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be used. Dissolve 9 lb of yellow prnssiate of potash is hot water,

and add the solution to the required quantity of water; then add 14 lb sulphuric acid, 6 lb sal-ammoniac, and about 6 oz. of crystals of protochloride of tin; the merino is placed in the mixture, and the temperature of the dye-bath gradually raised to the boiling point in five hours. The blue gradually formed on the cloth requires brightening in a fresh bath consisting of alum, persalt or tin, and cream of tartar, heated to nearly the boiling point. Red prussiate of potash is used in nearly the same way to dye dark Prussian blues upon wool, bnt as it is more easily decomposed than the yellow prossinto a weaker acid-bath suffices. Theso blues are frequently finished off with logwood to give them a deeper tone,

Prussian blues can also be obtained on such woollen goods as merinoes, by a process of padding, and the use of a colour nearly identical with the so-called French or royal blue used by calico printers. Amixture ispreparedasfollows. Haifa pound of wheaten starch is boiled with about half a gallon of water; in the thin paste thus made 13 oz. of powdered yellow prnssiate are dissolved, and afterwards 6 oz. of tartaric acid; when the mixture is quite cold 1 lb of prnssiate of tin in paste is added, 1J os. oxalic acid, and 3 oz. sulphuric acid; the whole is well mixed and strained. The woollens to be treated are first " prepared," as it is called, by impregnating them uniformly with oxide of tin, and then the above thickened mixture is applied by means of rollers, so that it shall be evenly and smoothly spread over the whole stuff; the cloth is then dried and exposed to the action of steam, which causes the acids to react upon the prussiates, and from a nearly colourless mixture develops an intense bine, which is found to be permanently fixed in the fibre.

Aniline blues.—There are several artificial bine dyes made from aniline and similar bodies, which, yield very brilliant colours on wool and silk. 'They can be easily applied, the goods simply requiring to be worked in their aqueous solution until they have acquired a sufficiently dark tinge. An artificial dye called Nicholson^ blue is differently applied; it is dissolved in an alkaline liquid, and forms then a colourless or nearly colourless solution, with which the goods to be dyed are impregnated; they are then passed into dilute acids, which develop the blue colour.

Litmus and logwood blues.—The other substances which have been used for blue colours, such, for example, as litmus, are of little importance, and are now nearly unknown to the practical dyer. A blue can be obtained from logwood which has some resemblance to indigo blue upon wool, but it is of a very low character both as to stability and shade, and is hardly ever employed by respectable dyers.

Yellow Colours.

Yellow textiles, being less pleasing to the eye, and more readily soiled, are not nearly so much in use as those dyed with the two simple colours blue and red. The chief yellow dyes, besides fustic, are quercitron bark or its concentrated extract flavine, Avignon or Persian berries, and the now almost disused indigenous product, weld. The general mordant for these is tin, sometimes with addition of alum. One or two illustrations will suffice to show the methods of using them.

Fustic yellow.—Fustic is probably the most generally employed yellow dye-stuff for wool; it gives yellewa inclined to orange. For light shades it is not necessary to mordant the wool; it is simply well cleansed, and then heated with fustic decoction and some cream of tartar. For darker shades the wool is boiled with solution of tin and tartar, washed, and then worked in the decoction of fustic.

Picric acid yellow.—Picric acid, one of the artificial colouring matters, gives pure though not deep yellow shades upon silk and wool without the aid of a mordant, the cleansed material being dyed by working it in a warm solution of the acid.

Chromatc of lead yellow.—The yellow most commonly employed for cotton goods is obtained by the use of salts of lead and bichromate of potash. The method of obtaining this colour differs somewhat from any previously described. The cotton, having been properly bleached, is impregnated with a salt of lead, usually by employing a solution of tbe acetate or sub-acetate of lead. The goods are next passed into a milk of lime solution, to which it is prudent to add some acetate of lead, in order to prevent the lime from dissolving the oxide of lead at first precipitated; the result of the lime treatment is that oxide of lead is evenly fixed upon the cotton, the excess of lime and lead is then well washed away, and the goods are passed into a solution of bichromate of potash, where they quickly acquire a bright and deep yellow colour, owing to the formation of the well-known pigment chrome yellow. To facilitate the combination, the bichromate of potash is mixed with as much sulphuric acid as suffices to liberate the whole of its chromium as chromic acid. The yellow-dyed goods require no further treatment than a good washing, the colour being quite fast This yellow is, however, in very little demand, and in ninety-nine

casoa out of s hundred It U immediately converted into »n orange, by passing it through boiling lime-water, which producea the basse chromate known aa chrome orange, which haa alway been in denial d for many articlea of wear

Compound Colour/.

The so-called simple colours—red, blue, and yellow— having now been dealt with, it remains to treat of their combinations, and this may be done brie8y, the processes employed being for the most part similar to those already described. The compound shades in Chevreul's chromatic nomenclature amount to nearly 15,000, and it is very probable that fully that number are produced by the dyers of the present day. For practical treatment, however, the compound colours can be reduced to comparatively few classes. Mixing the simple colours one and one we obtain three compound colours,—blue and yellow give green, blue and red give purple, yellow and red give orange; while there may be a normal green, purple, and orange, it is evident that all the varieties of these several colours will depend upon the proportions of their constituents. If the three simple colours be mired together, say in equal proportions, we may get a normal brown, or even a black; but if in unequal proportions, an immense number of shades, varying from the imagined normal brown to grey and drab, are produced. Although in many cases compound shades are produced by means of two or more simple colours, there are many natural as well as artificial dye stuffs which yield them ready formed, and frequently purer than they can be otherwise obtained. Most of these will be found mentioned in the following brief notice of practical processes in use.

Obb Colours.

Lo-lcao or Chinese green.—Until about the middle of the present century there was not an instance known of any green on textiles which was not composed of the two separate colours bine and yellow. About that time some green-dyed cottons, imported into France from China, attracted the attention of chemists, who were surprised that they could not separate the green into blue and yellow constituents. Inquiries showed that the Chinese employed a green colouring matter called Lo-kao, until then dnknown in Europe. It waa a costly dye-stun", selling in China for its weight of silver. Some quantity of it was imported and used in silk-dyeing by the French; it waa not, however, found altogether satisfactory, and has at length been quite abandoned for the aniline greens, which are in every respect preferable.

Aniline green.—There are two or three kinds of artificial green dyes in use, of which that known as methyl-aniline green, applied in silk dyeing, is most in request. The so-called iodine green has also been somewhat extensively employed for all kinds of fabrics.

These artificial and unstable materials are the only dye-stuffs for green possessed by the dyer, who is compelled to produce the colour by means of blue and yellow elements. The arsenical mineral green and the oxide of chromium green may be just mentioned as of extremely limited employ. The bluea used in dyeing green are indigo, Prussian blue, and the sulphate of indigo. The yellows are afforded by Persian berries, quercitron, fustic, or the yellow chromate of lead. The processes employed consist, for the most part, iu the separate application of the bine and yellow; for example, in dyeing a fast green upon wool from indigo and any of the yellow dye-stuffs, the blue is first produced as previously described, and the proper mordant for the yellow is then applied to the cloth, which is afterwards placed in the yellow colouring matter; the two colours are so intimately mixed as to be indistinguishable even by high magnifying powers. It may be observed that the reception of the blue does not to any perceptible extent dimininh the power of the cloth to combine with the yellow.

Prussiaie green Prussian blue ia employed aa a basis in the same

manner, only not being capable ot resisting chemical agents so well as indigo blue, it demands more care. The greens with Prussian blue bases are more lively than those made with indigo, but are not so fast. Sulphato of indigo is even less stable than Prussian blue. It is, however, cheap and easy of application, and gives rich colours. The greens made with chromate of lead are for the most part coalined to cotton goods, and are not in much demand.

Oranob Coloubs. For cotton the chief orange-dye is the chromate of lead compound already described, for other materials the orange colours employed

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Arnoito orange.—A warm solution of arnotto in weak alkalies is used without mordant to impart to silk an agreeable orange shade. Its colour is generally considered too yellow, but may be made redder by treatment with weak acids, or by previously mvinff the silk a light red foundation. * v ^

Picric acid orange.—Another orange on silk can be dyed by ■unerimposing on a light pink a yellow obtained from picric acid.

Nitric acid orange.—Bilk can also be permanently stained of a yellowish orange by means of moderately strong nitric acid, which most, however, be applied with great care, since a more than momentary contact would be very injurious to the strength of the fibre. This method of dyeing silk was formerly much used for handkerchiefs; by protecting certain parts from the add with melted wax or similar resists, white designs were produced upon an orange ground.

Purple Colours.

The purple colours may be held to include all shades produced by an admixture of red and bine, such for example as lilac, violet, mauve, 4c, and are of immense variety.

Aniline purple*.—8ince their discovery aniline colours have been almost exclusively employed for dyeing silk and wool purple, yielding as they do shades which for lustre and purity surpass any obtainable from the older colouring matters, and possessing also a fair amount of stability. An aaueous solution of the dye without mordant is all that is required, and the goods when dyed need very little subsequent treatment The aniline purples, violets, and mauves do not dye upon cotton without previous mordanting, and even then are so loose and unstable that they are only fitted for use where great fixity is not demanded, as for linings of clothing, &c. The most general mordant for the aniline purple colours on cotton consists of a tannate of tin obtained by first steeping the cotton in a solution of tannic acid, or in decoction of gall-nuts, sumach, or myrobalans, all of which contain tannic acid; after a few hours' contact a considerable quantity of tannic acid has become firmly attached to the cotton, and the goods, being now treated successively with stannate of soda and dilute sulphuric acid or in other ways, acquire a certain proportion of oxide of tin, and are prepared to receive the colours.

Madder purple.—But the purple colour par excellence upon cotton is obtained from madder or alizarin, the mordant being oxide of iron or a sub-salt of iron deposited on the fibre by treatment with the commercial pyrolignite of iron, commonly called iron liquor. This purple is remarkable for great permanency. It is very largely used in combination with black and white in the best kind of printed calicoes.

Archil purple.—Archil and cudbear are sources of purple colours on wool and silk. The shades produced are rich and beautiful; they are not, however, very permanent, and have been nearly superseded by the aniline colours. Of the few instances that can be cited of stuffs dyed purple by the direct union of red and blue colouring matters, the violet or purple woollen cloth used for ecclesi

astical purposes is an example. The indigo colour is first fixed and cleansed, and then the cloth is dyed with cochineal and tin mordants in the way already described for dyeing scarlet The purple thus obtained is a fast colour, but is very costly, and on that account is not much worked.

The common shades of purple, violet, lilac, Ac., upon wool are obtained from logwood with a mordant of alum and tartar: the red woods are sometimes employed in conjunction with logwood for these colours, which are "topped" with archil to give them more brilliancy.

The extensive range of colours, comprising all the shades of brown, bronze, chocolate, nut, wood, drab, and grey, which may be considered as compounded of the three elementary colours, some one of the three predominating, can;only be briefly treated of in this article. Most of them are actually produced by the use of dye-stuffs yielding the three simple colours; out there are colouring matters like catechu, which themselves yield brown colours, and others, such as logwood, which may be held to contain two or more of the simple colours, the blue predominating. A few illustrations will show how these triply compounded colours are produced by the dyer.

Brown Colours.

Rronu brown on wool.—The wool is mordanted with alum and tartar in the usual way, and is then dyed in a mixture of fustic and madder or other equivalent red and yellow dye-stuffs; for fast colours a blue part can oe communicated to it by the indigo vat. For a lower class of colours no indigo is used, but instead, a mixture of yellow wood (fustic or quercitron) with madder for the red, and logwood for the blue part; or again, the sulphate of indigo may be employed for the blue.

Tm broum.—Accordiaei to Mr Jairoain, the wool is mordanted

by boiling it for an hour with one per cent of its weight of bichromate of potash; it is then washed, and transferred to the dyeing vessel, with the following percentages of its weight of materials :— madder, 8*2: fustic 4*8; camwood. 2; barwood. 1*75; sumach, 2-1 : with these materials it is boiled for two hours.

Bark drab.—From the same authority we take the following as the weights required to dye 100 lb wooL previously mordanted with 1 lb of bichromate of potash:—camwood. 64 lb: sumach. 21b; madder. 24 lb ; fustic, 4 lb ; logwood. 2J tb ; boil for one hour and a half, and afterwards, to darken the colour, pass into water containing 1 lb ol sulphate of iron.

Black Colours.

Black, from a dyer's point of view, is compounded of the thrw simple colours, reo, yellow, and blue, in a state of concentration; but m reality the blue predominates in all good black colours, and

gives them their density and at the same time their lustre. What 1 called a dead black, crape black, or jet black, is the neanst approach to a neutral black, but even this would be brownish if the blue did not predominate. It is often extremely difficult to obtain a black dye to suit a particular market Of ten pieces appearing equally black to the uninitiated, an expert would, |*rhaps, pronounce one to be sooty, another purple, another red, another brown, another green, and so on.

We should have to go back some years in the history of dyeing, to find a time when black was actually dyed with the thrve elementary colours. In some processes blue from indigo was fin>t applied, and then, upon an alum mordant, red and yellow from madder and weld respectively; such a colour was unexceptionable for stability, but its great cost caused it to be disused.

At the present day, logwood is the chief dye-stun" for blacks upon wool or cotton, and gall-nuts and other astringents for silks. Aniline black, on account of obstacles to its application, cannot be said to have yet established itself in dyeing proper, though it is much and highly valued in calico printing.

Blade dye upon silk.—Silk easily takes a black by treatment first with decoction of gall-nuts, and subsequently with a salt of iron. For blue blacks the silk is usually first dyed with Prussian blue, and then with gall-nut black. Extract of chestnut-wood with an iron mordant gives a good black. In modern black silk dyeing, materials are heaped upon the fibre which are not necessary to its colour, but which increase its weight in an extraordinary manner, so as not only to compensate for the loss of 25 per cent of natural gum in the silk, but even, in some cases, to double or treble tho original weight The silk is, of course, much injured by the accumulation of foreign matters upon it, the fibre becoming harsh and brittle, and soon showing the effects of wear. The chief substances used for weighting are lead salts, catechu, iron, and galls, with soap or fatty matter, to soften in some degree the harshness these occasion.

Black upon wool. —Upon woollen cloth of fine quality, the black is dyed upon a basis of indigo blue, and, from the use of woad for this colour, such blacks are in England called " woaded blacks." The first process, therefore, in' producing the best black is to dye the wool in the indigo vat of a tolerably deep shade of blue, and afterwards boil it in a mixture of logwood and sumach, treating it with sulphate of iron; the latter process being two or three times repeated, a very perfect and durable black is obtained, provided the indigo basis is sufficiently deep, and only a minimum quantity of logwood has been employed, say about one-fourth the weight of the sumach.

Common black.—Common blacks upon wool have noindigo in their composition, but are dyed chiefly with logwood and iron salts; the wool and logwood are heated together for some time, and then sulphate of iron is added to the dye-bath. In other blacks of somewhat better quality, the woollen is boiled for some time with solution of iron, copper, and aluminium salts, together with tartar, and when the mordanting oxides have been fixed, the colour is dyed up in logwood. The bichromate of potash mordant can also be used for the black dye, and the cloth can be "bottomed " with camwood or barwood; it is then dyed up with logwood, to which fustic or sumach may be added.

Black upon cotton.—Almost the only ordinary black in cotton dyeing is obtained from logwood with iron mordant; sumach is sometimes used, and very rarely the black is dyed upon an indigo bine basis by means of sumach or galls and iron. As before stated, aniline black has not yet been practically applied in dyeing cotton. A common method is to first heat the goods for some hours with decoction of sumach, wash mordant in sulphate of iron, and then dye in logwood; another method consists in fixing an iron basis upon the cotton by the method given above (page 578), and dyeing in logwood, along with a portion of sumach or fustic, according to the shade required.

Velvet dyeing.—The most important branch of black dyeing upon cotton goods, is that employed for cotton velvets and velveteens, in which it is desired to produce a rich lustrous effect: the process is long, tedious, and uncertain, consisting of

applications of sumach, sulphate or acetate of iron, sulphate of copper, logwood, and fustic,—the end chiefly aimed at being the

Sreduction of a black with blush or violet bloom. The Manchester yers formerly held a monopoly of this blue-black upon velvet, as it is called, but of late years the German dyera have shown them- ■ selves very formidable competitors in dyeing this class of goods.

Theory Of Dyeing.

When the great variety of processes employed in dyeing is taken into consideration, it is apparent that there must be some difficulty in constructing a general theory which shall be applicable to every case.

The earlier writers who endeavoured to generalize the principles of the art considered that the particles of colour were mechanically deposited in the pores of the fibre. The use of chemical substances in dyeing was held necessary only to dilate the pores for the admission of the particles, to prepare the particles for entrance into the pores, or to close up the pores after the colouring particles had entered. Mordants were held to be necessary because they formed cavities in the fibre adapted by their size and shape to receive and retain different kinds of coloured particles. About the middle of the last century Bergmann, observing the dyeing of wool by sulphate of indigo; considered that what took place was a purely chemical action, and that the matter of the wool entered into chemical combination with the dye-stuff, changing it from a soluble into an insoluble substance, and showing therein the power of chemical affinity. From this time the mechanical or physical theory of dyeing was supplanted by a chemical theory, in which all the observed facts were explained by the assumption that chemical forces operated between the fibre and the mordant, or the fibre and the colouring matter. A closer consideration by a later generation of chemists of all the phenomena of dyeing and of the nature of the materials employed did not tend to support this theory. About 1840 Dumas, the celebrated French chemist, and Crum of Thornliebank, a skilful chemist and a practical dyer, formally disputed the existence of a chemical action in dyeing, and referred the phenomena to physical causes of attraction on the part of the fibre. Crum confined himself to the single case of the dyeing of cotton, and expressed himself convinced that it was owing either to surface contact of the dye stuff with the cotton or to its entrance into the hollow tubes of the same, the colours produced in the first case not being so stable as in the other, as far as resisting friction went. The power which cotton fibre evidently possesses of appropriating oxides from solutions, as well as colouring matters, such as indigo, was viewed by Crum as a case of surface attraction, similar to the power residing in charcoal of abstracting oxides and colouring matters from solutions, and he declared there was no such thing as a chemical combination between the cellulose of the cotton fibre and any of the chemical substances or dye materials. To controvert this statement is difficult, for, though the forces at work seem to be chemical forces, the products cannot be proved to be definite chemical compounds. On the other 'hand, the forces of catalysis, surface attraction, and powers of porous substances which Crum substitutes for the chemical forces of the older theories of dyeing, may be said to be merely names, without definite meaning, for indicating the existence of a class of phenomena not at all understood even at the present day. Dumas views the questions more broadly, and simply declines to accept as chemical phenomena actions which do not produce real chemical compounds. He considers that dyeing is more probably owing to a physical property of fibres by which they are enabled to attract and retain coloured bodies, much in the same way that animal charcoal does, and simply because the nature of the powers exercised by charcoal are not accepted as chemical, and no one knows what they are, dyeing cannot be considered as an effect of

chemical attraction or affiuity. He admits, however, thai there are some powers at work different from that possessed by charcoal. How is it, he asks, that wool takes up the scarlet dye so well under conditions where silk and cotton are barely tinged with colour 1 How is it that wool unites with the black precipitate formed with tannin and iron salts, while silk under the same circumstances is so difficult to dye 1 He asks, finally, how it is that certain colours can bo fixed better on some fibres than others; and whether it is not by some special action, not correctly called affinity, but which at any rate is an important force, or the resultant of several forces, that this is affected. But, he continues, to confound chemical affinity, properly so called, with the phenomena of dyeing is to confound two very different things. When silk unites with Prussian blue, or wool with indigo, the action is quite distinct from what takes place when sulphur combines with lead. But, on the other hand, again, fibres are not to be looked upon as acting simply the part of a filter in retaining colours.

Chevreul, at a later date, insists that in the present state of our knowledge the phenomena of dyeing can be explained only upon chemical principles. He admits that colour may be and in practice is frequently deposited upon the external parts of fibres, but there are numerous cases in which a soluble salt is decomposed by fibrous matters, as when silk is steeped in persulphate of iron; and he cannot consider as anything else thau chemical affiuity that power which enables a solid body to decompose a solution of elements, themselves united by chemical affinity, and which without the contact of the solid body would have remained in perfect union. Many other chemists, physicists, and microscopists have occupied themselves upon this vexed question, but without evolving any generally acceptable theory of dyeing. The balance of opinion may be said to be in favour of (he supposition that as far as regards the animal fibres, wool and silk, there are many cases of dyeing which can only be regarded as effected by chemical powers; with respect to the vegetable materials cotton and linen, the evidence is less certain, and we must wait for further research and investigation to seilie the disputed question.

Books of Reference.—Of the numerous works upon dyeing it may be sufficient to mention Bancroft's Philosophy of Permanent Colmtrs (2d ed. 1818); Berthollet's Elements de la Teinture, and lire's translation of the same into English (1841); Persoz's Traite de Vhnprasion dee Tissus (1846),—a most complete and accurate work for its date: O'Neill's Chemistry of Calico Printing and Dyeing (I860), and Dictionary of Dyeing (1862); Napier's Manual of Dyeing (3d ed. 187S); Schutzenberger's. TraiU dee Matures Colorantes (1867); Crookes'sDyeing and Calico Printing (1874); and Crace-Celvert'a Dyeing and Calico Printing (1875). Of periodicals specially devoted to the application of colouring matters to textiles there is only one in Great Britain, The Textile Colourisl; Germany has the Farber-Zeilung and the Muster-Zeitung; in France there are the Mbniteur de la Teinture and Le Teinturier pratique. Original articles upon the subject occasionally appear in the chemical journals, and especially in the Bulletins of the Industrial Societies of Mulhouae and Rouen. (C. O'N.)

DYER, John, English poet, was bom in 1639 or 1700 at Aberglasney, in Carmarthenshire, where his father, Robert Dyer, successfully practised as a solicitor. He was sent to Westminster school to be educated under Dr Friend, and was destined to succeed to his father's business. He showed, however, an inveterate dislike to the study of the law, and, having a taste for design, he induced his parents to allow him to adopt the profession of an artist He waudered about South Wales, sketching landscapes and occasionally painting portraits. In 1726 his first poem, Grongar Sill, appeared in a miscellany published by Richard Savage, the poet. It was an irregular ode in the so-called Pindaric style, but Dyer entirely rewrote it into a loose measure of four cadences, and printed it separately iu 1727. It had an immediate and brilliant success. Grongar Hill, as it now stands, is a short poem of only 150 lines, describing in language of much freshness and picturesque charm the view from a hill overlooking the poet's native vale of Towy. Artless in an affected age. the natural images which crowd upon ono another in this charming little poem are as admirable now as when they were written, and hold an assured place in English literature. Dyer's ambition to succeed as a pain .^r impelled him to visit Italy, and about ten years after the publication of Grongar Hill he seems to have attained this great desire, aud to have spent some time in the south of Europe. It was in consequence of this tour that he wrote his next poem, The Ruins at Rome, a descriptive piece in about 600 lines of Miltonic blank verse. Iu this work the phraseology is pompous and conventional, but there is considerable knowledge displayed, and the ardour of a true lover of antiquity. The Ruins of Rome appeared in 1740, and increased its author's reputation. Having fallen into bad health while painting in the Campagna, and finding that he was not destined to excel in the practice of art, he determined to enter into holy orders. In 1741 he was ordained by the bishop of Lincoln, and presented with the living of Calthorpe, in Leicestershire. He was married about this time to a lady descended from the brother of Shakespeare. In 1751 he was translated to the living of Belchford, in Lincolnshire, to which was added in 1752 that of Coningsby. In 1756 he exchanged Belchford for the wealthier incumbency of Kirby-on-Bane. In 1757 he published his longest work, the didactic epic of The Fleece, in four books, of which the first discoursed of the tending of sheep, the second of the shearing and preparatioa of the wool, the third of weaving, and the fourth-of trade in woollen manufactures. The subject was prosy, and the stately blank verse in which it was discussed gave the poem a ridiculous air. The town took no interest in it, and the wits facetiously prophesied that "Mr Dyer would be buried in flannel." He did, in fact, very shortly afterwards follow his poem to the grave, for he died of consumption on the 24th of July 1758, leaving a wife and four children. After his death his genius was defended and his writings analyzed by Scott of Amwell, who published a commentary on Dyer's poems. The latter were collected by Dodsley in 1770, but they only form one small volume. Grongar Hill has been compared with Sir John Denham's Cooper's Hill, which may in some measure have suggested it These two pieces remain the most important topographical poems iu English literature, if we exalude Ben Jonsoc's Pens/iurst.

DYNAMICS properly means that science which treats of the action of force. Defining force as that which affects the motion of matter, it appears that the Etudy of dynamics will lead to the consideration of the motion of material systems, and the laws in accordance with which this motion is changed by the mutual actions of the bodies forming such systems. But there is a sense iu which we may contemplate the geometrical results of the motion of bodies without studying the forces under which, or the time during which, it takes place; and hence there are many problems which at first sight we might be disposed to include under the head of dynamics, but which also belong to the domain of pure mathematics, and may therefore more projKjriy be considered as a branch of geometry. On the other hand, there is a branch of dynamics which treats of pure motion without taking any account of its subject or the means by which it is produced or changed. In this branch, to which the term kinematics, though first employed by Amjicre in a wider sense, may with propriety be confined, it may seem that no consideration of ihatter or of force is involved; but, unlike the class just alluded to, the problems which come under this head involve explicitly the element of time, and it is only after studying the laws of dynamics that we are able to furnish a theoretical measure

of time satisfying the demands of the human mind. Thus any Bubject in which the measurement of time is involved enters on this account into the domain of dynamics.

Measurement of Time.—For ordinary purposes the rotation of the earth furnishes a sufficiently exact means of measuring time, and the observation of the transit of a known star is the best method we possess of determining the error of a clock; but that the fundamental conception of the measurement of intervals of time is based upon other foundation than the diurnal rotation of our planet at onco appears from the fact that we see no inconsistency in asking whether the length of the day is the same now as it was 2000 years ago. H our primary conceptions of the measurement of time were derived from the earth's rotation, the absolute constancy of the length of the day would be amatter of definition. But it is not to the motion of the earth or of any other single body that we are indebted for our highest conception of the measurement of time—it is rather to the dynamical principle expressed in the first law of motion; and hence it is that the theoretical measurement of time, and of other physical quantities which explicitly involve time, most find a place under the head of dynamics. Kinematics may therefore properly be treated as a braucU of dynamics, and for its discussion, as well m for the euunication and explanation of the laws of motion, the reader is referred to the article on Mechanics.

Perhaps there is nothing which appears to present a subject for study simpler than that afforded by the properties of space, and hence it is that geometry attained so high a reputation and made such rapid advances among the ancients. It was easy to construct material standards of length and by their means to measure approximately the linear dimensions of limited portions of space, the human mind being only too ready to believe in the constancy of the dimensions of the standards constructed; and thus the properties of space presented a subject which, at the very outset, afforded a facility for investigation which was wantiug in the study of other physical quantities. The great simplification introduced by this belief in the permanence of the dimensions of material standards will be apparent if we consider the position in which we should be placed by the adoption of a different hypothesis. Once admit the supposition that the properties of a figure, as regards dimensions or form, depend explicitly on its position in space, or upon time, either by a process of growth in themselves or because space is changing its character, and the whole subject of geometry will require reconsideration.

Displacement.—A number of points or figures may be connected in accordance with such geometrical conditions that if one or more be displaced in a given manner the displacements of all the others may be determined. The determination of the displacement of each in terms of the given displacements is a problem in pure mathematics, aud the branch of geometry which treats of such questions may be called the science of displacement If we suppose the figures here contemplated to be material bodies, and the geometrical conditions to be determined by means of material constraints such as links, guides, teeth, and the like, the science of displacement thus applied becomes that of mechanism, and it is only necesary here to call attention to the following statements. First, in the study of displacements, or of pure mechanism, no account is taken, of any but the geometrical properties of the bodies displaced, while the forces engaged in producing the displacement are entirely neglected: the consideration of the mechanical properties of the materials of which the parts of a machine are constructed, the forces acting between those parts, and the best means of "fitting" them, belongs to applied mechanics and machine constniction. Secondly, the element of time is altogether left out of consideration j for, although it may be argued that the displacement of each part of the system takes place in the same interval of time, and that the geometrical conditions enable us to compare the displacements experienced by different parts during the same time, and thus lead us to a comparison of velocities, yet it must be observed that this is only a comparison amounting simply to a relation between corresponding displacements, aud does not involve time explicitly, since the whole displacement may take place in a time as long or as short as we please, for we do not consider it. Moreover, the actual motion of any part may be made uniform or varying in any arbitrary manner without any account being taken of it. In fact it is simply two or more configurations of the material system which are compared together, and, though for the sake of distinction we call one the initial aud another the final configuration, we might as well distinguish them in any other manaer and without stating which follows the other. Indeed we contemplate them as co-existent during the act of comparison. Hence we may complete the science of displacement or pure mechanism without ever considering force, or being able to measure time or even to define equal intervals.

Kinematics.—If to our conceptions of space and of displacement we couple that of time as a measurable quantity, wo are led to compare the rates of non-simultaneous as well as of simultaneous displacements, and are consequently obliged to measure the rate at which displacement occurs by the change of position experienced in a definite interval of time by the body, figure, or point we are regarding. Kate of change of position measured thus we call velocity. The next step in the same direction is the consideration of the rate at which velocity changes, or acceleration, and thus the association of our conception of space with that of time as a measurable quantity opens up to us that branch of dynamics which we call kinematics.

Matter.—Having considered displacement in connection with the time during which it occurs, the next step leads us to take account of the thing displaced, and here we are obliged to contemplate matter directly. Matter, like time and space, we do not attempt to define, but treat it as a primary conception, its more obvious properties making themselves known to all through daily experience.

Furce.—The change of the motion of material bodies brings us at once, through the introduction furnished by the first law of motion, to tho conception of force, which may be defined in terms of three primary quantities, viz., space, time, and matter. The second law of motion expresses the manner in which matter is affected by force, and teacher us how to measure force by the observation of its effects.

The science of dynamics in its restricted sense is that which treats of the consequences arising from the relations of matter to force, and before we can proceed in this science beyond the first step we must become acquainted with the second law of motion, while kinematics requires for its complete development only the first law of motion, its range being thereby sharply defined and separated from that of the rest of dynamics. The laws of motion, like other natural laws, must be understood to express merely the properties of natural bodies as we find them, and within the i degree of accuracy to which our experiments can be relied on. We might, of course, have started with any hypotheses we liked respecting the relations of force to matter, and upon these hypotheses and our conceptions of time and space have constructed a purely theoretical system of dynamics which would have been perfectly self-consistent; but our conclusions might, or might not, have agreed with observations of natural phenomena. If we found an agreement between the results of the application of our theory to special problems and the solutions of the corresponding problems as worked out objectively in nature,

we should have reason to believe that our hypotheses agreed with the facts, or, in other words, that they were true, and we should then raise them to the dignity of natural laws. It is on evidence of this kind that our acceptation of all natural laws is based. If our conclusions were inconsistent with natural phenomena our system of dynamics would be an abstract, instead of a natural, science—if, indeed, it might be called a science at all—and would be valuable merely as an intellectual exercise. In the case of such an abstract science we are not even bound to adopt the axioms respecting tho properties of space which are usually accepted, but may confer upon our "space" any number of dimensions and any properties we please.

Stress.—Though the conception of a single force is convenient, it nevertheless results from a mere process of mental abstraction. We never meet with a single isolated force in nature, but each is accompanied by an equal and opposite force acting in the same straight line, and when we speak of one without the other we do so merely for the sake of brevity. The third law of motion implies this statement, though it has also a wider signification. The action aad reaction which are thus always inseparably linked together may be conveniently called a stress, of which the two forces are opposite aspects. Thus it appears that there is nothiug in nature corresponding to what we are accustomed to call a single force; stresses, indeed, abound, and may be produced whenever we please, but we are completely ignorant of their existence except when they change the relative velocities of different portions of matter. Then, and then only, do they appeal to our senses.

Statics.—The investigation of the conditions under which a system of stresses produces no displacement of the'bodies between which they act constitutes the science of statics, and will be discussed under the head of Mechanics.

Measurement of Force.—Since force can be defined ia terms of cpace, time, and matter, it follow that the measurement of a force ought to involve measurements of these three quantities and of them only. Now it is plain that any force whatever may be chosen as the unit in terms of which other forces should be expressed, provided it is capable of being reproduced at all times and in all places with precision. We all now believe that the quantity of matter in a body is unchanged by changing it: position or by the simple lapse of time, and we also believe that the region of space which we inhabit is sufficiently homoloidal to allow us to compare distances in different directions, at different places, and at different times. Moreover, the first law of motion, as has been stated above, provides, when proper precautions are taken, a method of measuring time which satisfies the requirements of the miud, while the rotation of the earth affords a practical measure of time sufficiently exact for the most refined experiments we can execute. Therefore a unit of force which depends only on the units of length, mass, and time will be the same at all places, and, so far as our experience allows us to judge, at all times. Such a unit is termed an absolute unit. Not only force but every other quantity dealt with in dynamical science, as well as every physical quantity whose relations to space, mass, and time are known, can be measured in terms of a unit of its own kind which depends only on the fundamental units of length, mass, and time, and is then said to be expressed in absolute measure. The three primary units must be chosen in an arbitrary manner, and their permanence must be considered a matterNjf definition; but when these have been once fixed, all the absolute units derived from them are perfectly determinate and invariable. If a foot, a pound,"and a second be chosen as units, the corresponding absolute unit of force is called a poundal; while if the primary units be a centimetre, a gramme, and a second, the unit of force is called a dynt.

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