  Numerical and theoretical aspects of conformal mappings from a disk to a
circular-arc quadrilateral, symmetric with respect to the coordinate axes, are
developed. The problem of relating the accessory parameters (prevertices
together with coefficients in the Schwarzian derivative) to the geometric
parameters is solved numerically, including the determination of the parameters
for univalence. The study involves the related mapping from an appropriate
Euclidean rectangle to the circular-arc quadrilateral. Its Schwarzian
derivative involves the Weierstrass P-function, and consideration of this
related mapping problem leads to some new formulas concerning the zeroes and
the images of the half-periods of P.
