. Waring’s Obfervatlons
poffible roots. I believe alio, that I firft gave a rule in the
Milcell. Analyt. for finding the number of impoffible roots
from finding an equation, whofe roots are the fquares &c.
of the roots of a given equation, which rule in equations
of luperior dimenfions fometimes finds impoffible roots,
when Newton’s, Campbell’s, &c. rules fail, and fails
when they find them ; and alfo a rule for finding im-
poffible roots from an equation, whole roots are the Iquares
of the differences of the roots of the given equation ; this
rule (as has been obfeived by me in the Milcell. Analyt.
and 1 hilofophicalTranfa&ions) always difcovers whether all the
roots of the given equation are poffible or not ; and the laff term
of the refulting equation difcovers alfo, whether o, 4, 8, 12,
&c. or 2, 6, 10, 14, &c. impoffible too^s, are contained in the
given equation ; to which may be fubjoined, if the given equa-
tion has r poffible and n — r~2t impoffible roots, that the num-
ber of changes of figns from + to - and — to -f in the refulting
equation will not be lefs than r . , and the number of con-
tinued progreffies from -f to + and — to — will not be lefs than t :
whence, if the number of continued progrefifes be A, the
number of impoffible roots will not be greater than zt\ and
the number of poffible roots not lefs than n — 2/'. If the
number of changes of figns be //, the number of poffible roots
will not be greater than r\ where r' x Ludisthe greatefi poffible
number which does not exceed b\ and the number of impoffible
roots not lefs than n - /. Another rule was, I believe, firff given
by me in the Milcell. Analyt. 1 762, for finding impoffible roots
by finding an equation whofe roots are z, where x n —px nmmml +
q.x n ~ z — &c.. = %, and nx"~~' - n - 1 px”~~ z + n — 2 qx n ~ z - &c. = o.
In
on converging Seriefes. $3
In the Medit. Algebr. fomewhat has been added concerning
impoflible, affirmative, and negative values of the unknown
quantities in an equation which involves two or more unknown
quantities ; and alfo was firfl delivered a rule from the number
of affirmative, negative, and impoflible roots of an equation
being known to find the number of impoflible, negative, and
affirmative roots of an equation, whofe roots have a given
algebraical relation to the roots of a given equation ; on which
two lafl: fubjedts little, I believe, had been before publifhed.
M 2
[ *+ 3
XV. Experiments on the Production of Dephlogijlic cited Air from,
JVater with various Subjianccs. In a Letter from Sir Benjamin
Thompfon, Knt. F, R. S to Sir Jofeph Banks, Bart. P . R. S.
i
Read Feb. 15, 178-7.
DEAR SIR, Munich, Sept. 1, 1786.
■^"ARIOUS opinions having been entertained with refpedt to
the origin of the dephlogifticated air, produced by expo-
fing healthy vegetables in water to the adtion of th-e fun’s rays,
according to the method of Dr. Ingen-housz ; and not being
myfelf thoroughly fatisfied with any of the theories propofed,
I made the following experiments, with a view to throwing
fome new light upon that fubjedt.
Having found that raw filk polfelfes a power of attradling
and feparating air from water in great abundance, when expofed
in it to the action of light, it occurred to me to examine the
properties of this air, and to coniider more attentively the cir-
cumftances attending its production, thinking that this might
polfibly lead to fome further difeoveries, relative to the pro-
duction of the air yielded by water under other circumftances :
and though my fuccefs in thefe inquiries has not been equal to
my willies, yet, as in -the courfe of my refearches I have dis-
covered fome facts which I take to be new, and as I have con-
firmed others, already known, by a variety of new experi-
ments.
Sir Benjamin Thompson’s Experiments, &c. 85
ments, I flatter myfelf that you will not think an account of
my labours upon this fubjedt altogether uninterefting.
Before I enter upon the detail of my experiments it will be
neceflary to premile, that I fhall in general confine myfelf
merely to the fadts as they appear, without applying them to
the confirmation or refutation of the theories of others, and
• *
without entering into any fpeculative enquiries relative to their
remote caules ; and in defcribing the different appearances 1
fhall make ufe of the moll familiar terms. Thus, in fpeaking
ot the air produced upon expofing raw filk in water to the adtion
ot light, I fhall fometimes mention it as being yielded by the
filk ; and 1 fhall fometimes fpeak of the air furni filed by ex-
pofing water, which has previoufly turned green, in the fun’s
rays, as being immediately produced by the water, though it is
probable, that the green matter acts a very important part in
the produdfion of this air in the one cafe and in the other. But
how it adts is not well afcertained ; and I had in general much
rather confine myfelf to a fimple, and even an unlearned, de-
fcription of fadts, than by endeavouring to give more precife
definitions, at firff, to involve myfelf in all the difficulties
which would attend accounting for phenomena, whofe caufes
are but very imperfectly known.
You will, therefore, not be furprifed, if you fhould fome-
times find me fpeaking of appearances in the fame manner as
a perfon would mention them who faw them for the firff time,
and who did not know that others had dilcovered them before,
and how they had endeavoured to account for them. I fhall
take care that the fadts fhall be faithfully defcribed, and I flat-
ter myfelf you .will not think them the lefs intereffing on
account of their being unadorned. — But I haften to give you
an account of my experiments.
Expt -
S6 Sir Benjamin Thompson’s Experiments
Experiment N° i.
My firft objeCl was to collet a fufficieilt quantity of the ah*
feparated from water by lilk to determine its goodnefs by the
tefl of nitrous air; and to this end, having filled with clear
ipring water a globe of thin, white, and very tranfparent
glafs, 4 1 inches in diameter, with a cylindrical neck f of an
inch in diameter, and about 1 2 inches long, I introduced into
it grains of raw filk, which had been previoufly wafhed in
water, in order to free it of air ; and inverting the globe under wa-
ter, and placing its neck in a glafs jar, containing a quantity of
the fame water with which the globe was filled, I expofed it
in my window to the aCtion of the fun’s rays, and prepared
myfelf to examine the progrefs of the generation or production
of the air.
The globe had not been expofed ten minutes to the aCtion of
the fun’s rays, when I difcovered an infinite number of ex-
ceedingly fmall air-bubbles, which began to make their ap-
pearance upon the furface of the filk ; and thefe bubbles con-
tinuing to increafe in number, and in fize, at the end of about
two hours the filk, appearing to be intirely covered with them,
rofe to the upper part of the globe.
Thefe bubbles going on to increafe in fize, and running into
each other, at length began to detach themfelves from the filk,
and to form a collection of air at the upper part of the globe ;
but the meafure of my eudiometer being rather large, it was
not till after the globe had been expofed in the fun near four
days, that a fufficient quantity of air was collected to make the
experiment with nitrous air, in order to afcertain its goodnefs by
that teft.
1
on the Production of Dephlogijlicated Air .
Having at length colle&ed a fufficient quantity of this air
for that purpofe, 1 carefully removed it from the globe, and
mixing with i meafure of it 3 meafures of nitrous air, they were
reduced to 1,24 meafures; which fhews, that it was adtually
dephlogijYuated air , and that of a confiderable degree of purity.
Common air, tried at the fame time, 1 meafure of it with
I meafure of nitrous air were reduced to 1,08 meafure.
Having again expofed the globe with the fame water and filk
in my window, where the fun (hone the greateft part of the
day, at the end of three days 1 had collected 31 cubic inches
of air, which, proved with nitrous air, gave \a-yyi— 1,18;
that is to fay, 1 meafure of this air, added to 3 meafures of
nitrous air, were reduced to 1,18 meafure.
A fmall wax taper, which had been juft blown out, a fmall
part only of the wick remaining red-hot , upon being plunged
into a phial filled with this air, immediately took fire, and
burnt with a very bright and enlarged flame.
The water in the globe appeared to have loft fomething of its
tranfparency, and had changed its colour to a very faint
greenifh caft, having at the fame time acquired the odour or
fragrance proper to raw filk.
This experiment I repeated feveral times with frefh water
(retaining the fame filk) and always with nearly the fame re-
fult ; with this difference, however, that w r hen the fun (hone
very bright, the quantity of air produced was not only greater,
but its quality likewife was much fuperior to that yielded when
the fun’s rays were more feeble, or when they w r ere frequently
intercepted by flying clouds. The air, however, was always
not only much better than common air, but better than the air
in general produced by the frefh leaves of plants expofed in
water to the fun’s rays in the experiments of Dr. Ingen-
housz ;
38 Sir Benjamin Thompson's Experiments
housz; and under the circumftances the mod: favourable, it
was fo good that i meafure of it required 4 meafures of nitrous
air to faturate it, and 3,65 meafures of the two airs were de-
ll royed ; or, proved with nitrous air it gave ij + 472 = i ,35,
which, I believe, is better than any air that has yet been
produced in the experiments with vegetables.
The method I have here adopted of ufing algebraic cha-
racters in noting the refult of the experiments made to deter-
mine the goodnefs of air, though not ftriclly mathematical, is
very convenient ; and for that reafon, I fhall continue to make
ufe of it. a reprefents’the air which is proved ; 71 nitrous air ;
and the numbers which are joined to thefe letters fhew the
quantities, or the number of meafures, of the different airs
made ufe of in the experiment. The other number, which
Hands alone, or without any letter attached to it, on the other
fide of the equation, (hows the volume, or the number of
meafqres and parts of a meafure to which the two airs are
reduced after they are mixed. I fhall fometimes add a fourth
number, {hewing the quantity of the two airs deftroyed, as this
more immediately fliews the goodnefs of the air which is
Thus, in the experiment laft mentioned, 1 meafure of the
air proved, mixed with 4 meafures of nitrous air, were reduced
to 1,35 meafure, consequently 3,65 meafures of the two airs
were deftroyed ; for it is 1 + 4= 5 - 1,35 = 3,65, and the refult
of this trial I fhould write thus, i~~
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Vol. LXXVII.
B b b
&xpta-
Table IV. Deviations in the direction of the axis of the telefcope of the Equatorial Mi
Mr. Sme atom's Obfcrvation of Mercury
* 1 3
Explanation of the lefs obvious parts of the Tables of the Obferva~
tion of Mercury near his Elongation , Sept. 1786.
The third column of Tab. I contains the times of obferva-
tion as they were taken down from the half-fecond journeyman
clock, in minutes, quarters, and beats , according to the following
method ; which was, by taking up the beat when the fecond
hand came to 15, 30, 45, or 60, and then counting 30 beats re-
peatedly till the arrival of the object at the middle of the wire it
was approaching ; after its arrival, the beats (or interval be-
tween two beats) being retained in memory, and the eye cad
upon the dial-plate, it was eafily feen whether it was fo many
beats more than the quarter, the half, three-quarters, or the
whole minute, and was fet down accordingly. Thofe reduced
to minutes, feconds, and tenths of feconds, by allowing .2 or .3
for the quarter fecond, .5. the half, and .7 or .8 for the three-
quarters of a fecond, are contained in the fourth column. The
reduction of the fourth column to the f fth was by means of the
auxiliary Tab. II.; and Mercury being then nearly da tion ary
refpeffing the fun, the fun’s run was ufed for the planet in-
dead of that of a dar. The mean of each fet of obfervations
of the fifth column is carried into the fixth.
The feventh column contains the parts of the micrometer
as they were read off; to render which intelligible, it is to be
noted, that the declination wire A travels from the upper fide
of the field of view of the telefcope towards the center, and
fomewhat beyond it : and upon it are taken all the objects that
pafs the field of view on the upper fide, anfwerable (by inver-
fion of the objecd) to the font hern half of the field ; and in
like manner thofe that pafs the field of view on the lower
2 half
'With an Equatorial Micmftietefc $*9
half are taken upon the wire B, and for the fame reafon denote
a 'declination north. The fcale of the micrometers of each
wire begins from a point affirmed fomewhat without the field,
and the number increafes from thence towards the center of
•the field, and continues beyond it ; the integral parts are the
turns of the fcrew, and the centefimal the divifions of the
index plate, being divided into ioo parts. The point of the
fcale, anfwerable to the center of the field of view, having*
been found by obfervations on each fcale refpectively ; when
the wire A ( Aujiralis) {lands at 30.84, it is in the center of the
field ; and when the wire B ( Borealis ) is at 28.1 1, it alfo cuts
the fame center. Hence the parts of the micrometer being
refpectively taken from thofe two numbers (which may there-
fore be called ccnjiant numbers) the remainder will be the
diftance of each refpedtive wire from the center in parts of the
micrometer. Thus, in the obfervation of 0 Tauri upon the
23d, the parts are B 8.39; this taken from 28.11, leaves
N 19.72, which are placed in col. 8. as the diffance, in parts
of the micrometer, that 0 Tauri paffed north of the center of
the field of view, or axis of the telefcope.
In like manner, in the obfervation of Mercury on the 23d*
the parts are B 28.85 ; but this being greater than the conftant
number 28.11, the excefs will be .74 parts; which being the
parts reaching beyond the center, they will be fo much fouth
of it, and are fet down therefore in col. 8. S 0.74 : and in this
manner the declinations of the reft are made out, from their
refpedlive numbers of parts of the micrometer, and fet down
in col. 8.
The numbers of the fixth column of Tab. 1. are transferred
to the third column of Tab. III.; and the declinations fet down
in parts of the micrometer, Tab. I, col, 8. are transferred to
col. 7. of Tab. Ill,
Ebbs Cob
Ebbs
330 Mr. Sweat on’s Obfervaticn of Mercury
Col. 4, of this table contains the corre< 5 lions of the-
times deduced from the journeyman clock (as per col. 3.)
to reduce it to mean time; which corrections are made
out from the general account of the goings of the tranfit
clock, corrected by tranfits of the fun, taken the. 2zd, 23d,
27th, and 30th of September, 2nd the 12th, 13th., and 14th
of O&ober *. The journeyman deck was regularly com-
pared at nights and mornings with the tranfit clock ; and ge-
nerally immediately after the obfervation. The meridian and
rotative obfervatories in which the clocks refpeCtively were,
are at the diftance of 53 yards E. and. W. ; the comparifons
were made by a feconds flop watch 4-.
The numbers of the fourth column being properly applied
to thofe of the third produce the fifth ; and which, with the
fixth column, will be fufficientLy explained by their titles. The
parts of the micrometer in the feyenth column, being reduced
into minutes and feconds, are contained in col. 8. and reflec-
tively fhew the minutes and feconds at which each objeT
pafled to the north or fouth of the center of the telefcope.
The value of the parts of the micrometer were obtained by
previous obfervations, from whence the following rule was
deduced : the numbers of turns and centefimal parts being con-
iidered as integral, and divided by 1.08, the quotient will be
the number of feconds. Thus,, in the obfervation of 0 Tauri
* The tranfit clock was made by Hindley, and has a pendulum rod of
etdar wood.
t The journeyman clock was generally fet to the tranfit clock on Sunday
mornings; and when from home the former was fuffered to go down. The
journeyman will generally agree with the tranfit clock to 1" in 24 hours; but during
the period of thefe obfervations, went remarkably well.
upon
with an Equatorial Micrometer. 331
upon the 23d, the parts 1972, divided by 1.08, gives 1826"
= 3 q/ 7 ; and the parts of mercury .74, divided by i.o8=r~
, ' 6 S // ■= i / 8 // . Now the telefcope being fixed to one point of the
heavens during the whole period of thefe obfervations, without
any motion of any of the parts, the fcrews commanding
the declination wires A and B excepted, we are enabled to
judge of its fteadinefs to this point by the following remarks.
If it varied in declination, , this would.be fhewn by the paflage
of the fame ftar at a different diftance from the center of the
telefcope at different revolutions ; and if it varied in right afcen-*
fion, it would be fhewn by its not pafling the horary wires at
the due time, according to the acceleration of the ftars upon
the mean time of the. fun.. Both the right afcenfion and de-
clination may be varied by differences of refraction of the air
at the fame altitude ; and the right afcenfion is further liable to
be apparently varied, by the errors of the tranfit inftrument, -the
tranfit clock, the transferring of its time to the journeyman
clock, the intermediate errors of the fame, and of the obfer-
vation itfelf; and as there paffed an interval of. almoft .16
hours betwixt the paflage of Mercury over the field of. view of
the telefcope and that of x Ceti, whiclx was the nearefl: flar
wherewith a comparifon could be made, it will be a fatisfac-
tion to fee, as before intimated, what variations arofe in flill
greater intervals of time.
In right afcenfion.-
, „
Thus \ Ceti upon Sept. 23. paffed the horary wires at • - 9 II 28.3
an 4 — 26. • S 59 40*6
\ Ceti therefore came fooner in three days by' -
but - ought to accelerate on mean time - ~
therefore came after three days exadly to the time.
11 47-7
11 47.7
Again*
33^ Mr. Smeaton’s Obfervation of Mercury
Again, o Tauri upon Sept. 23. patted the horary wires at -
and • 26. — — — — -
e Tauri therefore came fooner after three days by — —
ought to accelerare on mean time - —
/ u
9 3 6 27-3
9 2 4 39-3
11 47-5
11 47.7
therefore came too late in rhree days by
.2
la declination.
/ //
0 Tauri upon Sept. 23. patted north of telefcope’s center » 30 26
26. — * ‘ — - 30 18
— — . — therefore patted lefs north, or more fouth, than before by 8
In like manner every companion that Tab. III. affords is par-
ticularly fef down in Tab. IV. which containing thirteen com-
panions in right afcenlion and ten in declination, the greateft
deviation -in right afcenlion is i // . 2 , and ii /; of a degree in
declination. This fuppofes every error before mentioned to
xefide in the inftrument, and every other inftrument and obfer-
vation, which were concerned in the refult, to be perfedf ;
which, from the fmallnefs of the total errors, feems to indi-
cate a degree of fteadinefs ill the inftrument unexperienced or
unnoticed before.
Deduction of the f option of Mercury from the ‘preceding
obfervatio?is as ft down in Tab. Ill,
In right afcenfion from col. 6.
in
6 Tauri followed X Ceti Sept. 2 %. - - - 24 59
— — — 26. - - 24 59.2
30. - - 2459.1
* oa. 13. - - 24 58.7
-■ at a mean 'of the four - - 24 59
» Orionis
•with an Equatorial Micrometer.
Orionis followed o Tauri Sept. 50.
' * Oct. 13.
333
h. ,
2 29 49.9
2 29 50.1
— - • ■ at a mean —
Now Mercury preceded x Ceti Sept. 23. —
X Ceti preceded 0 Tauri by mean of four
0 Tauri preceded « Orionis by mean of two
2 29 50
48 53.4
24 59
2 29 50
Mercury therefore preceded a Orionis by - — 18 43 42 ^
J11 declination from col. 8i
Sept. 23. A.M. Mercury parted the middle horary wire, fouthofits center I 8
Same evening 0 Tauri parted the middle horary wire, north of it — 50 26*
Therefore Mercury parted the middle horary wire more Si than 0 Tauri by 31 34..
But Sept. 26. x Ceti parted N. of center
■ 0 Tauri
30. x Ceti
* 0 Tauri — —
Oft. 13. x Ceti
0 Tauri — — ■
30 18 J
*7 nl
3° J
17 ”1
30 15/
/ u
J 3 7
J 3 6
! 3 *
From the fmallnefs of the above differences we may in fer^
that very little uncertainty in declination had attended that
palfage of 0 Tauri upon Sept 23.
P? Upon Sept. 30. 0 Tauri parted N
. « Orionis S
Upon Oft. 13. 0 Tauri parted N
« Orionis S
3° ^ l
24 20 J
3° *5]
24 20 j
/ it
Sunl 54 37
54 35
'3
* Orionis then at a mean parted more fouth than 0 Tauri , — « 54 36
Merc, therefore on the 23d parted with more N. declination than* Orionis 23 2
r
InveJUgation-
: 35-1- 'Mr. Smeaton’s Obfervation of Mercury
Invejligatlon of the efj'&Bs of refraCtion.
The preceding dedu&ions-and remarks v fhew the confifteney
of the obfervations with themfelves ; yet, * from' the poii-
tion of the telefcope, it being only elevated n°f above the
horizon?, it is necelFary to examine how far the deductions
above fpeeified were, capable of being affeCted by refraction.
And in this refpeCt'it will appear, that if it be fuppofed, there
-is no difference in the quantity ©f refraCtion of fuch objects as
appear within the limits of the held of view of this inftrument
(which is i° i y), then their relative pofitions to each other will
not be affeCted thereby : for if in fig. i . (Tab. XIII.) we fuppofe
the circle-X HRO to reprefent the boundary of the field of view,
HO being an horizontal and VR a vertical line, each, paffing
through, the ..center of the field at L; and if PLP denotes a
part of a parallel of declination, then BLX perpendicular
thereto, will be apart of an horary circle, both palfing through
the fame center. Now let d* be the apparent path of a flar,
fuppofing it unafFe&ed by refraCtion fill it comes to the vertical
line at *, and there to be lifted' up by refraCtion in the faid
vertical to L. Let e+ denote another ftar, alfo unaffeCted by
refraCtion, to pafs along the .different parallel of declination
e+ till it comes to + ; then, if it be fuppofed that the two
'Itars are both fituated in the fame horary circle, if at the point
+ refraCtion takes place, and by hypothefis • this is lifted up
equally with ’the other, in the perpendicular +/, then the
line +* being drawn through the places of the two Itars, will
• be cotemporary and parallel to LX; and the figure /+ #L
being evidently a rhomboides, the two Itars, fo altered by
* .This will readily be deduced by infpedion of the celeftial globe.
refraCtion,
ninth an Equatorial Micrometer. 335
refraction, will arrive together at the horary circle LX at the
(ame time, and with the fame difference of declination, as if
ho refraCtion had taken place. It is therefore only the difference
of refraCtion which takes place in objeCts at different heights
in the fame field , that can alter their relative fituations : how-
ever, it appears neceffary to examine what this may amount
to.
Let the letters in fig. 2. denote the fame things as before:
to which we will add, that a. A, B, C, D, denote the parallel
horary wires of the micrometer, and AA , BB, the declina-
tion wires, denoted A and B in the tables : now from the celcftial
globe we fhail alfo readily obtain the horary angle VLP — 54T
— L be. Let now an objeCt pafs along the wire A A from the
horizontal line at d to the vertical line at h \ in this it will pafs
through a difference of refraCtion, according as it gets more
and more elevated above the horizontal line HO; and let the
elevation Lb be half a degree or 30 minutes : then, according
to Dr. Bradley’s Table of RefraCtion*, the difference of
refraCtion betwixt the 78th and 79th degrees of zenith diffance
is 23". 6, half of which 1 i'A8, may be effeemed the difference
of refraCtion for a difference of half a degree of altitude at
78°! zenith diffance, or of u°| altitude: the objeCt, there-
fore, in paffing from the horizontal line at d to the vertical line
at b paffes through every difference of refraCtion from o x/ to
n'hS ; and the queffion is, how much it is at a medium , that
is, when it arrives at the middle wire at the point c ? F rom
this point let fall the perpendicular ce . Now, the proportion
of the {ides of the triangle db L being given from conffruction,
they may be taken off by a fcale, viz*
* Inferred in Dr. MasxelYne’s Obfervations, Vol. I. ]>. 13.
Vol. LXXVII. C c c Sup-
336 Mr, Smeaton’s Obfervation of Mercury
Suppofe 1 74
db — 299
d L =242
and afifuming the fide L£ = 30
the other Tides by proportion r db=$j.6
as above will be i^ 7 L = 4i.y
The triangles Lbc and dee are fimilar to dbL ; therefore fay,,
as db — 5 1.6 : dL — 41.7 :: Lb — 30 : Lc = 2 4 ; and as L b~
30 : Lit — 24 :: ^=41.7 : = 33.5 ; and again, as db —
51.6 : ^ — 33 5 :: L£ = 30 : r£ = 19.5 : but this will affeeff the
declination, only in proportion of the line ef drawn parallel
to LX ; and it will affect the right afcenfion according to the
lineyt: but the triangle ecf being fimilar to the original one
dbL , we fhall have db — 5 1 .6 : Lb — 30 ce = 19.5 :fc=: 1 1.3
for the line affecting the right afcenfion; and alfo, as db —
51.6 : dL =■ 41.7 :: ce— 19.5 : ef— 15.8 for the line affecting
the declination. But the effect of difference of refraction upon
the line Lb -=30' being only ii' 7 .8, the refpective effects of
the lines fc and ef will be in proportion ; that is,
/ / // //
as 30 : 1 1.3 :: 1 18 : 4.4 for the effect in right afcenfion,
and a3 30 : 15.8 :: 11.8 : 6.2 — declination ;
but as it has been determined, that when the line L b is 30
minutes, the line LC, or the correfponding declination, will be
only 24 minutes ; the effets of refration above Bated will be
therefore due to 24b
Correction for the poftion of the wires.
The above corretions take place on fuppofition that the
feveral wires of the micrometer were ffritly parallel to the
refpetive parts of the circles of declination, and horary circles
in the heavens ; but in the pra&ical ufe of this inffrument it
is
1
with an Equatorial Micrometer. 337
is found more convenient, on account of a ready and certain
adjustment, to place one of the wires AA or BB parallel to
the apparent track of the Star wherewith the planetary body is
to be compared: in confequence, when the Star * , fig. 1. is
lifted up to L, it will not Strictly purfue the line LP ; but
being lefs and lefs lifted up as it mounts higher, it will appa-
rently fall more and more below the line LP as it afcends above
the line HO, and will therefore take a courfe, fuppofe L p.
The wire PLP being therefore adj ufted to agree with pLp ; by
conftrudion of the instrument, the wire BLX will aStume the
pofition qLx perpendicular to pL p. The Star, therefore, that
ran along the parallel e + before it Suffered refraction, and at
+ was fuppofed to be lifted up to /, there not meeting LX
will take the courfe ly , nearly parallel to L p, and have fome
difrance, as lz, to travel before it arrives at the new- placed wire
Lx ; and it is now proper to examine what this quantity
may be.
Through the point % draw the line rzos parallel to HO, and
cutting the vertical RLV in 0, and let L 0 be afiumed = 30 / ;
then, lince the angle XLv is fuppofed to be minute, the grofs pro-
portions of the fides of the triangles L yz and Lyl may be, for
this purpofe, fuppofed the fame *, and the fame as Li be, dbL ,
fig. 2. to which the triangle L zo, fig. 1. will alfo be Similar ;
as likewife the triangle yzo, and alfo the little triangle zlv : but
making the Side Iv of the triangle zlv equal to the etteCl of
refraCtion in perpendicular = 1 1 " . 8 ; then, to find the Side lz,
* I 3m aware, that the fuppofition of the fides of the triangles L yz and Lyl
being the fame cannot be itri&ly lb; nor can they have the fame proportions ; nor
are any of the lines concerned right lines, that are fuppoled fuch ; but aflumptions
near the truth are allowable for the correction of an error in the grcatcjl part ,
that if uncorreCted would fcarcely amount to a grofs error .
C c c 2
the
33S Mr, Smeaton’s Observation of Mercury
the didance run from the firil to the lad fuppofed place of the
wire, we need only fay, as L.b= 30 : db — 5 1.6 :: lv — 1 i 7/ . 8 : /z
r=20 // .3 ; and this will be its value when the declination Lc*
fig, 2. is 24 / ; but then the declination L/ or L c ~, fig. 1.
being greater than the perpendicular fide 1^0 (alTumed 30 7 ) in the
proportion of L% : Lo, fay, by fimilarity of triangles converfely,
as dL = 4i.7 : db~ 51.6 :: ho — 3c 7 : Lz — f&'.i ; but as the
corredion before dated of 2o 7/ -3 is an angular error, taking place
in proportion to the didance from the center, or the declination ;
for the declination given of 2 f fay, as 38.2 : if :: 2o 7/ .3 : 13;
to which adding 4 7/ . 4, we (hall have for the whole error
in right afcenfion, fuppofing it in the equator, but mud be
again increafed in the proportion in which a dar having decli-
nation is dower than a dar in the equator ; that is, it mud be
increafed in the proportion of any of the numbers in the
fourth column of Tab. II. to the fimilar ones in col. 6. of
the fame table; that is, as T 4b 77 : T 47" or as 106 : 107,
:: 1 7 7/ .4 : 1 7 " 7 6 *.
As all thefe errors, arifing from difference of refradion, are
in proportion of the didance of theobjed from the center of the
telefcope, they will take place in proportion to the difference of
declination of the two objeds to be compared, whether they have
paded the field on the fame, or on different fides of the center.
Now the difference of declination of Mercury and u Orion is-
being only 'if 2 " •> and the quantities being made out for 24 /
fay (rejeding the 2 feconds), as 24 7 : 23 7 :: 17A4 :
which turned into time in the run of the dar will be i 7/ .i
in right afcenfion.
* My friend Dr. Maskelyne obferves, that in JtriHneJs each liar ought to
have its own proper reduftion, on account of difference of declination, which in
mtrem cafes will amount to a fenlible quantity,
3
Say
with an Equatorial Micrometer.
Say again, as 24' : 23' :: 6A2 : 6 7/ , the correction in de-
clination. From the near equality of the lines L / and Ls, it
is evident, that no correction of declination is neceflary on ac-
count of the inclination of the wires, the whole difference fallino*
£>
in right afcenAon. As therefore Mercury pafled with z j z"
more north declination than a. Orionis, and pafled through a
part of the medium that lifted him up lefs ; it therefore gave
him lefs north declination than it did to a, and therefore appa-
rently diminifhed the real difference ; hence muft be added
to the apparent difference 23' z'\ making it 23' 8" difference
of declination : and as Mercury was lifted up lefs than a>
he would not fo foon come to the middle wire by i 7/ .i as he
fhould have done, he therefore came too late by 1". 1, which
mufl: be fubtra&ed from the time of Mercury’s paflage the 2d
of Sept, which will increafe the time in which he preceded
u Orionis; that is, 18 h. 43' 42 /7 .4 increafed by 1.1 will be-
come 18 h. 43 7 4 3". 5 difference of right afeenfion.
I have been the more particular in the inveftigation of this
obfervation, firft of all to afeertain the degree of dependance
that may be formed on an inftrument of the kind ; and, fe-
condly, to infer fuch eafy and Ample rules, that other Amilar
obfervations may be the more eaAly reduced. Being therefore
latisfledof the liability of the inflrument j if we had concluded
the obfervation with that of Mercury in the morning, and of
0 Tauri in the evening of the 23d, then the refult from Tab.
111. fliould have been
/ //
Mercury pafled the wires at •* *- “ 22 34*9
And 0 Tauri pafled at - 9 3 6 2 7-3
Difference of right afeenfion
i5 J 3 52.4
which
34° Afr. Smeaton’s Obfervation of Mercury
which is the very fame as was before deduced from the 1
mean of the whole :
/ //
And if to Mercury’s declination fouth of telefcope s center — i 8
We add o Tauri’s north — 30 26
We fnall have for the difference of declination — - 3 1 34
the fame as before determined. Our obfervation would, there-
fore, in this cafe limply have been, that Mercury preceded
0 Tauri in right afeenfion 15b. if 5 2 ".4 mean time, and
palled the wire with more fouth declination than 0 Tauri by
0+ *
After this, 0 Tauri would have required to be compared with
fome Well rectified liar by meridian infhuments ; but in the
prefent cafe « Orionis, one of Dr. Ma^kelyne’s Catalogue of
34 principal liars happened to lie fufficiently near the fame pa-
rallel of declination, to admit of 0 Tauri to be compared
therewith by the fame inlfrument, while pointed to the fame
place of the heavens. The operations which were fubfequent,
therefore, mull be confidered as intended to fave thole of a
meridian inllrument.
Now had our obfervation concluded with the above, then
the correction would have taken place upon the difference of
declination of 0 Tauri with Mercury, inflead of the ultimate
one with a Orionis; but it mull be obferved, that whatever
quantity of correction the difference of declination would occa-
lion, it would be compenfated in the difference of refraCtion of
of 0 Tauri and « Orionis, when they came to be obferved on
the meridian ; however, in the prefent cafe it happens to be
more commodious, as both can be done under one.
Preparatory then to the laying down the limple rule for the
correction of refraction, it is proper to premife, that it is evi-
dent,
with an Equatorial Micrometer. 341
dent, the lines, fig. 2. L b, L c, ce, ef, being in continued
proportion L£ will be to ef in triplicate proportion of L b to
L c ; and that Lc will be to ef in duplicate proportion of
L b : L c. The difference of declination, therefore, due to
30' difference of elevation will be as L b to L c limply ; but the
efteCt of difference of refraCtion in declination will be lefs than
the difference of declination in the proportion of : Lc z ;
and that the effeCt of difference of refraction in right afcenfion
will be lefs than the difference of refraction in declination in
the proportion of L b : cb limply.
Now it has been remarked, that the elevation of the tele-
fcope’s center above the horizon, and the horary angle VLP,
will always be readily given near enough for the purpofe by
the globe. A triangle given L bd can therefore be cfonltruCted,
and the fide \J> being made 30' (or any convenient aliquot
part of a degree) the other fides will be found by propor-
tion : fay then, as in the prefent cafe, db= 5 1.6 : dL, = 4.1.7 ::
1^ = 30 : Lr=24, for the difference of declination correfpond-
ing to half a degree of altitude: fay then, as 51.6“ 41.7%
that is, as 2663 : 1739 :: 24 : 15.7 = ^ But without trou-
bling ourfelves with high numbers, if we take the proportion
51.6 to 41.7 by the Hide-rule twice, we fhall arrive at 15.7,
near enough for the value of the line ef : fay then, as L b~
30 : ef — 15.7 :: 1 T'.8 : 6". 2 for the refraCtion in' declination :
and as ^ = 41.7 : U— 30 :: 6A2 : 4". 4 for the refraction in
right alcenlion, according to the true pofition ot the wires :
and, for the correction of right afcenfion in the pofition of
the wires, lay,
Fig. 2. Fig 1.
t — A ^ / ' — ^
As L£z=30 : db ~ 5 1.6 :: h = 1 1 ".8 : lz— 20 " ;
and again, dJL = 4 i-J ; <#1=51.6 :: L1. LXXVIL lab. 3011- 342 .
Fig\ 2.
:
/
/
t
/
I
wit/j an Equatorial Micrometer. 343
Mercury in right afcenfion ; but if a ran the whole rotation
— 360° in 23 h. 5b 7 4 7/ . 1, what portion of it will be run in
5 h. i2 7 20 /7 .6= i8740 /7 .6 ?
But 24 h. = 86,400 feconds, and 360 = 1,296,000 feconds:
Time. Time. Of degrees. Of degrees 0
Say then, as 86400" : 18740". 6 :: 1296000" : 281 109"— — 78 5 9
But, according to Dr. Maskelyne’s feleft Catalogue, the right afcen-
ficn of a Orionis for Sept. 30, 178b, was, (which add) - 85 54 12
The right afcenfion of Mercury at the time of obfervation was therefore 163 59 21
According to Dr. Maskelyne’s feleft Catalogue a Orionis had decli- 0 y
nation north, corre&ed for precetfion — — 7 21 8.8
The fum of aberration and nutation from ConnoiJJance des Temps — •+■ 8.4
The correft declination north of a Orionis
To which add that Mercury pafled more north
7 21 17.2
23 8
Mercury’s declination therefore was
7 44 25.2
The refult.
1786, Sept 23. A.M. 1 Mercury , s f right afcenfion
at 5 h. 22' 35" M.T. J l declination north
163 59 21
7 44 25
Vol. LXXVII.
Ddd
[ 344 ]
XXXIV. A remarkable Cafe of numerous Births , with Obferva-
tions . By Maxwell Garthfhore, M. D. F* R. S. and A, S,
in a Letter to Sir Jofeph Banks, Bart. P. R, S.
Read June 21, 1787.
TO SIR JOSEPH BANKS, BART. P. R. S.
SIR, St. Martin’s-Lane. May 28, 1787.
'“T^HE following very extraordinary cafe, communicated to
JL me by Dr. Blane, F. R. S. I take the liberty, at his
delire, to tranfmit to you, with his letter to me, containing
the proofs of its authenticity ; hoping that it will appear to
you, as it did to us, worthy of being read at one of the meet-
ings of the Royal Society, as a fa£t in natural hiftory, w r hich is
equally uncommon, curious, and well vouched. In order, how-
ever, to make its lingularity more apparent, I have taken the li-
berty to fubjoin fome obfervations on births of this kind, with
fuch well authenticated accounts of limilar events as I have been
able to procure, confining myfelf chiefly to thofe which have
happened in our own country, where we are leafl: likely to be
deceived.
I have the honour to be,&c.
MAXWELL GARTHSHORE.
P. S.
Dr. Garthshore’s Remarks , See. 345
P. S. As one proof of its Angularity, I, many months
ago, employed various friends at Peterfburg, Berlin, Vienna,
Lyons, Paris, and Ghent, to collect for me well authenticated
cafes of this kind, and I have not as yet been able to procure
any.
Copy of a letter from Dr. Blane, Phyfician to his Majefty’s
Navy and to St. Thomas’s Plofpital, F. R. S. to Dr. Garth-
flaore, Phyfician to the Britifh Lying-in Hofpital.
D E A R S I R, * Sackville-Street, June 22, 1786.
A few days ago, I received from the country an account of a
woman who was delivered of five children at a birth in April
lafl. As your extenfive experience and reading in this line of
practice enable you to judge, how far this fa£t is rare or inte-
refting, I fubmit it to you, whether it deferves to be commu-
nicated to the Royal Society. Mr. Hull, the gentleman who
fent me the cafe, is a very fenfible and ingenious practitioner of
phyfic at Blackburn, in Lancafiaire. He attended the labour
himfelf from beginning to end, and his character for fidelity
and accuracy is well known to me, as he was formerly a pupil
at the hofpital to which I am phyfician ; fo that no fact can*
be better authenticated. He mentions alio, that he has pre-
ferved all thofe five children in fpirits; and, if delired, he will
fend them for the infpeftion of the Society *.
I am, with great regard, &c.
Gilbert BlAne.
* They were accordingly lent ; and having been exhibited to the Society when
this Paper was read, are now depolited in the Mule uni ol Mr John Hunter.
d d d 2
Margaret
346 Dr. Garthshoke’s Remarks on
\
Margaret Waddjngton, aged twenty-one, a poor woman
of the townfhip of Lower Darwin, near Blackburn in Lancaffiire,
formerly delivered of one child at the full term of pregnancy,
conceived a lecond time about the beginning of December
1785, and from that period became affedled with the ufual
fymptoms that attend breeding. At the end of the fir (l
month, fhe became lame, complained of conliderable pains in
her loins, and the enlargement of her body was fo remarkably
rapid, that fine was then judged by her neighbours to be almoft
half gone with child. At the end of the fecond month fhe
found herfelf fomewhat larger, and her breeding complaints
continued to increafe. When the third month was completed,
fine thought herfelf fully as large as fhe had formerly been in
her ninth month, and to her former fymptoms of hauled, vo-
miting, lamenefs, and pain of the loins, fine had now added a
diftreffing fhortnefs of breath. She continued to increafe fo
rapidly in lize, that fhe thought fine could perceive herfelf
growing larger every day, and file was under the frequent
neceffity of widening her cloaths. When fire reckoned herfelf
eighteen weeks gone, fhe firft perceived fomewhat indiftindtly
the motion of a child. By the 20th of April, 1786, all her
complaints were become much more diftreffing ; fhe had much
tenfion and pain over all the abdomen, her vomiting was in-
ceffant, and fhe now could not make water but with the utmofl
difficulty. The fymptoms being palliated by Mr. Lancaster,
fhe advanced in her pregnancy to Monday the 24th of April,
when being fuppofed to have arrived at the twentieth week,
fhe was feized with labour pains. Thefe continued gradually
to increafe till the next day, about two in the afternoon ; at
which time I was fent for, Mr. Lancaster being abfent,
and
a Cafe of numerous Births . 347
and (he was foon delivered of a fmall, dead, but not putrid,
female child. The pains continuing, this was foon followed
by a fgcond leis child ; to this very foon fucceeded a third,
larger than the firft, which was alive ; to thefe a fourth foon
followed, fomewhat larger than the firff, and very putrid ;
laft ol all, there loon lucceeded a fifth child, larger than any of
the fo rmer, and born alive. Thefe five children were all fe-
males ; two were born alive ; and the whole operation w r as per-
formed in the fpace of fifty minutes. The firft made its ap-
pearance at two in the afternoon, and the laft at ten minutes
before three. Each child prefented naturally, was preceded by
a iepaiate burft of water, and was delivered by the natural
pains only. In a fhort time after the birth of the lad, the
placenta was expelled by nature without any haemorrhage, was
uncommonly large, and in fome places beginning to be putrid.
It conlifted of one uniform continued cake, and was not divided
into diftinct placentulae, the tabulated appearance being nearly
equal all over. Each funis was contained in a feparate cell,
within which each child had been lodged ; and it was eafy to
perceive, by the fhate of the funis, and that part of the pla-
centa to which it adhered, in which fac the dead, and in which
the living children had been contained. I examined the fepta
of the cells very carefully, but could not divide them as ufual
into diflin£t laminae, nor determine which was chorion dr
which amnios. I could not prevail on the good women to
allow me to carry it home, to be more narrowly infpe&ed ;
and I fubmitted more readily to their prejudice for its being
burned, as its very foft texture- fee med to me to render it hardly
capable to bear injection. The two living children having fur-
vived their birth but a fhort time, I was allowed to carry them
home ; and I have prelerved the whole five in fpirits, and have
fince
3 48 jP r . Gahthshore’s Remarls on
fmce weighed and meafured them, and find their proportions
to be as follows in Avoirdupois weight, inches and parts.
The iff born dead
0 z. Dr.
6 J2 Length
Inchei.
9
The 2d — ■
— putrid
4 6
8|
The 3d —
— alive
8 1 2
94
The 4th —
— putrid
6 1 2
94
The 5th —
— alive
9 —
94
The mother, in fpite of the crowds with which her cham-
ber was continually filled, continued to recover, and was able
to be out of bed on the 27th and 28th, her third and fourth days ;
but finding herfelf then weak, by my advice, kept her bed till the
nth of May, when fhe went out of doors, and on the 2 iff
walked to Blackburn, two miles diflant. This was the 27th
day from her delivery, fhe having entirely recovered her
ftrength without any accident. It may not be improper to
add, that the hufband of this woman has been in an infirm ftate
of health for three years paft, and is now labouring under a
confirmed phthifis.
I am, &c.
Signed, JOHN HULL.
Blackburn, Lancalliire,
June 9, 1786.
Obfervations
a Cafe of numerous Births .
349
Obfervations on numerous Births .
%
THOUGH the females of the human fpecies produce
moft commonly but one child at a birth ; and though
their formation with only two breads, and one nipple to
each, renders it probable they were not originally intended to
produce in general more than two ; yet, from what we know
of the womb and its appendages, and what from the lated
experiments we are led to conjecture as to the mode of con-
ception, we cannot prefume a priori to fet limits to the
fertility of nature, nor determine decifively what number of
foetufes may be conceived and nourilhed to a certain period
in the human uterus at the lame time.
The prefent lingular and well-atteded cafe allures us, that
five have certainly been born at once, and we have no title
abfolutely to reject all the tedimonies of even more numerous
births, or to fay that, in fome rare indances, this number has
never been exceeded.
What has tended to render relations of this fort ridiculous,
and to throw a degree of diferedit on the whole, is the many
marvellous, and evidently ablurd and incredible hidories, which
not only the retailers of prodigies, but even the credulous
writers of medical obfervations, have colle&ed.
I need only refer thofe, who wilh to amufe themfelves with
furpriling relations of this kind, to the curious collections of
Schenkius, SchurigiUs, Ambrose Parey, and others.
But, in order to Ihew how very uncommon births of this
kind are, and how truly fingular the cafe communicated by
Mr. Hull to Dr. Blane is, I take the liberty to fubjoin a
Ihort
35>o Dr, Garthshore’s Remarks on
fhort view of -the ufual courfe of nature in this matter among
ouf own country- women, where we are lead likely to be
deceived.
Though female fertility certainly varies according to the
climate, fituation, and manner of life ; yet, 1 believe, it may
be taken for a general rule, that where people live in the moil
fimple and natural (fate, if they are the beft nourifhed, and if
they enjoy the firmeli health and ftrength, they will there be
the mod fertile in healthy children; but we have no data to
determine that they will there have the greatefl number at une
birth.
At the Britifh Lying-in Hofpital, where we have had
18,300 delivered, the proportion of twins born has been only
one in 91 births. In the Weftminfter Difpenfary, of 1897
women delivered, the proportion of twins has been once in
80 births; but in the Dublin Lying-in Hofpital, where above
21,000 have been delivered, they have had twins born once
every lixty-fecond time. The average of which is once in 78
births nearly, in thefe kingdoms.
The calculations made in Germany from great numbers, in
various fituations, Bate twins as happening in a varied propor-
tion from once every fixty-fifth to once every feveutieth time.
But in a more accurate and later calculation made at Paris,
by M. Tenon, Surgeon to the Salpetriere, we learn, that
in 104,591 births the proportion of twins was only one in
96, which is only a fmall degree lefs than we have calculated
at the Britifh Lying-in Hofpital.
It would be eafy to add other calculations, all differing from
thefe and from one another, more or lefs ; but I hope thefe are
fufficient to fhew that nature obferves no certain rule in this
matter ;
a Cafe of numerous Births. 35 x
matter ; and that even twins, the mofl ufual variation, is not
a very common occurrence.
When we advance to triplets, or three born at once, we
find comparatively very few inftances in this or any other
Country ; and though every one has heard of fuch events as
now and then happening, yet very few have feen them.
In all thofe 18,300 women delivered at the Britifh Lying-in
Hofpital, there has not been one fuch cafe. In the London
Lying-in Hofpital, where, being inflituted later, 'much fewer
have been delivered, they have had two fuch recorded as
prodigies. In the Weflminfter Dilpenfary, in 1897 women
delivered, there has been but one fuch event.
In the Dublin Hofpital, in 2 1 ,000 births, they have had triplets
born thrice, or once in 7000 times, but have never exceeded
that proportion or number, born at one time.
In a pretty extenfive pradticeof above thirty years, both in the
county of Rutland and in London, I have attended but one la-
bour where three children were born ; am perfonally acquainted
but with one lady who, at Dumfries, in Scotland, after bearing
twins twice, was delivered of three children at once ; and I was
Clever acquainted with any one who produced a greater number.
Yet fo much does this matter vary at Edinburgh, that Dr*
Hamilton, Profeffor of Midwifry, writes, he had feen trip-
lets born there, five or fix times in lefs than twenty-five years.
Mauriceau, in a long life of very extenfive practice at
Paris, with opportunities of knowing moft things extraordi-
nary that happened in his time in France, tells us, he had feen
triplets born but a few times ; had heard of four in that city
but once, and mentions no greater number.
One circumftance which he relates is fo far worthy of atten-
tion, as it accords with one fomewhat fimilar fubjoined to Mr.
Vol. LXXVII. E e e Hull’s
352 Dr. Garthshore’s Remarks on
Hull’s cafe now read, viz. “ That the hufband of one of
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