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Full text of "An account of experiments to determine the figure of the earth : by means of the pendulum vibrating seconds in different latitudes, as well as on various other subjects of philosophical inquiry"

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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 





















^ 


?c 


tN 


CTl 


CD 












c* 




fl 




— 2 (N 


. ; 


• 


• 


• 




• 


r- 


"^ 


rr 


»/5 




I 


^ 


• 


' 




« 


o 




























O 












o 


a> 










































^ 


^ 














„ 


CO 


o* 




CO 














0) 




^^ ^ ^ 


• 


• 


. 


• 


• 


• 


t- 


•^ 


~r 


»C 


■^ 


• 


• 




• 


• 


»-o 


o 


X> 




< 














o 


o 


o 


o 


o 












o 


II 


CO 

H 

% 




















<n 


05 


CN 


CO 












CM 






O e — ' 


- 


. 


. 


• 


* 




>- 


TJ- 


*o 


■^ 




• 


- 




• 




to 






CO - <r5 


Oi 












o 


o 


o 


o 


o 












o 


T3 
CO 




a> o o 


, 








. 












CD 

-7- 


, 






. 










r- 




»o 




<N - CO 


to " 












o 


o 


o 


O 


O 












o 
















c* 


00 


o* 


■^ 




oa 












b- 


aj 


S 
P 




CO o<^ 


• 




■ 


> 


> 


*- 


CD 






t^ 




■ 


• 


• 


• 


. 


CD 




C-l 2 <M 






' 




' 


o 


o 


o 


o 


o 


o 


" 


' 


* 






o 




CO 








































CD 
















o» 


00 


(N 


-H 




a 












t~ 


d 




1> o 00 


• 


• 


. 


• 




r- 


Cl^ 


CD 


CO 


t- 


CO 




• 


• 






CD 


1! 


■* 




<N - tN 












o 


O 


O 


o 


o 


o 












o 


-D 


o 








































K- 


^ 
















CN 






T 
















t- 


r- 

CC' 




CO o t~- 




. 








t- 


CO 


CD 


CT 


r- 


^ 












CO 


0) 




(N - C) 












O 


o 


O 


O 


O 


o 












o 




0) 










































fl 


(N 














CN 


X 








** 












CO 




c 


CO 


f 'o" CD 


. 










r- 


CO 


— ■ 


o 


<N 


o 


• 




■ 


• 


• 


o 




--^ 


CN - C^ 


71 * 


" 


' 


* 




^ 




_ 


^ 


^ 


„ 


* 




• 


* 








a 


'u 
























































CJO 


CO 


CO 


— 


CO 


Tf 




w 




0* 




a^ 


CO c. Tf 


• 


. 


- 


• 




. 


C4 


•o 


o 


o 


o 


o 


o 


^ 


o 


. 






D 


< 


CM - <N 


M • 


• 


• 


* 




' 


„ 


^ 


r-t 


_^ 


^ 


^ 


„ 


^ 


— ! 


" 


_ 




^ 


Urn 
O 






































o 




















GO 


CO 


00 


T^ 


GO 


■^ 




w 




ot 






C) CO 








. 


. 


. 


CN 


iO 


o 


C' 




o 


o 


— ' 


o 






r- 


H 


(1) 

T3 


cr» - iM 


m 












— 


- 


^ 


— 


^ 


— 


— 


— 


- 




- 


o 
















t- 


CO 


o 


CO 


-f 


CO 


-t* 




OJ 






Ji 


— o <N 
CO - CN 


« • 


• 


; 


• 


* 


• 


o 


o 


o 


o 








^ 


o 


* 


o 


01 
J3 


























































, 1 


CO 


CO 


rr 


00 


^ 




<N 




QO 




O 

o 


O o — 


• 


. 


a 


> 


• 


■ 


t- 


t* 


o 


o 


o 






^" 




• 


C5 


CAi 


CN " C) 


tn 












o 


o 


-- 


- 


- 


^ 


-' 


- 


~ 




o 
































































f 


















02 o O 


• 


* 


> 


. 




. 


t- 


t- 


o 


o 


o 


o 


o 


-H 


o 




Ol 


' ' 


O 


o 


— . 2 ^ 














o 


o 


-- 


-- 


^ 


-^ 


- 


- 


— 




o 












































t^ 


o 






















r- 


CC' 


-r 


-f 


so 






't 






** o tj> 


. 


. 




• 


• 


• 


• 


. 


. 


CO 


to 


CO 


CO 


CO 


iT- 


• 


CO 




Q 


J= 




m * 


• 




' 


* 


" 


* 


" 




o 


o 


o 


o 


Cfc 


o 




o 
















































»— 


"^ 


rf 


00 


« 


»^ 








ifi 


d 


as 


CO 


»o 


00 


00 










CO 5 ^ 


CO 


00 


00 


t- 






• 


• 




Cl 


o 


as 


Oi 


03 


a 


Oi 


Oi 










"o 


o 


o 


o 


o 


O 








C' 


-- 


o 


o 


O 


o 


o 


o 














































1^ 


•r 


^ 


00 


o» 


r- 










o 


C3 


CD 


»n 






e* 


Vj 




CO o t*' 


00 


00 

o 


00 

o 


o 


00 

o 


00 

o 


• 


• 




o 


o 


o 


o 


ai 
d 


d 


OS 

o 


o 


CO 

o 






•^ 




<X) 












•/5 


Cl 




en 




00 






h-9 




-1 o CO 


00 


CO 


CO 


t- 


00 


00 


> 


• 




O 


o 


Oi 


a 


05 


Oi 


OS 


as 


II 


PS 






"o 


o 


o 


o 


o 


o 








o 


- 


o 


o 


o 


o 


o 


o 


2 








































0^ 














00 












Cs 


c^ 




iO 


00 






T3 




O o — 


--^ 


1-" 


— * 


•-' 




— 


• 


• 






o 


Oi 


03 


o 


o> 


00 


o 


03 


U 






OT ^ 


^ 


J, 


^ 


— 


^ 


* 


' 


' 


o 


^ 


o 


o 


o 


o 


C' 


J 


iZ3 








































o 
















































-^ 


00 


■^ 










« 


Oi 


o* 


CO 


U!» 


00 


00 


»r> 








o^sS 




■^ 


CD 


lO 


tD 


lO 


; 


; 


; 


o 


o 


a> 


Ci 


o 


Cl 


Ol 


0» 




k-H 








^ 


•"■ 


"^ 


■"• 


^" 










"" 


o 


O 


o 


o 


o 


^ 




1— 1 






• 


• 


; 




: 


; 


; 


I 


; 


* 


I 


• 




^ 


: 


• 




' 


^ 


Ed 

n 






i 


"? 


O 


1 


2 

"c. 
o 


.2 

.c 
o 


S 
O 


'3 


_3 


'c 


'c 

i 


o 


a 
o 
>-* 
o 




> 


2 
"> 


1 












































H 






U 


p: 


O 


o 


o 


O 


O 


o 


(» 






o 


Oh 


fri 






t3 c 



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. 








S. 







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] 

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 







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. 


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 


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 







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. 







M. s. 


M. S. 


H. M. S. 


o 





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. 







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. 







M. S. 


M. S. 


H. M. s. 








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 




+2 
+ 2 
-7 


/ „ 
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 



-2 
+ 1 
-3 


/ 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 
18 51.5 



-1-4 


-2 
+5 
+5 



+3 


-3 
+ 5 
+ 4 


, <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 


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 





+ 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 

+ 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 

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 


+5 
-2 
-2 



+2 

+ 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 



-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 


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 

-3 
-1 


— 2 
+ 1 
-I 

-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 



-6 
-5 
+2 
+ 1 

-1 



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 


-1 


— 2 
+5 
-5 


-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 

-3 
-2 
-4 



-4 

-4 
-2 
-4 



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 



+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 .... 


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 



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 


— 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 


+ 2 
-5 
-2 


+6 
+8 

+ 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 




+ 3 
-4 
+4 
-6 




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 




+7 
+5 
-2 
-2 
— 2 


-1 
+9 
+7 


-4 




. .. 

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 



+ 8 
+3 
-9 

-2 




+ 7 
+ 2 
-10 
-I 




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 


-7 


+2 


+ 1 

+4 

-1 

-8 






. // 

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 





-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 


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 




+n 

— 4 

-2 

-6 




-1 
+ 4 
-6 
-3 
-8 



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 



+ 10 

-I 

-1 


-2 



f8 
-3 
-3 





* ^/ 
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 



+4 
— 4 

-1 

-1 




-1 
+3 
-3 
-2 
+ 2 


-1 


. // 
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 



i 2 
-2 
+ 1 


-1 


-1 

-3 
+3 
-2 
-2 


/ « 
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 





— 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 


* 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 

— 5 
-4 


, .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 


» ' ,' „ 

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. 




+4 


-0 
-3 
+ 2 




+2 
2 
7 
5 




— 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 





5 55 41.8 


-5 


-5 


6 01 02 


+ 1 





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 


-2 

— o 



+ 2 
-3 



2 

-3 




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 

+ 2 
+ 5 
-6 
-1 


-7 

+ 2 
+ 5 
-6 
-1 

— 7 


/ // 
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 .... 


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 


-8 


-5 


-3 



-9 


-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 





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 





+ 1 
— 4 
+ 1 
-5 




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 



+2 
-3 
+ 6 
-9 





+ 1 
-4 
+6 
-9 




< ,/ 

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 


+5 





+2 

+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 








-I 

-2 




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 





-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 


-4 
+4 
-4 


-2 


-3 
+ 3 
-2 


. */ 

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 




-1 











— 2 








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 

+ 3 
+S 
-10 


-6 
+ 5 

+4 
+4 
-8 


^ /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 


+5 


-10 

+ 3 


-2 


+ 7 


-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 


* 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 


* 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 




+5 
-9 
+9 
-8 





+7 
-7 
+ 11 
-6 


* 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 


+4 



3 



Mean . . . 
True time . 

Chron. fast 



10 59 48.27 
8 02 42.17 



00.1 



•1 



4 
+2 


+5 





— 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 


+ 1 
+ 5 



+8 



-4 
+5 





+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 




-2 

+ 2 





-2 




-1 

+ 1 





-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 


+ 1 


+ 2 



+ S 


+ 2 





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 


O - /< 

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 

-4 
+ 5 


+3 
+3 


-2 
+7 


' " 
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 

+4 


+4 
-1 
+ 1 
+2 

+5 


/ /. 
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 


* 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 






-4 



+3 

+2 






-2 



+2 

+4 


' 
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 

+2 
-1 


-4 

+7 
+2 

+2 
-1 


' 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 






-5 

-2 

+3 








-6 

-1 

+ 3 




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 


+ 


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 


. 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 

-5 
-5 
-I 
+ 6 


+4 

-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 





+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 


+2 
+4 


-1 

+2 
-13 


+ 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 



+5 
-3 
+8 
-3 





+4 
-3 
+7 
-4 




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 



+ 1 
+ 3 
-14 
+2 





+4 
+4 
-14 
+ 3 




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 





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 





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 



+2 
+5 
+ 6 

-2 
-4 



+ 2 
+ 5 
+6 
-2 
-4 


t ,1 

First Vernier 215 51 40 
Second „ 51 15 
Third „ 52 00 
Fourth ,, 51 10 


Mean . . 221 34 48 
Level ... 
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 





Mean . . .12 06 38 
True time . 7 59 39.1 


+7 


+7 





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 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 

-5 







-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 


-4 




+ 5 
+4 
-7 


-2 




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 





-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 

-12 
+2 
+4 


+3 
-3 

-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 

+7 
-2 
-4 
+ 1 


-2 

+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 





+4 







+ 3 




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 




-6 
-4 
+7 
+3 




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 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 



-7 
+2 
-3 
+7 
+ 1 



-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 







+ 1 

+ 1 


+4 







+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 





+ 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 



+ 3 
+2 
+ 5 
-2 
-3 



+ 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 



+8 


-3 


-2 



+ 8 


— 3 


-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. 





+2 

+ 2 





-4 









+ 2 

+2 





-4 







.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 




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. 





4 

7 

+6 

-7 

+ 2 




-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 

-3 
-2 
+2 
-2 



+ 3 

-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 



-5 

-3 

-2 
+ 6 



-2 

-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 


+ 2 
+ 3 
+ 1 


+2 


+ 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 



+2 
+5 
-2 
-8 
-4 






+7 



-6 

-2 


' '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 

+ 5 
-3 
+2 


+ 6 
+ 2 

+ 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 



+2 
-3 
+ 7 
-4 





+3 
-2 
+7 
-4 




. /. 

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 




+ 1 
-3 
+ 3 
— 3 
+ 2 



Mean . . 
True time 



11 50 37.27 
7 43 12.1 



+ 3 




+ 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 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 






+5 





+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 



-5 

+ 7 



-4 



-4 

+ 7 

2 





+ 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 


-4 
-2 
+4 
+6 


+2 

-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 


















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. ... 


Mean. . . 11 47 04.53 
True time. 7 39 30.07 


+7 


+ 6 


Mean. . . 12 59 44.57 
True time . 7 52 09.97 








+6.5 
9 o"l 


384 16 42 





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°; '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 

-4 
-1 



-1 




— 2 




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 

-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 








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 







— 5 
+ 10 
+2 
+2 
+ 3 






-i 

+ 10 

+1 

+2 

+2 

+ 11 


. .. 

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 



-2 
+2 
-2 
-4 
-2 
+2 
+5 
+5 
— 2 



-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. ... 


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 

+3 
-3 


+3 
-3 
+ 1 

+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 







+2 







+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 




/ // 

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 





+3 








+2 




* " 
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 



+ 2 



-4 

+ 4 





+ 1 




, 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 * // 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 



-6 








-6 






' « 
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 



+4 


+2 
+5 





+4 


+2 
+5 




^ // 
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 . 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 



+5 

+2 



+ 6 


-3 


+ 5 

+ 3 


+ 5 


/ " 
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 



-2 
+5 



■hio 





-2 

+7 


+ 10 




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 



+ 3 
+5 


+5 
— 3 



+4 

+ 5 



+ 5 

— 2 


. // 
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 



-3 
— 3 


-2 
-6 



-3 
2 


-3 

6 


/ */ 
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 





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 




-8 



n 

-2 




-9 




-2 




/ /' 

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 



-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 





+11 





+4 




+ 12 


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 



+ 4 


+ 6 


— 2 



+5 


+ 7 


-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 

+3 
-4 
-2 



+4 



+3 
+ 6 

+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 



+2 

+6 

2 

2 



— 5 



+ 1 

+ 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 






+ 3 


-2 






+4 


-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 






-5 

-4 






-3 

-3 


, // 
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 


/ 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 







+ 15 
+3 









+ 15 
+ 3 




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. 




-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 


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 



-2 
+2 


-2 
— 6 




/ // 
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 



/ // 
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 






/ // 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 





-6 


-7 


-10 



+ 4 


/ // 
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 


+ 8 

+ 2 


+ 15 






-1 

-8 



+2 


/ /' 
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 


' " 
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° ; '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 


+7 




-8 

-2 

-1 








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 

+6 


-5 
+ 1 
-3 

— 5 

— 8 
-1 


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 




-2 



+ 8 
+ 10 
+ 10 



-10 




+ 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 






+ 12 

-0 

+3 








+ 1 

+4 

-8 


, 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 



— 2 

— 4 


/ // 
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 





+9 




— 2 
-6 




— I 



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 




■fio 

-f-1 

f3 


-\i 




+ 1 
-8 
-6 


/ „ 
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 


/ // 
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 



+ 3 


+8 
-10 
+ 7 



-6 



-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 





-2 



+7 




-10 


1 


First Vernier 235 06 50 
Second „ 07 00 
Third „ 07 30 
Fourth „ 06 50 


Mean ... 131 35 30 
Index . . .+341 01 46 
Level ... 


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 


'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 

— 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 








+ 8 

-9 

+5 






-1 

-0 
-4 


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 ... 


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 





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 


+9 


+ 1 


— 9 
-4 


-2 


-10 


* " 
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 


-1 
+2 
-7 
-4 


/ . 
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 







-1 







. // 

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 

+ 3 
+ 6 
+3 



-3 

-5 
-2 
-5 



/ .' 
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 


/ // 








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 






+2 
+2 






-6 
-7 


/ ,/ 

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 



+9 


-6 

-8 

-7 








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 / // 

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. 





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 ; 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 



+ 7 


+5 


+ 6 



+ 3 



+ 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 


-2 
+4 
+3 










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 





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 



+ 5 



-5 
-5 


-6 
— 3 




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 



+ 2 
-1 
+6 


-2 



-5 
+5 

-1 



-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 

+6 



-I 
+ 1 
— 2 


-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 



+ 3 




-3 












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 ... 


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 





.372 11 34 





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 












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 





+5 

-5 

+ 3 












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 





+ 17 



— 5 
-11 


-1 
-5 





-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. 





+5 





— 5 

+7 



+ 14 







+2 





-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 . . 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 




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 



-3 
-1 
-2 
+2 
-5 



' " 
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 



+ 12 
-2 


+7 





+ 4 
-10 


-2 
-9 


/ « 
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 ... 


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 





.397 54 17.5 


Chron. slow 44 51 .56 


Chron. slow 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} 44 50.85 
Clock Slow of the Chronometer . 09 26.4 




Clock Slow of Mean Time . 


... 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 



+ 3 
-7 


-9 
-5 


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 


















, /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 ... 


Mean. . . 4 37 07 
True time . 5 21 59.9 


+ 32 


-22 


Mean. . . 4 S3 14.6 
True time. 5 38 07.34 








+ 5 


392 47 09 





397 02 37 


Chron. slow 44 52.9 


Chron. slow 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 44 52.82 
Her . 08 42.4 










Clock Slow of Mean Time 


. . . 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 




-3 

-3 

-6 

-2 



-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 








-3 

-1 

-7 





-6 


/ 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 44 49.9 


Chron. slow 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,> 44 51.32 
ter . 07 16.2 




. . . 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 

+4 
+ T 
+2 
+6 


-3 


-6 
— 2 
—7 
-4 


/ ,/ 
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 44 49.14 


Observed Z.D. 65 40 23.6 
Ref. and Paral. + 2 03 
Semidiam. . —15 45.5 


. // o 
360-346 42 06=13 






True Z.D. . . 65 26 41 






Chronometer, Slow. 
Clock Slow of Ciiron 


H. M. S. 

. 44 49.14 
3meter 06 33.1 








Clock Slow of Mean ' 


rime 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 



+ 10 

+7 

+6 


— 2 


+ 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 

-I 
+8 
+8 


— 5 
-5 


-9 


+ 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 44 50.83 


Chron. slow 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 


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/ 4* ^O-^S 
neter . 11 12 




Clock Slow of Mean Time 


... 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 

+ 10 

-11 


-3 

-3 

-3 



+ 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 ... 


Mean . . 5 41 27.37 
True time. 6 26 20.3 


+27 


-27 





421 02 39 


Chron. slow 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. 
... 44 52.93 
jometer 11 56.8 






Clock Slow of Mean 1 


"ime . 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 



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 



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 


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 
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^ 
. 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 







^•S 
















■*f 


























s 




; 


* 








• 






• 


fr- 


*- 


»^ 


•o 


»- 




CO 


CO 
























CO 


CO 




co 


CO 


CO 


CO 


CO 




CD 


CD 




^ 






„ 


„ 


„ 


00 


f« 




















»« 






(N 


s< 


OJ 




r- 






-— 


05 


• 










• 




* 


• 


o 


C3 








<2 




co 


CO 


t- 


^* 


O 




















CO 


CO 


















































^ 
















_ 


_ 






, , 


,_ 




, 








e> 


s? 


ffl 












' 


t~ 


CO 


CO 


on 


t^ 


'^ 


o 


t- 


• 








lA 


s 


ti-2 
















CD 


CD 


CO 


>o 


v> 


co' 


>ft 


o 




CO <D 










































3 


CO 








-* 






t- 


« 




















GO 


»iO 




bO 


(M 


oi 


00 


00 


1^ 


r- 




to 




















00 
CD 


CO 
CO 






^2 
















^ 


00 


J- 


»o 






■^ 


—. 




a 


,_, 


35 


in 






• 


• 






CO 


t- 


CD 


o 

GO 


• 




t- 


o* 


• 


t~ 


*^ 




OJ 


2 














































































•& 

<! 


N 


e — 




—. 


_ 


,« 


« 


_ 


o* 




















X 






<M 


^< 


ai 


"■ 




r~ 


"_ 


GO 


Ci 














* 






Ot 






ei5 








t- 


r- 


cc 


»* 


t- 


h- 




















t- 


r- 






















_ 




^ 


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1 


>o 






o» 


a 


N 


















o 


co 


-; 


— ' 






00 


00 




r- 


r- 


>» 


o 


0« 


















00 


00 


l- 


f- 






*- 


t* 




i- 




Q 


* 


o 








































;-H 








































„ 


CO 


s5 






**- 


-^ 


,_ 


00 


co 




















in> 


(^ 




CO 

<* 

6 


W 


tn 


• 


00 


o 

00 


t- 


a. 




• 


• 




• 


• 


• 








t^ 


t^ 


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_: 


















GO 




■^ 








>ri 




t^ 


O 


a 


o 


S:; 


rr 


• 






• 






o 




co 


CM 




: 


00 


00 


' 


o 


o 


GO 
CO 




w 


Co 


































X 






o 








































50 


.•s 






00 


CO 




^ 






















CD 


X 


H 


(N 


S^ 


W 


• 


CO 


CO 


^ 


■— 


CO 








• 


• 


' 




• 


" 






o 


H 




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l^ 


t- 


t- 


t- 


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t- 


t- 


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g 










































o 










































O 




















'^ 




00 








x 




00 r- 


-r 




o 


>-1 
0« 


s? 

»^": 


» 








; 






<£> 


CO 


CO 

CD 


O 
CD 






CO* 


CO 

KO 


CO* CD 


o 


o 




o 


2 








































a 








































PS 


■* 


^ 






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X 


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r-> 


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W 


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CD 


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cc 


























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<: 3 






cc 


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lO 


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rf3 


CO 

to 




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_. 






^ 








o* 


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03 




* 




• 






^ 


CI 


(N 


»C 






Cl 


f 


* 






c 


o 


IN 


~ B 
















CO 


ir> 


»o 


U5 






ID 


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y 

^ 


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'T^ 


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— . 




cc 




















00 




(» 


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CR 




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to 




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t- 

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_; 
















^ 




00 










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X 




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M 


s? 










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a 


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Cl 


■•r 










Cm 


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0« 


e- = 
















IT) 


m 


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V3 






lo 


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m 


lO 




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^ 


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00 


o* 




















^ 


CO 




(N 


s5 


3V 






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r- 


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O 




< = 






(Ti 


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CO 




















liO 


w 
























^ 










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if- 


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C5 


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CD 


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CO 






in 


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CD 




•^ 










































g 


S 


^^ 


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00 






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CD 


CD 




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•* 














































































^ , 






g^ 


































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1— 1 










































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2 










































^ 


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'S 








































•«! 


04 


5l 


n 






































M 










































fe; 


























































































• 






(2 








1 








Cm 

1 












o 




r 

5 






2 

1 


= 


o 


1 

c 
o 

C3 


o 




m 

3 
(-• 
3 




■f 


@ 


j 

o 


1 


8 
'5 


&0 


S .- 

o m 

■3 Uj 




' "i 






















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8 


t- 


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^ 




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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. 





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 
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. 







M. s. 


M. S. 


H. H. S. 








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 
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 


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 




32 


o 

51.5 




52 


o 

80 




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. 







M. S. 


M. S. 


H. M. 9. 








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. 








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 

1- 

. -o 

^ S 




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. 








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 




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. 







M. S. 


M. S. 


H. H. S. 








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. 





o 


S. 











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 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 






41.7 


M. S. 

53 16 


M. S. 

53 17 


H. M. S. 

U 53 16.5 


o 

1.311 





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 



'3 



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. 





51 


M. S. 

43 09 


M. S. 
43 14 


H. M. S. 

9 43 11.5 


s. 
1.32 





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 




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 


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 


9 50 


10 19 


10 48 28.5 


11 2 14 


11 30 


11 58 


12 27 


12 56 18 


2 48 33.5 


S 16 


3 44 


4 13 


4 42 42 


8 52 11 


9 20 


9 59 


10 28 


10 47 02 


2 9 01 


2 37 


3 05 


3 34 


4 3 37 


9 9 37.5 


9 38 


10 06 


10 35 


11 4 21.5 


1 35 52.5 


2 03 


2 32 


3 01 


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. 











M. S. 


M. 3. 


H. M. s 


o 





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. 







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 




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 


O 








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 





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 





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 





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. 




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. 




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 



+2 

+ 2 


-4 

+ 5 
-4 

+ 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 . . +^ 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 


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 


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. 








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 

-3 


+3 
+6 
+ 1 
-4 

-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 



+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 


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. 

28 49.6 
31 06 
32 36.4 
33 59.2 
35 46.4 
37 06.8 



Level. 



-5 







+ 2 

-1 









+ 3 

-2 



Mean. . . 


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 

+ 4 



+n 



-12 
+4 
-4 
+ 3 

+ 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. 


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 



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 




+8 





+8 

-0 



-2 




+ 1 




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 



+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 





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 





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. 


00 





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. 








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 





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 





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 





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 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 





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 




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. . — 
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. 

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 




. . . . 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 


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. 




24 42.3 


Junp lOtb Arcturu? 24 40.1 








Latitude . . 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 + 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 
31 

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 + 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. 








< << 


8 23 32 


3 14 


99 


— 7 


-9 




■ First Vernier . . .313 03 05 


8 26 45 


01 





+4 


+2 


Final. . . 


Second „ . . . . 02 50 
Third „ . . . . 03 30 


8 30 24 


3 38 


126 


+2 







Fourth , 03 30 


8 33 10 


6 24 


390 





— 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 . . . . - 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 





- 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 


57 


8 


- 8 


- 5 


Level .... —5 








- 3 














619 33 13.5 


12 53 53 

12 56 26 


6 34 
9 07 


410 
791 



— 3 


- 3 








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 
59 
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 



+ 1 

+2 

+ 6 

+2 

-1 







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. — 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 

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 — 
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 

+ 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 





-2 


S?9 


4-4 


+ 1 


220 


-2 


— 4 


12 


+5 


+3 


19 


-4 


-2 


172 


-7 


-9 


413 





_2 


998 





-3 


1551 


-3 






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 + 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 


- 1 
+ 5 
+ 11 

- 9 

- 3 

- 2 
+ 5 
+ 3 



+ 2 
+ 9 

- 11 

- 5 


+ 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 

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 


+ 12 

- 3 

- 1 
+ 5 

- 4 

- 1 
+ 9 


+ 2 



- 5 


+ 10 

- 5 

- 3 
+ 9 

- 6 

- 3 
+ 7 





-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 



+ 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 


- 4 
+ 2 

- 2 


+ 4 
+ 11 
+ 6 

- 7 

- 2 



- 7 
+ 2 



- 6 


- 4 


+ 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 
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 





+ 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 



47 

167 

350 

690 

1103 

1608 

2184 

3175 

4011 



Means. 



1132.2; 



- 2 
+ 9 

— 2 
+ 3 



— 5 
+ 3 

— 2 

— 2 
+ 3 

— 2 
+ 5 



- 1 
+ 7 

- 1 
+ 1 



- 7 
+ 1 

- 4 

- 3 
+ 1 


+ 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 
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 


+2 
-4 
+ 1 
-7 


+ 3 
+ 5 
+ 4 
+ 5 
-4 
-3 




+2 


+ 1 
-5 


-8 


+ 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 
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 



968 
2303 
2970 
3940 
6453 
7360 



-1 
+6 
-6 
-I 
~ 5 
+ 4 


-5 
— 5 


-4 
+8 
-7 
+ 7 

-6 

+7 
+ 2 
-1 
+ 6 
+ 7 



Means . 



3240.1 



-2 
+ 5 
-7 
-2 
-7 
+ 2 


-6 
-6 


-5 
+ 6 
-9 
+5 

-7 
+ 5 
+ 1 

+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 
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 



-I 

■+6 

-1 



-2 

+ 1 



+ 3 







+ 3 

-2 

+ 3 

+ 3 







+2 

+2 

-5 



-3 

+ 8 





+ 1 



-3 

-3 





+5 











+2 







+ 2 





-i-2 







+ 1 

+ 1 

— 3 



-I 

+ 6 





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 . . . . — 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 

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 





+ 5 

+5 





— 2 

-7 

-2 

+ 1 

+5 

+ 3 

-2 



+5 

+3 

+4 

-1 







-2 

+ 6 



+ 3 





+2 





-4 





+4 

+4 





-4 

-9 

-4 

+3 

+3 

+ 2 

-4 



+3 

+ 1 

+ 2 

-3 







-4 

+ 5 



+ 1 





-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 



. . 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 . . . - 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 






+3 
+2 


+9 
+7 


+6 
+ 7 
+8 
+8 






- 7 

- 7 
-10 



- 3 


- 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 










First Vernier . 


228 56 30 


18 13 13 


10 38 


1076 


+ 11 







Second „ . . . 


56 20 


18 15 32 
18 16 52 

18 19 02 


8 19 
6 59 

4 49 


658 
464 
221 






-11 





- 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 


33 


4 


+ 8 


- 4 


Final . . • 


Second „ . . . 
Third „ . . . 


37 00 

38 10 


18 23 14 
18 30 37 


1 23 
6 46 


18 
436 


- 9 



- I 





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 
- 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. 






/ " 


4 49 13 


14 46 


2075 










First Vernier . . . 128 22 40 


4 52 12 


11 47 


1321 


- 9 







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 



- 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 


45 


5 










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 



+ 10 


- 9 






Fourth „ . . . 
Mean .... 


31 20 


177 31 42.5 


5 13 24 


9 25 


844 


+ 10 





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 
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 





+ 3 





-10 

- 9 
-10 
+ 2 
+ 10 
+ 3 



- 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 




- 5 


+•6 



+ 5 


+ 5 


- 4 



- 5 

- 2 
+ 2 



- 3 


- 8 


+ 10 



+ 1 



+ I 






+ 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 


+ 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 

.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. 




+ 10 
+ 6 
+ 6 
+ 7 


+ 3 
+ 2 
+ 2 


+ 2 
+ 6 


+ 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 






+ 10 
1+0 
+ 10 
+ 10 
+ 2 
+ 10 
-10 

+11 

+ 2 







^ 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 . . . . + 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 










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 



+ 13 




+ 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 



- 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 










Second „ 


47 05 


11 1.5 -IS 
11 17 15 


3 48.5 
2 21.5 


138 
53 


+ 2 



- 7 



Final . .. 


Third „ 


47 30 


11 19 08 
1 1 20 36 


28.5 
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 

47 

1 33 

4 03 

5 31 
9 10 

10 49 
12 45 

14 26 



2010 
1625 
1117 

85 S 

535 

318 

140 

66 



23 

156 

289 

800 

1114 

1547 

1982 



+ 2 

+ 6 

+ 1 

+ 8 

+ 6 







+ 5 

+ 7 

+ 7 

+ 12 



+ 6 



+ 3 



- 6 

- 2 

- 7 

- 1 

- 2 

- 9 



- 3 

- 2 

- 2 
+ 4 



- 3 


- 5 



Means. Before Mid. 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 






+ 7 





+ 2 


+ 5 


+ 11 


+ 3 





+ 2 


+ 3 


+ 6 


+ 6 


+ 3 



2157.9 





- 2 


- 7 

- 3 
+ 2 

- 5 


- 7 

- 5 

- 2 

- 2 

- 5 

- 2 

- 6 

- 7 

- 8 
+ I 



- 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 . . 
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 










First Vernier . 


/ fl 

. 205 55 40 


23 17 03 
23 18 50 
23 20 25 


3 15.5 
I 28.5 
06.5 


101 

20 




+ 7 

+ 3 




- 1 

- 5 



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 

+ 2 
+ 7 


- 2 

- 8 
-6 



- 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 



+ 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 . + . 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 
+ 

+ 2 
+ S 
+ 10 
+■ 3 
+ 3 



- 6 

- 3 
+ 2 

- 3 


- 6 


+ 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 





+ 6 


1 17 16 


8 47 


734 


- 5 


+ 1 


1 19 22 


6 41 


425 


- I 


+ 5 


1 30 57 


4 54 


229 


- 6 





1 32 45 


6 42 


427 


- 1 


+ 5 


I 34 54 


8 52 


748 


- 6 





1 36 50 


10 47 


1107 


- 1 


+ 5 


1 38 33 


12 30 


1487 


- 2 


+ 4 


1 40 18 


14 15 


1932 


- 7 





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 

+ 6 
+2 
+4 
+ 2 
+8 


+ 9 
+ 8 
4-3 
+ 2 
+9 


+ 6 
+4 
+7 






2 

- 1 
-6 
-0 
-4 
-2 
-4 
+ 3 

+ 3 
+2 
-2 
-4 
+ 3 


-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 








Previous . • 


Third „ . . . 23 10 


6 57 30 

6 59 32 

7 01 02 


13 

2 15 

3 45 




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 










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 . . . + 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 








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^. 



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.)/ = 



— 0.002012 

— 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 . 






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 


= 







— 


00201 


+ 


X. 0.0000515 


+ 


y. 0.0000000 








- 


07593 


+ 


a. 0.0019464 


+ 


y. 0.0000038 








— 


7427S 


+ 


i-. 0.0190338 


+ 


y. 0.0003623 








— 


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 

24 41 


39.02074 


' 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 . . 





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 = 



350 



EXPERIMENTS FOR DETERMINING THE VARIATION 



0, 


.00201 


+ 


a. 0.0000515 


+ 


J/. 0.0000000 





.07593 


+ 


J. 0.0019464 


+ 


2/. 0.0000038 





.7427S 


+ 


X. 0.0190338 


+ 


y. 0.0003623 





.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 = 
0.20227 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' 

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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CD CTi 


X 


t^ 




<n 


Vi 


CM 


o 


CO 


o 


CO 


o 


W2 


oo 






-r 


CO 


CD 


to 


0» 




•-» 


o 


-H CN 


GO 


rj* 


TJ* 


TT 


v> 


o 




o 


>o 


o 


CM 


GO 


oo 


CM 


CM 


GO 


TP 


to 


o 


to 




!3 


s 


„ o 


o o 


O 


o 


00 


GO 


oo 


-I* 


•^ 


r- 


GO 


■^ 


-'J' 


'tf 


Oi 


Oi 


o 


o 


o 


o 


OJ 


X 




H 


° OS 


CI a 


Ci 


o 


o 


o 


o 


o 


o 




fr- 


t- 


fr- 


t" 


TP 


-^ 


X 


TP 

X 


■* 


■^ 


tj* 


TP 


OJ 
CJ 


•rajaqx 


° s 


^ ^ 


^ 


^ 


^ 




^ 


^ 


_ 


o 


o 


o 


o 


o 


X 


X 


X 


X 


X 


X 


o 


00 00 


X 


X 


X 


X 


X 

o 


X 


X 


X 


X 


X 


X 


X 


I:- 


fr- 


e^ 


t- 


I- 


r- 


b- 


>- 


3 

m 

Q 

X 




o 


o o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


i 

-a 
H 


i 




O CD 

o o 


o 
o 


o 

o 


o 
o 


o 

o 


o 
o 


o 
o 


o 

o 


o 
o 


Oi 
CD 


CI 
CT> 


OJ 

ci 


Oi 

ci 


o 
o 


o 
o 


o 
o 


o 


o 

o 


o 

CD 


o 
o 


o 

o 


n 


00 


CO 00 


oo 


oo 


oo 


oo 


CO 


00 


00 


CO 


CM 


0* 


o* 


CM 


GO 


CO 


GO 


GO 


GO 


GO 


CO 


GO 


GO 






















































3 


u 


■* r- 


lO t- 


Ci 


<N 


X 


04 


X 


./5 


X 


X 


CO 


o 


TP 


CD 


X 


t^ 


I—I 


CD 


CO 


CM 


X 


04 


o 




" w 


0» lO 


o 


■^ 


iO 




-5r 




0* 


QO 


o» 


W5 


'^ 


'^ 


CO 


»o 


Mi 


o 


to 


TP 


GO 


■V 


< 


fS 




CA 


«. -- 


Oi t- 


o» 


r- 


o 


CI 


t- 


CD 


•Tt< 


o 


CM 


X 


OJ 


^ 


o 


>o 


Vi 


o 


to 


CD 


, 


CD 


O 


--■ 


»c o 


o» 




CO 


o 




(N 


oo 


40 




—■ 


'^ 


■— ' 


-* 


oo 


CO 


GO 


TP 




TP 


o 


b1 


e<-> 


H 


a 


ft "?» 


t* 00 


o 


lO 


r- 


oo 


^ 


X 


Tf 


o 


CD 


o 


CN 


CD 


lo 


o 


h- 


-p 


o 


»^ 


X 


00 


% 


o 
3 




CA 


O CO 


»o »o 


Tf 


■* 


'J' 


■V 


T* 


GO 


CO 


CO 


m 


^ 


Tf 


GO 


CO 


t- 


CD 


CO 


CO 


to 


to 


CD 






5 *^ 


t- eo 


CO 


03 


\n 


CO 


X 


Oi 


^ , 


0» 


«* 


>o 


CO 


OS 


2 


X 


r- 


to 


TP 


fr- 


X 


to 


'■^ 


u 






04 CO 


^- 


o 


W) 


o 


lO 


'Tf 


^H 




o» 


■^ 


'^f 


Tp 




CM 


lO 


oo 


to 


tO 




CO 






c 
o 


- o 


(N ir> 


X 


„ 


CO 


o 


»i2 


X 


CO 


t- 


Ci 


Oi 


•K 


o 


X 


to 


GO 


CM 


o 


o 


X 


Oi 




a> 


c 


(» 


lo ao 


o 


40 


■t 


o 


<N 


« 


o* 


o 


o* 


^ 


CO 


^" 


.— 


CM 


lO 


rp 


CM 


o 


o 


04 




o> 


o CO 


o »« 


Ci 


CM 


»^ 


^ 


CO 


ID 


en 


o 


CD 


CO 


Ci 


CO 


X 


"^ 


r-. 


t- 


00 


X 


o 


-# 




1 


< 




CM 


OO GO 


oo 


■^J" 


CN 


00 


00 


CO 


CO 


CO 


^ 


lO 


«0 


CO 


»o 


»o 


CO 


CD 


r- 


r- 


t- 


CO 




«i 


I "'• 


TJ" 0> 


CO 




t- 


GO 


CM 


« 


Tf 


X 


m 


C5 


CO 


X 


^ 


X 


r^ 


(M 


X 


>o 


to 
o* 


00 


r^ 


5 = 


fr- 


lO o* 


ci 


IT- 


co" 


X 


Tf 


t* 


Tf 


»o 


r- 


GO 


CO 


o 


-rf 


o 


oo" 


TP 


r- 


CM 


_^ 


CD 




0) 


"3 


o 


^ o 


■V 


^ 


o 


^ 


o» 




c>* 


o 


o 




o 


Tf 




■^ 


o 




'S" 




TP 


to 




^ 


£3 




GO 1?* 


05 


CD 


X 


^ 


o 


Tf 


o 


^ 




,^ 


o 


X 


CD 


X 


»- 


to 


CM 


CJ 


h- 


Ci 






* c« 


CO T?. 


*?• 


in 


>o 


o 


o 




c>» 


CM 




CM 


oo 


GO 




o 


o* 


GO 


Tp 


■^ 


GO 


CM 




c 


0-" 


O 


o o 




o 


GO 


^ 


Tj* 


-r 


-* 


t- 


'^ 


■^ 


■*?• 


■^ 


o 


o 


o 


o 


o 


o 


CJ 


CJ 








<2 


05 


OS Ol 


o 


Ci 


o 


o 


o 


o 


o 


]~^ 


t' 


»^ 


*-* 


t- 


U3 


»o 


-^ 


^ 


"^ 


f 


■^ 


■<*• 






^ W3 


U5 W 


w 


o 


o 


o 


o 


W5 


o 


»n 


o 


o 


o 


o 


o 


o 


»o 


to 


o 


o 


to 


to 






•3 


- 00 


o oo 


w 


CO 


CN 


■^ 


»o 


CM 


rM 


Tf 


00 




■^ 




»n 




"^ 




o* 


CO 




o 




u 


* -a 


* <3i 


CI '^ 


*^ 


^M 


t- 


1^ 


CM 


,_ 


f' 


Ci 


CO 


C4 


o 


'tf 


Tf 


■^r 


^ 


■<p 


o 


o 


CM 


t' 




2 


S.O 


■^ 


GO CO 


lO 


o 


CO 


o 


u? 


»o 


o 




^ 


CM 


o 


TP 


^ 


'^ 


(M 


00 


to 


to 


CO 


to 




o 


o ^ 


rt 


cr> 00 


m 


t- 


t- 


X 


cs 


o 


X 


©1 


o 


X 


^ 


«o 


GO 




to 


o 


CM 


<?i 


to 


o 




^ 




O CO 


QO "X 


X 


co 


Tf 


■^ 


'?• 


o 


t- 




Oi 


GO 


OJ 


(Ti 


o 


o 


X 


GO 


GO 


X 


CJ 


Oi 




<*' 


o 


o o 


o 


CO 


o* 


o* 


CM 


CM 


X 




X 


oo 


X 


X 


CD 


CD 


TP 


t- 


b- 


•v 


to 


X 




>-9 

■5! 






— . .— . 




■■^ 


*"* 




—i 




•"" 


e» 




^" 
























■sooilUAJas 


o* 


C>( (M 


o» 


X 


0» 


CN 


CM 


CM 


X 


X 


CM 


X 


CM 


« 


o* 


CM 


c^ 


X 


X 


CM 


o» 


X 


Pi- 
Pi 


•qoJo'oN 


^^ 


(—1 ^^ 


^^ 


»— 1 


^^ 


■"* 


<— I 


"■ 


^^ 


■"■ 


■"■ 


^^ 


,— . 


-H 


'~* 


" 


f-H 


■"^ 


" 


"" 


*■" 


'"' 




















































H 


a ^ 


CO 


CO CO 


CO 


CD 


fi 


w 


to 


"2 


no 




(N 


CM 


04 


o* 


\n 


iO 
















i-i 


4) S 


« 00 


30 (X) 


X 


00 


Oi 


ci 


oi 


oi 


ci 


^ 


^ 


p-^ 


^ 


^ 


a 


ci 


(M 


o* 


CM 


CM 


Cs» 


CM 




C/3 


S'* 


T 


-- TT 


T 


•^ 


rr 


•* 


-7- 


-r 


"^ 


lO 


»o 


ir> 


m 


»o 


o 


o 


" 


■"■ 




r- 


— 


— ' 






co.S 


E 00 


<X> <Xi 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


CJi 


OJ 


OJ 


CTJ 


OJ 


Oi 


OJ 


OJ 






^ 


* •er 


TJ" 


■^ 


TJ* 


Tf 


-^ 


'^ 


Tj" 


Tl* 


■V 


■^ 


■^ 


Tf 


'^ 


^ 


"V 


Ti* 


■^ 


■^ 


Tp 








^E-" 


5 c 


o o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 




^ro 


X 


— O) 




^ 


CD 


T* 


lO 


Oi 


- 


CM 


05 


CM 


CD 


OJ 


c-» 


CO 


to 


Ci 


X 


GO 


Ci 


CM 






X OS 


oi CO 


U5 


oi 


»- 


CN 


^ 


t- 


■o 


Oi 


(N 


oo' 


t~ 


Ci 


r-^ 


t' 


ci 


to 


c^ 


r- 


rf 


t-* 






o» 


kO o 


TJ" 


o» 




GO 


o 


o 


I?* 


(N 


05 


CM 


e» 


VO 


«5 




o* 


CO 


to 






04 






«> 2 


n " 


— -r* 


o 


X 


Ci 


■^ 


CD 


X 


-« 


o 


r- 


CO 


00 


o 


GO 


r« 


■^ 


X 


^ 


^ 


„ 


■^ 






H J3 


•e^ CC 


U5 ^ 


CO 


■^ 


GO 


»o 


o 




CO 


U5 


CC 


o 


CO 


o 


■^ 


o 


CM 


■^ 


•— ■ 


GO 


■^ 


o 






^u 


S o» 


0« GO 


oo 


CO 


00 


oo 


Tf 


Tj- 


Tf 


TJ- 


X 


01 


Oi 


o 


X 


OJ 


X 


X 


C3J 


OJ 


^ 


04 




y 

^ 


. CO 


r s 






rt 


:; 






^ 


<M 


lO 


:; 


- 




Oi 

o* 


^ 


CM 


- 


^ 


s 


5 


:; 




a 


— U 








s 
























< 















GEOGRAPHICAL NOTICES. 



381 





■o 


J3 


























s 


O 


;; 


s 


K 


- 


o 


- 


d 


:; 


;; 


5 






«11 w 


U 










^ 




o 












Ed tf 


i 










J 




H 












S < 














a 








a* 




o S 


"5 
< 

B 
o 

a 

5 
5 


:; 


^ 


jj 


» 


S 

o 

a 
o 
o 


= 


a 
o 
o 


- 


a 


:: 


13 

a 
1 




w 








W5 


U5 








U5 


m 


-^ 


1^ 


■o 


J en 


00 


^ 


C5 


CO 


^ 


00 


X 


r- 


CM 


t- 


o 


— 


CM 


CO 


(N 


CO 




O 


Tf 


o 


<M 


CM 


o 


o 


:: 




^ CD 


„ 


CO 


, 


o 


r- 


■^ 


io 


<D 


CD 


a 


T) 




o 


'J' 


tT 


Tf 


Tf 


"S* 


TP 


Tf 


Tf 


Tf 


-^ 


Tf 


-^ 


■* 


hJ 






























o to 


o 


CO 


CO 


CD 


CO 


CO 


CO 


CD 


CO 


CD 


CD 


■if! 




























V 


GO 




■* 


_ 


CO 




CO 


t^ 




CO 


f- 




°o 


a 


^ CD 


^ 


c* 


>o 


_^ 


CO 


CO 


CO 


l- 


o 


o 




2 


rj- 


o 


o 


TT 


CO 


Tf 


CM 


Tf 


■"■ 


T 


CM 




0) 

1 




■* o 


„ 


o* 


iO 


00 


t- 


00 


CM 


CO 


»o 


o 




O 


o 


'^ 


CO 


o* 


co 


iO 


IT) 


Tf 


CO 


CM 








r, "^ 


-r 


Tf 


Tf 


"-f 


Tf 


-^ 


to 


CO 


CO 


«D 






H 


o CO 


CO 


CD 


CO 


CO 


CD 


CO 


o 


o 


o 


O 




3 

^ 
















■— ' 


-^ 


-" 


-^ 


o 
c 
iS 

Q 

o 

W5 


•oijaqj. 


- s 


CO 


QO 


CM 


CM 
00 


00 


00 


00 


QO 


QO 


00 


S 
o 
15 


. o 


o 


o 


o 


o 


(X> 


00 


o 


o 


O 


o 


n 


^ o 


o 


o 


o 


o 


o 

o 


o 
o 


o 


o 


o 


o 




K 


K 


CO 


GO 


CO 


GO 


GO 


CO 


GO 


GO 


CO 


CO 


o 














»o 










«3 


lO 




« 


% CO 


<N 


Ci 


Tf 


o 


CM 


»- 


CO 


CM 


t- 


»^ 


z 

C4 


o 


s 

H 


« 


> o 


o 

00 




o 

CI 


r- 


C>* 


GO 


o 


S 


CO 


*o 


c 


o 




-* 


O 


o 


CM 




CO 


(>♦ 


00 


o 


V3 


s 


(S 


t> 


a 


o f 


fr- 


„ 


&:> 


»n 


Tf 


T- 


o* 


CD 


o 


S 




s 

•^ 


< 


tn 


° Tf 


TT" 


*o 


o 


in> 


CO 


»o 


=>« 


o< 


CO 


CO 






















iO 


«o 




cd 


Z 




^ 


CO 


CI 


un 


^/^ 


o 


CO 


o 


CD 


^* 


o* 




0) 


u 




* CO 


>o 


o* 


(N 


o 


o 




o» 


lO 


GO 






3 


-1! 


o 


X ^ 


vr> 


GO 


i/S 


00 


»o 


t~ 


o 


Ci 


Si 


Oi 




O 


0. 


S 




CM 


O 


o 


CO 


GO 


— ' 


•^ 


O 


GO 


CM 




a 


<! 




o S 


O 


\n 


o< 


00 


C3 


r- 


Oi 


>o 


— 


00 








»c 


*iO 


-o 


■^ 


CO 


Tf 


Tf 


■* 


Tf 


CO 




s 






























i « 


tc 




rf 




Tj- 


T 


■^ 




CO 


^ 


^ 


m 


— ^ 




























Q a 


■* ■— ■ 


CO 


O 


>- 


Tf 


CO 


-f 


CO 


CO 


35 


r^ 




a 


-J 


" .— 


o 


o* 


o 






CJO 


Tf 


CO 




"^ 




S 




^ 


00 


CM 


00 


GO 


Ci 


CM 


■^ 


00 


CO 


00 






" t>0 


CM 


(N 






CM 




*o 


Tf 


^ 


GO 




01 
C 


O. g 


o ^ 


in 


W 


to 


lO 


O 


an 


CD 


CO 


to 


CO 




«;i 


<D 


CD 


CD 


CD 


CD 


CD 


CO 


o 


o 


O 


o 






X o 


W5 


»o 


»o 


O 


O 


o 


o 


o 


o 


•ft 






l-» 


" CN 


CO 


o 


CO 


CM 


Tf 


CM 




o 


»iO 


c^ 








^ O 


CO 


00 


r- 


00 


o 


CD 


t- 


Tf 


c^ 


»o 








S-f 


*o 


CO 


CM 


CO 


lO 


o 


Tf 


»o 


CO 


GO 


Tf 






o b 


CO 


lO 




CO 


CO 


lO 


IN 


(M 


c^ 


o 


o 




CO 




O 00 


00 


X 


00 


l- 


QO 


00 


» 


0* 


■x> 


r- 




<! 


■5 " 


t- 


r- 


b- 


t- 




h- 




CM 


en 


CM 


CM 


























































•saoiiBAjas 


(N 


i» 


C* 


o* 


00 


CM 


00 


CM 


00 


CM 


CSI 


-qo"jo-OM 


■"■ 


^ 


" 


•-~ 


— 


"-■ 


— 


^ 


^ 








H 






















































a t- 


lO 


« 


»o 


>o 


iO 


r- 


t- 












H 


S = 


M QO 


00 


00 


00 


00 


00 


00 


__ 


„ 


— 


„ 




IB 


S^ 


O 


o 


o 


o 


o 


•o 


»o 


4C 


U5 


iO 


»o 






c 


E g 


o 


o 


o 


o 


CJ 


Ci 


o 


CI 


C5 


CI 






o J 

II 


CO 


CO 


00 


GO 


CM 


(N 


CM 


CM 


CM 


o* 






■j o 


o 


o 


o 


o 


O 


o 


o 


O 


O 


o 






CO 


^ 


00 


CM 


t^ 


^ 


00 


■^ 


cc 


iO 


o 




^ . 


«■ ^ 


QO 


-T 


t- 


CO 


CI 


ci 


Oi 


o* 


-^ 


Tf 






^ TP 


CO 


CO 


CO 


Tj* 


CM 


■^ 


»o 


o 




o 






« p 
EJ5 


« w 


«M 


CM 


-f 


00 


>o 


CO 


u^ 


lO 


O 


CO 






« -^ 


6 


CM 


GO 


'* 


CM 


o 


o 


o» 


■^ 


lO 






PW 


B 00 


Cl 


o 


cs 


CI 


Ci 


o 


t- 


t* 


r- 


h- 








• Ol 










O 


^ 


o 






^ 






u 


o» O* 
















5 










H 


'^ -^ 










0) 
















< 


2 ^ 
s 










a 
















R 










3 
>-> 















382 



GEOGRAPHICAL NOTICES. 











<— 




■^^" 










^ 






^^^ 


^^^H 




MIM^ 
















W 

en 























3 

1 


0) 




tn 








o S 

a: 
a- 


■5 
c 

o 

C . 

O t- 


s 

B 

c 

< 

£ 

o 

.■-■ 

a . 
o t- 






"5 
< 

S 
o 






Ci 

s 

o 
«^ 

c . 


'S, 

£ 
o 

a . 






c 
< 

a 

o 




2 
a 

< 

s 

o 

-Q 




t 






o 


o i 






e*H 






o S 


o j; 






|« 


o <*- 




O '^ 




O 






s- 


s^ 






S° 






s- 


s- 






s ° 




s° 




S= 




^ 




>o 


\r> 


O 


»o 




O 






in 


>o 


»D 












in 


J» 


jj 


V *>» 


CD 


o 


_J 


O 


o 


CO 


CM 


00 


Ci 


f^ 


>D 


t^ 


-+• 


_.. 


in 


ID 




5 


* GO 


CO 


Tf 


GO 






GO 


O 


o 


CN 


oo 


(N 


O 


in 


o* 


o 


CO 


o 
^ 


"Ec 


(W 


o 


o» 


^ 


*4. 


Tf 


■^ 


>c 


00 


r- 


CO 


..0 


o 


00 


o 


o 


CO 


o 


* e* 


(N 


CM 


CM 


O 


c^ 


CM 


CN 


o» 


CM 


04 


CN 


CM 




04 


o* 


o» 


Vo 


h4 


o Z 


-f 


Tf 


Tf 


^ 


-<f 


^ 


•* 


Tf 


■^ 


'(f 


■rf 


■^ 


Tf 


'^ 


TJ" 


•^ 


o 






































(U 


CO 


0* 


CO 


00 


00 


— 


CM 


P^ 


c> 


Tf 


in 






CM 


-- 


r- 




OJ 


c 


■ i2 


^ 


VO 


ui 


X 


CO 


l^ 


o 


oo" 


GO 


Tf 


e» 


00 


00 


^ 


Ci 




-o 


m 




-r 


•iO 


ira 


00 


00 


T 


o 


o 


•O 


o 


ID 


"^ 


c^ 


-~' 


Tj- 




s 


ft 


* o 


t- 


Oi 


^ 


CM 


o 


m 


m 


in 


CO 


GO 


CM 


GO 


o 


o< 


CJl 




-— 


^ 


lO 


■^ 


■* 


rr 


00 


O* 


"" 


-■ 


CM 


CO 


CM 


c» 


oo 


in 


•D 




rt 


a 


° s 


CO 


CO 


GO 


CO 


CO 


CO 


(N 


CO 


00 


CO 


CD 


CO 


CO 


CO 


CD 




J 


H 


■•r 


rf 


-^ 


t- 


1^ 


t- 


CO 


*- 


t' 


t- 


in 


in 


in 


CD 


CD 


O 


•lUJoqx 


° S2 


o 


o 


O 


o 


o 


o 


o 


o 


o 


o 


<=> 


^ 


o 


o 


O 




cc 


00 


00 


00 


■» 


00 


00 


00 


00 


00 


00 


00 


X 


X 


X 






































w 


a 


i 

o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


Q 


m 


z ■"! 


■"■ 


""! 


■"; 


"■ 


^ 


"■ 


■"; 


^~ 


■"■ 


", 


*"" 


■"^ 


■"" 


*"■ 


""t 


CO 


OT 


« 


" o 


o 


o 


o 


o 


o 


o 


CD 


o 


o 


o* 


o 


o 


o 


o 


o 




o 


C3 


<w 


GO 


CO 


CO 


GO 


GO 


CO 


CO 


CO 


oc 


00 


oo 


oo 


00 


00 


CO 








































o 










o 




ID 






>o 




in 






iD 


\n 






o 




i 


V a 


c^» 


ci 


a 


ci 


C5 


b- 


00 


oo 


X 


^ 


00 


6 


CO 


r- 


t- 




a 


^ 


' <w 


O 


«o 


o 


-^ 


O 


c* 


-t 


— ' 


to 


•o 


TP 


»D 


o 


o 


in 


-4.4 


Q 
D 
H 


i. 


^ '^ 


(N 


-t< 


o 


o 


Tf 


■^ 


Cft 


r- 


fH 


CI 


ID 


CO 


-* 


o 


X 


S 




o 


CO 




o 


l^ 


CO 


« 


o 


CO 


CM 


■^ 


CO 


TP 


04 


o 


Tf 


04 


^ 


a 

9 


° g 


O 


<N 


^ 


— . 


00 


_^ 


00 


00 


CM 


a 


CO 


GO 




„ 


X 






u 


ui 


*o 


CO 


CD 


&•> 


GO 


'^ 


CO 


CO 


CO 


in 




CD 


CD 


■^ 


00 




0) 


-U 






































•5 


H 












w 




*n 






in 








i.^ 










Z 




V O 


CO 


_^ 


Ci 


CO 


CO 


00 


CM 


*^ 


CO 


in 


a 


GO 


Tji 


ID 


00 




CS 




d 




(N 


lO 


O 


o 


o 


o« 




■^ 




o 




O 


»D 


uO 






D 


•fl 


o 
o 


* C4 


CO 


_ 


c- 


r- 


o» 


■* 


t* 


CO 


03 


in 


Tf 


o» 


^ 


CO 


CD 






CL. 


m 


rj- 


o* 


lo 


O 


o 


TJ- 


o* 


o 


" 




in 


00 


o* 


^ 


w 


O 




-< 




o 5 


o 


CO 


GO 


05 


eo 


« 


t^ 


■* 


CI 


,~t 


00 


o 


CO 


00 


r- 








r- 


CO 


CO 


CO 


CD 


CO 


CD 


GO 


GO 


rf 


CO 


ID 


ID 


CO 


co 




CC 






































^ 


.si 


rj* 


o 


tn 


















»D 






r- 


CO 




o 


s O 


o 


in 


—4 


QO 


CD 


CO 


O 


o 


1- 


rf 


h- 


CO 


X 


X 


^- 




t« 


c^ 


O 




•* 


O 


O 


O 


CO 


Tj* 


GO 


*o 




O 




CM 


c^ 


o 




C 




































fr^ 


Si's 


V r- 


CO 




t- 


CO 


»~ 




O 


OJ 


o 


in 


o 


00 


C>» 


in 


o 




tS 


o* 


CM 


D* 




— . 


o 


o 




Tj- 


in 


w 


« 


o 




04 


CO 




n 




r. ^ 


-r 


'-4< 


n- 


r- 


r- 


r- 


CM 


GO 


CO 


CO 


CO 


■* 


*t. 


r- 


t- 




1) 


<2 


'^ »o 


'# 


-<}• 


■^ 


r- 


t- 


r- 


CD 


l- 


t* 


t- 


in 


ID 


in 


co 


CD 










































V *^ 


»ft 


>o 


o 


o 


o 


o 


O 


O 


o 


o 


o 


o 


o 


r- 


GO 




c 




- o 


— ' 


CO 




CM 


o 


o 




o 


00 


« 


CO 


'^ 


TP 


■^ 


■-• 




t-H 


WT) 


CO 


r- 


o 


^ 


» 


CD 


00 


in 


Oi 


04 


n 


CM 


■n* 


f 


o 






« s 


o* 


tN 


CO 


»o 






-* 


TT 


o 


0» 




o 


CM 


o 




o 






0.3 








































t- 


-# 


CO 


CM 


O* 




O 




I- 


00 


Cl 


CO 




CM 


■^ 


»D 






"■2 


o t- 


'Tf 


^ 




t- 


t- 


»- 


(N 


CO 


CO 


CO 


t- 




"^ 


t- 


r- 






•a; 


CD 


rf 


^ 


"3* 


r- 


t- 


t- 


CO 


*- 


r- 


»^ 


CD 


in 


in 


CO 


CD 




id 

o 






































•suopBAjas 


c* 


o 


o 


O 


o 


o 


o 


o 


o 


o 


o 


CM 


o 


o 


o 


o 




-qo io *oK 


^ 


■" 


" 


" 


" 






^ 


"■ 




~ 


"* 




^ 


*" 


" 








































H 


S »J 


'# 














lO 


tn 


in 


in 


ID 






in 


in 




o 




V} CO 


„ 


„ 


— 


CD 


CD 


CD 


00* 


in 


in 


in 


ID 


„ 


^ 


oo' 


eo 




CQ 




o 


1— i 


■-M 


^H 




^- 




CM 


o» 


CM 


04 


O* 


oo 


00 


00 


00 




-5! 


„• lO 


»c 


Ifl 


ifi 


in 


•o 


m 


*n 


in 


in 


in 


ID 


ID 


ID 


ID 


»D 








E lo 


to 


li^ 


in 


in 


lO 


Ui 


o 


in 


in 


in 


«D 


in 


»D 


m 


»D 






E O 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


O 


o 


O 


, o 


O 






-^H 




































4j «; ■ 




Oi 


-N 


CO 


f- 


CJ> 


GO 


(N 


CD 






■^ 


ID 


■^ 


o 


00 




■aS 


so — ' 


<N 


CD 


r- 


^ 


GO 


'■r 


«* 


r- 


CO 


ID 


JD 


GO 


ci 


cs 


00 






>.' 


(N 




CO 


o* 


— ■ 


o 


CM 


Tf 


tn 




CO 


■^ 


00 


04 




■V 






.o a 


H CO 


fr- 


C4 


00 


CM 


—. 


o» 


*- 


Oi 


' CD 


00 


CD 


04 


ID 


ID 


a 








S U5 


o 


CM 


CO 


o» 


o 


o 


iO 


in 




CM 


•D 


TJ- 


»D 


C4 


CO 










































S" 


B <^ 


o 


OS 


o 


o 


c:> 




o 


00 


05 


o 


























t— 










^^ 


■■ 


■"■ 










. CO 


r- 


^ 




Ol 


^ 


. 


04 


GO 


p 


;; 


;; 


in 


;; 


CD 


;, 




bi 


CM 0» 


o» 






CM 




























H 


c?* a, 














>i 






















*(! 


00 c 


^ 


^ 


^ 


^ 


^ 


^ 




^ 


^ 


^ 


^ 


^ 


^ 


^ 


„ 






Q 


" 3 

































GEOGRAPHICAL NOTICES. 



383 







V 












u 




*o 






u 














J3 












ffi 




■ 


















■s 


o 














^ 






3 

2 












iO 














'3 








R 


JZ 










li 


c 

3 

to 

S 
o 












< 




1 






1 






-D 
3 

'St. 

c 


Ci 














C I" 




c 






a Si 
o — 








■o 


&4 


c 
o 
o 












§J= 




o t; 










to 


IN 

3 


















^ 






1^ 






4) 




M5 


•o 




o 
























.^ 


•3 


5 -^ 


m 


CD 


CO 


o 


X 


CD 


o 


_M 


■^ 


o 


•o 


.^ 


'C 


Ci 


rt 


5 


00 


.— < 


00 


'^ 


o 


tT 


CO 


o 


UO 


CM 


CO 




»o 


T 


CO 


h-I 




■^ 


o» 


GO 


05 


•o 


05 


CO 


>o 


00 




05 


CO 






0* 


o 


* cw 


CO 


CO 


o» 


00 


<N 


CO 


00 


CO 


GO 


CN 


CO 


GO 


00 


CO 




1-3 


° §? 


00 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


X 


es 




CO 


GO 


CO 


CO 


GO 


CO 


CO 


CO 


00 


CO. 


CO 


CO 


CO 


CO 


i 


S 


r- 




-: 


t- 


cc 


-^ 


TT 


•o 


CD 


TT 


t^ 






^ 




■** 


o 


5 GO 


Co 


r- 


o* 


tT 


O 


CO 


^« 


go' 


CO 


co 


CD 


CD 


>o 




> 


o» 


•o 


c>» 


lo 


o 


^ 


CN 


U5 


CO 


CO 




■^ 


CO 






Q 


. »o 


^ 


t~ 


-r 


»^ 


o 


r- 


^ 


o 


CD 


„ 


CO 


X 


„ 




^^ 




o 


"" 


—' 


GO 


00 


T 


CN 


CM 






CM 


■^ 


GO 


CO 




« 


= 


„ t- 


t~ 


r- 


X 


X 


X 


a 


o> 


CO 


CO 


CO 


X 


X 


X 






tx 


o X 


X 


X 


O 


a 


o 


t^ 


fr- 


X 


X 


X 


**■ 


Tp 


•^ 




"a 
































Hi 
































CO 


•oiJaqj, 


o ^ 


f 


■^ 


-* 


•rf 


-^ 


CN 


CN 


o 


o 


o 


o 


o 


o 


a 

(5 


c 

o 




° fr- 


t- 


r- 


t- 


»- 


»- 


r- 


r- 


t- 


t^ 


r- 


t- 


t- 


t~ 


o 


iO 


1^ 


»o 


*- 


»- 


fr- 


X 


X 


»n 


iO 


ifi 


»o 


*n 


Iti 


^w 


z '^ 


o 


o 


o 


Ci 


Ci 


o 


C5 


c=> 


o 


o 


o 


o 


o 


V, 




" S 


2 


o 


m 


cs 


CD 


o 


O 


o 


o 


o 


o 


o 


o 


CD 


V 


C3 


CO 


90 


CO 


o» 


CN 


CJ* 


<N 


(N 


00 


00 


CO 


GO 


CO 


00 
























»/o 










■^ 
g 




_ 






























o 


•n 




5 <» 


QO 




o 


»o 


GO 


X 


O 


Oi 


CO 


X 


r- 


»- 


CO 




Cd 
Q 


ai 


" <N 


w 


" 




■^ 


^ 


GO 


CN 


o 


Tp 




■^ 


».o 




™ 


^ 


»o 


■3- 


Ci 


iO 


^ 


o* 


-r 


un 


*n 


CO 


Ci 


CO 


C3i 


(-J 


Et3 


H 


c 


" ^ 


co 


CM 


TP 


CO 


^ 


0--i 


CM 


o 




«o 


CM 


^ 


30 


s 


-^ 


H 




o «£ 




o» 


xn 




00 


CO 


CD 


CD 


CO 


o 


»o 


fr- 








< 


M 


'^ 


TT 


■3* 


GO 


CO 


GO 


T 


Tf 


e* 


CN 


o* 


CM 


CN 


00 




'C 

n 


H 


































iC 




, o 


t^ 


CI 


Tj- 


tc 


CD 


O 


lO 


X 


t- 


TJ- 


X 


t- 


X 




X 


B 


•- o* 


o 


o 


— 


»c 


T 


•o 


o 


CN 


o 


o 


<N 


o 


wo 




« 


< 


O 

o 


o 


CD 


CD 


CD 


CD 


CM 


o 


'*■ 


•V 


Tf 


r- 


CD 


00 


cs 




K 


P4 


s 


' "~ 


tc 


•:?■ 


V3 


(N 


c 


o* 


o* 


CO 


•iT 


co 


CO 


rN 






<J 




« oo 


« 


T* 


C4 


•*• 


CD 


CO 


CO 


»/3 


r- 


Ci 


CN 


*^ 


CO 




a- 






O CO 


■^ 


■^ 


■^ 


■T 


T 


to 


»o 


CO 


co 


CO 


t- 


t- 


t- 




^- 




c>* 




CN 


»o 


CO 




wo 






t- 






Ci 




OS 


5 X 


CO 


t- 


^ 


*- 


co' 


n 


00 


CO 


o 


CO 


a 


CD 


c^ 






•-•J 


o* 


o* 


CN 




<N 


CN 


■^ 


CM 


-T 


o 


CN 




or. 


o 






e" 
































a> 


a. ^ 




CO 


O 


O 


©J 




o 


r- 




>c 


t- 


CN 


o 


CD 




c 


— 


•-~ 


P* 


■^ 


'^T 


TJ- 




o 


" 






■^ 


CO 


GO 




a 


a.s 


o *- 


r- 


r- 


X 


X 


X 


Q 


o 


CO 


CO 


GO 


X 


X 


X 




.2 


<! 5 


" 00 


ca 


X 


Oi 


Ol 


03 


X 


X 


X 


X 


X 


■^ 


Tf 


TP 






00 


o» 


o 


lO 


o 


O 


o 


to 


o 


o 


o 


o 


o 


X 


«^- 


! ^ 


^ 


CO 


<N 


rj- 


CN 




•^ 


"T- 


o 






o 


»o 






s-5, 


QO 


GO 


-+ 


<— ' 


■^f 


CO 


X 


Tp 


b- 


o 


C5 


00 


CD 


o 




^-< 


H 


^ O 


-* 


o» 


o 


"" 


o» 


■^ 


—1 


•fl 


CO 




o 


00 


o 




> 


CO 


(N 


CO 


CM 


04 


c^ 


« 


« 


„ 


Ol 


CO 


1^ 


CO 


o» 




|> 




CN 


r- 


tr- 


Oi 


<J> 


<n 


o 


o 


00 


Oi 


CD 


X 


X 








<: 


lO 


00 


ee 


«o 


>o 


»o 


X 


X 


X 


■<t 


CD 


■^ 


rr 


Oi 




Cx 


































O 
0) 


































'SUOIlCAidS 


CD 


f~. 


o 


CD 


CO 


CO 


o 


o 


o 


CD 


X 


o 


o 


o 


en 
5 


-qOJO-oM 




~ 


" 






















CN 


































ffi 


c ,J 


lO 


•c 


Vi 


»o 


»c 


»o 






Vi 


IT) 


iO 


o 


W5 


iC 






S jS 


W (N 


(N 


o* 


■^ 


■^ 


■^ 


•o 


>o 


ai 


ai 


ci 


Oi 


Ol 


o> 




5^ 


O 


»o 


m 


»o 


U3 


lO 


»o 


*o 


o 


C' 


o 


o 


o 


o 




- 


=j CN 


(N 


CN 


CN 


o» 


(N 


(N 


CM 


CO 


so 


CO 


00 


CO 


GO 






O w 


« GO 


CO 


00 


CO 


GO 


GO 


GO 


CO 


00 


CO 


GO 


CO 


CO 


CO 




e 


CO a 


■ 






























1— 1 


^e 


X w 


0* 


<N 


CN 


CN 


C< 


CN 


o* 


<» 


CM 


CM 


rM 


CN 


tN 




H 


CO 


CO 


t- 


■* 


lO 


CO 


^ 


CD 


a 


r- 


ifi 


CO- 


CN 


r- 


a 


w ^ 


00 


o 


t^ 


(N 


cd' 


X 


»- 


TP 


CD 




oi 


t^ 


GO 






" o 

- S2 


r- 


Cs 


CO 


»o 


X 




-5* 




CO 


CO 

W5 


CM 


00 


o 




E CO 


-r 


»o 


C^ 


TT 


T" 




CN 


CO 


'J' 


tr> 




CN 


■^ 




•< 
































M 


H« 


E ^ 


Tf 


■^ 


»iO 


»C 


lO 


- 


^ 


- 


^ 


- 


c* 


CM 


c* 






W 




t 


* 


CO 
(N 


- 


, 


. 


J; 


CO 


. 


- 


;, 


, 


;; 








H 


(N S-^ 


































-t 


00 ^ 


K 


K 


» 


^ 


^ 


^ 


^ 


^ 


^ 


^ 




^ 











Q 


"^ '^ 






















ft 









384 



GEOGRAPHICAL NOTICES. 







a 










u 








a 






^ 






&=■ 






s 


cr 


- 




: 


;; 




^ 


:i 


:; 


3 


^ 


I; 




:; 


5 


in 

i2 






Z W 


< 








s 








o 






a 






a 


cj 




w « 


tj 








o 












< 






< 


-D 




a <! 










b 








t- 






s 

o 

— OJ 








s 




O K 

s 

Ph 


S 

o — 


:; 


o 

a 
o 


- 


= 


s 

o 


- 


- 


R 


g 


:; 


- 


:; 




a 

o 


o 




"i^ 






o =— 




o 






o '-^ 








o>- 






o<- 






o =— 


li 


CO 




s° 




s 






s ° 








s ° 






s° 






s" 


& 


%i 














v^v-^ 








' — v-' 






' — V — ' 






' — V — ' 








































<a 


■o 






U5 














»o 










in 




m 


•n 


. m 


o* 


•r 


ir> 


CD 


TT 


»- 


oo 


OS 


OS 


00 


O* 


o 


*f 


CM 


GO 


m 


3 


3 


- m 




CO 


-^ 


o 


CN 


in 




o 




TT 


TP 


o 


o 


GO 


CO 


CM 










































to 




o 


o 










CM 


CO 


CM 




o 




OS 


GO 


o 




ctf 


□ 

o 


- o» 


c?* 


o» 


!N 


c>t 


CM 


CN 


CM 


CM 


CM 


CM 


o* 


CM 




CM 


CM 


CM 


l_) 


ij 


„ Tf 


Tf 


Tf 


*f 


Tf 


-rp 


rf* 


■* 


■<^ 


-^ 


Tf 


■^ 


■rp 


■# 


■'f 


-TP 


TP 




- 


" TT 


■^ 


Tf 


■fl« 


■* 


Tj< 


'T 


TT 


'<?' 


TT 


Tf 


TP 


■^ 


Tf 


■^ 


-* 


-^ 


«; 


« 


.-. 


00 


(N 


CD 




__ 


lO 


•'J' 


'T 








t- 


in 


»n 

X 




3 


u 




































M 


2 






00 


GO* 


rf 


00 




CM 


o 


CO* 


CM 


CO 


t- 


CS 


f 


cri 




s 


' O 


o» 


CO 


CO 


CO 


CM 


>o 


O 


CO 


CM 


— ' 


go 


O 


TJ- 


in 


CO 




6 


Q 


~f 


w 


>ra 


OJ 


CO 


o 


•.-• 


t- 


o 


Tf 


OS 


■^ 


CO 


OS 


CO 


GO 






" T 


<N 


o 


o 


"— 


TT 


CO 


0» 


c* 


rr 


Tj- 


TP 


CO 


o 




O 




w 


9 


o C^ 


o» 


o» 


(N 


CM 


eo 


GO 


GO 


CO 


<?» 


^ 


,-, 


Tf 


in 


wo 


CM 




>j 


H 


° tD 


CD 


o 


o 


o 


t- 


t- 


r- 


t- 


UO 


lO 


m 


00 


00 


00 




01 


































a 


4) 


•lUiaqx 


= s 


CO 


o 


o 


o 


00 


00 


00 


00 


X 


00 


oo 


00 


00 


00 


»* 


c 


1^ 


fr- 


00 


00 


X 


r- 


r- 


r- 


r- 


t- 


t- 


r- 


t- 


l~- 


t- 


b- 


Q 


E 

o 


lO 


o 


o 


o 


o 


o 


m 


>o 


<ft 


lO 


lO 


vn 


wo 


wo 


»n 


in 


^O 


z ^ 


as 


o 


o 


o 


OS 


CJ 


OS 


OS 


OS 


OS 


cs 


OS 


OS 


OS 


OS 


X 
wo 






-■ a 


Ol 


o 


o 


o 


OS 


OS 


oi 


OS 


OS 


OS 


OS 


C3S 


OS 


OS 


c» 






CQ 


o» 


o» 


CO 


CO 


CO 


CM 


CM 


o» 


CM 


a» 


CM 


<N 


CM 


CM 


CN 


CM 




j2 




































tM 


c3 






































o 




^ 


« 


£. CO 


CO 


CO 


^ 


GO 


lO 


— . 


CD 


W 


ifi 


in 


CD 


M- 


in 


CD 


X 




N 
Q 


w 


*~ ■"■ 


" 


iO 


CO 


CO 


»ft 


CM 


O* 


■^ 


Tf 


o 


O* 


CM 


GO 


o» 


o 










c^ 


o 


CN 


CD 




t- 


CD 


UO 


OS 


go 


-P 


CD 


CS 


CM 


o 


•^ 


w 


H 


o 

c 

3 


^ o 


o 




■"■ 


o 


o 


O 


O 


CM 


in 


lO 


CO 




-^ 


O 


(N 


1*5 


H-( 


z 


^ 


00 


_H 


OS 


t- 


■^ 


t- 


O 


o* 


CO 


o 


CM 


O 


CO 


■Tp 


-r 




Hh 


j 


w 


° t- 


t' 


00 


C4 


o* 


TP 


Tf 


WO 


VO 


CM 


>o 


in 


or, 






CM 




a" 


























































« 
















M 


z 




^ « 




00 


■^ 


o 




cs 


O 


o 


tn 


n 


00 


CM 




OS 


CM 




u 


~^ 


* "O 


•— ' 




-■ 




o 


»o 


o 


'^ 


o 


CM 


■TP 


O 


'-' 


o 


in 






St 


o 


^ 


t- 


00 


t 


OS 


GO 


o 


CD 


CO 


_ . 


O 


t 


b- 


CO 


— i 


m 




J3 


?" 


GO 


co 




o 


CO 


CM 


»o 






o 


o 


o 


CO 


wo 


TP 


»n 




CJ 


< 


° ? 


-f 


GO 


1ft 


CD 


CD 


00 


O 


t- 


CD 


o» 


o 


t~ 


— 


-H 


OS 




a 






CO 


TJ- 


-5" 


■^ 


CO 


CO 


GO 


CM 


CD 


lO 


wo 


in 


r- 


1- 


00 




i, " 




»o 


o 






»o 










iiO 


WO 






in 




■2^ 

Pa 


V o 


co' 


Tf 


r- 


CO 


oo' 


oo 


CO 


o 


00 


^ 


CO* 


CD 


CM 


o 


OS 






^ r- 


■^ 


o 




■^ 


00 


o 


tn 


CM 


o 


■^ 


—' 


o 


O 


wo 


CO 




s^ 


. '^ 


Ol 


o^ 


o* 


•^ 


-* 


^ 


wo 


•-* 


,-m 


CO 


^ 


CO 


GO 


CD 


X 






Si's 


*• CO 




o 






CM 


c^ 




— ' 


IC 


CM 


CM 


Tp 


O 


O 


wo 




S-K 


" s 


CO 


04 


o» 


o» 


'^ 


•«r 


Tt< 


TP 


CM 


CM 


CM 


■^ 


in 


wo 


CM 






aS 


CD 


o 


o 


o 


1- 


t- 


I- 


r- 


«0 


m 


in 


00 


00 


00 






<I 








■"■ 


'"' 






















"■ 






































o 




V o 


«c 


u?> 


o 


o 


o 


o 


o 


O 


o 


UO 


in 


o 


o 


>n 


o 






■o 


- M 


rj- 


o 


»o 




CM 


oo 


Vi 


CM 


CO 


to 


^ 


o 


o* 


CM 


an 












































-■a 


in 


b- 


Ol 


o» 


»- 


CD 


o 


00 


CO 


o 


CD 


CM 




o 


■X 


CD 






2 =r 


- TT 




eo 


o 


0* 


o 


CO 


GO 


o 


CO 


>o 


00 




GO 


o 


"^ 




o 






































ffi 


u 


00 


co 




&» 


o* 


"^ 


CO 


CM 




00 


CO 


oo 


b- 


C3 




CS 




u "5 


O O 


CO 


o* 


CN 


o* 


rp 


T 


TT 


■^ 


CM 


CM 


CM 




»n 


»n 


0* 






<: 


»1^ 


CO 


o 


o 


o 


r' 


r- 


r- 


t' 


»o 


IC 


in 


00 


00 


X 






4) 






































■5 










































































•saoiiBAjae 


uo 


o 


o 


o 


o 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 




-qO jo-o^j 




"" 


^ 


'" 


" 


'- 


"" 


~" 


"■ 


"" 


^~ 


~ 


^ 


^ 


'" 


*"■ 








a „■ 






»o 


irt 


ifi 


»o 


m 


in 


»o 




















S ra 


,; -^ 


Oi 


o» 


IN 


o* 


GO 


co" 


go' 


00 


t- 


r- 


w 


00 


00 


X 


in 




. 


s'-*^ 


» ^ 


■^ 


115 


w 


in 


O 


U5 


Ui 


»o 


■o 


^ 


in 


o 


o 


CD 






a 


= -■: 


- "^ 


CD 


CD 


CD 


CD 


CD 


CD 


CD 


CD 


CD 


CO 


CD 


r- 


r- 


r- 


t- 




•^ 


CO = 

5?S 


E lo 


UO 


« 


lO 


wo 


O 


»0 


*o 


ir> 


O 


wo 


WO 


WO 


wO 


wo 


wo 




n 


B CN 


o* 


©* 


o* 


CM 


CN 


CM 


©» 


<yt 


0* 


CM 


CM 


o* 


CM 


CM 


(N 










































¥c.3 


CM 


- 


CD 


CO 


»- 


CM 


-tf- 


CM 


OS 


r- 


vi 


CM 


in 

00 


in 

T 


WO 


wo 

q 


< 


— CI 


r/ C* 


C5 


CD 


00 


CM 


W 


'^ 


•^ 


CO 


tn 


00 


IN 


r^ 


in 


CM 






^^ 


'^ O 


■^ 


90 


o 


o 


o 


CM 


CO 


»o 


CO 


OM 


w^ 


00 


— ■ 


■V 


m 




<U o 

Si 


• CD 


Ol 


00 


t- 


CD 


o 


CM 


OS 


CO 


CM 


CD 


CO 


CO 


r- 


OS 


wo 






a CM 




'^J' 


*-'i 


o 


o 




Ol 


rp 


CM 


CM 


GO 


ot 


CM 


GO 


■^ 






s ^ 


o» 


CO 


CO 


r- 


CO 


OO 


CO 


oo 


- 


y. 


CO 


CM 


CO 


GO 


CM 






. T- 




ifi 














^- 






^ 






CM 




H 


CH CM 


*^ 


(N 


•■ 


" 


" 


" 


" 


" 


CM 


•^ 


" 


w 


" 


" 








H 


<N 




































< 


CO bjD 


^ 


^ 


. 


^ 


^ 


^ 


^ 


^ 


^ 


„ 


^ 


^ 


^ 




a. 






O 


'^ < 

































GEOGRAPHICAL NOTICES. 



385 























■" ■ 






















OJ 








u 






o 

n 










^' 












•T3 

C 


o 








3 

2 








^ 






ffl 














































J= 




Ed ai 


c 

3 
IXl 








H 
o 






< 










1 












S ^ 








Cl< 






« 










8 








lb 


a" 


o s 


B 

p 








s 






s 

o 










s 

_ 4 








o 

Em 

o 




b 


c 
o 
o 






















a ^ 








to 












O e*- 






o s 










O s- 








c- 


■"oo 

CO 










s° 






^^ 










s = 








^ 




to 






ifi 


















»o 


in 










.s 


- ^ 


X 


r- 


■^ 


o 


o 


o 


00 


o 


rr 


X 


G^ 


GO 


t- 


r~ 


r- 


to 




5 


o 




CM 


CO 


no 


o 


o 


rr 




CN 


■V 


GO 


rr 


CO 




CN 




a; 






































'T3 


'Sii 


* C35 


X 


e- 


lO 


GO 


«o 


X 


X 


CD 


-r 


■^ 


CO 


CD 


«o 


•o 


r- 


CD 


s 


a 

3 


CC 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


oo 


CO 


CO 


GO 


co 


CO 




° s 


_ 


^ 


J , 


« 


^ 


^ 


— 




^ 


^ 


^ 


^ , 


__ 


__ 


_l 


_, 


ei 




CO 


CO 


CD 


CD 


CO 


CD 


CO 


CD 


CO 


CD 


CD 


CD 


CD 


CD 


CO 


CD 


u 














































00 






























^ 


Tf 


CO 


■-J 


00 


CO 






<o 


lO 






CO 




CD 




00 






a 


* *-* 


CO 


o 


c^ 


„* 


f 


,—, 


«" 


^* 


o» 


X 


^ 


o 


-f 


O 


oo' 




d 


S 


"if 


o* 


Tf 


Tf 


Tf 


Tf 


■— ' 


o 


00 


rr 


CN 


— ' 




CO 


o 


to 




'3 


Q 


^ CO 


,-. 


CD 


.-1 


^ 


rr 


m 


,—. 


w 


o* 


CD 


OJ 


lO 


o 


CN 


r- 




a, 


TJ- 


in 


»o 


o 


iO 


'^ 


CO 


•o 


rf 


GO 


r— 


o 


rr 


m 


o 


o 




xn 


a 


" g 


CO 


CO 


Tf 


»o 


»o 


»o 


-r 


tT 


^ 


rf 


•^ 


X 


X 


o 


o 






^ 


oi 


a> 


Oi 


iO 


•o 


o 


o 


>o 


«o 


lO 


*o 


wo 


m 


t* 


t- 




X. 




































CJ 




•rajsqj, 


-. o 


o 


o 


o 


X 


X 


X 


X 


X 


X 


X 


X 


■ X 


X 


t~ 


r- 


O QO 


x> 


00 


00 


r- 


r- 


t- 


»- 


^- 


t* 


r- 


»- 


t- 


r- 


fr- 


fr- 


1 
5 


s 


o 


o 


o 


o 


t^ 


1^ 


r^ 


CD 


CD 


CD 


CO 


CD 


»^ 


CD 


ee 


CD 


h 


. o 


o 


o 


o 


C5 


C3 


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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 





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. IS 


+ 0.43 




July 6 


Fa. 07 


+ 0.71 




Mar. 2 


,, 16 


+ 0.29 




„ 13 


„ 12 


+ 0.36 


■ At Sea. 


.., 9 


„ 18 


+ O.U 




„ 20 


„ 11.5 


+ 0.5 




., 16 


,, 19 


- 0.07 


!■ Sierra Leone. 


„ 27 


„ 18 


+ 0.43 


■ Bahia. 


„ 23 


., 18. S 


- 0.21 




Aug. 3 


,, 21 


+ 0.29 




„ 30 


„ 16 






„ 10 


„ 23 






April 6 
„ 13 


,. 16 
„ 19.5 



+ 0.5 




„ 17 

„ 24 


,, 22 
SI. 08 


- 0.14 

423 down, 
and reset. 


■ At Sea. 


„ 20 


,. 22 


+ 0.36 
- 0.07 




„ 31 


„ 07 


- 0.14 

- 0.36 


> Maranham. 


,. 2T 
May 4 


„ 21.0 
SI. 08 


423 down 
and reset. 

- 0.29 


■ At Sea. 


Sept. 7 
,. 14 


., 09.5 
„ 09.5 



- 0.21 


. At Sea. 


,. 11 


„ 10 


- 0.29 




„ 21 


,,0 11 


- 0.21 




,. 18 


., 12 


+ 0.43 




„ 28 


.. 12.5 





I Trinidad. 


„ 25 


„ 09 






Oct. 5 


„ 12.5 










+ 0.14 








+ 0.07 




June 1 


„ 08 






,. 12 


„ 12 













> St. Thomas. 






+ 0.5 


I At Sea. 


„ 8 


,, 08 


+ 0.21 




„ 19 


„ 08.5 


+ 0.29 




„ 15 


„ 06.5 






„ 26 


„ 06.5 






„ 22 


„ 03 


+ 0.5 
+ 0.57 


> At Sea. 


Nov. 2 


„ 05 


+ 0.21 
+ 0.43 


} Jamaica. 

J 


„ 29 


Fa. 01 


+ 0.86 


f Ascension. 


M 9 


,. 02 






July 6 


„ 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. 



53 01.8 W. 



27 00 E. 



H. M. S. 

Fa. 48 48 



> Ascension . 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. 



„ 49 12 
SI. 30 il.5 

„ 29 54 
Fa. 55 08 

„ 55 40 



357. 



H. M. S. 

Fa. 48 31 



,, 48 57 
SI. 30 OS 

„ 29 46 
Fa. 55 09 

„ 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 
„ 29.7 
„ 00.7 
Fa. 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 . . . 53 Ol.S W. 

By 150 Lunar distances at St. Thomas's referred, by 357 52 59.7 



Final Longitude . . . 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 20 57.9 E. 
By 150 Lunar distances at St. Thomas . . . . o 27 00. 
By 104 Lunar distances at Ascension, referred by 357 20 58.7 

Final Longitude . . . 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 57 30.4 W. 
By 104 Lunar distances at Ascension . . . . 57 34.3 
By 128 Lunar distances at Bahia, referred by 357 . . 57 34.7 

Final Longitude . . . 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. 

34 57.3 


; // 

141 17 07.45 


H. M. S. 

2 28 30.74 


H. M. S. 

1 21 49.82 


H. M. S. 

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 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 



2 






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O .2 

c ^ 

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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. 









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. 


. 


o / 


o 




June 15 


03 N. 


7 45 E. 


o 


|s. SOW. 29 miles. 
>West 48.5 „ 


Apr. 15 


6 40 N. 


11 48 W. 


84 





„ 16 


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 
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 


36 


5 22 


82.8 










].S. 71W. 14 „ 










>S.81E. 13 „ 


„ 16 


12 27 


32 51 




J 

In. 79 w. 1 1 „ 


„ 14 


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. 



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 





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 




76 


10 


9 A.M. 



83.1 



82 





,, 


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 o