SCIENCE 



Friday, j\'Lvy 19, 1911 



CONTENTS 

 The Bolyai Frize: 



Beport on the Works of Hubert: M. PoiN- 

 CARt 753 



Scientific Notes and News 765 



University and Educational News 769 



Discussion and Correspondence: — 



The Comparative Value of Methods for 

 Estimating Fame: Dr. C. A. Browne. 

 Dr. Woods 's Application of the Histometric 

 Method: Geo. H. Johnson. Metals on 

 Metals, Wet: Professor Edwin H. Hall . 770 



Scientific BooTcs: — 



Jordan on the Stability of Truth: Pro- 

 fessor A. W. Moore. Allen's Commercial 

 Organic Analysis: Professor W. A. Noyes 775 



Scientific Journals and Articles 777 



The Quie Demonstration System of Teaching 

 Qualitative Analysis: Professor Eaymond' 

 C. Benner 778 



Sumus in Dry-land Farming: C. S. Scofield 780 



Special Articles: — 



Some Experiments m the Production of 

 Mutants in Drosophila: Professor Jacques 

 LoEB, Dr. F. W. Bancroft. An Experi- 

 ment in Double Mating: Professor A^eb- 

 non L. Kellogg 781 



Societies and Academies: — 



The National Academy of Sciences. The 

 American Mathematical Society: Pro- 

 fessor F. N. Cole. The American Philo- 

 sophical Society. The Philosophical Society 

 of Washington : E. L. Paris 789 



MSS. intended for publication and books, etc., intended tai 

 leview should be sest to the Editor of Science, Qarrisoa-on- 

 HndsoB, N. Y. 



THE BOLYAI PBIZE^ 



The problems treated by Hilbert are so 

 varied and their importance is so evident 

 that a long preamble seems unnecessary. 

 It is preferable to enter immediately upon 

 the detailed exposition of his principal 

 memoirs. The reader in the presence of 

 results so important will himself draw con- 

 clusions. 



INVARIANTS 



The first works of Hilbert relate to in- 

 variants. We know with what passion this 

 part of mathematics was cultivated about 

 the middle of last century and how it has 

 since been neglected. It seemed in fact 

 that Clebsch, Gordan, Cayley and Syl- 

 vester had used up all that it was possible 

 to deduce from the old methods and that 

 after them there remained only slight 

 gleanings. But the progress of algebra 

 and arithmetic, and in particular the the- 

 ory of whole algebraic numbers, the exten- 

 sion soon made of it to integral poly- 

 nomials, and Kronecker's theory of moduli, 

 made possible the approach of the question 

 from a side still unexplored. 



This Hilbert did in attacking at first the 

 celebrated theorem of Gordan, according 

 to which all the invariants of a system of 

 forms can be expressed in a rational and 

 integral way as functions of a finite num- 

 ber of them. 



We could not better measure the ad- 

 vance made than by comparing the volume 

 Gordan had to devote to his demonstration 

 with the few lines with which Hilbert has 

 been satisfied. The method gained in gen- 



^ Report on the works of Hilbert by Poinearl. 

 Translated by G. B. Halsted. 



