll, di bibl. e st. delle sci. mat. 191 8, [2], 1, 52-62) 

 gives a very full account of F. Enriques's Lezioni sulla teoria 



