116 ON tHE POWER OF FLUIDS IN MOTION TO PRODUCfi 



elastic by regarding them as secured at each end and drawn into an initial po- 

 sition by the action of an evanescent stretching force. 



From which observations it is evident that if we consider the several cases 

 of perfect and imperfect elasticity in the directions of all the axes, and of 

 perfectly flexible bodies, drawn into an initial state by the action of an ini- 

 tial and evanescent force, we shall obtain the limits of the results that can prac- 

 tically happen. 



The several conclusions to which I have arrived for these cases may be 

 stated as follows : — 



1. It is convenient to distinguish between accumulative and instantaneous 

 loads, or between those which are gradually increased until the deflection due 

 to the ultimate load is obtained, and those which commence in their full effi- 

 cacy from the initial position of the support. 



2. Within the limits of perfect elasticity, instantaneous pressure produces 

 twice the effect of that which is accumulative, whether the result be to pro- 

 duce deflection or fracture. 



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

 ble in the other, instantaneous action at right angles to the axis of elasticity 

 produces a deflection which is to that of accumulative action as \J~4: to 1, whilst 

 the tendencies of fracture are as 4 to 1. But, should any case occur where the 

 law of elasticity follows an extremely 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 depart from 

 the law of perfect elasticity as we approach the limit of fracture, the ratio of 

 the effects of instantaneous and accumulative action will vary with the nature 

 of the substances, never being less, for elastic bodies, than 2 to 1, nor, for flexi- 

 ble, than 4 to 1, and more usually approaching 3 or 4 to 1 for the former case, 

 and 5 or 6 to 1 for the latter. 



5. Let a vase or conduit be acted upon by a load which is alone insufficient 

 to break it; and let this load be partly balanced by a small exterior force. Should 

 the great interior force suddenly cease, the small exterior action may crush the 

 vase or conduit inward, its energy in such case being the sum of the interior 

 and exterior forces. 



