Let us see now what the argument is, as it was worked out by the late Mr. J. W. Bosanquet, F.R.A.S. Shortly before the invasion of Judæa by Sennacherib—say in the beginning of the year 689 B.C.—Hezekiah was sick unto death. In answer to his fervent prayer for recovery the prophet Isaiah was sent to him with this message:—“Thus saith the Lord, the God of David thy Father, I have heard thy prayer, I have seen thy tears; behold, I will add unto thy days fifteen years ... and I will defend this city, and this shall be a sign unto thee from the Lord, that the Lord will do this thing that He hath spoken. Behold, I will bring again the shadow of the degrees, which is gone down in the sun-dial of Ahaz ten degrees backward. So the Sun returned ten degrees, by which degrees it had gone down.” (Isaiah xxxviii. 5-8). In these words we evidently have mention of some instrument erected in Hezekiah’s palace, in the days of his father Ahaz, for showing the change in the position of the shadow cast by the Sun from day to day. This statement is confirmed by a profane writer, Glycas, who states: “They say that Ahaz, by some contrivance, had erected in his palace certain steps, which showed the hours of the day, and also measured the course of the Sun.” The idea involved in “bringing again,” through “ten degrees backward,” “the shadow of the degrees” which had gone down, is very noteworthy. We seem intended to learn from these words several things. For one thing (to begin with) that the steps (as we must consider them to have been) on this sun-dial of Ahaz, were turned away from the Sun. For only in that position could they cast their shadow, or could the number of the illuminated steps be varied, upwards or downwards, according to the varying altitude of the sun. The only conceivable use of a fixed instrument so placed would be to show the rise and fall of the shadow from day to day, as the Sun on the meridian gradually rose higher between mid-winter and mid-summer, or descended lower between mid-summer and mid-winter, in passing of course through the winter and summer solstices in turn. No simple motion of the Sun in its ordinary diurnal progress would produce the effect described. On the other hand, it is equally clear that the shadow cast by a gnomon properly adjusted at the head of such a series of steps would travel upwards and downwards upon the steps “with the Sun,” from winter to summer and from summer to winter, indicating at each noon the meridian altitude of the Sun from day to day, the latitude of Jerusalem being 31° 47′, and the Sun’s altitude there on the shortest day being 34° 41′. If the gnomon were raised above the topmost step so as to bring the tip of the gnomon or any aperture in it so much above the step as would be the equivalent of 2° 54′ or slightly more, then the top of the shadow of the gnomon (or a spot of light passing through a hole in it) would, on the shortest day of the year, fall just beyond the lowermost step. An instrument