and Recording Earthquake- Motions. 211 



the end. This gives a displacement equal to -J x, and therefore 



an increase of weight on C = \ - hw8, where 8 is the density of 

 mercury in this case. & 



Now the increased elongation of the spring, c remaining 



stationary, is ~ h ; therefore the increased force is 



where W is the normal force on C. Hence we have 



h W lx . 



I hi by 



for an astatic arrangement. In this equation x, y, w, and 8 

 may vary; but y is generally determined with reference to a 

 convenient multiplication, and 8 will generally be either the 

 density of mercury or of a liquid whose density is approxi- 

 mately unity. Hence, x or w being decided on, the other 

 is determinate. 



The case in which the arm A is not used can evidently be 



got from the above by putting -j = 1. This arrangement with 



a long spring is, no doubt, best when the vertical displacement 

 is likely to be great. A round tube has an advantage over 

 the rectangular form of trough t for small motions, as it can 

 be arranged so as to render the system astatic when t is hori- 

 zontal, but to acquire stability when slightly displaced. For 

 large displacements, however, the rectangular form, when of 

 suitable depth, is no doubt best. 



Instruments of the class here described are not to be relied 

 on for static records, owing to the ease with which a large dis- 

 placement can be given to the lever. For such purposes an 

 instrument with a somewhat short natural period, controlled by 

 some kind of frictional resistance, acts best. 



Before the above method of compensation suggested itself 

 to me, I had attempted compensating by placing the axis B 

 below the line joining p and c. This method has the disad- 

 vantage, that generally a mass, either that of the weight or 

 the spring, has to receive a motion of translation in order that 

 the point C may remain at the same height. There is also 

 another disadvantage, namely that after a small displacement 

 the equilibrium becomes unstable. 



Several other methods have suggested themselves to me — 

 such as allowing the ring R to roll backwards and forwards, 

 on a properly proportioned axis, in a curve at the end of the 



