OPTICS. 
664 
with the fame facility. Farther, from the fimplicity of his 
rules, the whole tedious progrefs of drawing out plans 
and elevations for any objedt is rendered entirely ufelefs, 
and therefore avoided : for, by this method, not only the 
feweft lines imaginable are required to produce any per- 
fpedlive reprefentation, but every figure, thus drawn, will 
bear the niceft mathematical examination. Moreover, his 
fyftem is the only one calculated for anfwering every end 
of thofe who are practitioners in the art ofdefign; becaufe 
from hence they may be enabled to produce the whole, 
or only fo much of an object as is wanted, and, by fixing 
it in its proper place, may determine its apparent magni¬ 
tude in an inftant. It explains alfo the perfpedtive of 
lhadows, the refledtions of objedts from poliflied planes, 
and the inverfe pradtice of perfpedtive. 
Hamilton feems to be the firft writer who introduced 
the pradtice of fetting the radical, or parallel of the ori¬ 
ginal line, from the vanifhing point, upon the vanilhing 
line, and the original line from the interfedting point upon 
the interfedting line, in order to afcertain the reprefenta¬ 
tion of any point, or any part or parts of the original 
line, and to find the originals from the reprefentations 
given. This author is the firft who has applied the har- 
monical divifion of lines to perfpedtive. 
Noble’s Perfpedtive contains feveral inventions: his 
methods of drawing indefinite reprefentations to inac- 
cefiible vanilhing points, both by fcales and other means, 
are new. 
Thomas Malton’s treatife is an able performance. His 
theory is well arranged, and dennonftrated with true geo¬ 
metrical fpirit. The choice of his examples in the com¬ 
ponent parts of architedture, before uniting the whole 
into a complete edifice, are excellent. 
Though Mr. James Malton pretends to unite the prin¬ 
ciples of Dr. Brook Taylor with thofe of Vignola and 
Sirigatti, he might have referred them with more pro¬ 
priety to S’Gravefande’s invention of directors, as the ufe 
of the ftation-point, which is only a diredting point, can 
be more eafily explained upon the principles of the di- 
redting line, diredtor, and diredting point, than by any 
mechanical notion ; fo that the methods which he ufes 
may be referred entirely to the principles of Dr. Brook 
Taylor. In the method ufed in James Malton’s Perfpec- 
tive, every point of an object in the original plane is found 
in the pidture, by a line drawn between the interfedling 
and vanilhing point, or drawn from fome point already 
found, and the vanilhing point, and another line drawn 
by the diredting point and the diredtor: for, when the di- 
redtor of an original line coincides with the interfedtion 
of the vertical plane, the reprefentations diredted will be 
perpendicular to the interfedtion, or to the vanilhing line; 
therefore, lines thus drawn in the pidture will fall in the 
fame ftraight lines with original lines parallel to the pic¬ 
ture, and to the vertical plane, infilling upon the remote 
extremities of the lines drawn to the diredting point. 
This, therefore, admits of the plan of the object either 
being connedted with the pidture, or feparated from it, as 
conveniency may require. This circumftance has even 
been overlooked in the more excellent treatife of the fa¬ 
ther of the gentleman upon whofe work the remarks are 
now made. 
In order to underftand the principles of perfpedtive, it 
will be proper to confiderthe plane on which the repre¬ 
fentation is to be made as transparent, and interpofed be¬ 
tween the eye of the fpedlator and the objedt to be repre- 
fented. Thus, fuppofe a perfon at a window looks through 
an upright pane of glafs at any objedt beyond it, and, 
keeping his head fteady, draws the figure of the objedt 
upon the glafs with a black-lead pencil, as'if the point of 
the pencil touched the objedt itfelf; he would theh have 
a true reprefentation of the objedt in perfpedtive as it 
appears to his eye. 
In order to this, two things are neceflary : Firft, that 
the glafs be laid over with ftrong gum-water, which, when 
dry, will be fit for drawing upon, and will retain the traces 
of the pencil; and, fecondly, that he looks through a 
fmall hole in a thin plate of metal, fixed about a foot from 
the glafs, between it and his eye, and that he keeps his 
eye clofe to the hole; otherwife he might ftiift the pofi- 
tion of his head, and confequently make a falle delinea¬ 
tion of the objedt. Having traced out the figure of the 
objedt, he may go over it again with pen and ink ; and, 
when that is dry, put a fheet of paper upon it, and trace 
it thereon with a pencil; then, taking away the paper, 
and laying it on a table, he may finifli the pidture by giv¬ 
ing it the colours, lights, and fhades, as he fees them in 
the objedt itfelf; and then he will have a true refemblance 
of the objedt. 
To every perfon who has a general knowlege of the 
principles of optics, this muft be felf-evident; for, as vi- 
fion is occafioned by pencils of rays coming in ftraight 
lines to the eye from every point of the vifible objedt, it 
is plain that, by joining the points in the tranfparent plane 
through which all thole pencils refpedtively pafs, an exadt 
reprefentation muft be formed of the objedt, as it appears 
to the eye in that particular pofition, and at that deter¬ 
mined diftance. And, were pictures of things to be al¬ 
ways firft drawn on tranfparent planes, this fimple opera¬ 
tion, with the principle on which it is founded, would 
comprife the whole theory and pradtice of perfpedtive. 
As this, however, is far from being the cafe, rules muft 
be deduced from the fciences of optics and geometry for 
drawing reprefentations of vifible objedts on opaque 
planes ; and the application of thefe rules conftitutes 
what is properly called the art of perfpective. 
Previous to our laying down the fundamental princi¬ 
ples of this art, it may not be improper to obferve, that 
when a perfon ftands right againft the middle of one end 
of a long avenue or walk, which is ftraight and equally 
broad throughout, the fides thereof feem to approach 
nearer and nearer to each other as they are further and 
further from his eye; or the angles, under which their 
different parts are feen, become lefs and lefs, according as 
the diftance from his eye increafes ; and, if the avenue be 
very long, the fides of it at the fartheft end will feem to 
meet; and there an objedt that would cover the whole 
breadth of the avenue, and be of a height equal to that 
breadth, would appear only to be a mere point. 
The pradtice of this branch of optics is built upon the 
following 
Fundamental Theorem. Plate XVIII. 
Let abed , fig. i, reprefent the ground-plan of the figure 
to be thrown into perfpedtive, and efgh the tranfparent 
plane through which it is viewed by the eye at E. Let 
thefe planes interfedt in the ftraight line KL. Let B be 
any point in the ground-plan, and BE a ftraight line, 
the path of a ray of light from that point to the eye. 
This will pafs through the plane efgh in fome point b ; 
or B will be feen through that point, and b will be the 
pidture, image, or reprefentation, of B. 
If BA be drawn in the ground-plan, making any angle 
BAIC with the common interfedtion, and EV be drawn 
parallel to it, meeting the picture-plane or perfpedtive- 
plane in V, and VA be drawn, the point b is in the line 
VA fo fituated, that BA is to EV as bA to bV. For, fince 
EV and BA are parallel, the figure BAFVEZ>B is in one 
plane, cutting the perfpedtive-plane in the ftraight line 
VA; the triangles BA b, E \b, are fimilar, and BA : VE 
=6A : bV. 
Cor. i. IfB be beyond the pidture, its pidture b is above 
the interfedtion KL; but, if B be between the eye and the 
pidture, as at B', its pidture b' is below KL. 
Cor. 2. If two other parallel lines, BA', ES, be drawn, 
and A', S, be joined, the pidture of B is in the interfedtion 
of the lines AV and A'S. 
Cor. 3. The line BA is reprefented by bA, or bA is the 
pidture of BA ; and if AB be infinitely extended, it will 
be reprefented by AB. V is therefore called the vanijhing 
point of the line AB. 
Car. 
