198 M. A. Bravais on Right and Left-handed Oscillations, 



same direction as the rotation of the plane in which the lineal 

 vibrations are executed, that is from east to west, as when these 

 directions are opposed to each other. In the former case the 

 duration is shortened, in the latter case augmented. To the 

 circular oscillation of a pendulum it is therefore necessary to 

 apply a correction, the sign of which depends upon the sense iii 

 which the vibration is executed. 



We arrive at the same result when we discuss a priori the 

 effect of the rotatory motion of the earth upon the duration of 

 the circular oscillation of a pendulum. 



If t denote the duration of a complete lineal vibration of a 

 pendulum (two seconds in the case of a seconds' pendulum), and 

 T the duration of a sidereal day, then the angle of rotation of 



the earth during the time /, at the poles, is 27r ^, and in the 



. . t . 



latitude \ it is 2ir ^ sin X. 



If the same pendulum describes a circle, the apparent rotation 

 during the time t, when the direction of rotation is from east to 

 west, is 



27r + 27r ^ sin X, 

 and when the direction is from west to east, 

 27r— 27rppSinX. 



The change of the angle by the rotation of the earth during 

 the time T amounts therefore to + 27r sin X. The difference of 

 phase between the two motions left and right, after twenty-four 

 hours sidereal time, is therefore equal to the product of two 

 complete oscillations into the sine of the latitude. From this it 

 follows, that the conical seconds' pendulum, when it rotates from 

 east to west at Paris, moves about three seconds quicker than 

 when the rotation is from west to east, a quantity which far ex- 

 ceeds that which astronomers would think of neglecting. 



This difference would be still gi*eater in the case of long pen- 

 dulums. With the pendulum of 11 metres suspended by M. 

 Foucault in the Paris observatory, it would amount to at least 

 ten seconds daily. 



It is conceivable that this inequality might be proved in a 

 direct manner, if two isochronous pendulums were set swinging 

 simultaneously in opposite directions, so that their coincidences 

 on one and the same diameter might be observed ; for the rota- 

 tion of this diameter must be the same as that of the plane of 

 oscillation of a pendulum vibrating in a plane. 



The oscillations being always assumed as very small, what 



