ON THE THEORY OF HYDRAULICS. 215 



occupy a small part only of the vessel, and are placed near to each other, 

 ' the retardation will be much less considerable. Cases of this kind occur 

 very frequently in the passage of water through the pipes and valves of 

 pumps, and it is, therefore, of consequence to avoid all unnecessary expan- 

 sions, as well as contractions, in pipes and in canals, since there is always 

 a useless expense of force in restoring the velocity which is lost in the 

 wider parts. 



When a siphon or bent tube is filled with a fluid, and its extremities are 

 immersed in fluids of the same kind contained in different vessels, if both 

 their surfaces are on the same level, the whole remains at rest ; but if 

 otherwise, the longer column in the siphon preponderates, and the pressure 

 of the atmosphere forces up the fluid from the higher vessel, until the equi- 

 librium is restored ; provided, however, that this pressure be sufficiently 

 powerful : for if the height of the tube were more than 34 feet for water, 

 or than 30 inches for mercury, the pressure of the atmosphere would be 

 incapable of forcing up the fluid to its highest part, and this part remaining 

 empty, the fluid could no longer continue to run. (Plate XX. Fig. 258.) 



If the lower vessel be allowed to empty itself, the siphon will continue 

 running as long as it is supplied from the upper, with a velocity nearly 

 corresponding to the height of that portion of the fluid in the longer leg, 

 which is not counterbalanced by the fluid in the shorter : that is, to the 

 height of the surface of the upper vessel above that of the lower one, or 

 above the end of the siphon, when it is no longer immersed ; for the height 

 of the pipe is in all cases to be considered as constituting a part of that 

 height which produces the pressure. Thus the discharge of a pipe, descend- 

 ing from the side or bottom of a vessel, is nearly the same as from a similar 

 horizontal pipe, inserted into a reservoir of the whole height of the descend- 

 ing pipe and of the fluid above it ; and this is true even when the depth of 

 the vessel is inconsiderable in comparison with the length of the pipe, if its 

 capacity is sufficient to keep the pipe running full. It appears at first sight 

 extremely paradoxical, that the whole water discharged, each particle of 

 which is subjected to the action of gravitation in a pipe 16 feet long, for 

 half a second only, should acquire the velocity of 32 feet in a second, which 

 would require, in common circumstances, the action of the same force of 

 gravitation for a whole second, and this fact may be considered as favour- 

 able to the opinion of those who wish to estimate the magnitude of a force, 

 rather by the space through which it is continued, than by the time during 

 which it acts ; but if we attend to the nature of hydrostatical pressure, we 

 shall find that the effect of the column on the atmosphere is such as to pro- 

 duce, or to develope, a portion of accelerating force which is actually 

 greater than the weight of the particles immediately concerned. If a doubt 

 could be entertained of the truth of this theory, it might be easily removed 

 by recurring to the general law of ascending force, since it follows from 

 that law, that each particle, which descends in any manner through the 

 space of 16 feet, must acquire, either for itself or for some other particles, 

 af power of ascending to the same height ; and on the other hand, the event 

 of the experiment confirms the general law. For if we fix a shallow funnel 

 on a vertical pipe, and pour water into it, so as to keep it constantly full, 



