that may he employed in Earthquake Measurements. 41 

 and 



dt U ' 



from which it follows that 



CcosD = ^2J, 

 where 



and 



where 



E(N 2 -n 2 ) 



J - (N 2 -^ 2 ) 2 +4iv[y 2 ' 

 , =w . gJ+ «'/»(aj-sLy > 



n z —f z 



L= 2EN ' 



(N 2 -<) 2 + 4N 2 / 2 



It is obvious that we want the coefficients in the above equa- 

 tion for x to be proportional to nought, A 1? A 2 , A 3 , &c, and 



also the epochs tan -1 ^ 2 v 2 ? tan~* 2 2 3 ,&c. to be all nought 



if we are to have a perfect representation of the earthquake. 



Now for the epochs to be very small, / being a reasonable co- 



n 

 efficient of friction (say /equals Jw), we must have ^ either 



very small or very large. Examining the coefficients of the 

 second part in equation (3), 



?* 2 Ex 



v /^-n 2 ) 2 + 4Ny 2 ' 



?i 2 E 2 



; , &c, 



we see that the condition ^ being very small will make them 



proportional to A 1? A 2 , &c, as is required for a perfect repre- 

 sentation of the earthquake motion ; and if we put the coeffi- 

 cient C into the form 



n 2 



w 



C 2 = S 2 A 



('-» 



r 

 ^ N 2 



2 2 A- 





//- 



(i-J.)^ 



213 



/ 2 V NV N 2 



