46 Professors Perry and Ayrton on a neglected Principle 



Section E. 

 Let us now consider the case when 

 /=0; 

 then, unless n equals N, all the epochs are nought; so that, as 

 far as the epochs are concerned, no restriction is introduced 

 in making the seismograph-curve exactly represent the earth- 

 quake. C may be put into the form 



n £ ' 



so that if n is small compared with every N (that is, if the 

 springs are weak), then 



C = 2A nearly, 



= nearly, 



since 2A=0 is the condition of continuity; and the coeffi- 

 cients of the second part of the right-hand side of equation 

 (3) are 



AiN?, A 2 N* &c 



which are equal to A 1? A 2 , &c. Therefore weak springs give a 

 very good representation of the earthquake. 



It must, however, be remembered that, although in the case 

 of an earthquake motion having no discontinuity, weak springs 

 give good results, sometimes even better than strong springs, 

 still in the most complicated cases, if the natural vibrations of 

 the springs be quick, a little experience will enable easy cor- 

 rections to be made, which will allow the real earthquake mo- 

 tion to be read with much greater accuracy from the represen- 

 tations than might at first sight appear from the formulae. 



Section F. 

 Without the help of actual experiments made with the form 

 of seismograph we propose, calculation leads us to infer that 

 with a small amount of friction, such as that opposed to a lead 

 ball, of say 400 lbs. mass, surrounded by water or oil, and. 

 with the ball moving a simple recording apparatus, strong 

 springs will always give much more satisfactory results than 

 weak ones for earthquakes such as we have felt in Japan ; but 

 since friction will always cause the natural vibrations of the 

 ball to cease in a longer or shorter time according as the fric- 

 tion is small or great, it is possible that very satisfactory 



