PRIZE QUESTIONS. 



PEIZE QUESTIONS PKOPOSED IN 1805 BY THE ROYAL DANISH SOCIETY 



OF SCIENCES. 



MdtJiematical class. — The theory of rectilinear surfaces has been long since 

 carried to the height of perfection and elegance, so that not only has the full 

 and complete distribution of surfaces of this kind into species been divulged, but 

 for each class also, if the partial differential equation, by means of which classes 

 are distinguishable among themselves, be supplied, the geometric character of 

 the several classes may be determined. On the other hand, the theor}^ of those 

 surfaces which are generated by a movable circle, and which are hence called 

 ''circular surfaces," has not been so thoroixghly considered as is desirable ; for, 

 although certain surfaces of this kind have been adequately analyzed, and all 

 are readily susceptible of distribution into species and classes, yet the general 

 ti'eatment of this branch of the subject has been hitherto neglected. Hence the 

 Royal Danish Society of Sciences offers its gold medal, of the value of fifty 

 Danish ducats, for a satisfactory discussion of the following theme: 



" The analytical investigation of cii'cular surfixces, with a view to the distri- 

 bution of all such surfaces into proper species, each of which species again may 

 be distinctly defined by means of its own partial differential equation." 



Physical class. — It is proposed accurately to deteimine by actual experiments 

 what time is required in order that the blood, greatly diminished and diluted 

 through phlebotomy or arteriotomy, may be restored, both as to the whole 

 quantity and the quantity of red corpuscles, to its normal condition in the 

 animal. With this view a series of experiments on some species of mammalia, 

 nourished Vv'ith food of a certain quantity and quality, should be instituted ; the 

 alterations in the weight of the whole body should be noted, as well as the 

 quantities of urea daily s(xreted. 



In order to determine the quantity of blood which, remaining in the animal 

 after the effusion, cannot be directly measured, it will be competent to apply the 

 follo\ving method : The parts, after the spontaneous effusion of blood is ex- 

 hausted, are to be dissected, macerated, and washed in water to complete dis- 

 coloration, by which means the blood contained in the colored water may be 

 determined by using as a means of comparison a portion of the blood which 

 flowed at the beginning of the experiment, agitated Avith a certain quantity of 

 water to a corresponding degree of coloration with the former. For comparing 

 the red corpuscles also the different relative determinations may be employed 

 which result from a comparison of the blood agitated with the serum : 1, with 

 reference to the quantities of solid parts ; 2, the quantities of albumen ; 3, the 

 specific weights; and 4, the determination which is obtained from a comparison 

 of the quantities of blood necessary to color a certain quantity of water to a 

 certain degree. 



The prize will be the gold medal of the society, with the addition of one 

 hundred hnperiales. 



Historical class. — The questions proposed for the preceding year [Je con- 

 ventu UrncJioved) are continued for solution till the next. 



Classcniuii bequest. — As it is known that several metals which are deposited 

 in the electrical way possess peculiar properties which are of no little im- 

 portance in the technical arts, the society offers a premium of one hundred 



