202 FoucauWs Pendulum Experiment, 



tangents is the angle which the corresponding meridians make 

 with one another in the given latitude. The plane of vibration, 

 since it continues parallel to itself, will therefore change with I 



reference to the meridians, just the amount of the angle included 

 between these tangents. This is readily seen on the globe, mar- 

 ked otFas above explained, in which the Greenwich meridian is the 



starting point. The angle which one of the parallel lines drawn on ¥ 



I 



the globe (or its tangent) makes with the meridian it intersects is 

 (from the nature of parallel lines) equal to the angle between the 

 tangent to this meridian and that of Greenwich. The sum there- 

 fore of the angles between all the tangents to the meridians, will 

 be the amount of apparent variation in the plane of vibration for 

 24 hours. These tangents — which are strictly the cotangents of 

 latitude — form together the surface of a cone whose base is the 

 parallel of latitude, and whose angle of surface at summit is equal 

 to the revolution of the pendulum in 24 hours, li this cone be 

 supposed to be cut open and laid out on a flat plane, it will form 

 a sector of a circle, whose angle at the centre equals the angle 

 around the apex of the cone. The radius of this sector (or of its 

 circle) equals the cotangent of latitude, (cotL); and the circum- 

 ference of the sector is actually a parallel of latitude — a parallel 

 of latitude having been the base of the supposed cone. Now as 

 the number of degrees in any arc varies with the length of the arc 



Clf'C 



as related to the radius of the circle, or as -f^] and since the arc 



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here is a parallel of latitude and these paraflels vary with the co- 

 sine of latitude {cos L), and since also the radius [R) equals coL L 

 it follows that the number of degrees in the arc (or the number 

 expressing the apparent motion of the plane of vibration for 24 \ 



, ^ .„ cos L ' . 



hours,) Will vary as , an expression equivalent to the s%ne 



of latitude. 



Other demonstrations arrive at the same result, but none is more 

 simple or more conclusive. 



The theory thus involves no necessary consideration of the 

 forces engaged, by which many explanations of the experiment 

 are encumbered, but is simply a geometrical problem, based on the 

 position of the meridians of a revolving sphere, and the fact that > 



the pendulum moves in a fixed direction, parallel to the meridian 

 in which it is started. 



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The idea involved in Foucault's experiment " seems to have ! 



occurred long ago, and is mentioned in a paper in the Phil. Trans. 

 1742, No. 468, by the Marquis de Poli, in the course of some ob- 

 servations on the pendulum of a different kind. He remarks, 'I 

 then considered (adopting the hypothesis of the earth's motion,) 

 that in one oscillation of the pendulum there would not be de- 





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