12 



Lord Rayleigh on Bells. 



three tones is very nearly true. It must be remarked, how- 

 ever, that the tone fourth in order is scarcely heard in the 

 normal use of the bell, so that its pitch can hardly be of 

 importance directly, although it may afford a useful criterion 

 of the character of the bell as a whole. It is evident that the 

 first and second tones of Terling (1) are quite out of relation 

 with the higher ones. If the first could be depressed a semi- 

 tone and the second raised a whole tone, harmonic relations 

 would prevail throughout. 



Judging from the variety presented in the Table, it would 

 seem not a hopeless task so to construct a bell that all the 

 important tones should be brought into harmonic relation ; 

 but it would require so much tentative work that it could 

 only be undertaken advantageously by one in connexion with 

 a foundry. As to what advantage would be gained in the 

 event of success, I find it difficult to form an opinion . All I 

 can say is that the dissonant effect of the inharmonious 

 intervals actually met with is less than one would have ex- 

 pected from a. musical point of view; although the fact is to a 

 great extent explained by Helmholtz's theory of dissonance. 

 One other point I will touch upon, though with great diffi- 

 dence. If there is anything well established in theoretical 

 acoustics it is that the frequencies of vibration of similar bodies 

 formed of similar material are inversely as the linear dimen- 

 sions — a law which extends to all the possible modes of vibra- 

 tion. Hence, if the dimensions are halved, all the tones should 

 rise in pitch by an exact octave. I have been given to under- 

 stand, however, that bells are not designed upon this principle 

 of similarity, and that the attempt to do so would result in 

 failure. It is just possible that differences in cooling may 

 influence the hardness, and so interfere with the similarity of 

 corresponding parts, in spite of uniformity in the chemical 

 composition of the metal ; but this explanation does not 

 appear adequate. Can it be that when the scale of a bell is 

 altered it is desirable at the same time to modify the relative 

 intensities, or even the relative frequencies, of the various 

 partials ? 



Observations conducted about ten years ago upon the 

 manner of bending of bell-shaped bodies — waste-paper baskets 

 and various structures of flexible material — led me to think 

 that these shapes were especially stiff as regards the principal 

 mode of bending (with four nodal meridians) to forces applied 

 normally and near the rim, and that possibly one of the 

 objects of the particular form adopted for bells might be to 

 diminish the preponderance of the gravest tone. To illustrate 

 this I made calculations, according to the theory of the paper 



