46. This article is probably not Chaucer's. It is found in MS. Bodley 619, and in MS. Addit. 29250. The text is from the former of these, collated with the latter. What it asserts comes to this. Suppose it be noted, that at a given place, there is a full flood when the moon is in a certain quarter; say, e.g. when the moon is due east. And suppose that, at the time of observation, the moon's actual longitude is such that it is in the first point of Cancer. Make the label point due east; then bring the first point of Cancer to the east by turning the _Rete_ a quarter of the way round. Let the sun at the time be in the first point of Leo, and bring the label over this point by the motion of the label only, keeping the _Rete_ fixed. The label then points nearly to the 32nd degree near the letter Q, or about S.E. by E.; shewing that the sun is S.E. by E. (and the moon consequently due E.) at about 4 A.M. In fact, the article merely asserts that the moon's place in the sky is known from the sun's place, if the difference of their longitudes be known. At the time of conjunction, the moon and sun are together, and the difference of their longitudes is zero, which much simplifies the problem. If there is a flood tide when the moon is in the E., there is another when it comes to the W., so that there is high water _twice_ a day. It may be doubted whether this proposition is of much practical utility. 41_a_: This comes to precisely the same as Art. 41, but is expressed with a slight difference. See fig. 16, where, if _bc_ = 8, then BC = 12/8 EB. 41_b_: Merely another repetition of Art. 41. It is hard to see why it should be thus repeated in almost the same words. If _bc_ = 8 in fig. 16, then EB = 8/12 BC = 2/3 BC. The only difference is that it inverts the equation in the last article.] 42_a_ This is only a particular case of Art. 42. If we can get _bc_ = 3, and _b'c'_ = 4, the equations become EB = 4BC, E'B = 3BC; whence EE' = BC, a very convenient result. See fig. 17.] 43_a_: The reading _versam_ (as in the MS.) is absurd. We must also read '_nat_ come,' as, if the base were approachable, no such trouble need be taken; see Art. 41. In fact, the present article is a mere repetition of Art. 43, with different numbers, and with a slight difference in the method of expressing the result. In fig. 18, if _b'c'_ = 3, _bc_ = 4, we have E'B = 3/12 BC, EB = 4/12 BC; or, subtracting, EE' = (4-3)/12 BC; or BC = 12 EE'. Then add the height of E, viz. E_a_, which = AB.