168 Proceedings of the Royal Irish Academy. 



I have spoken of the physical sciences which have been actually brought 

 into the domain of ]\iathematies ; but as others become more perfect, they also 

 will reach this goal. Chemistry, on its physical side, is already highly 

 mathematical. ^Modern researches have abundantly shown that the space- 

 arrangement of the atoms, constituting a molecule, is of the utmost impor- 

 tance ; and the recent investigations of Professor J. J. Thomson and others 

 lead to the conclusion that the simplest chemical atom is in itself a most 

 complicated dynamical system. Such researches as those of Professor 

 J. J. Thomson could not have Ijeen carried on except by one who is a 

 most accomplished mathematician as well as an original and accurate 

 experimentalist. 



Xot a few have been the instances in which ^Mathematics has anticipated 

 the results of observation. I need scarcelj' remind the Academy of a remark- 

 able instance of this kind in which two of tlie most illustrious of its former 

 members were concerned — conical refraction foretold by Hamilton, and 

 realized by Lloyd. A discovery more interesting to the general public is 

 wireless telegraphy, the possibility of which was indicated by the equations 

 of Maxwell before it was shown by the experiments of Hertz. 



From all that we have been considering we cannot, I think, avoid being 

 convinced that Mathematics is a most essential part of Physical Science, and 

 that no scheme, national or otherwise, for the development of education in 

 science can be complete or satisfactory without fully recognizmg the value and 

 importance of mathematical training, and the necessity of securing, so far as 

 is possible, progress in ^Mathematics as well as in purely experimental 

 kuowledse. 



