222 PROFESSOR FORBES ON A SEISMOMETER FOR MEASURING 



but very elongated ellipses. Hence it will be easy to distinguish the mark made 

 by the first oscillation of the pendulum, which will always be contrary to the 

 direction in which the vibration of the ground takes place. 



There is one peculiarity arising from the construction of the instrument, 

 which, at first sight, perhaps, we should scarcely expect. The maximum dis- 

 placement we have seen to depend solely upon the time of one vibration, and it 

 may be the same (for small shocks) on whatever scale the instrument is con- 

 structed. We might expect, however, that the taller instruments would oscillate 

 longest, and be most easily set in motion ; but the contrary is the fact. This 

 arises from the circumstance, that the stiffness of the spring must increase with 

 great rapidity as the length of the pendulum becomes greater, that, consequently, 

 the elastic wire bends in all its length, unlike the feeble flat spring of HARDY'S 

 instrument, which doubles over almost at a point. The elastic wire, therefore, 

 tends to vibrate back and forwards many times before the inertia of its load has 

 suffered a complete vibration to take place, and even the flexure of the pendulum- 

 rod, by the powerful elastic action of the wire, will cause it to perform subordi- 

 nate oscillations, which have a tendency to destroy one another, and to bring the 

 whole to rest. This is a decided advantage when the object is (as in the present 

 case) merely to register the first or maximum displacement, and I find that, with 

 the size of the instrument which I have recommended (a 20-inch pendulum), the 

 effect is sufficient and well marked. 



In proceeding to investigate mathematically the action of such an instrument, 

 and to shew how it may be most advantageously adjusted to inform us of the 

 intensity of earthquake shocks, I must repeat, that I proceed upon the very limit- 

 ed hypothesis that the kind of shock desired to be measured consists in a lateral 

 heaving of the earth's surface through a certain space with a uniform velocity, 

 commencing and terminating abruptly. Except under such limitations, it is im- 

 possible to obtain rigorous conclusions. Experience alone can shew how far such 

 conditions correspond with fact ; but, unless theory indicate arrangements for 

 testing their admissibility, our knowledge is likely to remain as indefinite as it is 

 at present. 



I. The pendulum (Plate III. Fig. 1.) being displaced, to find the force tending 

 to redress it. 



Let F = the force in grains, which, when applied to the rod AB at distance 

 = 1 from the centre of motion (a point in the spring D), will balance the force 

 of the spring when the lateral displacement is also = 1. 



k = radius of gyration of the pendulum, which will be nearly equal to the 

 distance of the centre of the ball C from the middle of the wire D. 



M = weight of pendulum in grains. 



6 = angular displacement. 



