72 ANNUAL OF SCIENTIFIC DISCOVERY. 



in my opinion, can be worse than the bells of this shape, two or three feet 

 in diameter, which people seem to be so fond of buying for the new fashioned 

 cemeteries : whether from ignorance that they will sound very differently 

 on the top of a chapel and in the bell-founder's shop, or becavisc they think 

 a melancholy and unpleasant sound appropriate, or because they want to 

 buy their noise as cheap as possible, I do not pretend to say. These bells, 

 and thin bells of any shape, bear the same kind of relation to thick ones, 

 as the spiral striking wires of the American clocks bear to the common 

 hemispherical clock bells i. e., they have a deeper but a weaker sound, 

 and are only fit to be heard very near. A gong is another instrument in 

 which a deep note, and a very loud noise at a small distance, may be got 

 with a small weight of metal ; but it is quite unfit for a clock to strike upon, 

 not merely from the character of its sound, but because it can only be roused 

 into full vibration by an accumulation of soft blows. Gongs are made of 

 malleable bell-metal, about four of copper to one of tin, which is malleable 

 Avhcn cooled suddenly. The Chinese bells, some of which are very large, 

 may be considered the next approximation towards the established form ; 

 for they arc (speaking roughly) a prolate hcmispheroid, but with the lip 

 thickened ; whereby the sound is made higher in pitch but stronger, and 

 better adapted for sounding at a distance when struck with a heavy enough 

 hammer. But still the shape of the Chinese bells is very bad for producing 

 sound of a pleasing quality ; and generally it may be said, at least I have 

 thought so ever since I began bell ringing twenty-four years ago, that all 

 bells of which the slant side is not hollowed out considerably, are deficient 

 in musical tone. The Chinese bells are not concave but convex in the slant 

 side. 



If you make eight bells, of any shape and material, provided they are all 

 of the same, and their sections exactly similar figures (in the mathematical 

 sense of the word), they will sound the eight notes of the diatonic scale, if 

 all their dimensions are in these proportions GO, 53, 48, 45, 40, 36, 32, 

 30 ; which are merely convenient figures for representing, with only one 

 fraction, the inverse proportions of the times of vibration belonging to the 

 eight notes of the scale. And so, if you want to make a bell, a fifth above 

 a given one, it must be two thirds of the size in every dimension, unless you 

 mean to vary the proportion of thickness to diameter ; for the same rule 

 then no longer holds, as a thinner bell will give the same note v:ith a less 

 diameter. The reason is, that, according to the general law of vibrating 



plates or springs, the time of vibration of similar bells varies as - 



(diameter) 2 



When the bells are also completely similar solids, the thickness itself varies 

 as the diameter, and then the time of vibration may be said simply to vary in- 

 versely as the diameter. The weights of bells of similar figures of course 

 vary as the cubes of their diameters, and may be nearly enough represented 

 by these numbers 216, 152, 110, 91, 64, 46,33, 27. 



The exact tune of a set of bells, as they come out of the moulds, is quite 

 a secondary consideration to their tone or quality of sound, because the notes 

 can be altered a little either way by cutting, but the quality of the tone will 



