80 



EAETHQUAKES. 



The principles which guided him in making these 

 calculations will be understood from the following illus- 

 tration. 



If a column, A b c D, receive a shock or be suddenly 

 moved in the direction of the 

 arrow, the centre of gravity, 

 G, of this column will revolve 

 round the edge, and tend to 

 describe the path G o. If it 

 passes o, the column will fall. 

 The work done in such a case 

 as this is equal to lifting the 

 column through the height 

 oh. 



If G A = a, the angle 

 ^^^- ^^- G Ah = (j), and the weight 



of the body = w, then the above work equals 

 wa (1 — cos (p). 



This must equal the work acquired — that is to say, the 

 kinetic energy of rotation of the body, or 



wa (1 — cos cf)) = 



,2t^2 



2g. 



Where ^(; is the angular velocity of the body at start- 

 ing, K the radius of gyration round A, and g the velocity 

 acquired by a falling body in one second. Whence 



w"^ K^= 2 ga (1 — cos <j)), 

 but lu, the angular velocity, is equal to the statical couple 

 applied, divided by the moment of inertia, or, 



va CO? (f) 



IV = 



K\ 



squaring and substituting 



,-2 = 2<7 X — 

 a 



1 — cos <f) 



