68 VHILOSOPHICAL TRANSACTIONS. [aNNO \6Q5-6. 



observed to be dug in the mountains of Andria, Apulia, and other places ; and 

 thence he remarks how they were left there by the general flood ; why in 

 some places they remain uncorrupted, in others wasted and mouldered, in 

 others only by their impressed figures, and exact forms. That they all answer 

 in every delineation, and every part the very bodies they resemble, and are 

 truly the very same species. See Columna in his Observ. Aquat. et Terrestr. 

 Chap. 21, p. 43 to 55. Also de Purpura, Dissertat. de Glossopetris, p. 31 to 

 39; 4to. Romae impress. 10l6. 



y47i easi/ Demonstration of the Analogy of the Logarithmic Tangents, to the 

 Meridian Line, or Sum of the Secants : tvith various Methods for computing 

 the same to the utmost Exactness. By E. Halley. N° 2ig, p. 202. 



It is now near 100 years since our worthy countryman, Mr. Edward 

 Wright, published his Correction of Errors in Navigation, a book well de- 

 serving the perusal of all such as design to use the sea. Therein he con- 

 siders the course of a ship on the globe steering obliquely to the meridian ; 

 and having shown, that the departure from the meridian, is in all cases less 

 then the difference of longitude, in the ratio of radius to the secant of the 

 latitude, he concludes, that the sum of the secants of each point in the qua- 

 drant, being added successively, would exhibit a line divided into spaces, such 

 as the intervals of the parallels of latitude ought to be in a true sea chart, 

 where the meridians are made parallel lines, and the rhumbs or oblique courses 

 are represented by right lines. This is commonly known by the name of the 

 meridian line ; which, though it generally be called Mercator's, was yet un- 

 doubtedly Mr. Wright's invention, as he has made it appear in his preface. 

 And the table of it is to be met with in most books treating of navigation, 

 computed with sufficient exactness for the purpose. 



It was first discovered by chance, and as far as I can learn, first published by 

 Mr. Henry Bond, as an addition to Norwood's Epitome of Navigation, about 

 50 years since, that the meridian line was analogous to a scale of logarithmic 

 tangents of half the complements of the latitude. The difficulty to prove the 

 truth of this proposition seemed such to Mr. Mercator, the author of Lo- 

 garithmotechnia, tliat he proposed to wager a good sum of money, against 

 whoever woukl fairly undertake it, that he should not demonstrate, either 

 that it was true or fiilse : and about that time Mr. John Collins, holding a 

 correspondence with all the eminent mathematicians of the age, excited them 

 to this inquiry. 



The first that demonstrated the said analogy was Mr. James Gregory, in his 

 Exercitationes Gcometiicae, published anno lt)(J8, which he did, not witliout a 



