Weekly national intelligencer. [volume] (Washington [D.C.]) 1841-1869, 1851-06-07
COMMUNICATIONS.
ANALYSIS OF FoUcAU1Lrl,'ss EXPERIMENT lsE i,r

ANALYSIS OF FoUCAULTs EXPERIMENT.
Il rarely happens that. purely scientific experiment pos
sesses the elements Of popular interest An exemption from
all reprosch Of dune seems however, generally accorded
to FoucsuIs pendulum experiment, by which the earhs
durnal rotation is directly exhibited Though it really adds
nothing the creed Of philosophy, it has peculiar interest
from the grandeur Of its involved IDEAS In the hope Of illus
ang its rationale which of perplex all minds
not mathematicay trained subjoin simple geomecal
analysis Of the problem.
First as to the experimental fact. pendulum freely
suspended over horizontal table. concenicay graduated
seen, when carefully put in osclaon deva.e in its
successive oscillations constantly to the left Of its former
The plane Of oscillation has apparent rotation, which is
uniform, and depends on the latitude.
Now how does this prove the earhs durnal rotation
Simply because if this rotation exists the observed result
must follow and otherwise The experiment indicates
the relation between entirely distinct phenomena
y the earhs rotation and the oscillation Of the pendulum
If the earth did reyove, the pendulum would still osci
late, but constantly the line Of the table,
here important have clear idea Of what takes place
In the oscillation Of pendulum. When the ball is drawn
from beneath its point Of suspension component Of
weight acts along the wie and the other along the arc Of
vibration From the end Of this that component decreases
the ball descend becomes when the wire vertical
and negative the ball ascends This negative force
the inertia Of the ball. which has retained all the force
communicated in the descending branch When this stored
force exhausted the ball sgan descends and the osc
ton is continued In all this gravity incessant
force constant in intensity and direction Thus this force
governs the entire movement Of the pendulum.
Now, in rotation of the earth the line of direction Of
gravity at Washington describes the surface Of cone in
space whose veer the ears centre and whose base
10 parallel Of latitude Suppose the ideal sphere Of the
earth fixed in space rotation Of the actual earth carries
the point of pendulum suspension around our fixed ideal
parallel Of latitude So far the pendulum, (ds
regarding centrifugal force is the whether the earth
be conceived actually to rotate whether be fixed in
space and the point Of suspension be carried around on
parallel The forces, which entirely govern the oscla-
tons, act alike in the two cases.
Conceive the earth at rest and the pendulum carried around
any parallel In this movement the horizontal in the
ridan plane generates cone, having its the pro-
oDged axis Of the earth, and the parallel for its base Now
lot this be developed rolled tangent plane
will make sector whose radius equals the cotangen of the
latitude, and whose arc rec6ed, equals the reccaon Of
the parallel This development reduces the first cone
perpendicular cylinder through the of the sector This
the angular movement Of the plane Of osc
ation for pendulum during sdeeal day for suppose an
oscang pendulum carried around on the perpendicular
cylinder, while gravity acts along its elements just before
their Development the oscillations will be ia parallel planes
50 that table, bearing line pointing towards the CENTRE
and supporting the point Of SUSPENSION would relatively
to the oscillations, through the angle Of the sector.
In all this process Of reduction Of actual pendulum dur
ing day to pendulum carried around this sector nothing
done to change the relation between the plane oscillation
and the graduated table from that existing in Foucauls
pertinent Hence, in both cases, the plane of oscillation
would seem to traverse through the angle the above sector
Also, all the mechanical conditions in this movement are
uniform, the angular velocity be uniform for any period
Of time. aN
The sector 5000 - sim a radius and as degrees are
here proportional 10 veocies have the angular velocity
the plane eahs ang vel sin. lat radius or ang vel Of
plane earihs ang vel sim lat From this we see that
the time of complete revolution Of the plane the
table = IN i, AT the POLE sin lat. = l, or the time
of revolution is sdereal day. the EQUATOR Elm lat 0,
and the time Of revolution becomes infinite In latitude 800
this time two days. Between the pole and equator it
always than day. and fnie and be exactly found
by substituting the local latitude in the above formula.
If by actual experiment, this time Of revolution be
sured at any place. the latitude found from the formula by
substitution. From present appearances, however, the dis
tubing bear large relation to the whole pheno-
mena as 70 uouDtu the Pacca aPPcauon Of tns
experiment to determining ATTITUDES. Yet should not be
too easily abandoned. I" ".S
In the Complies Rends Of February 10 and II, NJ BIsEI
has reached the expression above for the angular
ociy the plane Of oscillation, by long discussion Of the
general equations Of the FoucAuLr has not published
his demonstration, BY reason Of il length and proay 10
justice him should be said that his il the Complies
RendYs is clear and The point making striking contrast
to his cloudy and mythical pepper translated in acknowledgement
The above reasoning will be readily followed by construct
ing the necessary diagrams, and will be fouad sufficiently
rigorous. Sundry minor points and illustrations omitted
for the sake Of breyity. u lts3 E. B. H.