TRANSACTIONS OF SECTION A. .")09 



them to Fresnel's wave-surface, and showed that the two sheets of the surface can 

 be expretised in the simple forms 



\" + v" - a- + b- — c' and X- + fi- = «- + b- — c-. 



By following the same method he succeeded also in adding au interesting new 

 triple system of orthogonal surftices to those already known. 



Richard Townsend was another of the J^ellows of Trinity of MacCuUagh's 

 school. He was known to us in College in my day as the great expositor of the 

 new geometry of Anharmonics and Involution. He wrote many valuable original 

 papers, but it was as a lecturer he was most remarkable. I never met a teacher 

 80 enthusiastic nor one who seemed to enjoy teaching more thoroughly. 



He inspired his pupils with much of his own ardour, and it is greatly owing to 

 Townsend's influence that the old name Trinity had for the study of Geometry was 

 so well kept up in his day. 



He published in the latter part of his life an extensive treatise on Modern 

 Geometry, which did good service in presenting the subject in the light of an 

 organised system and not as a collection of isolated problems. 



In this connection 1 must not omit to mention one of our most original Irish 

 geometers of recent days, l)r. John Casey. Where Casey learnt his Mathematics 

 is indeed a marvel. Up to middle life he was engaged in the engrossing labour of 

 a schoolmaster in Kilkenny under the National Board of Education. It was not till 

 he was nearly forty that by th(! advice of Townsend, to whom he used to send up 

 some of his ingenious geometrical solutions, he moved up to Dublin and entered 

 Trinity College. Cf his original papers his best known are those on Bicircular 

 Quartics and Cyclides. 



In elementary Geometry we owe to him a very elegant extension of Ptolemy's 

 famous theorem that for four points, A B C D, on a circle AC . BD = AB . CD 

 + AD . BC. Casey shows that the same equation is true if we replace the four 

 points by four circles touching a common circle and the lines joining the points by 

 the common tangents to the circles. He acquired so high a repute both as a 

 teacher and as a writer that he was oifered and accepted the post of Professor ot 

 Mathematics in the Catholic University 



It is not yet two years since George FitzGrerald was taken from us. The many 

 loving tributes to his memory which appeared in the scientific journals after his 

 death reveal to us how deep and widespread his loss was felt to be, but it is in 

 Ireland this loss is most serious. As long as he lived and worked, our country 

 could claim to own one of the foremost members of that select band who are 

 endeavouring to wrest from Nature her inmost secrets. 



You know how sedulous an attendant he was of the Meetings of this Section, 

 and Trinity College never sent you a representative of whom she had more reason 

 to be proud, for he has done more than any of her sons for many years to maintain 

 the reputation of her scientific school. This he has brought about, not by his 

 writings only, able and original as these were, but also by the encouragement and 

 stimulus he gave the younger men he gathered round him, and the self-forgetful 

 readiness with which he gave all the help he could to those who in any measure 

 shared his own genuine love for science. 



You will all rejoice that we are now in possession of a volume containing a 

 complete collection of FitzGerald's scientific papers. I am sure he himself could 

 not have wished for a better chronicler of his life and labour than his intimate 

 friend Dr. Larmor, more especially as Dr. Larmor's own far-reaching speculations 

 on the great mystery of the Ether qualify him in a very peculiar manner to 

 appreciate the Avork of his fellow-physicist. The admirable analysis of that Avork 

 in the opening pages of this volume renders any further account of it on my part 

 completely imnecessary. 



A few months before FitzGerald's death there passed away one of his most 

 distinguished pupils, Thomas Preston. Though cut off so young he had already 

 done much work, and of a quality which raised high expectations of his future. 

 His treatises on Light and on Heat are to be noted, not merely for the excellent 

 account they give of the recent additions to the subjects treated, but for the 



