This paper presents an empirical analysis of the geometry of the conal emission region for a total population of some 150 pulsars for which an adequate body of observations now exists. It continues the analysis begun in a previous paper that explored the geometry of the core emission region and provided a means of estimating the angle a between the rotation and magnetic axes of pulsars with core components. The various pulsars are thus divided into groups according to their morphological classification, and those species that have core components are treated first. Special consideration is given to the five-component (M) class and to those other, entirely conal species which are closely related to it, the conal triple (cT) and the conal quadruple (cQ). An adjunct appendix discusses the classification of these ''double-conal pulsars''-that is, the nearly 20 M pulsars as well as the four known cT stars and the five cQ candidates. The conal emission geometry of this group of five-component (M) stars is considered first. Their two pairs of conal components suggest that both an ''inner'' and ''outer'' hollow conal beam is emitted. For each pulsar several geometrical parameters are calculated: The angle alpha between the rotation and magnetic axes of the star is computed from the core width, the impact angle beta from the steepness of the polarization-angle traverse, and the radius of the conal emission beam rho from these quantities as well as the measured width of the conal component pair DELTAPSI. Finally, the emission height r is simply scaled according to the dipolar geometry of the ''last open'' field lines. The conal emission radii of the five-component M pulsars exhibit a behavior which is striking in its orderliness: The ''inner'' and ''outer'' radii have the following dependencies at 1 GHz, 4.-degrees-3P-1/2 and 5.-degrees-8P-1/2, respectively, where P is the pulsar period. As both the conal radii and the core width scale as P-1/2, the emission height (at a given frequency) is found to be independent both of the pulsar period and the magnetic inclination angle alpha. The ''outer'' cone then appears to be emitted at a 1 GHz height of about 220 km, and, if the ''inner'' cone is also emitted on this same set of field lines, its emission height is about 130 km. The other species also exhibit great regularity in their conal emission geometry. Virtually all of the core-single (S(t) pulsars which develop conal outriders at high frequency have a conal geometry which corresponds to the ''inner'' cone of the M stars. The triple (T) pulsars also have a conal emission geometry which closely matches that of the five-component pulsars; they divide in roughly comparable numbers between those which emit an '' inner '' and those which emit an '' outer '' cone. The final three, entirely conal classes entail additional difficulty because they lack a core component; therefore alpha cannot be directly determined. For these pulsars reference is made to the work of Lyne & Manchester, and, where possible, alpha-values were used which were close to those determined in their study. Generally, the cT and cQ pulsars seem to have conal geometries which are compatible with their classification-that is, they represent more peripheral sight-line trajectories through a double-conal emission pattern. Finally, among the conal double (D) and single (S(d)) pulsars most appear to emit ''outer'' cones, although a handful appear to have an '' inner '' conal emission geometry. It is not yet clear why some pulsars have an '' inner '' conal emission geometry, others an '' outer,'' and still others have both an '' inner '' and an '' outer '' geometry. Only the pulsar rotation period appears to distinguish, statistically, between these various groups. Pulsars with '' inner '' cones are generally faster, those with '' outer '' cones much slower, and the group of five-component (M) pulsars (which emits both cones) falls in between the other two. A major unanswered question is whether the '' inner '' cone is emitted at a lower height along the same group of peripheral field lines that produce the ''outer'' cone (as has been assumed, for purposes of calculation, in this analysis), or whether it is emitted at some greater height along a group of more interior field lines. Several different circumstances which might be capable of producing two conal emission beams are reviewed.
