Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4 : 1$ and force $F _ { 1 }$ is applied to $P$, an extension of $\Delta l$ is produced. The force which is required to produce same extension in Q is $F _ { 2 }$. The value of $\frac { F _ { 1 } } { F _ { 2 } }$ is $\_\_\_\_$ .