18. _episicle_, epicycle. To account for the planetary motions, epicycles were invented. The moon, for instance, was supposed to revolve round a _moving_ centre, which centre itself moved round the earth in a perfect circle. This came a little nearer to the true motion in some instances, but was hopelessly wrong, and nothing could be made of it, even when a _second_ epicycle, revolving about a centre which moved in the _first_ epicycle, was superadded. All that Chaucer says here is, that, whilst the centre of the moon's epicycle had a direct motion, the moon's motion in the epicycle itself was a reverse one, unlike that of the other planetary bodies. The subject is hardly worth further discussion, so I merely refer the reader to the Almagest, lib. iv. c. 5; and lib. ix. c. 5. § 36. The 'equations of houses' means the dividing of the sphere into _equal_ portions, and the right numbering of those portions or houses. The most important house was the first, or ascendent, just rising; the next in importance was the tenth, which was just coming on the meridian; then come the seventh or descendent, just about to set, and the fourth, just coming to the line of midnight. The next in importance were the _succedents_, or houses immediately following these, viz. the second, the eleventh, the eighth, and the fifth. The least important were the third, twelfth, ninth, and sixth. See Fig. 14. § 37. 18. _thise 3 howsez._ That is, the nadirs of the 2nd, 3rd, and 4th houses give the houses that 'follow,' i.e. the 8th, 9th, and 10th. The word 'follow' here seems to refer, not to position, but to the order in which the houses may most conveniently be found. Chaucer omits to add that the beginnings of the 5th and 6th houses can be found in a similar way, because it is sufficiently evident. It is all from Messahala. § 38. 1. _for warping, the brodere the bettre._ This may mean, either (1) to prevent warping, the thicker the better; or (2) to prevent the errors arising from warping (for fear of warping), the larger the better. I believe the latter to be the true interpretation; for it is better thus to guard against possible errors than to make the plate very thick and, at the same time, small. Besides which, the usual meaning of _brodere_ is _wider, larger, more ample_. Indeed, we find the very expression 'non sit tamen nimis parvus' in the 4th section of the Practica Chilindri of John Hoveden, published by the Chaucer Society; which see. 8. _fro the centre_, i.e. sticking up above the centre, the length of the wire being equal to a fourth of the diameter, or half the radius, of the circle. This proportion would do for many days in the year; but in the summer time, the pin would bear to be rather longer. Still, we need not alter the text. Cf. the Critical Note on p. 237. 10. _any-thing_, i.e. ever so little; so _ony-thyng_ in l. 13; cf. § 17. 6.