PRIZE QUESTIONS. 



QUESTIONS PROPOSED FOR COMPETITION BY THE ROYAL DANISH SOCI- 

 ETY OF SCIENCES, 1867. 



Class of Natural History asd Mathematics. — Question of natural 

 history. — Althougli the lichens have been the object, hi late years, of very pro- 

 found researches, (especially on the part of MM. Tulasne, Nylander, Th. Fries, 

 and Speerschneider,) there are still many points of great interest in their life and 

 development, respecting" which our knowledge remains very incom])lete. 



Although M. Tulasne had demonstrated in 1S52 that all the lichens arc fur- 

 nished with a special organ, (spermagorie with the spermatite,) and his researches 

 render it more than probable that this organ nmst serve for fecundation and cor- 

 respond to the male reproductive organ, tliere has, thus far, been no observation 

 made, nor experiment, which might establish conclusively that the organ in 

 question fulfils that function. AVe have, moreover, recent obsen'ations (of 

 MM. Hicks and Bary) which prove that there are certain species of coliraacese 

 which stand in generic relation to plants which have been heretofore considered 

 as types of algte, (Nostochacea, Chroococcacea?;) but the true nature of that 

 relation is still completely unknown. It results, lastly, from recent researches, 

 that there are reproductive organs (apothecite) without a. thallus, which apjjear 

 to subsist as parasites on the thallus of other species. They have been classed 

 as distinct species or genera in a family apart, (the pseudolichcns,) or considered 

 as champignons or special organs of the plants on which they live. The trae 

 nature of these organisms or organs is therefore still very enigmatical. The 

 society proposes its gold medal as a recompense for the solution, in a satisfactory 

 manner, of one or more of these three points. 



Question of mathematics. — The potential may be reduced to a more general 



form, A\»hen the variable,- //, in the function 2 — , is considered as a function of 



r 



t — — ,t beinff a new variable and a a constant. As the potential thus o'eu- 



eralized may receive applications much more r ^tended, the society desires that, 

 besides a recital of the principal propositions heretofore known in relation to this 

 function, an investigation of the same function should be submitted to it under 

 the form above indicated. 



Class of Histoey and Philosophy. — Question of history and pliiJohgii. — 

 How have the classical Latin authors been appreciated and how far have they 

 been made use of by the grammai'ians of tlic time of the empire and 1)y tlieir 

 schools ? What influence was exerted by this appreciation and this use on the 

 preservation or disappearance of literature, and how mucli of the literature of 

 antiquity may be estimated to have remained in circulation or to have been 

 accessible, about 500 years after Jesus Christ f 



The answers to these questions may be written in Latin, French, English, 

 German, Swedish, or Danish. The memoirs should not bear the name of the 

 author, but a motto, and be accompanied by a sealed note distinguished by the 

 same motto and enclosing the name, profession, and address, of the author. The 

 members of the society who reside in Denmark will take no ])art in the compe- 

 tition. The recompense accorded for a satisfactory reply to one of the projuised 

 questions, will be the gold medal of the society, of the value of 50 Danish ducats. • 

 The replies must be addressed, before the end of October, 1868, to the secretary 

 of the society, Professor J. Japetus Sm. Steenstrup. 



