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upon it with a diamond, they are to be timed by diminishing the thickness of those that are too sharp, which is dope by grinding them round from the neck towards the brim; comparing, by means of a welltuned harpsichord, the tone di awn from the glass by your finger with the note you want, as sounded by the corresponding string of the harpsichord. The largest glass in the instrument is G, a little below the reach of a common voice, and the highest G, including three complete octaves; and they are distinguished by painting the apparent parts of the glasses within side, every semitone white, and the other notes of the octave with the seven prismatic colours; so that glasses of the same colour (the white excepted) are always octaves to each other. When the glasses are tuned, they are to be fixed on a round spindle of hard iron, an inch in diameter at the thickest end, and tapering to a quarter of an inch at the smallest. For this purpose the neck of each glass is fitted with a cork, projecting a little without the neck: these corks are perforated with holes of different diameters, according to the dimension of the spindle in that part of it where they are to be fixed. The glasses are all placed within one another; the largest on the biggest end of the spindle, with the neck outwards; the next in size is put into the other, leaving about an inch of its brim above the brim of the first; and the others are put on in the same order. From these exposed parts of each glass the tone is drawn, by laying a finger upon one of them as the spindle and glasses turn round. The spindle, thus prepared, is fixed horizontally in the middle of a box, and made to turn on brass gudgeons at each end. A square shank comes from its thickest end through the box, on which sunk a , wheel is fixed by a screw: this will serve, like a fly, to make the motion equable, when the spindle is turned by the foot like a spinning-wheel. The wheel is eighteen inches in diameter, and conceals near its circumference about twenty-fire pounds of lead, and may be made of mahogany. An ivory pin is fixed in the face of the wheel, about four inches from the axis; overwliicli is put the loop of the string that comes up from the moveable step to give it motion. The box is about three feet long, eleven inches wide at the biggest end, and five inches at the smallest end ; it is made with a lid, which opens at the middle of its height, and turns up by back-hinges. The instrument, thus, completed, stands on

a neat frame with four legs. This instrument is played upon by sitting before it, as before the keys of a harpsichord, turning the spindle with the foot, and wetting the glasses, now and then, with a sponge and clean water. The fingers should be first soaked in water; and rubbed occasionally with fine chalk, to make them catch the glass, and bring out the tone more readily. Different parts may be played together by using both hands ; and the tones are best drawn out when the glasses turn from the ends of the fingers, not when they turn to them. The advantages of this instrument, says Dr. Franklin, are, that its tones are incomparably sweet beyond those of any other; and that they may be swelled and softened at pleasure by stronger or weaker pressure of the finger; and continued to any length: and, when it is once well tuned, it never again wants tuning. Franklin's Letters, &c.

Harmonica!, arithmetic, that part of arithmetic which considers musical intervals, expressed by numbers, in order to our finding their mutual relations, compositions, and resolutions.

Harmonical composition, in a general sense, includes both harmony and melody, i. c. of music or songs, both in a single part, and in several parts. In its more proper and limited sense, harmonical composition is restrained to that of harmony ; and may be defined the art of disposing and concerting several single parts together, so as to make one agreeable whole.

Harmonical interrul, in music, denotes the difference of two sounds, which is agreeable to the ear, whether in consonance or succession; and are, therefore, the same with concord.

Harmonical proportion, or tmaical proportion, is that in which the first term is to the third, as the difference of the first and second is to the difference of the second and third; or when the first, the third, and the said two differences, are in geometrical proportion. Or, four terms are in harmonycal proportion when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth. Thus 2, 3, 6, are in harmonical proportion, because * : 6 :: 1 : 3. And the four terms 9, 12, 16, 24 are in harmonical proportion, because 9 : 24 :: 3 : 8. If the proportional terms be continued in the former case, they will form an harmonical progression, or series, l. The reciprocals of an arithmetical progression are in harmonica! progres

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; ft e contra. 3. If three or

.oers in harmonical proportion be

multiplied or divided by some man-

, the products, or the quotients, will still

<e in hurmonical proportion. Thus, the

barmonicals 6, 8,12, multiplied by 3, give

12, 16, 34, or divided by 3, give 3, 4, 6,

which are also harmonical*. 3. To find a

harmonical mean proportional between two

terms: divide double their product by their

sum. 4. To find a third term in harmonical

proportion to two given terms: divide their

product by the difference between double

the first term and the second term. 5. To

find a fourth term in harmonical proportion

to three terms given: divide the product of

the first and third by the difference between

double the first and the second term. Hence,

of the two terms a and b the harmonical

mean is - , A; the third harmonical pro

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, also to a, b, c, the fourth

6. If there be taken

«a — b'

an arithmetical mean and a harmonical mean between any two terms, the four terms will be in geometrical proportion. Thus, between 2 and 6 the arithmetical mean is 4, and the harmonical mean is :',; and hence S : 3 :: t : 6. Also, between it and b the

arithmetical mean is ~\ , and the harnio

2ab Sab

meal mean is —T—t; but a : —r--:: u-f-o a-J-o

2

Harmonical scries, a series of many numbers in continual harmonical proportion. Thus, if there are four or more numbers, of which every three immediate terms are harmonical, the whole will make an harmonical

VOL. HI.

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series: such is 30 : 30 : 15 : 13 : 10. Or, if every four terms immediately nest each other are harmonical, it is also a continual harmonical series, but of another species, as 3,4, 6,9, 18, 36, &C.

Harmonical sounds, an appellation given to such sounds as always make a determinate number of vibrations in the time that one of the fundamentals, to which they are referred, makes one vibration.

Harmonical sounds are produced by the parts of chords, &c, which vibrate a certain number of times, while the whole chord vibrates once.

The relations of sounds had only been considered in the series of numbers, 1 : t, 2 : 3, 3 : 4, 4 : 5, &c. which produced the intervals called octave, fifth, fourth, third, &c. M. Sauveur first considered them in the natural series, 1, 3, S, 4, 5, &c. and examined the relations of sounds arising therefrom. The result is, that the first interval, 1 : 2, is an octave; the second, 1 :3, a twelfth; the third, 1:4, a fifteenth, or double octave; the fourth, 1 : 5, a seventeenth, the fifth, l : 6, a nineteenth, &c.

The new consideration of the relations of sounds is more natural than the old out-, and is, in effect, all the music that nature makes without the assistance of art.

HARMONICS, that part of music which considered the differences and proportions of sounds, with respect to acute and grave; in contradistinction to rhyme and metre.

HARMONY, in music, the agreeable result, or union, of several musical sounds, heard at one and the same time; or the mixture of divers sounds, which together have an effect agreeable to the ear. As a continued succession of musical sounds produces melody, so does a continued combination of these produce harmony. See Music.

Harmony »/' the spheres, or Celestial Harmony, a sort of music much talked of by many of the ancient philosophers and fathers, supposed to be produced by the sweetly-tuned motions of the stars and planets. This harmony they attributed to the various proportionate impressions of the heavenly globes upon one another, acting at proper intervals. It is impossible, according to them, that such prodigious large bodies, moving with so much rapidity, should be silent; on the contrary, the atmosphere, continually impelled by them, must yield a set of sounds proportionate to the impression it receives; consequently as they do not all run the same circuit, nor Ff

HAR

with one and the same velocity, the different tones arising from the diversity of motions, directed by the hand of the Almighty, must form an admirable symphony, or concert. They therefore supposed, that the moon, as being the lowest of the planets, corresponded to mi; Mercury, to fa; Venus, to sol; the sun, to lay ; Mars, to «; Jupiter, to cut ; Saturn, to re; and the orb ot the fixed stars, as being the highest of all, to mi, or the octave.

HARP, a musical instrument of the string kind, of a triangular figure, held upright between the legs of the person who plays upon it. See Musical Instruments. Harp, Eolian. See Acoustics. HARPINGS, in a ship, properly denote her breadth at the bow. Some also give the same name to the ends of the bends that are fastened into the stern.

HARPSICHORD, the most harmonious of all the musical instruments of the stringkind. It is played on after the manner of the organ, and is furnished with a set, and sometimes with two sets, of keys; the touching or striking of these keys move a kind of jacks, which also move a double row of chords, or strings, of brass or iron, stretched over four bridges, on the table of the instrument. See Music.

HARPOON, sometimes called harpingiron, a spear or javelin, used to strike the whales in the Greenland and South Sea fisheries. It is furnished with a long shank, and has, at the one end, a broad and flat triangular head, sharpened at both edges, so as to penetrate the whale with facility : to the other end of this weapon is fastened a long cord, called the whale-line, which lies carefully coiled in the boat, so as to run out without being entangled. See Fishery, whale.

The gnn-harpoon is a weapon used for the same purpose, but is fired out of a gun, instead of being thrown by hand. It is made of steel, and has a chain attached to it, to which the line is fastened.

HARTSHORN, spirit of. See AmMonia.

HARTOGIA, in botany, a genus of the Tctrandria Monogynia class and order. 'Natural order of Dumosa-. Rhamni, Jussieu. Essential character: calyx five-cleft; petals four, spreading; drupe ovale, inclosing two seeds. There is but one species, viz. H. capensis, found in the woods near the Cape of Good Hope. HARVEST/y, in zoology, a large four.

winged fly, of the cicada kind. See CiCada.

HASSELQUISTIA, in botany, so named, in memory of Frederick Hasselqnist, M. D. a genus of the Pentandria Digynia class and order. Natural order of Umbellate. Essential character: corolla radiated, in the disk, male: seeds in the circumference double, with a notched edge , in the disk solitan-, pitcher-shaped, hemispherical. There are two species.

HAT making. The materials for making hats, are rabbit's fur, cut off from the skin, after the hairs have been plucked out, together with wool and beaver.

The two former are mixed in various proportions, and of different qualities, according to the value of the article intended to be made; and the latter is universally used for facing the finer articles, and never for the body or main stuff. Experience has shown that these articles cannot be evenly, and well felted together, unless all the fibres be first separated, or put into the same state with regard to each other. This is the object of the first process, called bowing. The materials, without any previous preparation, are laid upon a platform of wood, or of wire, somewhat more than four feet square, called a hurdle, which is fixed against the wall of the work-shop, and is enlightened by a small window, and separated by two side partitions from other hurdles, which occupy the rest of the space along the wall. The hurdle, if of wood, is made of deal planks not quite three inches wide, disposed parallel to the wall, and at the distance of one-fortieth, or one fiftieth of an inch from each other, for the purpose of suffering the dust, and other impurities of the stuff, to pass through; a purpose still more effectually answered by the hurdle of wire.

The workman is provided with a bow, a bow-pin, a basket, and several cloths. The bow is a pole of yellow deal-wood, between seven and eight feet long, to which are fixed two bridges, somewhat like that which receives the hair in the bow of the violin. Over these are stretched a catgut, about one-twelfth part of an inch in thickness. The bow-pin is a stick with a knob, and is used for plucking the bow-string. The basket is a square piece of orier work, consisting of open strait bars with no crossing or interweaving. Its length across the bars may be about two feet, and its breadth eighteen inches. The sides into which the bars are fixed are slightly bonded into a circular curve, so that the basket may be set upright on one of these edges near the right hand end of the hurdle, where it usually stands. The cloths are linen and dyed of a dark olive brown. Besides these implements, the workman is also provided with brown paper.

The bowing commences by shovelling the materials towards the right hand partition with the basket, upon which, the workman holding the bow horizontally in his left hand, and the bow-pin in his right, lightly places the bow-string, and gives it a pluck with the pin. The string in its return, strikes part of the fur, and causes it to rise, and fly partly across the hurdle in a light open form. By repeated strokes, the whole is thus subjected to the bow, and this beating is repeated till all the original clots or masses of the filaments are perfectly opened and separated. The quantity thus treated at once, U called a batt, and never exceeds half the quantity required to make one hat.

When the batt is sufficiently bowed, it is ready for hardening, which term denotes the first commencement of felting. The prepared material being evenly disposed on the hurdle, is first pressed down by the convex side of the basket, then covered with a cloth, and pressed successively in its various parts by the hands of the workman. The pressure is gentle, and the bands are very slightly moved backwards and forwards, at the same time, through a space of perhaps a quarter of an inch, to favour, the hardening or entangling of the fibres. In a very short time, indeed, the stuff acquires sufficient firmness to bear careful handling. The cloth is then taken off, and a sheet of paper, with its corners doubled in, so as to give it a triangular outline, is laid upon the batt, which last is folded over the paper as it lies, and its edges, meeting one over the other, form a conical cap.

The joining is soon made good by pressure with the hands on the cloth. Another batt, ready hardened, is in the next place laid on the hurdle, and the cap here mentioned placed upon it with the joining downwards. This last batt being also folded up, will consequently have its place of junction diametrically opposite that of the inner felt, which it must therefore greatly tend to strengthen. The principal part of the hat is thus put together, and .now requires to be worked with the hands

a considerable time upon the hurdle, the cloth being also occasionally sprinkled with clear water. During the whole of this operation, which is called basoning, the article becomes firmer and firmer and contracts in its dimensions. It may easily be understood, that the chief use of the paper is to prevent the sides from felting together.

The basoning is followed by a still more effectual continuation of the felting, called working. This is done in another simp, at an apparatus called a battery, consisting of a kettle (containing water slightly acidulated with sulphuric acid, to which, for beaver hats,* a quantity of Die grounds of beer is added, or else plain water tor rinsing out), and eight planks of wood joined together in the form of a frustrum of a pyramid, and meeting in the kettle at the middle. The outer or upper edge of each plank'is about two feet broad, and rises a little more than two feet and a half above the ground; and the slope towards the kettle is considerably rapid, so that the whole battery is little more than six feet in diameter. The quantity «f sulphuric acid added to the liquor is not sufficient to give a sour taste, but only renders it rough to the tongue. In this liquor, heated rather higher than unpractised hands could bear, the article is dipped from time to time, and then worked on the planks with a roller, and also by folding or rolling it up, and opening it again; in all which, a certain degree of care is at first necessary to prevent the. sides from felting together; of which, in the more advanced stages of the operation, there is no danger. The imperfections of the work now present themselves to the eye of the workman, who picks out the knots, and other hard substances with a bodkin, and adds more felt upon all such parts as require strengthening.

This added felt is patted down with a wet brush, and soon incorporates with the rest. The beaver is laid on towards the conclusion of this kind of working. Some workmen say that the beer grounds used with beaver hats, by rendering the liquor more tenacious, the hat is enabled to bold a greater quantity of it, for a longer time; but others say that the mere acid and water would not adhere to the beaver facing, but would roll oft' immediately when the article was laid on the plank. It is probable that the manufacturers who uow follow the established practice, may not have tried what are the inconveniences this addition is calculated to remove.

The acid, no doubt, gives a roughness to the surface of the hair, which facilitates the mechanical action of felting. Nitrous acid is used in a process called carrotting; in this operation the material is put into a mixture of the nitrous and sulphuric acids in water, and kept in the digesting heat of a stove all night. The hair acquires a ruddy or yellow colour, and loses part of its strength. It must be remembered that our hat still possesses the form of a cone, and that the whole of the several actions it has undergone have only converted it into a soft flexible felt, capable of being extended, though with some difficulty, in every direction. The next thing to be done is to give it the form required by the wearer. For this purpose, the workman turns up the edge or rim to the depth of about an inch and a half, and then returns the point back again through the centre or axis of the cap, so far as not to take out this fold, but to produce another inner fold of the same depth. The point being returned back again in the same manner produces a third fold; and thus the workman proceeds until the whole has acquired the appearance of a flat circular piece, consisting of a number of concentric undulations or folds, with the point in the centre. This is laid upon the plank, where the workman, keeping the piece wet with the liquor, pulls out the point with his fingers, and pressed it down with his hand, at the same time turning it round on its centre in contact with the plank, till he has, by this means, rubbed out a flat portion equal to the intended crown of the hat. In the next place he takes a block, to the crown of which he applies the fiat central portion of the felt, and by forcing a string down the sides of the block, he causes the next part to assume the figure of the crown, which he continues to wet and work until it has properly disposed itself round the block. The rim now appears like a flounced or pnekered appendage round the edge of the crown, but the block being set upright on the plank, the requisite figure is soon given by working, rubbing, and extending this part. Water only is used in this operation of fashioning or blocking, at the conclusion of which it is pressed out by the blunt edge of a copper implement for that purpose.

Previous to the dying, the nap of the hat is raised or loosened out with a wire brush,

or carding instrument; the fibres being too rotten after the dying to bear this operation. The dying materials are logwood, and a mixture of the sulphates of iron and copper, known in the market by the names of green copperas and blue vitriol.

The dyed hats are, in the next place, taken to the stiffening shop. One workman, assisted by a boy, does this part of the business. He has two vessels, or boilers, the one containing the grounds of strong beer, which costs seven shillings per barrel, and is used in this and other stages of the manufactory as the cheapest mucilage which can be procured; and the other vessel containing melted glue, a little thinner than it is used by carpenters. The beer grounds are applied in the inside of the crown to prevent the glue from coming through to the face, and also to give the requisite firmness at a less expense than could be produced by glue alone. If the glue were to pass through the hat in different places, i t might be more difficult to produce an even gloss upon the face in the subsequent finishing. The glue stiffening is applied after the beer-grounds are dried, and then only upon the lower face of the flap, and the inside of the crown. For this purpose the hat is put into another hat, called a stiffening hat, the crown of which is notched, or slit open, in various directions. These are then placed in a hole in a deal board, which supports the flap, and the glue is applied Mwith a brush.

The dry hat, after this operation, is very rigid, and its figure irregular. The last dressing is given by the application of moisture and heat, and the use of the brush and a hot iron, somewhat in the shape of that used by tailors, but shorter and broader on the face. The hat being softened by exposure to steam, is drawn upon a block, to which it is securely applied by the former method of forcing a string down from the crown to the commencement of the rim. The judgment of the workman is employed in moistening, brushing, and ironing the hat, in order to give and preserve the proper figure.

When the rim of the hat is not intended to be of an equal width throughout, it is cut by means of a wooden or metallic pattern. The contrivance is very simple and ingenious. A number of notches are made in one edge of a flat piece of wood for the purpose of inserting the point of a knife, and from one side or edge of this piece of wood there proceeds a straight handle,

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