OPTICS. 
By the fame way of reafoning, when the refraction is di¬ 
vided between three glaffes, the aberration will be found 
to be but the ninth part of what would be produced from 
a finale glafs; becaufe, three times the cube of i is but f 
of the cube of 3. Whence it appears, that, by increafing 
the number of eye-glaffes, the indiltinftnefs which is ob- 
ferved near the borders of the field of a telefcope may be 
very much diminifhed.” 
The method of correcting the errors arifing from the 
refrangibility of light, is of a different confideration 
from the former. "For, whereas the errors from the 
figure can only be diminifhed in a certain proportion ac¬ 
cording to.the number of glaffes, in this they may be en¬ 
tirely corrected by the addition of only one glafs. A 1 fo 
in the day-telefcope, where no more than two eye-glaffes 
are abfolutely neceffary for ereCting the objeCt, we find, 
that, by the addition of a third, rightly fituated, the co¬ 
lours, which would otherwife make the image confufed, 
are entirely removed. This, however, is to be under¬ 
stood with fome limitation ; for, though the different co¬ 
lours into which the extreme pencils muff neceffarily be 
divided by the edges of the eye-glafles may, in this man¬ 
ner, be brought to the eye in a direction parallel to each 
other, fo as to be made to converge to a point on the re¬ 
tina ; yet, if the glaffes exceed a certain length, the co¬ 
lours may be.fpread too wide to be capable of being ad¬ 
mitted through the pupil or aperture of the eye; which is 
the reafon, that, in long telefcopes, conftruCfed in the 
common manner, with three eye-glafles, the field is al- 
wavs very much contracted. 
Thefe confiderations firft fet Mr. Dollond on contri¬ 
ving how to enlarge the field, by increafing the num¬ 
ber of eye-glaffes without affeCting the dilfinCf nefs or 
brightnefs of the image; and, though others had been 
about the fame work before, yet, obferving that fome 
five-glafs telefcopes which were then made w-ould admit 
of farther improvement, he endeavoured to conftruft 
one with the fame number of glaffes in a better man¬ 
ner; which fo far anfwered his expeditions, as to be 
allowed by the belt judges to be a confiderable improve¬ 
ment on the former. Encouraged by this fuccefs, he re- 
folved to try if he could not make fome farther enlarge¬ 
ment of the field, by the addition of another glafs, and by 
placing and proportioning the glaffes in fuch a manner as 
to correct the aberration as much as pofflble, without in¬ 
juring the diftinCfnefs ; and at laft he obtained as large a 
field as is convenient or neceffary, and that even in the 
longeft telefcopes that can be made. _ Thefe telefcopes 
with-fix glaffes having been well received, and fome of 
them beingcarried into foreign countries, it feemed a pro¬ 
per time to the author to fettle the date of his invention ; 
on which account he drew up a letter, which he addrefl'ed 
to Mr. Short, and which was read at the Royal Society, 
March 1, 1753. 
John Dollond was fucceeded in his bufinefs by his no 
lei's ingenious and indullrious fon, Peter Dollond, who 
improved the achromatic objeCt-glafs {fill further, by 
placing a double concave flint-glafs betw-een two convex 
ones of crowm-glafs, and by enlarging the aperture to 3$ 
inches in a 45-inch telefcope; of thefe a great number 
have been manufactured, and feveral of five feet focal 
length. His calculations of the radii of convexity, and of 
concavity were never publicly made known; and per¬ 
haps conflituted a fecreton which the continuance of his 
celebrity depended, when the time of his father’s patent 
had expired. The bufinefs is now' fuccefsfully conduced 
by G. Dollond, the nephew ; but at no period had any of the 
Dollonds an agent in Paris, as is faid in the new Supplement 
to the Encyclopaedia Britannica. For feveral years from 
the time of the eldeft Dollond’s death, the foreign Tranf- 
actions were crowded with diflertations and memoirs on 
the combinations of achromatic lenfes mathematically de¬ 
termined ; and the fubjeCt afforded ample fcope for the 
geometrical and analytical refearches of Euler, Clairaut, 
60S- 
and d’Alembert, as welt as for Bofcovich, Klingenftierna, 
Kaeftner, and Hennert; but, in this as in fome other fpe- 
culative invelfigations, the labours of the profound mathe¬ 
matician have not much benefited the practical advance¬ 
ment of the art to which thefe labours have been directed ; 
nay, they' have tended to keep at a diltance from each 
other the mathematician and the mechanic. 
Bofcovich’s eye-piece, however, may be confidered as 
conlfituting an exception to the preceding remark,and de- 
ferves here to be particularly noticed. According to one 
of his theorems, an eye-piece free from colours may be 
compofed of two fimilar lenfes of the fame glafs, provided 
they be placed from each other juft one-half of the fum of 
their focal diftances; which is very fimilar to the eye- 
glafs now commonly' adopted, in preference to a Angle 
lens, in the common aftronomical ref'raCting telefcope ; 
the only difference being, that in Bofcovich’s the lenfes 
are of equal convexity; whereas, in the common im¬ 
proved aftronomical eye-piece, the inner Jens has a longer 
focus than the outer one, in the ratio of 3 to 1; and, 
being both plano-convex, they both have their curved 
faces turned towards the objeCt-glafs. 
From the preceding experiments of the Dollonds have 
refulted all the advantages that the achromatic refracting 
telefcopes pofiefs over the long telefcopes with fimple ob- 
jeCt-glafles, and which have put them in competition 
with the beft refleCtors in the eflential qualities of pow-er, 
light, and diftinCtnefs of vifion. There is, however, an 
imperfection, notwithftanding Dollond’s great fk.il 1 and 
perfeverance, which remains yet to be overcome, if it be 
not in vincible ; which is, that;, while the colours occa- 
fioned by the extreme rays are corrected with fufficient 
accuracy by the compound objeCt-glafs, yet the interme¬ 
diate rays are not perfectly corrected ; and, if any- media 
can be fo modified as to correct all the rays that fall.on 
every point of the furface of the objeCEglafs,fo as to make 
them unite at the fame point in the line of the axis, then, 
and not till then, wall the objeCt-glafs be quite perfect. 
Peter, the fon of John Dollond, who, we have faid, fuc¬ 
ceeded to his father’s bufinefs, purified this fubject after 
his father’s death ; and in the year 1765 communicated 
to the Royal Society by letter the refult of his experiments. 
He remarks, that, when his father had made objeft« 
glaffes of one convex lens of crowm-glafs, and of one- 
concave of flint-glafs, to be ufed with convex eye-glafles, 
it was found that the excefs of aberration was in the 
convex portion of the compound objeCt-glafs, and that the 
equality of the counteracting aberrations could not be 
carried to any great diftance from the centre of the glaffes; 
he therefore attempted, about the year 1758, to make 
fhort objeCt-glaffes of the fame fort, to be uled with con¬ 
cave eye-glafles; but it was found, that, as the field of 
view, in tiling a concave eye-glafs, depended on the aper¬ 
ture of the objeCt-glafs, the limits of" the aperture were too 
confined with a double objeCt-glafs. This trial led the 
fenior Dollond to a conclulion, which the foil took up, 
and profited by; namely, that the excefs of fpherical aber¬ 
ration, occafioiied by one double convex lens of crowm- 
glafs, might be diminifhed, by fubftitutirig two plano¬ 
convex lenfes of fimilar glafs and curves, placed one at 
each fide of the double concave of flint-glafs. The fe¬ 
nior Dollond had fuccepded with this conftruCtion wdieri 
a concave eye-glafs was ufed, and when the compound 
focus was fhort; but it remained for the fon to complete 
a long objeCt-glafs of this conftruCtion, to be.ufed with 
convex eye-glaffes ; which he fucceeded in doing, firft 
with a telefcope of 5-feet focus, and 3! inches aperture, 
and afterwards with a 3^-feet one of the fame aperture, 
which he invited the Royal Society to fee, and which was 
the prototype of the numerous achromatic telefcopes of 
the fame dimeniions w'hich have been finee conftruCted s . 
and difperfed by fale through all the regions of" the globe. 
The largeft and beft telefcope of the achromatic kind 
ever made by P, Dollond, is that of ten feet focus, and 
3. five- 
