RECENT ADVANCES IN SCIENCE 369 



logical, statistical, and other observations, discusses from a 

 practical point of view the Fourier harmonic analysis and 

 gives some optical illustrations. " The tendency of recent 

 abstract analysis on related matters has been to explore the 

 general qualities of the various types of infinite assemblages, 

 rather than to determine the quantitative relations of average 

 or mean which offer themselves for the purpose of physical 

 theory, when the material is too complex for study in detail " 

 (p. 37). In some of the notes added at the end of the paper 

 (pp. 40-2) points of purely mathematical interest are dealt with. 



J. W. Nicholson {Nature, 191 7, 100, 15-16) gives an account 

 of, with some reflections on, the Addresses on connected subjects 

 of E. W. Brown to the American Mathematical Society and this 

 one of Sir Joseph Larmor to the London Mathematical Society 

 in 19 1 6. Brown's Address, which was on the relations of mathe- 

 matics to the natural sciences, indicated the types of work 

 really needed by the pure mathematician in this respect. 



P. R. Rider (Amer. Journ. Math. 191 7, 39, 241-56) treats 

 the problem of the calculus of variation for three dimensions 

 in a different form from Gernet (1902) and Bliss and Mason 

 (1908), and uses the results in considering certain generalised 

 definitions of angle and solid angle (cf. Science Progress, 191 7, 

 12, 11). 



A. Dresden {Trans. Amer. Math. Soc. 191 7, 18, 373-8) uses 

 methods analogous to those in a paper of his published in 191 6 

 (see Science Progress, 191 7, 12, 11) to obtain formulas for 

 the second derivatives of the extremal-integral arising in the 



theory of the integral jF{y ; y')dt. 



E. W. Chittenden {Amer. Journ. Math. 191 7, 39, 263-71) 

 studies certain relations treated by Hildebrandt (191 2), in his 

 paper on the functional calculus of Frechet. 



Some recent papers by F. L. Hitchcock may be mentioned : 

 " A Classification of Quadratic Vector Functions " {Proc. Nat. 

 Acad. Set. Washington, 1915, 1, 177-83), "Quaternion Investi- 

 gation of the Commutative Law for Homogeneous Strains " 

 {Proc. Roy. Soc. Edinburgh, 1915,35, 170-80), " On the Operator 

 Nabla in Combination with Homogeneous Functions " {Phil. 

 Mag. 191 5, 29, 700-8), and " A Classification of Quadratic 

 Vectors" {Proc . Amer .Acad. Arts and Sciences, 191 7 , 52, 369-454). 



In papers of 1885 and 1886, Poincare' showed that a solution 



