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We report new upper limits on any possible long-term time variation of theratio of the electron to proton masses, $(m_e/m_p)$, the fine-structureconstant, ($\alpha$), and the quantity $\alpha^2 g_p(m_e/m_p)$, where $g_p$ isthe proton gyromagnetic ratio. These limits are based on extremely highprecision observations of H$_2$, Si$^{3+}$, C$^0$ and H$^0$ in high-redshiftquasar absorption lines. They amount to 95\% confidence ranges of $(-7.6\to9.7) \times 10^{-14}$ yr$^{-1}$ for ($m_e/m_p$), $(-4.6\to 4.2)\times 10^{-14}$yr$^{-1}$ for $\alpha$\ and $(-2.2\to 4.2) \times 10^{-15}$ yr$^{-1}$ for$\alpha^2 g_p(m_e/m_p)$, where the elapsed time has been computed for acosmology with \hnought = 75 km s$^{-1}$ Mpc$^{-1}$ and \qnought = 0.5.Comment: 10 pages (w/ 2 tables) of text as 1 LaTeX file (aastex style macros:  aaspp.sty, flushrt.sty) plus 1 uuencoded compressed tar file of 2 PostScript  figures. To appear in the November 10, 1995 Astrophysical Journa

Astrophysical Limits on the Evolution of Dimensionless Physical Constants over Cosmological Time