CIRCULAR RELATIVE TO A MATHEMATICAL PRIZE. 



Prof. Spencer F. Baled, 



Sir : I beg to transmit to you the following communication, that will 

 shortly a})pear in the journal Acta Mathemaiica, of which 1 am chief 

 editor: 



"His Majesty Oscar II wishing to give a fresh proof of his interest 

 in the advancement of mathematical science, an interest already mani- 

 fested by his graciously encouraging the publication of the journal 

 Acta Mathematica, which is placed under his august protection, has 

 resolved to award a prize, on the 21st of January, 1889, the sixtieth 

 anniversary of his birthday, to an important discovery in the field of 

 higher mathematical analysis. This prize will consist in a gold medal 

 of the eighteenth size bearing His Majesty's image and having a value 

 of a thousand francs, together with a sum of two thousand five hun- 

 dred crowns (1 crown equal to about 1 franc 40 centimes). 



"His Majesty has been pleased to intrust the task of carrying out 

 His intentions to a commission of three members, Mr. Carl Weierstrass 

 in Berlin, Mr. Charles Hermite in Paris, and the chief editor of this 

 journal, Mr. Gosta Mittag Leffler in Stockholm. The commissioners 

 having presented a report of their work to His Majjesty, he has gra- 

 ciously signified his approval of the following final propositions of theirs: 



"Having taken into consideration the questions which from different 

 points of view equally engage the attention of analysts, and the solu- 

 tion of which would be of the greatest interest for the progress of 

 science, the commission respectfully proposes to His Majesty to award 

 the prize to the best memoir on one of the following subjects: 



"1. A system being given of a number whatever of particles attract- 

 ing one another mutually according to Newton's law, it is proposed, on 

 the assumption that there never takes place an impact of two particles, 

 to expand the co-ordinates of each particle in a series proceeding accord 

 ing to some known functions of time and converging uniformly for any 

 space of time. 



"It seems that this i)roblem, the solution of which will considerably 

 enlarge our knowledge with regard to the system of the universe, might 

 be solved by means of the analytical resources at our present disposi- 

 tion ; this may at least be fairly supposed, because shortly before his 

 death Lejeune-Dirichlet communicated to a friend of his, a mathema- 

 tician, that he had discovered a method of integrating the diflerontial 

 equations of mechanics, and that he had succeeded, by applying this 

 method, to demonstrate the stability of our planetary system in an ab- 



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