( 825 ) 



a point in common with 



an Sp s . 



An Sp g is determined by 



nine points. 



•oii!;iins a dynamoid reciprocal to 



a given rotoid. 



p spaces Sp a cut each 

 other according to Sp$— p . 



A rotoid can always be deter- 

 mined lying reciprocal with re- 

 spect to nine dynamoids. 



The dynamoids reciprocal to 

 the movements of a body with 

 j) degrees of treedon i form a 

 (9-/?)-fold infinite pencil. 

 Etc. etc. 



We shall now apply the above to the problem: "To decompose a 

 dynam according to ten given dynamoids", this problem being a tran- 

 scription of the following: 



"To apply to ten given points a distribution of mass so that the 

 centre of gravity finds its place in a given point." 

 We again put side by side the results. 

 To be defined successively : 



a. An Sp s through nine of the The rotoid reciprocal to nine 

 given points. of the given dynamoids. 



h. The right line through the The pencil of dynamoids through 

 remaining point and the centre of the remaining dynamoid and the 

 gravity. bearer of the given dynam. 



c. The point of intersection of The dynamoid on this pencil 

 this right line with the Sp e found reciprocal with respect to the 

 in a. rotoid found in a. 



d. The decomposition of the mass The decomposition of the given 

 in the centre of gravity according dynam according to the dyna- 

 to this point of intersection and moid found in c and the 10 th 

 the 10 th point named in b, which is dynamoid named in b, which is 

 possible, these three points being possible, these three dynamoids 

 collinear ; gives at once the mass belonging to one pencil, gives 

 to be applied in the last named at once the intensity of the 

 point. dynam on the last mentioned 



dynamoid. 

 The other must necessarily be- The other must necessarily bear 

 come the centre of gravity of the resultant of the dynam to 

 the remaining nine points. be applied to the remaining nine 



dynamoids. 



e. These treatments to be repeated These treatments to be repeated 

 for the determination of mass in for the determination of intensity 

 the other points. on the other dynamoids. 



Zalt-Boiumel, March 28, 1907. 



