3 6o ASTRO 
eight different fituations above defcribed, if we fuppofe 
the Earth to be at T, when Venus is at A, her dark he- 
inifphcre is towards the Earth, and the is therefore invili- 
ble, except the conjunction happens in her node, for then 
ibe appears like a dark fpot upon the difk of the Sun, 
which is called a tranfit. When Venus is at B, a little of 
her enlightened fide is turned towards the Earth, and there¬ 
fore flie appears (harp-horned; when (lie is at C, half her 
enlightened hemifphere is turned towards the Earth, and 
fhe appears like an half-moon; at D, more than halt her 
enlightened hemifphere is towards us, and (lie appears like 
the Moon about three days before it is full; at E, the whole 
enlightened hemifphere is towards the Earth, and Venus 
is then either behind the Sun, or fo very near him, that 
flie can hardly be feen ; but, if (lie ^ould, (he would ap¬ 
pear round, like the full-moon. At F, (he is like the 
Moon three days after the full; at G, like a half-moon 
again; at H, like a crefcent, with the points of the horn 
turned the contrary way to what they were at B ; all which 
phenomena are equally applicable to the planet Mercury. 
Hence Venus and Mercury have the fame phafes from 
their inferior to their fuperior conjunction, as the Moon 
has from the new to the full; and the fame from the fu¬ 
perior to the inferior conjunction, as the Moon has from 
the full to the new. 
The inferior planets do not fhine brighteft when they 
are full; thus Venus does not appear brighteft in her fu¬ 
perior conjunction, though her illuminated hemifphere be 
then turned towards us. Her fplendour is more diminilh- 
ed by her being at a greater distance troin us, than the 
confpicuous part of her illuminated difk is increafed. Dr. 
Halley has (hewn, that Venus is brighteft when her elon¬ 
gation from the Sun is about 40 0 . Mercury is in his great- 
elt brightnefs when very near his utmoft elongation. 
Of the Transits of Venus and Mercury. 
The principal ufe of the observations upon thefe tran- 
fits is accurately to determine the Sun’s parallax, or dif- 
tance from the Earth, which aftronomers have in vain at¬ 
tempted to find by various other methods; tor the mi- 
nutenefs of the angles required ealily eludes the niceft in- 
ftruments. But in obferving the ingrefs of thefe planets, 
particularly that of Venus into the Sun, and her egrefs 
from the fame, the fpace of time between the moments of 
the internal contacts, obferved to a fecond of time, may 
be obtained by the affiltance of a moderate telefcope, and 
a good pendulum-clock. And from two fuch obfervations 
rightly made, in proper places, the diltance of tire Sun 
from the Earth, to within a 500th part, may be certainly 
found. Dr. Halley, while at St. Helena, obferved a tran¬ 
fit of Mercury over the Sun’s difk ; and, by means of a 
good telefcope, it appeared to him that he could determine 
the time of the ingrefs and egrefs, without its being fub- 
jed to an error of a Single (econd; upon which he imme¬ 
diately concluded, that the Sun’s parallax might be de¬ 
termined by fuch obfervations, from the difference of the 
times of the tranfit over the Sun, at different places upon 
the Earth’s furfaee. But this difference is fo fmall in 
Mercury, that it would render the conclufion fubjeCt to 
a great degree of inaccuracy ; in Venus however, whofe 
parallax is nearly four times as great as that of the Sun, 
there will be a very conliderable difference between the 
times of the tranfits feen from different parts of the 
Earth, by which the accuracy of the conclufion might be 
proportionably increafed. Hence Dr. Halley propofed to 
determine the Sun’s parallax from the tranfit of Venus 
ever the Sun’s difk, obferved at different places on the 
Earth ; and, as it was not probable that he himfelf (hould 
live to obferve the next tranfits, which happened in 1761 
and 1769, he very earneftly recommended the attention of 
them to the aftronomers who (hould be alive at that time. 
Aftronomers were therefore fent from England and France 
to the mod proper parts of the Earth to obferve both thefe 
tranfits, from the refult of which, the parallax has been 
determined to a very great degree of accuracy. 
N O M Y. 
Kepler was the firft perfon who predicted the tranfits of 
Venus and Mercury over the Sun’s difk; he foretold the 
tranfit of Mercury in 1631, and the trairfits of Venus in 
1631 and 1761. The firft time Venus was ever feen upon 
the Sun was in the year 1639, on November 24, at H »wle 
near Liverpool, by our countryman Mr. Horrox. He 
was employed in calculating an Ephemeris from the Lanf- 
berge Tables, which gave, at the conjunction of Venus 
with the Sun on that day, its apparent latitude lefs than 
the femidiameter of the Sun. But, as thefe tables had fo 
often deceived him, he confulted the tables conftruCted by 
Kepler, according to which, the conjunction would be at 
8h. 1'. A. M. at Manchefter, and the planet’s latitude 
14' 10" fouth; but, from his own corrections, he expect¬ 
ed it to happen at 3I1. 57'. P. M. with 10' fouth latitude. 
He accordingly gave this information to his friend Mr. 
Crabtree at Manchefter, defiring him to obferve it; and 
he himfelf alfo prepared to make obfervations upon it, by 
tranfmitting the Sun’s image through a telefcope into a 
dark chamber. He defcribed a circle of about fix inches 
diameter, and divided the circumference into 360°, and 
the diameter into 120 equal parts, and caufed the Sun’s 
image to fill up the circle. He began to obferve on the 
23d, and repeated his obfervations on the 24th till one 
o’clock, when he was unfortunately called away by bufi- 
nefs ; but, returning at fifteen minutes after three o’clock, 
he had the fatisfaCtion of feeing Venus upon the Sun’s di(k, 
juft wholly entered on the left fide, fo that the limbs per¬ 
fectly coincided. At thirty-five minutes after three; he 
found the diftance of Venus from the Sun’s centre to be- 
13' 30" ; and, at forty-five minutes after three, he found 
it to be 13'; and the Sun fetting at fifty minutes after three 
o’clock, put an end to his obfervations. From thefe ob¬ 
fervations, Mr. Horrox endeavoured to correCt fome of 
the elements of the orbit of Venus. He found Venus had 
entered upon the difk at about 62° 30' from the vertex to¬ 
wards the right on the image, which, by the telefcope, was 
inverted. He meafnred the diameter of Venus, and found 
it to be to that of the Sun, as 1-12 : 30, as near as he could 
meafure. Gaffendus obferved the tranfit of Mercury 
which happened on November 7, 1631, and this was the 
firft which had ever been obferved; lie made his obferva¬ 
tions in the fame manner that Horrox did after him. Since 
his time, leveral tranfits of Mercury have been obferved, 
as they frequently happen; whereas only two tranfits of 
Venus have happened fince the time of Horrox. If we 
know the time of the tranfit at one node, we can determine, 
in the following manner, when they will probably happen 
again at the fame node. 
The mean time from one conjunction to another of Ve¬ 
nus or Mercury being known, and the time of one mean 
conjunction, we (hall know the time of all the future mean 
conjunctions; obferve therefore thofe which happen near 
to the node, and compute the geocentric latitude of the 
planet at the time of conjunction, in which cafe, if it be 
lefs than the apparent (emidiameter of the Sun, there 
will be a tranfit of the planet over the Sun’s difk * and we 
may determine the periods when fuch conjunctions hap¬ 
pen, in the following manner: Let P— the periodic time 
of the Earth, p that of Venus or Mercury. Now, in or¬ 
der that a tranfit may happen again at the fame node, the 
Earth mull perform a certain number of complete revo¬ 
lutions in the fame time that the planet performs a certain 
number, for then they muft come into conjunction again at 
the fame point of the Earth’s orbit, or nearly in the fame 
pofition with refpeCt to the node. Let the Earth perform 
x revolutions, whilft the planet performs y revolutions; 
x p 
then will Px—py ) therefore y=~^. Now P—365,256, and 
for Mercury £—87,968 ; therefore X —~— 87,96 (by 
y P 3^5>35 6 
refolvingitintoitscontinual fractions)^, i 2 ^* 
See. That is, 1, 6, 7, 13, 33, 46, &c. revolutions of the 
Earth are nearly equal to 4, 2.5, 29, 54, 137, 191, &c. re- 
-- 3 volutions 
