40 Professors Perry and Ayrton on a neglected Principle 



however, our experience of earthquakes in Japan leads us to 

 believe is rarely the case), then weak springs will give good 

 results. 



Section D. 



Let the earthquake motion be a periodic function of the 

 time ; then we know it may be expressed in the form 



z = A + 2 A cos (N* + F), 

 where A, N, and F may have any values we please in the 

 successive terms of the series. Or, generally, it may be ex- 

 pressed in the form 



z=2Acos(N* + F), 



one N having a value nought. 

 Let us take the restricted case 



-- = 2AcosN£; 

 then, if there is no discontinuity at the beginning, 



z=0, 



and 



when 



t = Q; 



from which it may easily be shown that 



2=0. 

 The differential equation of the motion of the centre of the 

 mass M relative to the box is 



f? + 2/^ + n^ = n^E cos N*, 

 dtr J dt 



where 



for each value of A and N taken in the successive terms of 

 the series. The solution of this differential equation is, if/ is 

 less than n. 



//XT'/! „9.\9 ■ JAT5 />2 ' ^ 7 



x = erfl C cos (\/ r? —f 2 t + D) 



Ecos^-f-tan" 1 ^^) 



v \N 2 - n y-^Wj 



the constants C and D being determined from the initial con 

 ditions, which are, when 



t = 0, 



a?=0, 



