226 FHILOSOPHICAL THANSACTIONS. [aNNO 1685. 



tion, the representation of places remote from the equator, was greatly distorted 

 -in those charts. For rectifying this in some measure, Mr. Wright advises, that 

 (the meridians remaining parallel, as before) the degrees of latitude, remote 

 from the equator, should, at each parallel, be protracted in like proportion with 

 those of longitude ; that is, as the cosine of latitude, which is the semidiameter 

 of the parallel, to the radius of the globe, which is that of the equator, so 

 should a degree of latitude, which is every where equal to a degree of longitude 

 in the equator, be to such degree of latitude so protracted, at such distance 

 from the equator; and so to be represented in the chart: that is, every where 

 in such proportion, as is the respective secant, for such latitude, to the radius: 

 for, as the cosine is to the radius, so is the radius to the secant of the same arch 

 or angle; as fig. 4, C : R::R:(r. So that, by this means, the position of 

 each parallel in the chart should be at such distance from the equator, com- 

 pared with so many equinoctial degrees or minutes, (as are those of latitude,) 

 as are all the secants, taken at equal distances in the arch, to so many times the 

 radius. Which is equivalent, as Mr. Wright observes, to a projection of the 

 spherical surface (supposing the eye at the centre) on the concave surface of a 

 cylinder, at right angles to the plane of the equator ; and the division of me_ 

 Vidians, represented by the surface of a cylinder erected on the arch of latitude 

 at right angles to the plane of the meridian, or a portion of it: the altitude of 

 such projection, or portion of such cylindric surface, being, at each point of 

 such circular base, equal to the secant of latitude answering to such point; 

 as fig. 5. This projection, or portion of the cylindric surface, if expanded 

 into a plane, will be the same with a plane figure, whose base is equal to a qua- 

 drantal arch extended, or a portion thereof, on which, as ordinates, are erected 

 perpendiculars equal to the secants, answering to the respective points of the 

 arch so extended: the least of which, answering to the equinoctial, is equal to 

 the radius ; and the rest continually increasing till, at the pole, it be infinite; 

 as at fig. 6. So that, as E R S L, a figure of secants erected at right angles on 

 E L, the arch of latitude extended, is to £ R R L, a rectangle on the same base, 

 whose altitude E R is equal to the radius; so is EL, an arch of the equator 

 equal to that of latitude, to the distance of such parallel, in the chart, from 

 the equator. For finding this distance, answering to each degree and minute 

 of latitude, Mr. Wright, as the most obvious way, adds all the secants, as they 

 are found calculated in the trigonometrical canon, from the beginning to the 

 degree or minute of latitude proposed. The sum of all which except the 

 greatest, answering to the figure inscribed, is too little; but the sum of all 

 except the least, answering to the circumscribed, is too great, which is what 

 he follows: and it would be nearer the truth than either, if, omitting all these. 



