3. _The fourthe part._ The true explanation of this passage, which Tyrwhitt failed to discover, is due to Mr. A. E. Brae, who first published it in May, 1851, and reprinted it at p. 68 of his edition of Chaucer's Treatise on the Astrolabe. His conclusions were based upon actual calculation, and will be mentioned in due order. In re-editing the 'Astrolabe,' I took the opportunity of roughly checking his calculations by other methods, and am satisfied that he is quite correct, and that the day meant is not the 28th of April, as in the Ellesmere MS., nor the 13th of April, as in the Harleian MS., but the 18th, as in the Hengwrt [133] MS. and most others. It is easily seen that _xviii_ may be corrupted into _xxviii_ by prefixing _x_, or into _xiii_ by the omission of _v_; this may account for the variations. The key to the whole matter is given by a passage in Chaucer's 'Astrolabe,' pt. ii. ch. 29, where it is clear that Chaucer (who, however, merely translates from Messahala) actually confuses the hour-angle with the azimuthal arc; that is, he considered it correct to find the hour of the day by noting _the point of the horizon_ over which the sun appears to stand, and supposing this point to advance, with a _uniform_, not a _variable_, motion. The host's method of proceeding was this. Wanting to know the hour, he observed how far the sun had moved southward along the horizon since it rose, and saw that it had gone more than half-way from the point of sunrise to the exact southern point. Now the 18th of April in Chaucer's time answers to the 26th of April at present. On April 26, 1874, the sun rose at 4h. 43m., and set at 7h. 12m., giving a day of about 14h. 30m., the fourth part of which is at 8h. 20m., or, with sufficient exactness, at _half-past eight_. This would leave a whole hour and a half to signify Chaucer's 'half an houre and more,' shewing that further explanation is still necessary. The fact is, however, that the host reckoned, as has been said, in another way, viz. by observing the sun's position _with reference to the horizon_. On April 18 the sun was in the 6th degree of Taurus at that date, as we again learn from Chaucer's treatise. Set this 6th degree of Taurus on the East horizon on a globe, and it is found to be 22 degrees to the North of the East point, or 112 degrees from the South. The half of this is at 56 degrees from the South; and the sun would seem to stand above this 56th degree, as may be seen even upon a globe, at about a quarter past nine; but Mr. Brae has made the calculation, and shews that it was at _twenty minutes past nine_. This makes Chaucer's 'half an houre and more' to stand for _half an hour and ten minutes_; an extremely neat result. But this we can check again by help of the host's _other_ observation. He _also_ took note, that the lengths of a shadow and its object were equal, whence the sun's altitude must have been 45 degrees. Even a globe will shew that the sun's altitude, when in the 6th degree of