and these tables chiefly considered the 'mene mote,' or average motion of the planets, and that only for periods of years. If you wanted the position of a planet at a given hour on a given day, you had to work it out by figures; the rule for which working was called a 'canon.' This very 'canon' is precisely given at length in sect. 44; and sect. 45 is only another way of doing the same thing, or, in other words, is an alternative canon. When all this is fairly and sufficiently considered, we shall find good grounds for supposing that these sections on the 'mene mote' are perfectly genuine, and that they really belong to Part iv. of the Treatise. I will only add, that the fact of sections 41_a_-42_b_ being thus placed after a portion of Part iv. is one more indication that they are spurious. § 23. CONCLUSION 40. But it may be objected, as Mr. Brae has fairly objected, that Conclusion 40 itself ought to belong to Part iv. So it ought perhaps, if Chaucer had followed out his own plan. But it is clear from its contents that the Prologue to the 'Astrolabie' was written _before_ the commencement of the treatise itself, and not, as prefaces generally are, afterwards. He was pleased with his son's progress. Little Lewis had asked him if he might learn something about an astrolabe. The father at once sent him a small astrolabe[50] by way of reward, constructed for the latitude of Oxford, and having 45 circles of latitude on the flat disc (see Fig. 5) instead of having 90 such circles, as the best instruments had[51]. This, however, was a 'sufficient' astrolabe for the purpose. But he believes the Latin treatises to be too hard for his son's use, and the Conclusions in them to be too numerous. He therefore proposes to select some of the more important Conclusions, and to turn them into English with such modifications as would render them easier for a child to understand, He then lays down a table of contents of his proposed five parts, throughout which he employs the future tense, as 'the firste partie _shal_ reherse,'--'the second partie _shal_ teche,' &c. This use of the future would not alone prove much, but taken in connexion with the context, it becomes very suggestive. However, the most significant phrase is in the last line of the Prologue, which speaks of 'other noteful thinges, yif god wol vouche-sauf & his modur the mayde, mo than I behete,' i.e. other useful things, _more than I now promise, if God and the Virgin vouchsafe it_. In accordance with his habits of seldom finishing and of deviating from his own plans at pleasure, we have but an imperfect result, not altogether answerable to the table of contents. I therefore agree with Mr. Brae that the 40th Conclusion would have done better for Part iv., though I do not agree with him in rejecting it as spurious. This he was led to do by the badness of the text of the MSS. which he consulted, but we can hardly reject this Conclusion without rejecting the whole Treatise, as it is found