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Theological Seminary,



CasSy
Slielf,



PRINCETON, N.J.



Book,




MEMOIRS

^^' O F T H E

Royal Society ;

Being a New Abridgment of the

Philofophical Tranfaftions:

Giving an A^ccount of the Undertakings, Studies, and
Labours of the Learned and Ingenious in many
confiderable Parts of the W o r l d 5 from the firft Inftitution
of that Illustrious Society in the Year i5(^5, to
the Year of our Lord 1735 inclufive.

The whole carefully abridg'd from the OriginalS;^ and the
Order of Time regularly obferv'd, with a Tranflation of the
L A t I N T R A c T s, and the Theoretical Parts apply'd to
Praftical Ufes ; alio an Explanation of the Terms of A a t as
they occur in the Courfe of the Work j being a Work of
general Ufe to the Publick, and worthy the Perufal of all
Mathematicians, Artificers, Tradesmen, ^c.
for their Improvement, in various Branches of Budneis.

By Mr. B A D D A M.

Illuitrated with a great Variety o f Copper Plates.
VOL. III.



Printed by G. Smith, in Stanhope-Jireety near Clare-marht, for the
Editor, one Door below the Black-Lyon Inn, IVater-Lane, Fleet-
Jfreeti and Sold by J. James, at Horace's Head, under the Royal
Exchange-, W. Shropshire, in Old Bond-ftreeti J. Millan,
Bookfeller, oppofite the Admiralty Office i T. Wright, Mathematical
InJlrumentMaker to His Majesty, Fleet-Jlreet\ N. Adams,
Optician to their Royal Highnesses the Prince and Princefs of
Wales, at the Golden SpeSiacles, Charing-Cro/s; C, Pickman,
Bookfeller, RatcliJ- Highway ^T^n^ B. Cole, Mathematical Injlfument*
Maker, Poppings-Court, Fleet- fir eet..

M.DCC.XXXIX.




MEMOIRS

O F T H E

ROYAL SOCIETY;

Being a New Abridgment of^he

Philosophical Transactions*




Of the Gochineel-Fly. Philofophical Tranfaaions N° ip^

p. 502.

HE infe6t, of which the coehineel is formed, is
affirmed to be the very fame, with what we call
the lady-bird, or cow-lady 5 it appears at firft
like a fmall blifler, or little knob upon the leaves
of the flirub, on which they breed, which after-
ward.s, by the heat of the fun, becomes a live
infe£^, or fmall grub 5 thefe grubs, in procefs of
time, become flies, and when come to maturity ( which muft be
found out by experience, in colleding them at leveral feafons )
they kill them, by making a great fmother of iome combuftible
matter, to the windward of the fhrubs, on which the iniefis are
feeding (having firft fpread fome cloths under the plants} where-
by all the infers being fmothered, and killed, by ihaking the
plants, they will fall down upon the cloths, and thus they are
gathered m great quantities with little trouble j then they fpread
them on the fame cloths in fome bare fandy place, or (lone-
pavement, and expofe them ro the heat of the tun, till they arc

A % ^0'»



4 M EM O 1 R S of the

dry, and their bodies fhriveled up, which, rubbed gently betwixt
one's hands, will crumble into grains, and the wings will fall
from them, which mufl be garbled out : Others, it is laid, expole
them to the fun in broad and fhallow copper balbns, wherein the
reflection of the fun will dry them fooner : The tree, or fhrub,
on which they breed, called the prickly-pear, or Indian Ffg, is
cafily and quickly propagated, by putting a fingle leaf, aCovc
half its depth, into the ground, which feldom fails to take root,
and emit other new leaves at the top thereof^ others fay, they
may be raifed from the feed or fmall grains, which are to be
found in the proper feaibn in the fruit, which is fomething like a
fig, arifing outof certain yellow flowers, or blofl'oms, that grow
out at the tops of the uppermoft leaves 5 which fruit is full of a
red pulp, that, when fully ripe, llains the hands, like mulberries,
with a purple or blood colour j on which, or on the bloflbms,
feme fay the infedts feed j which pofTibly may be the caufe of
that rich tincture within their bowels.

^^e "Prejfure 0/ Water in great Depthi. Phil. Tranf N° 193.

p. 504.

OFF of Tmtdlara^ near Sicily^ a bottle was let down
leventy fathoms, flopped with a very good tender cork, well
fitted, and the cork came up in the bettle, which was f full of
falt-water^ the bottle was again fitted with an excellent good
cork, but of a woodineis or hardnefs fome corks are of, with
which being let down in the fame manner, the cork continued in
its place, but bruiled, as it were 3 and the bottle, as before, about
\ full of f^lt watery whereupon, a good ox-bladder was bound
four-fold over the mouth of the bottle, without any cork at all,
only a piece of leather was put to prevent the glals's cutting the
bladder 5 and thus it was let down as before, but taken up with-
out any water, or the leafl moifture therein 5 at the diftance of
ibme leagues from the coaft o{ South Spai)U off the great hills of
Granada^ a leather was tied on the mouth of a bottle, tying
over that a fingle part of the bladder, and the bottle was funk 75
fathoms, but it came up again entire 3 then a hole was made in
the leather, about the bignels of a large pea, and the bottle was
zww limk 7 5 fathoms, but it came up perforated in the vacant^
place, where the leather had the hole* in if, and almoft full of
watery then another part of the bladder was bound fingle over it,
and let down but 50 fathoms, but it came up whole and entire;
after which it was funk 50 fathoms, and it came up broken, and
the bortlc full of watery then the bottle was fitted again, with

the



Royal Society. 5

the faid perforated piece of leather, and a double bladder, and
let down 50 fathoms, but it came up again entire 5 but upon fink-
ing it 75 fathoms, it then came up broken, and the bottle full of
watery in 39 f degrees of latitude, and about 150 leagues weft-
ward of ^Portugali a Florence flails was well flopped with a blad-
der over its mouth, and let down 30 fathom, but it was taken up
broken.

The Lumbricus Hydropicus; hy 'Dr. Edw. Tyfon. Phil.
Tranf. N° 193. p. 505.

IN the diiGfedion of a gaze! la or antelope, Dr. I'yfon oblerved
leveral Hydatides^ or fihus, filled with limpid water, about
the bignefs of a pigeon's egg, and of an oval form, faftened to the
Omentum^ and lome in the ^'Pelvis^ between the bladder of urine
and the Re£ium ^ he had obferved the like watry bags or hyda-
tides in other animals, and he lurpe6led them to be a particular
fort of infed bred in animal bodies, or at leaf! the embrio's or
eggs of them. i. Becaufe he oblerved them included in an exter-
nal membrane, like a Matrh, fo loofely, that by opening it
with the finger, or a knife, the internal bladder, containing the
LympJ'Jci or Serum^ feemed no where to have any connection with
it, but would very readily drop out, ftill retaining its liquor,
without fpilling any of it. 2. He obferved, that this internal
bladder had a neck, or white body, more opake than the reft of
the bladder, and protuberant from it, with an orifice at- its extre-
mity 3 by this it might, as by a mouth, ezchauft the Serum frora
the external membrane, and fo fupply its bladder, or ftomach,
5. Upon bringing this neck near the candle, it was found really
to move, and then fhorten itlelf Fig. i . Plate 1. reprefents
one of thefe watry bladders incloied in its external membrane, or
Chorion 3 its ihape was alm.oft round, only flatted as a drop of
quickiilver will be, by lying on a plane 3 a iliews the neck, \s^xi
thro' tne membrane, which m Fig. 2. is more plainly repreiented
(the external membrane being taken off) but as appearing to the
nake'd eye ^ where we may obierve an open orifice at its extremity,
and that it confifts of circular rings, or incifures, which ii\
Fig. 3. being viewed by a microfcope, do more evidently
diicover themlelvesj this part is granulated with a number of fine
eminences all over 3 the orifice at the extremity feems to be form.-
ed by rctradling itlelf inwards 3 and upon trial it was found fo^ for
in Fig. 4. is reprcfented the neck of this worm, drawn out its whole
length, and magnified j where may be obferved the leHcTang of the

lings,



6 MEMOIRSe/'/yS^

rings, and its tending to a point at the end 5 and opening it, there
was found within two firings aa^ proceeding from the neck, and
floating in the liquor 3 whole ufe may be to convey into the fto-
mach or bladder the moifture or nourifhrrient, which the worm,
by protruding its neck attra6ts from the external membrane 5 and
that this bladder is the ftomach, will appear lefs uiirealbnable, if
we confider how prodigioufly large the ftomach is in fome infers
in proportion to the other parts of the body 5 in a leech you may
oblerve not a (ingle, but above 20 llomachs, which empty out of
one into another, and run the whole length of the body ^ and
what Malpighi obferves of the filk-worm, that it would devour
in one day as much as the weight of its whole body, holds more
truly of a leech, that will do as much at a meal: Some will
poffibly be more inclined to think, that the whole is but an egg,
or embrio of another infect, and that this bladder is the Amtjion^
and the external coat that includes it in the Chorion -^ but for-
tnerly, in difle^-ing a rotten fheep, wherein Dr. ^fon foijnd
many of theie Hydatides., and opening feveral of them, he ob-
lerved the fame ftrufture in all ; and doubtlefs had they been real
embrios, iome of them would have come nearer to a flate of per-
fedion than others 5 he therefore thinks thefe Hydatides to be a Ibrt
cf worms or iuk^s fui Generis , and becaufe they contain fo much
water, and are ufually to be met with in rotten ilieep which are
hydropical, Dr. 7yf on calls them Lumhrici Hydrapici : But he
does not think that all the bladders to be found in morbid bodies,
are cf this fort 3 for in Ibme he did not oblerve this neck and
firufture of parts, but only a tranfparent bladder, filled with a
Lyriipha: Thus, upon opening the right fide of a patient, a little
below her fhort ribs, there iffued out a great deal of limpid
water, and tooether with it a great many Hydatides to the number
of 5005 moft of which were entire ana filled with limpid water,
the films of others, that were too large for the orifice were bro-
ken, but in none of them could he obferve the neck 5 which made
him think them ditferent from the prefent fubje6^, as are likewiie
thole he frequently met with in the Ovaria or telticles of women,
who have died hydropical, which he only takes to be the eggs,
contained therein, fvvelled to that bigneis by a great flux of hu-
mpurs into them.



7>?



Royal Society. 7

fhe viable Con]un5lions of the inferior Planets ivitb the Sun ^ by
Mr. Halley, Phil. Tranf. N° 1^3, p. 511. Tranjlatedfrm
the Latin.

THAT Mercury and F<?;7«5 do enter the diflc of the fun and
appear thereon like fo many black Ipots, is evident, both
from the principles of Ibund aftronomy, and undoubted oblerva-
tionsj but by what laws, or conditions, or in what period of
years thefe phienomena of^r themfelves to our view, has not been
determined by any of our modern aftronomers ; on which account
Mr. Halley thought it would not be unacceptable, if he ferioufly
applied himfelf to this difquifition, and cleared up a fubjedt fo
perplexed and fo little underftood.

It is felf-evident that thefo phafes of thefe planets always hap-
pen in their conjun<^ions with the fun, when rerroorade- viz,
when the fun is^ fo near their nodes, that the latitude of the
planet, in its conjunction with the fun, does not exceed the femi-
diameter of the latter 5 that the limits and conditions of theie
conjunctions may be the more eafily inveiligated, and fince the
elements of the calculation are entirely different, each planet is to
be treated of apart: And therefore to begin with Mercury^ it is
certain that according to late and accurate obfervations, the af-
cending node of this planet, in this century, viz. March i6'9r,
is found near the 15° of 'Taurus , or rather ato S. 15^ 44' from
the firft ftar of Aries 5 and the oppofite defcending at (j S. 1 5"*
44' from the fame ftar 5 the inclination of the plane of Mercury^
orbit to the ecliptic according to Kepler is 5° 54' which is nearly
exaCt : Now it appears from the moft approved hypothefes, that
the diftance of Mercury from the fun, when in the alcendin<y
node, is 31355 parts, of which the mean diftance of the fuS
from the earrth is 1 00000 5 but when it is in the other node, tha^
diftance, meafured in the fame parts, is 45908 : The fun, *wheQ
oppofite to the afcending node, is diftant from the earth, in con«
junaion therewith, 5^8955 parts, but in the other node, the fame
diftance becomes 101007 5 and therefore Mercury, in conjunaion
with the fun at the afcending node, is diftant from the earth
<)7 591 parts, bux at the defcending node 55(^995 which widely
differing from each other, thefe conjunaions, that happen in
different nodes, are alfo to be confidered feparately.

Let Mercury, when retrograde, be in a central conjiinaion
with the fun in the afcending node, in the month of 06iokrt
and from the above hypothefes we ihall have as follows 5

The



8 M E M O I K S of fie

S "" ' ff
The longitude of the fun from the firll ftar of 7 ,

^nVi - ^ - - -^1 ^ ^5 44 00
The longitude of Mercury feen from the fun 015 44 00
The diftance of J^fr^^ry from the fun 313(^5

. _. from the earth (^7591

The angle of the inclination of ilfe;Yw;ys orbit o <J 54 c©
The motion of Mercury, feen from the fun, ? i -o 8

in 6 hours — — — — 5 ^ ^

. of the fun in the fame 6 hours o o 1 5 5

Hence the motion of Mercury from the fun in?

d hours — — — - .^5^5 15 53
And his motion from the fun feen from the 7

earth in 6" hours — — — ^009512
And the angle of the viiible way o£ Jlfercury? ^,

within the fun with the ecliptic ^ -^ J° 3 15 00
Hence the motion of Mercury in his vifible 7

orbit in (J hours — -^ - ^ o o 35 40

Then the motion of Mercury in a fidereal year?

four revolutions beiides is, — — ■ — 5
Therefore in 1 5 years — — — 11
There are therefore wanting to 54intire revo-?

lutions — — — — 5

Which Ipace Mercury runs over in — —

By which the fun's place is advanced, and Mercury,
pofited in the node, is as much diflant from the
conjunction of the earth — — —
But that arch feen from the earth becomes —
Whence from the given angle of the vifible way S°
15' arifes the bafe ordinance from the vifible
conjunflion — — — — —

Which arch is run over by Mercury in — . —
But 13 fidereal years exceed fo many Julian ones with
3 intercalations by — — — —




Thereibre Mercury returns to the fun after 1 5 Ju- 7
lian years, and befides •— — — 3

Or, with four intercalations, if theprecceding year?
be the third after Siffc-^tik — -r- S ^



d. h.



m.



17 34
Bui



Royal Society. 5

But from the arch 5^' 10'' and given angle, the per-p ^ \ //
pendicular or nearcft diflance of Mercury from the^ o 8 3
lun becomes — • — — — — J

Therefore Mercury feen within the fun after 1 3 years
advances more northerly by 8' 3''

go'//

By the like realbning in ^6 fidereal years? u o 25 8

Mercury moves — — • — S
There are therefore wanting to 191 intire? ^

revolutions — — • — — S

h. m.

That is in time — - — — — 812

By which the liin is advanced — — — .02041
This arch feen from the earth becomes — — o 9 0^
The bafe anfwering thereto — — — 093^

h. m.
The time, in which Mercury runs over the bale, is i 30

But 4^ iidereal years exceed as many Julian with 11^^
intercalations by — -— — — 3 ^

And Mercury returns to the fun after 45 Julianl
years and befides — ■ — — — 5

Or, with 1 2 intercalations, that it becomes, when -o

the preceeding year is either the fecond or third > o 4 51
after Sijjet^tile _ >_ _™, — ^



But the perpendicular, by which Mercury advances?
to the north, becomes — > — — S



I 22,



The moil accurate period of Mercury to the fun 7
is abfolved in 2(53 fidereal years and befides _f

And thefe Iidereal years exceed as m.any Jidianl
with 66 intercalations by — ■ — - \



b. m, £
I II 30

[Q 20 O



-1. h. m, f



Whence after 2*^3 Julian years Mercury re

volves to the fun, but later by — 5° ^^ 33 5^

But if the preceeding year be ^/^xY/75', add i 11 31 30
Ar length after this interval it advances more?

northerly by _ - , _ _ ^^^^^^^

The other wider periods are eaiily dilcovered from what has
been juft new found, and they are either of 6 or 7 years 5 that of

Vol. III. B 7 years



years



lo ME M O IR S of the

7 years depreffes Mercury ii 47'' to the fouth^ and 7 whole
days, left by 9', Iboner, if there have been two intercalations 5
but with one intercalation, viz. when the former year is biflex-
tile, 6 days are to be fubdu»5ted, adding only 9' as before : It is
more rarely that after 6 years this planet is feen again in the fun*s
difk- after that period it palTes 50' 5c'/ more northerly 5 and
that later by 9 d. 17 h. 25 m. if the preceeding year be the fe-
cond or third after bifrextile3 otherwile 8 d. 17 h. 25 m. are to
be added.

Likewife if the conjun6iion happen at the defcending node in

^pril.

^ S ° If

The longitude of the fun from the firft ftar of 7 , , ^

^ries^ - - - - _|o 15 44 00
The longitude of Mercury feen from the fun 6 15 44 00
The diftanceof the planet from the fun - 45508
Its diilance from the earth — — 5 5/^99
The motion of Mercury feen from the fun in?

fixhouvs _ L _ _ I o o H ^9
The motion of the fun in the fame time — o o 45 21

. of il/^rr//r); from the fun — o o 28 52

Hence the angle of the vifible way of Mer-'^

cury within the difk of the fun with the^ o 10 i8 00

ecliptic is — — — — J
And the vifible motion from the earth in 6 hours o o 2 $ 52

Whence by following the method of the preceeding calculus, it
is evinced that Mercury, after 13 years and befides 5 d. 7 h. 57 m,
revolves to its conjunSiion with the fun; but if the preceeding
year be the third after biffextile, in that cale 2 d. 7 h. 37 m. are
only to be added 5 and then Mercury will be found to advance
16' 55'' more Ibutherly ; After ^6 years vA/ith 12 intercalations add
7 h. 14m. and Mercury will be in conjundlion with the fun 2' 23''
more foutherly 5 but if the former be biffextile, or the firfl after
ix, id, 7 h. 14 m. are to be added, in order to have the conjunc-
tion accurately: In like manner, after 2(^3 years, in which Aier-
ctiry declines o' 22'' to thefouth, either id. 11 h. 49 m. or ri h.
49 m. are to be added according to the rule prefcribed in the
farmer cale : But in d or 7 years, becaufe of the nearnefs of the
c?.rth and that planet, and therefore on account of the enlarged
arches at this node, it does not return to the fun, fo as to be leen
within its dift; After ^,3 years it pafles over the fun 14' 2.'! more
noitherlv, and the moment of the conjundion is had by lubflra£l-



Royal Society. ii

ing, from the time of the former, ^6,0 h. 23 m. if it be the
third year after biflextile^ otherwife fubftraft 2d. oh. 23m.
only: Having found thefe, it will be an eafy matter to continue
the calculus for all the conjunctions of Mercury with the fun, and
that with the greatclt certainty ; by addition only, the moments of
conjunctions and the diftances of the planet from the centre of
the Itin are obtained j whence likewile by the help of the table,
the durations of thefe ecliples, are difcovered, lb that nothing
feems to be wanting in this affair: As to the EpochdP-, thefe are
with more fafety had from the induftry of obfervers than by the
fubtileft calculations - therefore Mr. Halley chofe for the firil
cafe, that remarkable tranlit of Mercury which he himlelf had
fully obferved at St. Helena^ OBober 28, 1(^77 O. S. and whole
middle he determined there at o h. 4 m. p. m, but at London o h.
^%X£i.p.m. The way in which the planet leemed to advance
was 4' 40'' more northerly than the lian*s centre : In the other
cafe, viz. when Mercury was in conjunction with the fun
April 23, \66x O. S. he appeared at his lead diflance from the
fun's centre at 2)antzic <5 h. 8 m. p, m. and at London 4h. 52 m.
being then in the middle of his tranfit, and at the fame time was
diftant from the fame centre 4' 27'/ to the north 5 hence accord-
ing to the above rules, it was an eafy matter to exhibit in order
all the vilible conjunctions o^ Mercury with the fun.

A feries^ of the times wherein Mercury ^ being in conjunfiion
with the fun, is feen within his dillc, calculated for the prefent
and enfuing century, with the diftances of the planet from the
fun's centre.



In the month of A p r i l



Years


'i'lmes


ot LonjunCt.


Diit.tromthe 5un's C^entrel




d.


h. m.


' //




i5i5


22


21 38*


7 20


N.


161^


25


5 15*


9 35


S.


1661


-3


4 52 *


4 27


N.


1^74


16


12 29


12 28


S.


1707


24


12 6


I 34


N.


1720


26


19 43 *


15 21


S.


1740


21


II 43


15 35


N.


1753


24


19 20 *


I 19


S.


i']%6


22


18 57*


12 43


N.


^199


16


2 34*


4 12


S.



B



In



12



M E M O I R S of the

In the month of O c t o b e r.



Years


Times


r Conjunct.


Dilt. from the S


un' sCentre




d. h.


m.


/


//




i(5'05


22 8


29


12


48


S.


i6iS


25 2


4*


4


45


S.


16^1


27 19


37 *


3


18


N.


1^44


30 15


11


II


21


N.


16^1


23 13


20


II


16


S.


1664.


25 (J


54*


3


23


s.


1^77


28


28 * *


4


40


N.


i6(}0


30 18


2 *


12


43


N.


169-]


23 18


II *


10


4


S.


1710


16 II


45


2


I


s.


1723


29 5


19 *


(5


2


N.


1750


22 5


28


i(J


45


S.


i7B(J


30 22


53 * *


13


5


N.


1743


24 23


2 * *


8


42


S.


i75(T


z6 16


S6





39


S.


17^9


29 10


10


7


24


N.


177(5'


22 10
Nov,


19


15


23


S.


1782


I 3


44 *


15


27


N.




(9(^.










1789


^5 3


53*


7


20


S.



The tranfits marked with the fign * are partly vifible at Zon-
don^ but thofe with the lign * * are entirely to be leen there.

Note, that the fun's diameter at the afcending node of Mer-
cury in the month of OEfoher is 32' 34'^ 5 and therefore that the
greatefl duration of the central tranfit is 5 h. 29 m. but in April
the lim's diameter becomes 51' 54'^ whence on account of the
flower motion of the planet, the greateft duration is 8 h. i m.
But if Mercury fhould fall oblicjuely upon the difk, theie dura-
tions become fhorter in proportion to the diftance from the fun's
centre 5 and that the calculus might be the more perfefl, the fol-
lowing tables are fubjoincd, wherein are exhibited the half du-
rations of thefe eclipfes for each minute of diftance feen fram the
lun's centre, which added to, and fubftracled from, the moment of
conjunction found in the former table, exhibit the beginning and
end of the whole phaenoraenon.



O C TO-



Royal

October.



Society.

April.



13



Minut.


Semi-




Mmut.


Semi-


Dift.


dura t.




Dift.


durat.


'


h. m.


I


h. m.





2 44







4 oi


I


2 44




I


4


2


2 43




2


3 58i


3


2 41}




3


3 5^


4


^ 35>i




4


5 53


5


2 5^T




^ 5


; 48I


6


^,i.

d32


6


3 43


7


2 281




7


5 3^'


8


2 23




8


3 28


9


2 17




9


3 i8f


10


2 10




10


3 7


II


2 I


II


2 44


12


I 51




'-


2 58


13


I 39




13


2 19


14


I 24




H


I 55


15


I 4




15


I 21I


Mi

16


50
30


I5i 1


5'^









Thefe numbers do fitly reprefent all the obfervatlons hitherto
made, nor need we doubt of the future 5 feeing of all the planets
Mercury is the neareil to the fan, fo that it cannot in the leaft be
intercepted by the intervention of the centres of the other planets,
nor fenfibly difturbed by thole deviations, which a rile from their
fyflems, and to which the fuperior planets, particularly Saturn^
are obnoxious: Mr. Halley deiignedly omitted the parallaxes as
very inconliderable, and which being different, in different places,
could not be applied in a more general calculation, and becaufe
their quantity hath not hitherto been determinedi but from fuch
obfervations they may rather be more certainly derived ^ he had
alio as little a regard to Mercury ^ diameter, becauie, being ex-
tremely Imall, he leems to adhere for a very few minutes to the
limb ^ for by an accurate obfervation, OEiober 28, 1^77, he found,
that fcarcelytwo minutes were elapfed, when he entirely quitted



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