Mr. J. H. Cotterill on Elliptic Ribs. 21 



the left eye). There is general obscurity on one side; but the 

 tremor and boiling are so oppressive, that, if produced only in 

 one eye, they may nearly extinguish the corresponding vision in 

 the other. 



The duration of this ocular derangement with me is usually 

 from twenty to thirty minutes, but with one of my friends it 

 sometimes lasts much longer. In general, I feel no further in- 

 convenience from it ; but with my friends, it is followed by op- 

 pressive head-ache. 



In one instance it was remarked that the mouth of the person 

 afflicted was sensibly distorted on one side. And in one attack 

 on myself, which occurred while I was conversing with an ac- 

 quaintance in a railway- carriage, I soon became painfully sen- 

 sible that I had not the usual command of speech, that my 

 memory failed so much that I did not know what I had said or 

 had attempted to say, and that I might be talking incoherently. 



I entertain no doubt that the seat of the disease is the brain ; 

 that the disease is a species of paralysis; and that the ocular 

 affection is only a secondarv symptom. 



G. B. Airy. 



IV. On Elliptic Ribs. By James H. Cotterill, B.A., 



Scholar of St. John's College, Cambridge* . 



1. OINCE my last paper was written, I have seen a memoir 

 k3 by Professor W. Thomson (Phil. Trans. 1863), in the 

 appendix to which it is explicitly stated that the work done in 

 equilibrium of elasticity is a minimum. Had I been fortunate 

 enough to have seen this memoir earlier, I should probably have 

 been able to avoid the difficult task of discussing the general prin- 

 ciple, and have confined myself to its application to that class of 

 problems for which, as I have elsewhere said, I conceive it to be 

 peculiarly adapted. Enough has been said to enable an opinion to 

 be formed on this point, and I therefore should not have proceeded 

 further had I not, on application of the general method ex- 

 plained in a recent paper to the case of arched ribs of elliptical 

 form, obtained some results which appear to me interesting when 

 compared with Mr. Pairbairn/s experiments on elliptical boiler- 

 flues. The present paper will therefore be devoted to calculating 

 the stress on any section of an elliptical rib ; and the results 

 obtained may perhaps be of service in the theory of arches. 



In the paper referred to, it was shown that the stress on any 

 section of an arched rib may be expressed by the equations 



* Communicated by the Author. 



