700 PHILOSOPHICAL TRANSACTIONS. [aNNO J 763. 



the terraqueous globe ever yet invented, in which the meridians, parallels, and 

 rhumbs, are justly and truly projected in right lines, for the latter cannot be so 

 projected in Mercator." — If they cannot be so projected in Wright's, they 

 cannot in his ; for in both, the meridians are said to be right lines and parallel, 

 and therefore the rhumbs must be right lines also, or how can they intersect the 

 meridians so situated at equal angles ? He also says in his scholium, that " It 

 does not appear that Mercator or Wright ever thought of this projection ; for 

 the meridian line here is manifestly a line of tangents; whereas in their projec- 

 tion, it is a collection of secants." 



What Mercator's thoughts were on this matter when he formed his universal 

 map, I know not, as he has left us no account of it ; l)ut what Wright's were, 

 he has very plainly told us in his aforesaid book ; and whether his primary con- 

 ceptions, and preparative modulus, do not only take in the whole, but also the 

 very manner, of Mr. West's construction, will better appear on a due compari- 

 son of their respective methods. 



By comparing the two modes of construction together, it is not difficult to 

 discover that Mr. West's derives its original from Wright's ; for right lines 

 drawn from the centre through all the points in the spheric surface, and ter- 

 minating in the concave surface of the tube, are secants, and the tube becomes 

 a tangent line to all those respective secants : and, does not Wright's uniform 

 dilatation, by the 2d law of motion, produce the same ? West stops here, and 

 gives us a chart at once ; Wright calls these his geometrical lineaments only, by 

 which he obtains a rectilinear planisphere, and from which he demonstrates the 

 principles on which his table of meridional parts are founded. And that he 

 does not esteem this as a chart completed, but only his apparatus, and prepara- 

 tive work, which requires yet to be applied and moulded into a true nautical 

 chart, is evident from the next paragraph, " Now then (says he) let us dili- 

 gently consider of the geometrical lineaments, that is, the meridians, rhumbs, 

 and parallels of this imaginary nautical planisphere, that we may in like manner 

 express the same in the mariner's chart : for so undoubtedly we shall have 

 therein a true hydrographical description of all places in their longitudes, lati- 

 tudes, and directions, or respective situations each from other according to the 

 points of the compass in all things correspondent to the globe, without either 

 sensible or explicable error." 



And hence he proceeds to the proof and application of these his lineaments, 

 to the construction of his table of latitudes, as he calls it ; which is, in this 

 edition, computed to minutes of parallel distance, but with a little contrivance 

 in the calculus to reduce the same yet somewhat nearer the trutH. Notwith- 

 standing this care and nicety in computation, he is duly sensible that his incre- 

 ments of latitude calculated to minutes, though without any sensible errorj are 



