1884.] On the Dynamics of a Rigid Body in Elliptic Space. 219 



solution of sulphate of copper were placed in the negative and 

 positive compartments respectively of the apparatus. The positive 

 electrode consisted of a platinum wire, and the negative of a weighed 

 strip of metallic copper. 







Free sulphuric acid. 



Experiment. 



Time in hours. 











Pos. Compart. 



Neg. Compart. 



I. 



n 



•0766 



nil. 



ir. 



2 



•0936 



nil. 



in. 



3 



•1868 



•0191 



IV. 



3 



1501 



•0204 



y. 



3 



•2442 



•0237 



VI. 



3 



•2546 



•0372 



In none of these experiments was there any trace of hydrogen 

 visibly escaping from the negative electrode, while, as will be seen 

 from the table, there was no free acid formed in the negative compart- 

 ment till two hours or more had elapsed. By that time some admix- 

 ture in the horizontal part of the apparatus might reasonably be 

 expected, and even in the greatest instance it is small as compared 

 with the amount of salt decomposed. 



Similar experiments were made with the sulphate of zinc, with 

 similar results, no hydrogen being evolved, and little or no sulphuric 

 acid appearing in the negative compartment. 



We conclude, therefore, that it is not possible to determine the 

 composition, or even to show the presence of a hydrated salt in 

 aqueous solution by means of this electrolytic method. 



III. " On the Dynamics of a Rigid Body in Elliptic Space." 

 By R. S. Heath, B.A., D.Sc, Fellow of Trinity College, 

 Cambridge. Communicated by A. Cayley, LL.D., Sadlerian 

 Professor of Pure Mathematics in the University of Cam- 

 bridge. Received January 4, 1884. 



(Abstract.) 



This paper is an attempt to work out the theory of the motion of a 

 rigid body under the action of any forces, with the generalised con- 

 ceptions of distance of the so-called non-Euclidean geometry. Of 

 the three kinds of non-Euclidean space, that known as elliptic space 

 has been chosen, because of the perfect duality and symmetry which 

 exist in this case. The special features of the method employed are 



