VOL. L.] PHILOSOPHICAL TRANSACTIONS. 2 I Q 



was preferred, especially in nautical business; and has its uses at this day in to- 

 pographic constructions, as in bays, harbours, and very narrow zones. How- 

 ever, the errors in this were sooner discovered than corrected, both by mathema- 

 ticians and mariners, as by Martin Cortese, Petrus Nonius, Coigniet, and some 

 say by Ptolemy himself. 



The first step towards the improvement of this chart was made by Gerard 

 Mercator, who published a map about the year 1550, in which the degrees of 

 latitude were increased from the equator towards each pole ; but on what prin- 

 ciples this was constructed, he did not show. 



About the year 159O, Mr. Edward Wright discovered the true {principles on 

 which such a chart should be constructed; and communicated the same to one 

 Jodocus Hondius, an engraver, who, contrary to his engagement, published the 

 same as his own invention: this occasioned Mr. Wright, in ISQp, to show his 

 method of construction, in his book, intitled. Correction of Errors in Naviga- 

 tion; in the preface of which may be seen his charge and proof against Hondius; 

 and also how far Mercator has any right to share in the honour due for this great 

 improvement in geography and navigation. 



Blundeville, in his Exercises, p. 327, published anno 1594, gives a table of 

 meridional parts answering to even degrees, from 1^ to 80° of latitude, with the 

 sketch of a chart constructed from it: but this table he acknowledges to have 

 received from Mr. Wright. 



About the year 1720, a globular chart was published, said to be constructed 

 by Mr. Henry Wilson ; the errors in which were obviated by Mr. Tho. Haselden, 

 in a letter to Dr. Halley ; who at the same time exhibited a new scale, by which 

 distances on a given course may be measured, or laid off, at one extent of the 

 compasses, on Wright's projection; and was intended to render the same as easy 

 in practice as the plane chart. The above chart was published in opposition to 

 Mr. Wright's, which that author charged with imperfections and errors, and 

 that it represented places larger than they are on the globe. It is true, the sur- 

 face is apparently enlarged; but the position of places, in respect to one another, 

 are in nowise distorted; and it may be asserted, with the same parity of reason, 

 that the lines of sines, tangents, and secants, are false, because the degrees of 

 the circle, which are equal among themselves, are thus represented unequal. 

 Yet if a map or chart was so constructed, as to show the situation and true ex- 

 tent of countries, &c. prima facie (if I may be allowed the expression), and yet 

 retain all the properties, uses, and simplicity, of Wright's construction, it would 

 be a truly great improvement; but this seems to be impossible. 



The method exhibited by the Rev. Mr. Murdoch, in the preceding paper, 

 shows the situation of places, and seems better calculated for determining super- 

 ficial and linear measures than any other. He illustrates his theory with examplCvS 



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