42 N. W. Point of the Lake of the Woods. 
the two points by a straight line on the map, (projected ac- 
cording to Mercator.) _ If the angle formed by this line, and 
one of the parallels of the map, be more than an angle o 
45°, the northern point is the more northwest; if less, the 
southern is the more northwest; if 45° exactly, the two 
points are equally northwest. It will be easily seen, that if 
through the southern one of the two points, which are thus 
to be compared, a parallel of latitude be drawn, and through 
the northern one a meridian, and those lines be continued 
until their intersection, a right angled triangle will be form- 
ed, the hypothenuse of which is the straight line, connecting 
the two points in question, or the course from the one to the 
other, and the two cathetes the difference of longitude and 
the difference of latitude of the two points on the map. The 
angle formed by the connecting line of the two points with 
the parallel is exactly 45°, if the difference of longitude on 
the map is equal to the difference of latitude ; it is — = ; 
than 45°, if the difference of latitude be ia ns than the 
difference of longitude, both being measured on a map pro- 
jected on Mercator’s principles. If therefore the differences 
of latitude and longitude be expressed in figures, in the same 
manner, for example in minutes of a degree, on the principle 
of Mercator’s projection, these numbers will immediately | 
show which is the more northwestern one of the two points! 
The degrees of longitude are’ all equal on Mercator’s projec- 
tion, and may be easily expressed in any manner required. 
> degrees of latitude increase from the Equator to the 
Pole: the expression of the length of a meridian from the 
Equator to’ the latitude L., in minutes of a de. 
me 191 
: es'0 de b 
gation, under the-head of “meridional parts.” From all 
this, i appear, that in order to ascertain: which is the 
more northwestern one of two points, the longitude and lati- 
press it in minutes of a degree, (which numbers thus express 
