TKANSACTIONS OF SECTION A. 



491 



7. Oa the Tunes of Belb. By Lord Ratleioh, LL.D., Sec.R.S. 



Observations have been made upon a considerable number of bells of the usual 

 church pattern, including the five of the Terling belfry. The pitch of the various 

 tones, usually live for each bell, was fixed by comparison with a harmonium, and 

 with the aid of resonators. The results are friven in the accompanying table ; 

 where + or - after a note indicates that the pitch of the bell was a little higher 

 or lower respectively than the note of the harmonium. "Where two notes are re- 

 corded, the pitch of the bell was about midway between. 



The nominal pitch of the bells appears to depend upon the hu/hest of the tones 

 here recorded. When ringing in sequence, and heard from a distance, the bells of 

 the Terling peal were judged to give /5 , gt , «Jt > b, ct , no regard being had to 

 the octave. 



The various tones of any bell correspond, of course, to various modes of vibration. 

 Thus in the case of the first bell upon the above list the gravest note, e', corresponds 

 to a mode with 4 nodal meridians, viz. meridians along which the motion is purely 

 tangential. This is the ordinary mode of vibration of a finger bowl or glass receiver. 

 There is no nodal circle ; but this tone is at its loudest when the bell is Struck about 

 half-way up. The agreement of pitch with the harmonium is sutiiciently good for 

 the bellto respond when e' is sounded upon the instrument. 



The next note, c", may also be easily excited by the harmonium or by the voice ; 

 and again, in this case there are 4 (and but 4) nodal meridians. Hut now there is in 

 addition a nodal circle, situated about a quarter of the way up. If we tap along a 

 meridian, the tone in question disappears when the circle is reached, and reappears 

 when the circle is passed. The mode corresponding to/" + has 6 nodal meridians, 

 and no well-defined nodal circle of latitude. The sound becomes very faint when 

 the place of tapjung is much removed from the sound-bow. 



The tone b" flat is scarcely heard when the bell is struck on the sound-bow in 

 the normal manner. It comes out best at about half-way up. In this case also there 

 are G nodal meridians. The higb.est tone which could well be investigated, d'", 

 appears to be the one which characterises the bell. It is heard best when the 

 .sound-bow is struck and but little over the whole of the upper three-quarters of the 

 bell. In this mode there are 8 nodal meridians. 



From a musical point of view it would seem that all the bell.s are far removed 

 from perfection ; while the differences of relative pitch in the various cases recorded 

 in the table indicate that it may be possible to effect an improvement, even to the 

 extent of bringing all the five tones into harmonious relations. But the fourth 

 tone may probably he disregarded, as it is scarcely heard in the normal use of the 

 bell. The quality of sound is, however, very difficult to estimate ; and even the 

 imperfect octaves, of which several examples occur, give much less of a dissonant 

 effect than might have been expected. 



It is scarcely necessary to say that each of the tones recorded is in reality double, 

 and that from want of symmetry the components of each pair are usually separated 

 to a sensible degree. 



The .sequence of modes and tones differs altogether from what the theory of 

 thin shells would suggest, and this need not be a matter of surprise when we 

 consider how very considerable is the thickness of the sound-bow in comparison 

 with the distance between consecutive nodal meridians. 



A so-called hemispherical bell of Mears and Stainton gives results altogether 

 different from the above, and more in agreement with the theory of thin shells. 



