\ 



8 ART. 10. — S. KUSAKABE. 



scale-measurement. Let this distance be denoted by a, then tbe 



(I 

 above values of I' correspond to 1+ —^ where N is the number 



of loops contained in the observed segment of the string. Thus 

 a and I being two unknown quantities, they may be easily cal- 

 culated by the method of least squares. The result is : — 



I =23"^79. 



The result of the second experiment with another string and 

 smaller tension is 



Tf=20-908 



I =16-32. 

 The number of free vibrations of gravest mode for a perfectly 

 flexible string is given by 



1 / W.g 



where W is the suspended weight to which the tension is due. 

 But if we consider the string as not being infinitely thin, its 

 stiffness must be taken into account. In the case where the extre- 

 mity of the wire is constrained to be a node by stretching it over 

 a bridge but no couple acts to fix its direction, the correction 

 for a circular wire is given by 



_ T.imJE! 



where p' and E' are the specific density and the modulus of 

 elasticity of the wire respectively. 



Thus, the number of vibrations n of the specimen, which 

 is identical with that of the connected wire, is given by 



7:wE 1 



n=ni + 7io =ni + 



32/>'' n,l' 



