September 19, 1902.] 



SCIENCE. 



459 



and end of the stroke arising from the 

 inertia of the water. Mathematically the 

 effect is the same as that of the diaphragm 

 previously described. 



The operation of the diaphragm and air 

 chambers just considered is strictly anal- 

 ogous to that of capacity in an alternating- 

 current circuit, the diaphragm to capacity 

 in series, and the two air chambers to ca- 

 pacity in shunt, and by these self induction 

 may be neutralized to a greater or less ex- 

 tent, according to their relative amounts. 



We have thus far considered merely the 

 peculiarities of the transmitting or connect- 

 ing pipes in their relation to the double- 

 acting force pump regarded as the source 

 of energy. We need next to consider a re- 

 ceiving pump which shall take and utilize 

 the energy not expended in fluid friction. 

 Let the receiving pump be assumed at first 

 to be exactly like the force pump, and to 

 actuate a crank, fly wheel and other ma- 

 chinery on which energy is expended uni- 

 formly. The crank end of this second 

 cylinder is connected directly by a pipe 

 with the crank end of the force pump, and 

 the other ends likewise. In this case the 

 energy expended in fluid friction and iner- 

 tia may be neglected in comparison with 

 the energy transmitted; this arrangement 

 will transmit power from the driving crank 

 to the driven crank much as would a belt 

 or train of cog wheels. But suppose now 

 that the second cylinder is connected to 

 the first by very long pipes, miles long, 

 for example, in which the inertia of the 

 water becomes a controlling factor of the 

 transmission. It would evidently become 

 practically impossible to make the water 

 oscillate with any rapidity in such a closed 

 pipe under ordinary circumstances. But 

 let there be a series of air chambers uni- 

 formly distributed along the entire length 

 of the connecting pipes, or, what would 

 amount to nearly the same thing, let the 

 pipe be an elastic hose requiring pres- 



sure to enlarge or diminish its cross 

 section. 



This will at once entirely change the 

 circumstances of the case, for the air cham- 

 bers near the force pump will readily re- 

 ceive the water as it flows from the force 

 pump and transmit it to those next along 

 the line and so on, so that a wave of pres- 

 sure will pass along the pipe and at the 

 same velocity a wave of current will pass 

 having its maximum flow at points where 

 certain high pressure air chambers are dis- 

 charging into those next along the line. 

 By these progressive pressure and current 

 waves, energy will be transmitted to the 

 working cylinder which need not in this 

 case be of the same cubic capacity as the 

 force pump. Several complete waves may 

 be in progress of transmission along the 

 pipe at once. The frequency of oscillation 

 in the working cylinder will be equal to that 

 of the force pump, a number which may 

 be computed in any given case. But the 

 waves will lag in phase behind those of the 

 force pump to an amount due to the num- 

 ber of waves and fractions thereof in pro- 

 gress of transmission along the line, and to 

 the inertia of the working piston, etc. 



It is evident that when the two cylinders 

 are equal in every respect, except that the 

 piston of the second cylinder is of such 

 large mass that its inertia is great and 

 when in addition we may disregard fluid 

 friction, and the fly wheel of the second 

 cylinder is running idle, that no work is 

 expended in the system. In this case the 

 second piston will originate transmission 

 waves precisely as does the first but in op- 

 posite direction. The resultant of these 

 equal and opposite progressive waves will 

 be a system of stationary waves along the 

 line. Whenever the amount of energy 

 used at the working cylinder is small com- 

 pared with the total energy, kinetic and po- 

 tential, at and near the receiving apparatus 

 the waves originating there will approach 



