m 



h A A. Tlien the nii(l<lle point of the bar 

 moves in a line wliich k very approxi- 

 mately i^traight and parallel to A A, pro- 

 vided its excursions lie -withiu a range not 

 greater than the distance between the fixed 

 supports. These proportions will give 

 sensible astaticism when il ^ is horizontal ; 

 but by making the depth of the hanging 

 bar somewhat greater, or bj' placing the 

 centre of gravity of the hanging bar below 

 the lino of its attachment to the links BB, 

 we may give it any desired amount of 

 stability. 

 When BB are single cords the system is azimuthally unstable, but it is 

 easily jirevented from rotating about a vertical axis by making each of the 

 suspending links B double, in two parts which form a V whose vertex is at the 

 end of C, and whose base is a line through A ];erpendicular to the plane of the 

 paper. Further, this ])revents oscillation perpendicular to the plane of the paper, 

 and so leaves none but the desired freedom. To increase the steadiness we may 

 add a mass which should be as much as jiossible concentrated at the centre of C. 

 I'his may be pivotted about a horizontal axis perpendicular to C, through its 

 centre, and in that case the mass is equivalent to a particle concentrated there. 

 Figs. 47 and 4S, Plate XXIII, show this arrangement in elevation and plan. 

 There the hanging bar is a light ])latfom on which a heavy lead weight is 

 pivotted about the axis i i on the points of two steel screws, which press up into 

 a conical hole and V-slot in a bar _/ to which the weight is rigidly attached. 



Another plan is to use a pair of light suspended platforms, in line with 

 each other, and use them to carry a massive block by three sharp feet which 

 press into a hole and V-slot on one platform, and a V-slot jiarallel to these on 

 the ether. This arrangement is shown in figs. 49 and 50. 



But in both of these arrangements the friction at the ])ivots by which the 

 weight rests on the hanging platform is a disadvantage, wliich is all the more 

 felt because the platform tilts uj) through a considerable angle when displaced 

 from its mean position. For this reason the writer prefers the very simple form 

 .shown in figs. 51 and 52. There the bob or heavy mass is a piece of lead 

 rigidly fixed to the hanging bar. The effect of this is that when a horizontal 

 displacement of the ground occurs, in the line of the bar, the centre of the bar 

 does not remain at rest, but moves through a small determinate distance in the 

 same direction as the ground. 



Let M be the mass of the hanging piece (including the rigidly attached bob), 

 and let Mk^ be its moment of inertia about its central transverse axis. When 

 the hanging piece is displaced, its motion is one of rotation about its instantane- 

 ous axis, which is always situated at the intersection of the suspending cords 



