432 



Proceedings and List of Papers read. 



2. The ellipse with a key way cut into it of the shape of a rectangular 

 confocal hyperbola. 



3. The ellipse with a single slit cut into it. 



The most striking of the results is in reference to the reduction of 

 the torsional rigidity of the ellipse in case (3). This reduction of 

 rigidity decreases rapidly as the depth of the notch decreases. 



The rigidity, which is reduced by as much as 23 per cent, when the 

 depth of the key way is as great as 0*6 (semi-major axis), falls to about 

 1 per cent, when this depth is 042 (semi-major axis). 



Possibly this may throw some light on the fact that the effect of 

 cutting such slits into the material does not always give in practice 

 the reduction in the torsional rigidity which should have been expected 

 from Saint- Venant's results for the circle. Clearly the depth of the 

 keyway is a factor of the very first importance, and keyways of mode- 

 rate depth will produce a comparatively small effect on the torsional 

 rigidity. 



It is also shown that the effect of cutting two equal and opposite 

 slits is practically equal, in the two cases which I have calculated 

 (namely a = tt/6 and ot = tt/2), to twice the effect of a single slit. 



It seems, therefore, that the study of these sections brings to light 

 several interesting facts in the theory of elasticity, and will well repay 

 the trouble involved in dealing with the long and somewhat tedious 

 algebra and arithmetic which lead to these results. 



November 16, 1899. 



The LOED LISTEE, F.E.C.S., D.C.L., President, in the Chair. 



Professor W. F. Barrett and Mr. J. S. Gamble were admitted into 

 the Society. 



A List of the Presents received was laid on the table, and thanks 

 ordered for them. 



In pursuance of the Statutes, notice of the ensuing Anniversary 

 Meeting was given from the Chair. 



Professor Meldola, Professor Perry, and Dr. E. H. Scott were by 

 ballot elected Auditors of the Treasurer's accounts on the part of the 

 Society. 



The following Papers published during the recess, in full or in 

 abstract, in accordance with the Standing Orders of Council, were read 

 in title : — 



