10 ART. 10. — S. KUSAKABE. 



g =979-8 



/ =10-87 



whence 7ii = oô0"o 



7/2=0-2 

 n =350-5 

 The relation between the number of vibrations n and the 

 modulus of elasticity E of the specimen is given by the well 

 known formula 



k .IE 



where k is the radius of gyration and /■' is the specific density of 

 the specimen whose length is L ; while m is a constant satisfying 

 the equation 



cos m cosh m+ 1=0. 

 The smallest root, 1*875, corresponds to the gravest mode of 

 vibration. The first over-tone is ca. 2*6 octaves higher than the 

 gravest tone, so that in an actual case the succeeding roots of 

 the equation have no importance. 



Now, calculating the modulus of elasticity for the specimen 

 of soft iron from the above data, we have 



^= 2-029 xlO^' c.g.s. unit. 



In the above experiment, the direction of the motion of the 

 specimen was perpendicular to the elongation of the string. It 

 is well knowai that, if the direction of motion is parallel to the 

 string, the period of the vibration of the string becomes double 

 that of the specimen. That is to say, the frequency n of the 

 specimen is equal to twice the frequency {nx + n-ij of the string. 

 The second observation with another string and smaller tension 

 was made under the last mode of vibration, giving the following 

 result : — 



