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242 JOURNEY OF MAUPERTUIS.
the ecliptic, which caufes the preceffion of the equinox, and a change of declenfion in
the flars, which we can compute upon, in the matter of which we fpeak.
But there is in the ftars another change of declenfion, on which, although more re-
cently obferved, I believe we may reckon as fecurely as upon the other. Although
Mr. Bradley be the firft who difcovered the rules of the change, the exactnels of his
obfervations, and the excellence of the inftrument with which they were made, are
equivalent to many ages of ordinary obfervations. He found that every ftar obferved
during the courfe of the year, feemed to defcribe in the heavens a fmall ellipfis, of which
the great axis is about 40’. As there appeared at firlt to be a great variety in this
motion of the ftars, it was not till after a long fucceflion of obfervations that Mr.
Bradley difcovered the theory upon which this motion, or rather this appearance, de-
pends. If to difcover fo fimall a motion required his nicety of obfervation, his intelli-
gence as well was neceflary to find out the principle which produced it. We will not
attempt to explain the fy{tem of that celebrated aftronomer, which may be much better
feen by confulting No. 406 of the Philofophical Tranfactions ; all that we fhall obferve
on the fubject of this difference in the place of the ftars, obferved from the earth, is,
that it arifes from the motion of the light radiated by the ftar, and the motion of the
earth in its orbit, combined together.. Were the earth motionlefs, it would require a
certain inclination of the telefcope through which a ftar is obferved to permit the ray
emitted by the ftar to trayerfe its centre in coming to the eye. But if the earth, which
bears the telefcope, move with a velocity comparable to the velocity of the ray of light,
it isno longer the fame inclination which is neceflary to give to the telefcope ; its pofition
mutt be changed to allow the ray of light penetrating its centre, to reach the eye ; and
the different pofitions of the telefcope will depend on the different directions in which
the earth moves at the various feafons of the year. The calculation being made on this
principle, according to the velocity of the earth in its orbit, and according to the velo-
city of light, known by different experiments, the change of declenfion in the ftars is
found to be as ftated by Mr. Bradley from obfervation ; and one is enabled to fubtract
from the declenfion of every ftar the quantity neceflary for confidering it as fixed, dur-
ing the time that muft elapfe between the obfervations that are compared with each other
for determining an arc of the meridian.
Although the motion of every ftar in the courfe of the year follow very exaétly the
law which depends upon this theory, Mr. Bradley has difcovered yet an additional mo-
tion of the ftars, much fmaller than the two which we have mentioned, and which is not
fenfible until after the lapfe of feveral years. ‘To perfect nicety this third motion fhould
be reckoned; but for our work, in which the time that pafled between the obfervations
was very fhort, its effect is infenfible, or rather much fmaller than one can reafonably
hope to determine in thefe kind of operations. In fact, 1 confulted Mr. Bradley to
know if he had any obfervations upon the two ftars that we ufed for afcertaining the
amplitude of our arc. Although he had not obferved our f{tars, becaufe they pals too
far from his zenith to be obferved with his inftrument, he has been fo good as to com-
municate to me his laft difcoveries on the aberration and the third motion of the ftars,
and the correéted copy which he has fent for our amplitude, in which attention is paid
to the preceffion of the equinox, the aberration of the {tars, and this new motion, does
not fenfibly differ from the amended fcheme which we had made for the preceflion and
aberration alone, as in the detail of our operations will be feen.
Notwithftanding we might fafely rely upon the amendment for the aberration of light,
we were willing to make this amendment as little as poflible, in order to fatisfy thofe
(if any there fhould be) who might be unwilling to admit of Mr. Bradley’s theory, or
who
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