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CATHOLIC EMANCIPATION ACT.

not directly declared incapable of holding land, they were deprived of the right of acquiring it by purchase, or even by long lease; and if a Catholic chanced to occupy a place in a line of entail, he was passed over in favour of the next Protestant heir. No office of trust, civil or military, was now open to a Catholic; he was forbidden to vote at elections, to intermarry with a Protestant, or even to dwell in Limerick or Galway, except under certain conditions. But perhaps the most demoralising provision of all, was that which empowered the son of a Catholic to bring his father into Chancery, to force him to declare on oath the value of his property, and to settle such an allowance on him as the court should determine, not only for the father's life, but the son's.

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of 4. But the liberal view of the Roman Catholic claims was essentially the popular one—at least among the enlightened classes; and as a proof of this, under the hostile administration of the Duke of Wellington, the very same resolution which had been lost in 1827 by a minority of 4, was carried in 1828 by a majority of 6. The duke himself now began to waver in opinion, so that the beginning of the end was manifestly near. During O'Connell's famous canvass for the county of Clare, the duke declared in the House of Lords, 'If the public mind were now suffered to be tranquil, if the agitators of Ireland would only leave the public mind at rest, the people would become more satisfied, and I certainly think it would then be possible to do something.' O'Connell's return for Clare, notwithstanding the existence of the oaths which precluded him from taking his seat in the House, and the events which now followed in quick succession, made it clear that the something' of which the duke had spoken must be the passing of the emancipation bill in the ensuing session. The king's speech, which was read on the 5th February of the following year, accordingly contained a recommendation to parlia ment, to consider whether the civil disabilities of the Catholics could not be removed, consistently with the full and permanent security of our estab lishments in church and state.'

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Amongst the other burdens of this heavy time, may be mentioned the exclusion of Catholics from the profession of the law, and the regulation that if a Protestant lawyer married a Catholic, he should be held to have gone over to her faith: the prohibition against Catholics acting as schoolmasters, under the penalty of being prosecuted as convicts, by which the whole body was virtually excluded from the benefits of education: and the still more summary enactment, that if a priest celebrated marriage between a Protestant and a Catholic, he should be hanged. But as years passed away, the memory of the foul deeds of the Inquisition and the confessional, and of the other enormities of which Roman Catholics had been guilty in their days of power, waxed fainter; milder feelings began to prevail; and when Grattan appeared as the champion of their rights, the field was already in some degree prepared for his labours. Favoured by such influences, of which no one knew better how to avail himself, he suc-mittee, in which not one of the many amendments ceeded, in 1790, in carrying, in the Irish parliament, the famous resolution, that the king's most excellent majesty, and the Lords and Commons of Ireland, are the only competent power to make laws to bind Ireland. Many of the disqualifying statutes were now repealed, and the claim for complete equality with Englishmen and Protestants, or complete separation from the sister-country, was now formally urged. From this period till the final liberation was achieved, there was no rest. The Irish rebellion of 1798 brought home to the English nation the dangers to which it would constantly be exposed till the question was finally adjusted. The Act of Union of 1800 was the immediate consequence of that outbreak; and to this act the Irish were induced to consent by a virtual pledge entered into by Mr. Pitt, to the effect that the Catholic disabilities should be at once removed. But, like William of Orange, Pitt had pledged himself to more than he was able to accomplish. The king was seized with scruples regarding the obligations imposed upon him by his coronation oath, and made a vigorous stand against the proposals of his minister.

At a subsequent period, efforts were made in the direction of emancipation by Mr. Canning and Lord Castlereagh. About 1824, the press began to take up the question warmly; a Catholic Association was formed, to prepare petitions to parliament; the Irish priests stimulated their flocks to subscribe for the purposes of agitation; O'Connell rapidly became a power; and as early as March 1825, the importance of the question was so deeply felt, that Sir F. Burdett ventured to introduce a relief bill, which passed the Commons by a majority of 268 to 241, but was rejected by the Lords. A slight temporary reaction now took place, the superstitious fears of ignorant Protestants being excited by a 'no-popery' cry, and in consequence, a new relief bill, introduced in 1827, though supported by the last effort of Canning's eloquence, was lost in the Commons by a majority

On the 5th March, Mr. Peel brought forward the great measure. The majority on the motion in the Commons for going into committee was 188, in a house of 508 members; the debate on the second reading issued in a majority of 180; and the final majority, after the bill had passed through comproposed was carried, was 178 in a House of 462. In the Lords, the debate lasted three nights, the majority being 106 in favour of the second reading of a bill which, nine months before, the same House had refused, by a majority of 45, even to entertain -so rapid and threatening had been the progress of the agitation. On the 13th April 1829, this famous measure became the law of the land. It now only remains that, by mentioning the provisions of the act, we sum up the results of one of the most important controversies that ever agitated the inhabitants of this country. For the oath of supremacy, another oath was substituted, by which all Catholic members of parliament bound themselves to support the existing institutions of the state, and not to injure those of the church (see ABJURATION). Catholics were admitted to all corporate offices, and to an equal enjoyment of all municipal rights. The ariny and navy had already been opened to them. On the other hand, they were excluded from the offices of Regent, of Chancellor of England or Ireland, and of Viceroy of Ireland; from all offices connected with the church, its universities and schools, and from all disposal of church patronage. The most important security related to the franchise, in which a £10 was substituted for a 40s. qualification in Ireland. The clergy of the R. C. Church were left in the position of other dissenters, the government having declined either to endow them, or to introduce any machinery for prying into their relations to the pope. But the public use of their insignia of office, and of episcopal titles and names, was denied them; the extension of monachism was prohibited; and it was enacted that the number of Jesuits should not be increased, and that they should henceforth be subject to registration. For further information, see Miss Martineau's History of England during the Peace from 1815 to 1846. W, &. R. Chambers, 1858.

CATHOLIC EPISTLES-CATO.

CATHOLIC EPISTLES, the name given, according to Clemens Alexandrinus and Origen, to certain epistles, addressed not to particular churches or individuals, but either to the church universal or to a large and indefinite circle of readers. Originally, the C. E. comprised only the first epistle of John and the first of Peter, but at least as early as the 4th c. (as evinced by the testimony of Eusebius), the term was applied to all the apostolic writings used as 'lessons in the orthodox Christian churches. But this included the Epistle of James. of Jude, the 2d of Peter, and the 2d and 3d of John. These seven thus constituted the C. E., although the genuineness and authenticity of the last-mentioned five were not universally acknowledged; but this very incorporation with epistles whose canonicity was not questioned, naturally had the effect of confirming their authority, so that in a short time the entire seven came to be considered a portion of the canon.

CATHOLICOS, the title of the patriarchs or chief ecclesiastics in the hierarchy of the Armenian Church, and of the Christians of Georgia and Mingrelia.

remained in Rome, the chief of whom was Lentulus, were arrested, tried, condemned, and executed, December 5. The insurrections in several parts of Italy were meanwhile suppressed; many who had resorted to Catiline's camp in Etruria, deserted when they heard what had taken place in Rome, and his intention to proceed into Gaul was frustrated. In the beginning of January (62), he returned by Pistoria (now Pistoja) into Etruria, where he encountered the forces under Antonius, and, after a desperate battle, in which he displayed almost superhuman courage and enthusiasm, was defeated and slain. The appearance of Catiline was in harmony with his character. He had a daring and reckless look; his face was haggard with a sense of crime; his eyes were wild and bloodshot, and his step unsteady, from nightly debauchery. The history of the Catiline conspiracy is given by Sallust in a remark ably concise and nervous style.

CA'TION. See ANODE.

CATKIN (amentum), in Botany, a spike of numerous small unisexual flowers, destitute of calyx and corolla, and furnished with scale-like bractes instead, the whole inflorescence finally

Catkin of Willow.

Catkin of Birch.

falling off by an articulation in a single piece. Examples are found in the willow, hazel, oak, birch, alder, and other trees and shrubs, forming the natural order AMENTACEÆ (q. v.). In some, as in the oak and hazel, the male flowers only are in

catkins.

CATILI'NA, LU'CIUS SE'RGIUS, descended from a patrician but impoverished family, was born about the year 108 B. C. During his youth, he attached himself to the party of Sulla. His bodily constitution, which was capable of enduring any amount of labour, fatigue, and hardship, allied to a mind which could stoop to every baseness and feared no crime, fitted him to take the lead in the conspiracy which has made his name infamous to all ages. In the year 68 B. C. he was elected prætor; in 67 B. C., governor of Africa; and in 66 B. C., he desired to stand for thec onsulship, but was disqualified on account of the accusations brought against him of maladministration in his province. Disappointed thus in his ambition, and burdened with many and heavy debts, he saw no hope for himself but in the chances of a political revolution, and therefore entered into a conspiracy, including many other young Roman nobles, in morals and circumstances greatly like himself. The plot, however, was revealed to Cicero by Fulvia, mistress of one of the conspirators. Operations were to commence with the assassination of Cicero in the Campus Martius, but the latter was kept aware of every step of the conspiracy, and contrived to frustrate the whole design. In the night of November 6 (63 B. C.), Catiline assembled his confederates, and explained to them a new plan for assassinating Cicero; for bringing up the Tuscan army (which he had seduced from its allegiance), under Manlius, from the encampment at Fæsulæ; for setting fire to Rome, and putting to death the hostile senators and citizens. In the course of a few hours, everything was made known to Cicero. Accordingly, when the chosen assassins came to the house of the consul, on pretence of a visit, they were immediately repulsed. On the 8th of November, Catiline audaciously appeared in the senate, when Cicero-who had received intelligence that the insurrection had already broken out in Etruria-commenced the celebrated invective beginning: Quousque tandem abutére, Catilina, parientia nostra? &c. (How long now, Catiline, will you abuse our patience?') The CATO, MARCUS PORCIUS, surnamed Censorius scoundrel was abashed, not by the keenness of and Sapiens ('the wise'), afterwards known as CATO Cicero's attack, but by the minute knowledge he PRISCUS or CATO MAJOR-to distinguish him from displayed of the conspiracy. His attempt at a Cato of Utica-was born at Tusculum in 234 B. C. reply was miserable, and was drowned in cries of He inherited from his plebeian father a small farm execration. With curses on his lips he abruptly in the country of the Sabines, where he busied left the senate, and escaped from Rome during the himself in agricultural operations, and learned to night. Catiline and Manlius were now denounced love the simple and severe manners of his Roman as traitors, and an army under the consul, Antonius, forefathers, which still lingered round his rural sent against them. The conspirators who home. Induced by Lucius Valerius Flaccus to

was

CATMINT (Ne'peta cataria), a plant of the natural order Labiata, pretty common in England, in chalky and gravelly soils, but rare in Scotland and Ireland, widely diffused throughout Europe and the middle latitudes of Asia, and of North America; remarkable for the fondness which cats display for it. It appears to act upon them in a similar way to Valerian root; and when its leaves are bruised so as to be highly odoriferous, they are at once attracted to it, rub themselves on it, tear at it, and chew it. Its odour has been described as intermediate between that of mint and that of pennyroyal. It has erect stems, 2-3 feet high, dense whorls of many whitish flowers, tinged and spotted with rosecolour, and stalked heart-shaped leaves of a velvety softness, whitish and downy beneath.-Other species are numerous in the south of Europe, and middle latitudes of Asia.

CATO.

Immedi

remove to Rome when that city was in a transi- | (Berlin, 1833). Fragments of C.'s orations-of which tion epoch, from the old-fashioned strictness and as many as 150 were read by Cicero-are given in severe frugality of social habits, to the luxury and Meyer's Oratorum Romanorum Fragmenta (Zurich, licentiousness of Grecian manners, C. appeared to 1842). protest against this, to denounce the degeneracy of the Philo-hellenic party, and to set a pattern of sterner and purer character. He soon distinguished himself as a pleader at the bar of justice, and after passing through minor offices, was elected consul. In his province of Nearer Spain, where an insurrection had broken out after the departure of the elder Scipio (206 B. C.), C. was so successful in quelling disturbances and restoring order, that in the following year he was honoured by a triumph. C. exhibited extraordinary military genius in Spain; his stratagems were brilliant, his plans of battle were marked by great skill, and his general movements were rapid, bold, and unexpected. In 187 B. C., a fine opportunity occurred for the display of antique Roman' notions. M. Fulvius Nobilior had just returned from Ætolia victorious, and sought the honour of a triumph. C. objected. Fulvius was indulgent to his soldiers, a man of literary taste, &c., and C. charges him, among other enormities, with keeping poets in his camp.' These rude prejudices of C. were not acceptable to the senate, and C.'s opposition was fruitless. In 184 B. C., C. was elected censor, and discharged so rigorously the duties of his office, that the epithet Censorius, formerly applied to all persons in the same station, was made his permanent surMany of his acts were highly commendable. He repaired the water-courses, paved the reservoirs, cleansed the drains, raised the rents paid by the publicans for the farming of the taxes, and diminished the contract prices paid by the state to the undertakers of public works. More questionable reforms were those in regard to the price of slaves, dress, furniture, equipage, &c. His despotism in enforcing his own idea of decency may be illustrated from the fact, that he degraded Manilius, a man of prætorian rank, for having kissed his wife in his daughter's presence in open day. C. was a thoroughly dogmatic moralist, intolerant, stoical, but great because he manfully contended with rapidly swelling evils; yet not wise, because he opposed the bad and the good in the innovations of his age with equal animosity.

name.

In the year 175 B. C., C. was sent to Carthage to negotiate on the differences between the Carthaginians and the Numidian king Masinissa; but having been offended by the Carthaginians, he returned to Rome, where, ever afterwards, he described Carthage as the most formidable rival of the empire, and concluded all his addresses in the senate-house -whatever the immediate subject might be with the well-known words: Ceterum censeo, Carthaginem esse delendam' ('For the rest, I vote that Carthage must be destroyed').

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YOUNGER, or CATO UTICENSIS (from the place of
CATO, MARCUS PORCIUS, named CATO THE
his death), was born 95 B. C.
childhood, both parents, he was educated in the
Having lost, during
house of his uncle M. Livius Drusus, and, even
in his boyhood, gave proofs of his decision and
strength of character. In the year 72 B. C., he
served with distinction in the campaign against
Spartacus, but without finding satisfaction in mili-
tary life, though he proved himself a good soldier.
From Macedonia, where he was military tribune in
67, he went to Pergamus in search of the Stoic
to his camp, and whom he induced to proceed with
philosopher, Athenodorus, whom he brought back
him to Rome, where he spent the time partly in
sions. Desirous of honestly qualifying himself for
philosophical studies, and partly in forensic discus-
the quæstorship, he commenced to study all the
ately after his election, he introduced, in spite of
financial questions connected with it.
violent opposition from those interested, a rigorous
reform into the treasury offices. He quitted the
quæstorship at the appointed time amid general
applause. In 63 B. C., he was elected tribune, and
also delivered his famous speech on the Catiline
conspiracy, in which he denounced Cæsar as an
mined the sentence of the senate. Strongly dread-
accomplice of that political desperado, and deter-
ing the influence of unbridled greatness, and not
discerning that an imperial genius-like that of
Cæsar-was the only thing that could remedy
the evils of that overgrown monster, the Roman
Republic, he commenced a career of what seems to
us blind pragmatical opposition to the three most
Cæsar. C. was a noble but strait-laced theorist,
powerful men in Rome-Crassus, Pompey, and
who lacked the intuition into circumstances which
belongs to men like Cæsar and Cromwell. His
first opposition to Pompey was successful; but his
opposition to Cæsar's consulate for the year 59
formation of the first triumvirate between Cæsar,
not only failed, but even served to hasten the
Pompey, and Crassus. He was afterwards forced
connection with Cæsar, and become reconciled to
to side with Pompey, who had resiled from his
the aristocracy. After the battle of Pharsalia (48
B. C.), C. intended to join Pompey, but hearing the
news of his death, escaped into Africa, where he
but resigned the post in favour of Metellus Scipio,
was elected commander by the partisans of Pompey,
and undertook the defence of Utica, Here, when
he had tidings of Cæsar's decisive victory over
Scipio at Thapsus (April 6, 46 B. C.), C., finding that
his troops were wholly intimidated, advised the
Roman senators and knights to escape from Utica,
and make terms with the victor, but prohibited all
intercessions in his own favour. He resolved to die
rather than surrender, and, after spending the night
in reading Plato's Phado, committed suicide by
stabbing himself in the breast.

Though C. was acquainted with the Greek language and its literature, his severe principles led him to denounce the latter as injurious to national morals. He died 149 B. c. at the age of 85. C. was twice married. In his eightieth year, his second wife, Salonia, bore him a son, the grandfather of Cato of Utica. C. treated his slaves with shocking CATO, DIONYSIUS, is the name prefixed to a harshness and cruelty. In his old age, he became little volume of moral precepts in verse, which was greedy of gain, yet never once allowed his avarice a great favourite during the middle ages. Whether to interfere with his honesty as a state-functionary. or not such a person ever existed, is a point of He also composed various literary works, such as the greatest uncertainty. The title which the De Re Rustica (a treatise on agriculture)-much book itself commonly bears, is Dionysii Catonis corrupted, however. The best editions are by Gesnar Disticha de Moribus ad Filium. Its contents have and Schneider in their Scriptores Rei Rustica. His been differently estimated: some scholars have greatest historical work, Origines, has unfortu- considered the precepts admirable; others, weak nately perished; but some few fragments are given and vapid: some have found indications of a supein Krause's Historicorum Romanorum Fragmentarior scriptural knowledge; others of a deep-rooted

CATODON-CATOPTRICS.

and they are easily verified experimentally. Rays of all colours and qualities follow these laws, so that white light, after reflection, remains undecomposed. The laws, too, hold, whatever be the nature, geometrically, of the surface. If the surface be a plane, the normal is the perpendicular to the plane at the point of incidence; if it be curved, then the normal is the perpendicular to the tangent plane at that point. From these laws and geometrical consider ations may be deduced all the propositions of catoptrics. In the present work, only those can be noticed whose truth can in a manner be exhibited to the eye, without any rigid mathematical proof. They are arranged under the heads Plane Surfaces and Curve Surfaces.

paganism. The style has been pronounced the | laws are simple facts of observation and experiment, purest Latin and the most corrupt jargon. The truth would seem to be, that on a groundwork of excellent Latin of the Silver Age, the illiterate monks of a later period have, as it were, inwoven a multitude of their own barbaric errors, which preclude us from determining precisely the period when the volume was composed. It begins with a preface addressed by the supposed author to his son, after which come 56 injunctions of rather a simple character, such as parentem ama. This is followed by the substance and main portion of the book-viz., 144 moral precepts, each of which is expressed in two dactylic hexameters. During the middle ages, the Disticha was used as a text-book for young scholars. In the 15th c., more than 30 editions were printed. The best edition, however, is that published at Amsterdam in 1754 by Otto Arntzenius. Caxton translated it into English. CATODON and CATODONTIDÆ. CACHOLOT.

See

CATO'PTRICS. The divisions of the science of optics are laid out and explained in the article OPTICS (q. v.). C. is that subdivision of geometrical optics which treats of the phenomena of light incident upon the surfaces of bodies, and reflected therefrom. All bodies reflect more or less light, even those through which it is most readily transmissible; light falling on such media, for instance, at a certain angle, is totally reflected. Rough surfaces scatter or disperse (see DISPERSION OF LIGHT) a large portion of what falls on them, through which it is that their peculiarities of figure, colour, &c., are seen by eyes in a variety of positions; they are not said to reflect light, but there is no doubt they do, though in such a way, owing to their inequalities, as never to present the proper phenomena of reflection. The surfaces with which C., accordingly, deals, are the smooth and polished. it tracks the course of rays and pencils of light after reflection from such surfaces, and determines the positions, and traces the forms, of images of objects as seen in mirrors of different kinds.

A ray of light is the smallest conceivable portion of a stream of light, and is represented by the line of its path, which is always a straight line. A pencil of light is an assemblage of rays constituting either a cylindrical or conical stream. A stream of light is called a converging pencil when the rays converge to the vertex of the cone, called a focus; and a diverging pencil, when they diverge from the vertex. The axis of the cone in each case is called the axis of the pencil. When the stream consists of parallel rays, the pencil is called cylindrical, and the axis of the cylinder is the axis of the pencil. In nature, all pencils of light are primarily diverging every point of a luminous body throwing off light in a conical stream; converging rays, however, are continually produced in optical instruments, and when light diverges from a very distant body, such | as a fixed star, the rays from it falling on any small body, such as a reflector in a telescope, may, without error, be regarded as forming a cylindrical pencil. When a ray falls upon any surface, the angle which it makes with the normal to the surface at the point of incidence is called the angle of incidence; and that which the reflected ray makes with the normal, is called the angle of reflection. Two facts of observation form the groundwork of catoptrics. They are expressed in what are called the laws of reflection of light: 1. In the reflection of light, the incident ray, the normal to the surface at the point of incidence, and the reflected ray, lie all in one plane. 2. The angle of reflection is equal to the angle of incidence. These

R

MI

A

N

Fig. 1.

M

а

R

Plane Surfaces.-1. When a pencil of parallel rays falls upon a plane mirror, the reflected pencil consists of parallel rays. A glance at the annexed figure (fig. 1), where PA and QB are two of the incident rays, and are reflected in the directions AR and BS respectively, will make the truth of this pretty clear to the eye. The proposition, however, may be rigidly demonstrated by aid of Euclid, book xi., with which, however, we shall not presume the reader to be acquainted. The reader may satisfy himself of its truth practically by taking a number of rods parallel to one another and inclined to the floor, and then turning them over till they shall again be equally inclined to the floor, when he will again find them all parallel.-2. If a diverging or converging pencil is incident on a plane mirror, the focus of the reflected pencil is situated on the opposite side of the mirror to that of the incident pencil, and at an equal distance from it. Suppose the pencil to be diverging from the focus Q (fig. 2), on the mirror of the surface of which CB is a section. Draw QNq perpendicular to CB, and make qNQN, then q is the focus of the reflected rays. For let QA, QB, QC be any of the incident rays in the plane of the figure; draw the line AM perpendicular to CB, and draw AR, making the angle MAR equal to the angle of incidence, MAQ. Then AR is the reflected ray. Join gA. Now it can be proved geometrically, and indeed is apparant at a glance, that q▲ and AR are in the same straight line; in other words, the reflected ray AR proceeds as if from q. In the same way, it may be shewn that the direction of any other reflected ray, as BS, is as if it proceeded from q; in other words, q is the focus of reflected rays; it is, however, only their virtual focus. See art. Focus. If a B A N M pencil of rays converged to q, it is evident that they would be reflected to Q as their real focus, so that a separate proof for the case of a converging pencil is unnecessary. The reader who has followed the above, will have no difficulty in understanding

a

N

A

B

Fig. 2.

n m Fig. 3.

CATOPTRICS.

how the position and form of the image of an object placed before a plane mirror-as in fig. 3, where the object is the arrow AB, in the plane of the paper, to which the plane of the mirror is perpendicularshould be of the same form and magnitude as the object (as ab in the fig.), and at an equal distance from the mirror, on the opposite side of it, but with its different parts inverted with regard to a given direction. The highest point a, for instance, in the image, corresponds with the lowest point A, in the object. He will also understand how, in the ordinary use of a looking-glass, the right hand of the image corresponds to the left hand of the object.

When two plane mirrors are placed with their reflecting surfaces towards each other, and parallel, they form the experiment called the Endless Gallery. Let (in fig. 4) the arrow, Q, be placed

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be produced till they meet in C. Let SA, in the plane of A and B, be the ray incident on the first mirror at A, and let AB be the line in which it is thence reflected to B. After reflection at B, it will pass in the line BD, meeting SA, its original path, produced in D. The angle ADB evidently measures its deviation from its original course, and this angle is readily shewn to be double of the angle at C, which is that of the inclination of the mirrors. It is on this proposition that the important mathematical instruments called the Quadrant and Sextant (q. v.) depend.

Curved Surfaces.-As when a pencil of light is reflected by a curved mirror, each ray follows the ordinary law of reflection, in every case in which we can draw the normals for the different points of the surface, we can determine the direction in which the various rays of the pencil are reflected, as in the case of plane mirrors. It so happens that normals can be easily drawn only in the case of the sphere, and of a few surfaces of revolution,' as they are called. These are the paraboloid, the ellipsoid, and the hyperboloid of revolution. The paraboloid of revolution is of importance in optics, as it is used in some specula for telescopes. See arts. SPECULUM and TELESCOPE. The three surfaces last named are, however, all of them interesting, as being for pencils of light incident in certain ways what are called surfaces of accurate reflection-i. e., they reflect all the rays of the incident pencil to a single point or focus. We shall explain to what this property is owing in the case of the parabolic reflector, and state generally the facts regarding the other two.

P

G

vertically between the parallel mirrors, CD, BA, with their silvered faces turned to one another, Q will produce in the mirror CD the image q'. This image will act as a new object to produce 1. The concave parabolic reflector is a surface of with the mirror BA the image q, which, again, accurate reflection for pencils of rays parallel to the will produce with the mirror CD another image, axis or central line of figure of the paraboloid. and so on. Another series of images, such as q', This results from the property of the surface, that q, &c., will similiarly be produced at the same the normal at any point of it passes through the time, the first of the series being g', the image of Qaxis, and bisects the angle between a line through in the mirror BA. By an eye placed between the that point, parallel to the axis, and a line joining the mirrors, the succession of images will be seen as point to the focus of the generating parabola. Referdescribed; and if the mirrors were perfectly plane ring to fig. 6, suppose a ray incident on the surface and parallel, and reflected all the light incident on at P, in the line SP, parallel to the axis AFG. them, the number of the images of both series Then if F be the focus of would be infinite. If, instead of being parallel, the the generating parabola, mirrors are inclined at an angle, the form and join PF. PF is the position of the image of an object may be found in direction of the reflected precisely the same way as in the former case, the ray. For PG, the normal image formed with the first mirror being regarded at P, by the property A as a new (virtual) object, whose image, with regard of the surface, bisects the to the second, has to be determined. For a angle FPS, and therefore curious application of two plane mirrors meeting (angle) FPG = GPS. and inclined at an angle an aliquot part of 180°, But SPG is the angle of see art. KALEIDOSCOPE.-3. The two propositions incidence, and SP, PG, already established are of extensive application, as and FP are in one plane, has partly been shewn. They include the explanation and therefore, by the laws of all phenomena of of reflection, FP is the light related to plane reflected ray. In the same way, all rays whatever, mirrors. The third parallel to the axis, must pass through F after reproposition is one also flection. If F were a luminous point, the rays from of considerable utility, it, after reflection on the mirror, would all proceed though not fundamen- in a cylindrical pencil parallel to the axis. This retal. It is: When a ray flector, with a bright light in its focus, is accordingly of light has been re- of common use in light-houses. flected at each of two mirrors inclined at a given angle to each other, in a plane perpendicular to their intersection, the reflected ray will deviate from its original course by an angle double the

B

E

C

Fig. 5.

Fig. 6.

2. In the concave ellipsoid mirror there are two points-viz, the foci of the generating ellipse, such that rays diverging from either will be accurately reflected to the other. This results from the property of the figure, that the normal at any point bisects the angle included between lines drawn to that point from the foci.

3. Owing to a property of the surface similar to that of the ellipsoid, a pencil of rays converging to angle of inclination of the mirrors. Let A and B the exterior focus of a hyperbolic reflector, will be (fig. 5) be sections of the mirrors in a plane perpen-accurately reflected to the focus of the generating dicular to their intersection, and let their directions hyperbola.

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