in Bowed Stringed Instruments. 395 



Note dated the 8th of August added in proof. 



Since the paper was first written, several other interesting 

 effects have been noticed, o£ which the following is a 

 summary: — - 



(a) Cyclical forms of vibration of the Gr-string and belly 

 of a 'cello may also be obtained when the vibrating length is 

 double that required for production of the wolf-note, that is, 

 when the frequency is half that of the wolf-note. In this 

 case, when the pressure of the bow is sufficient to maintain 

 a steady vibration, the second harmonic in the motion of the 

 belly is strongly re-inforced. When the pressure is less 

 than that required for a steady vibration, cyclical changes 

 occur, the principal fluctuations in the motion, both of the 

 string and the belly, being in the amplitude of the second 

 harmonic. In this, as in all other cases, the cyclical changes 

 disappear and give place to a steady vibration, when the 

 bow is applied at a point sufficiently removed from the 

 end of the string. In this particular case, a large, almost 

 soundless vibration may be obtained by applying the bow 

 rather lightly and rapidly at a point distant one-fifth or more 

 of the length from the end ; the octave is then very weak in 

 the vibration of the string, but may be restored, along with 

 the tone of the instrument, by increasing the pressure 

 of the bow.' 



(b) The 'cello has another marked point of resonance at 

 360 vibrations per second. The pitch of this is also lowered 

 by loading the bridge. 



(c) When the vibrating length of the Gr-string or A-string 

 of the 'cello is about a fourth of the maximum or less, cyclical 

 forms of vibration may be obtained at almost any pitch 

 desired, by applying the bow with a moderate pressure rather 

 close to the bridge. 



(d) As the frequency of vibration is gradually increased 

 from a value below to one above the wolf-note frequency, 

 the phase of the principal component in the " small " motion 

 at the end of the string, that is also of the transverse hori- 

 zontal motion of the bridge, undergoes a change of approxi- 

 mately 180°. This is in accordance with theory. 



