328 Burhanl:—x\.pparent Variations of the Vertical. 



the distance z to a new position of e(|uilibi-iuin. The displacc- 

 nieiit of M is tiie same as that of a simple pendnl\im of length 

 CM snp])orted on the same pier. 



(2) Hence sin / 



z 

 CM 



= 



47r Z 







4,r' 



T 



sin t 



(3) or 2 = -/ T sin l (Parabola.) 



For a given value of /, s varies directly as T. 



If n be the multiplying ratio of the writing arm and z' the 

 displacement on the record, 



(4) s' = nz = T" sin i, (-i) can also be written 



I 



'■P2 



(5) z' = xn sin 1" — , which is the form used by Professor 



z 



Omori.* 



The pendulums used here have x 'about 75""^ and t about 

 1'74 seconds, and when T is 28 seconds and n equals 10 a 

 change of 1" in the level of the pier corresponds to a lateral 

 displacement of 9 millimeters on the record sheet. The cylin- 

 der revolves once per hour, and also moves laterally at the rate 

 of 3 millimeters per revolution, so that the pen traces a spiral, 

 the lines under normal conditions being spaced 3 millimeters 

 apart. Any tilting of the pier or pedestal in the line of free 

 motion of the pendulum would produce a crowding together 

 or separating of these lines. The amount of tilting during 

 short intervals of time, say 3 or 4 days, can be quite accurately 

 determined by measuring the excess or defect of the spacing 

 over the normal amount, 3 millimeters per revolution. 



A careful study of the records for the period Jan. 1906 to 

 Oct. 1907 shows that the piers on which the two components 

 were mounted were tilted by pronounced changes of temper- 

 ature. These piers were exceptionally well pi-otected against 

 sudden changes of temperature, aud the building would fur- 

 ther protect the ground around the piers from very sudden 

 changes of temperature. 



AVith gradual rise of temperature the top of the N-S pier 

 tipped toward the north and top of the E-W pier toward the 

 west. With falling temperature both sets of piers returned 

 toward their normal positions. 



A study of the diurnal tilting during Jan. 1906 to Oct. 1907 

 shows that it occurred on the E-W component on all clear days. 

 This relation was so definite that it was possible to tell by the 



* Publications of the Earthquake Investigation Committee, No. 21, 

 pp. 5-8. 



