344 Mr DAVIES on the Equations of Loci 



the equation of the point of projection. The same remark applies as is made 

 on equation (3). 



(c). b = a, the reversed Jordanian branch of the curve, denoted by 



v %a 



(d). b = inf. Then, as before the orthographic becomes 



1 k-* + kt 



v " Za ' 



XXXIV. 



I 



MERCATOR'S Projection or, more properly, WRIGHT'S Development 

 will next present itself to our consideration. 



The following process, for all cases of functional projection * on an 

 equatorial cylinder, will furnish the relation between the latitude and its 

 projection, if we admit the possibility of resolving the equations. 



Let x fy ...................... (1.) 



-=e ........................ (3.) 



The first of these is the equation of the development of the functional pro- 

 jection f on the equatorial cylinder, when that cylindrical surface is unrolled 



See note (D). 



f This very appropriate epithet seems to have been introduced into the science by 

 Mr GOMPERTZ. See his second tract on Imaginary Quantities, p. x. Some authors 

 have been so far from understanding the nature of " MERCATOB'S Projection," that they 

 have designated it as made " upon a plane at an infinite distance" ! DEALTRY'S Fluxions, 

 p. 427. This singular oversight originated, doubtless, in the want of a proper verbal dis- 

 tinction being made between the radial projection of a figure upon a given surface, and 

 the figure generated upon that surface, by taking as co-ordinates some function of the 

 curve said to be " projected." 



