In example the 3d they vary 1° 4´, on account of the high latitudes, which extend from 56° to 80° N.
However, I do not esteem this method so simple, easy, and concise, in the practice of navigation, as Mr. Wright’s construction, especially in determining the bearings or courses from place to place: nor will it (I presume) admit of a zone containing both north and south latitude.
Of these inconveniences Mr. Murdoch seems to be extremely well acquainted, when he expresses himself in the following very candid and ingenuous terms, viz. “As to Wright’s or Mercator’s nautical chart, it does not here fall under our consideration: it is perfect in its kind; and will always be reckoned among the chief inventions of the last age. If it has been misunderstood or misapplied by geographers, they only are to blame.”—And again, at the end of his nautical examples, he concludes thus, viz. “It is not meant, however, that it ought to take place of the easier and better computation by a table of meridional parts.”
I have the honour to be, with the greatest respect,
SIR,
The Royal Society’s, and
Your most obedient Servant,
William Mountaine.
Addenda to Mr. Murdoch’s Paper, Nº. LXXIII.
IF it is required “to draw a map, in which the superficies of a given zone shall be equal to the zone on the sphere, while at the same time the projection from the center is strictly geometrical;” Take Cx to CM as a geometrical mean between CM and Nn, is to the like mean between the cosine of the middle latitude, and twice the tangent of the semidifference of latitudes; and project on the conic surface generated by xt. But here the degrees of latitude towards the middle will fall short of their just quantity, and at the extremities exceed it: which hurts the eye. Artists may use either rule: or, in most cases, they need only make Cx to CM as the arc ML is to its tangent, and finish the map; either by a projection, or, as in the first method, by dividing that part of xt which is intercepted by the secants thro’ L and l, into equal degrees of latitude.
Mr. Mountaine justly observes, “that my rule does not admit of a zone containing N. and S. latitudes.” But the remedy is, to extend the lesser latitudes to an equality with the greater; that the cone may be changed into a cylinder, and the rumbs into straight lines.