Seamen's accidental deaths and injuries worldwide: a methodology and some estimates

If there is no information on the distribution of probable error, a position line of any shape simply divides the Earth's surface into two domains and the position is as likely to be in one as in the other. We may arbitrarily denominate them the + domain and the domain. The three position lines in Fig. 1 divide the surface of the Earth into seven zones. We follow the convention that the triangle itself is the 3 + zone ; every zone bounded by a side of the triangle is thus a 2 + , 1 — zone and each zone at a vertex of the triangle is a i-f, 2— zone. The 3— zone is conspicuous by its absence. If the true position were in the minus zone of each and every position line as they have severally been labelled, the cocked hat would necessarily be shaped as in Fig. 2 and the position would be within it. The fact that the cocked hat has taken the form of Fig. 1 and not that of Fig. 2 tells us that, by our convention, the position is in the 4domain of at least one position line. Given that we are in the + domain of one position line (p), and may equally be in either the + domain or the — domain of two other position lines (q, r), the four possibilities are shown in Fig. 3, but we have no idea which position lines correspond to p, q, r. Out of four, there is one chance that the position is in the 3+ zone, two chances that it is in a 2-I-, 1 — zone, one chance that it is in a 1 + , 2 — zone and no chance that it is in a 3 — zone. The probability of being in each zone is shown in Fig. 4.