458 



SCIENCE. 



[N. S. Vol. XVI. No. 403. 



parison with the resistance due to the 

 inertia of the water. The resistance due to 

 inertia is proportional to the product of 

 the mass of the water moved by its accelera- 

 tion. Since this acceleration is greatest 

 at the beginning of the stroke and vanishes 

 at the middle of the stroke, where it 

 changes to a retardation of amount increas- 

 ing to the end of the stroke, it is evident 

 that the phase of the current lags a quarter 

 of a revolution or period behind that of 

 the pressure, the pressure being a maxi- 

 mum at the beginning of the stroke, and 

 the current a maximum at the middle of 

 the stroke. During the retardation of the 

 piston the inertia of the water acts to drive 

 the piston forward, and (disregarding 

 friction) as much energy is returned to the 

 piston during retardation as is exerted by 

 it during acceleration, so that on the whole 

 no loss of energy occurs during the stroke. 

 In these particulars this case differs from 

 that previously considered, where the 

 pressure is in phase with the current and 

 energy is expended against resistance dur- 

 ing the entire stroke. 



Now suppose that fluid friction and 

 inertia coexist in the connecting pipe ; it is 

 evident that their coexistence does not 

 affect the separate actions which have been 

 described. The current or flow back and 

 forth is that due to the reciprocating 

 motion of the piston, and the pressure is 

 the resultant of the two pressures already 

 described, differing in phase by a quarter 

 of a period. The lag of the current will, 

 therefore, be less than a quarter of a 

 period. 



The inertia of the water is entirely anal- 

 ogous to the self-induction of an electric 

 circuit and the case of combined fluid fric- 

 tion and inertia is mathematically in every 

 particular the same as an alternating cur- 

 rent circuit having distributed ohmic re- 

 sistance and self induction. 



Next let us imagine the short by-pass 



first considered to be sufficiently increased 

 in diameter to make it a globular chamber 

 as large or larger than the cylinder itself, 

 and let it be furnished with an elastic dia- 

 metral diaphragm (of sheet rubber, for 

 example) which occupies a diametral posi- 

 tion whenever the piston is at the middle 

 of the stroke. It is evident that when the 

 piston is at the beginning of the stroke the 

 tension of the stretched diaphragm exerts 

 a negative pressure or suction to force the 

 piston forward in its stroke, which vanishes 

 at the middle of the stroke, after which the 

 pressure exerts a retardation whose amount 

 increases to a maximum at the end of the 

 stroke. But the total energy exerted by 

 the diai:)hragm and restored to it is equal. 



The action of the diaphragm differs from 

 the action of the inertia of the water pre- 

 viously considered in the one particular 

 only : it exerts its greatest forward pres- 

 sure at the instant the inertia exerts its 

 greatest bacls pressure, consequently when 

 we disregard fluid friction, the phase of 

 the current is one quarter of a period in 

 advance of the pressure. 



It thus appears that the eft'ect of such a 

 diaphragm is opposite to that of the inertia 

 of the water, so that a diaphragm having 

 sufficient tension would completely destroy 

 the effect of the inertia of the water. The 

 general effect of this arrangement is to re- 

 lieve to a greater or less extent the greater 

 pressures, positive or negative, at each end 

 of the stroke arising from the inertia of 

 the water. Furthermore it may be noticed 

 that a somewhat different device from that 

 .just mentioned might be employed, whose 

 resultant action would nevertheless be of 

 the same nature. For example, instead of 

 enlarging the by-pass let two equal air 

 chambers be placed on it, one at each end 

 of the cylinder. This is, in fact, the man- 

 ner in which relief is actually obtained in 

 pumping machinery, from the shock and 

 greatly increased pressure at the beginning 



