550 
OPT 
light by the glafs prifm to be almoft double of that by the 
water; for the image of the object was as much infected 
with the prifmatic colours as if it had been feen through 
a glafs wedge only whofe re fra fling angle was near 30 
degrees. Mr. Dollond was convinced, that, if the re- 
f'rafling angle of the water-veflel could have admitted of 
a fufficient increafe, the divergency of the coloured rays 
would have been greatly diminished, or entirely redtified ; 
and that there (would have been a very great refra&ion 
without colour ; but the inconvenience of fo large an 
angle as that of the prifmatic vellel mull have been, to 
bring the light to an equal divergency with that of the 
glafs prifm, whofe angle was about 60 degrees, made it 
necelfary to try fome experiments cf the fame kind with 
fmaller angles. He therefore got a wedge of plate-glafs, 
the angle of which was only nine degrees ; and, uling it 
in the fame circumftances, he increafed the angle of the 
•water-wedge, in which it was placed, till the divergency 
of the light by the water was equal to that of the glafs ; 
that is, till the image of the object, though confiderably 
refradled by the excefs of the refradtion of the water, ap¬ 
peared quite free from any colours proceeding from the 
different refrangibility of the light; and, as near as he could 
then meafure, the refradtion by the water was about £ of 
that by the glafs. 
As thefe experiments proved, that different fubftances 
caufecl the light to diverge very differently in proportion 
to their general refradtive power, Mr. Dollond began to 
fufpedl that fuch a variety might poffibly be found in dif¬ 
ferent kinds of glafs. His nextobjedl, therefore, was to 
grind wedges of different kinds of glafs, and apply them 
together; fo that the refractions might be made in con¬ 
trary directions, in order to difcover whether the refrac¬ 
tion and the divergency of the colours would vanifh toge¬ 
ther. From thefe experiments, which were not made till 
1757, he difcovered a difference far beyond his hopes in 
the refradlive qualities of different kinds of glafs, with 
• refpefl to the divergency of colours. The yellow or 
Itraw-coloured kind, commonly called Venice glafs, and 
the JEngUjh crown-glafs, proved to be nearly alike in that 
refpedi; though, in general, the crown-glafs feerned to 
make light diverge lefs than the other. The common 
Englilh plate-glafs made the light diverge more ; and the 
white cryffal, or Englilh flint-glafs, moll of all. He 
then examined the particular qualities of every kind of 
glafs that he could obtain, to fix upon two kinds in which 
the difference of their difperlive powers Ihould be the 
greateft ; and, proceeding in the manner related under 
Achromatic, vol. i. at length, after numerous trials, 
he was able to conftruft refracting telefcopes, with fuch 
apertures and magnifying powers, under limited lengths, 
as far exceeded any thing that had been produced before, 
reprefenting objects with great diffinftnefs, and in their 
natural colours. 
As Mr. Dollond did not explain the method by which 
he determined the curvatures of his lenfes, the celebrated 
M. Clairaut, who had begun to inveftigate this fubject, 
endeavoured to reduce it to a complete theory, from 
which rules might be deduced for the benefit of the prac¬ 
tical optician. With this view, therefore, he endeavoured 
to afcertain the refraftive power of different kinds of 
glafs, and alfo their property of difperfmg the rays of light. 
For this purpofe he made ufe of two prifms, as Mr. Doi- 
lond had done : but, inffead of looking through them, 
lie placed them in a dark room ; and, when the tranlinit- 
ted image of the. fun was- perfectly white, he concluded 
that the different refrangibility of the rays was corrected. 
In order to afcertain more eafily the true angles that 
prifms ought to have, in order to deitroy the effect of the 
difference of refrangibility, he conftruCted a prifm which 
had. one of its furfaces cylindrical, with feveral degrees of 
amplitude. By this means, without changing his prifms, 
he had the choice of an infinity of angles: among which, 
by examining the point of the curve lurface, which, re¬ 
ceiving the Tolar ray, gave a white image, he could eafily 
I c s. 
find the true one. He alfo afcertained the proportion in 
which different kinds-of glafs feparated the rays of light, 
by meafuring, with proper precautions, the oblong image 
of the fun made by tranfmitting through them a beam of 
light. 
In thefe experiments M. Clairaut was affifted by M. de 
Tournieres, and the refults agreed with Mr. Dollond’s in 
general; but/whereas Mr. Dollond had made the difper- 
fion of the ray's in glafs and in water to be as 5 to 4, (ac¬ 
knowledging, however, that he did not pretend to do it 
with exa&nefs,) thefe gentlemen, who took more pains, 
found it to be as 3 to 2. For the theorems and problems 
deduced by M. Clairaut from thefe new principles of op¬ 
tics, with a view to the perfection of telefcopes, we mult 
refer the reader to Mem. Acad. Par. 1756, 1757. 
The fubjeCt of achromatic telefcopes was alio inveftiga- 
ted by the illuftrious d’Alembert. This excellent mathe¬ 
matician propofed a variety of new conftruCiions, the ad¬ 
vantages and difadvantages of which he diftinCtly notes ; 
at the fame time that he points out feveral methods of cor¬ 
recting the errors to which thefe telefcopes are liable : as¬ 
hy placing the objeCt-glalfes, in fome cafes, at a fmall dif- 
tance from one another, and fometimes by ufing eye- 
glaffes of different refractive powers ; which is an expe¬ 
dient that does not feem to have occurred to any perfon 
before him. He even fliows, that telefcopes may be made 
to advantage, confuting of only one objeCt-glafs, and an 
eye-glafs of a different refraCtive power. Some of his con- 
ftruCtions have two or more eye-glaffes of different kinds 
of glafs. This fubject he confidered at large in one of 
the volumes of his Opufcules Mathematiques. We have 
alfo three memoirs of d’Alembert upon this lubjeft among 
thofe of the French Academy in the years 5764, 1765, 
and 1767. 
The inveftigation of Clairaut and d’Alembert do not 
feem to have affifted the exertions of foreign artifts. The 
telefcopes made in England, according to no exact rule, 
as foreigners fuppofed, were greatly fuperior to any that 
could be made elfewhere, though under the immediate di¬ 
rection of thofe able calculators. 
M. Euler, w ho firft gave occafion to this enquiry, hav¬ 
ing perfuaded himfelf, both by reafoning and calculation, 
that Mr. Dollond had difcovered no new principle in op¬ 
tics, and yet not being able to controvert Mr. Short’s tef- 
tirnony in favour of the achromatic telefcopes, concluded 
that this extraordinary effect was partly owing to the 
crown-glafs not tranfmitting all the red light, which 
would otiierwile have come to a different focus, and have 
diftorted the image ; but principally to his giving a juft 
curvature to his glafs, which he did not doubt would 
have produced the fame effeCt, if the lenfes had all been 
made of the fame kind of glafs. At another time he ima¬ 
gined that the goodnefs of Mr. Dollond’s telefcopes might 
be owing to the eye-glafs. “ If my theory,” fays he “ be 
true, this difagreeable confequence follows, that Mr. 
Dollond’s objeCl-glaffes cannot be exempt from the dif- 
perfion of colours ; yet a regard to fo refpeCiable a tefti- 
mony embarraifes me-extremely, it being as difficult to 
queftion fuch exprefs authority, as to abandon a theory 
which appears to me well founded, and to embrace an 
opinion which is as contrary to all the eftablilhed laws of 
nature as it is ftrange and feemingly abfurd.” He even 
appeals to experiments madeina darkened room; in which, 
he fays, he is confident that Mr. Dollond’s objeft-glalles 
would appear to have the fame defeCts to which others are 
fubjecl. 
Not doubting, however, but that Mr. Dollond had 
made fome improvement in the conftruCtion of telefcopes 
by the combination of glaffes, he abandoned his former 
project, in which he had recourfe to different media, and 
confined his attention to the correction of the errors 
which arife from the curvature of lenfes. But while he. 
was proceeding, as he imagined, upon the true principles 
of optics, he could not help expreffing his furprife that 
Mr. Dollond Ihould have been led to lb important a dif- 
covery. 
