218" PHILOSOPHICAL TRANSACTIONS. [anNO 1758. 



the middle point of the parallel sv in h. By this means too we shall gain more 

 space than we lose, while the map takes the usual rectangular form, and the 

 spaces GHV remain for the title, and other inscriptions. 



Another, and not the least considerable, property of our map is, that it may, 

 without sensible error, be used as a sea-chart; the rumb lines on it being loga- 

 rithmic spirals to their common pole /, as is partly represented in the figure: and 

 the arithmetical solutions thence derived will be found as accurate as is necessary 

 in the art of sailing. 



If it be required to draw a map, in which the superficies of a given zone shall 

 be equal to the zone of the sphere, while at the same time the projection from 

 the centre is strictly geometrical ; take ex to cm, as a geometrical mean between 

 CM and nw, 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 

 ex to CM as the arc ml is to its tangent, and finish the map; either by a pro- 

 jection, or, as in the first method, by dividing that part of xt which is inter- 

 cepted by the secants through l and /, into equal degrees of latitude. Mr. 

 Mountaine justly observes, " that my rule does not admit of a zone containing 

 K. and s. latitudes." But the remedy is, to extend the lesser latitudes to an 

 equality with the greater; that the cone maybe changed into a cylinder, and the 

 nimbs into straight lines. 



LXXIV, A short 'Dissertation on Maps and Charts. By Mr. Wm. Mountaine^ 



F. R. S. p. 563. 



Maps and charts are either curvilinear or rectilinear. Globular, or curvilinear, 

 are either general or particular. General are the hemispheres, for the most part 

 constructed stereograph ically. Particular contain only some part of the terra- 

 queous globe; and of this sort there are sundry modes of construction, which 

 for the most part are defective, so as not to be applied with accuracy and facility 

 to the purjjoses intended, in detennining the courses or bearings of places, their 

 distances, or both. 



Rectilinear were therefore very early adopted, on which the meridians were 

 described parallel to each other, and the degrees of latitude and longitude every- 

 where equal; the rumbs were consequently right lines; and hereby it was thought 

 that the courses or bearings of places would be more easily determined. But 

 these were found also insufficient and erroneous, the meridians being parallel, 

 which ought to converge: and no method or device used to accommodate that 

 parallelism. Notwithstanding the great deficiency in this plane map or chart, it 



