We have carried out a high-resolution x-ray study of the mass-density fluctuations and a light-scattering study of the bend-mode-director fluctuations associated with the nematic-smectic-$A$ phase transition in 4-cyano-4\ensuremath{'}-octylbiphenyl (8CB). This phase transition is found to be nearly second order with a first-order temperature jump of less than 10 mK. The peak scattering intensity, $\ensuremath{\sigma}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{0})$, with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{0}=(0, 0, \frac{2\ensuremath{\pi}}{d})$, where $d$ is the layer spacing, and the longitudinal correlation length, ${\ensuremath{\xi}}_{\ensuremath{\parallel}}$, exhibit single power-law divergences for $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}l|1\ensuremath{-}\frac{T}{{T}_{c}}|l2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ with critical exponents of $\ensuremath{\gamma}=1.26\ifmmode\pm\else\textpm\fi{}0.06$ and ${\ensuremath{\nu}}_{\ensuremath{\parallel}}=0.67\ifmmode\pm\else\textpm\fi{}0.02$, respectively. These exponents agree within the errors with the predicted $d=3$, $n=2$ values appropriate to de Gennes' superconductor analogue model. The ratio of the longitudinal to transverse correlation lengths, $\frac{{\ensuremath{\xi}}_{\ensuremath{\parallel}}}{{\ensuremath{\xi}}_{\ensuremath{\perp}}}$, increases gradually with decreasing reduced temperature, changing by a factor of 2.6 over the above temperature range. This corresponds to an effective exponent difference $\sqrt{\ensuremath{\parallel}}\ensuremath{-}\ensuremath{\surd}\mathit{\ifmmode\dagger\else\textdagger\fi{}}=0.16$. The bend mode elastic constant ${K}_{3}$, which is predicted to have a divergent contribution ${(\frac{{k}_{B}T{q}_{o}^{2}}{24\ensuremath{\pi}})}^{2}{\ensuremath{\xi}}_{\ensuremath{\parallel}}$, exhibits single power law behavior for ${10}^{\ensuremath{-}4}\ensuremath{\le}1\ensuremath{-}\frac{T}{{T}_{c}}l{10}^{\ensuremath{-}2}$, with ${\ensuremath{\nu}}_{\ensuremath{\parallel}}=0.62\ifmmode\pm\else\textpm\fi{}0.03$ in reasonable agreement with the x-ray results. The predicted amplitude is, however, wrong by a factor of four. Measurements of $B$, the layer compressibility coefficient in the smectic-$A$ phase, yield $\frac{B}{{K}_{1}}\ensuremath{\sim}{({T}_{c}\ensuremath{-}T)}^{\ensuremath{\varphi}}$ with $\ensuremath{\varphi}=0.26\ifmmode\pm\else\textpm\fi{}0.06$, in agreement with previous experiments in N-$p$-cyanobenzylidene-$p$-octyloxyanilene (CBOOA) and octyloxycyanobenzylidene (80CB), but in marked disagreement with the superconducting analogue model which predicts $\ensuremath{\varphi}={\ensuremath{\nu}}_{\ensuremath{\parallel}}^{1}=0.67$.
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