ltU4] on Improvements in Long-Distance Telephony 89 



making stationary waves on the string. By adjusting the tension we 

 can alter their velocity, and therefore the wave length or double the 

 distance from node to node. The number of vibrations of the cord 

 is given by a counter which records the speed of the motor. The 

 motion travels along the string a distance equal to one wave length 

 in the time of one complete vibration. We can with this apparatus 

 experimentally prove all the above statements. Taking a string of 

 known density or weight per inch or centimetre, and stretched by a 

 known weight or tension, we can find the square root of the quotient 

 of tension by density, which gives us the velocity of the wave, and 

 compare this number with the measured product of wave length and 

 frequency, which also gives us the wave velocity. 



The two numbers are found to be the same. If we employ a 

 string one-half of which is single and the other half four-fold, we 

 find on vibrating it that the waves are double as long on the part 

 which is single as they are on the part which is four-fold, thus 

 proving that the velocity varies inversely as the square root of the 

 density. By varying the speed of the motor whilst keeping the 

 tension of the string constant, we can obtain stationary waves of 

 various wave lengths, and prove that the velocity of the wave along 

 the string is the same for all wave lengths, (See Fig. 1.) 



In the case of this vibrating string, the mass per unit of length 

 corresponds to the inductance of an electric cable, and the tension 

 applied to the string to the inverse or reciprocal of the capacity of 

 the cable, but if the string is very flexible, there is no quality which 

 corresponds to the electric resistance of the cable, or to its dielectric 

 leakance. We must therefore turn for assistance to another case of 

 wave motion. 



If we attach to a horizontal steel wire a number of slips of metal 

 all soldered transversely to the wire, and if we give the end slip a 

 sudden displacement so as to twist the steel wire one way or the 

 opposite, a wave of twist, or a torsional wave, will run along it. 



In this case the torsional elasticity of the wire corresponds to the 

 tension in the case of the stretched string, and the mass of the 

 system per unit of length to the density of the string. This latter 

 corresponds also to the inductance of our telegraph cable, and the 

 torsional elasticity to the reciprocal of the cable capacity per unit of 

 length. If we suppose this arrangement to be immersed in water so 

 that the oscillatory motion of each transverse strip is resisted, the 

 water produces a decay or attenuation in the waves transmitted along 

 it which corresponds to the action of the electrical resistance of the 

 conductor in attenuating electric waves running along it. More- 

 over, it is clear, since fluid friction increases with velocity, the 

 attenuation of the waves propagated along this arrangement would 

 be greater for waves of short wave lengths or high frequency than 

 for long waves of low frequency. 



The point to notice is that by making these transverse strips 

 heavier we can give them a greater store of energy, and thus render 



