Equality of X-Ray and Light Scattering Measurements of Coherence Lengths at the Nematic-Smectic-APhase Transition

We have measured by light scattering the divergence of the elastic constants $K_2$ and $K_3$ at the nematic-smectic-$A$ transition in the liquid crystals 8OCB, $\bar{8}\mathrm{S}5$, and 8CB over a reduced temperature range ${10}^{-5\mathrm{}}<t<\mathrm{}{10}^{-2\mathrm{}}$. We find critical exponents ${\nu }_{\parallel }$ and ${\nu }_{\perp }$ and power-law coefficients ${\xi }_{\parallel }^0$ and ${\xi }_{\perp }^0$ which agree with values obtained from x-ray scattering within experimental error.