The geometrical conditions of an eclipse of the sun or moon are shown in fig. 1, which represents the earth E as casting its shadow towards C, and the moon M between the earth and sun as throwing its shadow towards some part of the earth and eclipsing the sun. The dark conical regions are those within which the sun is entirely hidden from sight. This portion of the shadow is called the _umbra_. Around the umbra is an enveloping shaded cone with its vertices directly towards the sun. To an observer within this region the sun is partly hidden from view. As the apparent path of the moon may pass to the north or south of the line joining the earth and sun, the axis of its shadow may pass to the north or south of the earth, and not meet it at all. An eclipse of the sun is called _central_ when the shadow axis strikes any part of the earth; partial when only the penumbra falls upon the earth. It is evident that an eclipse can be seen as central only at those points of the earth's surface over which the axis of the shadow passes. [Illustration: FIG. 2.] [Illustration: FIG. 3.] A central eclipse is _total_ when the umbra actually reaches the earth; _annular_ when it does not. These two cases are shown in figs. 2 and 3. In the first of these the sun is entirely hidden within the region uu'. In fig. 3 within the region aa' the apparent diameter of the sun is slightly greater than that of the moon, and at the moment of greatest eclipse a narrow ring of sunlight is seen surrounding the dark body of the moon. We shall treat the subject in the following sections:-- I. Phenomena of Eclipses of the Sun and conclusions derived from their observation. II. Eclipses of the Moon. III. The Laws and Cycles of recurrences of Eclipses of the Sun and Moon. IV. Chronological list of remarkable eclipses of the Sun, past and future, to the end of the 20th century. V. Description of the methods of computing eclipses. I. _Phenomena of Eclipses of the Sun._