ON THE EARTHQUAKE AND VOLCANIC PHENOMENA OF JAPAN. 127 



ment, but of a series of movements, which continually vary in 

 amplitude and period. 

 4. A series of earthquake waves is often accompanied by a series 

 of superimposed waves. 



OVEKTDRNING. 



The theoretical investigation of the OK^erturning of a body like a 

 column, which, although incomplete, has yielded results comparable with 

 those obtained from experiment, is due to my colleague, Professor C. D. 

 West. The result may be expressed as follows : — 



Let /= the acceleration in feet per sec. per sec. which may cause 



overturning, 

 y=the height of the centre of gravity of the column, 

 a;=:the horizontal distance of the centre of gravity of the column 



from the edge about which it may turn, 

 (7=:the acceleration due to gi'avity. 



Then f=n"^. 



y 



Experiments showed that the quantity /, which may be calculated 

 from the dimensions of a body, is closely related to the maximum 



acceleration, or — , which the body experienced at the time of over- 

 turning. 



When the period of motion is short / and — closely approximate, 

 but when the period is great (say two seconds) / may be 30 per cent. 



greater than — . 

 a 



Fracturing. 



A theoretically- derived formula, which showed a close relationship 

 with the results of experiment, was 



^^ gF°A^ 



where a=the acceleration necessary to produce fracture ; 



F°=the force of cohesion, or force per unit surface, which, when 



gradually applied, is sufficient to produce fracture ; 

 A=area of base fractured ; 

 y3=thickness of the column ; 



/=height of centre of gravity above the fractured base ; 

 W= weight of the portion broken off. 



Values for F° varying between 41 and 14-8 lbs. per square inch were 

 determined by pulling portions of the brick and mortar columns asunder 

 in a testing machine. 



Corresponding to these different values of F° different values of a were 

 obtained. 



Out of fourteen columns which were broken, in twelve cases the values 

 obtained for a, when F°=14-8 lbs., were fairly comparable with the quan- 



