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which he had been educated. Queen Mary, in 1553, repealed these laws, but they were re-enacted with fresh rigours by Elizabeth when she came to the throne in 1558. At the time these laws were made, it was not contemplated that there could be such a thing as dissent from the newly-established Church of England, but when the Puritans arose-the men who fought the battle of religious and political freedom against a Tudor queen, and against all the Stuart kings-fresh laws were framed to check them, and fetters the most oppressive and the most harassing were forged for them as they had been forged for the Roman Catholics. Every one within the realm was ordered to go to church on Sunday, or to be fined twelvepence -a sum in those days equal to more than two days' wages for a labouring man-and those who did not go for a month were fined £20. Subsequently, in the reign of Charles II. (1660-1685), it was ordered that no one should be admitted to office in any corporate town who had not within a year previously taken the Lord's Supper according to the rites of the Church of England, and certain oaths were prescribed to persons elected which no Romanist could take. The Book of Common Prayer was ordered to be used in every place for public worship, and no one was allowed to be a schoolmaster, or to have anything to do with the instruction of youth (dancing, for instance), unless he had signed a declaration of conformity to the Liturgy. Meetings of more than five persons for the purpose of worshipping God otherwise than by using the Prayer Book were liable to be broken up by force, and the preachers fined. The Test Act, passed in the twentyfifth year of Charles II., required all civil and military officers, and all persons in the service of the Crown, to take the oaths of allegiance and supremacy, to declare their disbelief in the doctrine of transubstantiation, and to receive the sacrament in the Church of England; and another law of the same king forbade any one to sit in Parliament or to vote for a member until he had taken such oaths as no Romanist could possibly take.

William and Mary (1688-1702) assented to a law granting Protestant dissenters the right of meeting for public worship if the place of meeting were duly registered; but the laws which gave this and certain other privileges to Protestants, welded yet closer the rivets of intolerance on the unfortunate Catholics, who were still forbidden to meet, or to celebrate the Mass. Statutes of George I. (1714-1727) and George II. (1727-1760) confirmed the odious Test Act, and extended it. Not only were all officers in the army and navy, and all persons in public posts still compelled to desecrate the sacrament of the Lord's Supper, and to take startling oaths, but all ecclesiastical and collegiate persons, all preachers, teachers, schoolmasters, lawyers, and high constables were compelled, under pain of deprivation, fine, and forfeiture, to take the oaths of supremacy and allegiance, and to abjure the Pope and the Pretender.

In 1779, the year before the words at the beginning of this article were spoken, an Act was passed relieving the Protestant dissenters from almost all their disabilities, those created by the Test Act and Corporation Act excepted. But the people thus enfranchised could not bear that a slight concession made the year before to Romanists, and allowing them to meet for worship under certain restrictions, should remain unrepealed. It was not enough that the Romanist should be shut out from every post of every kind in the public service, that he should be precluded from getting a living by instructing in any branch of knowledge, and that he should be unable to practise at the bar; the lately persecuted felt they could not enjoy their freedom if their fellow-sufferers by the law were also relieved, though only in part.*

A number of organisations, calling themselves Protestant Associations, had been formed in England and Scotland for the purpose of obtaining the removal of disabilities from Protestant dissenters. They chose Lord George Gordon for their chief, and had they searched the whole country over they could not have found a representative more thoroughly unsuited to guide

It was not till 1829 that the Catholic Emancipation Act allowed Roman Catholics to sit in Parliament, or to vote at elections, nor was it till the present reign that a full measure of freedom was meted out to the professors of all religions, including the Jewish religion, and that the law both in principle and practice ceased to perseoute.

them to their legitimate aspirations, though it must be confessed there was no fitter incarnation of their weaknesses and their folly. They were indignant at the slight concession given to their fellow-Christians, and they resolved, if possible, to procure the repeal of it, and if that was not to be, then they would do whatever their too ready hands might find to do. At the suggestions of Lord George, petitions were got up and numerously signed, begging the Legislature to deliver the land from the guilt of allowing certain of the inhabitants to pray together! Every means were taken to make the petition from the Protestants of London a "monster petition." Advertisements were issued, speeches were made to inflame the public mind, and personal entreaties were not wanting to induce the people to add their names.

Towards the end of May, 1780, a crowded meeting was held in Coachmakers' Hall, where Lord George spoke at length, addressing the people in a highly inflammatory harangue. He promised to present their petition to the House of Commons, of which he was a member, if they would attend him with not less than 20,000 persons, on the 2nd June. Resolutions were passed pledging the Association to meet with as many friends as they could muster on that day in St. George's Fields; and in order the better to distinguish those of the "true Protestant" party, it was agreed that the petitioners and their friends should wear blue cockades in their hats.

On Friday, the 2nd of June, Lord George Gordon met his followers, some 60,000 strong, in St. George's Fields, and after addressing them in a foolish speech, full of intolerant and strife-stirring words, marched them, six abreast, over London Bridge, up Fleet Street and the Strand to Palace Yard, of which they took riotous possession. The Houses had not yet met when the processionists arrived; there were not any police to keep order, and the troops had not any instructions.

Very soon the disposition of the assemblage was apparent. Thousands had only availed themselves of the Protestants' petition to indulge their natural instincts to commit robbery and violence, and as soon as the members of either House of Parliament began to arrive, these persons commenced to be natural. Earl Mansfield, one of the most upright and able Chief Justices England ever had, had agreed to preside over the House of Lords instead of Lord Chancellor Thurlow, who was ill at Tunbridge. As soon as his carriage came into Palace Yard it was attacked, the windows were broken, the body was much damaged, and the venerable old man with difficulty escaped into the House, with torn robes and disordered wig. The Archbishop of York was subjected to like violence, and the Bishop of Lincoln, whose carriage was literally demolished, was taken fainting into a house, whence he escaped in disguise over the leads. The Duke of Northumberland was pulled out of his carriage and robbed of purse and watch; the Lord President of the Council and other peers were also so roughly handled that they could hardly get into Westminster Hall. The Lords continued to arrive, and business commenced; but little progress had been made when Lord Montfort rushed in to say that Lord Boston was in the hands of the mob, and in imminent danger of his life. One who was present says:-"At this instant it is hardly possible to conceive a more grotesque appearance than the House exhibited. of their lordships with their hair about their shoulders; others smutted with dirt; most of them as pale as the ghost in Hamlet;' and all of them standing up in their several places, and speaking at the same instant. One lord proposing to send for the Guards, another for the justices or civil magistrates, many crying out, Adjourn, adjourn!' while the skies resounded with the huzzas, shoutings, or hootings in Palace

Yard."

Some

Lord Boston escaped from the crowd just as the House of Lords were proposing to go out and rescue him; but it being impossible to go on with business, the House adjourned at eight o'clock, and its members managed to get away unperceived by side ways and passages.

Some 200 members of the House of Commons assembled, but the noise of the Protestant rioters almost drowned their voices in debate. Lord George Gordon presented the monster petition, and moved that the House should consider it in com

mittee forthwith. An amendment was moved that it should not be considered till the 6th instant (four days on), but ti sense of the House could not be taken, because the rioter

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LESSONS IN GEOMETRY.-VIII. PROBLEM XVIII.-To draw a square upon a given straight

line.

Let A B be the given straight line upon which it is required to draw a square. By Problem III. (page 157), draw the straight line AX perpendicular and therefore at right angles to A B at its extremity A, and set off along A X a straight line A c equal to A B. Then from the point c as a centre, with c A as radius, draw the arc A E D, and from the point в as a centre, with the radius B A, draw the arc AFD, cutting the arc AED in the point D. Join D B, D C; the figure A C D B is a square, and it is described upon the straight line A B as required.

ANOTHER WAY.

Draw the straight line A X as above, and set off A c equal to A B. Then with the parallel ruler draw CD through the point c parallel to A B, and BD through the point B parallel to AC. The parallelogram ABDC is a square, and it is described upon the given straight line A B.

The angles at the four corners of a square are right angles, each containing 90 degrees. The diagonals which intersect each Death of the King. Jan. 29, 1820 other at right angles in the point a bisect the angles at the corners, or divide them into two equal parts. The angles CAD, D A B into which the right angle C A B is divided by the diagonal A D, contain each of them 45 degrees. If the learner will carefully construct a square on a large scale, as in Fig. 25, he will find that the angles C A D, B A D can be also divided into two equal angles by drawing straight lines from the point A through F and E, the points in which the diagonal C B is cut by the arcs AF D, A E D, and as these angles each contain 45 degrees the angles CAF, FAG, G A E, E A B, each contain 22 degrees. Again, in the triangle AF E, which is an isosceles triangle (see Definition 20, page 53) because the side A F is equal to the side A E, the angle FA E contains 45 degrees. Now, as the three interior angles of any triangle are equal to two right angles, or 180 degrees, the two angles A FE, A EF must together contain 18045, or 135 degrees, and as these angles are subtended by equal sides, they are equal A to one another, or, in other words, each contains 1352, or 67 degrees. From this we learn that if one angle of an isosceles triangle be known, we can easily determine how many degrees are contained by each of the remaining angles.

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Also, if two angles of any triangle be known, the third can be determined by adding together the degrees contained in the known angles, and subtracting them from 180 degrees. For example, in the triangle ACF we know that the angle FAC contains 22 degrees, and the angle A C F 45 degrees; the angle A F C is therefore equal to 180 degrees, less 671 degrees, the sum of the degrees contained in the angles FA C, A C F, or 112 degrees. The value of the angle AFC might also have been determined by subtracting the value of the angle A FE from 180 degrees, since by Theorem 3 (page 156) the angles A F C, A FE are equal to two right angles.

To construct a square, whose sides shall be of a given length, all that we have to do is to set off A B of the length required, and then proceed to form the square by the method of construction given above.

It will be a useful exercise for the learner to draw straight lines from the point D through the points E and F, cutting the sides A B, A C, as the lines A E, AF produced cut the sides B D, CD; and then determine the value of every angle he can find in the diagram thus formed from the method we have followed in the above remarks.

PROBLEM XIX.-To draw an equilateral triangle of a given altitude.

In Definition 24 (page 53) the learner was taught, that in any triangle a straight line drawn from the vertex of one of its angles, perpendicular to the opposite side or to that side produced, is called the perpendicular of the triangle. This straight line is also called the altitude of the triangle, from the Latin

ERRATUM.-In Lessons in Geometry VII. (page 209), in Problem XIV. line 17, for "the square of the length A by the length of B," read "the square of the length of в by the length of a."

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Fig. 26.

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altitudo, height, because it shows the height of the top or vertex of the triangle from its base. In Fig. 24 (page 209), c E is the altitude of the triangle A B C, and D E the altitude of the triangle A B D. If, then, we have to determine the altitude of an equilateral triangle already drawn, as in the triangle A B C in the same figure, it is manifest that we have only to draw a straight line from the point c perpendicular to the base A B; or, what is the same thing, bisect the base A B, and join the point of bisection and the point c, which is the top, vertex, or apex of the triangle. But to proceed with the problem under consideration. Let the straight line A represent the altitude of the equilateral triangle required. Draw any straight line B C of indefinite length, and from a point D, taken as nearly as possible in the centre of the line, draw D E at right angles to B C. Then, along the straight line D E set off D F equal to A, and from D as a centre with the distance D F, describe the semicircle HF G, cutting the straight line B C in the points & and H. Then from G as centre with the distance G D, describe the arc D I, cutting the semicircle H F G in L, and from H as centre with the distance H D, describe the arc D K, cutting the semicircle H F G in M. Through F draw the straight line I K parallel to B c, or, what is the same thing, touching the arcs D I, D K (see Problem X., page 192), and through the points L and M, draw the straight lines D N, Do, meeting I K in N and o. The triangle D NO is an equilateral triangle, having its altitude D F equal to the given altitude A.

If we join L F, the triangle D L F is an isosceles triangle, having the side D L equal to the side D f. As the sides D L, D F are equal, the angles which they subtend, namely, the angles D L F, D F L, are equal to one another. Now, the third angle, L D F, of the triangle D L F, is an angle of 30 degrees, and each of the angles D L F, D F L is therefore equal to 180-30 divided by 2, or 150÷2=75 degrees.

Again, in the triangle L N F, the angle L N F is an angle of 60 degrees; the angle F L N is equal to 180-75, or 105 degrees, since the angles F L N, F L D are together equal to two right angles, and of these the angle F L D has been shown to be an angle of 75 degrees; and the angle N F L is equal to 90-75, or 15 degrees, since the angle N F D is a right angle, and N FD an angle of 75 degrees. Its value can also be found by subtracting the value of the angles F N L, NLF from 180, thus: 180 (60+105)=180-165=15 degrees.

PROBLEM XX.-To draw an angle which shall contain a given number of degrees.

Although it is plain, from the preceding problems, that it is possible to draw many angles containing a given number of degrees without the aid of any instruments, except a pair of compasses and a ruler, it is necessary to resort to the protractor or scale of chords in drawing the great majority of angles when the extent of their opening is stated. The protractor has been described already (page 113). The scale of chords will be found on any "Plane Scale" of boxwood or ivory, sold by mathematical instrument makers, and consists of a line graduated or divided in such a manner as to show the opening of any angle from 1 degree to 90, in degrees only. The method of using the scale of chords is as follows:

B

On any straight line, x Y, set off a portion, A B, equal to the opening of an angle of 60 degrees, as marked on the scale of chords. Fig. 27. From the point A as a centre, with A B as radius, describe the arc B Z. Then, supposing it be required to draw an angle of 40 degrees, apply the compasses to the scale of chords, and open the legs to the extent of 40 degrees, as marked on the scale. From Bв as a centre, with the radius thus obtained, draw an arc, cutting the arc в z in the point c. Join AC; the angle B A C is an angle of 40 degrees.

To construct a scale of chords, a quadrant of a circle is drawn, and the arc of the quadrant is divided into ninety equal parts,

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corresponding to the number of degrees in a right angle. Straight lines are then drawn from one extremity of the arc to each of the points of division, and the length of each line in succession, from that which is drawn to the point nearest to the extremity of the arc from which the lines are drawn, to that which is drawn to the other extremity, is transferred to the scale. The radius of any circle, whether large or small, is the chord of an angle of 60 degrees; but the learner must bear in mind that no chord of an angle of 60 degrees, except that which is marked on his scale, will suffice for the length of the line A B, as the proportions of the chords of the other angles of the scale have been determined by the aid of the quadrant of a circle whose radius is equal to the chord of an angle of 60 degrees of the length laid down on the scale.

15 30 45 60 75 90

Fig. 28.

To render this perfectly intelligible, in Fig. 28 B A C is a quadrant of a circle, and the angle B A C is an angle of 90 degrees. As it would require an arc of considerable size to divide it clearly into 90 portions of equal size, let us be satisfied with dividing the arc B C into six equal parts in the points D, E, F, G, H. The straight lines drawn from A to each of these points divide the angle B A C into six equal angles of 15 degrees each, and the angles B A D, BA E, BAF, BAG, B A H, are respectively angles of 15, 30, 45, 60, and 75 degrees. Draw the lines B D, B E, B F, B G, B H, B c, from the extremity B of the arc B C through the points D, E, F, G, H, C. These lines represent the chords of the angles B A D, BA E, BAF, B A G, B A H, and B A C respectively, or chords of angles of 15, 30, 45, 60, 75, and 90 degrees, and by setting off the length of each in due order along any straight line, we construct a scale of chords for angles having these openings, based on the quadrant of a circle whose radius is equal in extent to the length of the chord of an angle of 60 degrees, as marked on the scale. To make an angle greater than 90 degrees by means of the scale of chords, it is only necessary to draw a semicircle instead of a quadrant of a circle, and having set off 90 degrees on the arc, to set off in addition the chord of the number of degrees by which the given angle exceeds 90. Thus, in Fig. 28, to draw an angle of 120 degrees, first draw the semicircle B X, with a radius equal to the chord of an angle of 60 degrees, as marked on the scale. Open the compasses to the whole extent of the scale, and setting one foot on B, with the other draw a small arc, cutting the arc B X in c. Then reduce the opening of the compasses to the extent of the chord of an angle of 30 degrees, and setting one foot on c, with the other cut the arc cx in K. Join A K; the angle B A K is an angle of 120 degrees, being formed by the angles B A C, CA K, the former of which is an angle of 90 degrees, while the latter is one of 30 degrees.

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A scale of chords can be readily constructed without drawing lines from one extremity of the arc of the quadrant to every point of section in succession between the extremity from which the chords are drawn and the other extremity. The method which we are now going to bring under the reader's notice has the advantage of simplicity; but in Fig. 28 the actual chords of the angles from 15 to 90 degrees are shown in succession, and the angles themselves that the chords subtend are also shown by straight lines drawn from the point в to the different points of section of the arc. In Fig. 29, having drawn a quadrant of a circle, A B C as before, join A B, the chord of the right angle A C B, and divide the arc A B into nine (or ninety, if it be large enough) equal parts in the points a, b, c, d, e, f, g, h. Then, setting one foot of the compasses at A, draw arcs through the points a, b, c, etc., in succession, cutting the straight line A B in the points numbered 10, 20, 30, etc. The distances along A B intercepted between the extremity A and each arc in succession are respectively chords of angles of 10, 20, 30, 40, 50, 60, 70, 80, and 90 degrees.

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I. VERTICAL SECTION OF HEAD OF PORPOISE, SHOWING THE NASAL PASSAGE. II. VERTICAL SECTION OF RABBIT'S HEAD, SHOWING OUTER WALL OF THE NASAL CANAL, LEFT SIDE. III. UNDER-SIDE OF HEAD OF SPOTTED DOG-FISH, IV. NASAL SAC OF STURGEON. Ref. to Nos. in Figs.-I. 1, 2, cavities of the skull; 3, septum between the lobes of the brain; 4, nasal passage; 5, slit-like orifice; 6, folded membrane; 7, upper end of air-passage, grasped by the sides of the nasal canal; 8, soft palate; 9, hard palate; 10, tongue; 11, valve. II. 1, cavity of the brain; 2, 3, ethmo-turbinals; 4, lower turbinal; 5, nostril; 6, palate; 7, nasal canal; 8, bulla of ear; 9, bristle running through Eustachian tube.

for a shorter time, and will not reproduce them at will. Mor over, these sensations furnish but few starting-points for thought, or speculation, or reason to proceed from. We seldom employ the smell in investigation, unless it be upon objects which give no indication whatever to any of the other senses; and when we do so, we are not satisfied until we have other confirmatory evidence as to the nature of those objects. The chemist in the laboratory will make use of this sense, as a rough-and-ready method of detecting gases which cannot be otherwise easily dealt with, but he always confirms their presence by other tests if possible. Any one who has presided over the practical experiments of

VOL. I.

detect pungent gases like ammonia and chlorine, but cannot distinguish between them, or between aromatic gases like alcohol and chloroform. On the whole, we make such little use of our organ of smell, its acuteness being as often an inconvenience as. an advantage to us, that we endure the loss of this sense with more patience and with less sense of privation than that of any other. The estimate we form from experience of the comparatively small value of this sense, is apt to make us misjudge its importance to the lower animals. But if we imagine that the impressions which this sense brings to animals are as dull, indistinct, and unreliable to their consciousness as to ours, a little

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