De proiectione geographica de Lisliana in mappa generali imperii Russici usitata

§. 20. Let us see, therefore, how great this maximum error will be at locations A, B, and X. For this purpose, let us calculate the error at A, which, since it is a $ω$ ( 90° - a + z ) - cos. a = 55 a $ω$ - 0,7660444, due to a $ω$ = 0,01410, will result in 0,00946; specifically, since the degree of the parallel at latitude A ought to be = 0,76604, it is somewhat larger in this projection: specifically 0,77550; and since that error is expressed in parts of one degree of the meridian, by assigning 15 miles to such a degree, that error will be worth 0,14190, that is, about the seventh part of one mile, or one Russian verst. That error, therefore, at terminus B or latitude 70°, where one degree of the parallel is 0,34202, is equal to only the thirty-eighth part, which can easily be tolerated in that region.

§. 21. For constructing the map of the Russian Empire, therefore, point O is most appropriately established on the middle meridian BA beyond the pole at a distance of 5 degrees, from which point the meridians AB will then be easily described through each degree of latitude, in which the degrees of longitude must be marked such that an angle of 48', 45'' corresponds to each around point O; whence, since the interval OA is = 55°, in the parallel drawn through terminus A, one degree of longitude will be = 55 . a $ω$ = 0,77550, or such a degree will be related to the degree of the meridian as 0,77550 : 1, whence this division can be completed quite expeditiously.

§. 22. Since in this projection all meridians are shown by straight lines, other great circles also, which one may conceive on the map, will not differ much from straight lines. The equator, indeed, would be a circle described with center O and radius = 95°, in which the individual degrees would be 95° . a $ω$ = 1,33950, which, however, ought to be equal to the degrees of the meridian; since, however, the equator does not occur in our map, that error does no harm to the projection. Let us see, therefore, by how much the great circles to be drawn on the map itself are to differ from straight lines.