346 Mr DAVIES on the Equations of Loci 



notice, as resulting from the total ignorance of the objectors. The two cases 

 I refer to, however, were the result of mistakes on the part of men of re- 

 spectable mathematical attainments for the times they lived, and the oppor- 

 tunities of cultivating this branch of study which they possessed. They were 

 Mr HENRY WILSON, in his proposal for Curvilinear Sea Charts, 1720."; and 

 the Rev. Mr WEST of Exeter, in his Posthumous Works, 1762, published 

 by the Rev. Mr ROWE. Of Mr WILSON'S book I can only speak from 

 the report of others ; but Mr WEST'S is certainly indicative of a degree of 

 mathematical acquirement, that shews the error was the result of haste 

 rather than incapability of investigation. He was led, by trusting too im- 

 plicitly to the unguarded verbal statements of WRIGHT, to suppose, 

 that if the loxodrome were gnomonically projected upon the equatorial cy- 

 linder, and this cylinder unrolled upon a plane, then this projection would 

 become a straight line. The error was pointed out by Mr SAMUEL 

 DUNN, in a letter to the Royal Society ; and this letter, and the report 

 made upon it by the Rev. WILLIAM MOUNTAINS (to whom the let- 

 ter had been referred by the Council of the Royal Society), were printed 

 in the Philosophical Transactions for 1763*. It was also noticed by Mr 

 GEORGE WITCHELL, who also determined the equation of the curve which 

 would be actually formed in] that case, in the Ladies' Diary for 1764 f . 

 I have no intention of entering anew upon this argument, and I allude to 

 it only as it affords me another opportunity of employing the method of 

 examining the relations between curves and their projections upon the 

 sphere, and its equatorial cylinder ; and that the cases before us afford a 

 good illustration of that very simple method. 



* Page 66. and 69. 



f- Vide Professor LEYBOURN'S edition of this curious, and in many respects valuable, 

 Miscellany, vol. ii. p. 249. We might, in a manner very similar to that just employed, 

 determine the development of the Stereographic projection of the Loxodrome upon the 

 equatorial cylinder, and should find, as is done in the Gentleman's Diary for 1820, p. 43. 

 that it is the logarithmic curve. 



