116 Royal Irish Academy. 



motion of the body is precisely the same as if it were rigidly attached 

 to the nut of a screw (in the ordinary sense of the word), which had 

 an appropriate position in space, and an appropriate number of threads 

 to the inch. Hence, it may be stated that the canonical form to which 

 all the forces acting on a rigid body can be reduced is a wrench on a 

 screw. By such conception it is shown by Dr. Ball the solution of 

 any problem in the dynamics of a rigid body may be presented. The 

 complete solution of such a problem must provide at each epoch a 

 screw by a twist about which, of an amplitude also to be specified, the 

 body can be brought from a standard position to the position occupied 

 at the epoch in question. I do not think it necessary, on this occa- 

 sion, to enter further into the details as to the methods employed, and 

 the results obtained by Dr. Ball in these researches ; suffice it to 

 observe, as to their power and generality, that, limited only by the 

 condition that the body, while the object of examination, remains in or 

 indefinitely adjacent to its original position, the restricted inquiry still 

 includes the complete theory of equilibrium, of impulsive forces, and 

 of small oscillations of rigid bodies. 



It would not, however, sufficiently indicate the services rendered 

 to Science by Dr. Ball were I to omit to state that, since the transfer 

 of his labours from the Eoyal College of Science to the University 

 Observatory at Dunsink, he has zealously devoted himself to those 

 astronomical researches for which a remarkable combination of mathe- 

 matical and mechanical ability have so highly qualified him. Already 

 he has laid before this Academy several memoirs embodying valuable 

 observatory work, and I understand that researches now in progress, 

 especially as regards the important subject of parallax, promise to 

 afford results which will redound to the credit of the University and 

 of this Academy, 



The Peesident then delivered the Medal to Dn. Ball, and pro- 

 ceeded : — 



The history of the gradual development of our knowledge of the 

 lower forms of animal and vegetable life presents a subject of great 

 and popular interest ; but on this occasion I feel it my duty to limit 

 myself to such observations as are requisite to explain to the Members 

 of the Academy the special grounds on which the Council decided to 

 signalise the services rendered by Mr. Archer to this department of 

 Science by the award of a Cunningham Medal. It is only since the 



