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not equally distant from the plane of the circle; they may be called respectively the nearer and further pole; sometimes the nearer pole is for brevity called the pole.

6. A pole of a circle is equally distant from every point of the circumference of the circle.

Let $O$ be the centre of the sphere, $AB$ any circle of the sphere, $C$ the centre of the circle, $P$ and $P'$ the poles of the circle. Take any point $D$ in the circumference of the circle; join $CD$, $OD$, $PD$. Then $PD=\surd (PC^{2}+CD^{2})$; and $PC$ and $CD$ are constant, therefore $PD$ is constant. Suppose a great circle to pass through the points $P$ and $D$; then the chord $PD$ is constant, and therefore the arc of a great circle intercepted between $P$ and $D$ is constant for all positions of $D$ on the circle $AB$.

Thus the distance of a pole of a circle from every point of the circumference of the circle is constant, whether that distance be measured by the straight line joining the points, or by the arc of a great circle intercepted between the points.

Definition. The length of the arc, measured along a great circle, from any point on a small circle to the nearer pole is called the spherical radius of the small circle.