444 UNIVERSITY OF VIRGINIA PUBLICATIONS 



conditions put the trial outside of the mathematical researches alluded to. 

 The results may be taken as agreeing with the eastward tendency, but 

 seem to give no satisfactory evidence of the meridian disturbance. The 

 experiment of course has no interest for one seeking for a lecture-room 

 demonstration. 



The spheroidal figure of the earth is another result and proof of its daily 

 rotation, but like the celestial movement, must be merely described to 

 the class. 



In this condition, it is difficult for us at this day to realize the sensation 

 produced in the whole reading world, when at the session of the French 

 Academy of Sciences, February 3, 1851, M. Foucault, a rising young 

 physicist, in a modest note of less than two pages, reported an experiment, 

 demonstrating the rotation of the earth by the use of a pendulum two 

 metres long. He observed that its plane of vibration showed a uniform 

 clock-wise turning at a rate demanded by the daily motion of the earth.* 

 Arago allowed him to repeat the trial with a pendulum 11 metres long in 

 the dome of the observatory. Finally he was permitted to install it on a 

 grand scale in the Pantheon, with a pendulum 67 metres long, having a 

 vibration-time of nearly 8 seconds. The experiment drew throngs of 

 observers and was repeated in the same place at short intervals for months, 

 being at last rudely interrupted by the Coup d'Etat of Louis Napoleon, 

 Dec. 2, 1851. 



As might be expected the apparent facility of the experiment and the 

 extreme simplicity of the apparatus required, caused it soon to be repeated 

 in every land, not only by scientists, but by every earnest student, who 

 could command a metal ball and a string. There were reported repe- 



* Foucault's sine formula may be deduced in a number of ways. Here is a 

 simple one. 



Let Pm P' oP be the parallel of latitude at Paris; PT the north and south line 

 there extended to meet the produced rotation axis of the earth at T (fig. 1). 



Then by the diurnal rotation the line PT will describe a cone, vertex at T and 



base equal to the parallel of latitude. The whole daily deviation (counter clockwise) 



of the line PT and of every line in the horizontal plane at P which makes a fixed angle 



with PT will be the cone surface angle at T developed into a plane, as in fig. 2, that is, 



the angle PTP. 



n t *i. 1 DTD SLTcPmP'oP UPD 



But the angle PTP = ^^^yp - = -^p- 



= 2x sin ip, where (p = ECP = latitude of Paris. Hence deviation in radians per 



, , 27r sin latitude 6.2832 . , ,., , 



mean solar second = ^^ ^—, , — = ———■ sin latitude. 



sidereal day m m. s. seconds 86164 



Hence the deviation clockwise of the vibration plane of pendulum per hour at 



Paris is 11?3; and at the University of Virginia 9?25. 



