506 REPORT— 1902. 



out the real significance of MacCullagh's function V ; that it coiTesponds to a stress- 

 strain system, but one of a very novel type ; one in which the stresses depend 

 entirely on the rotational displacements of the molecules, and are otherwise 

 absolutely unaffected by the ordinary deformation-strains. He further shows that 

 the difficulty under which MacCullagh's theory laboured, that it did not provide 

 for the rotatory equilibrium of the element, could be removed if we allowed our- 

 selves to assume the existence of a hidden torque acting on each element. 



As I understand tlie advocates of this theory, they maintain that an important 

 step has been made, even though in the present state of our knowledge we may 

 not be able to account for tlie existence of this hidden torque. They point out, 

 bowever, that such a torque is at least not inconceivable, whether its explanation 

 be sought in concealed kinetic phenomena, as in Lord Kelvin's material gyrostati- 

 cally constituted medium, or in quasi-magnetic forces supposed to reside in the 

 ethereal elements. 



Should this theory of a rotationally elastic ether obtain final acceptance, it 

 will of course be a matter of congratulation to MacCullagh's countrymen to find 

 that his labours, in this, perhaps the most important field of his researches, have 

 not been thrown away ; that they represent no mere play of elegant mathematical 

 analysis, but a real step in the progress of physical science. 



A few years after MacCullagh, two other well-known men, whose names for 

 half a century were associated with the Mathematical School in Dublin, were 

 elected Fellows — Andrew Searle Hart, afterwards Sir Andrew Hart, and Charles 

 Graves, subsequently Bishop of Limerick. They won their Fellowships in two 

 successive years, and both lived to an advanced age. 



Hart had a great reputation as a geometer. His examination papers were 

 specially noted for the number of original problems they contained. As specimens 

 of his work we may instance the following. Extending Feuerbach's theorem for 

 the nine-point circle, Hart showed that the circles which toucli three given circles 

 can be distributed into sets of four all touched by the same circle. He also showed 

 that Poncelet's beautiful porism for coaxal circles in piano held for the surface of an 

 ellipsoid, if we replace the rectilineal polygons by geodetic polygons and the coaxal 

 circles by lines of curvature. 



Ci raves became Professor of Mathematics on MacCullagh's resigning the Chair in 

 1843. He was largely influenced by the writings of Chasles, of whose two memoirs 

 on Cones and Spherical Conies he published a translation. In this were incor- 

 porated valuable original additions of his own, amongst others the remarkable theorem 

 that if two spherical ellipses are confocal the sum of the tangents drawn to the 

 inner from any point of the outer exceeds the intercepted arc between the points of 

 contact by a constant length, a theorem which of course includes the corresponding- 

 proposition for confocals in piano. Graves was one of the first to apply the method 

 of the Separation of Symbols to Hifterential Equations, and gave an elegant de- 

 monstration by this method of Jacobi's celebrated test for distinguishing between 

 maxima and minima in the Calculus of Variations. 



On the death of MacCullagh it was determined to strengthen the Natural 

 Philosophy department by the establishment of a second Professorship in that 

 subject, and.Tellett, one of the ablest of MacCullagh's pupils, was appointed to the 

 new Chair. 



His first published work "was his ' Calculus of Variations,' which at the time 

 it was written constituted the onlj^ systematic English treatise on the subject. It 

 is marked by that peculiar acuteness and power of fastening on essential points, 

 whether for criticism or exposition, which was the author's leading characteristic. 

 Apart from the excellent account he gives of the researches of Continental mathe- 

 maticians, I vvould notice especially his most interesting chapters on the conditions 

 of integrabilily and many valuable geometrical theorems on surfaces hence 

 resulting. In discussing his more properly original work we may arrange it in 

 three divisions : 1st, his papers on Elasticity ; 2nd, that on the properties of 

 Inextensible Surfaces; 3rd, those on the application of polarised light to the new 

 subject of Chemical Equilibrium. 



Jn tfvkirig \w the ppblem of an elastic mediu^p and tl^e propagation of wtvY^^ 



