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ladder; always slicing off the bark, as far as they can reach, before they fix a
new step; and thus they mount to the top, the Indian below gathering what
the other cuts; this they do by turns, and go from tree to tree, till their bag is
full ; which, when they have plenty of trees, is generally a day's work for one
Indian. As much care as possible must be taken that the bark is not cut wet;
should it so happen, it is to be carried directly down to the low country to dry,
otherwise it loses its colour, turns black, and rots; and if it lie any time in the
hut without being spread, it runs the same risk : so that while the Indians are
cutting, the mules, if the weather permits, ought to be carrying it down to
the place appointed for drying it, which is done by spreading it in the open air,
and frequently turning it.

Mr. Arrot had the curiosity to send above 50 seroons from the woods to the
city of Loxa, where he put it into a large open house, and dried it under cover,
never exposing it either to the sun or night air, imagining that the sun exhaled
a great many of its fine parts, and that the night air, or serene, was very
noxious to it; but he found the colour of the bark thus cured, not near so
bright and lively as that dried in the open air. He is of opinion, that a very
short time will put an end to this best sort, or at least it will be extremely hard
to be got, by reason of its distance from any inhabited place, the impenetra-
bility of the woods where it grows, and the scarcity of the Indians to cut it,
who, by the Spaniards' hard usage and cruelty, are daily diminishing so fast,
that in a very few years their race in that country will be quite extinct.

Mr. Arrot says, that the small bark which curls up like sticks of cinnamon,
and which in England is much esteemed, as being cut off the branches, and
therefore reckoned better and more effectual in curing fevers, is only the bark
of the younger trees, which, as it is very thin, curls in that manner; and that
the bark of the branches would not compensate the trouble and expences of
cutting. He also says, that after the bark is cut off any tree, it requires at



VOL. XL.] FHILOSOPHICAL TRANSACTIONS. 145

least 18 or 20 years to grow again ; which is directly contrary to what Dr.
Oliver says in N" 290 of the Phil. Trans. He added besides, that its fruit is
no ways like a chestnut, as the Doctor informs us in the same paper; but rather
like a pod, which incloses a seed somewhat like a hop-seed, and that he had
sent some of them to England.

He could not tell by what artifice or stratagem the Jesuits have got this bark
to be called after them, if not that they carried it first into Europe, and gave
themselves out as the first discoverers of its virtues : but he asserted, that the
current opinion at Loxa is, that its qualities and use were known by the Indians
before any Spaniards came among them ; and that it was by them applied in the
cure of intermitting fevers, which are frequent over all that wet unhealthy
country.

An Account, by Mr. John Eames, F. R. S. of a Booh entitled, A Mathematical
Treatise, containing a System of Conic-Sections, with the Doctrine of Fluxions
and Fluents, applied to various Subjects. By John Muller. N° 446, p. 87.

The ingenious author of this work,* observing how much time is necessarily
epent, and pains taken, in learning these valuable parts of mathematics, thought
it would be very well worth his while to lessen both, which he hopes he has
done considerably, in the following treatise. He has divided it into 3 parts,
contained in so many books.

In the first of these, he considers the properties of the 3 sections of a cone,
as well in, as out of the cone. And to make this part of the work of more
service to the reader, Mr. Muller has not only selected the most considerable
properties of these curves, that are to be met with in other writers, both anci-
ent and modern; but has added several new ones, which, as he informs us, are
inserted in their proper places. And that such gentlemen as are desirous to
read Sir Isaac Newton's Principia, but are at a loss for want of a sufficient ac-
quaintance with conic-sections, may be the more obliged, he has taken parti-
cular care to demonstrate such properties as Sir Isaac presupposes his reader to
be acquainted withal. Accordingly, he has prefixed a table of such propositions,
informing him as well where they are to be met with in this book, as in Sir
Isaac Newton's Principia Mathematica.

The proofs made use of in his demonstrations, are sometimes algebraical, at

* He was afterwards, for many years, professor of Fortification and Artillery, in tlie Royal
Military Academy, Woolwich, for the use of which, he published several books on those subjects,
which are still in great repute, being the best works extant of the kind.

VOL. VIU. U



IM6 philosophical transactions. [anno] 737.

other times geometrical, according as he finds the one to be plainer and shorter
than the other.

The second book treats of the direct method of fluxions. And here he
hopes the first principles of this method are laid down, not only in a new, but
very plain and concise manner. He proceeds to show the use effluxions in the
solution of the common problems of finding the maxima and minima of quan-
tities, the radii of the evolution of curves, and the radii of refraction and re-
flection. Under the first of these heads he says, particular care has been taken
to distinguish the maximums from the minimums, a thing which has not been
noticed so much as it ought to have been. And whereas some mathematicians,
having made use of what they call infinitely small quantities, are forced to re-
ject something out of the equation, for finding the fluxion of a rectangle, whose
sides are varying quantities, Mr. MuUer uses only finite quantities ; and finds
the fluxion of such a rectangle after a new manner, without rejecting any
quantity for its smallness. He does the same in finding the fluxion of a power.
And to avoid the use of infinitely small quantities, introduces a new principle,
viz. that a curve line may be considered as generated by the motion of a point
carried along by two forces or motions, one in a direction always parallel to the
absciss, and the other in a direction always parallel to the ordinate. Hence he
infers, that the fluxion of the ordinates is to the fluxion of the absciss, as the
ordinate is to the subtangent of the curve.

Having likewise proved from the first supposition, that if the describing point,
when arrived at any place given, should continue to move onwards, with the
velocity it has there, it would proceed in a right line, which would touch the
curve in that point ; he concludes that the direction of the force in that place,
is in the tangent to the curve : consequently, the 3 directions being known in
each place, the proportion between the velocities of the urging forces will be
likewise known. So that the nature of the curve being given, the law observed
by these velocities may be found ; and if the law of the velocities be given, the
nature of the curve may likewise be given.

In the third and last book, we have the inverse method of fluxions, with its
application to the several problems solvable by it ; such as the superficial and
solid contents of curvilineal figures, the rectification of curve lines, centres of
gravity, oscillation and percussion. Here also Mr. Cotes's tables of fluents are
explained and illustrated by examples.

He finishes this book with a great variety of problems, of a physico-mathe-
matical nature, several of which are new, and were proposed to him by Mr.
Belidor. Some indeed are not so, having been solved by Messieurs Varignon
and Parent ; but then he has solved them after a different, and, as he hopes, a



VOL. XL.] PHILOSOPHICAL TKANSACTIONS. . 147

more agreeable manner, the construction being more simple, and the process
much shorter.

Observations of the Maori's Transit by Aldebaran, ^pril 3, 1 736, at London.
.a .W. ,4W'»il . By John Bevis, M. D. N° 446, p. gO.

At 7'' 40"", apparent time, the moon's body and Aldebaran were seen to-
gether in the distinct base of the telescope.

ji Collection of the Observations of the Lunar Eclipse, Sept. 8, 1736, which
were sent to the Royal Society. N° 446, p. 92.

1 . In Fleet-street, London, by Mr. Geo. Graham, F. R. S. and by Mr. James

Short of Edinburgh, F. R. S. P. 92.
Apparent Time.
At 12" 58"" 0» Beginning of the eclipse. .

14 3 45 Beginning of total darkness.
The observation made with a 5|-inch reflecting telescope, magnifying
about 38 times.

2. In Covent-Garden, London, with a 5-foot telescope. By J. Bevis, M. D. p. 93.

Apparent Time.
At 12'' 56" 5(y Beginning of the eclipse.

14 2 25 Total immersion of the moon.

3. At Wittemberg in Saxony. By J. F, Weidler, R, S.S, &c. P. 94.

' l'' 50™ <y Beginning of the eclipse.

2 S3 00 The total obscuration.
4 44 00 Beginning of the emersion.

4. At Hudson's-Bay, by Capt. Christopher Middleton, F. R. S. P. q6.
Being in Hudson's-Bay, in the latitude 55° 34' north, and on the meridian

of the North-Bear-Island, which lies 30 miles to the westward of Charlton,
Capt. M. observed this total eclipse of the moon. The weather was very clear,
but the motion of the sea rendered his telescope useless, and he missed the
beginning.

Apparent Time,
gh 43m Total immersion of the moon into the shadow.

10 29 The emersion.

1 1 37 The end.

This same eclipse being qt)?(?rv^,f)y ^Pr.JBjevis.^t Lflp<iqn, when he made tjie

V2



148 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737.

true time of the total immersion of the moon's body into the shadow, M'' 2"
25* ; consequently the difference of longitude between London and North-Bear-
Island in Hudson's Bay, is 5*" IQ™ 25% or 79° 5l'.

A Solar Eclipse observed at London, Sept. 23, 1736. By J. Bevis, M. D.

N° 446, p. 98.

4'' 45™ 31' Beginning of the eclipse.

Observations of the Occultation of Mars by the Moon, Oct. 7, 1736.

N''446, p. 100.

1 . By Mr. Geo. Graham, F. R. S. in Fleet-street, London, with a refracting

telescope of 12 feet.

The first contact could not be seen for clouds.
Apparent Time.
At 14*' 24*" 44' Mars appeared about half covered.

14 25 21 Mars totally covered.

15 11 22 The moon appeared, but Mars was not seen, no part being

yet emerged.
15 15 11 Judged it was quite emerged, but clouds prevented the
moon's limb from being distinctly seen.

2. In Covent-Garden, by J. Bevis, M. D. p. 101.
Before the eclipse, he took several differences of right ascension and declina-
tion between <5 and i* Piscium, for ascertaining the true place of Mars : as
also several differences of right ascension and declination between the moon
and Mars, before and after the eclipse.
Apparent Time.

14*> 24™ 10" He was surprised to see Mars continue quite round, though

hardly, to appearance, disjoined from the scabrous edge of the

moon ; but that instant he thought it began to lose its figure.

15 14 46 The moon being just clear of a cloud, saw Mars partly emerged.

15 14 49 He seemed just half out ; then clouds came on again, so that the

final contact was not seen.

Observations of the Transit of Mercury over the Sun, Oct. 31, 1736.

N° 446, p. 102.

1. By Mr. George Graham, F.R.S. in Fleet-street, London, p. 102.

Apparent Time.

At 9*^ 22™ 00* Mercury not yet seen, then clouds.



TOt. XL.] PHILOSOPHICAL TRANSACTIONS. I49

Apparent lime.
At Q^ 23™ 37* He first saw Mercury for a few seconds, and judged he was
got entirely within the sun's disk, or perhaps a little more ;
then clouds again, with some intervals of a few moments
between, which allowed a sight of Mercury about 3 or 4
several times ; then quite cloudy till near 1 2, when we had
a sight of the sun for a few minutes, and took his transit
upon the meridian ; at which time we judged Mercury to be
about two of his diameters, or a little more, within the sun's
disk, and a little past the vertical line.
12 10 27 We had again a sight of the sun, but Mercury was gone off.

2. At the observatory of Bononia, by Sig. Manfredi, F. R. S. P. 103.

Beginning of Mercury's ingress 22** 7"* 56'

Ingress of the centre 22

Total ingress 22

Beginning of the egress O

Egress of the centre O

Total egress O

The mora of Mercury's centre on the sun's disk 2

Semimora 1

Middle time of the transit 23

3. Extracts of a Letter from Mr, Professor Weidler, F. R. S. &c. to Dr.
Mortimer, Seer. R. S. dated at Wittemberg, Jan. 1, 1737, n. s. P. 110.
Mercury appeared within the sun's eastern limb, as represented in fig. 17,
pi. 5.

.... at 1 12'' 4™ 30* at 5

5 abt 2 12 44 20 6

at 3 12 52 45 7



9


34


11


12


50


50


52


28


54


6


42


54


21


27


31


1



lO*'


49™ 20^


11


36 00


11


52 20


12


2 30



j4 Collection of Observations, relating to the Comet which appeared in January,
February, and March 1736-7. N° 446, p. 111.

1. Observations on that Comet made at Oxford, by J. Bradley, F.R.S. P. 1 j 1.
Mr. Bradley made several observations on the late comet, during the last 5
weeks of its appearance, which enabled him to find out the elements of a para-
bolic trajectory, on which a calculus might be founded, that would correspond
with each of his observations within about a minute of a degree : but the first of



150 PHILOSOPHICAL TRANSACTIONS. [anNO IJSJ.

them being taken many days after the time of the perihelion, and the whole
series comprehending but a very small portion of the trajectory ; he was sensi-
ble, that a little error, either in the observations themselves, or in the places of
the fixed stars, with which the comet was compared, might occasion a con-
siderable difference in the situation and magnitude, &c. of the orbit, deduced
from them alone ; and therefore he was desirous of having some earlier and ac-
curate observations, to determine those elements with more certainty : but not
having yet been able to procure such, he no longer defers laying before the So-
ciety the particulars of his own, with the comparison between the observed
places of the comet, and those computed from such elements as he had already
collected from his own observations.

Mr. B. first saw the comet on the 15th of February 1737, between 6 and 7 in
the evening, when its nucleus appeared small and indistinct, and its tail, extending
above a degree from the body, pointed towards the star in Lino Austral. Piscium,
marked g by Bayer. Applying the micrometer to a good 7-foot tube, he ob-
served, that at 7'' 32™, equal time, the comet preceded the said star 1° i' 40"
in right ascension, and was 20' 20" more southerly than the star. Note, That
the equal time is likewise made use of in all the following observations.

Assuming the place of this star, as it is settled in the British Catalogue, as
he likewise does others hereafter mentioned, it follows, that the comet's right
ascension was 23° 58' O*, and its declination 1° 3l' 55" north.

February 17, 7 hours 33 min. the comet followed a in Nodo Lin. Piscium
31 min. 25 sec. in right ascension, and was 52 min. 30 sec. more northerly.
Hence the comet's right ascension was 27 deg. 38 min. 20 sec. and its declina-
tion 2 deg. 21 min. 10 sec, north.

February 18, 7*" 14™, a small star (whose right ascension was afterwards found
to be 29° O' 5", and declination 2° 58' 30" north) preceded the comet 24' O" in
right ascension, and was 15' 30" more northerly. Hence the comet's right
ascension was 29° 24' 5", and its declination 2° 34' O" north.

February 21, 7^ 25", the comet preceded v Ceti 1° 6' 0'' in right ascension,
and was 38' 20" more southerly. Hence its right ascension was 34° 25' 10",
and its declination 3° 47' 20" north.

February 22, 7^ 45*", the comet followed n Ceti 30' 5" in right ascension,
and was 18' 45" more southerly. Hence the comet's right ascension was 30° l'
15", and its declination 4° 6' 55" north.

February 25, 7*^ 45", a small star (whose right ascension was afterwards
found to be 40° 34' O", and declination 5° 5' 30", north) followed the comet 2'
30" in right ascension, and was 2' 30" more northerly than the comet. Hence
the comet's right ascension was 40° 31' 30", and its declination 5° S'* 0" north.



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 154

The difference of right ascension and declination, between this star and the
comet, was taken with a 15-foot telescope ; but the place of the star was deter-
mined by one observation made with the 7-foot tube.

February 27, 8^ 45'", the comet preceded a small star, l" l6'0' in right
ascension, and was 2' 15" more southerly. The right ascension of this star was
afterwards, by a single observation, found to be 44° 37' 40", and its declination
5° 38' 30* north. Hence the comet's right ascension was 43° 2l' 40", and its
declination 5° 36' 15* north.

March 4, S** O™, a small star, whose right ascension was found to be 49°
30' 30", and its declination 6° 38' 30" north, preceded the Comet 7' 30* in
right ascension, and was lO' O" more southerly. Hence the right ascension of
the Comet was 49° 38' 0', and its declension 6° 48' 30".

March 12, 6^ 25™, the Comet preceded /* Tauri 2° 5' 50' in right ascension,
and was 4' 25" more northerly than the star. Hence the Comet's right ascen-
sion was 58° 12' 40", and its declination 8° 16' 30* north.

March 14, 9'' O™, the Comet followed the 47th star of Taurus in the British
catalogue 12' 30" in right ascension, and was O' 15" more northerly than the
star. Hence the Comet's right ascension was 6o° 8' b", and its declination
8° 34' 5" north. This, and all the following observations, were made with a
good 1 5-foot telescope, the Comet now appearing too faint to be well observed
with the 7-foot tube.

March 17, S'' 40™, the Comet followed y Tauri 25' 5" in right ascension,
and was 9' 40" more northerly. Hence its right ascension was 62" 47' 55", and
its declination 8° 58' 45'" north.

March 1 9, 7*" 50™, the Comet followed the same star 2° 4' 50" in right
ascension, being 23' 55'" more northerly. Hence its right ascension was 64°
27' 40"", and declination 9° 13' O* north.

The same night, at 9** O™, the Comet preceded d Tauri 47' 40'" in right
ascension, and was 22' 50'" more southerly. Hence its right ascension was
64° 30' 20", and declination 9° 12' 35" north.

March 20, S*" 5™, the Comet preceded d Tauri O' 30'" in right ascension,
and was 16' 35" more southerly than the star. Hence its right ascension was
65° 17' 30", and declination 9° 18' 50"" north.

March 22, 8'' 13'", the Comet followed the same star 1° 36' 10" in right
ascension, and was 3' 30" more southerly. Hence its right ascension was
66° 54' 10", and declination g° 3l' 35' north.

This was the last night that he saw the Comet; for the moon being then in
her increase, entirely obstructed its further appearance. The light of the
Comet was indeed, even in the moon's absence, so very weak, that he found



mo,



PHILOSOPHICAL TRANSACTIONS.



[anno 1737.

it difficult, in some of the latter observations, to take its place with any to-
lerable certainty; which is, in part, the cause of some little disagreement ob-
servable in the Comet's places taken from the same stars on different nights j
though there are likewise other irregularities that occur in this series of obser-
vations, which seem to arise from small errors in the assumed places of
the stars.

Supposing the trajectory described by this Comet to be nearly parabolical,
conformable to what Sir Isaac Newton has delivered in the 3d book of his
Princip. Math, he collects from the foregoing observations, that the motion of
this Comet, in its own orbit, was direct, and that it was in its perihelion,
Jan. 19, 6^ 20*" equal time at London. That the inclination of the plane of
the trajectory to the ecliptic, was ]8°20'45". The place of the descending
node b 16° 22'. The place of the perihelion ^ 25° 55'. The distance of
4;he perihelion from the descending node 80" 27'- The logarithm of the peri-
helion distance from the sun 9.347960. The logarithm of the diurnal motion
0.938 1 88.

From these elements, by the help of Dr. Halley's general table for Comets,
to which they are adapted, he computed the places in the following table;
which also contains the longitudes and latitudes of the Comet, calculated from
the observed right ascensions and declinations abovementioned, with the dif-,
ferences between the observed and computed places.



Oxon


. 1737,


Com. Longit.


Lat


. Aust. 1


Com.


Long.


Lat


. Aust.


DifF.


Diff.


Equal


Time.


Observat.


Observat. 1


Computat.


Computat.


Long.


Lat.


Feb. ISO jh


32"" .


r22'' 45' 7''.





53' 27"


r 22"


45'


0'..





53'


1".


.+


7'.


. +26"


17


7


33 ..


26 30 30 .


. 8


27 21


26


30


44 ..


8


28


6.


. —


14 .


.—45


18


7


14 ..


28 18 14 .


. 8


44 20


28


17


46..


8


43


57.


.+


28 .


. +23


21


7


25 ..


3 26 34 .


• 9


26 50


3


26


53 .


9


26


46.




19.


. + 4


22


7


45 .


5 4 53 .


• 9


40


5


5


28 ..


9


39


27.


. —


35 .


. -i-33


25


7


45 ..


9 42 18 .


. 10


12 21


9


41


I9 -


10


12


22.


.+


59.


.- 1


27


8


45 .


12 3643 .


. 10


31 42


12


36


16..


10


31


13.


• +


27.


.+29


Mar. 4


8


..


19 3 .


. 11


6 46


19


3


5..


11


7


8 .




5 .


.-22


12


8


25 .


27 49 58 .


. 11


43 3


27


49


53 ..


11


43


19.


.+


5 .


.-16


U


9


..


29 47 42 .


. 11


49 59


29


47


19-.


11


49


26.


. +


23 .


. +33


17


8


40 .


n 2 30 57 .


. 11


56 31


n 2


30


50 ..


11


56


49.


.+


7.


.—18


19


7


50 .


4 12 36 .


.12


19


4


12


45 ..


12





47 .


. —


9.


.-28




9


.


4 15 11 .


.12


1 12


4


15


13 ..


12





52 .


. —


2 .


. +20


20


8


5 .


5 3 10 .


. 12


3 5


5


3


32..


12


2


33 .


. —


22.


. +32


22


8


15 .


6 41 30 .


.12


6 15


6


41


19..


12


5


42 .


. +


11 .


.+33



From the small differences between the Comet's observed and computed
places, exhibited in t'ne last two columns of this table, we may reasonably
conclude, that the orbit, as above determined, cannot differ much from the
truth, and must therefore be near enough to enable future astronomers to
distinguish this Comet on another return, and thus to settle its period ; which



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 153

he cantiot at present pretend to do, not having met with an account of any
former Comet that seems likely to have been the same with this, a description of
which has been given particular enough to determine this point.

2. The same observed at the Aventine Hill at Rome. By Didaco de Revillas
Abb. Hieronym. R. S. S. p. 118. From the Latin.

Feb. 16, 1737, about 7 o'clock, p. m. the Comet appeared for the first
time in the western part of the heavens, 8 or 9 degrees lower than Venus, and
declining a little towards the south from her vertical circle. With the naked
eye nothing was perceived but a small whitish line, of a faint light : yet with a
very good telescope of Campani's, of 6 feet, besides the tail, which extended
to the opposite part from the sun, and appeared like a small line without the
telescope, was likewise espied the nucleus, though encompassed all round with
a thin atmosphere. As there was then no quadrant at hand, and not only a
fog intercepted, but the twilight deprived the view of the neighbouring fixed
stars, the apparent place of the Comet could not be determined for that night.

From the l6th till the IQth, as also after the 25lh, there happened other im-
pediments, which prevented observations. And in the nights between 19 and 26,
the Abbe could not otherwise determine the apparent place of the Comet, than
by comparing the phenomenon with Venus; as he only employed a small qua-
drant, whose tube was scarcely an English foot in length. From the vertical
altitudes therefore, both of the Comet and Venus observed at the same time,
were collected the vertical differences of both, as below.



Times.


Vert.


Differ.


scy' 7^ 59™





22'


22 7


3


56


23 7 20


3


13


24 6 15


2


30


25 7 30


I


47



3. Observations on the Comet, and of an Eclipse of the Sun, Feb. 18, 1736-7,
made at Philadelphia in Pennsylvania. By Dr. Kearsly, p. lig.



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