[ 5 68 ] 
te laft age. If it has been mifunderftood or mifap- 
tc plied by geographers, they only are to blame.” — 
And again, at the end of his nautical examples, he 
concludes thus, 'viz. “ It is not meant, however, 
“ that it ought to take place of the ealier and 
“ better computation by a table of meridional 
tc parts.” 
I have the honour to be, with the greateft refpedt, 
S I R, 
The Royal Societ y’s, and 
Your moft obedient Servant, 
William Mountaine. 
Addenda to Mr. Murdochs Paper , N°. lxxiii. 
TF it is required “ to draw a map, in which the fuperficies of a 
“ given zone (hall be equal to the zone on the fphere, while 
“ at the fame time the projection from the center is ftriCtly geo- 
“ metrical Take Cx to C M as a geometrical mean between CM 
and N n, is to the like mean between the cofine of the middle latitude , 
and twice the tangent of the femidifference of latitudes ; and project 
on the conic furface generated by xt. But here the degrees of lati- 
tude towards the middle will fall fliort of their juft quantity, and 
at the extremities exceed it : which hurts the eye. Artifts may 
ufe either rule : or, in moft cafes, they need only make Cx to 
CM as the arc ML is to its tangent, and finifh the map; either 
by a projection, or, as in the firft method, by dividing that part 
of xt which is intercepted by the fecants thro’ L and /, into equal 
degrees of latitude. 
Mr. Mountaine juftly obferves, “ that my rule docs not admit of 
“ a zone containing N. and S. latitudes.” But the remedy is, te 
extend the lejfer latitudes to an equality with the greater ; that the cone 
may be changed into a cylinder , and the rumbs into Jlra]ght lines. 
LXXV. 
