1819.] Royal Danish Society. 55 



becomes a very secure means of preventing the fraudulent waste 

 of valuable liquors. The Society voted its silver metal. 



Mr. Ai tiger's Self-Adjusting Crane. — This is a contrivance 

 tending to equalize the power applied to work a crane according 

 to the weight to be raised by it. The silver medal was awarded 

 to Mr. Ainger. 



ROYAL DANISH SOCIETY OF SCIENCES. 



View of the Transactions of the Royal Danish Society of Sciences, 



and of the Works of its Members, from May 31, 1817, to 



Mai/ 31, 1818. By H. C. (Ersted, Professor, and Knight of 



the'Cross of Dannebray. 



During last year, the following gentlemen were elected foreign 

 members : 



For the Mathematical Class.— Mr. Wiebeking, of Munich, 

 Privy-Councillor and Knight ; Mr. Flanti, of Naples, Professor. 



For the Physical Class.— Mr. Gieseke, of Dublin, Commander 

 of Dannebray ; Mr. Jameson, of Edinburgh, Professor. 



When Kepler had discovered the law for the motion of the 

 celestial bodies, viz. that the times in which given arches are run 

 through are proportional to the planes inclosed between the said 

 arches and the rays drawn to the centre of the powers, the pro- 

 blem of dividing a circle from a given point of the diameters in a 

 given proportion naturally occurred to him ; for if this problem 

 could be resolved with respect to the circle, the same must be 

 the case with the ellipsis. 



He proposed this question to the mathematicians, adding r 

 that he did not believe it could be resolved in a direct manner ; 

 and whoever could show him the contrary should be his magnus 

 Apollo. The problem afterwards bore his name, and has 

 since been considered by many mathematicians of the first rank. 

 The discovery and progress of the analysis furnished the mathe- 

 maticians with means enabling them to approximate more and 

 more to an accurate solution of this celebrated problem. 



Jeaurat had already set out the true anomaly by the middle 

 anomaly unto the sixth power ; Cagnoli unto the ninth ; but as 

 they merely gave results without any general formulas by which 

 the explanation of the results thus found out might be continued 

 at pleasure, no great progress was made as yet towards the real 

 object. 



It was reserved for the celebrated astronomer Schubert to 

 remedy this defect. By explaining the terms for the functions 

 of the eccentric anomaly, and by conveniently adapting it to the 

 terms of the true one, this great analyst succeeded in giving a 

 direct solution of Kepler's problem. In " Bode's Astrononuches 

 Jahrbuch," for the year 1820, this solution is found, together 

 with the numeral explanation for the true anomaly, and the radius 

 victor, unto the 13th power of the eccentricity. 



About the same time with Schubert, Professor Digin resolved 

 t > uudi ilake this explanation unto the 10th power of the eccen- 



