OPTICS. 
from the eye, to which the breadth of the pupil bears no 
fenfible proportion, the rays of light that come from a 
point in the object, and pafs the pupil, are fo little di¬ 
verging, that they may be conlidered as parallel. For a 
pi iff ure on the retina will not be fenfibly more confided, 
though the objeht be removed to a much greater diftance. 
2. "The moll general, and frequently the molt certain, 
means of judging of the diftance of objects is, he fays, by 
the angle made by the optic axis; for our two eyes are 
like two different ftations, by the alliftance of which dil- 
tances are taken ; and this is the reafon why thole perfons 
who are blind of one eye fo frequently mifs their mark in 
pouring liquor into a giafs, fnufting a candle, and fuch 
other actions as require that the diftance be exaftly diftin- 
guifhed. To be convinced of the utility of this method 
of judging of the diftance of objedls, he diretfs us to 
fufpend a ring in a thread, fo that its fide may be towards 
us, and the hole in it to the right and left hand ; and 
taking a fmall rod, crooked at the end, retire from the 
ring two or three paces, and, having with one hand co¬ 
vered one of our eyes, to endeavour with the other to 
pafs the crooked end of the rod through the ring. This, 
fays he, appears very eafy ; and yet, upon trial, perhaps 
once in a hundred times we (hall not fucceed, efpecially if 
we move the rod a little quickly. The ufe of this fecond 
method of judging of cTillances Dechales limited to 120 
feet; beyond which, he lays, we are not fenfible of any 
difference in the angle of the optic axis. 
3. A third method of judging of the diftance of objects, 
confifts in their apparent magnitudes, on which fo much 
ftrefs was laid by Dr. Smith. From this change in the 
magnitude of the image upon the retina, we ealily judge 
of the diftance of objecls, as often as we are otherwife ac¬ 
quainted with their magnitude; but, as often as we are 
ignorant of the real magnitude of bodies, we can never, 
from their apparent magnitude, form any judgment of 
their diftance. Hence we may fee why we are fo fre¬ 
quently deceived in our eftimates of diftance, by any ex¬ 
traordinary magnitude of objedls feen at the end of it; 
as, in travelling towards a large city, ora caftle, or a ca¬ 
thedral-church, ora mountain larger than common, we 
fancy them to be nearer than they really are. This alfo 
is the reafon why animals, and little objects, feen in val¬ 
leys contiguous to large mountains, appear exceedingly 
fmall. For we think the mountain nearer to us than if 
it were fmaller; and we Ihould not be furprifed at the 
fmallnefs of the neighbouring animals, if we thought 
them farther off. For the fame reafon, we think them 
exceedingly fmall when they are placed upon the top of 
a mountain, or a large building; which appear nearer to 
us than they really are, on account of their extraordi¬ 
nary fize. 
Dr. Jurin accounts for our imagining objedls, when feen 
from a high building, to be fmaller than they are, and 
fmaller than we fancy them to be when we view them at 
the fame diftance on level ground. It is, fays he, becaufe 
we have no diftindl idea of diftance in that direction, and 
therefore judge of things by their pictures upon the eye 
only ; but cuftom will enable us to judge rightly even in 
this cafe. Let a boy, fays he, who has never been upon 
any high building, go to the top of a lofty fpire, and look 
down into the ftreet; the objedts feen there, as men and 
liorfes, will appear fo fmall as greatly to furprife him. 
But, ten or twenty years after, if in the mean time he has 
ufed himfelf now-and-then to look down from that and 
other great heights, he will no longer find the fame ob- 
jedts to appear fo fmall. And, if lie were to view the 
fame objedls from fuch heights as frequently as he fees 
them upon the fame level with himfelf in the ftreets, he 
fuppofes that they would appear to him juft of the fame 
magnitude from the top of the fpire as they do from a 
window one ftory high. Fqr this reafon it is, that ftatues 
placed upon very high buildings ought to be made of a 
larger fize than thofe which are feen at a nearer diftance ; 
becaufe all perfons, except architedls, are apt to imagine 
5S7 
the height of fuch buildings to be much lefs than it 
really is. 
4. The fourth method by which Dr. Porterfield fays 
that we judge of the diftance of objedls, is the force with 
whiclv their colour llrikes upon our eyes. For, if we be 
affured that two objedls are of a fimilar and like colour, 
and that one appears more bright and lively than the 
other, we judge that the brighter objedl is the nearer of 
the two. 
5. The fifth method confifts in the different appearance 
of the fmall parts of objedls. When thele parts appear 
diltindl, we judge that the objedl is near; but, when they 
appear confided, or when they do not appear at all, we 
reckon the objedl to be at a greater diftance. For the 
image of any objedl, or part of an objedl, diminifhes as 
its diftance increafes. 
6. The fixth and laft method by which we judge of the 
diftance of objedls is, that the eye does not reprefent to 
our mind one objedl alone, but at the fame time all thofe 
that are placed betwixt us and the principal object whole 
diftance we are confidering; and, the more this diftance 
is divided into feparate and diftindt parts, the greater it 
appears to be. For this reafon, diltances upon uneven 
furfaces appear lefs than upon a plane; for the inequali¬ 
ties of the iurfaces, fuch as hills, and holes, and rivers, 
that lie low and out of fight, either do not appear, or 
hinder the parts that lie behind them from appearing; 
and fo the whole apparent diftance is dirninifhed by the 
parts that do not appear in it. This is the reafon that 
the banks of a river appear contiguous to a diftant eye, 
when the river is low and not feen. 
Dr. Porterfield very well explains feveral fallacies in 
vifion, which depend upon our millaking the diftances of 
objedls. Of this kind, he fays, is the appearance of parallel 
lines, and long villas confiding of parallel rows of trees; 
for they leem to converge more and more as they are far¬ 
ther extended from the eye. The reafon of this, he fays, 
is, becaufe the apparent magnitudes of their perpendicular 
intervals are perpetually diminifhing, while, at the fame 
time, we miltake their diftance. Hence we may fee why, 
when two parallel rows of trees Hand upon an afcent, 
whereby the more remote parts appear farther off than 
they really are, becaufe the line that meaiures the length 
of the villas now appears under a greater angle than when 
it was horizontal, the trees, in fuch a cafe, will leem to 
converge lefs, and fometimes, inftead of converging, they 
will he thought to diverge. 
For the fame reafon that a long vifta appears to con¬ 
verge more and more the farther it is extended from the 
eye, the remoter parts of a horizontal walk, ora long floor, 
will appear to afcend gradually; and objedls placed upon 
it, the more remote they are, the higher they will appear, 
till the laft be feen on a level with the eye ; whereas the 
ceiling of a long gallery appears to defcend towards a ho¬ 
rizontal line drawn from the eye of the fpe'dlator. For 
this reafon, alfo, the furface of the fea, feen from an emi¬ 
nence, feems to rife higher and higher the farther we look; 
and the upper parts of high buildings feem to (loop, or 
incline forwards over the eye below, becaufe they feem to 
approach towards a vertical line proceeding from the 
fpedlator’s eye ; fo that ftatues on the top of fuch build¬ 
ings, in order to appear upright, mull recline, or bend, 
backwards. 
Dr. Porterfield alfo (hows the reafon why a windmill, 
feen from a great diftance, is fometimes imagined to move 
the contrary way from what it really does, by our taking 
the nearer end of the fail for the more remote. The un¬ 
certainty we fometimes find in thecourfe of the motion of 
a branch of lighted candles, turned round at a diftance, is 
owing, he fays, to the fame caufe; as alfo our fometimes 
millaking a convex for a concave furface, more efpecially 
in viewing feals and impreflions with a convex-glafs or a 
double microfcope; and laftly, that, upon coming in a 
dark night into a ftreet in which there is but one row 
of lamps, we often miftkke the fide of the ftreet they are on. 
The 
