224 



Professor Sihanus P. Thompson 



[June 13, 



precisely four times as rajnd as the fundamental vibration of tlie 

 string as a whole. This would be true if the string were absolutely 

 uniform, homogeneous, and devoid of rigidity. Strings never are 

 60 ; and even if uniform and homogeneous, seeing that the rigidity 



Fig. 5. 



Graphic Record of Vibrations of Steel Wires. 



of a string has the effect of maldng a short piece stiffer in proportion 

 than a long piece, cannot emit true harmonics as the sounds of sub- 

 division. In horns and open organ-pipes the width of the column 

 (which is usually neglected in simple calculations) affects the 

 frequency of the nodal modes of vibration. Wertheim found the 

 partial tones of pij)es higher than the supposed harmonics. Dr. 

 Koenig found with an open organ-pij)e, about Ih feet long, that the 

 eighth partial tone (or sound of subdivision) was a whole major tone 

 higher than the theoretical eighth harmonic, and nearly agreed with 

 the ninth harmonic of the fundamental tone! Further, there are the 

 researches of Lord Eayleigh on the tones of bells, in which the 

 sounds of subdivision are most extraordinarily inharmonious ; afford- 

 ing us probably the reason why concerted hand-bell music is so 

 unendurable. I do not know what the musicians present would say 

 to such chords * as 



"^E 01* 



7) 



They are given by Lord Eayleigh as representing resi^ectively the 

 sounds emitted by two of the bells of the peal at Terling. 



* Tlie signs + or — signify tliat tlie actual tones were respfctively a httle 

 sharixT or a little Hatter than the note as written in the staif notation. 



