The figure of the projection is not always like that of the preceding: sometimes the loops become two ovals separated by a line which is continued through the middle of them, the part of this line between the ovals being a line on which nothing but a simple contact is seen. There is an excellent mathematical account of eclipses in general, with the full mode of calculating them, and examples, by Mr. Wool house, in the Supplement to the ' Nautical Almanac' for 1836. From this we extract the summary of the limits within which an eclipse, whether of the sun or moon, can happen.
At the time of full moon an eclipse of the moon will be certain when the moon's latitude is less than 51' 57", impossible when it is greater than 63' 45', and doubtful between these limits. For the doubtful cases an eclipse will result when the moon's latitude is less than 61 GO 8-1- 16" p and a being the equatorial horizontal parallax and semi-diameter of the moon, and w and er those of the sun.
At the time of new moon an eclipse of the sun will be certain when tho moon's latitude is less than l' 23' 15", impossible when it is greater than 1° 34' 52", and doubtful between these limits. For the doubtful cases, an eclipse will happen when the moon's latitude is less than p — + et + a + 25".
It is hardly necessary to state that eclipses of the sun are freqnently wholly partial, that is, not total for any one moment to any one part of the earth. Sometimes, though the eclipse be central, it is not total on account of the moon not being near enough to hide the whole of the sun ; in which case part of the latter is seen as a bright ring round the part hidden by the moon, and the eclipse is called annular.
Before prodeeding to give some account of the physical phenomena observed during total eclipses of the sun, it may be desirable to allude briefly to some of the more interesting eclipses of this nature recorded in history.
The ancient literature of Greece and Rome contains several incidental envisions to the occurrence of total eclipses of the sun. The most celebrated of these is the eclipse mentioned by Hcrodotus as having taken place during a battle between the Medes and Lydians. The historian relates that the two hostile armies were so much terrified by the spectacle of the eclipse, that they suddenly desisted from fighting, and concluded a treaty of amity and peace. lie further states that the eclipse had been foretold to the Ionians by Tide' the Milesian. The precise date of this eclipse has given rise to much discussion in modern times. In 1311 the late Francis Baily communicated a paper to the Royal Society, in which, by availing himself of Bilrg's lunar tables, lie endeavours to prove that a total eclipse of the sun which occurred on the 30th of September, 610 B.C., must have been the one alluded to by Ilerodotue. Ho acknowledges, however, that the ele ments of the lunar orbit employed in his investigation failed to exeunt also for a total eclipse of the sun which Diodorua Siculus mentions as baring occurred while Agatbocles, king of Syracuse, was proceeding with his fleet to Africa. In a paper published in the
' Philosophical Transactions of the Royal Society ' for 1852, Mr. Airy has taken up the subject of this eclipse. His researches are based upon a new determination of the elements of the lunar orbit derived from the Greenwich observations, and the values of the secular accele ration of the mean motion and node assigned by Professor Hansen.
The conclusion at which ho arrives is, that the eclipse referred to by lierodotus must have occurred on the 7th of September, 585 B.C. Ile aho ors that this date accords satisfactorily with tho eclipse of Aga thocles, and also with an eclipse briefly alluded to by Xenophon as having occurred at LarisEs, in Asia, during the retreat of the ten thousand Greeks.
Plutarch, In his `Dissertation on the Lunar Spots,' makes a brief but interesting allusion to a total eclipse of the sun which happened in his time. He mentions that it occurred about midday, that the dark ness was so great as to cause the day to resemble night, and that stars were everywhere visible. Kepler, who investigated the probable time • of the occurrence of this eclipse, is of opinion that it is identical with an eclipse which happened in the year 118 A.D.
The records of modern history contain a variety of interesting allusions to the occurrence of total eclipses of the sun.
Halley, in a paper on the total eclipse of the sun which happened at London in the year 1715, mentions, as an illustration of the rarity of such phenomena, that no previous eclipse of the same nature had been visible in the metropolis since the year 1140. This eclipse is recorded in the Saxon Chronicle ; a brief mention of it is also made by William of 31alinesbury. In the Saxon Chronicle it is stated that, "in the • • , Lent, the sun and the day darkened about the noontide of the day, when men were eating, and they did light their candles to eat by. That was the thirteenth day before the Calends of April. Men were very much struck with wonder." William of lifaimesbury states, "that while persons were sitting at their meals, the darkness became so great that they feared the ancient chaos was about to return ; and upon going out immediately, they perceived several stars about the sun." Total eclipses of the sun are mentioned in history as having occurred in the years 1187, 1241, 1415, 1433, 1485, 1506, 1530, 1544, 1560, 1567., 1598, 1605, 1652, and 1699. The eclipses of 1433, 1598, and 1652 were visible in the British Isles. The eclipse of 1433 occurred in Scotland. According to Maclaurin, there is a manuscript account of it preserved in the library of the Edinburgh University. The moon's shadow on the occasion of the eclipse of 1598 appears to have passed over the border counties of England and Sootland. The day of its occurrence, which was Saturday, was long remembered in both countries as Black Saturday. The eclipse of 1562 was visible in the north of Ireland and in Scotland.