With these preliminaries we will follow the lines which are marked out by the occurrence of the places in -_by_; beginning at a point on the coast of Lincolnshire, about half-way between the entrance to the Wash and the mouth of the Humber; the direction being south and south-west. Ander-_by_ Creek, Willough-_by_ Hills, Mum-_by_, Or-_by_, Ir-_by_, Firs-_by_, Reves-_by_, Conings-_by_, Ewer-_by_, Asgar-_by_,[27] Span-_by_, Dows-_by_, Duns-_by_, Hacon-_by_,[27] Thurl-_by_, Carl-_by_[27] take us into Rutlandshire, where we find only Grun-_by_ and Hoo-_by_. Neither are they numerous in Northamptonshire; Canons' Ash-_by_, Cates-_by_, and Bad-_by_ giving us the outline of the South-eastern parts of their area. For Huntingdon, Cambridge, and Beds, nothing ends in -_by_, whilst the other forms are in _sh_, and _ch_--as _Charlton_, _Shelton_, _Chesterton_ rather than _Carlton_, _Skelton_, _Casterton_. Leicestershire is full of the form, as may be seen by looking at the parts about Melton, along the valleys of the Wreak and Soar; but as we approach Warwickshire they decrease, and there is none south of Rug-_by_. More than this, the form changes suddenly, and three miles below the last named town we have Dun-_ch_ur_ch_ and Coa_ch_-bat_ch_. Tradition, too, indicates the existence of an old March or Debateable Land; for south of Rug-_by_ begins the scene of the deeds of Guy Earl of Warwick, the slayer of the _Dun_ Cow. Probably, too, the Bevis of Hampton was a similar[28] North-_amp_-_ton_-shire hero, notwithstanding the claim of the town of Southampton. The line now takes a direction northwards and passes through Bretby (on the Trent) to Derby, Leicestershire being wholly included. And here the frontier of the forest which originally covered the coal-district seems to have been the western limit to the Danish encroachments, Rotherham, Sheffield, and Leeds lying beyond, but with the greater part of Nottinghamshire and a large part of Derby within, it. In Yorkshire the East Riding is Danish, and the North to a great extent; indeed the western feeders of the Ouse seem to have been followed up to their head-waters, and the watershed of England to have been crossed. This gives the numerous -_bys_ in Cumberland and Westmoreland[29]--Kirk-_by_, Apple-_by_, &c. So much for the very irregular and remarkable outline of the area of the forms in -_by_ on its southern and western sides. In the north-east it nearly coincides with the valley of the Tees--nearly but not quite; since, in Durham, we have Ra-_by_, Sela-_by_, and Rum-_by_. The derivatives of _castra_, on the other hand, are in -_ch_-; _e.g._, Eb_ch_ester, _Ch_ester-le-street, Lan_ch_ester (Lan-_c_aster). In Northumberland there are none.