104, 105] FOTJCAULT'S PENDULUM EXPERIMENT. 323 



The particle falls to the east by an amount proportional to the square 

 root of the cube of the height of fall and to the cosine of the 

 latitude. This has been experimentally verified. 



1O5. Motion of a Spherical Pendulum. We have for the 

 pendulum the equation of constraint 



so that to the previous equations of motion are added terms 



giving 



245) 



Multiplying by -^i ~t -^ respectively and adding, then integrating, 

 we get the equation of energy, 



the gyroscopic terms disappearing, as usual. For a second integral 

 we get as in 23, 



If we assume that the oscillations are infinitely small, 



t i- 



is infinitely small, and the last term above is of the third order and 

 may be neglected. Integrating we have 



248 ) 



The equation of energy 246) becomes 



Inserting polar coordinates, 



| = r cos o, 



= r sn o, 



21 



