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here, with his instrument, in a fire which consumed the house helived in. Mr. E. Delaval, a most ingenious men.her of our RoyalSociety , made one in imitation of it, with a better choice and formof glasses, which was the first 1 saw or heard. Being charmedwith the sweetness of its tones, and the music he produced fromit, l wished to see the glasses disposed in a more convenient form,ami brought together in a narrower compass, so as to admit of agreater number of tones, and all within reach of hand to a personsitting before the instrument; which I accomplished after variousintermediate trials, and less commodious forms, both of glasses andconstruction in the following manner. The glasses are blown asnear as possible in the form of hemispheres, having each an openneck or socket in the middle. The thickness of the glass near thebrim is about the tenth of an inch, or hardly quite so much, butthicker as it comes nearer the neck ; which in the largest glasses isabout an inch deep, and an inch and a half wide within ; these di-mensions, lessening as the glasses themselves diminish in size, ex-cept that tlie neck of the smallest ought not to be shorter than halfan inch. The largest glass, is nine inches diameter, and thesmallest three inches. Between these are twenty-three differentsizes, differing from each oilier a quarter of an inch in diameter.To make a single instrument there should be at least six glassesblown of each size; and out of this number one may probablypick thirty-seven glasses (which are different for three octaves witlialJ the semitones) that will be each either the note one wants, or alittle sharper than that note, and all sitting so well into each otheras to taper pretty regular!y from the largest to the smallest. It istrue there are not thirty-seven sizes; but it often happens that twoof the same size differ a note or half a note in tone, by reason of adifference in thickness, and these may be placed in the other with-out sensibly hurting the regularity of the taper form. The glassesbeing chosen, and every one marked with a diamond the note youintend it for, they are to be tuned by diminishing the thickness ofthose tiiat are too sharp. This is done by grinding them roundfrom the neck towards the brim, the breadth of one or two inchesas may be required; often trying the glass by a well-tuned harpsi-chord, comparing the note drawn from your glass by the lingerwith the note you want, as sounded by that string of the harpsi-chord. When you come near the matter, be careful to wipe theglass clean and dry before each trial, because the tone is some-thing flatter when the glass is wet than it will be when dry; andgrinding a veryjitlle between each trial, you will thereby tune togreat exactness. The more care is necessary in this, because ifyou go below your required tone there is no sharpening it againbut by grinding somewhat oil' the brim, which will afterwards re-quire polishing, and thus increase the trouble. The glasses beingthus tuned, you are to be provided with a ease for them, and aspindle on which they are to be fixed. My case is about threefeet long, eleven inches every way wide within at the biggest end,and live inches at the smallest end; for it tapers all the way, toadapt it better to the conical figure of the set of glasses. This caseopens in the middle of its height, and the upper part turns up byhinges fixed behind. The spindle is ol hard iron, lies horizontallyfrom end to end of the box within, exactly in the middle, and ismade to turn on brass-gudgeons at each end. It is round, an inchin diameter at the thickest end, and tapering to a quarter of aninch at the smallest. A square shank comes from its thickest endthrough the box, on which shrink a wheel is fixed by a screw.This wheel serves as a fly to make the motion equable, when thespindle, w ith the glasses, is turned hv the foot like a spinning-wheel. My wheel is of mahogany, eighteen inches diameter, andpretty thick, so as to conceal near its circumference about 251b. oflead. An ivory pin is fixed in the face of this wheel, about fourinches from the axis. Over the neck of this pin is put the loop ofthe string, that comes up from the moveable step to give it motion.The case stands on a neat frame with four legs. To fix the glasseson the spindle, a cork is first to be fitted in lacli neck pretty tight,and projecting a little without the neck, that the neck of one maynot touch the inside of another when put together, for that wouldmake a jarring. These corks are to be perforated with holes ofdifferent diameters, so as to suit that part of the spindle on whichthey are to be fixed. When a glass is put on, by holding it stifflybetween both hands, while another turns the spindle, it may begradually brought to its place. But care must be taken that thehole be not loo small, lest in forcing it up the neck should split;nor loo large, lest the glass, not being firmly fixed, should turn or

move on the spindle, so as to touch or jar against its neighbouringglass. The glasses thus are placed one in another; the largest oilthe biggest end of the spindle, which is to the left hand : the neckof this glass is towards the wheel; and the next goes into it in thesame position, only about an inch of its brim appearing beyond thebrim of the first; thus proceeding, every glass when fixed shewsabout an inch of its brim (or three quarters of an inch, or half aninch, as they grow smaller) beyond the brim of the glass that con-tains it; and it is from these exposed parts of each glass that thetone is drawn, by laying a finger on one of them as the spindleand glasses turn round. My largest glass is G a little below thereach of a common voice, and my highest G, including threecomplete octaves. To distinguish the glasses more readily to theeye, 1 have painted the apparent parts of the glasses within-side,every semitone white, and the other notes of the octave with theseven prismatic colours; viz. C, red; D, orange; E, yellow; E,green; G, blue; A, indigo; B, purple; and C, red again; sotiiat the giasses of the same colour (the white excepted) are alwaysoctaves to each other. This instrument is played upon by siltingWore the middle of the set of glasses, as before the keys of aharpsichord, turning them with the foot, and welting them nowand then with a spunge and, clean water. The fingers should hefirst a little soaked in water, and quite free from all greasiness; alittle fine chalk is sometimes useful, to make them catch the glassand bring out the tone more readily. Both hands are used, bywhich means different parts are played together. Observe, tiiatthe tones are best drawn out when the glasses turn from the endsof the fingers, and not when they turn to them. The advantagesof this instrument are, that its tones are incomparably sweet be-yond those of any other; that they may be swelled and softenedat pleasure by stronger or weaker pressures of the finger, and con-tinued to any length ; and that the instrument, being once welltuned, never again wants tuning.” A farther account of this in-strument is inserted in the Annual Register, vol. iv. p. 149. Theauthor proposes to use cork instead of the finger, but this substitutedoes not seem capable of producing the same mellowness andequality of tone with the finger. Alum-water is also thought pre-ferable to chalk. From what has already been said, it will easilybe perceived, that this instrument requires to be tuned with thenicest degree of delicacy w hich the laws of temperament w ill pos-sibly admit. See Music, and Temperament. The same rules,however, which are observed in tuning a harpsichord, will beequally effectual in tuning the Harmonica ; with this only differ-ence, that greater delicacy in adjusting the chords should, if practi-cable, be attempted. On Plate LXXXV. fig. 3, is representedan instrument of this kind, made by Mr. Dobb of St. Paul’schurch-yard, London .

HARMONICAL ARITHMETIC, that part of arithmeticwhich considers musical intervals, expressed by numbers! in or-der to our finding their mutual relations, compositions, and reso-lutions.

IIarmonicai. Composition, in a general sense, includes bothharmony and melody, i. c. of music or songs, both in a singlepart and in several parts.

Harmonical Interval, in music, denotes the difference oftwo sounds, which is agreeable to the ear, whether in consonanceor succession ; and are, therefore, the same with concord. SeeConcord and Interval.

IIarmonicai. Proportion. See Proportion.

Harmonical Series, a series of many numbers in continualharmonical proportion. Thus if there are four or more numbers,of which every three immediate terms are harmonical, the wholewill make a harmonical series: sucli as 30 : 20 : 15 : 12 : 10. Or*if every four terms immediately next each other are harmonical, itis also a continued harmonical series, but of another species, as3, 4, (), 9, 18, 3(), &c.

IIarmonicai. Sounds, an appellation given, by Mr. Sauveur*to sucli sounds as always make a determinate number of vibra-tions, in the time that one of the fundamentals, to which they arereferred, makes one vibration*

HARMONICS, tiie concomitant or accessary sounds, which*upon the principles resulting from the experiments made on sono-rous bodies, attend any given sound, whatever, and render it ap'prctiable. Thus all the aliquot parts of a musical siring produceharmonics, or harmonical sounds.

HARMONY* [ajfzovio.] In the ancient treatises on music that