Maintenance of Vibration by Periodic Field oj lorce. 135 1 



F(y ) can only result in the amplitudes of all the components 

 of the impressed force being increased or decreased in the 

 same proportion, their phases remaining unaltered. The 

 non-uniformity of the field may thus affect the amplitude 

 of the vibration, but cannot alter its form, it being assumed, 

 of course, that the amplitudes are not so large as to alter the 

 free periods. This peculiarity of the action of a non- 

 uniform impulsive field is the explanation of certain 

 interesting observations described, but not explained, by 

 Klinkert in the paper referred to above. Klinkert experi- 

 mented with two wires, both electromagnetically maintained, 

 one of which was self-acting and the other was worked by 

 a current on separate circuit rendered intermittent by the 

 vibrations of the first wire. The vibration-curves of the 

 two wires showed a marked dissimilarity, a special feature 

 of interest being the fact that the vibration of the second 

 wire when at its maximum was practically similar to that 

 of a plucked string. In view of what has been said above r 

 this result will be readily understood. The magnetic field 

 is of appreciable strength only during a small fraction of 

 the period,' and may thus be regarded as of an impulsive 

 character. When there is an appreciable difference between 

 the natural and impressed frequencies of vibration, the form 

 of the motion approximates to that of a plucked string and 

 this is what is actually observed when the exciting current 

 s rendered intermittent by an independent interrupter. It 

 s when the natural frequency is somewhat greater than the 

 mpressed frequency that the vibrations of largest amplitude 

 md those that show the closest similarity to the vibrations 

 of a plucked string are obtained. For the vibrations are 

 then nearly in the same phase as the impulses, and as an 

 increase in the amplitude brings the position of the wire at 

 which the impulses act closer to the electromagnet, and 

 therefore still further increases the magnitude of the 

 impulses, a vibration of large amplitude may be maintained 

 in spite of the difference between the natural and impressed 

 frequencies of vibration. The increase of natural frequency, 

 due to a large amplitude, would also tend to encourage the 

 assumption of this form of vibration and to make it stable. 

 The conditions are, however, entirely different when the 

 vibrating wire is a self-acting interrupter which determines 

 the period and character of its own excitation, and a 

 detailed mathematical theory of the vibration-forms obtained 

 with it must be reserved for separate consideration. 



We may now pass on to consider the cases in which 

 the frequency of the vibration is not the same as the 



