In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation ${{dR} \over {d\ell }}$ of its resistance R with length $\ell $ is ${{dR} \over {d\ell }}$ $ \propto $ ${1 \over {\sqrt \ell }}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?