PROJECTION

A representation of the sphere on a plane, in which the meridians are represented by equidistant parallel straight lines, and the parallels of latitude also by straight lines perpendicular to the meridians. This projection, which IS universally adopted for nautical charts, by reason of the facilities which it affords in navigation from the circumstance that the rhumb, or sailing course between two points, is represented by a straight line, was invented by Gerard Mercat or (his true name was Kauffman, of which Mercat or is the Latin equivalent), a native of Rupelmonde, in East Flanders, bora in the year 1512. But, though Mercat or gave his name to the projection, it does not appear that he knew the law according to which the distance of the parallels from the equator increases. The true principles of the construction were found by Edward Wright, of Caius College, Cambridge, who explained them in his treatise, entitled The Correction of certain Errors in Navigation, published in 1599, and are as follows: — Suppose one of the meridians on the globe to be divided into minutes of a degree; one of these, taken at any parallel of latitude, will be to a minute of longitude, taken on that parallel, as the radius of the equator to the radius of the parallel; that is, as radius to the cosine of the latitude, or as the secant of the latitude to radius. This proportion holds true on the map in this sense, that if a minute of the equator be taken as the unit of a scale, and that unit be considered as the radius of the tables, then the representation of a minute of latitude will be expre ed by the number in the trigonometrical tables which is the secant of that latitude. Hence, in the map, while the degrees of longitude are all equal, the degrees of latitude marked on the meridian form a scale of which the distances go on increasing from the equator towards the poles, each being (approximately) the sum of the secants of all the minutes of latitude in the degree. The numbers resulting from the addition of the secants of the succe ive minutes reckoned from the equator form a scale of meridional parts, which is given in all books of navigation. The very remarkable property of this projection, namely, that the divisions of the meridian are analogous to the exce es of the logarithmic tangents of half the respective latitudes augmented by 45°, above the logarithm of the radius, was discovered by Bond about the year 1645; but was first demonstrated by James Gregory, in big Exercitationes Mathetnaticce, published in 1668. ( See the Script ores Logarithtnici, vols. ii. and iv.) [s. 745]