414 Mr. C. A. Bell on the Determination 



So far as can be judged from a cursory examination of 

 the literature of the subject , this method has been but little 

 used in the case of glass, doubtless because of the well-known 

 difficulty of obtaining perfectly uniform rods of this material 

 of any considerable length. The original plan of these experi- 

 ments was simply to determine the tones given by longitudinal 

 vibration of a number of rods (or tubes) of each kind of glass ; 

 to cut each of them into ten approximately equal segments ; 

 and by weighing and measuring the segments to construct 

 for each rod a diagram representing the variations in its 

 cross-section from end to end. It was expected that, of the 

 more nearly uniform of the original rods, a few might thus 

 be selected, from the tones of which Young's Modulus might 

 be calculated. 



Inspection of the diagrams showed, however, that of the 

 many rods examined not one showed such an approach to 

 uniformity as to be suitable for the object in view. But, 

 taking as a standard for comparison the mean value of the 

 product, number of vibrations per second x twice length of 

 rod, for each bundle, it was possible in a general way to 

 connect the variation from this mean exhibited by each rod 

 with its most marked irregularities ; and this observation 

 suggested that it might be possible, by the aid of the diagrams, 

 to calculate for each rod an " addition to length " which would 

 enable the velocity of sound through it to be calculated from 

 its rate of vibration as if the cross-section were constant — a 

 correction analogous to that given by Lord Bayleigh * for 

 tluid columns of slightly variable section. Trial showed that 

 this was certainly possible ; and on mentioning the matter to 

 Dr. Chree, to whom I am indebted for his cordial interest, 

 he kindly undertook to look into it, and has given in the 

 Appendix to this Note the mathematical proof that the cor- 

 rection, somewhat empirically applied, was strictly in accord- 

 ance with theory. The necessary correction is, in fact, given 

 by Lord Bayleiglrs formula with reversed sign. 



In the experiments quoted below, tuning-forks of high 

 frequency were not available ; the product n x 21 for the glass 

 rods was therefore determined as follows. Bessemer steel 

 rods of remarkable uniformity as regards diameter and texture 

 are now easily procurable. Three such rods from the same 

 drawing, § of an inch in diameter, when cut to exactly 

 the same length, about 11 feet, and clamped centrally by 

 means of corks in a vertical position f, gave, on being struck 



* ' Theory of Sound,' 1st edition, vol. ii. p. 61. 



f The note given by a rod of these dimensions is distinctly raised in 

 pitch when it is fixed horizontally. 



