WILLIAM L. CLEMENTS
LIBRARY OF
AMERICAN HISTORY
UNIVERSITY MICHIGAN



22
my bear
Mr. Winthrop's
LECTURES
On the USE of
THE TRANSIT OF VENUS.


TWO
LECTURES
ON THE
PARALLAX and DISTANCE of the Sun,
AS DEDUCIBLE FROM
The Tranſit of Venus.
Read in HOLDEN-Chapel at HARVARD-
COLLEGE in CAMBRIDGE, New-England,
in March 1769.
By JOHN WINTHROP, Esq.
HOLLISIAN Profeſſor of the Mathematics and
Philoſophy at Cambridge, and F. R. S.
Agite, mortales ! et oculos in Spectaculum vertite,
quod hucuſque Spectaverunt perpauciſſimi ;
Spectaturi iterum ſunt nulli.
Publiſhed by the general Deſire of the Students.
BO S T 0 N:
PRINTED AND SOLD BY EDES & GILL IN QUEEN-STREET,
MDCCLXIX.

ë
NUTO
DET
ot
To situs IT

The Use of the TRANSIT of VENUS.
bot
od
LECTURE I.
2
TRANSIT of VENUS UNDER THE
Sun is the moſt uncommon, and the
moſt important phænomenon, that the
whole compaſs of aſtronomy affords us. So un
common is it, that it can never happen above
twice in any century; in others, but once; and
in ſome centuries it cannot happen at all. And
the importance of it is ſuch as to ſupply us with
a certain and complete folution of a very curi-
ous Problem, which is inacceſſible any other
way. On both accounts it well deſerves a very
particular attention.
The phænomenon itſelf is, the paſſage of the
planet Venus acroſs the face of the Sun, from
caft to weſt, in the form of a round, black ſpor,
As we ſhall have the opportunity in a few months
of viewing one of theſe phænomena, if the wea-
ther permit, I ſhall adapt my deſcription of them
to the particular circumſtances of this Tranſit.
This planet then, having approached the Sun on
his eaſtern fide, and arrived at his limb or edge,
will,

6
Lect. l.
The Use of the
will, by being opake, make a ſmall, black notch
upon it; which, as ſoon as it is big enough to
be viſible,is called the firſt external contact. The
notch will immediately grow bigger, by the
planet's advancing, and in about 9 minutes
her centre will be got on the Sun's limb,and the
appearance will be that of a little black femi-
circle, which will occupy about 3 * degrees on
the circumference of the Sun. When the pla-
net is advanced above half, her circular figure
will cauſe an appearance as of a luminous horn
or cuſp on each ſide of it, with the points
turned towards each other, and gradually ap-
proaching, and in 9 minutes more Venus will
be wholly within the Sun's diſk, and the two
luminous cuſps running together at their points,
will form a narrow thread of light behind the
planet. The Sun's limb now recovers its light,
where it had been interrupted by the body of
the planet. This is called the immerſion, or the
firft internal contact. In about 3 hours the
planet will be in the middle of its courſe,
and neareſt to the Sun's centre, from which it
will be diſtant to the north about part of the
Sun's diameter ; its own diameter being ; part
of the Sun's. Then approaching the weſtern
ſide of the Sun, the thread of light between their
limbs will grow narrower till it breaks, and Ve-
nus again touches the Sun's limb, forming, what
is called, the beginning of emerfion, or the laft
internal contact. The light of the Sun's limb
will now again be interrupted, and two lumi-
nous

Lect. I. TRANSIT of VENUS, 7
nous cuſps formed, as before, which will recede
from each other as the planet moves off from
the Sun. In about 18 minutes, the laſt external
contact will be formed, the impreſſion made by
the planet upon the Sun's limb having become
gradually leſs & leſs, till it is quite impercepti-
ble. Theſe feveral phaſes will be very confpicu-
ous with any teleſcope, and even with the moſt
ordinary perſpective ; but few eyes are ſharp
enough to diſcern ſo ſmall an object as Venus
diveſted of her radiance ; her apparent diameter
being leſs than a minute of a degree. grida
You ſee what are the appearances in a Tranſic
of Venus. The theory of it is eafily under-
ſtood.-Venus circulates round the Sun,the ſame
way as the Earth does, that is, from weſt to eaſt,
but in a ſmaller orbit, and in a ſhorter period.
When Venus is in the ſame degree of the eclip-
tic with the Sun, ſhe is ſaid to be in conjunction
with the Sun; and as her orbit is incloſed within
the Earth's, it is plain, that a conjunction may
happen two different ways; either by the pla-
net's being beyond and above the Sun, and ſo in
the remoteſt part of its orbit from us, which is
called a ſuperior conjunction ; or being below
the Sun, and neareſt to us, and this is called an
inferior conjunction - The planet, having paſt a
fuperior conjunction will appear to move quickcr
to the eaſt than the Sun docs, whoſe apparent
velocity is the ſame as the Earth's real velocity
in its orbit; and thus will depart farther and
farther

8
Lect. 1.
The Use of the
farther from him, till ſhe has attained to the
diſtance of 48 degrees; and this is her greateſt
clongation from the Sun, her whole orbit being
included within two right lines drawn from the
Earth, at the diſtance of 48° eaſt and weſt of the
Sun. She will now appear ſtationary, in reſpect
of the Sun; and after this, while ſhe is deſcrib-
ing the neareſt part of her orbit contained be- :
tween the two right lines juſt mentioned,
will ſeem to move with a retrograde motion, or
the contrary way to what ſhe did before ; ap-
proaching the Sun from eaſt to weſt, and ſo will
paſs through an inferior conjunction with him.
Then running off to the diſtance of 48° weſt
from the Sun, ſhe will again appear ſtationary :
and after this, will be feen to reſume her direct
proper motion eaſtward, and will at length
arrive at another ſuperior conjunction.-In the
courſe of ſuch a revolution, ſhe puts on all the
phaſes of the moon. Near the ſuperior con-
junction ſhe appears round like the Full
moon, but ſmall; after this, waning, like the
moon after the Full; tho' her diameter grows
Jarger, becauſe ſhe is coming nearer the earth.
At her greateſt elongation ſhe reſembles the moon
in the Quarters, and from thence to the inferior
conjunction is cuſpidated or horned, like the
moon from the laſt Quarter to the Change; that
hemiſphere, which is enlightened by the Sun,
being turned more and more from the Earth,
till in the conjunction itſelf, it is wholly turned
Her diameter now appears largeſt -
In
or
from us.

Le&t. I.
9
TRANSIT of Venus.
In all this time, being on the eaſtern ſide of the
Sun, ſhe ſets after him; and for her extraordi-
nary luſtre, is called, by way of eminence, the
Evening-Star. She paſſes thro' the ſame ſeries
of changes, but in an inverted order, from the
inferior conjunction to the fuperior, juſt as the
moon does from the Change to the Full ; and
in this interval, being on the weſtern ſide of the
Sun, and riſing before him, ſhe is called the
Morning-Star, Such are the phænomena of
Venus. -It may be obſerved by the
way,
that
thoſe of Mercury are altogether ſimilar ; and
that they demonſtrate beyond all doubt, thar
theſe planets perform their revolutions round
the Sun, and not round the Earth.
FROM what has been ſaid 'tis obvious to col-
lect, that it is only in the inferior conjunctions
that Tranſits can happen.--If the orbit of Ve
nus lay in the ſame plane as that of the Earth,
or the ecliptic, there would be a Tranſit ar
every inferior conjunction ; for in this caſe, the
planet would paſs directly between the Sun and
the Earth; and only her unilluminated fide be-
ing turned towards us, ſhe muſt appear
like
black ſpot upon the Sun's diſk. But the fact
is otherwiſe. The orbit of Venus is inclined to
the ecliptic in a certain angle, tho' but a ſmall
one, and interſects it in two oppofite points,
called the nodes. At one of them, the planet
croſſes the ecliptic from ſouth to north, which
therefore is called the aſending node ; tha
В
other,

The Use of the
Lect. I.
other, where ſhe is moving from north to ſouth,
is called the deſcending node. 'Tis only at thoſe
inferior conjunctions which happen ſo near one
of the nodes as to make Venus's latitude, or her
diſtance from the ecliptic, leſs than the apparent
femidiameter of the Sun, that we can have a
Tranſit; at all others, Venus will paſs clear of the
Sun, either to the north or ſouth ; and that,at ſo
much
greater
diſtance as ſhe is farther from her
nodes. And for this effect, the Sun muſt be
within 2 degrees of a node ; which arc he goes
over in 2 days. In this
age
and the next, the
nodes being ſituated near the middle of Gemini
and Sagittarius, where the Sun is the 4th of
June, and 7th of December, Tranſits can hap-
pen only at thoſe times of the year ; that is, be-
tween the 2d and 7th of June; and between
the 5th and 1 oth of December. I ſhall confine
myſelf at preſent to thoſe which happen in
June, when the planet is at its deſcending node,
fince it is with theſe we are more immediately
concerned. The conjunctions ſuccede one ano-
ther after an interval of about 584 days, or
year and 7 months; as is caſily computed from
the period of the Earth, which is nearly 365
and that of Venus, which is 224.
When a Tranſit happens in the beginning of
June, there cannot be another at the ſame node,
till there is another inferior conjunction in the
beginning of June, within the limits of the
four days juſt ſpecified. This will not be, till
the interval of 584 days, repeated ſome number
of
I
days ;

Lect. I.
II
TRANSIT of VENUS.
years : More
er.
of times, will make nearly fome number of
years. To find when this may happen, reduce
the ratio, 584: 1365, to its leaſt terms, and
you
will find it to be as 8:5; which ſhews
that 5 of theſe intervals make 8
accurately, they make 8 years wanting 2 days,
7
hours, which defe&t falls within the limits
above aſſigned. This then is the ſhorteſt peri-
od in which one Tranſit can follow another..
The ſeveral conjunctions in this period ſuccede
in the following order; June 6 ; January 11 ;
Auguſt 14 ; March 25; October 25 ; and June
3. And this order is repeated in the next peri-
od ; only the conjunctions happen 2 days ſoon-
As the laſt of theſe Tranſits comes earlier
in the year, and ſo the planet is not got ſo far to
the eaſt as it was at the firſt, while the node re-
mains nearly in the ſame place, it neceſſarily
happens that the planet now deſcribes a differ-
ent path from what it did before. By calculation
we find that its path the laſt time is near 20 mi-
nutes more northerly than the firſt. And as the
femidiameter of the Sun is near 16 minutes, if
at the firſt of theſe conjunctions Venus paſt
more than 4 minutes to the South of the Sun's
centre, this laſt more northerly path will ſtill
fall within the Sun's diſk on its northern half,
and there will alſo be a Tranſit at the laſt of
the conjunctions. This was the caſe in the
Tranſit of June 1761, when Venus paft near
10 minutes South of the Sun's centre; which is
the reaſon why we ſhall have another in June
this
B 2

The Use of the
Lect. I.
this preſent year, in which the planet will paſs
10 minutes North of the Sun's centre. But if
in any, Tranſit Venus pafs within 4 minutes
South of the Sun's centre, or to the North-
ward of it, in the conjunction 8 years after ſhe
will paſs quite to the North of the Sun's diſk,
and there will be no Tranſit. Accordingly, in
the conjunction which will happen June 1, 1777,
Venus will paſs near 30" north of the Sun's
centre, and 14" from his northern limb. -
Thus you ſee that there cannot be another
Tranfit after two conſecutive periods of 8 years.
Let us inquire when there can be another.
ing lao: bo
From the foregoing account of the order in
which the conjunctions ſuccede one another, it
appears that the conjunction which happens
neareſt after the 3d of June, in the courſe of
the year, is on the 12th of Auguſt. There
will therefore be no other Tranſit at the def-
cending node, till the conjunction which falls on
the 12th of Auguſt, by anticipating at the flow
rate of 2 days, 7 hours, in 8 years, has got back
to the 7th of June ; which is 66 days. This
cannot be done in leſs than 29 of theſe periods
of 8 years, or 232 years, which make 235 years
from the preceding Tranſit. Nor will it be
done then, unleſs at the preceding Tranſit Ves
nus paſt above 5" north of the Sun's centre;
otherwiſe it will take 8 years more to ac-
compliſha it. Upon theſe grounds we find, that
beſide the two in 1761 and 1769, no Tranſit
has

Lect. I.
13
TRANSIT of VENUS.
has happened at this node, in the beginning
of June, ſince the year 1526, nor will again
till 2004.-The foregoing remark clears up
what at firſt fight appears fo paradoxical, that
there ſhould be two Tranſits at the ſame node
in 8 years, and no more in ſo long a period.
otodt oli ainsil13A
Minst lendu 20 on!
JUANOTHER may indeed happen before the
year 2004, at the oppoſite node. For, agreable
to the account of the order in which the con-
junctions ſuccede one another, we ſhall find
that, after a Tranfit on the 3d of June, the next
conjunction will fall on the oth of January;
which is but a month after the time of year
when Tranſits may happen at the aſcending
node. The conjunctions going back ſomewhat
quicker at this node, viz. 2 days and about it
kours in 8 years, this ſpace of a month may be
gone over in 13 of theſe periods, that is, in
104 years ; or, reckoning from the preceding
Tranſit
, in 105 years and an half. According-
ly, the next Tranſit will be on the oth of De-
cember in the year 1874; which will be fol-
low'd by another in 8 years, and then there will
be no more in December till the year 21-17.
Thus the 2oth century will paſs without a
Tranſit.
So extremely rare are theſe phænomena. And
in fact, till that which was obſerved in 1761,
there never had been but one ſeen ſince the cre-
ation. This was in December (N. St.) in the
year

14
Le&t. I.
av The Use of the
year 1 639; and it was ſeen by two perſons only;
Jeremiah Horrockes, a young Engliſh Aftrono-
mer, of an admirable genius, who was the only
perſon that predicted it, and a friend of his,
William Crabtree. And when this of nextJune
is paſt, the preſent race of mortals may take their
leave of theſe Tranſits; for there is not the
leaſt probability, that any one who ſees this, will
ever ſee another.
soiloqa
- 100 tit doitwa
i bio oro
On account of their rarity alone, they muſt
afford an exquiſite entertainment to an aſtrono-
mical taſte. But this is not all. There is ano-
ther circumſtance which ſtrongly recommends
them. They furniſh the only adequate mean of
ſolving a moſt difficult Problem,--that of deter-
mining the true diſtance of the Sun from the
Earth. This has always been a principal object
of aſtronomical inquiry. Without this, we can
never aſcertain the true dimenſions of the ſolar
ſyſtem and the ſeveral orbs of which it is com-
poſed, nor aſſign the magnitudes and denſities of
the Sun, the planets and comets; nor, of conſe-
quence, attain a juſt idea of the grandeur of the
works of GOD. Such as are unacquainted with
this ſcience, are apt to look upon every thing
that can be advanced with relation to this inqui-
ry, as at beſt but mere conjecture. 'Tis how-
ever true, that methods have been propoſed for
this purpoſe, which ſhew the great acuteneſs of
the inventors, and are founded on mathematical
demonſtration. The grand defect of them was,
that

Le&t. I.
IS
TRANSIT of VENUS.
that they required obſervations which could not
be made with ſufficient exactneſs. And this is
the reaſon why ſo capital a point has not as yet
been duly ſettled.---This important uſe of the
Tranſits of Venus was firſt pointed out by the
ſagacious Dr. Halley in the year 1691, and large-
ly explained by him in the Philoſophical Tranſ-
actions in 1716, when that great Aſtronomer,
deſpairing, by reaſon of his
age, to reach ſo
diſtant a period, moſt earneſtly left it in charge
to the Aſtronomers who ſhould be on the ſtage,
that with this view they would ſtrenuouſly and
with all their might apply themſelves to make
obſervations, in diſtant parts of the world, of
the Tranſit in 1761 ; but eſpecially, that of the
preſent year, on account of a peculiar advantage
attending it, which we ſhall hereafter explain.--
It will not be eaſy to give a diſtinct account of
the ſeveral ſteps in the method of applying theſe
phænomena to this purpoſe, without the uſe of
diagrams, which are not ſutable to this place. I
ſhall, notwithſtanding, endeavor to convey to
you as clear an idea as I can, of the general
inethod ; and, in order to it, ſhall trace things
from their firſt principles.
To find the diſtance of one object from ano-
ther, the firſt way that preſents itſelf is, to repeat
a known meaſure ſucceſſively till you have gone
over the whole ſpace between the objects. But
this ſuppoſes one of them to be acceſſible, from
the other, If it is not, the method is imprac-
ticable,

16
Lect. I.
The Use of the
ticable, and we muſt have recourſe to ſome
other. The properties of a plane triangle fup-
ply us with another. If two angles of a tri-
angle are given, the third is given too; and the
proportion of the ſides is alſo given; and there-
fore, if one of the ſides be given in magnitude,
the others are given in magnitude alſo ; as ap-
pears
from Euclid's Data. In other words, If
we can obſerve two angles of a triangle, and
meaſure the length of one ſide, we can find
the length of the other ſides. To apply this to
the caſe of meaſuring a diſtance on the land or
fea. Suppoſe we obſerv'd an object to bear
due north from us, but having moved one mile
to the eaſt, we find the object now bears N. W.
Here, by drawing lines thro' our ſtations and
the object, a triangle is formed, two of whoſe
angles are known ;-the angle at the firſt ſtati-
on, which is 90°; and the angle at the object,
which is 45º. One fide is alſo known, viz. the
diſtance between the ſtations. From theſe
Data, it is eaſy to find the diſtance of the ob-
ject, and that with the ſame degree of accuracy
as the obſervations can be made.
ſent ſuppoſitions, the diſtance of the object from
the firſt ſtation is equal to the diſtance between
the ſtations, that is, one mile. If the object
were moved, provided its motion were known,
its diſtance might be found on the ſame princi-
ples. This method is rendered univerſal by
trigonometry, and may be extended to aſtrono-
mical as well as geographical diſquiſitions. The
known
On the pre-

Lect. 1.
17
TRANSIT of VENUS.
known diſtance between the ſtations is uſually
called the baſe ; and the angle at the object, the
parallax. This is a greek word, which ſignifies
a change ; and is uſed to denote that change in
the apparent place of an object, which is occafi-
oned by changing the obſerver's ſtation.
CONCERNING this change or parallax, we
muſt make a few Remarks, which will be of
uſe to us in the ſequel.
11. That the parallax is always made the con-
trary way to that which the obferver has moved.
As, if he move Eaſt, the object feems to have
moved Weft ; if he move North, that moves
South; if he upward, that downward, &c.
2. The parallactic angle is ſo much the leſs, as
the baſe is more obliquely ſituated in reſpect of
the diſtance of the object. It is alſo leſs,
3. As the baſe is leſs than that diſtance.
THE firſt of thefe Remarks is evident from
the nature of parallax ; the two laſt, from the
properties of a triangle.
From the laſt Remark it appears, that this
method is fubject to limitations in practice jums
owing to the limits which nature has preſcribed
to our ſenſes. For when the bafe is the fanc,
the parallax is leſs, as the diſtance of the object
C
is

18
Lect. I.
The Use of the
is greater ; and vice verſa. Therefore if the
baſe be very fmall in reſpect of the diſtance of
the object, the parallactic angle may be ſo ſmall,
that it may be extremely difficult to obſerve it.
Thus, if we ſhould attempt to find the diſtance
of an object, which was 20 miles or more, by
changing our ſtation only 5 feet, the parallactic
angle would not be quite 10 ſeconds; which is
ſo ſmall that it can ſcarcely be obſerved, even
with
very
nice inſtruments. In ſuch ſmall angles,
the convergence of the lines is ſo flow, that a
fmall error in obſerving the angle will make a
great difference in the diſtance of the point of
interfection.
It is plain enough, that our hopes of finding
the diſtances of the heavenly bodies, with any
certainty, muſt be built on obſervations of their
parallaxes. If the diameter of the Earth bear
any ſenſible proportion to the diſtance of an
heavenly body, that body muſt be fubject to a
parallax, of ſome quantity or other ; that is, it
muſt appear in different points of the farry
heaven, when view'd from different parts of the
Earth. For this reaſon, Aftronomers reduce all
obſervations, wherever made, to the centre of
the Earth, which they conſider as the only true
point of view. The femidiameter of the Earth,
then, is the baſe which fubtends the parallactic
angle. Indeed, if we compare obſervations
made in oppoſite parts of this globe, then the
whole diameter of it will become the baſe, and
will

Lect. I.
19
TRANSIT of VENUS.
will ſubtend the ſum of the two parallaxes.
And this is the greateſt baſe we can poſſibly
get, for inveſtigating theſe parallaxes.
The immediate effect of parallax is, to make
a ſtar appear below its true place, according to
our firſt Remark; becauſe the Obſerver is above
the centre of the Earth. But while parallax
alters the poſition of a ſtar in reſpeat to the
horizon, it muſt alter it, to the other circles of
the ſphere too, as the equator, ecliptic, &c. and
thus it alters the times of the ſtar's arrival at
thoſe ſeveral circles. When a ſtar is in the
horizon, its parallax is greateſt ; that femidia-
meter of the Earth,at the end of which the ob-
ſerver is placed, being then directly oppoſite to
the parallactic angle, and perpendicular to the
diſtance of the ſtar. So that the horizontal
parallax of any ſtar is equal to the angle under
which the ſemidiameter of the Earth would
appear, if ſeen from that ſtar. As the ſtar riſes,
this femidiameter becoming more oblique, the
parallax diminiſhes, according to the ſecond
Remark. And if the ſtar comes to the zenith,
the parallax vaniſhes ; the ſtar then appearing in
the ſame place as if it were viewed from the
centre of the Earth. For the contrary reaſon,
when a ſtar is deſcending towards the horizon,
its parallax muſt increaſe.
Hence it appears, that if one perſon could
obſerve the place of the Sun or a planet, in the
Harry heaven, when in his zenith, and another
C 2

20
Lect. I.
The Use of the
at the ſame time, at the diſtance of 90', obſerve
it in his horizon, the difference of the two ob-
ſery'd places would be the horizontal parallax
fought. But this method, eſpecially with re-
gard to the Sun, tho' the moſt obvious of all, is
attended with inſuperable difficulties. And in-
deed, ſo are all other methods of attempting the
Sun's parallax, immediately. But, happily, we
are under no neceſſity of confining ourſelves to
this. As we know the proportion of the pa-
rallaxes of the ſeveral planets, if we can diſcover
the real quantity of any one of them, we diſ-
cover all the reſt. We are therefore at liberty
to chooſe that which we find moſt convenient;
and, according to our 3d Remark, thát planet
will be moſt convenient, which comes neareſt to
the Earth. This limits the inquiry to Mars, of
the fuperior planets ; and Venus, of the inferior.
Mars, in his oppoſition to the Sun, at his mean
diſtance, is but little more than half ſo far from
us as the Sun is, their diſtances being then near-
Jy as 11 to 21; and therefore his parallax then
is almoſt twice as great as the Sun's. But if he
bein his perihelion at the ſame time, f he comes
conſiderably nearer, his diſtance being to the
Sun's as about 8 to 21 ; and fo his parallax is
proportionally greater. Venus in her inferior
conjunction is but little more than one quarter
ſo far from us as the Sun is, and therefore her
parallax almoſt four times as great as his. This
therefore is the moſt advantageous circumſtance.
But
+ As he was 13th Aug. 1766; but will not be again in niany years.

Lect. I.
21
TRANSIT of VENUS.
But a Tranſit of Venus is the moſt favor-
able conjuncture of all, becauſe the limbs of
the Sun afford the beſt terms with which to
compare the planet; and inſtead of trying to
obſerve the parallactic angles, which are extremely
ſmall, it is much better to obſerve the differences
of time, occaſion'd by them, which are much
more ſenſible. For Venus on the Sun moves I
ſecond of a degree in 15 ſeconds of time.
Now a ſecond of time is very perceptible ; but
a ſecond of a degree can ſcarcely be diſcerned;
much leſs can i part of a ſecond be ſo. The
beſt obſervations will be, when the planet is in
contact with the Sun's limbs, at its immerſion
and emerſion ; the moments of which may be
determined with great accuracy, if the air be
clear, by ſuch as are furniſhed with good
aſtronomical inſtruments, and are expert in the
uſe of them.
If it be enquired, whether the Tranſits at
one node have any advantage above thoſe at the
other, the anſwer is, that, cæteris paribus, thoſe
in December, at the aſcending node, are pre-
ferable. The reaſon is, Venus is then about it
part nearer to us than in June. But this ad-
vantage, cho' real, may be much overbalanced
by other circumſtances, which we ſhall mention
when we come to explain the manner in which
the parallax may be deduced from ſuch obſerva-
tions. But this muſt be the ſubjest of another
diſcourſe.
Read, 1 March 1769.
LECTURE


(23)
LECTURE II.
IN
N the concluſion of the laſt diſcourſe we re?
marked that a Tranfit of Venus is the moſt
favorable conjuncture that can offer, for
inveſtigating the parallax of the Sun and
planets ;-a fundamental element in aſtronomy,
which neceſſarily enters into the theory of thoſe
bodies; and yet is extremely difficult to be fettled
with exactneſs by its being ſo very ſmall, as al-
moſt to eſcape the moſt critical obſervation. It
was farther remarked, that the beft method for
this inveſtigation is, to obſerve the differences of
time occaſioned by parallax, at the ingreſs and
egreſs of the planet. Our next buſineſs then is
to inquire, in what manner the times of theſe
phaſes will be affected by Parallax in differ-
ent parts
of the Earth. They will be affected
both by the difference of Longitude, and the
difference of Latitude. There is accordingly,
á parallax in Longitude, and a parallax in Lati-
tudet. The former alters the time,as thcObſerver
is
# In Geography, Longitude and Latitude are referred to the Equator;
in Agronomy, to the Ecliptic. This diſtinction was bere paſt.
over, to avoid embaraſſing the ſubject ; and there was the less
need to infift upon it, becauſe in the preſent caſe, the former
neceffarily involves the latter'.

24
Lect. II.
The Use of the
ás farther Eaft or Weſt; the latter, as he is far-
ther North or South. Their effects, tho'blended
together, muſt be examined feparately. We
begin with the parallax in Longitude.
HUTZ
Let us ſuppoſe an Obſerver on ſuch a place
of the Earth, as that he can ſee the firſt external
contact of Venus, when the Sun is in his Ze-
mith, and therefore at Noon : He fees this con-
tact without parallax, that is, at the fame inſtant
of time as he would, if he could ſee it from the
centre of the Earth. Suppofe another Obſer=
ver Weft from the former, and under a meridian
16 hours diftant. To him, the Tranſit will begin
at Sunriſe, in the lower half of the Sun. Both
the Sun and Venus being depreſs’d by parallax,
and Venus more than the Sun, becauſe nearer ;
at the time when the contact is formed to the
firſt Obſerver, it will not yet be formed to the
fecond ; but Venus's weſtern limb will be as
far diftant below the Sun's eaſtern limb, as her
parallax excedes the Sun's ; and the contact can-
not happen, till the planet has gone over this
diſtance, which is called her parallax from the
Sun. The contact therefore will not happen af
6 o'clock, but ſome time after. And if the two
Obſervers ſhould compare their obfervations ;
inſtead of finding the difference of the obferved
times of contact to be the ſame as the difference
of their meridians, viz. 6 hours, as they would,
if there were no parallax, they will find it to be
Jeſs than 6 hours.--Suppoſe a third Obſerver
6 hours

Leét. 11
25
TRANSIT OF VENUS.
6 hours Eaſt from the firſt. He will ſee the
Tranſit begin at Sunſet. As the Sun's eaſtern
limb, on which Venus eñters, is now the upper-
moft, 'tis evident that Venus, depreſs’d by pa-
rallax, will be brought into contact with this
limb, ſooner than if there were no parallax.
To this Obſerver, therefore, the contact will
happen before 6 o'clock; and upon a compäriſon
of this obfervation with the firſt, the difference
of the times will here alſo be found leſs than
6 hours, which is the proper difference of me
tidians; and as much leſs, as it was in the fore-
going caſe. But if the Weftern and Eaftern
obſervations ſhould be compared together, the
difference of their times from 12 hours would
be double of the preceding difference from 6
hours, when each of them was compared with
the Zenith obſervation. The fame thing is to
be ſaid of the firft internal contact ; as alſo, of
the two contacts at the egreſs. Each of theſe
phafes will happen later to thofe who ſee them
in the Eaſt, and ſooner to thofe who fee them
in the Weſt, than to thoſe who ſee them in the
zenith, or indeed, ticar the meridian.--You ſee
what a difference is made in the beginning and
end, by the parallax in Longitude:
From hence it follows, in the ſecond place,
that the whole duration of the Tranſit will be
alter'd by this parallax in Longitude. If oir
Weſtern Obferver, whơ fees the beginning in
the Eaſt, and therefore later, could travel fo far
Eaſtward as to fee the end in the Weſt, and
therefore

26
Leet. 11.
The Use of the
therefore fooner, it is plain that the duration of
the Tranſit would be ſhortened to him. The
rotation of the Earth produces thc fame effect :
It tranſports anObſerver from Weft to Eaſt, du-
ring the continuance of the Tranſit; fo that he,
who ſaw the beginning in the Eaſt, may ſee the
end in the Weft. On this account, the Tranſit
will be ſhorter to thoſe parts of this globe, which
have the beginning of it in the Morning, and
the end in the Afternoon, than it would be as
ſeen from the centre of the Earth. And it is
not neceſſary that the obſervation fhould be
made in a place where the middle of the
Tranſit happens juſt at noon - It is ſufficient, if
it be within an hour or two, before or after it.
The contraction of the duration will be much
the fanie, if the Latitude be the ſame. The du-
ration will be moſt contracted, on this account,
from the northern tropic, near which the Sun
will then be, to the equator. From theſe li-
mits, cither to the north or fouth, it will fill be
contracted, tho' not fo much; becauſe the de-
grees of the parallels of Latitude, which meaſure
the baſe of the parallactic triangle, or the ſpace
thro' which theObferver is carried eaſtward,grow
leſs as you advance toward either of the poles.
Sala
The reverfe will take place with refpect to ſuch
parts of the Earth as have the middle of the Tranſit
not far from midnight, and tlrerefore ſee the be-
ginning in the Weſt, and the end in the Eaſt ;
which will be the caſe with places ſo far North

Lect. II.
27
TRANSIT of Venus.
as to have their night ſhorter than the duration
of the Tranſit. For, the beginning in the Weſt
being accelerated by Parallax, and the end in
the Eaſt, retarded, it is manifeft that the whole
duration muſt be protracted, and be longer than
it would be, as feen from the centre of the
Earth. Or the thing may be conſidered in this
light. Where the middle is near noon, the Ob-
ſerver is carried, by the rotation of the Earth,
with a motion contrary to that of Venus; the
former being from Weſt to Eaſt, the latter from
Eaſt to Weſt. This accelerates Venus's apparent
motion on the Sun. But where the middle is
near midnight, the Obſerver, being on the op-
poſite ſide of the Earth, is carried in a direction
contrary to the former, and therefore the ſame way
as Venus ; and this retards her apparent motion
on the Sun. Theſe different effects of contrary
motions have been well illuſtrated by an ingenious
writer, Mr, Ferguſon (Aſtron. p. 39.).“ If two
6 birds, ſays he fly along fide of a ſhip under fail,
in contrary directions to each other, the bird
of which flies contrary to the motion of the ſhip
$$ will paſs by its whole fide fooner than the
o other bird will, which fies the ſame way as
© the ſhip fails,". The protraction of duration
in theſe northern parts on account of the paral-
lax in Longitude, will be diminiſhed as you ad:
yance toward the north pole, becauſe the pas
rallels of Latitude diminiſh. In the pole it-
ſelf, the protraction on this account would be
nothing; and it will be greateſt, in that Lati-
gude
D2

28
Lect. II.
The Use of the
tude where the night is but little ſhorter than
the Tranſit, and where confequently, the be-
ginning might be ſeen a little before Sunſet, and
the end a little after Sunriſe ; as it may be in
ſome places in the Latitude of 60°N. If theſe
lengthened durations, obſerved where the middle
is not far from midnight, he compared with thoſe
fhorten'd ones, where the middle is not far from
noon, the differences will be much greater than
if either of them were compared with the true
duration as ſeen from the Earth's centre.
The foregoing differences may be altered,
and made greater or leſs, by the parallas in
Latitude, which is the third particular we have
to ſpeak of. A perſon who ſees Venus in his
Zenith, fees her without parallax, and therefore
in the ſame place on the Sun as if th view
were taken from the centre of the Earth. One
to the Southward of the former, will ſee Venus
more Northerly on the Sun; and one to the
Northward, more Southerly ; according to the
firſt Remark we made concerning parallax,
For this reaſon, if a plane bé conceived to paſs
thro' the centre of the Earth and that little arc
of Venus's orbit which falls within the Sun's
diſk, all the inhabitants of the Earth, when to
the Southward of that plane, fee Venus with
Northern parallax of Latitude ; that is, they
ſee her more Northerly on the Sun, than the
would appear, from the centre of the Earth;
and all to the North ward of it fee her with a
Southern

Lect. II.
29
TK ANSIT of VẺ NƯs.
Southern parallax ; but all in the plane it ſelf,
fee her without any parallax of Latitude. Such
a plane, about the place which is in the middle
of the Earth's enlighten'd diſk, where the Sun
is in the Zenith, will croſs the furface of the
Earth juſt within the tropic of Cancer ; on the
Weſtern ſide of that place, it will paſs more
Southerly ; and on the Eaſtern, in general,
more Northerly ;
-by reaſon of the incli-
nation of Venus's orbit to the equator.—The
effect of this parallax is, to make the planet ap+
pear to pafs at different diſtances from the Sun's
centre, and conſequently to deſcribe chords of
different lengths on his diſk ; and thus it will
vary the duration of the Tranfit. The variations
on this account will be ſo much greater, cæteri
paribus,as the path of Venus on the Sun is farther
from his centre ; becauſe the farther the chords of
a circle are from the centre,ſo much quicker they
alter in length. The change of duration by
this parallax will not be made the fame way as
by the parallax in Longitude, if the Declination
of the Sun and the Latitude of Venus are of
differenç denominations, one North, the other
South ; but when they are of the fame deno-
mination, the change will be made the ſame
way ; and the difference of duration in diſtant
parts of the Earth will be more conſiderable in
the latter cafe than in the former. In June the
Declination of the Sun is North, If Venus paft
South of the Sun's centre, the inhabitants of
the Southern part of our globe, who would ſee
her

30
Lect. II.
The Use of the
her about noon with a Northern parallax of
Latitude, would ſee her paſſing nearer to the
Sun's centre, deſcribing a longer chord, and
conſequently continuing longer within the Sun.
But to the inhabitants of this part of the globe,
the duration would be ſhortened by the parallax
in Longitude ; as we ſhew'd under the ſecond
article.- On the other hand, where the middle
was near midnight, and where the duration
would be protracted by the parallax in Longi-
tude, the inhabitants being in a high North La-
titude, would ſee Venus with a conſiderable
Southern parallax of Latitude, which would
carry her farther from the Sun's centre, and by
making her deſcribe a ſhorter chord on his diſk,
would sorten the duration of her Tranfit.
Thus, in the ſuppoſition, that Venus paft South
of the Sun's centre, the parallaxes in Longitude
and Latitude would counteract one another
one would ſhorten the duration in the ſame
parts of the Earth where the other lengthens it ;
which would diminiſh the difference between
them. This was the caſe in 1761.-But in the
Tranfit of the preſent year, the contrary will
happen. Venus will now paſs North of the
Sun's centre; and therefore moſt of the inha-
bitants to the Southward of the tropic of
Cancer, who have the middle of the Tranſit
within an hour or two of noon, and ſo have
the duration of it contracted by the parallax in
Longitude, will ſee the planet, with a Northern
parallax in Latitude, in a more Northerly path,
that
;

Lect. II.
38
TRANSIT of VENUS.
that is,paſſing farther from the Sun's centre, and
confequently deſcribing a ſhorter chord, and
having a ſhorter duration within the Sun. And
tho' the parallax of Longitude is not quite fo
great in the high Southern Latitudes, as between
the equator and tropic of Cancer, yet the paral-
lax of Latitude is ſo much greater as to more
than make amends for it. On the other hand,
where the middle is near midnight, and the du-
ration protracted by the parallax of Longitude,
there the inhabitants, on account of their high
North Latitude, muft ſee Venus with a conſider-
able Southern parallax of Latitude. Her path
will therefore to them appear not ſo far to the
North, but nearer the Sun's centre, and conſe-
quently longer. In the caſe therefore of the
preſent Tranſit, the parallaxes of Longitude and
Latitude conſpire to produce the fame effects;
both of them ſhorten the duration in the
Southern parts of the Earth, and both lengthen
it in the Northern. This is the peculiar ad-
vantage, hinted in the preceding diſcourſe, which
the next Tranſit will have above the laſt, for af-
certaining the exact quantity of the Sun's paral-
lax. The general method of doing which you
may now eally underſtand.
FROM what has been ſaid, it appears that there
are two ways in which the obſervations of this
celebrated phænomenon are applicable to the
preſent reſearch. Obſervations of only the
beginning or end, made in different places,
may

.BUV The Use of the Lest. II.
5 10
may be compared ; or, obſervations of the
whole duration may be compared. It will be
cafy to obtain many more obſervations of the
former kind than of the latter, becauſe a great
number of places on the Earth are fituated, fo as
to fee one or other of theſe phaſes, which are not
able to ſee them both. You perceive that pa-
rallax differs in its operation in various parts of
the Earth, both in kind and in degree : In
fome, it accelerates ; in others, it retards ;
and that, more or leks, according to the dif-
ferent fituation of the places. And in each
place, its effect will be greater or leſs, in the
fame proportion as the Sun's total or hort-
zontal parallax is greater or leſs.od do
wel vloep
bn In the former way of proceding, the obu
ſerved times of the beginning or end muft
be compared with the difference of the meridi-
ans where the obfervations are made ; and any
exceſs or defect found between them is owing to
the operation of parallax; and from the quantity
of this exceſs or defect, the quantity of the
Sun's parallax may be calculated. The method
of calculation is indirect, or tentative. The
Sun's parallax is aſſumed to be of a certain
quantity, namely, that which from former
obfervations we know to be, either the truth,
or at left, very near it; and from hence, the
effects of parallax both in Longitude and La-
titude muſt be computed for each place
obfervation - the particular procefs of doing
which,
of

Lect. It.
33
TRANSIT of VENUS.
which, may more properly be explained elfe-
where. The total effect of both parallaxes
being thus found by computation, ſo as to get
the difference of times when the phaſes of the
Tranſit ſhould happen in each place ; if the oba
ſerved difference comes out the ſame as the cala
culated, it will be certain the Sun's parallax was
rightly aſſumed ; but if the obſerved difference
turns out greater or leſs than the calculated, it
will follow that the true quantity of the Sun's
parallax is greater or leſs than that which was
aſſumed. To explain this by an example. The
difference of meridians between the Royal Ob-
fervatory at Greenwich and this
, is 4' 44'. By
calculation we find, that aſſuming the Sun's pa-
rallax to be 8", 55, as it was found to be nearly
by the laſt Tranſit, the external and internal
contacts, at the beginning of the next, will be
accelerated by Parallax 7 minutes of time af
Greenwich ; happening there but a little before
Sunſet, when parallax has its greateſt effect.
With us, where it will begin aboué half an
hour after II, when the Sun is about $4° high in
the weſtern hemiſphere, the contacts will be ac-
celerated by parallax but 4 minutes. Therefore,
if obſervations be made in both places and con-
pared, the times ſhould be found to differ bue
4' 41'; which falls ſhort of the difference of
meridians, by 3'. This is on the fuppofition
that the Sun's parallax is 8", 55 ; a parallax of
this quantity being juſt fufficient to produce here
this defect of 3 minutes. A greater parallax
E
would
ز

34
Lect. II.
The Use of the
would produce a greater defect ; and a leſs pa-
rallax, a leſs defect. If therefore the obſerved
difference of the times ſhould be found greater
or leſs than 4' 41', and conſequently its defect
from the difference of meridians greater or leſs
than 3 minutes, the inference muſt be, that the
Sun's true parallax is greater or leſs than 8”,55, in
the fame proportion. Whereas ſhould this de-
fect appear to be exactly 3 minutes, we might
be affured that theSun's parallax is exactly 8", 55.
Thus ſhall we obtain the true value of the Sun's
parallax.—In this example, which is deſigned
purely for illuſtration, I have taken no notice of
the ſeconds of time. But it is of the higheſt im-
portance, that in making the obſervations they
ſhould be attended to with the moſt critical ac-
curacy. And herein lies one great advantage
of theſe Tranſits above every other phænomenon
that can be uſed for finding the parallaxes of
the planets, namely, that the obſervations can be
made with much greater exactneſs. For the times
of Venus's contacts with the Sun's limb
may
be
determined, by experienced Obſervers and in
favorable circumſtances, within a very few
feconds ; as was intimated before.
As the two places in this inſtance differ not
much in Latitude, which is North in both ; and
the obſervations in both muſt be made in the
Afternoon, and ſo the operation of parallax is
alike in both, viz. to accelerate the beginnings
there is a difference of only 3 minutes of time,
occafioned

Lect. II.
35
TRANSIT of VENUS.
occaſioned by the parallax. If the Greenwich
obſervation ſhould be compared with one made
in South latitude, and in a place ſo far Weſt as
to have the beginning happen in the Morning,
where the effet of parallax will be contrary,
and retard the beginning, the difference would
be more conſiderable. But to take the utmoſt
advantage of theſe obſervations, we ought to
make the difference of time as great as poſſible ;
and therefore, the afternoon obſervation ſhould
be made in ſome place where the beginning
happens not long before Sunſet, but yet long
enough to have the Sun of a ſufficient height;
and where the planet will be ſeen to enter on
the higheſt point of the Sun ; for then parallax
will have its full effect in accelerating the con-
taets, by depreſſing the planet directly downward
upon the Sun's limb. This place I find to be
near the latitude of 50° N, and about a quarter
of an hour Eaft of Greenwich. But Greenwich
itſelf, or indeed any part of Great-Britain or
Ireland, will ſerve very conveniently for this ob-
ſervation. The correſponding obſervation, to
be
compared with this, ſhould be made, if pof-
fible, in a place where the beginning happens
not long after Sunriſe, and the planet enters on
the loweſt point of the Sun ; for then parallax
has its full effect in retarding the contacts, by
depreſſing the planet directly downward from
the Sun's limb. The place where this will hap-
pen, is nearly oppoſite or antipodes to the
former, in the Southern part of the great South
Sea,

36
Lect. IL
The Use of the
Sca, nor far from which is marked on our
globes a tract of land but little known, called
New Zealand. If an obſervation could be
made there, it would be found to differ from
the Greenwich obſervation about 14 minutes of
time ; the difference being double of what it
would be, if each were compared with an ob-
ſervation in the Zenith, which might be made
on the weſtern coaſt of Mexico, juſt within the
tropic.-All this is as applicable to the egreſs of
the planet, as to its ingreſsi; Only the ſtations
muſt be different. The egreſs will happen ſooneſt,
in the loweſt point of the ſetting Sun, in the
South ſeą, near the tropic of Capricorn, and
meridian of California ; and lateſt in the
higheſt point of the riſing Sun, in Arabia ; the
difference being about 14 minutes, as before.-
To diſmiſs this head, it is plain, that in this way
of inveſtigating the Sun's parallax, it is abſo-
lutely neceſſary to have the Longitudes of the
places of obſervation determined with the moſt
rigorous exactneſs; for the ſucceſs of the
whole depends on comparing the obſerved dif-
ferences of time with the known difference of
meridians.
The other way of deducing the Sun's paral-
lax is, by comparing obſervations of the whole
duration of the Tranſit, made in diſtant places,
From the preceding diſcourſe it appears that to
the inhabitants of the Southern parts of this
globe, who have the middle of the Tranſit about
Noon,

Lect. II.
37
TRANSIT of VENUS.
Noon; as will be the caſe in the South Sea, the
duration of it will be ſhortened by both paral-
laxes; and that to the inhabitants of theNorthern
parts, who have the middle of the Tranſit in the
night, or when the Sun is near the North part
of the meridian, below the pole, the duration
will be lengthened by both. This will be the
caſe in Lapland. But here again, fuch ſtations
ſhould be choſen as will make the greateſt dif-
ference in the duration. The beſt places for
the latter obſervations will be near the polar
circle, rather within it, and about 20° or 30°
Eaſt from London ; between the bottom of the
gulph of Bothnia and the North Cape. There,
the duration between the internal contacts will
be about 5" 54'; and this is the longeſt that will
be any where ſeen. And the beſt for the former
will be in the ſouthern part of the South fea,not
far from the oppoſite meridian. It is not in-
deed known, whether there be any land ſituated
in that part of the globe. Nor is there any
known place, that can ſee the end of the Tranſit,
nearer to it than Mexico, in the Latitude of
20° N. and in that place there will be hardly
any parallax of Latitude, Mexico being very near
the plane paſſing thro' the centres of the Earth
and Venus. But by the parallax of Longitude
alone, the duration will be made about 18 mi-
nutes ſhorter there than in Lapland. If an ob-
ſervation could be procured in the Latitude of
55° S. where the parallax of Latitude as well as
that of Longitude will have a great effect, thedu-
ration

38
Lect. II.
The Use of the
ration would not be above 5* 30'; that is, no
leſs than 24 minutes ſhorter than in Lapland;
which is ſo conſiderable a difference, that the
Sun's parallax muſt be aſcertained by it to vaſtly
greater exactneſs than can be done any other
way. And in this way, there is no need of
being ſcrupulouſly nice as to the Longitudes of
the places of obſervation : A conſiderable error
in them, even of ſeveral degrees, will only make
the difference of a few ſeconds in the duration.
THERE is yet a third way of deducing the
parallax, and that is, from obſervations of the
leaſt diſtance of Venus from the Sun's centre, at
the middle of her Tranſit. But this diſtance
being uſeful, chiefly as it ferves to determine the
total duration, I need not enlarge upon it.-I
may add, however, that if an obſervation could
be made of this leaſt diſtance, in the Latitude of
63° N. and Longitude of 60° E. from London,
where the middle will happen at Sunriſe; and
another in the oppoſite place of the Earth,
where it will happen at Sunſet, the compariſon
of theſe two diſtances would give the double of
Venus's parallax from the Sun, immediately and
without calculation. The former place is in
Siberia, the latter in the unknown ſouthern
parts of our globe, and probably inacceſſible,
An obſervation at the former might, notwith-
tanding, be compared, to advantage, with a
fimilar

Lect. II.
39
TRANSIT of VENUS.
ſimilar one made in any high ſouthern Latitude.
-But enough of this.
In conſequence of Dr. Halley's recommen
dation, great endeavors were uſed to have the
Tranſit in 1761 duly obſerved. The approach of
this intereſting and long-expected phænomenon
excited the curioſity of every one who had the leaſt
reliſh for Science; & engaged Aſtronomers, where-
ever ſituated, to employ all their ſkill and care in
mak ſo critical and delicate an obfervation.
The moſt learned Societies & the firftMonarchs
in Europe exerted their influence and power
with emulation on this ſingular occaſion. It is
beſide the preſent purpoſe to give a detail of the
ſeveral obſervations that were made: They may
all be ſeen in the Philoſophical Tranſactions. I
ſhall content my ſelf with mentioning thoſe
which were made at the greateſt diſtances from
the Royal Obſervatory at Greenwich. The moſ
Northern place the Tranſit was obſerv'd at,was in
EUROPE, namely, Tornea in Lapland ; almoſt
under the polar circle.--In Asia, it was obſerved
at Tobolſk, the capital of Siberia, by a French
Aſtronomer, who performed a journey thither
of
4000 miles from Paris, at the inſtance of the
Imperial Academy of Sciences at Peterſburg, and
under
+ My ſubject did not lead me to ſpeak of the uſe of Tran lite
in determining Longitudes ; tho' thoſe of Venus, and
of Mercury too, of which laſt there are 13 or 14 in 100
years, are certainly one of the beſt means in the world
for this purpoſe, when once the parallax of the Sun is
exactly determined.
و

40 **U7 The Use of the Lect. Il.
under the Auſpices of the Czarina. This place
was fartheſt Eaſt. It was obſerved befides at
Madraſs, which was fartheſt South-eaſt, under
the direction of the Eaſt-India Company of
London. The French King alſo commiſſioned
two Members of his Royal Academy of
Sciences, to make the obſervation in the Eaſt-
Indies.-In AFRICA, it was obſerved only at
the Cape of Good Hope : It would have been
fo at St. Helena too, had not clouds pre-
vented; by Aftronomers fent to thoſe places by
the Royal Society, at the expence of his late
Majeſty K. GEORGE II. The Cape of Good
Hope was the fartheſt South.-In AMERICA, it
xvas obſerved only at St. John's Newfoundland;
and that at the expence of the Province of the
Maſſachuſetts-Bay. And this place was the
fartheſt Weft.
THESE obfervations and all the others were
collated, and the proper computations and con-
clufions made from theni; with incredible in-
duſtry and patience, by the late ingenious Mr.
Short of London, F. R. S. tho' he was able to
make but little uſe of the ſecond method, viz. by
the total duration; the greateſt difference ob-
ſerved, which was that between Tobolſk and
Madraſs, amounting only to 2 minutes, 50
ſeconds. In a Paper publiſhed in Phil. Tranſact.
for the year 1763, he has given the reſult of
the whole; which is, that the parallax of the
Sun, on the day of the laſt Tranſit, was 8", 56.
But

Led II.
41
TRANSIT of Vents.
But in a Letter he was pleaſed to write mie af
terward, dated London 23 July, 1966, he has
the following words. " I have, ſince the pub-
« lication of that Paper on the Sun's patallax
“ which you were pleaſed to approve of, col-
66 lected the obſervations of the late Tranſit
* made at many more places than I then had; ſo
" that by a compariſon of 43 places with the
"S obſervationi at the Cape [of Good Hope) the
“ mean reſult of the Sun's parallax, by the in-
“ ternal contacts, is 8", 545; and by the ex-
* ternal contacts, 8", 5518
ACCORDING to this laſt determination of
Mr. Short, I find the Sun's parallax at his mean
diſtance from the Earth to be 8", 68 ; and con-
fequently this mean diſtance to be 23,763 fe-
midiameters of the Earth. And as, by the
lateſt meaſures, à mean femidiameter of the
Earth is 3,957 miles, the intan diftance of the
Earth from the Sun is 94,030,000 miles nearly.
And in this we muſt acquieſce till the next
Tranfit; at which time, if the Aſtronomers
diſperſed in the ſeveral parts of this globe, prove
ſucceſsful in their obſervations, we ſhall be able
to determine the Sun's diſtance to a greater dea
gree of preciſion, and from thence aſcertain the
juft dimenſions of the whole fyftem. For,
CAR! has been taken in due feaſon to ſtation
Aſtronomers in ſome of the moſt ſuitable places
of the Earth. We are told that the Czarina
F
has

42
Lect. II.
The Use of the
has ſent out eight companies to the moſt northern
parts of her empiret, where the whole duration
will be viſible and of the greateſt length ; and
that the French King has fentObfervers to other
remote parts ; tho' we have not yet learned
the particular places of their deſtination.
The Royal Society with the aid of the Go-
vernment have fent feveral into the South
fea, who, it is to be hoped, will be able
to obſerve the duration where it will be ſhorteſt.
It was alſo propoſed to ſend fomeinto Hudfon's
Bay ; but whether they actually went, I am not
able to fay*. --The beginning may be feen in
Great-Britain and Ireland, and all over America ;
and the end, in the Eaſt-Indies ; but the begin-
ning happening before Sunriſe in the Eaſt Indies,
and the end after Sunſet with us, will prevent
obfervations of the whole duration. All Africa
and the biggeſt part of Eụrope will be entirely
deprived of this curious ſpectacle.
IT
+ It is a fortunate circumſtance for thoſe Northern Mif-
fionaries, who are gone to unknown parts of the Ruſſian
empire, that there is to be an eclipfe of the Sun on the morn-
ing of the Tranfit. This, if they have weather to obſerve
it, will enable them at once to fettle their Longitudes;
proper phænomena for which, feldom occur in thoſe re-
gions of perpetual day.-Extremely unfortunate it would
have been, had this eclipſe happened but 6 hours ſooner:
It would then have intercepted their view of the Tranſit.
* The equal-altitude and Tranfit-Inftruments for theſe
feveral aſtronomical Miffions, as well thoſe from France
and Ruffia as from Britain, were all made by the accu.
rate hand of Mr. Bird of London, who alſo made the
Inſtrument of that kind which lately arrived here for the
uſe of this College

Lect. II.
43
TRANSIT of Venus.
IT were greatly to be wiſhed that we could
obtain an obſervation of the whole duration, in
this quarter of the world. If made with ex-
actneſs, it would be a valuable addition to the
ftock of this ſort of obſervations, which, after
the utmoſt exertions, it is to be feared will be
but very ſmall; as there are but few places, at
leaſt that are acceſſible, in which both the be-
ginning and end will be viſible.* The neareſt
place to us at which an obſervation of this
ſort could be made, is Lake Superior, where the
end will happen a little before Sunſet. An ex-
pedition thither, I am ſenſible, would be at-
tended with difficulties ; but in ſuch an ex-
pedition, what are the difficulties, which love of
Science in Perſons poſſeſſed of wealth and
power, and reſolution in the undertakers, cannot
furmount ? I
2 !
CAT 077
I
* The only places which can ſee the whole of the Tranſit,
are, the South fea, thoſe parts of America which lie N.
W. of a circle drawn thro' the northweſt ſide of the
gulph of Mexico, Lake Huron, the ſouth end of James's
Bay, the eaſt end of Hudſon's ſtraits and the fouth part of
Greenland : Alſo, all within 67° of the N. pole, Kam-
ſhatka, Japon, the Ladrone Iſlands and New Zeland.
Extract of a Letter to the Author from a Gentleman of
the firſt diſtinction in the literary world, dated Lon-
don, July 2, 1768. " The Reverend Mr. Make-
“ lyne [ Aſtronomer-Royal at Greenwich ] wiſhes
« much that ſome of the Governments in North-
" America would ſend an Aſtronomer to Lake Superior
" to obſerve this Tranſit. I know no one of them more.
** likely to have a Spirit for ſuch an undertaking, or a
* Perſon and Inſtruments ſuitable, than the Maſſachu-
"5 ſetts. If your health and ſtrength were ſufficient for
"ſuch an Expedition, I ſhould be glad to hear you had
66 undertaken

The Use of the
Le&. II.
I CONCLUDE with the emphatical words of
the Rev. Mr. Horníby, the preſent Savilian
Profeſſor of Aſtronomy at Oxford, who, in a
diſſertation on this ſubject addreſs'd to the Royal
Society about three years ago, (Phil. Tranſ,
1765. p. 326) having ſủewn the neceſſity of
fending Obſervers into the South feąs, which has
accordingly been done, adds, “ An opportu-
$ nity of obſerving another Tranſit of Venus
will not again offer itſelf till the year 1874.
** It behoves us therefore to profit as much as
ço poſſible by the fayorable ſituation of Venus
" in 1769,* when, we may be aſſured, the
♡ ſeveral Powers of Europe will again contend
$ which of them ſhall be moſt inſtrumental in
el contributing
to undertaken it. Pofibly you may have an Eléve that
“ is capable. The fitting you out to obſerve the former
"Tranfit, was a public Act for the benefit of Science,
" that did your Province great honor."
Had it been poſſible, I would have undertaken this af-
fair with the utmoſt alacrity ; but my ſtate of health abe
folutely forbidding it, I was obliged, to my great mortifi-
cation, to decline all thoughts of it; and could only ea.
deavor to procure an obſervation by ſome other means.
Accordingly, I made a propoſal for that purpoſe, and
perſued it, as far as I could, and had the pleaſure to find
that it met with the approbation and countenance of many
Gentlemen of Rank and fortune. But ſince the above
Diſcourſe was read, I find that in literary expeditions as
well as others, there may be ſuch things as inſurmountable
difficulties. — A perfect obfervation was not likely to be
obtained : An imperfect one would be of little ſervice.
The propoſal failed of being carried into execution.
This fituation, from the principles laid down in p. 29.
find to be more favorable for the inveſtigation of paraf
Jax than any from the year 1526 till 2125.--Six hun
dred years!

Lect. II.
45
TRANSIT of VENUS.
60
şi contributing to the Solution of this grand
“ Problem, [finding the parallax.] Poſterity muſt
« reflect with infinite regret upon their negli-
gence
or remiſneſs; becauſe the loſs cannot
$ be repaired by the united efforts of induſtry,
$ genius, or power." ot bi bo bywni bresa
Read. 15th March 1769iy mudorld weit
IT moli nowad
bra lliw slooga on ento
yowolony T H E E N D. Bonito
no 01 DST in to
VS
8.
.397
90 9001 Homo
nombor bus
to be Advertiſement.
A
Sdi svilo za ulob pogu
A Sit is very probable, that a great number
of perſons may have the curioſity to
behold ſo uncommon a ſight as that
of Venus in the Sun, I think it neceſſary to
give a public caution, that no Body ſhould ven-
cure to look on the Sun, without defending his
eyes from the dazzling brightneſs"; whether he
uſes any kind of perſpective-glaſs or not. I
have known ſeveral perſons who have greatly
injured and impair'd their eyes by looking on
the Sun when eclipſed. A proper defence is fó
eaſily had, that no one need be without it. A
piece of common clear window glaſs, drawn a
few times thro' the flame of a candle or lamp,
till it be covered with ſmoke, will effe&tually
anſwer the purpoſe; and it may be cover'd
thicker

cumar (46)
HB,
thicker at one end than at the other, fo as to be
juft ſuited to the degree of the Sun's brightneſs
at any time. To prevent the ſmoke being
rubb’d off, when in uſe, it will be beſt to have
two ſuch pieces of glaſs, with their ſmoked lides
turn'd inward, and tied together, with a thread
between them. Thus guarded, a perſon may
view the Sun, without the leaſt danger to his
eyes. But to ſee Venus, moſt people will ſtand
in need of a perſpective. A very agreable way
of viewing the Tranſit, ſpots on the Sun, &c.
is to tranſmit the Sun's rays thro' a teleſcope or
perſpective, and receive them on a piece of
white paper, held a few inches from the end of
the teleſcope, and fhaded from all other light.
A perſon that deſires to obſerve the Tranſit, for
wſe as well as entertainment, ſhould be furniſhed
with a very good Teleſcope, and Clock, exactly
adjuſted to the true time by altitudes of the
Sun taken with an aſtronomical Quadrant or
Tranſit-Inſtrument for ſeveral days ; a common
meridian line not being ſufficient in this caſe.
He ſhould be free from every thing that may
diſturb or take-off his attention ; and therefore,
in profound ſilence, and without any company
but one or two aſſiſtants to watch the clock, and
write the obſervations.
giboto
ou 10
According to the lateſt corrections of Dr.
Halley's Tables, We expect that in this place
the phaſes will happen, as follows,
1
Lug
Venus
ol

( 47 )
Venus will firſt touch the Sun's
limb June 3,
24 25' 36"
She will be totally within
44
The middle, or Venus neareſt
the Sun's centre
5
03
36
8
The Planet being then 1o' to
the North of it.
True time of Sunſet
7
29 48
The firſt impreſſion of Venus will be made
in a point about 11 degrees of the circum-
ference of the Sun, to the right hand of the
higheſt point of the Sun. And there it will
appear in reflecting teleſcopes, and in the com-
mon ſort of perſpectives. But in aſtronomical
refracting teleſcopes; which invert objects, it
will appear as far to the left hand of the Sun's
loweſt point.
We heartily wiſh all curious Obſervers a les
rene ſky,

3
3 stions
re
sitive noted two
Vindm
2
conds and
si to rato
blo sat one
in
de mollis or
-Bolo 23 17 godion
oli to bod in one can od SAD
liw sa batori lonio od
- di baseret oslo ci 09
Simone di un veroon HORI
sido solitariat
enue on obna om
of rew
VA
1876



1269
Winthrop, John
1876
wi