the lower to the upper notes of the scale. The thinner the bell is in proportion to the weight of metal, it should be observed, the deeper is the pitch: so that if the same proportionate thickness were preserved in the treble as in the tenor of a peal, the former would have to be made of too small size and too little weight of metal to compete successfully with the tenor. By adding to the proportionate thickness of the treble, we are enabled to make it of larger size and heavier metal while preserving the high pitch. This effect of thickness on pitch is a thing to be borne in mind in ordering a peal of bells, and deciding what scale or pitch is to be adopted. The cost of the bells is in proportion to the weight of metal, and the question therefore is, given so much metal, in what form to cast it so as to get the best effect from it. This will often be best realised by not endeavouring to get too deep a tone from the peal; a peal tuned in the scale of E or of F may be equally cast with the same amount of metal, but will not be equally good, as either the E peal in that case must be too thin, or the F peal too thick. Where the amount of metal is limited, therefore, the higher pitch will give the best result, and enable the metal to be used to the best advantage.
The precise note which a bell of a certain shape, size, and weight will produce is almost a matter of experience; but the proportion between size and relative dimensions and pitch is capable of being approximately tabulated. The average modulus of the finest of the large bells of Europe, as between size and weight, is given by Sir E. Beckett (to whose work on Clocks and Bells the reader is referred for more detailed information on some of the points touched upon here), as 10 cwt. of metal for a bell 3 feet in diameter, and as the weight of metal varies as the cube of the diameter, a bell of 4 feet diameter would consume nearly 25 cwt., and one of 6 feet diameter 4 tons of metal. A bell of this last-named weight would, with the best and most effective disposition of the metal, give the note tenor C; and the pitch for other sizes may be deduced from this, on the rule that the number of vibrations per second in bells varies as (thickness)2 / diameter.
Where a set of bells are in precisely similar proportions throughout, their dimensions would be simply in an inverse ratio to the number of vibrations per second of the notes they were intended to sound. But as in practice the higher pitched bells are always made thicker in proportion to the diameter than the lower ones, for the reasons mentioned above, the problem cannot for practical purposes be stated in the simple form of inverse ratio. Bells, it may be observed, are tuned by turning out a small portion from the inner side of the thickest part or sound-bow, when they are too sharp, so as to reduce the thickness and thereby flatten them, or by similarly turning off a small portion from the edge of the rim, so as to reduce the diameter, when it is desired to sharpen them. This latter process, however, impairs the shape, and is apt also to injure the tone of the bell; and if the casting cannot be so accurately regulated as to give hope of ensuring correctness at first, it is better to let any excess be on the side of sharpness, which can be corrected without damaging the bell. In the case of large peals the plan has sometimes been followed of casting all the smaller bells a trifle thick, so that if the whole peal is not precisely in tune, the tuning may all fall on the smaller bells, which will be reduced in thickness till they are brought down to the pitch to range correctly with the larger ones. Bells are however now cast with considerable accuracy, and the turning out of a nearly perfect, or, as it is called, a 'maiden' peal, is not an uncommon occurrence; though it must be said that peals are not unfrequently so called which are not as perfectly in tune as they ought to be, but which are left untouched in order to claim the credit of being a 'maiden' set. This ought never to be allowed; in fact a much more rigorous standard ought to be maintained in tuning bells than is usual: the number of bells not properly in tune with each other which we hear is a constant annoyance to those whose ears can detect the falsity, and perhaps does something towards confirming other listeners in their deficiency of what is called 'ear.'
The casting of a large bell is an operation requiring considerable preparation and a great deal of nicety of workmanship. The first process is to form the model of the inside surface of the bell, or the core, which is done on a conical-shaped base of iron or brickwork; the clay, after being approximately modelled by hand, is brought to the correct mould by means of what is called a 'sweep,' which is a flat piece of hard wood with one of its edges cut to the section of the inside of the bell, and which is attached to a pivot fixed in the centre of the core, and then 'swept' round the clay until the model of the inside of the bell is correctly formed. The core is then thoroughly dried by heat, either by a fire lighted under it (if it is on a brick base), or by being placed bodily in an oven (if it is on an iron base). The next point is to obtain the outer shape of the bell, and its thickness. There are two ways of doing this. The method which used to be universally adopted was to make upon the core, after it was dried, a model of the thickness of the bell in clay, the outer shape of the bell being obtained by another sweep operating in the same way, and turning on the same centre as that which formed the inside shape; then upon this, when dry, to build a cover or cope, the inner side of which closely followed the outer shape of the bell. This cope, going like an extinguisher over the whole, was strengthened with haybands, or, in the case of large models, with pieces of iron worked into it, so that when made it could be bodily lifted off, the clay bell previously made on the core broken away, and the cope replaced, leaving between it and the core the precise shape and thickness of the bell. The difficulty however of getting a good external