OPTICS. 
Go 8 
fixed in a tube, or attached to each other in any other 
way, by moving the objedl QP, the image qp may be 
brought into the principal focus of the eye-glafs ; or into 
fuch afituation, that the rays may, after the latter refrac¬ 
tion, have a proper degree of divergency or convergency 
for the eye of the fpedlator. 
IMPERFECTIONS of OPTICAL INSTRUMENTS. 
Plate XVII. 
In explaining the conftruftion and effects of optical 
inilruments, we have fuppofed the images to be fimilar to 
the objects, and accurately formed in the geometrical foci 
of refracted or refiedted rays. Were thefe fuppofitions 
true, telefcopes and microfcopes would be perfedl;' no 
limit could be fet to their magnifying powers, but fuch 
as arife from the difficulty of forming fpherical furfaces 
of proper dimenfions; and, by their aftiftance, objedls 
might be feen as diftindlly as if they were viewed in plane 
reftedtors. The imperfedtions to which they are fubjedt 
arife from two caufes ; the fpherical figure of the refledt- 
ing and refradting furfaces, and the unequal refrangibi- 
lity of the different rays which conftitute the body of light 
by which objedts are feen. 
i. When any points in an objedl are feen by oblique 
pencils, that is, by fuch pencils as are not nearly perpen¬ 
dicular to the refledtingor refradting furfaces, thofe points 
do not appear in the places determined by the conitruc- 
tions and calculations hitherto given. 
This will be eafily underftood, by confidering the molt 
funple cafe of refradtion. Suppofe AB, fig. i, to be a 
plane refradting furface; PQR a ftraight line parallel to 
it; pqr the geometrical image of PQR ; O the place of 
the eye. Then, the rays which flow from P, after refrac¬ 
tion at the furface AB, are diffufed through all parts of 
the medium in which the eye is placed; and, if thofe rays 
of the pencil which pafs through O diverge accurately 
from p, they enter the eye as if they came from a real 
objedt there; andp is the vijihle image of P ; but, when 
the eye is at any confiderable diftance from the perpen¬ 
dicular PAZ, the point P is feen by an oblique portion of 
the general pencil, as PVO. Thofe oblique rays do not 
diverge accurately from any point; and therefore the vi- 
fible image will be indiftinft. But, if a: be the place where, 
if produced backwards, they occupy the fmallelt fpace, 
we may fuppofe this to be the vifible image of P ; artd the 
curve which is the locus of x to be the vifible image of 
the whole line PR. Again, if a diftorted image be formed 
by the object-glafs or refledlor of a, telefcope, different 
parts of it lie at different diftances from the principal 
focus of the eye-glafs; and, if one part can be feen dif- 
tindlly, the reit will appear confufed. Inftead of fpherical 
furfaces, it has been propofed to adopt fuch as are gene¬ 
rated by the revolution of the ellipfe, parabola, or hyper¬ 
bola ; but, independent of the difficulty of grinding thefe 
furfaces, little advantage can be expedled from them, as 
each furface will only refledt or refradt thofe rays accu¬ 
rately which belong to one particular focus, and the aber¬ 
rations in other cafes will generally be greater than thofe 
produced by fuch furfaces as are of a fpherical form. 
2.. Another and more confiderable caufe of imperfec¬ 
tion in optical inftruments, is the unequal refrangibility 
of differently-coloured rays. We have, in all our calcu¬ 
lations, fuppofed light to be homogeneal; that, whilft it 
pafles out of one given medium into another, the fine of 
incidence bears the fame invariable ratio to the fine of 
refradtion. But fir Ifaac Newton difcovered, that the 
common-light, by which objedtsare viewed, confifts of 
rays which differ both in colour and refrangibility; and 
that thofe rays' which differ in colour always differ in re¬ 
frangibility ; that is, if the fines of incidence be equal, 
the lines of refradtion are different, though the mediums 
remain the fame. Hence it follows, that, if the image 
of an objedt be diftindtly formed by the red, which are 
the leafi-refrangible rays, at one particular diftance from 
a refradtor, a diftindt image will be formed by rays which 
have a different degree of refrangibility, as the blue rays, • 
at a different diftance from it; thus, the rays of different 
colours, which flow from the fame point, being colledted 
at different diftances from the refractors, a confufed and 
coloured image of that point is neceffarily produced upon 
the retina, or upon any fcreen which receives the re- 
fradted rays. 
We are now to confider in what manner thefe imper- 
fedlions may in fome degree be remedied. And we 
fhall begin with the latter, which is of greater importance, 
as the errors it produces are much more confiderable than 
thofe which arife from 'the fpherical form of the furfaces; 
we may add, moreover, that its theory is more eafily ex- 
plained, and its effedts more likely to be corredled in 
pradtice. 
On the Aberrations produced by the Unequal 
Refrangibility of the Rays of Light. 
Prop. I. The fun’s light confifts of rays which differ in 
refrangibility and colour. 
This important difcovery was made by fir Ifaac Newt-on, 
who defcribes the experiment by which it is eftabliflied, 
in the following words. “ In a very dark chamber, st a 
round hole, about one-third of an inch broad, made in the 
fhut of a window, I placed a glafs prifm, whereby the 
beam of the fun’s light which came in at the hole might 
be refradted upwards toward the oppofite wall of the 
chamber, and there form a coloured image of the fun. 
The axis of the prifm was perpendicular to the incident 
rays. About this axis I turned the prifm flowly, and faw 
the refradted light on the wall, or coloured image of the 
fun, firft to defcend, and then to afcend. Between the 
defcent and afcent, when the image feemed ftationary, I 
flopped the prifm, and fixed it in that pofture, that it 
fhould be moved no more ; for, in that pofture, the re- 
fradtions of the light at the two fides of the refradting an¬ 
gle, that is, at the entrance of the rays into the prifm, and 
at their going out of it, were equal to one another. The 
prifm therefore being placed in this pofture, I let the re- 
fradled light fall perpendicularly upon a fheet of white 
paper at the oppofite wall of the chamber, and obferved 
the figure and dimenfions of the folar image formed on 
the paper by that light. This image was oblong, and not 
oval; but terminated with two redtilinear and parallel 
fides, and two femicircular ends. On its fides it was 
bounded pretty diftindlly, but on its ends very confufed- 
ly and indiftindlly, the light there decaying and vanilh- 
ing by degrees. The breadth of this image anfwered to 
the fun’s diameter, and was about two inches and the 
eighth part of an inch, including the penumbra. For 
the image was eighteen feet and a half diftant from the 
prifm; and at this diftance, that breadth, if diminifhed 
by the diameter of the hole in the window-fhut, that is, 
by a quarter of an inch, fubtended an angle at the prifm 
of about half a degree, which is the fun’s apparent dia¬ 
meter. But the length of the image was about ten 
inches and a, quarter, and the length of the redtilinear 
fides about eight inches ; and the refradting angle of the 
prifm, whereby fo great a length was made, was 64. de¬ 
grees. With a lefs angle, the length of the image was 
lefs, the breadth remaining the fame. It is farther to be 
obferved, that the rays went on in right lines from the 
prifm to the image ; and therefore, at their vely going 
out of the prifm, had all that inclination to one another 
from which the length of the image pijtceeded, that is, the 
inclination of more than two degrees and a half. And 
yet, according to the laws of optics vulgarly received, 
they could not poflibly befo much inclined to one another. 
“For, let F, fig. a, reprefentthe hole made in the win¬ 
dow-fhut, through which a beam of the fun’s light was 
tranfmitted into the darkened chamber, and ABC a 
triangular imaginary plane, whereby the prifm is feigned 
to be cut tranlverfely through the middle of the light; 
and let xy be the fun, MN the paper upon which the fo¬ 
lar 
