PRO 



II. StereograpJiic Projection. 



J. The projection of an arc, measured from the pole, is equal to the 

 tangent of half that arc. 



2. The projection of every circle is a circle. 



3. The projection of all circles parallel to the plane of projection will 

 be concentric circles, the radii of which are the tangents of % the dis- 

 tances of the circles from the pole. 



4. The projection of every great circle passing through the pole is a 

 straight line. 



5. The radius of projection of any other great circle is the secant of the 

 angle between the plane of the circle and the plane of projection. 



From these Arts, it appears, that the projection of the parts of the 

 sphere will not properly represent, in magnitude and situation, the parts 

 themselves. 



6. If the place of the eye be the pole of the earth, the meridians will 

 be projected into straight lines (Art. 4) ; and the parallels to the equator 

 will be projected into circles (Art. 3). This is called the Polar Projec- 

 tion. 



7. If the eye be placed in the equator 90 distant from the point from 

 which the longitude is reckoned, the projection of the radius of any me- 

 ridian will be the secant of its longitude (Art. 5). And the radius of 

 projection of the parallels of latitude is the cotangent of their latitude. 

 This is called an Equatorial Projection. 



The stereographic projection is chiefly used in delineating maps of the 

 world. 



III. Mercator's Projection. 



1. In this projection the meridians are parallel linos, the degrees of 

 longitude are all equal j the parallels of latitude are also parallel lines, 

 but unequal, a degree of latitude being to a degree of longitude '.'. rad. 

 I cos. latitude, and .*. the length of a degree of longitude being constant, 

 the length of a degree of latitude will be inversely as the cosine of lati- 

 tude, and will .", increase in going towards the pole. 



2. To find the length of the meridian on this projection for any num- 

 ber of degrees of latitude. 



Let x "= required length, r earth's radius then 



cot. comp. latitude 



% = r x n. 1. . 



r 



If .'. we take the latitude = 1, 20, ,3 , 90 we can construct a 



217 N 



