Oscillations in Straight Wires and Solenoids, 211 



detect any oscillations set up by the harmonics o£ the 

 generator. 



The centre of the solenoid is one of the points of maximum 

 current when the inducing coil is in the central plane, and 

 resonance is obtained when the wave-length of the funda- 

 mental oscillation of the generator is equal to that of one of 

 the normal modes of oscillation of the solenoid corresponding 

 to the odd numbers. 



The following table gives the wave-lengths of the free 

 oscillations as calculated by the formula (14), and also the 

 wave-lengths of the 1st, 3rd, 5th, 7th, and 9th obtained 

 experimentally. The mode of oscillation is indicated by the 

 number n in the first column, which is the number of points 

 on the solenoid at which a maximum current is obtained. 



Wave-lengths of Free Oscillations of Solenoid 227 metres 

 long, diameter 5 centimetres • 29 turns per centimetre. 



Calculated Observed 



wave-length. wave-length. 



1 773 870 



2 434 



3 315 338 



4 253 



5 217 231 



6 192 



7 175 184 



8 1(51 



9 150 15S 



The discrepancy between the observed and calculated 

 value, which is very marked in the longer waves, is due to 

 the effect of the ends and the increase of capacity produced 

 by neighbouring bodies. 



10. The increase in wave-length due to the ends may be 

 shown by measuring the distances between the points of 

 maximum current in the solenoid. These points are found 

 by moving the detector along the solenoid to the positions 

 where the current in the lamp is a maximum. Although 

 these positions cannot be determined very accurately by the 

 lamp indicator, the experiments show that the distances 

 between the points of maximum current are larger in the 

 middle than at the ends by an amount which cannot be 

 attributed to experimental error. An example is given in 

 fig. 4, where the curve indicates the distribution of current 



