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Fig. 4. is constructed from above data. The angle N P R is the complement of the easterly hour-angle and the point R is the centre of the 5h. Iim. easterly hour circle ; C is the centre of the equinoctial W QE; f is the centre of the parallel of declination, d d", and X the celestial object rising, and arc E X the rising amplitude.
N.B.-If a scale of secants is not handy, lay off from E. or W., on the primitive, the chord of the complement of the latitude, and from Z draw a line through the arc, measured by the chord, until it meets the tangent drawn from E. or W.; this line will be the secant required and is the radius of the equinoctial. It is obvious that as the latitude decreases to oo the radius of the equinoctial increases to infinity and the equinoctial would, for all practical purposes, be a straight line.
GEOGRAPHY AND NAVIGATION It is necessary to begin by introducing a few preliminary definitions connected with the sphere.
A SPHERE is a solid body, every part of the surface of which is equally distant from a fixed point within it which is called the centre.
A SPHEROID is a solid body, having the form of a sphere, but not quite round,-being flattened in some particular direction.
Every section of a sphere made by a plane is a CIRCLE of the sphere.
A DIAMETER of a sphere is any straight line passing through its centre, and extending in both directions to the surface.
The Poles of a circle on the sphere are those points on the surface of the sphere equally distant from the circumference of that circle. Every circle on a sphere has two poles, one on each side of its plane, and they are at the extremities of a diameter perpendicular to that plane.
A GREAT CIRCLE is any circle whose plane passes through the centre of the sphere, and every point on the great circle is 90 degrees from its pole on the surface of the sphere.
The centre of the sphere is the common centre of all its great circles, and no two great circles can have a common pole.
GREAT CIRCLES of the sphere are equal, and when they intersect they cut one another into two equal parts.
A SMALL CIRCLE is unequally distant from its two poles, since its plane does not pass through the centre of the sphere. Every point on the small circle is less than 90 degrees from one pole, and more than go degrees from the other pole of the sphere.
A sphere is divided into two equal parts by the plane of every great circle : and into two unequal parts by the plane of every small circle.
PARALLEL CIRCLES of the sphere are those circles the planes of which are parallel to the plane of some great circle ; and all these circles have the same pole.
The ARC of a circle is any part (small or large) of the circumference of a circle-it may be a degree or less, or many degrees, in length.
The shortest DISTANCE between two points on the surface of a sphere is the arc of a great circle passing through those points.
A SPHERICAL ANGLE is the inclination of two great circles of the sphere meeting one another.
A SPHERICAL TRIANGLE is a figure formed on the surface of a sphere by the mutual inter sections of three great circles.