490 



SCIENCE 



[N. S. Vol. LI. No. 1324 



upward at A is greater than that at D. The 

 liquid must therefore flow from A to D. 



It is evident from this discussion that a 

 siphon can not operate if AB is greater than 

 the barometric height for the liquid in ques- 

 tion. 



II. If we consider the pressures acting at 

 we will find that the pressure toward D is the 

 atmospheric pressure minus the pressure rep- 

 resented by a colirmn of liquid AB, while the 

 pressure toward A is the pressure of the at- 

 mosphere less the pressure represented by the 

 column of liquid DB. The resultant pressure 

 is therefore toward D, determining a flow in 

 that direction. 



It is evident from this discussion that a 

 siphon can not operate if AB is greater than 

 the barometric height for the liquid in ques- 

 tion. 



III. The end D being closed, and the siphon 

 filled, the pressure at D will exceed atmos- 

 pheric pressure by an amount represented by 

 the column of liquid DA, since all points at 

 the level of A are now at atmospheric 

 pressure. Ui)on opening D this excess pres- 

 sure causes the flow, and the atmospheric 

 pressure at A keeps the tube filled. 



It is evident from this discussion that a 

 siphon can not operate if AB is greater than 

 the barometric height for the liquid in ques- 

 tion. 



The refrain with which each treatment con- 

 cludes is a noteworthy element of uniformity, 

 to be considered below. Special features of 

 criticism are as follows. 



I. Pressure at a iwint within a body of 

 fluid is not upward or downward, to left or 

 to right, north, east, south or west. It is 

 without direction. 



The pressure at A, whether inside the tube 

 or outside, and whether the siphon be flowing 

 or not flowing, is never greater than the 

 pressure at D. 



The flow of a liquid between two points 

 does not necessarily take place from high to 

 low pressure. See the discussion below, based 

 on Bernoulli's principle, of this particular 

 case. 



II. As above stated, pressure in a body of 



fluid is without direction. The pressure at 

 is neither toward A nor toward D, and cer- 

 tainly does not have unequal components in 

 these two directions. 



m. Except the concluding refrain, this 

 treatment correctly represents the facts, and 

 shows at least why the siphon ought to start 

 flowing. Curiously enough, Bernoulli's prin- 

 ciple and the law of diminution of potential 

 energy having been known for a long time, 

 little attempt is made to show what happens, 

 and why, when the siphon is actually work- 

 ing, the discussions being chiefly hydrostatic. 



If we assume that the siphon gives an ex- 

 ample of steady frictionless irrotational flow 

 of an incompressible fluid, an assumption 

 probably justifled as a flrst approximation, we 

 can apply Bernoulli's principle. 



Then, for any given stream tube 



p + hdg + 4dti^ = constant, 



in which p represents fluid pressure, h height 

 above any assigned zero level, g acceleration 

 of gravity, d density of the fluid, and v the 

 speed with which it is moving. 



Considering now the siphon when in steady 

 flow, and assuming the reservoir indefinitely 

 large, we find that the stream lines begin at 

 the free surface, widely spread, the liquid 

 flowing here at a speed approaching zero; 

 converge into the orifice of the short limb, 

 with much increased speed; traverse the en- 

 tire length of the tube, supposed of uniform 

 cross section, without change in speed, and 

 that the stream emerges finally at this speed. 



At the surface A outside the tube the 

 pressure is atmospheric. Inside the tube it 

 is less than atmospheric, for the stream has 

 gained speed at the same level. As the 

 stream ascends, at uniform speed, the pres- 

 sure diminishes continuously, the least pres- 

 sure being reached at the highest point. 

 Descending, at constant speed, the pressure 

 increases until at the lower orifice D the 

 pressure is once more atmospheric, and the 

 stream emerges in pressure equilibrium with 

 the air surrounding it. 



Taking a stream tube beginning at surface 

 A outside the tube, and ending at D we have 



