134 Dr. C. Chree on the 



It will be seen that the instrument proved correct within 

 the limits of accuracy of the observations. 



The authors feel that the use of a calibrator of this kind will 

 facilitate accurate work in elasticity and lead to a greater 

 uniformity in the determination of coefficients. 



University College, Bristol. 

 June, 1904. 



yqrf 



XI. On the Lateral Vibration of Bars. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



HAYING recently, when dealing with the transverse 

 vibrations * of bars, made liberal use of the approxi- 

 mate method developed in Lord Rayleigh's ' Theory of 

 Sound/ I have read with interest Mr. Garrett's paper on 

 this subject in your November number. The use of photo- 

 graphy, to which Mr. Garrett's paper is mainly devoted, 

 seems not unlikely to be of material service, at least in cases 

 where no exact mathematical solution is obtainable. It is 

 even conceivable that it might supply the means for a 

 critical investigation as to the limits within , which the 

 ordinary Bernoulli-Euler solution for thin rods should be 

 restricted. 



The earlier part, however, of Mr. Garrett's paper seems 

 hardly to do justice either to Lord Rayleigh's method f or 

 to the subject of lateral vibrations. If the degree of closeness 

 of Rayleigh's assumed type to the actual type of vibration in 

 a clamped-free rod had required investigation, experiment is 

 not, as Mr. Garrett seems to think, the only or even the 

 most natural resource. The exact solution in this case is 

 known, and if necessary it could have been compared with 

 the simple type assumed by Rayleigh. This question, however, 

 does not really arise. The object of Rayleigh's method is to 

 obtain a close approximation to the frequency of the gravest 

 vibration in a simple way, and the justification required by 

 any assumed type of vibration is that the frequency derived 

 from it should be a close approach to the truth. The justifi- 

 cation for the method itself is the general theoretical result 

 established earlier in Lord Rayleigh's vol. i. §§ 88, 89, &c, 

 that a close approach is obtainable to the true period of 

 vibration even by comparatively crude hypotheses as to the 

 type of vibration, and that the frequency thus obtained must 



* Phil. Mag. May 1904, p. 504. 

 f ' Theory of Sound,' vol. i. § 182. 



