Acfessions property OF THE
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A
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AN ACCOUNT
EXPERIMENTS
TO DETERMINE
THE FIGURE OF THE EARTH,
BY MEANS or THE
PENDULUM VIBRATING SECONDS IN DIFFERENT LATITUDES
AS WELL AS ON
VARIOUS OTHER SUBJECTS
PHILOSOPHICAL INQUIRY.
By EDWARD SABINE,
rAPTilV IK THE ROYAL REGIMENT OF ARTILLERY; FELLOW OF THE ROYAL AND LINN^AN
SOCIETIES OF LONDON ^MEMBER OF THE ROYAL SOCIETY OF SCIENCES OF NORWAY;
CORRESPONDING MEMBER OF THE ROYAL SOCIETY OF SCIENCES AT GOTTIN-
GEN HONORARY MEMBER OF THE HISTORICAL. AND OF THE LITE-
' RARY AND PHILOSOPHICAL, SOCIETIES OF NEW YORK.
PRINTED AT THE EXPENSE OF THE BOARD OF LONGITUDE.
LONDON:
JOHN MURRAY,
BOOKSELLER TO THE BOARD OF LONGITUDE.
MDCCCXXV.
LONDON:
PRINTED BY VflLUAM CLOWES,
Nortbuoiberlaod'Court.
TO
DA VIES GILBERT, Esq., M.P.
TREASURER AND A VICE-PRESIDENT OF THE ROYAL SOCIETY,
AND A COMMISSIONER OF THE BOARD OF LONGITUDE;
WHO, IN THE SESSION OP 1816, MOVED AN ADDRESS OF THE HOUSE OP COMMONS TO THE CROWN,
PBAVING, " THAT HIS MAJESTY WOULD BE GRACIOUSLY PLEASED TO GIVE DIRECTIONS
FOR DETERMINING THE VARIATION IN THE LENGTH OF THE PENDULUM
VIBRATING SECONDS, AT THE PRINCIPAL STATIONS OF THE
TRIGONOMETRICAL SURVEY OF GREAT BRITAIN,"
THIS VOLUME,
CONTAINING AN ACCOUNT OP THE EXTENSION OP THE EXPERIMENTS, TO STATIONS INCLUDING
THE UTMOST ACCESSIBLE DISTANCE ON THE MERIDIAN OF A HEMISPHERE,
IS VERY RESPECTFULLY INSCRIBED.
CONTENTS.
EXPERIMENTS FOR DETERMINING THE VARIATION IN THE
LENGTH OF THE SECONDS' PENDULUM.
Section I. With Detached Invariable Pendulums.
Page
Description of the Instruments employed 3
Experiments at Sierra Leone 10
. St. Thomas 26
Ascension .....-•••• 40
. Bahia 52
Maranham ...••••• 71
— Trinidad . . 88
Jamaica ....•••••• 101
New York 113
Preparation of the Instruments for the Arctic Circle 131
Experiments at Hammerfest 137
— Spitzbergen ...•••••• 1^8
. Greenland .....-••• 157
— Drontheim ......... 172
Examination of the Thermometer employed in the Experiments . . 182
Experiments in London in 1821 and 1822 187
1823 191
1824 198
Experiments on the Expansion of the Pendulums by Heat . . . 204
Comparative View of the Rates of the Pendulums in 1821, 1822, 1823,
and 1824 211
VI CONTENTS.
Page
Dissertation on the Methods of observing Coincidences .... 213
Results with the Detached Pendulums ....... 234
Section II. With Attached Invariable Pendulums.
Description of the Instruments employed ....... 237
Experiments at Sierra Leone ......... 239
Ascension .......... 245
Bahia 249
Maranham 252
Trinidad 254
Jamaica .......... 257
New York , . 260
Hammerfest ......... 263
Spitzbergen ......... 265
Greenland 267
Drontheim 269
London 271
Results with the Attached Pendulums 273
Comparison of the Results with the Attached and Detached Pendulums . 281
Comparison of the Attached Pendulums at Melville Island in 1820, and at
Greenland in 1823 .285
Latitudes of the Pendulum Stations.
Description of the Instruments employed ....... 288
Latitude of Sierra Leone 291
St. Thomas 292
Ascension . ........ 294
Baliia . 297
Maranham 300
Trinidad . 306
Jamaica .......... 309
New York 311
— Hammerfest ......... 315
Spitzbergen .......... 316
Greenland . . . 322
— ■ Drontheim 327
CONTENTS. Vll
Application of the observed Variation in the Length of the Seconds' Pendulum
to the Determination of the Figure of the Earth.
Preliminary Remarks . . ........ 829
Deductions from the 13 Stations of the present Volume .... 334
from the Stations of the present Volume, combined with those of
the Trigonometrical Survey of Great Britian .... 341
from the Stations of the present Volume, combined with those of
the Arc of the Mei'idian passing through France . . . 347
from the combination of the Stations of the present Volume, of the
Trigonometrical Survey, and of the French Arc . . . 851
Collected View of the Deductions from the several Combinations . 352
On the Mean Length of the Pendulinn in the Latitude of 45° . . . 356
Suggestion of the IVIeasurement of a Portion of the Meridian at Spitzbergen 360
Connexion of the Pendulum Experiments recorded in this Volume, with the
Subject of a natural Standard of Linear Measure . . . . 364
GEOGRAPHICAL NOTICES.
Longitudes of the Pendulum Stations.
Description of the Instruments employed ....... 373
Abstract of 1350 Lunar Distances, observed at the Tropical Stations . 380
Practical Inquiry into the Value of Lunar Observations .... 387
Longitudes of Sierra Leone, St. Thomas, Ascension, Bahia, Maranham,
Trinidad, and Jamaica .......... 396
Suggestion of Measures required towards the most advantageous Employment
of Chronometers in Navigation ........ 401
Longitude of the Pendulum Station at New York ..... 402
Hammerfest . . . . . ib.
Spitzbergen ..... 404
Greenland ..... 409
Drontheim ..... 412
Memoir of a Chart of the East Coast of Greenland, between the Latitudes
of 72° and 76^ . . . 416
VIU CONTENTS.
HYDROGRAPHICAL NOTICES.
Page
Remarks on the Method of investigating the Direction and Force of the
Currents of the Ocean .......... 426
Presence of the Water of the Gulf Stream on tlie Coasts of Europe in Jan. 1822 429
Summary of the Currents experienced by His Majesty's Ship Pheasant . 436
Stream of the River Amazons crossed three hundred miles from the Mouth
of the River ............ 445
On the Depth at which the Water of the Ocean within the Tropics is found
at the Temperature of its greatest Density ...... 456
EXPERIMENTS FOR DETERMINING THE VARIATION IN THE
INTENSITY OF TERRESTRIAL MAGNETISM.
Preliminary Remarks .......... 460
Description of the Instruments and of the Mode of Experiment . . 464
Deduction of a general Law representing the Variations of Intensity at all
Parts of the Earth's Surface . . . . . . . . . 484
Comparison of the Law with the Experiments ...... 490
Map of the Northern Magnetic Hemisphere ...... 495
Suggestion of the Expediency of similar Experiments being made in the
Southern Magnetic Hemisphere ........ 496
Importance of taking into Account the actual natural Magnetic Intensities, in
computing the Corrections for cleai-ing the Compass from the regular effect
of a Ship's permanent Attraction ........ 498
Diurnal Oscillation of the Horizontal Needle at Hammerfest and Spitzbergen 500
ATMOSPHERICAL NOTICES.
On the Depression of the Horizon of the Sea over the Gulf Stream . . 503
On the comparative Intensity of the Radiation of Heat in the Atmosphere, at
Elevations, and at the Level of the Sea 506
Postscript 511
PREFACE.
In the year 1672, a pendulum, conveyed by Richer from Paris
to Cayenne, first made known the variation in the force of gra-
vitation in different latitudes ; and the progressive increase in
its intensity from the Equator to the Pole. The fact, thus evi-
denced, furnished, in the hands of Newton, an experimental de-
monstration of the deviation of the figure of the Earth from
perfect sphericity, and of its oblateness or compression at the
Poles.
In 1743, Clairault demonstrated his celebrated theorem, that
the sum of the two fractions, of which the one expresses the
Ellipticity of the Earth, and the other the ratio of the force of
gravity at the Poles to that at the Equator, is a constant quantity,
and is equal to | of the fraction expressing the ratio of the cen-
trifugal force at the Equator to that of gravity. From thence-
forward, the Ellipticity of the Earth was deducible, whenever
the difference between gravity at the Pole and at the Equator
should be ascertained ; and the pendulum became a means of
investigating the precise figure of the Earth, inasmuch as it
might be rendered an exact measure of the variation of inten-
sity, of which it had furnished the first general intimation.
X PREFACE.
Thus, a century and a half has elapsed since the earth has
been known to be compressed at the Poles ; during eighty years
of which period, we have recognised and possessed in the pen-
dulum a means of determining the exact measure of the com-
pression.
The progress which the inquiry had made in the first forty
years after the publication of Clairault's theorem, and the im-
portance which, in the judgment of the most eminent philoso-
phers of that period, attached to its further prosecution, cannot
be better stated than in the words of the admirable Memoire
redige par I'Academie Roy ale des Sciences (de Paris), pour
servir aux Savans embarques sous les ordres de M. de La Pe-
rouse, in which memoir experiments with the pendulum form
the first subject recommended to the attention of the naviga-
tors : " Une des recherches les plus interessantes est celle qui
concerne la determination de la longueur du pendule a se-
condes, a differentes latitudes. Les inductions que Ton a tirees
jusqu'ici de cet instrument, pour determiner les variations de la
Pesanteur, ont eu pour fondement des operations faites en petit
nombre par divers observateurs, et avec des instruments difFerens ;
et ce defaut d'unifoiinite dans les operations a d.h influer sur la
certitude des consequences deduites de la comparaison des
resultats. On sent de quel prix serait un ensemble dopirations
da ce genre, faites avec sain, par les memes personnes, et avec les
memes instrumens."
" The calamity, which terminated prematurely the researches
of M. de La Perouse and his associates, in an enterprise pre-
PREFACE. XI
eminent amongst Voyages of Discovery for the just and appro-
priate regard paid to the advancement of every branch of natural
knowledge, deprived the Academy and the public of the imme-
diate and justly-expected fruit of a memoir, in the preparation
of which so many eminent philosophers had participated ; but
the memoir itself has happily survived, to stimulate the exertions
and direct the researches of individuals of a succeeding gene-
ration, in this as well as in many other respects.
Early in the present century, a series of experiments to de-
termine the intensity of gravitation by means of the pendulum,
at the extremities and at some intermediate stations of the arc
of the meridian passing through France, and comprised between
Dunkirk andFormentera, was undertaken on the recommendation
of the Academy of Sciences, and carried into effect at the expense
of the French Government, by the Members of the Bureau des
Longitudes. Experiments in France were thus in progress, when,
in 1816, a corresponding undertaking was originated in Great Bri-
tain by an address to the Crown, moved in the House of Com-
mons by Mr. Davies Gilbert, praying that His Majesty (then
Prince Regent) "would be graciously pleased to give directions
for ascertaining the length of the pendulum vibrating seconds of
time in the latitude of London, as compared with the standard
measure in the possession of the House of Commons ; and for
determining the variations in length of the said pendulum at the
principal stations of the trigonometrical survey extended through
Great Britain" His Majesty's Ministers having requested the
assistance of the Royal Society, in carrying into effect the ob-
c 2
Xll PREFACE.
jects of the address, their accomplishment was undertaken by one
of the most distinguished members of that Society, and completed
in 1819 ; in which year the account of the experiments for deter-
mining the variation in the length of the pendulum vibrating
seconds at the principal stations of the trigonometrical survey of
Great Britain, was pubhshed by Captain Kater in the Philoso-
phical Transactions.
In 1821 the account of the experiments on the length of the
seconds pendulum at different points of the arc of the me-
ridian between Formentera and Dunkirk, in which MM. Biot,
Arago, Mathieu, Bouvard, and Chaix, had participated, in-
cluding a subsequent extension of the series by M. Biot to the
northern extremity of the British Islands, was published, forming
the close of the third volume of the Base du Systeme Metrique.
The suite of experiments thus executed in Great Britain
and in France, having, for their ultimate purpose, the highest
accomplishment of practical geometry, that of determining the
exterior configuration of the Earth, and conducted by the most
distinguished experimental philosophers in Europe, was never-
theless found to fail in arriving at a satisfactory conclusion. By
the improvements successively introduced in the apparatus and
in the methods of procedure, by the eminent mechanical skill
and ingenuity of the conductors, the pendulum was indeed ren-
dered an exceedingly precise measure of the relative intensities
of gravitation, at the several stations of experiment ; but the
regularity with which gravitation itself had been supposed to
vary in conformity with the general Ellipticity of the meridian,
PREFACE. XIU
was discovered to be greatly interfered with by inequalities in
the density of the materials which form the strata near the
surface of the Earth, the effects of which had not been duly
appreciated, or anticipated. The diminution of gravity from the
pole to the equator is derived theoretically from the decrease
observed to take place between any two given latitudes ; con-
sequently, if no irregular attraction occurred, the result deduced
from the comparison of the intensity at every two latitudes
whatsoever should be the same. The discrepancies, however,
in the results obtained by combining the lengths of the pendu-
lums observed at the different stations in Great Britain and in
France, were so great and so irregular, as to prevent any inde-
pendent conclusion whatsoever, relatively to the general figure
of the Earth, being drawn from the experiments, either of the
French philosophers, or of Captain Kater.
The state in which the inquiry into the figure of the
Earth by means of the pendulum, was left at the close of
the experiments in Great Britain and France, may be best
shewn by the following extracts from the respective pub-
lished accounts. The memoir of Captain Kater concludes with
this general remark : " It must be evident that nothing very
decisive respecting the general ellipticity of the meridian can
be deduced from the present experiments. For that purpose it
is requisite that the extreme stations should comprise an arc
of sufficient length to render the effect of irregular attraction
msensible ; and that effect might be diminished, if not wholly
prevented, by selecting stations of similar geological character.
XIV PREFACE.
and which should differ as httle as possible in elevation above
the level of the sea." Similar in effect is the conclusion of the
memoir of the French experiments. " La concordance des re-
sultats du Capitaine Kater avec les notres, lorsque les uns et les
autres ne peuvent pas se representer rigoureusement, par une
variation de la pesanteur proportionnelle au carre du sinus de
la latitude, acheve de mettre en evidence que cette impossibilite
est reel, et qu'ainsi Ton ne peut pas se flatter de representer
les longueurs du pendule pour tout le globe par une meme for-
mule, qui les reproduise avec une complette rigueur, mais seule-
ment dans les limites des differences que les variations locales
de la pesanteur peuvent y occasionner. Alors tout ce que reste
a faire consiste a employer toujours des precedes d'observation
assez exacts pour que les erreurs propres qu'ils comportent,
soient fort inferieurs en etendue aux effets reels des causes acci-
dentelles, afin de pouvoir deduire celle-ci de leur comparaison
avec la formule theorique construite sur I'ensemble de toutes les
observations."
Such was the state of the inquiry when the present experiments
were undertaken : their design was, to give the method of experi-
ment the advantage of being tried under the circumstances most
favourable for the production of a conclusive result ; to extend
the suite of stations, previously confined to Great Britain and
France, to the Equator on the one side, and to the highest
accessible latitudes of the northern hemisphere on the other ;
to multiply the stations at both extremities of the meridian, so
PREFACE. XV
that by their general combination, the irregular influences of
local density might mutually destroy each other, and the
variations of gravity due to the ElHpticity alone be eliminated ;
and to ensure the uniformity of procedure and strict compara-
bility of the results at all the stations, by the unity of the
observer, and the identity of the instruments. In effect, to
terminate the inquiry with the pendulum, — either by obtaining
decisively the result which it might be capable of furnishing, — or
by manifesting that no decisive result whatsover was attainable
by it, even under the most favourable circumstances of operation^
The success which has attended the attempt, and the conclu-
sive nature of the result which it has furnished, will be best
seen in the part of the following volume, in which the results
at the several stations of experiment are collected and applied,
with those at the stations in Great Britain and France, in
the deduction of the tota lincrease of gravitation between the
Equator and the Pole, and of the corresponding EUipticity of
the Earth.
The Reader is requested to correct the followinpr Errata before perusal.
Page
4 line 10, and page 187, line 22, for resistance read buoyancy.
45 line 19, for alternate read ultimate.
85 heading, /or Reduced Vibrations at 38o.l read 81°. 83.
86 heading, /or Reduced Vibrations at 82='.l read S2°.02.
115 line 3, for the strict relation of the force of gravity read tlie strict relation of tlie varia-
tion of the force of gravity.
148 last line, for 1 1° West read 9° East.
296 recapitulation, for Arcturus read a. Centauri.
305, 307, for a. Gruris read a. Gruis.
308 recapitulation, for a. Crucis read a. Gruis.
333 line 9 of text, for on the principle that the length read on the principle that the propor-
tion of the total difference in the length.
345 line 3 of Geological Characters, for computed read compact.
430 last line, for westward read eastward.
•360 line 22, for nearly two centuries read nearly a century,
AN ACCOUNT
OF
EXPERIMENTS FOR DETERMINING THE VARIATION IN THE LENGTH
OF THE PENDULUM VIBRATING SECONDS,
IN DIFFERENT LATITUDES;
MADE WITH A VIEW TO ASCERTAIN THE TRUE FIGTJRE OF THE EARTK.
B
SECTION I.
With detached Invariable Pendulums.
The pendulums employed in the experiments of the present section
were detached, or unconnected with machinery of any sort to maintain or
register their oscillations ; when set in motion, they vibrated by the in-
fluence of gravity alone, in arcs progressively diminishing by the re-
sistance of the air, until the pendulum arrived at rest; the continuance of
the vibration was sufficient, when commenced m an arc of moderate
dimension, to admit of its rate being very accurately determined.
The pendulums were so constructed as to be invariable in their length,
excepting by the expansion of the metal of which they were composed, due
to different degrees of temperature.
The rate of vibration of a pendulum of this description in an uniform
temperature in different parts of the globe, being strictly proportioned to
the force of gravity, furnishes the means of computing the variation in
the length of the pendulum vibrating seconds, at the respective stations
of experiment ; and, if at one of the stations, the absolute \eng\h of the
seconds' pendulum has been determined, by other processes and with
instruments purposely contrived, the true as well as the relative length
becomes also known at every other station at which the invariable
pendulum is employed.
The length of the seconds' perdulum in London has been deteimined
B 2
4 EXPERIMENTS FOR DETERMINING THE VARIATION
with great precision by Captain Kater, at Mr. Browne's house in Port-
land-place ; the rates of vibration of the present pendulums were obtained
at the same spot ; consequently their comparative rates at other stations
furnish respectively the true lengths of the seconds' pendulum, subject
to the errors (if any) of the original determination, and to their own
possible errors.
The rate of a pendulum is otherwise expressed by the number of
vibrations which it would make in any determinate period of time, (the
period throughout these experiments being twenty-four hours of mean solar
time), independently of the resistance of the air, and in arcs infinitely
small; this number, expressive of the rate, is deducible by certain known
methods from the number of vibrations acliuiUy performed in the same
period, in arcs of observed magnitude, and in the then existing cir-
cumstances of the atmosphere. The ascertainment of these particulars
with the necessary exactness constitutes a principal part of the experi-
ment ; and as it is impossible to command an uniform temperature at
different stations, and especially at those widely apart in latitude, it
is also necessary to be very accurately acquainted with the temperature
of the pendulums at the time of their observed vibration, in order to
remedy the only exception to their rigorous invariability; and by making
their expansion within the limits of the extreme differences of tem-
perature which occur in the course of the observations, the subject
itself of direct experiment, the value of the several reductions to a general
mean temperature is ascertained, and the results are ultimately rendered
strictly comparable with each other.
The method of ascertaining the rate of a detached pendulum, by ob-
serving the times of coincidence of its vibration with that of the pendulum
of an astronomical clock, which is itself duly compared with the heavens,
has been so recently practised and so fully described, both in Great
IN THE LENGTH OP THE SECONDS' PENDULUM. B
Britain and France, as to render a particular account of the process by
which it is accomplished unnecessary on the present occasion. The prin-
ciple of the method adopted in these experiments was the same as in the
instances alluded to ; but an alteration was made in the mode of observing
the coincidences which it was conceived would tend to greater accuracy ;
the nature of the alteration, and the reasons which induced its preference,
will be explained in a subsequent part of the volume, and in a place
more appropriate for their discussion.
The following were the instruments employed in the experiments with
the detached pendulums :
An astronomical clock, the property of the Royal Society, which was
lent by the President and Council for the occasion ; it was one of two
clocks made for the society in 1769, by Shelton, for the purpose of
accompanying Messrs. Baily and Dixon to the North Cape and Hammer-
fest, to observe the transit of Venus, It does not appear by any document
in the records of the Society, that these clocks were subsequently used,
until the expeditions of Arctic Discovery commenced in 1818, when
being fitted with invariable pendulums, they were employed in the experi-
ments of which I have given an account in the Philosophical Tramactiom {ov
1821*; the clock which was distinguished in that paper as No. 2, had
now its original compensation pendulum restored, and was thoroughly
cleaned and oiled afresh ; two iron plates were affixed to the case, one at
the top and the other at the bottom; the upper plate projected on each
side of the case to receive screws, by which the clock might be attached
to pickets of wood driven into a vertical wall ; a similar screw in the
* It is there stated, on the authority of Captain Kater, that they were the same clocks
which accompanied Captain Cook round the world: I have since been informed by
Mr. Lee, Librarian to the Royal Society, that the clocks which were lent lo Captain Cook,
one of which was also made by Shelton and the other by Ellicot, were sold by the
Society, in 1771.
6 EXPERIMENTS FOB DETERMINING THE VARIATION
middle of the lower plate secured the clock firaily to the wall when
finally adjusted, but admitted of a small motion of the case to the right
and left before the screw was tightened, for the purpose of putting the
clock in beat ; the lower plate was also furnished with screws acting
against the wall, to render the agate support of the pendulum truly
horizontal ; the ball of the pendulum was covered with a black varnish,
and had a circular disk of white paper pasted on the surface, near the
middle of the ball.
A transit instrument, by Dolland, with a telescope of thirty inches focal
length, and an aperture of two inches ; the transverse axis, being fifteen
inches, was supported on hollow brass cones ; the level was furnished
with a small cross level, and a graduated scale shewing tenths of seconds
of time at the zenith ; instead of the usual mode of placing wires or
cobwebs in the focus of the object and the eye-glasses, the telescope of
this transit was fitted with a piece of finely polished parallel glass, with
fine lines drawn upon it with a diamond at the proper intervals, whereby
the equality of distance, parallelism, and permanency, were designed to
be better secured than by the usual method.
A repeating circle, of six inches diameter, made by Dolland, upon the
same principles and construction as the one he made under the direction
of Captain Kater for the British Board of Longitude, and which was
originally designed for Professor Playfair.
Four chronometers, Nos. 357, 384, 423, and 493, which Messrs. Par-
kinson and Frodsham were so kind as to place in my charge, and entrust
to my entire disposal ; as the makers were yet desirous of other opportu-
nities of manifesting the excellency of their chronometers, than those of
the Arctic Expeditions, in which they had already obtained so much dis-
tinction : No. 423 was fitted for the pocket, and the other three were bo.x,
chronometers ; No. 357 was wound weekly, the others daily.
JN THE LENGTH -OF THE SECONDS PENDULUM. M
Two invariable pendulums, one of which was the property of the Board
of Longitude, as were also the transit and repeating circle: the other
pendulum was my own.
In entering on so extensive a series of experiments, the value of which
would depend entirely on their relation to each other being strictly main-
tained throughout, I could not but feel great anxiety in anticipating the
possibility of an injury taking place, in the course of so many embarkations
and disembarkations, to some essential part of the apparatus, and pre-
eminently to the pendulum; it is unquestionably a great disadvantage
attendant on the method of proceeding with invariable pendulums, in
such an inquiry as the present, that an accident befalling the pendu-
lum at any period of the experiments, not only interrupts their continuity,
but may prossibly render the whole previous labour of no avail ; in this
respect, and it is one which cannot fail to occasion continual and exces-
sive solicitude, the method of Borda, pursued in France, is much its
superior, as each determination obtained by it is in itself complete, and
is final ; it is a superiority, however, by no means uncompensated even
in sources of anxiety: by providing myself with a second pendulum,
and by employing both pendulums at every station, I hoped to avoid the
inconveniences, whilst I should avail myself of the advantages of the
method, which after much consideration I was induced to prefer.
The construction of the pendulums was precisely similar to that of the
one employed by Captain Kater, in determining the variation in the length
of the pendulum, at the principal stations of the trigonometrical survey
of Great Britain ; each pendulum was composed of a bar of plate
brass 1 .6 inch wide, and less than the eighth of an inch thick ; a strong
cross piece of brass was rivetted and soldered to the top, having a
prism of wootz, passing through a triangular hole in the bar, firmly secured
to it by screws of which the heads were sunk ; the angle of the prism on
8 EXPERIMENTS FOR DETERMINING THE VARIATION
which the vibrations were performed, and wliich is usually called a knife
edge, was ground to about 120 degrees ; it was fixed as nearly as could
b3 done at right angles to the bar ; the length of the bar from the knife
edge to the extremity was about five feet, but a flat circular weight, nicely
turned and pierced in the direction of its diameter to receive the bar, was
soldered at such a distance from the knife edge which served as the
point of suspension, that the pendulum made two vibrations less in about
eleven minutes than a clock keeping nearly mean time ; the part of the
bar which was below the weight was reduced to the width of 0.7
of an inch, and was varnished black to be more distincdy visible, in the
observation of coincidences, in contrast with the disk of white paper
on the pendulum of the clock ; the bar terminated in an angle, the point
of which served to indicate the magnitude of the vibration on an arc,
divided into degrees and tenths, which fitted into the opening of the door
of the clock-case.
The frame on which the pendulum was supported was of cast iron ; it
was designed to be fixed to the same wall with the clock, and at such a
distance above it, as would allow the end of the invariable pendulum to
.reach a little below the disk on the pendulum of the clock ; the upper and
horizontal part of the frame was nearly square, and stood out fi"om the
wall about twenty inches, in order to carry the pendulum clear of the
clock-case, when it should be suspended in front of the clock : the side
of the square which joined the wall was pierced with three holes, one in
the middle and the others at the extremities, to receive screws of nearly
five inches in length, which were intended to work into pickets of wood
driven into the wall ; the horizontal part of the frame received additional
support in brackets firmly screwed to its under side having strips of sheet
lead between ; the brackets were so contrived as to spread at the bottom
to the width of three feet, the more effectually to oppose any lateral motion
. IN THE LENGTH OF THE SECONDS PENDULUM. 9
arising from the vibration of the pendulum ; they were fastened to the wall
at their lower extremities by screws, similar to those already described ;
the weight of the frame exceeded ninety pounds.
The planes on which the knife edge immediately rested were of hard
Brazil pebble, and were fixed in a brass frame which screwed firmly to
the iron support with sheet lead intermediately ; the frame was fur-
nished with three adjusting screws, by which the planes could be ren-
dered truly horizontal, as shewn by a moveable level placed on them for
that purpose ; it had also the usual contrivance of Y's moveable by a
screw, to raise the pendulum when not in use, and to ensure its being
lowered on exactly the same part of the planes on every occasion.
The pendulums were numbered 3 and 4, and are distinguished ac-
cordingly.
A barometer, by Newman, and two thermometers, by Jones, having
their scales sufficiently large to admit a fair estimation of tenths of a
degree.
A small telescope, for the observation of coincidences, completed the
apparatus connected with the detached pendulums which was carried to
the stations in the neighbourhood of the Equator, where the accommodation
of a house with stone walls for the support of the clock and pendulum
frame could be depended on ; the provision which was subsequently
made for the same purpose in the northern stations, where no such accom-
modation existed, will be hereafter described.
I shall now proceed to detail the operations with the detached pendu-
lums, at the several stations, as they were successively visited.
10 EXPERIMENTS FOR DETERMINING THE VARIATION
SIERRA LEONE.
The Iphigenia arrived at Sierra Leone on the 22d of February ; I had
had the advantage of being previously known in England to His Excel-
lency Brigadier-General Sir Charles Mac Carthy, Governor of the British
possessions in Western Africa, who was resident at Sierra Leone, as the
seat of government ; and in the expectation of having to accomplish the
present purpose at some station within his command, I had received from
him the assurance of every assistance in his power ; I had now the plea-
sure of finding this assurance most amply realized, accompanied with the
utmost personal kindness.
On examination of the few stone buildings which have been as yet
constructed at Freetown, the officers' range of barracks at Fort Thornton
appeared on the whole the most eligible situation for the experiments,
being convenient and suitable in every respect, excepting in the height
above the sea, which was somewhat greater than could have been wished,
but was a minor consideration in comparison with the other circumstances
that determined the preference. Apartments in the barracks were accord-
ingly vacated and assigned me, being the Captain's quarter at the north
end of the range, immediately adjoining to and opening into the north-
west bastion : to these apartments the instruments were removed, as
soon as the necessary measures could be taken for their disembarkation
and conveyance.
Sir Robert Mends having assigned the Pheasant sloop of war for the
further prosecution of the service in which I was engaged, it was arranged
that Captain Clavering should return from a cruize to the harbour of Sierra
Leone, in the first week in April, by which time I engaged to have com-
pleted the experiments, and to be ready to embark.
IN THE LENGTH OF THE SECONDS* PENDULUM. 11
Captain Clavering was so kind as to land two of the marines of the
Pheasant's complement, and to leave them with me as orderlies ; an ar-
rangement which proved of material service to me.
The end waU of the range of barracks, which I had designed for the
pendulum and clock supports, was above three feet thick, composed of
irregularly shaped masses of granite imbedded in a strong cement ; I had
intended to have had a sufficient number of holes bored in the wall, and
at the proper distances, to have received separate plugs of wood for each
screw ; but after much perseverance and labour, the attempt was ob-
liged to be abandoned, in consequence of the extreme hardness of the
granite, which occasioned the stones to be loosened with the force neces-
sary to cut them : the supports were finally screwed to four-inch planks,
fixed to the wall by eight-inch spikes driven into the cement, the planks
being unconnected with the floor ; the supports were not less firmly at-
tached by this method, than if they had been fixed to the wall itself,
but the several screws of the clock and of the pendulum support, on one
side, were fastened into the same plank, an arrangement with which I was
hardly so well satisfied at the time, as I had afterwards reason to believe
that I might have been.
Glass windows not being in use at Sierra Leone, it was with some dif-
ficulty that a sufficient number of panes were obtained, which should give
the necessary light without admitting currents of air ; the room in other
respects was closed, and entered only for the purposes of observation ; the
telescope, for the determination of coincidences, was placed at nine feet
six inches from the front of the clock case, which distance was preserved
at all the subsequent stations.
By the kindness of Thomas Stuart Buckle, Esq., Surveyor and Civil
Engineer of the Colony, to whose assistance I was materially indebted
on this and other similar occasions, a very firm support of masonry was
C 2
12 EXPERIMENTS FOR DETERMINING THE VARIATION
erected for the transit instrument, on the parapet of the fort, adjoining the
bastion. On unpacking the transit, I had the mortification to find that the
female screw, into which one of the collimating screws worked, had be-
come unsoldered from the stop ; its repair occasioned some litde delay,
and might have been more difficult, and have caused further accidents of
more importance, if the system of wires had been of cobweb as is usual ;
but the lines cut on glass are much less liable to injury : the delay, how-
ever, and the inconvenience, might have been avoided altogether, if the
female screw had been made in the stop itself, cast in a proper shape for
that purpose, instead of being in a detached piece requiring to be sol-
dered to the stop; the repair being completed, and the coUimation perfect,
the instrument was placed in the meridian, or at least in a sufficient ap-
proximation to it, on the evening of the Gth of March, by transits of
Capella and Rigel, and proved by those of Castor, Procyon, and Pollux ;
and marks were taken for its subsequent adjustment and verification.
The rate of the clock appearing by the transits of the 7th, 8th, and
9th, to be sufficiently steady, the observation of coincidences was
commenced with pendulum 3 on the morning of the 10th, and con-
tinued in the fore and afternoons until the 14th, when the number of
observations, and their agreement with each other, being considered suf-
ficient, pendulum 4 was substituted on the support, with which a similar
series was completed between the 19th and 25ih.
Previously to my quitting England, the rates of the pendulums had
been ascertained in London, the details of which, reserved for the present,
will be found in a subsequent part of the volume ; as it has been deemed
a preferable arrangement, to connect together, in one view, the several
experiments made with the pendulums in London at different periods.
On examining the rates now obtained at Sierra Leone with those of
London, I was much surprised and disturbed to find that the retardation
IN THt; LENGIH OF THE SECONDS' PENDULUM. 13
was several seconds less than I had anticipated ; as I had left England in
the expectation, founded on the inferences drawn by Monsieur La Place,
that the variation of gravity would accoi*d, at least nearly, with an Ellip-
ticity of about 73-. My first impression was to suspect error in thj
experiments ; but on due consideration of every circumstance connected
with them, I could discover no reasonable ground of distrusting the general
applicability of the mode of experiment, or of supposing any peculiarity in
the present instance,which could render the results doubtful beyond a small
fraction of a second ; had I been furnished with one pendulum only, I
might have supposed that it had received some injury in the intermediate
voyage ; but the results of the two pendulums so nearly accorded as to
render such a supposition inadmissible, and I now felt the value of this
double provision, in the additional confidence which it authorised : I had
already reason to believe that the thermometers with which I had been
supplied were not very accurately graduated for tropical temperatures, but
error from this source could produce but a very small portion of the differ-
ence existing between the experiments and my previous expectation : re-
gister thermometers, in different parts of the room, shewed that the ex-
tremes of temperature in twenty -four hours, did not vary so much as three
degrees ; and pieces of floss silk, suspended in the neighbourhood of the
pendulum, manifested the absence of currents of air of sufficient note to
influence its motion : the horizontality of the agate supports had been
verified continually, and was as perfect at the close as at the commence-
ment : fortunately a few days yet remained before the Pheasant would
return, and I determined to employ them in putting up the apparatus afresh,
and in a new place, and in effecting an entire repetition of the experiments.
For this purpose I availed myself of the eastern wall of the same room,
which was sufficiently substantial, and being built of brick, permitted a
separate picket of oak to be driven into it for each screw, whereby a com-
14 EXPERIMENTS FOR DETERMINING THE VARIATION
munication between the detached pendulum and that of the clock was ren-
dered even more improbable than before : the preparations being com-
pleted, the observation of coincidences with No. 3 was commenced on the
morning of the 27th, and ended on the evening of the 29th ; and com-
menced with No. 4 on the morning of the 31st., and ended on the evening
ofthe2dof April.
The results of the second series accorded so closely with those of the
preceding as to be in effect identical, a circumstance not only highly
satisfactory, in increasing the dependence which may be placed on the
experiments at Sierra Leone, but also important, in giving additional con-
fidence to the mode of experiment generally ; as identity on repetition
renders highly improbable the existence of interfering causes dependant
on accident ; and strengthens the conclusion, that the rate of a detached
pendulum does indeed afford a just relative measure of the force of
gravity at the place of observation.
Being now fully persuaded that the true rates were obtained at Sierra
Leone, the pendulums were repacked for embarkation ; the experiments
having produced an impression, either that differences in the density of
materials near the surface and in the neighbourhood of the pendulum
station, have more influence on the rates than had been anticipated, or that
the Compression of the earth was itself greater than was generally sup-
posed ; and consequently that, in either case, it would be desirable to
repeat the experiments at a greater number of stations than had been
previously designed.
Mr. Buckle was kind enough to ascertain the height of the pendulums
above half tide to be 190 feet, by levelhng to the water side; the slope
was gradual towards the sea, and the fort stands on the highest ground in
its own immediate neighbourhood, except a small hill on which a mar-
tello tower is built, at a distance rather exceeding a quarter of a mile:
IN THE LENGTH OF THE SECONDS* PENDULUM. 15
the situation of Freetown, however, may be more generally stated to be
at the foot, on the northern side, of the range of mountains, which coming
from the interior, finds here its termination in the sea, and gives the
name to the cape, harbour, and colony of Sierra Leone; the general
height of the range, so far as it has been yet explored, is from two to three
thousand feet ; the principal geological feature, in the neighbourhood of
Sierra Leone, is a red granite, of easy and rapid decomposition.
The subjoined tables comprise the detail of the observations of which
the history has been thus related : Table L contains the times of transit of
stars, by which the rate of the clock was ascertained ; the transits were
observed by the chronometer, of which the times are entered in the table,
and consequently the record is direct ; they were noted by the beats
Avithout an assistant; the transit instrument being without shelter, and
the sun nearly vertical, the observations were confined to stars, and to
such as passed the meridian about sunset ; the telescope was removed
into the house during the remainder of the twenty-four hours from motives
of precaution, the pillars only being stationary. Table II. is annexed,
as affording evidence, that by means of the meridian marks, the teles-
cope was adjusted throughout to the same vertical plane. Table III.
contains the daily rate of the chronometers, deduced from the pre-
ceding transits : and Table IV. the comparisons of the chronometer and
clock at exact intervals each of twelve hours of mean time, whereby the
clock's rate on mean solar time was also obtained. The stoppage of the
clock, on the 1 5th of March, took place for the purpose of making a small
alteration in the position of the telescope for observing coincidences,
when the Series with No. 3 was completed and the pendulums changed,
as the telescope adjusted for the one pendulum was not precisely in the
prolongation of the line, connecting the disk on the clock pendulum and
the tail piece of the other detached pendulum ; the stoppage of the clock.
16 EXPERIMENTS FOR DETERMINING THE VARIATION
however, being inconvenient on many accounts, Avas dispensed with at
the subsequent stations, it being found equally easy, with a little practice,
to adjust the telescope when both pendulums were in motion, as when
they were at rest.
Tables V. and VI. comprise an account of the coincidences in the
double series with each pendulum. In these tables the times of disap-
pearance of the disk and also of its re-appearance are registered, and
a mean between the two is deemed and entered as the true time' of
coincidence ; the " time of disappearance " is the second which im-
mediately follows the first passage of the disc in entire obscuration ;
the " time of re-appearance " is the second immediately preceding the
re-appearance of the first portion of the disk, when passing the opening in
the diaphragm of the telescope. As each result is obtained from a mean
of ten successive intervals, the first and eleventh coincidence only are re-
<;orded, being those alone which are influencial on the deduction. The two
last columns are added for the purpose of shewing the accordance of the
particular results, when reduced to a mean temperature ; a degree of
Fahrenheit's scale being considered as equivalent to 0.42 of a vibration
in twenty -four hours.
The correction for the arc which added to the observed number of vibra-
tions in twenty-four hours, shews what they would have been in an arc
infinitely small, has been computed agreeably to the formula for that
purpose, given and demonstrated by Mr. Watts, in the seventeenth article
of the second number of the Edinburgh Philosophical Journal. If N be the
number of vibrations in twenty-four hours in circular arcs, and a and b
the commencing and concluding arcs, the corrected number of vibrations
will be JN+2«8so.o8iog(j)
IN THE LENGTH OF THE SECONDS' PENDULUM.
17
Table
I. TRANSITS OBSERVED .\T SIERRA LEONE.
1822.
STARS.
TIMES
OK TRANSIT BY THE CHRONOMETER 423.
Mean by the
Clironometer,
1st Wire.
and Wire.
Meridian
Wire.
4th Wire.
5lh Wire.
Mar. 6
Capella . . .
M. S.
55 25.6
56 03.2
H. M. s.
6 56 40.8
M. S-
57 IS. 4
M. S.
57 56
6 56 40.8
?)
Rigel
6 59 03.6
6 59 03.6
»T
Castor ....
14 56.4
15 27.2
9 15 oS.4
16 29.6
17 00.8
9 15 58.47
9)
Procyon . . .
21 48.4
22 14.8
9 22 41.2
23 07.6
23 34
9 22 41.2
J»
Pollux
26 OS. 4
26 38
9 27 07.6
27 37.6
28 07.2
9 27 07.73
9.
Capella . . .
43 40
44 17.6
6 44 55.2
45 33.2
6 44 55.3
)1
Rigel
46 52
6 47 18.4
47 44. S
48 11.2
6 47 18.4
1)
£ Orionis. . . .
7 34.4
S 00.4
7 08 26.4
8 53.2
9 19.2
7 07 26.67
))
f Orionis. . . .
13 09.2
12 35.6
7 13 02
13 2S.4
13 o4.8
7 13 02
9J
K Orionis. . . .
19 40
20 10-4
7 20 32. S
20 58. S
21 25.2
7 20 32.67
))
a. Orionis. . . .
25 52. S
26 19.2
7 26 45.6
27 12
27 38
7 26 45.53
)>
I Canis Maj. .
8 42 09.2
42 38.4
43 07.2
8 42 09.2
)>
\ Gemini ....
47 57.6
48 24. S
8 48 52
49 20
49 47.2
8 4S 52.27
?J
Castor
3 10. S
3 41.6
9 04 12.4
4 43.6
5 14.8
9 04 12.6
IT
Procyon . . .
10 02.8
10 28.8
9 10 55.2
U 22
11 4S
9 10 55.33
9T
Pollux ....
14 22
14 52
9 15 21.6
15 52
16 21.6
9 15 21.8
1)
K Navis
21 44.4
22 13.2
9 22 42
2Z 10. S
23 39.6
9 22 42
5?
e Navis
29 08.4
29 36.8
9 30 05.2
30 33.6
31 01.6
9 30 05.13
10.
Capella . . .
39 42.6
40 23.2
6 41 00.8
41 38.8
42 16.4
6 41 00.93
1)
Rigel
6 43 24
. . .
6 43 24
1)
£ Orionis. . . .
3 40.4
4 06.4
7 04 32.4
4 .58. 4
5 24.4
7 04 32.4
J1
f Orionis ....
S 15.2
S 41. G
7 09 07.6
9 34
10 00
7 09 07.67
)>
r. Orionis ....
15 45.6
16 12
7 16 38.4
17 04.8
17 31.2
7 16 38. 4
»»
a. Orionis
21 58.4
22 24.8
7 '22 51.2
23 17.6
23 44
7 22 47.2
11.
Capella . . .
35 50. S
36 28.4
6 37 06
37 44
38 21.6
6 37 06.13
?)
Rigel
39 02.8
6 39 29.2
39 55.6
40 22
6 39 29.2
»?
£ Orionis. . . .
59 45.2
00 11.2
7 00 37.6
01 04
01 SO
7 00 37.6
n
^ Orionis ....
04 20.4
04 46.8
7 05 12.8
05 39.2
06 05.2
7 05 12.87
l»
X. Orionis ....
11 50.4
12 17.2
7 12 43.6
13 10.4
13 36.8
7 12 43 67
?i
a. Orioni.s ....
18 03.6
IS 30
7 18 56.4
19 22. S
19 49.2
7 18 56.4
18
EXPERIMENTS FOR DETERMINING THE VARIATION
TRANSITS OBSERVED AT SIERRA LEONE,
continued.
1822.
STARS.
TIMES OF TRANSIT BY THE CHRONOMETER 423.
Mean by the
Chionometer.
1st Wire.
2nd M^ire.
Meridian
AVire.
4th Wire.
5tlL Wire.
Mar. 14
Capella . . .
,M. S.
2i 05.6
M. s.
24 43.6
11. M. S.
6 25 20.8
.M. S.
25 58.8
M. S.
H. M. S,
6 25 21
11
Rigel
27 17.6
6 27 44
28 10.4
6 27 44
»»
£ Orionis ....
. . .
48 26
6 48 52 4.
49 18.8
....
6 48 52.4
?i
^Orionis. . . .
.52 .35.2
53 01.2
6 53 27.6
53 53.6
54 19.6
6 53 27.47
»1
X Orionis. . . .
00 05.2
00 33
7 00 5S.4
01 24.8
01 51.6
7 00 58.4
T>
a. Orionis ....
06 IS. 4.
06 44. S
7 07 11.2
07 37.6
08 04.4
7 07 11.27
))
S Canis Maj..
21 36.4
22 05.6
S 22 34.4
23 03.2
23 32.4
8 22 34.4
11
^ Gemini. . . .
2S 24
2S 51.2
8 29 IS
29 45.2
30 12.4
S 29 18.13
Tl
Castor ....
43 36.4
44 07.2
8 44 38
45 08.8
45 39.6
8 44 3S
!'
Procyon . . .
50 27.6
50 54
8 51 20. S
51 43.8
52 13.2
8 51 20.53
?5
Pollux ....
54 47.6
55 17.2
S 55 47.2
56 16.8
56 46,4
8 55 47.07
1)
1 Navis
02 10
02 3S.4
9 03 07.2
03 36
04 04.8
9 03 07.27
)T
e Navis
09 33.2
10 02
9 10 30.4
10 58. S
11 27.2
9 10 30.33
19
Canopus . . .
20 29
21 11.6
7 21 55
22 38.6
■23 20.8
7 21 55
n
-/Gemini. . . .
2S 27.2
28 54.4
7 29 21.6
29 48. S
30 16
7 29 21.6
)i
Sirius
38 IS
3S 44.4
7 39 11.6
39 38. 8
40 05.6
7 39 11.67
?i
^ Canis Maj..
S 02 5S.2
. . .
8 02 58.2
u
A Gemini ....
S 46. S
9 14.4
S 09 41.6
10 OS. 4
10 36
8 09 41.47
!•»
Castor ....
23 59.6
24 30. S
S 25 01 .6
25 32.4
26 04
8 25 01 67
)»
Procyon . . .
30 52
31 IS
8 31 44
32 10.4
32 36.8
8 31 44.2
?)
Pollux ....
35 u.a
35 40.8
8 36 10.8
36 40.4
37 10
S 36 10.67
?J
1 Navis
42 34
43 02.8
8 43 31.2
44 00
44 28.4
8,43 31.27
21
Canopus . . .
12 36.8
13 20.4
7 14 04
14 47.6
15 31.2
7 14 04
5)
y Gemini ....
20 36.8
21 04
7 21 31.2
21 58.4
22 25.6
7 21 31.2
22
Canopus. . .
8 43.2
9 26.4
7 10 09.6
10 52. S
11 36
7 10 09.6
It
v Gemini. . . .
16 OS. 8
7 17 36.4
IS 03.8
7 17 36.35
24
a Orionis ....
27 07.6
27 34
6 28 00.4
28 26.8
28 53 2
6 28 00.4
»»
Canopus. . .
00 54
01 36.8
7 02 20
03 03.2
03 40.8
7 02 20.17
}f
y Gemini. .. .
08 53.2
09 20.4
7 09 47.6
10 14.8
10 42
7 09 47.6
Jt
Sirius
18 42.8
19 10
7 19 37.6
20 04.8
20 32
7 19 37.47
IN THE LENGTH OF THE SECONDS' PENDULUM.
19
TRANSITS OBSERVED AT SIERR.
\ LEONE,
continued.
1822.
STARS.
TIMES
OF TRANSIT BY THE CHRONOMETER 423.
Mean by the
Chronometer.
1st Wire.
2nd Wire.
Meridian
Wire.
llh Wire.
3th Wire.
Mar, 24
^CanisMaj..
.17. S.
42 25.6
yt. s.
42 54.4
H. M. S.
7 43 23.8
M. s.
43 53.2
M. S.
44 22
11. M. S.
7 43 23.8
1)
X Gemini. . . .
4S 12.4
49 39.6
7 50 07.2
50 34.4
51 01.6
7 50 03.07
»»
Castor ....
04 25.6
04 56.4
8 05 27
05 58.4
06 29.2
8 05 27.27
»1
Procyon . . .
11 IS
11 44
S 12 10
12 30
13 02.4
8 12 10.07
))
Pollux
15 36. S
16 06.8
8 16 36.4
17 06.4
17 36.4
S 16 36.. 53
n
1 Navis
22 59.2
23 28
S 23 56.8
24 25.6
24 54.4
8 23 56.8
26
y Gemini ....
01 03.6
01 30.8
7 01 58
02 25.2
02 52.4
7 01.58
n
Sirius
10 52.8
11 20
7 11 47.2
12 14.4
12 41.6
7 11 43.2
51
S CanisMaj..
34 36.4
35 05.2
7 35 34.4
36 03.6
36 32.4
7 35 34.4
11
A Gemini ....
41 22.4
41 50
7 42 17.2
42 44.8
43 12.4
7 42 17.33
20
a. Orionis
7 31.6
7 58
6 08 24.4
8 50.8
9 17.6
6 OS 24.46
M
Canopus . . .
41 IS
42 00.8
6 42 44
43 27.2
44 10
6 42 44
)i
y Gemini ....
49 17,6
49 44. S
6 50 12
50 39.6
51 06.8
6 50 12.13
)>
Sirius
59 06.8
59 34
7 00 01.4
00 28. 8
00 56
7 00 01.4
»
^CanisMaj..
22 50.4
23 19.6
8 23 48.8
24 18
24 47.2
7 23 48.8
11
A Gemini ....
29 37.6
30 04.8
7 30 32
30 59.2
31 26.8
7 30 32.07
April 2
Canopus . .
25 36.8
26 20
6 27 03.2
27 46.4
28 29.6
6 27 03.2
11
7 Gemini. . . .
33 25.8
34 03
6 34 30-2
34 57.6
35 24.8
6 34 30.2
»»
Sirius
■43 25.6
43 52.4
6 44 20
44 47.6
45 15.2
6 44 20.13
11
J CanisMaj..
07 08.4
07 37.6
7 OS 06.8
OS 36
09 05.2
7 OS 06.8
1'
X Gemini
13 55.2
14 22 4
7 14 50
15 17.2
15 44.8
7 14 49.87
D 2
20
EXPERIMENTS FOR DETERMINING THE VARIATION
TABLE II.
SIERRA LEONE.
DEVIATION of the TRANSIT INSTRUMENT from the MERIDIAN, on the under-mentioned Days of
March, IS22, as shewn by the Interval between the Transits of Stars, differing considerably in Declination,
but having nearly the same Right Ascension.
STARS.
Differeuces.
INTERVAL BETWEEN THE TRANSITS.
Mean Interval.
South
Star
too
soon.
Deviation
of the
Instrnment
from the
Meridian.
InR.A.
In Decliti.
8th.
mil.
lOlll.
lltlj.
Hill.
lOlli.
24tli.
Solar.
Sidereal.
Capella and ")
Rigel /
Castor and \
Procyon . . J
Procyonand ',
Pollux.... [',
M. S.
2 85.5
6 44.75
4 26.35
O /
54 13.25
26 85.75
22 46.5
M. S.
2 22.8
6 42.73
4 26.53
M. S.
2 23.1
6 42.73
4 26.47
M. S.
2 23.07
M. S.
2 23.07
M. S,
2 23
6 42.53
4 26.54
M. S.
6 42.53
4 26.47
M. S.
6 42.8
4 26.46
M. S.
2 23.01
6 42.66
4 26.49
M. S.
2 23.4
6 43.76
4 27.22
S.
2.1
0.99
0.87
S.
1.8
1.88
1.98
•
1.89
IN THE LENGTH OF THE SECONDS PENDULUM,
21
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22
EXPERIMENTS FOR DETERMINING THE VARIATION
Tabtv TV STKRRA TF.ONK r'nmnariqnns; nf fVip Astrnnnmirnl CAnrV with
X ■A. O IjIL XT* *>7XXjX VXVri nL^XJiV/X ■i XJi>' v>Ulll IJdl loUllo Ul lllv; rXO II {JllvUllt_Cil >_/lU\<tV It 1 111
the Chronometer No. 423, from the 9th to the 24.th of March, 1822; with the
Clock's Rate oti Mean Solar Time deduced.
1822.
Chronometer.
Clock.
Clock's Loss on 423.
DAILY RATES.
Chron.
Clock. 1
March 9 p. m.
H. M. s.
C 30 00
H. M. S.
6 10 21.4
Gaining.
Losing.
„ 9 P. M.
9 40 03 1
s.
„ 10 A. M.
9 39 00.9
. 124.7
„ 10 P. M.
9 37 5S.4
„ 11 A. M.
9 36 56
- 125
„ 11 P. M.
9 35 53.4
s.
S.
s.
„ 12 A. M.
9 34 51.2
■ 124.7
> 124 53
1.01
123.51
„ 12 P. M.
9 33 48.7
„ 13 A.M.
9 32 46. S
• 124.1
„ 13 P. M.
9 31 44.6
„ 14 A. M.
9 30 42.6
■ 124.1
„ 14 P. M.
• 10 00 00 .
9 29 40.5
„ 19 P. M.
9 49 43
„ 20 A. M.
9 48 41
• 124.1
„ 20 P. M.
9 47 38.9
„ 21 A.M.
9 46 37
123.6
21 P. M.
9 45 35.3
„ 22 a.m.
9 44 33.5
123.6
. 124.12
1.05
123.07
1
„ 22 P. M.
9 43 31.7
!
„ 23 A. M.
9 42 29.8
• 124 3
,, 23 P. M.
9 41 27.4
24 A. M.
9 40 24.9
125
84 P. M.
9 39 22.4
IN THE LENGTH OF THE SECONDS' PENDULUM.
23
SIERRA LEONE.— Comparisons of the Astronomical Clock with the Chronometer
No. 423, from the 26th of March to the 2d of April, 1822 ; with the Clock's Rate
on Mean Solar Time deduced.
1822.
Chronometer.
Clock.
Clock's Loss on 423.
DAILY RATES.
Chrou.
Clock.
March 26 p. m.
H. :\i. s.
H, M. S.
9 4S 41.6
s.
Grtioing.
Losing.
„ 27 A. M.
9 47 40
123.1
„ 27 P. M.
9 46 38.5
s
S.
s.
„ 28 A. M.
9 4o 37
■ 122.9
. 123.067
0.673
122.39
„ 28 P. M.
9 44 35.0
„ 29 A. M.
9 43 33.8
• 123.2
„ 29 P. M.
9 42 32.4
1
1
„ 30 A. M.
■ 10 00 00 ■
9 41 31
1
■ 122.61
„ 30 P. 31.
9 40 29.8
„ 31 A. M.
9 39 28.5
■ 123.3
„ 31 P. M.
9 3S 26.5
123.225
0.523
122.7
April 1 A. M.
9 37 24.4
• 123. S
1
„ 1 P. M.
9 36 22.7
2 A. M.
9 35 21
1
!■ 123. 2j
., 2 P. M.
I
9 34 19.5
i
24
EXPERIMENTS FOR DETERMINING THE VARIATION
T^
BLE V
. SIERRA LEONE.- — COINCIDENCES OBSERVED with PENDULUM 3.
1822.
MARCH.
Baro-
meter,
No. of
Coinci-
dence.
Tempe.
ratuie.
Time of
Disap-
pearance
Time of
Re-ap-
pearance
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
ratare.
Mean
Interval.
Correc-
tion for
the Arc
Vibrations
in 24 houre.
Reduction
to a mean
Tempera-
ture.
Reduced
Vibrations at
Sl.S" Faht.
First Series; Clock losing 123.51 seconds per diem.
+
S.
M. S. M. s.
11. M. s.
0
0
S.
0
10. A.M.
29.865<^
1
11
80.
80.8
19 38
07 03
19 40
07 12
8 19 39
10 07 07.5
1.22j
O.64J
80.4
644.85
1.35
86010.23
-0.38
86009.87
10. P.M.
29 835<
1
11
81.6
82 7
35 17
22 28
35 20
22 41
2 35 18.5
4 22 34 5
1.2 1
0.63J
82.15
643.6
1.33
86009.75
•fO.35
86010.16
10. P.M.
(bylampUgbt.)
29.850-^
1
11
81.2
81.2
10 39
57 45
10 41
58 03
8 10 40
9 57 54
1.271
0.67J
81.2
643.4
1.49
86009.81
-0 04
86009.77
11. A.M.
29'.885<
1
11
80.2
81.
31 09
18 28
31 10
18 38
8 31 09.5
10 18 33
1.291
o.esj
80.6
644.35
1.53
86010.23
-0.29
86009.94
11. P.M.
29.850-^
1
11
80.8
80.8
51 34
38 49
51 42
39 07
3 51 38
5 38 58
'■"I
O.61J
80.8
644.
1.31
86009.85
-0.21
86009 . 64
12. A.M.
29.900J
1
11
80.5
81.6
29 45
16 57
29 46
17 OS
8 29 45.5
10 17 02.5
1 231
0.66J
81.05
643.7
1.45
86009.89
-0.11
86009.78
12. P.M.
29. 850 j
1
11
82.3
82.9
UO 59
48 03
01 02
48 12
3 01 00.5
4 48 07.5
1.22)
0.64/
82.6
642.7
1 .35
86009.37
-1-0.55
86000.92
13. A.M.
29.76oi
1
11
80.6
80.7
20 02
07 21
20 04
07 30
7 20 03
9 07 25.5
1.22]
0.64]
80.65
644.25
1.33
86010.01
-0.27
86009.74
13. P.M.
29.880^
1
11
82.9
82.9
27 04
14 01
27 06
14 13
2 27 05
4 14 08.5
0.63 J
82.9
642.35
1 33
86009 19
■t-0.67
86009.86
14. A.M.
29.870.|
1
11
80.8
82.8
52 15
39 26
52 17
39 30
8 52 16
10 39 28
1.18]
O.62J
81.8
643.25
1 31
1.45
86009 . 57
86010.29
H-0.21
-0.57
86009.78
86009.72
Sec
ond Ser
ies; Clock losing 122.39 seconds per diem.
2T. A.M.
29.860J
1
11
79.8
80.1
49 30
36 26
49 31
36 37
9 49 30.5
11 36 31.5
1.25]
0.66J
79.95
642.1
27. P.M.
29.800-|
1
II
81.2
82.
22 47
09 31
22 51
09 43
2 22 49
4 09 37
1.22]
0 64]
81.6
640 . 8
1.35
86009 67
-hO.13
86009.80
29. A.M.
29.80o|
1
11
80.4
80.8
30 11
17 00
30 13
17 11
9 30 12
11 17 05 5
1.29]
0.68J
80.6
641.35
1.33
86010.07
-0.29
86009.78
29. P.M.
29.750-^
1
11
82.
82.2
43 05
29 43
43 08
29 53
•i 43 06.5
4 29 48
1.25]
0.66 J
82.1
640.15
1.45
86009.51
-1-0.34
86009.85
Means
29.840
81.3
86009.82
86009.82
IN THE LENGTH OF THE SECONDS' PENDULUM.
25
Table VI. SIERRA LEONE.— COINCIDENCES OBSERVED with PENDULUM 4.
]823>
March&Apbil.
Haro-
Dicter.
No.
of Co-
inci-
dence.
Tempe-
rature.
Time of
Disap-
pearance
Time of
Re-ap-
pearance.
TnieTime of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval
between
Ihe Coin-
cidences,
First Series; Clock losing 123.07 seconds per diem.
Mar. 20 A.M.
„ 20 P.M.
„ 21A.M.
22 A.M.
„ 22 P.M.
23 A.M.
„ 2 \ P.M.
„ 25 A.M.
29.842
29.920
29.88
29.912
29.600.
29 . 820
29.81
r
29.85 <
o
M. S.
M. S.
H. M. S.
O
0
82.1
43 48
43 54
8 43 51
1.181
11
82.1
34 44
34 58
10 34 51
0.62 J
82.1
80.8
00 03
00 04
3 00 03.5
1.29]
11
81.4
51 06
51 18
4 51 12
*
0.68J
81.1
81.7
41 16
41 20
8 41 18
1.281
11
81.9
32 11
32 2(
10 32 17.5
0.67|
81.8
79.6
19 59
20 02
6 20 00.5
1.281
11
81.1
11 13
11 26
8 11 19.5
0.67]
79.85
82.3
42 09
42 14
2 42 11.5
1.271
11
83.4
31 59
32 12
4 .32 05.5
0.66J
82.85
81.3
51 57
52 00
7 51 58.5
1.271
11
82.2
42 53
43 06
9 42 59.5
0.66 J
81.75
83.6
7 40
7 46
3 07 43
1.2 1
11
83.1
58 24
58 42
4 58 33
O.63J
83.35
81.3
47 32
47 38
9 47 35
0.63 J
11
82.6
38 31
38 46
11 38 38.5
81.93
666.
666.85
665.95
85 667.9
665.4
666.1
665.
666.35
Correc-
tion for
tbeArc.
S.
1.31
1.53
1.51
1.51
1.49
1.49
Vibrations
in 24 honrs.
Second Series; Clock losing 123.7 seconds per diem.
1.33
86019.13
86019.67
86019.33
86020.09
86019.09
86019.37
86018.77
86019.17
Reduc-
tion to a
mean
Tempe-
rature.
Reduced
Vibrations at
81.75 Faht
-(-0.15
-0.27
-fO.02
■0.80
-fO.46
„ 31 A.M.
April 1 P.M.
,. 2 A.M.
Means.
29.860<
29.83
29.860-
29.856
1
II
1
II
1
11
81.4
82
82
82.4
80.2
81
06 00
56 46
26 18
17 05
02 54
53 54
06 03
57 00
26 23
17 19
03 59
54 II
10 06 01.5
11 56 53
2 26 20.5
4 17 12
7 02 56.5
8 54 02.5
1.28
0.67
1.23
0.64
1.25
0.64
81.7
82.2
80.6
81.75
665.15
665.15
666.55
+ 0.67
-fO.08
1.51
1.30
1.44
86019.37
86019.22
86019.88
86019.37
86019.28
86019.40
86019.35
86019.29
86019.55
86019.37
86019.41
86019.25
-0.02
-f 0.19
-0.48
86019.35
86019.41
86019.40
86019.37
26 EXPERIMENTS FOR DETERMINING THE VARIATION
ISLAND OF ST. THOMAS.
The Pheasant having occasion to touch at the settlements on the Gold
Coast on her passage, did not arrive at St. Thomas's until the 15th of
May, on which day she anchored in the harbour of Santa Anna de
Chaves. The Island being a Portuguese possession, I had been fur-
nished with letters, obtained by the Admiralty through the Secretary of
State for Foreign Affairs, from the Marquess de Souza, Ambassador in
London, to the Governor of the Island, Senor Joao Baptiste, explanatory
of the purpose for which it was proposed that I should visit his command,
and requesting the good offices of the authorities in its promotion. On
anchoring, we were attended by Mr. John Fernandez, supercargo of a
British merchant ship in the harbour, who had received from Sir
Robert Mends a temporary appointment as vice consul ; and we were in-
formed by him, that the inhabitants, following the example of the larger
Portuguese Colonies, had recently established a provisional government,
in a Junta of three members, of which the former governor was the Pre-
sident ; his colleagues being, the principal Ecclesiastic entitled the
representative of the bishop, and a Colonel Andre, a native of the
Island, of mixed blood, who we further learnt was the efficient member
of the administration ; notwithstanding these proceedings, however, the
island still acknowledged the supremacy of Portugal.
Captain Clavering and myself, accompanied by Mr. Fernandez, waited
the same day on Senor Baptiste to present the Ambassador's letter, and
also one which Sir Charles Mac Carthy had been kind enough to give us ;
we were courteously and kindly received, as we had been led to expect
from the President's European birth and general character ; he assured
IN THE LENGTH OF THE SECONDS' PENDULUM. 27
US of his personal readiness to comply with the request which the
Ambassador's letter contained, but added, that it would be necessary
to be submitted in the first instance to the consideration of the Junta,
and concluded by desiring me to make known to Colonel Andr^ the par-
ticulars of the assistance which I should require. Our reception by that
gentleman was civil, but not so cordial as by the President ; we under-
stood that he had been a considerable sufferer, in the capture, by British
cruisers, of vessels which he had employed in the illicit trade in slaves,
which circumstance might have induced perhaps an indisposition to
forward the views of individuals of that nation; we left him, however,
with permission to examine the town and neighbourhood for a suitable
situation for the experiments.
The town of Santa Anna, which is much more extensive than it ap-
pears when viewed from the harbour, is built of wood with the exception
only of two stone houses ; one of these was occupied by Mr. Fernandez,
who was so obliging as to offer to resign it; but the situation was too
public, and the view of the heavens too confined, for the purposes of the
experiments ; it is the custom at St. Thomas's to surround the principal
mansion by the dwellings of the slaves, each of which has its separate
though small plantation, principally of cocoa nuts, and other lofty palms ;
great part of the town is thus entirely overshadowed, and the view of the
heavens is generally limited to a small space around the zenith. The
temporary circumstances of the family who inhabited the other stone house
placed it also out of the question ; so that there appeared no other choice,
than to apply for apartments in a stone fort situated on a sandy beach at
the entrance of the harbour, and which must have proved in many respects
a very inconvenient residence : the application was accordingly made.
It was late the following evening before the result of the consideration
of the Junta was made known, being not only a refusal of the accommo-
c s
28 EXPERIMENTS FOR DETERMINING THE VARIATION
dation in the fort, but a denial of permission to land the instruments at all
upon the island, grounded on the positive instructions of the Portuguese
Government to its Colonies generally, not to permit foreigners to make any
observations whatsoever in them, except by a special order from the Court
itself; instructions which, it was further observed, were of such general no-
toriety, and so positively enjoined, that if the Marquess de Souza had not
viewed the application from the British Secretary of State as made
solely on behalf of an individual, and not as one in the object of which
the Government itself was interested, the Marquess could not have failed
to have referred to his Court for the only proper and sufficient authority.
As this communication was made verbally by Colonel Andre, and
was not therefore necessarily conclusive, I endeavoured to see the
President on the same evening, and again on the following morning, but
in both instances without success, his secretary acquainting me that he
bad been obliged to decline public business for a few days, in consequence
of ah attack of fever. Having reason to suspect, that the unfavourable
disposition of the Junta might have been in some degree influenced by
the communications having hitherto passed through Mr. Fernandez,
whose acknowledgment as temporary vice consul, I found, had been
refused at the same time, I addressed a letter directly to the
Junta; in which, after recapitulating the circumstances, and refer-
ring to the presence of a ship of war as sufficiently indicating the in-
terest of the British Government, I requested, in the event of the
Junta persisting in a refusal, its communication in writing ; as
Captain Clavering would not feel justified in quitting the island with-
out an official document, which should enable the affair to be brought in
due course under the consideration, of the Court of Portugal, with
which it would rest to judge between the Government of St, Thomas
and the Marquess de Souza, and to decide by which of these authorities
IN THE LENTGH OP THE SECONDS* PENDULUM. 29
the request of the British Government, communicated with all due
formality, had been frustrated. Whilst awaiting a reply to this letter, the
Pheasant proceeded to Man of War Bay, a few miles to the westward of
Santa Anna, to wood and water.
Close to the landing place at Man of War Bay, is a large stone
mansion belonging to the extensive plantation of Fernandilla, which
had been uninhabited for some months before our arrival; and at a
short distance in-land, on the summit of an eminence of no great eleva-
tion, is a well-built brick church, at this time also unemployed ; we had
remarked these buildings in our passage along the coast a few days
before, as likely to answer the purpose of the observations, if nothing
better should offer at Santa Anna ; we now landed for their further
examination, and were not a little surprised to find them occupied by a
guard of sixty soldiers, which had been despatched from the town, at the
same time that the Pheasant sailed from the harbour, for the purpose of
watching her proceedings. The officer commanding, who spoke English
well, acquainted us, that he was ordered to oppose if possible, and other-
wise to remonstrate, in the sole case of our attempting to land instruments,
but that we were at liberty to cut wood, or to obtain any supplies of
which we stood in need, and that he should be happy to render us assist-
ance, or aid in making our stay agreeable ; we readily assured him that
we should not attempt to land instruments on the island without permis-
sion, and on this assurance he accompanied us to examine the buildings.
I found the mansion-house the best suited for my purpose of any that I
had seen, being too substantial for decay to have made much progress ;
it was also very convenient to the ship and well under her protection, as
she was moored immediately abreast of it, and near the shore. The
church would have been more healthy, but it was at a greater elevation
than I had supposed, and very difficult of access. The following morn-
30 EXPERIMENTS FOR DETERMINING THE VARIATION
ing I accompanied Captain Clavering to examine a small rocky island
about two miles off the shore, and uninhabited ; and finding that the
perpendicular face of the rock would admit of being bored to receive the
screws of the supports of the clock and pendulums, it was arranged, that
in the event of the refusal to land on St. Thomas's being persisted in,
we should take possession of this island, which is called in the charts the
Isla das Cabras, and build a protection from the weather with materials
from the ship ; the principal difficulty which we anticipated, and with
which we should have had to contend, would have been the regulation of
the temperature, which in spite of every precaution must have undergone
great fluctuations ; a much longer period than usual would therefore have
been required, to have obtained results equally satisfactory ; but the
delay would have been preferable to quitting the neighbourhood of the
equator, without at least an attempt to accomplish experiments, which we
had gone so far to make.
On returning to the Pheasant we received the reply of the Junta, in
-which the instructions of their Court, and the insufficiency of any other
than a direct authority to set them aside, were formally stated; but
the general effect of the communication Avas not that of a decided
refusal ; as it concluded by expressing regret that the British Government
had not obtained the proper authority for a purpose, which it was much
the inclination of the government of the island to forward ; and that in
consideration of its importance, and that St. Thomas's was the only
station in the immediate vicinity of the equator, on the African side of the
Atlantic, at which the experiments could conveniently be made, the
Provisional Government was still disposed to forward it, so far as their
responsibility could be extended.
I received at the same time a private message from Colonel Andr6
requesting me to return to Santa Anna to confer personally with him ;
IN THE LENGTH OP THE SECONDS* PENDULUM, 31
and on compliance, I had the satisfaction of finding that every difficulty
could be got over, except that of my admission into the fort : but it was
suggested that a convent, situated at a short distance in the country,
might contain suitable apartments, the occupancy of which, in such case,
was offered, and that they should be fitted up in any way that I should
direct I found the convent a large stone building, with a handsome suite
of reception rooms in tolerable repair ; these would have answered well,
had not the convent been entirely embosomed in wood, with no advantaf^e
over the house at Fernandilla to compensate for the greater distance from
the ship ; I therefore applied for, and obtained permission to occupy the
latter ; the officer with whom we were already acquainted, was ordered to
remain with half his guard in the rooms which were not required, and was
made responsible that no interruption should be offered, and nothing stolen.
From this gentleman, Senor Manuel Gomez, a native of Portugal, Captain
Clavering and myself received the most obliging and disinterested atten-
tion during our stay; having married the heiress of extensive plantations
on the Island, he possesses considerable influence ; and being partial to
England, of which he speaks the language well, his good offices, which
may be fully depended on, may prove of much avail to the ships
of war on the African station, when they may have occasion to visit
St. Thomas's.
In consequence of the delay caused by these preliminary measures, it
was not until the 23rd of May that the instruments were disembarked at
FernandiUa. The house was built of the compact basaltic stone of which
the island is composed, and which proved not less impracticable to chisels
than the granite of Sierra Leone ; fortunately the stones were individually
of less size, so that they could be removed without cutting, whenever it
was necessary to drive a wooden picket for the screws, and without
weakening the general strength of the wall, which exceeded a foot and a
32 EXPERIMENTS FOR DETERMINING THE VARIATION
half in thickness. A great advantage was derived from the substantial
nature of the walls, in the preservation of uniformity of temperature, to
which, also, the foliage of the surrounding and lofty trees contributed
in no small degree, so that although the range of the exterior thermo-
meter was greater than at Sierra Leone, in consequence of the descent
at night of the cold air from the very high land in the interior of the
island, the extremes in twenty-four hours of a register thermometer, in
the clock-room, were never so much as three degrees apart. *
It not being possible to supply the deficiency of glass here as at
Sierra Leone, the windows were closed with boards and matting, and
light admitted through a small opening when actually required in ob-
servation ; the clock and pendulum had also an additional protection from
currents, by a screen of African matting, which enclosed them above and
on either side.
The transit instrument was placed on a very substantial pillar of
masonry, which had been designed to support one of the corners of the
roof of a detached store, the building of which had not been proceeded in;
being distant a few feet only from the house, I connected the upper part
of it by a stage of communication with one of the windows of the clock
room, and as the pillar was above 12 feet high, the instrument was thus
inaccessible except from the house, and was consequently secure from dis-
turbance ; by cutting down the wood, in the direction of the meridian,
through a screen of about 200 feet which interposed between the house
and sea, an uninterrupted view was obtained of the north horizon ; the
transit was placed in the meridian on the 26th of May, and the going of
the clock having been ascertained to be sufficiently steady, the observation
of coincidences was commenced with No. 3 pendulum on the 28th of
May, and closed on the 3rd of June ; and with No. 4, on the 4th of June,
and terminated on the 10th. The weather during the whole of this
IN THE LENGTH OF THE SECONDS* PENDULUM. 33
period was very unfavourable for celestial observations, being continually
clouded, especially towards the horizon, but without rain ; of twenty -five
stars with which the transit list commenced on the 28th and 29th of May,
I was obliged to be content with intervals of time obtained by eight, (ex-
clusive of the sun,) on the 8th and 10th of June, their accordance being
such as did not justify the delay of another day, for the chance of unne-
cessarily multiplying observations.
The subjoined tables, containing the details, are arranged in a similar
manner to those of the preceding station, and do not appear to require
any particular explanation.
The height of the pendulums above half tide was ascertained by level-
ling to be 21 feet.
The Island of St. Thomas is about 30 miles in length from North to
South, and half as much in breadth ; the equator passes five or six miles
to the north of its Southern extremity ; it is composed of a very compact
and heavy Basaltic Rock, covered by a rich soil principally of vegetable
decomposition, and is thickly wooded in every part. The interior of the
Island is of considerable elevation ; when first seen by the Pheasant, on
the 13th of May, the principal peak subtended an angle of 13 minutes
with the horizon, when by careful chronometric observation it was not
less than 88 miles distant, whence its height may be inferred to exceed
7000 feet ; the ascent is practicable, the principal diificulty being the
absence of frequented paths.
The general result of the experiments at this Island indicated, as at
Sierra Leone, a greater compression than the prevailing expectation ; the
retardation of the pendulum was even comparatively less here than at
Sierra Leone ; which circumstance, however, I had been prepared to
expect, from the greater specific gravity of the Basalt of St. Thomas than
of the Granite of Sierra Leone.
34 EXPERIMENTS FOR DETERMINING THE VARIATION
It is with great concern that I have now to notice the distressing con-
sequences which attended on the experiments at this station. Captain
Clavering had been again kind enough at my particular request, and from
the obvious exigency, to land a guard of three marines, for the more
effectual protection of the instruments, and to render me such personal
attendance as was usually performed by my servant, who had been
trained in the Northern Expeditions to be a very useful assistant in an
observatory, but who had been taken ill at Sierra Leone, and having
suffered severely from the fever of the country, was not yet sufficiently
recovered to resume his duties ; the marines were stationed in the outer
room of the principal suite of apartments, the inmost of which was oc-
cupied by the clock and pendulums ; it was a large and airy room in
the first-story, the Portuguese guard occupying the ground-floor ; the
marines had no duties whatsoever to perform which required an ex-
posure to the chmate ; nevertheless, on the 9th of June, being the day
before the experiments were completed, one of the men shewed symptoms
of fever, a second on the following morning, and the third in the after-
noon, and unhappily all the cases proved fatal ; of the two m.arines who
had been landed to attend on me at Sierra Leone, one had died on the
passage to St. Thomas's, having been taken ill the day after his embar-
kation ; and the other was one of the present sufferers. It was thus
my misfortune to witness the death of every individual landed for my
assistance in Africa, with the exception of my servant, whose recovery
from a relapse which occurred at St. Thomas's, was long very doubtful ;
it will readily be imagined, that we rejoiced in departure from a climate,
which has shewn itself so generally fatal to European life.
The instruments were re-embarked in the afternoon of the lOth of June,
and the Pheasant sailed on the same evening for the Island of Ascension.
IN THE LENGTH OF THE SECONDS' PENDULUM.
35
TRANSITS OBSERVED AT THE ISLAND OF ST
. THOM.AS.
1822.
STARS.
TIMES OF TRANSIT BY THE CHRONOMETER 123.
Mean by the
ChroDometer.
1st Wire.
2ud Wire.
Meridian
Wire.
4tli Wire.
otli Wire.
May2S.
^ Leonis
M. S.
11 01.2
M. s.
11 2S
IM, S.
11 55.6
M. s.
12 23.2
M. s.
12 50.4
11 M. S,
6 11 55.67
JJ
I Leonis
20 45.6
21 13
21 38. 8
22 05.6
22 32
6 21 3S.S
11
g Leonis
4S 00
46 27.6
46 54. S
47 22
47 49.2
6 46 54,73
»l
S Corvi
. . .
27 27.2
27 54.4
28 21.6
7 27 27.2
»»
Spica
21 3(i
22 02.4
22 28.8
22 55
23 22
S 22 28.83
29.
fist Limb..
Sun's^
1 2(i Limb..
24 4fi.4
27 03.2
25 14.8
27 31.2
25 42. S
27 59.2
26 11.2
28 27.6
26 39. 2 1
28 56 \
23 26 51.15
j>
t Leonis
16 51.2
17 17.2
17 44
18 10. S
IS 37.6
6 17 44.13
u
V Leonis
30 00.8
30 27.2
30 53.2
31 19.2
31 45.2
6 30 53.13
57
£ Corvi
02 5S.S
03 26.8
03 54.8
04 22.8
04 50.8
7 03 54.8
?)
« Criicis
17 43.2
IS 3S.S
19 34.4
20 29.6
21 25.2
7 19 34.27
June 2.
0 Leonis
26 26. S
26 54
27 21.2
27 48.4
28 15.2
6 27 21.13
3.
fist Limb,.
Sun's<
(sd Limb..
25 34.4
27 50. S
26 02. S
28 19.2
26 30. S
28 47.6
26 59.2
29 16.4
27 27.6
29 44.8
23 27 39.33
i .
S Leonis
31 55.2
32 12
32 49.2
33 16. S
33 44
5 32 49.4
)»
I Leonis
41 39.2
42 06
42 32.4
42 59.6
43 26
5 42 33.6
ii
0 Leoni,s
G 53.2
7 20
7 47.2
S 15.2
8 42
6 07 47.67
s.
I Leonis
37 44. S
38 11.2
38 3S
39 04.8
39 32
5 38 38.13
?1
V Leonis
50 54.4
51 20.4
51 46. S
52 13.2
52 39.6
5 51 46,87
n
e Corvi
24 49.3
6 24 49.2
9.
Sun's 2d Limb
29 02.4
29 31.2
29 59.6
30 28
30 56. S
11 28 51.2
10.
S Leonis
20 12
20 39.2.
21 06.4
21 34
22 01.2
5 21 06.53
»i
E Corvi
16 04. S
6 17 00.8
15
a Crucis
. . .
31 45.6
32 41.2
33 36. S
6 32 41.2
1)
S Corvi
. . .
36 38.4
37 05.6
37 32.8
6 36 38,4
11
Spica
30 48
31 14
31 40
32 06.8
33 33.6
7 31 40.4
F 2
36
EXPERIMENTS FOR DETERMINING THE VARIATION
ISLAND OF ST
THOMAS
,
DEDUCTION of the RATE of the Chronometer Nb. 423 from TRANSITS ; between
the 2Sth of May and the 10th of June, 1S23.
28
29
30
31
1
2
3
4
5
6
7
8
9
STARS.
to
to
to
to
to
to
to
to
to
to
to
to
to
29
30
31
Ju.l
2
3
4
5
6
7
8
9
10
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
i Leonis . .
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.62
1.62
1.62
1 Leonis . .
1.21
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.11
1^ Leonis. .
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.28
1.28
(3 Leonis . .
1.19
1.19
1.19
1.19
1.19
1.22
1.22
1.22
1.22
1.22
••
£ Cotvi . . .
1.35
1.35
1.35
1.35
1.35
1.35
1.35
1.35
1..35
1.35
1.71
1.71
aCrucis . .
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
2 Corvi . . .
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.1
1.4
1.4
Spica. . .
The Sun 1
(solar.) J •
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.1
1.25
1.25
1.25
1.25
1.25
1.51
1.51
1.51
1.51
1.51
1.51
••
1.3
1.32
1.32
1.32
1.32
1.33
1.36
1.36
1.36
1.36
1.41
1.52
1.53
MEANS— ^
GaiDing per>
Diem 3
1 .318 (Sidereal) = l .322 in a Solar Day.
1 .42 (Sidereal)= 1 .424 in a Solar Day.
IN THE LENGTH OP THE SECONDS' PENDULUM.
37
ISLAND of ST. THOMAS.-
-Comparisons of the Astronomical Clock with the Chro-
nometer, No. 423, from Ihe 27th of May to the 10th of June, 1822; with the Clock's
Rate on Mean Solar Time deduced.
DAILY RATES.
1822.
Chronometer.
Clock.
Clock's loss on 423.
Chron.
Clock.
»1. M. S.
H. M. S.
S 31 13
8 30 11
8 29 08.9
rf^'iin inff
0
May 27 P.M.
(a.m.
„ 28]
(P.M.
> 124.1
J
Vvalllllig*
(a.m.
„ 29
(P.M.
8 28 07.5
8 27 04. 7
. 124.2
"1
(a.m.
„ 30]
(p.m.
8 26 03
S 25 01.2
I 123.5
i
J
1
1
s.
s.
s.
(a.m.
„ 31]
(P.M.
8 23 59.2
8 22 56.8
j- 124.4
J
1
' 124.1
1.32
122.78
^ (a.m.
June 1^
(p.m.
8 21 55
8 20 52.6
\ 124.2
j
1
f A. M.
„ 2
(P.M.
S 19 50.8
8 18 4S.6
> 124.
j
(a.m.
3]
(p.m.
. 8 00 00 .
8 17 46.8
> 124.3.
8 16 44.3
\
(a. m.
(p.m.
8 15 42.4
8 14 40
> 124.3]
J
(a.m.
„ 5
(p.m.
S 13 38.2
8 12 35.8
!• 124.2
J
1
fA.M.
(p.m.
8 11 34
8 10 31.5
I 124.3
1
(A.M.
7)
( p. M.
8 9 29.5
8 8 27.6
> 123.9
• 124.186
1.424
122.76
(A.M.
(p.m.
8 7 25.5
8 6 23.4
!■ 124.2
J
j- 124.
i 124.4,
(A. M.
>. 9 J
(p.m.
8 5 21 6
8 4 19.4
(A.M.
(p.m.
8 3 17.2
8 2 15
38
EXPERIMENTS FOR DETERMINING THE VARIATION
ISLAND OF ST. THOMAS.
COINCIDENCES OBSERVED witli PENDULUM No. 3; the Clock making 86277.22 Vibrations iu a M
eaii .Solar Day.
DATE.
Baro-
mtter.
No. of
Coinci
denct.
Tempe-
rature.
Time of
Disap-
pearance
Time of
Re--Tp-
pearauce.
True Time of
CoincideDce.
Arc of
Vibra-
tiou.
Mean
Tempe-
rature.
Meau
Interval.
Correc-
tion for
tbeArc.
Vibrations
in 24 hours.
Reduction
to a mean
Tempera-
ture.
Reduced
Vibrations at
S-i'.\ Faljt.
1822.
IN.
0
M. s.
M. S.
H. M. S.
o
0
s.
s.
30.06sJ
1
81.2
29 46
29 47
3 29 46.5
1.2 1
-1-
May 28 P.M.
\
81.45
614.8
1.38
86010.98
-0.27
8C010.71
II
81.7
17 10
17 19
5 17 14.5
0.66J
\
I
82.2
43 05
43 07
9 43 06
1.161
,, 29 A.M.
30.060<^
11
1
82.4
85.4
30 26
35 28
30 36
35 33
n 30 31
1 35 30.5
0.62]
1.161
82.3
644.5
1.26
86010.73
-i-0.08
S6010.81
„ 29 P.M.
30.02oi
f
11
1
85.8
80. e
22 20
25 49
22 29
25 51
3 22 24.5
8 25 50
0.62 J
1.2 1
85. G
641.4
1.26
86009.45
-H.47
86010.92
., 30. AM.
30.080<^
f
11
1
82.3
79.7
13 14
6 03
13 22
6 07
10 13 18
8 06 05
0.66]
1.16
81.45
644.8
1.38
SCO 10. 98
-0.27
86010.71
June 1 A.M.
30.020.^
80
646.9
1.26
86011.73
-0.88
8C010.85
1
11
80.3
53 48
54 00
9 53 54
O.62I
so.noj
1
84
00 20
00 22
1 00 21
1.24]
„ 1 P.M.
83.4
642.35
1.47
86010.06
-1-0.55
86010.61
11
82.8
47 19
47 30
2 47 24 5
0.68J
f
1
81.1
01 49
01 51
9 01 50
1.181
„ 2 A.M.
30.1.38<^
81.4
644.75
1.32
86010.89
-0.29
86010.60
[
\
11
1
81.7
80.6
49 12
2 41
49 23
2 45
10 49 17.5
9 2 43
0.63 J
1.2 1
„ S P.M.
30.110-^
11
81.6
50 07
50 16
10 50 11.5
o.eo]
81.1
644.85
1.38
86010.99
-0.42
86010.57
Mean s
30.076
82.1
86010. 72P
86010.726
.
IN THE LENGTH OP THE SECONDS' PENDULUM.
39
ISLAND OF ST. THOMAS.
COINCIDENCES OBSERVED with PENDULUM No. 4; the Clock making 8C277. 2 1 Vibrations in a Mean Solar Day.
DATE.
Baro-
meter.
No. of
Coinci-
dence.
Tempe-
rature.
Time of
Disap-
pearance
Time of
Re-ap-
pearance
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
ratore.
Alean
Interval.
Correc-
tion for
the Arc.
Vibrations
in 24 boors.
Reriuclion
to a mean
Tempera-
ture.
Reduced
Vibrations at
83.°iFaht.
1822.
IN.
0
M. s.
M. S.
H. M. S.
c
c
S.
s.
June 4 A.M.
30.09oi
11
81
81.8
50 58
42 30
51 03
42 43
9 51 00.5
11 42 36.5
1.2 1
0.66J
81.4
669.0
-f
1-38
86020.90
-0.71
86020.19
.. 5 A.M.
30.085^
11
80.6
83
25 19
16 45
25 23
16 58
9 25 21
11 16 51.5
LIS]
o.osj
81.8
669.05
1.32
86020.64
-0.53
86020.09
„ 5 P.M.
r
30.026<^
11
80.4
81.8
02 06
52 49
02 09
53 01
2 02 07.5
3 52 56.5
1.221
0.68J
85.6
661.9
1.44
86019.14
-H.05
86020.19
„ 6 P.M.
30.020-^
n
85.2
83
OS 05
59 06
08 09
59 20
3 08 07
4 59 13
1.181
0.63|
84.1
666.6
1.32
86019.70
-t-0.42
86020.12
., 7 A.M.
30.120^
1.
1.
11
81
83.8
07 36
59 13
OS 01
59 25
10 07 58.5
11 59 19
1.18]
0.63J
82.4
668.03
1.32
86020.24
-0.29
86019.95
„ 8 A.M.
30.120-!
11
83.8
8t
45 15
36 09
45 18
36 21
10 45 16.5
12 .S6 15
1 26]
0.7 J
83.9
665. 85
1.33
86019 63
4-0.34
86019.97
„ 8 P.M.
30.080<
11
84.4
81.4
40 59
31 53
41 05
32 09
3 41 02
5 32 01
"1
0.66J
84.4
665.0
1.38
86019.28
-fO.55
86019.83
,, 9 A.M.
30.10oJ
11
81.3
82.5
02 25
53 43
02 29
33 56
9 02 27
10 53 49.5
1.22]
0.68]
81.9
668.25
1.41
86020.44
-0.50
86019 91
„ 9 P.M.
so.iooi
11
83.2
83.2
49 22
40 31
49 29
40 47
2 49 25.5
4 40 39
1.18]
O.esj
83.2
667.35
1.32
86019.98
-fO.04
86020 02
„ 10 A.M.
30 lOoi
u
82.1
82.3
15 16
06 30
15 17
00 40
9 15 16.5
11 06 35
1.22]
0.68J
82.2
667.83
1.44
86020 . 30
-0.38
86019.92
Means
30.084
83.1
86020.02
86020.02
t-f
40 EXPERIMENTS FOR DETERMINING THE VARIATION
ISLAND OF ASCENSION.
The Island of Ascension, which was previously uninhabited, was taken
possession of by the British Government, in the year in which the late
Emperor of France was sent in captivity to St. Helena, and has since re-
mained in the occupation of a small detachment of seamen or marines, who
are its only inhabitants ; the Garrison, at the period of the Pheasant's visit,
consisted of a party of the Royal Marines, commanded by Major John
Campbell, whom we found in expectation of our arrival, in consequence of
a letter which had preceded us from Commodore Sir Robert Mends, on
whose command Ascension was considered a dependency ; it is scarcely
necessary to add that we were received by Major Campbell and the
officers under his command with the utmost kindness and hospitality, and
with a disposition to render every assistance in their power.
The only buildings on the island were those which had been erected
for the accommodation of the garrison ; they consisted of an officer's and
soldiers' barrack, and a store-house, forming three sides of a barrack
square, situated near the landing-place on the Northwest side of the island ;
the barracks had been described to me as being constructed of stone and
mortar, with walls exceeding a foot in thickness, and I had relied on this
information in selecting Ascension as one of the stations of experiment ;
I was therefore greatly disappointed on examining the walls, to find that
the mortar of which they were principally composed, (the stones being
comparatively few,) had been made without a due proportion of lime, and
that it was to be feared in consequence that they would not prove suffi-
ciently substantial to support such heavy weights as the clock and pen-
IN THE LENGTH OP THE SECONDS' PENDULUM. 41
' dulum-frame ; the walls of the store-house were indeed of an opposite
character, being built of large masses of the heavy volcanic rock of which
the Island chiefly consists, roughly squared so as to rest on each other,
. and forming a very compact wall of unusual thickness and great stability ;
from its ai)pt;aia[ice however, it was judged to present fewer facilities in
the operations of boring or driving pickets, than had been experienced
on any former occasion ; the house itself was also very ill adapted in other
respects for the experiments ; it contained the whole of the provisions and
stores of the garrison, including those of daily consumption ; and the
process of issuing and distributing the latter to the several messes took
place within its walls, and could not be removed elsewhere, without such
excessive inconvenience as amounted to impracticability ; the only light,
when the door was closed, was admitted through a small and grated
window at the end of the building, several feet from the ground, and so
inconveniently placed as to be quite unavailing in the observations, which
would have therefore to depend on the opening of the door-way for the
admission of light ; the store-house was however the only alternative if
the barracks should fail, rendering the prospect altogether so unfavourable,
as appeared scarcely to justify the double risk, of injury in landing and
putting up the instruments, and of the time which would have been con-
sumed in what might have proved an unsuccessful attempt, or at least an
unsatisfactory experiment ; but I had learnt by experience to confide in
the resources of a ship of war in surmounting difficulties almost of every
kind, and I was well assured of Captain Clavering's ready disposition
to spare no exertions which might assist me ; no time was therefore lost
in disembarking the instruments, which was accomplished on the evening
of our arrival, through a surf which frequently interrupts all communi-
cation between the anchorage and shore for days together, but which
was fortunately very' moderate on this occasion.
42 EXPERIMENTS FOR DETERMINING THE VARIATION
On the following morning a trial was made of the barrack wall, which
was found, as had been apprehended, too incohesive and unsubstantial
to answer the purpose ; a part of the wall of the store-house was therefore
selected for an attempt, and after considerable labour, by the joint
operation of chisels and wedges, three oaken pickets were established in
an horizontal interstice between two of the largest masses of stone ; the
pickets were of sufficient size, and at the proper distances, to receive
the three upper screws of the pendulum support ; one of the two remaining
screws at the ends of the brackets, happening to coincide with another
interstice, was secured to a picket the same evening ; and the other screw
on the following morning, by splitting off and removing a part of the
stone opposed to it, and substituting a junk of wood tightly wedged ; the
pendulum support, which was most important, was thus attached to the
wall as firmly as could be desired ; the clock was then fixed at the proper
distance beneath it, by removing the stones whinh were opposed to its
screws, (having previously wedged up the superincumbent stones,) and
supplying their places with junks of wood cut for the occasion and bound
in by wedges ; the clock was less securely fastened by this method than
the pendulum frame had been, but its immobility was of less consequence.
Aware of the inconveniences attendant on an unsteady and therefore
uncertain temperature, and that greater errors might be apprehended
from that source, than from any other whatsoever, every precaution was
taken which might contribute to impede its fluctuations ; the clock and
pendulum were enclosed above, and at the sides, by a double skreen of
African matting, stretched on a wooden frame, which projected about six
feet from the wall and was continued to the ground ; the light which was
admitted by a very small opening in the door-way, was reflected upon the
disk of the pendulum by mirrors properly disposed ; the store was closed
and the key remained in my possession, excepting for the short interval
IN THE LENGTH OP THE SECONDS' PENDULUM. 43
which was required in the daily issue of provisions, which took place in a
distant part of the room separated by a walled partition from the instru-
ments, and always at a certain hour of the forenoon, previously to which
I had completed the morning series of coincidences ; it was not pos-
sible, however, to prevent greater changes of temperature in the course
of the twenty-four hours, than had occurred at either of the preceding
stations ; the surface of the soil, or rather the rock, in the neighbourhood
of the barracks, being unprotected by foliage, and situated on the lee-
ward side of the island, became extremely heated during the day by the
power of the sun ; and although from the great thickness of the walls
his direct influence was little felt withinside, the occasional entrance
of the heated air from without could not be altogether prevented.
In the embarrassment which a range of 8 or 9 degrees of the thermo-
meter in the twenty-four hours produced, I felt the propriety of the de-
termination which I had formed in its anticipation, of confining myself,
whilst in the tropics, to those stations where the instruments could have
the protection of the roof and walls of a substantial house ; the store-room
was certainly far superior in this respect to any temporary covering which
could have been made with materials from the ship ; but the variations of
temperature were sufficiently perplexing, and required much watchfulness
and attention in selecting the most favourable periods of the day for the
observation of coincidences ; by these means, however, it may be seen that
the changes of temperature, whilst the pendulum was actually in vibration,
rarely exceeded 2°, and only in a single instance 3°; and as the
changes were progressive, and in opposite senses, being gaining in the
forenoon, and losing in the afternoon series, the errors which might be
apprehended from the pendulum being more slowly affected than the
thermometer, would in great measvire balance each other.
An unfinished wall near the Barrack-Square afforded a suitable and
G 2
44 EXPERIMENTS FOR DETERMINING THE VARIATION
convenient situation for the transit instrument ; the agreement in the
results with stars differing so widely in declination, as those in the table
of "observed transits," is a sufficient indication that the plane of the
vertical motion of the Instrument was preserved throughout.
It is but justice to the chronometers of Messrs. Parkinson and Frodsham,
that the attention of the reader should he directed to the opportunities,
which incidentally occurred in the course of these experiments, and are
exemplified in the Tables, of proving the steadiness of their going ; such
is the table shewing the rate of No. 423, at Ascension, deduced from the
transits ; the going of this chronometer is the more worthy of notice, as it
was almost incessantly employed in observations, and exposed in con-
sequence to continual changes of temperature and position. It would be
impossible indeed to express the advantage which these chronometers
proved to me on all occasions ; or how much the thorough reliance which I
could place on their time facilitated, and which is more important, how
much it conduced to the accuracy of, the variety of observations which
successively occupied my attention, and which I was usually pressed to
complete within the least possible time. I may take the present occasion
also to mention, as a circumstance well worthy of notice, that of twelve
chronometers, which Messrs. Parkinson and Frodsham have at different
times intrusted to my care in voyages of long duration and unusual ex-
posure, not only has there not been a single failure, but I should find it
difficult to say that any one chronometer has been decidedly inferior to the
others.
It has been already remarked that from the mode in which the clock
was attached to the wall and supported, it was not considered as per-
fectly secure from motion ; and it is probable that its weight acting on
the blocks of wood to which it was fastened, caused them to yield a little
for the first three or four days, until effectually stopped by the resistance
IN THE LENGTH OF THE SECONDS* PENDULUM. 45
of the wedges ; as the level which marks the horizontality of the hollow
cylinder in which the pendulum works, was observed to undergo oc-
casional slight derangements during that period ; whenever these were
noticed, they were immediately corrected by the screws in the lower
plate designed for that purpose, until the adjustment was no longer
disturbed ; but their effect on the rate of the clock in the first days of its
going may be perceived by its comparisons with the chronometer ; and
may be further traced, with remarkable correspondence, by a close examina-
tion of the table exhibiting the coincidences of Pendulum No. 3 ; in which
table as a mean rate is taken for the clock, its daily irregularities are
transferred in appearance to the Invariable Pendulum. Had the rate of
the clock, as indicated from day to day by the chronometer, been intro-
duced into the table, instead of the mean rate, the results with the
detached pendulum on the several days would have been shewn to be
not less in accord, than those of pendulum 4 appear in the succeeding
table, when the irregularities in the clocks going had ceased; and I
may remark, that this mode of constructing the table would have been
the more correct on this occasion, but as it is obvious that in either case,
the alternate result must have been the same, the form adopted at the pre-
ceding station has been adhered to.
The height of the pendulums above the mean level of the sea was
ascertained by direct measurement to be 17 feet.
The Pheasant arrived at Ascension on the 26th of June ; the observa-
tion of coincidences with No. 3, was commenced on the morning of the
30th, and ended on the evening of the 3rd of July ; and with No. 4, on
the morning of the 5th, terminating on the evening of the 8th ; the instru-
ments were re-embarked on the 9th, when we were again fortunate in the
state of the surf; and on the following day the Pheasant sailed for South
America.
46
EXPERIMENTS FOR DETERMINING THE VARIATION
TRANSITS OBSERVED AT ASCENSION.
1822.
STARS.
1
TIMES OK TRANSIT BY THE CHRONOMETER 423.
Mean by the
Chronometer.
1st Wire.
2nd Wire.
Meridian
Wire.
4th Wire.
5th Wire.
M. s.
M. S.
H. M. s.
M. S-
M. s.
H. M. s.
Juii.29
r 1st Limb.
Sun's<i
LM Limb.
56 04.8
58 22.4
56 33.2
58 50.4
12 57 01.6
12 59 18.8
57 30
59 47.2
57 58.4
00 15.2
12 57 01.6
12 59 18 8
»)
/3Crucis. . .
01 51.2
02 41.6
7 03 32
04 22.4
05 12.8
7 03 32
>»
£ UrsEe . . .
10 38
11 25.6
7 12 13.6
13 01.6
13 50
7 12 13.73
5»
7 Hydrae . .
34 20.4
34 49.2
7 35 17 6
35 46
36 14.4
7 35 17.53
5>
Spica . . .
40 56.8
41 23.6
7 41 50.4
42 17.2
42 44
7 41 50.4
)»
1 Virginis . .
. . .
51 10
7 51 36.8
52 02.8
. . .
7 51 36.6
)5
I Centauri. .
00 32.4
01 03.2
8 01 34
02 04.8
02 35.6
8 01 34
»»
» Ursse Maj . .
05 04.8
05 45.6
S 06 26.4
07 07.2
07 48
8 06 26.4
))
»)Bootis. . .
. . .
11 40.4
S 12 08.4
12 35.6
8 12 OS. 3
it
|9 Centauri . .
15 36
16 27.2
S 17 IS. 8
18 09.6
19 01.2
S 17 18 6
)J
wHydrse . .
21 12
21 41.2
8 22 10.4
22 39.6
23 OS. 4
S 2-2 10.33
)1
y. Virginis . .
28 24.4
28 51.2
8 29 18
29 44.4
30 11.2
S 29 17.87
J»
Arcturus . .
32 29.2
32 56.8
8 33 24.8
33 52.8
34 20.8
8 33 24.87
57
y Bootis . . .
49 36
50 09.6
8 50 43.2
51 17.2
51 50.8
8 50 43.33
f1
a Centauri 2 .
. .
. • .
8 54 27.2
. . .
8 54 27.2
t1
(A Virginis . .
58 36
59 04
8 59 30
59 56.4
00 22. S
8 59 30.2
H
£ Bootis. . .
02 00.8
02 30.4
9 02 59.6
03 29.2
03 59.2
9 02 59.8
IJ
a Librae 2 . .
05 56
06 23.2
9 06 50.4
07 17.6
07 54.8
9 06 50.4
July 4.
(3 Crucis . . .
42 25.2
43 15.6
6 44 06
44 56.4
45 46.8
6 44 06
1»
£ Ursae . . .
51 11.2
51 59.2
6 52 47.2
53 35.6
54 23.6
6 52 47.33
))
7 Hydrae . .
14 54.8
15 22.8
7 15 51.2
16 19.6
16 48
7 15 51.27
ii
Spica . . .
21 30.4
21 56.8
7 22 23.6
22 50
23 16.4
7 22 23.47
n
1 Virginis . .
31 18
31 44
7 32 10
32 36
33 02
7 32 10
)T
1 Centauri. .
41 06
41 36.8
7 42 07.6
42 38. 8
43 09.6
7 42 07.73
)»
»! Ursae . . .
45 37.2
46 18
7 46 58. S
47 39.6
48 20.8
7 46 58.93
»i
>i Bootis . . .
51 46
52 13.2
7 52 41.2
53 08. S
53 36.4
7 52 41.13
1)
y Bootis . . .
30 08.4
30 42
8 31 16
31 50
32 24
S 31 16.07
1
£ Bootis. .
42 33.6
.1
43 03.2
8 43 32.8
44 02.4
44 32
8 43 32.8
IN THE LENGTH OP THE SECONDS' PENDULUM.
47
TRANSITS OBSERVED AT ASCENSION, continued.
1822.
STARS.
TIMES OF TRANSIT BY THE CHRONOMETER 423.
Mean by the
Chronometer.
1st Wire.
2nd Wire.
Meridian
Wire.
4lh Wire.
5th Wire.
M. S.
M. s.
H. M. S.
M. S.
M. s.
H. M. s.
July 4
a Librae 2 . .
46 29.2
46 56.4
S 47 23.6
47 50.8
48 17.6
8 47 23.53
5
rlst Limb.
Sun's<!
LSd Limb.
57 27.6
59 45.2
57 56
00 13.6
12 58 24.4
1 00 42
58 52.8
01 10.4
59 21.6
01 38.8
12 58 24.47
1 00 42
8
plst Limb.
Sun's<
[2d Limb.
58 05
00 23.2
58 34.4
00 51.6
12 59 02.8
1 01 20
59 31.2
01 48.4
59 59.6
02 16.8
12 59 02.8
1 01 20
(3 Crucis . . .
26 51.8
27 42.2
6 28 32.6
29 23
30 13.4
6 28 32.6
£ UrsEe . . .
35 37.6
36 25.6
6 37 13.6
38 01.6
39 50
6 37 13.66
y Hydrse . .
7 00 17.6
. .
7 00 17.6
Spica . . .
05 56.8
06 23.6
7 06 50
07 16.8
07 43.6
7 06 50.13
1 Centauri. .
. . .
26 03.6
7 26 34.4
27 05.2
•
7 26 34.4
7) Ursse . . .
30 03.6
30 44.4
7 31 25.2
32 06.4
32 47.2
7 31 25.33
(3 Centauri . .
. . .
7 42 18.8
. . .
7 42 18 8
■jt Hydraj . •
46 12
46 40.8
7 47 10
47 38.8
48 08
7 47 09.93
X Virgiuis . .
53 24
53 50.8
7 54 17.6
54 44.4
55 10.8
7 54 17.6
Arcturus. .
57 28.4
57 56
7 58 23-6
58 51.6
59 19.2
7 58 23.73
y Bootis . . .
14 35.2
15 08 8
8 15 42.4
16 16.4
16 50
8 15 42.53
a. Centauri 2 .
. . .
8 18 27.7
. . .
. . .
8 18 27.7
»>
(iVirginis. .
23 36.8
24 03.6
8 24 30
24 56.8
25 23.2
8 24 30.07
>t
£ Bootis . . .
27 00.4
27 30
8 27 59.6
28 29.2
28 58.8
8 27 59.6
)i
a. Librae 2 . .
30 56.4
31 23.6
S 31 50.8
32 18
32 45.2
8 31 50.8
48
EXPERIMENTS FOR DETERMINING THE VARIATION
Ascension.— DEDUCTION of the RATE of the Chronometer, No. 423, from j
TRANSITS, between the 29th of June
, and the 8th of July, 1822.
STARS.
29
to
30
30
to
July 1
1
to
2
2
to
3
3
to
4
4
to
5
5
to
6
6
to
7
7
to
S
The sun (solar) . .
|3 Crucis
s.
2.6
2.^6
2.6
2.6
2.6
s.
2.6
2.72
s.
2.72
2.72
2.71
2.71
2.71
2.71
2.71
2.56
2.56
2.56
2.56
£ Ursse
2.63
2.63
2.63
2.63
2.63
2.49
2.49
2.49
2.49
7 Hydrae ....
2.66
2.66
2.66
2.66
2.66
2.5
2.5
2.5
2.5
Spica
2.52
2.52
2.52
2.52
2.52
2.57
2.57
2.57
■2.57
^ Virffinis ....
2 59
2.59
2.6C
2.59
2.66
2.59
2.66
2.59
2.66
2.58
2.58
2.58
2.58
1 Centauri ....
2.66
ti Ursse Maj. . . .
2.41
2 41
2.41
2.41
2.41
2.52
2.52
2.52
2.52
» Bootis
2.49
2.49
2.49
2.49
2.49
^ Centauri ....
2.59
2.59
2.59
2.59
2.59
2.59
2.59
2.59
2.59
TrHydrse ....
2.54
2.54
2.54
2.54
2.54
2.54
2.54
2.54
2.54
xVirginis ....
2.54
2.54
2.54
2.54
2.54
2.54
2.54
2.54
2.54
Areturus ....
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
2.46
y Bootis
2.46
2.46
2.46
2.46
2.46
2.54
2.54
2.54
2.54
a Centauri . . .
2.63
2.63
2.63
2.63
2.63
2.63
2.63
2.63
2.63
(xVirginis ....
2.56
2.56
2.56
2.56
2.56
2.56
2.56
2.56
2.56
E Bootis
2.51
2.51
2.51
2.51
2.51
2.61
2 61
2.61
2.61
a Librae
2.54
9.54
2.54
2.54
2.54
2.73
2.73
2.73
2.73
2.56
2.56
2.56
2.56
2.56
2.56
2.57
2.57
2.57
MEANS— Gaining per
Solar.
1
2.56:
= 2.57 '
2.t
69 = 2.
576 Sol
ar.
IN THE LENGTH OF THE SECONDS* PENDULUM.
49
Ascension. — Comparisons of the Astronomical Clock with
the Chronometer
No. 423, from the 30th of June to the 9th of July, 1S22 ; w
ih the Clocii's Rate
on Mean Solar Time deduced.
DAILY RATES.
1822.
Clironometer.
Clock.
Clock's Loss on 423.
Cluon.
Clock.
June 30 A. M.
H. M. S.
M. S.
41 12. G
Gaiuing.
Losiug.
„ 30 p. M.
Jul^- 1 A. M.
■!0 12 S
39 14.3
. lis. 3
„ ■ IP. M.
3S 15.1
. 117. S
s.
S.
S.
„ 2 A. M.
37 16.5
. 117.72
2.57
115.15
„ 2 p. M.
3(3 17.4
• 117.5
„ 3 A.M.
35 19
„ 3 p. M.
34 20.0
. 117.3
„ 4 A.M.
. 10 GO 00 .
33 21.7
„ 4 p. M.
32 23.5
117.3
„ 5 A. M.
31 24.4
„ 5 P. M.
30 2G
■ 116. S
„ 6 A. M.
29 27. G
•
„ 6 p. M.
2S 29
■ 116. S
„ 7 A. M.
27 30. S
• IIC.S
2.5S
114.22
„ 7 P. M.
2G 32.6
• 116. S
„ S A. M.
25 34
„ S P. M.
24 35.7
. 116.8
„ 9 A. M.
23 37.2
1
1
H
50
EXPERIMENTS FOR DETERMINING THE VARIATION
Ascension.— COINCIDENCES OBSERVED with PENDULUM No. 3 ; the Clock making
S62S4.85 Vibrations in a Mean Solar Day.
DATE.
Baro.
meter.
No.
of Co-
ioci-
deace.
Tempe-
ratare.
Time of
Disap-
pearance-
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
tlieArc.
Vibrations
in 24 hours.
Reduc-
tion to a
mean
Tempera-
ture.
Reduced
Vibrations at
81».47 Fabt.
1822.
IN.
0
M. S.
M. S.
H. M. s.
0
0
S.
S.
r
79.5
25 32
25 34
8 25 33
1.18'
-1-
June 30 A.M.
SO.HoJ
11
81
84
11 48
23 32
11 58
23 33
10 11 53
2 23 32.5
1.22
80.25
638
1.29
86015.65
-0.51
86015.14
„ 30 P.M.
30.130<j
30.180.!
11
83.5
79
09 12
30 08
09 21
30 09
4 09 16.5
8 30 08.5
>
0.64]
1.22]
83.75
634.4
1.35
86014.17
■fO.96
86015.13
July 1 A.M.
79.75
637.6
1.35
86015.55
-0.72
86014.83
11
80.5
16 19
16 30
10 16 24.5
0.64]
83.6
21 39
21 43
2 21 41
1.2 ]
1 p.:m.
30.12oJ
11
83.8
77
07 09
40 46
07 16
40 48
4 07 12.5
8 40 47
0.62
1 2 ]
83.7
633.15
1.32
86013.62
■fO.94
86014.56
„ 2 A.M.
SO.HoJ
I
11
79.2
837
27 17
24 35
27 28
24 37
10 27 22.5
2 24 36
0.62 J
1.2 1
78.1
639.55
1.32
86016.34
-1.39
86014.95
„ 2 P.M.
30.08oi
11
83.1
76.4
10 11
17 18
10 21
17 20
4 10 16
8 17 19
0.62
1.2 1
83.4
634
1.32
86013.96
-HO. 81
86014.77
„ 3 A.M.
30.1 70-!
77
640
1.32
86016.52
-1.88
86014.64
11
77.6
03 53
04 05
10 03 59
0.62
86.2
03 49
03 50
2 03 49.5
1.22
„ 3 P.M.
so. 120'
11
85.4
48 47
48 57
3 48 52
0.64 J
85.8
630.25
1.35
86012.37
-H.82
86014.19
Means
30.135
81.47
86014.77
86014.77
IN THE LENGTH OF THE SECONDS* PENDULUM.
51
Ascension— COINCIDENCES OBSERVED with PENDULUM No. 4 ; the Clock inakin<r
86283.78 Vibrations in a Mean Solar Day.
DATE.
Baro-
meter.
No.
of Co-
inci-
dence.
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Re-ap-
pearance,
True Time of
Coincidence.
Mean
Interv.il.
Correc-
tion for
llie Arc.
Vibrations
in 24 boors.
Reduc-
tion to a
mean
Tempe-
rature.
Reduced
Vibrations at
S2.87 Faht.
1822.
July 5 A.M.
„ 5 P.M.
„ 5 P.M.
(by lamp light.)
„ 6 A.M.
„ 6 P.M.
„ 7 A.M.
„ 7 P.M.
„ 8 P.M.
30.180^
30.150<^
30.130
30
170<!
30.140<
30.170^
30.140<
30.140<
Meana .
77.9
81.8
85. G
85.7
80
82
78.4
80.4
86
87.2
79.8
82.2
85.9
85
83.8
84.3
M. S.
14 34
04 14
34 42
23 16
57 00
46 19
40 08
29 45
58 20
46 44
55 17
44 50
21 18
09 55
7 43
36 40
M. S.
14 S9
04 26
34 43
23 28
57 02
46 33
40 09
.^0 00
58 22
46 58
55 20
45 05
21 23
10 07
7 48
56 56
H. M. S.
7 14 36.5
9 04 20
12 34 42.5
2 23 22
8 57 01
10 46 26
7 40 08.5
9 29 52.5
12 58 21
2 46 51
7 55 18.5
9 44 57.5
2 21 20.5
4 10 01
12 7 45.5
2 56 48
1.2
0.62
79.8!
85.65
79.4
86.6
i.ie
0.62
30.155
85.45
84.05
658.35
651.95
656.5
658.4
651
657.9
652.05
654.25
+
1.32
l.,35
1.54
1.54
1.54
1.29
1.32
1.29
82.87
86024.96
86022.41
86024.46
86025.20
86022.22
86024.73
86022.44
86023.31
86023.72
H 2
-1.27
-1-1.17
-0.79
-1.44
-H.57
-0.79
-1-1.08
■fO.49
86023.69
86023.58
86023.67
86023.76
86023.79
86023.94
86023.52
86023.80
86023.72
i
52 EXPERIMENTS FOB DETERMINING THE VARIATION
B A H I A.
Agreeably to the original design which I had given Sir Robert Mends,
and on which his instructions to Captain Clavering were founded, the
Pheasant should have proceeded from Ascension direct to Maranham
as her next station ; but, whilst at Ascension, Captain Clavering had
been induced to land all the provisions which could be spared from the
Pheasant, in consequence of a representation from Major Campbell that
the provisions of the Garrison were much reduced, and that he had
reason to apprehend that the vessel containing an expected supply
must have missed the island and gone to Leeward, which we after-
wards learnt to have been actually the case ; it became necessary there-
fore that the Pheasant should stop at Bahia on the passage to Maran-
ham to obtain a fresh supply.
On our arrival at Bahia on the 1 9th of July, we were apprized of the
revolution which had commenced in the Brazils in the preceding Fe-
bruary, and had already become so general, that the city of Bahia was
the only possession retained by the Portuguese ; we found them in daily
expectation of an attack by sea and land, as the Independant troops
were in force in the adjoining villages, awaiting the arrival of a squadron
from Rio to commence their operations in concert ; the city was in
great measure deserted by its principal inhabitants, whose slaves being-
left to provide for themselves, added much to the causes of alarm ; the
British merchants were anxiously looking for the arrival of the Blossom
sloop of war, which Sir Thomas Plardy, commanding at Rio, had pro-
mised for the protection of themselves and their property in case of
exigency ; she had not yet however appeared, and it was feared might
IN THE LENGTH OF THE SECONDS* PENDULUM. 53
not do SO before the attack should take place. In this state of general
insecurity and apprehension, the arrival of the Pheasant occasioned great
joy, and Captain Clavering was met with a most pressing solicitation
from the merchants, conveyed through Mr. Pennell, His Majesty's Con-
sul, to remain at Bahia until tranquillity should be restored, or at least
until he should be relieved by the Blossom : on Mr. Pennell's being
made acquainted with the particular service on which we were employed,
he readily undertook that the necessary accommodation and convenience
for obtaining the rates of the pendulums at Bahia should not be wanting,
if Captain Clavering would determine on remaining for a sufficient time :
the situation of the merchants being such as fully justified a compliance
with their request, and being desirous that the delay should not be
altogether unproductive of advantage to ourselves, Captain Clavering
acceded to this arrangement.
Having waited on General Madera, commanding the Portuguese
troops, and on the civil authorities, to obtain permission, the instruments
were landed and conveyed to Mr. PennelFs residence at Vittoria, where
Captain Clavering and myself were kindly invited to remain as inmates
during our stay. Vittoria is a suburb, a mile and a half from the city,
situated on a sandstone cliff which descends abruptly about 200 feet to
the sea ; the great road by the coast to Pernambuco and generally
towards the northward passes through the village, which at the time of our
landing was occupied as an advanced post by the Portuguese troops,
who were throwing up field works for its defence. The houses being
generally abandoned by the inhabitants, a suitable one for the recep-
tion of the instruments was easily obtained in the vicinity of Mr. Pen-
nell's, from which it was only separated by the road ; the walls being
of brick, the apparatus was quickly and very firmly put up in the man-
54 EXPERIMENTS FOR DETERMINING THE VARIATION
ner which I most approved, namely, by separate pickets for each screw ;
the house was altogether extremely well adapted for the purpose, except
that it possessed no convenient situation for a transit instrument, as
was also the case in the grounds belonging to Mr. Pennell's house, which
were on the rapid slope of the cliff; and as it would not have been
prudent, at such an unsettled period, to have stationed an instrument in
any public exposure, I was obliged to change the mode in which I had
hitherto proceeded, in comparing the time-pieces with the heavens, and
to substitute the Repeating Circle for the Transit.
As this was the first instance, I believe, of the application of the prin-
ciple of repetition to a circle of this description, of so small a diameter
as six inches, it may be proper to mention that, in consequence of its size,
both the level and telescope could be attended by the same person ; and
with so much ease that I was in ilie habit also of noting the times of the
observations myself, and of thus dispensing altogether with an assistant ;
which is not only an advantage in convenience, but also in accuracy,
as the instant of contact can be marked with more exactness to
parts of a second, by the observer himself by means of the beats of
a chronometer, than by an assistant to whom it must be notified by
voice or signal. In estimating the practical merits of this little instru-
ment in comparison with those of larger size, its portability is the most
obvious, and possibly may be the principal consideration; but the
advantage which it possesses in not requiring two observers, will be
acknowledged by those who have had much experience of both, to be
scarcely of less value.
The mode of comparing the chronometer with Astronomical Time
pursued at Bahia, furnished a much severer test of the uniformity of its
rate in short intervals, than the observation of Transits as at Ascension
IN THE LENGTH OP THE SECONDS* PENDULUM 55
at the commencement and at the close of the whole interval occupied by
the experiments, with few intermediate comparisons ; the Table which
exhibits the results must be regarded as highly creditable.
The height of the pendulums above the sea, being 218 feet, was as-
certained by several barometrical measurements, the particulars of which
are arranged in a table, and are subjoined.
The observations were continued from the morning of the 24th of
July to the morning of the 2nd of August ; the period being divided as
usual between the two pendulums.
General Madera having been re-inforced by troops from Lisbon, who
had arrived off the harbour nearly at the same time as the Independent
squadron from Rio, and had slipped past them, the intended attack was
converted into a strict blockade, which though slow in operation, was
ultimately successful. The Blossom having arrived, and the apprehension
of immediate danger having subsided. Captain Clavering felt himself at
hberty to pursue his voyage to Maranham, for which he accordingly
sailed on the 7th of August.
56
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia.— OBSERVATIONS to DETERMINE the RATE of the Chronometer No. 423, by ZENITH
DISTANCES of the Sun, -with a Repeating Circle ; from the 23tl of July to the 2d of August, 1822.
Latitude of the Place of Observation 12° 59' 22" S. ; Longitude 38° 32' W.
July, 23d, A.M. ; Barometer 29.98 ; Thennometer 73° ; 0's L.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
11. M. ,s.
10 45 07.2
10 47 53
10 50 22
10 52 07.5
+2
+4
+ 4
-5
0
+2
+ 2
-7
0 / „
First Vernier 263 06 40
Second ,, 06 10
Third ,, 07 00
Fourth „ 06 10
H. M. s.
10 59 01.5
11 00 57.5
11 03 34
11 06 20
+ 1
-1
+ 3
—4
0
-2
+ 1
-3
0 / i'
First Vernier 154 48 10
Second „ 48 05
Third „ 48 45
Fourth ., 48 20
Mean 10 48 52.42
True time .. 8 16 06.87
+ 5
-3
Mean 263 06 30
Level +1
Index +8.5*
Mean 11 02 29
True time.. 8 29 42.27
-1
-4
Mean 154 48 20
Index +96 53 30
Level — 2.5
+ 1
-2.5
Chron.fast . 2 32 45.55
Chron. fast . 2 32 46.73
263 06 39.5
251 41 48.5
Observed Z.D. 65 46 40
Ref.andParal. + 1 54.5
Semidiam.... — 15 46.5
360 - 263 06 30 = 9°6 53 30
Observed Z.D. 62 55 27
Ref.andParal. + 1 40.5
Semidiam.... —15 46.5
True Z.D 65 .32 48
True Z.D 62 41 21
Chronometer, Fast /^ ^^ 45.55]^ 2 "32' 46. 14
(2 32 46.73^
1
July 23d, P.M.; Barometer 29.96 ; Thermometer 77° ; 0"sU.L.
Chronometer.
Level.
Reading?, &c.
Chronometer.
Level.
Readings, 4c.
H. M. S.
6 09 50
6 U 23.5
6 14 10
6 15 55
6 17 35
0 18 51.5
0
-1-4
0
-2
+5
+5
0
+3
0
-3
+ 5
+ 4
0 , <i
First Vernier 13 25 45
Second „ 25 28
Third ., 26 00
Fourth ,, 25 12
H. M. S.
6 24 19
6 26 09
6 27 33
6 29 05
6 30 43
6 32 33.5
+ 2
+ 1
+ 2
— 2
_ 2
-2
+ 1
+ 4
+ 2
-2
-2
-3
0 1 II
First Vernier 41 12 10
Second „ 12 00
Third „ 12 30
Fourth „ 11 20
Mean 13 25 36.25
Level +10.5
Index -1-360 00 08.5
Mean 44 12 00
Level +1
Index ..+346 31 24
Mean 6 14 37.5
True time . . 3 41 50.13
+ 12-F9
Mean. ..... 6 28 23.75
True time.. 3 55 36.67
+ 2
0
+ 10.5
08.5
373 25 55
+ 1
390 46 25
Chron.fast.. 2 32 47.37
Chron. fast . 2 32 47.08
Observed Z.D. 62 U 19
Ref.andParal. + 1 37.5
Semidiam +15 46.5
Observed Z.D. 65 07 44
Ref.andParal. + 1 51.5
Semidiam.... + 15 46.5
360+03.5= 360 00
360-13 25 ,3'6 = 34°6 34
24
True Z.D 62 31 43
True Z.D 65 25 22
r9 32 47 37^ **' ^*' ^'
Chronometer, Fast J " ■* ^'••" , 2 32 47.22
[2 32 47.08J
1 • When the First Vcrni
r of the llepeathij Circle was set at Zero, tlie Index Correction, obtaiuert by reading the other Veruiers also, was H-0S".5
IN THE LENGTH OF THE SECONDS PENDULUM.
57
Bahia. Determination of the Rate of the Chronometer by Zenith Distances, continued.
July 2 Ith A.M. ; Barometer 29.97 ; Thermometer 71° ; ©"s L.L.
Chronometer.
Level.
Readings, &c.
Chronometer,
Level.
Readings, &c.
H. H. S.
10 57 06
10 59 26.5
11 02 13
11 04 34.5
11 06 49.5
11 08 09.5
1
+9
+7
+7
+ 3
+8
Mean 11 03 03.17
True time.. 8 30 It. 6
+ 33
-I
+ 7
+ 4
+4
0
+ 6
First Vernier
Second „
Third „
Fourth ,,
IR 20 55
35
50
20
+ 17
Chron.last.. 2 32 48.57
+25
363 + 08.5 = 360 00 08.5
Mean 16 20 40
Level +25
Index +360 00 08.5
H. M. S.
11 16 34
11 18 18
11 20 17
11 21 24.5
11 23 03
11 24 26
376 21 13.5
Mean 11 20 40.4
True time.. 8 47 51. G
-9
+ 10
-7
+ 5
+8
— 7
+8
-9
+3
+6
— 5
First Vernier
Second „
Third „
Fourth „
+4
Observed Z.D. 62 43 32
Ref. and Paral. + 1 39.2
Semidiam — 15 46.5
Chron.last.. 2 32 48.8
True Z.D. .
62 29 25
10
54
55
54
47
55
10
54
25
10
54
49
360 - 16 20 40 = 343 39 20
Level 0
Index +343 .39 20
354 34 09
Observed Z.D. 59 05 41.5
Ref. and Paral. + 1 24.5
Semidiam.... — 15 46.5
True Z.D 58 51 19.5
II. M. S.
f2 32 48.571 H. M. s.
Chronometer, Fast < > 2 32 48.68
l2 32 48.8 j
July 24th P.M.; Barometer 29.96 ; Thermometer 76°; G'sU.L.
Chronometer.
Level.
Readings, &;c.
Chronometer.
Rtatlings, &c.
II. M. S.
6 12 19
6 13 53.5
6 16 06.5
6 17 28.5
6 19 07
6 20 37
Mean 6 16 35.25
True time.. 3 43 45.13
Chron.fast.. 2 32 50.12
5
+ 3
0
+5
-2
-2
+2
0
+ 5
— 2
-2
-1.5
360 + 08.5 = 360 00 08.5
First Vernier
Second ,,
Third ,,
Fourth .,
15 13 40
13 28
14 00
13 10
Mean 15 13 34.5
Level —1.5
Index +360 00 08.5
375 13 41.5
Observed Z.D. 62 32 17
Ref. and Paral. + 1 39
Semidiam.... + 15 46.5
True Z.D 62 49 42.5
II. M. S.
6 27 11.5
6 28 25.2
6 30 07.5
6 32 01.5
6 33 47.2
6 35 00
+ 1
+ 2
-1
+ 5
+ 4
+ 4
Mean 6 31 00
True time . . 3 58 15.73
+i;
+ 1
+ 2
-1
+ 3
+ 3
+ 3
+ 13
Chron.fast. . 2 32 50.27
+ 14
360— 15 13 35 = 344 40 25
First Vernier 48 48 25
Second „ 00
Third ,, 30
Fourth „ 05
Mean 48 48 15
Level +14
Index +344 46 25
393 34 54
Observed Z.D. 65 35 49
Ref. and Paral. + 1 54
Semidiam .... + IS 46
True Z.D 65 53 30
II. M. s.
(2 32 50.121 "■ "• s-
Chronometer, Fast < > 2 32 50.2
12 32 50.27J
58
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia. — Determination of the Rate of the Chronometer by Zenith Distances, amtitiued.
July 25th A.M. : Barometer 30.05 ; Thermometer 71° ; 0's L.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. .S.
10 58 09.2
11 0! 13
11 02 36. S
ll 05 03.6
11 07 31.7
11 08 56.4
0
-1
-S
+5
—2
+ 2
-1
-3
— fi
-1-3
— 4
+ 1
o . //
First Vernier 14 43 00
Second ., 42 SO
TiMi-d „ 43 20
Fourth „ 42 40
11. M. S.
11 14 39.6
11 13 40
11 17 51.2
11 18 45.4
II 20 06.4
11 23 30
-4
-4
-4
_2
+ 2
+ 10
-5
-3
-5
— 2
+ 1
+ 8
O / //
First Vernier 11 30 15
Second „ 05
Third „ 30
Fourth „ 00
Mean . . . . 14 42 57.5
Level .... - 7
Index . . .+360 00 08.5
Mean .... 1 1 30 12.5
Level .... -5
Index . .+345 17 02.5
Mean . . .11 03 58.42
True time . 8 31 06.48
—4
-10
Mean . . .11 18 23.43
True time . 8 45 33.48
— 2
-8
-7
374 42 59
-5
356 47 10
Chron.fast . 2 32 51.94
Chron.fast. 2 32 51.97
Observed Z.D. 62 27 10
Ref. and Paral. + 1 38
Semidiam . . ■ — 15 47
True Z.D. . . 62 13 01
Observed ZD. 59 27 51.7
Ref. and Paral. +1 26
Semidiam . . —15 47
360 + 08.5 = 360 00
08.5
0 O / It o
360- 14 42 57.5 = 345
17 o'i.7
True Z.D. . . 59 13 31
H. M. S.
r2 93 51.941 "•"• s-
Chronometer, Fast < > 2 32 51.95
l2 32 51.97J
J
July 25th P.M.; Barometer 30.08; Thermometer 73"= ; Q'sU.L.
, Chronometer.
Level.
Readinijf, &c.
Chronometer.
Level.
Readings, &c.
11. M. S.
6 11 57.5
6 13 42.5
C 15 16
6 16 32.4
6 18 24.7
6 19 36
+ 3
+8
+ 2
-3
-1
-4
-f3
+ 8
+ 1
-3
-1
o / //
First Vernier 13 42 35
Second „ 20
Third „ 45
Fourth „ 10
H. M. S.
6 25 10
6 26 30
6 28 27.8
6 30 22.3
6 32 29
6 33 54.3
-1
+ 1
-1
0
-3
-1
— 2
+ 1
-I
0
-2
-1
-5
o / ;'
First Vernier 44 37 12
.Second „ 36 40
Third „ 37 12
Fourth „ 36 50
Mean .... 13 42 27.5
Level .... +4.5
Index . . .+360 00 08.5
Mean .... 44 36 58.5
I^vel .... -5
Index . . . .346 17 32.5
Mean ... 6 15 54.85
True lime . 3 43 01.5
+5
+4
Mean . . . 6 29 28.9
True time . 3 36 36.63
-5
+4.5
373 42 40.3
— 5
390 54 25
Cliron. fast . 2 32 53.. 35
Chron.fast . 2 .32 52.27
Observed Z.D. 62 17 07
Ref. and Paral. +1 37
Semidiam . . +13 47
Observed Z.D. 65 09 04
Ref. and Paral. +1 51
Semidiam . . +15 47
360 + 08.5 = 360 00
38.5
O O 1 II o
360 - 13 42 27.5 = 3 16
/ //
17 .32.5
True Z.D. . . 62 34 31
True Z.D. . . 65 26 42
[232 53.351 »• "■ «•
Chronometer, Fast < > 2 32 52.81
12 .32 52.27J
IN THE LENGTH OF THE SECONDS* PENDULUM.
59
Bahia. Determination of the Rate of the Chronometer by Zenith Distances, continued.
July 26 A.M.; Barometer 29.98 ; Thermometer 72°; Q'sL.L.
Chronometer.
Level.
Readings, &c.
Clironomcter.
Level.
Readings, &c.
H. M. S.
10 56 08
10 57 12.8
in 58 52.6
10 59 51.5
11 01 23
11 02 45.8
— 4
-3
+3
+2
-0
0
-6
-5
+2
+ 1
-1
0
First Vernier . 19 58 30
Second „ 58 20
Third „ 58 55
Fourth „ 58 30
H. M. S.
11 09 57.8
11 11 33
11 13 52.9
11 14 58
11 16 51. S
11 17 52.6
-2
+4
-3
0
0
-1
— 2
+5
-5
0
0
-1
O / //
First Vernier . 21 24 50
Second „ 24 40
Third „ 25 15
Fourth „ 24 40
Mean ... 19 58 34
Index . . . + SGO 00 08.5
Level ... —5.5
Mean ... 21 24 49
Index . . .+340 01 26
Level . . . —2.5
Mean. . . 10 59 22.3
True Time. 8 26 28.13
-2
-9
Mean. . . 11 14 11.52
True time. 8 41 17.27
-2
-3
-5.5
379 58 37
-2.5
361 26 13.5
Chron. fast. 2 32 51.17
Chron. fast. 2 32 54.25
Observed Z.D. C3 19 46
Ref. andParal. +1 42.5
Semidiam . . —15 46.7
Observed Z.D. 60 14 22
Ref. and Paral. + 1 29
Semidiam . . - 15 47
360+08'.'5 = 36°0 00
osl's
360-19 58 3"l = 34°0 o'l 26
True Z.D. . . 03 05 42
True Z.D. . 60 00 04
H. M. S.
TQ ^0 =.A 171 "• ^^' ^■
Chronometer Fast < " i>i.i'|_ g 32 54.21
12 32 54.25J
July 26 P.M.; Barometer £9 .98; Thermometer 75°; ©"sU.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
6 09 39
6 11 05.3
6 12 49.7
6 14 16.8
6 15 46.5
6 16 58.7
-4
0
-3
-2
-4
0
-4
0
-4
-2
-4
0
O . It
First Vernier . 9 58 10
Second „ 58 10
Third „ 58 25
Fourth „ 58 15
11. M. S.
6 23 36
6 25 03.2
6 26 26
6 27 42.4
6 29 46
6 31 12.7
+ 2
+4
— 1
+8
+4
0
+3
+ 4
-2
+ 7
+4
-1
O / H
First Vernier . 37 26 55
Second „ 26 35
Third „ 27 00
Fourth „ 26 50
Mean ... 9 58 15
Index . . .+360 00 08.5
Level . . . -13.5
Mean . . 37 26 50
Index . . .+350 01 45
Level ... +16
Mean. . G 13 26
True time . 3 40 31.73
-13
-14
Mean. . . 6 27 17.7
True time . 3 51 22.2 '
+ 17
+ 15
-13.5
369 58 10
+ 16
387 28 51
Chron fast. 2 32 54.27
Chron. fast. 2 32 55.5
Observed Z.D. 61 39 42
Ref. and Paral. +1 35
Semidiam . . +15 47
Observed Z.D. 64 34 48.5
Ref. and Paral. +1 48.5
Semidiam . . +15 47
Seo+Os'.'s = 360 GO 08
"s
36°0-9 58 15 = 35°0 o'l
45
True Z.D. . . 61 57 01
True Z.D. . 64 52 2 4
H. M. S.
Chronometer Fast 1^ ^^ ^*-^^i"'32 5^4.9
(.2 32 55.5 J
X 2
60'
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia.
-Determination of the Rate of the Chronometer hy Zenith Distances, continued.
July 27th A.M. ; Barometer 30.03 ; Thermometer 75° ; Q's L.L.
Chiononietcr.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
11 04 53
11 05 47.4
11 or 11.2
1 1 08 02
11 09 47.6
11 10 39.8
-4
+ 8
-2
+6
-1
-2
-5
+ 6
— 4
+5
-3
-4
O * "
First Vernier 8 54 .30
Second „ 54 15
Third „ 54 55
Fourth „ 54 10
II. M. s.
11 16 17.9
11 18 09.9
11 19 20.3
11 20 07
11 21 17.8
11 22 13.9
-6
+3
-7
-2
+5
+2
-8
+ 2
-9
-2
+3
+ 1
o - «
First Vernier 3 06 00
Second „ 05 55
Third „ 06 30
Fourth „ 06 00
Mean . ■ . . 8 54 27.5
Index . . .+360 00 08.5
Level .... 0
Mean .... 3 06 06
Index . . . + 351 05 32.5
Level .... -9
Mean . . . 1 1 07 43.5
True time . 8 34 47.2
+ 5
-5
Mean . . 11 19 34.47
True time . 8 46 37.9
-5
-13
0
08.5
368 54 36
-9
354 11 30
Chron.fast . 2 .32 56.3
Chron. fast . 2 32 56.57
Observed Z.D. 61 29 06
Ref.andParal. + 1 34
Semidiani . — 15 47
Observed Z.D. 59 01 55
Ref.andParal. + 1 24
Semidiam . . — 15 47
360+08.5 = 360 o'o
360 - S 54 27.5 = 351 05 32.5
True Z.D. . . 61 14 53
True Z.D. . . 58 47 32
H. M. S.
f2 32 56.3 1 "• »'• s.
Chronometer, Fast < > 2 32 56.43
L2 32 56.57J
July 27th P.M. ; Barometer 30.02 ; Thermometer 76= ; 0's U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
II. M. S.
6 13 29.7
6 14 33
6 15 54.5
6 16 59.5
6 18 15.3
6 19 24
-2
+8
+7
-1
+ 1
-3
-1
+7
+6
0
0
— 4
First Vernier 13 03 35
Second „ 03 10
Third „ 03 45
Fourth „ 03 00
H. M. s.
6 29 02.4
6 29 55.8
6 31 16.9
6 32 02.8
6 33 21 .8
6 34 16
+ 5
+ 10
0
+ 2
-5
-2
+6
+8
0
+ 1
-6
-2
o .
First Vernier 45 30 10
Second ., 29 45
Third ,, 30 10
Fourth „ 29 45
Mean .... 13 03 22.5
Index . . .+360 00 08.5
Level .... +9
Mean .... 45 29 57.5
Index . . . + 316 56 37.5
Level .... +8.5
Mean . . . 6 16 26
True time . 3 43 28.13
+ 10
i-8
Mean . . . 6 31 39.3
True time . 3 58 41.73
+ 10
+ 7
+ 9
08.5
373 03 40
+8.5
392 26 43 5
Chron.fast. 2 32 57.87
Chron.fast . 2 32 57.57
Observed Z.D. 62 10 36.7
Ref.andParal. + 1 37
Semidiam . . +15 47
Observed Z.D. 65 24 27.5
Ref.andParal. + 1 53
Semidiam . . +15 47
360 + 08.5 = 360 00
360 - 1°3 03 22.5 = 346
56 37.5
True Z.D. . . 62 28 01
True Z.D. . . 65 42 07
11. M. S.
<2 .32 57 871 H. M. s.
Chronometer, Fast < > 2 32 57.72
l2 32 57.57J
IN THE LENGTH OF THE SECONDS PENDULUM.
61i
Bahia. Determination of the Rate of the Chronometer by Zenith Distances, continued.
July 28th A.M.; Barometer 30 . 05 ; Thermometer 71°; Q'sL.L. (strong br fezes.)
Chronometer.
Level.
Readiogs, &c.
Chronometer.
Level.
Readings, &c.
H. H. S.
11 07 16.2
11 08 31.6
11 10 20.8
11 n 20
11 13 07.6
11 14 10
+7
-2
-0
-4
-0
+ 6
+5
— 5
-2
-6
-2
+4
O . "
First Vernier 4 29 20
Second „ 29 05
Third „ 29 50
Fourth „ 29 25
H. M. S.
11 20 29
11 21 28.7
11 22 48.8
11 23 46
11 25 10.5
11 26 16.8
-2
+ 2
+5
+6
+ 2
+ 8
-5
+ 1
+ 3
+ 4
+ 1
+7
First Vernier 353 24 15
Second „ 24 05
Third „ 24 35
Fourth „ 24 00
Mean .... 4 29 25
Index . . .+360 00 08.5
Level . . . +0.5
Mean ... 353 24 14
Index ... —4 29 25
Level . . . +16
Mean . . .11 10 47.7
True time . 8 37 48.07
+7
-6
Mean . . .11 23 19.97
True time. . 8 50 21.57
+21
+ 11
+0.5
,364 29 34
+ 16
348 55 05
Chron. fast. 2 32 59.63
Chron. fast.. 2 32 58.4
Observed Z.D. 60 44 56
Ref. and Paral. +1 30
Semidiam . . —15 47
Observed Z.D. 58 09 11
Ref. and Paral. +1 21
Semidiam . . — 15 47
360 + 08.5 = 360 00
08.5
Index — 4 2'9 2"5
True Z.D. . . 60 30 39
True Z.D. . . 57 54 45
H. M. S.
f2 32 59.631 "■ "• ■'•
Chronometer Fast < > 2 32 59.01
12 32 58.4 J
July 28th P.M.; Barometer 30. UO ; Thermometer 71°; ©'sU.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level. Readings, &c.
H. M. S.
6 06 28
6 08 02.4
6 09 44.8
6 11 18.8
6 13 16.8
6 14 46.8
-6
-3
-3
+ 3
-2
+2
-4
— 4
-5
+2
-S
+ 1
First Vernier 5 03 35
Second „ 03 10
Third ., 03 55
Fourth „ 03 05
Mean .... 5 03 26
Index . . . .360 00 08.5
Level .... -11
Mean ... 6 10 36.27
True time . 3 37 35.68
-9
-13
-11
365 03 23
Chron. fast . 2 33 00.59
Observed Z.D. 60 50 34
Ref. and Paral. +1 31
Semidiam . . +15 47
360 + 08.5 = 360 00
38.5
True Z.D. . . 61 07 52
H. M. S.
Chronometer Fast 2 33 00.59
62
EXPfiRIMENTS FOR DETERMINING THE VARIATION
—Dpfprminnfifin nf tViA Ralp nf tVip OironnriM^ter hv Zenith Distanpe.s. r.cmtinued. 1
1 July 29 A.M. ; Barometer 30 . 03 ; Thermometer 71°; Q'sU.L.
Chronometer.
Level.
Re.iding3, &c.
Chronometer.
Level.
Readings, &:c.
H. M. S.
11 09 03.6
11 11 00
11 13 08.8
11 14 27.2
11 IS 59.6
11 17 08.8
+2
+5
-2
+ 6
-3
0
0
+ 3
-4
+4
-6
0
O . tt
First Vernier . 00 31 00
Second ,, 30 50
Third „ 31 30
Fourth „ 30 40
H. M. S.
11 22 09.6
11 23 28.8
11 25 21.2
11 26 31.6
11 27 50
11 29 06.8
0
+7
+5
-2
-2
— 2
-1
+9
+7
0
-4
0
0 . ..
First Vernier. 345 50 10
Second ,, 03
Third „ 30
Fourth „ 03
Mean ... 00 31 00
Level . . . +2.5
Index . . .+360 00 08.5
Mean . . 313 30 12.5
Level . . . -fOS.o
Index ... -0 31 00
Mean. . . 11 13 28
True time. 8 40 26.38
+ 8
-3
Mean . . 1 1 25 44.67
True time. 8 52 42.32
+ 6
+ 11
+ 2.5
08.5
360 31 11
+ 8.5
345 19 21
Chron. fast. 2 33 01.62
Chron. fast. 2 33 02.33
Observed Z.D. 60 05 12
Ref. and Paral. +1 28
Semidiam . . —15 47
Observed Z.D. 57 33 13.5
Ref. and Paral. +1 18.3
Semidiam . . — 13 47
360+08.5=360 o'o
Index 0°0 s'l 00
True Z.D. . . 59 50 S3
TrueZ.D.. . 57 IS 43
Chronometer Fast < ""'•■'> 2 33 01.98
(2 32 02.35J
July 29 P.M. ; Barometer 30 -02 ; Thermometer 72° ; Q's U.L.
Chronometer.
Level.
Readings, &c.
Chionometer.
Level.
Readings, &c.
11. M. S.
5 51 32
5 53 23.6
5 55 34 4
5 57 54.8
6 00 00
6 01 26.8
0
+ 8
+3
-9
-2
0
0
+ 7
+ 2
-10
-I
0
o * «
First Vernier. 316 57 50
Second „ 57 40
Third „ 58 05
Fourth ,, 57 30
H. M. S.
6 09 12.4
6 10 42.4
6 12 35.6
6 14 15.6
6 16 22
6 17 42.4
+2
+ 5
0
-7
0
+2
+ 1
+4
-1
-8
0
0
0 . //
First Vernier. 334 57 55
Second „ 5S 00
Third „ 58 30
Fourth „ 58 05
Mean. ... 346 57 46
Level. ... -1
Index. . . . + 08.5
Mean ... 354 58 07.5
Level ... -1
Index . . . + 1 3 02 1 4
Mean. . . 5 56 38.6
True time. 3 23 35.2
0
-2
Mean. . . 6 13 28.4
True time. 3 30 23.47
+2
-4
-1
5
346 57 54
-1
368 00 22.5
Chron. fast. 2 33 03.4
Chron. fast. 2 33 02.93
Observed Z.D. 57 49 39
Ref. and Paral. +1 18
Semidiam . . +15 47
Observed Z.D 61 20 02
Ref. and Paral. + 1 33
Semidiam . . + 15 47
Index 00 00 08.
360—346 57 46=13 0
2 14
TrueZ.D. . . 58 06 44
TrueZ.D.. . 61 37 22
H. M. S. H M s
Chronometer Fast 1^ ^^ "^'^ \ 2 S3 03.16
12 33 02.93J
IN THE LENCTH OP THE SECONDS' PENDULUM.
Bahia. — Deterrninalion of the Rate of the Chronometer by Zenith Distances, conlimied.
Ju
ly SOtli P.M. ; Barometer 30. 10 ; Thermometer 72° ; 0's U.L.
Clironomeler.
Level.
Readings, &c.
CliroDometcr.
Level.
Readings, &c.
H. M. s.
e 25 S3. 6
G 27 33.2
6 29 13.6
6 30 45.6
6 32 29.2
6 33 56.8
0
+n
— 4
-2
-6
0
-1
+ 4
-6
-3
-8
0
o / «
First Vernier 28 22 .30
Second „ 22 05
Third „ 22 30
Fourth ,, 21 48
H. M. S.
6 45 19.6
6 46 42
6 48 32
6 50 28
6 52 15.6
6 55 38.8
0
+ 10
-I
-1
0
-2
0
f8
-3
-3
0
0
0 * ^/
First Vernier 82 37 50
Second „ 37 30
Third „ 38 10
Fourth ,, 37 40
Mean . . . . 28 22 13
Level .... —10
Index . . . + 360 00 08.5
Mean . . . . 82 37 47.
Ijcvel .... +3
Index . . .+331 37 47
Mean ... 6 29 55.33
True time . 3 56 49.63
-6
-14
Mean . . . 6 49 49.33
True time . 4 16 43.23
+4
!2
-10
388 22 11.5
+3
414 15 37.5
Cliron. fast. 2 33 03.7
Chron. fast . 2 33 06. 1
Observed Z.D. 64 43 42
Ref and Paral. + 1 49
.Semidiam . . +13 47
Observed Z.D. 69 02 36
Ref. and Paral. + 2 15
Semidiam . . +15 47
360 + 08.5 = 360 00
08.5
360 -2°S 22 13= 331
37 47
TiueZ.D. . . 85 01 18
True Z.D. . . 69 20 38
r2'3.3 05.7! "• "■ «■
Chronometer, Fast < > 2 33 05.9
[2 33 06. Ij
Ju
ly 31st P.M. ; Barometer 30.03 ; Thermometer 71° ; ©'s U.L.
Chronometer.
Level.
Readings, &c.
Clironometer.
Level.
■
Readings, &c.
H. M. S.
6 14 43.2
e 16 07.2
6 17 37.6
G 19 06.4
6 20 50
6 22 10.8
0
+4
— 4
-1
-1
0
-1
+3
-3
-2
+ 2
0
-1
0 . //
First Vernier 95 36 50
Second ,, 36 20
Third „ 37 00
Fourth ,, 36 25
H SI. s.
6 27 16
6 28 31.6
6 30 18.8
6 31 42
6 33 29.2
6 34 42.8
0
i 2
-2
+ 1
0
-1
-1
0
-3
+3
-2
-2
0 / «
First Vernier 124 45 15
Second „ 41 50
Third „ 45 45
Fourth „ 45 10
Mean . . . . 95 36 39
Level .... -1.5
Index . . . .277 22 14
Mean • . . .124 45 15
Level . . . —2.5
Index . . . .264 23 21
Mean ... 6 18 25.87
True time . 3 45 16.97
-2
Mean . . . 6 31 00.07
True time . 3 57 51.33
0
— 5
-1.5
372 58 53
-2.5
389 08 34
Chron. fast . 2 .SS 08.9
Chron. fast . 2 33 08,81
Observed Z.D. 62 09 49
Ref. and Paral. + 1 37
Semidiam . . +15 47
Observed Z.D. 64 51 26
Ref. and Paral. + 1 50
Semidiam . . +15 47
3G0 - 82 37 46 = 277
22 14
360 - 9°5 36 .39 = 264
23 2'i
True Z.D. . . 62 27 13
True Z.D. . . 65 09 03
H. »1. S.
[2 33 08.9 ! "• "• s.
Chronometer, bast <; > 2 33 08.87
L2 33 08.81J
64
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia. Determination of the Rate of the Chronometer by Zenith Distances, continued.
August 1 A.M.; Barometer 30. 10; Thermometer 71°; Q\ L.L.
CUroDometer.
Level.
Readings, &c.
Clironometer.
Level.
Readings, &c.
H. M. S.
11 03 28.4
11 04 56
11 06 49.2
11 08 36.8
11 14 59.6
11 16 47.6
-2
— 2
-r2
+4
-2
-5
-3
-3
+ 1
+3
-3
-6
O ' "
First Vernier . 87 03 10
Second „ 2 40
Third „ 3 20
Fourth „ 2 50
H. M. S.
11 21 13.6
11 22 58
11 25 22
11 26 43.6
11 28 26.4
11 31 28.8
-5
-0
+3
+5
-1
+3
-4
-1
+2
+ 4
— 2
+4
0 * ft
First Vernier . 69 51 35
Second „ 51 10
Third „ 5! 40
Fourth „ 50 50
Mean ... 87 03 00
Index . . 276 45 09
Level ... -8
Mean ... 69 51 19
Index ... 272 57 00
Level ... +4
Mean. . . 11 09 16.27
True time. 8 36 05.77
— 5
-11
Mean. . . U 26 02.07
True time. 8 52 51.77
+5
+3
-8
363 48 01
+4
342 48 23
Chron. fast. 2 33 10.5
Chron. fast. 2 33 10.3
Observed Z.D. 60 38 00
Ref. and Paral. +1 30
Semidiam . . —15 47
Observed Z.D. 57 08 04
Ref. and Paral. + 1 18
Semidiam . . — 15 47
360-83 14 51 = 276 '
3 09
360- 8°7 03 00 = 272 57 00
True Z.D. . . 60 23 43
True Z.D. . . 56 53 35
Chronometer Fast <- " '"'^ !. 2 33 10.4
2 33 10.3 j
August 1st P.M.; Barometer 30.05; Thermometer 73 ; ©'s U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
6 08 39
6 10 28
6 12 11.2
6 13 35.2
6 15 21.2
6 16 35.6
-3
+3
-3
-4
-3
-2
-1
+ 1
-1
0
— 5
-4
0 , .J
First Vernier 75 01 25
Second „ 01 05
Third ., 01 40
Fourth „ 00 50
Mean .... 75 01 15
Index . . . .290 08 41
Level .... -11
Mean ... 6 12 48.37
True time 3 39 37
-12
-10
-11
365 09 45
Chron. fast . 2 33 11.37
Observed Z.D. 60 51 37.5
Ref. and Paral. +1 31.5
Semidiam . . +15 47
» ' ,' „ 0
360 - 69 51 19 = 290
08 41
True Z.D. . . 61 08 56
Chronometer Fast 2 33 11.37
IN THE LENGTH OF THE SECONDS' PENDULUM.
65
Bahia. Determination of tlie Rate of the Chronometer by Zenith Distances, continued.
August 2d, A.M. ; Baronieler 30.10 ; Thermometpr 70° ; Q's L.L.
Chronometer.
H. H. .^.
U 15 30
n 17 04
11 19 07.4
11 20 46
II 22 22. S
11 24 04.4
Mean ....
True time
.11 19 49.1
. 8 46 35.6
Readings, &c.
+4
+4
+6
+6
-7
-3
+ 10
+2
+2
+ 4
+4
9
-5
Chron. fast . 2 33 13.5
+4
First Vernier 349 47 20
Second „ 47 20
Third „ 47 40
Fourth ,, 47 20
Mean 349 47 25
Level +4
Index +8.5
349 47 37
Observed Z.D. 58 17 56
Ref.andParal. + 1 23
Semidiam .... — 15 47
True Z.D 58 0."!
Chronouicler.
H. in. s.
11 28 32
11 29 46.4
11 31 46
11 32 54.4
11 34 40
11 36 40.4
Mean . . . . .
True time .
.11 32 23.2
8 59 09.85
Chron. fast . 2 33 13.35
Level.
Readings, &c.
0
+4
0
-0
-3
+ 2
0
+2
2
7
5
0
— 12
-7.5
360-349 47 25=10 12 35
o * //
First Vernier 323 59 20
Second „ 59 30
Third „ 59 50
Fourth „ 59 20
Mean 323 59 30
Index +10 12 35
Level - 7.5
334 II 58
Observed Z.D. 55 41 59.7
Ref.andParal. + I 14.3
Semidiam .... — 15 47
True Z.D 55 27 27
/Q go lo - 1 M. m. &.
" I, 2 33 13.42
33 13.35J
August 2d, P.M. ; Barometer 30.06; Thermometer 70° ; Q'sU.L.
Chronometer.
Level.
H. M. 8.
5 54 02.2
+ 1
0
5 55 41.8
-5
-5
6 01 02
+ 1
0
6 02 28.2
-4
— 5
6 04 13.2
-6
-7
6 05 34.8
+2
+ 1
Mean 6 00 34.37
True time.. 3 27 16.27
-11
-16
-13.5
Chron. fast.. 2 33 14.1
00 30
360 - S23 59 30= 3*6.
Readings, &c
First Vernier 312 56 00
Second „ 55 50
Third ,, 56 20
Fourth ,, 55 40
Mean 312 55 57.5
Index +36 00 30
Level +13.5
348 56 14
Observed Z.D. 58 09 23
Ref. and Paral. + 1 21
Semidiam +15 47
True Z.D 58 26 31
Chronometer.
Level.
Headings, &c.
H. M. .s.
Chronometer Fast 2 33 14.1
66
EXPERIMENTS FOR DETERMINING THE VARIATION
RATE DEDUCED from the PRECEDING OBSERVATIONS.
A.M. to A.M.
P.M. to P.M.
Dale.
S.
Date.
S.
Dale.
S. 1
Date.
S.
Date.
S.
July 23 to 24
2.55
July 25 to 20
2.51
July 23 to 24
2.98
July 25 to 26
2.09
July 27 to 31
2.79
25
2.9
,, Aug. I
2.63
25
2.79
27
2.46
>. Aug. 1
2.73
26
2.69
2
2.69
26
2.56
28
2.59
2
2.73
27
2.57
July 26 to 27
2.22
27
2.62
29
2.59
July 28 to 29
2.57
28
2.57
28
2.4
28
2.67
30
2. 62
30
2.65
29
2.64
29
2.59
29
2.66
31
2.68
31
2.76
„ Aug. I
2.7
,. Aug. 1
2.7
30
2.67
,, Aug. 1
2.65
„ Aug. 1
2.69
2
2. 73
2
2.74
31
2.71
2
2.66
„ 2
2.66
July 24 to 25
3.26
July 27 to 28
2.58
,. Aug. 1
2.68
July 26 to 27
2.82
July 29 to 30
2.74
26
2.76
29
2.77
2
2.69
28
2.84
., 31
2.85
27
2.58
,. Aug. I
2.79
July 24 to 25
2.61
29
2.75
.-. Aug. 1
2.74
28
2.58
2
2.83
26
2.35
30
2.75
2
2.73
29
2.66
July 28 to 29
2.97
27
2.51
31
2.8
July 30 to 31
2.97
„ Aug-. 1
2.71
,. Aug. 1
2.85
28
2.67
„ Aug. 1
2.74
,, Aug. 1
2.73
2
2.75
2
2.88
29
2.59
2
2.74
2
2.73
July 25 to 26
2.26
Ju.29toAu.l
2.81
30
2.62
July 27 to 28
2.87
Ju.SltoAu. 1
2.5
27
2.24
2
2.86
31
2.67
29
2.72
2
2.62
28
2.35
Aug. 1 to 2
3.02
), Aug. 1
2.65
30
2.74
Aug. 1 to 2
2.73
2
2.65
Means . . .
2.64
2.71
2.65
2.67
2.72
2.6T5
2.68
Gaining 2.68 Secon
3s per Diem.
IN THE LExVGTH OP THE SECONDS' PENDULUM.
67
Bahia. Comparisons of the Astronomical Clock with the Chronometer No. 423, j
from the 23d of July to the 2d of August, 1S22, inclusive; with the Clock's Rate'
on Mean Solar Time deduced.
1822.
Chronometer.
July 23 p. M.
„ 24 A. M.
,) 24 p. M.
„ 25 A. M.
„ 25 p. M.
,) 26 A. M.
,, 26 p. M.
„ 27 A.M.
» 27 p. M.
» 28 A. M.
,) 2S p. M.
„ 29 A. JI.
» 29 P. M.
„ 30 A. M.
„ 30 P. M.
„ 31 A.M.
„ 31 P. M.
Aug. 1 A. M.
„ 1 P. M.
„ 2 A. M.
). 2 P.M.
H. M. S.
;• 9 55 00 <
Clock.
H. M. s.
8 35 49
S 34 50.3
S 33 50.6
S 32 51.4
8 31 52.2
S 30 53.2
S 29 53.7
8 28 54.4
8 27 54.7
8 26 55.7
S 25 55.8
8 24 56
S 23 57
S 22 57.4
8 21 57.6
8 20 58
8 19 58. 1
S 18 58. 6
8 17 58.8
8 16 59
8 15 59.3
Clock's Loss on 423.
1
> 58. 7 !
\ \
> 59.7 j
1
59.2 1
59.2 ]
59
59.5
59.3 1
59.7 I
59
59.9
59.8 !
59
59.6
59.8 j
118.4
118.4
lis.
119
118.9
US. 8
D.\ILY RATES.
Chron.
Clock.
Gaiuiog.
> 2. 68
119.4
59. G )
59.9
59.5
59.8
59.8
59.7
!■ 119.5
Losius.
115.9
119.3
119.5
2.68
116.56
K 2
68
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia. COINCIDENCES OBSERVED with PENDULUM No. 3 ; the Clock making
S62S4.1 Vibrations in a Mean Solar Day.
Baro-
meter.
No.
of Co-
inci'
dence,
Tempe-
rature.
lime of
Disap-
pearance
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
ratore.
Mean
Interval.
Correc-
tion for
tbeArc.
Vibrations
in 24 bonrs.
Rednc-
tion to a
mean
Tempera-
ture.
Reduced
Vibrations at
75.2 Falit.
1822.
July 21 A.M.
,, 21P.M.
25 A.M.
25 P.M.
„ 26 A.M.
„ 26 P.JI.
27 A.M.
27 P.M.
29.970<
29.960-;
29- 960'^
29.990J
29.980.^
29.980<^
30.020-
30.020
1
11
1
II
1
11
1
11
1
11
1
11
1
11
1
11
74-2
75.7
75.7
75 9
75.2
75.2
76.8
76.8
73.3
75.7
74-2
75.2
73.5
74.3
70-2
75.7
M- s.
58 46
15 48
06 51
53 41
57 31
44 29
22 01
8 39
8 48
55 55
14 10
01 16
9 22
56 45
30 41
17 47
M. S.
58 48
45 56
06 55
53 56
,57 35
44 42
22 03
8 49
8 53
56 06
11 13
01 25
9 25
56 57
30 45
17 58
H. M- s.
9 58 47
11 45 52
3 06 53
4 53 46.5
9 57 33
11 44 35-5
3 22 02
5 8 44
8 OS 50-5
9 56 00.5
1 14 11.5
3 01 20.5
8 9 23.5
9 56 51
3 30 43
5 17 52.5
1.2
0-61
1.16
0-58
Means
29.990
74.95
75.8
75.2
76.8
74.5
74.7
73.9
75.95
75.2
642.5
641.55
642.25
640.2
613
642.9
644.75
642.95
-1-
1.33
1.S6
1.36
1.36
1.22
1.29
1.26
1.19
86016.83
86016.48
86016.78
86015.9
86016.92
86016.99
86017 72
86016.89
-0.10
-1-0.25
•t-0-67
-0.29
-0.21
-0-55
+ 0.S1
8C016-82
86016.73
86016.73
86016.78
86016.57
86016.63
86016.78
86017.17
86017.20
86016-82
IN THE LENGTH OF THE SECONDS' PENDULUM.
69
Bahia. COINCIDENCES OBSERVED with PENDULUM No. 4 ; the Clock making
86283.44 Vibrations in a Mean Solar Day.
70
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia.—
—BAROMETRICAL OBSERVATIONS to DETERMINE the HEIGHT of the
PENDULUM STATION.
DATE.
PENDULUM STATION.
AT THE SEA.
Heiglit above the Level
of Half Tide. |
REMARKS.
Baro-
meter.
Tliermometer.
Baro-
meter.
Thermometer,
Att.
Det.
Att.
Det.
1822.
IN.
o
o
IN.
o
o
1
Fathoms.
July 2 4, 6 A.M.
29.964
73
70.5
„ 21, 7 A.M.
30.176
72.4
72.4
12 ft. above J tide
35.4
„ 21, 8 A.M
29.976
73
71
„ 25, 6i A.M.
29.951
73
70
„ 25, 7 A.M.
30.177
72.5
72.5
do. do.
35.88
„ 25. 71 A.M.
29.987
74
71
„ 2R, 6J A.M.
„ 2R, 7J A.M.
29.976
69
69
30.196
70
70
atthelevelofi tide
35.2
Fms. Feet.
. 35.53 or 213
j'gtb of llie dif-
ference in the
Mercurial Co-
jDninsbasbeen
added, on ac-
count ufllie re-
„ 26, 8 A.M.
29.980
72
71
lative capaci-
ties of the tube
and cistern.
„ 31, 6iA.M.
30.068
70
69
., 31, 7 A.M.
30.302
71
71
do. do.
35.87
„ 31, 71A.M.
30.08G
71.5
69
Aug. 1, 6i A.M.
30.106
71.75
70.75
,, 1, 7 A.M.
30.329
71.5
71.5
do. do.
35.3
„ 1, 7iA.M.
30.114
72.75
71.75
IN THE LENGTH OF THE SECONDS' PENDULUM. 71
MARANHAM.
The City of Maranham is built on a low and chiefly alluvial island,
situated within the entrance of a large river of the same name. Being in
latitude 2° 12' S., it is only a few miles more distant from the equator
than the Pendulum Station at the Island of St. Thomas; but the cha-
racter of the two stations, in respect to the density of the materials near
the surface, could scarcely have been more dissimilar, if they had been
purposely selected ; I felt, therefore, a more than ordinary interest in
the experiments at Maranham, because I considered that, conjointly with
those at St. Thomas's, they were calculated to furnish a very notable,
practical exemplification of the influence which the superficial density has
on the general attraction of the mass ; and of the extent to which the rate
of a clock or pendulum may be made liable to differ, in the same lati-
tude, by the circumstances of the locality alone.
Even more than our usual good fortune attended us, in the exceeding
Kindness with which we were received by Mr. Hesketh, His Majesty's
Consul ; whose anxious desire to forward the inquiry in which I was
engaged, and to render our stay in every respect agreeable, cannot be
sufficiendy acknowledged, but will ever be most gratefully remembered.
The credentials with which I had been furnished by the Portuguese
Ambassador, were addressed to the authorities of Para, a city a few
miles nearer the equator, to which I had designed to have gone, before
I was aware that Maranham had advantages in many respects which
made it preferable. Through the good offices of Mr. Hesketh, the members
of the Provisional Government at Maranham, were induced to overlook the
72 EXPERIMENTS FOR DETERMINING THE VARIATION
informality, and to receive the introduction with the same consideration
as if it had been addressed directly to themselves.
A room on the ground-floor of Mr. Hesketh's house was better adapted
for the pendulums than any in which they had hitherto been accommo-
dated ; it was an inner room, with brick partitions, and borrowed light, in
which the temperature did not vary two degrees in the twenty-four hours ;
Mr. Hesketh was also kind enough to relinquish for my use an apartment
in the upper story, with windows opening in the four principal directions,
the sills of which were sufficiently stable to support the Repeating Circle,
and enabled me to employ it with great convenience in the determination
of the latitude, as well as in the comparison of the chronometers with
time : the house being in the middle of the city and without grounds, had
no situation in which a transit instrument might have been placed ; but it
adjoined a meadow belonging to the Cathedral, of which the Bishop, who
was also the President of the Provisional Government, offered me the use;
the times of sunrise and sunset, however, when a transit can be employed
to most advantage in tropical climates, are also the most healthy and
agreeable in taking exercise ; and as I had had experience of the suffi-
ciency of the repeating circle for the purposes for which a transit is used,
I determined to employ the former in preference, whilst in the latitudes in
which the heavenly bodies move most rapidly in altitude.
The tables, on this occasion, appear to require no particular comment,
as every part of the operation was very satisfactorily accomplished.
By repeated barometrical measurements, the particulars of which are
given in a table, the height of the pendulums above half-tide was shewn
to be 77 feet.
The discussion of the apparent irregularities in the action of gravity,
produced by the different quality of the superficial materials of the
globe, will be best pursued when the whole of the stations shall have
m THE LENGTH OP THE SECONDS' PENDULUM. 73
been gone through ; but without entering further into the discussion at
present, it may be proper to observe, that the result of the experiments
at Maranham confirmed both the inferences which I had drawn at Sierra
Leone; n-., that the effects of differences in the geological character of
the surface on the sum of the attractive forces are greater than had
been anticipated, or at least greater than any expressed anticipation-
and that the Ellipticity of the earth, as deducible by the pendulum
agreeably to the present modes of operation and deduction, appears greater
than the extreme limit within which previous expectation had been
bounded. I had also the satisfaction of perceiving by them, that althouo-h
the results, at the several stations which I had hitherto visited, were n'ot
strictly correspondent with each other, their deviations were systematic
and such as I should have assigned to each respectively, from a know-
ledge of Its geological character, agreeably to the scale of apportionment
with which the experiments at St. Thomas's and Maranham had fur-
nished.
In the increased confidence with which I now lool^ed forward to
a deduction of the figure of the Earth, of a far more satisfactory and
dec,s.ve character than had yet been obtained, as the ultitnate result of a
sufhcetnly extended muhiplication of the experiments, I ventured to write
from Marariram to Sir Humphry Davy, to propose the extension of the
senes to the higher latitudes in the summer of the follo,vi„o- year
We arrived at Maranham on the 21s. of August, and "quitted it with
much regret on the 7th of September.
74
EXPERIMENTS FOR DETERMINING THE VARIATION
1VT4R AviiAAF ORSFRV ATTOIVS in DFTFT^MfNF fhp R4TE nf tlif^ rhrnnomotpr Nn 42S hv ZENITH
DISTANCES of the Sun, with a Repeating Circle ; from the 21th of August to the 4th of September, 1S22.
[.atitiide cf ihe Place of Ohservation 2° .31' 41" S. ; Longitude 44° 21' W.
August 24lh A.M. ; Eaiomeler 30.05 ; Thermometer 80° ; ©'s L.L.
Chronometer.
Level.
Ktadiiigs, &C.
Chronometer.
Level.
Readings, &c.
II. M. S.
II 11 08.4
II 12 50
11 M 40.4
II 15 44.8
11 IT I'l
11 19 46.8
+ 3
— 2
0
-2
— o
0
+ 2
-3
0
2
-3
0
o - ;;
First Vernier 108 56 05
Second ,, 36 00
Third ,, 56 30
Founli „ 55 50
II. M. S.
11 28 05.2
11 30 32.4
11 S2 05.2
11 33 42.8
11 .35 42.4
11 38 03.6
+ 2
+ 2
+3
-1
-4
+ 1
+ 1
+ 1
+2
— 2
-4
+ 1
O / ,1
First Vernier 68 38 30
Second „ 20
Third „ 40
Fourtli ,, 15
Mean . . .108 56 06
Level .... - 5
Index . . .236 19 SI
Mean .... 68 38 26
Level .... +1
Index . . .251 03 54
Mean . . .11 15 19.07
True time . 8 IS 31.5
— 1
-6
Mean . . .11 33 01.93
True time . 8 36 14.23
+3
-1
-5
345 15 32
+ 1
319 42 21
Cliron.last . 2 sr, 47.57
Chron. fast. 2 56 47.7
Observed Z.D. 57 32 35
Ref. and Paral. + 117
Semidiaiii . . ■ — 15 51
True Z.D. . . 57 18 01
Obsei-vedZ.D. 53 17 03.5
Ref. and Paral. +1 05.5
Semidiam . . — 15 51
360 — 123 40 29 = 2.SC
19 s'i
O O 1 II o
360- 108 56 06 = 251
03 s'l
True Z.D. . . 53 02 18
H. M. S.
.l'2 56 47.571 H. M. s.
Chronometer, Fast < > 2 5G 47. C3
12 56 47.7 J
1
August 2 Ith P.5I.; Barometer 29.95; Thermometer 80° ; ©'sU.L.
Cltronoiiicter.
Lcvt-:.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M, S.
G 42 04
G 43 48.8
C 45 42
G 47 19.6
fi 49 14
G 50 40.4
-6
0
+ 2
+ 5
-6
-1
-7
0
+ 2
+ 5
-6
-1
— 7
0 / //
First Vernier 57 22 20
Second „ 21 50
Third „ 22 20
Fourth „ 21 .30
H. M. S.
6 55 30
6 56 34
6 58 22.4
7 00 29.2
7 02 23.2
7 04 26
-5
+2
-4
+4
-6
+7
-4
+3
-3
+5
-5
+7
O / /'
First Vernier 63 48 10
Second ,, 47 50
Third „ 48 10
Fourth „ 47 40
Mean .... 57 22 00
Index . .+290 00 31
Level .... -G.5
Mean .... 63 47 SS
Index . . .+302 38 00
Level .... 0
Mean ... 6 46 28.13
True time . 3 49 39.66
-6
Mean . . . 6 59 37.47
True time . 4 02 48.33
-2
+3
-6.5
347 22 28
+0
366 25 58
Chron.fast . 2 56 49.14
Chron.fast . 2 5R 48.47
o'o 34
Observed Z.D. 57 53 45
Ref. and Paral. + 1 20
Semidiam . . +15 51
Observed Z.D. 61 04 20
Ref. and Paral. +1 SI
Semidiam . . +15 SI
360 - 69 59 26 = 291)
O O 1 II o
360 - 57 22 00 = 302
38 o"o
True Z.D. . . 58 10 56
True Z.D. . . 61 21 42
H. M. S.
f2 56 48.471 "■»• »•
Chronometer, Fast < !■ 2 56 48.8
(2 56 49.14J
IN THE LENGTH OF THE SECONDS PENDULUM.
75
Maranham.-
Determination of the Rate of the Chronometer by Zenith Distances, continued.
August 25th A.M.; Barometer 30.05; Thermometer 80°; Q's L.L. |
Ctiroaometcr.
Level.
Readings, &c.
Clirouometer.
Level.
lleadin-^s, ic.
H. M. S.
10 54 38.4
10 56 36.8
10 58 34
11 00 20
11 02 01.2
11 04 40.8
-2
+2
0
-8
0
-5
-3
0
0
-9
0
-6
O , 1,
First Vernier 7 35 10
Second „ 35 00
Third „ 35 20
Fourth „ 34 40
H. M. S.
U ]3 16
11 15 07.6
11 17 09.2
11 18 57.6
1! 20 49.2
11 23 17.2
+1
+5
-3
-0
+ 1
+ 1
+ 1
+4
-3
-7
0
0
o , //
First Vernier 318 09 10
Second „ 09 10
Tliird „ 09 40
Fourth „ 09 20
Mean 7 ^5 02.5
Level -15
Index +360 00 08.5
Mean 348 09 20
Level - 3
Index -7 35 02
Mean 10 59 2S.53
True time.. 8 02 37.44
-13
-17
Mean 11 18 06.13
True time.. 8 21 1 1.5
-I
-5
-15
)8.5
367 34 55
-3
340 34 15
ChroD.fast. . 2 56 51.09
Chron.l'ast. . 2 56 51.63
Observed Z.D. 61 15 49
Ref. and Paral. + 1 30
Semidiam - 15 52
Observed Z.D. 56 43 43
Ref. and Paral. + 1 15
Semidiam — 15 52
360 + 08.5 = 360 o'o (
Index - 7 35 02
TrueZ.D 61 01 27
TrueZ.D 56 31 06 1
II. M. .S.
l2 56 51 .091 "■ "■ 5-
Chronometer, Fast < > 2 56 51.36
1,2 36 5I.63J
August 26tli A.M.; Barometer .SO. 05 ; Thermometer 8l)° ; Q's L.L.
Chronometer.
Level.
Headings, &c.
Chrcnometci*.
Level.
Readings, .Ic.
H. M. S.
10 43 37.2
10 45 29.2
10 47 17.2
10 49 34.8
10 51 50.8
10 54 09.2
+2
-4
+ 1
-5
0
0
+ 1
— 4
+ 1
-5
0
0
o / „
First Vernier 22 42 30
Second „ 42 20
Third ,, 42 40
Fourth „ 41 50
11. M. S.
11 05 51.2
11 07 06.8
11 09 04.8
11 10 49. C
11 12 41.2
11 14 24
0
+2
-3
+ 6
-9
0
0
+ 1
-4
+6
-9
0
0 < ,/
First Vernier 1 4 20 30
Second ,, 20 20
Third ., 20 ?,0
Fourth ,, 20 00
Mean 22 42 20
Level —6.5
Index +360 00 08.5
Mean . 14 20 90
Level — 5
Index +337 17 40
Mean 10 4S 39.73
True time.. 7 51 44.9
-6
-7
Mean 11 09 59.6
True time.. 8 13 05.9
-4
-6
-6.5
382 42 22
5
351 37 55
Chron.fast.. 2 56 54.83
Cliron.fast. . 2 56 53.7
08.5
Observed Z.D. 63 47 04
Ref. and Paral. + 1 42
Semidiam 15 52
Observed Z.D. 58 36 19
Ref. and Paral. + 1 22
Semidiam —15 52
360 + 08.5 = 360 00
O O 1 tl o
360 — 22 42 20 = 337
/ //
17 40
TrueZ.D 63 32 54
TrueZ.D 58 21 49
'
11. H. S. 1
„ f2 56 54.83! "■ "• «• J
Chronometer, Fast < }■ 2 56 54.26 1
i2 56 53.7 J 1
L 2
76
EXPERIMENTS FOR DETERMINING THE VARIATION
Maranham.
Determination of the Rate of the Chronometer by Ze
nith Tlistaiifps coniiiyitpd
August 27 A.M. ; Barometer 30 . 04 ; Thermometer 80°; O's
L.L.
Chronomcttr.
Level.
Eeadiags, &c.
'Chronometer.
Level.
Readings, &c.
H. M. S.
10 40 59.2
10 42 52
10 44 56
10 46 45.2
10 48 41.6
10 50 22
+3
0
+5
0
0
0
+2
0
+3
-1
-1
-1
o / //
First Vernier 40 37 45
Second ., 37 30
Third „ 38 00
Fourth „ 27 20
11. M. s.
10 55 45.6
10 57 44
11 00 43.6
11 02 49.2
0
0
0
0
-I
-2
0
0
o ' -/
First Vernier 285 01 10
Second „ 01 00
Third „ 01 40
Fourth „ 00 40
Mean ... 40 37 39
Index ... 345 39 40
Level ... +5
Mean . . .10 59 15.6
True time . 8 02 18.9
0
-3
Mean.. . . 285 01 07.5
Index . . . -40 37 39
Level ... —1.5
-1.5
Mean. . . 10 45 46
True time . 7 48 49
+8
+2
Chron. fast . 2 56 5G.7
+ 5
-.1
9 40
386 17 24
Index- 4°0 37 39
244 23 27
Cliron. fast. 2 56 57
Observed Z.D. 64 22 54
Ref. and Paral. +1 45
Seraidiam . . — 15 52
Observed Z.D. 61 05 52
Ref. and Paral. + 1 SO
Semidiam . . — 15 52
360-14 20 20 = 345 3
True Z.n. . . 64 08 47
True Z.D. . . 00 51 SO
Chronometer. Fast /^ ^'^ ^^ \ 2 56 56.85
i2 56 56.7 j
August 28 P.M. ; Barometer 29 -95 ; Thermometer 81° ; Q's
U.L.
Chronometer.
Level.
Readings, &;c.
Chronometer.
Level.
Re.idings, &c.
H. M. S.
6 01 55.6
6 03 15.2
6 05 00. S
6 06 21.2
6 08 00
6 09 44.4
-3
0
0
-4
+4
-4
-2
0
0
-3
+ 3
-2
0 . */
First Vernier 132 59 40
Second „ 132 59 30
Third „ 133 00 20
Fourth „ 132 59 50
11. M. s.
6 14 08.8
6 15 40
6 17 33.6
6 19 19.2
6 21 10.4
6 23 20.6
— 4
-15
+ 2
-6
+ 1
+6
— 2
- 12
+4
-4
+ 3
+7
O / .1
First Vernier 167 11 50
Second ,, 1 1 30
Third „ 12 10
Fourth ,, 11 40
Mean ... 132 59 50
Level .. . —5.5
Index . . .+242 26 37.5
Mean ... 167 11 47.5
Level ... -10
Index . . .+227 00 10
Mean. . . 6 05 42.87
True time. 4 08 44.2
-7 i-4
Mean. . . 6 18 32.1
True time. 4 21 33.07
-16
-4
— 5.5
375 26 22
-10
06 10
394 11 47.5
Chron.fast. 2 56 58.67
Observed Z.D. 62 34 23.7
Ref. and Paral. +1 37.3
Semidiam . . +15 52
Chron. fast. 2 56 59.03
Observed Z.D 65 41 58
Ref. and Paral. +1 52
Semidiam . . +15 52
2*6 37.5
360- in 33 z'a. 5 = 242
360-132 59 50 = 227
True Z.D. . . 62 51 53
True Z.D. T " 65 59 42
Chronometer, Fast J ^ ^^ 58.67]_ ^ jg jg.gj
[2 56 59.03J
IN THE LENGTH OP THE SECONDS* PENDULUM.
77
Maranhaim.-
Determination of the Rate of the Chrouometer by Zenith Distances, continued.
August 29th A.M.; Barometer 30.04; Thermometer 80° ; Q'sL.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. H. S.
10 54 36.4
10 57 02.8
10 58 50.8
11 00 12
11 02 00
11 03 25.6
0
-1
0
0
0
0
0
— 2
0
0
0
0
o . ..
First Vernier 141 40 20
Second „ 00
Third „ 20
Fourth „ 10
Mean ... .141 40 12.5
Level .... —1.5
Index . . . .223 23 00
Mean . . .10 59 21.27
True time . 8 02 20.07
-I
-2
-1.5
365 05 11
Chron. fast. 2 57 01.2
25 00
Observed Z.D. 60 50 52
Ref. and Paral. + 1 30
Semidiam . . —15 52
S60 - 136 .35 00 = 2°23
True Z.D. . . 60 36 30
11. M. S.
Chronometer Fast 2 57 01.2
Aug
ust 29th P.M.; Barometer 29.95 ; Thermometer 81° ; 0's U.L.
Chronometer.
Level.
Readings, &c. '"'
Chronotneler.
Level.
Readings, &c.
H. M. S.
6 24 19.6
6 26 28.8
6 28 32.8
6 29 51.2
6 32 16
6 33 42
-6
+4
0
+ 3
+S
-10
-6
+ 5
0
+4
+4
-8
0 ^ /y
First Vernier 90 28 40
Second „ 28 30
Third ,, 29 20
Fourth „ 28 30
H. M. S.
7 08 19.2
7 09 57.6
7 11 44.8
7 13 48.4
7 15 38.4
7 17 .36.4
-2
0
+5
0
-10
+ 3
-2
0
+ 7
0
-8
+4
First Vernier IIC 26 10
Second „ 25 50
Tliird „ 26 20
Fourth „ 25 55
Mean .... 90 28 45
Index . . .-1-231 42 45
Level .... -3
Mean . . . .116 26 04
Index . . .+269 31 15
Level .... -1.5
Mean ... 6 29 11.73
True time . 3 32 10.78
-6
-1
Mean ... 7 12 50.8
True time. . 4 15 48.57
-4
+ 1
-3
1 42 45
322 11 27
-1.5
385 57 17
Chron. fast . 2 57 00.93
Chron. fast.. 2 57 02.23
Observed Z.D. 53 41 54
Ref. and Paral. + I 07
Semidiam . . +15 52
—
Observed Z.D. 64 19 33
Ref. and Paral. + 1 45
Semidiam . . -15 52
360 - 128 17 15 = 23
360 - 90 2'8 45 = 269
i\ 15
True Z.D. . . 53 58 54
True Z.D. . . 61 37 10
H. JI. S.
[2 57 00.951 "■ "■ s-
Chionometer Fast ■! > 2 57 01.59
12 57 02.23J
78
EXPERIMENTS FOR DETERMINING THE VARIATION
Maranham. Determination of the Rate of the Chronometer by Zenith Distances, continued.
August 30th A.M.; Barometer 30.03 j Thermometer 80°; Q'sL.L.
1
Chronometei-.
Level.
Beadiugs, &c.
Cbronometei'.
Level,
Readings, &c.
H. M. S.
10 52 21.4
I 10 54 54.8
', 10 58 28.8
^ n 00 32.8
11 03 07.2
11 05 12.4
+ 3
+3
-8
-2
+ 2
-1
+ 2
+3
-9
-3
+3
-1
0 * 1'
First Vernier . S3 41 40
Second „ 41 15
Third ,, 42 00
Fourth „ 41 20
Mean .... 83 41 34
Index . . .+28! 05 37.5
Level .... —4
Mean. . . 10 59 06.23
True time . 8 02 02.42
-3 -5
-4
364 47 07
Chron. fast. 2 57 03.81
ObsL'rvedZ.D. 60 47 51
Ref. and Paral. + 1 30
Semidiani . . —15 52
360-7°8 54 22.5 = 281 C
5 s'Ks
True Z.D. . . 60 33 29
H. M. S.
Clironometer, Fast 2 57 03.81
August 30th P.M. ; Barometer 30.00 ; Thermometer 81° ; ©'s U.L.
Chionouieter.
Level.
Readiugs, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
6 28 27.6
6 29 52
6 32 06
6 33 31.4
6 35 50
6 37 25.2
+7
-2
+ 3
+ 3
-4
-5
+ 8
-2
+4
+4
— 2
-4
0 * ti
First Vernier 327 32 00
Second „ 31 50
Third „ 32 20
Fourth „ 32 00
11. H. S.
6 42 44.8
6 41 21.2
6 45 56.8
6 47 16
G 49 04.4
6 50 30.4
0
0
+5
-9
+9
-8
0
0
+7
-7
+ 11
-6
0 * 41
First Vernier 315 11 35
Second „ 11 20
Third „ 1 1 40
Fourth „ 11 00
Mean . . . .327 32 02.5
Index .... +08.5
Level .... +05
Mean . . . .315 11 24
Index . . . + 32 27 57 . 5
Level .... +1
Mean . . 6 32 52.53
True time 3 33 48.07
+2
+8
Mean. . . 6 46 38.93
True time. 3 49 34.27
-3
+5
+5
327 32 16
+ 1
347 39 22.5
Chron. fast . 2 57 04.46
Chron. fast. 2 57 04.66
Observed Z.D. 54 35 23
Ref. and Paral. + 1 08
Semidiam . . +15 52
Observed Z.D. 57 56 34
Ref. and Paral. + 1 22
Semidiam . . +15 52
360-327 32 02.5=32 2'
r 57.5
True Z.D. . . 54 52 23
True Z.D. . . 58 13 48
H. M. S. H M S
Chronometer, Fast/ ^ ^^ "''•^^ 1. 2' 57 04.56
[ 2 57 04.66]
IN THE LENGTH OF THE SECONDS* PENDULUM.
79
Maranham. Determination of the Rate of the Chronometer by Zenith Distances, continued.
Angust 31st A.M. ; Barometer 30 .05 ; Thermometer 80° ; ©"s L.L.
Chrononieler,
H. M. S.
10 51 30
10 5C 18.4
10 59 13.2
11 00 55.2
n 02 58
11 01 51.8
Level.
Readings, &c.
1
+2
0
+4
0
3
Mean . . .
True time .
Chron. fast
10 59 48.27
8 02 42.17
00.1
•1
4
+2
0
+5
0
— 0.5
3eo-6 59 11 = 353 00 49
First Vernier
Second „
Third ,,
Fourth .,
10 02 50
02 30
03 00
02 10
Mean
Index
Level
10 02 37
. + 353 00 49
-0.5
Chronometer.
363 03 25
Observed Z.D. 60 .SO 34
Ref. ami Paral. +1 30
Semidiani . . —15 53
True Z.D.
CO 10 11
II. M. S.
11 03 37.2
11 11 38.8
11 14 27.2
11 16 06
11 17 59.6
11 20 SI. 2
Mean. . .
True time .
II 15 03.33
S 17 57.4
Chron. fast 2 57 05.93
Headings, &<;
_2
+4
0
0
+ 1
+ 5
+8
-4
+5
0
0
+1
+ 5
+ 7
+7.5
Index - 10 02 37
First Vernier 350 45 00
Second
Third
Fourth
Mean .
Index .
Level .
45 00
45 40
45 00
350 45 10
-10 02 37
+07.5
310 42 54
Observed Z.D. 50 47 09
Ref. and Paral. + 1 15
Semidiani . . — 15 53
True Z.D.
56 32 31
n. M. s.
f2 57 06.1 1 "• '"■ ^'•
Chronometer, Fast < > 2 57 06.01
12 57 05.93J
August 31st P.M. ; Barometer 39
95; Thermometer 81^ ; ©
s U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. s.
6 18 08.4
6 19 49.2
6 21 46
6 23 24
6 24 59.2
6 26 10
0
-2
+ 2
0
0
-2
0
-1
+ 1
0
0
-1
O / //
First Vernier 302 59 20
Second ,, 59 20
Third ,, 59 50
Fourth „ 59 20
H M. S.
6 35 08.4
6 36 56
6 38 45. G
6 40 12.8
6 43 06.4
6 44 35.2
+ 7
0
+ 1
0
+ 2
0
+ S
0
+ 2
0
0
0
o , „
First Vernier 281 39 10
Second ,, .33 20
Third ,, 39 40
Fourth ,., 39 00
Mean ... 302 59 27.5
Index ... +9 14 50
Level ... -1.5
Mean . . 280 39 17.5
Index . . . +57 00 32.5
Level ... +10
Mean . . . 6 22 22.8
True time . 3 25 15.9
-2
-1
Mean ... 6 39 47.4
Truethne . 3 42 39.86
+ 10
+ 10
-1.5
312 14 16
+ 10
337 40 00
Chron. fast . 2 57 06.9
Chron. fast . 2 57 07.54
4 SO
Observed Z.D. 52 02 23
Ref. and Paral. +1 03
Semldiam . . +15 53
00 32.5
Observed Z.D. 56 16 40
Ref. and Paral. +1 15
Semidiam . . +15 53
0 O - /< 0
360 -350 45 10 = 9
360 - 302 59 27'. 5 = 5'7
True Z.D. . . 52 19 19
True Z.D. . . 56 33 48
H. M. S.
„ ^ f2 57 06.9 1 "• M- s.
Chronometer, Fast < > 2 57 07.2
L2 57 07..54J
80
EXPERIMENTS FOR DETERMINING THE VARIATION
Maranham.-
Oetermination of the Rate of the Chronometer by Zenith Distances, continued.
Spptember 1st P.M. ; Barometer 29.95 ; Thermometer 81° , Q's U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
6 21 15.6
6 26 50.4
6 28 41.2
6 30 22.4
6 32 21. G
6 33 51.6
+4
+4
-5
0
-4
+ 5
+3
+3
0
-2
+7
0 ' "
First Vernier 322 29 20
Second „ 29 .30
Third „ 30 00
Fourth „ 29 30
11. M. S.
6 40 40.4
6 42 37. G
6 44 26
6 45 59.6
6 47 56
6 49 29.2
+6
-2
+2
+4
0
+4
+4
-1
+ 1
+2
0
+5
0 / /.
First Vernier 308 07 20
Second „ 07 10
Third „ 07 50
Fourth „ 07 10
Mean . . . 322 29 35
Index . . . +08.5
Level . . . +0C
Mean ... 308 07 22
Index . . . +37 30 25
Level . . . +12.5
Mean. . . 6 23 23.8
True time . 3 32 13.2
+4
+8
Mean. . . 6 45 11.47
True time . 3 48 00 . 37
+ 14
+ 11
+ 6
322 29 49
+ 12.5
345 37 59
Chron.fast 2 57 10.6
Chron.fast 2 57 11. 1
.'
Observed Z.D. 53 44 58
Ref.andParal. + 1 06
Semidiam . +15 52
Observed Z.D. 57 36 17.5
Ref.andParal. + 1 21
Semidiam . . +15 52
360-322 29 35 = 37 30 25
TruoZ.D. . . 51 01 5R
TrueZ.D. . . 57 53 30
.f 2 '57' 10.6 1 «• M. s.
Chronometer, Fast < > 2 57 10.85
I 2 57 11 . 1 j
September 2d P.M. ; Barometer 29.94 ; Thermometer 81° ; © 's U.L.
Clironometer.
Level.
Readings, &c.
Chronometer.
Level.
Readi.ngs, &c.
11. M. S.
6 39 07.2
6 40 25.2
6 41 55.6
6 43 21.6
6 45 29.6
6 47 21.2
-5
+3
-4
-7
-7
+ 6
-5
+4
— 3
-5
-7
+7
0 * It
First Vernier 290 33 00
Second „ 32 5O
Third „ 33 20
Fourth „ 32 20
II. M. S.
6 52 31.6
6 53 58
6 55 38.8
G 57 04.8
G 58 32
C 59 52.4
0
0
-4
0
+3
+2
0
0
-2
0
+2
+4
0 '
First Vernier 292 33 15
Second „ 33 05
Tliird „ 3.i 30
Fourth „ 32 45
Mean ... 290 32 52.5
Index ... 51 52 38
Level ... -11.5
Mean ... 292 33 09
Index ... 69 27 07.5
Level . . . +2.5
Mean. . . 6 42 57.23
True time . 3 45 43.11
-14
-9
Mean. . . 6 5G 16.27
True time . 3 59 02.37
+1
+4
-11.5
342 25 19
+2.5
362 00 19
Chron.fast 2 57 13.9
Chron.fast 2 57 14.12
)2 38
Observed Z.D. 57 04 13
Ref.andParal. +1 17
Semidiam . . +15 53
Observed Z.D. 60 20 03
Ref.andParal. +1 30
Semidiam . . +15 53
360-30°8 17 22 = 5°1 .
360-290 32 52.5 = 69 2
7 07.5
True Z.D. . . 57 21 23
TrueZ.D. . . 60 37 26
H. M. S.
^ [2 57 14.121 H- »'■ 3.
Chronometer, Fast < > 2 57 14.01
[2 57 13.9 i
IN THE I.FNGTH OF THE SECONDS' PENDULUM.
81
Maranham. Determination of the Rate of the Chronometer by Zenith Distances, continued.
Sept
ember 3d A.M.; Barometer 30 . 05 ; Thermometer 80°; ©'s L.L.
Cbronometcr.
Level.
Readings, &c.
Cliruiiometer,
Level.
Readings, &c.
H. M. S.
10 49 28.4
10 51 32.8
10 53 18.4
10 54 57.6
10 57 32.4
10 59 07.6
-4
+8
+3
0
+2
-1
-4
+7
+2
0
+2
-1
0 ' II
First Vernier 192 51 !5
Second „ 51 00
Third „ 51 40
Fourth „ 51 00
B. M. S.
11 03 46.8
11 05 15.2
11 06 48.4
11 08 17.2
11 09 51.2
11 11 06
0
0
-5
-2
+3
0
0
0
-6
-1
+ 3
0
0 1 II
First Vernier 182 33 00
Second „ 33 00
Third „ 33 30
Fourth „ 32 30
Mean ... .192 51 14
Index . . . + 176 14 09
I-evel .... +7
Mean . . . .182 33 00
Index . . . + 167 08 46
Level .... -4
Mean. .. 10 54 19.53
True Time. 7 57 04.6
+8
+ 0
Mean. . . 11 07 30.8
True time. 8 10 11.54
-4
-4
+ 7
369 05 30
-4
349 41 42
Cliron. fast. 2 57 M.93
Chron. fast. 2 57 16.26
Observed Z.D. 61 30 55
Ref. andParal. + 1 30
Semidiam . . — 15 54
Observed Z.D. 58 16 57
Ref. and Paral. + 1 23
Semidiam . . - 15 54
360 - 183 45 5"l = 176
14 09
360-192 s'l 14 = 167
o's 4"g
True Z.D. . . CI 16 32
True Z.D. . . 58 02 26
II. M. S.
Chronometer Fast i"^ ^^ ''*-^^]. "'sV 15.59
12 57 16.26J
Sep
teniber 3d P.M. ; Barometer 29.95 ; Thermometer 81° ; ©"s U.L.
Chronometer.
Level.
Readings, &c.
Clironometer.
Level.
Readings, &c.
H. M. S.
6 23 07.6
6 24 35.4
6 26 26.8
6 27 44.4
6 29 20.4
6 30 52
+ !
+7
-4
+ 10
-5
-3
+0
+ 8
-3
+ 11
-5
— 2
0 . II
First Vernier 111 39 00
Second „ 38 40
Third „ 39 30
Fourth „ 39 00
H. M. S.
6 36 03.6
6 38 22.8
6 43 15.4
6 44 40.4
6 46 07.2
6 51 54.4
+ 2
0
-5
-5
-I
+ 6
+4
0
-5
-4
-2
+7
First Vernier 124 51 10
Second „ 51 00
Third ,, 51 20
Fourth „ 50 40
Mean . . . .141 39 02.5
Index . . . + 177 27 00
Level .... +7.5
Mean . . . .124 51 02.5
Index . . .+218 20 58
Level .... —1.5
Mean. . . 6 27 01.1
True time . 3 29 44.77
+6
+9
Mean ... 6 43 23.97
True time. 3 46 08.37
-3
0
+7.5
319 06 10
-1.5
S43 11 59
Chron. fast. 2 57 16.33
Observed Z.D. 53 11 02
Ref. and Paral. + 1 04
Semidiam . . +15 54
Chron. fast. 2 57 15.6
Observed Z.D. 57 11 59
Ref.andParaL + 1 17
Semidiam . . +15 54
360- i82 3*3 00 = 177
27 00
True Z.D. . . 53 28 00
True Z.D. . 57 29 10
H. _M. s. ^ ^ ^
Chronometer Fast i^ " 16.331^ 2' ^7 15.96
I2 57 15.6 j
M
82
EXPERIMENTS FOR DETERMINING THF. VARIATION
Maranham
-Deterinination of the Rate of the Chronometer by Zpnith Distaupp.s:. mntinnpfi
September4th A.M.; Barometer 30.04; Thermometer 80°; O'sL.L.
(Flying Clouds.)
Cbvonometer.
Level.
Readings, &c.
Cbrououieter.
Level*
Headings, &c.
H. M. S.
10 51 40
10 53 27.2
10 56 06.8
11 00 06
11 01 40
11 03 04.4
_o
+ 4
-13
0
+2
+4
-1
+2
-13
0
+ 2
+4
o * *'
First Vernier 128 18 00
Second „ 17 40
Third „ 18 20
Fourth „ 17 50
U. M. S.
1 1 06 44
11 07 57.6
11 09 58
11 15 26.4
11 17 02.4
11 18 44.4
0
+5
-3
+8
-3
0
0
+4
-3
+7
-4
0
C 1 .,
First Vernier 109 41 30
Second „ 41 10
Third „ 41 50
Fourth „ 41 00
Mean ... 128 17 57.5
Index . . .+235 08 57.5
Level . . . -5.5
Mean . . . 109 41 22.5
Index . . .+231 42 02
Level . . . +5.5
Mean. . . 10 57 40.73
True time . 8 00 23.67
-5
-6
Mean. . . 11 12 38.8
True time. 8 15 21.2
+7
+4
-5.5
363 26 50
+ 5.5
42 02
841 23 30
Chron. fast 2 57 17.06
Chron. fast 2 57 17.6
Observed Z.D. 60 34 28
Ref. and Paral. +1 28
Semidiam . . —15 54
Observed Z.D. 56 53 55
Ref. and Paral. +1 17
Semidiam . . — 1 5 54
300—124 s'l 02.5 = 2°35
08 57.5
360-128 17 58 = 2°31
True Z.D. . . 60 20 02
TrueZ.D.. . 56 39 IS
11. M. S. H M s
Chronometer Fast l'^ ^^ '^'"^l z' 57 17.33
12 57 17.6 j
September 4th P.M.; Barometer 29.95; Thermometer 81°; G
's U.L.
Chrouometer.
Level.]
Readings, &:c.
Chronometer.
Level.
Readings, &c.
H. M. S.
7 01 07.2
7 02 33.2
7 04 17.2
7 05 32.4
7 07 22.8
7 08 39.2
0
+ 1
+ 3
-14
+2
0
0
+4
+4
-14
+ 3
0
First Vernier 124 45 40
Second „ 45 SO
Third „ 40 10
Fourth „ 45 30
11. H. S.
7 15 10.4
7 16 58
7 18 08
7 19 19.6
7 21 04.4
7 22 31.6
+7
+ 1
+ 1
-7
-5
+5
+ 8
+2
+2
-6
-4
+7
o < «
First Vernier 160 19 40
Second „ 19 40
Third „ 20 00
Fourth „ 19 40
Mean ... 124 45 42.5
Index . . .+250 18 37.5
Level . . . -5.5
Mean ... 160 19 45
Index . . .+235 14 17.5
Level . . . +5.5
Mean. . . 7 04 55.33
True time. 4 07 37.77
-8
-3
Mean. . . 7 18 48.67
True time. 4 21 30.37
+2
+ 9
-5.5
375 04 15
+ 5.5
4 17.5
395 34 08
Chron. fast 2 57 17.. 56
Observed Z.D. 62 30 42.5
Ref. and Paral. +1 41
Semidiam . . +15 53.5
Chron. fast 2 57 18.3
Observed Z.D 65 55 41
Ref. and Paral. +1 59
Semidiam . . +15 54
360-109 4'l 22.S=2°50
18 37.5
360-124 45 42.5 = 235 1
TrueZ.D. . . 62 48 17
TrueZ.D.. . 66 13 34
H. M. S. j^j
Chronometer Fast 1^ ^^ "-^^1 2 57 17.93
\2 57 18 3 j
IN THE LENGTH OP THE SECONDS' PENDULUM.
83
RATE DEDUCED from the PRECEDING OBSERVATIONS.
A.M. to A.M.
P.M. to P.M.
Date.
S.
Date. :
S.
Pat5.
S.
Date.
S.
Aug.24toAu.25
3.73
Aug. 26 to Au. 31
2 35
Aug. 24 to 28
2.51
Aug. 29 to Sept. 2
3.1
26
3.31
Sept. 3
2.67
» "" 29
2.56
3
2.87
27
3.07
4
2.56
„ 30
2.63
4
2.72
29
2.71
Aug.27to Au.29
2.17
„ 31
2.63
Aug. 30 to 31
2.64
30
2.7
30
2.32
Sept. 1
2.75
„ Sept. 1
3.15
31
2.63
31
2.29
.. 2
2.8
Q
JJ -
3.15
„ Sept. 3
2.8
,, Sept. 3
2.69
), 3
2.72
3
2.85
4
2.7
4
2.59
). 4
2.65
4
2.67
Aug. 25 to Au. 26
2.9
Aug. 29 to Au. 30
2.61
Aug. 28 to 29
2.74
Aug. 31 to Sept. 1
3.65
27
2.74
31
2.4
30.
2 83
,> 2
3.4
29
2.46
„ Sept. 3
2.88
„ 31
2. 78
3
2.92
30
2.49
4
2.69
„ Sept. , 1
3.00
4
2.68
31
2.44
Aug. 30 to Au. 31
2.2
). 2
3.03
Sept. 1 to Sept. 2
3.16
„ Sept. 3
2.69
Sept 3
2 95
,, 3
2.85
3
2.55
4
2.60
4
2.7
,. 4
2.73
4
2.53
Aug. 26 to Au. 27
2.59
Aug.31 toSept.3
3.19
Aug. 29 to 30
2.57
Sept. 2 to Sept. 3
1.95
29
2.31
4
2.83
31
2.8
4
1.96
30
2.39
Sept. 3 to Sept. 4 1 . 74
Sept. 1
3.09
Sept. 3 to Sept. 4
1.97
Means 2.645
2.765
Gaining 2.7 Seconds per Diem.
M 2
84
EXPERIMENTS FOR DETERMINING THE VARIATION
Maraivham. Comparisons of the Astronomical Clock with the Chronometer, No.
423, from the 2^th of August to the 4th of September, 1S22; with the Clock's Rate
on Mean Solar Time deduced.
1822.
Chronometer.
Aug
24 A.M.
5)
24 P.M.
1?
25 A.M.
))
25 P.M.
11
2G A.M.
IT
2C P..M.
?J
27 A.M.
7»
27 P.M.
51
2S A.M.
))
28 P.M.
»
29 A.M.
H
29 P.M.
51
30 A.M.
11
30 P.M.
11
31 A.M.
11
31 P.M.
Sept. 1 A.M.
11
1 P.M.
11
2 A.M.
11
2 P.M.
11
3 A.M.
11
3 P.M.
11
4 A.M.
11
4 P.M.
V 12 05 00 <
IN THE LENGTH OF THE SECONDS' PENDULUM.
85
Maranham. COINCIDENCES OBSERVED with PENDULUM 3 ; the Clock making
SG2G6.G5 Vibrations in a Mean Solar Day.
DATE.
Baro-
meter.
No.
of Co.
inci-
dence.
Tempe-
rature.
Time of
,Dis:ip-
pearance.
Time of
Re-ap-
pearance,
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
ratnre.
Mean
Interval.
CorrL'c-
lion for
tile Arc.
Vibrations
in 24 hours.
Redac-
tion to a
Mean
Tempe-
rature.
Rediiceii
Vibrations at
38°.lFaht.
1822.
Auk. 24 A.M.
24 P.M.
25 A.M.
25 P.M.
26 A.M.
2G P.M.
27 A.M.
27 P.M.
28 P.M.
29 A.M.
30.050
29.960<
30.050<
29.950.^
30.050<^
29.970<
30.050.
29.950<
30.000,
30.050,
U
83
83.5
83.
83.8
82.8
82.9
81.9
il.'J
81.2
81.
82
81
81.2
81.6
80.9
80.2
80.4
80.8
80.9
M. S.
48 25
35 50
29 U
16 40
02 53
50 31
31 42
22 10
11 27
59 25
SO 48
18 11
8 OS
56 10
9 16
57 1 1
00 14
48 21
21 42
9 42
M. S.
48 26
36 00
29 17
16 49
03 00
50 40
31 47
22 49
11 28
59 36
30 51
18 51
8 09
56 20
9 IS
57 25
00 17
48 32
21 45
9 51
H. M. S.
10 48 25.5
12 35 55
2 29 15.5
4 16 41 5
8 02 59.5
9 50 35.5
2 34 44.5
4 22 41.5
8 11 27.5
9 59 30.5
1 SO 49.5
5 18 46
8 8 08.5
9
56
15
2
9
17
3
57
19
5
1
00
15
5
2
48
28
8
21
43.
5
0
9
46.
5
1.22
0.64'
1.18|
0.62 J
0.621
1.16
0.58
1.18
0.58
I.IS
0.58
1.18
0.58
1.2
0.6
1.18"i
0.58
1.18
0.58
83.25
83.55
82.85
81.8
81.35
82
81.1
81.25
SO. 3
80.85
641.95
611.9
645.6
648
648.3
647.65
648.65
648.25
619.25
648.3
+
1.3C
1 32
1.32
1.19
1.22
1.22
1.22
1.28
1 .22
1.22
86000.50
86000.42
86000.72
86001.57
86001.72
86001.46
86001.86
86001.78
86002.12
86001.72
-1-0.6
-1-0.72
-1-0.42
-0.20
•t-0.07
-0.31
-0.24
-0.64
-0.42
86001.10
86001.14
86001.11
86001.57
86001.52
86001.53
86001.55
86001.54
8600 1.48
86001.3
Means . . .
30.008
81.83
86001.39
86001.39
86
EXPERIMENTS FOR DETERMINING THE VARIATION
IN THE LENGTH OP THE SECONDS' PENDULUM.
87
Maranham
—BAROMETRICAL OBSERVATIONS to DETERMINE the
HEIGHT of the PENDULUM STATION.
At the Pendulum
The Cistern one foot above
datil;
Station.
High Water Marie.
Height
Baro-
meter.
Thermometer.
Baro-
meter.
Thermometer.
Mean
Tide.
REMARKS.
Alt.
Det.
Alt.
Det.
1822
IN.
o
0
l.N.
o
Feet.
H M.
Sept. 5, 8 00 A. M.
30.059
S3
82
„ 5, 8 20 A. M.
....
30 125
85
82
„ 5, 8 50 A. M.
30.059
85
82
. 8]
The difference in the Mer-
curial Column equal 67ft.
to which i2ft. are added
for half the Pall of Tide,
„ 5, 9 15 A. M.
30.124
85
82
and 1ft. for the Height of
the Cistern, above High
Water Maik.
„ 5, 9 45 A. M.
30.001
85
82
....
MEANS ....
30.060
85
82
30.125
85
82
/
88 EXPERIMENTS FOR DETERMINING THE VARIATION
TRINIDAD.
Having had the good fortune to meet Sir Ralph Woodford, Governor
of Trinidad, in London, soon after I had determined on undertaking the
present inquiry, he was kind enough to offer me letters of introduction
to Port Spain, the seat of Government in Trinidad, which should ensure
me a favourable reception, and the means of accomplishing the objects
which I had in view. Port Spain being very desirably situated near
the tenth parallel of latitude, I did not hesitate to avail myself of so ad-
vantageous an offer, and thus early anticipated the very agreeable and
satisfactory visit, which I had now the opportunity of making.
In the absence of Sir Ralph Woodford in Europe, the administration
was carried on by the Lieutenant Governor, Colonel Aretas WiUiam
Young of the 3rd West India Regiment, with whom I had had a former
though slight acquaintance, v»'hilst serving together at Gibraltar in
1805. The Pheasant arrived at Port Spain on the 18th of September,
which was a month later than Sir Ralph Woodford's letters had caused
her to be expected, being the consequence of her detention at Bahia ;
Colonel Young had been so kind as to provide me an apartment at his
house, and invited Captain Clavering and myself to be his guests during
our residence.
The pendulums were admirably accommodated in the Vestry-Room
of the new and very beautiful Protestant Church, which does so much
credit to the architectural taste and skill of Mr. Reinagle by whom it was
designed and built ; and is one of the many improvements and decorations
for which Port Spain is indebted to its present Governor, and which have
IN THE LENGTH OF THE SECONDS* PENDULUM. 89
rendered it one of the handsomest towns in the British Colonies. The
walls of the vestry being of an extraordinary thickness, the tempera-
ture was more than ordinarily uniform ; the going of the pendulums,
of the clockj and of the chronometer, at this station, deserve to be
particularly noticed.
Port Spain is built on a bed of gravel, between 30 and 40 feet deep,
resting on a substratum of clay ; it furnished therefore a second station
in the low latitudes, Maranliam being the other, in the opposite extreme
in respect of local density, to the stations of St. Thomas and Ascension ;
the number of stations in each extreme being thus the same, the undue
influence of either is counteracted, on the deductions which may be
derived from a general summary.
The height of the pendulums was ascertained by direct measurement
to be twenty-one feet above half tide.
It was with great regret that Captain Clavering and myself felt the
propriety of pursuing the voyage, as soon as the immediate object which
had occasioned our visit to Port Spain was completed ; as the very agree-
able society, and the many natural beauties and curiosities of Trinidad,
were strong incitements to delay : but our departure was pressed by an
anxiety to arrive in England as early as possible in the ensuing winter,
in order to make the necessary preparations for proceeding to the high
latitudes, as soon as the northern navigation should open in the sprino-,
so that we might have the whole of the following season at our disposal
in the Arctic Circle. The Pheasant therefore sailed for Jamaica as soon
as the instruments were embarked, for the purpose of undergoing in the
Dock Yard the repairs which she required, to enable her to encounter
the gales which might be expected in crossing the Atlantic at so late a
period of the year.
N
90
EXPERIMENTS FOR DETERMINING THE VARIATION
Trinidad. OBSERVATIONS to DETERMINE the RATE of the Chronometer No. 423, by ZENITH
DISTANCES of the Sun, with a Repeating Circle ; from the 23d of September to the 4th of October, 1S22.
latitude of the Place of Observation 10° 38' 43" N. ; Longitude 61° ,^6' W.
September 23d A.M. ; Barometer 29.97 ; Thermometer 81°; 0's L.L.
Cluoiiumeter.
Level.
Readings, &e.
Chronometer.
Level.
Readings, &c.
H. M. S.
11 45 40
11 47 36.8
11 49 40.4
11 51 23.2
11 53 16.4
11 54 44.4
+ 5
+ 1
+ 1
— 5
+1
— 4
+5
+ 1
+2
— 5
+ 1
First Vernier 221 31 40
Second „ 34 40
Third „ 35 20
Fourth „ 34 30
11. M. s.
12 01 .35.6
12 03 39.6
12 05 34
12 07 44
12 09 48.4
12 11 26.4
0
+2
+5
+ 6
-2
-4
0
+ 2
+ 5
+6
-2
-4
0 t ,1
First Vernier 215 51 40
Second „ 51 15
Third „ 52 00
Fourth ,, 51 10
Mean . . 221 34 48
Level ... 0
Index . . . + 156 29 58
Mean ... 215 51 31
Level ... +7
Index . . + 138 25 12
Mean . . .11 50 24.53
True time . 7 43 24
-1
0
Mean . . .12 06 38
True time . 7 59 39.1
+7
+7
0
378 04 46
+7
354 16 50
Chron.fast . 4 07 00.53
Chron.fast. 4 06 58.9
Observed Z.D. 63 00 4S
Ref. and Para I. + 1 41
Semidiam . . — 15 58
True Z.D. . . 62 46 31
Observed ZD. 59 02 48
Ref. and Paral. + 1 24
Semidiam . . —15 58
360 — 203 30 02 = 156
29 s's
O 0 1 It o
360-221 34 48= 138
25 12
TrueZ.D. . . 58 48 14
II. M. S.
.I"4 07 00.531 H- «• s-
Chronometer, Fast < >■ 4 06 59.7
14 06 58.9 J
September 23d P.M. ; Baiomcler 29 .97 ; Thermometer 86" ; Q'sU.L.
Cliioiioiiieter.
Level.
Reading?, &c.
Chronometer.
Level.
Readings, &c.
II. M, S.
8 23 04.4
8 84 35.6
8 26 IS
8 27 37.2
8 29 04.8
8 30 40
-2
+ 2
-3
+ 3
0
-5
0
0
0
0
0
-3
o / //
First Vernier 258 00 15
Second „ 257 59 40
Third „ 258 00 20
Fourth „ 257 59 40
H. M. S.
8 36 08
8 37 47.2
8 39 38
8 41 00.4
8 42 25.2
8 43 39.6
+2
+ 2
— 5
0
-4
0
+ 5
+4
-7
0
-2
0
o / //
First Vernier 319 31 35
Second „ 31 40
Third „ 31 50
Fourth „ 31 15
Mean ... 257 59 59
Index . . . + 14i 08 29
Level ... -4
Moan ... 319 31 35
Index . . . + 102 00 01
Level . . . —02.5
Mean . . . 8 26 53.33
True lime . 4 19 53.53
-5
-3
Mean . . 8 40 06.4
True time . 4 33 06
-5
0
-4
402 08 24
-2.5
421 31 34
Chron.fast . 4 06 59.8
Chron.fast . 4 07 00.4
Observed Z.D. 67 01 24
Ref. and Paral. +2 02
Semidiam . . +15 58
Observed Z.D. 70 15 16
Ref. and Paral. +2 26
Semidiam . . +15 58
360 - 215 51 31 = 144
08 29
360 - 257 59 59 = 102
00 o"i
True Z.D. . 67 19 24
TrueZ.D. . . 70 33 40
H. M. S.
U 06 59.81 H-"- s.
Chronometer, Fast < > 4 07 00.1
(4 07 00. 4J
IN THE LENGTH OF THE SECONDS PENDULUM.
91
1
September 24th A.M.; Barometer 30.01; Thermometer 81°,- O's L.L. 1
Ctironometer,
Level.
Readings, &c.
Ctironometei".
Level.
Readings, &c.
II. M. S.
11 25 40.8
11 27 01.6
11 28 41.6
11 30 31.2
11 32 34
11 33 57.2
+ 3
-3
0
-12
+2
+4
+3
-3
0
-11
+ 3
+ 5
O , II
First Vernier 7 56 10
Second „ 56 00
Third „ 56 10
Fourth „ 56 00
11. M. s.
11 39 00
11 40 16.8
11 42 17.6
11 43 40.8
11 45 16
11 46 46.8
-3
0
+7
-2
-4
+ 1
-2
0
+7
-1
— 2
+2
O / //
First Vernier 37 05 00
Second „ 05 00
Third „ 05 30
Fourth „ 05 00
Mean ... 7 56 05
In^.v J. J 40 28 25
loaex . • -I-J36Q 00 oO
Level .... - 4.5
Mean ... 37 05 07.5
Index . . .+352 03 55
Level ... +1.5
Mean. . . 1 1 29 44.4
True time. 7 22 41.83
-6
-3
Mean. . . U 42 53
True time . 7 35 50
-1
+4
- 4.5
408 24 25
+ 1.5
389 09 04
Chron. fast 4 07 02 . 57
Observed Z.D. 68 04 04
Ref. and Paral. + 2 08
Semidiam . . — 1 5 59
Cliron. fast 4 07 03
Observed Z.D. 64 51 31
Ref. and Paral. + 1 49
Semidiam . . — 15 59
28 25
360 - si 9 31 35 = 40
360 - 7 56 o's = 352 03 55
True Z.D. . . 67 50 13
True Z.D. . . 64 37 21
H. M. S.
■ f4 07 02.571 "•"• ^•
Chronometer, Fast < >■ 4 07 02.78
[4 07 03 J
1
September 25th A.M.; Barometer 30.01 ; Thermometer 80°; Q'sL.L.
Chronometer.
Level.
Readings, &c.
Cbronometer.
Level.
Readings, &c.
11. M. S.
11 22 18.8
11 23 46
11 25 13.2
11 26 17.2
11 28 36.8
11 29 46
0
0
0
+4
0
0
0
0
0
+ 3
0
0
o / ,/
First Vernier 91 01 45
Second „ 01 20
Third „ 01 45
Fourth ,, 01 10
H. M. s.
11 35 12
11 36 31.2
11 .'!7 50
11 33 04
11 40 21.2
11 41 34.8
-6
-5
+6
+ 2
0
0
-6
-4
+7
+3
0
0
o / ,/
First Vernier 126 46 00
Second „ 45 40
Third „ 46 20
Fourth „ 45 20
Mean ... 91 01 30
Index . . .+322 54 53
Level ... -+3.5
Mean ... 126 45 50
Index . . .+268 58 30
Level ... -1.5
Mean. . . 11 25 59.67
True time. 7 18 54
+ 4
+3
Mean. . . 11 38 25.53
True time . 7 31 19.4
-3
-0
+3.5
54 53
413 56 26
-1.5
395 44 19
Chron. fast 4 07 05.67
Observed Z.D. 68 59 25
Ref. and Paral. + 2 15
Semidiam . . — 15 59
Chron. fast 4 07 06.13
Observed Z.D. 65 57 23
Ref. and Paral. +1 55
Semidiam . . —IS 59
O O t 11 O
360 - 37 05 07 = 322
O 0 1 II o
360 — 91 01 30 = 268
/ //
58 30
True Z.D. . . 68 45 41
True Z.D. . . 65 43 19
H. M. S.
ll 07 05.671 "•"■ s.
Chronometer, Fast < > 4 07 05.9
1 (4 07 06.13/
■
N 2
92
EXPERIMENTS FOR DETERMINING THE V.\RIATION
)eterraination of the Rate of the Chronometer by Zenith Distances, continued.
September 26th A.M.; Barometer 30.00 ; Theimometer 81° ; 0'sL.L.
Cbronometer.
Level.
Readings, &c.
Cbronometer.
Level.
Readings, &:c.
H. M. S.
11 28 48
11 30 07.6
11 31 52.8
11 33 19.2
11 35 24
11 36 52.8
0
-7
+2
-3
+7
+ 1
0
-7
+2
-2
+ 8
+2
First Vernier 344 68 00
Second „ 07 50
Third „ 08 20
Fourth „ 08 00
H. M. S.
11 43 08
11 44 35.6
11 46 00
11 47 18.4
11 48 53.2
11 50 13.2
+ 3
0
0
0
+ 1
+ 1
+4
0
0
0
+2
+2
First Vernier 367 50 10
Second „ 50 00
Third „ 50 10
Fourth „ 50 00
Mean . . . 344 08 02.5
Index . . . +59 59 58
Level . . . +1.5
Mean ... 367 50 05
Index . . . +15 51 57.5
Level . . . +6.5
Mean. . . U 32 44.07
True time . 7 25 34.97
0
+ 3
Mean. . . 11 46 41.4
True time . 7 39 32.8
+5
+8
+ 1.5
404 08 01
+6.5
383 42 09
Chron. fast 4 07 09.1
Chron. fast 4 07 08.6
Observed Z.D. 67 21 20
Ref. and Paral. +2 04
Semidiam . . —16 00
Observed Z.D. 63 57 01
Ref. and Paral. +1 46
Semidiam . . —16 00
360-3o"o 00 02 = 59 5
9 s"s
36°0-344 08 o"2.5=15 s'l 57.5
True Z.D. . . 67 07 24
True Z.D. . . 63 42 47
H. M. S.
r 4 07 09.1 ) "• "• *•
Chronometer, Fast < > 4 07 08.85
I 4 07 08.6 J
Septer
iber 27th A.M. ; Barometer 30.01 ; Thermometer 80° ; Q's L.L.
'_ Chronometer.
Level.
Reading?, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
11 31 18
11 32 53.6
11 34 25.6
11 35 34.4
11 37 10.8
11 38 12.4
0
+ 3
+2
+ 5
-2
-3
0
+ 2
+ 1
+ 4
-1
-3
o . „
First Vernier 196 o7 20
Second ,, 37 20
Third „ 37 50
Fourth „ 37 20
H. M. S.
11 42 44
11 43 40.8
11 45 04.8
11 46 20
11 47 40
11 48 42
0
+8
0
-3
0
-2
0
+ 8
0
— 3
0
-2
O / „
First Vernier 221 52 40
Second „ 52 40
Third ,, 53 00
Fourth ,, 52 10
Mean ... 196 37 27.5
Index . . .+204 22 29
Level ... +4
Mean . . 221 52 37.5
Index . . . + 163 22 32.5
Level ... +3
Mean. . . 11 31 55.8
True time. 7 27 43.6
+ 5
+ 3
Mean. .. 11 45 41.93
True time . 7 38 29.8
+ 3
+ 3
+4
401 00 00
+ 3
385 15 13
Chron. fast 4 07 12.2
Chron. fast 4 07 12.13
Observed Z.D. 66 50 00
Rcf. and Paral. +2 00
Semidiam . . — 16 00
Observed Z.D. 64 12 32
Ref. and Paral. +1 46
Semidiam . . -16 00
360-155 37 3'l = 204
22 29
360-19°6 37 27.5 = 16°3
22 32.5
True Z.D. . . 66 36 00
True Z.D. . . 63 58 18
11. M. S.
[4 07 !2.2 1 "•"• s-
Chronometer, Fast < > 4 07 12.16
14 07 12.I3J
IN THE LENGTH OP THE SECONDS' PENDULUM.
93
Trinidad. Determination of the Rate of the Chronometer by Zenith Distances, continued.
September 28th A.M. ; Barometer 29.97 ; Thermometer 81° , Q's L.L.
Chronometer.
H. M. s.
11 58 50.8
12 00 01
12 01 53.2
12 03 31.6
12 05 00
12 06 08.8
Mean . , .
True time .
12 02 34.73
7 55 19.2
Chron. fast 4 07 13.53
Level.
0
+2
+ 2
0
0
-4
0
0
+ 2
+2
0
0
-4
0
.360-113 41 32.5 = 246 18 27.5
Readings, &c.
First Vernier 114 27 00
Second
Third
Fourth
Mean .
Index .
Level .
26 45
27 10
26 50
. 114 26 59
.-t-216 18 27.5
0
360 45 26
Observed Z.D. 60 07 34
Ref.andParal. +1 27
Semidiam . . — 16 00
True Z.D.
59 53 01
Clironometer.
H. M. s.
12 10 34.8
12 11 46.8
12 13 15.2
12 14 36
12 16 10
12 17 20
Mean ■ . .
True time .
12 13 57.13
8 06 41.17
Chron. fast 4 07 15.96
Level.
0
4
7
+6
-7
+ 2
0
-2
-6
+ 7
-6
+ 1
360-114 26 59 = 215 33 01
Readings, &c.
First Vernier
Second ,,
Third „
Fourth ,,
98 40 40
40 20
40 SO
40 20
Mean
Index
Level
98 40 32.5
.+245 33 01
-8
344 13 25
Observed Z.D. 57 22 14
Ref.andParal. +1 17
Semidiam . . - 16 00
True Z.D.
57 07 31
f4 07 15.531 "• »'■ s.
Chronometer, Fast < > 4 07 15.75
i4 07 15.961
September 29th A.M. ; Barometer 30.03 ; Thermometer 81° j © 's L.L.
Clironometer.
Level.
H. M. S.
11 45 35.2
11 47 10
11 48 29.2
11 49 49.2
11 51 12
II 52 13.2
Mean . . ,
True time .
11 49 05.8
7 41 46.73
Chron. fast 4 07 19.13
+ 3
0
-3
-2
+2
-2
+ 3
0
-3
-2
+ 2
-2
360-98 40 33 = 261 19 27
Headings, &c.
First Vernier 119 13 00
Second
Third
Fourth
Mean .
Index .
Level .
12 30
13 20
12 30
. 119 12 55
.+261 19 27
-2
380 32 20
Observed Z.D. 63 25 23
Ref.andParal. +141
Semidiam . . +16 00
True Z.D.
63 II 04
Chronometer.
Level.
H. M. S
11 59 30
12 00 47.2
12 02 20
12 03 33.2
12 04 59.2
12 05 59.2
Mean . . .
True time ,
12 02 51.47
7 55 32.1
Chron. fast 4 07 19.37
— 3
0
-5
-3
-2
+ 6
-2
0
-5
-2
-1
+7
Re.idi.ng3, &c.
First Vernier 119 43 20
Second
Third
Fourth
43 00
43 40
43 10
Mean .
. 119 43 17.5
Index .
.+240 47 05
Level .
— 5
360 30 17
360-119 12 55 = 240 47 05
Observed Z.D. 60 05 OS
Ref.andParal. +1 27
Semidiam . . +16 00
True Z.D.
59 50 30
II. M. S.
f4 07 19.131 "• "■ «•
Chronometer, Fast < > 4 07 19.25
14 07 19.37J
94
EXPERIMENTS FOR DETERMINING THE VARIATION
TaiNIDAD.—
I^ptprminatirm nf thp R.atp nf tlip rihrnnnrnpfpr hv Zpnith Dista
nr^« rn»/jn.wp//. 1
1
September 29th P.M.; Barometer 29 . 97 ; Thermometer 85°; 0'sU.L.
Clirononictcr.
Level.
Readings, &c.
Chronometer.
Leveh
Readings, &c.
H. M. S.
7 M 54.8
7 36 30
7 37 51.6
7 39 07.6
7 41 04.8
7 42 04.4
+3
0
0
+ 2
+ 3
+ 1
+2
0
0
+ 1
+4
+3
First Vernier 96 53 30
Second „ 53 10
Third „ 53 50
Fourth ,, 53 10
H. M. S.
7 50 10
7 51 06.8
7 52 30
7 53 43.6
7 55 03.2
7 56 16
0
+2
+5
-2
-8
-4
0
0
+7
0
-6
-2
0 ' '4
First Vernier 95 12 50
Second „ 12 20
Third „ 13 00
Fourth ,, 12 10
Mean ... 96 53 25
Index . . . + 240 16 50
Level . . . +6.5
Mean.. . . 95 12 35
Index . . .+263 06 35
Level ... -4
Mean. . . 7 38 35.53
True time. 3 31 15.2
+5
+ 8
Mean. . . 7 53 08.27
True time . 3 45 48.67
-7
- 1
+ 6.5
6 SO
337 10 21
-4
358 19 06
Chron. fast. 4 07 20.33
Chron- fast 4 07 19.6
Observed Z.D. 56 11 43
Ref. and Paral. +1 13
Semidiam. . +16 00
Observed Z.D. 59 43 1 1
Ref. and Paral. +1 27
Semidiam . . +16 00
3r0-119 43 10 = 210 1
36°0-96 S3 25 = 26°3 06 35
True Z.D. . . 56 28 56
True Z.D. . . 60 00 38
H. M. S. ^ ^ ^
Chronometer, Fast j'* "'' 20.33| ^ ^^- j^ gg
U 07 19.6 j
September 30th A.M. ; Barometer 30.01 ; Thermometer 81°; O'sL.L.
^Chronometer.
Level.
Beadings, &c.
Chronometer.
Level.
Readings, &c.
11. »I. .s.
11 20 52
1 1 22 02
11 23 38.4
11 24 41.2
11 26 12.8
11 27 56.4
+7
+ 3
0
+ 5
-3
+2
+ 6
+ 2
0
+ 5
-3
+ 2
First Vernier 152 07 20
Second „ 7 20
Third „ 8 10
Fourth „ 7 40
H. M. s.
11 32 18.4
11 33 33.6
11 35 08.8
11 36 23.6
11 37 54.8
11 39 00.8
0
+2
-3
+ 7
-4
0
0
+3
-2
+7
-4
0
0 . /.
First Vernier 192 17 40
Second „ 17 30
Third „ 18 00
Fourth „ 17 20
Mean ... 152 7 37.5
Level . . . +13
Index . . .+264 47 25
Mean ... 192 17 37.5
Level ... +3
Index . . .+207 52 22.5
Mean. . . 11 24 13.8
True time. 7 16 52
+ 14J+12
Mean. . . 1 1 35 43.33
True time. 7 28 20.8
+2
+4
+ 13
47 25
416 55 14
+ 3
400 10 03
Chron. fast. 4 07 21.8
Chron. fast. 4 07 22.53
Observed Z.D. 69 29 12
Ref. and Paral. +2 18
Semidiam . . -16 00
Observed Z.D 66 41 40.5
Ref. and Paral. +1 59.5
Semidiam . . - 16 00
S60-95 12 35=264
36°0-152 07 37.5 = 207
52 22.5
TiueZ.D. . . 69 15 30
True Z.D. . . 66 27 40
1
H. M. S.
f A 07 91 ft 1 **• "• ^■
Chronometer, Fast <■ ' " '^' ■" j. 4 07 22. 16
i.4 07 22.5SJ
IN THE LENGTH OF THE SECONDS* PENDULUM.
95
Trinidad. Deterraiuation of the Rate of the Chronometer by Zenith Distances, continued.
October 1st A.M. ; Barometer 30 OS; Thermometer 81° ; 0'sL.L.
Chronometer.
Level.
Readings, &c.
Clironometer.
Level.
Readings, &c.
II. M. S.
n 46 58
II 48 09.6
11 50 24.8
11 51 29.2
II 52 48
11 53 54
0
+ 1
-3
+ 3
— 3
+ 2
Mean . .
True time
11 50 37.27
7 43 12.1
+ 3
0
+ 5
— 2
+2
-I
+ 3
First Vernier 316 15 50
+7
Second
Third
Fourtli
Mean .
Level .
Index .
15 50
16 10
15 40
.316 15 52.5
+0.5
+62 20 00
H. M. S.
11 57 19.2
11 58 32
12 00 03.6
12 01 20
12 02 53.6
12 04 18
-3
+4
4
+2
-2
+ 6
378 35 57.5
Mean . .
True time .
12 00 44.4
7 53 19.6
+ 3
-2
+5
-3
+ 3
-0
r 8
First Vernier. 320 09 10
+ 11
Second
Third
Fourth
Mean .
Level .
Index .
09 20
09 50
03 20
Chron. fast. 4 07 25.17
S60 - 297 40 00 = 62 20 00
Observed Z.D. 63 05 59.6
Rcf.andParal. + 1 40.4
Semidiam . . — 16 01
Chron. fast. 4 07 24.8
+7
32D 09 25
+ 7
+43 44 08
3G3 53 40
360 - 316 15 52 = 43 44 08
Observed Z.D. 60 38 57
Ref. and Paral. +1 2S
Semidiam . . -16 01
True Z.D.
62 51 39
True Z.D. .
60 21 21
ni, . V , [4 oV 25.171 "•",' ^
Chronometer, Fast J -i n-r o
l4 07 24.8 I
4 07 24.98
October .3d .\.M.; Barometer 30 . 02 ; Thermometer 81° ; Q's L.L.
Chronometer.
H. M. S.
11 52 25.6
11 53 31.2
11 55 0 J
11 56 01.4
11 57 46.4
11 58 51.2
Mean . .
True time
.11 55 36.63
. 7 48 01 87
Chron. fast. 4 07 31.76
+3
+3
0
0
0
+5
0
0
+5
+4
360 - 319 01 05 = 40 58 55
Readings, &c.
First Vernier
Second „
Third ,,
Fourth „
Mean .
Index .
Level . . .
Observed Z.D.
Ref. and Paral
Semidiam . .
True Z.D. . .
330 44 30
44 20
45 00
44 10
330 44 30
+ 40 58 55
+ 4
371
43
29
61
57
15
. + 1
35
16
01
61
42
49
Ctironometer.
H. .M. S.
12 02 35.2
12 03 53.2
12 05 26.4
12 06 40.2
12 07 56.4
12 09 10.4
Mean . .
True time.
12 05 56.97
7 58 25.3
Chron. fast.. 4 07 31.67
Readings, &c.
-4
0
-5
+ 7
-4
0
-4
+ 7
2
0
+ 3
360- 330 44 30 = 29 15 30
First Vernier 327 30 20
Second „ 30 10
Third „ 30 40
Fourth ,, SO 10
Mean . . . .'i27 30 20
Index . . . +29 15 3tJ
Level ... — 4
336 45 46
Observed Z.D. 59 27 38
Ref. and Paral. + 1 26
Semidiam . . -16 02
True Z.D. .. 59 13 02
H. M. S.
f4 07 31.781 "• "• s-
Chronometer Fast < > 4 07 31.71
14 07 31.67J
96
EXPERIMENTS FOR DETERMINING THE VARIATION
Trinidad.-
Determination of the Rate of the Chronometer by Zenith Distances, continued.
October4th A.M.; Barometer 30.03; Thermometer 81°; Q'sL.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
11 43 03.2
11 44 43.2
11 46 21.6
11 47 38
11 49 26.4
11 51 14.8
+ 3
0
-4
-2
+4
+6
+2
0
-4
-2
+4
+ 6
First Vernier 91 17 30
Second „ 17 20
Third „ 18 00
Fourth „ 17 30
H. M. S.
11 56 06.4
11 57 24.4
U 59 06.6
12 00 25.6
12 02 03.2
12 03 21.2
0
0
0
0
0
0
0
0
0
0
0
0
o , <l
First Vernier 97 14 50
Second „ 14 30
Third „ 14 50
Fourth „ 14 40
Mean ... 91 17 35
Index . , .+292 59 01
Level . . . +6.5
Mean. ... 97 14 42.5
Index . . . +268 42 25
Level. ... 0
Mean. . . 11 47 04.53
True time. 7 39 30.07
+7
+ 6
Mean. . . 12 59 44.57
True time . 7 52 09.97
0
0
+6.5
9 o"l
384 16 42
0
363 37 07.5
Chron. fast. 4 07 34 . 46
Chron. fast.. 4 07 34.6
Observed Z.D. 64 02 47
Rof. and Paral. +1 45
Semidiam . . —16 02
Observed Z.D. 60 59 31
Ref. and Paral. + 1 SI
Semidiam. . . —16 02
360- 67 00 5'9 = 292 5
360 - 91 17'35= 268
42 25
True Z.D. . . 63 48 30
True Z.D. . .60-15 00
H. M. S.
Chronometer. Fast l* "^ 34.461^ 4*07' 34.53
14 m 34.6 j
October 4th P.M. ; Barometer 29 .96 ; Thermometer 81°; 0 's U.L.
Chronometer.
Level.
Readings, &:c.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 19 48
8 21 19.2
8 22 55.2
8 24 16
8 25 58.8
8 27 27.2
-2
-3
+ 2
0
-4
-1
0
-1
0
0
— 2
0
O 1 "
First Vernier 144 32 50
Second „ 32 40
Third „ 33 00
Fourtli „ 32 30
H. M. S.
8 33 20
8 34 37.6
8 36 23.2
8 38 15.6
8 39 49.6
8 41 04.8
+ 1
+2
-5
-6
-5
+4
+4
0
-3
-4
-3
+ 1
O , /,
First Vernier 211 41 25
Second „ is
Third „ 55
Fourth „ 05
Mean ... 144 32 45
Index . . .+262 45 18
Level . . . —5.5
Mean ... 211 41 25
Index . . .+213 27 15
Level ... _9
Mean . . 8 23 37.4
True time. 4 16 02.6
-8
-3
Mean. . . 8 37 15.13
True time. 4 29 40.8
-13
— 5
-5.5
5 18
407 17 57
-9
427 08 31
Chron. fast 4 07 34 . 8
Chron. fast. 4 07 34.33
Observed Z.D. 67 53 00
Ref. and Paral. +2 06
Semidiam . . +16 01
Observed Z.D. 71 11 25
Ref. and Paral. +2 30
Semidiam . . +16 02
»60-9''7 14 4'2 = 262 4
360—144 32 4'5 = 2l'5 2
7 15
True Z.D. . . 68 11 07
TrueZ.D. . . 71 29 57
U. M. S.
ft 07 ^S fi ) "■ ^'* ^*
Chronometer, Fast <■ * " ^'^ > 4 07 34.56
i4 07 34.33J
IN THE LENGTH OP THE SECONDS* PENDULUM.
97
RATE DEDUCED from the PRECEDING OBSERVATIONS.
Dale.
S.
D.ile.
S.
Dale.
S.
Date.
S.
Dale.
S.
A.M. to A.M.
Sept. 21 to 26
3.03
Sept. 25 to 30
3.25
Sept. 27 to 29
3.54
Sep.29toOc.3
3.11
Sept. 23 to 21
3. OS
27
3.13
„ Oct. 1
3.18
30
3.33
4
3.05
25
3.10
28
3.24
3
3.23
„ Oct. 1
3.20
„ oOtoOc. 1
2.82
26
3.05
29
3.29
4
3.18
3
3.26
3
3.18
27
3.11
30
3.23
Sept. 26 to 27
3.31
4
3.20
4
3.09
28
3.21
„ Oct. 1
3.17
„ 28
3.23
Sept. 28 to 29
3 50
Oct. 1 to 3
3.36
29
3.26
3
3.21
29
3.47
30
3.20
4
3.18
30
3.21
4
3.17
30
3.33
„ Oct. 1
3.07
Oct. 3 to 4
2.82
„ Oct. 1
3.16
Sept. 25 to 26
2.95
„ Oct. 1
3.23
» 3
3.19
P.M. to P.M.
3
3.20
., 27
3.13
3
3.27
n 4
3.13
Sept. 23 to 29
3.31
4
3.16
28
3.28
4
3.21
Sept. 29 to 30
2.91
„ Oct. 4
3.13
Sept. 24 to 25
3.12
29
3.34
Sept. 27 to 28
3.59
,, Oct. 1
2.87
Sep.29toOc.4
2.92
Means . . .
3.15
3.18
3.29
3.20
3.09
Gaining 3. 19 Seconds per Diem.
98
EXPERIMENTS FOR DETERMINING THE VARIATION
TuTTVTT^AT^ Pfi m nn r 1 dm 1 «: of ilif* Astrnnomical Clock with the Chronometer No. 423.
from the 23d of September to the 4th of October, 1822 ; with the Clock's Rate
on Mean Solar Time deduced.
1822.
Chronometer.
Clock.
Clock's Loss on 423.
DAILY RATES. 1
Chron.
Clock.
11. M. s.
11. M. S.
Gaioiog.
Losing.
Sept. 23 p. M.
S 33 15.2
1 '
\ 127
„ 24 P. M.
8 31 OS. 2
\ 127.2
[ 127
„ 25 P. M.
S 29 01
s.
s.
S
. 127.06
3.19
123,87
„ ^Q P. M.
8 26 54
J
. 127.1
„ 27 P. M.
S 24 45.9
. 127
„ 2S P. M.
8 22 39.9
■ 9 10 00 .
■ 127.1]
„ 29 P. 31.
8 20 32.8
■ 127
„ 30 P. M.
8 IS 25.8
127.1
Oct. 1 P. M.
8 16 18.7
• 127.1
• 127.12
3.19
123.93
„ 2 P. M.
8 14 11.6
■ 127.2
„ S P. M.
8 12 04.4
■■
„ 4 P. M.
8 09 57.2
. 127.2
IN THE LENGTH OF THE SECONDS' PENDULUM.
99
Teinidad. COINCIDENCES OBSERVED with PENDULUM No. 3 ; the Clock makiu<r
86276. 13 Vibrations in a Mean Solar Day.
O 2
100
EXPERIMENTS FOR DETERMINING THE VARIATION
Trinidad. COINCIDENCES OBSERVED with PENDULUM 4 ; the Clock
making
86276 . 13 Vibrations in a Mean Solar Day.
DATE.
Baio
meter-
No.
of Co.
inci-
dence.
Tempe-
rature.
Time of
Disap-
pearauce.
Time of
Re-ap-
pearaDce.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
lotervat.
Correc-
tion for
tUeArc.
Vibrations
in 24 hours.
Reduc-
tion to a
Mean
Tempe-
rature.
Reduced
Vibrations at
83.35 1 >.ht.
1822.
IN.
r
1
o
83
M. S.
29 37
M. s.
29 42
H. M. s.
10 29 39.5
o
!.2
0
0
S.
-f
Sept. 29 A.M.
30.010
f
11
1
83,2
S3
20 29
42 36
20 41
42 41
12 20 36.5
12 42 38.5
0.58
1.18]
83.1
665.7
1.26
86018.16
-0.10
86018.06
„ 29 P.M.
29.990.J
11
1
83.6
83.3
33 24
19 49
33 38
19 53
2 33 31
8 19 51
0.5SJ
1.22]
83.3^
665.25
i.22
86017.96
-0.02
86017.94
„ 30 A.M.
30.15oJ
11
1
83.3
83 S
10 31
41 18
10 47
44 22
10 10 39
2 44 20
O.62J
i.isl
0.58 J
83.3
661.8
1.31
86017.87
-0.02
86017.85
„ SO P.M.
29.97oJ
83.7
665.1
1.21
86017.89
-fO.15
86018.01
11
83.6
35 Ot
35 18
4 35 11
r
1
83
36 34
36 38
8 36 3G
i.is]
Oct. 1 A.M.
30.050<!
-
83.25
665.5
1.22
86018 04
-0.04
86018.00
11
83.5
27 23
27 37
10 27 31
0.58]
,
83.3
47 22
47 27
2 47 24.5
1.221
0.62]
„ 1 P.M.
29.980y
83.15
665.55
1.34
86018.16
-0.08
86018.08
11
83
38 !1
38 29
4 38 20
1
83
20 41
20 45
10 20 43
1.2 1
„ 2 A.M.
30.020.
>
83.5
665.1
1.28
86017.96
-1 0.06
86018.02
'
11
84
01 25
01 43
12 01 34
0.6 J
1
83
12 28
12 34
10 12 31
i.is]
„ 3 A.M.
30.020.
■
83.5
665.35
1.22
86017.98
-i-0.06
86016.04
11
81
3 17
3 32
12 3 24.5
0.58
1
83 2
14 01
14 07
I 14 01
1.18
„ 3 P.M.
30.020
>
I
83.3
GC5.45
1 22
86018.02
-0 02
86018.00
u
S3. 1
4 49
5 OS
3 4 58 5
0.58J
Means . .
30.023
83.35
86018.00
86018.00
IN THE LENGTH OF THE SECONDS' PENDULUM. 101
JAMAICA.
The Pheasant arrived at Jamaica on the 17th of October, when her
repairs were immediately proceeded in at the Dock Yard at Port
Royal, and ordered to be completed with all despatch, by Admiral
Sir Charles Rowley, commanding on the station ; it appearing, however,
on examination, that her refittal would require a detention of three weeks,
as she had been betw^een three and four years within the tropics, I availed
myself of the opportunity to determine the rates of the pendulums.
I was so fortunate as to obtain a house at Port Royal exceedingly well
adapted for the purpose, which was lent me by my friend Major William
Nicolls of the Royal Artillery, to whom it belonged in quality of acting
Governor of Fort Charles, but was at that period unoccupied, as Major
Nicolls was also in the temporary charge of the Quarter Master General's
Department, and resided at the Head Quarters of the forces at Kingston.
The proceedings at Port Royal differed in no respect from those at
the three preceding Stations : the Pendulums were in a room on the
ground floor, which was kept carefully closed and darkened, and in which
the temperature was consequently very uniform. October is accounted
one of the rainy months at Jamaica; but the rains at that part of the
season are not continuous, and proved no serious interruption to the
observations with the Repeating Circle. The yellow fever was prevalent
during our stay amongst the troops in Port Royal, and the daily deaths
were deemed considerable, even in Jamaica, in proportion to the strength
of the Garrison ; they certainly appeared very considerable to persons
unhabituated to the great and almost unceasing mortality of the West
102 EXPERIMENTS FOR DETERMINING THE VARIATION
India Islands ; happily the fever did not communicate itself to the
Pheasant, and she quitted Jamaica without] a single instance of its ap-
pearance amongst her crew.
Fort Charles is built on a calcareous rock, nearly on a level with the
surface of the sea, and at the extremity of the tongue of sand which forms
the harbour of Kingston, and on which Port Royal is situated. The
height of the pendulums above half tide, was nine feet.
The Pheasant's repairs being completed, she sailed under Sir Charles
Rowley's orders for Havanna, on the 6th of November, in convoy of
several British and American merchant vessels, as a protection against
the Pirates who infested the shores of Cuba ; and from Havanna she
proceeded to New York.
IN THE LENGTH OP THE SECONDS' PENDULUM.
103
Ta Af ATTA ORS'^RVATTrnvs; *^ t^ftfrmtatf *Iio pj att? ..r iU^ nu^r.
r,,„v.ofn,. 1V„ Aai U„ '7r"VTlT{I \
1 DISTANCES
of the Sun, with a Repeating Circle, from the 22d to the 30th of October, 1S22.
Latitude of the Place of Observation 17° 55' 55" N. ; Longitude 7f.° 54' W.
October 22d, A.M.; Barometer 30.05; Thermometer 80°; Q'sL.L. 1
Chronometer.
Luvel.
Readings, &c.
Chronometer.
Level.
Readings, &c.
II. M. S.
1 14 14
1 15 14.8
1 16 40.4
1 18 02
1 19 34.4
1 20 49.2
1 21 56.4
1 23 13.6
0
0
0
— 5
+ 10
+2
+2
+ 3
0
0
0
-i
+ 10
+1
+2
+2
+ 11
0 . ..
First Vernier 126 40 30
Second „ 40 10
Third „ 40 30
Fourth ., 40 10
H. M. S.
1 SI 13.6
1 32 27.6
1 33 37.2
1 34 57.6
1 S6 31.6
1 38 04.8
1 39 12
1 40 44
1 42 24.4
1 43 38.4
0
-2
+2
-2
-4
-2
+2
+5
+5
— 2
0
-2
+2
-3
-1
+2
+4
+4
-3
C 4 l»
First Vernier 33.5 15 50
Second „ _15 30
Third „ 15 50
Fourth ,, 15 K>
Mean ... 126 40 20
Index . . .+360 00 08.5
Level . . . +11.5
Mean. ... 335 15 42.5
Index. . . . 233 19 40
Level. ... 0
486 40 40
568 35 22.5
Mean. . . 1 18 43.1
True time. 8 08 52.57
+ 12
Observed Z.D. 60 50 o4
Ref.and Paral. + 1 29
Semidiam. . . —16 07
Mean. . . 1 37 17.1
True time. 8 27 26.37
+2
-2
Observer} Z.D. 56 51 32
Ref. and Paral. + 1 16
Semidiam. . . —16 07
+ 11.5
n
Chron. fast. 5 03 50.5.3
Chron. fast. 5 OS 50.74
True Z.D. . . 60 35 26
360 - 126 40 20 = 233 19 40
True Z.D. . . 56 36 41
II. H. S.
fS 09 50.531 H. M. s.
Chronometer, Fast I , „„ „ „ f'S 09 50.63
V5 09 50.74J
October 22d, P.M. ; Barometer 30.01 ; Thermometer 83°; 0'sU.L.
ChroDoraeter.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
9 21 46.4
9 23 06
9 24 41.2
9 26 09.2
9 27 27.6
9 28 28.8
+4
-2
+2
0
+3
-3
+3
-3
+ 1
0
+2
-4
o # »
First Vernier 74 1 1 30
Second „ 1! 15
Third „ 11 40
Fourth „ 11 00
H. M. s.
9 32 10
9 34 24.8
9 35 55.2
9 37 27.2
9 39 12.8
9 40 26.8
0
0
0
0
0
+2
0
0
0
0
0
+2
o , H
First Vernier 161 41 45
Second „ 41 30
Third „ 45 00
Fourth ,, 44 .30
Mean. ... 74 11 21
T„j.>, _L 5 1 00 00
Index. . +|3goOO 00
Level. ... +1.5
Mean. ... 164 44 41
Index. . . +2S5 48 39
Level. ... -2
Mean ... 9 25 16.53
True time . 4 15 24.2
+4
-I
Mean. . . 9 36 36.13
True time. 4 26 44.1
+ 2
+2
+ 1.5
435 11 23
+ 2
450 33 22'
Chron. fast . 5 09 52.33
Chron. fast. 5 09 52.03
Observed Z.'i>. 72 31 54
Ref.and Paral. + 2 42
Semidiam. . . +16 07
Observed Z.D. 75 05 34
0 0 / // 0
360-74 11 21=285 4
8 39
Ref.and Paral. + 3 14
Semidiam. . . +16 07
True Z.D. . . 72 50 43
True Z.D. . . 75 24 55
H. M. S.
rs 09 52.33] II. M. s.
Chronometer, Past <^ ^^ ^^.Osl ' "^ ^^''^
104
EXPERIMENTS FOR DETERMINING THE VARIATION
r
eter
til "ni^-irinr^oc- «^ii/;«,/«^ 1
.„„„.„ of ,he R..e or,he Ct™.n.e.„ b, Ze ™. ,
October 23(1 A.M.; Barometer 30.06; Thermometer 80°; Q'sL.L.
Ctironometer.
Level.
Readings, &c.
Chronometer.
Level.
Beading?, &c.
H. M. S.
00 30 31.4
00 41 32
00 43 38.8
00 45 04.4
00 48 42.8
00 50 09.6
0
0
0
+3
0
0
0
0
0
+2
0
0
0 * "
First Vernier 215 15 50
Second „ 15 40
Third „ 16 00
Fourth „ 15 40
H. M. S.
00 55 21.6
00 57 36.4
00 59 22.8
01 00 53.6
01 02 49.6
01 04 12.4
-4
+4
0
0
+ 2
0
-4
+ 4
0
0
+ 1
0
0 , t4
First Vernier 245 33 40
Second „ 33 30
Third „ 34 00
Fourth „ 33 20
Mean ... 213 15 48
Index . . . + 195 13 20
Level ... +2
Mean ... 245 33 38
Index . . . + 144 44 12
Level ... +1.5
Mean . . . 00 44 47
True time . 7 34 52.57
+3
+2
Mean. . . 01 00 02.73
True time . 7 50 08.2
+2
+ 1
+2.5
15 20
410 31 10
+ 1.5
390 17 51
Chron. fast 5 09 54.43
Chron. fast 5 09 51.53
Obsened Z.D. 68 25 12
Ref. and Paral. +2 10
Semidiam . . —16 07
Observed ^.D. 65 02 58
Ref. and Paral. + 1 49
Semidiam . . — 16 07
O 0 * // o
360—164 44 40=193
360-215 15 48= 1*44
I'-l Vi
True Z.D . " 68 1 1 13
True Z.D. . . 64 48 40
Chronometer Fast .; ^ ""^ •'■••'-■>. 5 09 54. !8
1.3 09 54.33J
October 2.3d P.M.; Barometer 30.02 ; Thermometer 83°; Q 's U.L.
Cbrouonieter.
Level.
ReadiDgs, &.C.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 43 28
8 47 29.4
8 49 32
8 51 11.6
8 52 58
8 53 08
0
-6
0
0
0
0
0
-6
0
0
0
0
0 ' «
First Vernier 288 23 10
Second „ 23 10
Third ,, 23 40
Fourth ,, 23 00
U. M. S.
9 06 21.2
9 08 30.8
9 10 28.8
9 11 56.4
9 13 53.6
9 16 03.2
0
+4
0
+2
+5
0
0
+4
0
+2
+5
0
0 ^ //
First Vernier 345 33 50
Second „ 33 40
Third „ 34 00
Fourth „ 33 30
Mean ... 288 23 15
Index . . . + 100 59 35
Level ... -6
Mean ... 345 33 43
Index . . . +71 36 45
Level ... +11
Mean. . . 8 50 17.83
True time . 3 40 21.33
Chron. fast 5 09 S6.5
-6
-6
Mean. . . 9 11 12.33
True time . 4 01 15.7
+ 11
+ 11
-6
59 35
389 22 44
+ 11
417 10 41
Chron. fast 5 09 56.63
Observed Z.D. 64 53 47
Ref. and Paral. + 1 48
Semidiam . . +16 07
Observed Z.D 69 31 47
Ref. and Paral. + 2 18
Semidiam . +16 07
360-259 00 25=100
360-288 23 l5 = 7'l Z
6 45
True Z.D. . . 65 1 1 42
True Z.D. . . 69 SO 12
Chronometer Fast P 09 56.5 1^ j" ^g jg ^g
l5 09 56.63J
IN THE LENGTH OF THE SECONDS PENDULUM.
lOc
Jamaica.—
-^Determination of the Rate of the Chronometer by Zenith Distances, continued.
October 24lh P.M.; Barometer 30 . 0 1 ; Thermometer 84° ; O'sU.L.
Chronometer.
Level.
Re.iding3, &:c.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 22 20.8
8 23 48.4
8 26 12.4
8 27 37. C
8 29 52.8
8 31 02
-3
0
+5
+2
0
+ 6
-3
0
+ 5
+ 3
0
+ 5
0 / "
First Vernier 345 21 50
Second ,, 22 00
Third „ \ 22 10
Fourth ,, 21 40
H. M. S.
8 42 08.8
8 43 44
8 45 36
8 47 03.2
8 48 39.6
8 50 37.6
0
-2
+5
0
■hio
0
0
-2
+7
0
+ 10
0
Of/*
First Vernier 25 07 35
Second ,, 07 20
Third „ 07 50
Fourth „ 07 15
Mean . . . .345 21 55
Index . . . +14 26 15
Level .... +9
Mean .... 25 07 30
1°-^- • ■ +I36O 00 00-'
Level .... +14
Mean ... 8 26 49
True Time. 3 16 48.1
+8
+ 10
Mean. . . 8 46 18.2
True time. 3 36 16.8
+ 13
+ 15
+9
26 15
359 48 19
+ 14
385 07 52
Chron.fast. 5 10 00.9
Chron. fast. 5 10 01.4
Observed Z.D. 59 58 03
Ref. and Paral. + 1 26
.Semidiam . . +16 07
Observed Z.D. 64 11 17
Ref. and Paral. + 1 35
Semidiam . . +16 07
360 - 345 33 45 = H
True Z.D. . . 60 15 36
True Z.D. . . 64 28 59
H. M. S.
Chronometer, Fast 1^ "^ '"^•"]. s'lo'oi'.lo
1,5 10 01. 4j
October 25th P.M.; Barometer 30.02 ; Thermometer 83°; Q's U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 28 14
8 30 46
8 32 37.2
8 34 14
8 36 14.8
8 37 56.4
0
+ 3
+5
0
+5
— 3
0
+4
+ 5
0
+ 5
— 2
0 . //
First Vernier 34 24 40
Second „ 24 20
Third „ 24 50
Fourth ,, 24 20
11. M. S.
8 42 25.6
8 43 58.8
8 45 43.2
8 47 25.2
8 49 13.6
8 50 31.6
0
-3
— 3
0
-2
-6
0
-3
2
0
-3
6
0 / */
First Vernier 60 52 40
Second „ 52 00
Third „ 52 45
Fourth „ 52 10
Mean . . . . 34 24 32
Index . . .+334 52 30
Level .... +12.5
Mean .... 60 52 24.5
Index . . .+325 35 28
Level .... —8.5
Mean. . . 8 33 20.4
True time. 3 23 16.17
+ 11
+12
Mean ... 8 46 33
True time . 3 36 28.73
-8
-9
+ 11.5
369 17 14
-8.5
386 27 43
Chron. fast. 5 10 04.23
Chron. fast. 5 10 01.27
$'2 3
— —
Observed Z.D. 61 32 52
Ref. and ParaL + 1 29
Semidiam . . +16 07
Observed Z.D. 64 24 37
Ref. and Paral. + I 43
Semidiam . . +16 08
360 — 2°5 07 .30 = 334
0
360-34 24 32 = 32°5 ;
J5 28
True Z.D. . . 61 50 28
True Z.D. . . 64 42 28
H. M. S.
Chronometer, Fast 1^ "^ 04.23|_ ^ jj ^^^ ^5
1.5 10 04.27J
106
EXPERIMENTS FOR DETERMINING THE VARIATION
Jamaica. Determination of the Rate of the Chronometer by Zenith Distances, continued.
Octobei-26tli A.M.; Barometer 30.06 ; Thermometer 80° ; Q's L.L.
Cbronometer.
Level.
Rcadiogs, &c.
Cbronometer.
Level.
Readings, &c.
H. M. S.
1 23 46.8
I 25 19
1 27 28
1 29 04.8
1 30 5G
1 .32 33.6
0
-8
0
n
-2
0
0
-9
0
0
-2
0
0 / /'
First Vernier 65 57 15
Second „ 57 10
Third „ 57 50
Fourth „ 57 15
il. M. S.
1 36 52.8
1 38 18.8
1 40 02
1 41 51.6
1 44 20.8
1 46 02.4
+0
-3
+5
+ 5
+ 2
+-5
0
-2
+ 6
+5
+ 1
7
First Vernier 46 08 00
Second „ 07 40
Third „ 08 10
Fourth „ 07 30
Mean ... 65 57 22.5
Index . . .+290 39 15
Level ... -10
Mean ... 46 07 55
Index . . .+294 02 37.5
Level . . . +15.5
Mean. . . l 28 11.37
True time . 8 18 04.3
-10
-11
Mean. . . 1 41 14.73
True time . 8 .SI 07.9
+ 14
+ 17
-10.5
356 S6 27
+ 15.5
340 10 48
Chron. fast 5 10 07.07
Chron. fast 6 10 06.83
Observed Z.D. 59 26 Ot
Ref. and Paral. +1 24
Semidiam . . —16 OS
Observed Z.D. 56 41 48
Ref. and Paial. +1 16
Semidiam . . -16 08
360— is 20 4'j = 29°0
39 lb
.360-65 57 22.5 = 234
02 37.5
True Z.D. . . 59 1 1 20
True Z.D. . . 56 26 56
H. M. S.
^5 10 07.07 "• "• ^•
Chronometer, Fast < > 5 10 06.95
1.5 10 06.83
October 26th P.M. ; Barometer 30.02 ; Thermometer 83° ; Q'sU.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. s.
8 11 06
8 12 34.8
8 14 20.8
8 16 05.6
8 18 00.8
8 19 33.6
0
0
+11
0
0
+4
0
0
+ 12
0
0
f5
+ 17
O i .1
First Vernier 33 21 15
Second „ 23 50
Third „ 24 20
Fourth „ 23 50
U. M. S.
8 23 26
8 25 02.4
8 26 53.6
8 28 12.8
8 29 39.2
8 31 20.8
0
+ 4
0
+ 6
0
— 2
0
+5
0
+ 7
0
-1
O / -/
First Vernier 36 06 45
Second „ 06 30
Third „ 07 10
Fourth „ 06 50
Mean ... 33 24 04
Index . . .+313 52 05
Level . . . +16
Mean . . 36 06 49
Index . . . + 326 35 56
Level ... +9
Mean. . . 8 15 16.93
True time . 3 05 08
+ 15
Mean. . . 8 27 25.8
True time . 3 17 17.43
+ 8
+ 11
+ 16
2 05
347 16 25
-J9.5
362 42 54
Chron. fast 5 10 08.93
Observed Z.D. 57 52 45
Ref. and Paral. + 1 16
Semidiam . . +16 08
Chron. fast 5 10 08,37
Observed Z.D. 60 27 09
Ref. and Paral. + 1 28
Semidiam . . +16 08
3C0-46 07 55 = 313 5
360-33 2*4 o"4 = 326 3
5 56
True Z.D. . . 58 10 09
True Z.D. . . 60 44 45
H. M. S.
fS 10 08.931 H. M. s.
Chronometer, Fast < > 5 10 08.65
l5 10 08.S7J
IN THE LENGTH OK THE SECONDS PENDULUM.
107
Jamaica. Determination of the Rate of the Chronometer by Zenith Distances, continued.
October 27th P.M.; Barometer 30.02 ; Thermometer 83° , Q'sU.L.
ChroDometer.
H. M. s.
8 15 25.2
8 16 54.8
8 18 ia.6
8 19 44
8 21 10.4
8 24 27.6
Mean . . .
True time .
8 19 20.93
3 09 08.1
Chron.fast 5 10 12.83
+2
-2
+2
+6
+5
-2
+ 3
-2
+ 1
+ 7
+ 6
— 1
+ 11 fl3
+ 13
360-36 06 48 = 323 53 12
Readings, &c.
First Vernier
Second „
Third „
Fourth „
29 34 30
34 20
34 40
34 10
Mean
Index
Level
2U 3t 25
.+323 53 12
+ 13
353 27 SO
Observed Z.D. 58 54 38
Ref. and Paral. +1 23
Semidiam . . +16 08
True Z.D.
59 12 09
CbrODometer.
II. M. s.
8 30 15.2
8 31 53.2
8 33 30.4
8 34 59.6
8 36 41.6
8 38 21.2
Mean . .
True time .
8 34 16.87
3 24 03.43
Chron.fast 5 10 13.44
Level.
+ 2
+5
0
+3
-4
-2
+4
+3
+ 6
0
+4
-2
-1
+ 10
+ 7
360-29 34 25 = 330 25 35
Readings, &Ci
First Vernier
Second „
Third „
Fourth „
42 01 10
04 00
04 15
03 .50
Mean
Index
Level
42 04 04
.+330 25 35
+7
372 29 46
Observed Z.D. 62 04 58
Ref. and Paral. +1 33
Semidiam . . +16 08
True Z.D.
62 22 38
H. M. S.
!5 10 12.831 "■ "■ s-
Chronometer, Fast < > 5 10 13.13
LS 10 13.44J
October 2Sth P.M. ; Barometer 30.01 ; Thermometer 83' ; ©'s U.L.
Chronometer.
H. M. S.
8 39 00
8 40 27.6
8 41 38.4
8 42 58
8 44 25.2
8 45 51.6
Mean . . .
True time .
8 42 23.47
3 32 06.07
Chron.fast 5 10 17.4
+ 2
0
+2
+6
2
2
— 5
+ 1
0
+ 1
+7
-1
-1
-7
-6.5
360-284 00 25 = 75 59 35
Readings, &c.
First Vernier 307 55 25
Second
Third
Fourth
Mean .
Index .
Level .
55 10
55 45
55 05
307 55 25
+75 59 35
+6
55 06
Observed Z.D. 63 59 il
Ref. and Paral. + 1 45
Semidiam . . +16 08
True Z.D.
64 17 04
Chronometer.
Level.
Readings, &c.
H. V. S.
Chronometer, Fast 5 10 17.4
p a
108
EXPERIMENTS FOR DETERMINING THE VARIATION
Jamaica. Determination of the Rate of the Chronometer by Zenith Distances, continued.
October 29th P.M.; Bar. 30.01; Therm. 83°; O'sU.L.
October 30th A.M.; Bar. 30.05 ; Ther 81°, Q's L.L.
Chronometer.
Level.
Beadiugs, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
9 16 57.6
9 18 16.8
9 20 01.6
9 21 13.2
9 23 05.6
9 24 35.6
0
0
0
+ 3
0
-2
0
0
0
+4
0
-0
0 # II
First Vernier 335 00 15
Second „ 00 10
Third ., 00 20
Fourth „ 00 00
H. M. S.
1 06 08.4
) 11 37.2
1 15 00
1 16 26.4
0
0
-5
-4
0
0
-3
-3
0 , //
First Vernier 168 26 40
Second ,, 26 20
Third „ 26 40
Fourth „ 26 20
Mean ... 335 00 1 1
Index . . . + 100 03 22.5
I.«vel ... +2.5
Mean. . . 1 12 18
True time . 8 01 54.17
-9
-6
Mean. ... 168 26 30
Index . . .+ 85 23 05
Level. . . . —07
-7.5
Mean. . . 9 20 41.73
True time . 4 10 20
+ 1
+4
Chron. fast. 5 10 23.83
""""
+2.5
435 03 36
253 49 28
Chron. fast. 5 10 21.73
(Cloudy.)
360 - 274 36 55 = S°5 23 55
Observed Z.D, 72 30 36
Ref. and Paral. +2 45
Semidiam . . +16 09
Observed Z.D. 63 27 22
Ref. and Paral. + 1 40
Semidiam. . . —16 09
360-259 03 22.5=100 (
)3 22.5
True Z.D. . . 72 49 30
True Z.D. . . 63 12 53
H. M. S.
Chronometer, Fast 5 10 21.73
11. M. S,
Chronometer, Fast 5 10 23.83
October SOlh P.M. ; Barometer 30 .02 ; Thermometer 83° ; Q's U.L.
Cbronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 18 27.6
8 20 06
8 21 50
8 23 S4.2
1
1 8 25 56.4
(
8 27 24.8
+2
+ 4
+ 5
-1
+ 2
+ 2
+ 1
+4
+ 5
-2
-2
+ 1
0 / II
First Vernier 169 23 20
Second „ 23 10
Third „ 23 40
Fourth „ 23 00
H. M. S.
9 06 12.4
9 07 23.6
9 08 42.8
9 09 54
9 11 11.2
9 12 31.6
0
0
0
+ 15
+3
0
0
0
0
+ 15
+ 3
0
0 1 II
First Vernier 230 12_50
Second „ 12 30
Third ,, 13 00
Fourth ,. 12 10
Mean . . . 169 23 17.5
Index . . . + 191 33 30
Level . . . +12.5
Mean ... 230 12 37.5
Index ... 190 36 42.5
l<;vel ... +18
Mean. . . 8 22 53
True time . 3 12 28.13
+ 14
+ 11
Mean. . . 9 09 19.27
True time. 3 58 54.03
+ 18
+ 18
+ 12.5
360 57 00
+ 18
420 49 38
Chron. fast. 5 10 24.87
360-168 ?'6 30=1°91
Chron. fast. 5 10 25.24
33 30
Observed Z.D. 60 09 30
Ref. and Paral. +1 27
Semidiam . . +16 09
Observed Z.D. 70 08 16
Ref. and Paral. +2 23
Semidiam . . +16 09
360-169 23 17 5=190
36 42.5
True Z.D. . . 60 27 06
True Z.D. . . 70 26 48
H. M. S. ^ jj ^
Chronometer, Fast < ^ "^ 24.871^ j' jj ^505
l5 10 25.24J
IN THE LENGTH OF THE SECONDS* PENDULUM.
109
RATE DEDUCED from the PRECEDING OBSERVATIONS.
Date.
S.
Dale. :
.S.
Dale.
s.
Date.
S.
P.M. to P.M.
October 23 to 26
4.03
October 25 to 26
4.40
October 27 to 30
3.97
October 22 to 23
4.38
2T
l.H
27
4.44
October 28 to 29
4.33
24
4.48
28
4.17
28
4.38
30
3.82
25
t4.02
29
4.19
29
4.37
October 29 to 30
3.32
26
4.12
30
4.07
30
4.1R
A.M. to A.M.
27
4.19
October 2 1 to 25
3.10
October 26 to 27
4.48
October 22 to 23
3.88
28
4.20
26
3.75
28
4.37
26
4.09
29
4.22
27
4.00
29
4.36
30
4.13
30
4.11
28
4.06
30
4.10
October 23 to 26
4.16
October 23 to 24
4.59
29
4.12
October 27 to 28
4.27
30
4.19
23
3.81
30
3.99
29
4.30
jOctober 26 to 30
4.22
4.22
3.96
4.33
4.01
MEANS.-GainiogJ
per Diem 3
4.14 Seconds.
IIQ
EXPERIMENTS FOE DETERMINING THE VARIATION
Jamaica. Comparisons of the Astronomical Clock with the Chronometer,
No. 423, from the 32d to the 30th of October, 1822; with the Clock's Rate on
Mean Solar Time deduced.
1
1822*
Chronometer.
Clock.
Clock's loss on 423.
DAILY RATES.
Chron.
Clock.
Oct. 23 A.M.
H. M. s.
f
M. S.
55 19.8
s.
Gaioing.
Losini;.
109.9
„ 23 A.M.
53 29.9
• 109.9
s.
S.
S.
„ 24 A.M.
51 40
■ 109.7
> 109.8
4.14
105.06
„ 25 A.M.
49 50.3
■ 109.7
„ 26 A.M.
■ 1 55 00
48 00.6
• 109.9
„ 27 A.M.
46 10.7
■ 109.8
„ 28 A. M.
44 20.9
109.5
109.45
4.14
105.31
„ 29 A.M.
42 31.4
• 108.6
„ 30 A.M.
40 42.8
J
IN THE LENGTH OP THE SECONDS* PENDULUM.
Ill
JAMAICA. COINCIDENCES OBSERVED with PENDULUM 3 ; the Clock making
86294.34 Vibrations in a Mean Solar Day.
DATE.T
Baro-
meter.
No.
ofCo-
inci.
dcnce.
Tempe-
ratore.
Time of
Disap-
pearance-
Time of
Re-ap-
pearance
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe.
ratore.
Mean
Interval.
Correc-
tion for
ttieArc
Vibrations
in 24 honr8.
Redac-
tion to a
Mean
Tempe-
rature.
Reduced
Vibrations at
81.77.
1822
,
81.1
M. 3.
13 31
H. s.
13 33
H. M. S.
10 13 32
o
1.22|
o
s.
0
-t-
Oct. 22 A.M.
30.060-
81.55
642.05
1.38
86026.90
-0.09
80026.81
{
11
82
00 26
00 39
12 00 32.5
0.66
'
81.8
19 08
19 12
1 19 10
1.2
„ 22 P.M.
30.010<
11
81.6
06 09
06 21
3 06 15
0.64
81.7
642.5
1.34
86027.06
-0
.03
86027.03
30.026S
80
25 29
25 33
7 25 31
1.18
„ 23 A.M.
>
80.5
643
1.28
86027.20
-0.53
86026.67
'•
11
81
81.6
12 33
U 06
12 49
11 11
9 12 41
2 11 08.5
0.62
1.18
„ 23 P.M.
30.020<
n
81.6
80.8
38 07
47 30
58 18
47 35
3 58 12.5
8 47 32.5
0.38
i.is]
81.6
0 12 . 4
1.22
86026.9
-0.07
86026.83
„ 24 A.M.
30.070<
I
f
11
81.2
81.8
34 34
18 35
3t 49
18 39
10 34 41.5
1 18 37
■
0.58J
1.14
81
642.9
1.22
86027.12
-0.32
86026.80
„ 24 P.M.
30.030<
/
81.85
642.25
1.14
86026.76
-fO.03
86026.79
11
81.9
5 32
5 47
3 05 39.5
o.sej
r
82.6
12 41
12 42
11 12 41.3
1.22J
„ 25 A.M.
30.070-^
11
83.2
59 24
59 36
12 59 30
>
0.64]
82.9
640.85
1.35
86026.37
-1-0.47
86026.84
[
83.2
18 38
18 40
S 18 39
1.22]
„ 25 P.M.
30.030-^
•
83.1
640.35
1.35
86026.19
-f 0.55
86026.74
11
83
81.2
5 14
57 49
5 31
57 51
5 05 22.5
9 57 51.5
0.64]
1.18]
„ 26 A.M.
SO.GToJ
11
82.3
44 38
41 54
11 44 46
0.6 j
81.75
641.45
1.25
86026.53
....
86026.53
Means . . .
30.043
81.77
86026.78
86026.78
112
EXPERIMENTS FOR DETERMINING THE VARIATION
Jam
POTivrr<Tnp'ivrr"'Pe npcT^cvpr*
,_:4l, Dr'lVTTkTTTTTlUr AT- A
. 4i,„ r<i„„i. ™~i-;„„
86294.69 Vibrations in a Mean Solar Day.
DATE.
Baro.
meter.
No.
of Co-
inci-
dence.
Tempe-
ralare.
Time of
Disap-
pearance
Time of
Rc-ap-
pcarauce
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
ratare.
Mean
Interval.
Correc-
tion for
the Arc
Vibrations
in ^ hours.
Reduc-
tion to a
mean
Tempera-
ture.
Reduced
Vibrations at
83.6.
1822.
IN.
1
o
83.5
M. s.
31 39
M. s.
31 45
H. M. S.
11 31 42
o
1.2
o
s.
S.
Oct. 27 A.M.
30.030-
11
1
S3. 5
83.5
22 01
44 19
22 21
44 24
1 22 11
3 44 21.5
0.64J
1.2 1
83.5
662.9
1.34
86035.69
-0.04
86035.65
„ 27 P.M.
30.010-
f
11
I
83.2
83.8
34 44
59 08
35 02
59 15
5 34 53
12 59 11.5
0.64
1.2 ]
83.35
663.16
1.34
86035.77
-0.10
86035.67
„ 28 P.M.
30.020-|
11
1
84.2
84.2
49 28
00 10
49 47
00 13
2 49 37.5
3 00 11.5
V
0.66
1.2 ]
81
662.6
1.38
86035.61
-fO.17
86035.78
28 P.M.
so.oooi
f
11
1
83.8
82
50 27
35 27
50 44
35 29
4 50 35.5
11 35 28
0.66]
1.3 1
84
662.4
1.38
86035.51
-t-0.17
86035.68
„ 29 A.M.
so.oeoJ
11
1
84
84.1
25 50
58 47
26 04
58 50
1 25 57
2 58 48.5
>
0.66
1.28]
83
662.9
1.52
86035.87
-0.25
86035.62
„ 29 P.M.
30.02oi
11
1
84.8
81.8
48 53
36 22
49 17
36 26
4 49 05
9 36 24
>
0.66
1.28]
84.45
661.65
1.48
86035.33
-hO.36
86035.69
„ SO A.M.
so.iooi
11
1
82.8
83.8
26 50
8 44
27 06
8 49
11 26 58
12 8 46.5
0.66]
1.28]
82.3
663.4
1.48
86036.03
-0.55
86035.48
„ 30 P.M.
30.080-|
11
84-2
58 57
59 17
1 59 07
0.66]
84
662.05
1.48
86035.44
+ 0.17
86035.61
Means
30.040
83.6
86035.65
86035.65
IN THE LENGTH OF THE SECONDS* PENDULUM. 113
NEW YORK.
Previously to entering into a detail of the proceedings at New York,
it may be proper to notice the considerations which induced me to attach
a more than ordinary interest to the experiments at that station ; and to
entertain a hope that the rates of the pendulums, obtained in one of the
principal cities of the United States, might have a value beyond that of
adding another station towards the more precise determination of the
figure of the earth.
The Government of the United States, excited by the assiduity with
which the principal governments of Europe were occupied in the regu-
lation of the weights and measures of their respective dominions, and
in devising methods of ensuring their perpetuity, had recently directed
its attention to the procurement of a national Scale of linear measure,
and to an inquiry into the modes of determining the value of its divisions,
so as to enable its verification at any subsequent period, or its replace-
ment in case of loss or accident. An official report on these subjects
had been drawn up in considerable detail, by one of the leading
members of the administration, and was published in 1821 ; the Scale,
which that report recommended to be obtained and adopted as a
standard, to which the several present measures of the States should
be referred, and by which they should be perpetuated, was pro-
posed to be itself a duplicate, so far as instrumental and executive
accuracy would admit, of the national Scale of France ; having con-
sequently its foundation, nominally, in a certain aliquot part of the
terrestrial meridian, but its real and practical verification in the length
114 EXPERIMENTS FOR DETERMINING THE VARIATION
of the pendulum vibrating seconds at the observatory at Paris ; the
report contained no specific recommendation of measures for determining
the value of the scale by a reference proper to the United States, nor were
indeed any proceedings for that purpose, apparently, contemplated in its
provisions ; but it could scarcely be deemed probable, that a Nation,
characteristically jealous of independence, and in which a disposition to
scientific discussion and inquiry existed, and was rapidly progressive,
would long rest satisfied with a means of verifying its scale, which would
require the operations, on any future occasion of reference, to be con-
ducted in a foreign Capital, and which would therefore be at the will of
a foreign Nation ; it was more reasonable to expect, that in the eventual
prosecution of the purposes of the government, of which the attainment
of a scale was necessarily the first step, the value of its divisions would
be ultimately determined by a reference to an invariable length in
nature which should exist within the territory of the United States ; and
that the length of the pendulum vibrating some definite portion of time at
some selected station would be adopted for that purpose, because the
pendulum exclusively possesses an essential quality in a natural stand-
ard, that of being easily accessible. In the event of so probable an
undertaking being carried into effect, it would become highly desirable
to compare the measurement thus made in the United States, with the
results of the similar operations in Great Britain and France; as by
the comparison, their accuracy would receive reciprocal confirmation, and
a decisive practical demonstration would be afforded, of the identity with
which the pendulum can be measured by diflferent experimentors, and
of its consequent effective value, in its application as a standard of
reference.
The experiments made at the principal stations of the European Arc,
have manifested that the difference in the length of the pendulum at two
IN THE LENGTH OF THE SECONDS' PENDULUM. • 115
places on the globe, cannot be inferred from a knowledge of their re-
spective latitudes, even were the general EUipticity of the meridian
correctly known; because the strict relation of the force of gravity to
the square of the sine of the latitude, does not exist in nature, being
interfered with by the variable density of the materials near the surface ;
the experiments contained in the present volume, afford still more de-
cisive evidence of the same fact, and manifest the great extent of the
irregularity which is induced thereby. A comparison, therefore,
between the measurements of the pendulum made at two places on the
globe, requires, and can only be accomplished by, a direct experiment.
By employing at New York the pendulums with which I was furnished,
I had it in my power to convey the measurement of the seconds' pendu-
lum in London, so carefully made by Captain Kater, and adopted by the
British Parliament to fix in perpetuity the divisions of its national Scale,
from the spot in which the measurement was actually accomplished, to
a station within the United States ; and I should consequently place on
record the length of the seconds' pendulum at that station measured on
the British Scale, with a precision only inferior to the original determi-
nation in London by the very limited errors which might be introduced
in the operations with the intermediate pendulums ; and as the relative
proportion of the British and French Scales has been very carefully
ascertained, the same process would also determine the length of the
pendulum at New York in parts of the French Scale, and also of the
American, presuming the execution of the latter to have been strictly
conformable to its design : whatsoever station, therefore, the government
of the United States might ultimately select for the operations of an
original measurement, the means would thus be presented of convenient
access and always within its command, of comparing the result with that
of the British measurement ; if reasons of expediency, unconnected with
Q 2
116 EXPERIMENTS FOR DETERMINING THE VARIATION
those of science, should determine the selection elsewhere than at New
York, a second proceeding with pendulums of comparison would be
required, intermediately between New York and the station so chosen ;
but if New York were itself the station, no other proceedings than those
of the original measurement would be required for the comparison ; and
as this consideration might possibly operate in determining the choice,
I was particularly desirous of obtaining permission to make the experi-
ments in some public edifice at New York, which might be equally
accessible on future occasions of similar or connected operations*.
* No comparison has yet been accomplished between the measurements of the natural
standards of different countries. The comparison of the measurements of the seconds' pen-
dulum in London and at Paris, the one effected by the method of Borda, the other by that
of Kater, was undertaken at the instance of tiie Bureau des Longitudes, by M. Arago, with
■whom were associated Messrs. Biot and Humboldt ; the execution was attempted by means
of two invariable pendulums, of which the rates were obtained in Paris in October 1817, at
Greenwich, in November 1817, and again at Paris in March and August 1818: from the
summary account of these experiments, published at the close of the third volume of the Base
du Systeme Metriquc, it is obvious that from some accidental cause or causes, the several
results were not attained with the precision which the occasion required, or of which the
mode of experiment is capable. The failure in a precise determination, is, however, the less
to be regretted, since if the rates of the invariable pendulums had been obtained at Paris
and at Greenwich, with the full accuracy which is practicable in such proceedings, the
comparison of the measurements in Paris and in London would not have been accomplished
thereby it is true that the latitudes of London and Greenwich are so nearly the same, that
the diflercnce in the length of their respective pendulums due to the Ellipticity of the earth,
may be computed by an assumed Ellipticity, without endangering a sensible error; but the
assumption that the disposition and nature of the materials near the surface at the observatory
on Greenwich Hill, and in Portland Place, London, are the same, and consequently that what
may be termed their irregular influence on the general attraction, is precisely alike in both
cases, is one which may involve error of too much consequence to be hazarded in an inquiry
which ou^ht to be so rigorously exact. It is not probable that this circumstance was over-
looked, although it is not expressly adverted to, by the eminent persons who conducted or
were concerned in the experiments, especially as M. Arago dwells on the importance of
effecting the comparison by a direct observation which should not involve supposition ; it may
rather be attributed to a circumstance, which if it be not timely attended to, may produce far
more serious inconveniences hereafter, namely, that the spot to which the Parliamentary
IN THE LENGTH OP THE SECONDS* PENDULUM. 117
A trigonometrical survey of the United States had also been for some
time in contemplation, to be conducted as a national undertaking upon
the same extended scale as that proceeding in Great Britain ; the prepa-
rations had so far advanced, that the instruments required for its exe-
cution, which had been ordered from* Europe, had already arrived at
Washington ; it was not unreasonable to hope, therefore, that the interest
which the experiments at New York might excite, in the inquiry con-
cerning the figure of the Earth, amongst persons of science in the United
States, might dispose the government to participate with those of Great
Britain and France in the operations for its determination, by directing
the variation in the length of the seconds' pendulum to be ascertained at
the principal stations of the American survey, in the same manner that
has been done in Great Britain. In that case New York would serve as
a connecting link between the American series, and the equatorial stations
which I had already visited, and those in the high latitudes which I had
it in prospect to visit ; it would also connect the operations in America,
with those of the British survey, and with those of the French philoso-
phers in France and Spain ; and might thus become the means, not only
of producing a considerable extension of the inquiry, but of combining
the whole operations into one general determination, the value of which
would far exceed the partial results of the several series, considered
independently of each other.
These were the motives, which being stated to Vice-Admiral Sir
Charles Rowley at Jamaica, prevailed with him to give his sanction
that the Pheasant should stop at New York on her way to England ; a
standard of Great Britain is referred, to which foreigners must resort to obtain a direct
comparison with the measurement on which the standard is founded, and in which alone it
can strictly be verified by posterity, is in the house of an individual, instead of being in a
public edifice.
118 EXPERIMENTS FOR DETERMINING THE VARIATION
measure which not having been contemplated when Sir Robert Mends's
instructions were drawn up, had not been authorized by him.
The Pheasant arrived at New York on the 10th of December ; I had
the advantage of being previously known to Dr. David Hosack, of that
city, whose ardour in the pursuit, and liberality in the promotion of
philosophical research, may justly entitle him to rank amongst its most
distinguished patrons ; I had soon, through his means, the satisfaction of
finding myself placed in a situation and in circumstances, which I could,
not but deem as highly favourable to the purposes which I had in view :
by the permission of the President and Council of Columbia College
most kindly tendered, an apartment opposite the door leading into the
gallery of the college chapel was assigned for the pendulums, being in
all respects extremely well adapted, and having an additional and g-reat
recommendation in the assurance that it would be equally accessible on
future occasions of a similar nature ; the use of the Cupola was likev/ise
permitted as a temporary observatory, for which it was well suited by-
having windows with firm and broad sills opening in the four principal
directions.
In one of the consequences of the accommodation which the instru-
ments thus received at Columbia College, 1 must ever deem myself to
have been most highly fortunate, namely, in the association which it pro-
cured me of the Professor of Natuial and Experimental Philosophy, and
of Chemistry, Mr. James Renwick, whose interest in the experiments was
so strongly excited as to induce him to give me his unremitting co-opera-
tion, a circumstance peculiarly desirable and satisfactory on an occasion
in which the results may hereafter come in question in the comparison
of the standard measurements of the two countries.
By favour of the gentlemen who superintend the administration of the
customs in New York the instruments were permitted to be landed
IN THE LENGTH OP THE SECONDS' PENDULUM. 119
without undergoing the customary formality of inspection ; they were dis-
embarked on the 11th of December, and were ready to have commenced
the observation of coincidences on the morning of the 15th, had not the
weather proved an obstruction until the 22nd ; the delay, however, may
ultimately have been beneficial, in giving time to the clock to take up a
more steady rate, than it might possibly have had in the earlier days.
The apparatus connected with the clock and pendulums, was in every
respect most satisfactorily set up ; the room appropriated to them was
entered only for the purposes of observation or of comparing the clock,
which operations were allowed to occupy no more time than they ab-
solutely required ; a precaution unnecessary withm the tropics, where
the general temperature is so nearly that of the human body, but which
becomes highly deserving of attention, where the disparity is so great
as in the severe winters of New York ; the room was also kept constantly
dark at other times by skreens of matting and baize suspended before
the windows ; by these means the variations of temperature of the apart-
ment rarely equalled a degree and half in the twenty-four hours.
No very suitable situation for a transit instrument occuring within a
convenient distance, the repeating circle was employed in the compa-
rison of the chronometer with astronomical time ; being desirous however
of the fullest corroboration of accuracy, an eighteen inch astronomical
telescope was firmly attached by a brass plate and screws to the side
wall of the eastern window of the College Chapel, having the vertical
side of the tower of the Presbyterian Church in its field of view, behind
which the times of disappearance of three stars in the constellation of
the Great Bear were observed by Mr. Renwick and myself on the 24th of
December and on the 2nd of January, comprising the interval through
which the observation of coincidences was continued.
120 EXPERIMENTS FOR DETERMINING THE VARIATION
New York is built on a bed of sand above one hundred feet in depth,
and resting on primitive rock ; the height of the pendulums above the
sea was obtained as follows :
Feet.
A station in Murray Street adjoining Columbia College
appears by the survey of New York to be above
high water-mark 20.8
Add, the ground line of Columbia College above the sta-
tion in Murray Street, by estimation - - - 14
Add, the pendulums above the ground line, by estimation 30
Add, the half risp nf the tides, immediate between the
springs and neaps - - - - - - 2.5
Total height of the pendulums above half-tide 67 feet.
An account of the experiments with the pendulums at Columbia
College, and of the corresponding series in London, was presented in
the spring of 1823 to the Literary and Philosophical Society of New
York, and will make a part of the second volume of their Transactions.
I have taken that opportunity of noticing the results in their connexion
with the incidental purposes, which I hoped they might be instrumental
in promoting ; and I am happy to be enabled to add, that Mr. Renwick
is proceeding, under the cognizance of the government of the United
States, and with its assistance, in the direct measurement of the seconds'
pendulum at Columbia College, by means of the pendulum with con-
vertible axes.
IN THE LENGTH OF THE SECONDS' PENDULUM.
121
New York. OBSERVATIONS to DETERMINE the RATE of the Chronometer No. 423, by ZENITH
DISTANCES of the Sun and Stars ; from the 22d of December, 1822, to the 2cl of January, 1S23.
Latitude of the Place of Observation 40° 42' 43" N.; Longitude 74° 03.5' W.
By Zenith Distances of the Sun, West of the Meridian.
December 22d ; Barometer 30.34; Thermometer 37° ; Q's U.L.
Clirononieter.
Level.
Readings, &c.
Chronometer. Level.
Readings, &c.
H. H. S.
7 55 00
7 56 41.2
7 58 56.8
8 00 27.6
8 02 44
8 04 23 2
+5
-5
-8
+5
+ 1
0
-2
+2
0
-2
— 6
0
0 / //
First Vernier 97 18 10
Second „ 18 10
Third „ 18 30
Fourth ,, 18 10
H. M. s.
8 10 17.2
8 11 58
8 14 07.6
8 15 42.4
8 17 43.2
8 19 08
+ 2
-2
+2
+ 9
t5
+7
— 5
-8
-5
+ 3
_2
0
0 / //
First Vernier 206 18 20
Second „ 18 10
Third „ 18 30
Fourth „ 18 20
Mean . . 97 18 15
Index . . .+360 00 08.5
Level . . -5
Mean . . . 206 18 20
Index . . . + 262 41 45
Level . . +3
Mean. . . 7 59 42.13
True time. 2 58 40.9
+ 13
-23
Mean. . . 8 14 49.4
True time. 3 13 47.33
+23
-17
— 5
457 18 18
+ 3
469 00 08
Chron. fast 5 01 01.23
Chron. fast 5 01 02.07
Observed Z.D. 76 13 03
Ref. and Paral. +3 54
Semidiam . . +16 18
Observed ZD. 78 10 01
Ref. and Para!. +4 32.5
Semidiam . . +16 17.5
0 0 / // oil'
360-97 18 15=262 41 45
True Z.D. . . 76 33 14
True Z.D. . . 78 30 51
H. M. S.
fS 01 01.231 "• "• S-
Chronometer, Fast < > 5 01 01.65
to 01 02.07J
i
1 December 23d; Barometer 30.26; Thermometer 20"'. 5; O'sl'-'-
Chronoroeter. Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 01 10
8 03 47.2
8 05 18.8
8 06 54
8 08 39.2
8 10 35.2
+3
0
0
0
0
-6
-7
0
-10
0
0
+ 4
0 / //
First Vernier 352 56 30
Second „ 56 20
Third „ 56 40
Fourth „ 56 30
H. M. S.
8 15 20.4
8 16 48
8 18 34
8 20 12.8
8 22 29.6
8 24 19.2
+ 10
0
+ 8
+ 2
0
+ 15
0
0
-1
-8
0
+2
0 / /'
First Vernier 105 20 45
Second „ 20 20
Third „ 20 50
Fourth „ 20 10
Mean . . . 352 56 30
Index . . . + 108 47 48
Level ... —8
Mean ... 105 20 31.5
a. f 7 03 30
Index . . +|„go Qg gg
Level . . . +12.5
Mean. . . 8 06 04.07
True lime. 3 05 04.07
-2;
+7
Mean. . . 8 19 .37.3
True time . 3 18 36.23
+3.
-9
-8
461 44.10
- +12.5
472 24 14
Chron. fast 5 01 00.00
Observed Z.D. 76 57 22
Ref. and Paral. +415
Semidiam . . +16 17.5
\ Chron. fast 5 01 01.07
Observed Z.D. 78 44 02
Ref. and Paral. + 4 56
Semidiam . . +16 18
360 - 251 12 12 = 10
3 47 48
0 0 ' " 0
360 — 352 56 30 = 7
03 30
True Z.D. . 77 17 54.5
True Z.D. . . 79 05 16
H. M. S.
f 5 01 00 1 "• "• ^•
Chronometer, Fast < > 5 01 00.53
is 01 01.07J
122
EXPERIMENTS FOR DETERMINING THE VARIATION
New York
T)pfprmination of the Rate of the Chronometer bv Zenith Distances, continued
By Zenith Distances of the Sun, West of the Meridian.
January 2d ; Barometer 30 .02 ; Thermometer 42° ; 0 's U.L.
Ciironomettr.
Level.
Readings, &c
Chronometer.
Level.
Readings, &c.
H. M. S.
S 02 24.4
8 04 40.4
8 06 22.4
8 07 52.8
8 09 29.2
8 11 25.6
+ 1
+ 6
+7
0
+7
0
-8
-2
-1
0
0
0
o t «
First Vernier 331 42 30
Second „ 42 10
Third „ 42 50
Fourth „ 42 00
H. M. S.
8 14 51.6
8 16 51.2
8 18 55.2
8 20 47.6
8 22 41.2
8 24 46
+2
+8
-10
+2
0
+6
-5
+ 1
-3
— 5
— 8
-1
0 t '1
First Vernier 78 17 50
Second „ 17 40
Third „ 18 20
Fourth „ 17 30
Mean . . . 331 42 22.5
Index . . . + 124 53 05
Level ... +5
Mean.. . . 78 17 50
\,.A^, J.? 28 17 37.5
- '"^'^^ • -+1360 00 00
Level ... —6.5
Mean. . . 8 07 02.47
True time . 3 06 29.27
+ 21
-11
Mean. . . 8 19 48.8
True time . 3 19 16.18
+ 19
-SS
+ 5
456 35 32
-6.5
466 35 21
Chron. fast. 5 00 33.2
Observed Z.D. 76 05 55.3
Ref. and Paral. +3 47.5
Semidiam. . +16 18
Chron- fast 5 00 32.62
Observed Z.D. 77 45 53
Ref. and Paral. +4 19
Semidiam . . +16 18
360-255 06 55=124 J
3 05
36°0-331 42 22.5=2°8
17 37.5
True Z.D. . . 76 26 01
TrueZ.D. . . 78 06 30
H. HI. S.
Chronometer, Fast | ^ °° ^^'^ \ 5 Oo' 32.91
15 00 32.62J
January 3d; Barometer 30.20 ; Thermometer 41° ; O'sU.L.
Chronometer.
Level.
' Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
8 07 50
8 09 16.8
8 10 51.8
8 12 03.2
8 13 32
8 18 31.6
0
-2
0
+ 8
+ 10
+ 10
0
-10
0
0
+ 2
+ 2
First Vernier 219 43 10
Second „ 43 00
Third „ 43 30
Fourth „ 42 50
Mean ... 219 43 07
Index . . .+239 55 S5
Level ... +10
Mean ... 81201.4
True time. 3 11 30.77
+ 32J-12
+ 10
459 38 52
ChroP.fast. 5 00 30.63
Observed Z.D. 76 36 29
Ref. and Paral. +3 57
Semidiam . . +16 18
360-120 o'4 25=239 S
5 35
TrueZ.D. . . 76 56 44
1
H. H. S.
Chronometer, Fast 5 00 30.63
IN THE LENGTH OF THE SECONDS PENDULUM.
123
New York. Determination of the Rate of the Chronometer by Zenith Distances, continued.
By Zenith Distances of the Sun, East of the Meridian.
December 24th ; Barometer 30 .
10; Thermometer 18°; G's L.L.
Chronometer.
Level.
Reartiogs, &c.
Chrouometei.
Level.
Readings, &c.
H. M. S.
1 36 58
1 38 40
1 40 30.4
1 41 45.6
1 43 50.4
1 45 00.8
0
0
0
+ 12
-0
+3
0
0
0
+ 1
+4
-8
0 , II
First Vernier 221 Ot 40
Second „ 04 30
Third „ 04 50
Fourtli „ 04 40
11. H. S.
1 47 48.4
1 49 18
1 51 00.4
1 .52 21.6
1 55 04.8
1 56 29.2
+S
+S
+3
+ 10
+9
+7
-4
-4
-8
0
— 2
— 4
0 / //
First Vernier 328 26 15
Second „ 26 15
Third „ 26 35
Fourth „ 26 10
Mean ... 221 04 40
Index . . .+254 54 45
Level ... +3
Mean ... 328 26 19
Index . . . + 138 55 20
Level . . . +11.5
Mean. . . 1 41 07.53
True time. 8 40 09.32
+ 20
-14
Mean. . . 1 52 00.4
True time. 8 51 02.6
+45
-2:
+ 3
475 53 28
+ 11.5
467 21 SO
ChroD. fast 5 00 58.21
Chron. fast 5 00 57.8
Observed Z.D. 79 19 55
Ref. and Paral. +515
Semidiam . . —16 18
Observed Z.D. 77 53 38
Ref. and Paral. + 4 19
Semidiam . . — 16 18
360 - 105 05 I'o = 25°!
54 45
.360-221 04 40= 138
55 20
True Z.D. . . 70 08 52
True Z.D. . . 77 41 59
H. M.
Chronometer, Fast <
[5 00
s.
58.21) "■ "• ^■
> 5 00 58
57.8 j
1
December 29th; Barometer 30.3
); Thermomeler 26"; Q'sL.L.
Chronometer.
Level.
Readings, &ic.
Chronometer. Level.
Readings, &c.
11. M. S.
1 47 44
1 50 13.2
1 51 54
1 53 12
1 54 44
1 56 26.4
+ 8
+5
0
0
+9
0
— 2
-6
0
0
— I
0
0 1 ,1
First Vernier 330 45 00
Second „ 45 00
Third „ 45 20
Fourth „ 44 40
11. M. S.
1 59 52.8
2 00 56
2 01 Z'0.8
2 0? 55.2
2 01 02
2 05 22.4 ■
— 3
0
0
■fio
-f-1
f3
-\i
0
0
+ 1
-8
-6
0 / „
First Vernier 70 53 35
.Second „ S3 10
Third „ 53 55
Fourth „ 53 00
Mean ... 330 45 00
Index . . . + 137 10 47.5
Level . . . +6.5
Mean ... 70 53 25
I J ^ if 29 15 00
Index . . +|36o 00 o,j
Level ... —7
Mean. . . 1 52 22.27
True time . 8 51 38.03
+22
-9
Mean . . 2 02 29.87 -
True time. 9 01 41.4 "
fl5
-29
+6
.5
467 55 54
_.
460 08 18
Chron. fast 5 00 44.24
Observed Z.D. 77 59 19
Ref. and Paral. + 4 35
Semidiam . . — 16 18
Chron. fast 5 00 45 . 47
ObservedZ.D. 76 41 23
Ref. and Paral. +4 07
Semidiam . . —16 18
360-222 49' 12'. 5= 137
6 17.5
0 0 / // 0
360 - 330 45 00 = 29 1
5 00
True Z.D. . . 77 47 36
True Z.D. . . 76 29 12
H. HI. S
[5 00 4
Chronometer, Fast <
[5 00 4
4.241 H-M- s.
> 5 00 44.85 !
5.47J
R 2
124
EXPERIMENTS FOR DETERMINING THE VARIATION
New York. Determination of the Rate of the Chronometer by Zenith Distances, continued.
By Zenith Distances of the Sun, East of the Meridian. !
January 2d; Barometer 29.98; Thermometer 32°; Q'sL.L. j
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
1 42 11.6
1 43 31.2
1 45 31.2
1 47 02
1 49 46
1 50 56
0
+ 3
0
+8
-10
+ 7
0
-6
0
0
0
-1
"o 1 '•
First Vernier 131 35 30
Second „ 5 20
Third „ 6 00
Fourth „ 5 10
H. M. S.
] 53 45.2
1 55 22
1 57 00.4
1 59 10.4
2 00 33.6
1 02 02
0
0
-2
0
0
+7
0
0
-10
0
0
1
First Vernier 235 06 50
Second „ 07 00
Third „ 07 30
Fourth „ 06 50
Mean ... 131 35 30
Index . . .+341 01 46
Level ... 0
Mean ... 235 07 02.5
Index . . .+228 24 30
Level ... -3
Mean. . . 1 46 29.7
True time . 8 45 55.3
+ 18
+ 17
Mean. . . 1 57 58.93
True time . 8 57 24 . 1
+7
-13
+0.5
472 37 16
— 3
463 31 30
Chron. fast 5 00 34.4
Chron. fast 5 00 31.83
Observed Z.D. 78 46 12.7
Ref. and Paral. + 4 46.3
Semidiam . . —16 18
Observed Z.D. 77 15 15
Ref. and Paral. +4 12
Semidiam . . -16 18
360-18 58 14 = 341 0
'l 46
360-131 35 30 = 228
24 s'b
True Z.D . . 78 34 41
True Z.D. . . 77 03 09
11. M. S.
Chronometer Fast 1^ "^ ^^•'' \ s' 00 31.61 *
[5 00 31.83J
By Zenith Distances of a. Lyra\, West of tlio Jleridian.
December 22d ; Barometer 30.30 ; Thermometer 35^.
January 2d; Barometer 30.02 ; Thermometer 32.5°.
Chrouonieter.
Level.
1
Readings, &c.
Clironometer. Level.
\
Readings, &c.
H. M. S.
11 31 56
11 34 06.4
11 36 14
11 38 26.8
11 41 48
11 44 08
+ 6
+2
-1
i9
+ 2
+7
-3
-7
-9
0
— 7
-2
O 1 II
t'TSt Vernier 251 12 30
Second ,, 12 00
Third „ 12 30
Fourth „ 11 50
H. M. S.
12 02 54
12 04 24.8
12 07 24
12 OS 35.2
12 11 32
12 12 55.2
0
0
0
+ 8
-9
+5
0
0
0
-1
-0
-4
0 1 II
First Vernier 291 50 00
Second „ 50 00
Third „ 50 30
Fourtli „ 49 30
Mean ... 251 12 12.5
Index . . . + 153 41 40
) Level . . . -1.5
Mean ... 291 50 00
Index . . . + 180 00 00
Level ... 0
Mean. . . 11 37 46.53
True time . 6 36 43.9
+2
3 -2J
Mean. . . 12 07 57.53
True time . 7 07 23.47
+ 13
-14
- -1.5
404 53 51
0
471 50 00
Chron. fas'. 5 01 02.63
Chron. fast 5 00 34.06
_ ,„ ,
Observed Z.D. 67 28 58
Refraction. . +2 26
Observed Z.D 78 38 20
Refraction. . +4 53
360-206 18 20=153 41 40
True Z.D. . . 67 31 24
360-180 00 00=lS0 00 00
True Z.D. . . 78 43 13
■A
11, M. S.
Chronometer, Fast 5 01 02.63
H. M. S.
Clironometer, Fast 5 00 34.06
IN THE LENGTH OF THE SECONDS' PENDULUM.
125
New York. Determination of the Rate of the Chronometer by Zenith Distances, continued.
By Zenith Distances of Uigel East of the Meridian.
December 23d ; Barometer 30.26; Thermometer 17°.
Chronometer.
Level.
Re.idings, &c.
Chronometer.
Level.
Readings, &c.
H. H. S.
12 21 39.2
12 24 53.6
12 27 21.2
12 30 15.2
12 32 24.8
12 35 02
+ 1
+ 8
0
+9
0
+ 1
— 9
-4
0
-2
0
-10
0 * "
First Vernier 53 20 30
Second „ 20 10
Third „ 20 30
Fourth _„ 20 00
II. M. S.
12 41 22.8
12 43 18
12 45 28
12 47 13.6
12 49 58
12 52 28.4
+ 6
+ 11
+ 10
+ 12
+S
+7
-4
0
-1
+2
-7
-4
0 / .
First Vernier. 89 43 10
Second „ 42 50
Third „ 43 20
Fourth „ 42 40
Mean .... 53 20 17.5
Level .... -3
Index . . .+360 00 08.5
Mean . 83 43 00
Level . +17.3
Index . . .+306 39 42.3
Mean . . .12 28 36
True time . 7 27 33.9
+ 19
-23
Mean. . . 12 46 38.13
True time. 7 45 37.17
+51
-16
-3
413 20 23
+ 17.5
396 23 00
Chron. fast. 5 01 02.1
Chron. fast. 5 01 00.96
Observed Z.D. 68 53 24
Refraction . . +2 41
Observed Z.D. 66 03 50
Refraction . . +2 20
True Z.D. . . 68 56 05
360 - 53 20 17.5 = 300 39 42.5
True Z.D. . . 66 06 10
H. >I. S.
Chronometer, Fast i^ "' u^-' 1 5 01 01.53
^5 01 00.96,
Januarj 2d; Barometer 30.02 ; Thermometer 28°.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
11. M. S.
12 25 43.2
12 27 15.2
12 28 39.6
12 30 01.4
12 31 57.2
12 34 13.6
-i-8
0
0
0
0
0
-1
0
0
0
0
0
0 . //
First Vernier 308 01 45
Second „ 01 35
Third „ 02 IS
Fourth „ 01 25
H. M. S.
12 38 39.2
12 40 01.0
12 41 31.2
12 42 43.2
12 44 54.4
12 47 40
+ 6
0
+ 3
+ 6
+3
0
-3
0
-5
-2
-5
0
0 / .'
First Vernier 313 26 10
Second „ 26 00
Third ,, 26 30
Fourth „ 25 50
Mean . . . 308 01 45
Index . . . +68 10 00
Level ... +3
Mean ... 313 26 07.5
Index . . .+ 57 3S 15
Level ... +1.5
Mean . . .12 29 38.87
True lime. . 7 29 04.23
+8
-1
Mean . . .12 42 34.93
True time . 7 41 39.94
+ 18J-13
+3.5
376 11 48
+ 1.5
305 24 2 1
Ohron.fast.. 5 00 34.64
Chron. fast . 5 00 3t.99
Observed Z.D. 62 41 5S
Refraction . . 1 57
Observed Z.D. 60 51 04
Refraction . . +1 49
0 0 / // 0
360-291 50 00 = 68 10 00
True Z.D. . . 62 43 53
360 - 308 01 45 = 51 58 15
True Z.D. . . 60 33 53
11. M. S.
„ .r5 00 34.641 "■ "• s-
Chronometer Fast < > 5 00 34.81
15 00 34.99J
126
EXPERIMENTS FOR DETERMINING THE VARIATION
New York.-
Determination of the Rate of the Chronometer by Zenith Distances, continued.
By Zenith Distances of Sirius, East of the Meridian.
January 3d ; Barometer 30.20 ; Thermometer 36 5°.
Chronometer.
Level.
ReadlDgSi &c.
Chruooineter.
Level.
Readings, &c.
H. M. s.
13 33 42.8
13 35 08
13 36 36
13 39 06.8
13 41 54
13 43 15.6
0
0
0
0
+2
+2
0
0
0
0
-6
-7
0 / ,/
First Vernier 343 24 00
Second „ 24 00
Third „ 24 30
Foutth „ 23 30
H. M. S.
13 46 24
13 48 26.4
13 50 17.6
13 53 46.8
J3 57 05.6
13 58 48
+3
+2
+2
0
0
+9
-6
-8
-7
0
0
0
o t II
First Vernier 43 02 10
Second „ 02 00
Third „ 02 35
Fourth „ 02 00
Mean. ... 343 24 00
Index. . . .+87 51 05
Level. . . . -3.5
Mean .... 43 02 1 1
Index + J 16 36 00
index. . -^ |ggo pg 00
Level. ... —2.5
Mean. . . 13 38 17.2
True time. 8 37 44.4
+4
-13
Mean. . . 13 52 28.07
True time. 8 51 54.77
+ 16
-21
-3.5
431 15 01.5
-2.5
419 38 09
Chron. fast . 5 00 32.8
Chron. fast . 5 00 33.3
1 03
Observed Z.D. 71 52 30
Refraction . +3 02
i'o 00
Observed Z.D. 69 56 $1.5
Refraction . . +2 43.5
SfiO-272 08 55 = 8°7 5
O O / // 0
360-343 24 00 = 16 ;
TrueZ.D. . . 71 55 32
True Z.D. . . 69 59 05
H. M. S.
r 5 00 32.8 "! H. M. s.
Chronometer, Fast < , „„ „„ o f" 5 00 33.05
L o UU oci. o J
New York. OBSERVATIONS to DETERMINE the RATE of the Chro-
nometer No. 423, from the 24th of December to the 2d of January, by the
DISAPPEARANCE of STARS behind the Steeple of the Presbyterian Church,
viewed in a Telescope fixed to the Wall, in the Eastern Window of the Chapel
of Columbia College.
Time of Disapp. by the Chron.
Inter-
Difference
Chronometer's Loss.
reuce.
val of
Sid.
Days.
between
9 Solar and
Sid. Days.
December 24.
January 2.
In the
Interval.
per Sid.
D.iy.
per Sol.
Day.
11. M. S.
H. M. s.
H. s.
M. S.
S.
s.
S.
1st. — Ursae Majoris
12 11 35.2
11 35 49.6
35 45.6
9
35 23.19
22.41
2.49
2.5
2d. — Ursae Majoris
12 15 16
11 39 29.6
35 46.4
9
35 23.19
23.21
2.58
2.59
3d. — Ursae Majoris
12 23 56.8
11 48 10.4
35 46.4
9
35 23.19
23.21
2.58
2.59
m THE LENGTH OF THE SECONDs' PENDULUM.
127
RESULTS of the PRECEDING OBSERVATIONS.
Interval.
No. of
Days.
Cbron.'s loss,
on Mean Solar
Time.
S.
December 22d to January 2d
II
2.61
„ 22d to „ 3d
12
2.59
By the Sun, West of the Meridian ....
„ 23d to „ 2d
10
2.76
23d to „ 3d
II
2.72
By the Sun, East of the Meridian. . . .
„ 24th to „ 2d
9
2. 59
By a. Lyrae, West of the Meridian. . . .
22d to „ 2d
11
2.59
By Rigel, East of the Meridian ....
23d to „ 2d
10
2. 67
By Rigel and Sirius, East of the Meridian .
23d to „ 3d
11
2.59
No. 1.
24th to „ 2d
9
2.50
By the Diappearance of Stars. . ■
No. 2.
,, 24th to „ 2d
9
2.59
No. 3.
„ 24th to „ 2d
9
2.59
Mean, — Chronometers' loss per Diem .
2.62
Intermediate.
December 24 to December 29.
5
2.63
By the Sun, East of the Meridian. . . <
„ 29 to January 2.
4
2.56
128
EXPERIMENTS FOR DETERMINING THE VARIATION
New York. Comparisons of the Astronomical Clock with the Chronometer No.
423, between the 22d of December, 1S22, and the 3d of January, 1S23; with the
Clock's Rate on Mean Solar Time deduced.
I82Z.
Chronometer.
Clock.
Clock's Loss on 42S.
DAILY RATES.
ChroD.
Clock.
n. M. s.
11. M. S.
Losing,
Losing.
Dee. 22 A. M.
S 50 03.9
s.
. 30.61
„ 23 A. M.
S 49 32.3
■ 30.3
„ 24 A. M.
S 49 52
s.
•30.4
> 29.98
„ 25 A. HI.
8 4S 31. G
.29.6
„ 26 A. M.
S 4S 02
. 29
„ 27 A. M.
S 47 33
s.
S.
S.
■ 30 1
• 30.01
2.62
32.63
„ 2S A. M.
• 7 00 00 .
S 47 03
. 29.9
„ 29 A. M.
S 46 33.1
.29.9
„ 30 A. M.
S 46 03.2
. 29
30.04
„ 31 A. M.
8 45 34.2
1S23
Jan. ) A. M.
S 45 04
. 30.2
. 30
„ 2 A. M.
8 44 34
. 31.3
„ 3 A. M.
8 44 02.7
J
IN THE LENGTH OF THE SECONDS* PENDULUM.
1-29
New York. COINCIDEXCES OBSERVED with PENDULUM No. 3
; the Clock making 86367.37
Vibrations in a Mean Solar Day.
DATE.
Observer.
Baro-
meter.
."O
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Menu
Interval.
Correc-
tion for
tlieAre.
Vibratious
in 24 lionrs.
Redac-
tion to a
mean
Tempe-
rature.
Reduced
Vibrations at
35.60=
1S22.
ts.
o
M. S.
M. s.
H. M. S.
0
o
S.
S.
Dec.
1
40.3
33 49
33 53
10 33 51
1.18
-1-
23 A.M.
Capt. Sabine
30.I4oJ
> 40.2
G84.15
1.22
86116.10
-Hi. 91
86118.01
1 >'
40.1
27 46
27 59
12 27 52.5
0.58
1
40.3
40 00
40 06
1 40 03
1.2
?S P.M.
Mr. Renwicfc
30.260S
•
40.25
684.25
1.25
S6!!6.15
-hi. 93
86118.08
i
11
1
40.2
33.7
33 56
11 02
34 15
11 05
3 34 05.5
9 11 03.5
0.58
1.2
24 A.M.
Capt. Sabine
30.40oJ
11
1
34.3
34.75
06 06
28 50
06 21
28 54
11 06 13.5
11 28 52
>
0.58
1.18
34
691
1.25
86118.63
-0.70
86117.93
24 A.M.
Capt. Sabine
30.400-^
11
1
36.25
36.8
23 36
35 41
23 47
35 45
1 23 41.5
1 35 43
0.6
1.26
35.5
688.93
1.25
86117.87
-0.07
86117.80
24 P.M.
Mr. Renwick
30.40oJ
11
36.3
30 01
30 21
3 .SO 11
>
0.66
36.55
686.8
1.46
86117.32
-1-0.37
86117.69
f
1
32.9
41 43
41 47
10 41 45
1.2
25 A.M.
Capt. Sabine
30.120<
11
1
33.6
33.5
36 49
59 30
37 04
59 37
12 36 56.5
12 59 33.5
0.6
1.21
33.25
691.15
1.28
86118.72
-1.01
86117.71
25 P.M.
Mr. Renwick
30.000-
'(
11
35.6
54 27
54 48
2 54 37.5
>
0.58
.34.55
690.4
1.26
86118.42
-0.47
86117.95
1 ,
32.6
51 20
51 25
10 51 22.5
1.2
26 A.M.
Capt. Sabine
30.000.
11
1
33
33.1
46 3T
58 26
46 49
58 30
12 46 43
12 58 28
>
0.6
1.24
32.8
692.05
] 1.28
86119.04
-1.20
86117.84
26 P.M.
Mr. Renwick
30.180-
11
34.6
53 31
53 52
2 53 41.5
0.59 J
33.85
691.35
1.31
86118.81
-0.76
86118.05
Means. .
30.210
35.66
86117.9
86117.9
130
EXPERIMENTS FOR DETERMINING THE VARIATION
New York. COINCIDENCES OBSERVED with PENDULUM 4 ; the Clock making 86367.37
Vibrations in a Mean Solar Day.
! [DATE.
5 ^Observer. ;
Baro-
mtter.
1822.
Dec.
27 A.M.
;27P.M.
28A.M.
^8 P.M.
29 A.M.
29 P.M.
! 30 A.M.
30 P.M.
Capt. Sabine
Mr-Renwick
Mr.Renwick
Mr.Renwick
Capt. Sabine
Mr.Renwick
Mr.Renwick
Mr.Renwick
31 P.M. Mr.Renwick
1823.
Jan.
1 A.M. Capt. Sabine
2 A.M. Capt. Sabine
30.420
30.420
30.290
30.290
30.290
z =
Tempe-
rature.
Time of
Disap-
pearance
Time of
Re-ap-
pearauce
TmeTimeof
Coincidence-
Arc of
Vibra-
tion.
Mean
Tempe-
ratore.
§9.290
30-460
30.560
30.790
30.510
29.980
2 P.M.
Means
Mr.Renwick
30.020
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
1
11
30.367
32.7
32.3
32.4
32.8
32.6
33
33 1
32.9
32
33.7
35
36.5
33.4
35.1
35.3
36.6
33
34.2
31.2
31.2
33.3
35.7
36.2
37.3
M. S.
11 33
11 23
22 57
22 39
13 22
12 59
36 43
36 25
7 22
7 20
30 32
29 52
3 35
3 03
25 16
24 26
47 02
46 35
31 44
31 52
15 33
15 10
21 01
20 05
M. S.
11 S9
11 40
23 04
23 10
IS 24
13 26
36 48
36 49
7 30
7 34
30 39
H. M. S.
11 11 36
1 11 31.5
1 23 00.5
3 22 54.5
10 13 23
12 13 12.5
12 36 45.5
2 36 37
9 07 26
11 07 27
11 30 35.5
30 10 1 30 01
3 40
3 29
25 22
24 46
47 09
46 57
31 53
.32 10
15 39
15 26
21 02
20 26
10 03 37.5
12 03 16
12 25 19
2 24 36
12 47 05.5
2 46 46
11 31 48.5
1 32 01
9 15 36
11 15 18
12 21 01.5
2 20 15.5
1.18
0.58
1.24
0.59
1.3
0.62
1.24
0.58
1.14
0.58
1.24
0.58
1.281
0.6 J
1.23
0.61
1.2)
o.soj
1 18]
0.6
1.2
0.6
1.29
0.61
.32.5
32.6
32.8
Mean
Interval.
Correc-
tion for
the Arc
32.85
35.75
34.25
35.95
33.6
31.2
34.5
36.75
33.81
s-
719.55
719.4
718.95
719.15
720.1
716.53
717.85
715-7
718.05
721.25
718.2
Vibrations
in 24 hours.
715. 4
+
1.22
1.31
1.44
1.30
1.17
1.30
1.38
1.33
1 27
1.25
1.28
1.41
86128.52
Reduc-
tion to a
Mean
Tempe-
rature-
Rednced
Vibrations at
33.31°.
86128.57
86128.56
86128.46
86128.63
86127-58
86128.12
86127.33
86128.05
86129.1!
86128.12
86127.31
86128.2
-0.55
-0 51
-0.42
86127.97
86128.06
86128. U
0.34 86128.12
-0.40
-fO.81
-fO.18
-HO. 90
-0 09
-1.1
-^0.29
•fO.81
86128.23
86128.39
86128.30
86126.23
86128.96
86128.01
86128.41
86128.12
86128.2
IN THE LENGTH OF THE SECONDS' PENDULUM. 131
The Pheasant anchored at Portsmouth on the 5th of February, 1823,
after an unusuaUy tedious passage of thirty-one days from New York ;
and proceeding to the river, landed the instruments at Deptford on the
18th of February.
On my arrival in London, I had the satisfaction of finding that
the letter which I had written to Sir Humphry Davy from Maran-
ham, proposing the extension of the experiments to the high latitudes,
had met the approbation of the Commissioners of Longitude, and that
Lord Melville's consent had been obtained for the employment of one
of His Majesty's ships in its prosecution ; accordingly the Griper sloop-
of-war, which had been one of the vessels engaged in the Expedition of
North- West Discovery in 1819-1820, on which occasion she had been
strengthened for the encounter of ice, was commissioned by Captain
Clavering on the 26th of February, and her equipment, for the particular
navigation for which she was destined, proceeded in.
The plan of the voyage, approved by the Admiralty, and conveyed in
their instructions to Captain Clavering, directed him to proceed in the
first instance to Hammerfest, near the north cape of Norway, as a pendu-
lum station adjoining the 70 degree of latitude ; from thence to a second
station in or near the 80"" parallel, on the northern coast of Spitzbergen ;
afterwards to make the east coast of Greenland in as high a latitude as
the barrier of ice, which renders that coast difficult of access, would
permit ; and having got within the barrier, and in the navigable channel
which is usually found in the northern seas in the neighbourhood of
land, to ascend the coast to the northward, as far as might be compatible
with a return to England in the same year, and to make a third pendulum
station at the highest latitude that might be thus attained ; Captain
Clavering was then directed to return to the southward in order to get
S 2
132 EXPERIMENTS FOR DETERMINING THE VARIATION
off the coast of Greenland before the advance of the season might en-
danger his detention during the winter ; after which he was at Uberty to
use his discretion in making a fourth station at Iceland, or elsewhere in or
about the same parallel, and then to return to England. In case the Griper
should be accidentally detained in the high latitudes during the winter,
she was ordered to be provisioned for eighteen months ; and the same
liberal supply of preserved meats and warm clothing was furnished for
the health and comfort of the seamen, and under the same regulations of
issue, as had taken place in the Voyages of Discovery.
The interval of the Griper's equipment was occupied in repeating the
trial of the pendulums in Portland Place, to ascertain that they had un-
dergone no alteration in the course and by the events of the preceding
voyage*; and in providing an apparatus for the support of the clock and
pendulums, and for their protection against the weather, required at the
stations of the north, where no other accommodation or convenience
could be expected, than the rock which might serve as a foundation.
It was desirable that the various parts of the apparatus for these pur-
poses should be contrived with as much regard to portability and con-
veniency of stowage, as was compatible with the stability of the supports,
and the sufficiency of the defence against the weather ; the preparation
for supporting the detached pendulums consisted of a cast-iron tripod
stand, the legs of which screwed into the angles of a strong triangular
frame which rested on the ground ; the vertical front was an equilateral
triangle, the sides of which were six feet and a half long ; the three legs
of the tripod screwed at the upper angle, opposite to the ground, to the
vertical sides and back of a rectangular frame, the upper and horizontal
side of which was fitted to receive the agate planes on which the pen-
* The particulars are reserved until the general account of the experiments with the de-
ached pendulums in London.
IN THE LENGTH OF THE SECONDS' PENDULUM. 133
duluDi vibrated ; by levelling the foundation so that the ground frame
was nearly horizontal, the side of the rectangle supporting the planes
was sufficiently so, to admit of their being brought into exact adjustment,
by means of the screws for fixing and levelling them, attached to the
brass box in which they were contained ; the ground frame was furnished
with screws at the angles, by which it could be raised from the ground on
a sufficiently hard foundation, if it were preferred that the rest should be
on three points of bearing, instead of on the frame generally.
The clock was provided with a similar support, but made of wood,
and so contrived as to stand withinside the iron tripod, beneath the
rectangular frame which carried the planes, and on the space compre-
hended by the ground frame ; thus when the pendulum was suspended,
and the clock placed in its proper position in relation to it, every part of
the apparatus belonging to the pendulum was detached from and uncon-
nected with the clock, and with its support ; the wooden stand was fur-
nished with a vertical and side adjustment, for placing the clock in beat :
both the stands were so constructed as to be readily taken in pieces, for
convenience in packing and carriage ; the iron tripod stand weighed
altogether above two hundred pounds ; they were contrived and executed
by Mr. Jones of Charing-Cross.
In providing a suitable cover for the instruments, I had the advantage
of having had much experience in the Northern Expedition, and particu-
larly at Melville Island ; I was aware that in the Arctic Circle, during the
summer months, a much less substantial protection would suffice, than in
the temperate or torrid zones, (and especially than in the latter), because
the constant presence of the sun above the horizon causes the range of the
external thermometer in the twenty-four hours to be much less than in
other parts of the globe ; in fact, in the very high latitudes, where the
difference in the sun's altitude on the northern and southern meridians
does not exceed 20 or 30 degrees, and whilst his inferior altitude is still
134 EXPEUIMENTS FOR DETERMINING THE VARIATION
sufficiently high to cause the balance of radiation to be in favour of the
earth, the temperature, independently of the variations occasioned by
changes in the weather, is very nearly the same at aU hours. It was thus
fortunate that accommodation was least needed where it was most
deficient, a.nd that the absence of houses could be supplied by a tem-
porary provision, which would not have been sufficient at the stations
of the preceding voyage, in a point of so much importance as the main-
tenance of an uniform temperature.
I obtained from the Ordnannft Department one of the large circular
tents used by the artillery for the purposes of the laboratory, consisting
of a canvass roof and walls without lining, and supported by a single
central pole ; the tent was of sufficient dimensions to include a wooden
house of twelve feet square and ten feet high, having the tent pole in the
middle ; the house was constructed of very substantial frame work, with
a boarded roof, floor, and walls, and was made to take in pieces and put
together at pleasure, the pieces which fitted to each other being marked
correspondingly ; the roof was flat and divided into 16 compartments,
each of which could be raised and folded back upon the adjoining one,
with which it was connected by hinges, so that the light passing through
the canvass of the tent might be admitted into the room in the direction
and quantity which might be desired ; the frame was every where
strengthened with diagonal pieces so as to be extremely firm ; the tent
pole passed through a hole made to receive it in a cross beam of the
roof, and was stepped into a very strong cross beam of the floor ; so that
besides the usual security against the weather of guys and tent-cords,
the tent had the additional support of the whole strength and weight
of the house ; it was intended that the room should be only partially
floored, in order that the clock and pendulum stands might rest on an
independent foundation on the ground or rock beneath, and be thus in-
sulated with regard to the house, as they already were with regard to
' IN THE LENGTH OF THE SECONDS' PENDULUM. 135
each other : the house was buih in the dock-yard at Deptford, by an order
from the Board of Admiralty, kindly obtained by Mr. Barrow ; and was
as firm and strong at the last station at which it was used, as when it
was first completed.
A small but extremely portable observatory for the transit instrument
was made under the direction of Mr. Dollond, the roof, sides, and floor,
of which were framed in separate pieces and fastened together by cop-
per screws ; the pedestal for the support of the transit, passed through
the floor, but was unconnected with it, so as to be entirely insulated ; it
exceeded four feet in length, of which a foot and a half was above the
ground, and the lower end wedged firmly into a frame sunk to the proper
depth for that purpose ; the pedestal was octagonal in shape, and being
hoUow was filled in with earth and stones to increase its firmness ; a flat
slab of free stone was screwed to the upper end, and rendered horizontal
by the insertion of wedges before the screws were tightened ; on this
stone rested a second slab of the same material to which the frame and
piUars of the transit fitted and were attached by screws ; the upper stone
was moveable upon the surface of the lower, until the instrument was
placed sufiiciently near the meridian to be within reach of exact adjust-
ment by its own means, when the stones were cemented to each other by
Plaister of Paris, which united the qualities of becoming dry immediately,
and of permitting them to be separated without injury, when the
experiments at the station were concluded. When the stones were
cemented, the transit and frame could be removed at pleasure, as the
screws ensured its correct replacement, and the observatory was thus
rendered disposable at such times for the use of other instruments ; as all
its fastenings were of copper, it was particularly adapted for experiments
connected with Magnetism.
A marquee for myself and a tent for my servant, both of which had
been supplied by the Ordnance Department at the commencement of
136 EXPERIMENTS FOR DETERMINING THE VARIATION
the Arctic Expeditions in 1818, completed the preparation for the northern
stations.
The compensation of the chronometers Nos. 423 and 493 requiring
adjustment, they were returned to the makers for that purpose on my
arrival in England, and Nos, 649 and 602 received in their stead ;
No. 619 was a pocket chronometer to be used in observation as No. 423
had been ; I also received No. 423 again, a day or two before my de-
parture for the north, having particularly requested that I might do so ;
its rate had not been examined by the makers since the adjustment of
its compensation, and I found it somewhat wider than it had been pre-
viously ; but as I used No. 649 from henceforth (with one accidental
.exception,) I did not take the pains to reduce the rate.
The equipment of the Griper being pressed with all the means which
Captain Clavering could obtain, she was ready for sea by the second
week in May, and sailed from the Nore on the 11th for Hammer-
fest, where she arrived on the 4th of June, having manifested in the
■passage that the heavy sailing by which she had been distinguished on
her former voyage, was in no degree improved.
IN THE LENGTH OF THE SECONDS* PENDULUM. 137
HAMMERFEST.
Hammerfest is a small trading and fishing town, built on one of the
numerous islands which adjoin the coast of Finmarken, and is distant
only a few miles from the northern extremity of Europe ; the town is
situated on the southern side of the harbour ; and on the opposite side
called Fugleness, Mr. John Crowe, an English merchant, has formed
within a few years past, a very promising commercial establishment,
occupying a long and narrow projection of rock, washed on each side by
the sea, and raised but little above its level. I had had the good fortune
to make Mr. Crowe's acquaintance in London during the spring, whilst
the Griper was fitting, and he had sailed on his return to Hammerfest,
some days before she was ready for sea : his arrival therefore, had pre-
ceded ours, and we found him prepared to receive us, with an hospi-
tality characteristic of the country in which he has made his summer
residence.
A spot was soon selected at Fugleness, in which the rock was suffici-
ently level for the few square feet required as a foundation for the house
and instruments ; the guys which stayed the tent pole, and the cords by
which the roof and walls of the tent were fastened down, were secured by
grapnels and ice anchors, and by heavy pieces of the rock brought for
the purpose ; the walls of the house were banked up with earth for a con-
siderable part of their height, and folds of canvass were nailed over every
crevice by which the air might gain admission into the room ; these precau-
tions were not unnecessary, as the weather proved most unfavourable dur-
ing the greater part of our stay, being almost an incessant gale, with rain,
T
138 EXPERIMENTS FOR DETERMINING THE VARIATION
sleet, and heavy fog ; nor were they in vain, as notwithstanding the violence
of the weather, the interior of the room remained perfectly dry, and free
from drafts ; even in the heaviest gale, floss silk suspended by the side
of the pendulum shewed that the air within the house was in a tranquil
state; the apparatus of the house and tent answered its purpose so
effectually, that the going of the clock and pendulums sustained no
inconvenience whatsoever. The comparison of the chronometer with
astronomical time was, however, very much impeded by the weather;
of twelve stars with which the transit list commenced on the 9th of June,
three only could be observed on the 22nd, and none on any of the in-
termediate days, except ^ UrSce, which was visible whilst passing two
of the wires on the 14th; the 23d continuing obscure, the series of coin-
cidences was closed on the preceding day, as the gain of the chronometer
in the interval between the observations on the 9th and 22nd, appeared
to have been satisfactorily determined by the transits of the sun and of
the three stars, and as the daily rate of the chronometer and of the clock
in the interim had been sufficiently uniform ; the transit observations
were also corroborated by the results deduced from those with the Repeat-
ing Circle, although the opportunities for the use of the latter instrument
were by no means favourable, as in addition to the slow motion of the
sun in altitude in the latitude of 70°, his limb became generally iU-
defined when at the proper distance from the meridian ; this interruption
of continuity, or ragged appearance of the disk is a frequent impediment
to exact observation in the Arctic Circle ; it affects both limbs, com-
mencing generally at about 30° or 35° of altitude, and increasing as the
sun descends.
The clock room not being of sufficient size to receive the telescope for
the observation of coincidences, when at the proper distance from the
pendulum, the stand for its support was placed between the house
and tent, and a window of a single pane was made in the wall which
IN THE LENGTH OF THE SECONDS' PENDULUM.
139
interposed between the telescope and its object ; a wooden porch was
built around the telescope, capable of containing a single observer, by
whom, when sealed at the telescope, the face of the clock was visible
through the open window.
Qualoen or Whale Island on which Hammerfest is situated, as weU as
the neighbouring islands and adjacent continent, are composed of primi-
tive rock ; that of Qualoen is principally Gneis. The height of the pen-
dulums above the sea was twenty-nine feet.
As the present occasion was the second in which Hammerfest had been
visited from England for astronomical purposes, and as from the pecu-
liarity of its situation in being the most northern town in the globe,
future occasions may occur of a similar nature, it may be useful to notice,
that the unfavourable weather, which we experienced during the month
of June, is said to be very prevalent in the summer months, but to be
confined to the islands; as we were informed, that at the same periods
the weather on the adjacent continent would present the remarkable
contrast of a serene and clear atmosphere ; on this account, Alten would
probably be a preferable station to Hammerfest for celestial obser-
vations ; but in otber respects, the harbour of Hammerfest is more easily
accessible, and as being the residence of Mr. Crowe, and of the other
members of his commercial establishment, Fugleness possesses an
advantage of much consideration to English visitors.
The instruments being re-imbarked on the morning of the 23d of June,
the Griper sailed in the afternoon, and anchored on the first of July in
Fair Haven on the north of Spitzbergen; the only ice which had been
seen on the passage, being a small stream, which frequently during the
summer season is found to set with the current round the southern shore
of Spitzbergen.
T -2
140
EXPERIMENTS FOR DETERMINING THE VARIATION
TRANSITS OBSERVED AT HAMMERFEST.
DATE.
STARS.
TIMES OF TRANSITS BY No. 649.
Mean by tlie
Chronometer.
Chron. Slow
on Mean Time.
1st Wire.
2d Wire.
Meridian Wire.
4tli Wire.
5th Wire.
1823.
H. M.
II. M.
II. M. S.
H. M.
H. M.
H. M. S.
11. M. S.
June 9
(l«'Limb
Sun^
(2'i Limb
25 03.2
25 31.6
22 26 00.4
26 28.8
26 57.6
(22 24 51.43
1 S3 47.82
j» j»
nUrsae ....
56 06.8
56 47.6
6 57 28
58 09.6
58 50
6 57 28.33
>J 3>
Arcturus. . .
23 30
23 58
7 24 25.6
21 54
25 22
7 24 25.87
it »
aLyrae ....
45 58
46 31.2
11 47 04.8
47 38
48 12
11 47 04.8
,. 10
fl"Limb
Sun <
(2'iLimb
22 58.8
25 15.6
23 27.2
25 44.4
22 23 56
22 26 13.2
24 24.8
26 42
24 53.2
27 10.8
[22 25 04.6
1 33 46.3
,, 12
fl"Limb
Sun i
(2<iLimb
23 25.2
25 43. G
23 54
26 12
22 24 22.4
22 26 40.8
21 51.2
27 09.6
25 19.2
27 38
(22 25 31.6
1 33 43.25
,, 13
f P'Limb
Sun{
(.2"' Limb
25 57.6
26 25.6
22 26 54.4
27 23.2
27 51.6
[22 25 45.57
1 33 41 63
„ 14
fl"Limb
Sun-J
1 2-1 Limb
23 53.2
24 21.6
22 24 50.4
25 18.8
25 47.2
[22 25 59.17
1 33 40.38
" )'
jiUrsffi ....
36 34.4
37 15.6
6 .. ..
6 37 56 13
,. 17
ri»'Limb
Sun<
t2<i Limb
24 36
26 53.2
25 04.8
27 22
22 25 33.2
22 27 50.8
26 02
28 19.6
26 30.4
28 48
[22 26 42
1 33 35.6
„ 22
n«Limb
Sun^
[2'! Limb
25 46.4
28 04.4
26 15.2
28 33.2
22 26 43.6
22 29 01.6
27 12
29 30
27 41.2
29 59.2
[22 27 52.67
1 33 29.33
M J»
jiUrsse ....
5 17.6
5 58.4
6 06 39.6
7 20
8 01.2
6 06 39.4
3» Jj
Arcturus. . .
32 41.6
33 09.6
6 33 37.6
34 05.6
34 33.2
6 33 37.53
) J)
a Lyrfe ....
55 08.8
55 42.8
10 56 15.6
56 49.2
57 22.8
10 56 15.8
IN THE LENGTH OF THE SECONDS PENDULUM.
141
Hammerfest. observations to DETERMINE the RATE of the Chronometer No. 649, on Mean
Time, between the 9th and 22d of June, 1S23, by ZENITH DISTANCES of the Sun, with a Repeating Circle.
Latitude of (he Place of Observation 70° 40' 04.5" N. ; Longitude 23° 45' E.
June 9th P.M.; Barometer 30 . 1 0 ; Thermometer 57° ; Q's
U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
S 54 15.2
3 56 02.4
3 58 07.6
4 59 55.2
4 01 28.4
4 02 54
0
+ 7
0
+5
0
+ 6
0
+ 3
0
0
0
+ 1
o / «
First Vernier 63 47 30
Second „ 47 10
Third „ 47 50
Fourth „ 47 10
H. M. S.
4 07 35.6
4 09 18.4
4 11 02
4 12 42.8
4 14 12.8
■ 4 16 06
+5
0
0
-2
+4
+3
0
0
0
0
0
0
O J jt
First Vernier 106 13 00
Second „ 12 50
Third „ 13 10
Fourth „ 12 20
Mean ... 63 47 25
Index . . .+332 10 22
Level ... +11
Mean ... 106 12 50
Index . . .+296 12 35
Level ... +5
Mean. . . 3 58 47.13
True Time. 5 32 35
+22
0
Mean ... 4 1 1 49 . 6
True time. 5 45 38.1
+ 12
-2
+ 11
395 57 58
+5
2 35
402 25 30
Chron. slow 1 33 47.87
Chron. slow 1 33 48.5
Observed Z.D. 65 59 40
Ref. andParal. + 2 00
Semidiam . . +15 47
Observed Z.D. 67 04 15
Ref. and Paral. + 2 06
Semidiam . . +15 47
360- 2°7 49 38 = 33°2 1
6 22
360- 6°3 47 25 = 296 1
True Z.D. . . 66 17 27
True Z.D. . . 67 22 08
H. M. S.
Chronometer, Slow 1' ^^ 47.87]_ j- gj ^gjg
Ll 33 48.5 j
June 22dP.M.; Barometer 29 .85 ; Thermometer 47°; O'
5 U.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readings, Sec,
H. M. s.
3 49 03.2
3 52 37.2
3 54 16.8
3 56 06.4
3 57 37.6
3 59 08
+3
+ 2
0
0
+ 5
0
-5
-5
0
-6
— 3
0
First Vernier 91 10 50
Second „ 10 00
Third „ 1 1 00
Fourth „ 10 15
H. M. S.
4 03 38
4 05 08
4 06 35.6
4 08 10
4 09 43.2
4 10 58.8
0
+ 2
-1
+6
0
-2
0
-5
+5
-1
0
-8
First Vernier 97 14 20
Second „ 14 00
Third „ 14 50
Fourth „ 14 15
Mean ... 91 10 31
Index . . .+268 48 02.5
Level ... +4.5
Mean ... 97 14 21
Index . . .+268 49 29
Level ... -2
Mean. . . 3 54 48.2
True time. 5 28 20.05
+ 10
-19
Mean. . . 4 07 22.27
True time 5 40 54.25
+ 13
-17
-4.5
359 58 38
-2
29
366 03 48
Chron. slow 1 33 31.85
Chron. fast. 1 33 31.98
Observed Z.D. 59 59 46
Ref. and Paral. +1 34
Semidiam . . +15 45
Observed Z.D. 61 00 38
Ref. and Paral. +1 38
Semidiam . . +15 45
360-91 11 57.5 = 268 4
8 o'2.5
360-91 10 3'l = 268 49
True Z.D. . . 60 17 05
True Z.D. . . 61 18 01
H. M. S.
[ 1 3S 31.85 ] H. M. s.
Chronometer, Slow ^ 1 33 31.98 [ 1 33 31.93
[ 1 33 31.97'J
* The particulars of Ibis observation are in the nest page.
1
142
EXPERIMENTS FOR DETERMINING THE VARIATION
Hajimerfk.st. Determiuation of the Rate of the Chronometer by Zenith Distances, continued.
June 22d P.M.; Bar. 29.85; Therm. 47°; Q'sU.L.
June 10th A.M. ; Bar. 29 .94 ; Thev. 57° ; Q\ X.L.
Chronometer-
Level.
Readiugs, &c
CUronometer.
Level.
Headings, &c.
JI. M. S.
4 15 59.6
4 17 04.4
4 19 16. 4
4 20 32
4 22 36
4 23 56.4
-7
+6
-7
+ 5
0
+6
0
-I
+ 1
— 2
0
-1
First Vernier 109 26 00
Second „ 25 30
Third „ 26 20
Fourth „ 25 50
H. M. S.
5 15 47.2
5 18 04.4
5 20 42
5 23 07.2
5 25 21.6
5 28 11.2
0
+ 3
0
0
-3
0
0
0
0
0
0
0
o . <l
First Vernier 129 51 20
Second „ 51 00
Third „ 51 40
Fourth „ 50 40
Mean ... 109 S5 55
Index . .+262 45 39
I level ... 0
Mean ... 129 51 10
Index . . .+253 46 42.5
Level ... -0
Mean. . . 4 19 54.13
Trae time . 5 53 26.1
+ 18
-18
Mean. . . 5 21 52.27
Trae time . G 55 41.1
+3
-3
0
.372 11 34
0
283 37 52.5
Chron. slow 1 S3 31 .97
Chron. slow 1 33 48.83
Observed Z.D 62 0! 56
Ref. and Paral. + 1 42
Semidiam . . +15 45
ObseiTed Z.D. 63 56 19
Ref. and Paral. + 1 50
Semidiam. . . — 15 47
Ce 42.5
3°G0-9°7 14 21 = 262
J5 39
360-10°6 13 17'.5=25°3 '
True Z.D. . . 62 19 23
True Z.D. . . 63 42 22
June lOtli A.M.; Barometer 29.94; Thermometer 57° ; Q's
L.L.
Chrouometer,
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
5 33 31.2
5 35 29.2
5 37 56
5 40 47.2
5 42 48
5 44 13.2
+ 3
+5
+2
-3
0
0
0
0
0
0
0
0
o . «
First Vernier 145 00 20
Second „ 00 00
Third „ 00 30
Fourth „ 00 00
H. M. S.
5 50 02.4
5 51 39. G
5 53 52.4
5 55 28.4
5 57 26
5 59 00
0
0
+5
-5
+ 3
0
0
0
0
0
0
0
O * if
First Vernier 152 38 20
.Second „ 38 10
Third „ 38 40
Fourth ,. 38 10
Mean . . . 145 00 12.5
Index . . .+230 08 50
Level . . . +3.5
Mean ... 152 38 20
Index . . .+214 59 47.5
Level ... +1.5
Mean. . . 5 39 07.47
True time . 7 12 55.7
+ 10
— 3
Mean. . 5 54 34.8
Trae time. 7 28 23. G
+8
-5
+3.3
375 09 06
+ 1.5
367 38 09
Chcon. slow 1 33 48.23
Chron. slow 1 33 48.8
Observed Z.D. 62 31 31
Ref. and Paral. + 1 43
Semidiam . . — 15 47
9 47.5
Observed Z.D. 61 16 21. S
Ref. and Paral. + 1 36.5
Semidiam . . — 15 47
360-129 51 l"o = 2°30
o's 5"o
360-145 00 l'2.5=21°4 i
True Z.D. . . 62 17 27
True Z.D. . . 61 02 11
H. M. S.
fl 33 48.83) H. M. s.
Chronometer, Slow < 1 33 48.23 1 I 33 48.62
[l 33 48.8 J
•
IN THE LENGTH OP THE SECONDS* PENDULUM.
143
Hammerfest. Determination of the Rate of the Chronometer by Zenith Distances, continued.
June 22d A.M. ; Barometer 29 .85 ; Thermometer 44° ; ©"s L.L.
Chronometer.
H. M.
6 09
6 11
6 12
6 15
6 17
6 19
s.
44
13.2
39.6
08
18
00.4
Mean. .
True time
6 14
7 47
10.53
39.4
Chron. slow I 33 28.87
+2
-3
+7
+ 6
+2
0
+ 17
— 5
-11
0
-1
-5
0
-25
— 4
360- 121 35 26=238 24 34
ncatliiigs, & ,
First Vernier 118 23 20
Second
Third
Fourth
Mean .
Index .
Level .
23 05
23 40
23 00
. 118 23 16
.+238 21 34
-4
356 47 46
Observed Z.D. 59 27 58
Ref, and Paral. +1 33
Semidiam . . —15 46
True Z.D.
59 13 45
Chronometer.
H. M. S.
6 24 40.8
6 26 13.2
6 28 00.4
6 29 38
6 31 56.8
6 33 55.2
Mean . . .
True time .
6 29 04.07
8 03 34.77
Chron. slow 1 33 30.
0
+5
0
0
— 5
+7
+ 14
0
0
+2
0
-7
+3.5
Readings, &c.
First Vernier 108 11 50
Second
Third
Fourth
Mean .
Index .
Level .
11 20
12 00
11 20
. 108 11 37.5
.+241 .36 44
+ 3.5
349 48 25
Observed Z.D. 58 18 04
Ref. and Paral. +1 28
Semidiam . . —15 45
True Z.D.
58 03 47
Chronometer, Slow <
H. M S,
fl 33 28.87) "• "• ^i-
il 33 30.7 J
1 33 29.79
RECAPITULATION.
June 9th P.M. ]
> Chronometer Slow
June 10th A.M. j \l 33 48.62
H. M. S.
1 33 48.191 H. M. s.
!■ 1 33 48.4 at Midnight, June 9th.
June 22d A.M. "j [l 33 29.791
> Chronometer Slow ', j- 1 33 30.86 at Noon, June 22d.
June 22d P.M. J [l 33 31.93^
Chronometer's Gain in 12i Days . . 0 00 17.54 = 1.4 Seconds per Diem.
144
EXPERIMENTS FOR DETERMINING THE VARIATION
Hammerfest. —
-DEDUCTION of the RATE of the Chronometer No. 649 from the
9th to 22d of June, 1S23.
9
10
11
12
13
14
15
16
17
IS
19
20
21
STAES.
(o
to
to
to
to
to
to
to
to
to
to
to
to
10
11
12
13
14
15
16
17
18
19
20
21
22
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
s.
The Sun . .
1.52
1.53
1.52
1.62
1.25
1.59
1.59
1.59
1.25
1.25
1.25
1.25
1.25
>i Ursse . . .
1.47
1.47
1.47
1.47
1.47
1.29
1.29
1.29
1.29
1.29
1.29
1.29
1.29
2
>->
CO
Arctunis . .
1.42
1.42
1. 12
1.42
1.42
1.4?
1.42
1.42
1.42
1.42
1.12
1.42
1.42
<t LyriE . .
1.K8
1.38
1.3S
1.38
1.38
1..38
1..38
1.38
1.38
1.38
1.38
1.38
1.38
By Zenith Dis-l
tances of the
Sun out of the f
Meridian . .j
i.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.44
1.41
1.44
1.4R
1..S8
1.42
1.42
1.42
1. 35
1.35
1.S5
1.35
1.35
MEANS— Gain-1
ingper Diem.J
_. .
1.43
1.38
IN THE LENGTH OF THE SECONDS' PENDULUM.
145
Hammerfest. Comparisous of the Astronomical Clock with the Chronometer
No. 649, from the 9th to the 22d of June, 1823 ; with the Clock's Rate on
Mean Solar Time deduced.
1823.
Chronometer.
Clock.
Clock's Loss on 649.
June 9 A.M
„ 9 P.M.
„ 10 A. W,
„ 10 P.M.
„ 11 A.M.
„ 11 P.M.
„ 12 a.m.
,, 12 p.m.
., 13 A.M.
„ 13 p.m.
„ 14 A.M.
„ 14 P.M.
„ 15 a.m.
„ 15 P.M.
„ 16 A.M.
„ 16 P.M.
„ 17 A.M.
„ 17 P.M.
„ 18 A.M.
,, IS P.M.
„ 19 A.M.
„ 19 P.M.
„ 20 A.M.
„ 20 P.M.
„ 21 A.M.
„ 21 P.M.
„ 22 a.m.
„ 22 P.M.
9 00 00
H. M. S.
9 05 IS. 7
9 05 52
9 06 25.4
9 06 58.6
9 07 32
9 OS 06.4
9 08 38.7
9 09 12.2
9 09 45.8
9 10 19 1
9 10 53
9 11 26
9 11 59.3
9 12 32.7
9 13 05.7
9 13 39.7
9 14 13.3
9 14 47
9 15 20.4
9 15 54.8
9 16 20.6
9 17 03
9 17 36.8
9 18 10.5
9 18 44.2
9 19 17.8
9 19 51.4
9 20 25
s,
33.3
33.4
33.2
33.4
33.4
33.3
33.5^
33.6
33.3
33.9
I 33
I 33.3
33.4
33
34
33.6
33.7
33.4
34.4
33. S
34.4
33.8
33.7
33 . 7"
33.6
33.6
33.6
66.7
66.6
66.7
67.1
67.2
66.7
67
67.3
67. S
D.MLY RATES.
Chron.
Clock.
Gaining.
66.77
1.43
^aiiiiiig.
68.2
68
2
67
5
67
3
67.
2
67.43
1.3S
68. SI
U
146
EXPERIMENTS FOR DETERMINING THE VARIATION
Hammerfest
—COINCIDENCES OBSERVED with PENDULUM 3; the Clock making
S646S.2 Vibrations in a Mean Solar Day.
IN THE LENGTH OF THE SECONDS* PENDULUM.
147
Hammerfest. ^COINCIDENCES OBSERVED with PENDULUM No. 4 ; the Clock making
S64GS.S1 "Vibrations in a Mean Solar Day.
DATE.
Baro-
meter.
No.
of Co-
inci-
dence.
Tempe-
Time of
Disap-
pearance.
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tenipe-
rntare.
Mean
Interval.
Correc-
lion lor
tile Arc.
Reduc-
Vibrations 11 tion to a
mean
in '24 hours. jlTempera-
ture.
Reduced
Vibrations at
44.34.
1823.
June 15 P.M.
„ 16 A.M.
„ 16 P.M.
„ 16 P.M.
„ 17 A.M.
,, 17 P.M.
„ 19 A.M.
„ 19 P.M.
„ 10 P.M.
„ 20 A.M.
20 P.M.
„ 21 A.M.
„ 22 P.M.
29.62
29.59
29.58
29.58
29.40
29.35
29.92
29.85
29.80
29.66
29.74
29.93
29.81
1
48
n
48
1
50
11
48.8
1
47
11
46.3
1
46.2
11
45.8
I
42.6
11
43
1
44.2
11
45.6
1
40
11
41.5
1
41.8
11
42
1
42
11
42
1
41.5
11
42
1
42.2
11
11.8
1
38.8
11
40
1
52
11
51.8
HI. s.
53 37
51 35
19 21
16 53
58 46
56 56
38 18
36 30
34 59
33 54
18 .33
16 57
32 21
31 44
27 51
26 51
50 09
49 04
54 37
53 44
12 59
12 00
15 51
15 21
2 37
59 31
M. S.
53 42
52 05
19 24
17 12
58 53
57 15
38 23
36 52
35 04
34 10
18 36
17 14
32 28
31 59
27 58
27 18
50 11
49 26
54 44
53 58
13 07
12 17
15 57
15 41
2 41
59 53
II. M. S.
5 53 39.5
7 51 50
9 19 22.5
U 17 02.5
1 58 49.5
3 57 05.5
5 38 20.5
7 36 41
9 35 01.5
11 31 02
2 18 34.5
4 17 05.5
10 32 24.5
12 31 51.5
1 27 54.5
3 27 06
4 50 10
6 49 IS
9 54 40.5
11 53 51
2 13 03
4 12 08.5
10 15 54
12 15 32.5
4 2 39
5 59 43.5
1.2 I
0.6 j
1.2
0.6
1 2
0.58 J
1.2
0.6
1.2
0.58/
1.2
0.6 I"
1.16
0.58
1.16
0.58
1.24
0.61
1.18
0.6
1.18
0.6
1.2
0.6
1.24
0.64
47
49.4
46.65
46
42.8
44.9
40.75
41.9
41.75
42
39.4
51 .9
709.05
706
709.6
710.05
714.05
711.1
716.7
715.15
714.5
715.05
714.55
717.85
702.45
+
1.28
1.28
1.25
1.28
1.25
1.28
1.19
1.19
1.40
1.25
1.25
1.28
1.40
86226.16
86225.12
86226.33
86226.52
86227.87
36226.88
86228.70
86228.20
86228.16
86228.19
86228.01
86229.16
86224.00
•fl.12
4-2.12
-fO.97
-fO.70
-0.65
-fO.23
-1.51
-1.02
-0.98
-1.09
-0.98
■2.07
86227.26
86227 . 24
86227.10
86227.22
86227.22
86227.11
86227.19
86227.18
86227.18
86227.10
86227.03
86227.09
-fS.lS 86227.18
Means
29.68
4 1 . 34
86227.18
86227.18
U 2
148 EXPERIMENTS FOR DETERMINING THE VARIATION
SPITZBERGEN.
The station selected for the pendulums at Spitzbergen was on one of
the islands, called the " Norways," situated to the north-west of the
main land of Spitzbergen, and forming with its coast the harbour of
Fair-Haven : it is the south-eastermost of the group, and the inner of
the two islands which are immediately to the eastward of Cloven Cliff,
a head-land well known to the navigators of the high latitudes ; as a
further means of its recognition, it is the second when viewed from Fair-
Haven, from Vogelsang, which is still, and probably will ever remain, as
pre-eminently entitled to its appellation, as when the distinction was
conferred nearly two centuries ago. The establishment of house, tents,
and observatory, occupied a low, but dry and tolerably level and well-
protected situation, at the south-western extremity of the island ; the
foundation on which the clock and pendulum supports rested was an
extensive bed of quartz rock. The height of the pendulums was twenty-
one feet above half-tide.
Captain Clavering, being desirous of employing himself during the
experiments in examining the state of the ice to the northward of
Spitzbergen, sailed for that purpose on the 4th of July, leaving Mr. Henry
Foster, midshipman, and Mr. Rowland, assistant surgeon, of the Griper,
with a boat and crew, and a sufficiency of fuel and provisions to have
made good her passage to Norway in the course of the autumn, had
any accident befallen the ship ; we had, however, the satisfaction of
witnessing her return on the 10th, having traced in the interval the
continuity of the ice, from its abutment on the land eastward of the
Norways, to the longitude of 11° west; the examination was not pur-
IN THE LENGTH OF THE SECONDS* PENDULUM. 149
sued further to the westward, because the line of the ice had taken the
south-westerly direction, in which we should again fall in with it on the
passage to Greenland. The experiments proceeded without interruption,
and were concluded on the 19th of July.
In illustration of the small extent of the range of the external ther-
mometer in the twenty-four hours in high latitudes in summer, I have
subjoined a table shewing the extremes of a register thermometer in
successive periods of six hours, from the 9th to the 18th of July ; the
thermometer was suspended in the open air about four feet from the
ground, and protected from the sun's rays by a roof at a considerable
distance above the thermometer : the exposure was free in every other
direction.
150
EXPERIMENTS FOR DETERMINING THE VARIATION
TRANSITS OBSERVED AT SPITSBERGEN.
TIMES
OF TRANSIT BY THE CHRONOMETER 649.
Mean by the
Cbrouometer.
DATE.
STARS.
CLOCK.
1st Wire.
2d Wire.
Meridian Wire.
4tii Wire.
5(h \rire.
1823.
'
M. s.
M. S.
H. M. S.
M. 8.
M. S.
H M. S.
H.
M.
s.
July 5
m.J.|2iiLimb
17 07.2
19 24 4
17 36
19 53.6
11 18 04.4
11 20 22
18 S2.8
20 50
19 01.2
21 18.8
[ll 19 13.06
11
09
33.97
,. 6
aCygni. . . .
52 36.4
S3 12.8
12 53 50
54 26.8
55 03 6
12 53 49.93
12
45
43.4
., ^
noon |2'i Limb
17 24.8
19 41.6
17 53.2
20 09.6
23 18 20.8
23 20 37.8
18 49.6
21 06.8
19 17.6
21 35 2
[23 19 29.63
23
12
00.51
» ?»
liUrsfe ....
54 50.4
55 31.2
5 56 12
56 52.4
57 33.2
5 56 11.87
5
49
06.22
M y>
Arcturus. . .
22 13.6
22 41.2
6 23 09.6
23 37.2
24 05.2
6 23 09.4
6
16
05.36
» ?-'
^Draconis . .
06 03.6
06 45.6
10 07 28
08 10
08 52 4
10 07 27.93
10
00
37.32
fs >J
aLyrae ....
44 41.2
45 14.8
10 45 48
46 21.6
46 55.6
10 45 48.2
10
38
59.9
V 8
(lUrsae ....
50 55.2
51 36.4
5 52 16.8
52 57.6
53 38.8
5 52 16.93
5
46
S7.14
., 10
„ (l"Limb
Sun J
noon j 2'' Limb
17 56
20 12
18 24
20 40.4
23 18 52.4
23 21 08.4
19 20.8
21 36.8
19 48.8
22 05.2
(23 20 00.46
11
16
53.02
)f jj
n Ursffi ....
43 04.8
43 45.6
5 44 26.4
45 07.2
45 48
5 44 26.4
5
41
41.96
» ?'
Arcturus. . .
10 28.4
10 56.4
6 11 24
11 52
12 20
6 11 24.13
6
08
41.32
j> jf
X Lyrse ....
10 34 03.8
34 37.4
35 11
10 34 03.8
10
31
33.26
ft }f
jeCygni. . . .
36 57.6
S7 34
12 38 10.8
38 47.6
39 24.4
12 38 10.83
12
35
51.44
V 11
>i Ursae ....
39 11.2
39 52
5 40 32.8
41 14
41 54.8
5 40 32.93
5
39
14.63
)• J'
Arcturus. . .
06 34.4
07 02.4
6 07 30
07 58
08 26
6 07 30.13
6 06
13.49
,, 12
Arcturus. . .
6 03 34.4
04 02.4
04 30
6 03 34.2
6
03
45.74
,, 13
„ f P^Limb
Sun )
noon [2'' Limb
18 24.4
20 40.4
18 52.4
21 08.4
23 19 20 8
23 21 36.8
19 49.2
22 05.6
20 18
22 33.6
[23 20 28.93
23
21
44.77
„ 14
„ fl*'Limb
Sun )
noon |2'i Limb
18 32
20 48.4
19 00.4
21 16.4
23 19 28.8
23 21 44.4
19 57.2
22 12.8
20 25.2
22 41.6
[23 20 36.65
23
23
21.22
,, IT
y Draconis . .
26 46.4
27 28.4
9 28 10.4
28 52.6
29 34.4
9 28 10.43
9
36
00.8
>f )J
aLyrse ....
05 24
05 57.6
10 06 31.2
07 04.8
07 38.4
10 06 31.2
10
14
23.92
„ 19
o (IstLimb
Sun )
noon (2'' Limb
18 55.6
21 10.8
19 23.6
21 38.8
23 19 51.6
23 22 06.8
20 20
22 34.8
20 48
23 03.2
[23 20 59.3
23
31
12.42
)J >J
>i Ursae ....
07 37.6
08 18.4
5 08 59.2
09 40
10 20.8
b 08 59.2
5
19
34.26
>} >J
Arcturus. . .
35 01.2
35 29.2
5 35 57.2
36 21. 8
36 52.4
5 35 57
5
46
33.78
» JJ
y Draconis . .
18 51.2
19 33.6
9 20 15.6
20 58
21 40.4
9 20 15.73
9
31
06.5
J» J>
aLyrje ....
57 29.6
58 02.8
9 58 36.4
59 10
59 43.6
9 58 36.47
9
09
29.63
>J »»
SunP^'L'-b
'"'''. (.2'" Limb
18 57.6
21 13.2
19 25.6
21 41.2
U 19 53.6
11 22 08.8
20 21.6
22 36.8
20 49.6
23 05.2
[11 21 01.3
11
31
59.61
» JJ
aCygni. . . .
01 29.6
02 06.4
12 02 4-^.6
03 20.4
03 57.2
12 02 43.47
12
22
07.02
IN THE LENGTH OF THE SECONDS' PENDULUM.
151
Spitzbergen. Comparisons of the Astronomical Clock with the Chronometer,
No. 649, from the 6th to the 20th of July, 1S23.
1823.
Chronometer.
Clock.
Clock slow or fast on 649.
July 6 A. M.
„ 6 P.M.
„ 7 A.M.
„ 7 P.M.
, S A.M.
, 8 P.M.
, 9 A.M.
, 9 P.M.
, 10 A.M.
, 10 P.M.
, 11 A.M.
, 11 P. M.
, 12 A.M.
, 12 P.M.
, 13 A.M.
, 13 P.M.
, 14 A.M.
, 14 P.M.
, 15 A.M.
I 15 P.M.
, 16 A.M.
, 16 P.M.
, 17 A.M.
, 17 P.M.
, IS A.M.
, IS P.M.
, 19 A.M.
, 19 P.M.
, 20 A.M.
, 20 P.M.
^ 3 00 00
II. M. S.
2 50 .33.6
2 51 17.6
2 52 01
2 52 43.8
2 53 26.9
2 54 09.8
2 54 53.8
2 55 38.5
2 56 22.7
2 57 05.6
2 57 49.3
2 58 31.8
2 59 16.2
3 00 00.2
3 00 44.7
3 01 29.6
3 02 13.7
3 02 5S
3 03 42
3 04 26
3 05 11.6
3 05 56.9
3 06 41.7
3 07 26.6
3 08 10.7
3 OS 56.7
3 09 41.7
3 10 27
3 11 12
3 11 56.8
Fast
Slow . 9
8
7
7
6
5
5
4
3
2
2
1
0
0
0
1
2
2
3
4
5
5
6
7
8
8
9
10
11
11
26.4
42.4
59
16.2
33.1
50.2
06 2
21.5
37.3
54.4
10.7
28.2
43.8
00.2
44.7
29.6
13.7
58
42
26
11.6
56.9
41.7
26.6
10.7
56.7
41 .7
27
12
.56.8
152
EXPERIMENTS FOR DETERMINING THE V.-iRIATION
Spitzbergen. OBSERVATIONS to DETERMINE the RATE of the Chronometer 649, and of the Astro-
nomical Clock, from Gth to 20th of July, 1823, by ZENITH DISTANCES of the Sun, with a Repeating Circle.
Latitude of the Place of Observation, 79° 49' 58" N. ; Longitude 1 1° 40' E.
July 6tli A.M.; Barometer 29 .96 ; Thermometer 41° , ©'sL.L.
Chronometer.
Level.
Reading?, &c.
Chronometer.
Level.
Readings, &c.
II. M. S.
5 31 55.2
5 34 00
5 33 55.6
5 37 58.8
5 39 46.8
5 41 50
+5
+7
+6
+ 10
-13
0
-3
-1
-2
+2
-5
0
0 ' "
First Vernier 176 41 40
Second „ 41 30
Third „ 41 50
Fourth „ 41 10
II. M. S.
5 48 37.2
5 50 24
5 52 11.2
5 54 00.8
5 53 37.6
5 57 26
0
+ 12
-2
0
+7
0
0
+ 4
-10
0
-2
-9
0 / «
First Vernier 214 35 45
Second „ 35 50
Third ,, 36 20
Fourth „ 35 30
Mean . . 176 41 32.5
Index . . . + 225 27 45
Level ... +3
Mean ... 214 35 50
Index . . .+183 18 27.5
Level ... 0
Mean. . . 5 36 54.4
True time . 6 21 45.96
+30
-24
Mean . . 5 53 02.8
True time. 6 37 52.94
+23
-23
+3
402 09 20.5
0
.397 54 17.5
Chron. slow 0 44 51 .56
Chron. slow 0 44 30.14
Observed Z.D. 67 01 33.5
Ref. and Paral. +2 11
Semidiam . . —15 45.5
Observed Z.D. 66 19 03
Ref. and Paral. +2 06
Semidiam . . — 15 45
Sfi0-is"l h 15 = 225 2
7 45
360-17°6 41 32 5=183
IS 27.5
True Z.D. . . 66 47 59
TrueZ.D. . . 66 05 24
H. M. S.
Chronometer, Slow |g ^' 50 '14} 0 44 50.85
Clock Slow of the Chronometer . 0 09 26.4
Clock Slow of Mean Time .
... 0 54 17.23
July 6th P.M. ; Barometer 29 .93 ; Thermometer 44° ; © 's U.L.
Clirononieter.
Level.
Readings, &c.
Chronometer.
Level.
Readings, &c.
H. M. S.
4 30 19.0
4 33 10
4 35 15.6
4 37 16.8
4 41 33.2
4 44 16.8
+ 8
+ 10
+ 1
+7
-1
+ 3
0
+ 3
-7
0
-9
-5
0 i tt
First Vernier 2 17 22 50
Second „ 22 45
Third „ 23 30
Fourth „ 22 30
H. M. S.
4 49 22.8
4 50 52.8
4 52 .33.2
4 54 01.6
4 55 35.6
4 57 01.6
0
0
0
0
0
0
0
0
0
0
0
0
0 , /t
First Vernier 284 25 30
Second ,, 25 30
Third „ 25 55
Fourth „ 25 10
Mean ... 247 22 54
Index . . . + 143 24 10
Level ... +5
Mean ... 284 23 31
Index . . . + 112 37 06
Level ... 0
Mean. . . 4 37 07
True time . 5 21 59.9
+ 32
-22
Mean. . . 4 S3 14.6
True time. 5 38 07.34
0
0
+ 5
392 47 09
0
397 02 37
Chron. slow 0 44 52.9
Chron. slow 0 44 52.74
Observed Z.D. 65 27 5i.5
Ref. and Paral. +2 00.2
Semidiam . . +15 43.5
Observed Z.D 66 10 26
Ref. and Paral. +2 04
Semidiam . . +15 45
360-214 33 5"o = l45
24 10
360-247 22 5'4=lf2
37 o"o
TrueZ.D. . . 63 45 37
TrueZ.D. . . 66 28 15
-
H. M.
Chronometer, SlowjJJ 'J] ^
Clock Slow of the Chrononx
;-;^l 0 44 52.82
Her . 0 08 42.4
Clock Slow of Mean Time
. . . 0 53 33.22
1
IN THE LENGTH OF THE SECONDS PENDULUM.
153
Detprminnfinn rtf tha "Rnfp nf flip PlirnnninpfAr fiJ.Q nnH nf f}ip Astronnmipal nifipli. hv 1
Zenith Distances, continued.
July 7th P.M. ; Barometer 29.80; Thermometer 40°; O's U.L.
Chronometer.
Level.
Rcidings, &c.
Chronometer.
Levcl.l
Readings, &c.
U. M. S.
4 29 53.6
4 31 37.6
4 34 12
4 36 04.4
4 38 00.4
4 39 52.8
+5
+ 5
+2
+6
+8
0
-3
-3
-6
-2
0
-7
o , «
First Vernier 162 23 00
Second „ 22 50
Third „ 23 30
Fourth „ 22 45
II. M. s.
5 00 08.4
5 01 43.2
5 03 20.4
5 05 35.2
5 07 15.2
5 10 01.2
+3
+7
0
0
0
0
-3
-1
-7
0
0
-6
0 / H
First Vernier 203 00 00
Second „ 202 59 40
Third „ 203 00 30
Fourth „ 202 59 50
Mean ... 162 23 01
Index . .+230 21 57.5
Level ... +2.5
Mean ... 203 00 00
Index . . . + 197 36 59
Level . . -2.5
Mean ... 4 34 56.8
True time. 5 19 46.7
+26
-21
Mean. . . 5 04 40.6
True time. 5 49 33.34
+ 12
-17
+ 2.5
21 57.5
392 45 01
-2.5
400 36 56.5
Chron. slow 0 44 49.9
Chron. slow 0 44 52.74
Observed Z.D. 65 27 30
Ref. and Paral. + 2 00.5
Semidiam . . +15 45.5
Observed Z.D. 66 46 09
Ref. and Paral. + 2 08.5
Semidiam . . +15 45.5
360-129 38 02.5=230
36°0 - 162 23 01 = 197
s'o s'g
True Z.D. . . 65 45 16
True Z.D. . . 67 04 03
H. M.
Chronometer, Slow i n tA
Clock Slow of the Chronome
Clock Slow of Mean Time
s.
19-j,> 0 44 51.32
ter . 0 07 16.2
. . . 0 52 07.52
1
Ji
ily 8th A.M.; (Sun in Eclipse) Barometer 29.75 ; Thermometer 33.5°; O's L.L.
Chronometer.
Level.
Readings, &c.
Chronointler.
Level.
Readings, &c.
11. M. S.
G 07 36.4
6 09 16.8
6 12 02.4
6 13 46.4
6 15 52.4
6 17 37.6
•+6
0
+4
+ T
+2
+6
-3
0
-6
— 2
—7
-4
0 / ,/
First Vernier 20 44 35
Second „ 44 20
Third „ 45 00
Fourth „ 43 50
Mean ... 20 44 26
L«vel ... +1.5
Mean ... 6 12 42
True time. 6 57 31.14
+25
-22
+ 1.5
17 s'l
394 02 21.5
Chton. slow 0 44 49.14
Observed Z.D. 65 40 23.6
Ref. and Paral. + 2 03
Semidiam. . —15 45.5
0 0 . // o
360-346 42 06=13
True Z.D. . . 65 26 41
Chronometer, Slow.
Clock Slow of Ciiron
H. M. S.
. 0 44 49.14
3meter 0 06 33.1
Clock Slow of Mean '
rime 0 51 22.24
154
EXPERIMENTS FOR DETERMINING THE VARIATION
Spitzbergen. Deteriuiiiatioii of tlie Rate of the Chronometer 649, and of the Astrouomical Clock, by
Zenith Distances, continued.
July 20th A.M.; Bavometer 29.70 ; Thermometer 42°; Q'sL.L.
CIuonomcttT.
LevL-l.
Readings, &c.
Chronometer.
Level,
Readings, &c.
H. M. S.
5 44 44.4
5 47 .38
5 49 34.4
5 51 32
5 53 52.4
5 55 53.2
+6
0
0
+ 10
+7
+6
— 2
0
0
+ 1
-2
-3
O / //
First Vernier 50 30 30
Second ,, 30 10
Third „ 30 10
Fourth „ 30 00
H. M. S.
6 00 34
6 02 04.4
6 04 06.4
6 05 28.8
6 06 57.2
6 09 05.6
+3
+3
0
-I
+8
+8
— 5
-5
0
-9
0
+ 1
First Vernier 97 17 40
Second „ 17 35
Third „ 18 10
Fourth „ 17 40
Mean ... .50 30 12.5
, , , ( 00 00 02.5
Index . .+|3gg poog
Level . . . +11 5
Mean .... 97 17 46
Index . . .+309 29 47.5
Level ... +1.5
Mean. . . 5 SO 32.4
True time. 6 35 23.23
+30
-7
Mean. . . 6 04 42.73
True time . 6 49 32.8
+23
-20
+ 11.5
410 30 26.5
+1.5
406 47 35
Chron. slow 0 44 50.83
Chron. slow 0 44 50.07
ObservedZ.D. 68 25 04.5
Ref. and Paral. +2 19
Semidiam . . —15 46.5
Observed Z.D. 67 47 56
Ref. and Paral. +2 14
Semidiam . . —15 46
300-359 59 5*7.5 = 00 0
b 02.5
360-50 30 l'2.5=309
19 47.5
TrueZ.D. . . 68 1 1 38
TrueZ.D. . . 67 34 24
II. »
Chronometer, Slow ^
Clock Fast of the Chronoi
4 so'. 83^ "■ '■• ,^- _
1 50.07/ 0 4* ^O-^S
neter . 0 11 12
Clock Slow of Mean Time
... 0 33 38.45
July 20th P.M. ; Barometer 29.70 ; Thermometer 42° ; O'sU.L.
^Chronometer.
^Level,
' Readings, &c.
Clironouieler.
Leve!.
Readings, &c.
H. M. S.
5 35 14.8
5 37 32
5 40 03.2
5 42 48
5 45 32.2
5 47 34
+5
+5
+5
0
+ 10
-11
-3
-3
-3
0
+ 2
-7
First Vernier 158 20 30
Second ,, 20 20
Third „ 20 40
Fourth „ 20 10
■
Mean ... 158 20 25
Index . . .+262 42 14
Level ... 0
Mean . . 5 41 27.37
True time. 6 26 20.3
+27
-27
0
421 02 39
Chron. slow 0 44 52.93
ObservedZ.D. 70 10 26
Ref. and Paral. +2 33
Semidiam . . +15 46
360 -9'7 n 46=262
12 14
TrueZ.D. . . 70 28 45
i
Chronometer, Slow .
Clock Fast of the Chroi
H. M. S.
... 0 44 52.93
jometer 0 11 56.8
Clock Slow of Mean 1
"ime . 0 32 56.13
IN THE LENGTH OF THE SECONDS* PENDULUM.
155
Spitzbergen. RATE of the ASTRONOMICAL CLOCK from the 7th to the 19th of
deduced from Transits.
J Illy, 1S23,
STARS.
7
to
S
S
to
9
9
to
10
10
to
11
11
to
12
12
to
13
1.3
to
14
14
to
15
15
to
16
16
to
17
17
to
18
18
to
19
7} UrssB
s.
86 83
87.89
88 26
87.67
87.92
s.
88.32
87.89
88.26
87.67
87.92
s.
88.32
87.89
88.26
87.67
87.92
s.
88.58
88.08
88.26
88.86
88.46
s.
88.36
88.16
88.26
88.86
88.46
s.
88.36
88.49
88.26
88.86
88.46
s.
88.36
88.49
88.26
88.86
88.46
s.
88.36
88.49
88.26
8S.86
88.46
s.
88.36
88.49
88.26
88.86
88.46
s.
88.36
88.49
88.26
88.86
88.46
s.
88.36
88.49
88.76
88 76
88.46
s
88.36
88.49
88.76
88.76
88.46
Arcturus
y Draconis
^J'S"'"Jon Solar Time. .
Sun, Noon. .
Sun, Midnight
Mean by the Sun ...
Mean by the Sun and!
Stars. — Gaining on Solar >
Time 3
87.71
87.95
88.01
88.25
88.01
88.25
88.45
88.69
88.42
88.66
88.49
88.73
88.48
88.72
88.49
88.73
88.48
88.72
88.49
88.73
88.56
88.80
88.57
88.81
87.94
88.44
87.94
88.44
87.94
88.44
83.00
88 44
89.00
88.44
89.00
88.44
89.10
88.44
88.44
88.44
88.44
88.44
88.44
88.44
88.44
88.44
88.44
88.44
88.19
88.19
88.19
88.72
88.72
88.72
88.77
88.44
88.44
88.44
88.44
88.44
88.02
88.23
:,88.23
88.70
88.68
88.73
88.73
88.65
88.64
88.65
88.70
88.70
88.555 Seconds.
Spitzbergen.— RATE of the ASTRONOMICAL CLOCK from the 6th to the 20th of July, deduced by ZENITH
DISTANCES.
P.M. to P.M.
s.
July 6th to July 20th ; Clock gaining per diem . . . 88.48
July 8th to July 20th ; „ ... 88.65
s.
July 6th to July 20th,- Clock gaining per Diem . . 88 5
July 7th to July 20th ; „ ... 88.57
ME AN.—Clock gaining per 1
88.565 88.535
88.55 Seconds.
X 2
156
EXPERIMENTS FOR DETERMINING THE VARIATION
Spitzbergen.
-COINCIDENCES OBSERVED with PENDULUM No. 3.
IN THE LENGTH OP THE SECONDS' PENDULUM.
157
Spitzbergen. coincidences OBSERVED with PENDULUM No. 4.
DATE.
Baro-
meter.
Clock
gaining.
a
"0 <U
6 "
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Re-ap-
pearauce.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
tlie Arc.
Vibratious
ID 24 hours.
Reduc-
tion to a
mean
Tempe-
rature.
Reduced
Vibrations at
1823.
July 14 P.M.
IN.
29.90
S.
88.73]
1
11
0
36.5
37.5
M. s.
23 32
24 36
M. s.
23 40
24 53
H. M. S.
12 23 36
2 24 44.5
1.22]
O.64J
0
37
s.
726.85
S.
-1-
1.35
86252.07
-0.21
86251.86
„ 14 P.M.
29.90
r
88.73<!
11
37
3S
43 40
44 37
43 41
44 55
5 43 40.5
7 44 46
1.32|
O.72J
36.5
726.55
1.66
86252.32
-0.42
86251.90
„ 15 A.M.
29.92
88.65<
11
34
33.4
52 00
53 32
52 07
53 55
1 52 03.5
3 53 43.5
I.22I
0.64 J
33.7
720
1.35
86253.05
-1.60
86251.45
,, 15 P.M.
29.93
88.65]
11
34.2
SI
53 58
55 31
54 06
55 49
0 54 02
2 55 40
1.24]
0.68J
34.1
729.8
1.47
86253.11
-1.43
86251.68
„ 15 P.M.
29.88
88.6sJ
11
33.5
33.4
48 27
50 03
48 33
50 23
7 48 30
9 50 13
1.28|
0.68]
33.45
730.3
1.51
86253.31
-1.71
86251.60
„ 16 A.M.
29.81
88.64]
11
32.2
32.8
53 57
55 46
54 05
56 04
1 54 01
3 55 55
1.28
0.68
32.5
731.4
1.51
86253.65
-2.10
86251.55
„ 16 P.M.
29.72
88.64]
11
37.2
37.6
25 28
26 27
25 36
26 41
10 25 32
12 26 34
0.62 J
37.4
726.2
1.31
86251.77
-0.05
86251.72
„ 17 A.M.
29.70
88.65]
11
39.5
38.4
8 6
8 42
8 14
8 59
10 8 10
12 8 50.5
1.22
0.64]
.38.95
724.05
1.35
86251.09
-t-O 60
86251.69
„ 17 P.M.
29.72
88.65]
11
38.8
38
15 06
15 48
15 13
16 10
3 15 09.5
5 15 59
'■'1
0.62j
38.4
724.95
1.31
86251.35
-^0.37
86251.72
,, 17 P.M.
29.72
r
88.65<
11
37.4
37.9
22 16
23 03
22 22
23 23
7 22 19
9 23 13
I.22I
O.64J
37.65
725.4
1.35
86251.45
-fO.06
86251.51
„ 18 A.M.
29.72
88.70]
11
39.5
38.9
31 16
31 46
31 23
32 08
4 31 19.5
0 31 57
0.6 J
39.2
723.75
1.28
86250.98
-HO. 71
86251.69
„ 18 P.M.
29.72
88.70]
11
39.1
39.4
24 01
24 42
21 11
25 01
10 24 07.5
12 2t 51.5
1.14^
0 . 56|
39.25
724.4
1.14
86251.06
-fO.73
86251.79
„ 19 A.M.
29.66
88.70]
11
41.8
43.5
31 44
31 35
31 51
31 52
10 31 47.5
12 31 43.5
1.18]
0.6 J
42.65
719.6
1.25
86249.57
-H2.16
86251.73
„ 19 P.M.
29.80
88.70]
1.
11
42 5
42
45 48
45 34
45 53
45 53
6 45 50.5
8 45 43.5
1.28|
0.66J
42.25
719.3
1.48
86249.70
-M.99
86251.69
„ 19 P.M.
29.70
88.70<
[
11
39.5
39.5
48 48
49 10
48 53
49 27
11 48 50.5
1 49 18.5
1.261
0.62 J
39.5
722.8
1.39
86250.79
-hO.84
86251.63
Means. .
29.79
37.51
86251.68
86251.68
15S
EXPERIMENTS FOR DETERMINING THE VARIATION
Spitzbergeiv. TEMPERATURE of the AIR in the SHADE.
DATE.
Thermometer.
Max. Min
MEAN-AND REMARKS.
DATE.
Thermometer.
Mas. Min.
MEAN-AND REMARKS.
July 8
„ 9
10
11
„ 12
13
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 P.M.
3 P.M.
9 P.M.
J.35.5
.>36
>38.5
l45
A2
J
1
>48
i.47
1.42
i.46
J
1
H7
141
J
1
.37
>38.5
J.3T
J
^
■-.37
j.32.5
.35
'>34
>34.5
31.5
31
34
37
36.5
35
37
41
40
40
40
36.5
35
35
31.5
32
31
31.5
33
32
33.5
33.5
36.25
4
36 Calmj with Fog.
11 i
40.7 Wind West J
Clear Weather.
39.251
I
38
42.5
43 :
" (
> 41.5 Wind West;
43.5 Clear Weather.
38.75
36
36.75
35.75
34.5
31.75
33.25
33.5
33.25
> 35.8 Calm; Thick
Fog.
i- 33 Wind East ;
Fog.
July 13
„ 14
„ 15
16
17
18
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
3 A.M.
9 A.M.
3 P.M.
9 P.M.
'>33
!'33
>35
J
1
V32
>31
31.5
i-32
f-30.5
J
1
i-29.5
j.34
J
>36
j
I36.5
I37
J
1
i-37
j
1
!.36
i-37
J
I37.5
!-37.5
J
>S3
31
31
32.5
31
30
30
30
29.5
29.5
29
32.5
35
34
32.5
35
34.5
33
35
36
34
32 1
32
34.25
31.5
30.5
30.75
31
30
29.5 1
31.5
33.75
35.5
35.25
34.75
36
35.25
35
36.25
36.75
35
32.4
Wind East ;
Fog.
30.5
Wind N.E.,
Fresh.
r 32.5
Wind East ;
Fog.
^ 35.3
Calm ; Thick
Fog.
■ 35.8
Calm ; Thick
Fog.
IN THE LENGTH OF THE SECONDS' PENDULUM. 159
GREENLAND.
Being desirous of preserving unbroken the continuity of the account of
the pendulum experiments, I shall confine myself at present to such a
brief notice of the outline of the Griper's voyage, from the time of her
quitting Spitzbergen, until her departure from Greenland at the close of
the season of navigation, as may be sufficient to explain the reasons
which determined the choice of the pendulum station on that coast ; and
shall reserve until a subsequent occasion, the few remarks which it may
be proper to make on the parts of Greenland, of which we were thus
accidentally the first visitors.
Captain Clavering, having succeeded in forcing a passage through
the barrier of ice, which impedes the access to the shores of East Green-
land, in a higher latitude than it is recorded to have been previously
traversed, arrived on the coast between the 74th and 75th degrees of
latitude in the second week in August ; he proceeded to ascend it in the
open channel within the barrier, experiencing no obstruction until he had
passed the 75th parallel, when his progress to the northward was checked
by ice, closely packed against the land, and sustaining, apparently, a very
heavy pressure from without, so as to be impassable, until an ofF-shore
wind should reUeve the pressure, and concur with re-action in producing
a set of the ice in an opposite direction; how soon this event might take
place was entirely conjectural, and there was an immediate necessity of
seeking a situation, in which to await the change, of less exposure than the
extreme advanced position, which from local circumstances, was one of
considerable danger ; Captain Clavering decided, therefore, to return to
a harbour of safe anchorage, in the latitude of 74° 30', which he had
160 EXPERIMENTS FOR DETERMINING THE VARIATION
examined in passing, and to station the ship there for the period which
the experiments should require ; after which, if the weather and the
state of the ice should authorize it, he might resume the attempt to
examine the coast to the northward as far as the navigation might
be open in the latter and more favourable part of the season. Captain
Clavering also determined on employing the boats, during the ship's
detention, in the examination of a very extensive opening in the coast,
between the harbour in which the ship was stationed and the latitude of
74° ; and on accompanying them himself.
The objects thus proposed being accomplished, the Griper sailed
again to the northward on the 31st of August ; but a continuance of the
profoundly serene weather which had prevailed almost uninterruptedly
during the preceding three weeks, and had been highly favourable for
the operations of the boats, as well as for those on shore, proved even-
tually the source of disappointment, as it had previously been of satis-
faction ; the inactivity which it compelled was the more vexatious, as the
state of the ice, when viewed from the hills which exceeded 3000 feet in
height, appeared sufficiently open for navigation as far as the eye could
reach, which was certainly beyond the 76th degree: what might have been
vindertaken with a favourable breeze and concurrent circumstances in the
first week in September, could not be attempted a few days later without
a most obvious risk of the detention during the winter, which Captain
Clavering was strongly cautioned against in his instructions ; he employed
therefore the short remainder of the season, in which the sun's presence
above the horizon for a sufficient number of hours of the day justified his
continuance on the coast, in extending its examination and survey from
the 74th to the 72d degrees of latitude. Having accomplished this purpose
on the 15th of September, and finding the vicinity of the land no longer
accessible, by reason of the ice which set in from seaward, and might
be expected to do so with increased pressure in the approaching autumnal
IN THE LENGTH OF THE SECONDS* PENDULUM. 161
gales, the Griper quitted the further examination of the coast to the
southward, and by favour of the first gale which had been experienced
for several weeks, repassed the barrier of ice on the evening of the
17th of September.
The harbour, in which the Griper remained from the 15th to the 31st of
August, was formed by the channel which separates the main land from
an island in which the experiments were made, and was secured from
the access of heavy ice from the ocean, by a smaller island, situated in
the mid-channel at the entrance. The groupe, of which these islands form
a part, consists of two, nearly of the same size, and of two others, much
smaller, being rather rocks than islands ; they extend from the latitude of
of 74° 30' to that of 74° 42', and were distinguished by the officers and
seamen of the Griper, by the appellation of the Pendulum Islands.
They partake in the character and general appearance of the main land,
which is that of the trap formation : although the principal islands are
in no direction so much as ten miles across, the greater part of their
surface exceeds 2000 feet in height, the elevated parts being remarkably
tabled on the summits. The anchorage was abreast of a plain of con-
siderable extent on the inner, or south westernmost of the two largest
islands ; the plain consisted of the debris of a sandstone rock, and was
generally swampy ; but a perfectly dry spot, which had been the site of
an Esquimaux village, was found for the pendulums on the shore close to
the anchorage.
As Captain Clavering was desirous of having a chronometer on which
he could depend for the determination of longitudes, during his excur-
sion in the boats, I supplied him with No. 649, which I had used in the
comparison of the clock with astronomical time at Hammerfest and at
Spitzbergen, reserving No. 423 for that purpose at Greenland ; and as
Messrs. Parkinson and Frodsham had led me to expect that No. 423
would keep a less uniform rate from day to day than in the former
Y
162 EXPERIMENTS FOR DETERMINING THE VARIATION
voyage, although an equally good mean rate in intervals of longer dura-
tion, in consequence of its not having been in their hands a sufficient
time, when returned to have its compensation corrected, I compared it
with astronomical time, by means of the transit instrument, from forenoon
to forenoon, and from afternoon to afternoon, and transferred the rate
thus daily obtained immediately to the clock.
Being desirous of ascertaining how near an approach could be
made by a sextant and mercurial horizon in so high a latitude to the
precision with which the daily rate is determined by transits, I made
the observations, the particulars of which are subjoined in a table ; they
present a confirmation, if any were needed, of the high opinion which the
most experienced observers have always expressed of the practical merits
of the sextant ; I have employed the method of absolute altitudes instead
of that of equal altitudes, from having had much experience of both,
which has induced me to give a decided practical preference to the
method of absolute altitudes, especially in the high latitudes.
The height of the pendulums above the sea was ascertained by direct
measurement, to be thirty-one feet and a half
IN THE LENGTH OF THE SECONDS' PENDULUM.
163
TRANSITS OBSERVED AT GREENLAND. 1
CO \ Yl C"
HMES OF TR.lNSrr BY THE CHRONOMETER 423.
Mean by the
D A'l E-.
STARS.
Ist Wire.
2d Wire.
Meridian Wire.
4lh Wire.
5Ch Wire.
CbroDometer.
1823.
M. S.
M. S.
H. M. S.
M. S.
M. s.
ir. M. s.
Aug
20
Capella (IkIow the Pole.)
33 16.8
8 33 54.4
34 32
35 10
8 33 54.4
If
?J
aCjgni ....
3 53.2
4 30
12 5 07.2
5 43.6
6 20.4
12 05 06.93
if
33
a Orionis ....
12 56.8
13 23.2
21 13 49.6
14 16
14 42
21 13 49.53
it
3»
a Lyrse (below the Pole).
57 58.4
58 31.6
21 59 05.2
59 38.8
00 12
21 59 05.2
' )J
21
(l»'Limb . .
Sun-}
(a'l Limb . .
24 49.2
25 16
1 25 42.4
2G 09.2
26 36
I 25 42.53
f
26 58.8
27 25.2
1 27 52
28 19.2
28 46
1 27 52.2
i
tt
y Draconis
. . .
9 18 48
19 30
20 12
9 18 48
> »
tt
a. LjTje ....
56 02.4
56 36
9 57 09.6
57 43.2
58 16.8
9 57 09.6
iy
33
a Aquilae ....
07 17.6
07 44
11 08 10.4
08 36.8
09 03.2
11 08 10.4
a
tt
Capella ....
. . .
.
20 27 32.8
28 10.4
28 48
20 28 10.4
31
J'
a Orionis ....
09 07.6
09 33.6
21 09 59.6
10 26
10 52.4
21 09 59.8
V
33
y Draconis (telowthe Pole).
15 30.8
16 13.2
21 16 55.2
17 37.2
18 19.6
21 16 55.2
it
33
a. LyrEe (below the Pole).
54 09.2
54 42.8
21 55 16.4
55 50
56 23.6
21 55 16.4
It
22
Arcturus
5 . .
. . .
31 35.2
5 30 39.6
tt
33
Capella {l>elow the Pole).
25 01.2
25 38.4
8 26 16
26 53.6
27 30.8
8 26 16
tf
3J
y Draconis . . .
13 34
14 16
9 14 58.4
15 40.8
16 22.8
9 14 58.4
tt
J'
uLyrae ....
52 12.8
52 46.4
9 53 20
53 53.2
54 26.8
9 53 19.87
3f
33
aCygni ....
50 14.8
56 51.2
11 57 28
58 04.8
58 41.6
11 57 28.07
ti
23
fp>Limb . .
Sun^
24 31.6
24 58.4
I 25 25.2
25 52
26 18.8
1 25 25.2
>
(2'JLimb . .
26 41.6
27 08.4
1 27 34.8
::28 01.6
28 28.4
1 27 34.93
JS
33
Aicturus . . .
25 53.2
26 21.2
5 26 49.2
27 17.2
27 44.8
5 26 49.13
tt
24
fl^'Limb . .
Sun \
24 22.4
24 49.2
1 25 16
25 42.8
26 09.6
1 25 16
t2'^Limb . .
27 32.4
26 59.2
1 27 26
27 52.8
28 19.6
1 27 26
a
tt
Arcturus
22 03.6
22 SI. 2
5 22 59.6
23 27.2
23 54.8
5 22 59.33
it
tt
Capella <Wow the Pole).
17 20.8
17 58.4
8 18 36
19 13.6
19 51.2
8 18 36
i
33
7 Draconis . . .
05 52.8
06 35.2
9 07 17.2
07 59.2
08 41.2
9 07 17.13
)>
3^
a Lyrje ....
44 32
45 05.6
9 45 39.2
46 12:4
46 46
9 45 39.07
Y 2
164
EXPERIMENTS FOR DETERMINING THE VARIATION
TRANSITS OBSERVED AT GREENLAND, continued.
DATE.
STARS.
TIMES OF TRANSIT BY 423.
1st Wire.
Meridian Wire.
4tli Wire.
Mean by the
Ciironometer.
1823.
Aug. 24
26
Sun.?
/2't Lin
sc Aquilfe
a Cygni . .
X Andi'omedse
yPegasi .
Capella
a Orionis .
y DraCOn is (below the Pole)
aL\TE6 (below the Pole),
Limb
Limb
Arcturus . . .
Capella Cb-low the PoIe;
^Diaconis .
X Lyrse . .
a Ai(uilee
a Cygn i . .
a Androraedse
yPegasi . .
a Arietis . .
Capella
a Orionis
^Dracon. (bolow the PoIe,
a LyrcB {below the Pole).
Limb .
Limb .
Capella (belowthePole)
y Draconis
Sun
r
(2'' 1
M. S.
55 17.6
48 S3. 6
12 07.2
17 04.8
15 25.6
04 00.4
42 S8.8
24 12.4
26 22
18 13.2
1.^ 30.4
02 03.2
40 42
51 57.6
41 43. 2
08 17.2
13 14.8
05 59.6
II 37.2
53 48.4
00 11.6
38 50
24 04.4
26 13.6
09 42.8
58 15.6
M. s.
56 14
49 10.4
12 36.8
17 31.6
16 03.2
04 42.4
43 12.4
24 39.2
26 48.8
18 41.2
14 08
02 45.6
41 l.').G
52 24
45 19.6
08 46.8
13 41.6
06 28
12 14.8
54 15.2
00 53.6
39 23.6
24 30.8
26 40.4
10 20.4
58 57.6
H. M. S.
10 56 40.4
11 49 47.2
15 13 06.4
15 17 58.4
20 16 40.8
20 58 30
21 05 24.4
21 43 46
1 25 06
1 27 15.6
5 19 09.2
8 14 45.6
9 03 27.6
9 41 49.2
10 52 50.8
11 45 56.4
15 09 16.8
15 14 08.8
17 06 56.4
20 12 52.4
20 54 41.6
21 01 35.6
21 39 57.2
1 24 57.6
1 27 06.8
8 10 58
8 59 40
M. S.
57 06.8
50 23.6
13 36
18 25.2
17 18.4
58 56.4
06 06.4
44 19.6
25 32.8
27 42.4
19 36.8
15 23.6
04 09.6
42 22.8
53 17.2
46 33.2
09 46.4
14 35.6
07 24.4
13 29.6
55 08
02 17.6
40 30.8
25 24.4
27 33.6
11 35.6
00 22.4
M. S.
57 33.2
51 00.8
14 05.6
18 52.4
17 56
59 22.8
06 48.4
44 53.2
25 59.6
28 08.8
20 04.8
IC 01.2
01 52
42 56 4
53 43.6
47 10.4
10 16
15 02.8
07 52.8
13 07.2
55 34
02 59.6
41 04.4
25 50.8
28 00.4
12 13.2
01 04.4
H. M. S.
10 56 40.4
11 49 47.13
15 13 06.4
15 17 58.47
20 16 40.8
20 58 30
21 05 21.4
21 43 46
1 25 06
1 27 15.53
5 19 03.07
8 14 45.73
9 03 27.6
9 41 49.2
10 52 50.67
11 45 56.53
15 09 16.67
15 14 08.73
17 06 56.27
20 12 52.27
20 54 41.47
21 01 35.6
21 39 57.2
1 24 57.6
I 27 06.93
8 10 58
8 59 40
IN THE LENGTH OF THE SECONDS' PENDULUM.
165
TRANSITS OBSERVED AT GREENLAND, continued.
DATE.
1823.
Aug. 26
STARS.
TIMES OF TRANSIT BY 423.
1st Wire.
27
Sun^
(2'» 1
)»
»
}*
y)
)»
jf
St
28
J'
?>
"
??
it
}t
f*
"
"
„
j»
.'J
a LjTfe.
Aldebaran .
Capella .
mOrionis .
a Lyrse (below the Pole)
Limb .
Limb .
Arcturus. .
Capella (below the Pole)
J- Diaconis
at Lyrae. .
a Aquila .
aCy^i .
Aldebaran
Capella .
a LyreB (below the Pole)
1" Limb .
2^ Limb .
Capella (below the Pole)
itLyree. .
Castor (below the Pole)
Pollux (below the Pole) .
a Aquilae .
Aldebaran .
Capella ....
aOrionis
T'Dracon, below the Pole.l
Sun
H. S.
36 54.4
30 23.2
07 48.4
50 00.8
33 02.4
23 55.6
26 04.8
10 37.2
05 55.2
54 27.2
33 05.6
4t 21.6
37 06.8
26 34.4
03 59.6
31 13.6
23 46.8
25 55.6
02 06.8
29 18
21 36.4
32 47.6
40 33.6
22 44.8
00 09.6
42 22.4
48 45.2
2d Wire.
Meridian Wire.
M. S.
37 28
30 50.4
08 25.6
50 27.2
35 35.6
24 22
26 31.2
11 04.8
06 32.8
55 09.2
33 39.2
44 48
37 43.6
27 01.6
04 37.2
31 47.2
24 13.2
26 22
02 44
29 51.2
22 07.2
33 17.2
41 00
23 14
00 47.2
42 48.8
49 27.2
H. M. S.
9 38 01.6
19 31 17.6
20 09 03.2
20 50 53.6
21 36 09.2
1 24 48.8
1 26 58
5 11 33.2
8 07 10.4
8 55 51.2
9 34 12.8
10 45 14.4
11 38 20.4
19 27 28.8
20 05 14.8
21 32 20.8
I 24 39.6
1 26 48.8
8 03 21.6
9 30 24.8
10 22 38
10 33 47.2
10 41 26.4
19 23 39.2
20 01 24.8
20 43 15.2
20 50 09.2
4lh Wire.
M. S.
38 35.2
31 41.8
09 40.8
51 20
36 42.8
25 15.6
27 24.8
12 00.8
07 48
56 33.2
34 46.4
45 41.2
38 57.2
27 56
05 52.4
32 54
25 06.4
27 15.6
03 59.2
.30 58.4
23 19.2
34 16.8
41 52.8
24 06.4
02 02.4
43 41.6
50 51.2
5th Wire.
M. S.
39 08.4
32 12
10 18
51 46.4
37 16.4
25 42
27 51.2
12 28.4
08 25.6
57 15.2
35 19.6
46 07.2
39 34
28 23.2
06 30
38 27.6
26 32.8
27 42.4
04 36.8
31 32
23 40.4
34 46.4
42 19.2
24 33.6
02 39.6
44 08
51 33.2
Mean by the
Clironometer.
H. M. S.
9 38 01.53
19 31 17.6
20 09 03.2
20 50 53.6
21 36 09.27
1 24 48.8
1 26 58
5 11 33.27
8 07 10.4
8 55 51.2
9 34 12.73
10 45 14.47
11 38 20.4
19 27 28.8
20 05 14.8
21 32 20.67
1 24 39.73
1 26 48.87
8 OS 21 67
9 30 24.87
10 22 38.2
10 33 47.07
10 41 26.4
19 23 39.2
20 01 24.73
20 43 15.2
20 50 09.2
166
EXPERIMENTS FOR DETERMINING THE VARIATION
i TRANSITS OBSERVED AT GREENLAND, continued.
DATE.
STARS.
TIMES OF TRANSIT BY 423.
Mean by the
Chronometer.
1st Wire.
2d Wire.
Meridian Wire.
4th Wire.
5lhWire.
1823.
91. S.
tt. a.
H. M. S.
M. s.
M. s.
H. M. S.
Aug.
28
a Lyrae (btiow the Pole) .
27 2S.2
27 56.8
21 28 30.4
29 04
29 37.2
21 28 30.33
fptLimb. .
23 34.8
24 01.6
1 24 28.4
24 55.2
25 21.6
1 24 28.33
}j
29
Sun^
(2'' Limb . .
25 44.4
26 11.2
1 26 38
27 04.4
27 31.2
I 26 37.87
' )>
93
Arctunis. .
02 59.6
03 27.2
5 03 54.8
04 22.4
04 50.4
5 03 54.87
j»
33
Capella (below the Pole)
58 17.2
58 54.4
7 59 32
00 09.6
00 47.2
7 59 32.07
' 3f
33
7 Diaconis .
46 48.4
47 30.8
8 48 12.8
48 54 8
49 36.8
8 48 12.73
J>
3t
aLyrae
25 27.2
26 00.8
9 26 34.4
27 08
27 41.2
9 26 34.33
it
33
Castor (below the Pole) .
17 46.4
18 17.2
10 18 48
19 18.8
19 49.6
10 18 48
}>
33
Pollux (below the Pole) .
28 57.6
29 27.6
10 29 57.2
30 27.2
30 56.8
10 29 57.27
9>
33
a Aquilae ....
36 43.2
37 09.6
10 37 36
38 02.8
38 29.2
10 37 36.13
99
93
Capella ....
56 20.4
56 58
19 57 35.6
58 13.2
58 50.4
19 57 35.53
>l
33
a Orionis ....
38 32.8
38 59.2
20 39 25.6
39 52
40 18.4
20 39 25.6
?>
33
y DraCOn . (below the Pole)
44 56.8
45 38.8
20 46 20.8
47 02.8
47 44.8
20 46 20.8
»
97
a LyrEe (helow the Pole) .
23 34.8
24 08
21 24 41.6
25 15.2
25 48.4
21 24 4J.6
ri*'Limb. .
23 24
23 50.8
I 24 17.6
24 44.4
25 11.2
1 24 17.6
}J
30
Sun \
(a"! Limb . .
25 34
26 00.4
1 26 27.2
26 54
27 20.4
1 26 27.2
>y
39
Arcturas. .
. . .
. . .
4 59 05.6
00 34
01 01.6
4 59 05.6
It
33
Capella (below the Pole)
54 27.6
55 04.8
7 55 42.4
56 20
56 57.6
7 55 42.47
if
31
at Lyrse
21 38
22 11.6
9 22 45.2
23 18.8
23 52.4
9 22 45.2
)»
«»
Castor (below the Pole) .
13 56.8
14 27.6
10 14 58.8
15 30
16 01.2
10 14 58.87
39
33
Pollux (below the Pole' .
25 08.8
25 38.4
10 26 08
26 38
27 07.6
10 26 08.13
tf
33
nAquilae ....
32 54
33 20.4
10 ,33 46.8
34 13.2
34 39.6
10 33 46.8
J»
3>
aCygni ....
25 39.2
26 16 11 26 52.8
27 29.6
28 06.4
11 26 52.8
IN THE LENGTH OP THE SECONDS' PENDULUM.
167
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O
'S
•«!
04
5l
n
M
fe;
•
(2
1
Cm
1
o
r
5
0
2
1
=
o
1
c
o
C3
o
m
3
(-•
3
■f
@
j
o
1
8
'5
&0
S .-
o m
■3 Uj
' "i
rt
>i
C3
CT"
<
8
t-
<
o
u
^
U
&.
<
8
8
** a.
168
EXPERIMENTS FOR DETERMINING THE VARIATION
Greenlan]
>i.^ 4V1/1 Pafa r^f iha Ohfnnr^maiiit* A.O*i
f^r^rr. 1
lUllO HJ U^L^lIIllUC IIJC .■-•.ixi.V. V/*
iwv, ^^,^.,^.„^.^. -.^^, WW.U 1
the 20th to the 30th of August, 1823, by Altitudes of the Sun, taken with a Sextant |
and Mercurial Horizon.
Latitude of tlie Place of Observation, 74° 32' 19" N.; Longitude, 18° 49' W. 1
DATE.
Chronometer.
App. Alt.
Sun's centre.
Baro-
meter.
Thermo-
meter.
Chron. fast on
Mean Time.
CHRON.'S RATE. 1
Alfi^.
Tran".
1S23.
H. .M. S.
O / //
IN.
0
II. M. S.
s.
s.
Aug. 20 P.M.
5 52 07.13
36 45 07
29.87
35
1 23 38.7
1 23 45.7 l
„ 21 A.M.
8 54 37.8
35 27 09
29.87
32
6 53
6.61
„ 21 P.M.
5 44 25.53
37 03 32.5
29.90
35
1 23 45.23^
16.7
6.49
„ 22 A.M.
S 46 41.8
33 50 45.5
29.90
36
1 23 52.4 i
'5.44
6.34
„ 22 P.M.
5 51 50.27
35 28 12.5
29.95
39
1 23 50.67
>5.91
5.93
„ 23 A.M.
....
. • . •
^5.5
1
5.6
„ 23 P.M.
5 37 17.27
36 3S 13
29.90
42
1 23 56.27
1
15.91
6.0
„ 24 A.M.
• • . •
....
.... f"
6.8
5.72
„ 24 P.M.
5 32 28.87
36 30 51
29.90
40
1 24 03.07
■5.91
5.83
„ 23 A.M.
9 23 08.53
36 26 52.5
29.71
33
1 24 10.13 ■
^5.26
1
5.96
„ 25 P.M.
5 29 35.73
36 10 48
27.73
30
1 24 08.23
6.7
7.38
„ 26 A.M.
9 14 06.73
34 42 43
29.68
36.5
1 24 16.83
8.84
8.09
„ 2G P.M.
5 36 19.67
34 40 39
29.73
45
1 24 17.17
[7.45
7.57
„ 27 A.M.
...
....
■^7.71
7.72
„ 27 P.M.
. . .
[7.45
7.3
„ 28 A.M.
9 IS 41.93
33 57 20
30.03
39
1 24 31.73
■'7.71
7.21
„ 28 P.M.
5 50 21.8
31 33 37
30.00
36
1 24 32.6 •'
U . 44 ■
6.35
„ 29 A.M.
9 18 12.07
33 14 10
30.15
34.5
1 24 38.17
MEANS — Gaining per Diem
6.64
6.68
The " Apparent Altitudes" are each a mean of six observations, three of the Upper, and
three of the lower Limb: they are corrected for an Index Error of l' 20". The Ther-
mometer was suspended in the air and in the shade, near the place of observation. The times
by the Chronometer were noted by the beats.
IN THE LENGTH OF THE SECONDS' PENDULUM.
169
Greenland. Comparisons of the Astronomical Clock with the Chronometer
No. 423, from the 20th to the 30th of August, 1823 ; with the Clock's Rate on
Mean Solar Time deduced.
1823.
Chronometer.
Aug. 20 p. M.
,, 21 A.M.
.1 21 p. M.
11 22 A. M.
,1 22 p. M.
1, 23 A. M.
„ 23 P. M.
„ 24 A. M.
„ 24. p. M.
„ 25 A. M.
„ 25 p. M.
11 26 A. M.
1, 26 P. M.
1, 27 A. M.
„ 27 p. M.
„ 28 A. M.
1, 28 P. M.
„ 29 A. M.
„ 29 P. I\I.
„ 30 A. M.
„ 30 P. M.
> 9 00 00 <!
Clock.
H. M. S.
9 44 24.2
0 45 00.2
9 45 36
9 4C 11.5
9 46 47.5
9 47 23.5
9 48 00
9 48 35.3
9 49 11.9
9 49 47.5
9 50 24.1
9 50 58.1
9 51 33.9
9 52 08.6
9 52 44.2
9 53 19
9 53 54.2
9 54 30,6
9 55 06
9 55 41.6
9 56 17.4
Mean .
CLOCK S GAIN.
F.M.loP.M.
71.3
72
71.8
72.2
70.6
TO. 5
70.4
71.6
71.8
71.5
72.5
71 .9
72.2
69.8
70.3
70
71.8
71.4
DAILY RATES.
Chron.
GainiDg.
g.
6.61
6.49
6.34
5.93
5.6
6.0
5.72
5.83
5.96
7.38
S.09
7.57
7.72
7.3
7.21
6.35
6.17
6.96
6.67
Clock.
Gaiuing.
s.
78.41
77.79
77.84
77.93
78. 1
77.8
77.62
78.03
78. 16
77.98
77.89
78.07
78.02
77.7
77.21
77.95
77.97
77.96
7S.07
77.94
170
EXPERIMENTS FOR DETERMINING THE VARIATION
Greenland. COINCIDENCES OBSERVED with PENDULUM 3 ;
86477.94 Vibrations iu a Mean Solar Day.
the Clock inakinor
DATE.
Baro-
meter.
1823.
Aug
.21 A.M.
»>
21 P.M.
)y
21 P.M.
»
22 A.M.
„ 22 Noon
„ 22 P.M.
„ 23 A.M.
„ 23 P.M.
„ 24 A.M.
„ 21 P.M.
„ 25 A.M.
„ 23 P.M.
29.885<
29.900
29.900
29.900^
29.935
29.950
29.880
29.888<
29.965.(
29 . 873
29.715
29. 720.
No.
of Co-
inci-
dence.
Tempe-
rature.
Time of
Disap-
pearance.
11
)
11
1
11
1
11
1
11
11
1
11
1
11
1
U
1
II
I
11
I
II
39.5
43.5
49.6
48.6
49.1
47.8
36.8
40
43.8
45
48
47.3
41.3
45
51.3
48.4
40
44.4
46.8
46.4
31
38.2
39.4
41.6
41 22
36 04
15 10
8 26
00 08
53 30
7 40
3 04
46 04
40 16
1 42
55 10
15 28
09 48
42 45
35 50
27 23
21 55
39 20
33 04
38 01
33 49
49 09
44 03
Time of
Re-ap-
pearance
M. s.
41 26
36 13
15 15
8 37
00 15
53 46
7 46
3 14
46 09
40 27
1 44
55 26
15 30
10 01
42 50
36 07
27 25
22 U
39 23
33 20
38 08
34 04
49 13
44 20
True Time of
Coincidence.
II. M. S.
8 41 24
10 36 08.5
2 15 12.5
4 8 31.5
6 00 II. 5
7 53 38
6 7 43
8 3 09
11 46 06.5
I 40 21.5
6 1 43
7 55 IS
10 15 29
12 9 54.5
5 42 47.5
7 35 58.5
10 27 21
12 22 03
4 39 21.5
6 ,33 12
6 38 04.5
8 33 56.5
11 49 11
I 44 11.5
Arc of
Vibra-
tion.
Mean
Tempe-
Mean
Interval.
0.58 J
1.18
0.58
1.18
0.58
1. 18
0.58
1.2
0.58
1.28
0.66
1.28
0.66
1.2
0.58
1.28
0.66j
1.26
0.64
1.18
0.58
1.22
0.62
41.5
49.1
48.4;
38.4
44.4
47.65
43.15
49.85
42.2
46.6
36.1
40.5
688.45
679.9
680.65
692.6
685.
681.5
686.55
679.1
687.9
683.05
695.2
690.05
Correc-
tion for
theArc.
1.25
1.22
1.22
1 .22
1.25
1.48
1.48
1.25
1.48
1.42
1.22
1.31
Vibrations
in 24 hours.
86227.95
86224.76
86225.06
86229.44
86226.87
86225.62
86227.50
86221.51
86228.00
86226.14
86230.38
86228.62
Reduc-
tion to a
Mean
Tempe-
ratnre.
-1.05
-1-2.14
+ 1.87
-2.33
-1-0. 17
-1-1.53
-0..36
+ 2. 46
-0.76
+ 1.09
-3.32
-1.47
Reduced
Vibrations at
86226.90
80226.90
86226.93
86227.09
86227.04
86227.15
86227.11
8C22C.97
86227.24
86227.23
86227.06
86227.15
Means .
29.876
44
86227.07
86227.07
IN THE LENGTH OF THE SECONDS* PENDULUM.
171
Greenland. COINCIDENCES OBSERVED with PENDULUM No. 4 ; the Clock making
S6477.94 Vibrations in a Mean Solar Daj-.
DATE.
Baro.
meter.
No.
of Co-
inci-
dence.
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Re -ap-
pearance.
Troe Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
tile Arc.
Vibrations
ill 2-1 hours.
Reduc-
tion to a
mean
Tempera-
ture.
Reduced
Vibrations at
41°. 14.
1823.
IN.
0
M. s.
M. S.
H. H. S.
0
0
S.
S.
Aug. 25 P.M.
29.71oJ
11
45.8
-14.8
33 26
31 55
33 34
.■^2 18
4 33 30
6 32 Ob. 5
1.181
0.56J
45.3
711.65
-1-
1.19
86236.07
+ I.T-,
86237.82
„ 26 A.M.
29.675J
U
34
38.2
58 47
59 08
58 55
59 22
5 58 51
7 59 15
1.2 1
0.58
36.1
722.4
1.25
86239.77
-2.12
86237 . 65
,. 26 P.M.
29.728J
11
4G.8
49.2
41 51
39 45
41 59
40 00
12 41 55
2 39 52.5
1 181
0 56|
48
707.75
1.19
'86234.75
-1-2.88
86237.63
„ 26 P.M.
29.728^
11
50
48
29 49
27 24
29 54
27 46
4 29 51.5
6 27 35
1.22
0.6
49
706.35
1.31
86234.39
•*-3.3
86237.69
„ 27 A.M.
29. 800 J
11
32.5
32.4
S3 47
34 48
33 49
35 07
4 33 48
6 31 57.5
1.281
O.64J
32.45
726.95
1.45
86241.49
-3.65
86237.84
„ 27 A.M.
29.900.!
11
39
42
10 58
10 23
11 05
10 40
9 11 01.5
11 10 31.5
1.181
0.56]
40.5
717
1.19
36237.89
-0.27
86237.62
„ 27 P.M.
29.900';
11
44
45
44 52
43 33
44 55
43 50
3 44 53.5
5 43 41.5
1.261
O.62I
44.5
712.18
1.41
86236.69
-r 1.41
86238.10
„ 28 A.M.
so.oooi
11
33.1
35.8
36 42
37 18
36 46
37 39
5 36 44
7 37 28.5
1.281
0.64J
34.45
724.45
1.45
86240.65
-2.81
86237.84
„ 28 A.M.
so.osoJ
11
38
40
42 35
42 25
42 39
42 41
9 42 37
11 42 33
1.221
0.58 J
39
719.6
1.28
86238.84
-0.9
86237.94
„ 28 P.M.
3O.OO0J
11
46
44.8
8 21
6 43
8 23
6 02
4 8 22
6 6 52.5
0.6lJ
43.4
711.05
1.48
86236.18
-I-I.79
86237.97
„ 29 A.M.
SO.looJ
11
37.2
41
45 22
45 06
45 23
45 22
8 45 22.5
10 45 14
1.28|
0.64J
39.1
719.15
1.45
86238.89
-0.86
86238.03
,, 29 P.M.
30.ieo.|
11
44.3
42.8
17 17
16 09
17 22
16 26
4 17 19.5
6 16 17.5
I.22I.
0.58 J
43.55
713.8
1.28
86236.92
-1-1.01
86237.93
„ .TO.-V.M.
so.oooi
11
36
39
34 33
34 37
31 34
31 54
7 34 33.5
9 31 45.5
'■n
0.64 J
37.5
721.2
1.48
86239.60
-1.53
86238.07
Means . . .
29.906
41.14
86237.86
86237.86
Z 2
172 EXPERIMENTS FOR DETERMINING THE VARIATION
DRONTHEIM.
It had been originally my intention to have made Reikivik in Iceland
the concluding station of the pendulum experiments in the high latitudes ;
but the difficulties which had been experienced in getting a complement
of seamen for the Griper, when fitting at Deptford, had delayed the com-
mencement of the voyage until the early part of the season had passed,
and had caused her to arrive later at every station than had been de-
signed ; consequently, when on the 17th of September, we found ourselves
finally disengaged from the Greenland ice, the season of navigation was
drawing towards a close ; the autumnal gales had already commenced,
and the nights were above sixteen hours long ; under such circum.stances
it would not have been prudent to have risked the approach to the coast
of Iceland, with which we were imperfectly acquainted, in a vessel which
sailed so heavily as the Griper ; and it was preferable to recross the
northern ocean to seek a pendulum station on the coast of Norway,
nearly in the same latitude as had been contemplated in Iceland ; and
as Drontheim, the ancient capital of Norway, appeared beyond compa-
rison, the most eligible situation for the purpose, the Griper arrived there
on the 8th of October.
As our visit to Drontheim was not premeditated, we were unfurnished
with official introductions to the authorities ; but our reception by his
Excellency Count Trampe, Governor of the province of Drontheim, was
not suffered to be the less cordial or unreserved, on account of the absence
of that formality ; the attentions which we experienced from that gentle-
man, and the facilities which we enjoyed in consequence of his sanction,
were in every respect such as might have been expected from a friend of
the late Sir Joseph Banks. Through the good offices of Mr. Schnitler,
IN THE LENGTH OF THE SECONDS* PENDULUM. 173
His Britannic Majesty's Consul, I obtained the necessary accommodation
and means of performing the experiments with great convenience and
advantage, in a villa in the environs of the tovv^n, belonging to Mr. Hans
Wensel, whose daughter Mr. Schnitler had married. Mr. Wensel was so
kind as to permit Captain Clavering and myself to occupy his villa as our
residence, and to allow me to take up the flooring of one of the rooms, to
enable the clock and pendulum supports to rest on the ground beneath,
and to be thus unconnected with the house or its foundation. Mr.
Wensel's villa is situated about an English mile from Drontheim, on
the right of the road which ascends the Steinberget hill, and is on a
foundation of mica-slate, approaching very nearly to clay-slate. The ob-
servatory containing the transit instrument was established on a small
eminence on the lawn belonging to the house.
It had been the good fortune of Captain Clavering and myself to have
experienced at each of the inhabited stations which we had visited the
most marked hospitality and kindness, but at none were our obligations
in these respects greater than at Drontheim ; to Mr. Schnitler especially
we were indebted for the most assiduous and unremitting endeavours to
render our residence agreeable ; and if I may be permitted in a single
instance to notice personal attentions, not directly conducing to the pro-
motion of the experiments, but contributing materially to our comfort and
pleasure whilst engaged in them, I would avail myself of the present occa-
sion, to express for Captain Clavering and myself our very grateful re-
membrance of the exceeding kindness which we received from Mr. Knut-
zon, and from the younger branches of his amiable and excellent family.
Mr. Mandall, an officer of Norwegian Engineers, was kind enough
at my request to undertake the trigonometrical measurement of the height
of the pendulums at Mr. Wensel's house, which he found to be 118
Norwegian, or 121.5 British feet above the level of mean tide.
174
EXPERIMENTS FOR DETERMINING THE VARIATION
TRANSITS OBSERVED AT DRONTHEIM.
TIMES OF TRANSIT BY No. 649.
Mean by the
Ciironometer.
DATE.
STARS.
CLOCK.
1st Wire.
2d Wire.
Meridian Wire.
4th Wire.
51h Wire.
1823.
M. S,
N. S.
H. M. 3.
M. 8.
M. S.
H. M. s.
H. M. S.
Oct. 15
aLyrae ....
16 40
17 13.6
4 17 46.8
18 20.4
18 54
4 17 46.93
4 24 54.27
..
iSLyrae ....
29 19 2
29 50.4
4 30 21.6
30 52.8
31 24
4 30 21.6
4 37 29.3
..
y Lyrae ....
38 05.2
38 36
4 39 07.2
39 38
40 08.8
4 .'9 07.07
4 40 15.07
y Aquils . . .
23 40.4
24 06.8
5 24 33.2
25 00
25 26.4
5 24 33.33
5 31 42.68
., ..
X Aquila; . . .
27 57.6
28 24
5 28 50.4
29 16.8
29 43.2
5 28 50.4
5 35 59.9
.,
3 AquiUe . . .
47 56.8
48 22.8
5 48 49.2
49 15.6
49 41.6
5 48 49.2
5 55 59.3
." j>
2x Capri. . .
53 53. 8
54 25.6
5 54 52
55 18.4
55 45.2
5 54 52
6 02 02.25
.,
aCygni. . . .
20 40.8
21 17.6
6 21 54
22 30.4
23 07.2
6 21 5 4
0 29 05.06
..
a. Aquarii . . .
42 09.4
42 S6
7 43 02
43 28
43 54
7 43 02
7 50 15.5
„ 16
a. LyrEe ....
12 41.8
13 18.4
4 13 52
14 25.2
14 58.8
4 IS 51.87
4 21 43.32
.> ,.
/S Lyrse . .
25 24.4
25 55.6
4 26 26.8
26 58
27 29.6
4 26 26.87
4 34 18.72
••
a LyrcP ....
34 09.8
34 41.2
4 35 12.4
35 43.2
36 14.4
4 35 12.23
4 43 04.36
,. .-,
X Pegasi . . .
37 18.8
37 45.6
8 38 12.8
.38 39.6
39 06.8
8 38 12.73
8 46 12.44
.. n
a Lyrae ....
08 49.6
09 22.8
4 09 56.4
10 30
11 03.6
4 09 56.-47
4 IS 32.95
..
/SLyrae ....
21 28.4
21 59.6
4 22 30.8
23 02
23 33.6
4 22 30.87
4 31 07.73
,. •.
yLyrae ....
30 14.4
SO 45.2
4 31 10.4
31 47.6
32 18. J
4 31 16.4
4 39 53.55
..
yAquilie . . .
15 49.6
16 16
5 16 42.4
17 08.8
17 35.6
5 16 42.47
5 25 21.01
a Aquila; .
20 07.2
20 33.6
5 21 00
21 26.4
21 52.8
5 21 00
5 29 38. C6
S Aquila . . .
40 06.4
40 32.4
5 40 58.4
41 24.8
41 51.2
5 40 58.6
5 49 37.9
2 a Capri. . .
46 07.6
46 34.8
5 47 01.6
47 28.4
47 55.2
5 47 01 53
5 55 41.07
aCygni. . . .
12 50
13 26. 8
6 14 03.6
14 40
15 16.8
6 14 03.47
6 22 43.86
« Aquarii . . .
34 18.8
34 45.2
7 35 11.6
35 37.6
36 03.6
7 35 11.4
7 43 54.33
X Pegasi . . .
33 22.4
33 49.6
8 34 16.4
34 43.6
35 10.4
8 34 16.47
8 43 01.28
,, 19
ttLyrae ....
00 58
01 3I.fi
4 02 05.2
02 38.4
03 12
4 02 05.07
4 12 11.53
V.
(3 Lyra; ....
13 .'!7.2
14 OS. 1
4 14 .39.6
15 10.8
15 42
4 14 .39.6
4 24 46.46
..
X Pogasi . . .
25 SI. 6
25 58.8
8 26 25.6
26 52.8
27 19.6
8 26 25.67
8 36 40.35
„ 23
X .\rietis . . .
1111 3G.4
12 04.4
12 32.4
11 11 36.4
11 21 SI. 4
IN THE LENGTH OF THE SECONDS' PENDULUM.
175
TRANSITS OBSERVED AT DRONTHEIM, continued.
DATE.
STARS.
TIMES OP TRANSIT BY No. 649.
Isl Wii
2d Wire.
Meridian Wire.
4th Wire.
5tb Wire.
Mean by the
Chronometer.
CLOCK.
182.^.
Oct. 23
28
Nov. I
-Tauri. .
-Tauri. .
Aldebaran
Capella .
/3 Tauri. .
^Draconis
X Lj Tie . .
(3Lyr£E . .
y Lyrje . .
yAquilse .
y Draconis
eLyrae . .
(3Lyr,E . .
yLyree . .
aAquilae
aPegasi. .
V Draconis
aLyrae . .
z Arietis .
-Tauri. .
-Tauri. .
Aldebaran
Capella .
/3 Tauri. .
38 51.2
16 15.6
2T 58
47 13.2
25 52.8
38 32.4
39 18.4
16 52.8
28 27.6
17 55.2
26 26
39 03.6
31 ,38.4
32 20.4
10 28.4
10 52
22 57.6
23 28.8
31 43.6
32 14.4
21 36.4
22 02.8
34 52
35 18.8
23 50.8
24 32.4
02 30.4
03 04
27 50.4
28 18.4
44 55.2
45 22.8
48 33.2
49 00.8
56 01.2
56 28.8
33 25.6
34 03.2
45 08.8
45 38.4
If .M. S.
13 28 39. G
13 32 18
13 39 43.6
14 17 30.4
14 28 57.2
2 48 37.2
2 26 59.6
3 39 34.8
3 48 20.4
4 33 46
2 33 02.8
3 II 25.6
3 24 00
3 32 45.6
4 22 29.2
7 35 46
2 25 14.8
3 03 37.6
10 28 46.8
12 45 50.4
12 49 28.4
12 56 56
13 34 40.8
13 46 08 I
M. S.
29 07.2
32 45.6
40 12.8
18 08
29 26.8
49 19.2
27 33.2
40 06.4
48 51.6
34 12.4
33 44.8
11 59.2
24 31.6
33 16.8
22 55.6
36 12.8
25 57.2
04 11.2
29 15.2
46 18
49 56
57 23.6
35 18
46 .37.6
M. s.
29 31.8
33 13.2
40 39.6
18 45.2
29 56.8
50 01.2
28 00.8
40 37.6
49 22.4
34 38.8
3J 26.8
12 32.8
25 02.8
33 47.6
23 22
36 .39.6
26 38.8
04 44.8
29 43.6
46 45.6
50 23.6
57 50.8
35 55.6
47 07.2
II. M. s.
13 28 .39.6
13 22 18
13 39 45.53
14 17 30.4
14 28 57.27
2 48 37.2
3 26 59.67
3 .39 34.93
3 48 20.4
4 33 46
2 33 02.67
3 11 25.6
3 24 00.13
3 32 45.6
4 22 29.2
7 35 45.87
2 23 14.8
3 03 37.6
10 28 46.87
12 45 50.4
12 49 28.4
12 56 56.07
13 31 40.67
13 46 08
II. SI. s.
13 41 58.74
IS 45 37.23
13 53 05.03
14 30 51.13
14 42 18.37
3 05 12.01
3 43 35.37
3 56 11.21
4 04 56.96
4 50 23.94
2 52 30.71
3 30 54.8}
3 43 29.79
3 52 13.34
4 42 00.69
7 35 23.46
2 46 09.42
3 24 33.36
10 49 55.39
13 07 03.28
13 10 41.4
13 18 09.57
13 55 55.34
1 1 07 22.98
176
EXPERIMENTS FOR DETERMINING THE VARIATION
Drontheim. Comparisons of the Astronomical Clock with the Chronometer No.
6-19, from the 15th of October
to the 3d of November, 1S23.
Clock's
Clock's
DATE.
Chronometer.
Clocli.
gain in 12
hours.
DATE.
Chronometer.
Clock.
gain in 12
hours.
1823.
11. M. S.
H. M. S.
1823.
H. M. S.
H. M. S.
Oct. 15 P.M.
4 00 00
4 07 06.8
Oct. 25 A.M.
1
7 14 13
1 21.8
1 22.1
1 21.5
!■ 21.5
., 15 P.M.
7 07 12.2
.S.
I 22
1 22.4
I 22.5
1 22.7
,. 25 P.M.
7 14 34.8
,. 16 A.M.
7 07 34.2
„ 26 A.M.
7 14 5C.9
.. If. P.M.
7 07 56.6
., 26 P.M.
7 15 18.4
„ 17 A.M.
7 08 19.1
„ 27 A.M.
7 15 39.9
J
j- 20.8
-1
.. IT P.M.
7 08 41.8
„ 27 P.M.
7 16 00.7
I 22.3
> 20.4
1 21.5
[ 21.9
1 21.4
1 21.7
1
,. 18 A.M.
7 09 04.1
,, 28 A.M.
7 16 21.1
1 22.8
,. 18 P.M.
7 09 26.9
„ 28 P.M.
■ 7 00 00 •
7 16 42.6
1 22.7
.. 19 A.M.
7 09 49.6
., 29 A.M.
7 17 04.5
\ 22.4
,, J9 P.M.
• 7 00 00 ■
7 10 12
„ 29 P.M.
7 17 25.9
I 22.5
,, 20 A.M.
7 10 34.5
„ 30 A.M.
7 17 47.6
I 22.2
1 21.6
} 21.6
1 21.6
1 22.1
.. 20 P.M.
7 10 56.7
„ 30 P.M.
7 18 09.2
I 22.2
,. 21 A.M.
7 11 18.9
„ 31 A.M.
7 18 30.8
1 21.8
,, 21 P.M.
7 11 40.7
„ 31 P.M.
7 18 52.4
I 22.1
,, 22 A.M.
7 12 02.8
Nov. 1 A.M.
7 19 14.5
,. 22 P.M.
7 12 24.2
1 21.4
I 21.5
I P.M.
2 00 00
2 19 27
> 22
,. 23 A.M.
7 12 45.7
J
\ 21.8
1 P.M.
7 00 00
7 19 36.5
1
1
,, 23 P.M.
7 13 07.5
1 P.M.
10 00 00
10 19 42
> 22.1
,, 23 P.M.
12 00 00
12 13 16.5
2 A.M.
7 19 58.6
} 22.1
1
■ 22.1
,, 24 A.M.
3 00 00
3 13 22.4
„ 2 P.M.
7 20 20.7
• 7 00 00 ■
|21
1 20.9
,. 21 A.M.
[
7 13 29.6
1 22.2
,. 3 A.M.
7 20 41.7
> 7 00 00 <^
.. 24 P.M.
1 1
7 13 51.8
., 3 P.M.
7 21 02.6
The Clock was found by Transits to be gaining on Mean Solar time 45". 47 per diem, and
by the above Comparisons 43" .7 per diem ou the Chronometer ; consequently the Chrono-
meter was saiiiina; l".77 on Mean Time.
IN THE LENGTH OF THE SECONDS' PENDULUM.
177
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178
EXPERIMENTS FOR DETERMINING THE VARIATION
Drontheim. COINCIDENCES OBSERVED with PENDULUM No. 3.
DATE.
1823.
Oct. 16 A.M.
„ 16 P.M.
„ 17 A.M.
„ 17 P.M.
„ 18 A.M.
„ 18 P.M.
„ 19 A.M.
„ 19 P.M.
,, 19 P.M.
(by lamp light.)
„ 20 A.M.
„ 21 P.M.
„ 22 A.M.
„ 22 P.M.
„ 22 P.M.
(b7 lamplight.)
„ 23 Noon.
„ 23 P.M.
(hj lamp light.)
,, 24 A.M.
Baro-
meter.
IN.
29.47
29.46
29.53
29.52
29.42
29.44
29.55
29.60
29. G7
30.00
30.06
30.34
30.30
30.30
29.92
30.17
30.17
Clock
gaining
Means
45.3,'i<
45.35-;
45.31<
r
45.31<
L
f
45.44'(
45.44<
I
r
45.44'i
I
r
45.44"!
29.82
f
45.44<
I
r
45.45<
f
45.45<
I
f
45.45<'
r
45.45-(
1.
f
45.45-^
I
r
45.45-;'
I
f
45.45<
f
45.49-;
I
Tempe-
rature.
47.4
48
48.2
48.7
46
46.1
46.3
46.4
45.1
45.9
46.4
46
45
46.3
46.9
46
47.5
47.5
46.2
47.2
46.9
46.9
46.1
46.3
46.2
46.2
46.6
46.6
50.1
50.1
51.2
51.4
52.2
52
Time of
Disap-
pearance
M. S.
59 24
53 22
34 21
28 10
47 40
41 50
16 36
10 45
32 30
26 50
52 34
46 42
19 08
13 26
4 10
58 11
35 52
29 46
55 02
49 06
09 40
03 40
21 07
15 09
4 00
58 00
28 43
22 40
41 00
34 23
2 23
55 22
17 56
10 54
Time of
Re-ap-
pearance.
True Time of
Coincidence-
Arc of
Vibra-
tion.
M. S.
59 29
53 38
34 25
28 26
47 41
42 06
16 41
U 03
32 35
27 04
52 39
47 08
19 13
13 42
4 15
58 36
35 55
30 02
55 07
49 21
09 45
03 56
21 09
15 25
4 05
58 31
28 47
23 01
41 07
34 44
2 24
55 40
17 59
II 13
H. M. S.
7 59 26.5
9 53 30
1 34 23
3 28 18
7 47 40.5
9 41 58
1 16 38.5
3 10 54
9 32 32.5
11 26 57
1 52 36.5
3 46 55
9 19 10.5
11 13 34
2 4 12.5
3 58 23.5
7 35 53.5
9 29 54
8 55 04.5
10 49 13.5
1 09 42.5
3 03 48
10 21 08
12 15 17
2 4 02.5
3 58 15.5
7 28 45
9 22 50.5
11 41 03.5
1 34 33.5
10 2 23.5
11 55 31
11 17 57.5
1 11 03.5
Mean
Tempe-
rature.
1.181
o.ssj
1.2 1
>
0.98J
1.26|
0.62 J
1.2 I
0.58 J
1.2 I
0.6 j
1.2 1
>
0.58J
1.2 1
0.6 J
1.2^
0.6 I
1.2 1
>
0.6 j
1.2 1.
>
0.58J
1.181
o.ssj
1.261
0.62 1
1.181
0.58 J
1.261
>
0.62J
Mean
Interval.
1.181
>
0.58J
1.281
0-64J
1.24!
>
0.62J
47.7
48.45
46.05
46.35
45.5
46.2
45.65
46.45
47.5
46.7
46.9
46.2
46.2
46.6
50.1
51.3
52.1
s.
684.85
683.5
685.75
685.55
686.45
685.85
686.35
685.1
684.05
684.9
684-55
684.9
685.3
684.55
681
678.75
678.6
Correc-
tion for
the Arc.
47.41
s.
■I-
1.22
1.25
1..39
1.25
1.28
1.25
1.28
1.28
1.28
1.25
1.22
1.-39
1.22
1.39
1.22
1.45
1.37
Vibrations
in 24 tioars.
86193.92
86193.65
86194.57
86194.37
86194.86
86191.63
86194.84
86194.36
86193.98
86194.27
86194.12
86194.41
86194.40
86194.29
86192.82
86192.21
86192.09
Reduc-
tion to a
Mean 1 Vibrations at
Tempe-
rature.
86193.99
■1-0-12
■^0.44
—0.57
-0.44
-0.80
-0.51
-0.74
-0.40
-t-0.04
-0.30
-0.21
-0-51
-0-51
-0.34
4^1.13
■f 1.63
■f 1.97
Reduced
47».41.
80194.04
86194.09
86194.00
86193.93
86194.06
86194.12
86194.10
86193.96
86191.02
86193.97
_86193.91
86193.90
86193.89
86193.95
86193.95
86193.84
86194.06
86193.99
IN THE LENGTH OF THE SECONDS' PENDULUM.
179
Drontheim. COINCIDENCES OBSERVED with PENDULUM No. 4.
DATE.
Baro-
meter.
1823.
Oct.25 A.M.
„ 25 P.M.
(bj lamp light.)
„ 26 A.M.
,, 27 A.M.
., 27 P.M.
(bj lamp light)
„ 28 A.M.
„ 28 P.M.
(by lamp tight.)
„ 29 A.M.
,, 29 P.M.
(by lamp light.)
„ 30 A.M.
31 A.M.
Nov. 1 A.M.
„ 2 A.M.
„ 3 A.M.
29.82
29.82
29.78
29.53
29.35
29.00
29.00
29.18
29.13
29.14
29.58
29.78
29.87
29.90
Clock
gaining.
Means.
45.49.
45.49<
45.49
45.49
45.49
45.49.
45.49
45.58
45.58.
gJ
45.5:
45.58
45.59
45.48.
45.48.
Tempe-
ratare.
47.8
47.8
46.9
46.6
50.3
50.8
53
52.8
52.9
51.4
50.1
50.8
51
51
48
47
47
47.2
43.8
43.2
42.7
43.8
40.5
40.5
39.8
41.2
40.. 3
40.3
Time of
Disap-
pearance,
!U. S.
20 15
18 23
8 47
7 00
15 11
12 45
45 23
42 30
14 08
11 24
15 46
13 25
37 58
35 23
44 27
42 37
01 02
59 17
57 54
56 55
47 15
46 17
19 12
18 47
07 05
06 42
13 08
12 46
Time of
Ue-ap-
pearance.
M. s.
20 23
18 47
8 51
7 18
15 19
13 10
45 31
42 57
14 15
11 47
15 55
13 47
38 03
35 41
44 35
43 03
01 07
59 41
57 59
57 15
47 21
46 40
19 15
19 05
07 12
07 09
13 11
12 59
True Time of
Coincidence.
Arc of
Vibra-
tion.
H. M. S.
11 20 19
1 18 35
5 08 49
7 07 09
11 15 15
I 12 57.5
U 45 27
1 42 43.5
10 14 11.5
12 11 ,35.5
11 15 50.5
1 13 36
8 38 00.5
10 35 32
10 44 31
12 42 50
9 01 04.5
10 59 29
10 57 56.5
12 57 05
4 47 18
1 46 28.5
II 19 13.5
1 18 56
11 07 08.5
1 06 55.5
11 13 09.5
1 12 52.5
Mean
Tempe-
rature.
1.18
0.60
1.28
0.64
1.22
0.6
1.22
0.6
1.22
0.62
1.2
0.6
1.28
0.64
1.2
0.6
1.22
0.6
1.24
0.62
1.2
0.6
1.24
0.62
1.18
0.58j
1.24
0.62
Mean
liiterv.il.
29.49
47.8
46.75
50.55
52.9
52.15
50.45
51
47.5
47.1
43.5
43.25
40.5
40.5
40.3
46.73
709.6
710
706.25
703.65
704.4
706.55
705.15
709.9
710.45
714.65
715.05
718.25
718.7
718.25
Correc-
tion for
the Arc.
+
1.25
1.45
1.31
1.31
1.33
1.28
1.45
1.28
1.31
1.37
1.28
1..37
1.22
1.37
Vibrations
in 34 bours.
86203.11
86203.47
86202.01
86201.11
86201.39
86202.08
86201.77
86203.32
86203.55
86205.11
86205.08
8C206.25
86206.16
86206.13
86203.61
Reduc-
tion to a
mean
Tempe-
rature.
-1-0.45
-1-1.60
-f-2.59
+ 2.28
-H.56
+ 1.79
+ 0.32
-0.15
■1.36
-1.46
-2,62
-2.62
-2.68
Reduced
Vibrations at
46».73
86203.56
86203.47
86203.61
86203.70
86203.67
86203.61
86203.56
86203.64
86203.70
86203,75
86203.62
86203.63
86203.54
86203.45
86203.61
2 A 2
180 EXPERIMENTS FOR DETERMINING THE VARIATION
RETURN TO ENGLAND.
The port of Drontheim is situated at the head of a fiord, and is distant
above ninety miles from the sea ; it was considered desirable, therefore,
to proceed to one of the outports, in order to await a favourable oppor-
tunity of putting to sea ; as the few hours of daylight, which were re-
duced to seven in the twenty-four, the general prevalence of westerly
winds towards the close of the year, and the very duU sailing of the
Griper, rendered a sufficient offing an object of importance, and diffi-
cult to be obtained. With this intention therefore we weighed from
Drontheim on the 13th of November with a head wind, and had suc-
ceeded on the 19th in beating down the fiord a distance of sixty miles,
when the increasing badness of the weather obliged us to anchor in a
small harbour between an island and the south shore of the fiord, and
detained us there, against every exertion to proceed, until the 4th of Decem-
ber ; on that day the wind sprung up from the E.N.E., and continuing
thirty-six hours, carried the Griper about one hundred miles to the west-
ward of the fiord, and thirty from the Stadtland, where the coast trending to
the southward enabled her to lay along the land with the wind at west, to
which quarter it had again shifted ; and on its coming on soon after to blow
with great violence, her situation became very critical upon a lee shore ;
by carrying a press of sail. Captain Clavering succeeded in making his
way good along the land, although nearing it, from the 62d to the 58th
degrees of latitude, when the line of coast opening to the Baltic relieved
us from immediate danger.
This gale which lasted three days, during which period there was no
intermission of its violence, was remarkable for the small amount of the
IN THE LENGTH OF THE SECONDS' PENDULUM. 181
effect produced on the barometer, either on its approach, during its con-
tinuance, or on its cessation ; and by the indications which were afforded
of its having originated in a disturbed state of electricity in the atmos-
phere ; it was accompanied by very vivid lightning, which is particularly
unusual in high latitudes in winter, and by the frequent appearance, and
continuance for several minutes at a time, of balls of fire at the extre-
mities of the yard-arms, and mast-heads ; of these not less than eight
were counted at one time.
Without further occurrence of note than a continuation of boisterous
weather, the Griper made Flamborough-head on the 13th of December,
and arrived in due course at Deptford on the 19th ; from whence the in-
struments were landed in London, and deposited in Portland-place.
182 EXPERIMENTS FOR DETERMINING THE VARIATION
LONDON.
Before I proceed in the detail of the observations of coincidences in
London, it is desirable to state the particulars of an examination which was
made of the thermometer that had been used throughout the experiments in
registering the temperature of the pendulums, with a view of ascertaining
the accuracy or otherwise of its graduation, and of determining the value
of the corrections, which might be required at different parts of the scale,
to produce the corresponding indications of Fahrenheit's thermometer.
In this examination, I had the advantage of the very valuable assistance
of my friend Mr. John Frederic Daniell, Fellow of the Royal Society.
The thermometer was made by Mr. Jones of Charing-cross, in 1821,
for the purpose of accompanying the pendulum belonging to the Board
of Longitude ; and as the occasion was one which required a more than
usual accuracy, proportionate pains were understood to have been
bestowed in its construction ; with the second pendulum I ordered and
received from Mr. Jones a second thermometer, which in appearance was
a duplicate of the first. The scales comprised a range from zero to
150°, and were divided into half degrees, of sufficient size to admit
a fair estimation to tenths. On my arrival at Sierra Leone, which was
the first opportunity I had had of carefully comparing the thermome-
ters with each other, I had the mortification to find that they differed
more than a degree in their indications, at the temperatures which I
might expect whilst within the tropics ; occasioning an uncertainty in the
deduction of the rate of the pendulum, amounting to not less than y^ ths
of a vibration per diem ; being greater, as I had reason to believe, than
the sum of the uncertainties due to all other causes whatsover. As I had
not the means at that time of referring any part of the scales to a natural
IN THE LENGTH OF THF SECOND'S PENDULUM. 183
standard, nor of comparing them with any other thermometer, in the
accuracy of which I could confide, I took the precaution of registering the
temperature of the pendulums, on all occasions, by both thermometers,
suspending them for that purpose, one on each side of the pendulum, at
equal distances from it, and at equal heights ; so that if any accident should
befall the one, which I could not but anticipate as an event of probable
occurrence, I might still retain the means of assigning the true tempera-
tures by the registry of the other, as soon as a favourable opportunity
should present itself, of effecting a rigorous examination of its scale.
The particular attention which was paid to the safety of the ther-
mometers, preserved them uninjured to the close of the experiments ;
as the registry of either, however, is suflScient for the record, I have
selected for that purpose the thermometer of which the tube was most
equable in its dimensions, and of which the ultimate correct graduation
was in consequence attended with the least inconvenience, although it
happened to have been the one in which the errors of greatest amount
had prevailed. As the scale did not reach higher than 150°, the freezing
point of water was the only point which could be verified by a direct
reference to a natural standard ; the reference was accordingly made,
and the graduation at 32° was proved, on several trials, to be exact. In
order to ascertain a second determinate point in the scale, it became
necessary to compare the thermometer, under circumstances which might
ensure a correct comparison, with one of which the scale should admit of
verification in two points by a natural standard ; for this purpose, Mr.
Daniell was so kind as to allow me the opportunity of employing a ther-
mometer in the construction and examination of which he had bestowed
much pains ; the points of boiling and freezing water had been determin-
ed experimentally, and proved by repeated subsequent trials ; the ac-
curacy of the intermediate division had been very carefully and minutely
scrutinized, by ascertaining that detached portions of mercury occupied,
184
EXPERIMENTS FOR DETERMINING THE VARIATION
in different parts of the tube, equal spaces as measured on the scale.
The two thermometers were placed in boiling ether, with their bulbs on
the same level and near the middle of the vessel which contained the
fluid ; the height of the mercury was then read on their respective scales,
at intervals of ten minutes, by Mr. Daniell, Mr. Newman (by whom Mr.
Daniell's thermometer had been made), and myself, as follows ; P. being
the pendulum thermometer, and D. the one belonging to Mr. Daniell ;
the barometer reduced to 32° stood at 30.368 inches.
sir. Newman.
P. 9S.9 D. 97.7
P. 99.6 D. 98.4
P. 100 D. 9S.7
Capt. Sabioe.
P. 98. S D. 97.5
P. 99.5 D. 98.2
P. 99.9 D. 98. 6
Mr. Daniell.
First Reading P. 99 D. 97.0
Second „ P. 99.5 D. 98. 4
Third „ P. 100 D. 9S.7
Whence the difference between the thermometers, at the part of the scale
which was under examination, appeared to be 1°.27 ; or 98°. 27 of the
pendulum thermometer corresponded with the 97th degree of Mr. Daniell's
thermometer, and consequently with the 97th degree of Fahrenheit's scale.
The space between the points of 32° and 97°, which were thus deter-
mined on the scale of the pendulum thermometer, was then divided by an
engine into sixty-five equal parts, on one side of the tube, the old division
being suffered to remain on the other side ; and the new graduation was
extended throughout the whole length of the scale. The following table
exhibits the comparative indications of the old and new divisions between
the degrees of 32 and 97, including the extreme range of temperature
during the pendulum experiments ; the comparison was made by means
of the micrometer screw of the dividing engine :
New Scale.
Old Scale.
New Scale.
Old Scale.
New Scale.
Old Scale.
o
32
0
32
o
51.5
0
52
o
80
0
SI
35
35.1
55
55.6
85
86.1
40
40.2
60
CO. 7
90
90.2
43
43.25
64
04.75
94
95.22
45
45.3
70
70.8
97
98.27
48
48.4
76
76.9
IN THE LENGTH OP THE SECONDS* PENDULUM.
185
Now if the points of 32° and 97° were correctly assumed as according
with Fahrenheit's scale, the first from experiment and the second from
Mr. Daniell's thermometer, and if the tube were every where of equal
capacity, then was the new graduation strictly that of Fahrenheit's
thermometer ; and the preceding table would furnish the corrections for the
degrees of the old division, or of that in which the temperature of the pen-
dulums had been recorded in the course of the experiments, into the true
degrees of Fahrenheit. To prove, therefore, the equal capacity, a column
of mercury was detached, and the tube gauged by Mr. Daniell and myself
as follows ; the degrees by which the length of the column in different
parts of the tube was measured, being those of the new division : —
Mr. daniell.
C
APT. SABINE
•
Upper end of
Lower end of
Length of
Upper end of
Lower end of
Length of
the Column.
the Cohimn.
the Column.
the Column.
the Column.
the Column.
o
o
o
o
o
o
99.23
64.25
34. 9S
101.15
66.23
34.92
94. 2S
59.3
34.98
96.5
61.28
35.02
89.3
54.4
34.9
91.3
56.4
34.9
S4.-i
49.55
34.85
86.37
51.5
34.87
79. G
44.7
34.9
81.6
46.65
34.95
74. S
39. S
35
70.7
41.75
34.95
69.9
34.9
35
71.85
36.85
35
05
30
35
66.98
32
34.98
Mean
....
34.93
Mean ....
34.95
Whence it appeared that the length of the detached column of mercury,
thus measured on a scale of equal divisions, was so nearly the same in all
parts of the tube, as to afford a satisfactory evidence, that the capacity of
2 B
186 EXPERIMENTS FOR DETERMINING THE VARIATION
the tube was sufficiently equable in the space included between 32° and
97° to justify the intermediate graduation into 65 equal divisions.
The want of a standard thermometer, verified at all points of its scale
by competent authority, having been felt in many other instances as well as
in the present, for purposes of reference, the superintendence of the con-
struction of such a thermometer has been undertaken by Mr. Daniell and
Captain Kater, at the instance of a committee of the Royal Society : as
soon as it shall have been completed, it is designed to obtain an additional
proof of the correctness of the 97th degree of the new division of the scale
of the pendulum thermometer (which rests at present upon the presumed
accuracy of Mr. Daniell's thermometer), by comparing its indication with
that of the standard during their immersion in boiling ether. As the
construction of a standard thermometer was undertaken early in the present
year (1824), it is hoped that its completion may be accomplished before
the publication of these experiments, so that a notice of the result of the
comparison may be appended at the close of the volume ; but as it is
confidently anticipated, from the habitual accuracy of Mr. Daniell, and
from his justly high authority in the construction of meteorological instru-
ments, that no difference, deserving of regard, will be found between the
thermometer on which he has already bestowed much pains, and the one
which he has undertaken to superintend, the comparisons in the table in
page 184 have been employed, in reducing the temperature of the pendulum
during the observation of coincidences at the several stations as registered
by Mr. Jones's thermometer, to the corresponding degrees which would
have been shewn by a correctly-graduated Fahrenheit's thermometer.
IN THE LENGTH OF THE SECONDS' PENDULUM. 187
EXPERIMENTS in 1821 and 1822.
It has already been noticed that, previously to the employment of the
pendulums at the stations adjoining the equator, their rates had been
obtained in London. The time which intervened between the date of the
order procured from the Board of Longitude for the construction of the
instruments and their embarkation, being not more than was neces-
sary for their preparation, it might have been very doubtful, whether so
desirable a measure, as a preliminary trial of the pendulums in London,
could have been accomplished, had I been obliged to await the completion
of their own apparatus ; fortunately, the provision which had been made
for Captain Kater's experiments with the pendulum with convertible
axes, had not been removed from Portland-place ; as soon, therefore, as
the pendulums themselves could be got ready, I availed myself of Capt.
Kater's permission to employ the agate planes belonging to his pendu-
lum, which still remained upon the support ; and with the assistance of
one of Mr. Browne's clocks, of which he was kind enough to supply the
rate, I made the observations contained in the following Tables, L and II.
The thermometer used to register the temperature of the pendulums was
one which had been employed by Captain Kater in his experiments, the
degrees of which were true degrees of Fahrenheit's scale. The corrections
for buoyancy, which express the value in vibrations per diem of the re-
tardation of the pendulums from their oscillating in a medium of variable
resistance instead of in a vacuum, have been computed on the data, that the
specific gravity of the pendulums is 8.6 ; that water is 836 times heavier
than air, when the thermometer is at 53'^, and the barometer, of which the
temperature of the mercury is also 53°, is at 29.27 inches ; and that in
observations which may be made in other states of the barometer and
thermometer, the number 836 will vary inversely as the height of the
barometer, and directly, its ^fo-th part, for each degree of Fahrenheit
that the thermometer differs from 53°.
2 B 2
188
EXPERIMENTS FOR DETERMINING THE VARIATION
Table I. Lon
DON
, 1821. COINCIDENCES OBSERVED ^vith PENDULUM No. 3.
DATE.
Baro-
meter.
Clock making
per Diem.
Is
= 1
z
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Re-ap-
pearaoce.
True Time of
Coincitlejicc.
Arc of
Vibra-
tion.
jMean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
the Arc.
Vibrations
in 24 hours.
Reduc-
tion to a
niewn
Tempe-
rature.
Reduced
Vibrations at
IN.
S.
0
M. S.
M. S.
H. M. 9.
0
0
s.
S.
July 6 P.M.
(Observed by Mr.
29.80
Aniold.
86399.44.
I
11
66.2
66.5
27 52
20 25
27 59
20 50
2 27 55.5
4 2-1 37.5
1.22)
0.64/
66.35
676.2
•f
1.35
86145.23
-f 0.29
86145.52
„ 7 A.M.
29.86
86399. 44<
1
11
65
66.3
25 38
18 22
25 43
18 32
11 25 40.5
1 18 27
1.26]
0.66]
65.65
676.65
1.46
86145.52
86145.52
„ 8 A.M.
30.04
86399. 44J
1
11
64.9
65.6
7 23
00 11
7 27
00 21
11 7 25
I 00 16
I.37I
0.71J
65.25
677.1
1.71
86145.95
-0.17
86145.78
„ !.■! A.M.
30.06
86399. 44^
1
11
65.2
65.6
00 15
53 00
00 22
S3 17
11 00 18.5
12 53 08.5
0.68 J
65.4
'^677
1.55
86145.75
-0.10
86145.65
Means . . .
29.94
63.66
86115.61
86145.61
The correction for Buoyancy is + 5.96, making 861.51 .57 Vibrations in vacuo, at the temperature of 65.66 Fahrenheit.
Table II. London
, 1821. COINCIDENCES OBSERVED with PENDULUM No. 4.
DATE.
Baro.
meter.
Clock making
per Diem.
s
6 u
Z.
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Reap.
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
theArc.
Vibrations
it) 24 boors.
Reduc-
tion to a
Mean
Tempe-
rature.
Hednced
Vibrations at
63°. 13.
IM.
S.
"
M. S.
M. S.
H. M. s.
0
0
s.
s.
Sep. 17 P.M.
30.10
-imoid. r
86400.3 ^
69
69
13 27
12 17
15 33
12 30
1 15 aO
3 12 23.5
1.36]
o.esj
69
701.35
+
1.64
86155.52
+ 0.37
86155.89
„ 18 P.M.
29.90
86400.4 i
69
69.8
28 45
25 18
28 50
25 33
2 28 47.5
4 25 25.5
1.38'|
O.71J
69.4
699.8
1.74
86155.22
■^0.53
86155.75
,, 19 A.M.
29.90
86400.6 J
66.7
67.8
01 34
57 35
01 40
57 50
10 01 37
11 57 42.5
1.34|
0.66J
67.25
702.55
1.57
86156.21
-0.37
86155.84
„ 20 P.M.
29.80
86400.7 J
67.3
67.7
37 27
34 18
37 33
34 31
2 37 30
4 34 26
1.36]
O.esj
67.5
701.6
1.64
86156.04
-0.26
86155.78
„ 21 A.M.
29.70.
86400.7 J
1
67 2
67.8
7 39
4 35
7 45
4 49
9 07 42
11 04 42
1.36]
0.68]
67.5
702.05
1.64
86156.22
-0.26
86155.96
Means . . .
29.88
68.13
86135.81
86155.84 j
The correction for Buoyancy is +5.94, making 86161.78 Vibrations in vacuo, at the temperature of 68.13 Fahrenheit.
IN THE LENGTH OP THE SECONDS' PENDULUM,
189
As the course of the experiments proceeded at Sierra Leone and at
the equatorial stations, I had occasion to remark, that whilst the difference
in the rate of the two pendulums in corresponding circumstances, or the
excess in the number of vibrations per diem of the one pendulum over that
of the other, due to their actual difference in length, was constant at the
several stations adjoining the equator, or as nearly so as the nature of
the observations would authorize an expectation, its amount deducible from
the experiments in London contained in the preceding Tables, appeared
a much wider departure from the subsequent experience, than could be
attributed to error in the observation of coincidences : this remark will
be best illustrated by the following collected view of the respective
differences at the stations visited in the voyage of 1822.
Stations.
Difference in the number of Vibrations,
per diem, of tlie two Pendulums.
St. Thomas . .
Maranham . .
Ascension . .
Sierra Leone .
Trinidad. . .
Bahia. . . .
Jamaica . . .
New York . .
London . . .
9.G9
9.39
9.51
9.74
10.00
9.90
9.60
9.59
11.25
- 9,6S Mean.
Two modes suggested themselves, whilst the equatorial stations
were in progress, of accounting plausibly for the difference which thus ap-
peared between London and the other stations : the pendulums had been
190 EXPERIMENTS FOR DETERMINING THE VARIATION
returned to Mr. Jones subsequently to the experiments in London, to be
fitted with cases, and packed for embarkation ; and it was possible that
an accident might have befallen one of them in the course of those opera-
tions, and have occasioned a slight alteration in its length, equivalent to
between one and two vibrations per diem ; or I might have transcribed
erroneously the sign prefixed to the rate of the clock during the coinci-
dences with No. 3, in Mr. Browne's memorandum which I had left in Eng-
land ; as a gaining rate of 0..56 parts of a second, instead of a losing rate of
the same amount, would have reduced the apparent difference within
the reasonable limit of errors of observation. Deeming the latter suppo-
sition the more probable, I wrote to Mr. Browne to request him to refer
to the rate of the clock at the period in question ; but on my return to
England in January, 1823, I received a fresh memorandum from him, by
which I perceived that I had not been mistaken in the original transcrip-
tion, either in the quality or in the amount of the rate. I then proceeded
to repeat the trial of the pendulums in London, expecting to discover
by the results compared with those of 1821, in which of the pendulums
an alteration had taken place. Captain Kater's agate planes were still
on the pendulum support, in Portland-place ; the screws, by which the
box containing the planes belonging to my own pendulums was fastened
on its support, did not correspond with the holes which had been made
to receive the screws of Captain Kater's planes in the mahogany plank
described in the Phil. Trans, for 1819, Part IIL, p. 41 ; and Mr. Browne
was unwilling that the strength of the plank should be impaired by fresh
perforations. I was induced, therefore, to employ Captain Kater's planes
a second time instead of my own, and to make no other difierence from
the proceedings of 1821, than by the substitution of my own thermometer
for Captain Kater's. Mr. Browne was again kind enough to permit me
to employ one of his clocks for the coincidences detailed in Tables III.
and IV., and to supply its rate.
IN THE LENGTH OF THE SECONDS PENDULUM.
191
Tauttt
IIT Tr>,v
DON, 1S2.
J rnTivrrTnFivri?s ORSFRVP.n with PF.NDTII.TIM No .<?
DATE.
Baro-
meter.
Clock making
per Diem.
u. a
0 1-
. -o
^ S
0
Teiiipe-
ralore.
Time of
Disap.
pearance.
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
the Arc.
Vibrations
in 24 hours.
Redac-
tion to a
mean
Tempe-
ratore.
Reduced
\ ibrations at
49^.1.
IN.
s.
•
M. S.
M. s.
H. M. s.
0
0
S.
S.
Feb. 28 A.M.
29.45
Bolton. f
86400. 43<
I
49.1
49.9
16 32
12 01
16 36
12 12
11 16 34
1 12 06.5
1.251
0.64 J
49.5
693.25
+
1.42
8G152.56
•fO.17
86152.73
„ 28 P.M.
29.45
r
86400. 43<
49
49.2
32 32
28 09
32 38
28 21
2 32 35
4 28 15
1-2 1
0.6 }
49.1'
694
1.27
86152.73
86152.73
Mar. 1 A.M.
29.90
86400. 74I
I
48.4
49.6
34 52
30 25
34 57
30 39
11 34 54.5
1 30 32
1.2 1
0.6 1
49
693.75
1.27
86152.94
-0.04
86152.90
„ 1 P.M
29.93
86400. 74 j
49.6
49
39 09
34 42
39 14
34 58
2 39 11.5
4 34 50
1.2 1
0.6 i
49.3
693.85
1.27
86152.97
■^0.08
86153.05
„ 2 A.M.
30.00
86400. 25<
L
48.1
49.1
41 04
36 42
41 09
36 59
11 41 06.5
1 36 50. S
1.251
0.64 J
48.6
694.4
1.4
86152.80
-0.21
86152.59
„ 2 P.M.
29.95
86400. 25|
I
49.1
49.1
16 41
12 20
16 46
12 SI
2 16 43.5
4 12 25.5
1.2 1
0.6 /
49.1
694.2
1.27
86152.60
86152.60
Means . .
29.78
19 . 1
86152.77
86152.77
The correction for Buoyancy is +6.15, making 86158.92 "Vibrations in Vacuo ; and 49.^1 of the scale of the registering
Thermometer is equivalent to 4S''.67 of Fahrenheit, being the temperature of the Pendulum.
T A WTT?
f\T Tr>»rT>rvi>x
1 COQ
rnnvrtriFivrrFS
, OBS
F.RVL
ffT\ ^itV. PFlVniTTTTM IVn 4.
DATE.
Baro-
meter.
Clock makin°
per Diem.
.•a
0
Tempe-
rature.
Time of
Disap-
pe.trance.
Time of
Re-ap.
pear.)nce.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion of
tUe Arc.
Vibrations
in 24 hours.
Rediic.
tion to a
me.tn
Tempe-
rature.
Reduced
Vibrations at
52«.39.
IN.
S.
0
M. S.
M. S.
H. H. S.
0
0
S.
S.
Mar. 4 A.M.
29. SO
Bolton. r
86400 . 47<
i
53
52.8
55 06
55 25
55 11
55 37
10 55 08.5
12 55 31
1.181
>
0.6 J
52.9
722.25
+
1.25
86162.51
+ 0.21
86162.72
„ 4 P.M.
29.35
86400. 47/
I
52.8
53
19 21
19 41
19 31
19 56
1 19 27.5
3 19 50
1.241
>
0.6 j
52.9
722.25
1.33
86162.59
-fO.21
86162.80
„ 5 A.M.
29.45
66400. 39I
I
11
51.6
52
45 16
45 53
45 25
46 04
11 45 20.5
1 45 58.5
1.181
0.6 j
51.8
723.8
1.25
86162.89
-0.25
86162.64
„ 5 P.M.
29.50
86400. S9I
I
52
52.7
58 31
58 56
58 37
59 14
1 58 34
3 59 05
1.2 1
0.6 j
52.35
723.1
1.28
80162.69
86162.69
„ 6 A.M.
29.75
86400. 29I
1
52
52
52 11
52 40
52 17
52 58
11 52 14
1 52 49
1.24|_
0.62J
52
723.5
1.36
86162.79
-0.16
86162.63
Means . .
29.47
52.39
86162.69
86162.69
The correction for Buoyancy is +6.02, making 86168.71 Vibrations in Vacuo ; and 52°.39 of the scale of the registering
Thermometer is equivalent to 51°.88 of Fahrenheit, being the temperature of the Pendulum.
192
EXPERIMENTS FOR DETERMINING THE VARIATION
London. COMPARISON of the VIBRATIONS of the PENDULUMS
in IS21 and 1S23.
Date.
Vibrations
per Diem.
Tempe-
rature.
Reduction
to a Mean
Tempera-
ture of 62°*
Reduced Vibrations at 62°.
Excess of
Vibrations
of Pendu-
lum 4.
Pendulum 3 . .}
Pendulum 4 .
1S21
1823
1S21
1S23
S6151.57
8615S.92
S6161.7S
86168.71
65.66
48.67
68.13
51.88
s.
+ 1.54
-5.61
+ 2.58
-4.26
86153.111
86133. 31j
86164.361
I 8615
3.21
> 11.20
86164.41
86164.45]
• The Reduction is in the proportion of 0.421 parts of a second per diem for each degree.
It is shewn by this comparison, that no alteration whatsoever had
taken place, either in the absolute or in the relative length of the
pendulums since their first construction ; and in so far as the experiments
just recorded afforded an evidence of this very important fact, their
results were highly satisfactory. The reason still, however, remained to
be inquired into, of the apparent difference in the length of the pendulums
with relation to each other, in London and elsewhere, in which error of
some kind was obviously involved, since it had been ascertained that
no real difference had existed. As the employment of Captain Kater's
agate planes was a departure from the strict correspondence of the pro-
ceedings in London with those at the other stations, it became the first
object of suspicion ; I caused, therefore, the box containing the planes
belonging to the pendulum to be fitted with screws to suit the holes already
existing in the mahogany plank, and having substituted them for Capt.
Kater's on the support, the coincidences of the succeeding Tables V. and
VL were observed.
IN THE LENGTH OF THE SECONDS' PENDULUM.
193
r* UT ¥7
\T 1 ,.^T
T-»/-k IVl
, isaa
rmivrpmPArrFs oRSFRVPn wwu PKNnTTTTTM iVr. q
LAlSLiU ». ±-tyj^^u\j^t
v^
DATE.
Baro-
meter.
Clock making
per Diem.
Si
11
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
interval.
Correc
lion for
tlieArc.
Vibrations
in 24 tiours.
Reduc-
tion to a
mean
Tempera-
ture.
Reduced
Vibration?al
53^.52.
IN.
s.
o
M. 3.
M. S.
U. H. S.
o
o
S.
S.
MarcliI9A.M.
29.75
Bolton.
86400.6 •
86400.6 <
I
11
1
53.5
53.7
53. 7
2t 57
20 10
53 51
25 02
20 21
53 58
11 24 59.5
1 20 15.5
2 53 51. 5
1.28]
0.64 J
1.28]
53.6
691.6
+
1.45
86152.21
-hO.03
86152.24
„ 19 P.M.
29.75
>
53.6
691.6
1.45
85152.21
-1-0.03
86152.24
11
53.5
49 03
49 18
4 49 10.5
0.64]
\
86400.65-;
1
51.2
17 23
17 28
11 17 25.5
1 28]
„ 20 .\.M.
29.60
>
51.05
694.5
1.45
86153.30
-1.04
86152.26
11
50.9
13 06
13 15
1 13 10 5
0.6lJ
f
1
51
30 33
30 41
2 30 37
1.26]
„ 20 P.M.
29.60
86400. 65<
f
51
695.15
1.41
86153.47
-1.06
86152.41
n
51
26 23
26 31
4 26 28.5
0.64]
r
I
55
18 16
18 22
12 18 19
1.3 ]
,. 21 P.M.
29.25
86400. SsJ
86100. e5<^
11
1
54-7
54.4
13 14
52 09
13 32
52 14
2 13 23
10 52 11.5
0.66]
1.3 ]
54.85
690.4
1.51
86152.10
-1-0.56
86152.66
,, 22 .\.M.
29.15
>
54.5
691.35
1.54
86152.24
-1-0.41
86152.65
11
51.6
47 20
47 30
12 17 23
0.60
r
86400. 65^
1
54.7
58 01
58 06
1 58 03.5
1.22]
„ 22 P.M.
29.15
0.62
54.8
691.65
1.33
86152.13
-^o.5^
86152.67
11
54.9
53 14
53 26
3 53 20
86400.1 ■
1
55
56 32
56 38
1 56 35
1.2
,, 24 P.M.
30.20
■
54.75
692.35
1.28
86151.78
-HO. 52
86152.30
11
54.5
51 52
52 05
3 51 58.5
0.6 J
r
86400.2 .
1
53
23 01
23 09
11 23 05
1.22
„ 25 A.M.
30 . 30
>
53.5
693.3
1.31
86152.27
86152.27
I "
54
18 31
18 45
1 18 38
0.6
Means .
29.64
53.52
86152.41
86152.41
The correction for Buoyancy is -f 6. OG, making SO 158.47 Vibrations in Vacuo; and 53°. 52 of the scale of the
registering Thermometer is equivalent to SS'.gT nf Fahrenheit's scale, being the temperature of the Pendulum.
2 C
194
EXPERIMENTS FOR DETERMINING THE VARIATION
Table VI. London
, 1S25
pruTvrr'Tnpivrrus ORSP'RVPn ,.,;<», PFNnTTTTTAi iVn j.
DATE.
Baro-
meter.
Clock making
per Diem.
Is
Tempe-
r.iture.
Time of
Disap-
pearance.
Time of
Re-ap-
pearance
True Time of
Coincideuce.
Arc of
Vibra-
tion.
Mean
Tempe-
ratare.
Mean
Interval.
Correc-
tion for
the Arc.
Vibrations
in 24 liours.
Reduc-
tion to a
Mean
Tempe-
ratnrc.
Reduced
Vibrations at
54°.9S
IN.
s.
Q
M. s.
M. s.
H. M. S.
0
o
S.
0
Mar. 23 A.M.
29.65
r
Bolton.
86400.3 <^
I
1
n
1
54.5
55
55
50 32
50 18
13 IS
50 39
50 41
13 51
11 50 35.5
1 50 29.5
2 13 47
1.24
>
0.62
1.22
54.75
719.4
+
1.36
86161.46
-0.10
86161. S6
„ 23 P.M.
29.65
86400.3 i
n
1
54.9
53..?
13 40
21 00
13 55
21 06
4 13 47.5
1 2! 03
>
0.6
1.28]
51.93
720.05
1.31
86161.61
86161.61
Apiil 5 P.M.
29.07
86399. 85<^
11
1
53.1
57
21 2S
35 43
21 38
35 50
3 21 33
12 35 46.5
>
0.64
1.3
53.2
723
1.15
86162.31
-0.75
86161. 5f.
„ CP.M.
29.25
86399. 85<^
11
37
35 25
35 36
2 .35 30.5
0.64
57
718.4
1.50
86160.84
+ 0.85
86161.69
Means . . .
29.40
54.98
86161.55
86161.55
The correction for Buoyancy is +6.02, making S6167.57 Vibrations in Vacuo ; and 54°.9S of the scale of the registering
Thermometer is equivalent to 54°.4 of Fahrenheit, being the temperature of the Pendulum.
DIFFERENCE in the VIBRATION of the PENDULUj^IS, on Captain
Kater's Planes, and on their own.
Pendulum 3.
Pendulum 4.
PLANES.
Captain Kater's.
Its own.
Captain Kater's.
Its own.
Vibrations
per Diem.
86153.21
86158.47
86164.41
861 67.. 57
Tempe-
ratnre.
62
52.97
62
54.4
Reduction
to a Mean
Tempe-
rature of
6-2« •.
-3. SO
-3.20
Reduced
Vibrations at
62". Falit.
86153.21
86151.67
86164. 11
86164.37
Difference in the
Vibrations of each
Pendulum, on Capt.
Kater's Planes and
on its own.
1.46
0.04
* The Reduction is in the proportion of 0.421 for each degree of Fahrenheit,
IN THE LENGTH OF THE SECONDS PENDULUM,
195
Difference in the number of the Vibrations of the two Pendulums
on their own Planes, in London, and at the Southern Stations.
StatioD,
Pendulum 3.
Pendulum 4.
Excess of
Vibrations of
Pendulum 4.
London . . .
S6154.6S
S6164.3S
9.70
9.6S
Southern Stations, Page 1S9
The cause of the want of correspondence in the rate of the one pendu-
lum compared with that of the other, in London and at the Southern Sta-
tions, had thus been traced to the accidental employment of Captain
Kater's planes of suspension in the experiments in London of 1821, and in
the first series in 1823. The most careful examination and comparison of
the two sets of planes, made after the diflference was known which their
respective employment produced, failed in discovering its occasion ; but
it may well be conceived, that inequalities or irregularities of various
kinds might exist, either in the planes, or in the knife-edges, or in both,
which might become sensible in the application of so delicate a test as the
vibration of a pendulum, though they might not be perceptible by other
means. It is remarkable that one pendulum should have been thus
, affected by the change of planes, whilst the other was not so ; that the
rate of No. 4 should have been uninfluenced, whilst that of No. 3 varied
so much as its 59-thousandth part : the knife-edges of the two pendulums
were precisely of similar dimensions, and the Y's, by which they were
lowered on the planes previously to oscillation, must have deposited them
at all times as nearly as possible on the same points of bearing. It may
not be superfluous to add, that the horizontal adjustment of the planes
was in every instance most carefully attended to, and examined occa-
2 0 2
196 EXPERIMENTS FOR DETERMINING THE VARIATION
sionally by Mr. Browne, as well as frequently by myself. Fortunately,
it is of the effect only, and not of the cause, that it is important to the
experiments to be assured ; and whilst the effect is placed beyond ques-
tion by repeated experiment, it may readily be conceded that the cause
may be too minute to admit of a satisfactory investigation.
Were an illustration wanting of the importance in experiments of this
nature, of maintaining the strictest correspondence in the proceedings at
the different stations, even in the most minute and apparently inconse-
quential particulars, this instance of the effect of the change of planes
upon the vibration of pendulum 3 affords a strong one. It is probable
that such instances might be of rare occurrence ; that the rates of pen-
dulums generally, as that of No. 4, would be the same on different planes,
supposing their construction to be similar, and the adjustments properly
regarded ; but in the evidence which is here presented of an alteration
being produced in a single instance, that condition of the experiment,
which requires the adoption of every precaution conducive to the
utmost attainable accuracy, is not fulfilled, unless the same planes are
used in all the experiments which are designed to be comparative.
I must not omit to notice, that the knowledge of the existence of error
in the earlier experiments with No. 3 in London, is one of the incidental
advantages derived from the employment of two pendulums ; had I
been furnished only with the pendulum belonging to the Board of
Longitude, I might not have been led to suspect the inaccuracy arising
from the use of Captain Kater's planes ; and I should thus have assign-
ed, from correct experiments elsewhere, an erroneous value to the length
of the seconds' pendulum at every one of the other stations which I
visited.
In the following Table, No. VII., the particulars are arranged which I
received from Mr. Browne, relative to the mode in which the rate of
the clock was deduced, with which the pendulums were compared in the
IN THE LENGTH OF THE SECONDS* PENDULUM.
197
observation of coincidences contained in Tables III., IV., V., and VI.
The clock, which was made by the late Mr. George Bolton, was com-
pared every day at 12 p.m. with two other clocks, which were regarded
as standards of comparison : one of these was the time-piece by Gum-
ming, noticed in the Phil. Trans, for 1819, part III. p. 41 ; the other was a
clock recently made by Molyneux on the same principle as Cumming's,
and in Mr. Browne's estimation, is not inferior to it in performance. The
standard clocks were regularly compared with astronomical time ; the
dependence placed on them being that of keeping an uniform rate from
one transit observation to another. The rate of Bolton, entered in
Table VII., is on mean time, as separately inferred from the comparison
with each of the standard clocks.
TABLE VII.
Rate o
Bolton
Rate o
Bolton
182S
deduced I'rom
Mean.
1823
deduced from
Mean.
Gumming
Molyneux
<'umming
Molyneux
12 P.M.
Gaining.
Gaining.
Gaining,
12 P.M.
Gaining.
Gaining.
Gaining.
Feb.
27
S.
|o.43
|0.75
1
y.
S.
March
14
S.
S,
S.
')
28
0.43
0.43
11
15
].0.5
)
0.4
0.45
0.73
0.74
1,0.6
0.4
0. 5
March
1
1»
16
J
n
2
|0.3
1-0.45
0.2
0.25
1»
17
l0.5
0.5
0.5
0.6
0.52
1>
3
J
1
11
18
l0.6
ii
4
|0.55
0.4
0.47
11
19
0.6
0.6
|o.38
0.4
0.39
T
0.6
0.65
)i
5
J
1
11
20
U
6
|0.3S
|o.6
1 «.
0.2
0.29
21
|0.8
0.9
0.85
11
7
0.6
0.6
11
22
|0.5
0.8
0.65
^O.S
0.8
0.8
lo.a
0.3
0.3
„
S
{
11
23
lo.s
0.8
0.8
|0.1
0.1
n.i
1)
9
•1
11
24
^0.3
0.2
0.25
l0.2
0.2
0.2
It
10
{
25
|0.3
0.2
0.25
}.0.2
0.1
0.15
)»
11
[o.oo
|o.35
1
jo.oo
26
11
12
0.00
0.00
April
4
Losing.
-1
Losing.
Losing.
0.35
0.35
l0.15
0.15
0.15
11
13
11
5
1
0.00
0.00
!>0.15
0.15
0.15
11
14
11
6
J
19S EXPEniMENTS FOR DETERMINING THE VARIATION
EXPERIMENTS ix 1824.
The experiments in London in the spring of 1823, the particulars of
which have been just related, were made when the pendulums had been
landed from the Pheasant on their return from the equatorial stations,
and before their embarkation in the Griper, for the Arctic Circle. On
the return of the Griper in the winter of 1823-1824, it became necessary
to repeat the trial of the pendulums a third time in London, for the
purpose of shewing that the attention given to their safe preservation
had been as effectual in the second voyage, as it had been found to
have been in the preceding one. There was also a second purpose,
essential to the strict comparison of the experiments at the several
stations with each other, Avhich remained to be accomplished on the final
return of the pendulums to England. Embracing climates so widely dis-
similar, the range of temperature, at which the various results had been
obtained, exceeded fifty degrees ; it became, therefore, an object of
primary importance, to determine experimentally, and with the utmost
exactness of which the experiment should be capable, the expansion of
the pendulums corresponding to the measures of heat. Two methods
of proceeding in the attainment of this object presented themselves ; one,
by immersing the pendulums successively in fluids of different tempe-
ratures, and measuring their intermediate expansion, by means of a
microscopical apparatus, which Captain Kater had devised on a similar
occasion, and of which he was so kind as to offer me the use, as well as
his own most valuable assistance in the operation ; and the other, by
ascertaining the effect of the expansion on the rate of the pendulums,
when vibrating in temperatures, of which the difference should equal the
extreme range which had occurred in the course of the experiments. The
IN THE LENGTH OF THE SECOXDS' PENDULUM. 199
latter method bore the more immediate relation to the purpose for which
the expansion was required ; but as I was more aware of the difficulties
which would oppose a sufficiently precise determination of the rate and
temperature during the vibration, than of those which are attendant
upon exact microscopical measurement, I should have preferred the
adoption of the former method, in reliance on the skilfulness and ex-
perience of Captain Kater, had I not possessed advantages, through the
kindness of Mr. Browne, in the use of his most excellent clocks, and in
his very accurate determination of their rates, which encouraged me to
an attempt, wherein I could otherwise have scarcely hoped to have suc-
ceeded ; and I was further induced by the consideration, that if I should
fail in determining with sufficient exactness the alteration of rate due to
differences of temperature, I should at least obtain a rate of the pen-
dulums in London, which would compare with the results in 1821 and
1823.
On my arrival in Portland-place in December, 1823, I found a clock of
Mr. Browne's, made by Arnold, being the same which Captain Kater had
used at the stations of the trigonometrical survey, in occupation of the re-
cess beneath the pendulum support, and keeping, as Mr. Browne informed
me, a tolerably good mean rate. Being anxious to take advantage of the
cold weather which then prevailed, and which was the coldest of the season,
in order to obtain the rate of the pendulums at the lowest temperature
which natural circumstances would enable, I determined to proceed im-
mediately in the observation of coincidences with the clock which was
already stationed ; hoping that by comparing it very carefully with
Cumming and Molyneux at short intervals, any deviation which might
take place from its mean rate might be detected and allowed for. By
keeping one of the windows of the clock-room constantly open, and
the shutters closed, and by discontinuing a fire in the adjoining room,
200 EXPERIMENTS FOR DETERMINING THE VARIATION
the temperature was lowered to little more than that of the external
atmosphere, and its fluctuations were reduced within very small limits.
As the observations proceeded, however, I had the mortification to
perceive, that the rate of the clock varied from hour to hour, so much,
and so continually, as to make it doubtful whether the vibrations of the
pendulums could be deduced from it with sufficient accuracy ; the irre-
gularity was shewn by the discordances in the partial results with the
detached pendulums, which form the severest test to which the unifor-
mity of a clock's going can be subjected, because they detect variation
in smaller intervals, than those in which it can be discovered by the
comparison with other clocks. I persevered, however, until ten results
with each pendulum had been obtained ; but finding on examination
that they contained differences with each other, amounting to a whole
vibration per diem, I was induced to reject them altogether, and to
undertake a fresh series with Gumming, which Mr. Browne consented to
remove into the recess for that purpose,
A further short delay took place, in furnishing the mercurial pendulum
of the clock with a small plate bearing a disk of the same diameter with
those on the pendulums of the other clocks ; the disk was of silver, and
was contrasted as usual by a coating of black varnish on the plate. The
door of the clock-case happening to be larger than those of the other
clocks of Mr. Browne's which had been used in the recess, the frame of
wood to which Captain Kater's arc, measuring the extent of the vibra-
tion of the detached pendulums, was fixed, was too small to fit into the
opening of the door-way. I had hitherto always used Captain Kater's
arc in London, because the frame of the arc belonging to the Board of
Longitude had been made to fit the clock which I had employed at the
other stations, and was much too large for Mr. Browne's clocks ; on this
occasion, however, I had the frame reduced to fit the door of Cumming,
IN THE LENGTH OF THE SECONDS' PENDULUM. 201
and happening to compare the arcs when thus accidentally brought toge-
ther, I perceived that I had too confidently presumed their radius to be
the same, in consequence of their having been made for pendulums of
equal length. The expansion of the pendulums, however, requiring all
my attention, I postponed for the time the inquiry into which was in
error, and into the exact amount of their difference.
From the time which necessarily elapsed in these previous arrange-
ments, it was not until late in March that I was able to resume the obser-
vation of the coincidences, the particulars of which are contained in
Tables VIII. and IX.
2 D
202
EXPERIMENTS FOR DETERMINING THE VARIATION
T.
T>X 17 V^TTT T AlMTIfilV Ift^'*
.rOTlVrrFnFNrF'2 nR«!17HVT7nmifV. PFlVniTTTTM TVr« -i
Liilif. Till. l.'UiVllUiVf 19
•\y\Jl.L\ \jLiJlljl\ KjF
DATE.
Baro-
meter.
Vibrations
i>f Cumroing
per Diem.
Z s
o
Tenipe-
ratme.
Time of
Disap-
pearance.
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
the Arc
Vibrations
in 24 boors.
Reduc-
tion to a
mean
Tempe-
rature.
Reduced
Vibrations at
44''.6e.
1821.
IN.
s.
86401. K
0
41.7
M. S.
53 16
M. S.
53 17
H. M. S.
U 53 16.5
o
1.311
0
s.
s.
-f
April 1 A.M.
29.88
42.35
704.15
1.51
86157.21
-0.97
86156.24
43
50 37
50 39
1 50 38
0.6oJ
86401. K
43.2
8 22
8 24
2 8 23
1.381
,, 1 P.M.
29.80
\
43.6
702.35
1.71
86156.81
-0.45
86156.36
t
f
41
45
5 26
21 34
5 27
21 39
4 5 26.5
10 21 36.5
0.7 J
1.2 1
„ 2A.M.
29.15
86401. iJ
L
r
45.2
45.2
18 26
32 06
18 34
.32 10
12 18 30
1 32 08
0.6 J
1.24]
45.1
701.35
1.28
86156.02
■(■0.18
86156.20
„ 2 P.M.
29.30
86401. ].|
44.5
701.3
1.36
86156.10
-1-0.07
86156.17
r
43.8
42.5
28 59
19 42
29 03
19 44
3 29 01
9 19 43
0.621
1..361
„ 3 A.M.
30.05
86400. 8<^
f
44.3
44.7
16 48
32 52
16 52
32 55
11 16 50
1 32 53.5
0.68J
1.4 1
43.4
702.7
1.64
86156.52
-0.53
86155.99
P.M.
30.08
86400. 8<^
\
45.1
44.8
29 39
03 37
29 43
03 40
3 29 41
10 03 38.5
\
0.7 J
1.241
44.9
700.75
1.74
86155.96
-HO. 10
86156.06
., 4 A.M.
30.26
86400.8-^
f
46
46
00 32
08 41
00 34
08 44
12 00 33
2 OS 42.5
0.62J
1.37J
45.4
701.45
1.36
86155.84
•1-0.31
86156.15
„ 4 P.M.
30.26
86400.8J
47
44.1
05 16
07 51
05 23
07 53
4 05 19.5
9 07 52
0.67J
1
46.5
699.7
1.62
86155.46
■fO.77
86156.23
„ 5 A.M.
30.44
86400.8]
44.9
701.5
1.5
86155.98
+ 0.10
85156.08
45.7
04 46
04 48
11 04 47
0.64 J
r
45.7
11 11
11 13
2 11 12
1.37|
„ 5 P.M.
30.44
86400.8^
46.2
07 52
07 55
4 07 53.5
0.67*
45.95
700.15
1.62
8G155.62
+ 0.54
86156.16
Means . . .
29.97
•
44.66
86156.15
86156.15
The correction for Buoyancy is +6.25, making S6162.40 Vibrations in vacuo ; p.iid 44.°.e6 of the scale of the registering
Thermometer is equivalent to 44°.3S of Fahrenheit, being the temperature of the Pendulum.
IN THE LENGTH OF THE SECONDS' PENDULUM.
203
1
Table IX. London, 1S24. COINCIDENCES OBSERVED with PENDULUM No. 4 ; the |
Clock (Cumming) making S6401 . 3 Vibrations iu a Mean Solar Day.
DATE.
Baro-
meter.
u
0 0
'3
0
Tempe-
rature.
Time of
Disap-
pear.ince.
Time of
Re-ap.
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion,
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
the Arc.
Vibrations
Id 34 bonrs.
Eedoc-
tion to a
Mean
Tempe-
rature.
Redaced
Vibrations at
47=.61.
1823.
IN.
0
51
M. S.
43 09
M. S.
43 14
H. M. S.
9 43 11.5
s.
1.32
0
s.
s.
+
Mar. 24 A.M.
29.95-^
[
50.6
50.2
43 24
58 24
43 28
58 28
11 43 26
1 58 26
0.66
1.35
50.8
721.45
1.55
86163.35
-H.34
86164.69
„ 24 P.M.
29.96<^
49.8
48.2
58 50
14 46
58 58
14 48
3 58 54
10 14 47
0.66
1.35
50
722.8
1.59
86163.81
■H.OO
86164.84
„ 25 A.M.
30.09<
48.5
48.5
15 33
23 39
15 37
23 43
12 15 35
2 23 41
0.66J
1.36
48.35
724.8
1.59
86164.49
-1-0.30
86164.79
,. 25 P.M.
30.06<
47.4
46.9
21 26
3.? 46
24 32
33 50
4 24 29
9 S3 48
>
0.66
1.32
47.95
724.8
1.60
86164.50
^-0.14
80164.64
„ 26 A.M.
so.ooJ
,
[
47.9
48
34 44
56 14
34 49
56 17
11 34 46.5
1 56 15.5
0.64J
1..32J
47.4
725.85
1.51
86164.75
-0.09
86164.66
„ 26 P.M.
so.ooJ
48.2
46
57 10
35 28
57 13
35 32
3 57 11.5
9 35 30
>
0.64
1.36
48.1
725.6
1.51
86164.66
■fO.20
86164.86
„ 27 P.M.
29.83J
f
47
44
36 40
46 50
36 44
46 53
11 36 42
8 46 51.5
0.66]
1.38]
46.5
727.2
1.60
86165.28
-0.47
86164.81
„ 28 A.M.
29.8sJ
44.5
728.95
1.67
86165.93
-1.31
86164.62
f
45
45
48 18
55 39
48 24
55 43
10 48 21
1 55 41
0.68J,
1 32]
„ 28 P.M.
29.88J
•
44.9
729.05
1.51
86165.81
-1.14
86164.67
1
44.8
57 08
57 15 3 57 11. 5I O.64J
Means . . .
29.96
47.61
86164.73
86164.73
The correction for Buoyancy is +6.2, making 86170.93 Vibrations in vacuo ; and 47°. 61 of the scale of the
registering Thermometer is equivalent to 47°. 24 of Fahrenheit, being the temperature of the Pendulum.
2 D 2
204 EXPERIMENTS FOR DETERMINING THE VARIATION
The next procedure was to raise the temperature of the clock-room by
artificial means, and to keep it steadily at an height which should exceed
80 degrees, the mean heat in the neighbourhood of the equator; for that
purpose a stove was placed in the apartment beneath, and the pipe brought
up through the floor into a part of the room most distant from the pendulum
recess ; the pipe was then bent in a right angle, about a foot and a half
above the floor, and carried across the room into a hole in the chimney-board
made to receive it ; a skreen of gauze was spread horizontafly a few inches
above the pipe, to prevent the immediate ascent of the heated air, and to
diff'use it more extensively in the lower stratum ; the windows and shutters
were closed, excepting when a part of one of the shutters was opened to
admit the light required in the observations ; the temperature of the ad-
joining room was raised by fires to between 70 and 80 degrees, so that
when the door of communication was opened for the purpose of entering
or quitting the clock-room, the temperature of the room might not be dis-
turbed ; the fire was kept up in the stove without intermission, and two
days were suffered to elapse before the observation of coincidences com-
menced, so as to allow the walls, as well as every part of the apparatus, to
become thoroughly warmed. Besides the usual register of the temperature
at the first and eleventh coincidences, three intermediate observations were
made at equal intervals, in order to obtain a more exact mean: by these
precautions, aided by the admirable going of the clock, the partial results
with each pendulum differed only in the hundredths of a vibration per
diem from their respective means ; the details are contained in the
following Tables, X. and XL
IN THE LENGTH OV THE SECONDS PENDULUM.
205
Tahttt V Inivnnivr m24, rOIN''"inp,Nr:P'S OKST'.RVF.n wifli PFNTITIT TTM No R : ihp
Clock CCurnmingJ raakin
g S6399.92 Vibrations in a Mean Solar Day.
DATE.
Baro-
meter.
<. a
Z =
o
o
Terape-
rature.
Time of
Disap-
pearance.
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
lioti.
Mean
Tempe-
rature.
Mean
Interval.
Correc-
tion for
the Arc.
Vibrations
in 24 liours.
Rcclnc-
tion to a
mean
Terape-
riture.
Reduced
Vibrations at
84^.56.
1824.
IN.
1
81
84.2
M. S.
7 26
M. S.
7 30
II. U. S.
1 7 28
1 34
0
1.21
o
S.
+
April 11 r.M.
29.37-
11
1
84.9
85
81.7
81.7
83.9
57 40
23 52
57 48
23 56
2 01
2 28
2 57 44
3 23 54
3 51
0.73.
1.2
84.55
661.6
1.55
86140.27
86140.27
,, U P.M.
29.37.
11
1
82.6
84.9
83.9
86.7
85.2
14 12
42 05
14 21
42 07
4 18
4 45
5 11 18
8 42 06
9 09
0.7
1.24
84
662.4
1.45
86140.51
-0.23
86140.28
„ 12 A.M.
29.42.
11
1
85.6
81.5
86.2
86.4
85.2
32 06
39 56
32 12
40 00
9 SB
10 03
10 32 09
11 39 58
12 07
0.73
1.271
85.64
660.3
1.55
86139.77
+ 0.45
86140.22
,, 12 Noon.
29.46-
11
1
81.6
83.2
82.4
82.8
82.6
30 11
38 26
SO 15
.38 29
12 31
1 02
1 30 13
2 38 27.5
3 06
0 74,
1.32
81.36
061.5
1.62
86 HO.. 34
-0.08
86140.26
,. 12 P.M.
29.48-
11
1
82.6
81.4
82.5
85.3
87.2
28 58
44 12
29 03
44 17
3 33
4 01
4 29 00.5
7 44 14.6
8 12
0.77.
1.2
82.4
663.3
1.75
86141.15
-0.91
86140.24
„ 13 A.M.
29.74-
11
87.2
85.6
86.8
34 10
34 16
8 40
9 07
9 34 13
0.7
> 86.42
659.85
1.45
86139.49
+0.78
86140.27
Means. . . .
29.47 = 29.38 at 53°
84.56
86140.26
86140.26
The correction for Buoyancy is +a.fi."), making 86145.91 Vibrations in vacuo ; and S4°.5C of the scale of
the registering Thermometer is equivalent to 83°.49 of Fahrenheit, being the temperature of the Penduluir.
206
EXPERIMENTS FOR DETERMINING THE VARIATION
Table XI. London, 1824. COINCIDENCES OBSERVED with PENDULUM No. 4; the
Clock (Cumwing) making S6399.9 Vibrations in a Mean Solar Day.
DATE.
Baro-
meter.
Tempe-
ratnre.
Time of
Disap-
pearance
Time of
Re-ap-
pearance.
True Time of
Coincidence.
Arc of
Vibra-
tion.
Mean
Tempe-
rature.
Mean
Interval.
Correc.
tion of
the Arc.
Vibrations
in 24 faonrs.
Rednc-
tiuu to a
mean
Tempe-
rature.
Reduced
Vibrations at
340.69.
Apr. 14 A.M.
„ 1 \ Noon
14 P.M.
„ 15 A.M.
., 15 P.M.
„ 16 A.M.
29.90<!
29.90<
29.90<^
29.80<!
29.80<^
29 . 30
16 P.M.
Means .
29.30.!
11
84
81.2
84
81.4
86
86
86.2
86
8T.5
89.5
82.4
82.1
85.7
91
90.8
82.2
81.6
81.25
83.8
83.6
83.2
83
83.3
84.5
84.5
82.2
84
83.4
82.5
83.2
84
86
84.8
87
86.3
M. S.
53 51
48 24
2 12
56 14
48 31
42 38
52 09
46 58
8 58
3 32
9 35
4 15
35 49
M. S.
S3 56
M, S.
53 53.5
48 33
2 16
56 22
48 36
42 46
52 13
47 06
9 04
3 42
9 40
4 28
35 56
SO 08
30 22
9 21 0
9 50 0
10 19 0
10 48 28.5
11 2 14
11 30 0
11 58 0
12 27 0
12 56 18
2 48 33.5
S 16 0
3 44 0
4 13 0
4 42 42
8 52 11
9 20 0
9 59 0
10 28 0
10 47 02
2 9 01
2 37 0
3 05 0
3 34 0
4 3 37
9 9 37.5
9 38 0
10 06 0
10 35 0
11 4 21.5
1 35 52.5
2 03 0
2 32 0
3 01 0
3 30 15
1.2
0.7
1.231
0.73 J
1.27
0.74
1.26
0.74
1.291
0.74j
1.34
0.78
1.221
0.74
84.52
687.5
87.04
684.4
86.4
684.85
82.49
689.1
83.7
687.6
83.06
688.4
85.62
686.25
■t-
1.45
1.55
1.63
1.61
1.68
1.76
1.51
86150.01
-0.07
86148.95
■1-0.99
86149.18
■f-0.72
86150.79
-0.92
86150.26
-0.42
86150.66
-0.68
86149.94
86149.94
86149.90
86149.87
86149.84
86149.98
86149.59
-fO.39
86149.98
29.70 =29.61 at 53°.
84.69
86149.92
86149.92
The correction for Buoyancy is +5.7, making 86155.62 Vibrations in vacuo; and 84°.69 of the scale of the
registering Thermometer is equivalent to S3°.62 of Fahrenheit, being the temperature of the Pendulum.
IN THE LENGTH OF THE SECONDS' PENDULUM. 207
The results then of the experiments to ascertain the effect of diflferences
of temperature on the vibrations of the pendulums, are as follows :
(86162.40 Vibrations at 4t.3S f86IT0.93 Vibrations at 47.24
Pendulum 3 \ Pendulum 4^
/86145.91 . . . 83.49 (86155.62 . . . 83.62
Differences. 16.49 . . 33.11 Differences. 15.32 . . 36.38
Hence it appears, that by the experiments with No. 3, a degree of Fah-
renheit is equivalent to 0.4216 parts of a vibration in twenty-four hours,
and by those with No. 4, to 0.4208 parts; the mean, or 0.4212, correspond-
ing to an expansion of the plate-brass of which the pendulums were com-
posed, of 0.021125 parts of an inch per foot in 180 degrees, may be taken
as the final deduction; the separate results are, of pendulum 3, 0.021117,
and of pendulum 4, 0.021133.
As the figure in the fourth place of decimals in the number 0.4212
amounts only to one hundredth of a vibration per diem in 50 degrees of
temperature, its consideration may safely be dropped, and 0.421 taken as
the equivalent to a degree of Fahrenheit, in the reduction of the experi-
ments to a general mean temperature.
The following notice was received by me from Mr. Browne, relative to
the rate of the clock used in obtaining the expansion of the pendulums:
" The rates from the 24th of March to the 16th of April were deduced
immediately from the observations taken with the transit instrument applied
to Gumming, as from the admirable going of this clock it was not thought
necessary to use the medium of any other: it cannot but be remarked,
however, that the difference in these rates in so short an interval is greater
than might have been expected from the general character of the clock:
the circumstance of its having been removed and put up in its new place
only on the 23d may account for the small change of rate between the 24th
of March and the 5th of April ; but the change which is observable from
the 10th to the 16th, v/hen the heated pipe was introduced, is greater than
208 EXPERIMENTS FOR DETERMINING THE VARIATION
can be properly due to any defect of compensation, and appears to be an
effect of the artificial heat, totally distinct from temperature, and arising
from the excessive dryness caused by it in the surrounding atmosphere :
how the dryness acted upon the clock, I must confess myself at a loss
to explain, but I believe myself perfectly correct in ascribing it to that
cause, as the new clock made for me by Molyneux upon the same prin-
ciple, with which Cumming's was regularly compared, was affected in
pecisely the same manner." H. B.
Before the rates of the pendulums which had been thus obtained could
be compared with those of the preceding year, it was necessary to in-
quire into the cause and amount of the difference which had been noticed
in the scale of the arcs belonging to Captain Kater and to the Board of
Longitude ; for that purpose both the arcs were referred for re-examina-
tion to Mr. Jones, by whom they had been made, when it appeared that
the length of the degrees in Captain Kater's arc was correct, each degree
measuring one inch and five hundredths, corresponding to a radius of five
feet and about half an inch ; but that the arc belonging to the Board of
Longitude had either been inadvertently graduated for a different radius,
or on a wrong calculation, if made designedly for the pendulum which it
accompanied, as the length of a degree was not more than 0.975 parts of
an inch*.
The following Table exhibits the reduction of the arcs registered in
Tables VIIL, IX., X., and XL by the erroneous scale, into the true
arcs in which the pendulums vibrated; the latter being in the inverse
proportion to the former of 42 to 39 : it contains also the corrections to
be applied to the number of vibrations per diem, calculated both for the
registered and for the true arcs.
* The division extended for two degrees on eacii side of the vertical ; the four degrees
occupied four inches two tenths on Captain Kater's, and three inches nine tenths on the one
belonging to the Board of Longitude.
IN THE LENGTH OF THE SECONDS* PENDULUM.
209
PENDULUM No. 3.
PENDULUM No. 4.
TABLE VIII.
TABLE IX.
TABLE X.
TABLE XI.
Arcs Registered. True Arcs,
1.31
0.6.5
I.S8
0.7
1.2
0.6
1.24
0.62
1.S6
0.68
1.4
0.7
1.24
0.62
1..S7
0.67
1.3
0.64
1.37
0.67
Arcs Registered.
Meant.
Differ-
ence .
■l.Sl
1.71-
1.28
1.36<
H
1.74
1.36<
1.62
l.SO
1.62'
1.22
0.6
r 1.28
0.65
1.12
0.56
1.15
0.58
1.26
0.63
1.30
0.65
1.15
0.58
1.27
0.62
1.21
0.60
1.27
0.62
1.53
K
30
1.46
1.11
1.18
1.41
.1.51
1.18
1.40
1.28
1.40
1.32
0.21
1.24
0.73
1.2
0.7
1.24
0.73
1.27
0.74
1.32
0.77
1.2
0.7
I.. 55
1.45
1.55
h'i
U.75.
1.45-
Troe Arcs.
Arcs Registered.
1.56
1.15
0.68
1.12
0.65
1.15
0.68
1.18
0.69
1.23
0.71
1.12
0.65
1.34
1.25
1.34
1.40
1.51
1.25
1.35
0.21
1.32
0.66
1.35
0.66
1.35
0.66
1.36
0.66
1.32
0.64
1.36
0.66
1.38
0.68
1..32
0.64
1.54
1.59-
1.59
>1.60
1.51
]'■"{
1.67
Troe Arcs.
Arcs Registered.
},.{
1.58
1.23
0.61
1.25
0.61
1.25
0.61
1.26
0.61
1.23
0.60
1.26
0.61
1.28
0.63
1.23
0.60
I,:
33
1..38
1.38
1.39
1.31
1.39
1.44
1.31
1.37
0.81
1.2
0.7
1.23
0.73
1.27
0.74
1.26
0.74
1.29
0.74
1.34
0.78
1.22
0.74
1.45'
1.55
1.62
1.61
1.68-
True Arcs.
I
76.
1.51
1.59
1.12
0.65
1.14
0.68
1.18
0.69
1.17
0.69
1.20
0.69
1.24
0.72
1.13
0.69
1.25
1.33
1.40
1.39
1.45
1.53
1.33
1.38
0.21
2 E
210 EXPERIMENTS FOR DETERMINING THE VARIATION
It is shown by this table, that in consequence of the arcs of vibration
having been registered by an erroneous scale, the corrections applied in
Tables VIII., IX., X., and XL, to reduce the number of vibrations per
diem performed in circular arcs into the equivalent number in arcs indefi-
nitely small, exceeds the corrections which were actually due by the same
amount in each instance, vis. by 0.21 parts of a vibration ; and that the
rate of the pendulum in each of those Tables, which is given as the mean
result of the experiments contained in them, ought, in strictness, to be
diminished by 0.21 parts of a vibration per diem.
As, however, the deductions which ought thus to be made, would be to
the same amoimt in each of the four instances, the differences in the rates
of the pendulums in high and low temperatures, obtained by the compa-
rison of the results with each other, remain the same, whether the deduc-
tions be made, or whether they be omitted.
The same remark extends to every purpose for which the comparative
rate only, and not the absolute rate, of the pendulums is required; that is
to say, to every purpose contemplated in these experiments.
By pursuing a similar investigation to the one contained in the pre-
ceding table, in every series in which the erroneous scale was used,
(which comprehends the whole of the experiments at every station, ex-
cepting those at London in 1821 and 1823,) it is found, that 0.21 is a
constant expression of the value of the difference between the corrections
due to the registered and to the actual arcs.
Omitting therefore, for the moment, the consideration of the experiments
in London in 1821 and 1823, no inconvenience whatsoever is occasioned
by an adherence to the original register, and to the rates of the pendulums
as they now appear in the several Tables : it being always remembered
that, if the absolute rate of either of the pendulums should be required at
any of the stations at which they were employed, 0.21 parts of a vibration
per diem should be deducted from the tabular rate.
IN THE LENGTH OP THE SECONDS* PENDULUM.
211
With respect to the experiments of 1821 and 1823, it is obvious that their
results may equally be brought into just comparison with those on all other
occasions, (and consequently w^ith the results in London in 1824,) whether
the number 0.21 be added to the former, or deducted from the latter.
In the following comparative view of the rates of the pendulums in
London, as obtained in 1821, 1823, and 1824, the difference of the scale
on which the respective arcs of vibration were measured, is compensated
by the addition of 0.21 to the results in 1821 and 1823.
Date.
Vibrations
per Diem.
Tempe-
rature.
Compen-
sation for
dift'erence
of Arc.
Reduction
to a Mean
Tempe-
rature.
Reduced
Vibrations
at 62".
Dilfereuce
of the par-
tial Results
from the
Mean.
Pendulum 3 . .
1821
1823
1823
1824
1824
[ With Ca
86158.47
86162.40
86145.91
ptain K
52.97
44.38
83.49
ater's Pla
+ 0.21
nes of Sus
-3.79
— 7.42
+ 9.05
pension *.
86154.89
86154.98
86154.96
— 0.05
+ 0.04
+ 0.02
Me
AN
86154.94
Pendulum 4 . .
1821
1823
1823
1824
1824
86161.78
86168.71
86167.57
86170.93
86155.62
68.13
51.88
54.4
47.24
83.62
+ 0.21
+ 0.21
+ 0.21
+ 2.5S
—4.26
— 3.2
-6.22
+ 9.10
86164.57
86164.66
86164.58
86164.71
86164.72
-O.OS
+ 0.01
-0.07
+ 0.06
+ 0.07
Me
AN
86164.65
• The experiments with Pendulom 3, in 1821, and iD the first series in 1823, which were made with Captain Eater's planes
of snspension, are not introduced into the table, on accoQnt of the effect which the employment of different planes was found
to produce on the rate of that pendolum, and which interfered to prevent the comparison of the results obtained on those
occasions, with those of the subsequent experiments on the planes belonging to the pendulum itself; they were, however,
strictly comparative with regard to each other, and their accordance has been already adduced in page 192, to show that no
change whatsoever had taken place in the pendalum between the first esperiments in 1821, and those of 1823.
2 E 2
212 EXPERIMENTS FOR DETERMINING THE VARIATION
The correspondence of the results in the preceding Table is much too
remarkable to be passed unnoticed, and the occasions are far too numerous
to admit of their accordance being attributed to accident, or viewed other-
wise than as a consequence of the method of experiment, and as an
evidence of the refinement of which it is capable: in fact, under circum-
stances which leave no uncertainty as to the temperature of a detached
pendulum, its rate may be determined to the utmost extent of the precision
to which the rate of the clock is known, with which the pendulum is com-
pared. It will be remembered, that the rate of the pendulum in twenty -four
hours is obtained from its comparison with the clock during an interval
which does not exceed in duration one twelfth part of the period for which
the rate of the pendulum is inferred; and as it is not possible to determine
the definite rate of a clock for so short an interval as that of two hours,
either by astronomical observation or by its comparison with other clocks,
it becomes necessary to rely on an uniform performance in an interval of
sufficient length to enable the mean gain or loss to be ascertained. The
degree of uniformity which is required in the clock's performance may be
appreciated by the consideration, that a departure from the mean rate,
amounting to the one hundred and twentieth part of a second in the two
hours in which the coincidences are continued, will make a difference of
one tenth of a vibration in the deduction of the rate of the detached pen-
dulum, which has been shown to be a very important quantity in these
experiments. The limit which the absence of a maintaining power
occasions in the period for which the oscillations of the pendulum of
experiment wUl continue, and in which consequently its rate must be
determined, throws the principal responsibility towards precise deduction
on the performance of the clock ; and in proportion as its regularity is
maintained in shorter intervals than are usually the objects of attention,
may the results of the coincidences in successive distinct experiments be
expected to be consistent. It is in this respect that the experiments in
IN THE LENGTH OF THE SECONDS' PENDULUM. 213
London, the account of which has occupied the preceding pages, have had
a peculiar advantage, in the employment and comparison w^ith Mr.
Browne's clocks, of which those in particular by Gumming and Molyneux
are probably unequalled in the preservation of a constant and uniform rate ;
it is to their excellence in this qualification, that the very remarkable agree-
ment in the results which is under notice may essentially be attributed.
The accordance of the results in the different years affords the best
practical proof that can be given that the pendulums had not sustained
injury from use or accident, from the commencement to the close of the
operations in which they have been employed. After the last experi-
ments, however, had been concluded, and before I had had leisure to
compare the several results, I requested Mr. Browne and Dr. WoUaston
to do me the favour of examining the knife edges of the pendulums ; when
neither by the eye, nor by a microscope, could the slightest effect of wear,
or injury of any sort, be perceived on the parts of the knife edges which
rest upon the planes.
I have deferred a statement of the reasons which induced me to prefer
the method of observing coincidences which I have adopted, viz., by taking
a mean of the times of disappearance and of the reappearance of the disk,
to that of observing the disappearances only and considering them as
times of coincidence, until the detail of the observations with the detached
pendulums had been gone through; because the difference of the methods,
and their respective influence on the strict relation of the several results to
each other, will perhaps be better understood by illustration than by
description; and it is important that the subject should be understood,
because it concerns the experiments of others, as well as those of mine.
If the oscillation of a detached pendulum could be really performed
in a vacuum, and if the motion at the point of suspension were perfectly
free, the vibration would continue indefinitely in an arc, of which the
214 EXPERIMENTS FOR DETERMINING THE VARIATION
magnitude would be determined by the impulse which first gave motion
to the pendulum, and would be thenceforward permanent.
In such case, the intervals comprised between successive disappear-
ances of the disk would be all of equal duration, whilst the rates of the
clock and pendulum remained the same ; and each would bear the strict
proportion of an interval between coincidences, to the difference between
the rates of the clock and pendulum.
If an alteration be supposed to take place in the arc of the clock during
the vibration of the detached pendulum in a vacuum, the effect on the in-
tervals between successive disappearances (independently of the influence
which the alteration might have on the rate of the clock) would be, to
render the one interval, during which the alteration took place, erroneous ;
but the original duration would be restored in subsequent intervals.
If the rate either of the clock or pendulum were to undergo a change,
the interval between coincidences would change correspondingly to the
difference of the rates. In this case, also, the interval between successive
disappearance, in which the change took place, would be rendered erro-
neous by reason of the alteration in the relative velocities of the pen-
dulums in their respective arcs, the effect of which would be equivalent to
an alteration in the magnitude of the arc of the pendulum that underwent
the change of rate ; but the succeeding interval would be of the correct
duration, and it would be successively maintained, whilst the relative
rates of the clock and pendulum were constant; and would shew the
exact period of time in which the pendulum of the clock gained two com-
plete vibrations on the detached pendulum, oscillating in a circular arc of
certain dimension; or in which the latter gained two complete vibrations
on the former, according as the detached pendulum might have been
constructed to vibrate more or less frequently than that of the clock.
If the case which has been thus supposed, of the vibration taking place
in a vacuum, could occur in practice, the times of successive disappearance
IN THE LENGTH OF THE SECONDS' PENDULUM. 215
might be considered as those of coincidence, and the rate of the pendukim
be deduced from the intervals between them, without producing more
than occasional irregularity ; because the intervals would be of the same
duration as those obtained by a more strict method of determining the
times of coincidence, excepting when changes occurred in the rate either
of the clock or of the pendulum, or in the arc of the clock, in which in-
stances a single interval only would be vitiated.
The pendulum, however, does not oscillate in a vacuum, but in a
resisting medium, which causes the arc, originally communicated, gra-
dually to diminish until the pendulum arrives at rest: the consequences
of the progressive diminution of the arc of the pendulum are, first, as
affects the actual rate of the pendulum itself, which continually accelerates
as the retardation lessens due to the vibration in circular arcs and in
proportion to their magnitude; and second, as the intervals between
successive disappearances are affected, independently of the rate of the
pendulum which they are designed to measure; for as the arcs diminish,
the pendulum moves with diminished velocity, occasioning the number of
seconds in which the disk passes the field of the telescope in entire ob-
scuration, to augment in successive coincidences ; and as the true time of
coincidence, i. e., when both pendulums are simultaneously at the lowest
point of their respective arcs, is the middle time between the disappearance
of the disk and its re-appearance, the successive intervals deduced from
the observation of the times of disappearance only will differ from those
deduced from actual coincidences, by half the amount which the time of
entire obscuration augments from one coincidence to the next.
The progressive increase in the rate of the pendulum occasions the
interval between successive coincidences to augment as the arcs diminish.
The increase in the time of obscuration occasions the interval between
successive disappearances, on the other hand, to diminish ; and according
to the amount of this diminution (which is proportioned to half the increase
216 EXPERIMENTS FOR DETERMINING THE VARIATION
in the period of obscuration in successive coincidences) does the rate
of the pendulum, deduced from the intervals between times of disap-
pearance, differ from the true rate of the pendulum*.
The object which is sought in these experiments is not necessarily the
absolute length of the pendulum at different stations, but its acceleration ;
and the acceleration may be obtained with equal correctness from nominal
rates, in which a constant diflference from the actual rates is maintained,
as from the actual rates themselves ; if, therefore, the increase in the
period of obscuration depended solely on the ratio of diminution in the
arc of the pendulum, and was therefore on all occasions the same, the
method of deduction from the times of disappearance might be substi-
tuted for those of more strictly assured coincidences, without occasioning
error : but the period in which the disk passes the field of the telescope
without being visible, is governed by a variety of considerations, amongst
the least influential of which, are those that depend on the relation which
the rates of the clock and pendulum bear to each other, or on that of
the respective velocities of the pendulums.
* In the usual practice of observing eleven coincidences in succession, in which the vibra-
tion is commenced in an arc whose dimension is between a degree and a degree and a half,
and terminates in one of six or seventh-tenths of a degree, the rate of the pendulum accelerates
by reason of the diminution of the arc, and is about one vibration and three-tenths per diem
faster at the close than at the commencement ; whence the interval between the 10th and 1 1th
coincidences should be longer than that between the 1st and 2d by nearly four seconds.
In the detached pendulum which I have employed, the period of obscuration of the disk
has varied on different occasions in the 1st coincidences from one to eight seconds, and in
the II th from eight to thirty seconds: as these numbers are adduced at present solely for
the sake of illustration, they may be supposed to average respectively four seconds and twenty
seconds. In substituting, therefore, the times of disappearance for those of true coincidence,
the first disappearance would take place two seconds, and the last ten seconds, before the
times when the two pendulums were in both cases strictly coincident ; making a dilTerence,
occasioned by the substitution, of eight seconds in the period due to the ten intervals ; whence
the rate of the pendulum obtained from the disappearances only, would be about three-tenths
of a vibration per diem less than the actual rate. With pendulums of which the difference
in rate on that of the clock with which they are compared is not so great as in mine, the
difference between the actual rates and those so deduced would be much more considerable.
IN THE LENGTH OP THE SECONDS* PENDULUM. 217
In the case of a pendulum oscillating in a resisting medium, and there-
fore in a progressively diminishing arc, the effect of an alteration in the
relative velocities of the pendulums in their respective arcs, on the intervals
between successive disappearances, differs from that which would take
place if the pendulum oscillated in a vacuum and in a constant arc, in
this respect, that it is not merely the single interval in which the alteration
occurs which is affected, but that every succeeding interval is influenced
as well as the first; and that the period of obscuration augments as the arc
of the pendulum diminishes, with greater or less rapidity, according to
the relation which the velocities bear to each other.
In order, therefore, that a constant difference might obtain between
the actual and the deduced rates of the pendulum on aU occasions, it
would be necessary that the relative velocities should be strictly main-
tained at the different stations ; which would require that both the
detached pendulum, and that of the clock, should vibrate every where
in the same respective arcs, and that the difference in the rates of the
two pendulums should be every where the same ; towards which, if
the inevitable imperfection of instruments could be entirely removed, a
stiU more serious embarrassment would present itself, in the necessity of
preserving an uniform temperature at every station, and on every occasion.
The only case, therefore, in which the method of obtaining the intervals
by observing the disappearance only could be rigorously correct in prin-
ciple, even as far as merely theoretical considerations are involved, is
one with conditions, which, it is probable, will prevent its ever being
of practical occurrence.
Tlie causes by which the period of obscuration is found in experience
to be principally affected, independent of, and unconnected with the
rates or velocities of the pendulums, are such as can scarcely fail to
introduce irregularity and error in every case in which the intervals of
disappearance only are employed.
2 F
218 EXPERIMENTS FOR DETERMINING THE VARIATION
It may readily be conceived, that if disks should be employed, of
which the diameters should not be precisely of the same magnitude,
whilst all other circumstances should remain the same, whatever vari-
ation might take place in the time of obscuration of the disks of dif-
ferent dimension in the first coincidences, would be greatly augmented
in the eleventh coincidences, because the value which a certain definite
space of the clock's arc bears to the whole arc of the pendulum, increases
as the latter becomes smaller ; thus, the rate of the pendulum deduced from
intervals of disappearance only, would be made to vary, according as disks
of different magnitudes were employed, whereas by the supposition the
rate is constant, and should appear so, by a perfect method of observation.
It may as readily be cuiiceived that the effect would be the same, whe-
ther the alteration in the magnitude of the disk were real, or apparent.
The apparent magnitude of the disk (as judged by the effect) is in-
fluenced by three considerations ; of which two interfere with the compa-
rison of observations made by different individuals, and the third with the
comparison of observations made at different times by the same individual.
First. — The length of the period of obscuration is different, cdtris
paribus, with different eyes; those persons who are what is usually
termed short-sighted, retain the view of the disk longer, and perceive
its re-appearance earlier than others.
Second. — The same remark applies, but in a much greater degree, to
eyes which have more or less practice in observation.
Third. — The duration of the period will vary to the same eye, accord-
ing to the quantity of light admitted into the room. In the experiments
recorded in this volume, a difference of fifteen seconds has been frequently
experienced in the time during which the disk was invisible when passing
the telescope, on occasions when the sole cause of the difference was
the greater or less portion of light by which it was rendered visible.
I proceed to exemplify, by instances drawn from the observations in the
preceding pages, some of the points which I have endeavoured to explain.
IN THE LENGTH OF THE SECONDS PENDULUM.
219
The diflference which takes place in the period for which the disk is
obscured, in the observations of persons equally practised, and where all
circumstances are correspondent, excepting the greater or less portion of
light by which the disk is rendered visible, may bewell illustrated by
the two earliest observations of coincidences recorded in this volume:
those of the afternoon of the 6th of July, 1821, observed by Mr. Browne,
and those of the following morning, observed by myself. To prevent
the inconvenience of a reference, the particulars are repeated, and results
are deduced from them by both the methods which are in question ; by
which the influence of the method of observation on the comparability of
results may be further judged :
London,
1821.-
COINCIDENCES OBSERVED with PENDULUM No. 3.
DATE.
Observer.
Tempe-
rature.
Time of
Disap-
pearance.
Time of
Reap.
pearance.
True Time of
Coiocideoce.
Arc of
Vibra-
tion.
Mean
Tempe.
rature.
Mean
Interval.
Correc-
tion for
the Arc.
Vibrations
in 24 hoQrt.
Redac-
tion to a
mean
Tempe-
rature.
Reduced
Vibrations at
65».66.
0
M. S.
M. 3.
H. M. s
o
0
S.
S.
July
1
C6.2
27 52
27 59
2 27 55.5
1.22]
-1-
6 P.M.
Mr. Browne.^
I
(
11
1
66.5
65
20 25
25 38
20 50
25 43
4 20 37.5
11 25 40.5
0.64 J
1.26'
66.35
676.2
1.3S
86145.23
■f 0.29
86145.52
7 A.M.
Capt. Sabine.
11
66.3
18 22
18 32
1 18 27
0.66J
65.65
676.65
1.46
86145.52
86145.52
8 P.M.
Mr. Browne.
I
66.2
27 52
1.22]
>
0.64J
1.26
66.35
675.3
1.35
86144.91
•fO.29
86145.20
11
1
66.5
65
20 25
25 38
7 A.M.
Capt. Sabine.
11
66.3
18 22
. . . .
>
0.66
65.6;
676.4
1.46
86145.44
86145.44
2 F 3
220 EXPERIMENTS FOR DETERMINING THE VARIATION
It is here seen that the time of obscuration in the first coincidence in
the afternoon series, exceeded by two seconds the corresponding time in
the noon series ; but that in the eleventh coincidences the excess had
augmented to no less than fifteen seconds. It happened that each obser-
vation was the first complete series of eleven coincidences which either
Mr. Browne or I had ever observed, and therefore in respect of practice
we were equal ; no part of the effect can be attributed to a difference of
eyes, since it was found on the contrary that in alternately observing
successive coincidences, when the circumstances, including those of light,
were similar, Mr. Browne invariably made the time of obscuration shorter
than I did ; yet so, that the intervals deduced from a mean of the times
of disappearance and re-appearance corresponded, notwithstanding the
change of the observer, whilst those resulting from the disappearances
only did not correspond ; that, in fact, Mr. Browne saw a minuter portion
of the disk, when following the pendulum previously to obscuration, and
again when preceding it in re-appearance, than was perceptible by me,
in consequence of a natural difference in our power of vision. The effect,
however, at present under consideration is of an opposite character, as
the periods of obscuration were longer in Mr. Browne's coincidences
than in mine, and as-it may be presumed, would have been still longer^
had our eyes been aUke in conformation ; the effect was caused by a
difference in the strength of the light, at the respective times of observa-
tion, in the room in which the experiments were made.
On a further examination of the table, it will be seen that when in
these observations a mean is taken between the times of disappearance
and re-appearance for the times of coincidence, the results deduced from
the intervals are identical notwithstanding the difference in the periods
of obscuration : secondly, that when the times of disappearance are con-
sidered as those of coincidence, the results which by the previous method
were shewn to be identical, would appear to differ 0.24- parts of a vibration
IN THE LENGTH OF THE SECONDS* PENDULUM. 221
per diem ; and consequently, that results, obtained by the method of dis-
appearances only are not strictly comparative unless the equality of light
can be assured : thirdly, that if different methods of observation be used
on different occasions, the employment of the results as comparative
may involve errors of still greater amount; if, for instance, the first
result be deduced by the method of disappearances, and the second by
that of the mean, they will appear to differ 0.32 parts of a vibration
per diem : and fourthly, that in experiments to obtain, not the relative,
but the absolute length of a pendulum, it is not indifferent which method
be employed, for if the one be correct, the other must be incorrect, since
the rates deduced from the mean of the two observations are shewn to
differ 0.2 parts of a vibration per diem, according to the method by which
they are derived.
Being desirous of obtaining a still more marked example of the in-
fluence of light on the period of obscuration, and on the respective inter-
vals deduced by the two methods, I took occasion, at Spitzbergen, to
submit the light, by which successive coincidences were observed, to con-
siderable changes, which I was enabled to accomplish by the division of
the roof of the pendulum-house into compartments, each of which was
removable at pleasure, so as to augment or diminish the aperture, by
which the light, passing through the canvass of the tent, was admitted
into the room : the compartments were opened about two minutes pre-
ceding a coincidence, and closed immediately after it ; and a day was
selected for the experiment, in which the temperature of the interiors of
the house and tent was nearly the same, and differed but little from that
of the external atmosphere, so as to be likely to remain steady.
222
EXPERIMENTS FOR DETERMINING THE VARIATION
Spitzbergen. 1823, July ISth, P.M. COINCIDENCES with PENDULUM 4.
This table appears to require no other explanation, than that the door
of the porch being open, in which the telescope for the observation of
coincidences was placed, and the consequent admission of light into the
porch, produced the same effect as a decrease of light in the room ; and
that a circumstance of practical occurrence which it illustrates, is the in-
fluence of the direction, as it regards the telescope, in which light enters
the room at difierent stations ; whether behind the observer when seated
for observation, or through a side window from whence it may have
direct access to the object-glass of the telescope.
IN THE LENGTH OF THE SECOND'S PENDULUM.
223
The influence which a greater or less degree of practice in different
observers will have on the period for which the disk is obscured,
may be exemplified by its amount in the coincidences observed by
Mr. Renwick and myself at New York ; in which it may be remarked
that the period in the eleventh coincidences was invariably longer with
pendulum 3, and in every instance except one with pendulum 4, in
Mr. Renwick's observations than in mine ; whilst in the first coincidences
the period differed much less, and was occasionally longer in mine than
in Mr. Renwick's.
NUMBER of SECONDS during which the DISK was OBSCURED in the
COINCIDENCES at NEW- YORK.
PENDULUM 3.
PENDULUM 4.
Mr. Renwicx.
Capt.vin Sabine.
Mk. Renwick.
CAPTAI^
Sabine.
1" Coin.
ilU'Coin.
I'« Coin.
11"" Coin.
1" Coin.
1 1"- Coin.
l^Coin.
11"" Coin.
S.
s.
S.
S.
s.
s.
s.
S.
0
19
4
13
7
31
4
20
3
15
2
27
6
17
7
21
4
11
5
24
8
14
4
21
4
15
7
IS
3
18
••
5
12
5
6
7
1
26
20
22
21
8
16
Means . .
5.2
20.5
4
13.2
5
24
7.2
10. 2
224
EXPERIMENTS FOR DETERMINING THE VARIATION
The error, which may arise in comparing the results of the obser-
vations of differently-practised individuals deduced from the times
of disappearance only, may be usefully illustrated by means of the first
five results obtained with pendulum 4 at New York, in page 130, wherein
the circumstances were as nearly similar, as can well be conceived ; and
as this series was the second in which Mr. Renwick had been engaged,
he could not be considered as entirely an unpractised observer: three of
these results, being the second, third, and fourth in the page, were from
the observations of Mr. Renwick ; the first and fifth were from mine.
Results Deduced.
From Mr. Renwick's
Observations
From Capt. Sabine's f
Observations . . [
From the Disappearances.
86187.64
86 127. 70 >86 127. 70
86127.76
86127.811
Ue
86128.19
128.00
From true Coincidences.
86128.061
8612S.14>S6128.11
861S8.12
86127.971
86128.23
j.86128.10
J
From the Re-appearances.
S6128.4S
86128.58
86128. 4S
86128.131
86128. 27J
86128.52
^86128.20
Difference between!
the Observers . . J
0.30
0.01
0.32
It is here seen, that the results obtained by Mr. Renwick and myself,
which agreed within one-hundredth of a vibration per diem when correct
intervals of coincidence were employed in the deduction, would have
appeared to differ no less than three-tenths of a vibration, if the times
of disappearance only had been observed, and regarded as those of
true coincidence.
If therefore the observations had been made by Mr. Renwick and
myself, seperately, and at different stations, a comparison of the results,
deduced from the disappearances only, would have involved an error
of three-tenths of a vibration; whilst the results obtained from the more
THE LENGTH OF THE SECONDS' PENDULUM. 225
correct intervals would have been strictly comparable, notwithstanding
the inequality of experience in the observers.
Further, if the observations of Mr. Renwick at New York had been
the commencement of a series of comparative experiments at different
stations, to be carried into execution throughout by himself, it is reason-
able to infer that as his practice would have increased, the periods of
obscuration would have become less, in so far as they are dependant on
a more or less experienced eye ; thus, by employing the disappearances
only, the error of three-tenths of a vibration might be equally involved in
the comparison of the earlier and later stations of the same individual, as
it has been shewn to be in the comparison of results obtained at the same
stations by observers with different degrees of practice : whereas, by
adopting the more correct method of a mean between the disappearances
and re-appearances, the earlier and later results of the same observer are
rendered as strictly comparable, as are the results of different observers
at the same station who may be unequally experienced.
This example affords also a still stronger illustration, than the former
one drawn from the observations of Mr. Browne and myself, of the pre-
ference which should be given to the latter method, in ascertaining the
rate of a pendulum of measured length, for purposes wherein it is essen-
tial that the rate ascertained should be due precisely to the length ; as in
the case of an experimental pendulum employed in the establishment of
a national standard. In this determination, it is the first importance that
the method of proceeding should ensure, as far as may be possible, the
attainment of identical results when conducted by different experimenters ;
and for that purpose that it should be as independent as it can be ren-
dered of individual skill and accidental circumstance. In the two in-
stances which have been adduced, wherein the same pendulum was used
in alternate observations by different persons, the one method is shewn
to have fulfilled the condition of agreement, the results being strictly
2 a
226 EXPERIMENTS FOR DETERMINING THE VARIATION
identical in the one case, and differing only the 100th of a vibration in the
other ; whilst by the other method, the disagreement, occasioned entirely
by the method of observation, amounted in the one case to two tenths, and
in the other to three-tenths of a vibration in the rate, equivalent to between
2 and 3,000ths of an inch in the length of the seconds' pendulum.
As an exemplification of the inaccuracy of the previously-received
method of observing coincidences is important towards the establishment
of the practice of a more correct method hereafter, as well as to an esti-
mation of the probable error which may have obtained in former experi-
ments, it may be useful to collect in one view the duration of the periods
of obscuration in the first and eleventh coincidences, in the several obser-
vations in this volume. It is probable that the variation in the length of
the periods thus exhibited may be much within its extent in general
occurrence ; since as the same clock was used at all the stations, the arc
was of the same dimension throughout : and as no alteration was made
in the length of the pendulum of the clock at different stations, its rate
underwent the same changes from the variations of gravity, as those of
the detached pendulums: and, lastly, as the light was endeavoured to be
equalized at the several stations, by regulating the space of its admission,
although, by the method of observation which was practised, its disturbing
influence was counteracted. It is reasonable to suppose that the variation
in the length of the period of obscuration may be far more considerable
on occasions, when different clocks are employed of which the arcs may
not be the same ; when the rate of the clock is reduced to keep mean
time at each station, whereby the length of the interval between the
coincidences must be greatly changed ; when care is not given to make
the commencing and concluding arcs of the detached pendulums the same
at each station ; when the observations are made by persons variously
practised ; and, finally, when precautions are not adopted to avoid
inequality of light.
IN THE LENGTH OF THE SECONDS* PENDULUM.
227
PENDULUM 3. TROPICAL STATIONS
SIERRA LEONE.
St.THOMAS.
ASCENSION.
BAHIA.
MARANHAM.
TRINIDAD.
JAMAICA.
ICoin
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
t Coin.
II Coin.
1 Coin.
U Coin.
■ Coin.
11 Coin.
1 Coin.
11 Coin.
S.
S.
s.
S.
s.
s.
s.
S.
B.
S.
S.
s.
s.
S.
s.
s.
2
9
2
9
I
9
2
10
2
8
1
10
4
14
2
13
3
13
2
9
2
10
I
9
4
15
3
9
2
8
4
12
2
18
2
4
S
9
I
11
4
13
1
9
3
12
4
16
i
10
1
11
2
8
4
7
2
10
5
9
5
20
5
11
8
18
4
12
4
12
2
11
5
11
I
11
3
10
5
15
1
U
2
11
2
11
2
10
3
9
3
10
6
15
4
15
S
9
3
10
2
11
2
12
3
12
I
10
3
15
1
12
:
••
4
9
1
10
4
11
2
3
3
11
8
9
3
5
15
14
2
5
17
16
Coiuci-_[lst, 2".6
dences, 1. 1 1th, 1 1"
2 8
10
2
10
3.4
11
2.3
9.6
3.8
13.7
3.6
14.1
Intervals, 643"
644"
636"
642"
617"
639"
642"
s
Obsc
iration in the 1st Coincidences S" ; in the
llth Coincidences 11". 3.
PENDULUM 3. NORTHERN STATIONS.
HAMMERFEST.
SPITZBERGEN.
GREENLAND.
DRONTHEIM.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
I Coin.
II Coin.
1 Coin.
11 Coin.
ICoin.
U Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
S.
S.
S.
S.
S.
s.
s.
S.
s.
3.
3.
s.
3.
s.
3.
3.
3
12
4
25
5
9
5
10
4
9
2
13
5
16
5
13
2
23
5
14
5
12
3
12
5
11
5
17
4
16
5
16
4
13
1
17
5
13
3
19
7
16
2
16
1
16
2
16
1
15
2
17
5
13
5
11
6
10
3
16
5
IS
5
31
2
15
4
18
5
11
4
12
5
11
7
15
5
14
4
21
5
16
5
15
4
11
4
13
2
16
4
17
5
16
7
21
1
18
5
12
5
3
12
11
3
1
12
13
5
3
16
25
16
1
3
18
19
..
a)
Coinci- rist, 3".l
d.nce3,1lUh,16".5
1st, 4".l; nth, 12". 1
1st, 4". 3; llth, 14"
1st
,4". I; llth.
ir
Intervals, 675"
690"
686"
684"
s
Obscuration in the 1st Coincidences 3" .9 ; in the 1 1th Coincid
pnces 1
s-.i.
2 G a
228
EXPERIMENTS FOR DETERMINING THE VARIATION
PENDULUM 4. TROPICAL STATIONS.
SIE. LEONE.
St. THOMAS.
ASCENSION.
BAHIA.
MARANHAM.
TRINIDAD.
JAMAICA.
1 Coin.
UCoin
1 Coia.
In Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
; 1 Coin.
S.
s.
s.
s.
s.
s.
s.
S.
s.
S.
s.
s.
9.
s.
6
14
5
13
5
12
5
12
1
14
5
15
6
20
I
12
4
13
1
12
1
13
2
13
5
14
5
18
4
13
3
15
2
14
1
12
3
12
4
16
7
19
3
13
4
14
1
15
7
18
4
12
4
14
3
17
5
13
S
12
2
14
4
13
3
14
4
12
2
14
3
13
3
12
3
15
5
13
6
12
5
18
3
24
6
18
6
16
5
12
2
13
2
12
4
18
4
16
6
15
4
13
5
16
4
23
5
10
6
15
5
20
3
14
7
16
4
15
6
12
6
19
5
14
1
10
5
17
•■
Means . , ■
4.3
14
4.2
13.4
3
14
3,7
15
3.5
12.3
5
16
4.4
19
Inter-
vals
666"
667"
655"
671"
672"
665"
662"
c
obscuration in
the 1st Coincidences 4"; in the 11th Coincidences 14".
8.
PENDULUM 4. NORTHERN STATIONS.
HAMMERFEST.
SPITZBEKGEN.
GREENLAND.
DRONTHEIM.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
1 1 Coin.
1 Coin.
UCoin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
1 Coin.
11 Coin.
9.
9.
9.
9.
9.
9.
s.
9.
9.
s.
9.
s.
9.
s.
s.
s.
5
30
7
26
8
17
7
22
8
23
4
21
6
24
8
26
3
19
7
22
1
18
6
20
8
11
4
16
4
18
5
2J
7
19
7
14
7
23
7
22
8
15
3
19
8
25
5
20
5
22
8
17
8
18
7
19
5
22
1
16
8
27
6
23
5
16
6
17
6
20
7
17
2
19
5
'7
7
23
3
18
3
17
4
lb
8
18
5
19
7
17
1
17
9
22
7
27
7
15
••
8
8
14
17
5
17
3
17
5
18
3
13
i-
2
Coinci-/ Ist,
dencea^litli
5". 3
19". 5
1st, 6". 5; nth, 18". 7
Ist, 4". 4; nth, 18"
Ist, 6"; nth, 22"
Intervals . .
713"
725"
716"
711"
Obscuration in the 1st Coincidences 5". 5; in the 11th Coincidences 19". 5.
IN THE LENGTH OP THE SECONDS' PENDULUM. 229
In these tables, the influence of the length of the interval between
coincidences on the period of obscuration, will be found to receive a
double illustration ; for which purpose the experiments with each pen-
dulum have been kept distinct, and have been arranged in two divisions,
one comprehending the tropical stations or those of high temperature,
and the other the northern stations, wherein the temperature was on
the average forty degrees lower, or equivalent to an increase of about
seventeen seconds per diem in the rates of the detached pendulums,
(which increase did not take place in the pendulum of the clock in
consequence of its compensation,) and to a consequent augmentation
exeeding forty seconds in the interval between coincidences ; the cir-
cumstances in the two divisions were strictly similar in all other
respects, excepting possibly in occasional inequalities in the light, not-
withstanding the prenantinns whiVh whth arlnptprh Tt is spfin that the
period of obscuration was augmented in every case in the longer intervals
by about one third of the average amount at the tropical stations.
It may be remembered that the number of vibrations made by pen-
dulum 4, exceeded those of pendulum 3, by rather less than ten vibra-
tions in the twenty-four hours; its coincidences with the clock were
consequently less frequent than those of No. 3 ; the difference of their
respective intervals amounted, on the average of the stations, to rather
less than thirty seconds; being the joint effect of the vibrations of
pendulum 4 having taken place at a somewhat lower mean tempe-
rature than those of No. 3, and of the actual difference in the leneth
of the two pendulums arising from their original construction. In this
instance also, the augmentation in the interval between coincidences
is shewn to have produced an increase in the period of obscuration,
corresponding to that occasioned by the augmented rate of both pen-
dulums from temperature.
QBO EXPEHIMENTS FOR DETERMINING THE VARIATION
In both instances, tlic illustration is not confined to the deductions
from the averages only, but may be traced in nearly its just proportion
into the several experiments at every station*.
In all the cases which have been thus illustrated, in which errors would
be involved by the comparison of results obtained by the method of
• The practical importance of this illustration will appear, by instancing the expe-
riments with a similar pendulum, made at Madras by Mr. Goldingham, and in London
by Captain Kater, and published in the Phil. Tr. for 1822, Part I., in which the interval
of coincidences difl'ered at the two stations not less than nine hundred seconds, being
725 seconds at Madras, and l630 seconds in London. In the evidence of the very
sensible eflect produced by a dilTerence of tiiirty or forty seconds, the liability to the
introduction of error of very serious consideration may be inferred, in the employment
of the method of disappearances where the intervals arc so widely dissimilar. Mr. Gold-
ingham appears to have adopted a mode of observing coincidences very nearly the same
as that which has been practised in the experiments in this volume, but without being aware
of the inaccuracies involved by the mnrp usual iripthod, or that the results obtained by
ditferent metiiods would not be comparable with each otiier. In gcnrral the errors of such
comparison would be greater tiian when the same method, altiiough defective, is employed
on both occasions ; in the latter case its amount is proportioned to the difference, at the
two stations, in the excess of half the period of obscuration in the eleventh coincidences over
half the period in the first coincidences ; in the former case, to the whole excess at the
station where the disappearances only are observed; that station in the present instance is,
the one in which the interval is of the longest duration.
Viewing the exceeding and admirable care with which the experiments appear to have
been conducted by Mr. Goldingham at Madras, it is much to be desired that the pendulum
and its apparatus should be returned to England, and that a series of experiments, strictly
comparable, should be made in London by the same method, and with the apparatus em-
ployed at Madras. It has been seen that the relation of experiments to each other may be
destroyed by the vibration of the pendulum on different agate planes ; and as other parts
of the apparatus, used at Madras, were furnished by the same maker as those which iiave
been shewn in the preceding pages to have been incorrect in their construction, it becomes
the more desirable that the same apparatus should be rigorously employed at botii stations ;
and that the thermometer in particular should be subjected to a careful examination. The
accomplishment of such a series in London is not less desirable, in regard to the great pains
which Mr. Goldingham has taken at Madras, tlian due to the work in which the experi-
ments are published in their present incomplete state ; for the rate of an invariable pendu-
lum at one station, however correctly obtained, possesses no value except in its combination
with strictly corresponding results elsewhere.
IN THE LENGTH OP THE SECONDS' PENDULUM. 231
disappearances only, the irregular influence of the circumstances which
occasioned error will counteract itself, when the re-appearances also are
observed and a mean is taken for the true time of coincidence.
As it might be imagined that the re-appearances may not be seen
with the same distinctness or certainty as the disappearances, and as a
difference in this respect might be deemed on superficial consideration
an objection to the method of which the re-appearances form a part of the
observation, it may be desirable briefly to trace the effect which such
a difference, supposing it to exist, would produce on the results.
The re-appearance in the first coincidence being much too decided to
admit of uncertainty in the observation, the possibility of such an occurrence
must be limited to the eleventh coincidence. Let therefore the times of
true coincidence be considered (as when they are deduced from a mean)
to take place when the centre of the disk passes the telescope in coinci-
dence with the middle of the tail-piece of the detached pendulum ; and
let it be supposed that the re-appearance in the eleventh coincidence is
observed one or even two seconds more distant from the true coincidence,
than the interval which took place between the disappearance and coinci-
dence ; the effect will be that the registered time of the eleventh coincidence
will be a second later than the true time, if the error of the observation be
two seconds, and half a second later if it be only a single second ; whence
the deduced rate of the pendulum will be four-hundredths of a vibration
per diem quicker than the actual rate in the one case, and two-hun-
dredths in the other ; but as the late observation of the re-appearance is
supposed to be a constant effect, as occasioned by a less facility in
noticing the first apppearance of an object than in following it until its
disappearance, however the deduction of the absolute rate might be
influenced, the relative rates would be every where similarly affected, and
the acceleration obtained from them would be as rigorously correct, as if
derived more strictly from the actual rates.
232 EXPERIMENTS FOR DETERMINING THE VARIATION
The observation of a coincidence is not however of the same nature as
that of the immersion and emersion of a satelHte, in which the object
is viewed until it gradually becomes invisible, and in which its re-ap-
pearance takes place through the same graduation of indistinctness : the
pendulum is visible only when passing the opening in the diaphragm of
the telescope, and therefore disappears to the eye and is seen afresh in
each cilternate vibration ; a reason does not readily present itself why
a minute portion of the white disk should not be seen with equal facihty,
during the passage across, whether it be on the preceding or on the
following side of the pendulum ; nor so far as my individual experience
is concerned, have I ever been able to perceive a difierence.
With respect to errors arising from inadvertency in the observer, or
from other similar causes depending on the individual, rather than a
consequence of the mode of proceeding, the possibility of their occurrence
may be supposed to be equal in each case: but their effect on the times
of coincidence deduced from two observations would be reduced to half
the amount, which would take place when the times depended on a single
observation.
The instant of coincidence is also capable of a more precise determina-
tion, when it is the mean of two, than when dependant on a single obser-
vation ; in the one case it is the second, and in the other the half second
of coincidence which is determined.
There are several other practical advantages in the method of the
double observation, of which an attentive observer would become sensible
in the course of a series of experiments ; but which I do not think it
necessary to particularize, having already exceeded the limits which I
had originally intended in this discussion, under a sense of the importance
of a correct appreciation being made of the relative value of different
methods of obtaining the rate of a free pendulum.
It will be remembered that in the various important purposes in which
IN THE LENGTH OP THE SECONDS* PENDULUM. 233
the pendulum is now employed, its peculiar value is as a very accurate
measure of very minute quantities; and that the inquiry into the best
method of procedure with it must in consequence be concerned in the
discussion of differences which may appear as extremely small ; but which
are by no means insignificant quantities in the purposes to which the
pendulum is appUed.
a H
234 EXPERIMENTS FOR DETERMINING THE VARIATION
RESULTS WITH THE DETACHED PENDULUMS.
The results obtained with the detached pendulums at the several stations
are collected in one view in the subjoined Table.
The particulars of the first nine columns appear to require no addi-
tional explanation to that which they have received in the several places
from whence they are collected.
The tenth, eleventh, and twelfth columns are occupied in a com-
parison of the results of the two pendulums at the several stations.
Column ten shows the excess of the vibrations of pendulum 4 over
those of pendulum 3 ; and in column eleven is inserted the mean
excess, which, in consideration of the number of observations from
which it is derived, may be deemed the precise amount due to the
actual difference in the length of the two experimental pendulums;
this amount ought consequently to have been constant, if the results
given by the pendulums had been every where strictly correspondent;
or, in other words, if the length of the seconds' pendulum deducible
from the experiments with No. 3, had been always precisely the
same with that deducible with No. 4. Column twelve exhibits the
several deviations from such perfect identity ; the amount of which, even
in the extreme cases, appears so small, that it may almost be deemed an
over-refinement to attribute its occurrence to any particular circumstance.
There is, however, one cause so much more prominent than others, that
if the deviations had been larger I should not have hesitated to have
ascribed them chiefly to it, and it may be proper therefore to be noticed.
It will be remembered that the rate of the clock with which the pen-
dulums were compared was determined by observations of Zenith Dis-
IN THE LENGTH OF THE SECONDs' PENDULUM, 235
tances or Transits for the whole interval through which the experiments
were continued ; and that the rate in the half intervals occupied by the
separate experiments with each pendulum, although apportioned under the
guidance of the observations and comparisons, must still be considered
as .having been less precisely determined by them than the rate for the
whole period, in consequence of the comparatively short duration of the
half intervals. Now if an inaccuracy be supposed in the division of the
rate into the half periods, its effect will be to cause an apparent dif-
ference of double its own amount in the rates of the detached pendulums;
because what is gained in the rate of the clock in the one half interval
must be taken from the other. The mean difference in the results
of the two pendulums (omitting the signs) is 0.16, and the extreme dif-
ference 0.37 parts of a vibration per diem, which are equivalent re-
spectively to an incorrect assignment of the clock's rate in the half intervals
(generally of five days) of 0.08, and 0.19 parts of a second per diem ;
which amounts are not merely within the limits of probable occurrence,
but are so small that the supposition of their non-occurrence must be
regarded as extremely improbable.
The effect, however, of incorrectness introduced, in the division of the
rate into the half intervals, ceases, when the separate results with the two
pendulums are united in a mean result, as in the succeeding colunrn.
Column thirteen exhibits a mean between the vibrations of the two
pendulums ; or rate of an imaginary pendulum supposed to oscillate in
a vacuum, and at a uniform temperature, at every station.
And finally, in column fourteen, are contained the respective lengths of
the seconds' pendulum at the several stations, corresponding to the vibra-
tions in the preceding column, and resting on the determination of the
length of the pendulum vibrating seconds in Portland-place, determined
by Captain Kater. These measures are expressed in parts of Sir George
Shuckburgh's standard scale, at the temperature of 62° Fahrenheit.
ana
236
EXPERIMENTS FOR DETERMINING THE VARIATION
RESULTS WITH THE DETACHED PENDULUMS.
STATIONS.
i
"a
Vibrations.
Barome-
Temperature.
Baoy-
ancy.
Reduction
to a Mean
Tempera-
ture.
Vibrations
in Vacuo
at 02".
Excess in the Vibrations
of Pendulum 4.
Vibrations
strictly
comparative.
Length of
the Seconds'
Pendulum.
ter.
Regis,
tcred.
Fahren-
lieit.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
St. Thomas. J
3
4
86010.73
86020.02
IN.
30.08
30.08
0
82.1
83.1
o
81.1
82.05
s.
5.79
5.79
s.
+ 8.04
+ 8.44
86024.56
86034.25
I 9.69
0.06
86029.40
IN.
39.02069
Maranham . J
S
4
86001.39
86010.70
30.01
30.00
81.83
82.02
80.82
81
5.78
5.78
+ 7.92
+ 8.00
66015.09
86024.48
I 9.S9
0.24
8601J.7S
39.01197
Ascension . .<
3
4
86014.77
86023 72
SO 13
30.15
81.47
82.87
80.47
81.83
5.81
5.80
+ 7.78
+ 8.35
86028.36
86037.87
>• 9.51
0.12
86033.11
39.02406
Sierra Leone J
3
4
86009.82
86019.37
29.84
29.86
81.3
81.75
80.3
80.74
5.75
5.75
+ 7.70
+ 7.89
86023.27
86033.01
[ 9.74
0.11
86028.14
39.01954
Trinidad . . J
3
4
86007.55
86018.00
30.01
30.02
84.45
83.35
83.4
82.3
5.75
5.76
+ 9.01
+ 8.55
86022.31
86032.31
[lO.OO
J
0.37
86027.31
39.01879
Bahia ....■!
3
4
86016.82
86027.61
29.99
30.06
75.2
72.9
74.3
72.1
5.86
5.90
+ 5.18
+ 4.25
86027.86
86037.76
> 9.90
0.27
86032.81
39.02378
Jamaica . . •<
3
4
86026.78
86035.65
SO. 04
30.04
81.77
83.6
80.77
82.55
5.79
5.77
+ 7.90
+ 8.65
86040.47
86050.07
I 9.60
■9.63.
0.03
86045.27
39.03508
New Yolk . .<!
3
4
86117.90
86128.20
30.21
30.37
35.66
33.81
.35.56
33.75
6.42
6.47
-11.13
-11.89
86113.19
86122.78
I 9.59
J
0.04
86118.48
39.10153
London . . -•
3
4
S. page 211
■■■{
62
62
86154.94
86164.65
> 9.71
0.08
86159.79
39.13908
Drontheim . .•<
3
4
86193.99
86203 61
29.82
29.49
47.41
46.73
47.06
46.38
6.19
6.13
- 6.29
- 6.^
86193.89
86203.16
[ 9.27
0.36
86198.52
39.17428
Hammerfest . <
3
4
86213.15
86227.18
29.93
29.68
55.05
44.34
34.47
44.06
6.11
6.20
- 3.17
- 7.53
86216.09
86225.83
> 9.74
0.11
86221.46
39.19512
Greenland . .^
3
4
86227.07
86237.86
29.88
29.91
44
41.14
43.73
40.93
6.24
6.28
- 7.69
- 8.87
86225.62
86235.27
[ 9.65
0.02
86230.44
39.20328
Spitzbergen . <
3
4
8R239.21
86251.68
29.89
29.79
45.2
37.51
44.9
37.36
6.23
0.31
- 7.20
-10.37
86238.24
86247.62
\ 9.38
J
0.25
86242.93
39.21464
IN THE LENGTH OF THE SECONDS' PENDULUM. 237
SECTION II.
With attached Invariable Pendulums.
IHE pendulums employed in the experiments of the present section
were attached to the machinery of a clock, by which their tendency to
arrive at rest in consequence of the resistance of the air was counter-
acted, the continuance of their oscillation maintained, and the number
of their vibrations registered.
The principle of their construction, in respect to invariability in length,
was the same as that of the detached pendulums ; they could undergo
no change but from the expansion of the metal of which they were com-
posed in different degrees of temperature.
The rate of a pendulum of this description is obtained by comparing
the clock to which it is attached, at the commencement and close of the
intervals for which the rate is desired, either with celestial time, or with
another clock which is itself duly compared with the heavens ; and by
observing, as frequently as may be thought necessary during the inter-
vals, the temperature and density of the atmosphere, the temperature of
the pendulum, and the arc in which it vibrates. The extent of the arc
is shown by a portion of a graduated circle affixed to the clock-case
immediately behind the lower extremity of the pendulum ; and the tempe-
rature of the pendulum, by a thermometer within the clock-case, suspended
as near the pendulum as it can conveniently be placed. From these data
may be computed the number of vibrations which the pendulum, being
238 EXPERIMENTS FOR DETERMINING THE VARIATION
of a certain temperature, would make in a vacuum, and in an arc inde-
finitely small.
The two pendulums, similar in construction, numbered 1 and 2, and
the clock in which they were successively used, were the same with
which I had been furnished in the Expeditions of Arctic Discovery, in
1818, and in 1819 — 1820; and have been particularly described in the
account of the experiments made in these voyages, published in the Phil.
Tran. for 1821 ; the following more brief notice may, therefore, suffice
on the present occasion.
The pendulums were each cast in one piece of solid brass, and were
furnished with knife-edges of hard steel, secured as in the detached pen-
dulums ; the vibration was performed on agate planes ground into por-
tions of hollow cylinders, and imbedded in a brass support firmly secured
to the clock-case. The clock was supported by a triangular wooden frame,
and was fitted with all the necessary and proper adjustments.
The knife-edges of the pendulums had been slightly corroded on their
return from the North, and it was apprehended that the injury might
increase so as to interfere with the vibration. They were therefore
ground afresh, and the clock cleaned and oiled previously to the com-
mencement of the present experiments. I had hoped that these opera-
tions might have been completed in sufficient time to have permitted a
trial of the going of the pendulums in the clock, before their embarkation
in the Iphigenia ; but from circumstances, which occasioned much vexation
at the time, but which it is needless now to particularize, this measure
could not be accomplished, and their first trial was at Sierra Leone.
IN THE LENGTH OF THE SECONDS' PENDULUM. 239
SIERRA LEONE.
The qualifications of a room suited to the reception of the pendulum
clock differ in some respects from those required in the apartment adapted
to the experiments with the detached pendulums; and it may be proper
to notice the two principal particulars of difference, because they influence
materially the greater facility with which accomodation can be procured
for the clock than for the pendulums. The support of the pendulum-clock
resting wholly on the ground, the nature and thickness of the walls are
no otherwise of consideration than as they may conduce towards an
uniformity of temperature : it is merely requisite that the flooring of the
room should be firm and substantial, or which is preferable, that the room
should be on the basement, and that the flooring should be removed so
as to allow the support to rest on the ground beneath. As the comparison
of the clock and registry of the arc and temperature can be accomplished
by the light of a taper as well as by the daylight, the admission of the
latter into the room is not a necessary qualification, and being preju-
dicial to steadiness of temperature may be better avoided.
The room in which the clock was set up at Sierra Leone was a kitchen
beneath the Officers' Quarter assigned for the pendulum experiments; the
floor was of brick, and the windows were permanently boarded up ; the
room was entered only at the times and for the purposes of comparison
and registry.
As the same methods of comparing the clock and of observing the
temperature and arc were pursued at the different stations with very little
variation, the following description may be considered to apply generally,
and the alterations only will be hereafter noticed.
The clock was compared at intervals of twelve hours of mean time
240 EXPERIMENTS FOR DETERMINING THE VARIATION
with a chronometer or clock the rate of which was determined by astro-
nomical observation. As soon as the comparison had been made, the door
of the clock-case was opened, and the temperature indicated by the pen-
dulum thermometer was read to degrees and tenths. It was then seen,
by means of the indices of a self-registering thermometer stationed also
in the clock-case, to what extent the temperature had varied in the pre-
ceding interval above and below the indication thus read ; the extremes
of temperature so obtained were entered in the table as corresponding to
the interval, and as those which the pendulum thermometer would have
shewn, had it possessed the means of registering its own extremes ; the
purpose of the self-registering thermometer was only to perform this
latter office, without regard to the agreement or otherwise of its scale with
that of the pendulum thermometer. The amplitude was next observed;
and as the graduated arc on which it was read was a fixture, and did not
admit the adjustment of its zero to the pendulum when at rest, the extent
of the arc was noticed in each semi-vibration, and the mean was entered
in the table as the angular deviation of the pendulum from the vertical. The
indices of the self-registering thermometer were then brought down to the
mercury, and the clock-case closed until the. next period of observation.
The clock was suffered to go for three or four days before the registry
was commenced, in order to allow the rate to become steady ; the observa-
tions with each pendulum were continued generally from five to seven days.
The following tables contain the particulars of the going of the two
pendulums at Sierra Leone ; and appear to require no other explanation
at present, than that the correction for the arc has been computed by the
same formula as in the detached pendulums: and that the reduction to
a mean temperature is in the proportion of 0.44 parts of a vibration per
diem for each degree of Fahrenheit; the chronometer with which the
clock was compared was No. 423 of which the rate on mean solar time
is taken from page 21.
IN THE LENGTH OF THE SECOND.S' PENDULUM.
241
Sierra Leone.
VIBRATIONS of PENDULUM No. 1, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.85 Inches.
Chrono-
reiidiilom
Clock's
liAlLX BATES.
Arc of
Correc-
Redac-
tion to a
Vibralloni
DATE.
loss on
Temperature.
tion for
per Diem at
melur.
Clock.
Chron.
Chron.
Clock.
Vibration.
lire Arc.
Temp.
81". 19.
1822.
H. M. s.
M. S.
Gainjng.
Losing.
O O 0
O 0
Mar. 9 P.M.
56 46.9
s.
S.
S.
[80. 7j
1.02
„ 10 A.M.
55 SI. 4
152.9
1.01
151.89
•81.2
[81 1
\ 81.3
1.00
"1.007
1.67
86249.78
1.00
'
„ 10 P.M.
54 14
[81.61
< >81.251
l80.6j
„ 11 A.M.
52 58
•152.2
1. 01
151.19
f81.28
{"■y. 1
[80. 9j
1.00
■1.00
1.65
-f 0.04
86250.50
„ n P.M.
51 41.8
[81.11
<; 1-80.551
1.00
[80 J
„ 12 A.M.
•10 00 00.
50 26.3
■152.1
1.01
151.09
^80.9
f 80.51
} ^81.25^
[82
0.98
^0.993
1.63
-0.13
86250-41
„ 12 P.M.
49 09.7
80.2
1.00-
„ 13 A.M.
47 54.5
•151.1
1.01
150.09
^ [81.15
rso.el
} S.81.2 J
[81. S
0.95
•0.983
1.59
86251.58
„ 13 P.M.
46 38.6
[81.8]
|81 f
1.00
„ 14 A.M.
45 23.4
•151. 1
1.01
150.09
>81.4
181 1
I 181.4 J
81.8
0.95
•0.983
1.59
■^o.o^
86251.59
„ 14 P.M.
41 07.5
I- J
1.00^
MEANS
150.87
81.19
0.993
1.63
86250.76
2 I
242
EXPERIMENTS FOR DETERMINING THE VARIATION
Sierra Leone. VIBRATIONS of PENDULUM No. 2 in the PENDULUM CLOCK.
Mean Height of the Barometer 29.85 Inches.
Chrooo.
Pendulam
Clock's
D&ILY RATES.
Arc of
Correc-
Redac-
Vibrations
DATE.
Temperatore.
linn fnr
tion to a
per Diem at
81°. 3.
meter.
Clock.
Cbron.
ChroD.
Clock.
Vibration.
Ul/M 1 Ui
the Arc.
Meao
Temp.
1822.
H. M. S.
M. S.
Gaining.
Losing.
000
0 0
s.
s.
Mar. 16 P.M.
23 22.5
1.10
S.
S.
a.
teW-n
+
„ 17 A.M.
23 01
"43
0.64
42.36
V81.6
1.07M.09
2.00
+ 0.04
86359 . 68
„ 17 P.M.
22 39.5
{ll:>- 1
1.07
„ 18 A.M.
22 18
'43.7
0.64
43.06
\^-> r'
1.06M.06
1.87
-0.11
86358.70
„ 18 P.M.
21 55.8
{l\>- 1
1.05
., 19 A.M.
21 S3. 8
.41.6
0.64
40.96
{^1.2}-. r
I.O5U.O5
1.83
-0.09
86360.78
„ 19 P.M.
21 14.2
{%:>- 1
1.05
„ 20 A.M.
20 53.4
■41.8
0.64
41. 16
[79 81 }''■"
{82:2/8' J
0.96ll.02
1.72
-0.26
86360. ."O
„ 20 P.M.
20 32.4
1.03
„ 21 A.M.
20 11.2
•42.2
1.05
41.15
1.02J.1.03
1.76
-0.04
86360.57
„ 21 P.M.
•10 00 00'
19 50.2
f^->-'y.
1.02
., 22 A.M.
19 30
■41.3
1.05
40.25
O.99I1.OI
1.68
-0.17
86301.26
I
{->.3/
„ 22 P.M.
19 08.9
1.02
,, 23 A.M.
18 47
5.44. 5
1.05
43.45
>82.22
1.04 •1.03
1.76
+ 0.31
86358.62
„ 23 P.M.
18 24.4
{ll->- 1
1.03
„ 24 A.M.
18 02.4
U4.4
1.05
43.35
ffi:?^^.. h-'
1. 04^1. 04
1.79
+ 0.26
86358.70
„ 24 P.M.
17 40
1.05
{l\:iy^ 1
1
„ 25 A.M.
17 19.3
Ui.i
1.05
40.05
«?.2h.er^^
1.04M.04
1.79
+ 0.06
86361.80
„ 25 P.M.
16 58.9
1.03
C.'lh- 1
„ 26 A.M.
16 39
Uo.i
J
1.05
39.05
{^y^r
I.O4I1.O4
1.79
86362.74
„ 26 P.M.
■*
16 18.8
1.05
MEANS
41.48
81.5
1.04
1.79
86360.31
IN THE LENGTH OF THE SECONDS* PENDULUM. 243
In the experiments which I had made with the same clock and pen-
dulums, during the voyages for the Discovery of a North-West Passage, the
action of the weight, transmitted through the wheels, had maintained an
amplitude always exceeding a degree and six-tenths ; whereas in these
experiments it may be seen that the amplitude with each pendulum
scarcely equalled a degree. As the weight was the same which had been
used on the former occasions, the diminution of its force appeared far too
great to be accounted for by any ordinary effect of the cleaning which
the clock had undergone intermediately ; but as this was the first time
that the clock had been set up since it had been cleaned, I thought it
possible that the effect might be, at least in part, occasioned by friction ;
arising either from a defective supply of oil, or from time being required
from the oil to work into the pivots : I supplied, therefore, a very small
quantity of prepared oil to the principal parts where its absence would
have occasioned the most resistance ; and having assured myself that
all the adjustments of the clock were perfect, and that the small fixed
level, by which the horizontality of the agate planes was shown, cor-
responded with the parts of the planes on which the knife edge rested,
the oscillation of pendulum 1 was suffered to proceed, and subsequently
of pendulum 2, as shewn in the preceding tables. At the close of the
experiments with pendulum 2, the clock had gone nearly a month, and
as no material alteration had taken place in the arc during that
period, it had become evident that none was to be expected from time.
The invariability of the sustaining force being a most important con-
dition, and within limits even an essential one, towards the success of '
the method of experiment, I felt extremely anxious to ascertain the
cause of the great variation which had appeared since the clock was
cleaned ; as if it arose from any accidental defect, or derangement
of the machinery (which I could not but suspect) it might yet admit of
being remedied ; whereas if I should fail in tracing it to an ostensible
2 12
244 EXPERIMENTS FOR DETERMINING THE VARIATION
cause, or if it should be one beypudjiiy power to remedy, it was scarcely
to be expected, that being of sufficient magnitude to have reduced the arc
to nearly the half of its original dimension, it should not be productive of
further fluctuations. Before the clock was re-packed for embarkation,
therefore, the works were submitted to a very close and careful examina-
tion ; but without my being able to perceive that any part of them was
misplaced or injured. As the whole of my attention, during the short
remainder of my stay at Sierra Leone, was occupied in a repetition of
the experiments with the detached pendulums as already described in
consequence of the results of the first series having differed so much from
previous expectation, I was obliged to postpone the further examination
of the pendulum clock until my arrival at another station, when I designed
to set it up in a room in which light should be admitted, for the purpose
of observing it, whilst in motion, with more advantage than I had been
able to accomplish at Sierra Leone. The next station which I visited
was the Island of St. Thomas : but in consequence of the difficulties which
were experienced in obtaining permission to land the instruments, and in
consideration of the irresponsible nature of the government of the Island,
I did not think it prudent to land more instruments than could conve-
niently be re-embarked by a boat's crew at the shortest notice ; and ac-
cordingly the pendulum clock was not landed.
IN THE LENGTH OF THE SECONDS' PENDULUM. 245
ASCENSION.
The room in the barrack- square at Ascension, which Major Campbell was
kind enough to give up to me, but of which the walls were not sufficiently
substantial to support the frame belonging to the detached pendulums,
possessed the qualifications of a brick floor and steady temperature which
rendered it suitable for the experiments with the pendulum clock : it
was accordingly set up, and was going on the afternoon of my arrival.
On .examining the movements of the clock on the following morning under
the advantage of a strong light, I had the satisfaction of discovering, and
of removing, the impediment to the free motion of the pendulum which had
caused so much anxiety, and which I shall endeavour to explain. The
cylindrical groove in which the knife edge vibrated was closed at the end
towards the back of the clock by the brass frame in which the planes were
imbedded, but was open at the other end: in order therefore to ensure
the replacement of the pendulum at all times in the same longitudinal
position, a brass cheek projected by a spring from the clock plate, and
acted as a termination to the groove at the open end, but without pressing
against or touching the side of the planes ; the length included between
the cheek and the opposite termination of the groove was designed to be
just sufficient to receive the pendulum, and to allow it to oscillate without
touching either extremfly ; and such was the space included before the clock
was cleaned ; but in putting the works together after that operation had
been performed, the brass cheek had not been replaced precisely in its
original position ; it had apparently escaped Mr. Arnold's notice, to whom
the clock had been intrusted to be cleaned, that the ends of the wootz
prism on which the pendulum vibrated were made to slope outwards com-
mencing from the top, so that the length at the knife edge visibly exceeded
that of the head-piece of the pendulum. In examining the vibration of the
knife edge in the cylinder, the lower part of the end of the prism, just at
246 EXPERIMENTS FOR DETERMINING THE VARIATION
the angle but not higher, appeared nearly if not quite in contact with the
cheek, although the latter stood well clear of the upper part of the prism
and of the head-piece. On pressing back the cheek towards the plate,
the arc immediately began to augment, and in a short time resumed and
maintained its former dimension of one degree and ^Vths. The contact
was so slight that I was not fully assured of its being actually the case,
until the effect which followed on the pressure being reUeved removed all
doubt ; and I then observed that the vibration at Sierra Leone had slightly
marked the brass. The two pendulums were tried successively, but when
the spring was at its full extent, the space included was not sufficient for
either to vibrate without touching at one extremity. Fortunately the re-
medy was simple and did not prevent the proper use of the cheek ; by
employing it at the full extent of the spring, when the clock was first set
up, the proper position of the pendulum was ensured : that object being
effected, its pressure on the pendulum was relieved, so that the oscillation
might be perfectly free.
It is from Ascension therefore that the comparative rates of the at-
tached pendulums commence. It appeared by subsequent comparison
with other stations, and by taking into account the acceleration as shewn
by the detached pendulums, that the rate of each pendulum at Sierra
Leone was accelerated about twenty-three seconds by the diminution of
the arc produced by the resistance to the free motion of the pendulum.
It is remarkable that no considerable irregularity should have taken place
in the daily going of the clock, under a disturbing influence of such mag-
nitude, by which its existence might have been indicated: had it not
been for my previous knowledge of the clock, I should certainly have had
no reason to have suspected from its going at Sierra Leone, that the
proper action of the weight was modified to so considerable an extent.
The height of the clock at Ascension was the same as that of the de-
tached pendulums; the rate of the Chronometer No. 423, with which it
was compared, is taken from page 48.
IN THE LENGTH OP THE SECONDS* PENDULUM.
247
ASCE
TMQTmv ^— -
VTRRATTONS nf PENDTTTTTM Nn 1 in fhp PENDTirUM rLOf'K
naiuiv . —
Mean Height of the Barometer 30.05 Inches.
DATE.
Chrouo-
Pendirlum
Clock's
DAILY RATES.
Arc of
Correc-
Reduc-
tion to a
Vibrations
per Diem at
toss OQ
Temperatare.
tion for
meter.
Clock.
Cbron.
Cbron.
Clock.
Vibration.
the Arc.
Temp.
SO'-.OS.
1822.
U. H. s.
M. s.
Gaining.
Losing.
O O 0
0
s.
June 28 P.M.
39 32.7
s.
S.
S.
[83. 5l
{ >8I.85i
180. 2j 1
f81.18
[82. Si
<^ Uo.5 i
1.751
1.75
+
,. 29 A.M.
■174.5
2.57
171.93
1.747
5.02
-1-0.50
86233.59
-■
[78.7]
„ 29 P.M.
36 38.2
■174.2
83 1
180.6 1
178.2]
1.74
,, 30 A.M.
2.57
171.63
>80.6
1.75
>1.747
5.02
-fO.24
86233.63
'83.81
>80.6 J
.77.4J
„ 30 P.M.
,33 44
[84 1
{ ?80.75>
[77. 5J
1.75
July I A.M.
•174
2.57
171.43
>80
fsi 1
< >79.25
[77. 5J
1.75
■1.747
3.02
-0.02
86233.57
,. 1 P.M.
30 50
[82.71
{ f80.251
[77.81
1.74
„ i A.M.
> 2 00 00 <
■174.7
2.37
172.13
^80.27
[77.8")
< (■80.3 J
[82. Sj
1.74
■1.743
5.00
•fO.lO
86232.97
„ 2 P.M.
27 55.3
[83.5
■! ^80.451
1.75
[77. 4)
„ 3 A.M.
•174.3
2.57
171.73
^80 . 28
1.75
•1.747
5.02
■fO.lO
86233.39
[77.4]
\ ^80.1 J
[82. sJ
„ 3 P.M.
25 01
[83.8]
1.74
■174.5
„ 4 A.M.
2.57
171.93
(>79.35
1.71
■1.743
5.00
-0.31
66232.76
[78.51
^78 J
|77.5
„ 4 P.M.
22 06.5
i:i""i
1.75
„ 3 A.M.
■174.5
2.57
171.93
>78.67
1.76
•1.7C.
5.10
-0.61
86232.56
|77.7|
1 f80 J
1.82.3
„ 4 P.M.
19 12
1.77
MEANS
171.81
80.03
1.748
5.03
86233.21
248
EXPERIMENTS FOR DETERMINING THE VARIATION
ASCEI
tfQTniV
— VI RRATTOIN'S of PENDULUM No 2 in tlip PENDULUM CLOCK
\ 13 1 U il .
Mean Height of the Barometer 30.07 Inches.
Cbrono-
Pendnlam
Clock's
DAILY BATES.
Arc of
Correc-
Reduc-
tion to a
Vibrations
DATE.
Tp til n f" I't t n r^
per Diem at
79°.44.
metcl".
Clock.
Cbron.
Cllton.
Clock.
M. CilJU^* (llUlf. I
Vibration.
the Arc.
Mean
Temp.
1822.
H. M. S.
M. s.
GaiQing.
Loung.
O O o
0 0
s.
S.
July 5 P.M.
1
4 38
8.
S.
a.
i::::i" i
1.75,
+
„ 6 A.M.
4 06.2
XA.i
2.55
61.82
/78.55
(76.71
1.75
.1.75
5.04
-0.39
86342.83
„ 6 P.M.
a 33. G
ILl""
1.75
„ 7 A.M.
3 01. S
■64.8
2.58
62.22
>79.45
[78.5]
{ >81.15
1,83.8]
1.75
.1.75
5.04
86342.82
„ 7 P.M.
■9 55 00-
2 28.8
f^ I78.25
i.79.75
1.75
^1.75
„ 8 A.M.
1 57.2
■64.8
2. 58
61.72
1.75
5.04
+ 0.14
86343.46
[78.5]
< }S\.25\
184 J
„ 8 P.M.
1 24.5
[79. 4)
>78 9
78. 4 J
1.75'
„ 9 A.M.
0 52.9
■64.6
2.58
62.02
180.02
j78.5|
< >81.15J
(83. 8j
1.75
>1.75
5.04
-^0.25
86343.27
„ 9 P.M.
0 19.9
1.75
MEANS
79.44
1 .7s
5.04
86343.09
IN THE LENGTH OF THE SECONDS* PENDULUM.
349
BAHIA.
The clock was set up in the same room at Bahia in which the experiments
with the detached pendulums were made: the floor was boarded, but as
the clock was situated in a part of the room which was not approached
except for the purposes of comparison and registry, and as the joists, on
which the floor was laid, rested directly on the foundation of the house,
the support was regarded as sufficiently firm.
The rate of the Chronometer No. 423 from the 23d of July to the
afternoon of the 2d of August is taken from the observations of which the
results are collected in page 66 ; the rate from the 3d to the afternoon of
the 5th is deduced from the zenith distances on the afternoon of the 2d in
page 65, and those which are subjoined, observed on the afternoon of
the 5th.
Bahia. -
—OBSERVATIONS to DETERMINE the RATE of the Chronometer 423, by ZENITH
DISTANCES of the Sun, observed with a Repeating Circle. — Latitude 12° 59' 21" S.
August 5th P.M.; Barometer 30.05 ; Thermometer 73° , 0'sU.L.
Chronometer.
Level.
Readings, &c.
Chronometer.
Level.
Readingf, &c.
Mean. . .
True time .
Chron. fast
H. M. S.
6 25 59.2
6 27 22
6 29 16.4
6 30 52.8
6 32 40.4
6 Si 13.6
+2
H-8
— 5
+2
+3
+ 2
+ 1
+8
-6
+2
+ 2
+ 2
First Vernier 24 54 45
Second „ 54 20
Third „ 55 00
Fourth „ 54 20
U. M. s.
7 01 28.4
7 02 54
7 01 40
7 06 17.2
7 07 40.4
7 08 50
-2
+6
-2
0
+2
+ 2
-4
+ 5
-4
0
+ 1
+ 1
O ' "
First Vernier 96 31 05
Second ,, 33 45
Third „ 34 20
Fourth ,, 33 30
Mean . . 24 51 36
T j„. 0-/360 00 00
Index . . +^ 0 og Qg 5
Level . . . +10.5
Mean ... 96 33 55
Index . . .+335 05 24
Level ... 2.5
6 30 04.07
3 56 41.13
+ 12
+9
Mean. . . 7 05 18.33
True time . 5 31 55.3
+ 6
-I
+ 10.5
384 54 55
+2.5
431 39 21
2 33 22. gf
Chron. fast 2 33 23.03
Observed Z.D. 64 09 09
Ref.andParal. +1 46
Semidiam . . +15 48
Observed Z.D. 7 1 56 33
Ref.andParal. +2 40
Semidiam . . +15 48
360 -2'4 s'l 36 = 335 0
5 24
True Z.D. . . 64 26 43
True Z.D. . . 72 15 01
f2 3*^ 22 Qll "• '*'■ ^'
Chronometer, Fast j^ 33 23'o3j '^ ^^ "^-^^
August 2d
„ 5th
H. w
P.M. Chronometer Fast 2 3,
. s.
i 14.1
P.M. Chronometer Fast 2 3.
i 22.98
Chronometer's Gain in
3 Days 8.88 =
2 .96 seconds per Diem.
2 K
250
EXPERIMENTS FOR DETERMINING THE VARIATION
RiHTA VTRRATFONS nf PKlVDrTTTTM No 1 in thp PENDULUM CIOCK
AJA m A*' ' V lUXfcilX Xv^i^ O Ul X XjJ.11 U \J ±j\J ITX l^U. X } 111 lUC X XJJ-^Xy U XjU ITX V^XjVVtXVi
Mean Height of the Barometer 39.93 Inches.
DATE.
Chrono.
Pendulum
Clock's loss on
D.IILY BATES.
Temperature.
Arc of
Correc-
tion for
Reduc-
tion to a
Mean
Vibrations
per Diem at
meter.
Clock.
the Cbron.
ChrOD.
Clock.
Vibration.
Ibe Arc.
Temp.
73''.2r
1822.
H. M. S.
M. S.
S. s.
Gaining.
Losing.
O o o
O 0
S.
S.
July 23 A.M.
30 06.7
J72.31
\ m.85
[75.4J
1.74
f85.7i
S.
S.
+
J 1
„ 23 P.M.
28 41
1 P^'l
2.68
168.42
>73.47
1.74
• 1.737
4.97
+ 0.09
86236.64
[74.7)
^85.4
\ ^73.1 J
I
J
1
>85.8i
1
171. sj
„ 24 A.M.
27 15.6
1.73
f72 )
{ )-73.5 1
hs J 1
„ 24 P.M.
25 49.8
1 f-l^'-S
2.68
169.22
173.35
1.73
.1.727
4.91
+ 0.04
86235.73
>86.l'
[74.4] I
\ n3-2
[72 j
„ 25 A.M.
24 23.7
1.72<
>84.9l
•' >871.2
f72.2)
1 n^-^ 1
175 J
„ 25 P.M.
•10 00 00'
22 58.8
2.68
168.52
p. 2
1.74
.1.73
4.93
-0.03
86236.38
1.86.3 J
[n.h ^
r
„ 26 A.M.
21 32.5
J
1.73
(.85. 7
J Vl71
[74. 6j
„ 26 P.M.
20 06.8
2.68
168.32
172. 9
f73 Sl 1
1.72
.1.727
4.91
-0.16
86236. 4S
Us. si
{,.,}"■•'
„ 27 A.M.
18 41.5
1
1
1.85.7
f72.7|
1.73
„ 27 P.M.
17 15.8
■• M71.5
2.68
168.82
>73.45
1.73
.1.73
4.93
+ 0.08
86236.19
1
[71.41
\ >73 J
|74.6J
1,85. 8-'
„ 28 A.M.
15 50
J
1.73.
M
EANS
168.66
73.27
1.73
4.93
86236.27
IN THE LENGTH OF THE SECONDS* PENDULUM.
251
Bahia. VIBRATIONS of PENDULUM No. 2, in the PENDULUIVI CLOCK.
Mean Height of the Barometer 30.00 Inches.
Temperature.
Arc of
VibralioD.
Correc-
tion for
tbeArc.
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
rT,.5|,
1.71
l72.8J
fTl.sl
72.15
f-71
2J
[70. Si
i >71.65
172. 8j
r72.5l
71.58
1.703
[71.
1.7O.5J
[71 )
< >71.65
172. 3j
■^-. ,S-71.05
L70.4J
r70.8l
< >71.55
172. 3J
r72.2l
170. 6J
{70.81, ,
i ^72.15,
r73.3l I
< S-72.5 J
171. 7j
.''71.71
58
71.35
71.47
32
173. 2j
^72. 45
65
72.05
57.44
r^-nti.
171 j
fTl 1
; >71.75i
172. 5J
!>71.5
r72.31 I
's >71.25J
i70.2j
f70.41
< j.71.85i
173. Sj
(71.92
172. 71
171. 3J
>72
1 70
1.70-
1.70M.70
1.70'
I.70M.703
1.71
I.7lil.71
1.7lj
1.7lll.71
1.71
1.71^.1.71
1.71
1.7lll.71
1.71]
+
4.79
4.77
4.79
4.83
4.83
4.83
1.7U1.71
,J
-0.06
-0.06
-0.16
-O.II
+0.26
+0.14
-0.10
+0.09
86347.21
86346.79
96346.91
86346.90
86346.87
86347.33
86347.09
86347.48
57.74
71.72
1.707
4.81
86347.07
2 K 2
259
EXPERIMENTS FOR DETERMINING THE VARIATION
MARANHAM.
The clock was set up at Maranham in the same room in which the de-
tached pendulums were used, the floor of which was paved with stone.
The rate of the Chronometer 423 is taken from page 83.
Maranham. VIBRATIONS of PENDULUM No. 2, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.92 Inches.
Chrono-
meter.
PvDilutura
Cluck.
Clock's loss
oa Cbron.
DAILY R.iTBS.
Chron. Clock.
Temperalure.
Arc of
Vibration.
Correc-
tion fur
llie Arc,
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
810.03.
1822.
Aug.SO P.M.
„ 31 A.M.
„ 31 P.M.
Sept. 1 A.M.
„ 1 P.M.
„ 2 A.M.
„ 2 P.M.
„ 3 A.M.
„ 3 P.M.
„ 4 A.M.
„ 4 P.M.
M. s.
10 12.7
^■39.!
9 32.8 1< |.80
HO . 1 '
•12 00 OoJ
8 52.7
8 12.8
7 32.5
6 52.5
6 12.6
5 33.3
4 53.9
4 14.5
3 34.9
•40.3
40
>39.9
39.3
J-.39.4
\
>39.C
1
^80.5
79.9
78.7
I79
s.
2.7
2.7
2.7
2.7
2.7
MEANS .
Losing.
77.3
77.5
77.2
76
76.3
.1^81 1
i >80.8
180. eJ
r80.4l
■! >80.8
L81.2J
80.8
f81.2]
180. 7J
(•80.95)
>80.95
1^80.71
". (•80. 95'
1.81. 2J
{81.21
I80.6r-^ I
1 r
76.86
[80.6
1-80.95
<
18I.3J
[81.51
I (-81.3
181. Ij
< ^81.15-'
181. 2j
fsi.s!
"i (•81.35
I.8I.2J
tSl 1
181. 3 j
!>81.15
80.92
81.22
81.25
1.75
1.75V 1.75
1.75
1.75> 1.75
I.75J
l-75> 1.75
81.03
1.75^
I
1.75> 1.75
1.75.
5.01 :-o.io
1.75
>• 1.75
I.75J
1.75
5.04
5.04
5.04
5,04
-0.03
-0.03
+0.08
+ 0.10
5.04
86327.64
86327.51
86.327.81
86329.12
86328.84
86328.18
IN THE LENGTH OV THE SECONDS PENDULUM.
253
Mad « ivrn AST VTRRATTmvrS ^r PTTlVmTTT TTM IVT^ i ir. <!,£. PF.lVnTIT TIIVT TT DPK 1
11±A
J.t./l.lV ±t.X^ltA. T AX^JLV'.^A X.I.V^X^KJ \J^ J. *JJ.^ M-f^ J^%^ ^'M. J.» u. i •»* H-tV* J. M^J.tM^ ^%^ .m^-^ A-.-. v^ .a^ -w t^^*..
Mean Height of the Barometer 29.93 Inches.
CbroQo-
Pendoium
Clock's loss
D4ILY BATES.
Arc of
Correc-
Reduc-
tion to a
Vibrations
DATE.
Temperature.
(ioalor
per Diem at
meter.
Clock.
on Cbron.
Obron.
Clock.
Vibration.
Ibe Arc.
Temp.
81°.39.
U. M. S.
H. «. S.
s. s.
Gaining.
Lo&ing.
0 0 0
0 0
9.
s.
Aug. 23 A.M.
12 01 51.8
■95
1^81. 61
1. 71,
S.
S.
82 1
[82.4]
ll89.6
., 23 P.M.
12 00 16.8
2.7
186.9
(■82.07
1.72
>1.713
4.85
■(•0.30
86218.25
' 1
94. 6J
^82. 4]
i (■82.15-'
[81 .9J
„ 24 A.M.
11 58 42.2
■95. 2i
[■81. 9I
) >82.051
82. 2]
1.71
„ 21P.M.
11 57 07
ll89.8
■94. 6J
2.7
187.1
f82.1
82.6]
f82.15
81. 7j
1.71
-1.71
4.83
+ 0.31
86218.04
„ 25 A.M.
11 55 32.4
1.71^
1
[81.4]
Igi 8
>, m.55]
[81. 7J
„ 25 P.M.
11 5S 57. G
ll89.4
2.7
186.7
>81.68
[82.11
1.71
■■1.71
4.83
■(■0.13
86218.26
.94. 6 J
J
[81. 5J
„ 26 A.M.
11 52 23
1.71
[81 1
■94.8
ll89.2
>81.I5]
[81. Sj
„ 26 P.M.
■12 00 00.
11 50 48.2
2.7
186.5
>81.3
1.71
■1.71
4.83
-0.04
86218.26
1
1
f81.7]
■94. 4J
J ^81.45'
[81. 2j
„ 27 A.M.
11 49 13.8
■94.3,
I188.8
81. 4]
J >81.2 1
81 J
1.71
„ 27 P.M.
11 47 39.5
2.7
186.1
'■ ^81.1
[81.2] 1
1.71
■1.71
4.83
-0.13
86218.60
■94. 5J
J Ul >
^__
80.8]
„ 28A.M.
U 46 05
J
L ■'
1.71
■94. 5^
(•80.8]
.. r 1
^ ^80.85
„ 28 P.M.
11 44 30.5
{ ll89
2.7
186.3
7.71
■1.71
4.83
-0.24
86218.29
1
i.94.5
[81 ] 1
J ^80.8 J
[80. 6 J
„ 29 A.M.
11 42 56
1.71
(■80.4]
U4.7
J ^80.55
[so. 7
„ 29 P.M.
11 41 21.3
' .189.4
[94. 7j
2.7
186.7
*■ ^80.65
(•80.91
1.7
•1.703
4.79
-0.33
86217.76
J 180.75
[80. 6j
„ 30 A.M.
11 39 46.6
1.7 '
MEANS
186.6
81.39
1.709
4.81
86218.21
254
EXPERIMENTS FOR DETERMINING THE VARIATION
TRINIDAD.
The station of the pendulum clock at Port Spain w^as in the vestry of the
Protestant church, which was paved with stone. The rate of the chro-
nometer 423 from the 23d of September to the 4th of October is taken
from page 97: and from the 4th, to the evening of the 8th of October,
the rate is deduced from the zenith distances on the morning of the 4th in
page 96, and the subjoined observations on the morning of the 10th.
Trinidad. OBSERVATIONS to DETERMINE the RATE of the Chronometer No. 423, by ZENITH
DISTANCES of the Sun, observed with a Repeating Circle.— Latitude 10° 38' 43" N.
October 10th A.M. ; Barometer 30.00 ; Thermometer 81° ; O's L.L.
Chronometer.
Level.
Readings, &c.
Cbronometer.
Level.
Headings, &c.
H. M.
11 25
11 26
U 28
11 29
11 30
11 31
s.
07.2
32.4
26.8
SO. 8
57.6
52.8
+4
+8
+2
-2
0
-3
+3
+6
+ 1
-4
0
-5
O 1 II
First Vernier 52 08 20
Second „ 08 00
Third „ 08 30
Fourth „ 08 00
H. M. s.
11 35 55.6
11 37 38.4
11 38 58.8
11 40 32.6
11 41 55.2
11 43 16
+7
+ 6
+ 16
-3
-3
0
+6
+5
+ 16
-5
-4
-1
First Vernier 88 25 40
Second „ 25 00
Third „ 25 50
Fourth „ 25 00
Mean ... 52 08 12.5
i„j „ . J360 00 00
Index . . -t-<^ (J gg pg 5
Level ... +5
Mean ... 88 25 22.5
Index . . .+307 51 47.5
Level ... +20
Mean. . . 11 28
True time . 7 20
42.93
51.55
+9
+ 1
Mean. . . 1 1 39 42.93
True time. 7 31 52
+23
+ 17
+ 5
412 08 26.5
+20
396 17 40
Chron. fast 4 07
51.38
Chron. fast 4 07 50.93
Observed Z.D. 68 41 24.5
Ref.andParal. +2 iO
Semidiam . . —16 04
Observed Z.D 66 02 56
Ref.andParal. +1 58
Semidiam . . — 16 04
360—52 08 12.5 = 307
51 47.5
True Z.D. . . 68 27 31
True Z.D. . . 65 48 48
H. M. S. 1^ ^j ^
Chronometer, Fastj^ °!| so'gs} "* "^ ^'''^
October 4th A.M. Chronometer Fast
10th A.M. Chronometer Fast .
H M.
4 07
. . . . . 4 07
s.
34.53
Sl.l.'J
1
Chronometer's Gain i
n 6 Days .... 16.6
2 = 5
.8 seconds per Diem
.
IN THE LENGTH OF THE SECONDS PENDULUM.
•255
Trinidad. —
-VIBRATIONS of PENDULUM No. 1, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.92 Inches.
DATE.
Chrono-
Fendalom
Clock-a
DAILY RATES.
Temperature.
Arc of
Correc-
Reduc-
tioB to a
"VibratioDs
per Diem at
loSSOQ
tion for
meter.
Clock.
Chron.
Cbron.
Clock.
Vibration.
the Arc.
Temp.
S2.93.
1822.
H. M. S.
M. s.
Gaining.
Losing.
o o o
O 0
s.
s.
Sept. 28 P.M.
38 33
8.
S.
3.
{Ih 1
1.76
+
„ 34 A.M.
•182.4
3.19
179.21
^8 2
83 1
^83.S5J
84. ij
1.76
>1.76
5.10
+ 0.11
86226.00
„ 24 P.M.
35 30.6
[81.71
} >83.051
[84. 4j
1.76
„ 25 A.M.
■183
3.19
179.81
>83.32
[84 1 1
^83.6 j
83. 2j
1.76
,1.76
5.10
+ 0.15
86225.44
„ 25 P.M.
32 27.6
[81.7]
1.76
i !>82.85l
[84 J
„ 26 A.M.
. 9 15 00.
■182.2
3.19
179.01
[83.6]
< >83.35J
■83.1
1.76
• 1.763
5.12
+ 0.05
86226.16
[83. l)
„ 26 P.M.
29 25.4
[81.91
< >82.7 1
1.77^
[83. 5j
., 27 .M.
■182.2
3.19
179.01
>82.8
r83.5] 1
|82.3]
1.76
■1.76
5.10
-0.08
86226.01
„ 27 P.M.
26 23.2
1.75
[81.3]
< f82.05
[82.8]
„ 28 A.M.
■182.4
3.19
179.21
\"-'y,
•82.58
1.75
.1.75
5.04
-0.18
86225.65
[83. 8j
„ 28 P.M.
23 20.8
1.75
1 MEANS
179.25
82.98
1 . T.W
5.09
86225.85
1
256
EXPERIMENTS FOR DETERMINING THE VARIATION
Trinidad. VIBRATIONS of PENDULUM No. 2, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.9 4 Inches.
DATE.
Chrono-
meter.
Pendulum
Clock.
Clock's
loss OD
Chron.
DAILY RATES.
Chron. Clock.
Teniperaluve.
Arc of
Vibration.
Correc-
tion for
the Arc.
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
82».82.
1822.
Sep. 29 P.M.
„ SO A.M.
„ 30 P.M.
Oct. 1 A.M.
„ 1 P.M.
,, 2 A.M.
„ 2 P.M.
„ .S A.M.
,, S P.M.
,. 4 A,M.
„ 4 P.M.
„ 5 A.M.
„ 5 P.M.
„ 6 A.M.
„ 6 P.M.
„ 7 A.M.
„ 7 P.M.
„ 8 A.M.
„ 8 P.M.
Vi 30 00<
M. S.
32 27.3
31 14.7
30 02.1
28 49.4
27 36.4
26 24.5
25 12.6
24 00.6
22 48.7
21 36.7
>72.6
72.6
U2.7
^73
171.9
71.9
L72
71.9
72
Gaining.
3.19
3.19
3.19
3.19
2.8
2.8
2.8
2.8
2.8
Losing.
69.41
3.41
69.51
69.81
69.1
69.1
69.2
69.1
69.2
o o
82.8
[83.6
('83.8
[82.5
-84.4|
82. 9 J
'84.41
82
83.2
83.15
^83. 65
>83.2
o o
1.72,
1.72>1.72
1.72
81. 6J
82. 3|
83. 7J
[82.7]
81.8]
'82.8]
81.9
■82.25
>82.35
82
■1,
81.8
81.3
1.74
1.75
1.76
1.77;
1.77
1.77'
1.77
1.77
1.77
1.77"
M.737
1.76
1.77
1.77
1.77
1.77
1.77
1.77
1 . 77'
1.77
1.77'
M.77
>1.77
M.77
+
4.86
4.96
5.10
5.16
5.16
5.16
5.16
5.16
5.16
•1-0.17
-1-0. 15
+ 0.36
■1-0.17
-1-0.08
-0.25
-0.21
-0.44
86335.62
863.35.70
86335.95
86335.52
86336.06
86336.14
863.35.71
86335.85
86335.52
MEANS
69.32 82.82
1.76
5.10
86335.79
IN THE LENGTH OF THE SECONDS PENDULUM.
257
JAMAICA.
The pendulum clock was set up at Port Royal in a room adjoining the
one in which the experiments with the detached pendulums were made;
it was on the same level, but had the advantage of a brick floor ; the
windows were darkened, and the room entered only for the purposes of
comparison and registry.
The rate of the Chronometer No. 423 from the 22d to the 30th of
October is taken from page 109 ; from the 30th of October to the 5th of
November the rate is deduced from the Zenith Distances on the morning
of the 30th in page 108, and those which are subjoined observed on the
morning of the 5th of November.
Jamaica. OBSERVATIONS to DETERMINE the RATE of the Chrouometer No. 423, hy ZENITH
DISTANCES of the Sun, observed with a Repeating Circle.— Latitude 17° 55' 55" N.
November 5lh A.M. ; Barometer 30 . 00 ; Tliermometer 81°; Q'sL.L.
Ctiiononiettr.
II. H. S.
0 28 49.6
0 31 06
0 32 36.4
0 33 59.2
0 35 46.4
0 37 06.8
Level.
-5
0
0
0
+ 2
-1
0
0
0
+ 3
-2
Mean. . .
0 33 14.07
7 22 30.47
-4
-5
True time .
-4.3
Chron. fast
5 10 43.6
m^^
Readings, &c.
First Vernier
Second „
Third „
Fourth „
34 23 10
25 10
23 40
25 00
360-.S17 44 19 = 42 15 41
Mean . . .
S»
25
15
Index . . +
Level . . .
360
42
00
15
00
41
-5
136
40
51
Observed Z.D.
72
46
49
Ref. and Paral
-f2
48
Semidiam . .
-
16
10
True Z.D. .
72 33 27
Chronometer.
H. M. S.
1 05 52.4
1 07 02.8
1 08 38.4
I 09 48.4
1 11 15.2
1 12 16
Mean . . .
True time .
1 09 08.87
7 38 25.8
Chron. fast 5 10 43.07
+ 3
+ 5
-5
+ 4
0
+ 4
+n
-12
+4
-4
+ 3
0
+ 3
+ 8
+9.5
360-316 13 32 = 43 46 28
Headings, &c.
First Vernier
Second „
Third „
Fourth ,,
346 45 50
45 30
46 00
45 40
Mean . . .
316
45
45
Index . . .
43
46
28
Level . . .
+ 9
390
32
22
Observed Z.D
65 OS
24
Ref. and Para!
. +
1
50
Semidiam .
-
16
10
True Z.D.
64 51 04
H. M. S.
Chronometer, Fast -jj jg 4307/ ^ '" '*^-^'
H. M. S.
October 30th A.M. Chronometer Fast 5 10 23.83
November 5th .4.M. Chronometer Fast 5 10 43.33
Chronometer's Gain in 6 Days
19.5 = 3.25 seconds per Diem.
2 L
258
EXPERIMENTS FOR DETERMINING THE VARIATION
Tamaipa vibrations of PENDUI TIM No 1 in
the PENDULUM CLOCK.
Inches.
Mean Height of the Barometer ^9.96
DATE.
Chrono-
meter.
Pendulum
Clock.
Clock's
loss on
Chron.
Daily rates.
Temperatme.
Arc of
Vibration.
Correc-
tion for
the Arc,
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
80°.%.
Cliron.
Clock.
1822.
H. M. S.
H. s.
s.
Gaining.
Losing.
0 c
c c
S.
s.
Oct. 22 A.M.
20 21.4
s.
s.
79
■80.25
81.5)
1.74
+
„ 22 P.M.
•164.8
4.14
160.66
> 1.735
4.98
-0.31
86244.01
„ 23 A.M.
17 36.6 <
81.3
1 . 7.V
„ 23 P.M.
■165
4.14
160.86
>80.3
[79. 3]
>1.725
4.92
-0.29
86243.77
„ 24 A.M.
14 51.6
'"si.sl
1.72-
„ 24 P.M.
. 1 50 00 ■
■165.1
4.14
160.96
< U0.8
[79.8]
>1.725
4.92
-0.07
86243.89
„ 2.5 A.M.
12 06.5
[80.2J
[82.6]
1.7,3-
„ 25 P.M.
.164.7
4.14
160.56
. .
■1.72
4.89
-HO. 19
86244.52
„ 26 A.M.
09 21.8
[83.6
1.71-
„ 26 P.M.
.165.8
4.14
161.66
<^ U2.O5
[so. 5
1.72
4.89
■f 0.48
86243.71
„ 27 A.M.
or, 36
1.73
MITiN.S
160.94
80.96
1 . 72.^
4.92
86243.98
IN THE LENGTH OV THE SECONDS PENDULUM.
259
Jamaica. VIBRATIONS of PENDULUM No. 2, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.96 Inches.
Chrono-
meter.
Pendulum
Clock.
Clock's
loss on
Chron.
DAILY RATES.
Chron. Clock
Temperature.
Arc of
Vibration.
Correc-
tion for
tlie Ac.
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
82''.28.
1822.
Oct. 28 A.M.
„ 28 P.M.
„ 29 A.M.
„ 29 P.M.
., 30 A.M.
„ 30 P.M.
„ 31 A.M.
„ 31 P.M.
Nov. 1 A.M.
„ 1 P.M.
„ 2 A.M.
„ 2 P.M.
„ 3 A.M.
„ 3 P.M.
„ 4 A.M.
„ 4 P.M.
„ 5 A.M.
> 6 00 00-^
M. s.
57 14. G
56 19
55 24.3
54 29.8
53 35.3
52 40.8
51 46.3
50 51.8
55.6
54.7
54.5
«4.5
^34.5
54.5
54.5
54.6
49 S7.2
Gaining.
4.14
4.14
3.25
3.25
3.25
3.25
3.25
3.25
Losing.
51.46
51.56
51.25
51.25
51.25
51.25
51.25
51.35
o o
80.5
83.7^
81. 6j
i
[83.8]
80. 8|
83. sj
81 1
83. 4|
82.1
82.7
>82.S
^82.2
0 o
1.70
1.705
1.71
1.72
1.71
M.715
1.715
1.71
r
^82.4
1.71
.. M.71
83. 4|
n
'83.51
80.9
^82.3
^82.2
1.71
.71'
1.71
U2.05
83.7
1.71
1.71
,1.71
1.71
4.80
4.86
4.86
4.83
4.83
4.83
4.83
4.83
-0.08
-HO. 18
-HO. 01
-0.04
-1-0.05
H-0.01
-0.04
-0.10
86353.26
86333.48
86353.64
86353.56
86353.65
86353.61
86353.56
86353.40
MEANS
51.31
82.28
1.71
4.83
86353.32
2 L 2
260
EXPERIMENTS FOR DETERMINING THE VARIATION
NEW YORK.
The experiments with the pendulum clock at Columbia College were
made in a room adjoining the library of the college, in the story beneath
the detached pendulums : the height above the sea was 53 feet.
The rate of the Chronometer No. 423 from the 22d of December to the
3d of January is taken from the observations of which the results are
collected in page 127; the rate from the 16th of December to the 22d was
obtained by Zenith Distances of the sun, west of the meridian, on the 16th
(which are subjoined,) compared with the corresponding observations on
the 22d, detailed in page 121.
New York. OBSERVATIOJNS to DETERMINE the RATE of the Chronometer No. 423, by ZENITH
DISTANCES of the Sun, West of the Meridian.— Latitude 40° 42' 4.3" N. Longitude 74" 03'.5 W.
December Ifith P.M.; Barometer 3
3.00; Thermometer 32° ; O'sU.L.
Chronometer.
>Level.
Readings, &c.
Chronometer.
Level.
Readings, Sec.
H. M. S.
7 59 29.6
8 00 53.6
8 02 35.2
8 03 51.4
8 05 51.8
8 08 00.8
0
+8
0
0
+8
-0
0
-2
0
0
+ 1
0
o * .*
First Vernier 281 33 20
Second „ 33 15
Third „ 33 50
Fourth „ 33 20
H, H. S.
8 12 38
8 14 05.2
8 15 44.8
8 17 15.6
8 20 05.6
8 21 48.4
-8
-2
-2
+ 9
-3
-3
0
+7
-11
+ 1
-12
+ 6
o / ,/
First Vernier 34 00 00
Second „ 33 59 40
Third „ 34 00 00
Fourth ,, 33 59 40
Mean ... 281 33 26
Index . . . + 180 13 00
Level . . . +03
Mean ... 33 51) 50
Index . . +{- 00 00
Level . . -09
Mean . . 8 03 28.07
True time . 3 02 19.4
+ 17-11
Mean . 8 16 56.27
True time . 3 15 48.23
-41
+23
+ 3
461 46 29
-9
472 26 IS
Chron.fast 5 01 08.61
Chron. fast 5 01 08.04
Observed Z.D. 76 57 45
Ref. and Paral. +4 08
Semidiam . . +16 17
ObservedZ.D. 78 44 22.5
Ref. and Para]. +4 48
Semidiam . . +16 17
360-179 47 00=180
13 00
360-281 33 26 = 7°8 2
6 s'l
TrueZ.D. . . 77 18 10
TrueZ.D. . . 79 05 27
H. M.
Chronometer Fast j'J °\
»"■"'-■-
December 16th P.M. Chronometer Fast .
December 22d P.M. Chronometer Fast .
11. M. S.
5 01 08.34
5 01 01.65
Chronometer's Loss
in 6 Days ... 6.6'
) = 1
. 12 seconds per Diem.
IN THE LENGTH OF THE SECONDS' PENDULUM.
261
The intervals at which the clock was compared, and the arc and tem-
perature registered, were of twenty -four hours duration instead of twelve,
in consequence of ray residence at New York being at some distance
from the College.
New York. VIBRATIONS of PENDULUM No. 1,
in the PENDULUM CLOCK.
Mean Height of the Barometer 30.20 Inches.
CLrono-
Pt-ndnlum
Clock's
DAILY RATES.
Arc of
Correc
Reduc-
\'ibralions
DATE.
loss on
Temperature.
tion for
tion to a
Mean
Temp.
per Diem at
nieter.
Clock.
Cbron.
Chron.
Clock.
Vibration.
the Arc
3;°.95.
1 822.
H. M. S.
M. s.
s.
Losing.
Losing,
« o
0 0
S.
s.
Dec, 16 A.M.
09 14.4
1.73
]
S.
S
[37.4]
1
11.73
+
(■68.4
1.12
69.52
<^ ^38.4
4.93
+ 0.20
86335.61
[39. 4j
1.731
„ 17 A.M.
08 06
[-68.7
J
[38 1
1
1.12
69.82 i<i J-38.85
j.1.73
4.93
-f 0.40
86335.51
[39. 7j
„ 18 A.M.
06 57.3
1.73-'
1
{■69. 3
J
[39.7]
il.73
1.12
70.42
"
4.93
+ 1.34
8C335.85
142. SJ
j
„ 19 A.M.
05 48
1.73^
[.71.4
[41.9]
1
[•1.725
1.12
72.52
U2.75
4.91
+ 2.11
86331.50
143. 6j
„ 20 A.M.
04 36.6
1
1
|41.2l
(-42. 45
I43.7J
1.72^
1
j
>71.4
1
1.12
72.52
.1.72
4.88
+ 1.98
86334.34
„ 21 A.M.
03 25.2
J
.69.6
[12.8]
1.72^
1
■ 7 10 00<
1.12
70.72
tl.S
>1.715
4.86
+ 1.47
86335.61
i.39.8j
„ 22 A.M.
02 15.6
J
[.68.6
[42 1
1.71;
2.C2
71.22
< ^39.6
1-1.70
4.77
+ 0.75
86334.30
[37.2]
\.GS>
„ 23 A.M.
01 07
J
Us. 8
[36.2]
)
2.62
68.42
I3. h
[•1.685
4.68
-1.91
863.34.35
„ 21 A.M.
00 01.2
J
1.68J
1-65.7
[31.2]
1
2.62
68. S2
i ^33. 7
[■1.68
4.64
-1.87
86334.45
136. 2j
„ 25 A.M.
58 55.5
1.68-'
1
[31.41
)
2.62
67.62
i ^33.05
[34. 7|
li.es
4.64
-2.16
86334.86
,, 26 A.M.
57 50.5
[.64.3
[31 1
1.68^
2.62
66.92
l34.4r-^
I1.68
4.64
-2.31
86335.41
„ 27 A.M.
56 46.2
J
1.68^
MEANS . . . . ,
69.82
37.95
1.707
4.80
86334.98
262
EXPERIMENTS FOR DETERMINING THE VARIATION
IVfw VnRK VTRTi ATTHIVS nf PPlVnTTl TTM IVn 9 in tliP PF.NnTTT.TTM TT-OrK.
iXliW I UXVK.. V
Mean Height of the Barometer 30.26 Inches.
DATE.
Chrono-
meter.
Pendulam
Clock.
Clock's
gaiaon
Cliton.
DAILY BATES.
Temperature.
Arc of
VibratioD.
Correc-
tion for
the Arc.
Rednc-
tiuD to a
Mean
Temp.
Vibrations
per Diem at
33°.88.
Chron.
Clock.
1822.
H. H. S.
M. S.
Lo«ing.
Gaining.
o o
0 0
s.
S.
Dec. 28 A.M.
42 50.5
S.
S.
S.
31.2
1.68
+
„ 28 P.M.
• 46
2.62
43.38
>32.05
34.7
. .
1.68
4.65
-0.41
86447.62
„ 29 A.M.
43 36.5
32 1
1.68
„ 29 P.M.
•44.9
2.62
42.28
f32.75
.3.S.5J
1.68
4.65
-0.50
86446.43
„ 30 A.M.
44 21.4
35.3
1.68
„ 30 P.M.
•45.6
2.62
42.98
i >32.S
[29.8
>\.G8
4.65
-0.69
86446.94
„ 31 A.M.
45.07
1.68,
[33.4]
„ 31 P.M.
■7 10 00'
....
•45.7
2.62
43.08
< U1.6
•1.69
4.71
-1.00
86446.79
1823.
[29.8
Jan. 1 A.M.
45 52.7
rs6
< Us. 5
,31 J
1.70
„ 1 P.M.
•45.3
2.62
42.68
.1.70
4.77
-0.15
86447.30
„ 2 A.M.
46 38
J
''37.3
1.70
„ 2 P.M.
■43.2
2.62
40.58
J ls6
[31.7
•1.70
4.77
-t-o.g.-J
86446.28
„ 3 A.M.
47 21.2
1.70
[36.8]
„ 3 P.M.
Us. 6
2.62
40.98
\ 138.05
39.3
•1.09
4.71
-hi. 81
86447.53
„ 4 A.M.
. 48 04.8
1.68
MEANS
42.28
33.88
1 .fifl
4.70
86446.98
IN THE LENGTH OF THE SECONDS' PENDULUM.
263
HAMMERFEST.
The framed house constructed for the pendulums at the Northern Stations,
and conveyed in the Griper, was of sufficient size to contain the pendu-
lum clock as well as the detached pendulums, and to permit them to be
set up at the same time without the interference of any part of their respec-
tive apparatus. The pendulum clock stood on the same side of the house
as the astronomical clock, and the triangular frame by which it was sup-
ported rested on the ground or rock beneath the flooring of the room.
The comparisons and registry were repeated at intervals of twelve hours
as usual. The Rate of the Chronometer No. 649, with which the clock
was compared, is taken from the observations of which the results are
collected in page 144.
HAMMERFEST. VIBRATIONS of PENDULUM No. 1, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.93 Inches.
Chrono-
meter.
Peiiduliim
Clock.
Clock's ^ain
on Chroii.
DAILY RATES.
Cliriin. Clock.
Temperalure.
Arc otf
Vibration.
Correc-
tion for
the Arc.
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
51^.9.
1822.
June 9 A.M.
„ 9 P.M.
„ 10 A.M.
„ 10 P.M.
„ II A.M.
„ 11 P.M.
„ 12 A.M.
„ 12 P.M.
„ 13 A.M.
„ 13 P.M.
,, 14 A.M.
8 55 00 <
M. S.
41 36
41 50.2
42 03.7
42 15.7
42 29
42 42.6
42 55.8
43 07.3
43 21
43 34.8
43 49
}14
}13
|,2
}.3.
}13.
},3.
},1.
}.3.
.5
27.7
■25.3
>2e.8
25.2
}13.81
I14.2I
Gaining,
1.43
1.43
1.43
1.43
1.43
Gaining.
29.13
26.73
28.23
26.63
29.43
/'♦'•'MR 7
151. 7/-*'^-'
:}51.7
{r.h-
41
51
153
1,50
[53
\59
56
47
;i7
151.
/SI
154.
rei.
1 53.
f53.
148.
f49
\52.
r50.
147.
2
2
^}56.45
■51.2
52.7
57.4
49.2
54 , 35
51.95
>51.l
}50.6 1
•' j>49.92
49. 25 J
1.67
1.68>1.687
,.„!
1.70M.70
1.69
1
1.67 >1. 68
i.osj
1.68>l-677
1.67
1.66'>l.r67
1.67-'
+
4.68
4.76
4.64
4.62
4.56
MEANS
28.03
51.9
1 .r,si!
4.60
■1.18
+ l.O-S
-HO. 97
-0.88
86432. P3
86432.57
•S6432.S7
864S2.22
86438.11
86432.68
264
EXPERIMENTS FOR DETERMINING THE VARIATION
HaMI"'='°^^<"^ VTRBATiniV.« «f PI7TVrr»TTT TTM 1V« Q ii i\,a PFlVnTTTTTM Ol OCK
Mean Height of the Barometer 29.70 Inches.
Chrono-
PeDdulnm
CIock*.s gain
DAILY R.tTES.
Arc of
Correc
- Reduc-
Vibrations
DATE.
TpmnfrntDrp
linn tnr
tion to a
per Diem at
43°.
meter.
Clock.
on Chron.
CbroD.
Clock.
.& CII) LICi atu J C«
Vibration.
the Arc
Mean
Temp.
1823.
H. M. S.
N. S.
s. s.
Gaining.
Gaining.
0 00
0 0
s.
s.
June 14 P.M.
r 25 49.4
1.67
1
S.
S.
[56.11
+
|>68.4,
ll38.S
< >52.55i
149 j
bo. 12
f49 1 1
< >47.7 J
1
„ 15 A.M.
26 57.8
1.38
139.68
1.62
■1.59
4.16
■1-3.13 ^ 86546.97
■69. 9I
[46. 4j
,. 15 P.M.
28 07.7
f48 1
< >46 ,
144 J
[48 1 1
< >16.6 J
1.48
•70. 3j
„ 16 A.M.
29 18
>140.5
■70. 2^
1.38
141.88
1.64
.1.69
4.16
■f-1.45
86547.49
1
i45.2j
„ 16 P.M.
30 28.2
.71.61
f45.2l
< > 14 1
142. 8j
^43.88
r42.5l
< >43.75-'
1.64
1
„ n A.M.
31 39.8
< M42.4
1.38
143.78
1.44
1.54
3.88
-HO. 39
86548.05
1
■70. 8^
„ 17 P.M.
32 50.6
.72.7,
1 iO J
[42.51
< >40.9 1
l39.3j 1
1.53
„ 18 A.M.
34 03.3
M43.9
.71.2'
1.38
145 28
>39.95
[39.3;
< >39 ■"
i.38.7j
1.4
■1.48
3.60
-1.34
86547:54
„ 18 P.M.
>8 55 00'
33 14.5
<
1.52'
■71. K
[38.61
1
< >39.1 1
[39. 6j
•39.93
[39.6]
< .•lO.S >
., 19 A.M.
36 25.6
< M41.3
1.38
112.68
1.67-.1.6S
J
1.31
-1.3J
8C5l5.fi8
1
■70.2
-12 J
„ 19 P.M.
37 35.8
1.70
'.n 1
■70 .
< >41.25i
41. 5j
„ 20 A.M.
38 45.8
M39.8
■69. SJ
1.38
141.18
[12 1
< >41 -'
i I'J j
1.69
1.69
4.70
-0.83
86315.05;
,. 20 P.M.
3J 55.6
<
(M.S'.
< >33.05i
L37.8J
!.67:
,. 21 A.M.
41 06.8
H41.1
U9.9.'
1.38
112.48
^ k39.2
r38.5l
<■ >39.35J
[40.2]
1.63
1.67
4.58
-1.67
86545.39
„ 21 P.M.
42 16.7
J
1.70 1
1
f39.3i
r™ 1
J >l0.55i
[41. 8j
., 22 A.M.
43 26.7
M39.8
■69. S-'
1.38
141.18
ks.e
[41.81
< >46.65J
i.51.5j
1.71
1.72^
1.71
4.83
■(■0-26
86546.27
„ 22 P.M.
44 36.5
MEANS
142.27
43
1.61
4.28
86546.55
IN THE LENGTH OF THE SECONDS' PENDULUM.
265
SPITZBERGEN.
At Spitzbergen the pendulum clock was compared directly with the
astronomical clock, at precise intervals of twelve hours of mean solar time
as shewn by the Chronometer No. 649. The rate of the astronomical
clock is taken from the transits and zenith distances, of which the results
are collected in page 155.
Spitzbergen. VIBRATIONS of PENDULUM No. l, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.90 Inches.
DATE.
Chrono-
Astronomical
Pcndalam
Pend.
Clock's
DAILY RATES.
Teraperatare,
Arc of
Correc- Reduc-
linn for ''"" " "
Yibr;ttion8
per Diem at
Hon tor
meter.
Clock.
Clock.
loss on
Astr. CI.
istr. CI.
Pend. CI.
Vibration.
he Arc.
Temp.
44''.07.
182S.
H. M. s.
H. M. s.
M. 5.
Gaining.
Gaining.
0 0 0
0 0
s.
s.
July 7 P.M.
2 52 43.8
35 24.fi
1.69^
8.
S.
S.
[48.21
.)-
< >46 1
1
[43. 8j
„ 8 A.M.
. 36.1
88.02
51.92
^45. 35
1.68
1.68
4.65
+ 0.56
86457.13
[43.8
< >44.7 >
i45.6j
,. 8 P.M.
2 54 09.8
3C 14.5
1.67
[47.61
l41.4l"-M
„ 9 A.M.
. 35.2
88.25
53.03
140.81 \''-'
<! >42.1 '
1.68
1.677
4.63
-0.34
86457.32
143. 4j
„ 9 P.M.
2 55 38.5
37 08
r43.4l
145.71 r-"
1.68
.. 10 A.M.
....
. 36.1
88.23
52.13
1.69
•1.69
4.71
+ 0.20
86457.04
<! .>43.7 J
[41. 7j
„ 10 P.M.
■3 00 00-
2 57 05.6
37 59
r45.71
< >4T.l 1
^''■'^ 47.65
1.70-
,, 11 A.M.
. 37.5
88.7
51.20
1.69
•1.697
4.75
+ 1.57
86457.52
r^-^l48.2 J
[50. 7 j
„ UP.M.
2 58 31.8
38 47.7
■
[51 1
■i >46.65i
142. 3j
M4.55
f41.41
.! >42.45-'
1.70
„ 12 A.M.
. 36.5
88.68
52.18
1.68
•1.69
4.71
+ 0.21
864,57.10
[43. 5j
,, 12 P.M.
3 00 00.2
39 39. G
|-'''-'l40.8.
1.69
„ 13 A.M.
I 34 188.73
54.73
f-'' I39.O5
1.67
•1.C8
4.65
-2.21
86457.17
[36.51
<! ^37.3 >
138.1 J
„ 13 P.M.
J
3 01 29.6
40 35
1.68'
MRAIVS
52.53
44.07
1.686
4.69
864.57.21
a M
266
EXPERIMENTS FOR DETERMINING THE VARIATION
Spitzbergen. vibrations of PENDULUM No. 2, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.80 Inches.
Chrono-
Astronomical
Pendulum
Fend.
Clock's
gain on
Aslr.CI
DAILY RATIOS.
Arc of
Correc
Reduc-
Vibrations
DATE.
meter.
Clock.
Clock.
Tpninpratnrp
Vibration.
tion fo
tlie Arc
tion ton
Mean
. Temp.
per Diem at
35°.63.
Astr. CI
. Pend.Cl
— A ciu ^^laiui ^.
1823.
H. M. S.
H. M. s.
M. s.
8.
Gaining
Gaining.
00 0
0 0
s.
July U P.M.
3 02 58
3t 20.6
[36.51
<^ 1.35.251
[34 ]
1.68
S.
S.
•1.677
+
„ 15 A.M.
U7.8
88.65
166.45
K34.48 1 1.67
4. 63
-1.39
86569.69
[.34 1
\ [33.7 J
[33. 4j
„ 15 P.M
3 04 26
37 06.4
J Us. 3 1
I32.6J
1.67
16 A.M.
..,
.78.4
88.64
167.04
>33.6
f32.6l
} ^33.9 J
[35. 2J
1.67
■1.673
4.61
-1.77
86569.88
„ 18 P.M.
3 05 56.9
39 55.7
[35.2
J, i>36.2 1
37. 2J
1.68
J
„ 17 A.M.
.77
88.65
165.65
[37.4
< ?38 J
[38. 6j
1.69
■1.687
4.69
-0.23
86570.11
„ 17 P.M.
3 07 26.6
42 42.4
f38 1
{ ^37.35
[,36. 7 1
1.69
„ 18 A.M.
• 3 00 00 •
.76.9
88.70
165.6
>37.4
[36.3"!
i >37.45J
1.69
■1.69
4.71
-0.11
86570.20
[38.6]
„ 18 P.M.
3 08 56.7
45 29.4
[38.6]
Ur 1
1.69
„ 19 A.M.
.75.9
88.70
164.6
>S8.95
1.69
>1.69
4.71
+ 0.5S
86569.89
■.37.4]
^39.9 J
42 J
„ 19 P.M.
3 10 27
48 15.6
\ MO. 751
[39. 5j
1.69
„ 20 A.M.
.75.1
88.70
163.8
f-40.75
[39.51
40.75
I42 J
1.69
1.69
4.71
+ 1.37
86569.88
„ 20 P.M.
3 11 56.8
51 00.5
42.6]
U1.6
40. ej
1.69-
„ 21 A.M.
■ • ■
>75
88.70
163.7
Ml. 12
^40 1
1.69
1.C9
4.71
+ 1.54
86569.95
U0.65J
l41.3j
„ 21 P.M.
3 13 26.3
53 45
1.69
MEANS
165.29 37.63
1.686
4.68
86569.97
IN THE LENGTH OF THE SECONDS PENDULUM.
267
GREENLAND.
The pendulum clock was set up in the pendulum house at Greenland, as
at the two preceding stations.
The rate of the Chronometer No. 423, with which the clock was com-
pared, is taken from the transits of which the results are collected in
page 167.
Greenland. VIBRATIONS of PENDULUM No, l, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.90 Inches.
DATE.
Chrono-
Pendulnm
Clock's
DAILY RATES.
Temperature.
Arc of
Correc
Redne- Vibrations
tion to a „ ri-
gain on
tioD for
vr«,« P^"^ Diem at
meter.
Clock.
Cbron.
ChroD.
Clock.
Vibration.
the Arc
jnean
Temp.
37°.7.
1823.
H. M. s.
H. M. s.
1
Gaining.
1
GAining.
O 0 0
0 0
s.
s.
Aug. 26 P.M.
8 53 43.9
S.
9.
S.
1.68
+
[45.11
i ^38.9 1
[S2.7J
„ 27 A.M.
8 54 02.4
1- 37.7
7.72
45.42
(■.38.3
[32.7]
1.68
■1.68
4.65
+ 0.26
86450.33
\ [37. 7 J
[42.7]
„ 27 P.M.
8 54 21.6
j
[42.3'
< >38.15l
[34 J
1.68
„ 28 A.M.
8 54 40.6
• 37.6
7.21
44.81
>38.45
f43.5]
< ^38.75J
1.66
.1.667
4.57
+ 0.33
86449.71
(34 j
„ 28 P.M.
•9 05 00-
8 54 59.2
< >37.9 1
1.66
I43.1J
,, 23 A.M.
8 55 19.6
■ 39.5
6.17 45.67
>3s.n
1.68
.1.673
4.61
+ 0.21
86450.49
f42.2j
< <38.45J
[34.7J
,. 29 P.M.
8 55 38.7
J30.4]
\ >35.5 1
140. 6j
1.68
,. 30 A.M.
8 55 58.7
• 39.7
6.67
46.37
>35.8
[30.6]
^36.1 J
1.68
1.68
4.65
-0.84
86450.18
1
,, 30 P.M.
8 56 18.4
i.es'
MEANS
45.57
37.7
1.67s
4.62
86450.18
2 M 8
268
EXPERIMENTS FOR DETERMINING THE VARIATION
Greenland. VIBRATIONS of PENDULUM No. 2, in the PENDULUM CLOCK.
Mean Height of the Barometer 29.90 Inches.
DATE.
Chrono-
meter.
Pendulum
Clock.
Clock's
gain on
Cbron.
DAILY RATES.
Chrc
Temperature.
Arc of
Vibr.ition.
Correc- Reduc-
,-„ .. lion to a
lion for .,
Mean
the Arc. Temp.
Vibratioos
per Diem at
39".
1823.
Auk. 20 P-M.
„ 21 A.M.
„ 21 P.M.
„ 2S A.M.
„ 22 P.M.
,, 23 A.M.
„ 28 P.M.
„ 24 A.M.
„ 24 P.M.
,, 25 A.M.
„ 25 P.M.
>9 05 00<
H. M. S.
9 42 57.8
9 44 12
9 45 26.4
9 46 40.5
9 47 54.2
9 49 09
9 50 23.4
9 51 37.8
9 52 53.4
9 54 08
9 55 23
M48.6
Gaming.
S.
6.61
M47.8
H49.2
M50
6.34
5.60
Gainiag.
S.
155.21
151.14
1.67
33.1
142. ij
34.6
44.6
36 1
42
41
44.2
34.5
40.5
.37.6 1
39.6
38.6
1.68
;.1.67
39 1
MO. 8
131.80
5.72
,>I49.6
5.96
135.72
42.6
37.
>39.42
155.56
36. 6|
46.1
f34
37 4
f37.4
41.6
33 1
37.4
>41.35
35.7
41
35.2
S38.35
1.66
1.66>1.R6
[37.41
I >40.5
l43.6j
\zT.
85
1.66
1.67^1.667
1.67
1.67>1.67
1.67
1.67>1.(;7
1.67
+
4. 51)
1.53
4.57
-0.18
86559.62
■1-0.79
•f 0.19
4.59
4.59
-0.29
-0.51
86559 . 46
86559.36
86560.02
86559.64
MEANS ,
155.08
S9
1.667
4.57
86559.66
IN THE LENGTH OF THE SECONDS* PENDULUM.
269
DRONTHEIM.
At Drontheim the pendulum clock stood in the same room and by the
side of the astronomical clock, with which it was compared at the usual
intervals: both clocks rested independently on the ground beneath the
flooring of the room which was removed for that purpose.
The rate of the astronomical clock is taken from page 177.
Drontheim. VIBRATIONS of PENDULUM No. 2, in the PENDULUM CLOCK.
*
Mean Height of the Barometer 29. S2 Inches.
CbroDO-
Astron.
Pendulum
Peud.Cl.onAat.Cl.
DAILY RATES.
Arc of
Correc
Feduc-
Vibrations
DATE.
tioQ to a
No. 649.
Clock.
Clock.
Slow.
GaiDiDg.
Aalr.Cl
Pend.CI.
Vibration.
EiOD for
the Arc
Mean
Temp.
per Diem at
i',oA.
1823.
H. M. S.
M. s.
M. s.
M. s.
s.
Gaining.
Gaining.
O O O
0
s.
s.
Oct. 13 A.M.
9 49.6
57 23.5
12 26.1
S.
s.
[44 ]
i .„ H5 1
146 J
1.69,
+
„ 19 P.M.
10 12
58 22.9
. . .
■73.5
45.44
118.94
J.45.17
.^41. 71 f
< „ >45..'?5J
146 j
1.691.1.69
4.7]
-0.98
86522.67
„ 20 A.M.
10 34.5
59 21.9
11 12.6
f44.2|
i >45.35i
U6.5J
1.69
., -'0 P.M.
10 56.7
00 21.1
-74
45.45
119.45
^45.35
r44.3
< >45.35^
146. 4j
1.69
•1.69
4.7!
-0.88
86523.28
., 21 A.M.
U 18.7
01 20.3
9 58.6
|44.3l
i >44.85i
145. 4J
U5.57
1.69
,. 21 P.M.
. 7 00 00 •
It -10.7
02 19.5
■74.4
45.45
119.85
1.70
•1.697
4.75
-0.81
8652.^.79
L44.8J
.. 22 A.M.
12 02.8
03 18.6
8 44.2
■
■
r47.8]
150. 8J
1.70
,, 22 P.M.
12 21.2
04 16.2
-71.8
■15.45
117.25
U9.9
rso ] 1
1.69
>1.697
4.75
+ 1.10
86523.10
■; ^50. 5 '
[51 j
., 23 A.M.
12 45.7
05 13.3
7 32.4
1.70
.r50.8!
■; (-51.3
151. 8j
„ 23 P.M.
13 07.5
06 12
■71.6
45.47
117.07
^51
r.50.n
■! >50.7 .1
l5I.3j
1.70
.1.70
4.77
+ 1.58
86523.42
„ 24 A.M.
13 29.6
07 08.8
6 20.8
1.70-i
MEANS
118.51
47.4
1 .6^^*=
4.74
86523.25
i/t/
270
EXPERIMENTS FOR DETERMINING THE VARIATION
nnmvTTHFiM VIRRATTONS nf PFTVDTILTJM No. 1. in the PENr>TTT TIM CI nCV
Ul\\J^ 1 Xl l!i 1. ITI • ▼ XUXVrl X X*_/iS O Ul J lim U*J 3^\J I'X A^u» i) tn mt x iJi
Mean Height of the Barometer 29 . 50 Inches.
DATE.
Cbrouo*
A3tron.
PeDdalum
Pend.;Cl.onA8t. CI.
DAILY
BATES.
Temperature.
Arc of
Correc-
tion lor
Reduc-
tion to a
Vibrations
per Diem at
440.7.
meter.
No. 649.
Clock.
Clock.
Slow.
Loss.
Ast. CI.
Pen. CI.
Vibration.
the Arc.
Mean
Temp.
H. M. S.
M. S.
H. 9.
M. s.
9.
Gaining.
Gaining.
O 0 o
o o
•s
s.
Oct. 25 P.M.
14 34.8
6 23.4
8 11.4
s.
9.
r44.71
148 !''■''
1.73
+
,. 26 A.M.
14 56.9
6 27.2
■37.1
45.49
8.S9
.r48 1 "•"
t5o r^^ J
1.72
■ 1.73
4.93
+ 1.31
86414.63
„ 26 P.M.
15 18.4
6 29.9
8 48.5
[49. 71
1.74
„ 27 A.M.
15 39.9
6 32.1
39.2
45.49
6.29
f51.2l P-'^
!52 ^'•''J
1 . 74
■ 1.74
4.99
■<-2.84
86414.12
.. 27 P.M.
16 00.7
6 33
9 27.7
1
.l"49.61
1.75:
„ 28 A.M.
16 21.1
6 34.7
■37.7
45.49
7.79
149 1 h-''
150 J ■"
1.75
• 1.75
5.05
+ 2.32
86415.16
„ 28 P.M.
16 42.6
6 37. 2
10 05.4
;49.31
i >47.85
1.75^
146. 4j ''
„ 29 A.M.
17 04.5
6 40.5
•37.2
45.58
8.38
148 J J
1.75
• 1.74
4.99
+ 1.20
86414.57
., 29 P.M.
17 25.9
6 43.3
10 42.6
[47. 4l
t42 j"-^
1.72
„ 30 A.M.
•7 00 00.
17 47.6
6 46.9
■35.3
45.59
10.29
r42.2i b'-'
l43.2h^-^ >
1.72
•1.72
4.86
-0.44
86414.71
„ 30 P.M.
18 09.2
6 51.3
11 17.9
.l'42.2! ,
i42.6r^-4 1
1.72^
„ 31 A.M.
18 30.8
6 55.7
35.5
45.58
10.08
141.81 «•'
143.4^^-'' '
1.72
•1.72
4.86
-0.97
86413.97
„ 31 P.M.
18 52.4
6 59
11 53.4
[43.51 1
< >41.5
I.39.5J
1.72
Nov. 1 A.M.
19 14.5
7 03.6
•34
45.59
11.59
{.37. 2l
■5 >38.5
1.72
•1.72
4.86
-2.07
86414.38
1
1.39. 8j ■■
„ 1 P.M.
19 36.5
7 09.1
12 27.4
f36 1
1.72
< '>37.5
139 j
„ 2 A.M.
19 58.6
7 14
•34
45.48
11.48
[39 1 ^''■''
< >40
1.72
!■ 1 72
4.86
-2.64
86413.70
i^" J
„ 2 P.M.
20 20.7
7 19.3
13 01.4
r40.81 ,
4. !''■'
1.72:
„ 3 A.M.
20 41.7
7 23.2
* * •
•34.7
45.48
10.78
r40.41 \''-''
[41. 6j
1.72
i- 1.72
4.86
-1.G5
86413.99
„ 3 P.M.
21 02.6
7 26.5
13 36.1
1.72
MEANS
9.45
44.7
1.729
4.91
864 14.. 36
IN THE LENGTH OF THE SECONDS' PENDULUM,
271
LONDON.
The pendulum clock was set up in Mr. Browne's library in Portland-
place, which is on the same level with the room in which the experiments
with the detached pendulums were made. The rate was obtained by
comparison with Mr. Browne's clock by Gumming.
LON
DON. VIBRATIONS of PENDULUBI No. 1, in the PENDULUM
CLOCK.— Mean Height of the Barometer 29.50 Inches.
Clock's
Rate on
Meau
Arc gf
Baro-
Correc-
Redtictiun
VibratioDs
DATE
Temperature.
tioD for
to a Mean
per Diem at
Solar time.
Vibration.
meter.
the Arc.
Temp.
54°. 1.
1823.
S.
o o
o o
IN.
s.
s.
Febniarj
21
1
f52.81
< > 53.7
154. 6J
..75^
+
> 35.34
j
> 1.745
j
4.98
-0.18
86369.46
>j
22
1
[53.21
1.74
1
> 35.24
< > 54
[54. 8j
> 1.745
j
4.98
-0.04
86369.70
w
23
1
[53 1
1.75-'
1
> 35.44
< i- 54.3
} i.74
4.95
+ 0.09
86369.60
24
J
L55.6J
I.73J
j> 36.04
[53.81
I 1.7S5
• 29.33 .
4.92
+ 0.22
86369.10
J
i.55.4J
j
»>
25
1
[52.41
1.74
1
,> 35.84
i } 53.7
[55 j
j- 1.745
j
4.98
-0.18
86368.96
»»
26
1
[52.41
1.75
> 35.34
J
<! > 53.7
155 J
> 1.745
4.98
-0.18
86369.46
27
1.74
"
1
[51.61
1
(■ 35.24
i !> 5.^.1
154. 6j
V 1.745
J
4.98
-0.44
86369 . 30
»
28
1.75
1824.
January
21
1
[53.21
1.78
1
> 34.4
< > 53.5
[53. 8j
;> 1.78
5.20
-0.26
86370.54
22
1.78
j>
[53 1
1
■> 34.6
i > 53.5
154 j
> 1.775
J
5.17
-0.26
86370.31
23
1.77,
**
[55 1
1
> 35.6
<^ }■ 55.5
[56 J
> 1.77
j
. 29.65 .
5.14
+ 0.62
86370.16
24
1.77
"
rss 1
1
;• 35
< > 54
[55 J
j 1.765
5.11
-0.04
86370.07
»
25
155 1
< S- 55.5
[56 j
1.76
> 35.6
> 1.76
j
5.07
+ 0.62
86370.09
»
26
1.76^
MEANS. .
35.31
54.1
1.754
5.04
86369.75
272
EXPERIMENTS FOR DETERMmiNG THE VARIATION
London. VIBRATIONS of PENDULUM No. 2, in
the PENDULUM CLOCK.
Mean Height of the Barometer 29.53 Inches.
DATE,
Cumniiug.
Peodulum
Clock.
Clock's
gaiaon
Cumm.
DilLT B4TBS.
Temperature*
Arc of
Vibration.
Correc-
tion for
tbeArc.
Reduc-
tion to a
Mean
Temp.
Vibrations
per Diem at
530.9.
Cumm.
Pend.CI.
1823.
H. N. s.
N. s.
s.
Losing.
Gaining.
o o
0 0
s.
s.
Mar. I P.M.
07 42.6
1
1
1.72
9.
S.
52.6]
+
„ 2 A.M.
■75.3
0.24
75.06
Us. 4
54. 2j
>1.72
4.83
-0.21
86479.68
„ 2 P.M.
08 57.9
53.8| .
1.72-^
„ 3 A.M.
•74.3
0.24
74.06
>54.5
55. 2J
► 1.72
4.83
•fO.26
86479.15
„ 3 P.M.
10 12.2
53.4]
1.72:
„ 4 A.M.
•74
0.24
73.76
«4.15
54. 9]
► 1.725
4.86
+ 0.10
86478.62
„ 4 P.M.
11 26.2
53.3]
1.73;
„ 5 A.M.
■74.2
0.24
73.96
«4.6
55. 9J
>1.73
4.89
•fO.31
86479.16
,. S P.M.
12 40.4
■53.8]
1.73
„ 6 A.M.
• 2 00 00 •
■74.3
0.24
71.06
>54 . 5
55. 2J
1.73
4.89
+ 0.26
86479.21
„ 6 P.M.
13 54.7
53.2]
1.73
„ 7 A.M.
■75
0.24
74.76
«3.8
[54. 4J
•1.73
4.89
-0.04
86479.61
„ 7 P.M.
15 09.7
52.8]
1.73
,^ 8 A.M.
■75.5
0.24
75.26
^3.5
[54.2
•1.73
4.89
-0.17
86479.98
„ 8 P.M.
16 25.2
[52.7
1 r^
1.73
„ 9 A.M.
75.3
0.24
75.06
•1.73
4.89
-0.40
86479.55
[53.3
„ 9 P.M.
17 40.5
J
[52.8
1.73
„ 10 A.M.
•75.3
0.24
75.06
i >53.5
[54.2
■1.73
4.89
-0.17
86479.78
„ 10 P.M.
18 55.8
1.73
MEANS
74.56
.oi.g
1.728
4.87
86479.43
IN THE LENGTH OF THE SECONDS' PENDULUM. 273
RESULTS WITH THE ATTACHED PENDULUMS.
The results with the attached pendulums at the several stations are
collected in one view in the subjoined table.
The reduction of the vibrations to a general mean temperature of 62°
in column 7 is in the ratio of 0.44 parts of a vibration per diem for
each degree of Fahrenheit; correspondent to an expansion of the cast
brass of which the pendulums were composed of 0.0220 parts of an inch
per foot in 180 degrees.
In column 8 are inserted the vibrations finally corrected of each
pendulum at the several stations of experiment; and in column 9 the
excess of the vibrations of pendulum No 2 over those of pendulum No 1 ;
whence it appears that supposing the effect of the sustaining force of the
clock to have been the same on both pendulums, the actual difference in
their length was equivalent to 109.97 vibrations per diem ; and that the
greatest deviation from identity, in the ultimate deduction from the separate
results with each pendulum, at any one of the stations, corresponds to a
difference of 0.41 parts of a vibration per diem, and the mean deviation
(omitting the signs) to a difference of 0.17 parts.
The tenth column exhibits a mean between the vibrations of the two
pendulums ; or the rate of an imaginary pendulum supposed to have oscil-
lated in the clock in a vacuum and at an uniform temperature at every
station. These vibrations are consequently the final results of the expe-
riments with attached pendulums; and were the method of experiment
certain, and the execution sufficiently exact, the several lengths of the
seconds' pendulum should be to each other in the duplicate ratio of the
numbers in this column.
The first of these preliminary questions, namely, that which concerns
the sufficiency of the method of experiment, is much the more important
2 N
^4 EXPERIMENTS FOR DETERMINING THE VARIATION
consideration ; it is dependant on the assurance that can be entertained,
that the influence on the rate of the pendulum, of the force applied to sustain
and register its oscillations, has been uniform at every station.
When, in the year 1818, it was determined to take advantage of the
opportunity afforded by the expedition of Northern Discovery then in pre-
paration, to extend the inquiry into the figure of the earth, by means of the
pendulum, into the latitudes of the Arctic Circle, the method of attached
pendulums was chosen as that of procedure, by the committee of the Royal
Society to whom the consideration of the subject was referred ; and the
clock and pendulums which have been now experimented with were pre-
pared under the direction of that committee : my part on that occasion was
to obtain the results which the method thus selected might produce, with
the utmost correctness which the nature of the experiment should permit.
The publication of the experiments made in the voyages of 1818, 1819,
and 1820, revived the objection to the employment of pendulums attached
to clocks in the prosecution of the inquiry, which several years antece-
dently, had induced in France the substitution of free pendulums. The
following summary of the objection may not, perhaps, be deemed an in-
correct statement. It was admitted that no very decisive reason could be
assigned why the action of the weight, transmitted through the wheels,
might not be a constant force ; but it was urged that no sufficient proof
of the affirmative existed ; and that, as, in tlie absence of such proof,
had the compression deduced by the clocks deviated widely from the
result of methods not liable to the objection, or from received opinion,
there would have been no hesitation in attributing the difierence to an
effect of the sustaining force, and in rejecting altogether the results of the
attached pendulums, so, in the existing case, which happened to be that
of near accordance, the results could not be considered as entitled to the
weight of an independant authority, in confirmation of the compression
towards which they approximated.
IN THE LF.NGTIl OK THb; SECONDS' PENDULUM. 275
The question of the invariability, or otherwise, of the sustaining force,
could obviously receive no other than an experimental solution: the
opportunities which my subsequent prosecution of the inquiry with
detached pendulums presented, of exhibiting the acceleration deduced by
pendulums vibrating in clocks, in comparison with that of free pendu-
lums, promised to be sufficiently extensive, to enable a fair practical
decision on a point of considerable interest in the history, and in the
employment of clocks. It was accordingly undertaken, and has been
carried through, in the operations which are now recorded.
There is one indication afforded in the going of a pendulum attached
to a clock, by which an inference may be drawn a priori, and inde-
pendently of the comparison with free pendulums, as to the constancy of
the sustaining force. The resistance of the air to the motion of the
pendulum is the impediment which the action of the clock has to over-
come, and the vibration is therefore maintained in an arc of such dimen-
sion, that the force and the resistance are exactly in equilibrio: the
steadiness of the arc is consequently an evidence of the preservation of
their relative proportion to each other, and its variation, of changes in
the proportion, occasioned by an alteration of either : now the alterations
to which the resistance of the air is liable, are necessarily of very small
amount, and their causes are equally cognizable by other means ; if then
a difference in the arc takes place which exceeds in amount that which
may reasonably be ascribed to the variation of the resistance, or if it
happens when the resistance must be presumed to have been un-
changed, the difference must be regarded as indicating an irregularity in
the sustaining force ; and in like manner, the steadiness of the arc, or
the confinement of its fluctuations within the small limits by which it may
be supposed to have been affected by variations in the resistance, will
indicate a regularity of the sustaining force.
It may be seen by the tables containing the details at the several
2 N 2
276 EXPERIMENTS FOR DETEKMININO THE VARIATION
stations, that the differences in the arc of vibration at the eleven stations,
of which the results are collected in the subjoined table, were compre-
hended between 1°.76 and l°.61 ; those of pendulum No. 1 varying from
1°.76 to r.67, and those of pendulum No. 2 from r.76 to l°.6l * ; and
further, that this small diminution of the arc obtained progressively from
the equatorial to the polar stations. Now, the effect of the increased
velocity of the pendulum, due to the increase in the force of gravity in
proceeding from the equator towards the pole, would be to augment the
resistance of the air, and consequently to contract the arcs ; the increased
density of the atmosphere in the colder latitudes would operate in like
manner to augment the resistance, and would tend still more to contract
the arcs ; to the joint operation of these two causes, modified by the very
effect which they tended to produce, may doubtless be ascribed the small
and apparently systematic variation of the arcs; leaving the inference that
the proper action of the clock was constant throughout the experiments.
The influence which the inconsiderable variation that took place in the
arcs of vibration may have had on the respective rates of the pendulum,
can scarcely be supposed to have been otherwise than very small ; it must,
however, be admitted that no very certain authority can be adduced for
estimating the correction to be applied in compensation of the difference :
there can be little doubt that the effect would vary in dependence
* l°.6'l, in a single case only, i. e., at Hamraerfest; omitting that instance, tlu' lowest arc
to which No. 2 was reduced was between 1°.66 and 1°.67. The irregularity at Hammerfest
was occasioned by one of the legs of the clock-frame having rested on a fragnunt of rock
which had been disunited from the general mass, but remained imbedded in its original
position : part of the foundation of the pendulum-house rested also on this fragment, near
one of its extremities ; and during the violent gales which were experienced, communicated a
slioht tremulous motion to the whole fragment. As soon as the cause of the irregular action
of the clock was discovered, the contact of the house with the slab on which the leg of the
clock rested was relieved, when the arc was immediately restored to its original dimension,
which was subsequently maintained. To the same cause may be attributed the unusual
discordances of the partial results with pendulum 2 at Hammerfest.
IN THE LENGTH OF THE SECONDS* PENDULUM. 277
on the causes by which the difference in the arcs might be occasioned ;
and that the same causes would produce diiFerent effects in different
clocks, according to the mode in which the action of the sustaining force
is applied to the pendulum ; or in other words, according to the nature
of the escapement.
The corrections for the arc which have been applied in the tables to
the rates of the attached pendulums at each station, and which have had
for their object the reduction to the supposed corresponding rates in arcs
infinitely small, have been in all cases those which would be due to the
difference between the vibration in a circular and in a cycloidal arc of
the same dimension as the observed arcs. This correction for an arc
of 1.76, is + 5.10, and for 1.66 + 4.53; the uncertainty which affects
the results of these experiments, is only as to the value of the difference
between these corrections, namely, whether the quantity 0.57 should be
more or less. Were it of consequence to pursue the investigation, it
might possibly be shewn from the detail of the clocks going, that if
the quantity 0.57 is erroneous, it is probably so in defect, that the
retardation increased in the larger arcs in a ratio somewhat greater than
the difference between the vibration in circular and cycloidal arcs ; but
the quantity is altogether so small, that the evidence of probability could
not be very satisfactory.
Before the comparison of the results with those of the detached pen-
dulums is proceeded in, it may be proper to notice another source of
inexactness, by which the precision of the former may have been
slightly affected. In the estimated value of the corrections applied to
the rates at the several stations to reduce them to a general mean tem-
perature, errors of small amount may have obtained in two ways ; first,
in the method pursued of registering the temperature, which was not a
strictly comparative one at stations widely differing in climate ; and,
secondly, in the assignment of the equivalents to the effects produced
278 experiments' for determining the variation
on the rates by differences of temperature. The mean of the extremes
taken twice in twenty-four hours, may afford a strict comparative tem-
perature, whilst the observations are confined to adjoining latitudes or
similar climates ; but as a mean so taken does not bear precisely the
same proportion to the true mean temperature in all climates, and
as the observations included a very extensive range, a nearer ap-
proximation by a more frequent registry would have been requisite,
had the utmost attainable accuracy of the method of experiment been
sought ; as at Melville Island for instance, where the temperature in the
clock case was registered every hour for six weeks ; but the object now
sought by the attached pendulums, in relation to the ultimate purpose to
which the acceleration was to be applied, was at the utmost, a general
corroboration of the results obtained with the detached pendulums ; and
as no hope could be entertained that the utmost devotion of time or
attention could have enabled the former method to compete in minute ac-
curacy with the latter, the registry was confined to a sufficient frequency,
to obtain the temperatures at the several stations comparable within
limits, by which the general conclusion might not be affected. The same
consideration influenced the adoption of an expansion of the pendulums
by heat, drawn from the general result obtained by former experimenters
on the expansion of cast brass (of which the pendulums were composed),
instead of an attempt to determine it by special experiment, as was done
in the case of the detached pendulums. The determination, by the rate
of vibration in extreme temperatures would have been much more difficult
of precise accomplishment with pendulums vibrating in clocks ; and if
artificial temperatures had been employed, the conclusion would have
been far less certain in its practical application, than when the results
were unembarrassed by the machinery and action of a clock. Under any
probable supposition, the assumed expansion will not occasion error of
greater amount than one tenth of a vibration per diem.
IN THE LENGTH OF THE SECONDS* PENDULUM. 279
Having premised the causes, occurring in the execution, by which the
precision of the results with the attached pendulums may have been
interfered with, I proceed to their comparison with those of the free pen-
dulums, which is exhibited in the 10th, 1 1th, 12th, 13th, and 14th columns
of the subjoined table.
The 10th column has been already described as presenting a mean
of the vibrations of the two attached pendulums, or the rate of a supposi-
titious pendulum, oscillating in a clock in a vacuum, and at an uniform
temperature, at every station.
The 1 1th column contains the corresponding vibration of a suppositi-
tious detached pendulum, oscillating also in a vacuum, and at an uniform
temperature, brought forward from the 13th column of the table in p. 236.
In column 12 is inserted the excess of the vibrations at each station of
the attached over those of the detached pendulum ; and in column 13 the
mean excess. Had the length of the seconds' pendulum deducible from
the results of the two methods of experiment been everywhere strictly
identical, the values in column 12 would have corresponded in every in-
stance with the mean excess in column 13. The deviations from identity
are inserted in the 14th, or final column.
The deviations are obviously greater on some occasions than can be
ascribed to inaccuracy in the corrections for the arc and temperature :
when all circumstances are duly considered, there can be no hesitation
in believing them to have been occasioned by accidental and temporary
affections of the action of the weight, in its transmission to the pendulum,
through the machinery of the clock.
When the various processes are borne in mind, which the clock under-
went in its removal from station to station, the production of occasional
irregularities in the action of the machinery would seem to be scarcely
avoidable ; and when it is further considered that the account of its going
was usually commenced on the second or third day after it had been set
280 EXPERIMENTS FOR DETERMINING THE VARIATION
up, and concluded before it had gone a fortnight, the small extent of the
limits, within which the amount of the deviations are comprised, will ap-
pear a remarkable testimony of the excellence of the clock.
That the irregularities were occasioned by accidental and temporary
causes, and that the influence of the sustaining force on the rate of the
pendulums underwent no permanent change during the operations, may
be shewn by the usual process of grouping several results into a mean,
whereby the accidental irregularities, with which, what will then become
the partial results were affected, will counteract each other, and cease to
embarrass the comparison. In column 14, the results at the five stations
within 20° on either side of the equator (which were also the first ob-
tained in the order of time), are thus collected into one group ; and
the remaining six stations, between the latitudes of 40° and 80°, into a
second group ; and it is then seen, that although the acceleration at a
single station obtained by attached pendulums, may be in error (inferred
from the comparison with free pendulums) to an amount, in an extreme
case, of two seconds per diem, yet, if the stations of experiment are
sufficiently multiplied, to extinguish, in^an average result, the influence of
the partial irregularities introduced by the machinery of the clock, the
two methods of experiment produce an identical result.
Thus then, the objects designed by the employment of the attached
pendulums appear to have been most satisfactorily effected ; first, as a
method of experimenting upon the figure of the earth, it is seen to be
less exact in single determinations, but equally so, in extensively mul-
tiplied operations, as is the method with detached pendulums ; secondly,
in regard to the authority of the present experiments, the agreement of
two methods, the processes of which are totally distinct, and which have
only in common a reference to the same determination of astronomical
time, can scarcely be deemed less than evidence of proof, of the correct-
ness of the general result in which they agree.
IN THE LENGTH OF THE SECONDS' PENDULUM.
281
RESULTS WITH THE A'lTACHED PENDULUMS.
STATIONS.
=
-c
c
Vibrations.
Baro-
meter.
Therm 0-
meter.
Correc-
tioD for
Buoy-
ancy.
Reduc-
tion to a
Mean
Temp.
Vibrations
in a Vacuum
at 62°.
Escesa in
the Vibr.
of PencJ.2.
Vibr. strictly comparative.
COMPARISON of the METHODS.
Att. Pend.
Det. Pend.
(page 836.)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
IN.
O
S.
s.
1
86218.21
29.93
81.39
5.80
+ 8.53
86232.54
1
Maranham .<
^109.81
86287.44 | 86019.78
167.66
-0.7
2
86328.18
29.92
81.03
5.80
+ 8.37
86342.35
J
f
1
86233.21
30.05
80.05
6.82
-1- 7.94
86246.97
1
Ascension .<
2
86343.09
30.07
79.44
6.85
+ 7.67
86356.61
M09.64
86301.79
86033.11
168.68
-hO.3
f
1
86225.8.5
29.92
82.98 5.77
■f 9.23
86240.85
1
1 109. 88
J
Trinidad . .<^
86295.79
86027.31
168.48
-hO.l
•-^0.04
[
2
se.sss.rg
29.94
82.82
5.78
+ 9.16
86350.73
1
86236.27
29.93
73.27
5.89
•f 4.96
86247.12
]
Bahia ■ ■ A
2
1
86317.07
86243.98
30.00
29.96
71.72
80.96
5.92
5.80
+ 4.28
•f 8.34
86357.27
86258.12
mo. 15
lllO.Il
86302.19
86032.81
169.38
-1-1.0
Jamaica . .<
86313.17
86045.27
167.90
-0.5
2
8635.S.52
29.96
82.28
5.79
+ 8.92
86368.23
f
1
86331.98
30.20
37.95
6.33
-10.58
86330.73
New York J
f
2
1
86416.98
86369.73
30.26
29.50
33.88
54.1
6.50
6.11
-12.37
- 3.48
86441.11
86372.36
[no. 38
1
86385.92
86118.48
167.44
•I 68.4-
-I.O
London . .<
r
2
1
86479.43
86414.36
29.53
29.50
53.9
44.7
6.07
6.15
- 3.46
- 7.61
86482.04
86412.90
U09.68
1
86427.20
86159.79
167.41
-1.0
Drontheim .<
2
1
86523.25
86432.68
29.82
29.93
47.4
51.9
6.2!
6.12
- 6.42
- 4.44
86523.04
86434.46
W10.14
1
86467.97
86198.52
169.45
+ 1.0
!•- 0.04
Hammerfest •;
2
86546.55
29.70
43
6.22
- 8.36
86544 41
M09.95
86489.43
86221.46
167.97
-0.4
Greenland J
1
86450.18
29.90
37.7
6.35
-10.69
86445.84
ll09.97
86500.8!
86230.44
170.37
+ 2.0
2
86559.66
29.90
39
6.27
-10.12
86555.81
J
1
86457.21
29.90
44.07
6.24
- 7.89
86455.56
I1IO.O2
Spitzbergen <
86510.57
86212.93
167.64
-0.8
2
86569.97
29.80
37.63
6.33
-10.72
86565.58
1
2 O
283 EXPERIMENTS FOR DETERMINING THE VARIATION
There is yet a third source from which a corroboration may be adduced
of the general correctness of the results with the detached pendulums ;
and which it may be interesting therefore briefly to examine. It is by
their comparison with the acceleration shewn by the astronomical clock.
The pendulum of this clock was on the principle which is usually termed
the gridiron compensation ; it had the ordinary contrivance for regulating
its length by means of a screw and circular nut at its lower extremity;
the ball of the pendulum rested on the nut, which was divided and figured
round its circular rim, corresponding to fractions of a second of time ; the
vibration was performed on a knife edge, working in a cylindrical groove
ground in agate ; presuming the compensation to have been perfect in
temperatures fifty degrees apart, and the position of the nut unchanged,
this pendulum was strictly invariable in its length.
The exact relation of the rate of this pendulum to the force of gravity at
the several stations may have been affected, first, by irregularities inherent
in the attachment to machinery ; secondly, by defective compensation ; and
thirdly, by variations in the arc of vibration. As no intention was enter-
tained of using the rate of the astronomical clock for any other than its
immediate purpose at each station, no registry was made of the extent of
the arcs : all that can be said of them now therefore is, that they certainly
did not vary to any considerable amount, but that they probably under-
went the small alterations due to the variable resistance of the atmosphere :
and that no correction has been attempted for them.
The length of the pendulum, as dependant on the regulating screw, was
kept the same at all the stations, except at Ascension, where the nut was
accidentally turned, and was not discovered to be so until the clock was in
motion, when it was not deemed of consequence to be rectified; the rate
at Ascension, therefore, is not included in the comparison.
The columns in the subjoined table exhibit respectively, the rate of the
IN THE LENGTH OF THE SECONDS PENDULUM.
283
astronomical clock brought forward from preceding pages ; the corrections
for buoyancy, and the rates corrected ; the comparative vibration of the
detached pendulums from column 13 in the table in page 236 ; the differ-
ences between the clock and the detached pendulums; the mean differ-
ence ; and finally the discordances.
STATIONS.
Vibrations
of the
Ast. Clock.
Correc-
tion for
Buoy-
ancy.
Vibrations
per Diem.
Vibrations
per Diem.
Detached
Pendulums.
Differ-
ence.
Mean
Differ-
ence.
Discordances.
St. Thomas
Maranham .
Sierra Leone
Trinidad .
Bahia . .
Jamaica .
New York
London .
Drontheim
Hammerfest
Greenland
Spitzbergen
86277.23
86266.83
86276.8
86276.1
86283.77
86254.. 5
86367.37
86408.20
86445.46
86468.50
86477.94
86488.55
5.79
5.78
5.75
5.75
5.88
5.78
6.45
6.00
6.16
6.16
6.26
6.27
86283.02
86272.61
86882.55
86281.85
86289.65
86300.28
26373.82
86414.20
86451.62
86474.66
86484.2
86494.82
86029.40
86019.78
86028.14
86027.31
86032 81
86045.27
86118.48
86159.79
86198.52
86221.46
66230.44
86242.93
253.62
252.83
254.41
254.54
256.84
255.01
255. 3J
254.41
253.10
253.20
253.76
251.89
>254.08<
-0.5
-1.3
-(■0.3
■I-0.4
-H2.7
+ 0.91
+ \.2
•f 0.3
-1.0
-0.9
-0.3
-2.2.
> + 0A
-0.5
The evidence, which is afforded by this comparison, of partial irregu-
larities in the rate of pendulums attached to clocks, and of general
agreement with detached pendulums, when the stations are sufficiently
multiplied to reduce the effect of accidental interferences, is very similar
to that furnished by the corresponding table in page 281.
The number of stations required to produce a mean result, in which the
influence of partial irregularities may be neutralized, must depend on the
amount of error which may be liable to occur in an extreme case ; it may
2 O 2
284 EXPERIMENTS FOR DETERMINING THE VARIATION
be inferred from the comparisons that both the average and the extreme
irregularity was about one-fourth or one-fifth greater in the astronomical
than in the pendulum clock, and it might be expected therefore that the
same grouping of stations, which produced a correspondence between the
detached and solid pendulums, would not be sufficient to extinguish alto-
gether the influence of extreme cases in the astronomical clock ; and ac-
cordingly the effects of the discordancies at Bahia and Spitzbergen are not
wholly destroyed by the five stations combined with each, but are still
visible in the means.
In the following table are collected in one view the discordancies of the
results of the detached pendulums at the several stations, 1 st, with those
of the attached solid pendulums ; 2dly, with those of the attached com-
pensated pendulum ; and 3dly, with the mean of the three distinct me-
thods, ascribing to each for the moment an equal weight. The object
of this table will be more fully apprehended when the accidental irregu-
larities in the force of gravity, as evidenced by these experiments, shall
be under consideration ; its purpose is to exhibit the utmost error which
could be attributed to the results with the detached pendulums at each
station, were each of the distinct and separate methods employed of equal
authority * ; and the consequent limit, within which they must be pre-
sumed, on such concurrent testimony, to be exact ; it will be seen in the
sequel that the utmost errors fall far short of the anomalies which will be
manifested in the application of the results, and consequently that it
* It is hardly necessary, but it may be pro])er to state expressly, that it is not intended to
represent the methods as being really equal in authority; on the contrary, the results with
the detached pendulums must be esteemed as far more exact than even the mean of the three
methods. It is hoped that the details of the experiments throughout are sufficiently ample, to
enable every person to form his own estimate of the probability of error in each determination.
IN THE LENGTH OF THE SECONDS PENDULUM.
•285
must be regarded as extremely improbable that the causes of the anoma-
lies should be in the experiments.
The Detached Pendu
lums in
The Detached Pendu
urns in
STATIONS.
excess or defect
by
STATIONS.
excess or defect
by
The Solid
Pendalums.
The Com-
pensated
Pendulum.
The Mean
of the three
Methods.
The Solid
Pendulums.
The Com-
pensated
Pendulum.
The Mejn
of the three
Methods.
St. Thomas .
s.
s.
+ 0.5
+ 0.2
New York .
+ 1.0
-1.2
-0.1
Maranham .
+ 0.7
+ 1.3
+ 0.6
London . .
+ 1.0
-0.3
+ 0.2
Ascension
-0.3
-0.1
Dronthetm .
-I.O
+ 1.0
0.0
Sierra Leone
. . .
-0.3
-0.1
Hammerfest
+ 0.4
+ 0.9
+ 0.4
Trinidad . .
-0.1
-0.4
-0.2
Greenland .
-2.(1
+ 0.3
-0.5
Bahia . . .
-1.0
-2.7
-1.3
Spitzbergen
+ 0.8
+ 2.2
+ 0.9
Jamaica . .
+ 0.5
-0.9
-0.1
The following table, in which the going of the pendulums in their
employment during the Expedition of Discovery in 1819 and 1820, is
compared with their subsequent going at the same or corresponding
stations recorded in this volume, appears of sufficient interest to merit in-
sertion, from its bearing on some points of the preceding discussion.
The particulars in the first nine columns would seem to require no
other explanation, than that the vibrations of the pendulums in 1819 and
1820 are brought forward from the details published in the PMl. Trans.
for 1821 ; two clocks were then employed, in both of which the pen-
dulums were tried, with results of which the means coincided within 0.2
of a vibration per diem ; the vibrations in the clock which was then con-
sidered to deserve a preference, for reasons adduced in the memoir, are
those introduced in the present table ; the weights of the two clocks were
of the same amount.
286 EXPERIMENTS FOR DETERMINING THE VARIATION
It has been noticed that on the return of the pendulums from the north
in 1820, their knife edges were ground afresh, in consequence of injury
which they had received from rust ; it is to that cause that the differ-
ences in column 13 are due, (presuming that as the arcs were equal, the
influence of equal weights on the rate was uniform also) ; the pendulums
appear to have been lengthened by the operation, an amount equivalent
to about eight vibrations per diem ; and No. 2 rather less than No. 1.
The small correction for ellipticity in column 11, is the difference of
vibration between the latitudes of Melville Island and Greenland, which
would be occasioned by an ellipticity of -a-iT^h ; it is introduced for the
purpose of comparing the acceleration between London and Melville
Island, with that between London and Greenland, which in conformity
to a compression of -j-l-gth should differ 0.5 per diem. It is seen by the
final column that the comparative acceleration obtained in 1819 — 1820,
and 1823, differed 0.54 parts of a vibration per diem ; being much
within the limit of the differences to which the results of attached pen-
dulums have been shewn to be liable, from accidental irregularities in the
sustaining force.
The most interesting column, however, is that which exhibits the arcs
of vibration ; it is seen that on both the occasions, in which the clock and
pendulums were taken from the latitude of London to that of between
seventy-four and seventy-five degrees, the arcs diminished to the same
amount ; presenting a strong testimony of the systematic nature of the
cause of the diminution, and confirming the probability, that it has been
correctly ascribed to the increased velocity of the pendulum in the higher
latitudes, and to the consequently increased resistance of the atmosphere.
In' the uncertainty which is involved in the comparison of the vibra-
tions of attached pendulums performed in different arcs, it might,
perhaps, be desirable, should they be again employed in this or similar
IN THE LENGTH OF THE SECONDS* PENDULUM.
287
inquiries, to employ a variable, instead of a fixed weight ; and to pro-
portion the sustaining force in such manner, that the arcs might always
be maintained of the same dimension.
Statious.
Latitudes.
Dates.
i
Arc of
Vibra-
tion.
Tem-
pera,
tare.
Vibrations.
Excess of
Pendulum
No. 2.
Mean
Vibration.
Corrections.
Comparative
Vibrations.
1^'ff"- Difference
sices of between
'end. in theAcce-
1820 & leration in
1823 '8M 51 1843.
Temp.
Ellipj.
f
18I9<
1
1.76
0
4S
86388.10
•108.89
86442.54
-7.4
86435.14
2
1.73
45
86496.99
London . . .
51 31 08. 4'
1823-;
1
1.75
62
86372.36
1
ll09.68
86427.20
86427.20
■7.94
2
1.73
62
86482.04
1
J
0.54
1
1.65
45
86462.53
"1
M09.33
Melville Island.
74 47 12.1
1820-
86517.19
-7.4
-0.5
86509.29
r
2
1
1.67
1.67
45
62
86571.86
86445.84
1
J
•8.48
Greenland. . .
74 32 19
182 3 J
M09.97
86500.81
86500.81
2
1.67
62
86555.81
288 EXPERIMENTS FOR DETERMINING THE VARIATION
LATITUDES OF THE PENDULUM STATIONS.
The instruments employed in determining the latitudes were a repeating
circle of six inches diameter; a repeating reflecting circle of eight inches
diameter; and a sextant of eight inches radius.
The repeating circle was made by the direction, and at the expense of
the Board of Longitude, for the purpose of exempUfying the efficacy of
the principle of repetition when applied to a circle of so small a diameter
as six inches, carrying a telescope of seven inches focal length and
one inch aperture; and of practically ascertaining the degree of accu-
racy which might be retained, whilst the portability of the instrument
should be increased, by a reduction in the size to half the amount, which
had been previously regarded by the most eminent artists as the extreme
limit of diminution to which repeating circles, designed for astronomical
purposes, ought to be carried.
The excellent workmanship of Mr. Dollond, and the many ingenious
and useful contrivances which he has applied to the repeating circles of
his latest construction, rendered this little instrument extremely com-
plete, and by no means inconvenient in use; the arrangement, in par-
ticular, of the screws was such, that each could be managed without the
liability of interfering with or of being mistaken for others, and with
full room for the fingers even under very unfavourable circumstances ; as at
New York where the temperature was frequently below 20°, and obliged
the use of gloves.
It has already been noticed that the diminution in the size of this
instrument brought the several particulars of an observation, being the
contact, the levels, and the time, within the command of a single observer;
IN THE LENGTH OF THE SECONDS' PENDULUM. 289
and that the advantages gained in those respects are scarcely of less im-
portance than the increased portability. The observations vi^ith the circle,
detailed in the following pages, were made without an assistant.
The practical value of the six inch circle may be estimated by com-
paring the differences of the partial results from the mean at each
station, with the correspondence of any similar collection of observations
made with a circle on the original construction and of large dimension;
such for instance as the latitudes of the stations of the French Arc recorded
in the Base du Systeme Metrique; when if due allowance be made for the
extensive experience and great skill of the distinguished persons who
conducted the French observations, the comparison will scarcely appear
to the disadvantage of the smaller circle, even if extended generally
through all the stations of the present volume ; but if it be particularly
directed to Maranham and Spitzbergen, at which stations the partial
results were more numerous than elsewhere, and obtained with especial
regard to every circumstance by which their accuracy might be affected,
the performance of the six inch circle will appear fully equal to that of
circles of the larger dimension ; the comparison with the two stations,
at which a more than usual attention was bestowed, is the more appro-
priate, because it was essential to the purposes for which the latitudes
of the French stations were required, that the observations should always
be conducted with the utmost possible regard to accuracy.
It would appear, therefore, that in a repeating circle of six inches, the
disadvantages of a smaller image enabling a less precise contact or
bisection, and of an arch of less radius admitting of a less minute subdi-
vision, may be compensated by the principle of repetition ; whilst the
advantage is obtained, of a less pressure on the centre work, and of a
more free and independent motion of the several parts of the instrument,
in consequence of the reduction in size; which advantage is of much
practical consideration.
2 p
290 EXPERIMENTS FOR DETERMINING THE VARIATION
The repeating reflecting circle will be particularly described in a
subsequent part of the volume, in an account of the Longitudes of the
several stations, in which determination it was principally employed.
The sidereal chronometer used in noting the distance of stars from the
meridian, corresponding to their zenith distances observed with the
repeating circle, was made by Molyneux, and was lent me by Captain
Frederic Marryatt of the Royal Navy ; its rate appeared, by the compa-
risons at the several stations, to be losing about 5 seconds on a sidereal
day, and to be tolerably steady.
The corrections for astronomical refraction, employed in the following
calculations, are taken from Dr. Thomas Young's table, published in the
Nautical Almanac for 1822, and subsequent years ; the temperature of the
table being considered 48° instead of 50°.
The corrections for aberration and nutation applied to the stars, of which
the true apparent places are not inserted in the Nautical Almanac, have
been computed by Mr. Groombridge's Universal Tables, published in the
first volume of the Transactions of the Astronomical Society of London.
IN THE LENGTH OF THE SECONDS' PENDULUM.
291
SIERRA LEONE.
Place of Observation. — The West Bastion of Fort Thornton.
March Sth, 1822. Barom. 29.90 ; Ther. 80°. The Chroii. 423 fast 48'
AR. 6'' SY 19".4, on the Meridian at S" 22' 17" by the Chronometer.
Distances observed with a Repeating Circle.
50". Sirius,
The Zenith
Chronometer.
Hor.-iry
Angles.
N. V.
Sines.
Level.
Headings, &c.
H. M. S.
8 10 10
8 13 51
8 16 22
8 20 01
8 24 24
8 26 25
8 28 53
8 31 26
M. S.
12 07
8 26
5 55
2 16
2 OT
4 08
6 36
9 09
Means ,
1.39T
677
333
49
43
163
415
797
-3
+ 3
+ 3
+5
-6
+ 4
+8
-5
-4
+ 2
+2
+4
-7
+3
+8
-6
484,2
+ 5.5
La t. 8° 29' 30" Cosine .... 9.9952127
Dec. 16° 29" Cosine .... 9.9817744
Z.D. 24°58' Cosecant . . . 10.3745940
Log. Sine 1" A.C 5.3168000
Log. 484.2(+4) 6.6850248
Correction 3" 45' .6 Log. 2.3534059
Previous
Final.
First Vernier
Second „ .
Third „ .
Fourth „ .
Mean
First Vernier
Second
Third
Fourth
Mean
Index
Level
Observed Z.D. .
Refraction +0' 27"
Barometer. . — 0
Thermometer — 1
Correction .
True Z.D. . .
Star's Declio. .
Latitude North .
90 25 00
24 48
25 15
24 40
90 24 66
290 37 10
37 00
37 50
37 10
290 37 17.5
-90 24 56
+5.5
200 12 27
25 01 33.4
+0 25
-3
45
6
24
58
13
3
16
28
45
4
8 29 27.9
2 P 2
292
EXPERIMENTS FOR DETERMINING THE VARIATION
St. THOMAS.
Place of Observation. — ^The Mansion House of Fernandilla ; Man of War Bay.
June 7th, 1S22. Bar. 30. 10; Ther. 78°. The Chron. 423 slow, 29' 3G" : a. Crucis
(AR. 12'' 16' 52". 4) on the Meridian at 6'' 44' 33", by the Chronometer. The
Altitudes observed with a Repeating Reflecting Circle, and a Mercurial Horizon.
Cbronometer.
Horary
Angles.
N.V.
Sines.
Re:idings, &c.
H. M. S.
6 45 20
6 49 18
M. S.
0 47
4 45
6
215
o y M
Arc passed through 1 1 o nn .^rt
- . . . 97 sn 07 .';
Mean ....
110.5
Refraction - 1' sr'.S
Barometer . . -0.4
Thermometer + 6.4 .
...... -1 45.5
+0 12.1
Lat.0°25' Cosine. 9.999988
Dec. 62° 07' Cosine . 9 . 669942
Alt. 27° 28' Secant . 10.051939
Log. Sine 1" A.C. . 5.316800
Log. 110.S(+4) . . 6.043362
Star's South Polar Dista
Prec. Aber. and Nut,
27 28 S4.1
nee, 1st Jan. 1818 . 27 54 32 1
— 1 15.6
Latitude North
. . . . 0 24 42 3
Correction 1
2".l = .
1.082031
IN THE LENGTH OF THE SECONDS PENDULUM.
293
29' 50"; Arcturus (AR. U'' 07' 35". 5) on the Meridian at s"" 23' 1 5". 5 by the
Chron. The Altitudes observed by a Repeating Reflecting Circle, and a Mercurial
Horizon.
Meridian Double Altitude
0 4 *S
110 36 44
Apparent Altitude
70 18 22
Refraction . . —20". 9
Barometer . . —0.1
Thermometer +1.2
-19.9
True Altitude
. _ . . . . . . _ . . . 70 18 02. I
North Polar Distance . fi9 .^.^ 22
Latitude North
n 24 40 \
RECAPITULATION.
0 24 42.3
Junp lOtb Arcturu? 0 24 40.1
Latitude . . 0 24 41.2 North.
294
EXPERIMENTS FOR DETERMINING THE VARIATION
ASCENSION.
Place of Observation. — The Barrack Square.
June 26th, 1S22. Bar. 30.14; Ther. 80°. The Chron. No. 423 fast 55' 08". a
Centauri (AR. U** 28' 13"), on the Meridian at S*" 05' 45", by the Chron. The
Altitudes observed with a Sextant and Mercurial Horizon. Index Correc. — 1'.
Chronometer.
Horary
i^ngles.
N.V.
Sines.
Observed Double
Altitudes.
Deduction.
U. M. S.
8 57 20
8 59 .S3
9 01 45
9 03 20
9 04 23
9 08 27
9 09 44
9 n 05
M. S.
8 25
6 12
4 00
2 25
1 22
2 42
3 59
5 20
Means
674
366
152
56
18
63
151
271
75 39 20
75 40 20
75 41 20
75 42 00
75 42 20
75 41 55
75 40 50
75 39 40
219.6
75 40 58
Lat. 7° 56' Cosine . . . 9.9958235
Dec. 60° 07' Cosine .... 9.6974347
Alt. 37° 49' Secant . . . . 10.1023857
Log. Sine 1" A.C 5.3168000
Log. 219.6 (+4) 6.S41632.S
Correction 28". 5 = Log. 1.4540762
Observed Double Altitude . . 75 40 58
Index - 1 00
Apparent Altitude 37 49 59
Refraction — 1 1 5 1
Barometer — O.sl . . .— Ill
Thermometer + 4 . 3 j
Correction + 0 28.5
True Altitude 37 49 16.5
South Polar Distance, lat Jan. 1818 29 54 33
Prec. Aber. and Nut — 1 05.6
Latitude South 7 55 49 . 1
IN THE LENGTH OP THE SECONDS' PENDULUM.
295
Ascension. July 2d, 1822. Bar. 30.15; Therm. so°. The Chron. 423, fast
55' 22". aCentauri (AR. U"" 28' 13") on the Meridian at S"" 42' 20' by the Chron.
The Altitudes observed with a Sextant and Mercurial Horizon. Index Correc. — 1'.
Chronometer.
Horary
Angles.
N.V.
Sines.
Observed
double Altitudes.
Deduction.
U. M. S.
8 32 42
8 34 17
8 35 40
8 36 57
8 38 10
8 39 29
8 40 29
8 41 49
8 42 57
8 44 12
8 45 26
8 47 41
8 48 46
8 49 54
8 51 12
Means
M. s.
9 38
8 OS
6 40
5 23
4 10
2 51
1 51
0 31
0 37
1 52
3 06
5 21
6 26
7 34
8 52
883
617
423
276
165
77
33
3
4
33
92
272
394
545
748
304. S
75 38 10
75 39 35
75 40 00
75 41 05
75 41 25
75 41 30
75 41 50
75 42 10
75 41 50
75 41 30
75 41 00
75 40 25
75 39 50
75 39 05
75 38 45
75 40 32.7
Latitude 7° 56" Cosine . . 9.9958235
Declination 60° 07' Cosine . . . 9.6974347
Altitude 37° 49' Secant. . . 10.1023857
Log. Sine 1" A.C. . . . 5.3168000
Log. 304.3 (+4) 6.4833020
Correction 39".4 Loj. 1.5957459
Observed double Altitude . . . 75 40 32.7
Index Correction — 1 00
Apparent Altitude 37 49 46.3
Refraction -1' 11". 9 i
Barometer - 0.3 ^ . . . - 1 10.7
Thermometer + 4.5 J
Correction + 0 39.4
True Altitude 37 49 15
South Polar Dist., 1st Jan. 1818. . 29 51 33 -i
Prec. Aber. and Nut — 1 05. 6j
Latitude, South 7 55 47.6
296
EXPERIMENTS FOR DETERMINING THE VARIATION
Ascension. July 6th, 1822. Bar. 30.15; Therm. 80°. The Chron. 423, fast
55' 32". « Centauri (AR. 14" 2S' 13") on the Meridian at s'' 26' 46" by the Chron.
The Zenith Distances observed with a Repeating Circle.
Chronometer.
Horary
Angles.
N.V.
Sines.
Level.
Readings, &c.
H. M. S,
M. S.
0 < <<
8 23 32
3 14
99
— 7
-9
■ First Vernier . . .313 03 05
8 26 45
0 01
0
+4
+2
Final. . .
Second „ . . . . 02 50
Third „ . . . . 03 30
8 30 24
3 38
126
+2
0
Fourth , 03 30
8 33 10
6 24
390
0
— 3
Mean 313 03 14
8 35 47
9 01
774
+6
+6
Index + 08.5
8 38 42
11 56
1355
+5
+2
Level +4
Means ....
457.3
+ 4
313 03 26.5
Lat.7°56' Cosine. . . . 9.9958235 Refraction + 1' 14". g-j
Barometer + O.Sj. +1 10.7
Dec. 60° 07' Cosine. . . . 9.6974347 Thermometer - 4.5J
Z.D. 52" ir Cosecant . . . 10.1023857
Correction . . . . - 0 59.2
Log. Sine 1" A.C 5.3168000
TrueZ.D. . . . 52 10 45.9
Star's Decl. 1 Jan. 1818. 60 05 27 / |
Log. 457.3 (+4)
6.6602012
Prec. Aber. and Nut. . + 1 05.6)
Correction 59". 2 Log.
1.7726451
Latitude, South. . . 7 55 46.7
RECAPITULATION.
D 1 >i
7 55 49.1
July 2, a Centauri
7 .55 47.6
July 6, a. Centauri
7 55 46.7
7 55 47.8 South.
IN THE LENGTH OF THE SECONDS* PENDULUM.
297
BAHIA.
Place of Observation. — At Mr. Pennell's House at Vittoria. The Zenith
Distances observed with a Repeating Circle.
July 2.3cl, 1S22.
Barom.
30.04; Therm. 71°. The Chron. 4a;i fast 2" 32' 47",
(page oG) ; a. Ly
rae (AR.
is" 30' 57'. 8) on the Meridian at 12" o
9' 00" by the
Chronometer.
Chronomtter.
Horary
Angles.
N. V.
Sines.
Level.
Readings, &c.
H. M. S.
M. s.
O * //
12 46 15
12 45
1547
0
- 4
First Vernier
156 18 50
12 51 46
7 14
49S
+ 3
+ 1
Second „
18 55
i2 53 50
5 10
251
- 6
— 5
Final . ■
Third „ . .
19 35
12 56 34
13 00 13
S 26
1 13
56
14
+ 1
- 2
- 2
- 5
Fourth „ .
Mean
19 00
156 19 05
13 02 30
3 30
117
+ 3
+ 1
Index
+ 360 00 08.5
13 05 12
13 OT 11
6 12
8 11
366
637
+ 10
- 6
+ 7
- 3
Level
+2
13 10 32
13 13 37
11 32
14 37
1266
2033
+ 15
-11
+ 15
- 8
Observed Z.D. .
Refraction + r \T .i
516 19 15.5
51 37 55.6
i
Means .
678.8
+ 2
Barometer. . -hO.
• +1 10.2
1
1 iiermoraeter — 3.i
J
Lat. 12° 59' Cosine
Dec. 38° 37'. 5 Cosine
. 9.9887531 Correction . . .
. 9.8927885 „ „_
True Z.D.
-2 16.7
51 36 49.1
Z.D. 51° .37' Cosecan
. .
. 10,1057537 c , r> ■•
Star's Declin. . .
38 37 29.7
Log. Sine 1" A.C..
Log. 678.8 (+4). .
Correction 2' 16". 7
. 5.3168000
Log
. 6.8317418
Latitude South .
12 59 19.4
. 2.1358371
•2 Q
298
EXPERIMENTS FOR DETERMINING THE VARIATION
Bahia. July 26th, 1S22. Barom. 29. 9S ; Therm. 73°. The Chron. 423 fast
21' 32' 55", (page 59) ; a. Lyrae (AR. ISi- 30' 57". S) on the Meridian at 12'' 47' 19"
by the Chronometer.
Chronometer.
Horary
Angles.
N.V.
Sines.
Level.
Readings, &c.
H. M. S.
M. S.
o / •<
12 35 26
11 53
1344
— 5
- 8
First Vernier . . 259 33 05
12 37 40
9 39
886
-10
-12
Second „ . . . 33 00
12 40 15
7 04
475
- 1
— 4
Final. . <
Third ,, . . . 33 35
12 42 15
12 44 27
5 04
2 52
244
78
+ 4
+ 4
+ 1
-h 1
Fourth „ . . 33 00
Mean . . . . 259 33 10
12 46 17
1 02
10
— 1
- 4
Index . . . .+360 00 08.5
12 48 16
12 51 33
0 57
8
- 8
- 5
Level .... —5
- 3
619 33 13.5
12 53 53
12 56 26
6 34
9 07
410
791
0
— 3
- 3
0
Observed Z.D. . . 51 37 46.1
12 58 55
11 36
1281
- 5
- ^
Refraction +l'ir.3 i
Barometer \ -fl 09.9
13 00 43
13 24
1709
- 1
- 4
Thermometer —3.4 J
Means .
617.3
- 5
Correction . . . —2 04.3
True Z.D. . . . 51 36 51.7
Star's Declin. . . 38 37 30.5
Lat. 12° 59' Cosine .... 9.9887531
Dec. 38° 3T. 5 Cosine .... 9.8927885
latitude South . . 12 59 21.2
Z.D 51° 37' Cosecant ... 10 1057537
Log. Sine 1" A.C 5.3168000
Log. 617.3 (+4) ....
. 6.790496;
i
Correction
2' 04". 3
Lo
g . 2.094591*
■
IN THE LENGTH OF THE SECONDS PENDULUM.
299
Bahia. July 31st, 1S22. Barom.
a"" 33' 09", (page 63); a Pavonis (AR.
by the Chronometer.
30.05 ; Therm. 71°. The Chron. 423, fast
ao"" 11' 36") on the Meridian, at Ui- OS' 14''
Chronometer.
Horary
Angles.
N. V.
Sines.
Readings, &c.
H. M. S.
14 02 58
14 04 52
14 07 15
14 08 47
14 11 IS
14 12 52
14 16 20
14 20 49
14 23 21
14 27 49
M. S.
5 16
3 22
0 59
0 33
3 01
4 38
8 06
12 35
15 07
19 35
Means
264
108
9
3
87
204
624
1507
2175
3648
-4
+5
-I
+3
+ 5
+9
+5
+2
+ 3
+ 2
-6
+2
0
+ 1
+2
+ 6
+2
-1
0
0
862.9
+ 17.5
Lat. 12° 59' Cosine .... 9.9887531
Dec. 57° 17' Cosine .... 9.7327837
Z.D. 44° 18' Cosecant . . . . 10.1558863
Log. Sine 1" A.C 5.3168000
Log. 862.9 ( + 4) 6.9359605
Correction 2' 14".9 Log. 2.1301836
Final .
First Vernier
. . 83 15 10
Second „
14 40
Third „ . .
. . 15 15
Fourth „ .
14 40
Mean
. . 83 14 56
Index
. + .360 00 08.5
Level . . .
. . + 17.5
443 15 22
Observed Z.D. . . . 44 19 32.2
Refraction +0' 56". 8"]
Barometer +0.1 ' +54.4
Thermometer — 2.5 J
Correction . . . — 2 14.9
TmeZ.D 44 18 11.7
Mean Decl. Jan. 1, 1818. 57 18 23
Prec. Aber. and Nut. — 0 48.9
Latitude. South. . . 12 59 22.4
RECAPITULATION.
July 23, a Lyra; 12 59 19.4
July 26, <t Lyra; 12 59 21.2
July 31, a Pavonis 12 59 22.4
12 59 21 South Latitude.
2 Q 2
300
EXPERIMENTS FOR DETERMINING THE VARIATION
MARANHAM.
Place of Observalion. — In Mr. Heskelh's House.
The observations were made with the six inch repeating circle belonging to
the Board of Longitude, and vv^ere designed to afford a fair example of the
accuracy of which that Instrument is capable. The circle was supported
on the v.'indow-sills, and was always suffered to remain several minutes
after the adjustments were perfect, before the observations were commenced.
The temperature was registered by a thermometer freely suspended near
the circle, and its height was observed before the mercury had risen in
consequence of the approach of the lamp, by which it was read. The
screws for slow motion, of the circle, level, and telescope, were turned in
opposite directions, in successive pairs of observation.
August 28th, 1S22. Barometer 29.95; Thermometer S0°. The Chron. 423, fast
2i> 50' 59'', (page 76) ; a. Ljrie (AR. 18'" 30' 57". 4) on the Meridian, at 8'' 04' 35"
Mean Time, and at 1 li> 01' 34" by the Chronometer.
Ciironometer.
H. M. S.
10 49 06
10 52 40
10 55 50
10 57 44
11 00 49
11 03 42
n OR 52
II 09 17
Horary
Angles.
M. s.
12 28
8 54
5 44
3 50
0 45
2 08
5 18
7 43
Means
N.V.
Sines.
Lat. 2° 32' Cosine
Dec. 38° 37' Cosine
Z.D. 41° 09' Cosecant
Log .Sine 1" A.C. .
Log. 4!6(+4) . .
Correction V 19'. 7
1479
754
S13
1 4 1
5
43
267
567
416
+ 3
- 2
- 4
- 1
- 8
-h 4
- 8
+ 7
+ 1
- 4
- 6
- 2
-10
+ 2
-10
+ 5
16.5
Loff
9.9990753
9.8928395
10.1817526
5.3168000
6.6491349
2.010.?023
Readings, &c.
Previous
Final
First Vernier
Second „ .
Third „ .
Fourth „ .
Mean .
C First Vernier
Second „
\ Third „
' I Fourth „
[ Mean
Index
Level
Observed Z D. .
Refraction — 1' 50"
Barometer — 0
Tliermometer — 3
Correction .
True Z.D. .
Star's Decl. .
South Latitude
167 11 50
11 30
12 10
11 40
. 107
11
47.
5
. 136
35
00
34
30
35
30
35
00
. 136
35
00
+ 192
48
12
.5
16.
5
329
22
56
41 10 22
+ 0 47.7
- 1 49.7
41 09 20
38 37 37.6
2 31 42.4
IN THE LENGTH OP THE SECONDS* PENDULUM.
301
Maramham. August 29, 1S22. Bar. 30.00; Therm. 80°. The Sidereal Chron.
No. 702, slow on Sidereal Time S'' 23' 38". a Lyrse (AR. IS" 3o' 57".-l) on the
Meridian at 10'' 7' 19" by the Chronometer.
Chronompter,
Horary
Angles.
N. V.
.sines.
Level.
Readings, &c.
M. M. s.
9 -18 35
9 51 00
9 54 20
9 57 OJ
9 59 15.5
10 02 30.5
10 06 11.5
10 08 i3
10 n 31
10 14 08.5
10 17 33.5
10 20 OS
M. S.
18 44
16 19
12 59
10 IS
7 31.5
4 48.5
1 07.5
I 24
4 15
e 49.5
10 H.5
12 46
3339
-3
-1
2533
+4
+ 2
1604
-2
-4
1000
0
-2
S?9
4-4
+ 1
220
-2
— 4
12
+5
+3
19
-4
-2
172
-7
-9
413
0
_2
998
0
-3
1551
-3
0
Means
1035.8
■11.5
Lat. 2°32' Cosine .... 9.9995753
Dec. 38° 37' Cosine . . . . 9.8928395
Z.D. 41°09' Cosecant . . . 10.1817526
Loj. Sine 1" .\.C 5.3144251
Log. 1035.8 (+4) 7.0I527S9
Correction 4' 13".4 Log. 2.4038R84
Previous
Final
First Vernier
Second „
Third „ .
Fourth ,,
Mean .
116 26
10
25
SO
26
20
25
65
116 26 04
First Vernier . . . 250 59 50
Second „ . . . .250 59 30
Third „ . . . .251 00 10
Fourth , 250 59 20
Mean 250 59 42.5
Index .... +243 33 56
Level - 14.5
494 23 24
Observed Z.D. . . . 41 12 47
Refraction ■+()' 50" .9 1
Barometer ...I + 0 47.9
Thermometer — 3.o'
Correction .... — 4 13.4
True Z.D 41 09 21.5
Star's Declination . . 3S 37 37.7
South Latitude ... 2 31 43.8
302
EXPERIMENTS FOR DETERMINING THE VARIATION
Maranham. August 29th, 1822. Baroni. 30.00 ; Therm. 80°. The Sidereal
Chron. 702 slow on Sidereal Time s" 23' 39". a. Pavonis (App. AR. ao"" 1 1' 36") on
the Meridian at 1 1"" 47' 57" by the Chronometer.
Chronometer.
Horary
.Angles.
N. V.
Sines.
Level.
Headings, &c.
H. M. S.
11 39 28
11 42 54.5
11 46 55
11 49 12
11 54 45
11 56 42
U 58 58
12 01 11
12 06 56
12 08 51
N. s.
8 29
5 02.5
1 02
1 15
fi 48
8 45
685
242
10
15
440
729
11 01 ' 1155
13 14
18 59
20 54
Means .
1667
342S
4155
1252.6
- 1
0
- 1
+ 5
+ 11
- 9
- 3
- 2
+ 5
+ 3
+ 2
+ 9
- 11
- 5
0
+ 6
+ 1
-0.5
Lat. 2° 32' Cosine 9.9995753
Dec. 57° 17' Cosine 9.7327837
Z.D. 54° 46' Cosecant . . . 10.087879."!
Log. Sine 1" A.C 5.3144251
Log. 1252.6 ( + 4) 7.0978124
Correction 2' 50" 8 Log . 2.2324758
First Vernier
Second „
Previous ^ Third „
Fourth „
Mean .
First Vernier
Second „
Final . . ■; Third .,
Fourth „
Mean .
250 59 50
250 59 30
251 00 10
250 59 20
250 59 42.5
78 54 20
54 20
54 40
54 10
78 54 22.5
[109 00 17.5
Index .... +<
[360 00 00
Level
+0.5
547 54 40.5
Observed Z.D. . .
54 47 28
Refraction +1' 22" 4 i
Barometer . . . . >
1
+ 1 17 6
Thermometer -4.8 J
Correction.
-2 50.8
True Z.D
54 45 54.8
Star's Dec. iJan. 1818
57 18 23 1
Prec. Aber. and Nut.
-0 43. 7J
Latitude South .
2 31 44.5
IN THE LENGTH OF THE SECONDS' PENDULUM.
303
Maranham. August 31st, 1S22. Bar. 29.97 ; Ther. 80°. The Sidereal Chron.
slow on Sidereal Time 8" 23' 50". x Lyrae (AR. is" 30' .57'..3) on the Meridian at
10" 7' 7" by the Chronometer.
Chronometer.
H. M. s.
9 52 35
9 55 46
9 58 43
10 00 48.5
10 04 12
10 06 11.5
10 09 37.5
10 II ,37.5
10 16 05
10 18 14
10 21 03.5
10 25 17
Horary
Angles.
N.V.
Sines.
14 32
II 21
8 21
6 18.5
2 55
0 55.5
2 30.5
4 30.5
5 58
II 07
15 56.5
18 10
2010
1226
672
379
81
8
60
194
765
1176
1850
3140
Means
963.4
Level.
- 3
0
+ 12
- 3
- 1
+ 5
- 4
- 1
+ 9
0
+ 2
- 5
0
+ 10
- 5
- 3
+ 9
- 6
- 3
+ 7
0
0
-10
- 2.5
Lat. 2° 32' Cosine .... 9.9995753
Dec. 38° 37' Cosine .... 9.8D28395
Z.D. 41°09' Cosecant . . 10.1817526
Log. Sine 1" A.C 5.3144251
Log. 963.4 (+4) 6.98.38066
Correction 3' 55".7 Log. 2.3723991
Readiogs, &c.
Previous
Final
First Vernier . . . 280 39 10
Second ,,.... 39 20
Third „ . . . . 39 40
Fourth ,,.... 39 00
Mean 280 39 17.5
First Vernier
Second „
Third „ .
Fourth ,,
55 09 25
09 15
09 50
09 10
Mean 55 09 25
79 20 42.5
360 00 00
- 2.5
Index
Level
.+ ■
494 30 05
41 12 30.4
+ 0 47.9
Observed Z.D. . .
Refraction +0'50".9i
Barometer • • • f
Thermometer _ 3.0 J
Correction . . . . — 3 55.7
True Z.D 41 09 22.6
Star's Declination . 38 37 38
South Latitude . . 2 31 44.6
304
EXPERIMENTS FOR DETERMINING THE VARIATION
r
Maranham. August 31st, 1S22. Barom. 29.97; Therm. S0° ; the Sidereal
Chron. slow on Sidereal Time S"" 23' 50"; a Cygiii (AR. 20'' 35' 25") on the
Meridian at 12'' 11' 35" by the Chronometer.
Chronometer. I '
Angles.
N.V.
Sines.
Level.
II. M. S.
11 57 46.5
12 00 03.5
12 02 26.5
12 04 33. 5
12 07 59.5
12 10 12
12 13 09
12 16 03.5
12 20 31
12 22 40
12 25 45.5
12 27 19
M. s.
13 48.5
11 31.5
9 08.5
7 01.5
3 35.5
1 23
1 34
4 28.5
8 56
11 05
14 10.5
15 44
Means
1814
1264
795
470
123
18
23
190
760
1169
1912
2355
- 5
+ 4
0
- 4
+ 2
- 2
0
+ 4
+ 11
+ 6
- 7
- 2
- 7
+ 2
0
- 6
0
- 4
0
+ 1
+ 9
+ 4
- 9
- 4
907.7 -3.5
Lat. 2° 32' Cosine 9.9995753
Dec. 44° 39' Cosine 9.8521218
Z.D. 47° IV Cosecant 10.1345808
Log. Sine 1" A.C 5.3144251
Log. 907.7 (+4) 6.9579423
Correction 3" 01". 4 . . . Log. 2.2586453
Previous
Final
Readings, 6
c.
o ' /'
First Vernier .
55 09 25
Second „
09 15
Third „
09 50
Fourth „
09 10
Mean
. 55 09 25
First Vernier .
. 261 45 20
Second „
45 00
Third „
45 40
Fourth „
Mean .
44 40
. 261 45 10
Index .
+ 304 50 35
Level
-3.5
566 35 41.5
Observed Z.D. 47 12 58.5
Refraction +1 02.91
Barometer . . . > +0 59.2
Thermometer — 3.7j
Correction . —3 01 .4
True Z.D. . . 47 10 56.3
Star's Declin. . . 44 39 14.2
South Latitude . 2 31 42.1
IN THE LENGTH OF THE SECONDS' PENDULUM.
303
r
Maranham. September 2d, 1 822. Barom. 29.95 ; Therm. 77°; the Sidereal
Chronom. 702 slow on Sidereal Time S" 24' 02"; a Gruris (App. AR. 21'' 57' 03")
on the Meridian at 13'" 33' 01" by the Chronometer.
Cbrooometer.
Horary
Angles.
N.V.
Sints.
Readings,
ike.
First Vernier
. 183 45 40
Second „
. . 45 40
Third
46 20
Fourth „
45 45
Mejin .
. 183 45 51
Index .
+360 00 08.5
Level . .
+ 18
543 46 17.5
H. M. S.
IS 18 50
13 21 44.5
13 25 08
13 27 33.5
13 31 15
13 33 45
13 35 59
13 39 18
13 41 24
13 43 23
13 47 32
13 49 26.5
M. S.
14 II
II 16.5
7 53
5 27.5
1 46
0 44
2 58
6 17
8 23
10 22
14 31
16 25.5
Means
1914
1210
592
283
SO
5
84
376
669
1023
2005
2567
896.5
+ 2
+ 6
- 5
+ 5
- 8
+ 4
- 4
- 1
+ 8
+ 5
+ 18
0
+ 1
+ 5
- 7
+ 3
-10
+ 2
- 6
- 3
+ 6
+ 3
+ 13
- 1
+ 18
Final
Lat. 2" 32' Cosine
Dec. 47° 49' Cosine .
Z.D. 45° 17' Cosecant
Log Sine 1" A.C. . .
Log 896.5 (+4) . .
Correction 2' 54". 6 .
9.9995753
9.8270493
10.1483780
5.3144251
6.9525503
Log. 2.2419780
Observed Z.D. . 45 18 51.5
Refraction +58". 7 1
Barometer — 0".1> +0 55.4
Therm. . — 3". 2 J
Correction . . . —2 54.6
True Z.D. ... 45 16 52.3
Star'sDec.lJan.1818 47 49 59
Prec. Aber. Nut. . —1 24.5
Latitude South . 2 31 42.2
RECAPITULATION.
August 28,
a Lyrae
. ... 2 31
42.4
August 29,
a. Lyrae
... 2 31
43.8
August 29,
a. Pavonis
... 2 31
44.5
August 31,
a Lyrae
... 2 31
44.6
August 31,
" Cygni
... 2 31
42.1
Septem. 2,
a Cruris
... 2 31
42.2
2 31
43.3 South.
2 R
306
EXPERIMENTS FOR DETERMINING THE VARIATION
TRINIDAD.
Place of Observation. — In Colonel Young's House, in the second ground-lot West
of the Protestant Church in Port Spain. The Zenith Distances were observed
with a Repeating Circle.
September 30th, IS22. — Barom. 29. 9S ; Therm. 77°. The Sidereal Chron. 702 slow
of Sidereal Time 7'' 17' 30". Achernar (Apparent AR. l'' 31' 07". 5) on the Meridian
at is'' 13' 37". 5 by the Chronometer.
Chonometer.
Horary
Angles.
N.V.
Sines.
Level.
Readings, &c.
H. M. S.
IS 09 01.5
18 11 18.5
18 13 48.5
18 15 51.5
18 17 49
18 19 41.5
18 22 08.5
18 24 23.5
18 26 37.5
18 28 46.5
18 31 53.5
I 18 34 09.5
M. S.
4 36
2 19
11
2 14
4 11.5
6 04
8 31
10 46
13 00
15 09
18 16
20 32
201
51
0
47
167
350
690
1103
1608
2184
3175
4011
Means.
1132.2;
- 2
+ 9
— 2
+ 3
0
— 5
+ 3
— 2
— 2
+ 3
— 2
+ 5
- 1
+ 7
- 1
+ 1
0
- 7
+ 1
- 4
- 3
+ 1
0
+ 3
Previous
+ 2
Final
First Vernier
Second „ .
Third „ .
Fourth ,, .
l Mean
f First Vernier.
Second ,, .
Third „ .
Fourth „ .
Mean
Index
Level
192 17 40
17 35
17 55
17 30
192 17 40
297 40
20
40
00
40
20
40
00
297
.40
10
[167
42
20
1360
00 00
+ 2
825 22 32
Lat. 10''39' Cosine 9.9924539
Dec. 58° 08" Cosine 9.7225881
Z.D. 68° 47' Cosecant .... 10.0304823
Log. Sine 1" A.C 5.3144251
Log. 1132.25 (+4) 7.0539400
Correction 2* 10" . . . Log. 2. 1 1 38894
Observed Z.D. . . 68 46 52.7
+ 2 20.7
Refraction + 2.28.8]
Barometer . . . j.
Thermometer — 8.1 J
Correction
True Z.D. . . .
. - 2 10
. . 68 47 03.4
Star's Dec. IJan. 1818. 58 09 51
Prec. Aber. and Nut. — 1 43.7
Latitude North . . 10 38 56.1
IN THE LENGTH OP THE SECONDS* PENDULUM.
307
Trinidad. October 3d, IS22. Barom. 29 .98 ; Therm. 78°. The Sidereal Chron.
702 slow of Sidereal Time 7'' 17- 47"; a. Gruris (Apparent AR. 21" 57' 03") on the
Meridian at l*"" 39' 16" by the Chronometer.
ChroDometer.
H. M. s.
14 20 19
14 22 38
14 25 05
14 26 49
14 29 13
14 32 14
14 35 01
14 37 32
14 39 62
14 41 35
14 43 51
14 45 41
14 48 51
14 51 07
Horary
Angles.
18 57
16 38
14 11
12 27
10 03
7 02
4 15
1 44
0 36
2 19
3 35
6 25
9 35
11 51
N. V.
SiDes.
3416
2632
1914
1475
961
471
172
29
3
51
122
392
874
1 336
Level.
+ 1
+4
0
+2
-4
+ 1
-7
0
+ 3
+ 5
+ 4
+ 5
-4
-3
0
+2
0
+ 1
-5
0
-8
0
+ 2
+ 3
+ 2
+ 3
-6
-5
Means .
989.1
-2
ReadiDgs, &c.
Lat. 10° 39' Cosine .... 9.99245.39
Dec. 47° 49' Cosine .... 9.8270493
Z.D. 58° 27' Cosecant . . . 10.0694667
Log. Sine 1" A.C 5.3144251
Log. 989.1 ( + 4) . . ■. •. ■. 6.9952402
Correction 2' 38" Log. 2.1986352
Previous
Final
First Vernier
Second „ .
Third „ .
Fourth „ .
Mean
O / It
328 20 20
20 10
20 40
20 10
328 20 20
First Vernier
Second ,,
Third „ .
Fourth „ .
Mean
Index
Level
+
67 10 30
01 00
01 40
01 10
67 01 20
r 31 39 40
[720 00 00
- 2
818 40 58
Observed Z.D. . . 58 28 38.5
Refraction + r 34". 8 1
Barometer . . . > +1 29.3
Thermometer — 5 . 5 J
Correction ... —2 38
True Z.D. ... 58 27 29.8
Star's Dec. IJan. 1818 47 49 59
Prec, Aber. and Nut. — 1 21.4
Latitude North .
10 38 52.2
2 R 2
308
EXPERIMENTS FOR DETERMINING THE VARIATION
Trinidad. October 4th, 1S32. Barom. 29.96; Therm. 76°. The Sidereal
Chron. 702 slow of Sidereal Time 7'' 1/ 53".5. Acheriiar (App. AR. l" 31' OT'.e)
on the Meridian at IS'' 13' 14" by the Chronometer.
Chronometer.
H. M. s.
17 42 19
17 45 19.5
17 48 15
17 50 42
17 53 15
17 55 13
17 57 41
17 59 05:5
18 02 20.5
18 04 17.5
18 07 02.5
18 08 41.5
18 11 35.5
18 13 09
Lamp trimmed.
18 23 19
18 28 47.5
18 30 54.5
18 33 35
18 39 17
18 41 03.5
Horary
Angles.
M. S.
30 55
27 54.5
24 59
22 32
19 59
18 01
15 33
14 08.5
10 53.5
8 5C.5
6 11.5
4 32.5
1 38.5
0 OS
10 05
15 33.5
17 40.5
20 21
26 03
27 49.5
N. V.
Sines.
Level.
9070
7405
5936
4H29
.S799
3088
2301
1903
1130
761
365
196
25
0
968
2303
2970
3940
6453
7360
-1
+6
-6
-I
~ 5
+ 4
0
-5
— 5
0
-4
+8
-7
+ 7
-6
+7
+ 2
-1
+ 6
+ 7
Means .
3240.1
-2
+ 5
-7
-2
-7
+ 2
0
-6
-6
0
-5
+ 6
-9
+5
-7
+ 5
+ 1
0
+5
+ 5
Readings, &c.
-5.5
Lat. 10" 39' Cosine 9.9924539
Dec. 58° 08" Cosine 9.72258S1
Z.D. 68° 47' Cosecant .... 10.0304823
Log. Sine 1" A.C 5.3144251
Log. .3240.1 (+4) 7.5105584
Correction 6.12 Log . 2.5705078
Previous ■
First Vernier
Second ,,
Tliird „
Fourth „
Mean .
Final .
First Vernier
Second ,,
Third „
Fourth „
Mean .
Index
Level
211 41 25
41 15
41 55
41 05
211 41 25
148 41 10
40 50
41 20
40 50
148 41 02.5
, / 148 18 35
~II0>*0 00 00
-5.5
1376 59 .32
29". 3
Observed Z.D.
Refraction +2'
Barometer
Thermometer —7.8
Correction
True Z.D. . . .
Star's Dec. 1 Jan. 1818
Prec. Aber. and Nut.
Latitude North
68 50 58.6
-1-2 21.5
-6 12
68 47 08.1
58 09 51 j
>
— i 42.2,'
10 38 59.3
RECAPITULATION.
o / //
September 30th, Achernar 10 38 56.1
October 3d, a Crucis 10 38 52.2
„ 4th, Achernar 10 38 59.3
10 38 56 North.
IN THE LENGTH OF THE SECONDS' PENDULUM.
309
JAMAICA.
Place of Observation. — Fort Charles. The Zenith Distances observed with a
Repeating Circle.
October 25th, 1S22. Bar. 30.01 ; Therm. 7S°. The Sidereal Chron. slow on Sidereal
Time s"" 18' is". Polaris (AR. 5S' 14". 2) on the Meridian at IS'" .39' 56" by the Chron.
Horary
Angles.
N. V.
Sines.
Readings, &c.
H. M. S.
18 08 52
18 II 4i
IS I I 38
18 16 40
18 19 01
18 21 5-1
18 23 55
18 26 04
18 28 43
18 30 38
18 33 40
18 35 42
18 37 49
18 39 S3
18 42 32
18 46 22
IS 48 00
18 50 04
18 52 04
18 53 45
18 55 27
18 56 56
18 58 22
18 59 26
19 01 25
19 02 56
19 04 25
19 05 08
19 07 33
19 09 27
M. S-
31 04
28 11
25 18
23 16
20 55
18 02
16 01
13 52
11 13
8 38
6 16
4 14
2 07
0 23
2 36
6 26
8 04
10 08
12 08
13 49
15 31
17 00
18 26
19 .30
21 29
23 00
24 29
25 12
27 37
29 31
9178
7552
6087
5149
4162
3093
2441
1830
1197
765
374
171
43
1
64
391
619
977
1101
1817
2291
2750
3233
3618
4S90
5031
5701
6039
7251
8282
Means
3183.4
+ 3
+ 1
-5
-2
0
-I
■+6
-1
0
-2
+ 1
0
+ 3
0
0
0
+ 3
-2
+ 3
+ 3
0
0
0
+2
+2
-5
0
-3
+ 8
0
+ 1
0
-3
-3
0
0
+5
0
0
0
0
0
+2
0
0
0
+ 2
0
0
-i-2
0
0
0
+ 1
+ 1
— 3
0
-I
+ 6
0
Lat. 17° 56' Cosine .
Dec. 88° 22' Cosine .
Z.D. 70° 26' Cosecant
Log. Sine 1" A.C.
Log. 3183.4 (+4)
Correction 18".9
f First Vernier
Second „
Previous \ Third „ .
Fourth „ .
I Mean . .
r First Vernier
Second „
Final . A Third „
Fourth „
t Mean .
Index.
Level .
9.9783702
. . 8.4548934
. . 10.0258327
. . 5.3144251
7.3028912
Log. 1.2764126
. 117 31
25
31
10
31
35
31
00
. 117 31
17.5
. 69 21
05
20
40
20
50
20
25
. 69 20
45
, / 242 28 12. 5
^ l.'800 00 00
+ 12
2111 49 39.5
Observed Z.D. . . . 70 23 39.3
Refraction + 2' 42". .31
Barometer ■ • ■ i" + 2 3.'? . 1
Thermometer — 9. 2 J
(^rrection . . . . — 0 18.9
-i-I2
True Z.D 70 25 33.3
Star's Decl 88 22 02.1
Latitude North . . . 17 56 08.6
310
EXPERIMENTS FOR DETERMINING THE VARIATION
Jamaica.— — November 3d, 1822. Bar. 30.00; Therm. 78°. The Sidereal Chron.
slow on Sidereal Time 6'' 19' 06". 4. Polaris (AR. 5S' 12."4.) on the Meridian at
IS*" 39' 06" by the Chronometer.
Chronometer.
Horary
Angles.
N.V.
Sines.
Readings, &c.
H. M. S.
17 53 18.5
17 56 36
17 59 41
18 02 15
18 04 50
18 07 09
18 09 11
18 10 56
18 13 47
18 15 55
18 18 44
18 20 26.5
18 22 30.5
18 24 36
18 26 42
18 28 11
18 30 16
18 31 46
18 33 31.5
18 35 12
18 37 18
IS 38 42
18 40 19
18 41 39.5
18 43 32
18 45 00.5
18 47 29
18 50 01
18 52 25.5
IS 54 07.5
M. s.
45 48
42 30
39 25
36 51
34 16
31 57
29 55
28 10
25 19
23 11
20 22
18 40
16 36
14 30
12 24
10 55
8 50
7 20
5 35
3 54
1 48
0 24
1 13
2 33
4 26
5 54
8 23
10 55
13 20
15 01
Means
19902
17144
14754
12899
11157
9702
8508
7543
6093
5112
3946
3315
2622
2001
1463
1134
743
512
297
145
31
2
14
62
187
331
669
1134
1692
2146
-2
0
0
+ 5
+5
0
0
— 2
-7
-2
+ 1
+5
+ 3
-2
0
+5
+3
+4
-1
0
0
0
-2
+ 6
0
+ 3
0
0
+2
0
-4
0
0
+4
+4
0
0
-4
-9
-4
+3
+3
+ 2
-4
0
+3
+ 1
+ 2
-3
0
0
0
-4
+ 5
0
+ 1
0
0
-0
0
4508.7
+ 10
Lat. 17°56' Cosine 9.9783702
Dec. 88° 22' Cosine 8.454893
Z.D.70°26' Cosecant .... 10.0258327
Log. Sine 1" A.C. . . . . . 5.3144251
Log. 4508.7 (+4) .... 7.6540513
Correction 26". 8 Log. 1.4275727
Previous
Final
First Vernier
0
. . 5
48 40
Second „ .
48 10
Third „ . .
48 50
Fourth „ . .
Mean ....
48 00
5
48 25
r First Vernier
. . 317
44 25
Second „ .
44 10
Third „ . .
44 40
Fourth „ . .
■ Mean.
44 00
. . 317
44 19
Index
, 5 354 11 35
^ 11440 00 00
Level . . .
• •
+ 10
2111
56 04
Observed Z.D. .
. . 70
23 52.1
Refraction + 2' 42". 3"!
Barometer •■ • f + 2 33.1
Thermometer — 9.2J
Correction . . . - 0 26.8
True Z.D 70 25 58.4
Star's Decl 88 22 05
Latitude, North.
17 56 06.6
RECAPITULATION.
October 25, Polaris
November 3, Polaris
17
17
56 08.6
.56 06.6
17 56 07.6 North.
IN THE LENGTH OF THE SECONDS PENDULUM.
.311
NEW YORK.
Place of Observation. — ^The Cupola of Columbia College. The Zenith Distances
were observed with a Repeating Circle.
December 24th, 1822. Barom. 30.40 ; Therm. 20°.5. The Chronometer 423 fast
5'' 00' 57' (page 123) ; Sun on the Meridian at 23'' 59' 53" Mean Time, 5'' 00' 50"
by the Chronometer.
Chroaometer.
Time from
Noon.
N.V.
Sines.
Level.
Readings, &c.
II. M. S.
4 45 27
4 49 06
4 51 50
4 57 23
4 59 40
5 03 10
5 05 25
5 07 10
5 09 10
5 10 38
5 12 54
5 15 00
M. s.
!.■; 23
11 41
9 00
3 27
1 10
2 20
4 35
G 20
8 20
9 48
12 04
14 10
2252
1310
771
113
13
52
200
382
661
914
1386
1910
Means. After Nooo 1 23
830.3
0
0
+3
+2
0
+9
+7
0
+6
+ 7
+8
+8
0
0
- 7
- 7
-10
0
- 3
0
- 4
- 3
+5.5
H. M.
App. Greenwich time at Noon ... 4 56.2
Observation later than Noon ... 1.4
App. Greenwich time, correspondine\ . ,, „
to the Mean Z.D j" 457^
Lat. 40° 42' 43" Cosine . . . 9.8796683
Dec. 23° 26' 34" Cosine . . . 9.9625861
Z.D. 64° 09' 15' Cosecant. . . 10.0457718
Log. Sine 1" A.C 5.3144251
Log. 830.3 (+4) 6.9192350
Correction 2' 12". 3 . . . Log. 2.1216863
Previous •
Final
First Vernier
Second „
Third „
Fourth .,
Mean .
First Vernier
Second „
I Third ,.
Fourth „
Mean .
Index .
Level .
338 26 20
26 20
26 50
26 00
328 26 22.5
21 34 50
34 30
35 10
34 30
21 ,34 45
I r 31 S3 37.3
"^ 1720 00 00
+5.5
Observed Z.D.
773 08 28
64 25 42.3
Refraction +2'or'.l i
Barometer . . +1.6 i . , „, ,
Thermometer. +6.7 f +2 01.5
Parallax . . . —7.9 j
Seinidiam .
Correction
-16 17.7
2 12.3
64 09 13.8
Decl. at 4h .57' 6 • I 23 25 33.7
App. Greenwich time J
North Latitude . . 40 42 40.1
312
EXPERIMENTS FOR DETERMINING THE VARIATION
New York. December 24th, 1822. Barom. 30.40; Therm. 21°.
The Sidereal
Chron. 702 slow on Sidereal Time 6'' 33' 53 " ; Polaris (AR. O" 57' 46".3) on the |
Meridian at IS'' 23' 51" by the Sidereal Chronometer.
Chronometer.
Horary
Angles.
N.V.
Sines.
Level.
Readings, &c.
H. M. S.
M, s.
o f tt
18 09 48
U 03
1879
0
0
First Vernier .
228 56 30
18 13 13
10 38
1076
+ 11
0
Second „ . . .
56 20
18 15 32
18 16 52
18 19 02
8 19
6 59
4 49
658
464
221
0
0
-11
0
0
- 1
Previous ■
Third „ . . .
Fourth „ . . .
Mean
57 00
56 30
228 56 ,35
18 20 48
3 03
89
+ 10
+ 1
First Vernier .
80 37 40
18 23 12
0 33
4
+ 8
- 4
Final . . •
Second „ . . .
Third „ . . .
37 00
38 10
18 23 14
18 30 37
1 23
6 46
18
436
- 9
0
- I
0
Fourth „ . . .
Mean
37 30
80 37 35
18 33 00
18 35 08
9 09
11 17
797
1212
+ 9
+ 8
+ 2
- 4
Index . . . . +
Level
fl31 03 25
[360 00 00
+ 13
18 H7 09.5
13 18
1683
+ 9
- 2
571 41 13
Means . . .
711.4
+ 13
Observed Z.D. . .
47 38 26.1
+ 1 08.2
- 0 04.3
Lat. 40° 42' 43" Cosine . . . 9.8796683
Dec. 88° 22' 18" Cosine . . . 8.4535622
Z.D. 49° 39' 30" Cosecanl . . . 10.1312705
Log. Sine 1" A.C 5.3144251
Refraction +1' 0.3".8l
Barometer +0.9>
Thermometer + 3 . 5 j
Correction
True Z.D. . . .
Polar Distance . .
Co. Latitude . . .
Log. 711. 4 (+4) ....
. 6.8521139
47 39 30
I 37 41.1
Correction 0' 04".3 . . . Lo
g. 0.6310400
49 17 11.1
North Latitude .
40 42 48.9
IN THE LENGTH OF THE SECONDS PENDULUM,
313
New Yobk. December 31st, 1822. Baroni. 30.76; Therm. 20°. The Chroii.
423 fast 5" 00' 40" ; the Sun on the Meridian at o'' 03' 19" Mean time, 3'' 03' 59"
by the Chronometer.
Chronometer.
Time from
Noon.
N.V.
Sines.
Level.
Readings, &c. .Sun's L.L.
H. M. s.
H. s.
0 / "
4 49 13
14 46
2075
0
0
First Vernier . . . 128 22 40
4 52 12
11 47
1321
- 9
0
Second „ . . . 22 20
4 54 26
9 33
868
+ 7
- 2
Previous <
Third „ ... 23 10
4 56 45
4 59 20
5 00 47
7 M
4 39
3 12
498
206
97
•1-12
+ 9
+ 6
+ 3
0
- 4
Fourth „
Mean ....
22 20
128 22 37.5
5 02 45
1 14
14
- 3
-12
First Vernier ... 177 31 50
5 04 44
0 45
5
0
0
Second ., . . . 31 40
5 07 00
3 01
87
+ 3
- 7
Final. . •
Third „ . . . 32 00
5 08 32
5 10 52
4 33
6 53
197
451
0
+ 10
- 9
0
Fourth „ . . .
Mean ....
31 20
177 31 42.5
5 13 24
9 25
844
+ 10
0
f231 37 22.5
Index . . . . +<^
(360 00 00
Level .... +7
Means. Before Xoon 1 39
555.25
+ 7
1
H. H.
769 09 12 1
Observation earlier than Noon .
1.7
Observed Z.D. L.L. . 64 05 46 1
App'. Greenwich time corresponding!
to the Mean Z.D J
4 54.5
Refraction +1'59".3
Barometer . . +3.0
Thermometer +5.3
• +1 59.7
Lat. 40° 42' 43" Cosine . . . . 9.8796683
Parallax . . -7.9 J
Dec. 23° OT 17" Cosine . . . . 9.9636344
Semidiam .... -16 17.8
Z.D. 63° 50' 00" Cosecant . . . 10.0469582
Correction ... —1 28.9
f.ng. Sinel" AC . . S.3141951
Log. 555.25 (+4) 6.7444886 True Z.D. ... 634959
Correction 1' 28".9 . . . Loj
'. 1.9491746
App. Greenwich time j
23 07 17.6
North I^atitude .
40 42 41.4
2 S
314
EXPERIMENTS FOR DETERMINING THE VARIATION
New York. January 3d, 1823. Barom. 30.20; Therm. 36°. The Sidereal
Chron. 702 slow on Sidereal Time 6" 34.' 55". B Ursffi Minoris (AR. u'' 51' 17".5)
on the Northern Meridian at 20'" 16' 22" hy the Chronometer.
Chronometer.
Horary
Angtes.
N. V.
Sines.
Level.
Readings, &c.
II. M. S.
20 05 40
20 08 IS
20 11 00
20 12 32
20 16 36.5
20 20 57
20 24 14.5
20 26 12.5
20 28 02
20 29 53.5
20 32 06.5
20 34 55
M. 9.
10 42
8 04
5 22
3 50
0 14
4 35
7 52
•J 50
11 40
13 31
15 44
18 33
Means .
1090
619
274
140
I
200
589
920
1295
1739
2355
3274
0
+ 3
0
0
-10
- 9
-10
+ 2
+ 10
+ 3
0
- 9
First Vernier
Second „
Previous I Third „
Fourth „
Mean .
Final .
First Vernier
Second „
Third „
Fourth „
Mean .
Index
Level .
219 43 00
43 10
43 25
42 50
219 43 OR
272 08 50
08 50
09 30
08 30
. 272 08 55
, M40 16 54
''"1360 00 00
— 19.5
772 25 29
1041.3
-19.5
Lat. 40° 42' 43" Cosine . . . . 9.8796683
Dec. 74° 52' 19" Cosine . . . . 9.4166026
Z.D- 64° 25' 00" Cosecant . . . 10.0448136
Log. Sine 1" A.C 5.3144251
Log. 1041.3 ( + 4) 7.0175759
Correction 0' 17". 1 Log. 1.6730855
Observed Z.D.
Refraction +2'
Barometer
Thermometer
Correction .
True Z.D. . .
Polar Distance
Co. Latitude .
Latitude North
00". 7
+0.8 .
+2.9J
64 22 07.4
> -f2 01.4
+0 47.1
64
24
58
9
15
07
41
2
49
17
17
7
40 42 42.3
RECAPITULATION.
December 24, the Sun 40 42 40.1
December 24, Polaris 40 42 48.9
December 31, the Sun 40 42 41.4
January 3, e UrsE Minoris, S.P 40 42 42.3
40 42 43.2 North.
IN THE LENGTH OF THE SECONDS' PENDULUM.
315
HAMMERFEST.
Place of Observation.-— M Fugleness. The Zenith Distances observed with a
Repeating Circle.
June 12th, 1823. Bar. 29.90; Ther. 61°. The Chron. No. 649, slow 1" 33' 44".5.
Sun on the Meridian at 2S^ 59' 15 " Mean Time, and at 22"' 25' 30".5 by the Chron.
Chronometer.
Horary
Angles.
H. M. S.
22 07 28
22 08 55
22 10 38
22 13 07
22 14 45
22 16 08
22 32 48
22 33 50
22 35 08
22 36 27
22 38 05
22 39 26
22 41 15
22 42 13
22 44 00
22 45 34
18 02.5
16 33.5
14 52.5
12 23.5
10 45.5
8 22.5
7 17.5
8 19.5
9 37.5
10 56.5
12 34.5
13 55.5
15 44.5
16 42.5
18 29.5
20 03.5
N.V.
Sines.
Means. After Noon. . 3 14
3096
2620
2105
1461
1101
668
506
660
881
1140
1505
1845
2357
2656
3253
3827
1855
- 1
+ 1
+ 6
0
0
- 5
0
+•6
0
0
+ 5
0
+ 5
0
- 4
- 5
- 2
+ 2
0
- 3
0
- 8
0
+ 10
0
0
+ 1
0
+ I
0
0
+ 3
Apparent Greenwich time at Noon 22 25
Observations later than Noon . . 3.2
Ap'. Greenwich time, corresponding! „„
to the Mean Zenith Distances. . J ***•*
Lat. 70°40' Cosine .... 9.5199112
Dec. 23° 08" Cosine .... 9.9635957
Z.D.47°32' Cosecant . . 10.1321377
Log. Sine TA.C 5.3144251
Log. 1855 (+4) • 7.2683439
Correction 2' 37".9 Log. 2.1984136
Readings, &c. Son's L.L.
Previous
Final
! J irst Vernier
. 266 10 20
Second „ .
9 43
. Third „ .
10 20
! Fourth „ .
Mean . . .
9 40
. 266 10 00
First Vernier
. 311 26 10
Second „ .
26 20
Third „ .
26 40
Fourth „ .
Mean . .
25 45
. 311 26 14
Index . . .
■ r 93 50 00
■^ \3G0 00 00
Level .
L.L.
+ 3
765 16 17
Observed Z.D
. 47 49 46
Refraction+r
04"
21
Barometer .
-0
.2
Thermometer
- 1
4
+ 0 56.3
Parallax
-6
3
Semidiam
.
,
. - 15 46.4
Correction .
. - 2 37.9
True Z.D. .
. 47 32 IS
Declination at Za"" 28'
(June 11th) App'. \ 23 07 47.
Greenwich time .
Latitude North
70 40 05.3
2 S 2
316
EXPERIMENTS FOR DETERMINING THE VARIATION
SPITZBERGEN.
Place of Observation. — At the Observatory on the Inner Norway Island.
The Zenith Distances were observed with a Repeating Circle.
July 5th, 1823. Bar. 30.10; Therm. 41°. The Chron. 649, slow 44- Sl'.S, (page
152); the Sun on the Southern Meridian at O'' 04' 00" Mean Time, and at
23ii 19' OS. 5 by the Chronometer.
Chronometer.
H. M. s.
22 55 .S8
22 57 54
23 00 00
23 02 00
23 04 13
23 05 45
23 08 00
23 11 04
23 13 17
23 16 IG
23 18 38
23 20 28
23 22 26
23 2 t 02
23 25 36
23 27 08
23 28 47
23 31 48
23 33 52
23 35 45
Times
from Noon.
III. s.
23 30.5
21 U.5
19 08.5
17 08.5
14 55.5
13 23.5
11 08.5
8 04.5
5 51.5
2 52.5
0 .30.5
1 19.5
3 17.5
4 53.5
6 27.5
7 59.5
9 38. 5
12 39.5
14 43.5
16 36.5
Before Noon
3 01
N. V.
Sines.
5250
4292
3486
2796
2119
1707
1182
620
327
79
3
17
103
228
397
608
885
1525
20C3
2625
1515.9
Level.
0
+ 10
+ 6
+ 6
+ 7
0
+ 3
+ 2
+ 2
0
+ 2
+ 6
0
+ 6
+ 7
+ 6
-10
+ 8
+ 7
+ 3
+
Readings, &c. Sun's L.L.
Apparent Greenwich time at Noon . 23 13.3
Observations before Noon ... - 3
Apparent Greenwich Time corres-lg- , , „
ponding to the Mean Z.D. . . 1
Lat. 79° 50' Cosine 9.2467746
Dec. 22^ 52' Cosine 9.9644537
Z.D. 56° 58' Cosecant 0.0765728
Log.Sine 1"A.C 5.3144251
Log. 1515.9 (+4) 7.180670G
Correction 1' 00". 7 Log. 1.7828968
Previous •
First Vernier
Second „ .
Third „ .
Fourth ,, .
Mean
39 18 20
18 10
IS .30
18 10
39 18 17.5
Final
J
f First Vernier
Second „
Third „ .
Fourth „
Mean
Index
Level
+
Observed Z.D. L.L. .
Refraction + 1' 30". 3")
Barometer + 0.3
Thermometer + ! . 3
Parallas
Semidiam. .
Correction .
. 103 39 05
38 45
39 30
38 50
. 103 39 02.5
r.320 41 42.5
1 720 00 00
+ 5
1144 20 50
, 57 13 02.5
\-l\
+ 1 24.0
— 15 45.5
— 1 00.7
TraeZ.D 56 57 40.8
Decl.at23"10;.3App.l g^ 5, ,5.5
Greenwich Imie j
North Latitude . . . 79 49 56. i
IN THE LENGTH OF THE SECONDS' PENDULUM.
317
Spitzbergen. July 6th, 1823. Bar. 29.90; Therm. 3S°.5. The Chronometer
649, slow 44' 51" (page 152). The Sun on the Northern Meridian at 12'' 04' IG"
Mean Time, and at ll'' 19' 25" by the Chronometer.
Chronomeler.
II. M. S.
11 05 2B
11 07 35
II 10 07
11 12 00
11 \4 47.5
11 17 07
11 20 45.5
11 22 44
II 25 OG
II 27 37.5
11 30 IS
11 32 17
Time from
Midoi^ht.
SI. s.
IS 53
11 50
9 18
7 25
4 37.5
2 18
1 20.5
3 13
5 41
8 12.5
10 53
12 52
Meaiii- Before Mid. 0.35
N. V.
sines.
Level.
ISCl
1333
823
521
203
51
17
105
307
641
1127
1575
714
0
0
0
+ 10
1+0
+ 10
+ 10
+ 2
+ 10
-10
+11
+ 2
0
0
^ 2
+ 1
+ 1
+ 1
- 7
+ 3
_ 2
+ 3
- 6
+ 13.5
Readings, &c. Sun's U.L.
App. Greenw''. Time at Midnight . 11 13.3
Observations earlier than Midnight . 0.6
App. Greenwich Time correspond- 1 .i 19 ^
ing to the Mean Z.D. j '
Lat. 79° 50' Cosine .
Dec. 22° 44' Cosine .
Z.D. 77° 26' Cosecant
Log. Sine 1" A.C. . .
Log. 71 4 (+4). . .
Correction 0' 24". 6
Log
9.24677 46
9.9648785
0.0105308
5.3144251
6.8536982
Previous
Final
First Vernier
Second ,,
Third ,, .
Fourth ,, .
. 284 25 20
25 10
25 50
25 00
Mean 284 25 20
First Vernier
Second „
Third ,, .
Fourth ., .
Mean
Index . . . . +
Level ....
129 38 00
37 50
38 25
38 05
129 38 05
75 34 40
720 00 00
+ 13.5
925 12 58. 5
Observed Z.D. U.L. . 77 06 04.9
Refraction +4' 09". 4
Barometer —0 00.8
Thermometer+0 04.9
Parallax —0 08.6.
Semidiam +15 45.5
Correction . . . . + 0 24.6
> + 4 04.9
True Z.D 77 26 19.9
1.3903072
Decl. at llh 12'.7 App.
Greenwich Time
North Latitude .
102 33 40.!
22 43 44.2
79 49 55.9
318
EXPERIMENTS FOR DETERMINING THE VARIATION
Sui'ryRRRfjFiv Jiilv 7lli 1 S2.S Raroni 29.74- Therm 34°
TliP niirnn. r.4.q
slow 44' 49".5 (page 253); the Sun on the Northern Meridian at 12'' 04' 26" Mean J
Time, and at 11' 19' 36".5 by the Chronometer.
Chronometer.
Time from
Miduight.
N.V.
Sines.
Level.
Readings, &c. S
in'« U.L.
II. M. s.
H. s.
O ' ff
10 52 43
26 53.5
6876
0
0
First Vernier
. 203 00 00
10 5G 03
23 33.5
5278
+ 6
- 3
Second „
. 202 59 40
10 57 56
11 00 12
21 40.5
19 24.5
4469
3.584
0
+ 13
0
+ 4
Previous.
Third „
. 203 00 30
11 02 57
11 04 27
11 07 38
11 10 32
16 39.5
15 09.5
U 58.5
9 04.5
2G40
2187
1365
783
+ 2
+ 13
+ 7
- 7
+ 3
0
- 3
Fourth „
Mean .
202 59 50
203 00 00
11 12 35
7 01.5
470
+ 2
- 7
First Vernier
. 306 47 20
11 11 00
5 36.5
300
0
0
Second „
47 05
11 1.5 -IS
11 17 15
3 48.5
2 21.5
138
53
+ 2
0
- 7
0
Final . ..
Third „
47 30
11 19 08
1 1 20 36
0 28.5
0 59.5
2
10
+ 8
-12
- 2
- 3
Fourth „
Mean . .
46 50
306 47 11.2
11 30 27
11 31 51
10 50.5
12 14.5
1118
1426
+ 6
+ 3
- 3
- 7
Index .
f 157 00 00
4^
11 34 08
14 31.5
2008
+ 2
- 7
[1080 00 00
11 35 18.
15 41.5
2312
+ 9
- 1
Level . .
+ 12
11 37 09
11 38 36
17 .32.5
18 59.5
2928
3431
+ 2
+ 10
- 7
+ 1
Observed Z.D.
1
U.L.
543 47 23.2
Meaiu. Before Midnight 3 38
2070.4
+ 12
77 11 22.2
Refraction +4'
11"
Apparent Greenwich Time at Midnight . 1
Observation earlier than Midnight . .
1 13.3
3.6
Barometer . —2.2
Thermometer +7.3
Parallax . -8.5
• +4 07.6
Apparent Greenwich Time corresponding],
lo the Mean Z.D. J
1 09.7
+ 15 45.5 1
Lat. 79° 50' Cosine 9.2467746 Correction
Dec. 22° 38' Cosine 9.9651953 True Z D
Z.D. 77° 32' Cosecant 10.0103624
1
+ 1 11. S
77 32 26.6
02 27 33.4
Log. Sine 1" A.C 5.3144251 Decl. at 1 lb 09'.7
!f 22 37 34.8
Los. 2070.4 (+4) . . . 7.3160543 App. Greenwi^T
imej
o
Correction 1'
11". 3 . .
. . Lo
?. 1.8528117
North Latitude
79 49 58.6
IN THE LENGTH OF THE SECONDS PENDULUM.
319
Spitzbehgen. July 9th, 1S23. Barom. 29.93; Therm. 37°. The Chron. GI9,
slow 44' 48" ; the Sun on the Northern Meridian at la"" 04' 45' Mean Time, and at
1 1*" 19' 57" by the Chronometer.
ChroDometer.
Time from
Midnight.
N.V.
Sines.
Readings, &c. Sun's U.L.
H. M. S.
II 05 25
1 1 06 5.^
11 09 07
11 10 29
II 12 27
U 14 10
n 16 07
II 17 19
11 19 10
11 21 30
11 24 00
11 25 28
11 29 07
II SO 46
II 32 42
11 34 23
M. s.
14 32
13 04
10 50
9 28
7 30
5 47
3 50
2 38
0 47
1 33
4 03
5 31
9 10
10 49
12 45
14 26
2010
1625
1117
85 S
535
318
140
66
0
23
156
289
800
1114
1547
1982
+ 2
+ 6
+ 1
+ 8
+ 6
0
0
0
+ 5
+ 7
+ 7
+ 12
0
+ 6
0
+ 3
- 6
- 2
- 7
- 1
- 2
- 9
0
0
- 3
- 2
- 2
+ 4
0
- 3
0
- 5
Means. Before Mid. 0 38
786.3
+ 12.5
.Apparent Greenwich Time at Midnight 11 13.3
Observation earlier than Midnight . 0.6
App. Greenwich Time corresponding!
to the Mean Z.D / " '^•'
Lat. 79° 50' Cosine
Dec. 22° 24' Cosine
Z.D. 77° 46' Cosecant
Log. Sine 1" A.C. .
Log. 786.3 (+4) .
Correction 0' 27".! .
9.2467716
9.9659285
0. 0099753
5.3141251
6 8955883
Previous •
Final
' First Vernier
Second „
Third „
Fourth „
Mean .
First Vernier
Second „
Third „
Fourth „
Mean
Index
Level .
176 08 55
09 00
09 3J
08 50
176 09 03.7
334 57 40
57 50
58 00
57 25
334 57 43.7
flS3 50 56.3
[720 00 00
+ 12,5
1238 48 52.6
Observed Z D. U.L. . 7T 25 33.3
Refraction +4' 15" 1
Barometer . . —0.6
+ 5.8
-8.5 J
Thermometer
Parallax
Semidiam .
Correction .
True Z.D. .
+ 4 11.7
+ 15 45. G
-fO 27.1
77 45 57.7
102 14 02.3
Decl. at III' 12". 7
22 24 03
App. Greenwich Time J
Log. 1.4326918
North Latitude
79 49 59.3
320
EXPERIMENTS FOR DETERMINING THE VARIATION
Spitzbebqeiv. July lOth, 1823. Barom. 30.00; Therm. 45°. The Chron.
423 fast of No. 649, 3' 25", slow of Mean Time 41' 23". The Sun on the Northern
Meridian at 12'> 04' 54" Mean Time, and at 11" 23' 31" by 423.
Chronometer.
Time from
MidDigbt.
N. V.
Siues.
Level.
Readings, &c. Son's U.L.
H. M. S,
10 54 42
10 56 56
iO 59 5 4
11 02 51
1 1 05 25
11 07 28
II 10 15
11 12 28
11 15 15
11 17 10
11 19 21
]1 22 00
11 25 48
11 27 45
11 30 42
11 32 31
11 34 47
11 36 52
11 39 17
11 40 40
M. S.
28 49
26 35
23 37
20 40
18 06
16 03
13 16
11 03
8 16
6 21
4 10
1 31
2 17
4 14
7 11
9 00
U 16
13 21
15 46
17 09
Means. Before Midnight. 4 55
7894
6719
5305
4063
3117
2451
1675
1162
6S0
384
165
22
50
171
491
771
1208
169G
2365
2793
0
+ 7
0
+ 2
+ 5
+ 11
+ 3
0
+ 2
+ 3
+ 6
+ 6
+ 3
2157.9
0
- 2
0
- 7
- 3
+ 2
- 5
0
- 7
- 5
- 2
- 2
- 5
- 2
- 6
- 7
- 8
+ I
0
- 1
Previous .
+
Final
H. M.
App'. Greenwich Time at Midnight . 11 13.3
Observation earlier than Midnight . . 4.9
App". Greenwich Time corresponding! ,] /lo ^
to the Mean Zenith Distance . . j" " ^J'-"*
Lat. 79°50' Cosine .... 9.2467746
Dec. 22° 17' Cosine .... 9.9662920
Z.D. 77° 53" Cosecant . . 10.0097845
Log. Sine 1" A.C 5.3144251
Log. 2157.9 (+4) 7.3340313
Correction 1' 14". 3 Log. 1.8713075
First Vernier
334 57 10
Second
57 50
Third „ . . .
58 00
Fourtli „ . . .
Mean ....
57 25
334 57 43.75
First Vernier
85 40 50
Second „ . . .
40 20
Third
41 00
Fourth
Mean ....
40 20
85 40 37.5
{ 25 02 16.25
Index . • . +■!
[ 1440 00 00
Level ....
+ 8.5
1550 43 02.25
Observed Z.D. U.L.
77 32 09.1
Refraction +4' IS" i
Barometer . . 0
Thermometer +1.6
. + 4 11.1
Parallax . . — 8.5
Semidiam
+ 15 45.6
Correction . . .
+ 1 14.3
True Z.D. . . .
77 S3 20.1
Decl. at nil 08". 4 1
102 06 39.9
App. Greenw^.timeJ
22 16 44.1
North Latitude . .
79 49 55.8
IN THE LENGTH OF THE SECONDS' PENDULUM.
321
Spitzbergen.
-July 12th, 1S23.
Barom. 29.94 ; Therm. 37
\5. TheChron.
No. 649 slow 44'
4S". The Sun on the Southern Meridian at 00'' 03' 06".5 Mean |
Time, SS"" 20' IS".
5 by the Chronometer.
Chronometer.
Time from
Noon.
N.V.
Sines.
Level.
Readings, &c. Sun's U.L.
H. M. S.
23 15 10
M.S.
5 08.5
252
0
0
First Vernier .
0 / fl
. 205 55 40
23 17 03
23 18 50
23 20 25
3 15.5
I 28.5
0 06.5
101
20
0
+ 7
+ 3
0
- 1
- 5
0
Previous ■
Second „
Third „ .
55 40
56 15
23 22 22
23 23 32
23 25 04
23 27 33
23 29 00
23 31 35
2 03.5
3 13.5
4 45.5
7 14.5
8 41.5
U 16.5
40
99
216
499
719
1210
+ 7
+ 1
+ 3
0
+ 2
+ 7
- 2
- 8
-6
0
- 7
2
Fourth „
Mean .
First Vernier .
Second ,,
55 20
. 205 55 43.75
. 175 35 15
35 15
23 33 34
13 15.5
1673
+ 1
- 8
Final . . ■
Third ,. .
35 40
23 36 10
15 51.5
2392
+ 3
- 6
Fourth „
Mean .
Index .
34 50
Means. After Noon 4 42
601.8
-5.5
. 175 ,^5 15
1 [154 04 16.2
^ 1360 00 00
App. Greenwich Time a
Observation after Noon
App. Greenwich Time, c
to the Mean Z.D. .
Lat. 79° 50' Cosine .
H. M.
t Noon . . 23 13.3
d 7
Level .
-5.5
Observed Z.D. U
Refraction +1' 3
Barometer . . —
Thermometer . -f
Parallax . . . —
689 39 25.7
orrespom
L. 57 28 17.!
".2 1
r.i\ +>2s.5
7.4 J
'"?} 23 18
9.2467746
Dec. 22° 05' Cosine .
. . . 9.9669101
Semidiam .
+ 15 45.8
Z.D. 57° 45' Cosecant .
Log. Sine 1" A .C. . .
Log. 601.8 (+4) . .
. . . 10.0727694
. . . 5.3144251
. . . 6.7794522
Correction
-00 24
57 45 04.4
Decl. at 231" 18'. ..!„„„. . ,
App. Greenwich Ti-o r 22 04 57.1
Correction 00' 24" . .
Log. . 1.3803314
North Latitude .
79 50 01.5
RECAPITULATION.
July 5, Sun
on the Southern Meridian . . .
... 79 49
56.1
July 6, Sun
on the Northern Meridian . . .
... 79 49
55.9
July 7, Sun
on the Northern Meridian
... 79 49
58.6
July 9, Sun
on the Northern Meridian
... 79 49
59.3
July 10, Sun
on the Northern Meridian
... 79 49
55.8
July 12, Sun
on the Southern Meridian
. , . 79 50
01.5
79 49
57.8 Noith.
a T
322
EXPERIMENTS FOR DETERMINING THE VARIATION
GREENLAND.
Place of Observation. — At the Observatory on the Inner Pendulum Island.
1
August 21st, 1823. Bar. 29.90 ; Ther. 39°. The Altitudes observed with a Sextant
and Mercurial Horizon. The Chron. No. 423 fast l*" 23' 45" (page 168) ; the Sun
on the Meridian at 0'' 03' 03" Mean Time, and at l*" 26' 48" by the Chron.
Chronometer.
H. M. S.
1 18 00
1 13 00
1 33 40
1 35 00
Time from
Noon.
M. S.
8 48
7 4S
6 52
8 12
Means. Before Noon 23
N.V.
Sines.
737
5S2
4 19
640
602
56 07 58 ^
55 04 50 O
55 04 30 Q
56 07 45 ^
55 36 IG
Observed Double Altitude
Index
55 SG 16
- 1 20
55 34 .i6
Apparent Altitude 27 47 2S
Refraction 1' 50". 1
Barometer +0.4
App. Greenwich Time at Noon .
Observation earlier than Noon
Apparent Greenwich Time corres-
ponding to the Mean Altitude J
H. M.
1 15.3
0.4
1 14.9
Thermometer — 2
Parallax +7.7
Correction .
1 44
+ 0 36.6
True Altitude 27 46 20.6
Zenith Distance ...
. . . . 62 13 39.1
Decl. at 11" 14'.9 app. Greeni". Time 12 18 39
I^t 74°32' Cosine .... 9.4259867
Dec. 12° 19' Cosine .... 9.9898873
Alt. 27° 46' Secant 10.0531293 North Latitude 74 32 18.4
Log. Sine 1" A.C 5.3144251 ~"^
Log. 602 (+4) 6.7795965
Correction 36". 6 Log. 1.5630249
IN THE LENGTH OF THE SECONDS' PENDULUM.
323
Greenland. August 22nd, 1823. Bar. 29.95; Therm. 39°. The Altitudes ob-
served with a Repeating Reflecting Circle of six inches diameter, and a Mercurial
Horizon. The Chrou. No. 423, fast l"- 23' 51', page 168. The Sun on the Meridian
at 0''02' 48" Mean Time, and at l^ 26' 39" by the Chronometer.
Cbronomeltr.
H. M. s.
1 20 30
1 21 50
1 32 20
1 33 24
1 35 08
1 36 30
Time from
NooD.
M, S.
6 09
4 49
5 41
6 45
8 29
9 51
Means. Afwr Noon. S 17
N. V.
Sines.
360
221
307
434
685
923
488.3
H. M.
Apparent Greenwich Timel, ,, „
at Noon /^ '*-^
Observation later .
3.3
App. Greenw' Time cor-1
responding to the MeanW 18.6
Altitude ...
•J
Lat.74''32' Cosine. 9.4259867
Dec. 1 1" 59' Cosine . 9.9904312
Alt. 27°2e' Secant .10.0518084
Log. Sine 1" A.C. . 5.3144251
Log. 488.3 (+4) . 6.6886867
Correction, 0' 29".6Ix)g. 1 .4713381
DedactioD. (The Limbs observed aileroately.)
Arc passed through
O / //
329 31 10
54 55 11.7
Apparent Altitude 27 27 35.8:
Refraction - 1' 51". 6i
Barometer . + 0 . 2 I
> • . . . - 1 45.8;
Thermometer — 2.1
Parallax . + 7.7J
Correction +0 29.6
True Altitude
27 26 19.6
Zenith Distances 62 33 40.4
Deelin. at 1" 18". 6 1
f
App. Greenwich Time J
North Latitude
11 58 36.2
74 32 16.6
2 T 2
324
EXPERIMENTS FOR DETERMINING THE VARIATION
Greenland. August 23d, 1823. Barom. 29.90; Therm. 37°.5 ; the Altitudes
observed with a Repeating Reflecting Circle of six inches diameter, and a Mercurial
Horizon. The Chronometer No. 423 fast l"- 23' 5G" (page les). The Sun on the
Meridian at O"" 02' 33" Mean Time, and at l"" 26' 29" by the Chronometer.
Chronometer.
Time from
Nooc.
N.V.
Sines.
Deduction. (The Limbs observed allernalely.)
11. M. s.
1 12 07
1 14 45
1 18 20
1 19 50
1 35 45
1 38 15
1 41 15
1 42 50
M. 3.
14 22
11 44
8 09
6 39
9 16
11 46
14 46
16 21
1964
1310
632
421
817
1318
2075
25 44
Lat. 74"32' Cosine 9.4259867
Dec. 1 1° SS" Cosine 9.9909839
Alt 27° 06' Secant . ... 10.0505062
Lo" Sine 1" \.C 5.31442S1
Log. 1385 (+4) . . .
Correct. 1' 23".S
7.1414498
Log. 1.9233537
o / />
Means. ATter Noon 1 24
1385
Arc passed through
433 44 00
54 13 00
. _,. H. M.
. . . . 27 06 30
Apparent Greenw". I im
at Noon . . . ■
Observations later . .
H 1 15.3
1.4
Refraction . -1'53".3
Barometer . . . +0.4
Thermometer . - 2.4
Parallax . . . . + 7.7
Correction ....
- 1 47.6
+1 23.8
App. Green. Time corres
ponding to Mean Alt.
'1 1 16.7
27 06 06.2
. . . . 62 53 53.8
Decl. at 1'' 16". 7 app. Gre
enwichTime . . 11 38 26.2
74 32 20
IN THE LENGTH OF THE SECONDS' PENDULUM.
325
Greenland. August 25th, 1S23. Barom. 29.72 ; Therm. 3S°. Zenith Distances
with a Repeating Circle. The Chron. 423 fast 1" 24' 09 " (page 16S) ; the Sun on
the Meridian at 02' 02" Mean Time, and at 1" 26' 11" by the Chronometer.
Chronometer.
H. M. S.
I IS 10
1 IS 45
1 17 45
1 20 10
1 31 45
1 33 32
1 35 30
1 37 12
1 38 45
1 40 28
Time from
Noon.
M. S.
13 01
10 26
8 26
6 01
5 34
T 21
9 19
11 01
12 34
14 17
N.V.
Sines.
1612
1036
677
345
295
514
826
1155
1503
1941
Means. After Noon 2 IS
990.4
+ 3
+ r.
+ 10
+ 0
0
+ 2
+ S
+ 10
+■ 3
+ 3
- 6
- 3
+ 2
- 3
0
- 6
0
+ 2
- 6
- 6
Readings, &c. Alternately upper and lower Limbs.
+- 12.5
Apparent Greenwich Time at Noon
Observation earlier than Noon
U. M.
1 15.3
2.2
.\pp. Greenwich Time corresponding to\ , ,. ,
the Mean Z.D. . . . . . . f ' ''-^
Lat. 74° 32' Cosine .
Dec. 10° 58" Cosine .
Z.D. ea" 35' Cosecant
Log. Sine 1" A.C. .
Log. 990.4 (+4)
Correction 0' 59". 7
9.4259867
9.9919956
10.0478945
5.3144251
6.9958106
Previous •
First Vernier
Final . . i
Second „
Third „ .
Fourth „ .
Mean . . .
First Vernier .
Second „
Third „ .
Fourth „
Mean .
Index .
. +
Level . .
179 58 00
57 50
58 20
58 00
179 58 02,5
95 37 30
37 20
38 00
37 20
95 37 32.5
180 01 57.5
360 00 00
+ 12.5
635 39 42.5
Observed Z.D. . . 63 33 58.25
Refraction +1'56".5
Barometer —1.1
Thermometer +2.4
Parallax . . -7.9 J
Correction . . . —0 59.7
• +1 49.9
True Z.D. . . . 63 34 48.45
Log. 1.7761125
Decl. at 1" 17'. 5 . }
App. Greenwich Time J
North Latitude . .
10 57 31.5
74 .32 19.95
326
EXPERIMENTS FOR DETERMINING THE VARIATION
Greenland. August 2Glh, 1823. Uarora. 29.74 ; Therm. 44°. Zenith Distances
observed with a Repeating Circle. The Chron. 423 fast I'' 24' 17" (page 168) ;
Sun on the Meridian at 01' 46" Mean Time, and at l" 2G' 03" by the Chronometer.
Chronometer.
Time from
Noon.
N. V.
Sines.
he\
e\.
11. M. S.
M. s.
1 7 33
18 SO
3256
- 4
+ 3
1 10 07
15 56
2416
+ 13
+ 7
1 12 10
13 53
1834
- 4
-U
1 14 40
11 23
1233
0
+ 6
1 17 16
8 47
734
- 5
+ 1
1 19 22
6 41
425
- I
+ 5
1 30 57
4 54
229
- 6
0
1 32 45
6 42
427
- 1
+ 5
I 34 54
8 52
748
- 6
0
1 36 50
10 47
1107
- 1
+ 5
1 38 33
12 30
1487
- 2
+ 4
1 40 18
14 15
1932
- 7
0
Means. Before N
001. 1 26
1319
+ 1
Readings, &c. Limbs alternately observed.
Previous
Final .
H. M.
Apparent Greenwich Time at Noon . 1 15.3
Observation earlier than Noon . . 1.4
App. Greenwich Time corresponding to \ , ,„ „
the Mean Z.D j- 1 ici.y
Lat. 74° 32' Cosine 9.4259867
Dec. 10° 37' Cosine 9.9925013
Z.D. 63" 55' Cosecant .... 10.0466485
Log. Sine 1" A.C 5.3144251
Log. 1319 ( + 4) 7.1202448
Correction 1' 19".4 . . . Lo,::. 1.8998064
First Vernier
95 37 30
Second „ .
37 20
Third „ .
38 00
Fourth „ .
37 20
Mean . .
95 37 32.5
First Vernier
112 30 40
Second „ .
36 30
Third „ .
. •
37 00
Fourth „ .
36 30
Mean
142 36 40
Index
+{
264 22 27.5
360 00 00
Level . .
+ 1
766 59 08.5
Observed Z.D.
63 54 55.7
Refraction +1' 58". 4
Barometer —1.0
Thermometer +1.0
Parallax -7.9
Correction .
True Z.D. . . .
Decl. at 1'' 13". 9
App. Greenw"" Time
North Latitude .
+ 1 50.5
-1 19.4
63 55 26.8
10 36 51.1
74 32 17.9
RECAPITULATION.
O t dt
August 21st, Sun on the Southern Meridian. Sextant 74 32 18.4
„ 22d, „ „ Repeating Reflecting Circle 74 32 16.6
„ 23d, „ „ Repeating Reflecting Circle 74 32 20
„ 25th, ,, „ Repeating Circle . . . 74 32 19.9
„ 26th, „ „ Repeating Circle . . .74 32 17.9
North Latitude
74 32 18.6
IN THE LENGTH OF THE SECONDS PENDULUM.
327
DRONTHEIM.
Place of Observation. — Mr. Hans Wentzel's Villa. The Zenith Distances were
observed with a Repeating Circle.
October leth, 1S23. Barom. 29.4.G ; Therm. 41°. The Chron. G-19 slow 39' 3o".j.
The Sun on the Meridian at 11'' 06' OS" by the Chronometer.
Chionomeler,
Time from
Noon.
N. V.
Sines.
LevL'I.
Readings, &c. Limbs alternately observed.
H. M. s.
10 48 15
10 49 15
10 52 01
10 53 21
10 55 25
10 56 44
10 58 41
11 01 01
II 02 58
II 04 11
II 09 01
11 10 II
II 12 03
II 13 II
II 15 Of,
II 16 04
II 17 56
II 19 01
II 20 51
II 22 08
H. 5.
17 53
16 23
U 07
12 47
10 43
9 21
7 27
5 07
3 10
1 57
■i 53
4 03
5 57
7 03
8 58
9 56
11 48
12 56
II 43
16 00
Means. Before \oon. 0.16
3043
2354
1896
1555
1093
841
528
249
93
36
79
156
3.17
473
7P5
939
1325
1392
2061
2436
1102.65
-6
+ 6
+ 1
+2
0
+ 6
+2
+4
+ 2
+8
0
+ 9
+ 8
4-3
+ 2
+9
0
+ 6
+4
+7
0
0
2
- 1
-6
-0
-4
-2
-4
+ 3
0
+ 3
+2
-2
-4
+ 3
0
0
-2
+2
+30
Lat. 63°26' Cosine 9.6505395
Dec. 8° 41' Cosine 9.9919933
Z.D. 72°0r Cosecant .... 10.0215073
Log. Sine 1" A.C 5.3144251
Log. 1102.65 (+4) 7.0424370
Correction 1' 4.5".6 Log.. 2.0239022
Previous ■
Final.
First Vernier
Second ,,
Third „
Fourth „
Mean .
First Vernier
Second „
Third „
Fourth „
Mean .
Index .
Level .
210 21 00
20 30
21 20
20 25
210 20 49
212 19 40
19 30
20 10
19 20
212 19 40
\ 149 39 11
L1080 00 00
+ 30
1 44 1 39 21
Observed Z.D.
Refraction +2' 58". 6
Barometer —3.3
Thermometer +3.3
Parallax . . -8.2
Correction
True Z.D. . . .
Declination South
Latitude North .
72 05 58
-f2 50.4
-1 45.6
72 07 02.8
8 41 11.5
63 25 51.3
328
EXPERIMENTS FOR DETERMINING THE VARIATION
Droatheim. November lOth, 1S23. Bar. 30.44; Therm. 30°. The Chron.
No. 649 slow 38' 53". a Ursse (Apparent AR. 10'' 52' 47") on the Meridian below
the Pole at 6'' 57' 17" by the Chronometer.
Chronometer.
Horary
Angles.
N.V.
Sines.
Level.
Readings, &c.
H. M. S.
M. s.
O / t/
6 50 45
6 32
406
+ 8
- 3
' First Vernier . . 209 22 40
6 53 06
4 11
167
+ 7
- 3
Second „ . . . 22 30
6 5» 56
2 21
53
0
0
Previous . •
Third „ . . . 23 10
6 57 30
6 59 32
7 01 02
0 13
2 15
3 45
0
48
134
+ 10
+ 4
+ 6
- 1
- 6
- 4
Fourth „ . . . 22 20
Mean . . . . 209 22 40
First Vernier . . 135 27 00
7 03 23
6 06
354
+ 6
- 4
Second ,. . . . 26 30
7 04 42
7 25
524
+ 8
- 3
Final . .
Third „ . . . 27 20
7 06 30
9 13
809
+ 2
- 8
Fourth ,, . . . 26 40
7 OS 17
11 00
1152
+ 8
- 2
Mean . . . . 135 26 62.5
7 U 03
13 46
1804
+ 2
— 8
7 14 40
17 23
2S75
0
0
r„j„. J. /ISO 37 20
Index . . • + IseO 00 00
Level . . +9.5
Means
694
+ 9.5
646 04 22
Observed Z.D. . . 53 50 21.8
Lat. 63°26' Cosine 9.6505395
Refraction +1' 19".5j
Barometer +I.2i. + 1 23.9
Dec. 62° 42' Cosine .... 9.6614810
Thermometer +3.2J
Z.D. 53°52' Cosecant .... 10.0927784
Log. Sine 1" A.C 5.3144251
Correction . . . + 0 36.3
True Z.D. ... S3 52 22
Altitude .... 36 07 38
Log. 694 (+4)
6.8413595
Apparent North P.D. 27 18 19.2
Correction S6".35 . . . Log. 1.5605835
Latitude North . . 63 25 57.2
RECAPITULATION.
October 16, The Sun I . ■
.... 63 25 51.3
s.p
. . . . 63 25 57.2
63 25 54.2 North.
IN THE LENGTH OP THE SECONDS' PENDULUM. 329
APPLICATION OF THE OBSERVED VARIATION IN THE LENGTH
OF THE SECONDS' PENDULUM TO THE DETERMINATION OF
THE FIGURE OF THE EARTH.
The elements, required towards the determination of the figure of the
earth, are the ratios of the length of a pendulum vibrating equal por-
tions of time, at the level of the sea, in different latitudes.
The values, which the operations recorded in the preceding pages have
experimentally determined, are the lengths of the pendulum vibrating
seconds of mean solar time, at stations of ascertained latitude, but
elevated, in all the instances, more or less considerably above the sea.
In order, therefore, to render the results applicable to the proposed
determination, it is necessary that each should receive a small correction
proportionate to the elevation at which it was obtained.
The value of the corrections which may be actually due in the several
cases, is, unfortunately, not susceptible of a very exact determination,
either by calculation or by experiment. Were the surface of the earth
an unbroken plain, of uniform density, and were the space between its
level and that of the station of experiment unoccupied by matter, the re-
duction of the length of the pendulum at the upper level to that of the
lower level, would be strictly proportioned to the squares of their re-
spective distances from the earth's centre : but the materials composing
the eminence on which the pendulum is placed, as well as those which
are adjacent, will influence the vibration by virtue of their own attrac-
tion ; whence the difference in the length of a pendulum required to
vibrate in equal times at the level of the sea, and at an elevation, must in
all cases be less than would be due to a variation of gravity proportioned
2 u
330 EXPERIMENTS FOR DETERMINING THE VARIATION
to the squares of the distances ; and as the existing arrangement and
disposition of the materials at the surface of the earth is one of much
irregularity, both in figure and density, and as it is obviously impossible
to calculate with exactness the peculiar attraction due to each locality, the
value of the employed corrections must necessarily be assigned in some
measure on arbitrary assumption, and must, therefore, be deficient in
that precise experimental determination, of which all other parts of the
operation appear to be capable.
The uncertainty, to which the results, to be adopted in the general
conclusion, are liable from this source, may however be altogether
avoided, or reduced within limits of inconsiderable amount, by the selec-
tion of stations but little removed from the level of the sea: but as
stations cannot always be obtained in which this important advantage
may be combined to its fiiUest extent with the other necessary qualifica-
tions, it may be proper to shew the limit of elevation at which the
uncertainty produces a sensible effect on the results, as well as the extent,
to which the correction for elevations exceeding that limit, may be con-
sidered as uncertain.
The co-efficient of a formula, which should correctly represent the
modification, which the decrease of gravity at elevations proportioned to
the square of the distance from the earth's centre undergoes, by reason
of the attraction of the masses which surround and on which the opera-
tions take place, must vary in its amount in relation both to their external
configuration and density : with respect to the first consideration, it has
been stated by Dr. Young in the Philosophical Transactions for 1819, that
if a station be situated on a tract of table land of two thirds the mean
density of the earth, its attraction would equal half the diminution of gra-
vity occasioned by receding from the earth's centre ; and that in almost
any country which could be chosen for the experiment, wherein the inequa-
lities of surface might be excessive, the correction for elevation would
IN THE LENGTH OF THE SECONDS* PENDULUM. 331
not equal three fourths of the amount deducible from the duplicate pro-
portion of the distances from the centre : now as the general disposition
of the surface is much more conformable to the first supposition, than to
the second extreme, (which is that of a station raised on a sphere), and
as stations of experiment are rarely chosen in situations deviating much
from what may be deemed a level surface broken by occasional small
irregularities ; if the co-efRcient, due to an average superficial density, be
assumed at ^ths, it is probable that the correction would be in no in-
stance in error, from the circumstances of figure, more than ^th of the
amount deducible from the squares of the distances, excepting in a very
extreme case, when a special allowance might be made.
The lengths of the pendulum at the several stations determined by
these experiments, are given to the fifth place of decimals, and may be
presumed to be correct in their relation to each other, as far as the figure
in the fourth place, corresponding to tenths of a second in the daily rate ;
if the elevation be under twenty feet, an uncertainty amounting to ^th
of the correction due to the squares of the distances, will not affect even
the figure in the fifth place of decimals, and it is not until the figure in
the fourth place is affected, that the presumed correctness of the ex-
perimental determinations is interfered with.
In the view that has been thus taken, the variation of the co-efficient
due to the form of the eminences which rise above the general level of
the earth's surface, has alone been taken into the account ; it remains to
consider the variation which may be occasioned by the different densities of
the materials of which the eminences are composed. The first difficulty
that would present itself, in an attempt to vary the co-efficient in this
relation, would be found in the estimation of the density itself, or of
its proportion to the average superficial density ; of this, the pendulum
may be considered to furnish the best evidence which is attainable ;
and however inexpedient it may appear, to derive from an eflfect
2 u 2
332 EXPERIMENTS FOR DETERMINING THE VARIATION
produced, a correction of that effect proportioned to itself, the evi-
dence which the pendulum affords of the influence exerted by the
peculiar attraction of a locality, in modifying the mean force of gravity,
ascribed to the parallel by a combination of experiments in different
localities, may present the best practical means of approximating towards
a true estimation, where the object of the determination requires an
especial accuracy. A second difficulty would exist in appreciating the
effect of different densities on the co-efficient ; if a judgment may be
formed from the present experiments, the bearing of which on the point
in question will be discussed in the sequel, the local variations of gravity
are influenced far more considerably by the density of the masses on
which the pendulum is immediately placed, than on the general disposi-
tion of the surface.
To attempt a modification of the co-efficient of ^ths, in consideration
of the presumed variations of local attrantinn. either from form or density,
at the stations of the present experiments, would be a refinement beyond
the occasion ; at four of the stations only, an error of twice the
amount of the uncertainty, supposed in reference to the form of the
eminence, would affect by a single unit the figure which has been pre-
sumed to have been accurately determined at the station ; and at the
remaining nine stations the possible errors may be regarded as wholly
insignificant.
In the subjoined table the corrections have been inserted, both as
derived from the squares of the distances, and as modified by a constant
co-efficient of 0.6. The utmost facility is thus afforded for the sub-
stitution of any other co-efficient which may be deemed preferable,
either generally, or in individual cases ; the modified corrections are those
which have been employed in reducing the lengths of the pendulum at
the several stations, to the supposed corresponding lengths at the level of
the sea, inserted in the final column.
IN THE LENGTH OP THE SECONDS' PENDULUM.
333
STATIONS.
Latiluiles.
Height
above the
Sea.
Leugth of (he
Seconds*
Pendulum.
Corrections for Elevation.
Deduced Peu-
duluni at the
level of the Sea.
O ' "
FT.
IN.
St. Thomas
0 24 41 N.
21
39.02069
.00008
.00005
33.02074
Maranbam
2 31 43 S.
77
39.01197
.00029
.00017
39.01214
Ascension .
7 55 48 S.
17
39.02406
.00006
.00004
39.02410
Sierra Leone
8 29 28 N.
190
39.01954
.00071
.00043
.39.01997
Trinidad .
10 38 56 N.
21
39.01879
.00008
.00005
39.01884
Bahia .
12 59 21 S.
213
39.02378
.00079
.00047
39.02425
Jamaica .
17 56 07 N.
9
39.03508
.00003
.00002
39.03510
New York
40 42 43 N.
67
33.10153
.00025
.00015
39.10168
London
51 31 08 N.
92.5
39.13908
.00035
.00021
39.13929
Drontheim
63 25 54 N.
121.5
39.17428
.00046
.00028
39 . 1 7456
Hammerfest .
70 40 05 N.
29
39.19512
.00011
.00007
39.19519
Greenland
74 32 19 N.
31.5
39.20328
.00012
.00007
39.20335
Spitzbergen .
79 49 58 N.
21
39.21464
.00008
.00005
39.21469
In order to obtain from the lengths of the pendulum contained in the
final column of the antecedent Table, the Ellipticity, which may represent
in the best possible manner their combined indication, when considered
as expressing the direct ratios of gravitation in the respective parallels
of latitude, it is desirable to employ the method of least squares in the
deduction ; by that method, the values of the equatorial pendulum, and of
the total increase of gravitation between the Equator and the Pole, are
determined in such manner, that the variation in the lengths of the pen-
dulum deduced from the combination (on the principle that the length
varies as the square of the sine of the latitude,) being compared with the
observed variation, the sum of the squares of the several differences, may
be less, than by any other possible determination.
In the ensuing calculation, the values of the equatorial pendulum, and of
the total increase of gravitation, are represented by x andy; and the
differences between the partial and the combined experimental determi-
334
EXPERIMENTS FOR DETERMINING THE VARIATION
nations at each station by T>\ D^ D^ ^-c. The sum of the first series of
conditional equations, divided by 13, and made equal to zero, expresses
the equation of minimum in respect to x; the sum of the second series
(which are the first thirteen equations, severally multiplied by the co-effi-
cient of y in each equation) divided by 13, and made equal to zero,
expresses the equat
St. Thomas
Maranham .
Ascension .
Sierra Leone
Trinidad
Bahia . .
Jamaica . .
New York .
London . .
Drontheim .
Hammerfest
Greenland .
Spitzbergen
on of minimum in respect to^.
0 24 41
2 31 43
7 55 48
8 29 28
10 38 56
12 59 21
17 56 07
40 42 43
51 31 OS
63 25 54
70 40 05
74 32 19
79 49 58
39.02074 — X — 0.0000515.)/ = D'
39.01214 — X — 0.0019464.)/ = D^
39.02410 — X — 0. 0190338. y = D*
39.01997 — X — 0. 0218023. jr = D*
39.01884 — X - 0.0341473.?/ = D'
39.02425 — X - 0. 0505201. v = D°
39.03510 — X — 0.094S286.)/ = D'
39.10168 - X — 0.4254385.)/ = D°
39.13929 — .T - 0.6127966.)/ = D'
39.17456 — X — 0.7999544.)/ = D'"
39.19519 — X — 0.8904120.)/ =: D"
39.20335 — X — 0.9289304.)/ = D'^
39.21469 — X — 0.9688402.^ = D'^
39.09107 — X — 0.3729771.)/ = 0
— 0.002012
— 0.075934
— 0.742773
— 0.850725
— 1 . 332390
— 1.971510
— 3.701643
— 16.635365
— 23.984428
— 31.337865
— 34.899873
— 36.417184
— 37.992760
+
+
+
+
+
+
+
+
+
+
+
+
a:. 0.0000515
a;. 0.0010464
a;. 0.0190338
a-. 0.0218023
a;. 0.0341 473
a;. 0.0505201
a;. 0.0948286
.T. 0.4254385
.T. 0.6127966
.T. 0.7999544
.r. 0.8904120
a;.0.92S9304
a;.0.96S8402
— 14.611113 + a;. 0.3729771
+ )/. 0.0000000
-I- y. 0.0000038
+ y. 0.0003623
+ )/. 0.0004753
+ y. 0.0011660
-1- y. 0.0025523
-1- y.Q. 0089924
+ y. 0.1809980
-1- y. 0.3755200
-I- y. 0.6399270
+ y. 0.7928336
-I- y. 0.8629118
+ y. 0.9386515
-1- y. 0.2926457=0
From the equations of minimum the value of .t is found = 39.01568 inches, the
pendulum at the equator; and y = 0.20213, the increase of gravitation between the
equator and pole. The ellipiicity corresponding to these values, is j^^ of the equatorial
diameter.
IN THE LENGTH OF THE SECONDS* PENDULUM.
335
The following table exhibits in the second column the lengths of the pen-
dulum in the several latitudes, computed from the preceding values of x
and 1/, or those corresponding generally with the experiments ; the third
column contains the lengths actually observed at each station ; the fourth
column, the excess or defect of the individual results on those of the com-
bined determination (or the values respectively of D', D\ D', ^-c); and
the fifth column, the number of vibrations per diem corresponding to the
excess or defect in the preceding column.
STATIONS.
».Sin.2 Lat.
Lengthfi
individually
determined.
Individual
determinations
in excess or
defect.
The excess
or defect
in Vibr.
GEOLOGICAL CHARACTER.S.
St. Thomas .
39.01568
39.02074
+ .00506
+ 5.58
Basaltic rock.
Maranham
39.01607
39.01214
- .00393
-4.34
Alluvial.
Ascension . .
39.01953
39.02410
+ .00457
+ 5.04
Compact volcanic rock.
Sierra Leone
39.02009
39.01997
-.00012
-0.12
A soft and rapidly disintegrating
granite.
Trinidad . .
33.02258
.39.01884
- .00.374
-4.12
Alluvial.
Babia . . .
39.02589
39.02425
-.00164
-1.80
A deep soil on a sandstone basis.
Jamaica . .
39.03485
39.03510
+ .00025
+ 0.28
Calcareous rock.
New York .
39.10167
39.10168
+ .00001
0.00
fA stratum of 100 feet of sand, on
\ serpentine.
London . . .
39.13954
39.13929
-.00025
-0.28
Gravel and chalk.
Drontheim .
39.17738
39.17456
-.00282
-3.10
Argillaceous soil on mica slate.
Hammerfest .
39 . 19566
39.19519
- .00047
-0.52
Mica slate.
Greenland . .
.39.20344
39.90835
-.00009
-0.08
Sandstone.
Spitzbergen .
39.21151
39.21469
+ .00318
+ 3.50
Quartz.
The most remarkable circumstance which this table presents to the
view, is the extensive range in the amount of the differences between the
individual and the combined experimental results ; indicating either errors
of experiment far more considerable than those which have hitherto been
brought in question, or actual irregularities in gravitation much greater
than have been previously evidenced.
That the differences are not altogether occasioned by errors of experi-
336 EXPERIMENTS FOR DETERMINING THE VARIATION
ment, and that, in fact, the utmost portion of them must be very small,
which, without an extreme violation of probability, can be attributed to
that source, may be affirmed from the strong support which the individual
results receive in the correspondence of a second, and totally distinct me-
thod of experiment, in that of the attached pendulums. The instances of
extreme irregularity are, in defect at Maranhara and Trinidad, and in
excess at Spitzbergen, Ascension, and St. Thomas. At Maranham and
Trinidad, the vibrations of the detached pendulums appear in defect no
ess than 4^4 and 4.12 seconds per diem respectively; the attached
pendulums (as evidenced in the comparative table, in page 281) shew
in like manner a defect at Maranham of 5.04, and at Trinidad of 4.22
seconds. At Spitzbergen and Ascension, the detached pendulums are in
excess 3.50 and 5.04 seconds respectively ; the attached are also in excess
2.70 seconds at Spitzbergen, and 5.34 seconds at Ascension. At St.
Thomas's, the solid pendulums were not employed ; but in their absence
a corroborative testimony of the same nature is afforded by the rate of
the astronomical clock, relatively to its rate at all the other stations : the
excess of vibration shewn by the detached pendulums is 5.58 seconds,
and by the astronomical clock 5.08 seconds. An objection might be
raised to the full authority of the astronomical clock as an independent
corroboration, in the possibility, although extreme improbability, of a
mutual influence having subsisted from proximity, or by communication
through the respective supports ; but no such possibility can be supposed
between the detached and the solid pendulums ; nor have the two methods
a single point of connexion in which a common error could obtain, except
in being referred to the same determination of astronomical time, which
determination rests on observations much too extensively varied and
multiplied to be questionable. When it is considered that the differences
include a range between extreme cases of 10 seconds per diem, and that
they are manifested alike in every instance (the discordances being abso-
lutely insignificant in the comparison) by two decidedly distinct methods
IN THE LENGTH OP THE SECONDS' PENDULUM. 337
of procedure, and even by a third, of which the claim to be considered as
an independent authority will not be refused by those who carefully exa-
mine the details, the conclusion that the irregularities do not originate in
the experiments, but in the natural phenomena which are the objects of
experiment, appears inevitable.
Viewing the differences, then, as indicating the existence of irregulari-
ties in gravitation itself, and as measures of the local excess or defect at
each station, over the mean force in the respective parallels corresponding
to the experiments generally, it is desirable to inquire into the relation
which they may appear to bear, to the peculiarities of the superficial
strata, in form and density.
The three stations, at which the force of gravitation would appear in
principal excess, are St. Thomas, Ascension, and Spitzbergen ; the cha-
racter of these stations, in regard to the disposition of the attractive mat-
ter near the surface, is similar and peculiar : they are situated on islands
of small extent but considerable elevation, the sides of which, both above
and below the water, are abrupt and almost precipitous : they may be
considered, therefore, as resembling stations on the declivity of an emi-
nence, intermediate between the summit and the foot ; and to be especially
opposed to stations on an extensive tract of table-land. Now the effect of
such a locality on the sum of the attractions, derived from considerations of
form alone, should be, to produce a weaker force than the mean gravitation
of the parallel, whereas the experiments indicate an increased force.
Again, Maranham and Trinidad, the stations where the force was in prin-
cipal defect, are also bordering on the sea, but being situated near the
mouths of extensive rivers, the coasts continue shallow at a great distance
from the land ; those stations, therefore, have little inequality of eleva-
tion, and may be regarded as approximating very nearly to that state of
the surface, in which the influence of form is at a maximum in augment-
2 X
338
EXPERIMENTS FOR DETERMINING THE VARIATION
ing the attraction : here, again, the effect evidenced by the experiments
is of a totally opposite description.
The conclusion is far otherwise, however, when the respective densities
of the materials near the surface are viewed in connexion with the excess
or defect of local gravitation, and regarded as the circumstances of prin-
cipal influence. It is fortunately not required for this purpose, that the
estimation of the density should be very precise, as, independently of the
pendulum, it would not be easy to be ascertained ; it is sufficient to com-
pare the particulars of the column indicating the irregularities of gravi-
tation, with the geological characters of the several stations, to perceive^
their general, and ahnost to trace their individual, connexion. In arrang-
ing the stations agreeably to the order of the densities evidenced by expe-
riment, the compact volcanic rock of Ascension, the still more compact
basalt of St. Thomas, the quartz of Spitzbergen, and the alluvial soils
of Maranham, and Port Spain, in Trinidad, are found in their appropriate
places at the opposite extremities of the succession ; whilst of the inter-
mediate stations (of which the correctness of the arrangement, relatively
to each other, does not admit of the same positive testimony), not one can
be said to differ materially from the position which would be assigned it,
from the best estimation that can be formed of the density of the strata
situated immediately beneath the pendulums.
Excess or de-
Scale of
STATIONS.
fect of Vibr.
density.
St. Thomas . .
+ 5.58
100
A compact and very weighty basalt.
Ascension . .
+ 5.04
94
A compact volcanic rock.
Spitzbergen . .
+ 3.50
79
An extensive and deep bed of quartz.
Jamaica . . .
+ 0.28
45
Calcareous rock.
New York . .
0.00
43
A stratum of 100ft. of sand, resting on serpentine.
Greenland . .
-0.08
43
The debris of a compact sandstone rock.
Sierra Leone .
-0.12
42
J A stratum of several feet of earth, resting on soft and
\ rapidly disintegrating granite.
London . . .
-0.28
41
Gravel and chalk.
Hammerfest .
— 0.52
37
rMica slate on a peninsula nearly surrounded by deep
\ water.
Baliia ....
-1.80
26
Several feet of soil resting on sandstone.
Drontheim . .
—3.10
12
An argillaceous soil resting on rocks of mica slate.
Trinidad . . .
-4.12
2
Alluvial soil and sand.
Maranham . .
-4.34
1
.'Alluvial soil and sand.
IN THE LENGTH OF THE SECONDS' PENDULUM. 339
Amongst the many interesting inferences which may be drawn from the
view that has been thus presented, the following may deserve to be
especially noticed :
1. If the irregularities in the force of gravitation are principally
owing to the different densities of the materials near the surface, and if
the influence of exterior configuration is so inconsiderable in comparison,
as not to be recognisable in the results of experiments, the assumption
of a co-efficient, for reducing the vibration at heights to that at the level
of the sea, varied in relation to the form alone, cannot be supposed to
meet the difficulties attendant upon a correct assignment ; so far other-
wise indeed, that in estimating the counteracting effect of the attraction
of the eminence on which the experiment is made, on the regular de-
crease of gravitation in receding from the earth's surface, proportioned to
the squares of the distances from the centre, it would appear that the
consideration of its form may be safely neglected.
2. If a clock, or pendulum, is liable to vary 10 seconds in the same
latitude, according to the nature of the materials on which it rests (in-
cluding such only as are commonly found at the surface of the earth,)
the length of the seconds' pendulum at the level of the sea, correctly
determined at two places on land in the same parallel, may differ as much
as .01 of an inch ; and as the force of gravitation at alluvial stations may
be supposed to exceed that which prevails over the extent, and at the
surface, of the ocean, nearly as much as it falls short of the force at the
stations of greatest local density, the actual variation of gravity in the
same parallel may be considered as not less than equivalent to 20 seconds
per diem, or to ^th nearly of the difference between gravity at the pole
and at the equator due to a compression of ^ig, or to rroVoth of the whole
attraction of the earth.
3. To obtain the force of gravitation corresponding to a parallel, to be
2X2
340 EXPERIMENTS FOR DETERMINING THE VARIATION
employed in the deduction of the total increase between the equator and
the pole, due to the Ellipticity of the Earth, it is requisite, therefore,
that several stations in or near the parallel should be grouped, so as to
produce a mean result, in which the irregularities that render single
stations unavailing in the deduction, may mutually destroy each other ;
it is desirable also that stations in either extreme of local density should
be avoided as far as may be possible ; or that if accidentally included, that
an equal number of stations in each extreme should be comprehended in
a group : thus, in the present experiments, St. Thomas and Maranham,
Ascension and Trinidad, Drontheim and Spitzbergen, are respectively
opposed to each other ; it is preferable however, to confine the experi-
ments to stations, at which the differences from the mean may be less
considerable ; as a general guide, perhaps, to where the specific gravity
of the superficial strata may be between 2.25 and 2.75.
4. If the length of the pendulum assigned to a particular latitude, by
the combined results of the experiments at the thirteen stations of this
volume, be regarded as an approximate representation of the mean
gravitation in the part of the parallel which is occupied at the surface by
land ; and if its amount, over the part which is occupied by the ocean,
be supposed less than at alluvial stations, by more than half the differ-
ence between the stations of greatest and of least local density ; and, if
the parallel be equally occupied by land and ocean, the true mean pen-
dulum of the latitude will be even less than the shortest of the individual
deductions: thus, the equatorial pendulum, or the length representing
the mean gravitation at the equator, will be less than 39.01568 (the
value of X in page 334,) which is its length in situations only where the
disposition and density of the materials near the surface correspond with
the general average of the stations ; and less even than 39.01175, which
is the length deducible from Maranham, the station of least local attrac-
IN THE LENGTH OF THE SECONDS* PENDULUM. 341
tion. It follows also, that although the ratio of gravitation in different
latitudes may be determinable, by multiplying sufficiently the experiments
in and near the respective parallels, — as well as the total increase between
the equator and the pole, by making the groups sufficiently distant from
each other, — the multiplication of stations on the land alone will not
approximate towards a knowledge of the true equatorial pendulum.
Fortunately, this length is not required to be very accurately known for
the determination of the figure of the earth ; since, if 39.01 were substi-
tuted for 39.01568 as the value of x, its combination with y = 0.20213
(the total increase between the equator and the pole,) in page 334, would
produce an ellipticity of y^ ; the difference between which deduction
and 7^, resulting from x = 39.01568 and j/ =: as before, is too small to
be significant in the present state of our knowledge.
5. The scale afforded by the pendulum for measuring the intensities
of local attraction, appears to be sufficiently extensive, to render it an
instrument of possible utility in inquiries of a purely geological nature.
It has been seen* that the rate of a pendulum may be ascertained by
proper care to a single tenth of a vibration per diem ; whilst the variation
of rate, occasioned by the geological character of stations, has amounted
in extreme cases to nearly ten vibrations per diem; a scale of 100
determinable parts is thus afforded, by which the local attraction, de-
pendant on the geological accidents, may be estimated.
The lengths of the seconds' pendulum determined by Captain Kater,
at the principal stations of the trigonometrical survey of Great Britain, in
* Vide, the Table in page 211.
342 EXPERIMENTS FOR DETERMINING THE VARIATION
pursuance of an address of the House of Commons to the King, and
published in a memoir in the Philosophical Transactions for 1819, may
be connected and compared with the thirteen results contained in this
volume, by means of the station in London, which is common to both
series.
The experiments, by which Captain Kater's determinations were
effected, were made with an invariable detached pendulum, and by a
procedure similar in all respects to that which has been adopted in the
operations recorded in this volume, excepting in the mode of observing
coincidences ; the rate of the pendulum used at the stations of the survey,
having been deduced throughout from the intervals between the disap-
pearances only ; except in this one circumstance, the united series of
nineteen results (London being a common station) are (it is believed)
strictly comparable.
The following table contains the names of the stations of the Survey,
with their respective latitudes, elevations, and pendulums, determined at
the station; the corrections for elevation in two columns, as in the similar
table in page 333; exhibiting, first, the corrections due to the duplicate
proportion of the distances from the earth's centre, and, second, the
corrections reduced by a co-efficient of 0.6* ; and in the final column, the
* Captain Kater has employed a co-efficient, varying from five to seven-tenths according
to what he supposed might have been the influence oi the form of the eminences on which
the pendulum was placed, and without regard to the variations of density. The constant
co-efficient of 0.6, which is here employed in the reduction of his results to the level of the
sea, is not introduced in preference, as presumed to represent Letter the actual attraction of the
several eminences, but inasmuch as it was necessary towards the just comparison of Captain
Kater's results with mine, either that mine should be reduced by a variable co-efficient also, or
that all should be reduced by the same constant quantity. Now, as the influence of the form
does not appear to be recognisable in the actual variations of local attraction, it would have
been superfluous at the least to have varied the corrections in relation to it, whilst the
consideration of the density, which is the really influential circumstance, is omitted.
IN THE LENGTH OF THE SECONDS' PENDULUM.
343
deduced lengths of the pendulum in the respective latitudes at the level of
the sea.
The height of the pendulums in Mr. Browne's house, in London, being
here described as 92.5 feet above the level of the sea, whilst in Captain
Kater's memoir, in the Philosophical Transactions, is stated to be 83 feet
only, it is necessary to explain that Captain Kater's estimation of the
height was founded, in part, on the understanding (on the authority of
the Royal Society) that the elevation of their barometer at Somerset-house
is 81 feet above low-ivater mark; but as the latter elevation has been
since corrected by Mr. Bevan, who has determined it by levelling to be
90.5 feet above the mean level, the height of the pendulums must now be
considered as 92.5 feet, and is so esteemed by Captain Kater. It may
be proper also to notice that Captain Kater's elevations are occasionally
measured from low water, whereas mine are invariably measured from
the mean level of the sea. The difference, however, may be safely
disregarded in the comparison.
STATIONS.
Latitudes.
Elevation.
Pendulums
at the Stations.
Corrections for Elevation.
Deduced Pen-
dulums at tbe
level of the sea.
Unst . . .
60 45 2S
28
39.17145
.00010
.00006
39.17151
Poitsoy . .
57 40 59
94
.39.16140
.00035
.00021
39.16161
Leith . . .
55 58 41
68
39.15540
.00026
.00016
39.15556
Clifton . .
53 27 43
339
39.14517
.00127
.00076
39.14593
Arbury Hill .
52 12 55
737
39.14057
.00276
.00166
39.14223
London
51 31 08
92.5
39.13908
.00035
.00021
39.13929
Shanklin .
50 37 24
212
39.13551
.00091
.00055
39.13606
The stations of the Survey are combined in the following page with
those of the present volume, in producing their corresponding Ellipticity
by the method of least squares :
344
EXPERIMENTS FOR DETERMINING THE VARIATION
St. Thomas .
0 24
41
; 39.02074
—
a- - 0. 0000515. y
=
D-
Maranham .
2 31
43
; 39.01214
—
X - 0. 0019464. y
z^
D'
Ascension
7 55
48
; 39.02410
—
a- — 0.019033S.y
nr
W
Sierra Leone
S 29
28
39.01997
-
X — 0.021S023.y
=:
D*
Trinidad
10 3S
56
; 39.01884
—
X - 0-0341473. y
=
D'
Bahia . .
12 59
21
39.02425
—
X - 0. 0505201. y
=
D'
Jamaica . .
17 56
07
39.03510
—
X — 0. 0948286. y
rr
D'
New York
40 4-2
43
39.10168
—
X — 0. 4254385. y
=
D"
Shanklin . .
50 37
24
39.13606
—
X — 0.5975163. y
=
D»
London . .
51 31
08
39.13929
—
X - 0. 6127966. y
zr:
£)16
Arbury Hill
52 12
55
39. 14223
—
.1- — 0. 6246044. y
=
D"
Clifton , .
53 27
43
39.14593
—
X — 0. 6455676. y
=
D'=
Leith . . .
55 58
41 ;
39.15556
—
X — 0. 6869473. y
=:
D.3
Portsoy . .
57 40
59
39.16161
—
X — 0. 7141988. y
=
D"
Unst . . .
60 45
28
39.17151
—
a- - 0. 7613667. y
=
D"
Drontheira
63 25
54
39.17456
—
X — 0. 7999544. y
=
J)10
Haminerfest
70 40
05;
39. 19519
—
X - 0.S904120.y
=
D'-
Greenland . .
74 32
19 ;
39 . 20335
—
X — 0. 9289304. y
=
J)18
Spitzbergen
79 49
58 ;
39.21469
-
.r — 0.96SS402.y
:=:
D"
39.11036
-
a- - 0. 4673107. y
=
0
— 0
00201
+
X. 0.0000515
+
y. 0.0000000
- 0
07593
+
a. 0.0019464
+
y. 0.0000038
— 0
7427S
+
i-. 0.0190338
+
y. 0.0003623
— 0
85072
+
.r. 0.021 8023
+
y. 0.0004753
— 1
33239
+
a.'. 0.034 1473
+
y. 0.0011660
— 1
97151
+
a;. 0.0505201
+
y. 0.0025523
— 3
70164
+
X. 0.0948286
+
y. 0.0089924
- 16
63536
+
a:. 0.4254385
+
y. 0.1809980
- 23
38443
+
a-. 0.5975163
+
y.O. 3570258
— 23
98443
+
.r. 0.6 127966
+
y. 0.3755200
— 24
44841
+
a. 0.6246044
+
y. 0.3901308
— 25
.27135
+
a:. 0.6455676
+
y. 0.4167575
— 26
S97S0
+
a-. 0.6 86 9473
+
y. 0.4718966
— 27
96918
+
X.0.71419SS
+
y. 0.5100800
- 29
823S9
+
j; 0.7613667
+
y. 0.5796793
— 31
33786
+
a. 0.799 9544
+
y. 0.6399270
— 34
S99S7
+
a. 0.8904120
+
y.0.79 2S336
— 36
41718
+
a.-. 0.9289304
+
y. 0.8629118
- 37
99276
+
X. 0.9688402
+
y. 0.9386515
—
IS
30208
+
X. 0.4673107
+
y.0.3436S23 -0.
Whence x = 39.01566, the Seconds' Pendulum at the Equator ; y = 0.20265, the
increase of gravitation from the Equator to the Pole; and the EUipticity = jj^.
IN THE LENGTH OF THE SECONDS' PENDULUM.
345
The following Table exhibits the pendulums, computed for the several
latitudes of the stations from the values of x and_y, as in the last page;
with the differences between the individual and the combined experimental
determinations, expressed in linear measure, and in the correspondent daily
vibrations ; the differences are presented in accompaniment with the geo-
logical characters of the stations, on which they are considered to depend.
STATIONS.
j(.Sin.2 Lat.
Excess or
defect of the
iudividoal
Determi-
nations.
Excess or
defect, io
Vibrations.
GEOLOGICAL CHARACTERS.
St. Thomas
39.01566
+ .00508
+ 5.60
Basalt.
Maranham
39.01605
-.00391
- 4.32
Alluvial.
Ascension
39.01952
+ .00458
+ 5.03
Computed volcanic rock.
Sierra Leone
39.02008
-.00012
- 0.12
A soft and rapidly disintegratinggranite.
Trinidad .
39.02258
-.00374
- 4.12
Alluvial.
Baliia
39.02590
-.00165
- 1.81
A deep soil on a sandstone foundation.
Jamaica . .
39.03488
+ .00022
+ 0.25
Calcareous rock.
New York
39.10187
-.00019
- 0.20
100 feet of sand, resting on serpentine.
Shanklin .
39.13675
- .00069
- 0.76
Chalk.
London .
39.13984
-.00055
- 0.60
Gravel and nal<c.
Arbury Hill
39.14223
-.00000
0.00
Chalk, in the vicinity of primitive rocks.
Clifton .
39.14648
-.00055
- 0.60
Clay and shale.
Leith. .
39.15487
+ .00069
+ 0.76
Sandstone and scattered basaltic rock.
Portsoy .
39.16039
+ .00122
+ 1.32
Serpentine and granite.
Unst . .
39.16995
+ .00156
+ 1.72
Serpentine.
Drontheim
39.17777
-.00321
— 3.54
Argillaceous earth, resting on mica slate.
Haramerfest
39.19610
-.00091
- 1.00.
Mica slate.
Greenknd
39.20391
- .00056
- 0.60
Sandstone.
Spitzbergen
39.21200
+ .00269
+ 3.00
Quartz rock.
The following arrangement exhibits a mode of grouping the stations
into partial results corresponding to particular latitudes, from the subse-
quent comparison of which with each other, the Ellipticity of the earth
2 y
346
EXPERIMENTS FOR DETERMINING THE VARIATION
may possibly receive even a more satisfactory elucidation, than from their
general combination according to the method of least squares. The
middle group comprises the six stations contained within the limits of
England and Scotland, and assigns, from their several experimental
determinations, the length of the pendulum in the latitude of 54 degrees.
The first group comprises in like manner the five stations nearest the
equator, and the third group the five most northern stations, from which
are respectively assigned the pendulums corresponding to the latitudes of
5 degrees, and of 70 degrees.
STATIONS.
Latitudes.
Pendulums.
Mesa
Latitudes.
Correspondiug reduced
Pendulums, y = 0.20245.
St. Thomas . .
O 1 It
0 24 41
39.02074
0 ' ti
r 39.02227
Maranham . .
2 31 43
39.01214
39.01329
Ascension . . .
7 55 48
29.02410
\ 5 00 00 ■
39.02179
■ 39.01758
Sierra Leone .
8 99 28
39.01997
39.01710
Trinidad . . .
10 38 56
39.01884
39.01347
Shanklin . . .
50 37 24
39.13606
39.14760
London ....
51 31 08
39.13929
39.14774
ArburyHill . .
Clifton . .
52 12 55
53 27 43
39.14223
39.14593
• 54 00 00 •
39.14829
39.14774
> 39.14832
Leith
55 58 41
39 . 15556
39.14900
Portsoy ....
57 40 59
39.16161
39.14953
Unst
60 45 28
39.17151
39.19614
Drontheim . .
63 25 54
39.17456
39.19138
Uammerfest . .
70 40 05
39.19519
■ 70 00 00 -j
39.19370
39.19405
39.19452
Greenland . . .
74 32 19
39.20335
Spitzbergen . .
79 49 58
39.21469 ^
39.19732 '
(
From the combination of the mean restilt of the first and second grotips, the value
of y = 0.20210, and the Ellipticitj- ^3.
From the first and third groups, y = 0.20212, and the EUipticity -^,.
From the second and third groups, y = 0.20218, and the EUipticity j^.
IN THE LENGTH OF THE SECONDS* PENDULUM. 347
I proceed to the comparison of the lengths of the seconds' pendulum at
the stations which have been hitherto under notice, with the similar
determinations at several points of the arc of the meridian comprised
between Formentera and Unst, effected conjointly by MM. Biot, Arago,
Bouvard, Mathieu, and Chaix, in a suite of operations undertaken at the
instance of the Academy of Sciences of Paris, and carried on under the
authority and support of the late and present governments of France,
having commenced in 1807, and terminated in 1817. An account of the
operations is published in detail at the conclusion of the third volume of
the Base du Systime Metrique.
The experiments of the French philosophers were made with an
apparatus on the principle invented by Borda for the measure-
ment of the seconds' pendulum at Paris, and by the process devised
by that eminent philosopher ; its distinctive peculiarity from the method
employed at the stations of the British survey, and at those of this
volume, is, that the absolute length of the pendulum is separately de-
termined at each station, instead of the relative lengths to a particular
station, serving as a common basis. If, however, the fundamental length
on which the several determinations in the one mode of operation de-
pend be correctly measured, and if the process by which the separate
measurements at each station are effected in the other mode, be without
an inherent error, the several results, when reduced to the same measure,
ought to be strictly comparable, with the exception of the uncertainty
which must prevail in the several reductions to the level of the sea.
The first of the two following tables comprises the names of the eight
2 Y 2
348
EXPERIMENTS FOR DETERMINING THE VARIATION
Stations at which experiments were made by the French philosophers ;
the latitudes of the stations, and their elevation above the sea in metres ;
the lengths of the decimal pendulum observed at the station, expressed in
millimetres, and the names of the experimentors. The second table
exhibits the corresponding lengths of the sexagesimal pendulum, as well
in millimetres as in parts of Sir George Shuckburgh's scale at the tem-;
perature of 62 degrees* ; it contains also, the elevation in British feet,
and the respective corrections to the level of the sea, computed first, by the
duplicate proportion of the distances from the earth's centre, and second,
by the same proportion with a co-efficient of 0.6 ; the pendulums at the
level of the sea, as inserted in the final column, are obtained by employing
the corrections computed with this co-efficient f.
STATIONS.
UDSt
Leith
Dunkirk
Paris
Clermont . . .
Bordeaux . . .
Figeac . . . .
Formentera . .
Latitudes.
o ' "
60 45 25
55 58 37
51 02 10
48 50 14
45 46 48
44 SO 26
44 36 45
38 39 56
Ele.
vation.
Metres.
9
21
4
70
406
17
223
203
Decimal
Peniluluin.
ItlilUmetres.
742.721034
742.408533
712.07610
741.90112
741.61059
741.60464
741.56033
741.20540
OBSERVERS.
Hiot.
Biot.
Biot, Mathieu.
Biot, MathieUj Bouvard.
Biot, Mathieu.
Biot, Mathieu.
Biot, Mathieu.
Biot, Arago, Chaix.
* The metre is accounted 39.37079 inches of Sir George Shuckburgh's scale ; the metre
being at the temperature of melting ice, and the British scale at that of 62° of Fahrenheit.
t The allowance for the elevation of the stations used in the memoir in which the expe-
riments are recorded, is in the first of the above proportions ; the second is introduced here,
solely with a view of rendering the results in the final column more strictly comparable with
the others, in which the co-efficient of 0.6 has been employed.
IN THE LENGTH OF THE SECONDS PENDULUM.
349
STATIONS.
Sexagesimal Pendutum.
Eleva-
tion in
feet.
Corrections
for Elevation.
Reduced
leimhsot tile
Seconds' l*eiid.
at the level of
In Milli-
IQ British
metres.
Measiire.
the Sea.
Unst
994.94308
39.17170
30
.00011
.00007
39.17177
Leith
994.52145
39.15522
69
.00026
.00016
39.15538
Dunkirk . . .
994.07913
39.13769
13
.00004
.00002
39.13771
Paris
993.84473
39.12843
230
.00085
.00051
39.12894
Clermont . . .
993.45554
39.11313
1332
.00499
.00299
39.11612
Bordeaux . . .
993.44756
39.11282
56
.00021
.00013
39.11295
Figeac ....
993.38822
39.11048
732
.00274
.00164
39.11212
Formentera . .
992.91275
39.09176
CO 6
.002 48
.00149
39.09323
In the ensuing calculation, the stations of the French Arc are combined
with the thirteen stations of this volume, in the deduction of the corres-
ponding Ellipticity by the method of least squares.
St. Thomas . .
0
24
41;
Maranham . .
2
31
43;
Ascension
7
55
48;
Sierra Leone
S
29
28;
Trinidad . . .
10
38
56;
Bahia ....
12
59
21 ;
Jamaica . . .
17
56
07;
Formentera . .
3S
39
56;
New York . .
40
42
43;
Figeac ....
44
36
45;
Bordeaux . .
44
50
26;
Clermont . . . .
45
46
48;
Paris ....
48
50
14;
Dunkirk . . .
51
02
10;
London . . .
51
31
08;
Leith ....
55
58
37;
Unst ....
60
45
25;
Drontheim . .
63
25
54;
Hamraerfest . .
70
40
05;
Greenland . .
74
32
19;
Spitzbergen . .
79
49
58;
39.02074 - X — 0. 0000515. y = D'
39.01214 — X - 0. 0019404. y = I>
39.02410 — X - 0. 0190338. y = D''
39.01997 — X — 0.0218023. J/ = D'
39.01884 — X - 0. 0341473. y = D''
39.02425 — .r - 0. 0505201. y = D^
39.03510 — X - 0. 0948286. y = D'
39.09325 - X - 0. 3903417. y = D"
39.10168 — X — 0.4254385.?/ =: D'
39.11213 — X — 0. 4932.370. y = D'"
39.11295 - a- — 0. 4972172. y = D"
39.11612 — X — 0.5136118. J/ = D'^
39.12894 - X — 0. 5667721. y = D'='
39.13771 — X - 0. 6045723. y = D"
39.13929 — X — 0. 6127966. y =: D"
39.15538 — X — 0. 6869301. y = D'"
39.17177 — X - 0. 7613525. y = D
39.17456 - X — 0. 7999544. y =: D'"
39.19519 - .r — 0.8904120.y = D"
39.20335 — X — O.92S9304.y =: D"
39.21469 - X - O.96SS402.y = D^'
39.10534. - X - 0. 4458446. y = 0
350
EXPERIMENTS FOR DETERMINING THE VARIATION
0,
.00201
+
a. 0.0000515
+
J/. 0.0000000
0
.07593
+
J. 0.0019464
+
2/. 0.0000038
0
.7427S
+
X. 0.0190338
+
y. 0.0003623
0
.85072
+
.T. 0.0218023
+
?/. 0.0004753
1,
.33239
+
X. 0.0341473
+
J/. 0.0011660
I
.97151
+
x. 0.0505201
+
y. 0.0025523
3
.70164
+
X. 0.0948286
+
y. 0.0089924
15
.25973
+
X. 0.3903417
+
y. 0.1523667
IS
.63536
+
X. 0.4254385
+
y.O. 1809980
19
.29154
+
.T. 0.4932370
+
y. 0.2432827
19.
, 44764
+
X. 0.4972172
+
2/. 0.2472250
20
.09049
+
X. 0.5136118
+
y.O. 2637970
22.
17718
+
X. 0.5667721
+
y.O. 3212305
23.
.66157
+
X. 0.6045723
+
y.O. 3655076
23
.9S443
+
X. 0.6127966
+
y. 0.3755200
26
.89702
+
X. 0.6869301
+
y.O. 4718730
29,
.82353
+
X. 0.7613525
+
y.O. 5796577
31
.33786
+
X. 0.7999544
+
y.O. 6399270
3i.
S99S7
+
X. 0.8904120
+
y.O. 7928336
36
.41718
+
X. 0.9289.304
+
y.O.S6291IS
37
.99276
+
X.0.96SS402
+
y.O. 9386515
y.O. 30711115 = 0
0.20227 the total increase of
— 17.456817 + X.0.445S446 +
Whence x=: 39.01516 the equatorial pendulum; y =
gravitation ; and the Ellipticity =
In the four first columns of the table in the following page, are collected
in one view the whole of the stations which have been thus severally
considered, their latitudes, observed pendulums, and the names of the
observers ; the values of x and y , which best correspond with their com-
bined indication, are stated at the bottom of the page, the details of the
calculation by the method of least squares being omitted, as the equations
corresponding to each station have been already inserted in the preceding
pages : the fifth column contains the pendulum in the respective latitudes
computed from the values of x and y ; and the sixth column, the discord-
ances between the individual and combined experimental determinations,
expressed in Mnear measure.
IN THE LENGTH OF THE SECONDS' PENDULUM.
351
STATIONS.
Latitudes.
Experimental
Pendulums.
Observers.
Computed
Tenduiums.
Esperilnental
Pendulums in
excess or defect.
St. Thomas .
O 4 1'
0 2141
39.02074
Sabine
39.01520
+ .00554
Maranham . .
2 31 43
39.01214
Sabine
39.01559
-.00345
Ascension . . .
7 55 48
39.02410
Sabine
39.01905
+ .00505
Sierra Leone .
8 29 28
39.01997
Sabine
39.01961
+ .00036
Trinidad . . .
10 38 56
39.01884
Sabiae
39.02211
-.00327
Bahia ....
12 59 21
39.02425
Sabine
39.02543
-.00118
Jamaica . . .
17 56 07
39.03510
Sabine
39.03440
+ .00070
Formentera , .
38 39 56
39.09176
Biot, Arago, Chaix. . .
39.09422
-.00246
New York . . .
40 42 43
39.10168
Renwick, Sabine . .
39.10133
+ .00035
Figeac . • .
44 36 45
39.11212
Biot, Mathieu ....
.39.11506
-.00294
Bordeaux . . .
44 50 26
39.11295
Biot, Mathieu ....
39.11586
-.00291
Clermont . . .
45 46 48
39.IIC12
Biot, Mathieu ....
39.11918
- .00306
Paris
48 50 14
39.12894
Biot, Mathieu, Bouvard
39.12994
-.00100
Shanklin . . .
50 37 21
39.13606
Kater
39.1.3617
- . 000 1 1
Dunkirk . . .
51 02 10
39.13771
Biot, Mathieu . . .
39.13760
+ .00011
London ....
51 31 08
39.13929
Kater, Sabine ....
39.13926
+ .00003
ArburyHill . .
52 12 55
39.14223
Kater
39.14165
+ .00058
Clifton ....
53 27 43
39.14593
Kater
39.14590
+ .00003
Leith
55 58 33
39.15547
r Biot . . . 39.15538 \
I Kater . . . 39.15556/
39.15127
+ .00120
Portsoy ....
57 40 59
39.16161
Kater
39 15979
+ .00182
Unst
60 45 26-5
39.17164
f Biot . . . 39.17177 1
\ Kater . . . 39.17151 J
39.16931
+ .00230
Drontheim . .
63 25 54
39.17456
Sabine
39.17715
-.00259
Hammerfest . .
70 01 05
39.19519
Sabine
39.19516
-.00027
Greenland . .
74 32 19
39.20335
Sabine
3D. 20326
+ .00009
Spitzbergcn . .
79 49 58
39.21469
Sabine
39.21134
+ .00335
Whence x =
39.01520, t
he equatorial pendulum : y = 0.20245 the in
crease of
gravitation
between th
1
'
•P"-"J 2
3 9.f
352
EXPERIMENTS FOK DETERMINING THE VARIATION
In the following table are collected in one view the deductions from
the several combinations which have been examined in the preceding
pages.
the Equatorial
Peodulum, a-.
The total increase
of gravitation, y.
The Ellipticitv.
a:8cy=a&in
the respective
Columns.
3/=aa before,
i=39.01.
IN.
.39.015(iS
IN.
0.20213
1
1
From the thirteen stations of this volume.
2 381
288-3
From the same, combined with the eight )
stations of the French PhUosophers. j
39.01516
0.20227
1
1
288-7
288-6
From the same, combined with the seven !
stations of the British Survey. j
39.01566
0.20265
1
1
2 8 VI. 5
289-1
From the comparison of the pendulum of the 1
Latitude of 5" deduced from the five sta-
tions nearest the Equator, with the Pendu-
39.01606
0.20210
I
1
288-ii
lum in the Latitude of 54° deduced from
the six stations in England and Scotland.
From the comparison of the Pendulum of the
Latitude of 5°, deduced as before, with the
pendulum of the Latitude of 70° deduced
39.01599
0.20312
1
288 1
1
2 8 8 - -i
from the five most Northerly stations.
From the comparison of the pendulum of the
Latitude of 54°, with that of the Latitude
of 70°, both deduced as above.
39.01599
0.2021S
1
288-5
288-1
From the general combination of the stations
of this volume, of the British Survey, and
of the French Arc ; in all twenty-five
39.01520
0.20245
1
1
288-9
289-1
stations.
MFANS
0.20227
1
1
288-6
288-7
The attempt to determine the figure of the earth by the variations of
gravity at its surface, has thus been carried into full execution, on an arc
of the meridian of the greatest accessible extent ; and the results which
IN THE LENGTH OF THE SECONDS' PENDULUM. 353
it has produced are seen to be consistent with each other, in combinations
too varied to admit a probability of the correspondence being accidental.
The Ellipticity to which they conform differs more considerably than could
have been expected from 3-^7^, which had been previously received on
the authority of the most eminent Geometrician of the age, as the con-
current indication of the measurements of terrestrial degrees, of pendulum
experiments, and of the lunar inequalities dependant on the oblateness of
the earth. In flirther attestation of the irreconcilability of the variation
of gravity now manifested, with the Ellipticity inferred in the memoir
in which the Marquis de Laplace has discussed the results of previous
observation and experiment, it may be noticed, that if each of the
tropical stations which I have visited be severally combined with each
of the stations within 45 degrees of the pole, no one result, amidst all
the irregularities of local attraction, will be found to indicate so small a
compression as that of previous reception.
The consideration, which the Ellipticity indicated by these experiments
may receive from the public, as a final determination, will depend, first,
on the conclusiveness which may attach to it, as the ultimate result of the
method of experiment ; and, second, on the conclusiveness of the method
itself, in regard to the determination sought.
It is not easy to anticipate what accumulation, or what variety of
experimental evidence will be required in a final determination of
such magnitude as that of the exterior configuration of the earth ; and
(as a consequence) of the laws of density according to which the at-
tractive matter of which it consists is distributed in its interior ; the
inquiry has been actively and unremittingly pursued for more than a
century and a half, and has been deemed of sufficient importance to
receive the co-operation of governments, where the undertakings have
been beyond the power of individuals, or of associations, to accomphsh ;
* 2 z
354 EXPERIMENTS FOR DETERMINING THE VARIATION
and it may be confidently presumed that the subject will not be allowed
to drop, until the object of the inquiry is deemed to be most thoroughly
and satisfactorily ascertained.
The individual who has conducted the experiments, is peculiarly dis-
quahfied for anticipating the general opinion as to their conclusiveness, by
reason of his intimate knowledge of the sources from whence error might
have arisen, and of the efficacy of the means which were adopted to guard
against its occurrence. The conviction which this knowledge produces
on his own mind, cannot be imparted in its full force even by the most
careful and extended detail : he cannot, therefore, anticipate what may
be the impression on the minds of others, and the decision must remain
with those, in whom maturity of judgment gives authority to opinion.
Should more evidence, however, appear to be yet desirable, in con-
firmation of the difference between the polar and equatorial gravitation
shewn by the experiments which have been under notice, it may conduce
to the completion of the inquiry, to point out by what measures it may
be most satisfactorily procured.
It is presumed to have been sufficiently shewn, that single stations
are quite unavailing in the assignment of the length of the pendulum
due to a particular latitude; and that a group of not less than six or
seven stations is requisite for that purpose : it may be further observed,
that in the present advanced stage of the inquiry, no result ought to
be admitted to have weight, which has not been obtained with due
regard to all the minute circumstances by which error in experiment
may be avoided. A reflection on the progress of the inquiry hitherto,
will abundantly shew, that inexact experiments have tended but to
perplex, and even to mislead : the irregularities of gravitation present a
sufficient difficulty in the determination, without the additional embar-
rassment of irregularities of experiment.
IN THE LENGTH OP THE SECONDS' PENDULUM. 355
1. There is already an experimental pendulum at Madras; were it
conveyed to five or six stations of various geological character between
the latitudes of Madras and the equator, and returned to England to
have its corresponding rate in London correctly ascertained, with such
arrangements as should manifest the intermediate invariability of the
pendulum of comparison, a second tropical group would be obtained,
doubhng the evidence at the one extremity of the arc.
2. The seabord of the United States presents every requisite facility
for the execution of a third group in the middle latitudes, varied almost
at pleasure, in regard to the circumstances of locality. This group would
possess the more interest, as the length of the pendulum on the average
of the stations in the corresponding parallels in Europe, has hitherto
fallen short of the general ratio in latitudes both to the north and to the
south. It might be accomplished with great convenience by the Govern-
ment of the United States, should a disposition be felt to cooperate with
Great Britain and France in the prosecution of this important inquiry ;
and New York would, in such case, form a connecting station with the
experiments in Great Britain, in France, within the Tropics, and in the
Arctic Circle.
.3. An additional group in the high latitudes would be comparatively a
more arduous undertaking ; the west coast of Greenland, and the north-
ern shores of Baffin's Sea, would be suitable localities in which it might
be accomplished, however, in a single season ; the stations on the Green-
land coast from 60° to 74° would consist of primitive rocks, and might be
visited between April and July ; those in still higher latitudes, which are
accessible towards the close of July, and for which the months of August
and September would remain, would consist of transition and secondary
rocks. We know, on the authority of Baffin, who is yet our only authority for
the northern limits of the sea which bears his name, that the experiments
might be carried in that direction, at least as far as the latitude of 78°.
2 z 2
356 EXPERIMENTS FOR DETERMINING THE VARIATION
It may be reasonably presumed that the three groups which have been
thus suggested, combined with the four which have been already accom-
plished, would terminate the inquiry into the figure of the earth by means
of the pendulum, as far at least as regards the northern hemisphere ; by
producing a result which would be decisive in the estimation even of the
most cautious judgment; or by shewing (what the present experiments
must render exceedingly improbable) that a decisive result is not at-
tainable by it.
Having thus considered the deductions, in regard to the increase of
gravitation between the equator and the pole, and the corresponding
Ellipticity of the earth, furnished by the experiments at the twenty-
five stations enumerated in page 351, as well in their general as in
their partial combination, it may not be uninteresting, briefly to ex-
amine the correspondence of the mean ratio of gravitation at the
surface of the earth, as it may be severally inferred from the ex-
periments of the French philosophers, from those of Captain Kater, and
from mine.
If the length of the pendulum in the latitude of forty-five degrees be
deduced from the experimental lengths at each of the stations, by the
aid of the co-efficient^ = 0,20227, and if the stations of each distinct
series of experiments be collected into a mean result, their correspond-
ence or otherwise will be manifested on comparison: thus,
The Pendulum in the ^ The French Philosophers at S^^ggjj^g^ _ ^^^jj^
^ Stations j
lati'"'^^"*''^^ '^"'■■icapt. Kater at 7 Stations =39.117-29 +.00075
responding to the | Q^pt. Sabine at 6 Northern Stations = 39.11664 + .00010
experiments of [ Capt. Sabine at 7 Southern Stations =39.11688 -1- .00034
Mean. 39. u 654
IN THE LENGTH OF THE SECONDS' PENDULUM. 357
It is here seen that the mean ratio of gravitation deducible from the
eight stations of the French philosophers is considerably in defect,
when viewed in comparison either with Captain Kater's, or with mine ;
from Captain Kater's, especially, it differs not less than would influence
the going of a clock two seconds in a day. It can scarcely be sup-
posed that the discrepancy is occasioned by the different mode of ex-
periment adopted by the French philosophers, and still less by any
inexactness in the execution, where such consummate skill was dis-
played: that portion of it, then, which, on a due consideration of the
circumstances at the several stations, shall appear beyond the utmost
uncertainty which can attach to the respective conclusions, must be
regarded as proceeding from, and evidencing an actual deficiency of
gravitation on the average of the eight stations, when compared with
the average of nearly twice their number; aU the stations having
been selected without reference to the peculiarities of local attraction.
Unless, therefore, some adequate cause for the discrepancy can be
found in the experiments themselves, it must appear, that if the pen-
dulum of a particular latitude be supposed to have been determined by
the mean of eight measurements at different stations in the parallel indis-
criminately selected, — and if the process be subsequently repeated at
eight other stations as indifferently chosen, in the expectation of obtaining
a mean result identical with the former,— the expectation may be defeated
by a difference not less in amount than .002 parts of an inch. It is
unnecessary to show by how much this difference may be exceeded,
where single determinations only are employed.
The principal, and it may almost be said, the only source, from
whence the individual results may have been liable to material inaccu-
racy, is in the reduction of the pendulums actually determined by the
experiments at the stations, to the presumed corresponding lengths
at the level of the sea ; in which respect the magnitude of the possible
358 EXPERIMENTS FOR DETERMINING THE VARIATION
inaccuracy may to a certain extent have been proportionate to the height :
now the elevation of Clermont, one of the stations of the French arc,
being 1332 feet, far exceeds that of any other of the stations with which
it is included ; and the doubt which must be allowed to exist, respecting
the co-efficient which it might be most proper to use, in reducing the
pendulum of that height to the corresponding one at the sea, renders the
reduced result uncertain to a much greater amount than is involved
elsewhere*. If therefore the influence of the experiments at Clermont
be withdrawn from the pendulum of the latitude of forty-five degrees
deduced from the French stations, the comparison may, perhaps, be
deemed to take place under circumstances more strictly corresponding
to each other ; when it will be seen that some portion of the apparent
discrepancy is removed.
ThePendulumofthe 'The FreHch Philosophers, (omitting 1^^ 39.11563 - .00098
Clermont) — 7 Stalions j
Capt. Kater — 8 Stations = 39.11729 + .00068
Capt. Sabine — 6 Northern Stations = 39.11664 + .00003
Capt. Sabine — 7 Southern Stations = 39.11688 + .00027
latitude of 45° cor-
responding to the
experiments of
Mean. 39.11661
It may be inferred, then, from the premises in the foregoing pages,
that 39.1166 is the approximate mean length of the seconds' pendulum
in the part of the parallel of 45 degrees which is occupied by land :
that in consequence of the inequalities of local attraction, the length,
correctly measured at individual stations in the parallel, may be liable
to vary from 39.1221 to 39. 1132: that if the several densities of the
strata near the surface at the twenty-five stations of experiment, be
* It is probable that at such considerable heights, the value of the co-efficient, if one be
used, should be varied in relation to the height, as well as to the disposition of the surface,
and to ihe density of the substances composing the eminence.
IN THE LENGTH OF THE SECONDS' PENDULUM. 359
supposed to be comprehended (as it is probable they may) between
1.8 and 3, the length of the pendulum over the sea, could it be there
measured, — or which is the same thing, the ratio of gravitation over the
surface of the ocean, — might possibly be found as low as 39.1042* : and
on the further supposition that the parallel consists of equal surfaces of
land and ocean, the mean pendulum of the latitude may not differ consi-
derably from 39 . II .
The same method of inference will assign 39.1391 as the mean
length of the pendulum in the latitude of London (51° 31' 08".4), re-
quired to vibrate seconds on the land, 39. 1267 on the ocean, and 39.1329
as the mean pendulum ; also, that the length correctly measured at
different stations in the parallel on land at the level of the sea, might
vary from 39.1446 to 39.1357.
It will also assign 39.01 as at least an approximate mean length of
the pendulum at the equator, corresponding to gravitation at all points
of the circumference ; whence the space which a body would fall
through in one second of time is equal to 16.04223 feet ; and the cen-
* Had circumstances permitted, it was my intention, whilst at Spitzbergen, to have obtained
the rate of the pendulum clock on one of those vast accumulations of ice and snow which are
occasionally met with, filling entire valleys, and presenting towards the ocean a front of five or
six hundred feet, and sometimes even more, in perpendicular height. The summit of a
Glacier is frequently a level surface, connecting the mountain ridges by which the valley is
enclosed ; and on one of the larger Glaciers a clock might be so placed, resting on pickets
blunted at the end and driven into the snow, that the sides of the hills might be more distant
from it than the bottom of the valley, and thus that no materials of a specific gravity greater
than unity might be within five or six hundred feet of the clock. Its comparative going, when
so stationed, and when supported at the same elevation above the sea on the adjacent land,
miorht have afforded a more highly interesting illustration of the influence of superficial
density on the general gravitation, than any which has been hitherto produced. Had the
Griper commenced her voyage earlier in the season of 1823, this experiment would have
been at least attempted; and it is now noticed, in the hope that it may yet be accomplished
by some future voyager to Spitzbergen (which on account of its geographical position is
occasionally visited for purposes of science), to whom time may be an object of less conse-
quence than it was to me.
360 EXPERIMENTS FOR DETERMINING THE VARIATION
trifugal force at the equator is TiTijn of gravitation, or 'aggloai of gravity.
The correspondence betw^een these fractions, and that which has been
found to express the Ellipticity of the Earth, or, in other words,
between gravitation at the pole and at the equator in terms of the
equatorial gravitation, and the radius of the earth at the pole and at
the equator in terms of the equatorial radius, is too remarkable a
coincidence to escape notice.
The success which has thus attended the attempt to carry into effect,
under the conditions most favourable for the experiment, the method of
investigating the figure of the earth by means of the pendulum, and the
consistent and precise result, far exceeding previous expectation, which,
under such circumstances, it has been found to afford, encourage the
belief that an equally satisfactory conclusion, and one highly interesting
in the comparison, might be obtained by the measurement of terrestrial
degrees, performed also under the requisite conditions to give its due
efficiency to the method of experiment. Experience has fully shewn, that
no result of decisive character is to be expected from the repetition or
comparison of measurements in the middle latitudes ; and that it is only
from operations carried on in portions of the meridian widely separated
from each other, that such an event can be regarded as of probable ac-
complishment. The project of the original experimentors, — of those
eminent men who, nearly two centuries ago, devised and executed
corresponding measurements at the equator and at the arctic circle,
— ^was of far more vigorous conception, than the steps of their suc-
cessors have ventured to follow, even to the present period ; and it is
due to their memory to recognise that the failure on that occasion was
IN THE LENGTH OF THE SECONDS* PENDULUM. 361
not from insufficient extension of view, or from deficiency in the spirit of
enterprise ; but from the attempt having been made in the infancy of
practical science, when the instruments were inferior, and the modes of
their most advantageous employment less understood, than they have
since been rendered.
The discordancies, which appear in the comparison of the measure-
ments hitherto accomplished, are not so great as those which had resulted
from the comparison of pendulum experiments, previously to the present
attempt to give the latter method its full and efficient trial : it has been
also seen that in proportion as the arcs have been enlarged, so as to
include the continuous measurement of more extended portions of the
meridian, and as the processes of operation have been conducted with
improved means, and increased attention to accuracy, the anomalies have
progressively diminished ; the prospect, therefore, that they may be
made wholly to disappear, by combining the interposition of the greatest
interval between the measurements that the meridian of an hemisphere
will admit, would seem sufficiently probable to justify and induce the
undertaking.
Through the munificent liberality and splendid patronage of the East
India Company, India already presents a determination of the arc con-
tained between the 10th and 20th parallels: and as a consequence of the
political changes which have recently taken place in South America,
there is reason to hope, that the impediments to a measurement between
the equator and the 10th degree, in the quarter of the globe best suited
for the operation, will speedily be removed.
In regarding the polar extremities of the meridian, the attention is
naturally directed in the first instance to Spitzbergen, as the land of
highest convenient access in either hemisphere ; its qualification, in that
respect, is indeed far beyond comparison with other lands, and is a point
of very principal importance ; its high latitude and conveniency of access
3 A
362 EXPERIMENTS FOR DETERMINING THE VARIATION
do not, however, form its only suitability ; for, on due consideration, it
will be found to possess many very peculiar advantages for the operations
of a triangulation.
The general geological character of Spitzbergen is a group of islands of
primitive rock, the ordinary hills of which are from 1000 to 2000 feet in
height, commanding generally extensive views, and unencumbered with
the vegetation which presents so great an obstacle to the connexion of
stations in the more genial climates. The access to all parts of the
interior is greatly facilitated by the extensive fiords, and arms of the sea,
by which the land is intersected in so remarkable a manner ; these, whe-
ther frozen over, as in the early part of the season, or open to navigation,
as in the later months, form routes of communication suited to the safe
conveyance of instruments either in sledges * or in boats ; the fiord, in
particular, which separates the western and eastern divisions of Spitz-
bergen, would be of great avail ; it extends in a due north and south
direction for above 120 miles, with a breadth varying from ten to thirty
miles, and communicates at its northern extremity, by a short passage
across the land, with the head of another fiord proceeding to meet it from
the northern shores of the island, and afibrding similar facilities for carrying
on either a triangulation, or a direct measurement, on the surface of
the ice at the level of the ocean. It is hardly necessary to add, that the
latter operation would be unembarrassed by the inequalities of surface, and
uncertain temperature of the apparatus, which occasion so much trou-
ble, and require so much precaution in the usual determination of a base.
The extent of the arc in the direction of the meridian, between the
* Sledges with rein-deer trained to draft, and the Fins by whom they are managed, may be
hired for the season, at Haramerfest, in any number that might be required. Spitzbergen
abounds more in the food of the rein-deer, and is more plentifully stocked with the animals
themselves in their wild state, than any other arctic country which I have visited. The offi-
cers of the Griper killed more than fifty deer on the small islands which form the northern
part of the harbour of Fairhaven.
IN THE LENGTH OF THE SECONDS' PENDULUM. 363
southern shores of Spitzbergen and the islands on its northern coast
in the eighty-first degree of latitude, is between four and five degrees.
At the period of the celebrity of Spitzbergen as a fishing station, in the
middle of the seventeenth century, when above 200 vessels, manned by
10 or 12,000 seamen, annually resorted to its vicinity, and frequented its
harbours for the purposes of boiling oil, and when the harbours were di-
vided by convention amongst the vessels in consequence of their numbers,
according to the nation and towns to which they belonged, all parts of the
coast were known to and visited by the hardy and enterprising Dutch and
German seamen, by whom the fishery was then principally conducted. The
whales have long since deserted the haunts which their kind had enjoyed
for ages before in unmolested security, and have sought retreats less
accessible to man ; the graves, which occupy every level spot around the
harbours, contain the only and in that climate the almost imperishable
memorials of the once busy scene, which has reverted to its original
solitude ; even the accidental presence of a whaling ship in the western
harbours is an event of rare occurrence*, and it is probable that more
than half a century has elapsed since any vessel has passed to the
North-eastern shores ; it is not surprising, therefore, that the dehneation
of land, represented in the charts of the period when Spitzbergen was
so greatly frequented as existing to the East of the seven islands, and
to extend in a northerly direction far into the eighty-second parallel,
should neither have been estabhshed nor disproved by modern au-
thorities ; those persons who have had opportunities of becoming
acquainted, by examination on the spot, with the remarkable cor-
* During the Griper's stay of three weeks in the neighbourhood of the harbour of
principal resort in earlier times, and in the middle of the fishing season, not a single whale
fish or whaling ship were seen. The only vessels which now frequent the shores of Spitz-
bergen, are Norwegian sloops in quest of sea-horses and eider down. Their visits have been
hitherto confined to the fiords and the islands on the southern and western coasts: they arrive
early in March, and remain as late as November, making occasionally three voyages in a season.
3 A 2
364 EXPERIMENTS FOR DETERMINING THE VARIATION
rectness of the older charts in general, in the insertion and in the re-
lative position (when not separated by much extent of ocean) of lands
then recently discovered, will hesitate too hastily to reject their testimony,
until it has been satisfactorily disproved ; should land exist as repre-
sented in the charts of the period alluded to, even though not visible
from Spitzbergen, its triangular connexion might be estabished on the
surface of the ice, and latitudes yet unattained be included in the ope-
rations of the survey ; nor would it be safe to assign too confidently the
northern limit of such operations even in the absence of land, in our
present ignorance of the facilities which the ice itself may aflford for their
extension towards the pole.
The measurement of a portion of the meridian in the higher latitudes is,
however, one of the many experimental inquiries, beyond the reach of
individual means to accomplish, for which the advancement of natural
knowledge is delayed ; if its accomplishment may be hoped for by that
nation which has been most forward in exploring the regions of the north,
— to whom its climates and its natural difficulties are familiar, — it must
still await the existence of a channel in one of the departments of the
state, through which the liberal disposition of the British Government to
forward every undertaking worthy of a great nation, and by which it may
occupy an additional page in history, shall be rendered available to other
branches of scientific research, than those which are immediately con-
ducive to the interests of navigation.
As the Pendulum experiments which have been related, bear in several
points both theoretically and practically on the subject of a natural
standard of linear measure, it may be useful to bring their connexion
with it in such pomts directly under notice, rather than to leave it to be
inferred incidentally.
IN THE LENGTH OF THE SECONDS' PENDULUM, 365
In selecting a length in nature as a reference for a national linear
scale, there are two qualities in particular the possession of which is
essentially requisite ; first, it must be an invariable length ; and second,
it must be also easily accessible.
The quadrant of the meridian, of which the French metre was designed
to be the ten millionth part, possesses the first requisite ; but is inap-
plicable to its purpose, in consequence of the difficulties which impede
the actual determination of its magnitude, and the great time and labour
which would be required in the operation, even if it were possible that the
impediments to its execution could be overcome. The relation of the
metre to the length in nature to which it professes to bear a certain pro-
portion, exists, therefore, only in the name ; and, if the measurement of
the quadrant were hereafter to be actually accomplished, and the metre
should be found to differ from its nominal proportion, it cannot be
doubted, that it would be the proportion, and not the established scale,
which would undergo the change.
Failing the actual determination of the quadrant of the meridian, its
magnitude, and that of its aliquot part, the unit of the French scale,
have been assigned from the measurement of an arc of the meridian,
comprising about a tenth part of the quadrant, and by the assumption of
a certain ellipticity : now, as the length of a definite portion of the cir-
cumference is as invariable as the circumference itself, the re-measure-
ment of the arc which supplied the foundation of the scale, might serve
equally for its recovery if lost, or for its restoration if injured by accident
or wear, provided that the labour, time, and expense attendant on such
an operation (admitting the certain identity of the result on repe-
tition) did not render such a natural standard one that is not easily ac-
cessible ; which consideration has occasioned its practical abandonment
as a reference, by the distinguished persons themselves whose lives
have been engaged in the original measurement, and by whom the
366 EXPERIMENTS FOR DETERMINING THE VARIATION
pendulum is now proposed as the means of defining and determining the
metre.
In the act which passed the British Legislature in the session of 1824,
entitled " An Act for ascertaining and estabUshing uniformity of Weights
and Measures," the British imperial yard is declared to be in the pro-
portion of 36 inches to 39.1393 (ten thousandths) of an inch, when com-
pared with a pendulum vibrating seconds of mean time in the latitude of
London, in a vacuum at the level of the sea. In thus designating and
adopting the pendulum of a particular latitude as the natural standard of
British measure, the act necessarily assumes that the length so adopted is
of an uniform magnitude ; namely, that the seconds' pendulum at the
level of the sea and in a vacuum is of the same length every where in
the same latitude ; this assumption, however, is directly opposed by the
evidence of the facts which have appeared in the course of the present ex-
periments, and which is particularly summed up in the second, third, and
fourth inferences in pages 339 and 340, and again in pages 358 and 359.
In the third report of the commissioners appointed by his Majesty to
consider the subject of weights and measures, dated March, 1821, on
which report the act of the legislature of 1824 was founded, it is re-
commended that the authentic legal standard of the British Empire should
be identified, by declaring that 39.1393 inches of the standard, at the
temperature of 62° of Fahrenheit, have been found equal to the length of
a pendulum supposed to vibrate seconds in London, at the level of the
sea, and in a vacuum. The recommendation of the commissioners is a
nearer approximation than the act itself, to that more simple standard
of determinate and determinable magnitude, and which is, in fact, the
only experimental foundation of the provisions either of the act or of the
report, the pendulum of a particular spot ; and it is observable, that just
inasmuch as the specification of the report departs from the simplicity of
its foundation, does it fail in precision, and in substituting that which is
IN THE LENGTH OF THE SECONDS' PENDULUM. 367
supposititious and uncertain, for that which is susceptible of direct and
experimental proof This is seen, first, in the attribution of a certain
definite length to the pendulum vibrating seconds in London, whilst the
subject of the experiment was, more precisely, that of the pendulum vi-
brating seconds in a certain part of London ; wherein the expression sub-
stituted is in strictness incorrect, except on the supposition that the se-
conds' pendulum is of the same length in all parts of London ; which it
would not be safe to assume even for meridians under the same parallel ;
and which is theoretically opposed (and doubtless also practically) to the
sensible variation in the length of the pendulum in the northern and
southern parts of London, due to the Ellipticity of the Earth : secondly, in
the substitution of a supposititious pendulum by the reduction to the level
of the sea, for the real pendulum measured at the spot, wherein two
suppositions are involved, both open to question ; namely, first, that the
elevation was correctly ascertained, and secondly, that it was correctly
allowed for. With respect to the elevation itself, it is now admitted (page
343) that the height was incorrectly assigned to the amount of
several feet, by the error of one (and that the only one which has
been subsequently examined) of the data on which it rested ; and in
regard to the correction, the present experiments have rather increased
than diminished the uncertainty that previously prevailed as to the proper
co-efticient to be employed in the reduction. Were the reference made
to the pendulum which was actually the subject of experiment, with the
understanding that all fixture repetitions, designed to produce identical
results, should be made identically at the same spot, the accuracy or
otherwise, both of the elevation and its correction, would be immaterial,
because those particulars would be omitted in the specification, as super-
fluous ; but in the case obviously contemplated by the report, and implied
in its language, that the standard should be recoverable by measure-
ments made elsewhere in London, the elevation and its just correction
368 EXPERIMENTS FOR DETERMINING THE VARIATION
are essential, and require to be known with the same accuracy as the
length of the measured pendulum itself.
In the twenty-first Number of the " Journal of the Royal Institution
(April, 1821), is a communication from Professor Schumacher to the Secre-
tary of the British Board of Longitude, armouncing the adoption, for the
Danish standard of length, of the pendulum vibrating seconds of mean
solar time in the latitude of 45° north, and in the meridian of Skaagen,
at the level of the sea, and in a vacuum. If this specification is to be
understood literally, the geographical position to which it refers is in
Italy, not far from Mantua ; and as its pendulum would require an arbi-
trary correction to reduce it to the level of the sea, in order to fulfil the
conditions of the specification, it could not become the subj ect of a .direct ex-
perimental determination. But it is more probable that the understanding
should be, and that the intention is, to ascertain the length of the seconds'
pendulum at the level of the sea at some spot in the Danish dominions,
possibly at Skaagen itself, and to deduct a certain proportion of its length
from the measurement, corresponding to the effect of the supposed
Ellipticity of the Earth between the parallel of the experiment and of 45°.
If the latter understanding be correct, the Danish measure will be
identified by the pendulum of the spot where the experiment is made,
and the same spot must be recurred to for its recovery ; and the Danish
natural standard will be the pendulum of that spot, and not the pendulum
of the latitude of 45°. The correspondence of the divisions of the scale
with the aliquot parts of the supposed pendulum of 45°, will indeed
establish a relation between them ; but it will be like that of the metre
to the quadrant of the meridian, a nominal relation to an inferred, but not
determined length, having no practical superiority over an assumption more
purely arbitrary. If it be designed that the Danish standard should be
the representative of the mean ratio of gravitation between Ihe equator
and the pole, which is the probable intention, it does not necessarily follow
IN THE LENGTH OF THE SECONDS' PENDULUM. 369
from the proposed mode of determination that it should be so, even if the
elKpticity were correctly known, because it would also be requisite that the
materials near the surface at the place of experiment in the Danish do-
minions, should be a mean in the scale of the general superficial density*.
It is by France only that the experimental length itself, the measured
pendulum of a spot, has been distinctly recognised as the subject of
reference, and as the means of identifying the national scale ; nor is it in
that respect only, that France has advanced beyond other nations in the
preliminary steps towards the establishment of a reference which may live
through succeeding generations, and become available to distant posterity ;
she has repeated the measurement, which was supposed to have fixed in
perpetuity the value of the metre ; and the capability of the process of
Borda to produce an identical result in the hands of other experimenters,
has undergone a practical examination ; the length of the sexagesimal
pendulum at the observatory at Paris, by Borda's measurement, is
39.12776 inches of British measure, and by that of Messrs. Bouvard,
Biot, and Mathieu, 39.12843 ; concerning which measurements, differing
so considerably, M. Arago has remarked, that it would be difficult to
pronounce to which the preference should be given. We are thus enabled
to form a practical estimate of the extent to which the metre may be
considered as identified, and may be capable of recovery on repetition
by the present process of reference ; the knowledge that the metre
is not yet referred with certainty to the third place of decimals of a
British inch, is an advance, in comparison with the erroneous ppfnion that
might otherwise have been entertained, that being gi^-en to the fifth
place it was correct in the fourth.
We are thus also furnished with evidence, if evidence were required for
* See page 358, where the mean seconds' pendulum in the part of the parallel of 45°
which is occupied by land, is inferred from the mean of 24 stations, and the probable amount
of difference at single stations or from fewer combinations is fully discussed.
3 B
370 EXPERIMENTS FOR DETERMINING THE VARIATION
conviction, how essential the experiment itself of repetition is to enable
a correct judgment to be formed of what repetition will produce.
It is seen that it is not sufficient, that a certain scale has been found
to bear a certain proportion to a certain length in nature; it is also
necessary, that it should be proved, that it will be so found again by
repetition in other hands, in order that the purpose of identification,
which is that of recovery, should be fulfilled.
There is reason to believe that the method for which science is indebted
to the ingenuity and mechanical skill of Captain Kater, will be found
capable of greater precision than that of Borda ; it is on the proceed-
ings of that method that the details of these experiments have much
practical bearing, since what is true generally in regard to the accidents
of experiment with the pendulums which I have used, is also appli-
cable to the convertible pendulum. Thus the reasoning and experi-
ments in pages 213 to 233, apply equally to the convertible as to the
comparative pendulum, and shew, that according to the method that is
practised of observing coincidences, will a pendulum of determinate and
invariable length appear to possess different rates ; and that unless the
re-appearances of the disk be observed as well as its disappearances,
neither the true rate corresponding to the length will be obtained, nor
will the results of different experimentors be independent of individual
peculiarity or accidental circumstance, and consequently that they will
not be identical.
So also does the evidence, commented upon in pages 195 and 196, that
the experimental rate of a pendulum may be influenced by an accidental
peculiarity in the agate planes on which it vibrates discoverable only by
a trial on other planes, bear on the convertible pendulum with more
force, perhaps, than on the simple invariable pendulum ; first, because
it has two axes of suspension instead of one ; and second, because
the sliding weight is more likely to interfere with the uniform bearing of
IN THE LENGTH OF THE SECONDS* PENDULUM. 371
tlie knife edges on the planes. The existence of such and similar
inaccuracies is best disproved by identity on repetition with different
instruments ; but they may certainly exist unsuspected in an unrepealed
experiment.
It is in the same view that the comparison of diflFerent methods of
ascertaining the length of the pendulum is highly important, and by con-
sequence, the invention of new modes of procedure. It is understood that
a third method has been proposed by Dr. Young, by means of a weight
sliding on a rod, or bar, with a single axis of suspension, as a yet more
convenient method of obtaining a correct standard, than the processes
of Borda and Kater. It would be highly interesting to ascertain, bv
competent trial, the relative values of the three methods, and to examine
the correspondence of their results ; or, rather, to work at them until
they should correspond, or until the reason of a difference should be ap-
parent. The transmission of our measures to those distant times when
our manufactured scales shall have perished (and such is the object of
the reference to nature), is a purpose of such magnitude in all respects,
as to require the utmost evidence which the ingenuity and labour of the
age can supply : on its exact accomplishment depends the value to
posterity of every attainment of the present age, in which linear measure
is concerned ; and it may be reasonably expected that the habits, in
regard to accuracy in experiment, of the times when our proceedings
shall be examined, for the purpose of recovering by them that which is
lost, will be incomparably more precise than at the present period.
In selecting a spot, the pendulum of which is to supply an invariable
length in perpetuity, it is expedient to avoid, as far as may be possible,
the causes which may interfere with the permanency of local gravitation ;
for which reason great cities, or their vicinity, may be considered generally
as objectionable stations. It may be reasonably doubted, for instance,
3 B 2
372 EXPERIMENTS FOR DETERMINING THE VARIATION, SfC.
whether the present pendulum, in any particular spot in London, is
sensibly the same as it was before that part of the city was built ; since
an alteration in the density of the materials at the surface, equivalent
to only 100th part of the natural differences which actually prevail in
various localities (page 339), would be sufficient to influence the pendulum
in the fourth place of decimals. We have recently seen the substitution
attempted of masses of iron for the paving stones of London ; and it is
obviously impossible to anticipate the changes, which the ingenuity of
man in constant operation may hereafter effect, to promote the interest
or convenience of an immense population collected within a small com-
pass. A station sufficiently distant from dwellings, and not likely to
become their site, and yet not so remote as to be of inconvenient resort
to foreigners, who may desire to compare the standards of their respec-
tive countries with that of Great Britain, would seem to be much
preferable.
Even the changes which the accidents of nature may produce, admit of
being provided against, by the well-established comparison of the standard
pendulums of different countries with each other; whereby the means
are furnished of recovering the standard of any particular country, even
if the spot of its original determination should be destroyed.
GEOGRAPHICAL NOTICES.
LONGITUDE OF THE PENDULUM STATIONS.
The longitude of the Pendulum Stations was required to be known, in
order to deduce the time at Greenwich corresponding to that at the
several stations. For such purpose, I might have availed myself in some
instances of the received longitude, as being probably sufficiently correct ;
but as original determinations would have been necessary in many cases,
and as I was desirous that the memoir should be in all respects as
complete in itself, and as independent as it could be made of the ob-
servations of others, it was deemed preferable to undertake an original
ascertainment of the longitude at all the stations.
In the prosecution of this undertaking, it was conceived that a useful
service might be rendered to navigation and geography, by affording
an extensive practical exemplification of the value of lunar observations,
when made with instruments of the best construction, and their results
computed with due regard to what are usually termed the minute
corrections.
It is well known that the instruments employed in the British navy
and marine for observing lunar distances, are almost universally
sextants, and that circular instruments are very rarely to be met
with. Now, angular distances observed with sextants are liable to
certain errors, caused by defects of construction, for which the circular
completion of the arc enables a remedy : three sources of error may be
374 GEOGRAPHICAL NOTICES.
specified in particular ; first, from imperfect graduation ; second, from
the index and horizon glasses not being parallel when the index of the
limb is at Zero, constituting what is termed index error; and third,
from defective centring of the limb with respect to the arch. The great
improvements which have been made of late years in the art and practice
of graduation have rendered the errors arising from that source much less
significant than they were formerly, but those who have carefully exa-
mined modern sextants, know, that this imperfection is by no means
wholly removed. — The index error admits of its amount being de-
termined, and when known, it may be allowed for by an equal in-
crease or diminution of the angle read on the arch ; in good sextants, and
with due precaution, the index error is not very liable to change, but it
requires constant examination, and occasions, therefore, at the best,
much additional trouble. — The third source of error, however, that of the
eccentricity of the limb with regard to the arc, is a much more serious
evil, being extremely prevalent, and admitting of no very easy method of
detection, or of having the value of the error at different parts of the arc
ascertained*. The reflecting circle devised by Mr. Troughton, on which
construction the very few circles which are met with in British ships are
made, was designed expressly to obviate these defects ; but its use has
been found to be attended with so much practical inconvenience, as in
* The best mode with which 1 am acquainted of practically examining a se.xtaiit in this
respect, is by observing the meridian altitudes of several stars of known declination at different
altitudes at the same station. If the centring is correct, the latitudes deduced from the several
observations will agree ; if it is not so, the errors occasioned by it at different parts of the arc
may be ascertained and allowed for in future observation, in addition to Inde.x Error. By
employing a mercurial horizon, and a telescope magnifying from ten to fourteen times, and
by deducing the meridian altitudes from several observations made whilst the star is near the
meridian, noting and correcting for the horary angles, this examination may be made with
much exactness, by a tolerably practised observer. I may add that of many se.xtants which I
have myself examined, of makers in most repute, I have met with only two, which had the
same error at all points of the arc.
GEOGRAPHICAL NOTICES. 375
great measure to counterbalance the superiority of its principle, and to
have impeded its general adoption : it may be sufficient to particularize,
that the errors of imperfect graduation and defective centring are coun-
teracted in that circle by a multiplication of verniers, making three
distinct readings necessary in each observation ; whilst in practice, the
reading the arc, especially in night observations, is by far the most in-
convenient and irksome part of the whole process of observation, the
frequency of which it is most desirable to diminish, rather than
to increase. A more convenient reflecting circle than Mr. Troughton's
was therefore a desideratum of much practical importance; and it was
particularly to be wished that the principle of repetition should be intro-
duced, as a means of dispensing with the necessity of reading the arc,
until the close of the several observations of a series.
In the spring of 1821, Mr. Dollond, to whom practical astronomy has
so many obligations, was kind enough to show me the design of a re-
peating reflecting circle, which was then in progress of execution : as this
instrument appeared, so far as could be judged from the design, to pro-
mise to supply precisely what was wanting, I requested him to make a
second on my account, intending to give it an extensive trial. Without en-
tering minutely into the details of the construction of Mr. Dollond's circle,
it may be sufficient to notice, that it consists of two concentric circles in
the same plane and nearly in contact, the one of which moves within the
other: both circles are graduated, the outer into 720° subdivided into
spaces of 10 seconds; the inner, at every tenth degree on both sides of
Zero to 180°, referring for its subdivisions to those of the outer circle:
the inner circle carries the telescope, horizon glass, and a vernier applying
to the graduation on the outer circle, to which it clamps and is furnished
with an apparatus for slow motion, placed with the clamp near the te-
lescope : the index glass is carried on a limb moving freely round upon
its own centre, having an apparatus for slow motion, a clamp by which it
376
GEOGRAPHICAL NOTICES.
may be attached to the outer circle, and a vernier applying to the inner one.
This part of the circle corresponds with, and is similar to the limb of a
sextant, and may be used accordingly. To employ the circle in its more
extended application as a repeating instrument, the vernier of the inner
circle is clampt and read off, or set if it is preferred at the primary di-
vision; the telescope and horizon glass, which are both fixtures to this
circle, are then directed to either of the objects, and the limb carrying the
index glass is moved on its own centre, until the reflected image of the
other object is in the field, when the limb is clampt, and the contact
effected. So far the process is the same as in an ordinary sextant, with this
advantage, that the angle may be observed on either side of the Zero,
avoiding the necessity of the inversion of the instrument, (which at sea is
frequently very inconvenient,) and the value of the angle thus measured may
be read by the vernier of the limb, as already noticed. This reading, how-
ever, is an unnecessary step, where it is purposed to proceed in repetition,
which is done as follows: the inner circle is now unclampt and moved round,
(the limb with the index glass remaining fixed to the outer circle) until
its vernier has passed through twice the angle which is measuring ; it is
then clampt, and the telescope and horizon glass being directed to the
object which was reflected in the first observation, (or to the same as
before, accompanied by the inversion of the circle, if it best suits the
nature of the observation, or the convenience of the observer,) the objects
are again perceived in the field, and their contact is effected as usual.
The vernier of the circle becomes then charged with the sum of the two
observed angles, which, if it is not wished to proceed further in the
repetition, may be read off, and being divided by two, the quotient is
the distance corresponding to the mean time between the observations.
The angle so obtained is free from index error, but is still liable to be
affected by those of imperfect graduation, and eccentricity, although their
effect has been diminished by the process already gone through. In
GEOGRAPHICAL NOTICES. 377
order wholly to extinguish these errors also, the repetition of the same
double process must be continued, until the vernier of the circle has
progressively completed the entire round, or as nearly so as the amount
of the measured angle will admit; when a single reading, divided by the
number of observations, will shew, as before, the angle corresponding to
the mean time of observation.
When used as a sextant only, this instrument possesses the following
advantages over sextants of the ordinary construction ; first, it enables
the angle to be measured alternately on each side of zero, whence the
index error is compensated, and the liability to those of imperfect divi-
sion and centring diminished ; secondly, by clamping the vernier of the
circle successively at primary divisions, about a third of the circle apart,
in succeeding pairs of observation, the errors of centring may be de-
stroyed ; and thirdly, the angle which may be measured is not limited
by the extent of the arc, but may be carried to the utmost amount in
which the relative position of the glasses will admit of reflection.
When used as a circle, the following additional advantages are gained ;
the process of observation is shortened at least a half, by dispensing with
the reading off and writing down the angle at each repetition. The
errors which are frequently introduced in those operations are avoided ;
those of imperfect graduation and eccentricity are rendered insensible ;
and in night observations especially, the eye is spared the alternate
reference to a strong artificial light, necessary for reading the arc, but
extremely prejudicial to the most favourable state of the eye for
observation.
An incidental advantage arising from thus shortening the process of
observation is, that it places the whole operation within the power of
an individual to accomplish by himself; whereas it previously consisted
of too many distinct parts, and was consequently too laborious and
fatiguing for accuracy. The subjoined observations were made (with
3 c
378 GEOGRAPHICAL NOTICES.
very few exceptions) without an assistant, the times being noted by the
beats of a chronometer. The satisfaction is great to an observer to have
all the parts of an observation thus within his own command ; it is con-
venient also, because assistance is not always to be obtained ; and it is
conducive to accuracy, because the attention of an assistant is rarely
equal to that of the observer.
In the subjoined tabular abstract, the " Time by the Chronometer" is
a mean of the number of observations expressed in column 4, the details
of the time corresponding to each observation being omitted. The cor-
rection of the chronometer No. 423, to the mean time at the several
stations inserted in column 3, is taken from the preceding pages of this
volume; in column 5 is shewn the whole arc passed through by the
vernier of the circle in the process of repetition ; and in column 6, being
the whole arc divided by the number of repetitions, is the apparent
distance corresponding to the mean chronometer time in column 2.
Columns 7 and 8 exliibit the apparent altitudes of the moon and sun, or
star, calculated for the known apparent time at the station. The correc-
tions for refraction, or the differences between the true and apparent
altitudes, have been computed for the states of the atmosphere shewn in
columns 9 and 10, by Dr. Young's table in the " Nautical Almanac" for
1 822 ; much pains was taken to obtain the true temperature of the air,
uninfluenced by radiation on the thermometer from the surfaces around ;
for which purpose the thermometer was enclosed in a highly-polished
metal cylinder, pierced with holes in the top and bottom, and placed in
the shade. The true distances in column 11 have been deduced by
Dr. Maskelyne's method, published in the preface to " Taylor's Loga-
rithms," with corrections introduced, — of the horizontal parallax on account
of the Ellipticity of the Earth, — and of the distance, where the oblique
semi-diameters were sensibly affected by refraction.
In deducing the time at Greenwich, corresponding to the true distances,
GEOGRAPHICAL NOTICES. 379
from those inserted in the "Nautical Almanac" for every third hour,
the second differences of the moon's motion in relation to the sun or star
have been duly taken into the account. It sometimes happens that the
second difference of the distances of the moon and stars inserted in the
Nautical Almanac for every third hour, amounts to more than one minute
of space ; in such instances the correction due to the second difference
will exceed six seconds of space during more than half the intermediate
interval, and consequently, if neglected, will occasion an error of about
three minutes of longitude in the deduction. This circumstance is thus
specially adverted to, because its notice is omitted in the very useful
summary of the minute corrections, requiring attention where precision
is desired, published by the secretary of the British Board of Longitude
in the Journal of the Royal Institution for July, 1820.
The circle with which the distances were observed was ten inches
in diameter, and weighed five pounds ; the telescope was furnished with
a magnifying power of fourteen. The observations at Sierra Leone
were not strictly its first employment, as I had observed sixty-four dis-
tances with it at Madeira, on the outward passage ; with the exception
of these, however, the use of the circle was new to me at Sierra Leone,
and the awkwardness which attends the employment of a new instrument
was stiU to be overcome.
The sixty-four distances at Madeira, of which forty were of Regulus
west of the moon, and twenty -four of the Sun east of her, made the
British Consul's house, at Funchal, in 16° 55' 00" W.*; the longitude of
the Consul's garden has since been ascertained by the mean of sixteen
chronometers, specially sent for the purpose, at the direction of the Com-
missioners of Longitude, and has been found 16° 54' 45". 3 W.
* Letter to Sir Humphry Davy, P.R.S., dated Goree, January, 1822, printed in the Journal
of the Royal Institution, April, 1823.
3 C 3
380
GEOGRAPHICAL NOTICES.
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o
GEOGRAPHICAL NOTICES.
387
The preceding tabular statement comprises the results of 1350 dis-
tances, divided into 1-23 sets, and distributed through seven stations.
The following table collects in one view the mean results, and exhibits
a summary of the differences of the individual sets on the general mean
at each station.
STATIONS.
No. of
Dis.
tances.
No. of
Sets.
Individual Sets differing from tiie Meau
MEAN
LONGITUDES.
Les.
Ihan 1
mile.
Less
than 2
miles.
Less
tliai 3
miles.
Less
than 4
miles.
Less
than 5
miles.
Less
than 6
miles.
Less
than 7
mi lee.
Sierra Leone.
St. Thomas .
Ascension . .
Bahia. . . .
Maranham
Trinidad . .
Jamaica . .
318
150
164
128
158
162
270
23
11
16
14
16
16
27
4
2
5
5
12
5
15
7
4
4
3
6
7
4
1
2
3
1
5
4
7
2
5
2
1
2
2
1
O ' n
13 15 26.8 W.
6 45 00.4 E.
14 23 35 W.
38 32 39 W.
44 21 25.5 W.
61 36 15 W.
76 53 15 W.
Total . . .
1350
123
48
33
20
17
4
0
1
Whence it may be inferred that in similar circumstances of observation,
— i. e., on shore, and within the tropics, the observer being previously
accustomed to lunar observation with sextants, and furnished with a
correct knowledge of the time at the station, — it is about 2 to 1, that a
single set composed of 10 or 12 distances observed with Mr. DoUond's
circle, will give a result within two miles of the longitude, deduced from
an extensive series, including the various states of the atmosphere occur-
ring in such climates, and at different periods of the moon's age ; that it
is about 2 to 8 that the result will be within one mile ; and that a
difference, amounting to so much as between 4 and 5 miles, may not be
expected to occur oftener than about once in 25 sets.
3 D 2
388 GEOGRAPHICAL NOTICES.
The improvement which practice will make in the habits of ob-
servation, (and consequently on the inferences that have been thus
stated,) is evident on an inspection of the table ; for if the three last
stations only are regarded, the chances will appear more than equal, that
the result of a single set is within one mile, and 4 to 1 that it is within
two miles of a general mean ; whilst the extreme difference, occurring
only once in 59 sets, is under four miles.
No attempt has been made to correct the distances inserted in the
Nautical Almanac, by a more exact knowledge of the moon's place
derived from the Greenwich observations ; because the design has been
to afford a practical inference of the degree of accuracy which an observer
may expect with the means with which he is furnished on the spot. It
may be proper to mention also, that the table includes every set of dis-
tances observed at the stations to which it refers.
The conveniency of the circle in observation, and the facility with
which it may be managed by those who will accustom themselves to its
use, may be judged by the observations at Jamaica ; where it may be
seen that 60 distances of the sun and moon were observed within the
hour, or one in each minute, including the observation and entry of the
time of each distance, and the reading off at every tenth distance, and
writing down the arc passed through. In the repetition of the same
process with the moon and Aldebaran at night, the number of distances
observed in an hour was 50, or, on an average, one in a minute
and twelve seconds. Of the six sets into which the distances of
the sun and moon under notice were divided, three are within one
mile of the combined result of twenty-seven sets, and the two others
within two miles ; and of the five sets of the moon and Aldebaran,
four, are within one mile, and the fifth within two miles : this is
stated to shew that accuracy was not sacrificed to expedition ; both the
GEOGRAPHICAL NOTICES. 389
instances were without the advantage (in expedition certainly) of an
assistant.
The observation of the angular distance of the moon from certain fixed
stars, has long and universally been regarded as the best means of de-
ducing the longitude of a vessel on the ocean from celestial phenomena ;
but it has not been so generally recognised as it deserves to be, as the
most eligible of all the methods which present themselves to the choice
of the geographer, or the practical astronomer, for determining positions
on land, wherever time or the conveyance of instruments form a part of
the consideration. It combines, in a degree far beyond comparison with
any other method, the very important qualities of convenience, expedition,
and accuracy. The whole apparatus which is required, — a circle, a
chronometer, and an artificial horizon, — does not weigh twelve pounds ;
no temporary observatory is required for its protection, and all situa-
tions are equally convenient for its use ; the latitude and longitude
may both be determined in the first twenty-four hours after the
arrival at a station, during three-fourths of every lunation ; and as
the observations by which the determinations are accomplished may be
multiplied within that interval at the pleasure of the observer, so as to
comprise, in respect to latitude, every important variety of circumstance,
and almost every variety in regard to longitude, no sacrifice of accuracy
to expedition is called for, but the precision will be proportionate to
the labour which is bestowed.
There are occasions in which the qualities of convenience in por-
tability, expedition and accuracy in determination, are almost equally
essential. Such is the design which is understood to be entertained,
of forming the basis of a survey of central India, by the celestial deter-
mination of the geographical position of stations, selected at proper in-
tervals over that very extensive portion of the globe. Admitting the
space to contain 130 or 140 square equatorial degrees, and the stations
390 GEOGRAPHICAL NOTICES.
to be on an average 100 miles apart, above eighty such determinations
must be made. Those who are acquainted with the apparatus which
would be required, in any other mode of deducing the position from
celestial observation than the one under notice, and will pursue in
detail the consideration of the conveyance of such an apparatus over such
an extent of country, independently of the accidents and interruptions to
which it would be liable, — and who can appreciate the time which would
be occupied in obtaining an equally precise determination at each station,
as lunar distances would give in 24 hours, — will, I think, arrive at the
conclusion, that it is only by lunar distances that the design is likely
to receive its accomplishment.
With respect to the degree of accuracy to which the mean results of
the lunar observations at the seven tropical stations may be considered
to have been obtained, additional evidence may be aflforded, by exhibit-
ing their mutual accordance when connected with each other chronome-
trically. I have employed for that purpose the chronometer No. 357
of Messrs. Parkinson and Frodsham, which, having a small and con-
venient rate, and being wound weekly, was selected as a standard of
comparison for the chronometers in the Pheasant. No. 357 was
stationary on board, and was suspended in a cot from the deck, in a part
of the cabin where the motion was least, and where it remained undis-
turbed, except for the purposes of comparison, and of being wound. Its
treatment, therefore, was as favourable to the preservation of a steady
and uniform rate, as that of No. 423, with which its weekly comparison
is shown in the following table, may be esteemed to have been the
reverse. The immediate purpose of the table is to enable the transfer
to No. 357 of the comparisons of No. 423 with astronomical time,
recorded in former pages, and thus to furnish the means of examining in
detail, the chronometrical connexion of the lunar longitudes with each
GEOGRAPHICAL NOTICES. 391
Other, to those who may be disposed to take that trouble. The testimony,
however, which the table incidentally bears to the excellence of the
chronometers, so liberally lent by Messrs. Parkinson and Frodsham, and
to which the accuracy of the observations contained in this volume is so
essentially indebted, will probably be an object of more general interest.
It can rarely have happened to any chronometer to have undergone so
great a variety and such constant practical exposure, whilst its rate
was submitted to so severe a scrutiny, as that of No. 423. It is known
that the rates of chronometers are frequently found to vary on embarka-
tion in vessels, insomuch as to have given rise to the distinctive terms of
Land Rates, and Sea Rates * ; no such variation can however be traced
* An opinion has lately prevailed, that the change in the rate of chronometers on em-
barkation, which used to be considered as a consequence of the motion of a ship, is principally
occasioned by the magnetic influence of the iron which she contains ; and it has been assumed
by some of the writers, who have taken part in the recent discussions on the subject, that the
effect so attributed is one of general experience. I believe, on the authority of others, rather
than from my own observation, that a difference does sometimes, and even frequently, take place
between the land and sea rates of thronometers; but from whatever cause the irregularity may
arise, I must regard its occurrence as an evidence of the inferiority of the particular chrono-
meter, to the advanced state to which the art of their construction has attained ; because,
amongst the many with which I have at different times been furnished by Messrs. Parkinson
and Frodsham, and which I have frequently translerred from the ship to the shore, for two
and three weeks at a time, for the purpose of trial, I have never been able to discover any
systematic variation whatsoever, consequent on their removal.
With regard to the influence of the iron as a cause of the irregularity, a more decisive
evidence can scarcely be imagined of its not being practically discovered under the mo^t
favourable circumstances for its CNhibition, than took place in the four chronometers of
Messrs. Parkinson and Frodsham, of which I have given an account, in the appendix to
Capt. Parry's Voyage of Discovery, in 1819-1820, pages vii to xii, .wiii, xix, and xx. On
that occasion the Hecla was stationary and immoveable, being frozen up, for more than ten
months in the vicinity of the magnetic pole, the dip being between 88 and 89 degrees ; such
is the situation and such the circumstances, which are supposed to be best adapted for the de-
velopment of magnetism in the stanchions and other vertical iron of a ship ; the chronometers
were kept on board during the whole winter, and their rates, preparatory to the navigation of
the following summer, were assigned from the average of the four months immediately preced-
ing her extrication from the ice ; at the expiration of an equal period of four months of na-
vigation, the Hecla arrived at Leith, having experienced much bad weather in crossing the
392 GEOGRAPHICAL NOTICES.
in the going of No. 423, in any one of the six voyages in which it was
embarked between April and November, and which alternated with
nearly equal periods on land, when it was employed incessantly in ob-
servations, including those of magnetism. The uniformity of rate which
it preserved from day to day, under every circumstance of change or
exposure, was indeed admirable; and is deserving of regard, as an
evidence of the high degree of perfection to which the mechanism and
workmanship of chronometers have attained.
Atlantic, having been entirely dismasted on one occasion, and (which might have been expected
to have had even a more prejudicial effect on the chronometers,) having sustained very frequent
severe shocks from collision with ice ; but on comparing the four chronometers at the Ob-
servatory at Leith, their Greenwich time, employing the Winter Harbour rates, proved less
than two seconds in error. On the arrival of the Hecla in the Thames, the chronometers
were returned to Messrs. Parkinson and Frodsham's house in London, where, after a month's
interval, they were found to be still going at the same rates, as in the Hecla whilst in the har-
bour of Melville Island. These particulars are stated in detail in the pages referred to; but
the circumstance is thus again generally noticed, because it appears to have been overlooked
by many, whose ingenuity has been exerted in devising contrivances to remedy an evil
which has no practical existence, where the common discretion of life is exercised, in ob-
taining the better article at an equal price. Had the especial purpose of the Hccla's voyage
been to inquire whether the iron of a ship, in its ordinary distribution, would, under extreme
circumstances, exert a sensible intluence on the chronometers, better adapted arrangements
could scarcely have been devised for the experiment, nor could a more decisive result in the
negative have been obtained.
GEOGRAPHICAL NOTICES.
393
WEEKLY COMPARISON of the Chronometers 357 and 423 between February
and November, IS22 , with the average Daily Rate in each Week of 423 on 357.
DATE.
423 011 357.
423'3 R.ite
on 357.
STATION. 1
DATE.
423 on 357.
423's Rnte
on 357.
STATION.
1822.
M. S.
1822.
H. S.
Feb. 23
Fa. 0 IS
+ 0.43
July 6
Fa. 0 07
+ 0.71
Mar. 2
,, 0 16
+ 0.29
„ 13
„ 0 12
+ 0.36
■ At Sea.
.., 9
„ 0 18
+ O.U
„ 20
„ 0 11.5
+ 0.5
., 16
,, 0 19
- 0.07
!■ Sierra Leone.
„ 27
„ 0 18
+ 0.43
■ Bahia.
„ 23
., 0 18. S
- 0.21
Aug. 3
,, 0 21
+ 0.29
„ 30
„ 0 16
„ 10
„ 0 23
April 6
„ 13
,. 0 16
„ 0 19.5
0
+ 0.5
„ 17
„ 24
,, 0 22
SI. 0 08
- 0.14
423 down,
and reset.
■ At Sea.
„ 20
,. 0 22
+ 0.36
- 0.07
„ 31
„ 0 07
- 0.14
- 0.36
> Maranham.
,. 2T
May 4
„ 0 21.0
SI. 0 08
423 down
and reset.
- 0.29
■ At Sea.
Sept. 7
,. 14
., 0 09.5
„ 0 09.5
0
- 0.21
. At Sea.
,. 11
„ 0 10
- 0.29
„ 21
,,0 11
- 0.21
,. 18
., 0 12
+ 0.43
„ 28
.. 0 12.5
0
I Trinidad.
„ 25
„ 0 09
Oct. 5
„ 0 12.5
+ 0.14
+ 0.07
June 1
„ 0 08
,. 12
„ 0 12
0
> St. Thomas.
+ 0.5
I At Sea.
„ 8
,, 0 08
+ 0.21
„ 19
„ 0 08.5
+ 0.29
„ 15
„ 0 06.5
„ 26
„ 0 06.5
„ 22
„ 0 03
+ 0.5
+ 0.57
> At Sea.
Nov. 2
„ 0 05
+ 0.21
+ 0.43
} Jamaica.
J
„ 29
Fa. 0 01
+ 0.86
f Ascension.
M 9
,. 0 02
July 6
„ 0 07
"
3 E
394 GEOGRAPHICAL NOTICES.
From the comparisons in the preceding table, and the transits and
zenith distances observed at the different stations with No. 423 and
detailed in former pages, the particulars are supplied which are arranged
in the next table, and furnish the necessary data for conveying the lunar
longitude of each station to the next on either side of it, and thus of
comparing them with each other, as is done in the subsequent memo-
randa .
The 1st column of the tables states the earliest and latest days at
each station, in which the correction of No. 423 to mean time was as-
certained with precision, its amount being shewn in the 4th column ; the
5th contains the corresponding correction of 357, and the 6th its difference
from the mean Greenwich time obtained by lunar observations ; in the 7th
column is inserted the number of days included by the observations of
rate at each station, and in the 8th the average daily rate of 357, de-
duced from the direct comparison of 423 with astronomical time, and
transferred to 357.
The rates of both the chronometers appear to have accelerated in a
very regular and uniform progression, which may not improbably be
attributed to the gradual adaptation to each other of the several parts
of the workmanship, in the process of wear, as both the chronometers
were of recent construction. The acceleration being regular, an interme-
diate rate between that of the station on either side has been assumed
for the intervals of passage from station to station.
GEOGRAPHICAL NOTICES.
395
A TABLE
Shewing the RATE and CORRECTIONS of No. 357 to MEAN TIME at the
several TROPICAL STATIONS, and its Corrections to the Mean Greenwich
Time obtained by the Lunar Observations.
DATE.
STATIONS.
1822.
March 6
April 2
May 27
June 10
„ 26
July 9
„ 23
.\ugust 5
„ 24
Sept. 4
„ 23
Oct. 10
, 22
Nov. 5
Lunar Longitude.
On Mean Time at the Station.
423.
Sierra Leone
St. Thomas.
0 53 01.8 W.
0 27 00 E.
H. M. S.
Fa. 0 48 48
> Ascension . 0 57 34.3 W
Bahia .
Maranham.
Trinidad.
Jamaica. .
2 34 10.6 W. ■
2 57 25.7 W.
4 06 25 VV. •
5 07 33 W.
„ 0 49 12
SI. 0 30 il.5
„ 0 29 54
Fa. 0 55 08
„ 0 55 40
357.
H. M. S.
Fa. 0 48 31
,, 0 48 57
SI. 0 30 OS
„ 0 29 46
Fa. 0 55 09
„ 0 55 29
2 32 46.5 „ 2 32 31.2
,, 2 33 00
„ 2 56 56
„ 2 27 25
„ 4 07 12.5
„ 4 08 04.5
„ 5 09 58.5
„ 5 10 48
357 on Mean
Greenwich
Time.
„ 2 33 22
„ 2 56 48
„ 2 57 17.5
„ 4 07 00
„ 4 07 52
„ 5 09 51.5
„ 5 10 44
SI. 4 30.8
„ 4 04.8
„ 3 03
„ 2 46
„ 2 25.3
„ 2 05.3
„ I 39.4
„ 1 10.6
„ 0 29.7
„ 0 00.7
Fa. 0 47.5
,, 1 39.5
„ 2 25.5
„ 3 15
Inter-
vals.
Daily
Rate.
Da3S,
27
14
13
13
U
Gaiuing.
0.96
1.21
1.54
2.22
2.63
!„
f"
.06
3.54
3 E 3
396 GEOGRAPHICAL NOTICES.
COMPARISONS OF THE LONGITUDE OBTAINED BY DIRECT LUNAR
OBSERVATION AT EACH STATION, AND THE LUNAR LONGITUDE
OF THE ADJOINING STATIONS, REFERRED BY MEANS OF THE
CHRONOMETER No. 357.
Sierra Leone. — In the West Bastion of Fort Thornton.
h. ra. s.
By 318 Lunar distances at Sierra Leone . . . 0 53 Ol.S W.
By 150 Lunar distances at St. Thomas's referred, by 357 0 52 59.7
Final Longitude . . . 0 53 00.75=13° 15' U" W,
In a letter received in 1S23, from the late Thomas Stewart Buckle, Esq., Civil Engineer and
Surveyor of the colony of Sierra Leone, the Geographical bearing of Fort Thornton from Cape
Sierra Leone, is stated to be S. 83° E., and the distance about 7,000 yards, or 3.8 geographical miles.
Whence the longitude of the Fort referred to the Cape, would make the latter in 13° 19' 00" West.
St. Thomas. — At the Mansion-House of Fernandilla, Man-of-War Bay.
Ii. m. s.
By 318 Lunar distances at Sierra Leone, referred by 357 0 20 57.9 E.
By 150 Lunar distances at St. Thomas . . . . o 27 00.
By 104 Lunar distances at Ascension, referred by 357 0 20 58.7
Final Longitude . . . 0 20 58.9 = 0° 44' 43.5" E.
The Roadstead of Santa Anna de Chaves is about 4^ geographical miles east of the meridian of
Man-of-War Bay ; whence the longitude of the Roadstead is 6° 49' 13' E.
Ascension. — In the Barrack-Square.
h. m. s.
By 150 Lunar distances at St. Thomas's, referred by 357 0 57 30.4 W.
By 104 Lunar distances at Ascension . . . . 0 57 34.3
By 128 Lunar distances at Bahia, referred by 357 . . 0 57 34.7
Final Longitude . . . 0 57 35.1 = 14° 23' 40.5" W.
By a recent trigonometrical survey of Ascension by the officers of the garrison, the particidars
of which are in the Hydrographic Office of the Admiralty, tlie Barrack-Square bears from Cross-Hill
about N.W. the distance being less than 4,000 feet ; whence the longitude of Cross-Hill may be
taken at 14° 23' 20^' W.
GEOGRAPHICAL NOTICES. 397
Bahia. — At the House of William Pennell, Esq., British Consul ; Vittoria.
h. m. s.
By 164 Lunar distances at Ascension, referred by 357 . 2 34 10.2 \V.
By 128 Lunar distances at Bahia 2 34 10.6
By 158 Lunar distances at Maranham, referred by 357 . 2 34 15.8
Final Longitude ... 2 34 12.2=38° 33' 03" W.
Mr. Penuell's house is situated about half a mile east of the meridian of Fort St. Antonio ; whence
the longitude of the fort may be inferred 38° 33' 30' W.
Maranham. — At the House of Robert Hesketh, Esq., British Consul, adjoining
the Cathedral.
h. m. s.
By 128 Lunar distances at Baliia, referred by 357 . . 2 57 20.5 W.
By 158 Lunar distances at Maranham . . . . 2 57 25.7
By 1G2 Lunar distances at Trinidad, referred by 357 . 2 57 31.5
Final Longitude . . . 2 57 25.9 = 44° 21' 2S."5 W.
The longitude may be referred to the Cathedral without sensible error.
Trinidad. — On the Second Groimd Lot,West of the Protestant Church, Port Spai7i.
h. m. s.
By 15S Lunar distances at Maranham, referred by 357 . 4 06 19.2 W.
By 162 Lunar distances at Trinidad . . . . 4 06 25.
By 270 Lunar distances at Jamaica, referred by 357 . 4 06 18.6
Final Longitude . . . 4 06 20.9=61° 35' 13."5 W.
The longitude of the Protestant Church maybe inferred 61° 35' 00" W.
Jamaica. — At the Governor\s House, Fort Charles, Port Royal.
h. ni, s.
By 162 Lunar distances at Trinidad, referred by 357 . 5 07 39.4 W.
By 270 Lunar distances at Jamaica . . . . 5 07 33.
Final Longitude ... 5 07 36.2=76° 54' 03" W.
The spot at which the observations were made is marked by the position of the Flagstaff at Fort
Charles.
398 GEOGRAPHICAL NOTICES.
I proceed to compare the longitudes of the stations thus obtained with
their previously-received longitudes, as given in the Connaissance des
Terns, (No. for 1823,) and in Professor Lax's Nautical tables, (edition
of 1821,) which works are presumed to contain the tables of longitude of
the most approved authority in Great Britain and France.
Cape Sierra Leone is not found in the table of the Connaissance des
Tems ; in Professor Lax's table, it is given on the authority of the late
Hydrographer of the Navy, 13° 18' 00" W., and by the present observa-
tions is in 13° 19' 00" W.
The longitude of the Roadstead of Santa Anna de Chaves, in the
Island of St. Thomas is stated, in the Connaissance des Terns, on
chronometrical authority, to be 7° 32' 22" East of Greenwich Obser-
vatory ; but by the present observations, it is only in 6° 49' 13" East.
Man-of-War Bay is placed by Professor Lax, on the authority of the
Hydrographic Office, in 6° 44' 00" East, and by the present observations
is in 6° 44' 43".5 East.
In the Connaissance des Tems, the longitude of the Island of Ascen-
sion is inserted 13° 58' 45" W., but without specification of the part of
the Island to which the geographical position refers. Professor Lax
has repeated the longitude of the French table, with the same uncertainty
of position; but has also given that of Cross-Hill from the Hydro-
graphic Office, 14° 13' 30" W. It appears from the recent trigono-
metrical survey, the particulars of which are deposited in that office,
that the eastern extremity of the island is less than 8 miles east of
the meridian of the Barrack-Square, or Cross-Hill ; whence^ it may be
inferred that if 14° 23' 46".5, the present determination, be the true lon-
gitude of the Barrack- Square, no part of the Island is in a less Western
longitude than 14° 15' 00"; and that the authority for the position as-
signed by Professor Lax to Cross Hill is about ten miles, and that
of the French table nearer twenty miles in error. The correct longi-
GEOGRAPHICAL NOTICES. 399
tude of Ascension is of value, because the island is frequently made by
vessels on the homeward passage from the East Indies, and a de-
parture is taken from it ; the error of former determinations is also on
the side of danger.
The longitude of Fort St. Antonio is given in Professor Lax's table,
38° 28' 00" West, on the authority of the Hydrographic Office. The table
in the Connaissance des Terns, does not notice Bahia or its environs ;
but in a memoir entitled " Navigation aux cotes du Bresil," published
in Paris, in 1821, by M. Le Baron Roussin, then Capitaine de Vaisseau,
and since Admiral, in the service of France, (who was employed in the
command of a small squadron, in the survey of the coasts of Brazil, in
1819 and 1820, and subsequently in 1822, when the Pheasant was at
Bahia,) Fort St. Antonio is placed provisionally in 38° 30' 12" W., de-
pendant upon the longitude of Fort Santa Cruz d'Anhatomirim ; the differ-
ence of meridians between the stations being inferred chronometrically, and
the longitude of Fort Santa Cruz derived from lunar distances, which are
stated in the memoir to require to be more rigidly computed, before their
correct result should be known. In the additions to the Connaissance des
Terns for 1826, a memoir is printed by M. Givry, in which the longitudes
of M. Le Baron Roussin on the coasts of Brazil are discussed ; in that me-
moir Fort St. Antonio is placed in 38° 31' 35" W., being a chronometrical
inference from Rio Janeiro, and dependant upon the true longitude of Rio,
which is assumed from the mean of various sources differing not less than
22 miles from each other. It will be observed that the longitudes of Fort
St. Antonio, assigned in the memoirs of MM. Roussin and Givry, are
in neither case from direct observation at the meridian itself, but in both
from the provisional longitudes of distant meridians referred to Bahia by
means of a chronometer ; if, however, the lunar observations made at
Bahia itself by M. Roussin and his officers, be regarded as a more direct
400 GEOGRAPHICAL NOTICES.
authority for the longitude of Fort St. Antonio, the following would
appear the result : —
%57 series of eastern distances of the Moon from the ) „ o .,/ ,o// «
> 3S 41 4o 2
Sun observed on the 1 1th and 1 2th of October at Bahia ^
By 51 series ot western distances observed at the same "i oi' qc
spot on the 25th and 27th of October. ^
Longitude of Bahia, west of Greenwich 3S 36 40. S
and that of Fort St. Antonio would differ not more than a few seconds
to the westward. It has been seen that the lunar observations with
Mr. Dolland's circle made Mr. Pennell's house at Vittoria in 38° 32' 33";
those at Ascension chronometrically referred to the same spot 38° 32' 39";
and those at Maranham similarly referred 38° 33' 57"; whence Fort St. An-
tonio may be deduced from the mean of the three determinations to be in
38° 33' 30" W. Navigators will exercise their own judgment, in selecting
the longitude amongst these various authorities which may appear most
satisfactory ; but it may be presumed that a mean of the six deductions,
or 38° 33' 15", may be within one mile of the truth.
Maranham does not appear in the table in the Connaissance des
Tems ; but in that of Professor Lax the town of St. Luiz Maranham is
placed in 44° 05' 00" W., on the authority of the Hydrographer of the Ad-
miralty. This longitude however can scarcely be regarded as otherwise
than very erroneous ; the town itself is small, and the cathedral, to which
the lunar observations at Bahia, Maranham, and Trinidad, have severally
assigned with little variation the longitude of 44° 21' 28'. 5, is situated
nearly in the middle of the town.
The longitude assigned to Port Spain in Trinidad in the Connaissance
des Tems is 61° 38' 00" W. on chronometric deduction; and in Professor
Lax's table is the same longitude, referring to the Connaissance des Tems
as authority ; the present determination is 61° 35' 00", referred to the
meridian of the Protestant church, which nearly divides the town.
GEOGRAPHICAL NOTICES. 401
The Connaissance des Tems places Port Royal, Jamaica, in 76° 45'
15" W., from astronomical observations; Professor Lax's table in
76° 52' 30" W. from the Hydrographic office ; and the lunar observations
at Trinidad and Jamaica in 76° 54' 00" W. The result of the 270 dis-
tances observed on the spot, being 76° 53' 15", is, perhaps, in this in-
stance, a more satisfactory determination, than the mean between the
lunars of Trinidad and Jamaica.
The advantage to navigation, of the very accurate determination of the
longitude of places of frequent resort, consists in the means which it
provides for the regulation of chronometers. In making a port, it is com-
paratively of little consequence that its longitude should be knovra nearer
than to a few miles ; but since the use of chronometers has become so
general, (and much has navigation benefited by their introduction, even
more perhaps in the time that is saved, than in the dangers that are
avoided,) it is a great desideratum to furnish a ready means, at the
different ports which ships are accustomed to visit, of obtaining a correct
comparison with Greenwich time. For that purpose, however, it is ne-
cessary that the longitude should have been accurately determined ; because
if an error exists, its amount will be charged against the previous going of
the chronometer, and will occasion the assignment of an erroneous rate in
continuance ; which may be productive of far more inconvenience than
the original error itself, if the succeeding voyage should be of much longer
duration than the preceding one was. The comparison of chronometers
with Greenwich time, by means of established geographical positions, is so
much more convenient and certain, than by celestial observation on board,
that the full value of chronometers to navigation will not be derived, until
the small number of stations which have been as yet determined with
sufficient care for that purpose, are extensively increased ; when lunar ob-
servations at sea will only be resorted to as a check in long passages, or
3 P
402 GEOGRAPHICAL NOTICES.
on the approach to land. A revision of the geographical position of those
stations, which are most frequently visited, would be a very important
service, and is well worthy of accomplishment under the direction of
the Board of Longitude of the first maritime nation. The revised tables
should contain an additional column to those in the tables at present
esteemed as of the best authority, for the purpose of specifying the spot
to which the geographical position refers ; without such specification,
it is quite superfluous to insert the data, as is now done, to seconds of
space. The spots should also be selected, as far as might be possible,
'with reference to their conveniency of access, with instruments, from
vessels in the harbour.
Longitude of Columbia College, New York.
By 70 lunar distances, 40 of Pollux east, and 30 of Aldebaran west
of the moon, the longitude of Columbia College appeared 74° 03' 27"
West. The result alone is stated, because the observations are not con-
sidered as sufficiently entitled to confidence, to justify their publication
in detail. The transition from a residence of several months within the
tropics, to the severity of a New York winter, was too sudden for the
requisite attention to ensure accuracy in night observation.
Longitude of Hammerfest.
The practical as well as theoretical merits of the reflecting circle on
Mr. Dollond s construction having been thus manifested by extensive
trial, it was conceived, that in order to derive the full benefit from the
application of the principle of repetition, the diameter, and consequently
the weight, of the circle would admit of reduction. Accordingly, on the
return of the Pheasant to England, and whilst the Griper was fitting,
Mr. Dollond consented to receive back the ten-inch circle, and to make in
exchange one of six inches diameter only ; which was completed a day
GEOGRAPHICAL NOTICES. 403
or two before the Griper sailed. Whilst at Hammerfest, I observed
with it about the usual number of lunar distances, but not having
leisure to compute the results on the spot, the observations v^rere put by
until the passage between Hammerfest and Spitzbergen, when, in the
course of reduction, I was surprised by finding discordances much be-
yond the ordinary occurrence. On a careful examination of the circle'
their cause was traced to a connexion which had been established
between the horizon-glass and the collar of the telescope, by a part of the
frame-work to which the skreens of the index glass were attached. In
consequence of this connexion, the pressure of the face against the eye
tube of the telescope, which assists in steadying the instrument during
the observation of lunar distances, deranged the verticality of the horizon
glass ; but as, on the pressure being removed, it instantly returned to its
adjustment, the occasional derangement had escaped notice. The lunar
observations at Hammerfest having been thus vitiated, the longitude of
Mr. Crowe's establishment at Fugleness has been deduced by five chrono-
meters of Messrs. Parkinson and Frodsham, dependant on the pro-
visional longitude of the pendulum station at Spitzbergen, (11° 40 30"
East,) and employing a mean between the observed rates at Hammerfest
and Spitzbergen, for the intermediate period of fourteen days from the
22nd of June to the 6th of July ; this longitude is 23° 45' 45" East, the
different chronometers varying from 23° 44' 30" to 23° 46' 30".
The six-inch circle was not employed subsequently in lunar distances ;
but the latitudes recorded in pages 323 and 324 were observed with it'
being sufficiently steadied by the handle for the observation of altitudes.
Mr. DoUond has recently made a circle on the same principle of construc-
tion for Mr. Renwick of New York, of eight inches in diameter, which
weighs four pounds, and has the same telescope and glasses as the circle
often inches. The eight-inch circle appears, and will probably prove,
the most eligible of the three in respect to size.
3 F 2
404
GEOGRAPHICAL NOTICES.
LONGITUDE OF THE PENDULUM STATION AT SPITZBERGEN.
I. By the Transits of the Moon and Regulus, observed with No. 649 on
THE loth OF July, the Apparent Meridian Altitudes of the Moon and
Star being respectively 22° 26' and 23° oi'.
TIMES OF TRANSIT BY THE CHRONOMEIER, No. 649.
Mean by the
Chronometer.
1st Wire.
•2d Wire.
Meridian Wire.
4th Wire.
5lh Wire.
Moon's Western Limb ....
Regulus
u. s.
27 36.8
02 30.8
M. S.
28 04.1
02 57.2
H. M. S.
1 28 32.4
2 03 24
M. S.
29 00.4
03 50.8
M. S.
29 28.4
04 17.6
H. M. S.
1 28 32.47
2 03 24.07
DATE.
transits.
649 Slow of
Mean Time
by the Star's
Transit.
Mi
Sidereal
Interval be-
tween ihe
Transits.
Moon's AR. at
tlie Transit of her
Limb.
Corresponding App. Time.
Difference of
Meridians.
Spitsbergen.
Greenwich.
July
10
Moon's Western
Limb, and Re-
gulus.
H. M. s.
■0 44 48.7
S.
0.7
H. M. S.
0 34 57.3
0 ; //
141 17 07.45
H. M. S.
2 28 30.74
H. M. S.
1 21 49.82
H. M. S.
0 46 40.92 E.
II. By the Solar Eclipse.
The termination of the solar eclipse, which took place on the 8th of
July, was observed in front of the pendulum house, by Mr. Henry Foster
and myself: by Mr. Foster with an achromatic telescope, made by Mr.
DoUond, of 2 feet 6 inches focal distance, and 2| inch aperture, with a
power of 51 ; and by me, with the telescope attached to the repeating
circle, of 6 inches focal distance, and one inch aperture, with a power of
forty ; the eye in both instances being protected by a deep red glass.
GEOGRAPHICAL NOTICES.
405
The chronometers employed were No. 423 by Mr. Foster, and No. 649
by me ; the corrections of both to mean time being derived, as follows,
from the transits and zenith distances observed with No. 649, recorded in
pages 150 and 158.
July 7th at the Sun's transit 649 slow 44 51.27
„ at the transit of i Ursse ... 44 50.67
jj „ Arcturus . 44 50.52
„ y Draconis . 44 50.03
^, „ a LjrEB ... 44 50.45
8 „ 1 Urste ... 44 49.7
7 P.M., by the Repeating Circle 44 51.32
8 AM 44 49.14
whence at 7 A.M., on the Sth 44 50.49
44 50.17
44 50.03
44 49.7
44 50.15
44 50.2
Mean
44 49.96
Slow 44 50.11
No. 423, Fast of 649 by comparisons made before and after the end of the Eclipse 3 15.3
No. 423 . . Slow 41 34.S
h. m. s. h. m. s.
Termination of (by Mr. Foster at 7 1 1 10.8 by 423, or at 7 52 45.61 A.M. mean time,
the eclipse |by Capt. Sabine at 7 07 55.4 by 649, or at 7 52 46.51 A.M. mean time.
Mr. Foster's observation may be regarded as preferable to a mean
of both, on account of the superiority of the telescope with which he
observed.
The longitude which this observation would assign for the observatory
at Spitzbergen has been computed by Mr. Foster on the suppositions, that
the moon's place is correctly given in the tables for that day, — that the
ellipticity of the earth is 75-; th, — and that the observation was not affected
by irradiation or by the inflection of light: the result, under such circum-
stances, would be 11° 37' 58". 5, East.
Mr. Foster has permitted me to insert the following memorandum of a
series of distances of the sun east of the moon, and of a second series
of the sun west of the moon, observed by him at the same spot as the
solar eclipse and lunar transit were observed ; their mean result appears
to confirm the accuracy of the deduction from the moon's transit, rather
than that from the eclipse, according to the computation.
406
GEOGRAPHICAL NOTICES.
III. By Lunar Distances observed by Mr. Foster.
At the Observatory on the inner Norway Island, the following Lunar
Observations were taken with a sextant of eight inches radius, made by
Dollond; the highest power was applied to the telescope, and the same
red-coloured screen glass was used in both Lunations.
July 3, P.M. 1823. Barometer 29.78. Thermometer 38. S Sun East of Moon.
Apparent Time at
the Place of
Observation.
H. M.
4 43
4 48
4 49
4 51
4 52
4 54
4 55
4 57
4 59
5 1
s.
13.2
9.2
42
16.5
46.5
17.7
57.7
49
37
20.7
59.2
36
3.2
28.7
55.5
40.5
Observed Dis-
tance between Sun
ami Moon's
nearest Limbs.
63 38 41
63 35 38
63 34 45
63 33 57
63 33 8
63 32 15
63 31 12
63 30 7
63 29 10
63 28 13
63 27 20
63 26 23
63 25 38
63 24 40
63 23 43
63 23 10
Error
of
Sextant.
+ 10
True Distance of cen-
tres computed by
the direct method.
63 49 32
63 46 36
63 45 47
63 45 3
63 44 19
63 43 29
63 42 29
63 41 25
63 40 32
63 39 38
63 38 46
63 37 54
63 37 12
63 36 14
63 35 22
63 34 48
Apparent Time at
Greenwich in-
terpolated by se-
cond diflcrences.
H. M. S.
3 55 50.2
4 1 16.8
2 47.6
4 9.5
5 31.1
7 3.9
8 55.2
4 10 54.4
4 12 32.7
4 14 13.3
4 15 49.5
4 IT 26.4
4 18 43.9
4 20 31.6
4 22 8.5
4 23 11.1
Longitude
of the
Place of Observation.
11 50 45 E.
1143 6
11 43 36
11 46 45
II 48 51
11 48 27
11 45 37
II 43 39
11 46 4
11 46 51
11 47 25
11 47 24
11 50 4
II 44 16
II 41 45
11 37 21
Longitude of Place of Observation by Lunars O East of 5 = 11 45 44.7 E,
GEOGRAPHICAL NOTICES.
407
July U, P.M., 1S23, Barometer 30.02, Thermometer 41.5, Sun West of Moon.
Apparent Time at
the Place
of Observation.
Observed Dis-
tance between San
and i^loon's
nearest Limbs.
H. M. S.
3 59 32.6
4 1 6.3
4 2 35.8
4 4 0.4
4 7 0.5
4 8 41.9
4 10 19.5
4 11 48.6
4 13 5.1
4 16 31.2
4 18 11.5
4 19 50.2
4 21 32.9
4 23 14.7
4 24 26.4
4 26 32.5
46 36 35
46 37 30
46 38 20
46 39 8
46 40 42
46 41 28
46 42 15
46 43 5
46 43 50
46 45 28
46 46 18
46 47 17
46 48 13
46 49 12
46 49 53
46 50 58
Error
of
Sextant.
+ 10
True Distance be-
tween the centres
computed by
the direct method.
Apparent Time at
Greenwich in-
terpolated by se-
cond differences.
Longitude
of the
Place of Observation.
46 48 25
46 49 23
46 50 16
46 51 8
46 52 47
46 53 38
46 51 28
46 55 23
46 56 9
46 57 55
46 58 48
46 59 51
47 0 50
47 1 54
47 2 36
47 3 46
H. M. S.
3 12 52.7
3 14 36.9
3 16 12
3 17 45.4
3 20 43
3 22 14.4
3 23 44
3 25 19.2
3 26 45.9
3 29 55.2
3 31 30.7
3 33 23.6
3 35 9.4
3 37 4.3
3 38 19.7
3 40 25.2
II 39 59 E.
II 37 21
11 35 57
11 33 45
U 34 22
11 36 52
11 38 52
11 37 21
1 1 .34 48
II 38 55
11 40 12
11 36 39
11 35 52
II 82 36
II 31 40
11 31 49
Longitude of Place of Observation by Lunars O West of 5= 1 1 36 3 . 7 E.
408
GEOGRAPHICAL NOTICES.
Longitude of the Observatory, Sun East of Moon = 11 45 44.7 E*.
Ditto ditto, Sun West of Moon =1136 3 . 7 E *.
Mean Longitude by Lunar Distances = 11 40 54.2 E.
RECAPITULATION.
By the Transits of the Moon and Regulus II 40 13. S E.
By Lunar Distances II 40 54.2
By the Termination of the Solar Eclipse II 37 58. 5
O * w
Longitude inferred 11 40 30 E.
* The difference which Mr. Foster found mi the longitude derived from liis Eastern and Western
distances, amounting to 39 seconds of time, or to about 20 seconds of angular distance, may be adduced in
illustration of the errors to which 1 have alluded, as occurring in sextants even of the best makers, and not
compensated by the most careful ascertainment of the index correction at the zero end of the arc.
It will be seen by the following memorandum, that nearly the same amount of error was found to obtain
in the angles of altitude, measured with the same instrument, and read from nearly the same part of
the arc .
DATE.
Sun's meridian
double Altiuule
L.L.
Index
Correction.
Barom.
Tlierm.
Lntitude dedaced.
O / It
„
IN.
o
o
,
„
July
5 Midnight.
24 56 10
+ 10
30.00
38.5
79
50
13.2] o .
■ 79 49 59.
45.6
3 N.
"
7 Noon . .
65 13 00
+ 10
29.82
39.5
79
49
The mean latitude differs only 2 seconds from the results with the repeating circle, in page 321 ; but the
particular observations are 27.6 seconds apart, making an error uncompensated by the index correction,
which was very carefully and repeatedly examined, of about 14 seconds in each angle, if divided equally
between them. The error shewn by the distances and altitudes is of the same description ; and indicates
that the angles read between the 40lh and GOth degrees of the arc, and corrected for the index error ob-
served at the zero end, were in excess of the truth from 10 to 14 seconds.
GEOGRAPHICAL NOTICES.
409
LONGITUDE OF THE PENDULUM STATION IN GREENLAND.
I. By Luwar Transits.
STARS.
TRANSITS BY THE CHRONOMETER 423.
Mean by the
DATE.
1st Wire.
ad Wire.
Meridian Wire.
41h Wire.
5tli Wire.
Chronometer.
M. S
M. s.
H. M. S.
M. s.
M. S.
H. M. S.
Aug. 21
» Aquilae ....
07 17.6
1
07 44
11 08 10.4
08 36.8
09 03.2
11 08 10.4
„ „
Moon's E. Limb .
34 43.2
35 10.4
13 35 37.6
36 05.2
36 32.2
13 35 37.73
„ 22
aCygni
56 14.8
56 51.2
11 57 28
58 04.8
58 41.6
11 57 28.07
}J J»
Moon's E. Limb .
16 53.6
17 21.2
14 17 48.4
18 15.6
18 42.8
14 17 48.33
„ 23
Arcturus ....
25 53.2
26 21.2
5 26 49.2
27 17.2
27 44.8
5 26 49.13
>j jy
Moon's E. Limb .
50 17.2
59 44
15 00 11.2
00 38.4
01 05.2
15 00 11.2
„ 24
ot Andromedee . . .
12 07.2
12 36.8
15 13 06.4
13 36
14 05.6
15 13 06.4
?) JJ
Moon's E. Limb .
42 56.8
43 24
15 43 51.2
44 18.4
44 45.6
15 43 51.2
„ 23
Moon's E. Limb .
28 54.8
29 22.8
16 29 50.8
30 18.4
30 46
16 29 50.6
J J !»
X Arietis
05 59.6
06 28
17 06 56.4
07 24.4
07 52.8
17 06 56.27
,, 26
Moon's E. Limb
18 13.6
18 42
17 19 10.4
19 38.8
20 07.2
17 19 10.4
J J -V
Aldebaran . . .
30 23.2
30 50.4
19 31 17.6
31 44.8
32 12
19 31 17.6
„ 27
Moon's E. Limb .
11 34.4
12 03 6
18 12 32.8
13 06
13 31.2
18 12 32.8
t> JJ
Aldebaran . . .
26 34.4
27 01.6
19 27 28.8
27 56
28 23.2
19 27 28.8
„ 28
Moon's E. Limb SP.
39 50.4
40 20.4
6 40 50
41 20
41 50.4
6 40 50.2
>j »
Pollux SP. . . .
32 47.6
33 17.2
10 33 47.2
34 16.8
34 46.4
10 35 47.07
" »
Moon's E. Limb .
09 04
09 34
19 10 04
10 34
11 04
19 10 04
)j jj
Aldebaran . . .
22 44.8
23 12
19 23 39.2
24 06.4
24 33.6
19 23 .39.2
„ 29
Moon's E. Limb SP.
39 09.6
33 40
7 40 10.4
40 40.8
41 01.2
7 40 10.4
i> »
Pollux SP. . . .
28 57.6
29 27.6
10 29 57.2
30 27.2
30 56.8
10 29 57.27
V ''
Moon's E. Limb .
09 52
10 22
20 10 52
11 22.4
11 52.4
20 10 52
)) ■'
a Orionis ....
38 32.8
38 59.2
20 39 25.6
39 52
40 18.4
20 39 25.6
„ 30
Moon'sE.LimbSP.
40 56.8
41 27.2
8 41 57.6
42 28
42 58.4
8 41 57.6
jj .J
Pollux SP. • . .
25 08.8
25 38.4
10 26 08
26 38
27 07.6
10 26 08.13
3 G
410
GEOGRAPHICAL NOTICES.
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GEOGRAPHICAL NOTICES.
411
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412
GEOGRAPHICAL NOTICES.
LONGITUDE OF THE PENDULUM STATION AT DRONTHEIM.
I. By Lunak Transits.
TIMES OF TR.\NSIT BY THE CHRONOMETER 649.
Meao by the
DATE.
STARS.
I8t Wire.
2d Wire.
Meridian Wire
4tb Wire.
5lli Wire.
Chronometer.
REMARKS.
182S.
U. s.
H. 91. S.
M. S.
M. s.
H. H. s.
Oct. 15
2 a Capricomi .
53 58.8
54 25.6
5 54 52
55 18.4
55 45.2
5 54 52
«Cygni
20 40.8
21 17.6
6 21 54
22 30.4
23 07.2
6 21 54
., „
Moon'sWestern Limb
58 49.2
59 16.4
7 59 43.6
00 10.8
00 38
7 59 43.6
„ 16
a Pegasi ....
37 18.8
37 45.6
8 38 12.8
38 39.6
39 06.8
8 38 12.73
}t y>
Moon'sWestern Limb
41 19.6
41 46.4
8 42 13.2
42 40
43 06.8
8 42 13.2
,. 17
2 a Capricomi
46 0T.6
46 34.8
5 47 01.6
47 28.4
47 55.2
5 47 01.53
,, ,.
a Cj-gni ....
12 50
13 26.8
6 14 03.6
14 40
15 16.8
6 14 03.47
„ .,
X Cephei ....
51 00.4
51 55.6
6 52 51.6
53 46.8
54 42.8
6 52 51.47
.. „
a Aquarii
31 18.8
34 45.2
7 35 11.6
35 37.6
36 03.6
7 35 11.4
V ,.
a Pegasi
33 22.4
33 49.6
8 34 16.4
34 43.6
35 10.4 j
8 34 16.47
Moon'sWestein Limb
24 38
25 05.2
9 25 32
25 59.2
26 26
9 25 32.07
,. 19
aPegasi
25 31.6
25 58.8
8 26 25.6
26 52.8
27 19.6
8 26 25.67
., ..
Moon'sWestern Limb
58 01.6
58 29.2
10 58 57.2
59 24.8
59 52.4
10 58 57.07
f Moon less than one
I hour past Ibe full.
)» >f
Moon's Eastern Limb
• • •
11 01 12.8
01 40.4
11 01 12.8
(Observations iodif-
1 ferent from Clouds.
„ 23
Capella
16 15.6
16 52.8
14 17 30.4
18 08
18 45.2
14 17 30.4
,. ..
Rigel
19 02
19 28.4 14 19 54.8
1
20 21.6
20 48
14 19 54.93
,, ..
fiTauri ....
27 58
28 27.6
14 28 57.2
29 26.8
29 56.8
14 28 57.27
>' jj
Moon's Eastern Limb
49 32
50 02
14 50 32
51 01.6
51 31.6 '
14 50 31.87
GEOGRAPHICAL NOTICES.
413
DEVIATION of the TRANSIT INSTRUMENT from the MERIDIAN, at DRONTHEIM,
as shewn by the Interval between the Transits of Stars, differing considerably in Declination,
but having nearly the same right Ascension.
DATE.
STARS.
DIFFERENCES.
Solar Interval
between the
Transits.
Chronometer's
Daily Kate.
True Sirtereal
Interval.
— o
= 2
Devia-
tion.
In R.A.
In Decl.
1823.
M. s.
o /
M. S.
S.
M. s.
S.
Oct. 15
2 !t Capri. & a Cephei.
27 08.85
57 44.5
27 02
G. 1.4
27 06.41
2.44
4.47
.. IT
2 X Capri. & a. Cygni.
27 08.83
57 44.5
27 01 94
Mean Time.
27 06.37
2.46
4.98
" .'.»
2 aCapri.& a Cephei.
1 06 05.72
74 55
1 05 49.94
Mean Time.
1 00 00.75
4.97
5.29
3> M
a Cephei. & a Aquarii.
42 22.43
63 00
42 19.93
Mean Time.
42 26.89
4.46
5.28
„ 23
Capella and Rigel.
2 22. 3S
54 13
2 24 S3
Mean Time.
2 24.93
2.6
4.93
Mean Deviation of the Transit Instrument to the West, when pointed to the Southern Horizon . .
4.99
414
GEOGRAPHICAL NOTICES.
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GEOGRAPHICAL NOTICES. 415
For the purpose of referring the latitude and longitude of the pen-
dulum station at Mr. Wenzel's house to the Cathedral at Drontheim. a
base of 684 feet was measured with a Gunter's chain, in an intermediate
plain on the bank of the river, and a trigonometrical operation accom-
plished with a repeating circle. The bearing of the cathedral from the
observatory was S. 85° 27' E., and the distance 5010 feet, or 0.82 of a
geographical mile ; whence the difference of latitude is deduced 3". 6 S.
and of longitude 1° 50' E., making the Cathedral in N. latitude 63° 25'
50".4, and in E. longitude 10° 24' 50". The geographical position as-
signed in the Connaissance des Terns to Drontheim generally, is
63° 25' 50" N. latitude, and 10° 23' 25" E. longitude ; but as no specifi-
cation is made of the spot, to which the position, thus given to seconds,
refers, no more particular comparison can be made with it.
416 GEOGRAPHICAL NOTICES.
MEMOIR OF A CHART OF THE EAST COAST OF GREENLAND,
BETWEEN THE LATITUDES OF 72° AND 76°.
The longitude of the Lands contained in this chart are referred to, and
rest on the longitude of the observatory on the inner pendulum island,
considered as a first meridian ; the difference of meridians between the
observatory and "Greenwich having been ascertained by the observations
in page 411.
The chart may be divided into three sections, in respect to the mode
in which the survey of each section was accomplished. The first
comprises from the latitude of 76° to that of 74° 30' ; the second, from
74° 30' to 73° 40' ; and the third from 73° 40' to 72°.
The coast of the main land to the north of 74° 30', and of the islands,
with the exception of Shannon Island, has been delineated by astrono-
mical bearings from two hills, one on the outermost, and the other on the
innermost of the Pendulum Islands, aided by the view and bearings from
a hill on Shannon Island.
The geographical distance between the two stations on the Pendulum
Islands, being 9,010 miles, and their position relatively to each other
and to the observatory was determined by a trigonometrical operation,
in which the repeating circle was used in obtaining the value of the
angles, and the extent of the levelled base was 2019.6 feet.
The positions of the Bluff" headland to the north of Roseneath Inlet, and
of the islands named from their appearance, Ailsa, and the Haystack,
have been laid down by the intersection of bearings ; the island placed
in latitude 76° was seen only from the station on the Inner Pendulum
Island, and was decidedly more distant than the other lands.
MttoawMVaHMMiMMiVW
GEOGRAPHICAL NOTICES. 417
The position of the south eastern extremity of Shannon Island was
determined by observations on the spot ; the eastern side of the Island
was coasted by the ship ; the north-western side was viewed from the
hill at the north-east extremity ; and the southern side from the hills on
the Pendulum Islands, and from Cape Philip Broke ; the island itself
consists of low land, with five eminences, which at a short distance
resemble a group of islands ; the whole is so low as not to have been
discovered from the Griper, until she had passed to the northward of Cape
Desbrowe.
The character of the main land, which throughout the chart is com-
posed of rocks of the order usually termed the trap formation, is lofty,
bold, and precipitous, with summits frequently tabled, and rising
abruptly from the sea to 3 and 4000 feet of elevation. The most northern
point to which the land was seen continuous, was by Capt. Clavering
and myself, from the eminence at the northern extremity of Shannon
Island, and in a direction N. 26° W. true ; the coast was also visible
from the same spot, in a direction N. 20° W., being seen indistinctly
through clouds, but still high and bold, and apparently trending a few
degrees to the westward of north ; the Ice Horizon to the eastward of
N. 20° W., was clear and uninterrupted.
Cape Desbrowe, which rises from the sea at a slope scarcely admitting
of ascent, to a tabled summit nearly 3000 feet in height, is the land
earliest seen, and most conspicuous in approaching the coast in the 74°
parallel ; the expectation, that it might prove the north-eastern extremity
of Greenland, was not destroyed, until the Griper had passed to the
northward of its parallel.
The middle section of the chart, from 74° 30' to 73° 40', or more exactly
from Cape Wynn to Cape James, was surveyed by Captain Clavering
with the boats of the Griper, in an expedition undertaken for that pur-
pose, between the 19th an*^ 30th of August, whilst the pendulum ex-
3 H
418 GEOGRAPHICAL NOTICES.
periments were in progress ; the track of the boats is marked by a faint
dotted line on the chart.
The longitudes of this portion of the coast were determined by Capt.
Clavering, with the chronometer No. 649, corrected to the mean time of
the observatory ; it is justly due to the makers of that excellent watch,
as well as proper in regard to the accuracy of the longitudes deduced
by it, to notice, that on the return of the boats after an absence of eleven
days, during which period the chronometer was unavoidably exposed to
very many circumstances and incidents unfavourable to its steady going,
its error on the observatory time, after the allowance of its previous and
ordinary rate, was less than two seconds.
The large bay, or fiord, the recesses of which were explored by Capt.
Clavering, is without doubt the inlet of Gael Hamkes, the situation of
which has been shifted at the caprice of modern chart-makers, be-
tween the latitudes of 73° and 75°, but which appears in its proper
latitude of 74° in the charts of the period when the discovery was
recent. In the oldest of these with which I am acquainted*, entitled
" De Carten van Noorwegen, Finmarken, Laplandt, Spitzbergen, Jan
Meyen, Eylandt, Yslandt, als mede Hitland," engraved at Amsterdam
by Pieter Goos, in 1666, being only twelve years subsequent to the
voyage of Gael Hamkes, the " Landt door Gael Hamkes, opgedaen in't
Jaer 1654," forms an inlet corresponding so well, both in latitude and
general outline, with the one to which the name of the old Dutch navi-
gator has been in consequence preserved, that no doubt of their identity
can be entertained.
The shores of the fiord are in general lofty, and the water deep ;
there is a good and well protected anchorage, on the northern side, above
the spot marked in the chart as the summer residence of Esquimaux.
The fiord was entirely clear of ice ; nor was the progress of the boats
* In the possession of James Smith, Esq., of Jordan Hill, near Glascow.
GEOGRAPHICAL NOTICES. 419
embarrassed by the formation of bay ice, which took place to a very con-
siderable thickness, in more exposed situations and in shallower water,
during the hours in which the sun was low*.
The third section, from Cape James to the southward, was delineated
during the progress of the Griper down the coast, in the track which is
shewn in the chart. The exact position of the Cape Broer Ruys of the
* The following experiments on the amount of the cooling influence of radiation, are illus-
trative of the reason why bay ice did not form in the fiord, whilst in the open sea and in
the roadstead in which the Griper was anchored, the surface of the water was covered for
several hours in each day with a coating sometimes an inch and half thick : —
" August 25th. Prepared a circular piece of black wool 2 inches diameter and flattened,
which weighed, when dry, very exactly 8 grains ; at half past nine P.M., when the sun was
obscured by the hills on the northern side of the island, and the bay ice began to form in the
roadstead, I placed the piece of wool on a grass plat, and a thermometer with its bulb
also covered with black wool, by its side. A similar thermometer freely suspended in the
air, three feet from the ground, and protected from the effects of radiation by a linen cloth
stretched horizontally two feet above it, shewed 30 degrees, and was itself dewed at that
temperature, probably from the air at that height being chilled by its proximity to the sur-
face of the ground, which was cooling so rapidly by radiation ; the wooled thermometer on
the grass fell in a few minutes to 20 degrees ; as did also a black wooled register thermometer
placed in the focus of a polished metallic mirror : after 4^ hours' exposure, the sheltered
thermometer was at 29°- 5 ; the thermometer on the grass 20°, and the register had been at
19° ; the wool had increased in weight 3 grains, and on being carefully dried, recovered
exactly its original weight; being again replaced on the grass plat, it gained rather less than a
grain in the one hours' exposure which preceded the re-appearance of the sun on the eastern
side of the hills.
" August 28th. The experiments of yesterday were repeated, with the difference, tiiat the
wool was allowed to remain on the grass during the whole period of the sun's obscuration,
between 6 and 7 hours, when it was found to have gained 5i grains, weighing at the close 13J
grains. The sheltered thermometer was 29°, the wooled thermometer on the grass 20°, and
the register in the mirror 19°.
"August 29th. Experiments repeated ; the thermometers shewed respectively 30°, 21°,
and 19°. — The weather was always clear and calm."
It appears, therefore, that the surface of the water, in all situations of fair exposure to the
heavens, was subject, when the sun's rays were shaded, to a cooling influence which would
have sunk a thermometer to 20°; but that in the fiord, where the radiation into space was
greatly reduced by reason of the elevated and nearly perpendicular banks, the temperature to
which the surface water was exposed, was probably very little less at any time, than that of
the air with which it was in contact.
3 H 2
420 GEOGRAPHICAL NOTICES.
old charts, was determined by observation on the Cape itself ; that of the
most prominent points, and the general outline of the great bay com-
prised between Capes Broer Ruys and Parry, by astronomical bearings
fi-om the former cape, and from an ascertained station on the ice, in the
neighbourhood of Cape Parry. The Bontekoe Island of the Dutch charts
was recognised by the correct relative position in which it is placed in
them to Cape Broer Ruys, and to the coast generally.
The names inserted in previous charts have been preserved wherever
it was possible to recognise with confidence the spot to which they were
designed to belong ; they are distinguished by a line beneath. The
names not so distinguished, which have been assigned by Capt. Claver-
ing to a few of the most prominent features of the land, will probably
be sufficient for every practical purpose, on a coast so little visited. I
have to acknowledge his kind attention, in having attached my name, in
his manuscript chart, to the remarkable cape on the outer pendulum
island, and in his having subsequently changed it, at my request, to
Cape Desbrowe*.
So far as the experience of a single season may have influence, the
voyage of the Griper does not encourage a hope, that the immediate
neighbourhood of the land, in the latitudes of the chart, may prove a
successful fishing ground ; on one occasion only were whales seen, being
five or six in number, near the northern entrance of Gael Hamkes Bay ;
otherwise, as far as its navigation is concerned, it is a coast remarkably
free from dangers, and in which the nature of the soundings is in-
variably indicated by the character of the land.
It is probable that the east coast of Greenland is rarely, if ever, ac-
cessible directly from the westward, in a higher latitude than that in
* So named after the late Edward Desbrowe, Esq., M.P. for Windsor, and Vice Cham-
berlain to her late Majesty, Queen Charlotte ; to which gentleman I was indebted for my
entrance into the army.
GEOGRAPHICAL NOTICES. 421
which the barrier of ice was crossed by the Griper, namely, a few miles
to the northward of 74 degrees ; it was Captain Clavering's wish to have
crossed it higher if possible, and he accordingly entered the ice in 77° 30'
on the 28th of July, its eastern boundary being found in that parallel, in
2" West longitude ; his western progress was however almost immediately
impeded by an unbroken field, the Eastern and continuous side of which
was coasted for sixty miles, until it conducted again into the open sea,
nearly in the same longitude in which the ice had been first entered,
and a degree further to the southward. In latitude 76° the boundary of
the ice receded considerably to the westward, and on the 2nd of August
Capt. Clavering again entered it in 75° 30', and in 8° West, and proceeded
through sailing ice in a S.W. direction, along the margin of fields in which
no lane was visible, to the latitude of 74" 05' and longitude of 15° West,
where the first practicable breach of continuity presented itself, by
which a passage to the land was ultimately effected. The character of
the field ice was heavier than that which occupies the middle of Davis's
Strait, and Baffin's Sea in the early part of the season of navigation ; but
was not so heavy as the field ice in the Polar sea, in the neighbourhood
of the North Georgian Islands. The barrier of fields, which in 77
degrees must have been about 200 miles across, was reduced to 60 miles
in the latitude of 74°, and required five days of much exertion to cross ;
an attempt which would have been scarcely prudent in a ship less ad-
mirably strengthened and equipped than the Griper.
The circumstance of principal geographical interest, the knowledge
of which was obtained by the Griper's visit to East Greenland, was, the
non-existence of the current which has been stated to prevail, if not
throughout the year, at least constantly in the summer season, and to
carry the overflowing waters and the ice of the Polar Sea, with great
velocity, down the coast of Greenland to the southward ; on this
current much stress has been laid in the recent discussions on the pro-
422 GEOGBAPHICAL NOTICES.
bability of a north-west passage. The desire which was felt to ascer-
tain the velocity, extent, and depth of the supposed current, as well as
the fear of being carried by it much to the southward of the latitude in
which we were desirous of making the land, induced the comparison of
observations with the reckoning, which in the Griper was kept with the
utmost care, on every possible occasion, and could not have failed to have
discovered a current of the tenth part of the velocity attributed to the one
in question, even if an additional means of comparing the ship's daily
position had not been furnished by the land, which was in sight from
the first day on which she entered amongst the fields of ice. But neither
in crossing the barrier, nor on any subsequent occasion in the seven
weeks during which she remained on the coast, could the slightest in-
dication of a southerly current be perceived, either by her own experi-
ence, or by the ice viewed from day to day from the summits of hills of
2 and 3000 feet of elevation. The only observable motion of the great
body of the ice was to press occasionally upon the land, an effect which
was probably caused by the influence of the wind or sea on its eastern
or outward side ; at other times, and especially when an ofi-shore wind
prevailed, the ice retired, so as to leave a channel between the land and
ice of one or two leagues in breadth ; but there was no general set what-
soever to the southward ; and it was quite remarkable to observe, at the
close of the season, how much less disintegration the fields had undergone,
than ice which has been itself in motion, or which has been subject, as
in Davis's Strait, to the destructive agency of icebergs.
,The fact, however, of the absence of current at, and within, the barrier,
and the stationary condition of the fields which formed it during the
season of 1823, is not irreconcilable with the occasional existence of a
southerly current amongst the broken fields and packed ice on the east-
em boundary, and in the vicinity of the open sea. Geographical inves-
tigation has traced the cause of currents generally, to the drift of the
GEOGRAPHICAL NOTICES. 423
superficial waters of the ocean from the impulse of the wind ; the agency
of this cause is peculiarly operative and conspicuous within the Arctic
Circle, where not only the surface of the sea is exposed to the action of
the wind, but also a seventh portion of each of the masses of ice which
float upon its surface. The drift of the loose ice in the direction of the
wind commences immediately a breeze springs up, and if followed by
a calm, continues for some time after the exciting cause has subsided ;
the motion of the six-sevenths of the ice which are below the surface
must communicate an impulse, greater both in velocity and in depth,
than the action of the wind upon the surface of the water alone would
produce ; it is not surprising, therefore, that currents in the direc-
tion, and in accompaniment with wind, should be more particularly ex-
perienced in seas encumbered with ice, than in the open ocean ; and as
easterly and north-easterly winds are prevalent in the summer months,
in what may be called the Greenland and Spitzbergen sea, it cannot be
doubted that a current in a southwest direction along the margin of the
main body of the ice must frequently prevail. It is not impossible also
that the main body of the ice itself in the parallels of 74°, 75°, and 76°,
being certainly not fixed, may not be so stationary in all seasons as it
was in 1823, which must certainly be regarded as a remarkable season
in respect to the weather, the serenity of which was scarcely interrupted
by more than a gentle breeze, from the beginning of August to the
middle of September. The wind, however, rarely blows with strength
over an extent of Ice, and it must be a north wind of both strength and
continuance, to set in motion such extensive masses, the surfaces of which
present to its action little more than an unbroken plain. The causes
which have been thus noticed are, however, very distinct from that to
which the existence of a constant current down the coast of Greenland
has been attributed, and which would move the largest floating masses
424 GEOGRAPHICAL NOTICES.
equally with the smallest ; namely, the overflowing of the Polar Ocean ;
of such a current no trace was discernible.
The extraordinary distances at which land has been stated to have
been seen in the Arctic Circle, rendered it an object of some curiosity, to
ascertain correctly the distance at which the coast of Greenland should
become first visible, for which observation the circumstances proved par-
ticularly favourable : the weather was remarkably clear when the Griper
entered the ice on the 2nd of August, and continued uninterruptedly so,
until long after the coast was seen ; it was certainly at no time visible
on the 2nd or 3rd of August, during which days the Griper neared the
land from 180 miles to 60, by navigating amongst the sailing ice ; and it
was not until the forenoon of the 4th, that even the appearance of land
was recognised ; when distinctly made out. Cape Desbrowe was, both
by observation of the ship's place, and by the angle subtended by
stations subsequently ascertained, about 55 miles distant, which, for
land of nearly 3000 feet of elevation, was by no means an extraordinary
occurrence ; nor was the mode of its appearance in any respect unusual,
being first recognised, but not without doubt, by the most experienced
eyes, and the outline becoming gradually more and more distinct as the
ship made progress, until all on board admitted its reality. A still
more favourable opportunity of investigating the visibility of distant land
from the level of the ocean, presented itself during the progress of the
experiments on the Pendulum Islands ; on ascending the hills which rose
to the northward of the observatory, the nearly insulated hill which forms
Cape Broer Ruys, was seen in the horizon clear of the general Hne of
the coast, and was then supposed to be an island ; its bearing from the
observatory being ascertained, a telescope was stationed accordingly,
and the appearance of the supposed island was looked for both by the
GEOGRAPHICAL NOTICES. 425
naked eye and with the telescope, at almost all hours of the twenty-
four, in the foUowing twelve days ; twice during that period, it was de-
cidedly seen, but much distorted by refraction, and was once besides
doubtfully visible ; the weather during the whole time was perfectly clear,
and the sky ahnost without a cloud. The distance in a direct line was
about 73 miles. The particulars of a Barometrical measurement of the
height of Cape Broer Ruys, which was ascended by Captain Clavering
and myself for the purpose, have been unfortunately mislaid, but accord-
ing to a rough calculation from the particulars made on the spot, it was
between 2700 and 3000 feet; the observatory was 30 feet above the
sea.
It is by no means designed in this statement to imply a doubt of the
extraordinary facts that have been alluded to, but merely to show that
it was not from inattention that we are not able to corroborate them by
a similar experience.
3 I
426
HYDROGRAPHICAL NOTICES.
Previously to my leaving England in 1821, I had had the great ad-
vantage of much conversation with Major Rennell, on the subject of
the currents in the Northern and Southern Atlantic Oceans, and of hav-
ing my attention directed by him to those points in particular, concerning
their velocity, limits, and temperature, on which further inquiries might
conduce to the advancement of hydrographical knowledge.
The method of ascertaining the existence, direction, and velocity of a
current, where land is not in sight, and a ship cannot be rendered sta-
tionary by anchorage, is to compare her position at intervals of sufficient
length, (generally of 24 hours,) by observation and by reckoning. By
the former is learnt her real change of geographical position in the inter-
val ; by the latter, the course and distance that she has gone through the
water ; should the position by the reckoning not agree with the position
by the observation, the diflference (presuming both to be correct) is the
indication and measure of current.
To determine a ship's position from day to day by observation, or
rather her relative position on one day to the preceding, has become,
since the introduction of chronometers, a matter of very simple accom-
plishment, and capable of much precision. It is far otherwise with the
reckoning, however, when more is sought by it than such a rough ap-
proximation as may serve the ordinary purposes of navigation ; it must
in fact, require the most assiduous and unremitting attention, as well as
considerable nautical experience and judgment, to estimate correctly the
continually varying effects of the winds and sea, on a body that is also
HVDROGRAPHICAL NOTICES. 427
continually varying the measure of her exposure to their influence. It may
be in the power of an individual in a vessel, to obtain, by his own exertions
alone, that portion of the materials towards the evidence of currents,
which depends on her real change of position ; but the completion of the
evidence by a sufficiently correct reckoning must be the result of an
interest participated in by all the executive officers of a ship ; or by the
establishment of such habits of accuracy, under the authority of her com-
mander, as are not of usual practise, because they are not necessary for
the general purposes of navigation ; the employment of chronometers, by
which the position of a ship is ascertained and a fresh departure taken
on every day that the sun shines, has superseded the necessity of that
vigilant and scrupulous regard, which the older navigators paid to all
the details of the reckoning, on which alone they had to depend ; and has
tended to substitute general habits of loose and vague estimation, for the
considerate and well-practised judgment with which allowances were for-
merly made for the incidental circumstances of steerage, leeway, making
and shortening sail, &c., &c., on a due attention to which the accuracy
of a reckoning so materially depends.
In ships of war especially, the reckoning is further embarrassed by a
difficulty, less obvious but not less generally operative, by which, if not
properly provided against, the knowledge of the true course which the
ship has made is necessarily rendered very uncertain ; it arises from the
usual practice of directing the course by the binnacle compasses, which
are two in number for the convenience of the hehnsmen, and being placed
one on the larboard and the other on the starboard side of the midship,
with a space between them of greater or less extent according to the size
of the vessel, can scarcely fail, and are in fact generally influenced dif-
ferently by the ship's iron ; and being subject to different st/sie7ns of at-
traction, the compasses not only disagree, but their disagreement varies
according to the direction of the ship's head, the amount of the dip of the
3 12
428 HYDROGRAPHICAL NOTICES.
needle, and the force of terrestrial magnetism. It is customary always to
steer by the weather compass, and thus each is liable to become in its
turn the directing compass for periods of more or less duration, and the
corrections of the courses for the disturbing influence of the ship's iron
become so various and complicated, as to render the deduction of a cor-
rect reckoning practically unattainable. For example, the binnacle com-
passes of the Iphigenia, on her passage from England to Madeira, were
observed to differ from each other half a point in one direction when on
south-westerly courses, and less than half a point in the opposite direc-
tion when on easterly courses, the indications of the compasses having
crossed each other, and agreed at some intermediate point : it was re-
quisite, therefore, that the correction to be allowed on every course by
each of the two compasses should be ascertained, and that the compass
by which each course was directed should be specially recorded, in order
that the true course should be known.
The most obvious mode of preventing so much inconvenience and
trouble, as well as the more correct practice, is to direct and note the ship's
course by one compass only, stationed permanently in some convenient
situation without reference to the helmsmen, and to use the binnacle
compasses solely to steer by, on the point which may be noticed at the
time to agree with the magnetic course of the standard compass ; and by
employing an azimuth compass for the latter purpose, the advantage is
gained of enabling the variation to be observed directly with the compass
by which the course is governed, and thus of avoiding intermediate com-
parisons, in which time is occupied, and errors frequently introduced.
This arrangement of a standard compass was adopted by Captain
Clavering in the Pheasant, and subsequently in the Griper, and was
found to answer its purpose perfectly, and to be attended with no prac-
tical inconvenience whatsoever.
Although from the causes above noticed no satisfactory investigation
HYDROGRAPHICAL NOTICES.
429
of the direction or velocity of currents could be made in the Iphigenia,
in her passage from England to the coast of Africa, a remarkable and
very interesting evidence was obtained, by observations on the tempera-
ture of the sea, of the accidental presence in that year of the water of the
gulf stream, in longitudes much to the eastward of its ordinary extension.
The Iphigenia sailed from Plymouth on the 4th of January, after an
ahnost continuous succession of very heavy westerly and south-westerly
o-ales, by which she had been repeatedly driven back and detained in the
ports of the channel ; the following memorandum exhibits her position at
noon on each day of her subsequent voyage from Plymouth to Madeira,
and from thence to the Cape Verd Islands, the temperature of the air in
the shade and to windward, and that of the surface of the sea ; it also
exhibits in comparison, the ordinary temperature of the ocean at that
season, in the respective parallels, which Major Rennell has been so kind
as to permit me. in insert on his authority, as an approximation founded on
his extensive inquiries ; the last column shews the excess or defect in the
temperature observed in the Iphigenia's passage.
Longitude W.
Air.
Surface
Water.
Excess or
DATE
Latitude N.
Defect.
Observed.
Usual.
1»22.
0
o
o
Jan. 5
47 30
7 30
47
49
50
- 1
,. 6
44 20
9 30
52.5
55.7
52.5
+ 3.2
Plymouth
,, ■?
41 22
n 37
54
58.2
54
+ 4.2
to
Madeira.
,. 8
38 54
13 20
54.2
61.7
55.7
-1- 6
,, 9
No Ob
servation.
56
63
58
+ 5
„ 10
33 40
15 30
60.7
64
60
+ 4
„ 19
26 GO
17 50
66
65.5
67
- 1.5
Madeira
„ 20
24 30
18 50
68
67
68.4
- 1.4
to the
,, 21
23 06
20 00
69
69
69 5
- 0.5
Cape Verds.
„22
21 02
21 27
69.5
69.5
71.2
- 1.7
„ 23
19 20
23 00
70.6
70.2
71.6
- 1.4
430 HYDROGRAPHICAL NOTICES.
It is seen by the preceding memorandum, that in the passage from
Plymouth to Madeira, the Iphigenia found the temperature of the sea,
between the parallels of 441° and 33f° several degrees warmer than its
usual temperature in the same season ; namely, 3°.2 in 44^°, increas-
ing to 6° in 39°, and again diminishing to 4° in 33f°; whilst at the
same period, the general temperature of the ocean in the adjoining
parallels, both to the northward, and to the southward, even as far as the
Cape Verd Islands in 19f°, was colder by a degree and upwards than
the usual average. The evidence of many careful observers at different
seasons and in different years, whose observations have been collected
and compared by Major Rennell, has satisfactorily shewn, that the water
of the Gulf stream, distinguished by the high temperature which it brings
from its origin in the Gulf of Mexico, is not usually found to extend to
the eastward of the Azores. Vessels navigating the ocean between the
Azores and the continent of Europe, find at all seasons a temperature
progressively increasing as they approach the sun ; the absolute amount
varies according to the season, the maximum in summer being about
14 degrees warmer than the maximum in winter ; but the progression in
respect to latitude is regular, and is nearly the same in winter as in
summer, being an increase of 3° of Fahrenheit for every 5° of Latitude.
It is further observed, that the ordinary condition of the temperature, in
the part of tlie ocean under notice, is little subject to disturbance, and
that in any particular parallel and season, the limits of variation in dif-
ferent years are usually very small ; after westerly winds of much
strength or continuance, the sea in all the parallels is rather colder than
the average temperature, on account of the increased velocity communi-
cated to the general set of the waters of the North-eastern Atlantic
towards the southward. To the heavy westerly gales which had prevailed
almost without intermission in the last fortnight in November, and during
the whole of December, may therefore be attributed the colder tern-
HYDROGRAPHICAL NOTICES. 431
peratures observed in the latitude of 47|°, and in those between 26°
and 19i°.
If doubt could exist in regard to the higher temperatures between
44i° and 33|-°, being a consequence of the extension in that year of
the Gulf stream in the direction of its general course, it might
be removed by a circumstance well deserving of notice, namely, that
the greatest excess above the natural temperature of the ocean was
found in or about the latitude of 39°, being the parallel where the middle
of the stream, indicated by the warmest water, would arrive, by continu-
ing to flow to the eastward of the Azores, in the prolongation of the great
circle in which it is known to reach the mid Atlantic.
One previous and similar instance is on record, in which the water of
the Gulf stream was traced by its temperature quite across the Atlantic
to the coasts of Europe ; this was by Dr. FrankUn, in a passage from the
United States to France, in November, 1776*. The latter part of his
voyage, i.e., from the meridian of 35° to the Bay of Biscay, was performed
with little deviation in the latitude of 45° ; in this run, exceeding 1200
miles, in a parallel of which the usual temperature, towards the close of
November, is about 551°, he found 63° in the longitude of 35° W., dimi-
nishing to 60° in the Bay of Biscay ; and 61° in 10° West longitude, near
the same spot where the Iphigenia found 55°. 7 on the 6th of January,
being about five weeks later in the season. At this spot then, where
the Iphigenia crossed Dr. Franklin's track, the temperature in Novem-
ber, 1776, was 51°, and in January, 1822, 3°.2 above the ordinary
temperature of the season.
There can be little hesitation in attributing the unusual extension of
the stream in particular years to its greater initial velocity, occasioned
by a more than ordinary difference in the levels of the Gulf of Mexico
and of the Atlantic ; it has been computed by Major Rennell, from the
* Franklin's works, 8vo., London, 1S06, Vol. II., pages 200, 201.
432 HYDROGRAPHICAL NOTICES.
known velocity of the stream at various points of its course, that in the
summer months, when its rapidity is greatest, the water requires about
eleven weeks to run from the outlet of the Gulf of Mexico to the Azores,
being about 3000 geographical miles ; and he has further supposed, in
the case of the water of which the temperature was examined by
Dr. Franklin, that perhaps not less than three months were occupied
in addition by its passage to the coasts of Europe, being altogether a
course exceeding 4000 geographical miles. On this supposition, the
water of the latter end of November, 1776, may have quitted the Gulf of
Mexico, with a temperature of 83°, in June ; and that of January, 1822,
towards the end of July, with nearly the same temperature. The summer
months, particularly July and August, are those of the greatest initial
velocity of the stream, because it is the period when the level of the
Caribbean sea and Gulf of Mexico is most deranged.
It is not difficult to imagine that the space between the Azores and the
coasts of the old continent, being traversed by the stream, slowly as it
must be, at a much colder season in the instance observed by the Iphigenia
than in that by Dr. Franklin, its temperature may have been cooled
thereby to a nearer approximation to the natural temperature of the
ocean in the former than in the latter case ; and that the difference be-
tween the excess of 5°.5 in November, and of 3°.2 in January, may be
thus accounted for.
If the explanation of the apparently very unusual facts observed by
Dr. Franklin in 1776, and by the Iphigenia in 1822, be correct, how
highly curious is the connexion thus traced between a more than ordinary
strength of the winds within the tropics in the summer, occasioning
the derangement of the level of the Mexican and Caribbean seas, and
the high temperature of the sea between the British channel and Madeira,
in the following winter.
Nor is the probable meteorological influence undeserving of attention.
HYDROGRAPHICAL NOTICES. 433
of SO considerable an increase in the temperature of the surface water
over an extent of ocean exceeding 600 miles in latitude and 1000 in
longitude, situated so importantly in relation to the western parts of
Europe. It is at least a remarkable coincidence, that in November
and December, 1821, and in January, 1822, the state of the weather
was so unusual in the southern parts of Great Britain and in France,
as to have excited general observation ; in the meteorological journals
of the period it is characterized as " most extraordinarily hot, damp,
stormy, and oppressive;" it is stated "that an unusual quantity of rain
fell both in November and December, but particularly in the latter ;"
that, " the gales from the W. and S.W. were almost without intermis-
sion," and that in December, the mercury in the barometer was lower
than it had been known for 35 years before*.
• The following description of this very remarkable winter is extracted from Mr. Daniell's
Essay on the climate of London, {Meteorological Essays, London, 1823,-pages 297 and 298)
and becomes highly curious when viewed in connexion with the unusual temperature of the
ocean in the direction from which the principal winds proceeded.
" November 1821 differed from the mean, and from both the preceding years, in a very
extraordinary way. The average temperature was 3° above the usual amount; and althou-h
lU dryness was in excess," [the relative dryness, in consequence of the increased temperatur"]
" the quantity of rain exceeded the mean quantity by one half. The barometer on the whole
was not below the mean. All the low lands were flooded, and the sowing of wheat very
much interrupted by the wet.
" In December the quantity of rain was very nearly double its usual amount. The ba-
rometer averaged considerably below the mean, and descended lower than had been known
for thirty-five years. Its range was from 30.27 inches to 28.12 inches. The temperature
was still high for the .season, and the weather continued, as in the last month, in an uninter-
rupted course of wind and rain ; the former often approaching to an hurricane, and the latter
inundating all the low grounds. The water-sodden state of the soil, in many parts, prevented
wheat sowing, or fallowing the land at the regular season. The mild temperature pushed
forward all the early sown wheats to an height and luxuriance scarcely ever before witnessed.
The grass, and every green production increased in an equal proportion.
"January, 1822. This most extraordinary season still continued above the mean tem-
perature, but the rain, as if exhausted in the preceding month, fell much below the usual
quantity in this. There was not one day on which the frost lasted during the twenty-four hours.
" Serious apprehensions were entertained lest the wheats, drawn up as they had been by
3 K
4§4 HYDROGRAPHICAL NOTICES,
On leaving the Cape Verd Islands, the Iphigenia proceeded to make
the continent of Africa at Cape Verd. The distance between the Cape
and the Islands is about 400 miles, both being in the same parallel of
latitude. This passage afforded an interesting opportunity of observing,
on the approach to land, the influence of its vicinity on the temperature
of the sea. The general temperature of the surface in that parallel and
at that season may be considered 71°.?, the observations made at sunrise,
noon, and sunset, in the first 350 miles of the passage, varying from 71° to
72° A : but at sunrise on the 31st of January, being then at the distance of
26 miles vpest of Cape Verd, with no land as yet in sight, the surface water
had lowered to 69°.6. On approaching nearer it progressively diminished,
until at one mile from the shore, it had fallen as low as 64 degrees, and
continued from 64 to 65 degrees, between Cape Manoel and Goree.
Cape Verd is situated nearly at equal distances, exceeding 70 miles,
from the mouths of the Senegal and Gambia, the one being to the north
and the other to the south. It is probable that the water of both these
rivers is always colder at their entrance into the sea, than the ocean
temperature of the parallel ; that of the Gambia certainly was so at that
season, but it was not so cold as the sea in the vicinity of Cape Verd, as
on approaching the entrance of the Gambia, the temperature of the surface
rose to 67°. 5, and varied in the river itself at different hours from 66° to
67°.5 ; and at the depth of 36 feet, being within six feet of the bottom, a
self registering thermometer indicated at high water less than a degree
colder than the surface. The coast in the neighbourhood of Cape Verd
is every where low and sandy, and is covered with trees to the water's
warm and moist weather, without the slightest checii from frost, should be exhausted by
excessive vegetation, and ultimately be more productive in straw than corn.
"The month of February, still five degrees above the mean temperature, ended a winter
which has never been paralleled."
It would not be difficult to trace in detail, each of the efi'ecis described in the preceding
extract, to the cause which has been thus placed in connexion with them.
HVDBOGRAPHICAL NOTICES. 435
edge. Such indeed is the general character of the shores of western
Africa, with the exception of Cape Sierra Leone ; but at no other part
of the coast was the diminution of the temperature of the water, on ap-
proaching the land, so great, as in the instance which has been men-
tioned. Between the Gambia and Sierra Leone are a succession of
rivers, originating in land of less elevation than the Senegal and Gam-
bia, and much exceeding them in the temperature of the waters which
they convey into the ocean ; in the mid-channel of the Rio Grande, at a
few miles from its mouth, the surface was never less than 74°, and oc-
casionally as high as 77.°5, and at the depth of thirty or forty feet was
less than a degree colder than the surface. At the entrance of the
River Noonez the surface water was 77°.5, and at that of the Rokelle 80°.
To the south of the Rokelle, and from thence to the extremity of the
Gulf of Guinea, the coast is swept by a current of considerable rapidity,
which renders the cooling effect of the land less apparent; but in
the bays of the coast, where the current sweeps from point to point,
and leaves still water in the inside, a difference is commonly found
amounting to three and four degrees *.
* The passage from the Cape Verd Islands to Cape Verd and the Gambia afforded a not
less interesting opportunity of observing the difference in the hygrometrical state of the
atmosphere at sea and in the vicinity of the continent, in the region of the trade winds. We
had entered the N. E. Trade in the latitude of 24° N., nine degrees to the Northward of the
Cape Verd Islands, and did not lose it until the afternoon of the day on which we quitted the
Gambia, the strength declining on the approach to the continent, but the direction continuing
unchanged. On the 28th, 29th, and 30th of January, in navigating the first 350 miles of the
passage from the Islands to the continent, the air in the shade and to windward varied at dif-
ferent hours of the day from 70.2 to 71'2, and the dew point from 63 to 64.5. At sunrise on
the 31st when at twenty-six miles West of Cape Verd, the Dew Point was 6l.5, and lowered to
57.5 on nearing the land, the temperature of the air not being sensibly affected. Off the en-
trance of the Gambia on the 1st of February, and in the river on the 2nd, 3rd, and 4th, the
Dew Point was never higher than 51°, and occasionally as low as 48.5, the air over the water
and in the shade being generally during the day from 69° to 70°- When about to quit the
Gambia on the morning of the 5th of February, we experienced, although in a very slight de-
3 K 2
436 HYDROGRAPHICAL NOTICES.
The following summary account of the direction and force of the currents
experienced in each day's navigation, commences with the appointment
of the Pheasant to convey the clocks and pendulums from Sierra Leone
to the subsequent stations. Captain Clavering entered with much in-
terest into the inquiry, and by his judicious arrangements, and personal
superintendence, until habits were established, the reckoning of his ship
was rendered little inferior, as an element in the deduction of currents,
to the observed difference of latitude and the chronometrical difference
of longitude. On leaving England, I had obtained from the Admiralty a
supply of the logs invented by Mr. Massey, which being towed at a
sufficient distance astern to be clear of the back-water occasioned by a
ship's progress, register her way by the revolutions of a spiral acted upon
by the water through which it is drawn. The self- registering log was
used as a check upon the estimated reckoning, and proved the value and
efficacy of the attention paid to the latter, by its being a very rare cir-
cumstance to find a difference between them, amounting to a mile, in
twenty-four hours. The comparison between the ship's run by observa-
tion and by reckoning was usually made by Capt. Clavering from fore-
noon to forenoon, and. by myself from afternoon to afternoon ; and the
results being each reduced to noon and compared, served for the detec-
grce, the peculiar wind called the Harmattan, of which the season was nearly over ; its direction
■was one or two points to the North of the trade wind, or about N.N.E. ; the air during its
influence fell to 66.5, and the Dew Point to 37-5 ; affording a reasonable inference, that in a
genuine Harmattan, and before it reaches the sea, the constituent temperature of the vapour
may be at least as low as 32°. lu the progress to Cape Ro.xo, on the afternoon of the same day,
we lost the Harmattan, and with it the continuance of the trade wind. The sea breeze which
followed, raised the temperature of the air to 70°,and of the Dew Point to 6\.5.
It appears, therefore, that when the North East wind first cumes off the continent of Africa,
it contains only 53 parts in 100 of the moisture which would be required for repletion at the
existing temperature; that in blowing over the sea its proportion of moisture rapidly augments,
until at fifty miles from the land, it has acquired 80 parts in 100; which proportion is not
subsequently increased by its passage over 350 additional miles of ocean. In the Harmattan
the air contained only 38 parts in 100 of the proportion of moisture required for its repletion.
1
r 1 I I
HYDROGRAPHICAL NOTICES.
437
tion and correction of errors, on either side. The table exhibits the
ship's true position at noon on each day ; the temperature of the surface
water ; and the direction and amount of the difference of her position, by
observation and by reckoning, from noon to noon. On days when the sun
was obscured, the direction of the apparent set is deduced from intervals
of 48 hours instead of 24, but the rate is that due to each interval of
24 hours.
Tempera-
Tempera-
DATE.
Latitnde.
LoDgilDde.
ture of the
Surface
Appareot Set in each
24 boars.
DATE.
Latilade.
^-S"-"- 'sT.r"face^
Apparent Set in each
24 hours.
Water.
Water.
From the River Gaboon to Ascension. 1
From C
APE M0C>
T to Cap
E Three Points.
1822.
1
O /
o f
1822.
0 .
o /
o
June 15
0 03 N.
7 45 E.
o
|s. SOW. 29 miles.
>West 48.5 „
Apr. 15
6 40 N.
11 48 W.
84
0
„ 16
0 44 S.
5 50
• •
„ 16
Sun ob
scured.
83
S-S.53E. 32miles.
„ 17
Sun ob
scured.
73
„ IT
4 53
9 04
83
>S.84E.24 „
1
„ 18
„ 19
1 00
1 45
2 07
0 19
74
72.5
}s. 86W.29 „
}n. 88W.37 ,,
|s. 81W.47 „
„ 18
4 S8
8 18
■>N.79E.40 „
,, 20
2 34
1 55W.
72.8
., 19
4 18
6 36
84.8
J
1
„ 21
3 48
4 54
74.5
Is. 81 W. 32.5 .,
>N.76E. 51 „
„ 20
4 37
S 48
84.5
J
„ 22
5 10
7 50
77.5
J
|n. 6SW. 16 .,
JN. 57W.18.25,,
„ 23
6 21
10 43
77.5
.) 24
7 27
13 22
78
From Lag
OS to St.
Thomas.
From Ascension to Bahia. |
May 8
5 22 N.
2 51 E.
83.5
1
1 °
>S.45E. Smiles.
July 10
7 57 S.
14 24W.
|n. 74 W. 11 miles.
|North 2 „
., 9
5 00
2 32
84.5
J
1
VS.84E. 17 „
,. 11
9 16
17 00
., 10
4 46
2 49
84
J
1
» 12
10 10
19 45
>S.24E. 16 „
|n. 35W. 6 „
., "
3 46
2 5T
83.2
1
• S. 89 E. 22 „
]
„ 13
10 35.5
22 25
IWest 16 „
Is. 82W. 14 „
.. 12
Sun ob
scured.
83
,. 14
11 05
25 53
» 15
11 42
29 08
„ 13
0 36
5 22
82.8
].S. 71W. 14 „
>S.81E. 13 „
„ 16
12 27
32 51
J
In. 79 w. 1 1 „
„ 14
0 16
6 24
82.8
j
„ n
13 05
36 31
438
HYDROGRAPHICAL NOTICES.
DATE.
Latitude.
Lon^tude.
Tempera-
ttiieof the
^Surface
Water.
Apparent Set in each
24 boure.
DATE.
Longitude
Temperature
of the
Surface Water.
Apparent .Set in cacb
24 hours.
1822.
Aug-. 8
. 9
. 10
, 11
, !2
, 13
, 14
Axig. 15
> 16
. 17
, 18
. 19
Sept. 8
, 9
, 10
, 11
, 12
. \^
, H
, 15
, 16
, IT
From Bahia to Pernambuco.
13 SOS,
Sun ob
13 48
12 36.5
11 03.5
10 15
9 33
o »
o
38 22 W.
• •
scured.
77.2
37 59
77.1
3T oz
7T.2
36 20
78
35 53.5
78
35 13
78
>N. 69 W. 13 miles.
J
>N. 12\V. 2.5
JN.SIW. 14
N.33E. 13
N.27\V. 15
Fjom Pernambuco to Maramiam.
5 04 S.
6 15
3 22
2 17.5
1 55
34 54 W.
78
34 36
78.4
36 45
78. S
40 17
77.8
43 06
77.8
North 22 miles
|n.44W.62 „
N.70W.41
N.66W.13
From Maranham to Trinidad.
0 21 N.
2 59
5 18
7 01
7 05
7 24
7 43
8 12.5
9 29
8 00
45 58W.
79.8
48 07
80.8
50 .39
81.8
52 38
81.5
53 32
83
54 19
83.3
55 55
81
57 22
84
59 30
84
61 00
81
N.49W. 48 miles,
N.54W.99 „
|N. 38W.68 „
}n. 41E. 5 „
}s. 47W. 18 „
|s. 87W. 17 ,,
|n. 72W.28 „
In. 33 W. 48 ,,
J
In. 52 W. 57 ,,
Flora Trinidad to Jamaica.
18S2.
Oct. 10
„ 11
„ 12
,. 13
„ 14
„ 15
,, 16
10 55
12 24
13 18
"3 53
IS 02
Sun obs
17 50
O f
0
61 56
63 43
. . S3
65 56
. . 83
67 59
. . 82.8
70 45
. . 82.9
cured.
. . 83
76 08
. . 83
|n. 52 W. 49 miles
].N. 53W.12 „
N. 79W.16 „
S. 83W.16 „
■>N. 41 W.19
From Havannah to New York.
Nov
.27
23 09
5'
28
23 52
ft
29
25 20
»
30
28 38
Dec
1
32 02
?»
2
Sun obs
•••
3
35 04
if
4
Sun obs
)•
5
36 38
fi
6
37 00
-')
7
37 35
•»
8
38 44
-"
9
40 08
82 23
81 42
79 47
!
79 32
78 33
cured. •
74 54
f
:ured. ■!
{
72 29
73 46
74 33
74 26
74 07
8A.M.
Noon.
9 P.M.
8 A.M.
3 P.M.
8 P.M.
8 A.M.
Noon.
3 P.M.
8 A.M.
Noon.
6 P.M.
8 A.M.
Noon.
80.5
80.7
,80.8
80.5
80.1
79.2
80.1
79.5
78.2
78.7
78
77.5
77.6
77.3
77.5
77.5
62.4-
60.6
59.5
I S. 85 E. 14 miles.
N. 31 E. 22.5 „
4W.70 „
U.
N. 17E.38
^N. 47 E. 44.5
I.N.55E. 77
West
16
1
1
Is. 55 W. 10
Is. 5 W. 15
Is. 45W. 6
HYDROGRAPHICAL NOTICES. 439
REMARKS ON THE PRECEDING SUMMARY.
In the voyage between Capft Mount and Cape Three Points, the
Pheasant's progress appears to have been accelerated about 180 miles,
by the current, which, during the season when the S. W. winds prevail
on that part of the coast of Western Africa, runs with considerable rapidity
in the direction of the land, round Cape Palmas to the eastern parts of the
Gulf of Guinea. The breadth of this current abreast of Cape Palmas varies
with the season, and has been found as much as 180 miles ; but, in its
subsequent course to the eastward, it enlarges to nearly 300, and occupies
the whole space between the land on one side, and the equatorial current
running in an opposite direction on the other ; the velocity abreast of
Cape Palmas and Cape Three Points, and in the vicinity of the land, was
in May, about two knots an hour ; and further to the eastward, where the
Pheasant crossed its breadth from Cape Formosa to St. Thomas, and
where its velocity had been much diminished by the dissipation of its
waters, it was found still to preserve a general rate of rather less than
a mile an hour ; and a direction, a few degrees to the southward of east.
Between Cape Three Points and Lagos, the observations were sus-
pended in consequence of the greater part of the officers and men being
absent in the boats, examining merchant vessels anchored on the coast,
and suspected of being engaged in the trade in slaves. The little effect
of the current experienced between the 8th and 9th of May, was occa-
sioned by the slack water in the Lagos bight, from which the Pheasant
did not re-enter the fair stream until the morning of the 9th. There
appears to have been a southerly deflection between the 10th and 11th.
for which no very obvious reason presents itself The general tem-
perature of the stream in the mid-channel in the Gulf of Guinea, in April
and May, exceeds 84 degrees, diminishing to 82 and 83, on its south-
ern border, where it is in contact with the colder water of the equa-
440 HYDROGRAPHICAL NOTICES.
torial current ; and occasionally to, 79°, and frequently to between 79°
and 8r.5, on its northern side, in the proximity of land.
In the passage from the coast of Africa to the Island of Ascension, the
Pheasant appears to have entered the equatorial current, almost imme-
diately after her departure from the entrance of the River Gaboon ; as
she was decidedly under its influence when passing the southern extre-
mity of the Island of St. Thomas. This current is formed by the drift
water impelled by the trade winds in the southern Atlantic, (which in
the neighbourhood of the continent of Africa are very much southwardly,)
towards the eastern part or head of the Gulf of Guinea ; where, being
opposed by the waters brought to the same spot by the Guinea current,
the drift water streams off in the direction of the equator and principally
on its southern side ; and being continually fed in its western progress
by the drift from the S.E., (becoming more and more inclined to the me-
ridian, as the influence of the continent on the regular direction of the
trade wind lessens from distance,) the stream pursues its course quite
across the Atlantic to the continent of South America, where one portion
of it proceeds along the northern coast, (if Brazil to the Caribbean Sea
and Gulf of Mexico, and contributes in part to raise the level of those
seas, and thus to lay the foundation of the Gulf Stream.
The Pheasant's voyages from the coast of Africa, successively to Ascen-
sion, Bahia, Pernambuco, Maranham, Trinidad, and Jamaica, were per-
formed principally in the current, the origin and progress of which have
been thus stated.
The equatorial current is not usually met with so far to the northward,
at its commencement on the coast of Africa, as it was found by the
Pheasant in the month of June : but it is probable that at the season
when the trade winds are strongest, and approach nearest the equator, the
drift water may be impelled into a more northern parallel than at other
seasons, before the opposition to its direct course becomes so strong, as to
HYDROGRAPHICAL NOTICES. 441
occasion it to stream oif to the westward. Its more usual northern limit,
in the meridian of the Island of St. Thomas, is considered by Major Ren-
nell to be in the second or third degree of south latitude. The direction
of the stream was as nearly west as could be inferred from the observa-
tions, and its rapidity between the meridians of 7 ^ East, and 7 g West,
averaged forty miles a day. We appear to have passed out of the stream
on the 22nd of June in latitude 5°+, S., and longitude 8°+, W., into the •
drift current from the S.E., which contributes to its supply and to preserve
its velocity across the Atlantic ; it may be seen that the drift water was
pressing on the southern border of the stream with a force of 16 and 18
miles in 24 hours, in a direction oblique to and accelerative of its course.
In the passage between the River Gaboon and Ascension, being a
distance of 1400 geographical miles, the Pheasant was aided by the
current above 300 miles, in the direction of her course.
In consequence of the southing of the trade wind in the vicinity of the
continent of Africa, the water impelled before it, which forms the com-
mencement of the Equatorial Stream, arrives from a more remote south-
ern parallel, and is therefore of a colder temperature than the drift water
which successively falls into it from the S.E., impelled more obliquely
to the meridian, and consequently arriving from latitudes less distant from
the Equator. Thus the temperature of the stream varied from 72.5 to 74°,
whilst that of the drift current was 77.5 and 78°. But the more important
distinction, both in amount and in utility in navigation, is between the
waters of the Equatorial and of the Guinea currents. These exhibit the
remarkable phenomenon of parallel streams, in contact with each other,
flowing with great velocity, in opposite directions, and having a diiFerence
of temperature amounting to ten and twelve degrees. Their courses con-
tinue thus parallel to each other and to the land for above a thousand
miles ; and according as a vessel, wishing to proceed along the coast in
either direction, is placed in one or the other current, will her progress
3 L
442 HYDROGRAPHICAL NOTICES.
be aided from forty to fifty miles a day, or retarded to the same amount :
the practical advantage, therefore, derivable from the difference of tem-
perature, in enabling vessels to discriminate at all times in which current
they are situated, is as great as it is obvious*.
* The occasional advance of the cold water of the Equatorial Current to the Island of St.
Thomas, may assist in explaining an apparent peculiarity in the climate of that island, when
compared with the climate of the Coast of Western Africa generally. At all the British pos-
sessions, from the Gambia in 13° north latitude to the Forts on the Gold Coast, June, July,
and August are accounted the unhealthy months; whilst at St. Thomas, on the contrary, they
are the most healthy in the year to Europeans, although they are not so to the Negroes, who
suffer much from colds and rheumatism during their continuance. It has been seen, that the
water of the Equatorial Current is from 10 to 12 degrees colder than that of the Gulf of
Guinea, and that its northern border, which at other seasons passes the meridian of St. Thomas
at a distance from 120 to 180 miles south of its southern extremity, was found in June in
contact, or very nearly so, with the island itself; and it is not improbable, from a conside-
ration of the causes which occasion its advance towards the equator when the sun is in the
northern signs, that in July it may extend so far, as even to include the whole island within
its limits.
The temperature of the air is known to be immediately dependant on that of the surface
water of the sea, and to be influenced nearly to the full extent of any alteration that may
take place therein. In crossing the Gulf of Guinea from Cape Formosa to St. Thomas, the
air, over the surface of the Guinea current, observed in the shade and to windward, at sun-
rise, noon, and sun-set, averaged Sl°.5, the extremes being 79° and 83°. 5 ; whilst in the
passage from the river Gaboon to Ascension, over tiie Equatorial Current, the air averaged
only 74°, the extremes being from 73°. 5 to 7-l°.5 ; a part of the passage being, moreover, on
the very edge of the two currents, and within sight of St. Thomas. The vicinity of the Equa-
torial Current, therefore, when the sun is in the northern signs, cannot fail materially to
influence the temperature of the island, (particularly as the wind is always from the south), and
thus to affect its climate. Situated on the equator, St. Thomas has naturally two cold seasons,
or winters, in the year, the sun being equally distant in June and in December ; but in June,
July, and August, is superadded the influence of the surface water of the ocean several
degrees colder than in November, December, .ind January ; rendering the months of June,
July, and August, pre-eminently the winter of St. Thomas ; in which the natives complain
of colds and rheumatism, and the health of Europeans is less affected than at other seasons,
because the climate is then less dissimilar than usual to their own.
The comparative unhealthiness of Prince's Island to St. Thomas, and of both to Annabona,
as the residence of Europeans, has been frequently and particularly noticed by Portuguese
authorities, and is universally recognised at Prince's Island and at St. Thomas. It may be a
sufificientexplanationto remark, that Annabonaisalways surrounded by the Equatorial Current;
Prince's always by the Guinea Current ; and that the position of St. Thomas is intermediate.
HYDROGRAPHICAL NOTICES. 443
The voyage from Ascension to Bahia commenced in the continuation
of the same drift current from the S.E., in which the latter part of the
passage to Ascension was performed ; but on the 13th of July, the
Pheasant appears to have re-entered the southern border of the equa-
torial current, in the longitude of 22^ W., and latitude of lOi S. The
evidence of many voyages in different years, the journals of which have
been submitted to Major Rennell's examination, have led him to the
conclusion, that it is the ordinary course of that stream, to divide into
two branches about the twenty-third degree of west longitude, the
and its climate is occasionally influenced by both. In tropical climates a very few degrees of
temperature constitute an essential difference in the feelings of the natives, and in the health
of Europeans.
The point of deposition varied over the differently-heated surfaces of water, in correspond-
ence with the difference in the temperature of the air ; so that, although the quantity of mois-
ture was diminished in the colder air over the Equatorial Current, the proportion of the quan-
tity to that which would have been required for repletion, was as nearly as possible the same
as over the Guinea Current, being on the average S4.°.o parts in 100° in both instances.
The air, therefore, was equally moist over the Equatorial as over the Guinea Current, although
in the one case the weight of vapour in a cubic foot (derived from the averages) was 10 grains,
and in the other 7.93 grains only. The cold air incumbent on the Equatorial stream, being
borne by the south wind over the surface of the Guinea Current, caused the deposition, which
generally obscured the horizon to the north of St. Thomas, during the pendulum observations,
as noticed in page 33 ; and which fell, as we understood, in heavy rain in the offing. The
quantity of vapour in the atmosphere over the island being less than that over the nearly
surrounding water of the Guinea current (an effect of the high land of which the island con-
sists), no deposition took place on the island itself. The hygrometer indicated the temperature
of its superincumbent vapour to be between the extremes of 7l° and 74°.5, observed three
times a day between the 26th of May and the 12th of June. The range in the Gulf of Guinea
was from 76° to 80°.
It is worthy of notice to what little distance the colder air, impelled by the constant south
wind, attained over the Guinea current, before it became itself heated by the condensation of
the vapour of higher constituent temperature. The great bodies of the air and of the vapour
over the respective currents, though so dissimilar in temperature, were as little affected by
their contiguity, as the surface waters of the currents themselves. By their mutual and
opposite action, the air in condensing and thus reducing the temperature of the vapour, and
the heat liberated in the condensation of the vapour in raising that of the air, the mi,\ture
speedily destroyed the differences ; and the effects of the contiguity were thus limited to a very
few miles within the border of either stream.
3 L 2
444 HYDROGRAPHICAL NOTICES.
northern portion flowing in a N.W. direction, and diffusing its waters in
the basin of the Atlantic, and the southern, which is the largest portion,
proceeding in a direction to the southward of west, until it reaches the
coast of the continent of South America ; where it is again subdivided
by the projecting part of the coast between Cape St. Roque and Cape
St. Augustin, the northern branch coasting the north of Brazil and
Guiana to the West Indies, and the southern branch proceeding down
the eastern side of the continent towards Terra del Fuego. The Phea-
sant's experience corresponded in all respects with this general view.
The direction of the southern part of the equatorial stream, into which
she entered on the 13th of July, became gradually more and more to the
southward of west on approaching the continent ; being due west be-
tween the longitudes of 22°i and 26' ; S. 82 W. between 26° and 29° ;
and S. 71 W. between 29° and 33° ; and the apparent set between the
noons of the 16th and 17th of July is obviously compounded of the in-
fluence of the equatorial stream, (then probably become still more south-
wardly) during the first part of the twenty-four hours, and of the
northerly current, during the latter part, which the observations between
Bahia and Pernambuco shew to prevail in the vicinity of the coast includ-
ed between those stations. The Pheasant may therefore be considered
to have crossed the whole breadth of the branch of the stream which pro-
ceeds to the S.W., by having passed out on its western side between
the longitudes of 33° and 36°, and to have ascertained its general velocity
to have exceeded half a mile an hour, by the according observations of
the 14th, 15th, and l6thof July.
From Pernambuco to Cape St. Roque, the northerly current rapidly
accelerated, until in passing the Cape it may be considered that the
Pheasant had entered the full stream of the other branch of the equatorial
current ; namely, of the one which pursues its way along the northern
coast of Brazil and Guiana to the West Indies. Between the noons of the
Hydrographical notices. 445
16th and 17th, she was set 44.5 to the north, and 42.5 to the west, making
a general effect in the twenty-four hours of N. 44 W., 62 miles ; but
as she did not round Cape St. Roque until midnight, the course having
been altered for that purpose at half past eleven p.m., it must be understood
that the direction of the current was probably more northerly in the first
part of the interval, and more westerly in the latter part, than the general
eflfect ; and that the velocity may in like manner have been less than
the rate of 62 miles to the south of Cape St. Roque, and more than
that amount after passing the Cape. The purpose of stopping at
Maranham obliged the Pheasant to draw nearer the land on the follow-
ing day, than would have been expedient, had she been bound direct to
the West Indies, and been desirous of preserving the full advantage of
the current in her favour ; on examination of the tabular results, it will
be obvious, that by thus nearing the land, she quitted the full strength
of the stream, and that she did not re-enter it again until the day after
her departure from Maranham, Avhen it was found to be running with
the astonishing rapidity of ninety-nine miles in twenty-four hours. It
may also be seen that although in the space comprised between the
direct course of the stream from Cape St. Roque to the West Indies, and
the coast of Brazil, the velocity progressively diminished on approaching
the land, no counter current was found to take place, but the westerly
direction was still maintained, though at the reduced rate of less than
half a mile an hour, when very near the land. It may be attributed to
the rapidity with which the water is thus swept along the shore, that no
change is perceptible in its temperature, on approaching a coast which
is so remarkably shallow, as to have not more than seventeen fathoms
water at thirty-six miles in the offing.
At 10 A.M. on the 10th of September, whilst proceeding in the full
strength of the current, exceeding, as already noticed, four knots an hour,
a sudden and very great discoloration in the surface water a-head was
446 HVDROGRAPHICAL NOTICES.
reported from the mast-head, and from the very rapid progress which the
ship was making, was almost immediately afterwards visible from the
deck. Her position in 5°. 08' north latitude, and 50°. 28' west longitude,
both known by observation, sufficiently apprized us that the discoloured
water which we were approaching could be no other than the stream of
the river Amazon, preserving its original impulse at a distance of not
less than 300 miles from the mouth of the river, and its waters being
not yet wholly mingled with those of the ocean of greater specific
gravity, over the surface of which it had pursued its course.
We had just time to secure some of the blue water of the ocean for
subsequent examination, and to ascertain its temperature, before we
crossed the line of its separation from the river water, the division being
as distinctly preserved as if they had been different fluids.
The direction of the line of separation was N.W. by N., rather nor-
therly ; great numbers of gelatinous marine animals, species of the
Genus Physalia, were floating on the edge of the river water, and
many birds were fishing apparently on both sides of the boundary.
The temperature of the ocean water was 8r.l, and of the river water
81°.8, both within a short distance of the division line ; the specific
gravity of the former was 1.0262, and of the latter 1.0204, distilled
water being unity : the ocean water had also been found 81° at seven
A.M. on the same morning. At noon, having advanced considerably
within the boundary, so that it was no longer in sight from the ship, the
specific gravity of the surface water was 1.0185, and its temperature
81. °8.
Being desirous of ascertaining the depth at which the water of the
ocean would be found unmixed with the river water. Dr. Marcet's very
simple and practical apparatus was employed to bring up water from
fifty fathoms, the specific gravity of which proved 1.0262 ; the bottle was
then sent down a second time to twenty-one fathoms, at which depth the
HYDROGRAPHICAL NOTICES. 447
f
specific gravity was also 1.0262, limiting the depth of any admixture of
the fresh water to less than 126 feet. Its superficiality was further evi-
denced by the colour of the water in the ship's wake, which was much
more blue than that of the general surface. The temperature of the water
from fifty fathoms was 77°.2, and from twenty-one fathoms, 80°.5 ; we
had no bottom with 105 fathoms.
From noon on the 9th, till 10 a.m. on the 10th, we had found the cur-
rent of the ocean running with an average velocity of four knots in a direc-
tion N. 54° W, ; the ship's true course had been very nearly N. 45° W. ;
the division line of the streams trended about N. 33° W. It was obvious,
by the general appearance of the respective surfaces, that the current
of the river water was running with considerable rapidity, in a direction
inclined to that of the ocean, and nearly coinciding with the line which
marked their separation ; the ship's course was, therefore, altered a point
westerly. During the afternoon of the 10th, and morning of the 11th,
the colour and specific gravity of the surface water indicated that we con-
tinued in the river stream ; but that it was becoming latterly more and
more mixed with the sea water. At noon, in latitude 7°.0r, and longitude
52° 38'.5, the specific gravity was 1.0248, temperature 8r.5 ; and from
twenty fathoms, 1.0262. Between noon on the 10th and noon on the 11th
the ship was set N. 38° W., sixty-eight miles, or rather less than three
miles an hour ; which may, therefore, be considered the general direction
and rate at which the water of the Amazon was proceeding, at the dis-
tance of 300 miles and upwards from its natural banks. The original
impulse at its discharge into the ocean is to the eastward of north ; so
much, therefore, had its course been deflected, by having to sustain the
continual pressure of the current of the ocean on its eastern side. As the
initial velocity must have greatly exceeded that which it had preserved
after a course of 300 miles, and as the force of the current which presses
on it is much less in the neighbourhood of the land than it subsequently
448 HYDROGRAPHICAL NOTICES.
becomes, it is probable that the deflection may have been scarcely sensi-
ble in the early part of the course, but much more rapid latterly than
would be due to the whole effect divided by the distance ; and that a
further deflection of the 16 degrees, which measured the inclination of the
streams where the Pheasant crossed the division line, might not require
much more distance for its accomplishment ; when the course of the
streams being parallel, the obstacle to the diffusion of the river water on
its eastern side would be removed, and the marked line of the separa-
tion of the streams would gradually cease to exist. In the early part of
the river's marine course, as it may be termed, and where the force of the
current of the ocean is comparatively weak, the greater obliquity of its
direction may compensate for its want of force, in enabling it to oppose
the diffusion of the river water. On the western side the fresh water is
gradually and insensibly lost in that of the sea ; at noon on the 12th,
the specific gravity of the surface water was 1.0253, in latitude 7' .05',
and longitude 53°|.
The effect which the stream of the Amazons produces on the current of
the ocean in thus crossing its course, is to accumulate the water brought
by the equatorial current, until it streams off with a rapidity which gra-
gually deflects, and ultimately overpowers the obstacle, which opposes its
more regular flow ; it is to the accumulation from this cause, that the
partial velocity of ninety-nine miles in twenty-four hours, much exceeding
the average rate of the branch of the Equatorial current between Cape St.
Roque and the West Indies, is to be attributed. The southern border of
the current is also removed by it to a distance from the land, leaving a
space of the ocean, bounded by the river water on the east, the land on
the south, and the Equatorial current on the north, which is occupied by
irregular streams of various and uncertain strength and direction, as
shown by the Pheasant's experience between the 11th and the 14th of
September. It is desirable that vessels bound from the Brazils to the
HYDROGRAPHICAL NOTICES. 449
West Indies should, therefore, keep well off the land of Guiana, in order
to preserve the strength of the Equatorial current in their favour ; whilst
others, endeavouring to make a passage along the coast to the eastward,
should be especially cautious to keep in the space within the current.
The Pheasant re-entered the current about the eighth degree of latitude,
and in the fifty- seventh of longitude, and was subsequently indebted to
its influence, between two miles and two miles and a half an hour, until
her arrival in the Gulf of Paria*.
The observations in the passage from Trinidad to Jamaica indicate a
general set of the surface water across the Caribbean Sea towards the
Gulf of Mexico, averaging about sixteen miles in each twenty-four hours.
The northerly inflexion, on approaching Jamaica, was occasioned by the
indraft between Cape Tiburon and Point Morant.
From Jamaica to the Havannah the Pheasant was engaged in conduct-
ing a convoy, which obliged a suspension of the observations.
In crossing the Caribbean Sea from Trinidad to Jamaica, between the
9th and 17th of October, the temperature of the surface water, observed
always at 8 a.m., and occasionally at other hours, was never less than
82°. 8, nor more than 83° ; between Jamaica and Grand Cayman, on the
10th and 11th of November, the minimum was 83°, and the maximum at
3 P.M., 83°.8 ; from the Cayman Islands to the entrance into the Gulf of
* In the passage from Maranliam to the West Indies, and in crossing the mouth of one of the
largest rivers of the globe, the hygrometrical state of the atmosphere was the subject of very
frequent and careful observation on each day ; no effect of the river, however, on the state of
the aqueous vapour was perceptible: the point of deposition varied only between 12°. 5 and
74°, and the air between 7^)° and 82°, the higher temperatures of botli taking place when
we had arrived abreast of Surinam, and the surface water had increased to 83°. In the Gulf
of I'aria, where the general temperature of the surface is raised to 84°.5 by the admixture of
the healed water from the smaller branches of the Orinoco, the air was further augmented to
84°, and the Point of Deposition to 75°..5. Between Point Galeotta and Port Spain, we
crossed the stream of one of the branches of the Orinoco, the temperature of which was
ibP.S, an<l the specific gravity not more than 1.0064; the general surface of the Gulf
being 1.0204.
3 M
450
HYDROGRAPHICAL NOTICES.
Mexico, between Yucatan and Cuba, and in the open part of the Gulf
itself, the surface varied from 82° to 82°. 5* ; but on approaching Havan-
* The particular observations were as follows, and are accompanied by the temperatures of
the air, and of the point of deposition, observed at the same hours.
Between Trinidad and Jamaica.
PoRr Royal, i
AMAICA
Be
ween Jamaica and Havannah.
Oct.
Time.
Water.
Air.
Point of
Depo5.
Oct.
Time.
Water.
Air.
Point of
Depos.
Nov.
Time.
Water.
Air.
Point of
Depos.
11
8 A.M.
o
83
o
83.2
o
77.5
20
10 A.M.
8°3.7
0
76
10
9 A.M.
0
83.1
0
82
0
,,
21 P.M.
83
83
78.5
22
noon.
o «
83.5
76.5
»
3 P.M.
83.8
83.2
12
8 A.M.
83
82
76.5
23
7 A.M.
ji d
78.8
76
n
8 A.M.
83
81.8
74
13
8 „
82.8
83
77.5
j»
2 P.M.
'c CO
C 00
(u ...
82.5
76
13
H „
82.5
80.8
72
14
8 „
82.9
82
78
24
noon.
83
77
14
Si „
82.2
79.7
72
15
8 ,,
83
82
rain.
25
91A.M.
■5 g
81.7
75
»J
3 P.M.
82
78
rain.
16
8 „
83
83.4
77.5
29
noon.
3
85.5
78
15
SiA.M.
80
78.8
72.5
17
8 „
83
82
30
10 A.M.
00 «
84.5
78
17
8^ „
82
80.3
74.5
w
noon.
82
77
31
Nov.
1
2
3
10 „
10 ,,
6 „
6 „
6X1"'.
Co
c 2
83
82.5
78
78.5
76
75
75
76
18
21P.M.
8iA.M.
82.1
80.5
80.2
78.9
71.5
73
The light rain which fell on the afternoon of the 14th of November, in the passage between
Jamaica and Havannah, was a precipitation from an height above the earth's surface, as the
air near the surface was very far from being replete with moisture at the time. It was pro-
duced by the commencement of a wind from the N.E. (the same, I believe, which is called at
Havannah, El Norte), which almost instantly lowered the temperature of the air two degrees
at the surface, and of course correspondingly in its ascending progression, whilst the dew
point and its progression remained unaltered. The height, therefore, at which the tempera-
tures of the air and vapour would coincide (by reason of the difi'erence in their respective
ratios of cooling), would at once descend a space equivalent to that required to diminish
the temperature of the air two degrees in its ascending progression, and a precipitation would
take place throughout that space too copious to be altogether re-dissolved by falling into a
warmer atmosphere ; and thus some portion of it would reach the surface, forming the light
rain which we experienced. It was not, however, of long continuance, the superfluous mois-
ture being disposed of, and the atmosphere speedily adapting itself to the new order of cir-
cumstances, by the processes which have been so well pointed out by Mr. Daniell, in his essay
on the habitudes of an atmosphere of permanently elastic fluid mi.xed with aqueous vapour.
I am not able to assign with confidence the cause of the surface water being only 80° on
the morning of the 1 3th ; but I suspect that it evidenced the presence of a thread of the cur-
rent which descends from the northern shores of the Gulf of Mexico along the coast of
Florida ; and of which a small portion from the western border is sometimes turned to the
I
HYDROGRAPHICAL NOTICES.
451
nah, on the morning of the 18th, we were apprised by the colder tempe-
rature of 80°.5, that during the preceding night we had entered the cur-
rent, which descends from the northern shores of the Gulf of Mexico
along the coast of Florida, and forms the head of the Gulf stream. In
the subsequent passage from Havannah to the Straits of Bahama, on the
27th, 28th, and 29th of November, we crossed the narrow sea formed by
the northern shore of Cuba and the Florida reefs, in which the waters of
the stream are comprised, previously to their discharge into the Atlantic :
the surface water in this passage varied from 80°.5 to 80°. 7, which may
therefore be considered as the initial temperature of the gulf stream to-
wards the end of November. The strait between the Bahama's and
the eastern side of Florida, which forms the outlet of the stream, is rather
less than 200 miles in length, and from 33 miles at the narrowest part of
the water-way, to 50 miles at the widest, in breadth. The Pheasant was
at the southern extremity of the strait at noon on the 29th, and at the
northern extremity at noon on the 30th, with good observations of the
latitude on both days, and with especial care given to the intermediate
reckoning. The rate of three miles an hour (or more exactly seventy
miles in twenty-four hours) may, therefore, be regarded, with confidence,
as the initial velocity of the Gulf stream at that period.
The maximum of its temperature in the strait was 80°.8, and the mini-
mum observed 80°. 5 ; but the Pheasant did not approach the shore on
either side, where the surface is known to be colder, by reason of the
vicinity of land.
The diminution in the rapidity of the stream on the 1st, 2d, and 3d of
December, is the consequence of its expansion after the outfall into the
westward by the northern coast of Cuba on which it impinges, and takes a course towards
Cape St. Antonio. The charge of a convoy in a sea so much infested with pirates was
incompatible with the measures which would have been necessary to have ascertained more
particularly the cause of the decrease in temperature of the surface water.
3 M 2
452 HYDROGRAPHICAL NOTICES.
Atlantic ; it is probable, however, that on neither of the three days was
the Pheasant in the full strength of the current, being nearer the inner
border, where the velocity is checked, and the waters accumulated,
by the direction of the coast of America between Charleston and Cape
Hatteras ; the consequence of the accumulation is seen in the increased
rate on the 2d and 3d, in comparison with that on the 1st of December ;
and in the very remarkable circumstance, that after passing Cape
Hatteras, the velocity experienced between the 3d and the 5th of
December was actually greater than the initial velocity at the outlet,
being 3.2 miles an hour on the average of the forty-eight hours, or
seventy-seven miles in each twenty-four hours ; and was, doubtless, con-
siderably greater than the average during a part of the time. The
accumulation of the water of the stream in the neighbourhood of Cape
Hatteras, to such an extent as to occasion it to flow off with even
greater rapidity than on its discharge into the ocean from the Gulf of
Florida, is a fact which I believe had not been previously observed, but
which may be explained by a brief notice of the different states, at
different seasons, of the current, and of the ocean through which it
pursues its course. In the summer months, the stream issues from the
outlet with a velocity nearly one-third greater than at the period of the
Pheasant's voyage ; its original northerly direction, received from the
Bahama channel, is turned considerably to the eastward of north, (about
N. 50° E.) by the coasts of Georgia and South Carolina, in which new
direction it passes Cape Hatteras, and pursues an unobstructed course,
until it impinges upon the St. George's bank to the eastward of Nan-
tucket, by which it is turned still more to the eastward ; but as it
strikes the bank very obliquely, it is deflected without material accu-
mulation of its water, or increase of velocity. The St. George's bank
is the last obstruction that the stream encounters, as it never afterwards
approaches land. There is, therefore, no accumulation in the summer
HYDROGRAPHICAL NOTICES. 453
months in the neighbourhood of Cape Hatteras ; but on the contrary the
western border of the stream expands into the great Bay between Cape
Hatteras and Nantucket, and occasions a diminution rather than an
increase in the velocity at the surface; accordingly it is found that the
force originally communicated at the outlet is progressively diminished
from above eighty miles in twenty -four hours in the first 180 miles after
its discharge into the Atlantic, usually to less than seventy miles when
abreast of Cape Hatteras.
On the approach of winter, the disparity in the general level of the
Gulf of Mexico and the Atlantic is diminished by the reduction in the
level of the Gulf, and the impulse communicated to the stream at its fall
into the Atlantic is proportionably lessened. At that season, also, an
alteration takes place in the level of the part of the ocean towards which
the course of the stream is directed. The heavy autumnal gales from
the north and north-east impel before them the superficial waters of the
north-western Atlantic into the space comprised between the coast of
America and the Gulf stream : this space, which is of considerable width
between Cape Race in Newfoundland and the northern border of the
stream, narrows towards the westward, and has no outlet ; the drift
water consequently accumulates, and presses wholly against the northern
and western borders of the current, and by raising the usual level of the
ocean, prevents the surface water of the stream from reaching the
Nantucket and St. George's banks, and opposes the expansion of the
western border into the recession of the coast of the continent between
Cape Hatteras and Nantucket ; the accumulation of the Gulf water is
thus occasioned, which streams off to the north east with the augmented
velocity experienced by the Pheasant between the 3d and 5th of
December. It is probable that the occasional effects thus noticed are
very superficial, and that the great body of the water which issues from
the Gulf of Florida, and is of considerable depth, is governed, both in
454 HYDROGRAPHICAL NOTICES.
direction and velocity, solely by the original impulse, and the banks
on which it impinges ; but navigation is more immediately concerned
with the surface current only.
On the 5th of December, between 10 a.m. and noon, the Pheasant
quitted the gulf stream, passing out on its northern side. At 8| a.m. she
was in longitude by observation 72° 25' W., and in latitude, deduced from
the subsequent noon, 36° 14' ; the temperature of the surface water was
74°, and of the air 60°.5. At 10 a.m., the temperatures being still the
same, the depression of the horizon, observed with a dip sector from the
Pheasant's gangway, where the height of the eye was 15 feet 3 inches
above the sea, was 4' 56". 6, being an excess of 1' 05".6 above the usual
computed and tabular depression. On repeating the observations at noon,
it was found that a change of great magnitude had taken place interme-
diately ; the horizon, viewed from the same height, making an angle,
on the second occasion, of only 3' 36". 6 with the horizontal line passing
through the eye. As the ship was in both instances very steady, and
the horizons perfectly clear, the observations were decided and certain ;
and the utmost error of which either might be suspected could not be
more than 5". So great an alteration in the refractive quality of the
atmosphere led to the immediate suspicion, that the temperature of the
surface water of the sea must also have greatly altered, and that we must
have passed from the warm water of the stream into the colder surface of
the general ocean. This suspicion was confirmed on trial, the temperature
having fallen from 74° at 10 a.m. to 62.°4 at noon, being a difference of 1 r.6.
As a measure of precaution on such a sudden and great decrease, Captain
Clavering immediately sounded, but had no bottom with 120 fathoms :
the temperature at 110 fathoms, indicated by a register thermometer
attached to the line above the lead, was 51°. 5. The distance from the
nearest banks noticed in the charts was sixty-five miles.
The northern boundary of the stream, where we had thus quitted it, was
HYDROGRAPHICAL NOTICES. 455
between the latitudes of 36° 26' and 36° 38', and in the meridian of 72° 30'W.
The surface water on which we entered was in motion to the westward, at
the average rate of sixteen miles experienced in the following twenty-
four hours, and generally to the west and south-west between the north-
ern side of the stream and the banks on the coast of Maryland. This
motion may be more properly characterized as a drift current, occasioned
by the prevalence and strength of recent northerly gales, than as a counter-
current. In approaching the banks, the surface water at 8 a.m. and at noon
on the 7th of December was 59°.5 ; at 3 p.m. it had fallen to 54°.2, on
which we immediately sounded, and found bottom in thirty-three fathoms :
on the following morning, in thirty fathoms, the surface was 53°. 5, and at
8 A.M. on the 9th in twelve fathoms, but still with no land in sight (being
twenty miles off the coast), 49°.5. In the afternoon of the same day,
when about two miles distant from Sandy Hook, the water had finally
lowered to 45°. Thus in a space of the ocean scarcely exceeding 200
miles in direct distance, we found the heat of the surface progressively
diminish from 74° to 45°.
On a general review of the influence of the currents which have been
thus particularized, on the Pheasant's progress, in her voyage com-
mencing at Sierra Leone, and terminating at New York, it may be seen,
that she was indebted to their aid on the balance of the whole account,
and in the direction of her course from port to port, not less than 1600
geographical miles, the whole distance being under 9000 miles ; affording
a very striking exemplification of the importance of a correct knowledge
of the currents of the ocean to persons engaged in its navigation ; and
consequently of the value of the information, in the acquisition and arrange-
ment of which Major Rennell has passed the later years of his most
useful life. The publication of the charts of the currents in the most
frequented parts of the ocean, which he has prepared with his accustomed
and well-known indefatigable assiduity, and strict adherence to the
456 HYDROGRAPHICAL NOTICES.
evidence of facts, — as soon as he shall deem them sufficiently complete
for the public guidance, — will be a most important service rendered to
practical navigation.
On the Depth at ichich the Water of the Ocean within the Tropics is found at
the temperature of its greatest density.
The greatest density of sea water resulting from its temperature takes
place at 42°, or thereabouts : if heated above, or cooled below that
amount, it is rendered specifically lighter, and in the natural progression
must be found incumbent on water of 42°.
In the existing state of the ocean, the temperature of 42° may be con-
sidered as the mean heat of the surface of the sea in a parallel between
the latitudes of 65° and 70°; from whence the influence of external
causes renders the surface colder towards the pole, and warmer towards
the equator, and in both cases specifically lighter, than water of 24°.
In approaching the equator, (or rather, more generally the space
within the tropics, to every part of which the sun is periodically vertical,)
the warmth of the surface water increases, and the heat penetrates to
greater depths ; in descending beneath the surface, the temperature
progressively decreases and the density augments, until the term of 42°
(or thereabouts) is reached ; beneath which no further alteration of either
takes place, dependent on influences operating on the surface. It was to
ascertain the depth at which the term of this progression might be met
with in the tropics, that the following experiment was made.
In the Caribbean sea, in latitude 20| N. longitude, 83^ W., nearly
midway between the Cayman Islands and Cape St. Antonio at the
west end of Cuba, in the afternoon of the 1 3th of November, 1822, a
HYDROGRAPHICAL NOTICES. 457
Six's self-registering thermometer, enclosed in an iron cylinder, having
holes in the top and bottom to admit the free access of the water, was
lowered to a depth exceeding 1000 fathoms. A weight of 75 lbs.
was attached to the end of the line, and 11 coils of 113 fathoms each,
and 3 fathoms of a 12th coil were veered, making altogether 1246
fathoms. The weather being very favourable, with light airs and little
swell, the ship's drift was bodily to leeward, without either head or stern
way. The 1246 fathoms were veered in rather more than twenty-five
minutes, at the expiration of which time the line was fairly on the ship's
qua ter. Under such circumstances, the depth to which the thermometer
was sunk must have exceeded a thousand fathoms, as an allowance of
246 fathoms for stray line would be more than ample, if no bight of con-
sequence existed in the rope, which, from the rapidity with which the
weight drew out the line, appeared to be the case ; 246 fathoms of stray
line would be an equivalent to a drift of four-fifths of a mile in twenty-
five minutes, whereas that of the ship did not exceed half a mile an hour.
The line was hauled in in fifty-three minutes, when it appeared that
the thermometer had registered 45°.5, the surface being 83°; whence it
may be reasonably inferred that 100 fathoms more line would have sunk
the thermometer to 42°, the rate of cooling being on the average of the
whole depth about twenty-eight or twenty-nine fathoms to a degree of
Fahrenheit ; and thus that the sea water would have been found at its
maximum of density, dependent on temperature, at about 1200 fathoms
below the surface.
The thermometer used in this experiment was made expressly for the
purpose to which it was applied ; it was of the ordinary construction, ex-
cept that the top of the tube, in which is contained the index of heat, was
hermetically sealed instead of being closed by a cork, as is sometimes
the case. I have since sunk the same thermometer in the same apparatus
to 650 fathoms, accompanied by a similar thermometer enclosed in a
3 N
458 HYDROGRAPHICAL NOTICES.
strong iron cylinder without perforations, and of which the top screwed
down upon leather, so as to exclude the access of the water to' the interior
of the cylinder, and thus to prevent any effect which might be supposed
to be occasioned in the indications of the free thermometer, by the in-
creased pressure of water at great depths upon its exterior surface.
The two thermometers were suffered to remain below above an hour,
to allow the air in the inside of the closed cylinder to adjust itself to the
temperature of the surrounding water ; and on their being drawn up,
they were found to have registered precisely the same indication.
A notice of the preceding experiment in the Caribbean Sea was read
before the Royal Society in April, 1823, and published in the Philoso-
phical Transactions of that year. I have since learned that a similar
experiment had been made in the ocean between the tropics, in 1816, by
Capt. Wauchope of the Royal Navy, then commanding His Majesty's
ship Eurydice ; and as the interest and value of each of the results,
separately considered, are greatly increased by the very remarlcable cor-
roboration which they afford to each other, I have obtained Captain
Wauchope's permission to insert the following detailed account of his
experiment.
The thermometer used was a common one of Fahrenheit ; it was en-
closed in the middle of six cases, all of tin except the outer one, which
was of wood : each of the cases had valves at the top and bottom opening
upwards, so that the valves might remain open whilst descending, but
would close on being drawn up through the water ; there was also a
small spring to the upper valve, which prevented it from opening when
once shut. The four inside cases were separated from each other
about a quarter of an inch all round, allowing the water to pass freely
between them ; the fifth case was distant from the one next to it on the
inside by about half an inch, which space was filled with tallow. The
outer case was of wood an inch in thickness, and separated about
IIYDROGRAPHICAL NOTICES. 459
an inch from the one next to it by a column of water. The size of
the apparatus was two feet high, and ten inches diameter, having a
weight of 721bs fastened to the bottom, and the end of a coil of two inch
rope to the top. Of this rope 779 fathoms were veered, then 390 of
two and a half inch, and then 266 of three inch, making in all 1435 fa-
thoms veered overboard. A 321b shot was attached to every 200 fathoms,
and the whole was run out twenty-two minutes. It was allowed to
remain twelve minutes before the hauling in was commenced, that the
whole might have time to sink ; and it took an hour and twenty minutes
to draw the thermometer to the surface, when it stood at 42°, the sur-
face water being 73'. Latitude 3° 20' S. and longitude 7° 39' E. ; date,
September, 1816*. Capt. Wauchope is of opinion that the thermometer
must have sunk about 1300 fathoms, provided there was no curve in the
rope, as the ship's drift was about five knots in twenty-four hours.
Both experiments, therefore, concur in assigning a depth of 1200 or
1300 fathoms as the term of the augmentation, occasioned by external
influences within the tropics, of the temperature of the sea water above
that of its greatest density.
In a previous experiment of the same kind, which Captain Wauchope
made in latitude 10° N. longitude 25° W., the quantity of rope veered
was 966 fathoms, the temperature of the surface water was 80°, and the
enclosed thermometer shewed 51° ; corresponding to a diminution of tem-
perature averaging one degree in about 29 fathoms, being very nearly
the same ratio as appeared by the experiment in the Caribbean Sea.
* From the geographical position, and the temperature of the surface water, Capt. Wau-
chope was in the equatorial current near its commencement. In his case the surface water was
thus accidentally colder than is due to the parallel, whilst in mine it was warmer; the acci-
dents beinc; in both cases the effect of currents.
3 N 2
460 EXPERIMENTS FOR DETERMINING THE VARIATION
EXPERIMENTS FOR DETERMINING THE VARIATION IN THE
INTENSITY OF TERRESTRIAL MAGNETISM.
The inquiry into the laws which regulate the phenomena of terrestrial
magnetism has occupied, successively, the attention of many of the most
eminent mathematicians and philosophers of the last and present cen-
turies ; whose endeavour it has been to elicit, from the facts collected in
different parts of the globe, an experimental law, which, embracing the
whole, should represent by calculation each individual observation, within
such limits as might reasonably be ascribed to accidental causes of dif-
ference.
There are three distinct classes of phenomena, in which the influence
of terrestrial magnetism is found by observation to vary in different parts
of the globe : these are — 1st. The direction which a needle, freely sus-
pended, assumes in relation to the geographical meridian ; 2d. the direc-
tion, in regard to the horizon ; and 3d. the intensity of the attraction by
which it is solicited. These are termed respectively the magnetic varia-
tion, dip, and force. The phenomena of the variation and dip have
hitherto received the principal attention, and indeed almost the exclusive
regard, of the experimentalists, as well as of those who have sought to
submit the results of experiment to a systematic arrangement.
The necessity of ascertaining the direction of the compass needle in re-
gard to the geographic meridian, for the purposes of navigation, has caused
the variation to become known in almost all parts of the globe, and far
more extensively than the dip, which is an object purely of physical re-
search ; it happens unfortunately that the class of phenomena with which
we are thus best acquainted, is the one least susceptible of systematic
reduction; the skill of the many eminent mathematicians, by whom
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 461
the observed variation of the needle has been considered, has failed in
deducing any general law by which the observations may be represented ;
and it may be concluded, in the words of one of the most distinguished
existing authorities, that it is impossible to find any places for two, or even
for a greater number of magnetic poles, which will correctly explain the
direction of the needle (in regard to the meridian) in every part of the
globe.
The prospect of a better success, founded on the phenomena of the
dip, was entertained at the commencement of the present century ; it had
been learnt by observation, that a needle suspended by its centre of
gravity, and having perfect freedom of motion, assumed an horizontal
position in certain parts of the globe, which, in the absence of very pre-
cise observation, appeared to form a great circle of the sphere, inclined
at about 12 degrees to the equator ; that in receding from this circle in
either direction, the horizontal position was departed from ; one of the
poles dipping beneath the horizon if the recession was towards the North,
and the other if towards the South : and as the amount of the departure
from horizontality appeared, as far as was then known, to bear a certain
proportion to the distance from the circle, it was deemed probable that at
its poles the position of the needle would be vertical. Reasoning
then on certain hypothetical considerations, in which the circle of no dip
was regarded as the magnetic equator, and its poles as the magnetic
poles, of the earth, it was inferred, that between the equator and the poles
the tangent of the dip should be equal to twice the tangent of the magne-
tic latitude. On submitting this law, partly experimental and partly hy-
pothetical, to more extensive experience, it has not been found, however,
so correct a representation of the facts as it had been expected to prove.
M. Biot, to whose original suggestion it was substantially due, had in-
ferred from the position on the globe of the circle (or rather, as it is now
known to be, the inflected curve) of no dip, that the spot in the northern
462 EXPERIMENTS FOR DETERMINING THE VARIATION
hemisphere, in which the needle would be vertical, would be found in 76°
north latitude, and 25° west longitude of Paris, It was shewn, however,
by the observations which I had an opportunity of making in the longi-
tudes west of Baffin's Bay, in the years 1818, 1819, and 1820 (and which
h'lve been since confirmed by other observers with other instruments),
that the dips of greatest magnitude are found in meridians nearly 90°
distant from M, Biot's supposition ; and (which is more directly to the
point, because amidst the many irregularities of the dip it by no means
follows that there might not be two places in the northern hemisphere,
each with a dip of 90 degrees) I had a further opportunity, in 1823, of
observing within a very few miles of the actual spot assigned by M. Biot
as that of the maximum of dip, when it was found not to exceed 80
degrees and a few minutes. Nor is this instance of difference between
the facts and the computation from the formula which was designed to
represent them, an extreme case. M. Biot has attributed the failure of
the formula, in its general application, to the existence of certain se-
condary centres of magnetrc attraction, which are supposed to interfere
with and disturb the regularity of the effects under the general law * ;
however that may be, it is certain that no two positions can be assigned
to the magnetic poles, which shall enable a calculation of the dip by any
function of the polar distance, in which differences from fact shall not be
found of 10 degrees and upwards ; and that whatever circle may be
assumed as that of the magnetic equator, if the magnetic latitudes are
parallels, stations will be found having the same magnetic latitude, (and
not insulated stations only, but districts,) in which the dip may be shewn to
differ from 10 to 15 degrees. It must be conceded, therefore, that the dip
cannot be considered in strictness even as an approximate indication
of the magnetic latitude, of the magnetic equator, or of the magnetic poles
in the assumed hypothesis.
* Precis de Physique Exp^rimentale, Edition of 1821. Vol. II. chap. ix.
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 463
In tracing the progress of our experimental acquaintance with the
principal phenomena of the earth's magnetism, it is impossible to avoid
remarking the little attention that has been paid to the intensity of the
force by which the magnetic needle is solicited, in comparison with the
pains which have been bestowed to ascertain its direction.
We learn by the memoir drawn up by the Academy of Sciences at
Paris, for the instruction and guidance of M. de la Perouse and his as-
sociates, that previously to the year 1782, observations had been made
at Brest, at Cadiz, at TenerifFe, and at Goree, and subsequently at Brest
and Guadaloupe, in which no sensible difference had appeared in the
intensity of the magnetic force at those stations. We now know that ob-
servations by which a difference was thus not discovered, must have
been defective ; and such appears to have been the suspicion of the
members of the Academy, by whom the memoir was drawn up, if a
judgment may be formed from their recommendation that such experi-
ments should be repeated, and especially that the comparative force of
magnetism should be ascertained at those places on the globe, where the
dip was most considerable, and at those where it was least so.
The recommendation thus made had little effective operation until the
beginning of the present century, when it fortunately attracted the notice,
and obtained the attention of M. de Humboldt, to whom almost every
branch of natural knowledge has so much obligation: his comparative
experiments in Europe and in South America, published in 1805, first
made known a diminution of intensity on approaching those parts of the
globe, where the dipping needle is horizontal ; and further appeared to
indicate, though with considerable irregularities, that the diminution was
progressive, coincidently with the decrease of dip. M. de Humboldt's
experiments, with a much fewer number made by M. Rossel, in the
voyage of Admiral D'Entrecastreaux, (but published subsequently to
those of M. de Humboldt, and inclining to the same indications, though
464 EXPERIMENTS FOR DETERMINING THE VARIATION
less decidedly,) include, it is believed, the whole of our experimental
knowledge in regard to the intensity, previously to the year 1818 ; when
the determination of the British government to re-attempt the discovery
of a North West Passage between the Atlantic and Pacific Oceans, opened
a field of great interest for researches of every kind connected with
magnetism, in countries to which the access had previously been ex-
tremely inconvenient.
The interest which I had felt in the perusal of M. de Humboldt's ex-
periments, induced me, on my appointment to conduct the scientific
operations of the Voyage of Discovery of 1818, to feel much solicitude
in the preparation of the instruments by which the magnetic dip and
force should be ascertained. The dipping-needles officially supplied by
the government were of very inferior construction ; but Mr. Browne was
kind enough to allow me to employ a dipping-needle belonging to him-
self, the workmanship of the late Messrs. Nairne and Blunt, artists of
deserved celebrity in the construction of such instruments : it has sub-
sequently remained in my possession, and has accompanied me in three
northern, and one equatorial voyage : the results obtained with it are
now to be discussed.
In the voyages of 1818, and of 1819-20, the first to Baffin's Bay,
and the second to Melville Island, the same needle served for both the
purposes of the dip and force. It was furnished with a means of
adjusting the centres of gravity and of motion to each other, by small
screws on a cross of wires attached to the axis, as described in the
Philosophical Transactions for 1772, article 35 ; and was adjusted
with great care, and probably as well as that very difficult opera-
tion is ever performed, before its embarkation in 1818 ; since which
period its magnetism has never been interfered with, nor has it im-
dergone a change. The observations on the intensity of the force
made during those two voyages, are consequently strictly comparable
I
IN THE INTENSITY OF TERRESTRIAL MAGNETISM.
465
with each other ; the dips observed in those voyages are probably also
entitled to as much confidence as can attach to observations made with
needles in which the influence of gravity is supposed to be wholly
destroyed by an instrumental adjustment. It is scarcely possible that
such an adjustment should be quite perfect, and there will always remain
a liability to errors, amounting perhaps to a few minutes.
The magnetic observations made in the voyage of 1818, were pub-
lished in detail in the Philosophical Transaction's for 1819, and those of
the voyage of 1819 — 20, (or at least a portion of them, as the space
allotted for the purpose did not admit of the whole being so published,)
in the appendix to the narrative of that voyage. As those on the inten-
sity of the force will be employed on this occasion, in the discussion of
the ratio of its variation in different parts of the earth, the following
abstracts of them are now given.
ABSTRACT in the VOYAGE of 1818.
STATIONS.
Latitude,
Longitude.
Dip.
Time of 100
Vibrations in
the Magnetic
Meridian.
London ....
Shetland . . .
Davis Straits, on Ice
Hare Island .
Baffin's three Islands
Baffin's Sea, on Ice
Baffin's Sea, on Ice
Baffin's Sea, on Ice
Baffin's Sea, on Ice
Baffin's Sea, on Ice
Baffin's Sea, on Ice
Davis Strait, on Ice
51 31 N.
60 09.5
68 22
TO 26
74 04
75 05
75 51.5
75 59
76 32
76 45
76 08
70 35
0 08 W
1 12
53 50
54 52
57 52
60 23
63 06
64 47
73 45
76 00
78 21
66 55
70 33 N.
74 21 *
83 08
82 49
84 09
84 25 *
84 44'
84 52
85 44
86 09 *
86 00
84 39
3 O
M. S.
8 02
7 49.75
7 20
7 21.3
7 25.5
7 23.25
7 IS
7 16
7 16
466
EXPERIMENTS FOR DETERMINING THE VARIATION
ABSTRACT in the VOYAGE of 1819— 1820.
STATIONS.
Latitude.
Longitude.
Dip.
Time of 100
^ ibratioils in
tlie Magnetic
Meridian.
London
Davis Strait, on Ice ...
Baffin's Sea, on Ice
Possession Bay
East Shore of Regent's Inlet .
Regent's Inlet, on Ice .
North Shore of Barrow's Strait
Byam Martin's Island .
Polar Sea, on Ice .
Bay of the Ilecla and Griper
On Melville Island ....
Observatory, Winter Harbour
Davis Strait, on Ice
51 31 N.
64 00 N.
72 00
T3 31
72 45
72 57
73 33
75 10
74 55
74 47
74 27
74 47
68 30
0 08
61 50 W.
60 00
77 22
89 41
89 30
88 18
103 44
104 12
110 34
111 42
110 48
64 21
70 33
83 04 *
84 15
86 04 *
88 27
88 23 *
87 36 *
88 26
88 29
88 30
88 37
88 43
84 21.5
M. s.
8 02
7 17.4 t
7 19.5 t
7 19 t
7 22.5 t
7 24.3 t
7 26.25
In the seven observations of the dip which are marked with an asterisk
in the foregoing abstracts, Captain Parry had the kindness to accompany
and remain with me, whilst I was engaged in making the observations ;
and to confirm the correctness of my reading of the division of the arc,
to which the needle settled at each repetition, by going over that part of
the process himself. Our separate readings are recorded in the original
detailed accounts, where it may be seen that in no one of the seven
instances they differed more than one minute in a mean result ; affording
a satisfactory proof of the precision with which the divisions of the circle
of Mr. Browne's dipping instrument are capable of being read. It is
proper to add, that the unity of the observer, in all the respects in which
it is of consequence that the same individual should conduct all the
experiments of a suite, was equally preserved in those observations, as
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 467
in the others in which I had not the pleasure of such an accompaniment.
In recording so extensive a series of observations on the dip and force,
covering nearly a fourth part of the northern magnetic hemisphere, it is
not unimportant to notice such particulars, as might otherwise be thought,
and more particularly by those who are themselves practical observers,
to constitute an occasion of dissimilarity.
The time of 100 vibrations of the dipping-needle at the stations in
the second abstract, marked with a f , are now first published.
On the return of the expedition of Arctic Discovery in 1820, and
before my departure for Africa, in 1821, a conviction of the imperfection of
the usual method of observing the dip, with needles in which it is a
necessary condition to the accuracy of the result, that the axis of motion
should pass through the centre of gravity, but which condition is pro-
bably never strictly fulfilled, induced me to cause a needle to be made
on a principle recommended by Professor J. Tobias Mayer, in his
treatise " De imi Accuratiori acus indinatoricB Magneticee," published in
the Transacliom of the Royal Society of Sciences at Gottingen, for 1814.
In this needle, the centres of motion and gravity are designedly sepa-
rated, so that inequalities of workmanship in the axis, or in the planes of
suspension, are rendered of less effect, being opposed by the joint in-
fluences of gravity and magnetism ; whilst by a peculiar process of
observation, and an appropriate formula, the joint operation of the two
forces is resolvable, and the position which the needle should assume
from that of magnetism alone, deducible with precision. This needle,
being found on trial to deserve the preference in practice, which had been
inferred from its superiority in principle, was subsequently employed in
the determinations of Dip ; and Mr. Browne's needle was reserved solely
for the indications of the Force.
In order that the observations made with the needle on Professor
Mayer's construction, may be understood in the condensed form in which
3 o 2
468 EXPERIMENTS FOR DETERMINING THE VARIATION
they are given in the following tables, it is necessary to prefix a descrip-
tion of the needle itself, of the mode of observation with it, and of de-
ducing the results.
The needle was a parallelopipedon of eleven inches and a half in
length, four-tenths in breadth, and one-twentieth in thickness ; the ends
were rounded ; and a line marked on the face of the needle passed
through the centre to the extremities, answering the purpose of an
index line.
The cylindrical axis on which the needle revolved was of bell metal,
terminated, where it rested on the agate planes, by cylinders of less
diameter ; the finer these terminations can be made, so long as they do
not bend with the weight of the needle, the more accurate will be the
oscillations ; small grooves in the thicker part of the axis received the Y's
which raised and lowered the needle on its supports, and ensured that
the same parts of the axis rested on the planes in each observation.
A small brass sphere traversed on a steel screw, inserted in the lower
edge of the needle as nearly as possible in the perpendicular to the
index line passing through the axis of motion ; by this mechanism the
centre of gravity of the needle, screw, and sphere, may be made to fall
more or less below the axis of motion, according as the sphere is screwed
nearer or more distant from the needle, and according as spheres of
greater or less diameter are employed.
The object proposed in thus separating the centres of motion and
gravity, was to give to the needle a force arising from its own weight,
to assist that of magnetism in overcoming the inequalities of the axis ;
and thus to cause the needle to return, after oscillation, with more cer-
tainty to the same point of the divided limb, than it would do were the
centres strictly coincident.
The centres of motion and of gravity not coinciding, the position which
the needle assumes, when placed in the magnetic meridian is not that of
IN THE INTENSITY OP TERRESTRIAL MAGNETISM. 469
dip ; but the dip is deducible, by an easy calculation, from observations
made with such a needle, according to the following directions.
If the needle has been carefully made, and the screw inserted truly
as described, the centres of motion and of gravity will be disposed as in
the lever of a balance, when a right line joining them will be a perpen-
dicular to the horizontal passing through the extremities, (or to the index
line ;) this condition is not indeed a necessary one, but it is desirable to
be accomplished, because it shortens the observations, as well as the
calculation, from whence the dip is deduced ; its fulfilment may be as-
certained with great precision, by placing the needle on the agate planes
before magnetism is imparted to it, and observing whether it returns to
a horizontal direction after oscillation, in each position of the axis ; if it
does not, it may be made to do so at this time with no great trouble.
With a needle in which this adjustment can be relied on, two obser-
vations made in the magnetic meridian are sufficient for the determination
of the dip ; the two faces of the needle are turned successively towards
the observer, by reversing the position of the axis on its supports in such
manner, that the edge of the needle which is uppermost in the one observa-
tion becomes lowermost in the other ; the angles which the needle makes
with the vertical in these two positions being read, the mean of the
tangents of those angles is the co-tangent of the dip.
But when needles are used in which this adjustment has not been
made, or where its accuracy cannot be relied on, four observations are
required ; two being those which are already directed ; the two others
are similar to them, but with the poles of the needles reversed ; calling
then the first arcs F and /, and those with the poles reversed G and g,
and taking tang. ,,- + t^„g ^ ^ ^
tang. F - fang. / = B
tang. G + tang, g = C
tang. G — tang, g = D
A.D.B.C , . I
B +T> B + D ~ '^ co-tangent of the dip.
470 EXPERIMENTS FOR DETERMINING THE VARIATION
In reversing the poles, it is not necessary that the magnetic force im-
parted to the needle should be the same in amount as it possessed pre-
viously to the operation.
By adopting the precaution of placing the needle in a groove to prevent
its lateral motion, and by confining the sides of the magnet by parallel
strips of wood, so that in moving along the needle they may preserve
its direction, the poles may always be ensured to coincide with the ex-
tremities of the longitudinal axis.
If the distance between the centres of motion and of gravity be con-
siderable, the arcs in the alternate observations will be on different
sides of the vertical, especially when the dip is great ; in such cases the
arcs to the south of the vertical are read negatively.
The arcs in each of the four, positions, forming the elements from
whence the dip is deduced, are the arithmetical mean of (usually)
six observations, half of which were with the face of the circle towards
the east, and half with the face towards the West ; the needle being
lifted by the Y's and lowered gently on its supports between each
observation ; the arcs indicated by both ends of the needle were also
read, to correct the errors arising from inequality in the divisions, or
from the axis of the needle not passing correctly through the centre
of the circle.
The observations, of which the following table presents an abstract,
were made in the summer of 1821, for the double purpose of deter-
mining the dip in London, and of affording a satisfactory evidence
of the consistency of the results obtained with Mayer's needle. The
experiments were made with spheres differing considerably in magni-
tude, with a view of discovering if any limit of proportion between
the respective forces of magnetism and gravity was desirable to be
maintained ; it is obvious that in proportion as the spheres are larger,
the arcs read will deviate more and more from the position which the
IN THE INTENSITY OF TERRESTRIAL MAGNETISM.
471
needle would assiime from the force of magnetism alone ; but it does
not appear that the ultimate result, deducible from the readings by
means of the formula, is affected even by differences which might be
considered as excessive.
ABSTRACT of OBSERVATIONS with MAYER'S NEEDLE on the
DIP, in the Regent's Park, London, August, 1S21.
DATE
The MARKED END of the NEEDLE being
Dip deduced.
A North Pole.
A South Pole.
The Weight.
The Weight.
l^ppennost.
Undermost.
Uppeimost
Undermost.
1821.
S.
O /
F.
o
o *
G.
0 /
August 3
+ 9 22.3
31 08.2
+ 6 17.1
29 41.3
70 03.3 N.
6
- 22 22
49 11.7
- 20 09
40 58.7
70 04.7 „
6
+ 10 08.3
30 36.8
+ 7 46.6
28 47.7
70 01.4 „
,, 11
— 14 49.1
45 58
- 11 28.7
41 50.7
70 00 . 1 „
„ IS
+ 14 07.2
27 24.3
+ 13 21.7
24 14.2
70 05.9 ,,
., .13
+ 10 17.2
30 36 . 2
+ 9 15.3
27 12.6
70 03.5 „
15
+ 8 03.4
32 00.2
+ 7 40.9
28 57.4
70 05.2 „
IS
+ 17 34.1
24 14
+ 15 34.8
22 17.5
70 00.9 „
20
- 19 25
48 24.7
- 17 19
44 57.1
70 00.3 .,
20
+ 17 38.5
24 27.6
+ 15 22
22 04
70 03.8 „
ME
Kti • .
70 02.9 „
472 EXPERIMENTS FOR DETEKMINING THE VARIATION
At the same time that Mayer's needle was provided for the purpose
of introducing greater accuracy in the observations of the dip, several
other alterations were made in parts of the apparatus employed in the
determinations both of the dip and intensity, which it may be proper to
premise. To ensure the perfect horizontality of the agate planes which
support the axis of the needle, a spirit level was attached to a circular
brass plate, of the proper diameter to be placed upon the planes them-
selves, with adjustments to bring it parallel to the plate : the errors of
the level are shewn by placing the plate in various positions hori-
zontally, and of the planes by turning the whole instrument upon its
horizontal centre; when these errors are adjusted, and the planes and
plate perfectly horizontal, the apexes of two cones, which proceed
perfectly at right angles from the plate uniting them at their base,
and are equal to the diameter of the divided circle of the instrument,
should coincide with the divisions 90° and 90° of the circle ; if they
do not, the cones afford the means of correcting the adjustment in
that respect also.
Mr. Browne's needle appearing unnecessarily encumbered about the
axis, having two adjusting weights on each wire of the cross, and the
wires themselves being needlessly long, and consequently liable to de-
rangement, the weights were removed altogether, and the needle re-ad-
justed by shortening all the wires one-half, and one of the pairs more than
a half, and unequally. Having since had opportunities of observing the
direction of this needle in dips of nearly every amount, I am able to say
with confidence, from its correspondence with the results of Mayer's
needle, that the re-adjustment of the centers of motion and gravity were
very satisfactorily accomplished. The alteration occasioned a small
difference in the time of vibration, making its oscillation in the two
subsequent voyages not directly comparative with those in the two pre-
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 473
ceding : this circumstance, however, is of no moment whatsoever, be-
cause the whole suite of experiments are equally comparable with each
other, by means of the station in London common to both, at which
the time of vibration was very correctly ascertained before and after
the alteration was made.
A moveable ring was fitted into the great ring of the instrument, and
close to the back of the divided circle, for the purpose of retaining and
releasing the needle at any arc at which it might be desired to commence
the vibrations for determining the intensity of the force. To one part of
the ring a double lever was attached, acted upon by a spring throwing
one end of the lever within the divided circle, so as to support the needle
at any division that might be required ; a string was attached to the
other end of the lever, passing through a hole in the great ring, which
when drawn tight released the needle, by pulling the lever from under
it. The needle was always retained, previously to oscillation, both in
the meridian and in the perpendicular vibrations, at 70 degrees from its
natural position ; the account of the time of vibration was commenced
when the arc had diminished to 60 degrees ; and concluded when it had
further diminished to less than 10 degrees. The number of vibrations
which Mr. Browne's needle usually made between these arcs, was from
90 to 110 ; from which the average time of 10 vibrations was inferred as
entered in the tabular abstracts ; the times of commencement, and of
every subsequent 10th vibration, were noted by a chronometer of
small and steady rate, to the nearest beat, i. e., to the nearest four-
tenths of a second.
The following table presents an abstract of the observations on the
Dip, made principally with Mayer's needle in the voyages of 1822 and
1823 :—
3 P
474
EXPERIMENTS FOR DETERMINING THE VARIATION
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I
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 475
The next table contains an account of the average time of ten
vibrations of Mr. Browne's needle in similar arcs at the several stations
enumerated in the first column ; the second column exhibits the .time of
vibration in the plane of the magnetic meridian, the squares of which
numbers express the inverse ratio of the intensity of terrestrial mag-
netism ; the third column contains the corresponding times of vibration
in the plane perpendicular to the meridian ; the squares of the numbers
in this column should correspond with the squares of those in the pre-
ceding, divided by the sine of the dip ; consequently the dip itself is
deducible as an observation, from a comparison of the times of vibration
in the meridian and perpendicular to it ; the results so obtained are in-
serted in the 5th column, until the dip arrives at an amount when, from
the reduced ratio of the increase of the sines, this method of deduction
ceases to be practically useful. The fourth column shews the times of
vibration of the same needle, suspended by an assemblage of untwisted
silk fibres attached to one extremity of the axis, and limiting the needle
to an horizontal motion ; the vibrations were performed under the pro-
tection of a wooden cover with glazed windows, the silk suspension
being fifteen inches in length : the squares of these times should corre-
spond with the squares of the times in column 2, divided by the cosine
of the dip ; affording a third method of deducing the dip by observation,
which becomes available when the preceding fails ; the 6th column con-
tains the dips so deduced ; the seventh exhibits the results obtained by
the direct method brought forward from the preceding tabular abstract,
and placed in comparison with those in the 5th and 6th columns ; in
the eighth is inserted the Dip finally deduced from a mean of the methods
thus compared.
3 p a
476
EXPERIMENTS FOR DETERMINING THE VARIATIONS
TiMR OF Ten Vibrations.
Dip deu
c'CED.
Dip deducfd
in the urdi-
UHiy ITHMtf.
(Page 474.)
Dip finally
deduced.
STATION.
In llie
maoneiic
iiieiiUiaii.
Perp. to
tlie iiiei-'ui.
^nspendcd
liinizon-
tally.
«! = .i„.D.
COS. D.
1.
2.
= M.
3.
= P.
4.
= H.
5.
6.
7.
8.
s.
s.
s.
O '
0
'
0 '
0 '
Islandof St. Thomas.
61.652
Stationary.
00 04 S.
03 04 S.
Maranham ....
58.66
93.744
23 03
23 07.75
23 06 N.
Sierra Leone . . .
58.012
81.017
30 50.5
31 02.25
30 57 „
Trinidad
53.262
67.1
39 03.3
39 02.5
39 03 „
Jamaica
49.667
58.15
46 51
46 58.25
46 55 „
Grand Cayman . . .
49.61
57.288
48 35
48 48.3
48 42 „
Havannah ....
48.177
51.2
.52 11
51 55.3
52 03 „
London
49.453
51
70 05.8
70 03.5
70 01. 5„
New York ....
44.667
45.687
72 55
73 05
73 00 „
Drontlieim ....
49.643
50 . 5.52
96.75
74 40
77
44
74 43
74 42 „
Hammerfest ....
48.885
49.435
103.8
77
11
77 13.3
77 13.3,,
Greenland ....
48.05
48.4
116.507
80
12.7
80 12
80 12 „
Spitzbergen ....
47.562
47.9
121.36
81
10
81 11
81 10 5„
In the Voyage of Discovery of 1819-1820, I had made experiments
on the intensity of the force with needles limited by their mode of sus-
pension to an horizontal motion, of which an account is given in the ap-
pendix to the narrative of that voyage ; it has not been thought necessary
IN THE INTENSITY OP TERRESTRIAL MAGNETISM. 477
to include those experiments in the present summary, because, on occa-
sions where the dip so nearly approaches 90 degrees, the employment of
horizontal needles is more curious, as evidencing to general apprehension
the diminution of directive force which the compass needle undergoes
in such situations, than usefiil towards a knowledge of the real inten-
sity of magnetism*; the reverse, however, is the case in the parts of
the earth where the horizontal differs little from the natural direction of
the needle ; in such situations they afford, perhaps, a more exact compa-
rison of the relative intensity than the dipping needle, which by reason
of the resistance of the planes supporting its axes, sooner arrives at rest
than needles suspended by silken fibres ; and the greater duration of the
period through which the vibrations continue, enables the average time
of vibration to be obtained with greater exactness. It is for this reason
also that a silken suspension is preferable for the horizontal needles to
an agate resting on a point.
The apparatus which I provided for the horizontal needles in the
voyages of 1822 and 1823, was preferable in many respects to that
which had been employed in 1819-20; and being simple, of little cost,
and fully equal to its purpose, the following description may promote the
further extension of experiments of the same nature : it consisted of a
mahogany box, made, for convenience, in an octagonal shape, with a top
of stout glass ; the height was fifteen inches, and the diameter sufficient
to allow a bar of seven inches in length to vibrate freely, when suspended
by a silk line passing through a brass button inserted in a perforation
in the middle of the glass top ; a metal circle fixed in the bottom of the
* Their employment should cease, whenever the uncertainty to which the observation of
the dip is liable induces a corresponding uncertainty in the reduction of the time of vibration
dependant upon it, equalling i,, amount, and superadded to the probable mean error of obser-
vation with the horizontal needles themselves.
478 EXPERIMENTS FOR DETERMINING THE VARIATION
box, of rather more than seven inches diameter, marked the arc of vi-
bration ; the bar or needle was carried in a light stirrup, into which it
slid until correctly balanced ; the silk thread, of fifteen inches in length,
consisted of a sufficient number of silk fibres to sustain the weight, and
was always allowed to untwist itself, in the first instance, with a brass
needle, of equal weight with the magnetic lieedles ; and was so adjusted,
by moving the button round, that the brass needle should settle, when
at rest, in the magnetic direction. The box was usually placed on the
ground, in a sheltered situation, far from buildings or other sources of
local interference ; the only adjustment required, (except that of the silk
thread,) was to render the divided circle horizontal, which was accom-
plished by a pocket spirit level, and wooden wedges placed beneath the
box ; the silk being thus without twist, and one of the magnetic bars in
the stirrup, and known to be horizontal by its accordance with the circle,
the degree to which it settled was registered as the zero ; it was then
drawn about 40 degrees out of the meridian, and retained by a copper
wire passing through the glass top, and capable of being moved in
azimuth from the outside, and of being raised so as to release the needle
at pleasure, to commence its oscillations ; these were not noticed until
the arc had diminished to 30 degrees, when the registry commenced,
and was repeated at the close of every tenth vibration, until the arc
had still further diminished to 10 degrees, when the experiment was
concluded.
The six needles which were used in this apparatus differed from each
other considerably both in rapidity of vibration, and in the duration of
the interval of oscillation between 30 and 10 degrees ; Nos. 1, 2, 3, and 5,
were similar in shape ; being bars 7 inches long, 0.25 broad, and 0.15
thick ; No. 4 was a bar of the same magnitude in the middle, but gra-
dually tapering to points at the extremities ; No. G was cylindrical.
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 479
flattened in the middle to fit the stirrup ; they were all magnetised with
very powerful magnets in the summer of 1821, and being tried in
London, in 1823, on their return from the Equator, and in 1824 on their
return from the Arctic Circle, were found to have preserved throughout
the same average time of vibration as in 1821, with the exception of
No. 2, which from some cause that was not obvious had changed its rate
materially between 1821 and 1823, and was therefore discontinued in
subsequent use, and the experiments made with it, although inserted
with those of the other needles in the tabular abstracts, are rejected in
the conclusions drawn. When not in use, the needles were kept in pairs
in the customary manner, Nos. 1 and 3, 2 and 6, 4 and 5, being com-
bined, with their opposite poles united, in separate boxes ; and each
needle was placed by itself in the direction of the meridian for two or
three hours before its time of vibration was ascertained. The times
were registered to fractional parts of a second by the beats of a chrono-
meter, having a rate inappreciable in the interval. The detail of the
experiments at a single station will suffice to explain more fully the
manner in which they were proceeded with ; at the remainder of the
stations, the results only are collected, and are presented in one view in
a tabular abstract.
480
EXPERIMENTS FOR DETERMINING THE VARIATION
TIMES of VIBRATION of the SEVERAL NEEDLES observed with No. 423, on
the Beach at
Man-of-War
Bay, Island of St. Thomas, May, 1S22.
Needle 1.
Needle 2.
Need le .3.
Needle 4.
Needle 5.
Needle 6.
Vibra-
tions.
Time.
Interval.
Time.
Interval.
Time.
Interval.
Time.
Interval.
Time.
Interval
Time.
Interval.
M. S.
M. s.
IM. S.
M. S.
M. s.
M. S.
0
0 00
s.
117.6
0 00
s.
73.8
0 00
s.
119.2
0 00
S.
39
0 00
S.
53.6
0 00
S.
45.6
10
1 57.6
117.2
I 13.8
73.6
1 59.2
118
0 39
39
0 53.6
53.4
0 45.6
45.6
20
3 54.8
116.4
2 27.4
73.2
3 57.2
117. 6
1 18
39
1 47
54
1 31.2
45.2
30
5 51.2
116.8
3 40.6
73.4
5 54.8
117.6
1 57
38
2 41
53
2 16.4
44.6
40
7 48
116
4 .54
73
7 52.4
117
2 35
38
3 34
53.6
3 01
44.0
50
9 44
116
0 07
73
9 49.4
117
3 13
.38
4 27.6
53.4
3 45.6
45.2
60
U 40
116.2
7 20
72.8
11 46.4
116. 8
3 51
38
5 21
53.6
4 30.8
44.8
70
13 36.2
116.2
8 32.8
72.6
13 43.2
116.4
4 29
38
6 14.6
53.4
5 15.6
44.6
80
15 32.4
115.4
9 45.4
72.8
15 39.6
116.4
5 07
38
7 08
53
0 00.2
44.6
90
17 27.8
115.4
10 58.2
72.8
17 36
116. 4
5 45
39
8 01
53
6 44.8
44.6
100
19 23.2
115.6
12 11
72.6
19 32.4
116.8
6 24
39
8 54
53
7 29.4
44 6
110
21 18.8
116
13 23.6
72.4
21 29.2
7 03
9 47
52.6
8 14
120
23 14.8
115
14 36
72.6
10 39.6
52.8
130
25 03.8
115.4
15 48. 6
72.6
• • •
11 32.4
140
27 05.2
115.6
17 01.2
72.6
150
29 00. 8
18 13.8
.
■ •
Time of
t™ V
Vihra- 1
tions. J
116.05 Seconds.
72.92 Seconds.
117.2 Seconds.
38.45 Seconds.
53.26 Seconds.
44.9 Seconds.
IN THE INTENSITY OF TERRESTRIAL MAGNETISM.
481
AN ABSTRACT of EXPERIMENTS on the INTENSITY of MAGNETISM,
with Needles suspended Horizontally.
STATIONS.
Average Time of 10 Horizontal Vibrations between the Arcs of 30° and 10°.
No. 1.
No. 2.
No. 3.
No. 4.
No. 5.
No. 6.
St. Thomas
Bahia
S.
116.63
s.
72.92
73.87
117.2
119.5
s.
38.45
39.07
S.
53.26
S.
44.98
46.07
Ascension
38.75
Maranham
73.17
53 . 87
52.88
45.04
Sierra Leone
74.08
119.76
38.93
53.56
45.67
Trinidad
116.43
73 75
117.44
38.73
52.95
45.24
St. Mary's River Gambia . .
122.26
. . .
39.8
54.566
Port Praya
125.49
40.7
55.25
Jamaica
114.3
72.31
114.31
37.4
51.9
44.39
Grand Cayman
116.84
73.16
115.6
44.8
Havannah
117.5
73.41
118.07
38.41
45.27
Teneriffe
84.136
45.6
62.366
53.2
Madeira
141.8
46.2
1821
159
92.6
165.9
54
72.95
61.95
London -l.
1823
161.33
103.6
164
53.24
74.37
C3.42
1824
161.5
163.2
52.4
73.9
62.74
New York
156.09
156
50.64
70.55
60.36
Drontheim
180.84
182.67
60.2
70.46
Haramerfest
195.84
• • .
196.86
63.43
87.64
75.73
Greenland
220.8
221.42
71.78
84.76
Spitzbergen ....
229.26
231.81
75.11
10.39
88.17
3 Q
482 EXPERIMENTS FOR DETERMINING THE VARIATION
In any application that it may be proposed to make, of the times of
vibration of needles limited to an horizontal motion, towards a knowledge
of the ratio of variation in the force of terrestrial magnetism, it is a
preliminary step, alike necessary in all cases, to obtain from the observed
times of horizontal vibration, the corresponding times in which an equal
number of vibrations would have been performed, had the needles been
free to have oscillated in the direction of the force itself. This purpose
is accomplished by reducing the squares of the respective times of hori-
zontal vibration in the proportion of the radius to the cosine of the Dip ;
the results so obtained are inserted in the following table ; which ex-
hibits in effect the times of vibration of the same needles, supposing that
they had been fitted as dipping needles, and had been made to vibrate
in the plane of the meridian ; the errors only excepted, which may have
been introduced by an inaccurate knowledge of the Dip, affecting the
cosine used in the reduction ; this consideration becomes of moment only
where the Dip is great ; it may be accordingly remarked in pages 474-
476, that the endeavours to obtain that element correct were increased
in reference to the occasion.
IN THE INTENSITY OF TERRESTRIAL MAGNETISM.
483
REDUCED TIMES, in which TEN VIBRATIONS would have been performed
in the direction of the DIPPING NEEDLE, by each of the Needles of which
the Horizontal Vibration was observed.
STATIONS.
No. 1. No. 2.
No. 3.
No. 4.
No. 5.
No. 6.
St. Thorans . . . .
S.
116.65
s.
72.92
s.
117.2
6 .
38.45
S.
53.26
s.
44.98
Bahia
73.77
119.3
38.96
53.96
46
Ascension ... ...
38.67
53.75
Maranham
50.7
43.19
Sierra Leone
68.6
110.9
36.05
49.6
42.29
Triuidad
102 6
64.99
103.5
34.13
46.67
39.87
St. Mary's
106.7
34.74
47.63
Port Praya
105.1
34.09
46.28
Jamaica
94.46
59.76
94.47
30.91
42.9
36.69
Grand Cayman
94.92
59.44
93.91
.36.4
Havannah
92.14
57.57
92.57
30.12
35.5
Teneriffe
59.64
32.32
44.21
37.71
Madeira
96.88
31.56
r 1S21
93
54.09
96.88
31.54
42.60
36.18
London < 1823 '
94.22
60.78
95.77
31.1
43.43
37.04
1- 1824
94,33
95.31
30.6
43.16
36.64
New Yoik
84.40
84.. 35
27.38
38.15
32.64
Dronthcim
92.89
93.84
30.92
36.19
Hammerfest
92.1
92.58
29.83
41.22
35.61
Greenland
91.12
91.35
29.62
34.97
Spitzbergen
89.8
'
90.8
29.42
42.7
34.54
The squares of the numbers in each column of the above table, are to each other, in
the inverse ratio of the intensity of the magnetic force at the respective stations, as
severally indicated by the different needles.
3 Q 3
484 EXPERIMENTS FOR DETERMINING THE VARIATION
Having thus obtained the experimental relation of the magnetic force,
at stations distributed over and comprehending an eighth of the surface
of the globe, (pages 465, 466, 476, 481,) I proceed to employ the results
in their designed application, — as facts collected towards the establishment
of a general law, which shall represent by calculation the relative
intensity in all parts of the globe.
It is assuredly deserving of remembrance, and highly creditable to the
sagacity of the philosophers who drew up the admirable memoir for the
guidance of M, de la Perouse, a memoir unparalleled in the annals of
voyages of discovery, that at a period when so high an authority in physical
knowledge as Mr. Cavendish believed and maintained the invariability
of the magnetic force at all parts of the Earth's surface, and when that
belief was apparently confirmed by experiments at various stations
widely removed from each other (page 463), the authors of the memoir not
only manifested doubt, but even implied the expectation that the force
would be found to vary in accordance with the dip.
Since the publication of the experiments of M. de Humboldt in the
present century, the latter opinion had gradually gained ground, but no
suggestion of a specific relation was made until 1820, when Dr. Thomas
Young, in one of the numbers of the Astronomical and Nautical Collec-
tions, published in the Journal of the Royal Institution, inferred from
certain hypothetical considerations, that the force would probably be
found to vary, inversely, as the square root of 4, less three times the
square of the sine of the Dip. In founding this inference, however.
Dr. Young had assumed as a fact, that the Dip itself varied in conformity
with M. Biot's hypothesis, or at least that a sufficient approximation to
the phenomena was furnished by it ; an assumption, the correctness of
which is far from being agreeable to experience; on the contrary, indeed,
the computation and facts are so frequently and so much at variance, as
to have pressed the alternative, either of giving up the hypothesis, or of
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 485
rejecting^the phenomena of the Dip as an evidence in its support or con-
tradiction. The course pursued by M. Biot himself has been to preserve
the hypothesis, by enlarging it so as to include the existence of secondary
and local centres of attraction, interfering with and destroying the syste-
matic correspondence of the Dip with the primary and general attraction ;
implying consequently the rejection of the phenomena of the Dip as a test
of the hypothesis ; and which indeed is expressly done in the admission
by the same authority, that the irregularities to which the Dip is liable,
and consequently its amnnnt at any particular station, can only be known
by actual experiment.
Under these circumstances, then, it may be proper to examine in the
first instance, whether the variations of the Intensity are, in fact, in any
correspondence with those of the Dip. For that purpose the relation be-
tween them suggested by Dr. Young may be assumed, as that which
would subsist in the event of both the phenomena being in conformity
with the original hypothesis. And it will be sufficient to exhibit the com-
parison of the experimental results with a single needle with the ratio
so computed, because the differences between the several needles are in-
significant, compared with those which wiU appear between the calculation
and experiment.
The most exact method of examining the accordance of a body of ob-
served results with a formula proposed to represent their differences, would
doubtless be, by comparing the ratio at each station severally with that at
all the others both by experiment and calculation ; the process however
is tedious, and would be needlessly precise in the present case ; it may
be preferable therefore to substitute a more ready mode of approximative
comparison, by reducing the times of vibration observed at each station
to the corresponding times which would be required agreeably to the
formula where the dip should be = 0 ; if the formula and experiments
agree, the reduced times should all be the same ; otherwise, as the squares
486
EXPERIMENTS FOR DETERMINING THE VARIATION
of the reduced times represent the magnetic force where there is no Dip,
severally conformable to the observations from whence they are derived,
the arithmetical mean of the several squares may be taken as the equi-
valent to unity ; and being combined with the squares of the times actually
observed at the several stations, will give the experimental ratio at each,
to be compared with the computed ratio.
Thus if T, T, T*", ^-c, be the times of vibration of a needle in the plane of
the magnetic meridian at stations where the sine of the dip is respectively
S, ^, §, ^c, then will f '-, f -, f^ ^c, represent, inversely the force of
magnetism at those stations, and agreeably to the formula of Dr. Young
a t" 2 f ' 2 f"
v/4 -3 8" v^4 - 3 S^ V^4. - 3 S^
should be equal to each other, and to T^, which is the force where the ho-
rizontal direction is the natural position of the needle.
But should the several values of T^, thus obtained, be found to diflfer,
their arithmetical mean may be assumed to represent the force where
there is no Dip, as deduced from, and corresponding suitably, with the
whole of the experiments.
i
I
A TABLE exhibiting a COMPARISON of the RATIOS of
the MAGNETIC
INTENSITY, to unity when the Dip
=; 0, as deduced, 1st,
by Computation
from the Dip; and 2d, by the Experiments with Mr. Browne's Needle.
ST.iTlONS.
Dip.
Ratios
CompQta-
tion ill
Excess
or Defect.
ST.\T10NS.
Dip.
Ratios
Compnta-
tion in
Excess
or Defect.
Com-
puted.
Experi-
mental.
Com-
puted.
Expcri-
nieotal.
Dip = 0
0 . r
0 00<
T2 =
3
61.3
1
i
i
I
1
Havannah . .
52 03
1.37
1.62
-0.25
St. Thomas . .
0 01
1
0.99
+0.01
London . . .
70 03.5
1.72
1.54
+0.18
Maranham . .
23 06
1.06
1.09
-0.03
j New York . .
73 00
1.79
1.88
-0.09
Sierra Leone .
30 57
1.12
1.12
-0.00
Drontheim
74 42
1.82
1.52
+0.30
Trinidad . . .
39 03
1.19
1.33
-0.14
Hammerfesl .
77 13
1.87
1.57
+ 0.30
Jamaica . . .
46 55
1.29
1.52
-0.23
Greenland . .
80 12
1.92
1.62
+0.30
Cayman
18.42
1.32
1.53
-0.21
Spitzbergen .
81 10.5
1.93
1. 66
+0.27
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 487
The diflferences between the experimental and computed ratios shewn
in the preceding table, are obviously far greater than can be attributed
to any probable errors of observation ; the defect of the computation at
all the West India stations, for example, and its excess at the northern
stations, are so great and so systematic, as to be decisive against the sup-
posed relation of the Force to the observed Dip, and equally so against
any other relation whatsoever, in which the respective phenomena might
be supposed to vary in correspondence with each other.
It is further observable, that if an attempt be made to compute the dip
at the several stations of experiment, on the supposition that its tangent is
equal to twice the tangent of the magnetic latitude, the differences between
the Intensities, as evidenced by experiment, and as computed from the ob-
served Dip, will be found to take place at the same stations and nearly in the
same degree, as the observed Dips will differ from those of computation ;
that in fact the Intensity does not correspond with the Dip, when the
variations of the latter deviate from the general law of the hypothesis ;
and that, in consequence, the secondary local attractions, conceived to be
influencial on the direction of the needle, must be further conceived to have
little or no sensible effect on the general Intensity of magnetism.
It is desirable therefore, in the next place, to examine, whether the
original supposition of two magnetic centres, infinitely near to each other
and to the earth's centre, acting on all points of its surface in the
inverse ratio of the squares of the distances, a supposition stron^-Iy
supported by the analogous magnetism of an iron sphere, may not afford
a general law of magnetic Intensity, capable of representing within cer-
tain small limits, incidental to the experiments themselves, all the varia-
tions of Intensity which have been thus observed.
In the supposed magnetic sphere, the Intensity would be at a minimum
in a great circle representing the magnetic equator, and at a maximum
at each of the poles of that circle ; and by pursuing a similar course of
488 EXPERIMENTS FOR DETERMINING THE VARIATION
demonstration to that which has been adopted by mathematicians in
regard to the supposed variations of the Dip, the force between the
equator and the poles should vary in the proportion of 1 to 2, and inter-
mediately as V~i + 3 COS." i, i being the itinerary distance from either of
the magnetic poles.
To refer this arrangement to the terrestrial sphere, in order to examine
its conformity or otherwise with the actual phenomena, the magnetic
equator must be sought by connecting those points on the Earth's surface,
where the Intensity is observed to correspond, and to be at a minimum in
regard to all other points ; or, the geographical position of the maximum of
Intensity in either hemisphere must be determined, to fix the place of the
magnetic pole : the latter operation requires the less extensive experi-
mental inquiry, and on examination the observations in the northern
hemisphere recorded in the preceding pages will be found sufficient for
the purpose.
The experiments in the two voyages of North-western Discovery (pages
465-466), will alone furnish the means of assigning an approximate
position for the maximum of Intensity ; as first, in regard to its geogra-
phical longitude, the force was observed to increase, in sailing to the
westward on or near a parallel of latitude in Baffin's and the adjoining
seas, until about the meridian of 80° West longitude ; but, in proceeding
still further to the westward, it was found to diminish : now, as the amount
of the force is supposed to be in inverse proportion to the itinerary dis-
tance, the point of any particular parallel where the force will be greatest
must be at the intersection of the geographical meridian passing through
the maximum in the hemisphere, or, in other words, through the magnetic
pole ; whence the situation of the pole may be inferred to be in or about
80° West longitude, whatever may be its latitude. Second, in regard to
its geographical latitude, it was further noticed, that in ascending Davis
Strait on a meridian or nearly so, and, generally, wheresoever in the
countries or seas adjacent opportunities presented themselves of com-
IN THE INTENSITV OF TERRESTRIAL MAGNETISM. 489
paring the magnetic force at stations nearly in the same meridian, but in
different parallels, the intensity diminished as the latitude increased :
indicating that even the most southerly stations (between 60° and 70° N.
latitude) were to the North of the parallel in which the magnetic pole
was situated.
Having this approximate position, it was not difficult to fix the more
precise spot which should best correspond with the general body of
observations collected in the four voyages. After a few trials, it was
found that the latitude of 60° N., and longitude of 80° W., would fulfil
the purpose decidedly better, than when either 59° or 61° of latitude were
substituted, or than when 85° W. longitude was employed instead of 80°;
a greater precision than to degrees of latitude, and to 5° of longitude (150
miles), might have appeared a refinement beyond the occasion, other-
wise 78° of longitude might have been preferred to 80°. From the spot
thus indicated, therefore, /. e., in 60° N. latitude, and 80° W. longitude,
the itinerary distances of the several stations of experiment were com-
puted, as entered in the fourth columns of the subjoined Tables; as well
as the computed ratios of the force to unity at the equator, varying in
the direct proportion of v i + 3 cos.' u, and inserted in the last column
but one of each of the three tables. In obtaining the corresponding
experimental ratios, a similar process has been followed to that already
described in page 486 ; thus T". ^ i + 3 cos.^ «", T"^ ^1 + 3 cos.' i",
T"'l ^1 + 3 cos.^ i'", ^-c, is the force at the magnetic equator correspond-
ing to the several experiments, the arithmetical mean of which gives the
values of T^ for each of the needles, as inserted at the head of their respec-
tive columns ; these values being again compared with the experiments
at each station, the inverse proportion which the experiments severally
bear, to the force at the equator regarded as unity, is inserted in the
columns opposite to the stations to which the experiments belong. In the
final column of each Table, the ratios by experiment and calculation at
the several stations are compared, and their differences stated.
3 R
490
EXPERIMENTS FOR DETERMINING THE VARIATION
Table. I. —
-COMPARISON of the EXPERIMENTAL and COMPUTED RATIOS of the
MAGNETIC INTENSITY, at the Stations visited in the voyages of 1822 and 1S23.
STATIONS.
Geograpbical
Position.
Com-
puted iti-
nerary
Distance.
RATIO OF INTENSITY BY EXPERIMENT.
Ratio.
Espe-
rimcntal
Ratio
in excess
or defect.
Horizontal Needlks.
Mean
liy the
Horizon.
.Needles.
Dip.
ping
Needle.
LatitDde.
Longitude.
by Ex.
periin.
by Com
pntat.
1
3
4
5
6
Magnetic Equator .
o
0
2
T =
o *
120.27
130.81
39^24
54^05
46^4 1
2
63.4
St. Thomas . .
00. 5N.
6.75E.
87 58
1.06
1.06
1.04
1.03
1.06
1.05
1.04
I.QIS
1.005
+ 0.04
Ascension . .
8. S.
14.5 W.
85 08
1.03
1.01
1.02
1.02
1.01
+ 0.01
Bahia . .
13. „
38.5 „
80 16
1.03
1.02
1.
1.02
1.02
1.02
1.04
-0.02
Sierra Leone .
8.5N.
13.5 „
71 02
• •
1.19
1.18
1.19
1.2
1.19
1.19
1.19
1.15
+ 0.04
Maranham .
2.5 S.
44. „
68 31
1.14
1.16
1.15
1.17
1.16
1.18
-0.02
Gambia . .
13.5 N.
16.75,,
65 07
1.27
1.28
1.29
1.28
1.28
1.24
+ 0.04
Port Piaya . .
15. „
23.5 „
60 48
1.31
1.32
1.36
1 33
1..33
1.31
+ 0.02
Tenerifife . .
28.5 „
16.25,,
52 36
1.47
1.49
1.51
1.19
• •
1.49
1.45
+ 0.04
Trinidad . .
10.5 „
61.5 ,.
51 23
1.37
1.36
1.32
1.34
l.,36
1.36
1.42
1.39
1.47
-0.08
Madeira
32.5 „
17. „
48 52
• •
1.55
1.55
1.55
1.55
1.52
+ 0.03
London . . .
51.5 „
....
42 57
1.64
1.59
1.59
1.58
1.61
1.60
1.64
1.62
1.62
Jamaica . .
18. „
77. ,,
42 03
1.62
1.64
1.61
1.59
1.6
1.61
1.63
1.62
1.63
-0.01
Cayman
19.25,,
81.5 „
40 43
1.61
1.65
1.63
1.63
1.63
1.63
1.65
-0.02
Drontheim .
63.5 ,,
10. E.
39 14
1.68
1.66
1.61
1.65
1.65
1.63
1.64
1.67
-0.03
Hammerfest
70.5 „
24. „
39 01
1.71
1.7
1.73
1.72
1.7
I.7I
1.68
1.63
1.68
+ 0.01
Havannah .
23. „
82.5 W.
36 53
1.70
1.70
1.70
1.71
1.705
1.73
1.72
1.71
+ 0.01
Spitzbergen . .
80. „
11.5 E.
31 46
1.79
1.77
1.78
1.76
1.80
1.78
1.78
1.78
1.78
• • •
Greenland . .
74.5 „
19. W.
26 09
1.74
1.75
1.76
1.76
1.75
l.TJ
1.75
1.85
-0.10
New York .
40.5 „
74. „
19 40
2.03
2.05
2.05
2.01
2.02
2.03
1.96
1.99
1.91
+ 0.08
IN THE INTENSITY OF TERRESTRIAL MAGNETISM.
491
Table II. COMPARISON of tlie EXPERIMENTAL and COMPUTED
RATIOS of the MAGNETIC INTENSITY, at the Stations visited in the
voyage of 1818.
STATIONS.
GnOCRAPHICAL
Position.
Com-
puted iti-
nerary
Distance.
Time of
Ten Vibra-
tions,
(page 465.)
Ratios op
Intensity.
Expe-
rimental
Ratio
ill excess
or defect.
REMARKS.
Lrttitude
North.
Longiliide
West.
by E\-
periin.
by Cal-
ciilaiion.
Magnetic Equator -
1. LontJon ....
o '
51 31
o •
0 08
o /
90 00
s.
48.2
1.62
1.
o '
42 57
1.62
2. Shetland ....
60 09
1 12
37 01
46.975
1.70
1.70
3. Davis Strait . . .
6S 22
51 00
13 53
44.
1.94
1. 95
-0.01
On an iceberg.
4. Hare Island .
70 26
55 00
14 36
44.13
1.94
1.95
-0.01
S. Davis Strait . . .
70 35
67 00
11 50
43.6
1.98
1.97
■1-0.01
On an iceberg of im-
mense size.
6. BafiSn's Sea . . .
75 05
GO 30
16 17
44.55
1.90
1.94
-0.04
On field ice.
7. Baffin's Sea . . .
75 51
63 00
16 56
44.325
1 .92
I.9J
-0.02
On field ice.
8. Baffin's Sea . . .
76 08
78 21
16 08
43.6
1.98
1.91
H-O.Ol
On an iceberg.
9. Baffin's Sea . . .
76 45
76 00
16 49
43.5
1.99
1.94
-fO.05
On an iceberg.
Table III. COMPARISON of the
EXPERIMENTAL and COMPUTED
RATIOS of the MAGNETIC INTENSITY, at the Stations visited in the |
voyage of 1819— 1S20.
STATIONS.
Geographical
PosirioN.
Com.
pitted iti
nerary
Distance.
Time of
Ten Vibra-
tions,
(page 46G.)
Ratios op
In-i ensity.
Expe-
rimental
lialio
in excess
or defect.
REMARKS.
Latitude
Nortli.
LoniriliKle
West.
by Ex-
perlm.
by Cal-
culation.
Magnetic Equator .
London
O '
51 31
o /
0 08
O t
9ll 00
s.
48.2
1.63
1.
+ 0.01
O '
42 57
1.62
Davis Strait
64 00
61 50
, 9 22
43.74
1.98
1.98
On ice.
Possession Bay
73 31
77 22
14 20
43.95
1.95
1.96
-0.01
Regent's Inlet .
72 45
89 41
13 17
43.9
1.96
1.96
Byam Martin's Island .
75 10
103 44
17 22
44.25
1.93
1.93
Melville Island
74 27
111 42
18 30
44.43
1.92
1.92
Winter Harbour .
74 47
no 48
18 30
44.C25
1.90
1.92
— 0.02
3 R 2
492 EXPERIMENTS FOR DETERMINING THE VARIATION
On viewing the differences between the calculation and experiments,
contained in the final columns of the three preceding Tables, and on duly
considering the delicate nature of such experiments, and their liability to
various sources of error of observation, — as well as the possible local
and accidental disturbing attractions which may occasionally have been
encountered in the course of so extensive a series, — the accordance of the
experimental results with the general law proposed for their represen-
tation cannot be contemplated as otherwise than most striking and
remarkable.
The general applicability of the law to all the stations of the present
experiments, is further strengthened by a more attentive consideration
of the differences themselves, and of the causes which may seem to have
occasioned them ; there are three of principal note in Table I., in two of
which, at Trinidad and Greenland, the calculation is in excess, and in
the third, at New York, in defect. The differences at Trinidad and
New York are produced principally by the results with the horizontal
needles, which differ more from the results with the dipping-needle in
those instances than upon any other occasion, and more in fact than the
latter does from the calculation : now a difference between the results of
the two methods of experiment will be occasioned by, and is indicative
of, the presence of some partial or accidental attraction at the station in
question, the effect of which will necessarily be more conspicuous in the
vibrations of the horizontal needles, on which only a portion of the regular
terrestrial force acts, than in those of the dipping-needle, on which the
whole unresolved force operates. It is, indeed, this very difference that
furnishes the best means with which I am acquainted of detecting the
presence of a disturbing force ; and accordingly the agreement of the two
methods at all the other stations may be with propriety referred to, as
evidencing the general success of the caution which was at all times
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 493
observed, in selecting a situation for the experiments sufficiently distant
from iron.
That the discrepancy at Trinidad was occasioned by some such acci-
dental cause, may also be inferred from the correspondence of the ex-
periments and calculation at the neighbouring stations on opposite
sides, and nearly at equal distances, of Maranham and Jamaica.
With respect to the correctness of the experiments themselves at
Greenland and Trinidad, the opportunities were excellent ; the place of
observation at Trinidad was on the lawn of the Government House, far
distant from buildings, and above a mile from Port Spain ; at Greenland
there were no houses to remove from, and nothing indeed to suspect,
except the soil, which was everywhere strongly impregnated with iron.
The circumstances were not so favourable at New York, the weather
being extremely cold, with snow falling during the time that the needles
were in use ; so that the observations on the Dip with Mayer's needle
were not repeated, as at the other northern stations, where, from the con-
siderable amount of the Dip, it became an important element in the re-
duction of the times of horizontal vibration, and where consequently its
correct knowledge was materially conducive to the accuracy of the infer-
ences which might be drawn from the horizontal needles, in regard to the
intensity of the force in the direction of the dipping needle : for this
reason, the results at the horizontal needles at New York are not perhaps
entitled to the same consideration as elsewhere, and the Intensity de-
duced by the dipping needle alone, may with more propriety be regarded
as furnishing the experimental ratio at that station.
The differences next in rank in Table I., and the only remaining ones
in that table worthy of notice, are at St. Thomas, Sierra Leone, the
Gambia, and TenerifFe, at all of which the calculation is in defect nearly
to the same small amount ; these stations are situated nearly alike in
respect to the assumed position of the magnetic pole, of which it has
494 EXPERIMENTS FOR DETERMINING THE VARIATION
already been remarked, that preserving the latitude of 60°, the longitude
of 78° west would have accorded better with the general body of the
experiments than that of 80° ; it is particularly in regard to these four
stations that the longitude of 78° would have been preferable, as the
removal of the pole two degrees to the eastward of its assumed position
would reconcile the calculation and experiments at them, with compa-
ratively very little effect on the itinerary distances of any of the other
stations.
Of the nine stations comprised in Table II., the experiments made on
land are entitled to principal confidence ; those on ice were on occa-
sions when the vessels were detained by circumstances of weather, and
may have been affected either by the presence of the ship, anchored to
the iceberg on which they were [necessarily] made, — by a vibrating mo-
tion of the ice from the impulse of the waves, affecting the horizontality
of the planes, — or, if on field or floe ice, by a circular motion of the whole
mass, only sensible to the observer, by perceiving, at the close of the
observations, that the instrument had moved in azimuth perhaps several
degrees from the meridian during their course. One of the ice stations
should be excepted from this remark, the experiments having been made
on an iceberg of immense size very securely grounded in Davis Strait,
on which I remained during great part of a day, whilst the ships were
distant under sail. It is the 5th station of the Table ; and with the land
stations, being the 1st, 2d, and 4th, will be found to present the best
accord between the experiments and calculation ; whilst at the other
stations the differences are not greater than might very reasonably have
been expected from the causes above noticed.
The experiments comprised in Table III. were made generally under
more favourable circumstances than those of the preceding voyage, and
with an attention to particulars, suggested by experience, and conducing
to greater accuracy in the mode of observation ; their results present,
.IT KlRIOUS ST.1TIO.YX.
I'innpulpd,
<IAIi'/ '^-"!'>,/^/J
I S . 73
Jl . So .
J3 . J7
J3 . S3
/.( . 2o
14 ■ 3V
iS . oS
le . jj
Iff . u*
36 . S6
iZ . 27
1 ■ ^8 fktvi.* Stroir
1..9S Davi.f .Vf/ntf
J..tS Jtetjrnte /nfr/
1 .ff-t J>nvi.r ,\'rr*ttt
J . .94 Jfa/y /.tia/ui
1..98 Bttmn." Sen
1 .fio Baffin^: Sra
i ■ 9& BdtTifhf Sni
2 . ff7 Baffin.^ Sra
J .fl3 £ji(tm Mo/-fi/h,* /jtlnntt
1 . 93 MrivU/f Itlnjtfi
J .fto Winter ilarbniir
1 ..Qf} Ncwyork-
J ?6' .Off 2 . ■;5 Qrr/'ji/atif/
3o . i3
i 31 . Oft
37 . S3
3't . 14
./^ . 43
43 .n3
^9 ■ 4S
j S2 . 33
I 52 . 3ff
2 . '8 Spt'tzhrrvfrei
2 . 7? Jiavtitinn
I 70 ShdittRfl
. t ,6g Hammrrrhat
. 1 .^4 Jirontheiin
t .S3 Grami fatfiiutn J'f
t . S3 Jamairff
1 . f!s J.nnftntt
i . 3fl Tfinittnti
. 2 .4*} TenrHffir
Go . 4S 2 . 33 rort J'mt/n
try . 3o
I 6W . 3j
'\ ^1 . OS
J . 2/t fiiimhin
J . i/i .t'lrr/Yi ZfO/ir
fin
tO ..
,-. i .oi
I!fi/uii
S5
oa .
- 2 . t>2
. t.W>-/l.ffMI
";
sa
2 .at
StTAoma.*
\ -
Kqiiatnr
/\t.iu.ftfJ uj-t/u uit Mfit^-Jiine t8»i.biifj0hnMuj .>xy ^lihri-uttfr yftr^f ZonJan
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 495
therefore, as might be expected, a closer accordance with the calculation,
than those of the preceding voyage : several of the stations in this table
are peculiarly interesting, from their proximity and relative bearing to
the assumed position of the magnetic pole.
In taking a general review of the experiments on the intensity of
magnetism contained in the preceding pages, and of the inferences that
have been drawn from them, it appears, that if the earth be considered a
magnetic sphere, with poles analogous to those of the induced magnetism
of an iron ball, and if in the year 1822, or thereabouts, the geographical
position of the pole in the northern hemisphere be assumed in 60° N.
latitude, and 80° (or more exactly in 78°) W. longitude, — and if the
magnetic force be supposed to vary between the pole and the equator
in the proportion of two to one, and intermediately, as the square root of
one increased by three times the square of the cosine of the distance from
the pole, measured on a great circle of the sphere, — the relation of the
intensities actually observed at thirty -three stations, distributed over, and
comprehending a space equal, or nearly so, to a fourth part of the surface
of an hemisphere, will be represented within such small limits as may
reasonably be ascribed to the unavoidable uncertainties of experiment.
The annexed map of the northern magnetic hemisphere has been con-
structed for the purpose of producing a more distinct impression than
can be conveyed by verbal description, first, of the arrangement of the
intensities under the supposed law ; second, of the portion of the hemis-
phere in which the phenomena have been proved in conformity to it ; and
third, of that portion which yet remains for a more extended experience.
The map is a correct delineation, on a polar projection, of the land in an
hemisphere, having its pole in the latitude of 60° north, and in the longi-
tude of 80° west ; the parallels are those of equal magnetic intensity, and
are drawn at the proper intervals, to express the ratios of the force
496 EXPERIMENTS FOR DETERMINING THE VARIATION
under the respective parallels of 1.1, 1.2, 1.3, ^c, to the force at the
equator considered as unity ; the space comprehended by the experi-
ments, and over which they are distributed, is shewn by the insertion of
the names of the stations. This map furnishes also a ready means to tra-
vellers in the northern hemisphere, of perceiving the relation of the mag-
netic force according to the law which the present experiments have
suggested, at any two or more stations which they may design to visit ;
and by thus facilitating comparison, may conduce towards the obtain-
ment of further experimental testimony.
Meanwhile, the evidenced agreement over so considerable a portion
of the hemisphere affords a reasonable ground of expectation, that the
phenomena may equally be found in correspondence with the law at
other parts of the same hemisphere ; and that the law may even prove,
still more extensively, one of general application over the whole surface
of the globe, the intensities in the southern hemisphere being computed
from the southern magnetic pole. It would assuredly be an highly in-
teresting subject of physical research, to ascertain by direct experiment,
whether the magnetic force varies in the southern hemisphere in the same
ratio as it has been shewn to do in the northern ; and if so, to determine,
by a sufficiently extensive series of comparative experiments, the geo-
graphical position of the southern magnetic pole, as that of the northern
has now been deduced. Presuming the supposed regularity of the
phenomena, it would be an additional advantage, that the situation of the
two poles should be ascertained as nearly contemporaneously as possible ;
and if the same instruments which have already traversed so large a
portion of the one hemisphere were employed for a similar purpose in
the other hemisphere, and if on their return to England, they should
be found to have preserved their magnetism unchanged, as on former
occasions, their employment would further shew whether or not the ge-
neral intensity of magnetism is the same in each hemisphere.
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 497
Experience has shown, in all countries where sufficiently precise ob-
servations have been made, that both the dip and variation undergo an
apparently systematic periodical oscillation, sensible in its annual pro-
gression, but of which the extent and period have not yet been determined
at any station on the globe. It may be inferred that the intensity is subject
to an analogous variation, but the evidence of experiment is yet wanting.
Were it ascertained that the absolute intensity at any particular place
had undergone an alteration in a certain number of years, a circum-
stance far more difficult of experimental proof than the changes in the
dip and variation, the cause might be ascribed either, to a fluctuation in
the general magnetic intensity of the globe, — or to such an alteration in
the system of terrestrial magnetism in regard to its geographical rela-
tions, as the changes of the dip and variation are usually ascribed to ;
namely, to a change of position of the magnetic poles. The existence
of the latter cause, however, as producing the effect, may become the
subject of a distinct and decisive experiment, if the inferences which
have been drawn in the preceding pages shall be estabhshed by more
extensive experience ; as by the repetition of a similar series of experi-
ments in a future year, the position of the maximum of intensity in
the northern hemisphere may be shewn either to have been stationary in
the interim, or to have advanced to a spot, of which the geographical
relation may be determined in the same manner as on the present occa-
sion ; when, if the number of years elapsed have been sufficient, the
difference of position and the interval may become the elements of ascer-
taining the nature of the progression to which the magnetic pole is sub-
ject ; and to which the alteration of intensity, at any particular station,
should have been conformable, if thegeneral magnetic intensity of the
globe is a constant force.
3 S
498 EXPERIMENTS FOR DETERMINING THE VARIxVTION
The experiments recorded in the preceding pages have placed beyond
question the fact, that the variation in the intensity of the magnetic force
in different parts of the globe cannot be represented by any function of
the known dip ; consequently, whenever it may be desired to trace with
precision the compound effect of the forces acting on the compass needle
in ships, the intensity must be regarded as an essential element of the
computation, distinct from the dip, and necessary to be known by obser-
vation, until that necessity shall be superseded, by the law of its variation
having been thoroughly ascertained.
There are two forces which act on the compass needle of ships ; the
natural force of terrestrial magnetism, and the disturbing force of the
ship's iron. The latter is usually considered constant in different parts
of the globe ; the former varies in its influence on the horizontal needle,
inversely as the cosine of the dip, and directly as the intensity. Now
as the intensity doubles between the equator and the pole, it is obvious
that its variation must by no means be omitted in the computation ;
and a reference tn the experiments with the horizontal needles at New
York and at London will suffice to shew, that the magnitude of the
horizontal force cannot be assumed to vary as a function alone of the ob-
served dip, as is done in Dr. Young's " Table of corrections for clearing
the compass of the regular effect of a ship's permanent attraction," pub-
lished in the Journal of the Royal Institution, vol. ix., page 375, without
incurring occasionally very considerable error. The dip at New York
being 73°, and at London 70°, the natural force acting on the horizontal
needle should be reduced at New York, according to that computation,
in the ratio of 0.85, to 1 in London, and the influence of the disturbing
force proportionally increased ; whereas, the experiments shew that the
natural horizontal force is actuafly greater at New York than in London
(in the proportion of 1.1 to 1), notwithstanding the increase of three
degrees in the inclination of the dip ; and it is so because the absolute
IN THE INTENSITY OF TERRESTRIAL MAGNETISM. 499
force of magnetic attraction is greater at New York in the proportion of
1.96 to 1.62 in London, as shewn by experiment, instead of being in the
proportion of 1 .78 to 1 .72, in which it would be inferred to vary by the
author of the article in the Journal of the Institution. The effect of the
increased, instead of diminished, magnitude of the natural force acting on
the compass needle at New York, in comparison with London and its
vicinity, was further obvious in the amount of the disturbing influence of
the iron in the Pheasant, which was observed by Captain Clavering to be
less at New York than in the River Thames, notwithstanding the differ-
ence in the dip. In fact, if the maximum disturbance at the Nore
were 16°, it should be augmented to upwards of 18° by the table of
corrections which has been referred to, but under the actual magnetic
circumstances was really reduced to little more than 1 5°. A much stronger
practical example of error produced by neglecting the consideration of the
actual intensity might doubtless be furnished by situations of equal dip,
chosen in the North Sea and in the Gulf or River St. Lawrence ; and is
the reason why comparatively so much fewer complaints have been made of
the errors of the compasses in the latter navigation, than might have been
expected from the amount of the dip in the vicinity of the St. Lawrence.
It is indeed a fortunate circumstance for navigation generally, that the
amount of the dip of the needle is not always commensurate with that of
the intensity of the force ; and that the dips of greatest magnitude in both
hemispheres are confined to regions, which, from other natural causes, are
rarely traversed. Had the dip, for instance, in the West Indies, in the
homeward passage from thence by the course of the Gulf Stream, and
o-enerally on the coasts of the United States and of the British North
American possessions, been in correspondence with the intensity, the
irregularities in the direction of the compass needles would have proved
a most serious embarrassment, instead of being a consideration of very
little practical importance, in the navigation of those extensive and
greatly-frequented districts of the ocean.
3 s 2
500 EXPERIMENTS FOR DETERMINING THE VARIATION
Observations on the Diurnal Oscillation of the Horizontal Needle at
Hammerfest and Spitsbergen.
The few satisfactory observations which time and opportunity enabled me to
make on the diurnal oscillation of the needle, are appended to the preceding
memoir, in the hope that, from the localities in which they were made, and
I may venture to add from the extreme care that was taken to obtain results
worthy of confidence, they may prove of service to those persons who are
engaged in the investigation of the nature and causes of that phenomenon.
The observations were made with a very complete and delicate
apparatus, the property of Mr. Browne, made by Mr. DoUond. The
needle is suspended by a silk line of several inches in length, passing
over a pulley, and having a weight attached to the other extremity, which
may be either a counterpoise for the whole weight of the needle, or for a
portion of it, so that the weight may be either partially or entirely re-
lieved from the central pivot on which the needle is otherwise supported ;
the graduated circle is of seven inches diameter, and is divided into
spaces of ten minutes, which are again sub-divided to single seconds by
micrometer wires in the field of two compound microscopes, one of which
is fixed to see the north end, and the other the south end of the needle, at
the same time with the nearest divisions of the circle. The adjustments
required are, — of the horizontality of the circle, and of the needle when
suspended, — the freedom from tension in the silk suspension, — and the
coincidence of the micrometer wires, when at zero, with the nearest primary
division to the indication of the needle. The whole apparatus requires
to stand on an insulated and very firm support, and to be approached,
and the micrometer screws touched, with great caution. It was protected
from the weather by a circular canvass tent, of which the wood work was
copper fastened ; and situations were selected for the tent, where the
needle might be undisturbed by accidental visitors. Both ends of the
needle were observed, but the movements of the north end alone recorded,
IN THE INTENSITY OF TERRESTRIAL MAGNETISM.
501
as those of the south end corresponded, in consequence of the counterpoise
being rather less than the weight of the needle. The primary division
with which the micrometer wire coincided when at zero, was to the west
of the north end of the needle, both at Hammerfest and Spitzbergen ; so
that the higher numbers of the registry indicate its greatest oscillation
to the eastward, and the lower numbers the limit to the westward. The
following tables comprise the observations.
OBSERVATIONS on the DIURNAL OSCILLATION
of a NEEDLE SUSPENDED
HORIZONTALLY.— Hammerfest,
June, lS-23
Latitude 70° 40' N. Dip 77° 13' N. Variation 1 1° 26' W.
June
12th
1 3th
14th
15th
16th
17th
18th
19th
20th
2Ist
22d
2E
° %
Mean Place
of Hie
Needleattht
respeclive
hours.
Deviation of
the North end
of the Needle
from its average
Mean Place.
H.
6 A.M.
• "
. '/ t It
' "
'.." 12 00
' "
10 30
12 10
12 10
10 00
5
I'l i"i
2 14 Ey.
n „
■•
.. 12 00
10 30
2
11 15
2 18
9 „
13 50 12 00
10 55
n 20
10 00
5
11 37
2 41
10i„
12 25 12 00
12 00
11 25 10 40
9 10
9 15
U 00
8
10 59
2 02
Noon.
3 00
4 45
9 30
8 50 5 00
9 15
5 23
6 43
6 16
5 08
10
6 23
2 34 Wf.
14 P.M.
3 20
••
8 40
8 20 7 40
2 50
6 43
5 45
7
6 11
2 46
3 ,.
5 00
4 45
8 00
8 20 7 45
5 30 3 40
6 43
6 14
9
6 15
2 42
4| ,,
6 30
4 00
7 30
8 50 7 00
6 30 5 23
6 43
6 30
9
6 34
2 23
6 „
8 10
4 40
8 20
7 00 8 25
8 20
8 IS
7 34
6 40
9
7 30
1 27
Ti „
8 20
7 00
5 00
9 10
6 .30 8 25
7 30
8 40
7 34
6 40
10
7 29
1 28
9 „
8 20
5 00
5 40
8 20
8 00 8 25
7 30
8 40
7 31
6 40
10
7 25
1 52
\0h „
9 30
8 30
8 20
8 00 ' ..
8 30
9 00
8 40
C 40
8
8 24
0 S3
Midnight.
12 45
12 20
21 30*
8 40
8 00 1 . .
9 40
9 30
8 40
6 40
8
9 32
0 35 Er.
IJ A.M.
••
12 00
••
10 30 1 . .
9 40
10 07
8 40
5
10 II
1 14
s „
12 00
10 50
10 30 , . .
o
11 07
2 10
4J „
12 10
11 00 ..
1
12 00
11 00
9 25
5
11 05
2 08
Me*n Place of
the Needle .
8 57
• There
direction a
wlien I eiu
d.iy, at 104
occurred in
ippears r
tlie sam
•red it w
A.M., i
tbe ten
0 reason to doabt, that the deviation of the needle at midnight of the
e hour, arose trotn some natural c.nise. No one had been ne.ir llie Obst
ith tile usual care to avoid disturbance, I found the needle perfectly ste;
had returned of its own accord to its ordinary indication. This observe
lays, bas been omitted in the Mean.
I4lh 10 or 12 min
rvatory Tent sine*
rly at the recordet
lion, being the on
ties to
ll.ep
divis
ly irre
the e.istwar*
receding obst
on; and on
gularity of a
of itP usual
rvHtii'ii, aud
he folluwing
niuuiit which
502
EXPERIMENTS FOR DETERMINING THE VARIATION, ^C.
OBSERVATIONS on the DIURNAL OSCILLATION of a NEEDLE SUSPENDED
HORIZONTALLY.— Spitzbergen, July, 1S23.
Lat. 79° 50' N. Dip 80° !0' N. Variation 25° 12' W.
■^■^^— -
i-
July
4th
5th
6th
7th
8th *
9th
10th
11th
ii
Mean TLice Deviation of
of llie tile Noitii end
•Needle .at tiie of tiie Neeriie
respective from its average
lioura. Mean Place.
, „
* „
/ rr
/ //
/ /.
r ff
1 '/
, /.
, „
6 A.M.
n „
9 ,,
10 34
10 00
9 .30
10 20
10 20
10 15
3
10 23
2 42 Ey.
10 18
3
10 13
2 32 „
8 56
9 30
9 00
4
9 14
1 S3 „
10| .,
8 30
7 40
8 08
8 30
7 28
5
8 03
0 22 „
Noon.
7 SO
6 00
7 35
8 00
7 58
5
7 25
0 16 Ws.
IJ P.M.
4 44
6 00
6 25
6 30
5 48
5
5 53
1 48 ,,
3 ,,
4 35
6 20
6 SO
5 44
5 12
. . .
5
5 41
2 00 „
4i „
3 35
5 30
6 30
5 53
5 08
5 42
6
5 23
2 IS ,,
6 .,
5 08
5 07
5 43
5 53
4 54
4 53
5 31
7
5 18
2 23 „
n »
4 13
5 07
S 40
0 12
5 27
5
4 56
2 45 „
9 „
4 13
4 35
6 50
5 44
4
5 20
2 21 „
lOi „
6 30
6 33
6 SO
7 20
6 14
G 20
6 52
7
6 37
1 04 „
Midnight.
7 37
7 20
8 50
8 00
8 00
. . .
5
7 57"'
0 16 EJ.
•J A.M.
3 „
8 50
U 36
8 45
9 34
3
9 03
1 22 .,
11 37
10 46
10 37
10 30
10 15
9 14
7
10 40
1 59 ,,
4J „
11 50
10 50
11 30
10 15
9 31
12 00
10 20
7
10 54
2 13 „
Mean Place of the Needle .
7 41
• Snn eclipsed at 7 A.M.
503
ATMOSPHERICAL NOTICES.
On the Depression of the Horizon of the Sea over the Gulf Stream.
In estimating the depression of the horizon of the sea, corresponding to
the different heights of an observer's eye, the horizon is supposed to be
raised by terrestrial refraction one-fourteenth part of the depression due
to the spherical figure of the earth; and the corrections for different
heights, rigorously computed from the dimensions of the earth, are re-
duced, accordingly, in that proportion, in the tables of the most approved
authorities. Experience has shewn that, in general, when the tempe-
rature of the air is colder than that of the surface of the sea, the tabular
depressions, so computed and reduced, are in error, in defect, — and when
the air is warmer than the sea, in excess, — of the true depression : the
proportion of the error to the difference of temperature being, however,
too irregular, and the inferences themselves subject to exceptions of too
decided a character, to allow any practical rule to be established for
a corresponding allowance in correction. So long as the error of the
tables is confined to a few seconds in amount, its occurrence may be
safely disregarded in all the ordinary purposes of navigation; but it
was a question, only to be solved by experiment, whether in cases
of an extreme difference between the temperatures of the air and
water, the amount of error might not be so considerable as to require
attention, especially in deducing a ship's place by chronometrical ob-
servations within three hours of noon. It was for the purpose of having
504 ATMOSPHERICAL NOTICES.
this question tried in the Gulf Stream, where the sea is frequently many
degrees warmer than the air, that Dr. Wollaston contrived the dip
sector, an instrument now too well known to need description, but which,
from accidental circumstances, had not been applied in its original de-
sign until the present occasion.
The dip sector which I employed was the property of the Admiralty,
and was one of those originally made for the northern expeditions ; pre-
viously to my leaving England in 1821, I had it fitted with a telescope of
much larger field than before, so that the spaces of the opposite horizons
to be brought into contact were greatly augmented, and the observations
rendered thereby much more exact ; with the instrument thus improved,
used under proper circumstances, and with due repetition, the results
may be confided into less than five seconds.
The following table presents an abstract of the observations, by which
it will be seen, that so far as their evidence can determine, a navigator
may be right nine times in ten, in apprehending a tabular error in defect
when the sea is warmer than the air ; but that with differences in the
temperature of the air and water, frequently amounting to between 10
and 20 degrees, and once even as great as 29 degrees (the sea being
always the warmer), the error of the tables was not found even in a
single instance so great as two minutes.
ATMOSPHERICAL NOTICES.
505
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3 T
506 ATMO^ilMIERKJAr. NOTICES,
0)1 the Iiiteimlj/ in Effect of the RarJiatio/i uf Heat in the Atniofiphere, at
Heights, and at the Level of the Sea.
The following attempt to compare the heat produced by the radiant
power of the sun at the level of the sea and at a considerable elevation, —
and, conversely, the cooling influence of nocturnal radiation in a calm
and clear sky, — was made at Jamaica, The stations selected for the ex-
periment were on the Glacis of Fort Charles at Port Royal at an eleva-
tion of 8 feet, and on a plateau near the summit of the ridge of the Port
Royal Mountains, 4080 feet above the sea.
The thermometers employed to measure the opposite extremes of the
radiating influences, were a mercurial thermometer, having an index re-
gistering the maximum, and a spirit thermometer, having an index regis-
tering the minimum of heat ; the stems only were attached to scales, and
the bulbs were coated with lamp-black and covered with black wool. The
same thermometers were used at both stations, and were placed for ex-
posure on thick vegetation, by the filaments of which they were supported
horizontally, without being screened ; the vegetation on the mountain was
meadow grass, and at Port Royal the plant called TibuUus Maximus,
by which the ground between Fort Charles and the extremity of the Point
is over run. The exposure to the heavens was equally perfect in both
cases; the height above the ground, at which the thermometers were
supported by the vegetation on the mountain, was between three and
four inches, and at Port Royal about ten inches.
The extremes of the true atmospheric temperature, the maximum in
the day and the minimum at night, were registered by a thermometer
suspended at about five feet above the ground, in a situation shaded from
the heavens by a roof, but open in all other directions ; the thermometer
ATMOSPHERICAL NOTICES. 507
was enclosed in an highly-polished metaUic cyhnder of eight inches dia-
meter, protecting it from the influence of radiation from surrounding
bodies, and pierced with large holes in the top and bottom to admit a
thorough draft.
The observations, of which the particulars are collected in a table,
shew, that whilst a blackened thermometer, exposed during six days to
the sun at the level of the sea, did not rise higher on any occasion than
36.5 above the temperature of the surrounding atmosphere, the same
thermometer similarly exposed at an elevation of 40S0 feet, rose on a
single day of experiment 59 degrees higher than the surrounding atmo-
sphere ; and that, notwithstanding the reduction at 4080 feet of 13 degrees
in the temperature of the atmospheric medium in which the thermometer
was exposed, and which medium was constantly operating in counter-
action of the measure of heat produced by the absorption of the rays, the
exposed thermometer was actually nine degrees higher on the one day
in the mountains than its maximum had been in any one of the six days
at the level of the sea. It is also shewn, that whilst a thermometer,
fairly exposed to the heavens at night, at the level of the sea, fell on the
average of seven nights nine degrees below the temperature shown by a
thermometer protected from radiation into space (the greatest partial
effect being 11.5 degrees), the same thermometer similarly exposed on a
single night at 4080 feet, fell eighteen degrees below the protected
thermometer. And thus, that the vegetation on which the thermometer
was placed was respectively subject, — at Port Royal, to a difference of
55°. 5, — and in the mountains to a difference of 77°, — of temperature in
each twenty-four hours ; evidencing a far greater intensity in the action
of radiation at the elevation, than at the level of the sea.
The circumstances of the weather were favourable for the experiments
at both stations ; that is to say, the weather was clear and calm during a
portion of each day and of each night.
3 T 2
508
ATMOSPHERICAL NOTICES.
EXPERIMENTS upon SOLAR and TERRESTRIAL RADIATION
at Jamaica.
On tlie Glacis of Fort Charles at Port Royal, 8 feet above the Sea.
DATE.
DAY OBSERVATIONS.
Maximutn of Heat.
NIGHT OBSERVATIONS.
Minimum of Heat.
Extreme Differences
in each 24 boms.
Blackened
Therm,
in the 8un.
Atmosph.
Temp.
Difference.
Blackened
Therm,
exposed.
Atmosph.
Temp.
Difference.
Of the
exposed
Therm.
Of the
Atmosph.
o
o
o
o
0
0
0
o
Oct. 25
122
86
36
72
76
4
50
10
,, 26
123
87
36
69
76
7
54
11
>. 27
122
86
36
65
76
11
57
10
28
122
86
36
66
76
10
56
10
., 29
123
86.5
36.5
65
76.5
11.5
58
10
„ 30
123
86.5
36.5
65
76
11
58
10
Nov. 3
67
76
9
Means .
122.5
86.3*
36.2
67
76
9
55.5
10.25
Ou a plateau near the summit of the Port Royal Mountains, 4080 feet above the Sea.
Nov. 1
132
73
59
45
63
18
77
10
• A Diercnrial thermometer snspended freely in the air, about live feet above the ground and ia the 8un,
was carefully observed at intervals of the fore and afternoon, from the 25th lo the 301h of Oct., and was
never seen to rise higher than 92% being a difference of 6" Faht. above the shaded thermometer, occa-
sioned by the absorption of the rays in the bulb, which was naked and not blackened. This thermometer
usually attained 9^^ at 10 A.M., before the sea breeze eet in : on the commencement of the breeze it fell,
but regained the same height in the afternoon, although the breeze had freshened intermediately.
The evidence which the preceding experiments furnish, of the greater
intensity in the effect of the sun's rays at an elevation than at the level
of the sea, was further strengthened by the indications of a differential
thermometer in vacuo exposed to the sun at both stations. The sentient-
ball of this thermometer was of dark-coloured glass, designed to ab-
sorb the rays ; the other ball was pellucid, and was protected by a
double case of polished silver, with no part of which it was in contact :
the whole instrument was enclosed in a glass cylinder hermetically
ATMOSPHERICAL NOTICES.
509
sealed at the lower end, and containing a tolerable vacuum. The degrees
of the thermometric scale were millesimal, the interval between the boil-
ing and freezing of water being divided into 1000 degrees. On placing
the thermometer in a fair exposure to the sun, and on removing the
wooden cover by which it was usually protected, the fluid in the stem
adjoining the sentient ball fell rapidly, until it reached an amount propor-
tioned to the influence to which the thermometer was subjected, when it
remained stationary for some minutes. This amount being registered,
ihe cover was restored and the instrument re-placed in a secure and
shaded situation.
EXPERIIVIENTS upon SOLAR RADIATION with a DIFFERENTIAL THERMOMETER
in VACUO at Jamaica.
AT PORT ROYAL.
AT AN ELEVATION OF 4080 FEET.
Date.
Hoori.
Therm.
Effect pro-
duced in
Remarks.
Date.
Hours.
Therm.
Effect pro-
duced in
Reuarks.
Oct. 24
noon.
o
88
Strong breeze, very clear.
Nov. 1
8 50A.M.
74
1| min.
Faint haze.
„ 21
li P.M.
88
do. do.
„ 1
9 50 „
100
\\ min.
Clear.
„ 26
91 A.M.
82
Calm. do.
,. 1
10 45 „
84
14 min.
Light clouds.
„ 26
noon.
88
2 min.
Fresh sea-breeze.
„ 1
11 45 „
no
I^ min.
Very clear.
„ 29
noon.
90
2 min
Almost calm, clear.
„ 29
2 P.M.
86
2 min.
Freshening, clear.
„ 30
10 A.M.
88
2 min.
Calm, very clear.
„ 30
4 P.M.
91
2 min.
Very strong sea-breeze.
„ 30
H „
7 1
2 min.
do. do.
Nov. 3
8 A.M.
68
Calm and clear.
„ 3
9 „
82
do.
„ 7
7 „
48
do.
POSTSCRIPT.
Juno, 1825.
An intention having been expressed in page 186, of appending, at the
close of this volume, a notice of a comparison of the thermometer em-
ployed in the pendulum experiments, v^^ith a standard thermometer which
was understood to be in preparation under the superintendence of the
members of a committee of the Royal Society, in the expectation that
the completion of the standard would be accomplished before the pub-
lication of the experiments, — it is necessary to state, in explanation of
the non-fulfilment of that intention, that no such standard thermometer
has yet been completed.
lONDON
PRINTED BY W : CLOWES
Northumberlaad-court.
/
r
BOSTON PUBLIC LIBRARY
3 9999 06561 040 2
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