^{page 243 note 1} After the junction of these two the river is called the Mawddach. But the Eden is clearly the principal branch, inasmuch as it maintains its direction unchanged.

^{page 244 note 1} It will be noticed that this line is almost exactly parallel to the general trend of the coast of Cardigan Bay, a fact which seems to point to some community of origin.

^{page 244 note 2} If the radial valleys existed before the formation of the transverse valleys, we might expect that where the lines joining the remnants of the radial valleys cross the intervening ridges, there should be a col or depression ; and this is, indeed, very commonly the case. Moreover, opposite each important stream where it enters a transverse valley, there is generally a little valley running down from the col and entering the transverse valley on the opposite side. For example, opposite the point where Afon Lliw enters the valley of the Bala fault, a valley runs in from the col called Bwlch-y-pawl, which is situated at the head of the River Vyrnwy. Opposite Afon Tryweryn is the valley of the Hirnant, and from this we pass across a col into the head of Afon Tanat. Similarly, in the line of the Ceirw we find Afon Trystion entering the valley of the Dee from the opposite side ; and from the head of Afon Trystion a decided depression leads us to the head of the Ceiriog.