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Page 33, col. 1, vol. II.-Exglish-Larix.

Felicitas virtute nititur; nititur ne hominibus felicitas; no felicitas Deo nititur; excolere virtutem eniti debemus: Po" iiium complexusest; filius patris mortem ultus est; rex Poo" policitusest; sororituae regina pollicita estine praemian; milites tumulatam gloriam adipiscinitentur, mane exerreoti so." discessee; benevitae officiis functi sunt; Aristoteles et Zoo praeceptorum officiis functi sunt; quando amici tui domum rever tent? heri domum reverterunt; e patriá profecti sunt, et nun?” revertent; pestis haec hominum in animis nata est (born); * patria : patria mea est mundus; in animis mortalibus so! seniina innata vitiorum; dux cum hostibus congressus est; quotio duces Arglici cum hostibus congressi sunt, semper disces: superiores; optimi cujusque pueri animus maxime Poro . amat; boni in salutem animae nituntur; lacte pueri “ Fo vescuntur; discipuli officiis suis functi sunt; O Deus; missio lapsorum; succurite pauperibus; proprium est stuititi" " prodesse.

Page 39, col. 1, vol. II.-LATIN-ENGLISH.

Caesar feared to oppose his army to a liver of such o: Caesar is of opinion that it should be attempted, and a trial made; Caesar, although he feared to oppose his army to a stream." . o magnitude, yet is of opinion that it should be attempted ; d: triai made; nor did they fear that they should be so : they said that they feared not the enemy; they said that * feared the narrow road; they said that they feared that." . not supplied conveniently enough; they said that they o the enemy, but the narrow road, and that they were afrai • not provisions could not be supplied conveniently enough; ben

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afraid, the ship is safe; I fear greatly on account of the republic; he had no fear on account of his own peril and the peril of the legion; you are not afraid you will lose the place; he feared he should not succeed.

Page 39, col. 1, vol. II.-ENGLISH-LATIN.

Timeone operam perdideris; timeo as domus cadat; timeout frumentum in urbem supportetur dux ; metuebatut exercitus ejus veniret; de sua puellulá pulchrá metuunt; de fortuna tuá nihil timeo; rex ducesque timent ne circumveniantur; Cicero experiendum judicat; timeout experiri possit.

Page 54, col. 2, vol. II.-LATIN-ENGLISH.

The forehead, the eyes, and the countenance often lie, but the speech lies very often; whatever arises has its origin from nature; the sun bestows the same light and the same warmth on all; how many are unworthy of light! and yet the day arises; whence, at length, do you appear to us so suddenly? O soldiers, if we break out in fierce assault upon the enemy, the victory is in our hands; while we attempted to assault the city, the enemies attacked us from behind ; each one measures dangers by his own fear; the wise man both remembers past things with pleasure, and so possesses present things, as to perceive how great and how pleasant they are; take care you do not obtain honours by flattery; orators, before they begin, premise certain things; in all matters, before we begin, we #od employ careful preparation; all the citizens had adorned and clothed their houses with flowers and wreaths, because they were waiting for the king; while the hostile army was demolishing the private and public buildings of the city, the citizens were filled with the greatest grief; while the enemies were dividing the spoil amongst themselves, we charged them with the greatest impetuosity; the general exhorted the soldiers, that they should try all methods by which they might relieve the city from the blockade; because a fierce tempest arose, great fear seized upon all the sailors.

Page 55, col. 1, vol. II.-ENGLISH-LATIN.

Saeva tempestas coorta est; saeva tempestas coorietur; saeva tempestan coorítur; saevae tempestates cooriebantur, saeva tempestas cooriebaturi nautae multos labores experti sunt; hostes domum tuam demolientur, mean sororem opperiar; mater nea herime opperiebatur; illi eblanditi sunt honores; honores eblandieris ne? nolo honores chlandiri; prius quam oidiaris, adhibenda tibi est industria; tellure potitur; omni urbe potitus cat ; libris patris mei potiar; mi puer, cave no mentiaris; solun mali mentiuntur; malum est mentiri; O pater, nunquam mentiar; illi mentiti et puniti sunt ; turpe est mentiri; sol et bonis et malis orítur, tanta bonitas Deo est; rex fortibus militibus honores langitur; inter duo filios bona partitus est; quicquid a telluru writur, wenit a manu diviná.

Page 55, col. 1, vol. II.-LATIN-ENGLISH.

Those are to be laughed at, who teach others that which they themselves have not tried; every animal loves itself, and as soon as it appears, aims at preserving itself; nature has bestowed so great a productive power on the conveniencies and necessaries of men, in order that those things which are begotten may seem to have been given to usadvisedly (consulto), and not to have arisen by chance; Herodotus passed through many lands, and certainly (quodom) related many marvellous things, but these he himself invented not, but others (invented them) from whom he heard them; now, for three months we had been waiting for a friend, when his death was announced to us; Sulla suddenly appeared to the Romans, and began a most flightful civil war; a wise man will never flatter bad men, never invent any false thing, never occasion injury to others; if we attack the enemy quickly, there is no doubt that in a short time we shall get possession of the city; as soon as the sun has risen, we shall set out; take care that you do not flatter bad men; the enemies hastened to get possession of the city; an even number is easy to divide; the sun rising, we set out; a fierce tempest having arisen, great fear seized all the sailors; with the greatest pleasure we behold the sun when about to rise (oriturum).

Page 55, col. 1, vol. II.-ENGLISH-LATIN.

Sole oriente, tenebrae diffugiunt; solem oriturum magná cum voluptate specto; coortà tempestate, naves nostrae sparsae sunt; mulli calamitatem moliar, non etiam malis; ortusne est solo hotă octavāsol orietur ; repente hostem adortus est; meam ordiar orationem; orator orationem ordiebatur, quum judex intrabat; non est dubium quintuis potituti sitis; simulatgue nati sumus, movemus; omnes hominesse ipscs diligunt, ac simulatgue facultatibus potiti sunt, inter se eas partiri debent; inter egentes facultates partitus est; multi Britanniam emensi, ignorant quam sit felix potensque; spero te nunquam mentiturum esse; tempestas orieturi omnes existimant, tempestatem coorituram esse.

Page 55, col. 2, vol. II.-LATIN-ENGLISH.

The arts support themselves; we shall always pity wretched men; when you are sick, you ought to comply with the instructions of the physician; foolish men perceive }. faults of others, (but) forget their own; the principal charm of springs from modesty; 0 boys, reverence old age; Q boy, I confess the truth; take pity on the destitute; let the scholars reverence their teachers; } doubt not that you will promise me your protection ; we behold (intuemur) with great pleasure the noble examples of virtue which have been recorded in history; who knows not how many abuse eloquence 2 we have enjoyed peace during many years; all the citizens fear that the enemies will attack the city; as soon as we have arisen, we proceed to our business; the citizens, having obtained liberty, will enjoy the greatest pleasure; aid the fallen; converse as boldly with your friend as with yourself; be not angry with those whom you ought to love; if we always pursue the path of virtue, access to heaven will sometimes lie open to us; perform your part well; by concord small things increase, by discord the greatist things fall to pieces: glory, like a shadow, follows virtue; do not flatter bad men; we measure great men by their worth, not by their fortune; pleasure flatters our senses; I fear that my friend is dying.

Page 55, col. 2, vol. II.-ENGLISH-LATIN.

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Heri amicus meus mortuus est; metuo he amicus tuus moriturus sit; ne largitor malis pueris; Deus piis largietur; aditus in coelum semper bonis patet; metuo ut aditus in coelum Alexandro pateat; quamdiu patria tua pace fruebatur quamdiu regis exercitus in patria nostra erit, pace fruémur; esne munere functus he abutere patris gratiâ; loquartecum, sed non tibi, blandiar; regi blanditus, laudem adeptus est; filius me laudem adipiscétur 2 filius meus gloriam maximam adeptus est; gloria virtutem eximiam sequitur ; se rediturum esse, mihi pollicitus est; ille rediit; non, cras redibit; pueri se ipsi tuentur, pueri se ipsi tueri debent; misereor et miserebor miserorum; ne obliviscere vitionum tuorum; intra paucos dies proficiscar; quando revertes? weremini senes, O pueri, weremini patrem; vereinini Deum; peccatum suum fassus est; tempestate coortà, pavor animos nostros occupavit.

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The violin consists of 58 different pieces; the wood is generally of three sorts; the back, neck, sides, and circles, are of sycamore; the belly, bass-bar, sound-post, and six blocks, of deal; and the finger board and tail piece, of ebony. Six cremona violins (namely those made by Amati or Straduarius) that came * my possession, were made after the following proportions. The belly was thickest where the bridge rests; then it diminished about a third at that part where the holes are cut, and where the belly rests on the sides it was half as thick as in the middle. The same proportion is observed in the length. . The thickness is o maintained all along that part in which the bass-bar is fixed;

A. Thomson.

thence to the upper and under end blocks, the thickness decreases to one half, so that the cheeks are three-fourths the thickness of the breast, and the edges all round only one half. These proportions are best for imparting a full, powerful, and sonorous sound. ...The back is worked out much in the same proportion as the belly. If you feel desirous of more information on this subject, I advise ou to purchase “Otto's Treatise on the Violin.” Published by t. Cocks and Co., New Burlington-street, London. The price, I believe, is 3s. Yours, &c. H. M. S.

ANSWERS TO CORRESPONDENTS.

Elswick: Right in the lean horse query.—A STUDENT IN ENGLisu, and his friends in Sheffield, are strongly advised to commit the lists of profires and affires with their meanings to memory; this will give them such a hold, as it were, of the most important part of the language, as will enable them to speak and write with the greatest accuracy.-WALLAser Bideton (Liverpool): We hope that Mr. Cassell's Latin Dictionary, edited by Dr. Beard, will be the best and cheapest, when it is ready.—W. Bush {y. mouth) wishes to know where he can obtain designs %. wood-carving.— S. HEATH (Barnetby) should read Virgil before Horace. As an introduction to the Horation metres and style, he would do well to read George Buchanan's Latin translation of the Psalms of David, a most elegant book, and written in the purest Latin, that of the Augustan age: good copies of it may be had at o old book-stall in London for sixpence.—H. Eaves (Preston) wishes to know of some work on the art of grinding glasses for telescopes: can any of our readers assist him? A Subscalagh (in Buckingham) will have some lessons on Mapping, &c. in the P. E.-J. Y. (Preston) will find his wants supplied in the Lessons on Chemistry, when they appear.-AMicus. (Stepney): The subjects for Examination in Natural Philosophy, and Chemistry, in the University of London, are always the same, but the particular questions vary every year. The classical subjects for the Pass Examination in 1851 are stated in No. 41, p. 215, col. 2, line, 34.-W. Ash (Holborn): His penmanship is really not, so bad as , he thinks; we advise him to buy two or three copy. books for large-hand, ready ruled, at a stationer's shop, and imitate our large copies by writing them from A to Z two or three times. Then, do the same with the half-tert hand; and, lastly, do the same with the small or court-hand, and he may rest assured that by slow and careful perseverance he must improve. He ought, of course, to read most carefully our instructions as to the mode of holding the pen and sitting at the table.-W. Butleh (Southwark); The sentence “I had known the deceased some years prepious to his death,” is the most correct.—A Subscrimea (Isle of Man) should buy the latest edition of Smart's Walker's Dictionary. Encyclopaedias very soon get out of date; we cannot recommend any one in particular, as you might be disappointed in the first article you turned up. The P. E. will be better than any encyclopædia. Incola, the sentence beginning Regibus is quite right:-Agricola ought to have known that littera in the singular is a letter of the alphabet, and that a letter in the sense of an epistle is in Latin litterie, being in the plural.—F.T. An adjective pronoun is a pronoun which, like an adjective, stands with a noun, as si qui (for si aliqui) homines, if any persons; the genitive case of the personal pronoun ego, that is mei, of me, or mine, denoting possession, and so is the same as mei of what is called the possession pronoun meus; they are indeed the same word; similar tenses are such as denoting corre. sponding times, may go together; dissimilar tenses are the reverse, corresponding times are such as in the nature of things stand in the same relation as the presents, and the presents hold the same position in time or in regard to eternity; in the same o are the past and the past related, the future, and the future; the supine differs from the infinitive chiefly in form and in construction; the supines are really nouns, the one in the accusative case, the other in the ablative; the infinitive also has sometimes the force of a noun, as Amo legere libros, I love to read books, is the same as Amo lectionem librorum, I love the reading of books. Hennicus (Taunton): Should write to Mr. Bagster for what he wants; Simeon's Horae Homiletica is the book he means, but we don't know any thing about prices. Your suggestion about publishing the figures of Euclid by themselves is good for many purposes; it will be taken into con sideration.—John McCulloch (Edinburgh): Thanks for his answers to Cassell's Arithmetic.—B. B. (Yorkshire): must really buy and read the Spectator for himself. Gregory's letters we doubt not are good, and recommendable to a student.—T. MoRLEY (Bromley): Thanks for his answers to the questions in Cassell's Arithmetic.-E. SMITH (Little Cookham, Surrey) shall have the first copy of the answers to Cassell's Arithmetic.—GEit. MAN1ces, received and under consideration.-Paulo (Dundee): Right; not is terroris. GEnxian.-EDw ARD Eves should study more the rules of declension. In exercises 3, 4, and 10 you have made mistakes. The other sentences are very correct; every syllable beginning with an s must be written with a long fo-A Sunscainen; Etcetera, &c. x., is written in German generally u. f. m., but also like the English etcetera.-T. S. W. R. B. F. will find it in this week's lesson.-T. W.; Do not know; have never seen it. 8. DAvies (Cayo): We believe Matthiae's Greek Grammar to be the most complete.-PHILoMAth, (Bath): Received.—A STUDENT (Halifax.): in the German, as in the French Lessons, there are references to the Second Paar yet to come.-J. Colquhoun (Tolcross): Practice does wonders.-W. h. {Apsley-bridge) should write to the bookseller he mentions for his catalogue; he will be only too happy, to send it to him.—A Constant READER, &c. (Leeds), is informed that the two editions of the P.E. are exactly the same; the only difference is in the paper, and the heading of the first page. Eranata. Vol. I. p. 411, Col. I: Exercises 2, line 2, for divitissime, read divitissimi, for dissisilim read dissimiles; Line 17, Jor modestur read modestior; line 19, Jor similissima read simillima; line T, for contamus read cantamus.

LITER A R Y NOTICE S.

GIN AND WATER; a pair of pictorial designs by Kenny Meadows, portray. ing the effects arising from the indulgence of those potent liquids. In the first, GIN, we have the interior of the drunkard's home, with a glimpse of the horrors which belong peculiarly to such homes; in the second, Wareh, we see how comfort, cleanliness, and peace attend the steps of the temperate man. The contrast is well sustained, and the pictures—which measure 24 inches by 16 inches—cannot but be popular. We have had too many songs and pictures in praise of the drinking customs of our country, and we are glad to perceive that our poets and artists are beginning to discover that they may get inspiration even out of water— “Wine, wine, thy power and praise Have ever been echoed in minstrel lays; But water, I deem, hath a mightier claim To fill up a niche in the Temple of Fame?" These pictures, which should be framed and hung over every cottage chimney-piece, and on the walls of every factory, and workshop, and ragged school throughout all the land, can be obtained of every bookseller for one shilling... They are exquisitely engraved on wood, by Messrs. Henry Linton and William Measom. THE AUToGRAPHs for FREEdox; containing, in addition to a New Story by Mrs. Stowe, authoress of “Uncle Tom's Cabin,” entitled “The Two Altars; or, Two Pictures in One;—The Altar of Liberty, or 1776; The Altar of , or 1850,"a thrilling Narrative by FREpenick Douglass, entitled “The Heroic, Slave;” “Passages in the Life of a Slave Woman," by Annie Parker; “Placido, the Cuban Slave,” by Professor W. G. Allen; “The Heroic Slave Woman,” by the Rev. J. S. May, &c.; also, Coutributious from the leading Writers in America on the Question of Negro Eunancipation; and, on this side of the Atlantic, from the Earl of Carlisle, the Bishop of Oxford, Wilson Armistead, Joseph Sturge, &c.; with fac. similes of the Autographs of all the Contributors, Price Is., in boards; or bound in cloth, with Eight beautiful Engravings from designs by Gilbert and Willis, pricels. 6d. ATHEIsM ConsidekkD THEoLogically AND Politically. This Volume, consists of thirteen Lectures, by the Rev. LYMAN Borcuen, D.D. (father of Mrs. H. B. Stowe.) These Lectures enter fully into the momentous question now at issue, or, at least, under discussian, between “Secularism” and Christianity. For close reasoning and eloquent declamation, these Lectures have rarely been surpassed. The Wolume, just issued, is well printed, and is sold for 2s. 6d. bound in cloth. The ALTAR of the Household: a Series of Services for Domestie Worship for every Moruing and Evening in the Year; Select Portions of Holy Writ, and Prayers and Thanksgivings for Particular Occasions; with an Address to Heads of Families. Edited by the Rev. John Harris, D.D., Principal of New College, St. John's Wood; Author of “The Great Teacher;" "Mammon;'''“Pre-Adamite Earth,” &c. &c., assisted by eminent contributors, The following are among the Ministers engaged in the p ation of Tur ALTAR of THE Household :-The Rev. J. Sherman, the Rev. W. Urwick, D.D., the Rev. W. H. Bunting, M.A., the Rev. R. Ferguson, LL.D., the Rev. F. A. Cox, D.D., LL.D., the Rev. Professer Lorimer, the Rev. Newman Hall, B.A., the Rev. B. S. Hollis, the Rev. W. Chalmers, A.M., the Rev. J. Beaumont, M.D., the Rev. Samuel Martin, the Rev. William Brock, the Rev. John Kennedy, A.M., the Itev. William Leask, the Rev. Charles Williams, the Rev. W. W. Ewbank, A.M., the Rev. J. Stoughton, the Rev. W. Reid, the Rev. George Smith, &c. &c. The Work will be completed in Two Parts, one to appear on the First day of each successive month; the whok forming One Handsome Volume, with Frontispiece engraved on steel by a first-rate Artist. Parts I, to III. are now ready, price is, each, or in one Quarterly Section, price 3s. Cassell's Euclid.—The ELEMENTs or GeoMErax. Containing the First Six, and the Eleventh and Twelfth Books of Euclid, Edited by Rober Wallace, A.M., price ls. in stiff covers, or 1s. 6d. neat cloth. The SELF AND CLAss ExAMINER IN Euclid, containing the Enuncis' tions of all the Propositions and Corollaries in Cassell's Edition, for the use of Colleges, Schools, and Private Students, is now ready, price 3d. Cassell's Elements of Aarthmetics(uniform with Cassell's Euclip) is now ready, pricels, in stiff covers, or 1s. 6d. neat cloth. THE ANsweks to ALL THE Questions in cassell's Akitnotorio for the use of Private Students, and of Teachers and professors who use this workin their classes, is preparing for publication, price 3d. The Ladies' Wonk Book, containing full instructions for every kind." Ladies'.Work, in Point Lace, Knitting, Netting, Embroidery, Crochet, & forming the most splendid Book for the Work-table ever issued. This work contains an immense number of the newest Designs for Ladies' work, a 3.3% description, and is produced in a style perfectly unique, Prio 2s. 6d. The Ladies' Drawing-Room Book, in which are introduced to: choicest Engravings from the “Illustrated Exhibitor and Magazine of Aro and the “Ladies' Work Book;" the whole forming a beautiful Volume of the Prawing-room.. The work is printed on fine Fiate Paper, and got up " the first style of Art. Price 10s. 6d. Uncle Tom's Cabin, with Twenty-seven Illustrations on wood." George Cruikshank, and an elegant Portrait of the Authoress-rho Editions of this popular work are now on sale at our omes—a pro Room Edition, demy 8vo., price 4s. 6d. elegantly bound, with gilt edge; crown 8vo., neatly bound, gilt edges, 3s.6d, or plain binding, 33. ... THE ILLUSTRATED ExiiinitoR AND MAgazine of ART-The First 1. Parts of a new and improved Series of this work, under the title "" Illustraten Magazine of Ant, are now ready, price one shillio. Weekly Numbers are now enclosed in a meat wrapper, price 3d Insolio to numerous Engravings in the text, each number contains a fine o: ing, worked on Plate Paper. With the first Part was presented a * View of the Interior of St. Paul's Cathedral, during the Interment."." late Duke of Wellington, printed upon fine Piate Paper, measuringo inches by thirteen, in addition to four separate Engravings, and ** number of choice Illustrations, with which each Partis embellished.

Printed and Published by John cassell, 9, La Belle sauvage” Ludgate-hill-March 5, 1853,

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PREviously to entering on the details of Perspective, we shall show, by a few easy lessons and experiments, that a certain knowledge of the principles of this department of the art of drawing may be readily acquired. Take your seat at a table, having a wall opposite to it, at the distance, say, of five feet from the eye, and having the edge of the table parallel to (that is, in every part equally distant from) the wall. Make a mark on the edge, in order to determine your position exactly, and to enable you to replace yourself in the same spot at pleasure. Now, using one eye only, make a mark on the wall directly opposite to the eye— suppose this point to be c, in fig. 71, your own position being at A. Next, lay a book near A, at right angles to the edge of the table, and the sides will appear to your eye.to take such directions that, if they were sufficiently prolonged, they would meet in the point c. Take another book near B, also at right angles to the edge of the table, and consequently parallel to the first book near A, and you will find that its sides will in like manner appear to meet in the point c, if sufficiently prolonged. Lines which meet in one point in this manner,

are said to converge to the point; and you will find, on layin another book beyon B, that its sides will also converge to c, if only it shall be parallel to the book A. Points to which parallel lines appear to converge are called, in perspective, vanishing points; and you will perceive from the preceding observations, that for parallel lines at right angles to the wall, or, which is the same thing, at right angles to the edge of the table (these parallel lines being also in horizontal planes), the vanishing point is directly opposite the eye. In the next place, take a book E, and place it on the book near B, so as to make an angle of 60°, with the edge of the table. Place yourself as before, with the eye opposite to c, and you will find that at this angle of 60°, the Yanishing point is no longer opposite to the eye, but that it lies in a horizontal line drawn through c, namely II H ; and, supposing, as before, that the eye is about five feet frcm 9, the new vanishing point v will be about three feet from c, in this horizontal line. Again, a book near G, placed parallel to E, will have the same vanishing point v. By a similar process, you will find that a book lying at an angle of 45° with the edge of the table, will have its vanishing point on the horizontal line H H, at the distance of about five feet from c. With these instructions you may continue similar observations on the convergency of the parallel lines of books placed at other angles. All the preceding examples are but particular instances of a general #. about to be explained; it will,

WOL. II.

therefore, be sufficient to have indicated here a method by which the student may practically verify much of our observations, which will immediately follow, relating to vanishing points and vanishing lines.

[1..] If you look through a pane of glass at any object on the other side of it, and with a diamond, or any other suitable instrument, you trace upon the glass the apparent outline of the object, as it appears to the eye, it will be correctly drawn; and, if the colouring and shading were added, you would have upon the glass an exact image of the original. Perspective is generally divided into Linear and Aerial. Aerial Perspective relates to such changes as take place in the colour and the depth of shadow, according to the distance of any object from the eye, and other modifying circumstances. This branch of perspective will be treated of when considering Colour and CHIARo-scubo, or LIGHT and SHADE. Linear Perspective explains the laws which modify such an outline as we have just supposed to be drawn upon a pane of glass. The end contemplated in this kind of perspective is to produce such an outline as shall convey to the mind a just idea of the original. Linear Perspective, then, is the art by which upon a plane (such as the surface of a sheet of paper) an outline (or tinear) representation may be drawn so as to produce the same image in the eye as the object itself would do, under certain given conditions.

[2.] Rays of light proceed from one point to another in straight lines. Upon this fact, and upon another, which the treatises on Optics explain, namely, that the rays from all objects to which we direct the eye converge to a point in the interior and at the back of that organ, the principles of , perspective are founded. The following remarks will illustrate this subject:-

In fig. 72, the triangle n c_n is the object, and the lines BA, cA, D.A, represent luminous rays proceeding to the eye at A. Rays of light proceed in all directions from any object whatever, but, on directing the eye to an object, we perceive. it only by means of those rays which arrive at the eye, and are there converged. This being premised, the lesson conveyed by fig. 73, will be understood by the following explanations, and, as these contain the elements of the - practical methods now in use for producing drawings in perspective, the student is requested to study them with attention.

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H. H. Go is the plane of the picture, and is generally taken in a position vertical to that of the ground plane.

v H H is the vanishing plane; it always passes through v, the place of the eye, and is always taken parallel to an original plane. The line in which the vanishing plane cuts the plane of the picture (or, as it is sometimes called, the plane of projection) is the vanishing line of an original plane.

The line H H is consequen { the vanishing line of the ground plana, and of all planes parallel to the ground plane. It is commonly called the horizontal line; and in it are found the vanishingpoints of lines in the groundplane, making any angle whatever with go, which we shall call the ground line. This line g g is evidently the intersection of the plane of the picture with the ground plane, H H being the vanishing line of planes parallel to the ground plane, the vanishing points of all lines lying in such parallel planes will also be found in H. H.

§f The vanishing point of any original line, that is, a line lying in any original plane, as, for example, the line q R is found by supposing a plane to pass through the line, and through the point v, the place of the eye; this plane evidently cuts the vanishing plane in a line parallel to the original line; for example, v c is evidently p el to a R, and the point c, where this line v c meets the vanishing line of the plane in which Qalies, is the vanishing point of a R, and of all lines in the same plane which are parallel to am. As HH is the vanishing line of all planes parallel to R G s q, it follows that the point g is the vanishing point for all the lines in those planes which are parallel to q R. The image, or projection of the line a R, is at once ascertained when the vanishing point and the original line are given. Produce q R to the ground line, and join P, the point where it cuts this line, with q, the vanishing point; draw R v and q v, to the point v; then q r is the projection or perspective representation of q R.

[4.] When the three planes are brought into one, in a manner to be explained in the next section, these constructions are very easy, and if the reader familiarises himself with the figure referred to in [3.], all the practical methods in use will be understood without difficulty. Indeed, fig. 73, with the explanations now given, contains, in as concise a form as possible, the constructions on which all modern treatises on Perspective are founded; and forms the key to all that is to follow in this series of lessons, It is, therefore, recommended to the best attention of the student, with the assurance that a clear conception of its construction is in itself the substance of all theoretical perspective; for, by looking at any object * a pane of glass, and supposing it to represent H H ag, the plane of projection (confining, in the first place, his observations to lines at right angles to the ground line), he will see how consistent this construction is with the natural appearances.

5.] In fig. 73, the vanishing point for a R at light angles to

the ground line a q, was shown to be at c, the point where v c cuts it H at right angles. In fig. 74, if T N is at an angle of 60° with the ground line, its vanishing point M will be found

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n t the representation of T N. Now suppose the plane go to be turned round upon the line g g as on a hinge, until it is in the same plane with H H g g : and suppose also the plane.” to be turned in like manner on H H until it also is in the plane H H a g-the three planes are brought into one, and the lio v M., PN, retain their direction mutually parallel as before, the intersections also at P and M with the horizontal and the ground line have suffered no change. In fig-75 is shown on ‘. ment very commonly adopted in perspective drawing four ed upon this.

Fig. 75.

c 2 is the ground line; the line it it is determined to ing ng equal to the height of the eye above the ground line this sorresponding strictly with the lines Hg in the " *. ceding figures; the line v c is the distance of the eye from the plane of the picture, and in this arrangement, as . the two preceding figures, the vanishing point of any line so o: a given angle with the ground line, is found by do parallel through v, the place of the eye, to out the hor o: fine in M, bringing T N up to the ground line to out i o joining r and M, and then determining the length of thby drawn to v from T and N. this mood is the picture, and the spaces above and o. l are used for the necessary constructions effected by o: ruler, the set square, the T square, compasses, and o sson: ments described, with explanations of their uses, * their on Practical Geometry in vol. I. of this work. irranishits Lines at right angles to the groundline have their . the point in c, where a line from v the place of the eye, meet toy horizontal line at ; angles; this point is called the Po sight or the centre of the picture. - - *#. parallel 'sthe o line or horizontallino, o: parallel to the plane of the picture, have no yo.: because a parallel drawn through v, as is at onto. ioni never meet the horizontal line. Such lines in perspect be parallel to their eriginals.

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