Royal SodMf^ i 7S 



rupt the eye of ttiie observer from the vertical piine'pa^^iHg through 

 the diameter, and ill which plane the wire 'Oi'tlM Its positions 

 remains. '* "'■'■ ' 



When the upper end of the wire is placed at '90°, tfilit is when it 

 coincides with the axis of rotation, if the wire be caused to vibrate 

 in any given plane, say from N. to 8., it will continue to do so what- 

 ever rotation may be comniunicatefl ; so that with respect to the 

 moving wheel, or the axis of the wire, tiie plane of vibration will move 

 with the same velocity and in the opposite direction. When the 

 rider is fixed at 30°, and the wii-e makes therefore an angle of 60° 

 with the axis of rotation so as to describe in it^ motion the'surface of 

 a cone having this inclination to the vertical, it will be observed 

 that tiie plane of vibration makes one complete rotation during two 

 rotations of the wheel; this is best observed by fixing the eye to a 

 line in the same plane with the wire, while walking round with the 

 wheel during its rotation. When the rider is fixed at 19,',°, the 

 ))lane of vibration makes one rotation during three rotations'of the 

 wheel ; when fixed at 1 i,l^°, it makes one rotation during four of the 

 wheel, &c. ; and when it is fixed at 0°, the wire lying horizontally, 

 no rotation of the plane of vibration occurs. It is needle.-^s to observe 

 tiiat the sines of 90°, aO°, 19^°, 144% 0°. correspond to tiie numbers 

 1' 2' h h ^'> '^^ reciprocails of ttie nimbersexprtjssing tlie respective 

 times of rotation. 



The axis of a flexible pendulum can only as^sume a position ver- 

 tical to the point of the earth's surface over which it is placed. 

 Were it possible to maintain the vibration of a stretched wire occa- 

 sioned by an original impulse, for a sufiicient length of time, the 

 apparent rotation of its plane of vibration would vary with the in- 

 clination of the wire to the axis of the earth ; placed in this axis it 

 would make a rotation in 24 hours, it would become progressively 

 slower according to the law above given, as it approaches tiie plane 

 of the equator, and when anywhere in this plan* the' 'vibrations 

 would always be performed in the same direction. I" >lir' 



The experiment which led M. Foucault to his ingenious and in- 

 teresting researches relating to the rotation of the earth, is stated 

 by him thus:— " Having fixed on the arbor of a lathe and in the 

 direction of the axis, a lound and flexible steel rod, it was jmt 

 ill vibration by deflecting it from its position of ecjuilibriuni and 

 leaving it to itself. A jilane of oscillation is thus determined, which, 

 from the persistence of tlie usual impressions, is clearly delineated 

 ill space; now it was remarked that on turning the ai'bor which 

 serves as a support to this vibrating rod by the hand, the plane of 

 oscillation is not carried with it." .uui ...;)., (>. i/j ■..) ,.;! 



Tills persistence of the plane of oscillatioh oi'A VibvitJOff vikl, 

 notwithstanding the rotation of the point to which its end is fixed, 

 does not appear to have hitherto been made the subject of philo^so- 

 pliical observation. Ordinary notions even .seem to have been 

 opposed to this now recognised fact. Chladni in his treatise on 

 Acoustics, in the chapter "On the co-existence of vibrations with 

 other kinds of motion," states as follows:— 



