480 



Mr. L. Southerns on the 



A = 0, r = oo; thus if P is brought into the same vertical 

 as Q, the effect is equal to that of raising w to infinity. Thus 

 whatever (finite) stability the beam may have when the fibres 



Fig. 3. 



are at an initial distance say A apart, it will become unstable 

 or infinitely sensitive for some smaller but still finite value 

 of A. If the balance is originally very stable, this of course 

 will only apply to extremely small values of i/r, since the above 

 only holds for small values of <£, which is great compared 

 with ^jr when h is very small. In order then to make the 

 stable balance as sensitive as we please, we need only move 

 up P towards the vertical through Q by means of its adjusting- 

 screw. This may be done from the outside of the balance-case 

 without touching or even arresting the beam. 



Now suppose that in a given case, in order to reduce the 

 balance to the point of instability, it would be sufficient to 

 raise iv to a height r above the knife-edge. The same result 

 will be produced by decreasing the value of A to A', as shown 

 in fig. 3. Short of this, say for the value A, the sensi- 

 tiveness as measured by the deflexion of the beam for a given 



small load in one scale-pan will be proportional to -r-5 on 



the diagram, for AB represents to some scale the vertical 

 distance of the centre of gravity of the beam below the 

 knife-edge, which is clearly zero when w is at the level A, 



