374 Mr. E. Beckett Denison, [March 6, 



16 tons, within 174 lbs., and raised the note from E flat to E. 

 Fortunately the same ratio of increase was made throughout, and 

 the waist is 3^ in., or one-third of the sound-bow, as it ought to 

 be ; and therefore the only effect of the mistake is, that the bell is 

 heavier and more powerful ; for it being cast the first, the alteration 

 of the note did not signify, as the four quarter bells can as easily 

 be made to accord with E natural as with E flat. And as they 

 will be rather smaller in consequence, the aggregate weight of the 

 whole five will be about 24 tons, as I originally estimated. I have 

 only to add, with reference to this part of the subject, that the width 

 of the bell at the top inside is half the width at the mouth, as it 

 generally is ; though in some bells, for instance, the great clock 

 bell at Exeter, it is the outside diameter that is made half tiie 

 diameter at the mouth. It is of no use to state here the precise 

 geometrical rules by which the pattern of a bell of what we now 

 call the Westminster pattern is drawn, as they are purely empirical. 

 I mean, that having got a bell, by trial, which we all agreed was 

 better than any other, I made out some sufficiently simple rules 

 for drawing the figure of its section by means of a few circles 

 whose radii are all some definite numbers of 24th parts of the 

 diameter of the bell : but there is no kind of a priori reason, that 

 I know of, why a bell whose section or sweep is made of those 

 particular curves, should be better than any other ; and therefore I 

 call the rules for tracing the curve merely empirical ; and as they 

 would be of no use to any one but bellfounders, who know them 

 already, or easily may, if they like, I shall say no more on this part 

 of the subject. 



As I have been asked many questions about the mode of 

 calculating the size of a bell, so as to produce a particular note, and 

 the answer is very simple, I may as well give it, though it may be 

 found already, with other information on this subject, in the only 

 English book I know of which contains such information, I mean 

 the second edition of my Lectures on Church Building., to which a 

 chapter on bells is added. 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 — 60, 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 — for instance, the B bell to our E, it 

 must be |rd 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 with 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 .-y, f~\3' When the bells are also completely similar 



