MDDM Ch. 75 Difficult History with Plumb-lines

Sun Sep 8 11:57:42 CDT 2002

"'At the request of Maskelyne, I am coming North a
Mountain of suitable Gravity to seek, whose presum'd
Influence might deflect a Plumb-line clearly enough to
be measur'd without Ambiguity.-- Tho' given the A.R.'s
difficult History with Plumb-lines, I feel
Apprehension for the Project.'" (M&D, Ch. 75, p. 733)

Cf. ...

"'The Attraction of Mountains,' Maskelyne Jobates,
whilst slowly 'round him The Moon becomes a Dormitory,
'-- according to Newton, these Peaks may hold enough
Mass to deflect our Plumb-lines, thereby throwing off
our Zenith Obs.  We must therefore repeat these Obs at
the other side of the Island, and take the Mean Values
betwixt 'em.'
   "'The Other Side,'-- it does give Mason a Chill. 
If the Cape of Good Hope be a Parable about Slavery
and Free Will he fancies tho' not quite grasp'd, then
what of this Translocation?  That Maskelyne's
Obsessedness in the Article of Plumb-lines, may be a
factor in the change, will not become apparent till
too late.  Days in a row now pass in which Maskelyne
speaks of little but the faulty Suspension of the
Sisson Instrument.  'My career, my Life,-- hanging
from a damn'd Pin!'  He takes to accosting strangers
in The Moon and then in other taverns, subjecting them
to long wearying recitations describing the
malfunction in numbing detail, and what he has
instructed be done to correct it, and how others have
complied, or not,-- a history without sentiment or
suspense (save that which the Plumb-line, as it proves
faultily, hangs upon its Loop, and that upon its
Pin)." (M&D, Ch. 15, p. 158)

A la a yo-yo ...

>From  Silvio Bedini, "The Transit in the Tower:
English Astronomical Instruments in Colonial America,"
Annals of Science 54 (1997): pp. 161-96 ...

   "The sector Bird made for Penn was the first
example of the instrument to incorporate improvements
previously suggested by the Astronomer Royal Nevil
Maskelyne.  These consisted of a modification of the
manner of suspending the plumb-line that corrected a
situation which had introduced an error of many second
per angle." (p. 172; cf. M&D, Ch. 30, p. 297)

http://waste.org/mail/?list=pynchon-l&month=0201&msg=64597&sort=date

Maskelyne proposed to the Royal Society in 1772, an
experiment for determining the Earth's density with
the use of a plumb line. He was not the first to
suggest such an experiment. Bouguer and La Condamine
had tried such an experiment over 30 years before.
Maskelyne carried out the experiment in 1774 on
Schiehallion, a mountain in Perthshire, Scotland.
Schiehallion was chosen because it was surprisingly
regular and conical in shape so its volume could be
determined accurately. From his observations Maskelyne
computed that the Earth's density is approximately 4.5
times that of water. He was awarded the Copley medal
of the Royal Society in 1775 for this work.

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Maskelyne.html

The Reverend Neville Maskelyne, Astronomer Royal, came
up with a plan to prove that Newton's Law of Gravity
holds for matter on the Earth as well as in the
heavens. For this he needed a symmetrical mountain -
Schiehallion appeared to be perfect.

Maskelyne argued that if the earth was totally smooth,
then a plumb line would point down towards the centre
of the earth because of the force of gravity on the
bob. But if there was a pimple on the earth's surface
(a mountain) then gravity would pull the plumb line
very slightly towards it.

Over a period of four months, he and his colleagues
camped out on Schiehallion - first on the south side
then on the north - collecting data on the apparent
altitude of the stars. If gravity did exist, then when
Maskelyne was taking measurements on the south side of
the hill, the plumb line should be deflected towards
the north effectively decreasing the apparent altitude
of the stars. The opposite should occur when he was on
the north side of the hill. The difference between the
two sets of readings would be the gravitational pull
of the mountain.

Two hundred and thirty-seven measurements and many
calculations later Maskelyne discovered that the
mountain did in fact have a gravitational pull on the
plumb line of 11.7 seconds of arc.

The surveyors took thousands of measurements to
determine the relative volumes and positions of the
mountains. Charles Hutton was a leading figure in
analysing this data, and as part of this he divided
the landscape into a number of vertical pillars around
the observatories, thus inventing the concept of
contour lines - essential to modern hillwalkers!

http://www.jmt.org/cons/sch/sch_ref_maskel.html

In 1772 he proposed to the Royal Society a mode of
determining the attraction of mountains by deviations
of the plumb-line (ib. lv. 495), and Schiehallion in
Perthshire was fixed upon as the subject of
experiments, skilfully conducted by Maskelyne from
June to October 1774. Their upshot was to give 11Ó×6
as the sum of contrary deflections east and west of
the hill, whence Hutton deduced for the earth a mean
density of 4×5 (ib. lxviii. 782). The Copley medal was
in 1775 awarded to Maskelyne for his curious and
laborious observations on the attraction of mountains.

http://www.hyperarts.com/pynchon/mason-dixon/extra/maskelyne_bio.html

>From The Earth's Density, by K.E.Bullen, FRS: 

In 1772, Nevil Maskelyne proposed a repetition of the
Chimborazo (Peru) experiment in Scotland, and a Royal
Society Committee selected Mt Schiehallion in
Perthshire for the purpose. The mountain has a short
east-west ridge, with steep slopes to the north and
south. (The name was spelt Schehallien in Maskelyne's
paper. Referring to the differences in spelling, Dr.
P.L. Willmore tells me that he has the impression that
"the early English explorers had some difficulty in
transliterating the sounds made by the local
inhabitants, particularly as the climate in the area
is very conducive to colds.") 

Careful surveys were first made during the period
1774-1776. Two observing stations were then set up on
the same meridian, one on the northern and the other
on the southern slope. At each station, Maskelyne made
some 170 observations of the apparent zenith distances
for more than 30 stars, and arrived at a mean
difference of 54".6 for the two stations. The excess
of this difference over the measured latitude
difference 42".9 was attributed to the plumb-line
deflection caused by the mountain. 

... The density of the mountain was estimated as 2.5
g/cm^3, thus yielding 4.5 g/cm^3 for the mean density
of the earth. 

NB, the accepted value today is about 5.5 g/cm^3 

http://www.hyperarts.com/pynchon/mason-dixon/extra/info.html

And for the mathematically and/or interactively
inclined ...

Pierre Bouguer was a French scientist who was the
first to attempt to measure the density of the Earth
using the deflection of a plumb line due to the
attraction of a mountain. He made measurements in Peru
in 1740. A more successful use of this method by the
astronomer Maskelyne placed the density between 4.5
and 5. 

http://www-gap.dcs.st-and.ac.uk/~history/Curves/Pursuit.html

This animation simulates Maskelyne's experiment to
demonstrate the deflection of a plumb line by the mass
of a mountain in order to estimate the mass of the
Earth. 

http://www.scienceprof.com/geophysics_2.html

http://www.scienceprof.com/docs/geoPhys/geoPhys.html#maskelyne

And see as well ...

Maskelyne, Nevil.  "A Proposal for Measuring the
   Attraction of some Hill in this Kingdom by
   Astronomical Observation."  Phil. Trans. of the
   Royal Soc., Vol. LXV (Dec. 1775): 495-99

http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=7&size=1&id=pt.1775.x.x.65.x.495

Maskelyne, Nevil.  "An Account of Observations made
   on the Mountain Schehallien for finding its
   Attraction."  Phil. Trans. of the Royal Soc.,
   Vol. LXV (Dec. 1775): 500-42.

http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=7&size=1&id=pt.1775.x.x.65.x.500

Not to mention ...

Howse, David.  Nevil Maskelyne: The Seaman's
   Astronomer.  New York: Oxford UP, 1989.

And note that it is now Dixon rather than (in addition
to?) Mason who feels "Apprehension" ....

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