Septkmbkk 19, 1902.] 



SCIENCE. 



457 



ture's energies; and the inventions of a 

 new century shall justify every one of 

 Charles Sumner 's ' prophetic voices, ' from 

 those of Seneca to those of Cobden, De 

 Tocqueville and that orator, seer and 

 prophet, Sumner himself. Seneca's conti- 

 nent has appeared and there are no more 

 geographical worlds to conquer; but there 

 are greater worlds still accessible to the sci- 

 entific explorer. The prophecy of the 

 'bought servant,' George Webb, became 

 true with the birth of a new nation: 

 Rome shall lament her ancient fame declined 

 And Philadelphia be the Athens of mankind. 



Meantime, the nation, as prophesied by 

 Sheridan, shall thus maintain a ' name and 

 government rising above the nations of 

 Europe with a simple but commanding dig- 

 nity that wins at once the respect, the con- 

 fidence and the affection of the world. ' 



And, in all this, the man of science, seer, 

 revealer and prophet, shall play the noblest 

 part. 



E. H. Thurston. 



Cornell Univeksitt. 



ATTENUATION AND DISTORTION ON LONG- 

 DISTANCE TELEPHONE AND POWER 

 TRANSMISSION LINES REGARDED 

 AS HYDRODYNAMIC PHE- 

 NOMENA.* 



The analogy between a steady flow of 

 water in a long pipe under the action of 

 the constant head and a continuous current 

 of electricity under some constant pressure 

 such as is furnished by one or more cells 

 of a battery, has often been employed to 

 give a clear elementary physical conception 

 of the mathematical relations expressed by 

 Ohm's law. In this case the applied pres- 

 sure is gradually consumed by the resist- 

 ance experienced by the current, and in 

 strict analogy with the flow of water, the 



* Abstract of paper read before the American 

 Association for the Advancement of Science by 

 Professor Henry T. Eddy, University of Minne- 

 sota, Pittsburgh meeting, Jime, 1902. 



loss per unit of length is proportional to the 

 product of the square of the current and 

 the first power of the resistance. So far 

 as the mathematical relations are concerned 

 the two problems are identical. 



It is the object of this paper to extend 

 this hydrodynamic analogy to the more 

 complicated case of long-distance trans- 

 mission by alternating currents in general. 



Telephone transmission has been specifi- 

 cally mentioned in the title in order to 

 include the general case of variable fre- 

 quency. The importance of thus extending 

 and enlarging this analogy will be evident 

 when we reflect that all the complicated 

 phenomena of long-distance electrical 

 power transmission, by any combination of 

 land lines and cables with their sending 

 and receiving apparatus, may be completely 

 reproduced in all its details of operation 

 by simple pumping machinery with its 

 transmission pipes and air chambers, whose 

 manner of operation may be made clear t© 

 any one without the aid of higher analysis. 

 Let us first take the case of a double-acting- 

 pump cylinder and piston in which the two. 

 ends of the cylinder are connected by a, 

 simple pipe or by-pass without valves. 

 When this apparatus is filled with water 

 and the piston is moved back and forth by 

 a uniformly rotating crank, the water is 

 forced through the by-pass alternately 

 from one end of the cylinder to the other. 

 If the by-pass is short, the resistance to 

 motion may be taken as due to fluid fric- 

 tion only, since the inertia of the water 

 may then be disregarded. This is in every 

 particular analogous in the manner of its 

 operation to a sinusoidal electromotive 

 force acting in a circuit whose induction 

 and capacity may be disregarded in com- 

 parison with its ohmic resistance. 



But in case the pipe connecting the ends 

 of the pump cylinder be made very long 

 and the size sufficient to greatly reduce the 

 friction, we may disregard this in com- 



