The mode of absorption of light by a coloured substance is often eminently characteristic of the substance, but can be judged of only very imperfectly by the tint of the transmitted light. It is easily determined by analysing the transmitted light by means of a prism. When a body is not homogeneous in structure, but (like chalk or paper) is filled with surfaces capable of reflecting light, a considerable portion of the whole reflected light ordinarily proceeds from a greater or less depth beneath the outer surface. If the material of which the body is composed be one capable of absorbing light, the light reflected from the interior suffers absorption both in penetrating into the body and in getting out again. Accordingly, those colours which the material is least disposed to absorb are found predominating in the reflected light. It is thus that absorption operates in the case of pigments, the petals of flowers, dyed clothes, &c., which exhibit more or less lively colours by reflected light, though in these cases the light reflected strictly at the outer surface is colourless. The tint of the reflected light has a general agreement with that of the light transmitted through a sufficiently thin stratum of the coloured material.

Metals may for most purposes be regarded as absolutely opaque; yet even they can sometimes be rendered so thin as to transmit light. Thus, gold-leaf transmits a green or bluish-green light; and the coloration of the light shows that the transmission does not take place merely through the minute holes with which gold-leaf is filled, but actually through the metal. There are good reasons for believing that the strong reflecting power of metals is intimately connected with their intense absorbing power. Thus gold, which absorbs the more refrangible colours with most energy, reflects them also in greatest abundance, so that it is yellow by reflected, while it is bluish-green by transmitted light. Some intensely coloured substances (murexide and platinocyanide of magnesium are good examples) absorb the colours of a part of the spectrum almost as intensely as metals, while for other parts they are comparatively transparent, and reflect the colours for which they have an intense absorbing power with an energy comparable with metals while other colours are reflected only as they would be by vitreous substances. Hence the regularly reflected light is brilliantly coloured; but the predominant colour is that of the light most intensely absorbed. This is just the reverse of what takes place in the case of the light reflected from the petals of flowers, &c., where the coloration is due, not to reflection, but to absorption, and the colour is that due to the light for which the absorbing power of the colouring substance is least. (See a paper by M. Haidinger in the Proceedings of the Academy at Vienna. Sitzungsberichte,' Bd. 8, S. 97. See also 'Phil. Mag., S. 4, vol. vi., pp. 284 and 393.) When a doubly refracting crystal is coloured, it often happens that the two pencils which, in any given direction within the crystal, are capable of being transmitted independently of each other, are very differently absorbed. Thus a plate of tourmaline cut parallel to the axis stops more or less completely light polarised parallel to the axis, constituting the ordinary ray, and lets through light polarised perpendicularly to the axis, constituting the extraordinary ray. In some specimens, with plates of a suitable thickness, the stoppage and transmission respectively are tolerably perfect, which makes such a plate very valuable in experiments on polarisation. That the effect is really one of absorption may be shown by using, instead of a plate bounded by parallel surfaces, a thin wedge tapering to a mere line, and viewing it separately by light polarised parallel and perpendicularly to the axis. It is found that quite close to the edge the crystal is colourless and transparent for both pencils; but that as the distance from the edge increases, the ordinary pencil becomes rapidly more and more absorbed, while the absorption of the extraordinary comes on but slowly. As usual in absorption, the different colours are unequally absorbed, and not only so, but the colours which are most absorbed are different for the ordinary and extraordinary rays, so that the crystal is commonly differently coloured with regard to the two pencils, which may be observed at the same moment, but separately, by viewing the crystal through a double-image prism. The mode of absorption changes, not only in a given direction within the crystal in passing from the ordinary to the extraordinary ray, but also in passing from one direction to another. Dr. Wollaston appears to have first observed (Phil. Trans.,' 1804, p. 428) that the light transmitted along the axis of a crystal of tourmaline had a colour different from that of the light transmitted perpendicularly to the axis. Several uniaxal crystals (such as smoky quartz, &e.) agree with tourmaline in the general character of the absorption which takes place in them. The colour, and generally the mode of absorption, of the ordinary ray is alike in all directions; that of the extraordinary varies from that of the ordinary, which it has in the direction of the axis, to that most different from the ordinary, which it has in any direction perpendicular to the axis. Many biaxal crystals have a similar property, but the variation of the colour with the direction is more complicated, and in particular some very curious appearances are observed about the optic axes. (See a paper by Sir David Brewster, Phil. Trans.,' 1819, p. 11.) M. Haidinger has shown that in biaxal crystals (or at least in those which are symmetrical with respect to three rectangular planes) there are three fundamental modes of absorption, symmetrically related to the principal axes, seen each in any direction perpendicular to the axis in question by light polarised perpendicular to that axis.

M. de Senarmont has recently shown ('Annales de Chimie,' S. 3,

tom. xli. p. 319) that the power of double absorption may be conferred on naturally colourless crystals by a small amount of foreign impurity. A very remarkable example is afforded by nitrate of strontia coloured red by crystallising out of an infusion of logwood.

ABSTINENCE, from abstineo, to abstain. The term abstinence signifies a total, or an excessive privation of food. The constituent matter of the body is in a state of continual change-the old particles are constantly taken up and carried out of the system, while new particles are as regularly deposited in their room to repair the loss. The source of these new particles is the aliment or food; but a second office is performed by the aliment scarcely less important than that of furnishing new matter for the renovation of the system. All the organs of the body are excited to the performance of their functions by certain external agents, which are called stimulants; such as air, water, heat, and so on; but of these stimulants the aliment is among the most indispensable and the most powerful. Upon the quantity and quality of the aliment depend the quantity and quality of the blood, and upon the quantity and quality of the blood depends in a great measure the energy of all the functions of all the organs. Any material change in the diet must necessarily produce a powerful impression on the system. Life can be maintained but for a short period under the total privation of food, while the excessive privation of it produces effects upon the system which have not been often observed with accuracy, but which are remarkably uniform, and highly curious and instructive. Opportunities occasionally occur of noting these effects with correctness and completeness, when, for example, the passage to the stomach is closed up by disease; or when, owing to an unsound state of mind, the individual refuses to take nourishment. During the first two or three days after the total abstinence from food, in a person previously in sound health, the suffering from hunger is generally severe. The thirst is also at times distressing, but thirst is not constantly attendant. The pulse during this period remains natural and so does the temperature of the body. All the evacuations are scanty, and take place at distant intervals. After the first two or three days the wasting of the body becomes visible, the fresh colour characteristic of health disappears, and the features and the limbs, instead of being plump and round, are sunk and collapsed. The loss of weight, which increases rapidly, is appreciable, and the progress of the emaciation is striking. The physical debility increases in exact proportion with the emaciation: and the mind becomes weak, confused, wandering, irritable, and at length almost deprived of reason. All this time there is little or no pain from hunger or thirst, or these uneasy sensations return only at intervals, and are seldom acute and never lasting. The pulse at this stage may be a little quickened; it is certainly easily excited; and in like manner the heat, which seldom sinks below the natural standard, is readily parted with, so that a slight change of the temperature of a room is felt acutely, and produces very uneasy sensations, a fact which demonstrates to the physician the feebleness with which the functions are carried on, no less clearly than the physical debility itself. The most remarkable and curious phenomena which next supervene, are those connected with the intellectual faculties. The loss of power to perceive accurately, and to connect the trains of thought, is followed by decided delirium, which is at first of a low muttering character, similar to that which takes place in the last stage of typhus fever; but this sometimes passes rapidly into furious and even maniacal delirium, requiring coercion, just as a violent paroxysm of madness itself. Generally the delirium is preceded by a state of painful watchfulness and restlessness, it being impossible to procure sleep or quiet; and, finally, the skin becomes intensely hot, the pulse extremely rapid, the emaciation frightful, the debility so great that scarcely the slightest movement can be performed, and at length the individual sinks exhausted, commonly into a state of stupor amounting to that complete and profound insensibility which is technically called coma.

This history of the progressive changes which take place in the system on the total abstraction of food, is illustrated in the most perfect manner, by two cases which fell under the notice of physicians capable of accurately observing and duly appreciating each successive event. Many wonderful stories are on record, of the truth of which there is no sufficient evidence; but the cases to which we refer were observed and recorded by men whose veracity is beyond question, and who were endowed with more than ordinary discrimination and judg ment. The record on this account is invaluable, while in itself it is highly curious and instructive.

For the first case we are indebted to Dr. Currie, of Liverpool. In August, 1795, a gentleman of Yorkshire, aged sixty-six, applied to this physician for his assistance, on account of an obstruction in his swallowing food, with which he had been afflicted for ten or twelve months. At first the complaint was slight; it occurred only when he attempted to swallow dry and hard substances; it afterwards extended to solids of every kind; and, at the time he was first seen by his physician, although he was still able to pass down liquids, the quantity he could swallow was not sufficient for his nutrition, and he was considerably reduced. On the introduction of a bougie into the gullet, it passed about two inches easily, but then met with an obstruction which, by a moderate pressure, was overcome. It then passed easily seven or eight inches more, but at the lower part of the tube, towards its termination in the cardia, it met with a firm resistance, which no

patience or skill could surmount. This obstruction proceeded from a schirrous tumour, which, gradually increasing at first, diminished the passage, and at length closed it wholly.

On the evening of the 17th of October, a sudden increase of the obstruction came on, and from this time he was able to swallow only a table-spoonful of liquid at a time, and at long intervals. It was with difficulty that he got down seven or eight spoonsful of strong soup in the day, and this quantity gradually diminished. On the thirteenth day from this sudden increase of the obstruction, the passage appeared to be wholly closed.

The patient himself, to the last, was far from despairing of his recovery; and the affectionate friends around him, though they could not but see the issue of the case, yet desired that his life might be prolonged to the uttermost. The following plan was, therefore, adopted with this view. Every morning a clyster was administered, consisting of eight ounces of strong broth, made chiefly of the membranous parts of beef, these being considered the most nutritious, into which were rubbed two yolks of egg, and to which were added forty drops of laudanum. This was repeated in the afternoon, and again in the evening, previously to which, in the evening, he was placed up to the neck in a tepid bath, of which one-fourth was milk, and the rest water; the whole quantity amounting to twenty-four gallons. The temperature was fixed at 96°, to accommodate his sensations, and the time of immersion was gradually prolonged from forty-five minutes to an hour. After a few days it was found that the retention of the rectum improved, so that the clysters were enlarged to ten ounces of broth, and three yolks of eggs each; to which were added eight ounces of white wine, and the laudanum, which was added to the evening clyster, was gradually increased from sixty to two hundred and fifty drops. Thus the whole of his nutriment for twenty-four hours consisted of thirty ounces of broth, twenty-four ounces of wine, nine yolks of eggs, and from 250 to 380 drops of laudanum, and administered by clyster; with what liquid might be supposed to be taken up in the bath by the absorbents of the surface of the body. When in tolerable health, at the commencement of his complaint, this gentleman, who was a tall man, and naturally corpulent, weighed 240 lbs. Before the obstruction had become complete, imperiect nutrition had reduced him to the weight of 179 lbs. In twenty days, from the period of the sudden increase of the obstruction, he was reduced to 154 lbs. ; on the twenty-fourth day he had lost 5 lbs. more; and at the period when his delirium commenced, that is on the thirtysecond day from the night that he ceased to swallow, he weighed 138 lbs., having lost upwards of 100 lbs. of his original weight. He lived four days longer, that is, thirty-six days from the period when the obstruction was supposed to be complete; but during these last four days, no nutriment, in any form or of any kind, was administered; for the rectum no longer retained the clysters, and the administration of the bath appeared, under these circumstances, to be wholly useless. For a month after the total obstruction of the passage the temperature and the pulse were natural; but on the thirty-second day the pulse became small and frequent; on the following day the eyes lost their common direction, the axis of each being turned towards the nose; he complained that he sometimes saw double, but the sensibility of the retina was increased rather than impaired; for, on the admission of the light of the window, he screamed out, though he had before been accustomed to this light. On the next day there was considerable incoherence of mind; this incoherence passed rapidly into delirium, during the prevalence of which there was a perpetual and indistinct muttering, with great restlessness and agitation; the skin and the extremities were sometimes of a burning heat, and sometimes clammy and cold; the pulse became feeble and irregular; the respiration, which hitherto had been singularly undisturbed, became laborious; and in ninety-six hours after the clysters and all other means of nutrition had been abandoned, he ceased to breathe.

During the whole of this melancholy progress to inevitable death, this unfortunate gentleman complained very little of hunger: occasionally he expressed a wish that he could swallow, but not often nor anxiously; and, when questioned on the subject of his appetite, he always declared that he had no hunger which occasioned any uneasiness. The clysters evidently relieved the sense of hunger, and the opium they contained seemed to have a powerful share in producing this relief. It occasioned quiet and rest after each clyster, and allayed every kind of desire or appetite. Neither was he much disturbed with thirst. This sensation was, indeed, troublesome during the first days of his abstinence; but it abated, and, as he declared, was always removed by the tepid bath, in which he had the most grateful sensations. His spirits were uncommonly even, and his intellect perfectly sound. He occupied himself a good deal in his private concerns; and, as usual, interested himself in public affairs. In order to husband his strength he was confined a good deal to bed; but, till the last few days of his life, he dressed and undressed himself daily, and walked, not only about his room, but through the house. His nights were quiet; his sleep sound, and apparently refreshing. Just before his delirium set in he had very lively dreams, which were all of a pleasant nature; and, in the last conversation he had with his physician, he told him he had had a very gay evening with two Yorkshire baronets whom he named; that they had pushed the bottle about freely; that many

jokes had passed, at the recollection of which he laughed heartily, a thing uncommon with him; but it was observable that he was unable, longer than a moment or two, to distinguish this scene which had passed in sleep from a real occurrence; and this state of mind lapsed into delirium from which he never recovered. At this period he was so weak as to be scarcely able to turn himself in bed, to which he had been entirely confined several days, previously to his death.

The second case, which is no less interesting, occurred to Dr. Willan. It was that of a young man of studious and melancholic turn of mind, who being affected with indigestion, undertook voluntarily to live without food. He drank nothing but water flavoured with a little orange juice. He was seen by Dr. Willan on the sixty-first day of his fast: at that time he was emaciated to a most astonishing degree; the muscles of his face were entirely shrunk; his cheek bones stood prominent and distinct, affording a most ghastly appearance; the abdomen was concave from the collapsed state of the intestines; the limbs were reduced to the greatest possible degree of tenuity, and the processes of their bones were easily distinguishable. His whole appearance suggested the idea of a skeleton prepared by drying the muscles upon it in their natural situations. His mind had become imbecile. Unfortunately the treatment adopted was injudicious, the quantity of food allowed him being much too large; yet, for the first few days, he appeared to improve, regaining flesh and strength, and acquiring firmness and even cheerfulness of mind; but on the night of the fifth day he was sleepless and restless; on the morning of the sixth, he began to lose his recollection, and before midnight he was quite frantic and unmanageable; at the same time his pulse was increased in frequency, with considerable heat of the skin, and tremors. During the following day he continued raving, and talking very incoherently, as he had done during the preceding night. He remained nearly in the same state, scarcely ever sleeping, and taking very little nourishment, his pulse becoming daily smaller and feebler, and beating at length 120 strokes in a minute, and his emaciation still increasing, until the eleventh day from the period that he began to take food and medicine, and the seventy-second from the commencement of his abstinence, on which day he died, quite exhausted.

There is no authentic case on record in which the duration of the abstinence was as long as this, and both these cases taken together, afford an excellent history of the disorder of the functions, and the exhaustion of the powers of life on the total and continued abstraction of food. The mind in the first case was naturally firm and strong; in the second it was supported by an enthusiasm amounting to insanity. When the mind is feeble, and especially when it is under the influence of fear, anxiety, despondency, or any other depressing cause, the duration of life is greatly abridged. It is instructive to observe the absence of severe suffering from hunger and thirst; the absence of all acrimony of the fluids; the absence of all violence and turbulence of mind until delirium set in, the precursor of death.

From the powerful influence of abstinence on the system, it is obviously capable of becoming a most energetic remedy in various diseases. When the mass of the fluids and solids of the body is too abundant, abstinence is capable of reducing them to almost any extent that can be required; and if the abstinence be judiciously commenced and conducted, not only is it unattended with any diminution of the strength or injury to the health, but it contributes to the improvement of both. Numerous instances are on record which place this fact beyond question. The case of Cornaro the Venetian nobleman, and that of the Essex miller, which afford evidence of this more complete than it would be easy to invent, are universally known. The body, whatever be its bulk or weight, provided the health be in other respects sound. may be reduced to almost any degree of thinness, and kept at that point by an appropriate regulation of diet and exercise. The physician, at his pleasure, can make no one fat, but he can make any one as thin as he chooses, frequently improving at the same time the health and vigour both of body and mind. Seldom is he called upon to put this art into practice, and seldomer than he ought does he insist upon carrying it into practice; but it is something to know that the resources of his art place this in his power.

In ali acute diseases, such as the various forms of fever and inflammation, abstinence is a most powerful remedy, not only because the abstraction of nutriment diminishes the mass of the fluids and solids (since the process of absorption goes on though the supply of new matter is stopped), but also because it withdraws one of the main stimulants of the system, and consequently subdues the increased actions which accompany, and which for the most part constitute, acute diseases.

In some chronic maladies, especially in that large class which depend on what is termed plethora, that is, too great a quantity of solids and fluids, particularly in the plethoric state of the blood-vessels of the brain, predisposing to and producing apoplexy, in some morbid affections of the stomach itself, in some derangements of the liver, and in several diseases of the heart, abstinence is an invaluable remedy. In other chronic diseases it is injurious, as in diseases of debility, in diseases which depend on irritation in contradistinction to those which depend on inflammation, and in various nervous maladies.

Abstinence is not equally borne by all persons, nor at all times by the same person. By the corpulent and plethoric it may be endured longer, and carried farther, than by the thin and the spare; in the

middle or mature age, it is less injurious than in infancy, youth, or extreme old age. A degree and duration of it, which are highly beneficial in a fever or an inflammation, would be fatal in the state of health. It is curious, and it is highly important to bear in mind, that abstinence and excess produce symptoms so nearly alike, that it often requires the utmost care and sagacity on the part of the physician to distinguish the one case from the other; and as the one requires opposite remedies from the other, a mistake may be fatal, and must be injurious. A man, addicted to drunkenness, was cast into prison for theft, and reduced, at once, to a diet of bread and water. After the first week, a disorder of the intellectual faculties took place; his countenance became pale and expressive of languor, his flesh wasted, and his strength declined; his nights were sleepless; shortly after wards there was delirium, which was mild at first, but subsequently furious. These symptoms might have been easily mistaken for those which denote inflammation of the brain; but the true nature of the affection was discriminated, and brandy was administered. Immediately the affection of the brain disappeared, and the flesh and strength returned.

Some time ago an alarming epidemic broke out in the Milbank Penitentiary, London. The prisoners confined in this prison were suddenly put upon a diet, from which animal food was almost entirely excluded. An ox's head, the meat of which weighs eight pounds, was made into soup for one hundred people, which allows one ounce and a quarter of meat to each person. The prisoners were at the same time subjected to a low degree of temperature, to considerable exertion, and were confined within the walls of a prison, situated in the midst of a marsh, which is below the level of the adjoining river. The consequences were, first, loss of colour, of flesh, and of strength; next, this simple debility of constitution was succeeded by various forms of disease-scurvy, dysentery, diarrhoea, low fever; and, lastly, affections of the brain and nervous system-namely, headache, vertigo, delirium, convulsions, apoplexy, and even mania. When bleeding was tried, the patients fainted after losing five, four, or even fewer ounces of blood. Abstinence will sometimes produce a train of symptoms exactly similar to those of the disease which it is employed to remove. Persistence in the abstinence will aggravate the malady, which will baffle every mode of treatment as long as the abstinence is persevered in; but which will disappear with surprising rapidity on the administration of a generous diet. This is especially the case with those affections of simple irritation which assume the appearance of inflammation, and which are attended with headache, noise in the ears, giddiness, restless ness, sleeplessness, and delirium. A professional man was seized with fever; rigid abstinence was enforced, not only during the continuance of the fever, but also during the stage of convalescence. Delirium, which had been present in the height of the fever, recurred in the convalescence. A physician of eminence in maniacal cases was consulted, who recommended him to be removed to a private asylum. Before this advice was carried into effect, another physician saw him: a different treatment and regimen, with a gradual increase of nourishment, were adopted; the patient was well in a few days, and within a fortnight returned to his professional avocations. It is the common belief that abstinence is conducive to longevity, and many stories are on record which are conceived to establish the truth of this opinion. It is stated, for example, that the primitive Christians of the east, who retired from persecution into the deserts of Arabia and Egypt, lived healthfully and cheerfully on twelve ounces of bread per day, with mere water; that, with this diet, St. Anthony lived 105 years; James the Hermit, 104; Arsenius, tutor of the Emperor Arcadius, 120; St. Epiphanius, 115; Simeon the Stylite, 112; and Romauld, 120: to which are added many others. But we should remark that the evidence for these instances of longevity is not very satisfactory. [FOOD, in NAT. HIST. DIV.]

From these remarks it is evident that abstraction, being a merely arbitrary act of the mind, by which a certain attribute is considered apart from any other attributes with which it may happen to be associated, does not represent to us images or notions to which there is anything corresponding in the nature of things; there is nowhere an abstract man or tree which has no colour, dimensions, or other incidents not entering into the abstract notion signified by these general terms. Whenever we recognise in any object those peculiarities which we consider as characteristic of a certain class, we refer it to that class, without taking any heed of the other attributes with which they may happen to be combined. Thus, if in some unexplored part of the world there should be discovered a race of animals resembling some known variety of the human race in every particular except the colour of the skin or the hair, they would be doubtless called men, although there is no such thing as an abstract man whose skin or hair is devoid of colour.

The circumstance of there not being any sensible object, or any conception of our mind, which we can image to ourselves without its attributes, has given rise to considerable perplexity on the subject of abstraction. For instance, when we think of a horse, we represent to ourselves an animal of certain colour, shape, and size; though we should equally give the name of horse to an animal of different colour, shape, and size. So, when we think of a plane triangle, although a triangle is any plane figure bounded by three straight lines, yet we cannot help representing to ourselves a triangle which is either rightangled, or acute-angled, or obtuse-angled, or equilateral or scalene, The truth is, that the process by which the mind abstracts is, that it conceives or represents to itself the object of thought as an individual of its class, together with certain particular attributes which must belong to all individuals; and it considers apart from the rest only that attribute which is required for the matter in hand. Thus, if it is a question whether a newly-discovered skeleton is that of an animal belonging to the class of elephants or of deer, the comparative anatomist calls to his mind an elephant or deer, such as actually exists, but considers only the structure of his bones; and, if there is a close agreement in this respect, he pronounces the skeleton to have belonged to one of those classes. So, likewise, when a mathematician, by means of a figure described on paper, proves that the square of the hypotenuse equals the sum of the squares of the other sides of a right-angled triangle, although the image in his mind is that of a triangle of a definite size, yet he considers only the relation of the sides and angles, without paying any attention to the length of the lines.

This process, by which the mind generalises a particular notion, by considering only a part of it, might be illustrated by many examples of changes in the meaning of words. Thus, there stood formerly on the bank of the Thames, in London, a palace called Bridewell; this, in the reign of Elizabeth, was converted into a penitentiary, or prison for hard labour; whence the term bridewell has been extended, and is now sometimes used as a general name for such penitentiaries. So the name palace has been extended to all sumptuous houses, having originally been confined to that on the Palatine hill, at Rome. It has been remarked that, although brute animals have, like men, the faculty of reasoning or drawing conclusions from premises, yet they have not, like men, the faculty of abstraction. Nevertheless, it is plain that some animals go through a process of which the effects exactly correspond with that of abstraction in men; for example, they can count, and are aware of the recurrence of certain numbers; and a dog who has once been beaten with a stick, or pelted with a stone, will run away from all sticks or stones, of whatsoever size, shape, or colour. That they cannot found, on abstraction, the admirable gift of language, the most important distinction between men and beasts, is owing apparently not to the absence of the power of forming general notions, nor yet to the inability of making articulate sounds, as we may perceive in the instance of the parrot. [NOMINALISTS.]

ABSURDUM, REDUCTIO AD, is that species of argument which proves, not the thing asserted, but the absurdity of everything which contradicts it. It is much used in geometry, in order to demonstrate the converse of a proposition already proved. One of two things must be true; either the proposition asserted, or something which contradicts it. If the opposing party deny the proposition, he must affirm that which is contradictory. Let his counter-proposition be taken for granted; then, if by the legitimate use of it some absurdity can be deduced, it is evident that his contradiction is wrong, and the original proposition right. As an instance of this method of proceeding, let us suppose it has been proved, and is not denied, that whenever a iş B then c is D. We may then affirm that when c is not D, A is not B. For if A were B, C would be D; but c is not D, therefore A is not B. The full form of the Reductio ad Absurdum, in this case, is as follows:

But

the consequence that, when c is not D, A is not B; that is, you say that o may not be D, and yet A may be B. Let this, then, be as you say, that is, let c not be D, and yet let a be B. But in supposing that A is B, the admitted proposition obliges you to say that c is D. you have supposed that c is not D: you therefore say at the same time that c is D, and that c is not D, which is absurd. Consequently, if it be true that whenever A is B then c is D, it follows that when c is not D, A is not B.

The Reductio ad Absurdum has been objected to as not equally

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conclusive with direct demonstration. For this there is no foundation; though it must be admitted that direct demonstrations are more pleasing and more elegant. But it is obvious that, if everything which contradicts a proposition be false, the proposition itself must be true. The student of logic must distinguish between that which is only contradictory, and that which is contrary to a proposition. Thus, to the proposition that "all squares are equal," it is contradictory that some squares are not equal," and contrary, that "no squares are equal." The contrary is the most complete contradictory, and affirms that the proposition is true in no one instance. It is not correct to say that, if a proposition be false, its contrary is true; for example, it is false that all squares are equal, and equally false that no squares are equal. But of a proposition and its contradictory one must be true; thus either all squares are equal or some squares are not equal. Hence, whatever disproves a proposition proves something contradictory, and whatever disproves everything contradictory proves the proposition. The Reductio ad Absurdum is, therefore, as conclusive as direct demonstration.

The Reductio ad Abeurdum, in Euclid, is wholly unnecessary to all who can see that contra-positive propositions are identically the same. The following forms are contra-positive:

Every A is B

Every not-B is not-A.

Thus (Euclid I. 4) two sides equal to two sides understood, proves that equal angles give equal areas: that is, unequal areas give unequal angles. He then has to prove I. 6, which he does by Reductio ad Absurdum. His form is, equal base angles give equal opposite sides: its equivalent contra-positive is, unequal sides give unequal opposite angles. From the unequal sides it may immediately be shown, as in Euclid, that two triangles having two pairs of sides equal, each to each, have unequal areas, and therefore unequal angles. Thus it is shown that the angles opposite unequal sides are unequal: which is but saying that the sides opposite equal angles are equal. Had logic been cultivated concurrently with geometry, the Reductio ad Absurdum would long ago have disappeared, in nearly all the cases in which it is now used. ABUTMENT, in building, is that which receives the end of, and gives support to, anything having a tendency to thrust outwards in a horizontal direction. The piers against which an arch that is less than a semi-circle rests are abutments; while the supports of an arch of any other figure, which springs at right angles to the horizon, are imposts. The piers of the arches of Southwark and Vauxhall bridges are abutments or abutment-piers; whereas those of London, Blackfriars, and Waterloo bridges, and of the old Westminster bridge, are imposts or impost-piers. Nevertheless, the piers at the extremities of a bridge, of whatever form its arch or arches may be, are always termed its abutments; that is, abutments of the bridge itself.

ABUTMENT, in machinery, is a term applied to a fixed point from which resistance or re-action is obtained. In an ordinary steam-engine, for example, each end of the cylinder acts alternately as an abutment. The steam, being unable to expand itself in the direction of the fixed obstacle, that is, the end of the cylinder, expends the whole of its elastic force in the opposite direction, against the movable obstacle or piston. In like manner the breech of a gun forms an abutment for the expansive force of the ignited powder; although in this case, the abutment not being absolutely a fixed point, its recoil occasions some loss of power. Even a rotatory steam-engine, with a continuous circular action, must have an abutment to render the force of the steam effective. Springs, whether used to impel machinery, as in the case of a watch, or to measure or control force, as in the various contrivances noticed under SPRING-BALANCE, must have their abutments or points of resistance; as also must all mechanical combinations in which power is transmitted by means of screws, of which it is sufficient to cite as an example the nut in the fixed head of an ordinary screw-press. In all these cases an analogy may be traced with the use of the term abutment in architecture. With a similar meaning the name is applied in carpentry to a joint in which two pieces of timber meet so that the fibres of one piece run in a direction oblique or perpendicular to the joint, and those of the other parallel with it.

ABUTTALS, from the French abutter, to limit or bound, are the buttings and boundings of lands to the east, west, north, and south, showing by what other lands, highways, hedges, rivers, &c., such lands are in those several directions bounded.

The bour laries and abuttals of corporation and church lands, and of parishes, are usually preserved by an annual procession. ABYSSINIAN CHRISTIANS. The discovery of a body of Christians in so remote a country excited, in no small degree, the attention of Europe in the 15th century, which was again revived by Salt's last mission, in 1810. From the 'Tareek Negushti,' or 'Chronicle of the Abyssinian Kings,' combined with the evidence of the ecclesiastical writers, we learn that Christianity was introduced into Abyssinia in the time of Constantine, by Frumentius, or Fremonatos, as the chronicles call him. Frumentius, after residing some years in the country, was raised by Athanasius the patriarch of Alexandria, to the dignity of bishop. He arrived in Abyssinia, perhaps about the year A.D. 330, and probably in the reign of the King Aizanas, whose name still exists in the inscription of Axum. It is, however, not certain to which king of the Abyssinian chronicles we ought to apply the

names of Aizanas and his brother Saizanas, both of which occur in the inscription, and also in a letter of the Emperor Constantine, addressed to them A.D. 356. When the Greek merchant Cosmas visited Abyssinia, A.D. 525, it was completely a Christian country, and well provided both with ministers and churches. Of the Abyssinian churches, which probably belong to the earlier periods of their conversion, or at least are eight or nine hundred years old, there are still some remains. The most remarkable is Abuhasubha, hewn out of the solid rock, which at this place is soft and easily worked. The Portuguese, Alvariz, describes ten such churches as these, of which he has given a plan, and one of them is probably the same as that which Mr. Pearce visited at Jummada Mariam. (Salt, p. 302.) The great church at Axum is comparatively modern, though parts of it, such as the steps, clearly belong to a prior edifice. Mr. Salt describes the wellbuilt remains of a church or monastery near Yahee, which he assigns to the 6th century of the Christian era.

The monastic, and also the solitary life, spread into Abyssinia from the deserts of the Thebais, and when the Portuguese Jesuits entered the country they found it full of such devotees; many of them seemed, however, to be monks only as far as celibacy was concerned, for they cultivated the ground and lived in villages.

With the Christian religion, the Abyssinians received the Holy Scriptures, which they now possess in the ancient Ethiopic version, made, according to Ludolf, from the Greek Septuagint, though nothing is known of the date of this version. As to the New Testament (says Ludolf), no entire copy has been yet brought to Europe. Mr. Bruce brought with him from Abyssinia a complete copy of the Scriptures in the Ethiopic language, and also a set of the Abyssinian Chronicles. The Abyssinians divide the Scriptures, which they have entire, differently from what we do, making four principal parts of the Old Testament, and mixing what we call the Canonical with the Apocryphal books. The New Testament is also divided into four parts, to which they add the Book of Revelation as a supplement. The old written language is of the Semitic stock, and is written from left to right, but the language is not now spoken; there are two languages now in use, the Tigré and the Amharic. For other information respecting the Abyssinian liturgies, and the religious opinions of the Abyssinians, we refer to Ludolf, Book iii. chaps. 4, 5. Ludolf denies the existence of the Book of Enoch, because he had only seen a spurious copy. A knave who got possession of an Ethiopic book, wrote the name of Enoch upon it, and sold it to Peiresc for a considerable sum of money, and this was the book that Ludolf saw. Bruce brought home three copies of the book of Enoch; one of which he gave to the Bodleian Library at Oxford. This book was originally written in Greek, but the original is lost-all but one large fragment. In the epistle of Jude reference is made to the prophecies of Enoch; and Mr. Bruce says, "the quotation is word for word the same in the second chapter of the book." This, however, will not prove the genuineness of the prophecies of Enoch, as Mr. Bruce has very well argued. An English translation of the book of Enoch was published by Dr. Lawrence, Oxford, 8vo. 1822. The High Priest (or sole bishop) of Abyssinia is called Abuna, which signifies Our Father; and as Frumentius, the first bishop, received his appointment from the Patriarch of Alexandria, this dignitary has, probably, always been a foreigner. The king is the head of the Church. Polygamy, though not allowed by the ecclesiastical canon, is common enough in practice; and Mr. Salt mentions an instance of one gentleman who had five wives at once. The king, of course, marries as many as he pleases: the clergy, also, who are not monks, may marry, but only once. A second marriage renders them unworthy of their sacred office, according to the ancient canons. Circumcision, according te Bruce, is practised in Abyssinia, and baptism of infants and agape or love-feasts have been in use ever since the introduction of Christianity. The creed of the Abyssinian Church is what is called the Monophyiste; i. e., admitting the divinity of our Saviour, but acknowledging in him only one nature.

It would appear, from what we know of the Abyssinian Church, that its priests, at present, are not well informed, nor are the people in general well acquainted with the principles of the Christian religion, though they may be Christians in name; yet some of their ceremonies are conducted with great decency, and very much resemble those of the Church of England. When Salt was at Chelicut, Lent was strictly observed for fifty-two days, and no flesh was eaten during this period, though fish and various dishes were always plentiful on the table: the people always fasted till sunset. A feast followed this severe and protracted fast, in which they all seemed anxious to make up for lost time, by over eating and drinking. The Sacrament is also administered in Abyssinia, in a very decorous manner; and red wine made of a grape which is common in some parts of the country, is used on the occasion. Formerly (says Mr. Salt) if a man married more than one wife, he was excluded from participating in this rite, but wealth and power have induced the Church to relax its severity in this respect. Marriage itself in Tigré, appears a mere civil institution: the woman keeps her name, and the parties can separate whenever they agree to do so. In this case the woman has her dowry back, which is not forfeited unless she is manifestly guilty of adultery. The higher classes are subject to no rule, but what may be considered as imposed by the relatives of the male and female. The priests are forbidden to marry after ordination. The Abyssinians bury their dead immediately after