RUPTURE OF THE VESSELS WHICH CONTAIN THEM. 115 



The pressures that maintain the equiUbrium between the load and strain 

 may vary incessantly from the operation of those minute vibrations that every 

 where render absolute rest impossible; nearly all the cases that are practically 

 regarded as states of rest, or uniform motion, are really examples of periodic 

 vibrations which escape the senses. Motions so small are often sufficient to 

 make the pressures pass through all degrees of intensity, and even to become 

 negative; but the practical mathematician, who only looks to ultimate results, 

 cannot take notice of this delicate and hidden machinery, and finds it conve- 

 nient to regard the load as invariable, and to estimate the strain, not by its 

 mean, but its greatest amount. These remarks will sufficiently explain the 

 necessity of the distinction which I have made between the pressure and the 

 mean pressure, or load : and I have only to add one or two farther observations, 

 in order to render the terms I have employed sufficiently clear and precise. 

 The first of these regards a species of action that occurs frequently in the 

 strains we are discussing, or rather, which forms a convenient limit to the 

 mixed strains that are met with in nature. To understand this action, let us 

 suppose a fluid of finite mass, as water or mercury, to be contained in a tube 

 of some very flexible and imponderable material ; a sudden tremor propagated 

 in the fluid would then cause, at the point where the wave passed, a pulsation 

 of very limited extent, compared with the expansive power of the tube; and 

 which would have its single advance and single regression regulated by laws 

 proper to the fluid, and little involving the inconsiderable resistance of the con- 

 duit. Such an action we shall describe as " an exterior, or interior, vibration 

 of immense momentum and infinitely little extent, compared with the motions 

 and mass of the support." 



A clear idea of this species of force will be necessary to what follows ; and 

 the only further observation for which we shall have occasion has reference, 

 not to the forces exerted, but to the nature of the structure which sustains them ; 

 and chiefly to the distinction that must be made between elastic supports and 

 those which unite with this quality a large degree of flexibility. Every ma- 

 terial, it is well known, when wrought into rods or plates sufficiently thin,, 

 loses its tendency to return to a primary, or unloaded position, and must be re- 

 garded as flexible. Flexibility itself is merely an elasticity, more or less per- 

 fect, acting according to a single axe; and flexible bodies may be allied to the 



