422 Dr. 0. Chree on the Determination 



specimens from the same works, but of density 3*136 at 

 10°/4°, an indirect determination of W gave 5*39 x 10 11 . 



The foregoing list includes all the rods and tubes that have 

 been examined, with only one exception, where some gross 

 blunder had evidently been committed. Inspection shows 

 that discrepancies between the uncorrected products nx2l 

 are reduced by 90 per cent, in the corrected values of a, 

 and it is highly probable that the calculated values of E / are 

 correct to three figures. 



When a glass can be obtained in thin rods or tubes — a 

 diameter o£ 5 or 6 mms. seems most desirable — the experiments 

 are easily and rapidly carried out, since no great accuracy is 

 required in the weighing or measurement of the segments. 

 Thick rods or tubes naturally give more trouble, especially 

 when of hard glass, and here some care in selecting suitable 

 specimens is desirable. Tubes which do not give persistent 

 notes when struck should be at once rejected. Perfect 

 uniformity is no,t to be expected ; failing this, the best results 

 are obtained with rods or tubes which taper continuously 

 from one end to the other. 



Appendix by C. Chree, F.R.S. 



Taking the axis of the tube as axis of z, the origin being 

 at one end, we have for the longitudinal displacement in the 

 fundamental free-free vibration 



io = A cos kt cos 7r.:/l, (1) 



where A is a constant, I the length, and hftir the frequency. 



In reality iv varies slightly over the cross-section, but for 

 the purpose of the present correction we may neglect this 

 variation and also the energy answering to the lateral 

 motion. 



If the section S were uniform we should have — neglecting 

 the correction for finite area of section — 



kj'ir=ajl > where a^^/E/p. 



Here p denotes the density, E Young's modulus, and a 

 the " velocity of sound " in the nomenclature employed by 

 Lord Rayleigh. 



S, it should be noticed, means the sectional area of the 

 material ; in a circular tube whose outer and inner surfaces 

 are circles of radii r and r' , & = 7r(r 2 — r' 2 ). 



Let 



S = S + SS, 2) 



