ON SEISMOLOGICAL INVESTIGATIONS. 75 



The magnification of impulsive horizontal displacements of the ground 

 may be found in two ways : — 



(1) The easier way is to obtain it from the period of undamped 

 oscillation, together with the sensitivity to static tilt (' Modern 

 Seismology,' by G. W. Walker, page 23). 



According to Mr. Shaw's advice, when observing the period, the 

 damping magnets were entirely removed, not merely tied up to the pillar, 

 lest their weight should bend the latter. The period came to 9-88 sees. 

 for small swings, 10 08 for large ones, and 9 9 has been taken in the 

 subsequent calculation. 



The arrangements provided for determining tilt are very convenient. 

 The pitch of the tilting screw, the distances between the feet and the 

 lengths of the path of light, were all measured, and the scale of tilt thus 

 verified to ^ per cent. The sensitivity to static tilt was found to be 

 e-Sgmm. on the paper per 10"^ radian. Now the magnification for 

 sudden lateral displacements is 



(cms. on paper) x iv^ , • , , non 



, — - ^.,^f- ^ - , --- . -,,„, which comes to 282. 

 (radians- tilt) X g X (period)^ 



(2) As a check, the same magnification was calculated independently 

 from the lengths of the levers and the radius of gyration of the boom 

 about its pivot. In the sketch, BR is the boom pivoted at R. CB is a 

 link, CD a lever pivoted at D, and D is also the mirror. P is the photo- 

 graphic paper. 



Lengths of Levers.— The small length CD was measured by a 

 travelling microscope. The distance from the mirror D to the photo- 

 graphic paper was diminished by ^ of the thickness of the cylindrical 

 lens. The length of the equivalent mechanical pointer was taken as 



2 (DP - ^K) (BR), , ^ on A . Tr T. • n . • , 



— ^^ CD^ ^^^^ metres. Here K is the thickness 



of the cylindrical lens. 



B T R 



w 



> 



Fig. 1. 



Radius of Gyration. — To find this, the moments of inertia about 

 the pivot R of the several parts were measured separately, added up, 

 and divided by the total mass. 



The moment of inertia of the boom was found from the position of its 

 centre of mass, together with its period of vibration, when hung up 

 vertically by a short thread attached at W and set to oscillate about a 

 horizontal axis through R. 



The heavy dumb-bell shaped mass was at first pivoted upon the boom, 

 as in some Milne instruments ; the intention being to diminish the 

 moment of inertia. The gain in this respect is less than 20 per cent, 

 of the whole moment of inertia of the moving system. On the other 



