ABE 
fradted by a lens, by which they are prevented from meet¬ 
ing or uniting in the fame point, called the geometrical 
focus, but are fpread over a fmall fpace, and produce a 
confufion of images. Aberration is either lateral or lon¬ 
gitudinal : tire lateral aberration is meafured by a perpen¬ 
dicular to the axis of the fpeculum or lens, drawn from 
the focus to meet the refradted or reflected ray: the lon¬ 
gitudinal aberration is the diftance, on the axis, between 
the focus and the point where the ray meets the axis.— 
There are two fpecies of aberration, diftinguifhed accord¬ 
ing to their different caufes : the one arifes from the figure 
of the fpeculum or lens, producing a geometrical difper- 
iion of the rays, when thefe are perfectly equal in all re- 
fpedts; the other arifes from the unequal refrangibility of 
the rays of light themfelves; a dilcovery that was made by 
Sir lfaac Newton, and for this reafon it is often called the 
Newtonian aberration. As to the former fpecies of aber¬ 
ration, or that arifing from the figure, it is very fmall, and 
ealily remedied, in comparifon with the other, arifing 
from the unequal refrangibility of the rays of light, which 
is very great; and, hence it may feem ftrange that objects 
appear through telefcopes fo diftindt as they do, conlider- 
ing that the error arifing from the different refrangibility 
is almoft incomparably larger than that of the figure. 
In confequence of the difcovefy of the unequal refrangi¬ 
bility of light, and the apprehenlion that equal refradtions 
muff produce equal divergencies in every fort of medium, 
it was fuppofed that all fpherical objedt-glaffes of telefcopes 
would be equally aft'edted by the different refrangibility of 
light, in proportion to their aperture, of whatever mate¬ 
rials they might be conftrudted: and therefore that the 
only improvement that could be made in refradting tele¬ 
fcopes, was that of increafing their length. So that Sir 
lfaac Newton, and other perfons after him, defpairing of 
fuccefs in the ufe and fabric of lenfes, diredted their chief 
attention to the conftrudtion of refledting telefcopes. 
However, about the year 1747, M. Euler applied himfelf 
to the .fubjedt of refradtion; and purfued a hint fuggefted 
by Newton, for the defign of making objedt-glafles with 
two lenfes of glafs incloiing water between them; hoping 
that, by conftrudting them of different materials, the re- 
fradlions would balance one another, and fo the ufual aber¬ 
ration be prevented. Mr. John Dollond, an ingenious 
optician in London, minutely examined this fcheme, and 
found that M. Euler’s principles were not fatisfadtory. 
M. Clairaut likewife, whofe attention had been excited to 
the fame fubjedt, concurred in opinion that Euler’s fpecu- 
lations were more ingenious than ufeful. This controverfy, 
which feemed to be of great importance in the fcience of 
optics, engaged alio the attention of M. Klingenftierna 
of Sweden, who was led to make a careful examination 
of the eighth experiment in the fecond part of Newton’s 
Optics, with the conclufions there drawn from it. The 
confequence was, that he found that the rays of light, in 
the circumftances there mentioned, did not lofe their co¬ 
lour, as Sir lfaac had imagined. This hint of the Swe- 
dilh philofopher led Mr. Dollond to re-examine the fame 
experiment; and after feveral trials it appeared, that dif¬ 
ferent fubftances caufed the light to diverge very different¬ 
ly, in proportion to their general refradtive powers. In 
the year 1757, therefore, he procured wedges of different 
kinds of glafs, and applied them together fo that the re¬ 
fradtions might be made in contrary diredtions, that he 
might difcover whether the refraction and divergency of 
colour would vanilli together. The refult of his firft trials 
encouraged him to perfevere; for he difcovered a diffe¬ 
rence far beyond his hopes in the qualities of different 
kinds of glafs, with refpedt to their divergency of colours. 
The Venice glafs and Englifh crown glafs were found to 
be nearly allied in this refpedt: the common Englifh plate 
glafs made the rays diverge more; and the Englifh flint 
glafs mod of all. But without enquiring into the caufe 
of this difference, he proceeded to adapt wedges of crown 
glafs, and of white flint glafs, ground to different angles, 
to each other, fo as to refradt in different diredtions: till 
VOL. I. No. 2. 
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the refracted light was entirely free from colours. Having 
meafured the refradtions of each wedge, he found that the 
refradtion of the white glafs was to that of the crown glafs, 
nearly as 2 to 3 : and he hence concluded in general, that 
any two wedges made in this, proportion, and applied to¬ 
gether fo as to refradt in contrary directions, would refradt 
the light without any aberration of the rays. 
Mr. Dollond’s next objedt was to make fimilar trials with 
fpherical glafles of different materials, with the view of 
applying his difcovery to the improvement of telefcopes : 
and here he perceived that, to obtain a refradtion of light 
in contrary diredtions, the one glafs muff be concave, and 
the other convex ; and the latter, which was to refradt the 
mod, that the rays might converge to a real focus, he 
made of crown glafs, the other of white flint glafs. And 
as the refradtions of -fpherical glafles are inverfely as their 
focal diftances, it was neceflary that the focal diftances of 
the two glafles fiiould be inverfely as the ratios of the 
refradtions of the wedges ; becaufe that, being thus pro¬ 
portioned, every ray of light that paiies through this com¬ 
pound glafs, at any diffance from its axis, will conftantly 
be refradted, by the difference between two contrary re¬ 
fradtions, in the proportion required; and therefore the 
different refrangibility of the light will be entirely removed. 
But in the applications of this ingenious difcovery to prac¬ 
tice, Mr. Dollond met with many and great difficulties. 
At length, however, after many repeated trials, by a re- 
folute perfeverance, he fucceeded fo far as to conffrudt re¬ 
fradting telefcopes much fuperior to any that had hitherto 
been made; reprefenting objedts with great diffinctnefs, 
and in their true colours. 
M. Clairaut, who had interefted himfelf from the be¬ 
ginning in this difcovery, now endeavoured to afcertain 
the principles of Mr. Dollond’s theory, and to lay down 
rules to facilitate the conffruction of thefe new telefcopes. 
With this view he made feveral experiments, to determine 
the refradtive power of diff erent kinds of glafs, and the 
proportions in which they feparated the rays of light: 
and from thefe experiments he deduced feveral theorems 
of general ufe. M. d’Alembert made likewife a great 
variety of calculations to the fame purpofe; and he fhewed 
how to corredt the errors to which thefe telefcopes are 
fubjedt, fometimes by placing the objedt-glaffes at a fmall 
diftance from each other, and fometimes by ufing eye- 
glafles of different refradtive powers. But though fo¬ 
reigners were hereby fupplied with the molt accurate cal¬ 
culations, they were very defective in pradtice. And the 
Englilh telefcopes, made, as they imagined, without any 
precife rule, were greatly fuperior to the belt of their 
conftrudtion. 
M. Euler, whofe fpeculations had firft given occafion 
to this important and ufeful enquiry, was very reludtant 
in admitting Mr. Dollond’s improvements, becaufe they 
militated againft a pre-conceived theory of his own. At 
laft however, after feveral altercations, being convinced 
of their reality and importance by M. Clairaut, he af- 
fented; and he foon after received farther fatisfadtion 
from the experiments of M. Zeiher, of Peterfburgh.—• 
M. Zeiher fhewed by experiments that it is the lead, in 
the compolition of glafs, which gives it this remarkable 
property, namely, that while the refradtion of the mean 
rays is nearly the fame, that of the extreme rays con fide r- 
ably differs. And, by increafing the lead, he produced 
a kind of glafs, which occafioned a much greater repara¬ 
tion of the extreme rays than that of tiie flint glafs ufed 
by Mr. Dollond, and at the fame time confiderably in- 
creafed the mean refradtion. M. Zeiher, in the courfe of 
his experiments, made glafs of minium and lead, with a 
mixture alfo of alkaline falts; and he found that this 
mixture greatly diminiftied the mean refraction, and yet 
made hardly any change in the difperfion: and he at length 
obtained a kind of glafs greatly fuperior to the flint glafs 
of Mr. Dollond for the conftrudtion of telefcopes; as it 
occafioned three times as great a difperfion of the rays as 
the common glafs, wliilft the mean refraction was only as 
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