574 Royal Society. 



" Vibratory motions may co-exist with all other iiinds of motions 

 in an infinity of difierent manners, as has been demonstrated by 

 Dan. Bernouilli and L. Euler in vols. xv. and xix. of the Nov, 

 Comment. Acad. Petrop,, and confirmed by experiment. These co- 

 existences of different motions occur in all sonorous bodies without 

 exception : we may, for example, produce the sound of a string 

 stretched on a board, or that of a plate, a tuning-fork, a bell, &c. ; 

 and while the vibrations still last, impress on this sonorous body a 

 motion of rotation round its axis, and at the same time a progres- 

 sive motion : thus all these motions may be performed in the same 

 time, without one being hindered by the other; but the absolute 

 motion of each point will be very complicated." 



Now this is true only when the vibrating body is constrained to 

 vibrate in one direction. When the rod or string is equally flexible 

 in every direction, the plane of vibration given to it from any origi- 

 nal impulse is constantly maintained whatever may be the velocity 

 of rotation communicated to its point of support, provided the axis 

 of vibration remains in the same position or moves only parallel to 

 itself. 



This observed independence of the plane of oscillation on the point 

 of attachment led M. Foucault to assume, that were a flexible pen- 

 dulum suspended from a fixed point in the prolongation of the axis 

 of the earth, that is above one of the poles, and maintained con- 

 stantly in vibration, the plane of oscillation maintaining an inva- 

 riable position in space would appear to a spectator on the earth's 

 surface and moving with it to make an entire revolution in twenty- 

 four hours, but in the opposite direction to that of the rotation of 

 the earth. 



What takes place at other points of the earth's surface is more dif- 

 ficult to determine ; but M. Foucault, from mechanical and geome- 

 trical considerations, was led to the conclusion that the angular dis- 

 placement of the plane of oscillation is equal but opposite to the 

 angular motion of the earth multiplied by the sine of the latitude. 

 According to the theory of rotation, first established by Frisi and 

 more fully developed by Euler and Poinsot, the velocity of rotation 

 of the earth may be considered as the resultant of two angular velo- 

 cities, one round the vertical of the point where the observer is 

 placed, and the other round the meridian or horizontal line lying N. 

 and S. The component of the angular velocity estimated round 

 the vertical axis is n sin y, and the plane of oscillation not partici- 

 pating in this motion remains at rest with respect to it, and there- 

 fore appears to an observer moving with the point, to rotate with 

 the same velocity in the contrary direction. 



It is not necessary that one end of the wire be fixed in the axis 

 of rotation; if it be parallel to a wire so fixed, the rotation of the plane 

 of vibration will be exactly similar ; in such case the wire or axis of 

 vibration will describe the surface of two cones having their com- 

 mon apex in the axis of rotation. 



