<2f84 LECTURE XXIII. 



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 cor- 

 responding 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 si- 

 phon, 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, descending 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 descending 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 gravi- 

 tation in a pipe 16 feet long, for half a second only, should acquire the velo- 

 city of 32 feet in a second, which woukl require, in common circumstance.% 

 the action of the same force of gravitation for a whole second, and this fact 

 may be considered as favourable to the opinion of those, who wish to esti- 

 mate the magnitude of a force, rather by the space through which it is con- 

 tinued, 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 produce, or to develope, a portion of accelerating force 

 M'hich is actually greater than the weight of the particles immediately con- 

 cerned. 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, niust acquire, either for itself or for some other 

 particles, a 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, while the pipe discharges itself into a reservoir, out of which the water runs 

 through a second pipe, placed horizontally, of exactly the same dimensions 

 with the first, the height, at which the water in the reservoir becomes sta- 

 tionary, will be very nearly equal to the height of the funnel above its sur- 

 face, so that the same height produces the same velocity in both cases. 

 ^Plate XX. Fig. 259-) 



