This is a correspondence between the Irish physicist and mathematic...
You can find Stoke's paper "On the Variation of Gravity at the Surf...
I highly recommend taking a look at [Stoke's paper](https://archive...
As Stokes describes, gravity at the new sea level is influenced by ...
After this letter, in 1888 Edward Hull [wrote a report](https://boo...
PROPOSED CONNEXION OF EUROPE WITH AMERICA 313
the name was not known. I cannot at present tell whether my
letter reached you. Your last letter was dated from Ithaca, but
the telegram was dated from New York.
I said I was sure the Committee would be extremely glad if
you could come over to swing the pendulums at Kew and perhaps
also at Greenwich. It would seem indeed to be an almost
necessary supplement to the American work. Obviously the
value of this would be greatly enhanced if a thoroughly trust-
worthy connexion were established between American and
European stations. A connexion has indeed been made by
Col. Herschel but he employed a new method of adjusting the
agate planes, which d priori would seem to be rather precarious,
and at any rate has not yet received that degree of examination
which would seem requisite to inspire full confidence.
It would be most desirable as you have been swinging the
pendulums at American stations that you should yourself complete
the connexion by swinging them in this country, as that would
ensure the strict comparability of the observations on the two
sides of the Atlantic Ocean.
It has been suggested to me that if I put "
U.S.
Coast and
Geodetic Survey" on the letter it would be pretty sure to
find you.
I am, dear Sir, yours very faithfully,
G. G. STOKES.
DISTURBANCE OF GRAVITY BY CONTINENTS.
To PROF. E. HULL.
26 Feb., 1887.
I am afraid you will think I have forgotten the question you
asked me in your letter. It is not so, but I thought that before
answering it I would look into Professor Suess's book if I could
find it....But if I had found it I do not know that I should have
been much the wiser, for as you say he gives no numerical data as
to the dimensions of the supposed continent, nor does he specify
what the continent actually is if he is dealing with a real, not an
ideal, continent.
314 CAUSE OF DEFECT IN GRAVITY OVER CONTINENTS
In
a
paper
"
On
the
Variation
of
Gravity
at the
Surface
of the
Earth*," which
I
wrote long ago,
and
which
is
published
in the
Transactions
of
the Cambridge Philosophical Society,
and in my
Collected Papers,
of
which
as yet
only two volumes have appeared,
I showed that
the
effect
of a
continent would
be to
make
a
slight
apparent diminution
of
gravity
in
continental stations
as
compared
with detached oceanic islands.
It
operates
in
this way:—that
the attraction
of the
land causes
the
surface
of the sea
level,
the level surface, that is, which would
be
determined
by a
system
of geodetic levelling carried from
the
coast inwards,
to
stand
higher from
the
centre
of the
earth than
it
would have done
had
the place
of the
continent been occupied
by
ocean. The raising
of
the sea
level
is
greatest inland,
but it is
quite sensible,
and
even important,
at the
coast itself
of the
continent.
How much
the
raising amounts
to,
depends
of
course
on
the dimensions
you
attribute
to the
continent
and the
height
you give
it
above
the
undisturbed level
of the sea. To
take
a
numerical example,
I
suppose
the
case
of a
circular island,
or
continent, whichever you please
to
call
it,
1000 miles
in
diameter,
and elevated
a
quarter
of a
mile above
the sea
level.
I
suppose
the depth
of the
ocean
in
which this island
is
supposed
to be'
placed
to be 2
miles.
I
make
the
usual suppositions
as to the
average density
of the
rocks
&c, in the
neighbourhood
of the
earth's surface, atid
as to the
mean density
of the
earth, which
is
fairly well ascertained.
I
find
the
elevation
of
the
sea
level
in the
interior
of the
island
or
continent (Australia),
a
good
way
from
the coast,
to be
about 400 feet.
Of
course
in a
great continent
it
might
be
considerably greater. This would cause
an
apparent
diminution
of
gravity
in
continental stations,
I
mean
of
course
in
gravity
as
reduced
by the
usual methods
to the
level
of the sea.
In
the
first place
in
reducing
to the
level
of the
sea we leave
out
of consideration
the
attraction
of the
stratum
of
earth between
the actual
sea
level
and
what
the sea
level would have been
if
the continent
had
been away.
As far as
this goes, corrected
gravity ought
to
appear
too
great.
But in the
second place,
in
reducing
to the
level
of the sea we
reduce
to a
point further
from
the
centre
of the
earth than
we
should have done
if the
sea level
had
been unchanged,
and
therefore
in
correcting
we
* Cambridge Phil. Trans,
vol.
viii. (1849),
pp.
672—695. [Math,
and
Phys.
Papers, vol.
ii. (p.
155).]
NUMEBICAL ILLUSTRATION 315
don't add enough to bring it up to what it would have been if
ocean had been beneath us instead of land. On this account
therefore gravity should appear too small, I mean reduced gravity.
The two effects on apparent gravity are antagonistic, but the
second is the stronger, so that on the whole gravity ought
caeteris paribus to appear a little less on continents than on
detached islands. Sabine and Airy have pointed out that such
appears to be the result of observation, but so far as I know I
was the first to point out that such a result ought to follow from
the attraction of a continent, by disturbing the sea level.
Far inland, the thing could only be tested in those cases
where the sea level has been accurately determined by geodetic
operations. We could not accordingly throw much light on the
question by means of pendulum observations in Thibet.
I am, dear Sir, yours very truly
P.S.
You will find Airy's discussion in his article
"
Figure of
the Earth
"
in the Encyclopaedia
Metropolitana.
An elevation of 400 feet, even if there had been no intervening
attraction to reduce the resulting diminution of gravity, would
only alter the number of vibrations per diem of a seconds'
pendulum by about one and a
half.
Of course apart from
disturbance the difference in the number per diem at two
stations on the same parallel of latitude would be nil, and
therefore the small difference of 1*5 would be infinity times
that. I do not know what the term of comparison used by
Fischer may be.
To E. F. J. LOVE.
7 QUEEN'S PARADE, BATH,
6 August, 1891.
DEAK
MR LOVE,
I have come here for a week or two, and have brought
your letter of June 19 with me to answer it from this house,
which is that of one of my sisters.
You do not say expressly, but I take for granted that in the
contemplated gravity survey [of Australia] you mean to use
invariable pendulums, not Kater's pendulum or some other form
available for absolute determinations. It is generally, I think,
This is a correspondence between the Irish physicist and mathematician G. G. Stokes and Edward Hull, an Irish geologist, who held the position of Director of the Geological Survey of Ireland.
The effect of the rise of the sea level due to the attraction of continental land had been historical disregarded by a lot of British geographers due to the widespread influence of Lyell's hypothesis that the ocean-surface was uniform all over the globe. Hull, however was exposed and intrigued by the work of German geographers Suess and Fischer, who had been studying the difference between the periods of pendulumns at islands and continental stations. It was after finding Suess and Fishcher's work that Hull decided to write a letter to Stokes.
In this letter, Stokes shares some of his research on how continental masses affect the sea level thus disturbing gravity.
I highly recommend taking a look at [Stoke's paper](https://archive.org/stream/transactionsofca08camb#page/682/mode/2up) in which he actually tried to derive the gravitational potential taking into account several factors that might influence gravity at the surface of the Earth, including:
- Moon's gravitational force
- Earth's spheroidal form
- Earth's Rotation
It's a great example of Stokes extraordinary skills both as a mathematician, using countless analytical methods without the aid of numerical simulations, but also as a Physicist, interpreting and discussing which factors play a relevant role in the problem and which can be disregarded.
As Stokes describes, gravity at the new sea level is influenced by a few factors: it's further from the centre of the Earth and thus less attracted, but also attracted by two new slabs of land, one in between the the old and new sea level ($g'$) and another one above the new sea level ($g''$).
After calculating the magnitude of the effects, Stokes concludes that the dominant one is the decrease on gravity due to the new sea level being further away from the centre of the Earth.
After this letter, in 1888 Edward Hull [wrote a report](https://books.google.com/books?id=zC8_AQAAMAAJ&pg=RA1-PA596&lpg=RA1-PA596&dq=stokes+force+of+gravity+continental+and+islands&source=bl&ots=XciffJe5Tb&sig=ACfU3U2FAjgNhg5qYvB1I7ZhlEbNCFqTvw&hl=en&sa=X&ved=2ahUKEwj3x6jctsboAhXPsZ4KHRfsCIgQ6AEwDHoECAkQAQ#v=onepage&q=stokes%20force%20of%20gravity%20continental%20and%20islands&f=false) to the British Association for the Advancement of Science sharing the effect and his discussions with Stokes.
You can find Stoke's paper "On the Variation of Gravity at the Surface of the Earth" [here](https://archive.org/stream/transactionsofca08camb#page/672/mode/2up).