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about two months. When it begins to flower, it is cut with pruning knives, an operation which is repeated about six weeks afterwards in wet weather. It is seldom suffered to continue more than two years, being then supposed to degenerate; when it is dug up, and a new crop sown in its stead.

From the leaves of the small branches is prepared that excellent dye which is known by the name of INDIGO. The leaves, when cut down, are thrown into large vats of water, where they are suffered to remain till a considerable fermentation ensues, and the water progressively acquires a violet colour. This happens in about sixteen or eighteen hours from the commencement of the infusion, at which time the water is conveyed by means of cocks at the bottom of the vat into another vessel, in which it is constantly agitated by a kind of churn till it becomes frothy all over the surface, and every part is intimately blended with every part. It is then allowed to settle, and the superincumbent water being drawn off, the indigo remains at the bottom of the vessel like a sediment or feculence.

The negroes on the coast of Guinea gather the leaves of the plant at any season of the year, pound them into a paste which they dry and preserve in the form of loaves. When they want to use them for the purpose of dyeing, they dissolve them in a ley, for which they usually prefer the ashes of the sea purslane, the fortulaca minima latifolia of Plumier, by the negroes called rheme. This ley imbibes a tincture of the indigo, into which they dip their linen cold, and repeat the immersion according to the depth of coJour they intend to give it. Indigo, or a substance very similar to it, both in external colour and chemical test, may be obtained from various other plants, and especially from different species of amorpha, sophora, and isatis, but not in equal quantity nor equal excellence with the indigo of the indigofera or real indigo plant.

INDIGO is a soft powder, of a deep blue, without either taste or smell. It undergoes no change, though kept exposed to the air. Water, unless kept long upon it, does not dissolve any part of it, nor produce any change. When heat is applied to indigo, it emits a bluish red smoke, and at last burns away with a very faint white flame, leaving behind it the earthy parts in the state of ashes. Neither oxygen nor the simple combustibles have any effect upon indigo, except it is in a state of solution; and the same remark applies to the metallic bodies. The fixed alkaline solutions have no action on indigo, except it is newly precipitated from a state of solution. In that case they dissolve it with facility. The solution has at first a green colour, which gradually disappears, and the natural colour of the indigo cannot be again restored. Hence we see that the alkalies, when concentrated, decompose indigo. Pure liquid ammonia acts in

the same way. Even carbonate of ammonia dissolves precipitated indigo, and destroys its colour; but the fixed alkaline carbonates have no such effect. Lime-water has scarcely any effect upon indigo in its usual state; but it readily dissolves precipitated indigo. The solution is at first green, but becomes gradually yellow. When the solution is exposed to the air, a slight green colour returns, as happens to the solution of indigo in ammonia; but it soon disappears.

The action of the acids upon indigo has been examined with most attention, it certainly exhibits the most important phenomena. When diluted sulphuric acid is digested over indigo, it produces no effect, except that of dissolving the impurities; but concentrated sulphuric acid dissolves it readily. One part of indigo, when mixed with eight parts of sulphuric acid, evolves heat, and is dissolved in about twenty-four hours. According to Haussman, some sulphurous acid and hydrogen gas are evolved during the solution. If so, we are to ascribe them to the mucilage and resin which are doubtless destroyed by the action of the concentrated acid.

The solution of indigo is well known in this country by the name of liquid blue, or sulphat of indigo. While concentrated it is opaque and black; but when diluted, it assumes a fine deep blue colour; and its intensity is such, that a single drop of the concentrated sulphate is sufficient to give a blue colour to many pounds of water. Bergman ascertained the effect of different re-agents on this solution with great precision. Dropped into sulphurous acid, the colour was at first blue, then green, and very speedily destroyed. In vinegar it becomes green, and in a few weeks the colour disappears. In weak potash it becomes green, and then colourless. In weak carbonate of potash there are the same changes, but more slowly. In ammonia and its carbonate, the colour becomes green, and then disappears. In a solution of sugar, it became green, and at last yellowish. In sulphate of iron, the colour became green, and in three weeks disappeared. In the sulphurets the colour was destroyed in a few hours. Realgar, white oxide of arsenic, and orpiment, produced no change. Black oxide of manganese destroyed the colour completely. From these and many other experiments it was inferred, that all those substances which have a very strong affinity for oxygen, give a green colour to indigo, and at last destroy it. Hence it is imagined, that indigo becomes green by giving out oxygen. Of course it owes its blue colour to that principle.

M. Haussman, in a letter addressed to M. Berthollet, gives an account of the manner in which the solution of indigo is prepared, by means of an alkaline solution of red arsenic, for the use of calico printers.

He merely makes a caustic alkaline solu

tion of red arsenic, to which he adds, while it is still boiling, a sufficient quantity of indigo bruised, in order to obtain a very deep shade; which it is still easy to render more or less intense, as the object may require, by diluting the solution of indigo with a weak ley of caustic potash, which is preferable to pure water, because it retards a little the absorption of the oxygen of the atmosphere, and consequently retards the regeneration of the indigo. The beauty of the blue in the stuffs requires that this regeneration should not be too sudden or too tardy. The too slow absorption, proceeding from a too great excess of caustic alkali, should be avoided in the blue for pencilling with, as well as in the stone blues, which advantage we procure by passing the stuffs printed with bruised indigo, mixed with a gummy solution of sulphate of iron, alternately through vats of caustic potash, sulphate of iron oxidated at the minimum, and finally through a vat acidulated by the sulphuric or muriatic acids. On exposing to the sand bath a mixture of bruised indigo and muriatic solution of tin with excess of acid, and oxidated at the minimum, the colouring substance is decomposed, liberating a gas of an insupportable and pernicious smell, which ought to be examined.

If indigo, treated with the muriatic solution of tin oxidated at the minimum, without the assistance of a caustic alkali, is of no use in dyeing, this is not the case with sulphat of indigo treated or mixed in different proportions with the same solution of tin, after having previously absorbed the sul phuric acid; the latter being made use of in printing-honses for producing all sorts of blue and green shades (Annales des Arts et Manuf.).

INDIRECT. a. (indirectus, Latin.) 1. Not straight; not rectilinear. 2. Not tending otherwise than obliquely or consequentially to a purpose. 3. Wrong; improper (Shakspeare). 4. Not fair; not honest (Daniel). INDIRECTION. s. (in and direction.) 1. Oblique means; tendency not in a straight line (Shakspeare). 2. Dishonest practice: not used (Shakspeare).

INDIRECTLY. ad. (from indirect.) 1. Not in a right line; obliquely. 2. Not in express terms (Broome). 3. Unfairly; not rightly (Taylor).

INDIRECTNESS. s. (in and directness.) 1. Obliquity. 2. Unfairness; dishonesty. INDISCERNIBLE. a. (in and discerni ble.) Not perceptible; not discoverable (Denham).

INDISCERNIBLY. ad. (from indiscernible.) In a manner not to be perceived.

INDISCERPTIBLE. a. (in and discerpti ble) Not to be separated; incapable of being broken or destroyed by dissolution of parts.

INDISCERPTIBILITY. s. (from indiscerptible.) Incapability of dissolution.

INDISCOVERY. s. (in and discovery.) The state of being hidden (Brown). INDISCREET. a. (indiscret, French.) Imprudent; incautious; inconsiderate; injudicious (Spenser).

INDISCREETLY. ad. Without prudence; without consideration (Sandys). INDISCRETION. s. (indiscretion, Fr.) imprudence; rashness; inconsideration (Hayw.)

INDISCRIMINATE. a. (indiscriminatus, Latin.) Undistinguishable; not marked with any note of distiction.

INDISCRIMINATELY, ad. Without distinction (Government of the Tongue). INDISPENSABLE. a. (French.) Not to be remitted; not to be spared; necessary (Wooward).

INDISPENSABLENESS. s. State of not being to be spared; necessity. (from indispensable.) Without dispensation; without remission; necessarily (Addison),

To INDISPOSE. v. a. (indisposer, Fr.) 1. To make unfit (Atterbury). 2. To disincline; to make averse (Smith). 3. To disorder; to disqualify for its proper functions (Glanville). 4. To disorder slightly with regard to health (Walton). 5. To make unfavourable (Clarendon).

INDISPÒ'SEDNESS 8. (fromindisposed.) State of unfitness or disinclination; disor dered state (Decay of Piety).

INDISPOSITION. 8. (indisposition, Fr.) 1. Disorder of health; tendency to sickness; slight disease (Hayward). 2. Disinclination; dislike (Hooker).

INDISPUTABLE. a. (in and disputable.) Uncontrovertible; incontestable (Rogers). INDISPUTABLENESS. s. The state of being indisputable; certainty; evidence.

INDISPUTABLY. ad. (from indisputable.) 1. Without controversy; certainly (Brown). 2. Without opposition (Howel).

INDISSOLVABLE. a. (in and dissolvable.) 1. Indissoluble; not separable as to its parts (Newton). 2. Obligatory; not to be broken; binding for ever (dyliffe).

INDISSOLUBILITY. s. (indissolubilité, French.) 1. Resistance to a dissolving power; firmness; stableness (Locke). 2. Perpetuity of obligation.

INDISSOLUBLE. a. (indissoluble, Fr.) 1. Resisting all separation of its parts ; firm; stable (Boyle). 2. Binding for ever; subsisting for ever (Bacon).

INDISSOLUBLEŃESS. s. Indissolubility; resistance to separation of parts (Hale). INDISSOLUBLY. ad. (from indissoluble.) 1. In a manner resisting all separation(Boyle). 2. For ever obligatory.

INDISTINCT. a. (indistinct, French.) 1. Not plainly marked; confused (Dryden), 2. Not exactly discerning (Shakspeare),

INDISTINCTION. 8. (from indistinct.) 1. Confusion; uncertainty (Browa.). Omission of discrimination (Sprat),

INDISTINCTLY. ad. (from indistinct.) 1. Confusedly; uncertainly (Newton). 2. Without being distinguished (Brown). INDISTINCTNESS. s. (from indistinct.) Confusion; uncertainty; obscurity (Newton). INDISTURBANCE. s. (in and disturb.) Calmness; freedom from disturbance (Tem.) INDIVIDUAL. a. (individu, individuel, French.) 1. Separate from others of the same species; single; numerically one (Watts). 2. Undivided; not to be parted or disjoined (Milton).

INDIVIDUALITY. s. (from individual.) Separate or distinct existence (Arbuthnot). INDIVIDUALLY. ad. (from individual.) 1. With separate or distinct existence; numerically (Hooker.) 2. Not separably; incommunicably (Hakew.).

To INDIVIDUÁTE. v. a. (from individuus, Latin.) To distinguish from others of the same species; to make single (More). INDIVIDUATION. s. (from individuate) That which makes an individual (Watts). INDIVIDUITY.s. (from individuus, Lat.) The state of being an individual; separate existence.

INDIVI'NITY. 8. (in and divinity.) Want of divine power: not in use (Brown). INDIVISIBILITY. 8. (from indiviINDIVI'SIBLENESS. Jsible.) State in which no more division can be made (Locke). INDIVI'SIBLE. a. (indivisible, French.) What cannot be broken into parts; so small as that it cannot be smaller (Digby).

INDIVISIBLES, in geometry, those indefinitely small principles or elements, into which any body or figure may be supposed to be ultimately resolved.


The method of comparing magnitudes invented by Cavalerius, called indivisibles, poses lines to be compounded of points, surfaces of lines, and solids of planes; or, to make use of his own description, surfaces are considered as cloth consisting of parallel threads, and solids are formed of parallel planes, as a book is composed of its leaves, with this restriction, that the threads, or lines of which surfaces are compounded, are not to be of any conceivable breadth, nor the leaves or planes of solids, of any thickness. He then forms these propositions, that surfaces are to each other, as all the lines in one, to all the lines in the other; and solids, in like manner, in the proportion of their planes.

For instance, every sphere is two-thirds of a circumscribing cylinder. Let the hemisphere BCM, the circumscribing cylinder BDKM (pl. 88. figs. 8, 9), and the inscribed cone DAK of the same base and altitude, be supposed to consist of planes as HEGH pa. rallel to the base. Since HF-AE2-EF2 + FA2=EF2+GF2; and since the circles of which HF, FF, and GF are the radii, are as the squares of those radii; the area of the circle in the cylinder whose radius is HF, is equal to the sum of the areas of the circles in the hemisphere and inscribed cone, whose

radii are EF and GF. Therefore the sum of all the circular planes, which are supposed to compose the cylinder, is equal to the sum of all the circular planes which compose the hemisphere, together with the sum of those which compose the inscribed cone. But the inscribed cone is one-third part of the cylin der; therefore the inscribed hemisphere is two-thirds of the same.

But this method of indivisibles, however true the conclusion is in this case, is manifestly founded on inconsistent and impossible suppositions. For while the lines, of which surfaces are supposed to be made up, are of no breadth, it is obvious that no number of them can form the least imaginable surface; if they are supposed to be of some sensible breadth, they are in reality parallelograms, how minute soever their altitude, and then the assumed proportion of Cavalerius may fail, for surfaces are not always in the same proportion with the parallelograms inscribing them. And the same contradictory suppositions obviously attend this composition of solids, or of lines. This kind of reasoning has, therefore, led to error; as in the case of pendulums vibrating in very small circular arcs, concerning which Keill and others maintain that the times of vibration in such arcs are equal to those of descent down the chords: whereas, in fact, the descents down the arcs are less than those along the chords, in the ratio of a quadrantal arc of a circle to its diameter.

INDIVI'SIBLY, ad. (from indivisible.) So as it cannot be divided.

INDO CIBLE. a. (in and docible.) Unteachable; insusceptible of instruction.

INDO'CIL. a. (indocile, French.) Unteachable; incapable of being instructed (Bentley). INDOCILITY. s. (indocilité, French.) Unteachableness; refusal of instruction.

To INDOCTRINATE. v. a. (endoctriner, old French.) To instruct; to tincture with any science, or opinion (Clarendon).

INDOCTRINATION. 8. (from indoctrinate.) Instruction; information (Brown).

INDOLENCE. s. (in and doleo, Latin; I'NDOLENCY. Jindolence, French.) 1. Freedom from pain (Burnet). 2. Laziness; inattention; listlessness (Dryden).

INDOLENT. a. (French.) 1. Free from pain. 2. Careless; lazy; inattentive; listless (Pope).

INDOLENTLY. ad. (from indolent.) 1. With freedom from pain. 3. Carelessly; lazily; inattentively; listlessly (Addison).

INDORSEMENT, in law, any thing written on the back of a deed; as a receipt for money received. There is likewise an indorsement, by way of assignment, on bills of exchange and notes of hand; which is done by writing a person's name on the back thereof.

To INDO'W. v. a. (indotare, Latin.) To portion; to enrich with gifts.

INDRA'UGHT. s. (in and draught.) 1. An opening in the land into which the sea

flows (Raleigh). 2. Inlet; passage inward (Bacon).

INDRE, a department of France, which includes the late province of Berry. It has its name from a river, which rises in this department, and passing into that of Indre and Loire, falls into the Loire between Chinon and


INDRE and LOIRE, a department of France, which includes the late province of Touraine. To INDRENCH. v. a. (from drench.) To soak; to drown (Shakspeare).

INDUBIOUS. a. (in and dubious.) Not doubtful; not suspecting; certain (Harvey). INDU BITABLE. a. (indubitabilis, Lat.) Undoubted unquestionable (Watts),

INDU/BITABLY, ad. (from indubitable.) Undoubtedly unquestionably (Sprat). INDU BITATE. a. (indubitatus, Latin.) Unquestioned; certain; evident (otton).

To INDUCE. v. a. (induire, French; induco, Latin.) 1. To persuade; to influence to any thing (Hayward). 2. To produce by persuasion or influence (Bacon). 3. To offer by way of induction, or consequential reasoning (Brown). 4. To inculcate; to inforce (Temple). 5. To cause extrinsically; to produce (Bacon). 6. To introduce; to bring into view (Pope). 7. To bring on; to superinduce (Decay of Piety).

INDUCEMENT. s. (from induce.) Motive to any thing; that which allures or persuades to any thing (Rogers).

INDUCER. 8. (from induce.) A persuader; one that influences.

To INDUCT. v. a. (inductus, Latin.) 1. To introduce; to bring in (Sandys). 2. To put into actual possession of a benefice (Ayliffe).

INDUCTION. s. (induction, Fr. inductio, Latin.) 1. Introduction; entrance (Shaks.) 2. The act or state of taking possession of an ecclesiastical living.

INDUCTION, in logic, is that process of the understanding by which, from a number of particular truths perceived by simple apprehension, and diligently compared together, we infer another truth which is always general and sometimes universal. In the process of induction, the truths to be compared must be of the same kind, or relate to objects having a similar nature: every one knows that physical truths cannot be compared with moral truths, nor the truths of pure mathematics with either.

The method of induction is admitted by British philosophers to be the only method of reasoning by which any progress can be made in the physical sciences; for the laws of nature can be discovered only by accurate experiments, and by carefully noting the agreements and the differences, however minute, which are thus found among the phenomena apparently similar. It is not, however, commonly said that induction is the method of reasoning employed by the mathematicians; and Dr. Robison long thought, with others, that in pure geometry the reasoning is strictly syllogistical. Mature reflection, however, led him to doubt, with Dr. Reid, the truth of the generally received opinion, to doubt even whether by categorical syllogisms any thing whatever can be proved.

To the idolaters of Aristotle we are perfectly aware that this will appear an extravagant paradox; but to the votaries of truth, we do not despair of making it very evident, that for such doubts there is some foundation.


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The fundamental axiom upon which every categorical syllogism rests, is the well known proposition, which affirms, that "whatever may be predicated of and of every individual comprehended under that a whole genus, may be predicated of every species This is indeed an undoubted truth; but it cannot constitute a foundation for reasoning from the genus to the species or the individual; because we cannot possibly know what can be predicated of the genus till we know what can be predicated of all the individuals ranged under it. Indeed it is only by ascertaining, through the medium of induction, what can be predicated, and what not, of a number of individuals, that we come to form such notions as those of genera and species; and therefore, in a syllogism strictly categorical, the propositions which constitute the premises, and are taken for granted, are conclusion, which the logician pretends to demonthose alone which are capable of proof; whilst the strate, must be evident to intuition or experience, otherwise the premises could not be known to be true. The analysis of a few syllogisms will make this apparent to every reader.

Dr. Wallis, who, to an intimate acquaintance with the Aristotelian logic, added much mathematical and physical knowledge, gives the following syllogism as a perfect example of this mode of reasoning in the first figure, to which it is known that all the other figures may be reduced :—

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Omne animal est sensu præditum. Socrates est animal. Ergo

Socrates cst sensu præditus.

Here the proposition to be demonstrated is, that Socrates is endowed with sense; and the propositions assumed as self-evident truths, upon which the demonstration is to be built, are, that every animal is endowed with sense;" and that Socrates is an animal." But how comes the demonstrator to know that " every animal is endowed with sense?" To this question we are not aware of any answer which can be given, except this, that mankind have agreed to call every being, which they perceive to be endowed with sense, an animal. Let this, then, be supposed the true answer: the next question to be put to the demonstrator is, How he comes to know that Socrates is an animal? If we have answered the former question properly, or, in other words, if it be essential to this genus of beings to be endowed with sense, it is obvious that he can know that Socrates is an animal only by perceiving him to be endowed with sense; and therefore, in this syllogism, the proposition to be proved is the very first of the three of which the truth is perceived; and it is perceived intuitively, and not inferred from others by a process of reasoning.

Though there are ten categories and five predicables, there are but two kinds of categorical propositions, viz. Those in which the property or accident is predicated of the substance to which it belongs, and those in which the genus is predicated of the species or individual. Of the former kind is the proposition pretended to be proved by the syllogism which we have consi

dered; of the latter, is that which is proved by the truths known by experience, from which, by the


Quicquid sensu præditum, est animal. Socrates est sensu præditus. Ergo Socrates est animal.

That this is a categorical syllogism, legitimate in mode and figure, will be denied by no man who is not an absolute stranger to the very first principles of the Aristotelian logic; but it requires little attention indeed to perceive that it proves nothing. The imposition of names is a thing so perfectly arbitrary, that the being, or class of beings, which in Latin and English is called animal, is with equal propriety in Greek called wor, and in Hebrew w. To a native of Greece, therefore, and to an ancient Hebrew, the major proposition of this syllogism would have been wholly unintelligible; but had either of those persons been told by a man of known veracity, and acquainted with the Latin tongue, that every thing endowed with sense was by the Romans called animal, he would then have understood the proposition, admitted its truth without hesitation, and have henceforth known that Socrates and Moses, and every thing else which he perceived to be endowed with sense, would at Rome be called animal. This knowledge, however, would not have rested upon demonstrative reasoning of any kind, but upon the credibility of his informer, and the intuitive evidence of his own senses.

It will perhaps be said, that the two syllogisms which we have examined are improper examples, because the truth to be proved by the former is selfevident, whilst that which is meant to be established by the latter is merely verbal, and therefore arbitrary. But the following is liable to neither of these objections:

All animals are mortal.
Man is an animal; therefore
Man is mortal.

Here it would be proper to ask the demonstrator, upon what grounds he so confidently pronounces all animals to be mortal? The proposition is so far from expressing a self-evident truth, that, previous to the entrance of sin and death into the world, the first man had surely no conception of mortality. He acquired the notion, however, by experience, when he saw the animals die in succession around him; and when he observed that no animal with which he was acquainted, not even his own son, escaped death, he would conclude that all animals, without exception, are mortal. This conclusion, however, could not be built upon syllogistic reasoning, nor yet upon intuition, but partly upon experience and partly upon analogy. As far as his experience went, the proof, by induction, of the mortality of all animals was complete; but there are many animals in the ocean, and perhaps on the earth, which he never saw, and of whose mortality therefore he could affirm nothing but from analogy, i.. from concluding, as the constitution of the human mind compels us to conclude, that nature is uniform throughout the universe, and that similar causes, whether known or unknown, will in similar circumstances, produce at all times similar effects. It is to be observed of this syllogism, as of the first which we have considered, that the proposition, which it pretends to demonstrate, is one of those

process of induction, we infer the major of the premises to be true; and that therefore the reasoning, if reasoning it can be called, runs in a circle.

Yet by a concatenation of syllogisms have logicians pretended that a long series of important truths may be discovered and demonstrated; and even Wallis himself seems to think, that this is the instrument by which the mathematicians have deduced, from a few postulates, accurate definitions, and undeniable axioms, all the truths of their demonstrative science. Let us try the truth of this opinion by analyzing some of Euclid's demonstrations.

All our first truths are particular; and it is by applying to them the rules of induction that we form general truths or axioms; even the axioms of pure geometry. As this science treats not of real external things, but merely of ideas or conceptions, the creatures of our minds, it is obvious, that its definitions may be perfectly accurate, the induction by which its axioms are formed complete, and therefore the axioms themselves universal propositions. The use of these axioms is merely to shorten the different processes of geometrical reasoning, and not, as has sometimes been absurdly supposed, to be made the parents or causes of particular truths. No truth, whether general or particular, can, in any sense of the word, be the cause of another truth. If it were not true that all individual figures, of whatever form, comprehending a portion of space equal to a portion comprehended by any other individual figure, whether of the same form with some of them, or of a form different from them all, are equal to one another, it would not be true that "things in general, which are equal to the same thing, or that magnitudes which coincide, or exactly fill the same space," are respectively equal to one another; and therefore the first and eighth of Euclid's axioms would be false. So far are these axioms, or general truths, from being the parents of particular truths, that, as conceived by us, they may, with greater propriety, be termed their offspring. They are indeed nothing more than general expressions, comprehending all particular truths of the same kind. When a mathematical proposition therefore is announced, if the terms of which it is composed, or the figures of which a certain relation is predicated, can be brought together and immediately compared, no demonstration is necessary to point out its truth or falsehood. It is indeed intuitively perceived to be either comprehended under, or contrary to some known axiom of the science; but it has the evidence of truth or falsehood in itself, and not in consequence of that axiom. When the figures or symbols cannot be immediately compared together, it is then, and only then, that recourse is had to demonstration; which proceeds, not in a series of syllogisms, but by a process of ideal mensuration or induction. A figure or symbol is conceived, which may be compared with each of the principal figures or symbols, or, if that cannot be, with one of them, and then another, which may be compared with it, till through a series of well known intermediate relations, a comparison is made between the terms of the original proposition, of which the truth or falsehood is then perceived.

Thus in the forty-seventh proposition of the first book of Euclid's Elements, the author proposes to

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