174 SCIENCE PROGRESS 



Algebra and Analysis. — C. Lallemand {C.R., 174, 1922, 82, 

 253) gives an account of the development and the present 

 state of nomography ; other papers on the subject are by 

 D'Ocagne {ibid., 146, 1664), and by W. Margouhs {ibid., 1684). 



M. Lecat {C.R., 174, 1922, 728) has a note on cubical 

 determinants. 



G. Andreoli {Rend. Napoli, 27, 192 1, 280-7) determines a 

 class of determinants which can be decomposed into factors 

 involving radicals, and thus a class of algebraical equations 

 solvable by radicals. 



P. Levy {C.R., 174, 1922, 855, 1682) and J. W. Lindeberg 

 {ibid., 1400) discuss the part played by Gauss's law in the 

 theory of errors. 



O. Perron {Sits. Heidelberg, 1921, Abh. 4 and 8) discusses 

 the approximation to irrational numbers by rational numbers ; 

 and G. Valiron {C.R., 174, 1922, 1530) Hermite's approxima- 

 tions to an irrational. 



M. Auric {C.R., 174, 1922, 24, 145, 279, 439), in a series of 

 notes, gives a generalisation of continued fractions, with 

 applications. 



E. Noether {Math. Ann., 85, 1922, 26-33), P- Furtwangler 

 {ibid., 34-40), and A. Ostrowski {Math. Zs., 12, 1922, 317-22) 

 are concerned with the ordinary and absolute irreducibility 

 of algebraic polynomials. 



F. S. Macaulay {Proa. L.M.S., 21, 1922, 14-21) has a note 

 on the resultant of a number of polynomials of the same 

 degree. 



G. Szego {Math. Zs., 13, 1922, 28-55), following J. H. Grace, 

 and A. J. Kempner {Math. Ann., 85, 1922, 49-59) deal with the 

 distribution of the complex roots of algebraic equations. 



S. Breuer {Math. Ann., 86, 1922, 108-13) investigates 

 cyclic equations of the sixth degree. 



E. Helhnger {Math. Ann., 86, 1922, 18-29) applies the 

 theory of systems of equations with infinitely many unknowns 

 to Stieltjes' continued fractions. 



The ordinary extension of the invariant theory of binary 

 forms is to ternary forms, but another way is to consider 

 several series of variables, giving them independent linear 

 transformations. E. Schw^artz {Math. Zs., 12, 1922, 18-35) 

 does this for the form P = {ax){^y), with a geometrical inter- 

 pretation in space of seven dimensions. 



M. Janet {C.R., 174, 1922, 432, 991) obtains invariant 

 canonical forms for algebraic systems. 



In a report on the theory of divergent series, W. A. Hurwitz 

 {Bull. Amer. Math. S., 28, 1922, 17-36) gives special attention 

 to the mutual consistency of two summations, i.e. whether 

 they give the same value. 



