8. L. Pen field — Stereographic Projection. 



from the pole. Thus, referring to figures 1 and 2, p. 3, the 

 distances at which the lines of projection of arcs of 110° and 

 135° would meet the diameter can be taken directly from this 

 scale. Various examples of the uses of scale No. 3 will appear 

 during the course of this article. 



Owing to the size of the sheets upon which the divided 

 circle and scales are printed, there is a limit to the number of 

 stereographically projected degrees which can be given. As 

 seen in figure 3, the end of scale No. 3 indicates the 156th 

 degree from the pole. Since in some operations it may be 

 necessary to carry the projection beyond the limits of this 

 scale, the distances from the pole to the remaining projected 

 degrees are given in millimeters in the following table : 



157°-344-l mr 



158 -360-1 



159 -377-7 



160 -397-0 



161 -418-3 



162 -442-0 



163°-468-4 mi 



164 -498-1 



165 -531-7 



166 -570-1 



167 -614-4 



168 -666-0 



169°-727-0 mm 175°-1603-3 I 



170-800-1 



171 - 889-4 



172 -1001-0 

 1-73 -1144-5 

 174 -13357 



176 -2004-5 



177 -2673-2 



178 -4010-3 



179 -8021-2 



180 Infinity 



The Possible Circles on a Spherical Surface. — About a 

 point p located anywhere on the surface of a sphere, two 

 kinds of circles may be described ; an indefinite number of 

 small circles, whose distance from p is less than 90°, and one 

 great circle, at a distance of 90° from p. If p is located at 

 either the north or the south pole of a sphere, the small circles 

 described about p correspond to the parallels of latitude of a 

 terrestrial globe, and the great circle answers to the equator. 

 If the sphere is oriented with its north and south poles in a 

 vertical direction, and p is located on the equator, the small 

 circles described about p will have a vertical position and will 

 be referred to as vertical small circles. A vertical great 

 circle, on the other hand, will pass through the north and 

 south poles, and will thus correspond to some north and south 

 meridian of a terrestrial globe. A great circle, whatever its 

 position, corresponds to some circumference of a sphere, and, 

 moreover, every great circle has this peculiarity, that it crosses 

 the horizontal great circle, or equator, at two points which are 

 antipodal. 



The Stereographic Projection of Small Circles. — The upper 

 portion A of figure 5 is intended to represent a vertical sec- 

 tion through the center of a sphere ; hence, the graduated 

 circle corresponds to some north and south meridian. X Y \& 

 the trace of the plane of the equator, and _ZV and 8 are the 

 north and south poles, respectively \p is some fixed point on 

 the meridian, the figure representing it as 36° north of the 

 equator. Around p, a small circle is supposed to be described, 



