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+.help refv Jun99 "Slalib Package"
+.nf
+
+      SUBROUTINE slREFV (VU, REFA, REFB, VR)
+
+     - - - - -
+      R E F V
+     - - - - -
+
+  Adjust an unrefracted Cartesian vector to include the effect of
+  atmospheric refraction, using the simple A tan Z + B tan**3 Z
+  model.
+
+  Given:
+    VU    dp    unrefracted position of the source (Az/El 3-vector)
+    REFA  dp    tan Z coefficient (radian)
+    REFB  dp    tan**3 Z coefficient (radian)
+
+  Returned:
+    VR    dp    refracted position of the source (Az/El 3-vector)
+
+  Notes:
+
+  1  This routine applies the adjustment for refraction in the
+     opposite sense to the usual one - it takes an unrefracted
+     (in vacuo) position and produces an observed (refracted)
+     position, whereas the A tan Z + B tan**3 Z model strictly
+     applies to the case where an observed position is to have the
+     refraction removed.  The unrefracted to refracted case is
+     harder, and requires an inverted form of the text-book
+     refraction models;  the algorithm used here is equivalent to
+     one iteration of the Newton-Raphson method applied to the above
+     formula.
+
+  2  Though optimized for speed rather than precision, the present
+     routine achieves consistency with the refracted-to-unrefracted
+     A tan Z + B tan**3 Z model at better than 1 micro-arcsecond within
+     30 degrees of the zenith and remains within 1 milliarcsecond to
+     beyond ZD 70 degrees.  The inherent accuracy of the model is, of
+     course, far worse than this - see the documentation for slRFCO
+     for more information.
+
+  3  At low elevations (below about 3 degrees) the refraction
+     correction is held back to prevent arithmetic problems and
+     wildly wrong results.  Over a wide range of observer heights
+     and corresponding temperatures and pressures, the following
+     levels of accuracy (arcsec) are achieved, relative to numerical
+     integration through a model atmosphere:
+
+              ZD    error
+
+              80      0.4
+              81      0.8
+              82      1.6
+              83      3
+              84      7
+              85     17
+              86     45
+              87    150
+              88    340
+              89    620
+              90   1100
+              91   1900         } relevant only to
+              92   3200         } high-elevation sites
+
+  4  See also the routine slREFZ, which performs the adjustment to
+     the zenith distance rather than in Cartesian Az/El coordinates.
+     The present routine is faster than slREFZ and, except very low down,
+     is equally accurate for all practical purposes.  However, beyond
+     about ZD 84 degrees slREFZ should be used, and for the utmost
+     accuracy iterative use of slRFRO should be considered.
+
+  P.T.Wallace   Starlink   26 December 1994
+
+  Copyright (C) 1995 Rutherford Appleton Laboratory
+  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
+
+.fi
+.endhelp