438 



SURFACE WAVES. 



[CHAP, ix 



or for any homogeneous liquid globe of about 5 times the density 

 of water, the half-period is 47 m. 12 s.*" 



" A steel globe of the same dimensions, without mutual gravi- 

 tation of its parts, could scarcely oscillate so rapidly, since the 

 velocity of plane waves of distortion in steel is only about 10,140 

 feet per second, at which rate a space equal to the earth's diameter 

 would not be travelled in less than 1 h. 8 m. 40 s.'f- " 



When the surface oscillates in the form of a zonal harmonic spheroid of the 

 second order, the equation of the lines of motion is #z<7 2 = const., where w 

 denotes the distance of any point from the axis of symmetry, which is taken 

 as axis of x (see Art. 94 (11)). The forms of these lines, for a series of equi- 

 distant values of the constant, are shewn in the annexed figure. 



242. This problem may also be treated very compactly by the 

 method of 'normal coordinates' (Art. 165). 



The kinetic energy is given by the formula 



^d8 



(H), 



* Sir W. Thomson, I. c. 



t Sir W. Thomson. The exact theory of the vibrations of an elastic sphere 

 gives, for the slowest oscillation of a steel globe of the dimensions of the earth, a 

 period of 1 h. 18m. Proc. Lond. Math. Soc., t. xiii., p. 212 (1882). 



