EARTHQUAKE MOTION DEDUCED FROM OBSERVATION. 8 1 

 and since the length, of the corresponding pendulum is 



\^=2gl X 



1— cos (j) 



COS^ </). 



To apply this to any given case we must find the value 



of I or of — , 

 a 



. Mallet finds these values for the cube, solid and hollow 

 rectangular parallelopipeds, solid and hollow cylinders, 

 &c. In these formulae we have a direct connection be- 

 tween the dimensions and form of a body and the velocity 

 with which the ground must move beneath it to cause its 

 overthrow. 



Not only is the case discussed for horizontal forces, 

 but also for forces acting obliquely. Similar reasonings 

 are applied to the productions of fractures in walls, but 

 as there is uncertainty in our kno\^ledge of the co- 

 efficient of force necessary to produce fracture through 

 joints across beds of masonry, the deductions ought not 

 to be applied as the measures of 

 velocity. Where the fractures 

 occur at the base or in horizontal 

 planes, or in those of the con- 

 tinuous beds of the masonry, or 

 through homogeneous bodies, the 

 uncertainty is not so great, and for 

 cases like these Mallet gives several 

 illustrations. The distance to 

 which bodies had been projected, 



as, for example, ornaments from the tops of pedestals, 

 coping-stones from the edges of roofs, were also used as 

 means of determining the angle at which the shock had 



Fig. 15. 



