APPENDIX.

EXPLANATION OF CHANGES OF AMPLITUDE OF THE RISINGS OF STARS.

If a top (Fig. I) is spun and slightly tilted over, it will perform a number of slow gyrations, and the highest point will slowly describe a horizontal circle (shown by the dotted line) round a centre E, which is vertically above the lowest point.

Take a precessional globe (Fig. II), which has around it a vertical brass circle: another brass circle revolves inside it on an axis of which N is one of the pivots; and an ordinary celestial globe is pivoted inside this circle, E being one of its pivots. EN subtends about 23 at the centre C of the globe.

One revolution of the globe inside the inner circle corresponds to the slow precessional gyration of the earth, which is only completed in about 26,000 years.

One revolution of the globe and inner circle clamped together corresponds to one revolution of the earth on its axis in twenty-four hours. Clamp the globe and inner circle together so that N becomes the north pole (N being elevated about 30° to suit the latitude of Memphis in Egypt), it will then represent the heavens at the present time; the star (Arcturus) rising at P when revolution ensues. Unclamp the globe, revolve it through 623 and clamp it again to the inner circle, so that N' takes the place of N as the north pole; then the condition of things about 4500 years ago (B.C. 2596) is represented, because

62.34 4500

360 26000

Through N' runs the constellation Draco, and a Draconis was then very near the pole, and was the pole star for a long period before and after that time; it will also be noticed that the constellation of the Great Bear was then nearer to the pole than it is now.

When revolution ensues the star (Arcturus) will rise at P instead of P, for as N' has been moved to the right, the star must shift also, since N'P must equal NP'.

Thus the magnitude of the horizontal angle PCP' represents the change in amplitude in the rising of Arcturus at latitude 30° in that period of 4500 years, and the angle consequently is a measure of time. E and the dotted circles have the same meaning in both Figs. I and II.

This slow gyratory movement of the axis of the earth also causes the sun at the equinoxes to appear to move through the belt of stars called the signs of the zodiac, of which Aries is one; as the whole belt is arbitrarily divided into twelve equal parts or signs, the movement through each sign takes a twelfth part of 26,000 years, or about 2,166 years. This apparent movement of the equinoxes was known long ago, and consequently the gyration received the name, now established by long usage, "the precession of the equinoxes."

L

DISCUSSION.

The SECRETARY.-I should like to mention that the author of the paper, Lt.-Col. G. Mackinlay, is not unacquainted with practical astronomy, as he was second observer in the British expedition to make observations on the transit of Venus in 1882 in Jamaica, when he took independent observations. Dr. Copeland, the present Astronomer-Royal for Scotland, was the first observer. You will thus see that Colonel Mackinlay is well qualified to deal with the subject of Biblical Astronomy.

Mr. HARDING.—Mr. Chairman, ladies and gentlemen, I have been asked to give my testimony as to the astronomical ideas of the people of Palestine to-day, and more particularly of the Bedouins. After some years in contact with the Bedouins, I have come to the conclusion that their ideas are very vague indeed. They know the names of the signs of the zodiac, but I doubt whether they could point out the signs in the heavens. However, they can tell the time by the stars. When one has been travelling by night, and has asked them the time, looking around they would make a fairly good guess as to what the time of night was. During the day they certainly would tell the time by the sun, but they never could tell with any accuracy when the sun was more than halfway up from the horizon. They hold the hand at arm's length between the face and the sun, and show how many fingers the sun is from the horizon. But I have noticed and was struck by the regard that the Bedouin had for the morning star. I think that if that friend of Colonel Mackinlay's who doubted the possibility of rejoicing in the light of Venus had ever spent a night on the open desert, with its discomforts, he would rejoice in the light of the morning star. Always when a Bedouin comes into the tent before dawn the first thing he is asked is, "Has the star risen?" Just as a lazy British workman, we may say, turns over to his friend and says, "Is it six o'clock yet?" so the lazy Bedouin turns round and says, "Has the star risen?" I can fully corroborate what Atallah Athanasius has said about the travellers in Egypt rejoicing in the light of the morning star. On a night when there is no moon, the light of Venus

does make a decided difference. I have proved that when riding with one's back to the east, I have been able to tell that the star had risen by the difference in the light.

There are just two points in Colonel Mackinlay's paper that I should like to draw attention to with a view to getting a little information from any Hebrew scholars who may be present. In connection with the points of the compass, the Bedouins and the Arabic speaking peoples evidently originally fixed their points of the compass by the way they were looking, that is to say, to the east. The universal word for north in all Arab dialects is the word for left hand, and in certain parts the word for the right hand also indicates the south. In connection with this see the verse in the xxiii chapter of Job, quoted by the lecturer. It is extremely probable that the points of the compass are here indicated, and some versions (including modern Arabic) translate accordingly. But I should like the opinion of Hebrew scholars as to whether we should take the south as the place of hiding. I do not know very much about Hebrew, but it seems to me that the north is the place of hiding. The common word for north, tsaphon, means hidden. It is strange that the same idea should be connected with the south. In the passage in Job ix, 9, we get two words both meaning south. We get cheder and teman; teman must mean the south; cheder is given by the lecturer as one of the words used for south, and it also means a secret place or chamber.

And then the second point was with reference to "yam," the sea, which usually means west. In this particular passage in Psalm cvii, 3, it is translated south. There is no doubt that it means south. How does it come to have this meaning? It is connected with the word north, tsaphōn, and the same collocation occurs in Isaiah xlix, 12, where our translators translate it north and west. But it struck me at once on looking at this, and I think it is an idea that is supported by some scholars, that the word "yam" here is really a contraction of "yamin," which is the ordinary word for south. Possibly as this is the only instance in which "yam" seems to mean south, that might be the explanation. One would like to hear what Hebrew scholars have to say about it.

Commander W. F. CABORNE, C.B., R.N.R.-While glad of the opportunity afforded me for saying a few words in appreciation of Colonel Mackinlay's thoughtful, valuable, and interesting paper, I