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89) Log. 0.8726650 (=50 degrees to radius 1)------- -1,9408476
    Log  MF (Sine 35 degrees)---------------------- -1,7585913
    Log  MT (tang. 55 degrees---------------------- [[underline]] 0.1547732  [[/underline]] 
    Take the sum ----------------------------------  -1,8542121
    from log.Nn (=.6923772)------------------------   [[underline]] -1,8403427  [[/underline]] 
    the remainder ---------------------------------  -1,9861306
    is the logarithm of Cx. And because 1: Cx::MT:xt, to this add the log. MT ------------------------------------[[underline]]  0,1547732 [[/underline]] 
    The sum ---------------------------------------   0.1409038
is the log. of xt = 1.383260; and xR (= xr =1/2 Ll) being .4363325, Rt will be 0.9469275, rt = 1,8195925.  Whence having fixed upon any convenient size for our map, the center t is easily found.  As, allowing an inch to a degree of a great circle, or 50 inches to the line Rr, Rt the semidiameter of the least parallel will be 54,255 inches, and that of the greatest parallel 104.255 inches.
    Again, making as radius to MF so the longitude 110 [[degrees]] to the angle StV, that angle will be 63 [[degrees]]..5' 3/5.  Divide the meridians and parallels, & finish the map as usual. 
    [[underline]] Note [[/underline]] , The log. MT being repeated in this computation with a contrary sign, we may find xt immediately by subtracting the sum of the logarithms of Ll and MF from the log. of Nn.
VI.  A map drawn by this rule will have the following properties:
1.  The intersections of the meridians and parallels will be rectangular.
2.  The distances north and south will be exact; and any meridian will serve as a [[strikethrough]] [[illegible]] [[/strikethrough]] scale.
3.  The parallels thro' Z and Y, where the line Rr cuts the arc Ll, or any small distances of places that lie in those parallels, will be of their just quantity.  At the extreme latitudes they will exceed, and in mean latitudes, from X towards Z or Y, they will fall short of it. But unless the zone is very broad, neither the excess nor [[inserted]]the [[/inserted]] defect will be anywhere considerable. 
4.  The latitudes and the superficies of the map being exact, by the construction, it follows, that the excesses and defects of distance, now mentioned, compen=sate each other; and are, in general, of the least quantity they can have in the map designed.
5.  If a thread is extended on a plane, and fixed to it at its two extremities, and afterwards the plane is formed into a pyramidal or conical surface, it may be easily shewn, that the thread will pass thro' the same points of the surface as before; and that, [[underline]] conversely [[/underline]], the shortest distance between two points in a conical surface is the right line that joins them, when that surface is expanded into a plane.  Now, in the present case, the shortest distances on the conical surface will be, if not equal, always nearly equal, to the corresponding distances on the sphere: and therefore, all rectilinear distances on the map, applied to the meridian as a scale, will, nearly at least, shew the true distances of the places represented.
6.  In maps, whose breadth exceeds not 10 [[degrees]] or 15 [[degrees]], the rectilinear distances may be taken for sufficiently exact.  But we have chose our example of a greater breadth than can often be required, on purpose to shew how high the errors can ever arise; and how they may, if it is thought needful, be nearly estimated and corrected.
    Write down, in a vacant space at the bottom of the map, a table of the errors of equidistant parallels, as from five degrees to five degrees of the whole latitude; and having taken the mean errors, and diminished them in the ratio of radius to the sine of the mean inclination of the line of distance to the meridian, you shall find the correction required; remembering only to distinguish the distance into its parts that lie [[underline]] within [[/underline]] and [[underline]] without [[/underline]] the sphere, and taking the difference of the corresponding errors, in [[underline]] defect [[/underline]] and in [[underline]] excess [[/underline]].
But it was thought needless to add any examples; as, from what has been said, the intelligent reader will readily see the use of such a table; and chiefly as, whenever exactness is required, it will be more proper, and ended  

Transcription Notes:
09-19-14-BW Changed 'line' to 'lie' in sect. VI. 3. All else okay. Added a period after rectangular in VI., item 1.