  New analytical expressions and numerical results for the mode coefficients,
the directivity and the quality factor as well as computationally convenient
expressions for the input admittance of a symmetrical biconical antenna of
arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality
factor for a wide-angle biconical antenna is evaluated using three alternative
formulations: (i) the evanescent energy stored outside the circumscribing
sphere, (ii) the total evanescent energy stored in all space and (iii) by
equivalent circuit model, and these are all compared with Chu's lower limit for
an ideal antenna. Numerical calculations based on the analytical formula for
antenna admittance confirm the conjecture that Foster's reactance theorem
remains invalid even for perfectly conducting antennas. Furthermore, the
variation of directivity of a wide-angle biconical antenna is a slowly varying
function of its electrical length and is shown to depart significantly from
that of a thin cylindrical dipole. Lastly, the ratio of directivity to $Q$ of
an electrically small biconical antenna is shown to approach 78\% of the value
of an ideal omnidirectional antenna.
