i i.q. 4 I'
I iii ii
il.
II :
.Ciii-'
I
320 APPENDIX.
that any one had suddenly varied from its rate, its result was onritted
in the determination.
The method of interpolating for the alteration of the rates which I
have adopted, is one that was successfully employed by Captain
Flinders in his sur\'ey of New Holland ; and one that I have been
for many year's in the habit of using with most satisfactory results.
In cases where chronometers alter their rates suddenly, the rule
cannot be apphed; but, in general, the alterations are caused by
changes of temperature; and as these changes are 'gradual, so the
rates alter in the same progressive manner.
The correction has, therefore, been obtained by an arithmeticid
progression; in which the first term, the number of terms, and the
common difference, are given to find the sum of the terms.
l l i e difl^erence between the two rates divided by the number of
days that have interi'ened, called the daily variation of rate, is the first
term F ; as well as the common difference D : the interval between
the determination of the errors of the watches, in mean time, of the
place left and arrived at, is the number of terms N : and the sum of
the terms is the correction required, S. The formula, when reduced
to its simplest form, is F (N+1) |-=S.
The places which I was instructed to visit for the purpose of measuring
their respective meridional differences were Madeha, Santa
Cruz in the island of Teneriffe, the north-east end of San Antonio,
and Port Praya in the island of St. Jago, in the North Atlantic ;
and the island of Trinidada, Rio de Janeiro, and Monte Video, in
the South Atlantic Ocean.
After the chronometers had been carefully rated at the Ohservator)',
they were embarked on board H.M.S. Adventm-e, on the 23rd
April, 1826; but as the ship was detained at Deptford and Northfleet
until the 4th May, an opportunity was offered of ascertaining
what change had been produced by the alteration of the place; and
it turned out to be by no means inconsiderable. Five of the watches
had accelerated, and the remaining four had retarded rates. It
would be difficult to assign any other reason for this change than
the effect of the ship's local attraction.
With this newly found rate we sailed for Plymouth; and, after
five days' passage, amved in the Sound; and, on the 9th May, ob^
tained a set of coiTesponding altitudes upon the Breakwater, upon a
stone marked ^ ; which, by the Ordnance map, is 0' 31"-5 in longi-
APPENDIX. 321
tudeto the eastward of the flag-staff of Drake's Island ; 10" 2 to the
westward of Plymouth old church, and 0' 25"-1 to the westward of
the new church. The longitude, therefore, of the station, by the
Ordnance survey,would be 4° 7' 41"'7, but by applying a proportion
of the error detected by Dr. Tiarks, in Ids chronometrical observations
between Greenwich and Falmouth, viz., 4®'09 or 1' 11""3, the
corrected longitude of the station wiU be 4° 8' 43". Our chronometers
made it 0' 40"- 2 to the eastward of the corrected longitude,
and 0' 19"-6 to the westward of the original determination by the
Ordnance survey.
The Breakwater being the point from whencc all my differences are
measured, I have considered its longitude west of Greenwich to bo
as above stated, namely, 4° 8' 43".
It now remains to record the results, the details of which are
given in another form.*
Madeira.—The observations were made at Mr. Veitch's garden.'
house, that being the spot used by Dr. Tiarks with ten chronometers.
The difference between it and the Breakwater is 12<'45'4o"
west: the longitude mU therefore be 16° 54' 28" W.
which is 0' 17''-4 to the eastward of Dr. Tiarks's determination.
Tenehiffe (Fort San Pedro)—^by eleven chronometers is 0° 40' 6"
to the eastward of Madeira, and will therefore be ... 16°14' 22" W.
St . Jago (landing place at Port Praya)—by ten chronometers
it was found to he 7° 15' 55" west of Teneriffe, and therefore
23° 30' 17"
Rio DE Jankiho (Villegagnon Island)—by fourteen chronometers the
difference was found between it and Port Praya to be 19° 34' 46"
which will make its longitude 43° 05' 03"
St . Aktonio (Terrafal Bay at the south-west end).—In consequence
of unfavourable weather we were unable to land at the north-east
end, and, therefore, made our observ'ations atTerrafal Bay; the longitude
of which was found by eleven chronometers to he 9° 05' 39"
to the westward of Teneriffe which makes it 25° 20' 01"
Tbinidada.—On account of the south-east trade being scant, we were
prevented from makmg this island.
Monte Video (Bat Island).—The difference of longitude between
this place and Rio de Janeiro was measured, on various occasions,
* These details are lodged in the Hydrographical Office. R, F;