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produce Rupture of the Vessels, which contain them, and on 

 the Distinction between Accumulative and Instantaneous Pres- 

 sures; by Charles Bonny castle, Professor of Mathematics in 

 the University of Virginia," reported in favour of its publica- 

 tion in the Transactions of the Society, which was ordered ac- 

 cordingly. 



Mr. Bonnycastle's investigation was suggested by a paper read by 

 Dr. Hare, and printed in the Transactions of the Society, entitled 

 " On the Collapse of a Reservoir, whilst apparently subject within to 

 great Pressure from a Head of Water." Dr. Hare pointed out the 

 circumstances attendant upon this curious occurrence, and showed 

 how the vessel might have been momentarily relieved from the pres- 

 sure of the water within, so as to make that of the surrounding air 

 efficient in producing the collapse. The principal object of Mr. Bon- 

 nycastle's paper is to investigate the precise nature and degree of the 

 forces brought into action in this and similar cases. 



The results at which Mr. Bonnycastle arrived, are stated by him 

 as follows : — 



1. It is convenient to distinguish between accumulative and in- 

 stantaneous loads, or between those which are gradually increased 

 until the deflection due to the ultimate load is obtained, and those 

 which commence in full efficacy from the initial position of the sup- 

 port. 



2. Within the limits of perfect elasticity, instantaneous pressure 

 produces twice the effect of that which is accumulative, whether the 

 result be to produce deflection or fracture. 



3. In regard to supports perfectly elastic in one direction, and per- 

 fectly flexible in the other, instantaneous action, at right angles to the 

 axis of elasticity, produces a deflection which is to that of accumula- 

 tive action as >/4 to 1, whilst the tendencies to fracture are as 4 to 1. 

 But should any case, occur when the law of elasticity follows an ex- 

 tremely high power of the deflection, then the singular result will 

 follow, that the deflections are the same, whether the force be exerted 

 from the initial state or the state of load, but that the tendency to 

 fracture will be immensely greater in the former case, than in the 

 latter. 



4. In producing the fracture of natural substances, which all de- 

 part from the law of perfect elasticity as we approach the limit of 



