PRIZE QUESTIONS. 



QUESTIONS PROPOSED FOR COMPETITION BY THE ROYAL DANISH SOCI 

 ETY OF SCIENCES, 1867. 



Class of Natural History and Mathematics. — Question of natural 

 Mstonj. — Although the lichens have been the object, in late years, of very pro- 

 found researches, (especiallj' 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 incomplete. 



Although M. Tulasne had demonstrated in 1852 that all the lichens arc fur- 

 nished witn a special organ, (speiTnagorie with the spennati^e,) and his researches 

 render it more than probable that this organ nmst sei've for fecundation and cor- 

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

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

 question fulfils that fvmction. We have, moreover, recent observations (of 

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

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

 as types of algse, (Nostochacese, Chroococcacese;) but the true nature of that 

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

 that there are reproductive organs (apothecipe) without a thallus, which appear 

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

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

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

 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, when the variable, //, in the function 2"— ,is considered as a function of 



t — — , t being a new variable and a a constant. As the potential thus gen- 

 eralized may receive applications much more f ^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 History and Philosophy. — Question of history and philology. — 

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

 been made use of by the grammarians of the time of the empire and by their 

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

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

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

 accessible, about 500 years after Jesus Christ? 



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 part in the compe- 

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

 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. 



