By many thoufand comparifons he has 
proved, firft, that periodical inequalities 
-previoufly determined, were only fufcep- 
tible of very flight melicrations. He in- 
troduced fome equations indicated imper=- 
fefily, afterwards neglected by Mayer and 
-Maion, and certain others much more im- 
‘portant, indicated in the laft volumes of 
La Connoiflance des Tems, by Citizen 
Laplace : they rendered the Tables much 
better, but did not correct the inequality 
of the mean mation. 
‘It remained to try the equations with a 
long period ; theory not having furnifhed 
‘any, our author attempted to determine 
the law of obferved anomalies empirically : 
she was lof in an imexticable labyrinth ; 
butat the very time when, fatigued with fo 
many ulelefs efforts, he had given up all 
hope, he learned that Citizen Laplace had 
jult difcovered the form and the arguments 
of two new equations, the more precile-de- 
termination of which he referred to fubfe- 
“quent ohfervation. With this almoft un- 
-hoped-for affiftance, our author undertook 
a new labour, and was enabled to fix the 
value of two equations, which explained 
every. thing in’ ihe happief manner.— 
Hence refulted a more corre&t knowledge 
of the mean motion-—a more perfect agree- 
ment between the calculations and the ob- 
feryvations—and, above all, a well-founded 
hope that this agreement will be kept up, 
and that we fhall no longer fee, as of late 
years, errors increafe in a rapid man- 
her. ese 
This is not the place to enter into nu- 
merical details ; they will be found in a 
paper, and in Tables, laid: down by the 
Commifiaries before the Bureau. To give 
an idea of the precifion of the new Tables, 
it will be fufficient to fay, that the errors 
attributable to them, go very rarely to 
12"; from whence it follows, that the 
aftronomer who fhall obferve the Moon, 
will rarely find, between the real place 
-and the calculated place, a greater diffe- 
rence than the thicknefs of the very fine 
thread which is at the fecus of his pro- 
fpective-glafs ; and to fhow of what im- 
portance this exactitude is for navigation, 
we fhall fay that thefe 12” of motion do 
net require half a minute of time, the na- 
vigator will not err eight minutes in his 
longitude, at leaft, through the fault of the 
Tables ; fo that if he is enabled to beftow 
the fame accuracy on his obfervations, he 
will be able to confider the problem of the 
longitudes as fufficiently refolved for prac- 
fice. 
_ The Commiffaries conclude, that the 
Proceedings of Learned Societies. 
[O& 1, 
new Tables, from the immenfity of the 
labour which they pre-fuppofe—from the 
intelligence which has direéted this la- 
bour—from the great fuperiority whicls 
they have over other tables—and, laftly, 
from the utility which they will daily af- 
ford to aftronomers and to navigators, are, 
in every refpect, worthy of the prize an- 
nounced. 
Signed, LaGRaNnce, LaPpLACE, ME- 
CHAIN, and DELameEre;: the Reporter. 
THE ROYAL SOCIETY OF 
LONDON. 
OPTICS aud ASTRONOMY. - 
R. WOLLASTON; inthe Bakerian © 
Lecture, préfented this learned body 
with ‘¢ Obfervations on the quantity of 
horizontal. refraction ; and a method of 
meafuring the dip at Sea.” From thefe 
it appears that the quantity of refraétion: “35a 
varies in general with any change of the 
thermometer or hygrometer. The inftru- 
ment with which he made his experiments 
was a plane reflector, fitted to the objeét- 
end of a {mall telefcope, at an angle of 
45°, fo that, when the telefcope is held 
vertically, it gives a horizontal view at 
any level that-is- found moft eligible. - 
‘When the water was calm he fometimes 
obferved that the greatelt refraétion was 
vifible within an inch or two of its fur- 
face, it has been feen equal to fix or feven_ 
minutes in the {pace of 300 or 400 yards ; 
at other times it was greatelt at the height 
of a foot or two; but in this cafe, a more 
extenfive view becomes neceflary. Dr. 
Wollafton’s experimeats were made on 
the River Thames; on the 234 of Sep- 
tember 1800, when the water was 2°% 
warmer than the air, the refraction was 
equal to 4’. In O&tober the difference of 
temperature was 3°, and the refraétion 
was 3’. Five days afterwards the water 
was 11°2 warmer than the air, yet the 
quantity of refraction did not exceed 3/,, 
but the fmallnefs of the refraction, in this 
cafe, was probably owing’to the drynefs 
of the atmofphere. . , 
From a Table, which is given, and 
which was the refult of a variety of obfer- 
vations, Dr. Wollafton infers that when - 
the water is warmer than air fome increafe 
of deprefiion of the horizon may be ex- 
pected ; but that its quantity will be 
greatly influenced, and in general dimi- 
nifhed, by the drynefs of the atmofphere. 
On fome occafions, the quantity of refrac_ 
tion is, very different from what the ftates 
of the thermometer and hygrometer would 
indicate. Once when the difference of 
: _ temperature 
a 
