TRANSACTIONS OF SECTION A. 507 



in such medium, Jellett follows the example of MacCullagb, who had made this 

 subject one of special interest to the Dublin school. In these memoirs he draws 

 attention to a remarkable dirt'erence in the mode of regarding the molecular con- 

 stitution of the medium, a difference corresponding to what is now known as the 

 distinction between the Rari-constant and Multi-constant theories. AVe may, Jellett 

 points out, regard the action between two molecules as only conditioned by the 

 relative position of these molecules, or as dependent also on the position of the 

 neighbouring molecules. The first is termed by Jellett tlie hypothesis of indepen- 

 dent action, and this he shows to lie at the basis of Cauchy"s theory, whereas the 

 theory of Green, the English elastician, essentially involves the second hypothesis 

 which Jellett calls ' modified action.' fie established in the same papers the im- 

 portant theorem that if a Work function exists the three directions of vibration, 

 corresponding to a plane-wave, are rectangular, an<l vice versa. 



In his memoir on luextensible Surfaces various interesting questions are 

 discussed. Tie proves that in the case of a synclaslic surface if a closed curve 

 on the surface be held fixed, the entire surface will be immovable ; that on the 

 other hand on an anticlastic surface it is possible to draw a curve which may be 

 held fixed without involving the immovability of the surface, the conditions being 

 that the curve will be that formed by the successive elements of the inflexional 

 tangents. The mathematical theory of such curves had been already studied, but 

 Jellett seems to have been the first to signalise their importance in the theory of 

 deformation, and, on account of the property referred to, he proposed to call them 

 Curves of Flexure. It is interesting to remark that Maxwell was attracted by the 

 same subject of Inextensible Surfaces, and in one of his earliest papers confirms by 

 an entire!}' ditierent method several of Jellett's conclusions. 



At the close of Jellett's paper a remarkable proposition is laid down, apparently 

 for the first time, that a closed oval surface cannot be inextensibly deformed ; in 

 other words, that if such a surface be perfectly inextensible it is also perfectly- 

 rigid. I think we must admit that the proof of this striking theorem offered by 

 Jellett is by no means satisfactorj'. Subsequent attempts by others to establish 

 this proposition can hardly be said to be more successful. But the fact that it 

 can be rigorously proved true for a .sphere or more generally for any ellipsoid 

 seems to indicate that we have here to do with a real and important theorem, but 

 one which needs, as is so often the case, to have the limits of its application more 

 clearly defined. 



Many experimental physicists will know Jellett best by the beautiful and 

 delicate instrument he invented, ' The Double-plane Analyser,' an instrument which 

 he devised in order to secure the more exact determination of the rotation of the 

 plane of polarisation than could be obtained by the polariscopes hitherto in use. 

 Jellett was actuated here by the consideration that he saw in this phenomenon of 

 the rotation of the plane of polarisation a means of attacking the interesting 

 problem of chemical equilibrium. Chemical equilibrium he defines thus: 'Two 

 or more substances may be said to be in chemical equilibrium, if they can be 

 brought into chemical presence of each other (as in a solution) without the forma- 

 tion of any jiew compound or change in the amount of any of the former com- 

 pounds which ha\e thus been brought together.' In a mixed solution of sundry 

 bases and acids where all the possible salts are soluble, what are the proportions in 

 which the acids are distributed amongst the bases ? Such was Jellett's question, 

 and in aiiswering it he arrives by a remarkable train of quasi-mathematical 

 reasoning at certain laws governing this distribution, and proceeds to establish the 

 truth of these laws by observation with his new polariscope. 



He also discusses in the same papers two alternative theories which we can 

 hold of chemical combination, the ' statical ' and the ' dynamical,' and shows from 

 the consideration of the number of equations which yubsist that the 'dynamical 

 theory' is alone admissible. 



When the Association met in Belfast twenty-eight years ago Dr. Jellett 

 occupied this Chair, and at the close of his Address, in which he took for his subject 

 certain fresh applications of Mathematical Analysis to Physical Science, he touched 

 upon these yery researches in which hp was at the time ejigaged. 



