THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



JANUAR Y 1890. 



I. On Bells. By Lord Rayleigh, Sec. B.S.* 



THE theory of the vibrations of bells is of considerable 

 difficulty. Even when the thickness of the shell may 

 be treated as very small, as in the case of air-pump re- 

 ceivers, finger-bowls, claret glasses, &c, the question has given 

 rise to a difference of opinion. The more difficult problem 

 presented by church bells, where the thickness of the metal 

 in the region of the sound-bow (where the clapper strikes) is 

 by no means small, has not yet been attacked. A complete 

 theoretical investigation is indeed scarcely to be hoped for ; 

 but one of the principal objects of the present paper is to 

 report the results of an experimental examination of several 

 church bells, in the course of which some curious facts have 

 disclosed themselves. 



In practice bells are designed to be symmetrical about an 

 axis, and we shall accordingly suppose that the figures 

 are of revolution, or at least differ but little from such. 

 Under these circumstances the possible vibrations divide 

 themselves into classes, according to the number of times the 

 motion repeats itself round the circumference. In the gravest 

 mode, where the originally circular boundary becomes ellip- 

 tical, the motion is once repeated, that is it occurs twice. The 

 number of nodal meridians, determined by the points where 

 the circle intersects the ellipse, is four, the meridians corre- 

 sponding (for example) to longitudes 0° and 180° being 

 reckoned separately. In like manner we may have 6, 8, 10 . . 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 29. No. 176. Jan. 1890. B 



