  The electro-optical Kerr effect induced by a slowly-varying applied electric
field in liquid helium at temperatures below the $\lambda$-point is
investigated. The Kerr constant of liquid helium is measured to be $(1.43\pm
0.02^{(stat)} \pm 0.04^{(sys)})\times 10^{-20}$ (cm/V)$^2$ at $T=1.5$ K. Within
the experimental uncertainty, the Kerr constant is independent of temperature
in the range $T=1.5$ K to 2.17 K, which implies that the Kerr constant of the
superfluid component of liquid helium is the same as that of normal liquid
helium. Our result also indicates that pair and higher correlations of He atoms
in the liquid phase account for about 23% of the measured Kerr constant. Liquid
nitrogen was used to test the experimental set-up, the result for the liquid
nitrogen Kerr constant is $(4.38\pm 0.15)\times 10^{-18} $(cm/V)$^2$. The
knowledge of the Kerr constant in these media allows the Kerr effect to be used
as a non-contact technique for measuring the magnitude and mapping out the
distribution of electric fields inside these cryogenic insulants.
