(I Digitized by the Internet Archive in 2012 with funding from Research Library, The Getty Research Institute http://archive.org/details/criticalexaminatOOhigh A CRITICAL EXAMINATION OF THE PAINTINGS On the CIE LING of the Banqueting-houfe at Whitehall* . , A CRITICAL EXAMINATION OF THOSE TWO PAINTINGS On the C I E L I N G of the Banqueting-boufe at Whitehall: IN WHICH Architecture is introduced, fo far as relates to the Perspective; TOGETHER WITH The Discussion of a Question, which has been the Subject of Debate among Painters. Written many Years fince ; But now firft Published. By 7. HIGHMORE. LONDON: Piinted for J. Nourse, at the Lamb againft Cathari?te~ Jireet, in the Strand. M. DCC. LI V. [i] PREFACE. THE following Piece has lain by me, finiihed, many Years, as well as a larger Work on the general Subbed of Perfpe&ive ; both which I have, at leverai times, intended to publifn, either feparateiy, or together; and, in the latter View, had defigned this as an Appendix : But it appearing, ibme time ftnce, by feveral Advertifcments, that Mr. Kirb\ y of Iffwichj was then printing a Treatife on this Subject, I delayed mine till I mould lee whether his Performance, in the Principles and InftrucUons, was juft and complete, Co as to anfwer all the Purpofes of what I had written ; relblring, in that Cafe, intirely to iurprei's my own. This, which I now offer to the Public, is only that imall Part which was defigned as an Appendix to the larger Work ; and con- tains an Examination of the Cieiing in the Banqueting-houfe, to- gether with the Conilderation, and Solution, of a Quetlion which hath occaiioned frequent Difputes among modern Artifts; vi& Whether a Range of Columns, fianding on a Line parallel to the Picture, ought to be painted according to the ftrict Rules of Per- spective; that is, whether thoie Columns, in proportion as they A recede ii PREFACE. recede from the Centre of the Picture, (hould be drawn broader than that diredly oppoilte to the Eye, as the Rules require 5 or whether [became they really, in Nature, appear lefs, in propor- ., .; :: rr.ey are BOOK du"hnt' itacj cugh: not to be made lefs, or, a: mod, equal to each other, in the Pidure ? This Point I had determined, as is above remarked, many Years iinee, afad now give it in the manner I then wrote it, without any A. rcraticn. on account of the prefent Occafion ; and the rather, as I rind that M: A>. who has undertaken the fame Queftion) vs thofe very Notions which I therein fuggefted to be the mod probable Groure c: Ac Miitakes of feveral Authors and Painters : For he fays, /. 70. of his FirftParr, tl Since the Fallacies of Vifion •* are lb many and great, &c. — it feems reafonable not to comply " w;:- : :.t ttt 7_.es of mathematical Perfredive, in lbme parti- '* cular Cafes (as in this before us), but to draw the Reprefenta- : ons of Ob^eds as they appear ioihe Ere, &c." But I would ask, how- cy J. ;.: ;; by fim Ku.ei and if by any, by what Rule are they to be drawn, contrary to, or different from, the ftrid mathematical Perfpedive Rules? — Befides, he owns, f. 72. "That ** what he had faid, related only to round or cylindrical Obieds; : at that, as to fquare, they fiould continually grow larger, the " Oak ::.-:■; are removed from the Centre of the Pidure, &c" > and adds, u thai As Dfifepfeal o: a Square k longer than its Side; rat the Diameter, which is te Mek6ttt,Wi a Circle, is always of :ne tame Length." This is true* and is the Reafon why th& --.■■■■ :: a Bafe appears wider than the 7Vr*J, when feen ob- t ; . though bat equal in Breadth, when feen diredly; and this will be /:. I ::-. rboBgh the Columns are made as much wider as true Penpc&ive requires f md therefore can be nothing to the Purpofe; PREFACE. m Purpofe; foe if (according to him) the Squares of the PHntc: i the Bafc of the Columns, as well as the Pedeftab, -are made con- tinually wider, while the Columns arc preserved all of me iame Breadth, what will be the Reprefetatlon of the round Part -of die Bales, and of the Columns within thofe Squares! and h owflian ge> will die Angles of die Plinths, and the Pedeftals, (hoot out be- yond the Breadths of thofe Columns, and dhcovcr a Difpropor- tion not to be prerented by any Expedient? When I wrote this laft Paragraph, I had no Sufpkion, that he would have propofed any thing like a Rule founded on inch mif- taken Notions; and therefore was the more furprifed to find what he Offers in/, y y. of his Second Part. His Words are ; ** Firfr, Rnd the Representation of that Column which " neareft the Centre of the Picture— then fet off the Diftance for •* the Centres of the other Columns, and draw the Sqnares for * die Plinth, Capital, &a and then, upon each Side of the Axis, " let off at the Bottom of each Column Half the Diameter of the " Corner Column (tbmt is, tftkeFbf, *r wemjit* theCemtr* m afthePffiwre)* and, at the Top of the Column, fet off H: : * the Width of the Neck of the Corner Column : Finally, draw ■ Lines from thence fo as to diminHh the Column in a proper " manners and thereby we may make all the Columns that are pa- rallel to the Eye, wftbefime Big*?fs. As to the great ProjedioQ of their Bales, they will not look ar all prepofteroas, if they are done : any one who has but a tolerab : Z fc for Drawing and is careful in taking a proper DifUnce for th: Z e A 2 .. iv P R JE F A € E. Now, bcfides that every Column, except the ncarefl: to the Centre, will be falfe, his Rule appears inconiulcnt with itfelf, and with his own Intention; for either the whole Building may be confidcrably removed from the Centre of the Picture, or Part of it may cover that Centre : In the former Cafe, that which is ::;:.: eft to it may be i'o diuant as to become much wider than he :::...": allow, on his Principles: and, in the latter Call: (how lone; foever the Range or" Columns may be), the mod dillant will be no wider than the mere geometrical Breadth ; becaufe that which covers the Centre of tnc Picture will be the Meafure of all the reft. r^z:.zi i: fellows, mat if he was to reprefent a Building, one Column of which fhould cover the Centre of the Picture, the reft be continued to the Extremity of the fame Picture, every Column would be of the geometrical Breadth, and no m are : Whereas, had the fame Building besun at aDiftance from the Centre of the Pielure, the lirft Column would .according to own Rule; be much wider than one (landing in the fame Place, if the Building had begun at the Centre. Such Incongrui- ties pill be unavoidable in deviating from the true Rules of Per- ;:f::ve.---He fays, " If they ate done by a Perfon having a toie- Ki rable Eye for Drav.ir.g, they will no: look preposterous f '---but, -. ::uth, Skill in Drawing has nothing to do in this Cafe, where Measures are concerned ; the moft skilful and the meft ignorant, in Drawing, are equally d::t::cd, by him, to make the Plinths, Pe- tals, ire. progreiuveiy wider, according to true Terfpectrje ; and the Columns on thole Plinths all equal, contrary to the Rules. v can an Eu for c Dr^n;?g, or any Ability whatfoever, recon- cile thefe Di:p: : usl As PREFACE. : .t :'iv5. i: '.■-':. c: : :::::: I. .'::.■.:: .:.:;:; . will prevent all Inconveniencies ; bat do Difiance will reduce then: co ecniil Z::zz:':.i. He furely forgets what his Author, Brock Taylor, lays in the Preface of his Book, /- n, and 12. • : The executive Part of Painting is wholly coofiaed, and (tricHy C€ tied to the Rules Art, which cannot bedifpenled with upon " aaj account i and therefore, in this, the Artiifc ought to govern €c hirnfelf jntirelj by the Rules of Art, not to tate any Liberties '•■ -j. : :6t ;.'•'.: r:: ::y :../._ :n:: is /.:: ::„ y z:ir:r. :::::;. nz te to the Rules of Peripccnve, or not truly coloured, or truly ** (haded, does not appear to be what the Artifr intended, but :; :bxe:h..:: el.e. \Vr.e:efo:e. ::. :: any :i~e. tne A:: J: ni:- c< pens to imagine, that h : -s Pifiurc would look better, if be '■• ':.: : i ' verve 1 lirzle rrcrn ::.;-.": Ponies, he may i^"_;: r.irr.A.: " that the Fault belongs to his original Deilgn, and not to the •• 5::. ::.:': d: :he ZLn.ef - ::: .:: .; perfectly tjrreei'iie i.zi -It c - in tr.e :;:. :. _.. :. - : :c~ts tlicrr.felvef, cm never zzzzi: ce- •'• fective in : r.n;:c. we:: :n:fe O: :e~:5 ::e exiftly ccziec. And the Firu Seciioa of both his Editions is as ftrong,anc "etc. and particular, as potable, to the lame Purpole. It is therefore very e:::::::r.r.::y. z'r.iz Mr. ±\. ::.:z.z icy::: :':;:.: :ne Principles ef n.i Author, whom he profefles to follow and explain, etpedally in a ttei wherein this Author hath taken care, at the rerj Entrance of his Work , to precaution his Reader in ib explicit a manner. Not thsr the Authority of Brock. Taylor, or of any Man, ought to be decifive, .: can re fewn that he was miflaken 5 but if he was not, it mull be confeifed, that his Explainer is, and {though -n:e- vi PREFACE. undesignedly) mifleads thofe whom he undertakes to inftrnd. His Reafoning appears altogether groundlcfs, and as inconfiftent with the general Principles of Perfpective, as with the Syftem of his Author j and affe&s many other Cafes, befides that which is the immediate Occafion of it. As for Inftance; The Reprefentation of a long Wall on a Titlure parallel to it, mould l?e made of the fame Height at its utmoft Extent, as directly oppofite to the Eye, notwithstanding it appears of lefs Height, the farther it is extended 5 for the Repre- fentation will appear as much Jefs, in proportion, at the Extent, as the Original appears; they being both feen under the fame Angles, and in, exa&ly, the fame oblique Dire&ion. Yet there are many Examples of Errors of this Kind, in the Works of celebrated Artifts, who have otherwife great Merit $ particularly in feveral Prints of Views [by Rigaud]; and, among others, in a View of Greenwich Hofpital (the Spectator being fuppofed on the River oppofite to the middle Space between the Two Fronts) he has drawn the upper Lines of the Cor- nices, inclining towatds the Ground, at the Extremities, thus ww*"" •*-*- : So that if thefe Lines were continued, inwards, till they mould meet in the Middle, between the Fronts, they would make an obtufe Angle, inftead of one right Line. To thefe may be added another Example, which, being very fimple, will be intelligible to every Reader. In the Reprefentation of a fquare Pavement, if a very fmall Diftance be taken, the for- warded Squares will be deeper than wide; which, though they may appear odd, when feen at a greater Diftance than that taken, are PREFACE. vii arc neverthclefs ftri&ly true, and ought to be (o reprefented, when the Place or Station of the Spe&ator is limited, as may, in certain Cafes, happen; and then, inftead of calling the Reprefentation a Forejhorteningt the Term need only be changed to that of Fore- lengthening 5 which, in fuch Inftances, will be as juft Perfpetlive as any whatever ; and this is hinted at Fig. i . in the Beginning of the following Difcourfe : But when the Painter is at Liberty to choofc his Diftance, as on a Picture with refpect to which the Spedator is not confined, it will, no doubt, be more eligible to take a Station from whence hisObje&s will appear more nearly of their original Proportion 5 but, in all Cafes, the drift Rules will never fubjetl: him to any Inconveniencies, much lefs to any Abfurdities. Notwithstanding the Freedom of my Remarks in refpeel: to the Paffagcs to which I have referred, if my Leifure had permitted me to read and examine the whole Book, I doubt not but I (nouid have found much to commend, and very little to cenfure; and, as far as I can judge by a curfory View of the greateft Part, believe it to be an ingenious and ufeful Performance, although the Author may have entertained a few miftaken Notions, in common with fome of the greateft Mailers, whofe general Excellencies fufficiently atone for them. I have carefully endeavoured to avoid any Expreflions that might give Pain to the Author on whom I animadvert; that being the fartheft from my Intention ; and I fhould be very forry, if the Terms I have ufed, for the fake of Truth and Perfpicuity, fhould produce any other Effect than what I deftgn. Juftice viii PREFACE. Jufticc and Candor oblige me to obferve, that he expreffes him- felt with great Modefty 5 and, for that very Rcafon, he may re- trad with the better Grace, when convinced of his Miftake, as I doubt not he will be, on reconfidering the Point in Queftion 5 and as every Man is liable to Error, fo he only deferves Reproach who perfifts in it after Conviction. And if it can be fhewn, that the Miftake is on my Side, I am ready to acknowlege it as frankly as I have remarked (what I prefume to be) that of another. I mall make no other Apology for the Length of the Preface to fo friort a Work, but that the immediate Occafion of publiming it required feveral Quotations, and Reafonings upon them. A ['} C R I ■ T I C A L EXAMINATION,^. NO Painting can appear perfectly true, unlefs feen from the Point intended by the Painter ; becaufe the Picture, being always confidered as a tranf- parent Surface, or Medium, through which the vifual Rays are fuppofed to pafs, if the Spectator changes his Situation, thofe Rays (in Nature) will interfect that Sur- face in different Points ; and therefore (in the Pi8lure) y being determined to fuch certain Points, the Station of the Spectator becomes neceffarily fixed, and unalter- able, and the Picture muft appear falfe feen otherwife j which may be illuftrated as follows. Suppofe an original, that is a real, Cube placed di- rectly oppofite to the Spectator's Eye, and fomewhat below it : in this Situation, he will fee only Two Faces of it, one in Front, the other at the Top ; which latter will be forefhortened ; and, if he moves to the Right or Left, he will fee a Third Face alfo forefhortened ; but B iL 2 A Critical Examination if, inftead of an original Cube, this Firft Appearance was a Pi&ure reprefenting a Cube in fuch Situation, the Spectator would never fee more or his by changing his Place; nor ever fee it truly but from one certain Point: There, indeed, it might exactly reprefent the Original, and deceive. Hence it is evident, that tho' a Pi&ure may be perfectly true from one certain Point of View^ it cannot from any other ; becaufe the Spectator would ftill have the fame Appearance, though he expe&ed a different; which is mentioned, to (hew the Neceffity of regarding a Pi&ure as intended by tire Painter; and alfo to mew the Miftake of thofe, who imagine that it is often advifeable to deviate from the Stri&nefs of the Rules, left, in fome Cafes, Things mould appear dif- agreeable ; which, however, no Pi&ure will, that is true, and truly feen ; but, if made falfe, for this Rea- fon, muft appear falfe every-where, being really true no- where. Some particular Cafes, however, have been thought to require this Liberty ; fuch asj for Inftance, a long Gallery, through which the Spe&ator is fuppofed to walk: If this were painted, to be viewed from a given Point, though with the utmoft Truth, as the Spe&ator moves on, it would appear falfe, it is allowed.; but this is unavoidable in the Nature of Things.; and the fame would happen, if any other Point had been chofen,when not feen from fuch Point. The Queftion is, Whether it mould be painted true from fome one Point, or falfe from all? If the Painting muft be one conti- nued Pi&ure, and could be all feen at a View, there would of Two Paintings, &c> 3 would be no room to doubt, but that it ought to be painted truly from one Point: But if it were allowed to divide the Gallery into feveral diftincT; Pictures, in that Cafe, each Picture might have its proper Point of Sight, and every one be viewed feparately $ which, per- haps, is to be preferred. And thus much is faid r to obviate any Objections which might poffibly be ftarted againft the Manner of treating the Subject of the following Pages ; and to mew, that how plaufible foever thefe Confederations may be thought in fome fuch Cafes as that juft men- tioned, yet they can have no Place here— -this Cieling . being actually divided into Nine feparate Pictures, evi- dently intended to be viewed fingly, and having each its own proper Point of Sights from which only it cam be truly feen ; and therefore ought to be ftridly true from thence, especially if the Painter really deiigned^ this, as, it is prefumed, will appear by what flbalLbe offered. B 2 THESE 4 A Critical Examination '"jp H E S E Paintings are plainly defigned to reprefent ■"- Pieces of Architecture ftanding perpendicularly on an horizontal Plane, and feen from given Points below ; for the Plane is in reality horizontal, and therefore ought to be fo confidered ; and the Forefhortening of the Columns in the Pictures, as they are there painted, cannot be true on any other Suppoiition, befides that the human Figures are all proportionably foreshortened; but if they were intended as Pictures on perpendicular, or vertical Planes (in which manner feveral great Mafters have formerly painted on Cielings), then all perpendi- cular Objects ought to lofe no more of their geometrical Heights, than of their geometrical Breadth?, and the for- ward eft Objects would be equal to their Originals in both ; which is not the Cafe here ; for the Columns, &c. are not quite One- third of their geometrical Heights ; by which it is evident, that the Intention was to reprefent them as is here fuppofed. This Circum- ftance alfo determines the very Point from whence the Picture ought to be viewed ; which having found, a judicious Spectator will be enabled to examine the Whole. Fig. i.] Let C H be the Section or Profile of the Cieling, A C a Column, or any original perpendicular Object, of its geometrical Height; C#, being One- third of the Length of C A, is taken to reprefent it -> a being the of Two Paintings, tfc. $ the Reprefentation of A, then, I fay, the Spectator's Eye muft be fomewhere in the Line A D ; and if D is fup- pofed to be the Height of the Eye from the Floor, then D is that Point ; for, fuppofmg D E to reprefent a Line, in which the Spectator's Eye might move backwards or forwards, it is evident, if C A be reprefented within the Space C a y that D muft be the Place where the Spectator ought to flop. Otherwife imagine the Eye to be removed back as far as E ; fo that the vifual Ray A E may cut the Cieling in an Angle of 45 Degrees ; then the painted Object will be equal in Length to its Original (though on -fcke- horizontal Plane), and in all Places of D E back- warder than E ; i. e. 45 Degrees ; the Reprefentation of A C will be longer than its Original, as, in all Places forwarder than E, the Reprefentation will be fhorter than its Original. It is of no Confequence whether the Floor be the true Diftance, or whether that were taken away, and the Picture feen from the Ground : In both Cafes, the Eye muft be in fome Point of the indefinite Line ADj and fo will fee a as the Reprefentation of A ; for if the Eye were at ^, that would make no Alteration in the Perfpective Length of C a ; as is evident. Fig. 2.] And now, having found the Point D, or the Spectator's Eye, it will be neceffary, in order to ex- amine the Picture, to fuppofe the Cieling feen not fide- wife, as in the Scheme above, but in Front, over the Spe- ctator's Head ; and, in this View, let C, S, C, be taken for the Plane of the Cieling; and, from S, let S, D, be drawn 6 A Critical Examination drawn perpendicular to that Plane below it, and C A, C A, be drawn, of equal Lengths, perpendicular to the fame Plane, above it. Nov/, fuppofe D, S, the Din 1 a nee of the Eye from the faid Plane, or Picture, of which S will consequently be the Centre, and the Lines S D and C A, C A, will be all parallel to one another (by 6. of the ii. Euclid) \ then will the Eye fee C A, C A, upon the Picture, in the Lines C S, C S, where C a, C a, will will be the Reprefentations of C A, C A ; for A D and A D, in this Scheme, are vifual Rays, as A D in the former. But as one principal Error in thefe Paintings, is the falfe Direction of the Columns (for they are drawn pa- rallel to the Sides of the Picture,, and to each other, in- ftead of tending both to the fame Point), it may be proper to conflder this Circumftance more particularly. A C, and A C, being thus raifed perpendicularly, are in the Pofition of the original Columns ; and D S is drawn parallel to them, cutting the Cieling, or Picture,, in S, directly over the Spectator's Head. Now, fup- pofing the Cieling, or Picture, traniparent, it is impof- fible the Spectator, in this Situation, mould fee the Tops or Capitals of the Columns in any other Lines or Dire- ctions than thofe of C S, and C S ; for each Triangle, C A D, is a Plane cutting the Cieling, or Picture, in that Line C S ; the Point C touching it, and the vifual Ray D A cutting it in a ; and if theipColumns were ever fa high, even infinitely continued, upwards, their whole Repre- of Two Paintings, &V. 7 Reprefentations would be in the Lines C S, and C S, and their Top, at an infinite Diftance, would coincide with S. Or thus : The Lines C A, and D S, being parallel to each other, a Plane will pafs through them both; and as C A touches the Picture in C, and D S touches it in S, the Plane paffing through thefe Lines will neceflarily cut the Picture in C and S ; that is, in the Line C, S ; and the Line A D is, in this Plane, A C, S D, and (with it) cuts the Picture in the Line G S, their common In- terferon ; u e. at the Point a* Though nothing more is absolutely neceflary to the prefent Purpofe, yet the following Demonftration may be acceptable to fome Readers. The Two Triangles CAD, CAD, are equal, being on equal Bafes, and between the fame Parallels [See Prop. 3 8. of the Firft Book of Euclid] ; and C S D, C S D, are equal, becaufe on the fame Bafe, and between the fame Parallels (Prop. 37.); Wherefore the whole Figures C A a S D, CA^S D, are equal (each being compofed of Two Triangles, already proved to be respectively equal) ; and therefore, laftly, taking away the Two equal Tri- angles C S D, G S D, the remaining Triangles CA^, C A #, muft be equal ; and eonfequently, having equal Bafes on the fame Line, muft be between the fame Pa- rallels: For which Reafon, Ca y Ca 9 are of equal Height ; 8 A Critical Examination Height ; i. e. a. Line drawn from a to a will be parallel to one drawn from C to C ; and would be fo, tho' the Obliquity, and confequently the Lengths, of C 3> 4? is a triangular Plane cutting the Picture in 1, 2 5 which of Two Paintings,, &V. p which Picture is parallel to the original Square [See 16, and 17 Prop, of the nth Book of Euclid's Element s\ ; and fo of every other Line compofing the whole Square, and of the whole Circle. From what has been faid above, it is evident, that a Pi&ure on a Cieling, reprefenting fuch Pieces of Archi- tecture, as thofe which have occafioned thefe Refle- clions, ought to appear as K (Fig, 4.) ; whereas they are painted as L (Fig. 5.) ; which does not reprefent the Thing intended, but fomething elfe ; for if, in K, the Columns reprefent Perpendiculars to the horizontal Plane (the Originals of which are confequently parallel to each other], then, in L, they reprefent Columns di- verging from each other at the Top, thus \ / : More- over, the Plinths of the Bafes not being Squares, but Trapeziums, and the Circles not being Circles, but El- lipfes, do reprefent Trapeziums and Ellipfes ; for, fince they are on a Pi&ure parallel to the Origi- nals, they muft reprefent Figures fimilar, or of the fame Forms. It remains only to point out the probable Caufes of the Errors here remarked ; in order to which it muft be considered, as hath been obferved, that, when the Pidure is a Plane parallel to the original Objects, it will receive their Reprefentations in a parallel Manner; that is, the feveral Parts will be in the fame Proportion to each other as in the Originals : For Inftance ; they will neither be fhortened nor lengthened, but always keep C their io A Critical Examination their geometrical Proportions in what manner foever the Spectator's Eye is placed; but when the Picture makes a right (or any other) Angle with the Original, it will receive their Reprefentations either longer or fhorter than fuch Originals, according to the Situation of the Spectator's Eye ; as hath been {hewn at Fig, i. Now, the apparent Caufe of thefe Miftakes is a ge- neral Notion, that all Objects ought to be reprefented as they appear to the Eye ; which, though in a certain Senfe true, is far from being fo, as frequently applied to Practice; that is, without confidering the Polition of the Picture, or Medium through which thefe Objects do appear to the Eye, whether parallel, perpendicular, or inclined, with refpect to the original Objects ; the Un- derstanding of which thoroughly, would prevent all poffible Errors, as the neglecting, or not underftand - ing this, has occafioned thefe, and many more. In the Cafe before us, the Painter muft have con- sidered, that, if he had feen Columns in the Situation in which he has fuppofed the Originals of thefe, from the Station which he has chofen, they would appear fhort- ened : And herein he judged rightly ; and hath given them a Length fuitable to the Plane on which, or Me- dium through which, they are feen from below ; but then he has made the Columns parallel to each other ; which they never can be on an horizontal Plane. From hence it appears, that his Miitake is owing to what has been already taken Notice of ; viz. not confidering the Neceffity Of TWO POINTINGS, &C. II Neceffity of finding the Points of Interfe&ion of all the Parts of the Objects, on the fame Medium, from one and the fame Station. Again, The Circles and Squares are falfe, for the fame Reafon ; for though it be true, that a Square or Circle, feen obliquely, will not appear as when feen di- rectly, yet it does not follow (as hath been remarked), that they muft not be reprefented by Squares and Circles ; on the contrary, they are to be reprefented by fimilar Figures ; for the Obliquity of the Spectator's Situation, in refpect of the Painting, being exactly the fame as in refpect of the Original, will produce the fame Effect; i. e. in both Cafes, the Image in his Eye will be the fame : So that, tho' it be not true, that all Objects are to be reprefented, in all Cafes, as they appear (without regard to the Medium through which they are feen) ; yet it is true, that all Objects are to be painted fo, on the Medium through which they are feen, or fuppofed to be feen, as that they fhall appear, as the Originals appear. For want of thefe Considerations, or want of fuffi- cient Knowlege, the Painter hath reprefented the Ob- jects here, in dome Circumftances, as on an horizontal Plane; in others, as if on a perpendicular Plane; in fuch manner that the Pictures are falfe on any Plane whatfoever; and eminently fo on the Plane where they are. C 2 Tho 5 12 A Critical Examination Tho' it is prefumed, that what has been undertaken is fufficiently proved ; yet fince it might be expected, that thofe Pieces of Archite&ure, which are condemn- ed, fhould be exhibited as, it is pretended, they ought to have been painted ; to fatisfy fuch Curiofity, they are added, both as reprefented on the Cieling, and alfo as they ought to have been reprefented : But, in the Firft, marked O, O, the Wreathing of the Columns is omitted, to fhew the Perfpective more nakedly; and, as they are mere Sketches, Regard is had only to the Per- fpe&ive. The Squares of the Bafes of the Pedeftals, in the Firft, are left vifible, to fhew the Effect, and convince the Reader of their Truth ; tho' other wife they ought to be fupported, appearing here in the Air. In the Second, marked P, P, the Columns are fup- pofed cut afunder, for the fame Reafon ; that is, to fhew the Circles. The Reader will judge better of the Effect, by hold- ing the Prints over his Head, for a few Moments. And tho', in this fmall Treatife, the Principles, in ge- neral, were only intended to be afcertained, and not the Practice ; which latter is amply and explicitly taught in a larger Work; yet, that the Second Figure may be more readily underftood, and the Operation comprehended, let it beobferved, that the Line, marked f of Two Paintings/ 6V. 13 ! > 2 > 3? 4> 5> 6, * s tne Axis °f a Cylinder, and the nu- merical Figures are Centres of the feveral Circles ; each of which is a Plane parallel to the Picture : For In- ftance, N° I. is the Centre of the Circles a and b\ which are considered as concentrical ; 2 is the Centre of c> — 3 is the Centre of d> — 4 is the Centre of e andy*; which are concentrical ; — 5 is the Centre of g' y -'- and 6 is the Centre of h and /; which Circles are alfo concentrical. The fame Principles, and the fame Kind of Reafon- ing, will determine the Queftion, Whether, in repre- fenting a Row of Columns, {landing on a Line parallel to the Picture, thofe which are more diftant from the Centre of fuch Picture, mould be made equal to, lefs or bigger than, the nearer ? It is allowed they appear lefs ; but the Anfwer to this Queftion is, that they ought to be made bigger ; and, though fo painted, they will really appear as much lefs as they appear in Nature 1 For (Fig. 6.) let A, B, and C, be Three Columns, either fquare or round ; and firft fuppofe them fquare ; it is evident, that the Reprefentation of them will take up the Space marked by the vifual Rays, from the ex- treme Angles to D, the Spectator's Eye, on the Line E F, which may be confidered as the parallel Picture ; that is, the Reprefentation of A will fill the Space g> h\ that of B will fill the Space /, k ; and that of C, the Space /, m. If 14 A Critical Examination If the Columns are round, the feveral Spaces, which their Reprefentations employ, will be determined by the Rays which are Tangents to the Circles : Thefe Spaces are marked with a double, or blacker Line : But if the Picture be placed on the Line E, H, or any other Line between H and D (the End E remaining unmoved), the Reprefentations of the more diftant Columns will then be in lefs Spaces of the Picture, in certain Propor- tions, according to their feveral Distances : But, on all thefe Pictures, they will be truly reprefented 7 and will exhibit the Images of the Originals to the Eye of the Spectator at D; who will neceffarily form the fame Ideas of the Proportions and Diftances of the Objects from any one of thefe Pictures, as from any other of them ; which may all be considered as tranfparent Planes, or as one fuch Plane moveable on a Hinge, at E, from F to H, or to any other Point on the Arc F H ; which Plane or Planes (being fuppofed tranfpa- rent) no more hinder tj^e Spectator from difcerning the original Objects than the common Medium of Air ; and as all the vifual Rays are neceffarily right Lines, the Picture, or Medium, makes no Alteration in their Di- rections ; which are continued, without Interruption, from the feveral Parts of the Originals, to D, through one or more tranfparent Planes, however placed; and, whichfoever be chofen, the Reprefentations can be de- termined by nothing but the Interferons of thofe vifual Rays, and cannot poflibly be falfe, if thefe Interferons are truly found. And lince every Reader, even the leaft intelligent, will readily allow, that the Reprefent- ations of Two Paintings, &c> tq ations on the Picture E, H, muft truly exhibit the Images of their Originals ; a little Attention, and Reflections will alfo convince him, that thofe on the Picture E, F, muft neceffarily exhibit them with equal Truth, becaufe they are determined by the very fame Rays. But as fomething of this Kind has been already faid, in the Ex- amination of the Banqueting-houfe, no more need be here added. JV. S. The Rays for the round Columns are deter- mined by making Tangents to the feveral Circles from D, and the Points in which they touch are found, by bifecting the Line from D to the Centre of each Circle ; that is to fay, the Lines D A, D B, and D C, and with the Lengths a A, bB^ and c C, as Radii, making an Arc through the Centre of each Circle, cutting the Circumference in the Points fought. If the Circles were nearer each other, and D at a greater Diftance, the Difference would be proportion-ft//// ^j&fy- lefs, and, at a fufficient Diftance, not at all offen- five ; as indeed nothing, that is truly reprefented, can* be ; but even at this, or any Diftance, the Rule (being demonftrably and univerfally juft) cannot vary. FINIS, f&'*' /*?■*' f&- *■ c )ful