ON SEISMOLOGICAL INVESTIGATIONS. 77 



must not be too large. The measurements were made on the photo- 

 graphic record, and gave 45 : 1 for the ratio of successive displacements 

 on opposite sides of the zero. From these data the curve in fig. (2) was 

 plotted. 



Comparison of the Magnification with that of a Galitzin Instrument 

 having Galvanometric Registration. — This was done by selecting a 

 point of time at and near which the natural disturbance was of a 

 regular sinusoidal character on the seismograms of both the Milne-Shaw 

 and Galitzin instruments. The two instruments were in the same room 

 (though on separate piers) and their booms were parallel to one another, 

 so that we may assume that the ground motion was the same for both. 

 The amplitude and period of the Galitzin chart were measured, and from 

 these and from the known constants of the Galitzin instrument the 

 amplitude of the ground motion was deduced. Dividing this quantity 

 by the amplitude on the Milne-ShaAv record we get the magnification of 

 the latter instrument. The figures so obtained have been represented by 

 the crosses in fig. 2. The agreement of the crosses, with the curve 

 obtained by consideration of the Milne-Shaw instrument alone, is nearly 

 as good as could be expect'^d, considering the uncertainties involved in 

 measuring the small amplitudes of 1 or 2 mm. on the Milne-Shaw record. 

 The constants of the Galitzin instrument were obtained in May 1915 by 

 the method of tapping the boom (Gahtzin's 'Lectures,' ch. vii. § 3) and 

 differ only slightly from those obtained in previous years. 



Direction on the Paper. — The boom is suddenly pulled to the west. 

 The light spot therefore moves as if the ground had been jerked to the 

 east. This test is made on every sheet. 



Lag of Maximum. — The usual theory of lag begins by assuming that 

 the ground is in a regular and constant state of sinusoidal motion. Each 

 wave is by hypothesis exactly like its neighbours, and therefore it is 

 impossible to distinguish one wave from another, and the lag is indeter- 

 minate as to an arbitrary number of whole wave-lengths. This is the 

 only arbitrariness. The theory usually ends, however, in a formula 

 which gives the tangent of the angle of lag, and the angle is therefore 

 unspecified as to a whole number of half wave-lengths. On going back 

 and examining the sine and cosine of the angle of lag this uncertainty 

 disappears, in so far as it concerns the phase relations of the quantities 

 represented by the symbols in the theory. But there is still a practical 

 uncertainty of half a wave-length until we have connected the symbols 

 to our practice in reading records, by defining the relation of east and 

 west ground-motion to up and down the record. The definition here 

 adopted is that when all is at rest and the ground suddenly moves, then 

 the initial displacement of the trace on the developed photographic 

 record is conventionally said to be in the same direction as the initial 

 motion of the ground. The actual test is made by pulling the boom 

 in the opposite direction, as stated above. 



Now the equation of motion of a ' critically aperiodic ' boom is 



(i-r^--f- <'> 



where 6 is the angle turned through by the boom. 

 Here x is the displacement of the ground. 



n and I are positive constants. 



