De proiectione geographica de Lisliana in mappa generali imperii Russici usitata

that the degrees of the parallels everywhere maintain the just ratio to the degrees of the meridians which is observed on the spherical surface, it seemed advisable to deviate slightly from that method rather than renounce the aforementioned advantages. Hence, therefore, the following question of the greatest importance arose: how should the meridians be set with the parallels so that the true ratio, which the degrees of longitude and latitude maintain between themselves on the sphere, might be departed from as little as possible throughout the entire extent of the map? So that, indeed, errors could scarcely be perceived, since such an aberration could easily be pardoned, provided only that the mentioned advantages are obtained.

§. 6. The most celebrated Astronomer and Geographer of that time, Delisle, to whom the care of such a general map was first entrusted, endeavored to satisfy this requirement in such a way that he established a just proportion between the degrees of longitude and latitude for two more notable parallels, judging that if they were equidistant from the middle parallel of the entire map as well as from the extremes, the aberration could nowhere be notable. It is therefore asked here, which two parallels should be chosen for this purpose, so that the maximum errors arising therefrom may become the smallest of all.

Tab. II. Fig. 1.

§. 7. Let A B, therefore, be a portion of any meridian passing through the Russian Empire, whose most southerly terminus is at A, and the northerly at B, and let the latitude be set at A = a, and at B = b, such that, for instance, a = 40° and b = 70°; then let δ denote the quantity of one degree in all meridians. Furthermore, let points P and Q be those places where the degrees of longitude should maintain the just ratio to the degrees of latitude, and let the latitude for point P be set = p, and for place Q = q. Since, therefore, the degrees of any parallel on the sphere relate to the degrees of the meridian as the cosine of the latitude is to the total sine, for place P, the degree of longitude should be taken as Pp = δ cos. p, and for place Q, one degree of longitude Qq = δ cos. q.