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\write 0 {8.  TIDAL VARIATIONS IN THE EARTH'S ROTATION 
\noexpand\dotfill\the\pageno\noexpand\break}
\noindent{\large CHAPTER 8}  {\bf TIDAL VARIATIONS IN THE EARTH'S
ROTATION}
\bigskip

     Periodic variations in UT1 due to tidal deformation of the
polar moment of inertia were derived by Yoder {\it et al.} (1981)
including the tidal deformation of the Earth with a decoupled
core.  This model uses effective Love numbers that differ from 
the bulk value of 0.301 because of the oceans and the fluid core
giving rise to different theoretical values of the ratio $k/C$ for
the fortnightly and monthly terms.  However, Yoder {\it et al.}
recommend the value of 0.94 for $k/C$ for both cases.  Oceanic tides 
also cause variations in UT1 represented by models given by Brosche 
{\it et al.} (1991, 1989), Dickman (1993, 1991, 1990, 1989), 
Gross (1993), Herring and Dong (1994), and Ray {\it et al.} (1994).  
The contribution of the oceanic tides is split into a part which is 
in phase with the solid Earth tides and an out-of-phase part.

     Table 8.1 provides corrections for the tidal variations in
UT1$-$UTC with periods between five and 35 days.  This is identical
to tables in IERS Technical Notes 3 and 13 which defined UT1R$-$UTC,
$\Delta-\Delta$R, and $\omega-\omega$R.  Table 8.1 continues to
define UT1R$-$UTC, $\Delta-\Delta$R, and $\omega-\omega$R.

$${\rm UT1-UT1R} =  \sum^{41}_{i=1}A_i\sin\xi_i$$
$$\Delta-\Delta{\rm R} = \sum^{41}_{i=1}A'_i\cos\xi_i$$
$$\omega-\omega{\rm R} = \sum^{41}_{i=1}A''_i\cos\xi_i$$
$$\xi_i = \sum^5_{j=1}a_{ij}\alpha_j$$
$a_{ij} =$ integer multipliers of the $\alpha_j$ ($l$, $l'$,
$F$, $D$ or $\Omega$) for the $i^{\rm th}$ tide given in the
first five columns of Table 8.1.
$A_i$, $A'_i$, $A''_i$ are given in columns 7-9 
respectively in Table 8.1.

     Table 8.2 is identical to Table 8.2 in IERS Technical Note
13 which defined UT1S$-$UTC, $\Delta-\Delta$S, and $\omega-\omega$S
except that the table below corrects one misprint in the out-of-phase
term for the 18.6-year tide.  Table 8.2 provides corrections for the
tidal variations with periods from five days to 18.6 years and
incorporates the most significant effects of oceanic tides using
the model of Dickman (1993).

$${\rm UT1-UT1S} =  \sum^{62}_{i=1}B_i\sin\xi_i + C_i\cos\xi_i$$
$$\Delta-\Delta{\rm S} = \sum^{62}_{i=1}B'_i\cos\xi_i + C'_i\sin\xi_i$$
$$\omega-\omega{\rm S} = \sum^{62}_{i=1}B''_i\cos\xi_i + C''_i\sin\xi_i$$
$\xi_i$ are defined the same way as for UT1R above except the 
$a_{ij}$ are given in the first five columns of Table 8.2.
$B_i$, $C_i$, $B'_i$, $C'_i$, $B''_i$, and $C''_i$ 
are given in columns 7-12 respectively in Table 8.2.

     Table 8.3 provides corrections for daily and sub-daily tidal
variations in the Earth's rotation from Ray (1995).  Values 
corrected using Table 8.3 are referred to as UT1D, 
$\Delta-\Delta$D, and $\omega-\omega$D.  Those corrected using 
Table 8.1 and 8.3 will then be called UT1DR, $\Delta-\Delta$DR, 
and $\omega-\omega$DR, and those corrected using Table 8.2 and 8.3
will be called UT1DS, $\Delta-\Delta$DS, and $\omega-\omega$DS.

$${\rm UT1-UT1D} =  \sum^{8}_{i=1}D_i\sin\xi_i + E_i\cos\xi_i$$
$$\Delta-\Delta{\rm D} = \sum^{8}_{i=1}D'_i\cos\xi_i + E'_i\sin\xi_i$$
$$\omega-\omega{\rm D} = \sum^{8}_{i=1}D''_i\cos\xi_i + E''_i\sin\xi_i$$
$$\xi_i = \sum^6_{j=1}c_{ij}\gamma_i + \phi_i$$
$c_{ij} =$ integer multipliers of the $\gamma_j$ ($l$, $l'$, $F$,
$D$, $\Omega$, or $\theta$) for the $i^{\rm th}$ tide given in columns
2-7 of Table 8.3.  $\phi_i =$ the phase given in column 8 of Table 8.3.

     Table 8.4 provides corrections for daily and subdaily tidal
variations in polar motion from Ray (1995).  Values corrected by
using this table are referred to as xD and yD and are obtained by

$$x - xD = \sum^{8}_{i=1}F_i\sin\xi_i + G_i\cos\xi_i,$$
$$y - yD = \sum^{8}_{i=1}H_i\sin\xi_i + K_i\cos\xi_i,$$

\noindent where $F_i$, $G_i$, $H_i$, and $K_i$ are given in the
table and

$$\xi_i = \sum^{6}_{j=1}c_{ij}\gamma_i+\phi_i.$$

\noindent $c_{ij}$ = integer multipliers of the $\gamma_i$ ($l$, $l'$,
$F$, $D$, $\Omega$, or $\theta$) for the $i^{th}$ tide given in
columns 2-7 of Table 8.4.  $\phi_i$ = the phase given in column 8 of
Table 8.4.

\vfil\eject
%\bigskip
\noindent Table 8.1. Zonal Tide Terms With Periods Up to 35 Days. UT1R,
$\Delta $R, and $\omega $R represent the regularized forms of UT1,
the duration of the day $\Delta$, and the angular velocity of the
Earth, $\omega$.  The units are $10^{-4}$ s for UT, $10^{-5}$ s for
$\Delta$, and $10^{-14}$ rad/s for $\omega$.
\hrule

\noindent\kern3pc ARGUMENT*\kern4pc PERIOD \kern1pc UT1$-$UT1R \kern1pc
$\Delta-\Delta $R \kern1.5pc $\omega-\omega $R\hfil\break
\hbox{}\kern17pc Coefficient of \kern2pc Coefficient of\hfil\break
\hbox{}\kern.5pc$l$\kern2.2pc$l'$\kern2pc$F$\kern2pc$D$\kern2pc$
\Omega$\kern2.1pc Days\kern1pc Sin (Argument)\kern1pc Cos (Argument)
\halign{\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&
\hfil#\kern2pc&\hfil#\kern3pc&\hfil#\kern3pc&\hfil#\kern3pc&\hfil#\cr
  1&   0&   2&   2&   2&     5.64&      -0.02&        0.3&     -0.2\cr
  2&   0&   2&   0&   1&     6.85&      -0.04&        0.4&     -0.3\cr
  2&   0&   2&   0&   2&     6.86&      -0.10&        0.9&     -0.8\cr
  0&   0&   2&   2&   1&     7.09&      -0.05&        0.4&     -0.4\cr
  0&   0&   2&   2&   2&     7.10&      -0.12&        1.1&     -0.9\cr
  1&   0&   2&   0&   0&     9.11&      -0.04&        0.3&     -0.2\cr
  1&   0&   2&   0&   1&     9.12&      -0.41&        2.8&     -2.4\cr
  1&   0&   2&   0&   2&     9.13&      -0.99&        6.8&     -5.8\cr
  3&   0&   0&   0&   0&     9.18&      -0.02&        0.1&     -0.1\cr
 -1&   0&   2&   2&   1&     9.54&      -0.08&        0.5&     -0.5\cr
 -1&   0&   2&   2&   2&     9.56&      -0.20&        1.3&     -1.1\cr
  1&   0&   0&   2&   0&     9.61&      -0.08&        0.5&     -0.4\cr
  2&   0&   2&  -2&   2&    12.81&       0.02&       -0.1&      0.1\cr
  0&   1&   2&   0&   2&    13.17&       0.03&       -0.1&      0.1\cr
  0&   0&   2&   0&   0&    13.61&      -0.30&        1.4&     -1.2\cr
  0&   0&   2&   0&   1&    13.63&      -3.21&       14.8&    -12.5\cr
  0&   0&   2&   0&   2&    13.66&      -7.76&       35.7&    -30.1\cr
  2&   0&   0&   0&  -1&    13.75&       0.02&       -0.1&      0.1\cr
  2&   0&   0&   0&   0&    13.78&      -0.34&        1.5&     -1.3\cr
  2&   0&   0&   0&   1&    13.81&       0.02&       -0.1&      0.1\cr
  0&  -1&   2&   0&   2&    14.19&      -0.02&        0.1&     -0.1\cr
  0&   0&   0&   2&  -1&    14.73&       0.05&       -0.2&      0.2\cr
  0&   0&   0&   2&   0&    14.77&      -0.73&        3.1&     -2.6\cr
  0&   0&   0&   2&   1&    14.80&      -0.05&        0.2&     -0.2\cr
  0&  -1&   0&   2&   0&    15.39&      -0.05&        0.2&     -0.2\cr
  1&   0&   2&  -2&   1&    23.86&       0.05&       -0.1&      0.1\cr
  1&   0&   2&  -2&   2&    23.94&       0.10&       -0.3&      0.2\cr
  1&   1&   0&   0&   0&    25.62&       0.04&       -0.1&      0.1\cr
 -1&   0&   2&   0&   0&    26.88&       0.05&       -0.1&      0.1\cr
 -1&   0&   2&   0&   1&    26.98&       0.18&       -0.4&      0.3\cr
 -1&   0&   2&   0&   2&    27.09&       0.44&       -1.0&      0.9\cr
  1&   0&   0&   0&  -1&    27.44&       0.53&       -1.2&      1.0\cr
  1&   0&   0&   0&   0&    27.56&      -8.26&       18.8&    -15.9\cr
  1&   0&   0&   0&   1&    27.67&       0.54&       -1.2&      1.0\cr
  0&   0&   0&   1&   0&    29.53&       0.05&       -0.1&      0.1\cr
  1&  -1&   0&   0&   0&    29.80&      -0.06&        0.1&     -0.1\cr
 -1&   0&   0&   2&  -1&    31.66&       0.12&       -0.2&      0.2\cr
 -1&   0&   0&   2&   0&    31.81&      -1.82&        3.6&     -3.0\cr
 -1&   0&   0&   2&   1&    31.96&       0.13&       -0.3&      0.2\cr
  1&   0&  -2&   2&  -1&    32.61&       0.02&        0.0&      0.0\cr
 -1&  -1&   0&   2&   0&    34.85&      -0.09&        0.2&     -0.1\cr}
\smallskip
\hrule
\bigskip
\noindent Table 8.2. Zonal Tide Terms. UT1S1, $\Delta $S1, and
$\omega $S1 represent the regularized forms of UT1, the duration of
the day $\Delta$, and the angular velocity of the Earth, $\omega$. The
units are $10^{-4}$ s for UT, $10^{-5}$ s for $\Delta$, and $10^{-14}$
rad/s for $\omega$.
\hrule

\noindent\kern3pc ARGUMENT* \kern4pc PERIOD \kern4pc UT1$-$UT1S
\kern3.6pc $\Delta-\Delta $S \kern2.7pc $\omega-\omega $S\hfil\break
\hbox{}\kern27pc Coefficient of 
\halign{\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&
\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&
\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\kern2pc&\hfil#\cr
$l$&$l'$&$F$&$D$&$\Omega$& Days& Sin& Cos& Cos& Sin& Cos& Sin\cr
 1& 0& 2& 2& 2&     5.64&    -0.02&     &   0.3&    &   -0.2\cr
 2& 0& 2& 0& 1&     6.85&    -0.04&     &   0.4&    &   -0.3\cr
 2& 0& 2& 0& 2&     6.86&    -0.10&     &   0.9&    &   -0.8\cr
 0& 0& 2& 2& 1&     7.09&    -0.05&     &   0.4&    &   -0.4\cr
 0& 0& 2& 2& 2&     7.10&    -0.12&     &   1.1&    &   -0.9\cr
 1& 0& 2& 0& 0&     9.11&    -0.04&     &   0.3&    &   -0.2\cr
 1& 0& 2& 0& 1&     9.12&    -0.40& 0.01&   2.7& 0.1&   -2.3&  -0.1\cr
 1& 0& 2& 0& 2&     9.13&    -0.98& 0.03&   6.7& 0.2&   -5.7&  -0.2\cr
 3& 0& 0& 0& 0&     9.18&    -0.02&     &   0.1&    &   -0.1\cr
-1& 0& 2& 2& 1&     9.54&    -0.08&     &   0.5&    &   -0.5\cr
-1& 0& 2& 2& 2&     9.56&    -0.20&     &   1.3&    &   -1.1\cr
 1& 0& 0& 2& 0&     9.61&    -0.08&     &   0.5&    &   -0.4\cr
 2& 0& 2&-2& 2&    12.81&     0.02&     &  -0.1&    &    0.1\cr
 0& 1& 2& 0& 2&    13.17&     0.03&     &  -0.1&    &    0.1\cr
 0& 0& 2& 0& 0&    13.61&    -0.30&     &   1.4&    &   -1.2\cr
 0& 0& 2& 0& 1&    13.63&    -3.20& 0.09&  14.7& 0.4&  -12.4&  -0.4\cr
 0& 0& 2& 0& 2&    13.66&    -7.73& 0.21&  35.6& 1.0&  -30.0&  -0.8\cr
 2& 0& 0& 0&-1&    13.75&     0.02&     &  -0.1&    &    0.1\cr
 2& 0& 0& 0& 0&    13.78&    -0.34&     &   1.5&    &   -1.3\cr
 2& 0& 0& 0& 1&    13.81&     0.02&     &  -0.1&    &    0.1\cr
 0&-1& 2& 0& 2&    14.19&    -0.02&     &   0.1&    &   -0.1\cr
 0& 0& 0& 2&-1&    14.73&     0.05&     &  -0.2&    &    0.2\cr
 0& 0& 0& 2& 0&    14.77&    -0.72& 0.02&   3.1& 0.1&   -2.6&  -0.1\cr
 0& 0& 0& 2& 1&    14.80&    -0.05&     &   0.2&    &   -0.2\cr
 0&-1& 0& 2& 0&    15.39&    -0.05&     &   0.2&    &   -0.2\cr
 1& 0& 2&-2& 1&    23.86&     0.05&     &  -0.1&    &    0.1\cr
 1& 0& 2&-2& 2&    23.94&     0.10&     &  -0.3&    &    0.2\cr
 1& 1& 0& 0& 0&    25.62&     0.04&     &  -0.1&    &    0.1\cr
-1& 0& 2& 0& 0&    26.88&     0.05&     &  -0.1&    &    0.1\cr
-1& 0& 2& 0& 1&    26.98&     0.18&     &  -0.4&    &    0.3\cr
-1& 0& 2& 0& 2&    27.09&     0.44&     &  -1.0&    &    0.9\cr
 1& 0& 0& 0&-1&    27.44&     0.53&     &  -1.2&    &    1.0\cr
 1& 0& 0& 0& 0&    27.56&    -8.33& 0.12&  19.0& 0.3&  -16.0&  -0.2\cr
 1& 0& 0& 0& 1&    27.67&     0.54&     &  -1.2&    &    1.0\cr
 0& 0& 0& 1& 0&    29.53&     0.05&     &  -0.1&    &    0.1\cr
 1&-1& 0& 0& 0&    29.80&    -0.06&     &   0.1&    &   -0.1\cr
-1& 0& 0& 2&-1&    31.66&     0.12&     &  -0.2&    &    0.2\cr
-1& 0& 0& 2& 0&    31.81&    -1.84& 0.02&   3.6& 0.0&   -3.0&   0.0\cr
-1& 0& 0& 2& 1&    31.96&     0.13&     &  -0.3&    &    0.2\cr
 1& 0&-2& 2&-1&    32.61&     0.02&     &   0.0&    &    0.0\cr
-1&-1& 0& 2& 0&    34.85&    -0.09&     &   0.2&    &   -0.1\cr
 0& 2& 2&-2& 2&    91.31&    -0.06&     &   0.0&    &    0.0\cr
 0& 1& 2&-2& 1&   119.61&     0.03&     &   0.0&    &    0.0\cr
 0& 1& 2&-2& 2&   121.75&    -1.88&     &   1.0&    &   -0.8\cr
 0& 0& 2&-2& 0&   173.31&     0.25&     &  -0.1&    &    0.1\cr
 0& 0& 2&-2& 1&   177.84&     1.17&     &  -0.4&    &    0.3\cr
 0& 0& 2&-2& 2&   182.62&   -48.84& 0.11&  16.8& 0.0&  -14.2&   0.0\cr
 0& 2& 0& 0& 0&   182.63&    -0.19&     &   0.1&    &   -0.1\cr
 2& 0& 0&-2&-1&   199.84&     0.05&     &   0.0&    &    0.0\cr
 2& 0& 0&-2& 0&   205.89&    -0.55&     &   0.2&    &   -0.1\cr
 2& 0& 0&-2& 1&   212.32&     0.04&     &   0.0&    &    0.0\cr
 0&-1& 2&-2& 1&   346.60&    -0.05&     &   0.0&    &    0.0\cr
 0& 1& 0& 0&-1&   346.64&     0.09&     &   0.0&    &    0.0\cr
 0&-1& 2&-2& 2&   365.22&     0.83&     &  -0.1&    &    0.1\cr
 0& 1& 0& 0& 0&   365.26&   -15.55& 0.02&   2.6& 0.0&   -2.2&   0.0\cr
 0& 1& 0& 0& 1&   386.00&    -0.14&     &   0.0&    &    0.0\cr
 1& 0& 0&-1& 0&   411.78&     0.03&     &   0.0&    &    0.0\cr
 2& 0&-2& 0& 0&  1095.17&    -0.14&     &   0.0&    &    0.0\cr
-2& 0& 2& 0& 1&  1305.47&     0.42&     &   0.0&    &    0.0\cr
-1& 1& 0& 1& 0&  3232.85&     0.04&     &   0.0&    &    0.0\cr
 0& 0& 0& 0& 2&  3399.18&     7.90&     &   0.1&    &   -0.1\cr
 0& 0& 0& 0& 1&  6798.38& -1637.68&-0.10& -15.2& 0.0&   12.8&   0.0\cr}
\bigskip
\hrule
\bigskip

\noindent Table 8.3.  Diurnal and subdiurnal zonal tide terms.  The
units are $10^{-4}$ s for UT, $10^{-5}$ s for $\Delta$, and $10^{-14}$
rad/s for $\omega$.
\hrule

\noindent\kern1pc Tide \kern1pc $l$ \kern1pc $\l'$ \kern1pc F
\kern1pc D \kern1pc $\Omega$ \kern1pc $\theta$ \kern0.4pc phase
\kern0.4pc Period \kern0.7pc UT1$-$UT1D \kern1.3pc $\Delta-\Delta$D
\kern2.5pc $\omega-\omega$D
\hfil\break
\hbox{} \kern25pc Coefficients of \hfil\break
\hbox{} \kern13.6pc (deg.) \kern0.0pc (hours) \kern1.1pc Sin 
\kern1.2pc Cos \kern1pc Cos \kern1.3pc Sin \kern1.2pc Cos \kern1.2pc Sin
\halign{\kern1.3pc#\hfil\kern1.1pc&\hfil#\kern1.2pc&\hfil#\kern1.3pc&
\hfil#\kern1.5pc&\hfil#\kern1.2pc&\hfil#\kern1.3pc&\hfil#\kern1pc&\hfil#
\kern1pc&\hfil#\kern1pc&\hfil#\kern1pc&\hfil#\kern1pc&\hfil#
\kern1pc&\hfil#\kern1pc&\hfil#\kern1pc&\hfil#\cr
Q$_1$&-1& 0&-2& 0&-2& 1&-90& 26.868& 0.02& 0.05&-1.4& 2.8&  1.2& -2.4\cr
O$_1$& 0& 0&-2& 0&-2& 1&-90& 25.819& 0.12& 0.16&-7.1& 9.4&  6.0& -7.9\cr
P$_1$& 0& 0&-2& 2&-2& 1&-90& 24.066& 0.03& 0.05&-1.8& 3.2&  1.5& -2.7\cr
K$_1$& 0& 0& 0& 0& 0& 1& 90& 23.935& 0.09& 0.18&-5.4&11.2&  4.6& -9.4\cr
N$_2$&-1& 0&-2& 0&-2& 2&  0& 12.658&-0.04&-0.02& 4.5&-1.8& -3.8&  1.6\cr
M$_2$& 0& 0&-2& 0&-2& 2&  0& 12.421&-0.16&-0.07&19.6&-8.7&-16.6&  7.4\cr
S$_2$& 0& 0&-2& 2&-2& 2&  0& 12.000&-0.08& 0.00& 9.5&-0.5& -8.1&  0.4\cr
K$_2$& 0& 0& 0& 0& 0& 2&  0& 11.967&-0.02& 0.00& 2.5&-0.5& -2.1&  0.4\cr}
\bigskip
\hrule
\bigskip
\item{$\theta$} $ = 100^\circ\d4606184 + 360^\circ\d98564737$(MJD-51544.5)
Earth's rotation angle

\vskip-1pc
See Chapter 5 for definitions of $l$, $l'$, $F$, $D$, $\Omega$.
\bigskip

\vfil\eject
\noindent Table 8.4.  Diurnal and subdiurnal tide terms for 
polar motion.  The units are msec. of arc for $\Delta x$ and
$\Delta y$.
\hrule
\noindent\kern1pc Tide \kern1pc $l$ \kern1pc $\l'$ \kern1pc F
\kern1pc D \kern1pc $\Omega$ \kern1pc $\theta$ \kern0.4pc phase
\kern0.4pc Period \kern3.0pc $\Delta x$ \kern5.0pc $\Delta y$
\hfil\break
\hbox{} \kern23pc Coefficients of \hfil\break
\hbox{} \kern13.6pc (deg.) \kern0.0pc (hours) \kern1.3pc Sin 
\kern1.7pc Cos \kern1.7pc Sin \kern1.9pc Cos
\halign{\kern1.3pc#\hfil\kern1.1pc&\hfil#\kern1.2pc&\hfil#\kern1.3pc&
\hfil#\kern1.5pc&\hfil#\kern1.2pc&\hfil#\kern1.3pc&\hfil#\kern1pc&\hfil#
\kern1pc&\hfil#\kern1pc&\hfil#\kern1pc&\hfil#\kern1pc&\hfil#
\kern1pc&\hfil#\cr
Q$_1$&-1& 0&-2& 0&-2& 1&-90& 26.868&-0.026& 0.006&-0.006&-0.026\cr
O$_1$& 0& 0&-2& 0&-2& 1&-90& 25.819&-0.133& 0.049&-0.049&-0.133\cr
P$_1$& 0& 0&-2& 2&-2& 1&-90& 24.066&-0.050& 0.025&-0.025&-0.050\cr
K$_1$& 0& 0& 0& 0& 0& 1& 90& 23.935&-0.152& 0.078&-0.078&-0.152\cr
N$_2$&-1& 0&-2& 0&-2& 2&  0& 12.658&-0.057&-0.013& 0.011& 0.033\cr
M$_2$& 0& 0&-2& 0&-2& 2&  0& 12.421&-0.330&-0.028& 0.037& 0.196\cr
S$_2$& 0& 0&-2& 2&-2& 2&  0& 12.000&-0.145& 0.064& 0.059& 0.087\cr
K$_2$& 0& 0& 0& 0& 0& 2&  0& 11.967&-0.036& 0.017& 0.018& 0.022\cr}
\bigskip
\hrule
\bigskip


\noindent{\bf References}

\nobreak

\item{}\kern-2pc
Brosche, P., Seiler, U., S\"undermann, J., and W\"unsch, J., 1989,
     ``Periodic Changes in Earth's Rotation due to Oceanic Tides," 
     {\it Astron. Astrophys.}, {\bf 220}, pp. 318--320.

\item{}\kern-2pc
Brosche, P., W\"unsch, J., Campbell, J., and Schuh, H., 1991,
     ``Ocean Tide Effects in Universal Time detected by VLBI," 
     {\it Astron. Astrophys.}, {\bf 245}, pp. 676--682.

\item{}\kern-2pc
Dickman, S. R., 1989, ``A Complete Spherical Harmonic Approach to
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\item{}\kern-2pc
Dickman, S. R., 1990, ``Experiments in Tidal Mass Conservation"
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\item{}\kern-2pc
Dickman, S. R., 1991, ``Ocean Tides for Satellite Geodesy," {\it Mar.
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\item{}\kern-2pc
Dickman, S. R., 1993, ``Dynamic ocean-tide effects on Earth's
     rotation," {\it Geophys. J. Int.}, {\bf 112}, pp. 448--470.

\item{}\kern-2pc
Gross, R. S., 1993, ``The Effect of Ocean Tides on the Earth's Rotation
     as Predicted by the Results of an Ocean Tide Model," {\it Geophys.
     Res. Let.}, {\bf 20}, pp. 293--296.

\item{}\kern-2pc
Herring, T. A. and Dong, D., 1994, ``Measurement of Diurnal and 
     Semidiurnal Rotational Variations and Tidal Parameters of Earth,"
     {\it J. Geophys. Res.}, {\bf 99}, pp. 18051--18071.

\item{}\kern-2pc
Ray, R. D., Steinberg, D. J., Chao, B. F., and Cartwright, D. E., 
     1994, ``Diurnal and Semidiurnal Variations in the Earth's 
     Rotation Rate Induced by Oceanic Tides," {\it Science}, 
     {\bf 264}, pp. 830--832.

\item{}\kern-2pc
Ray, R. D., 1995, Personal Communication.


\item{}\kern-2pc
Yoder, C. F., Williams, J. G., Parke, M. E., 1981, ``Tidal Variations
     of Earth Rotation," {\it J. Geophys. Res.}, {\bf 86}, pp. 881--891.

\vfil\eject
