Meaning of ‘means of a mine’

The passage below is from Feudal England by John Horace Round.

Breaching of the Walls 439

Returning now to sober fact, let us ask how the city of Exeter came into William's hands. This is the pivotal point on which the whole story revolves. On this point Mr. Freeman spoke with no uncertain sound : the city was " taken by means of a mine."17 It was, he wrote, "by undermining the walls that William at last gained possession of the city," the citizens being thus forced "to submit unreservedly."18 He added, contrasting the success of William with the failure, in 1003, of Swend:

William might have been beaten back from Exeter as Swend had been, if the military art of Normandy in William's days had not been many steps in advance of the military art of Denmark in the days of Swend.

This allusion to "Swend" involves a perfect tangle of confusion. Turning back a couple of pages, we are reminded that on Penhow, "sixty-seven years before (1001), Swend, of Denmark, driven back from the city, had found his revenge" (p. 154). Guided by a footnote, we turn for information to the earlier volume to which the author refers us, only to learn that it was not Swegen, but the adventurer Pallig who was driven back from Exeter in 1001 (i. p. 307), while "of Swegen himself we hear nothing in English history for nine years (994-1003)"19 Moreover, when Swegen did come—in 1003—invading England to avenge the massacre of Saint Brice, he was not "driven back from the city," but, on the contrary, "stormed and plundered it" (p. 315), for "tne citizens who had beaten back Pallig had no chance of beating back Swegen" (Exeter, p. 27).

This passage is 439th page of the book.

I have some questions about it.

One, the meaning of the underlined ‘means of a mine.’

I cannot figure the meaning of ‘means& mine.’ Does ‘means’ mean ‘method’? (Am I right?) But about ‘mine’ I can’t even produce any guesswork. (Could you help me?)

Still, I have more questions. In this book’s index, there’s the entry named “on the Conqueror’s earldoms 439 page;”

Does ‘Conqueror’ mean William in this page? (Am I right?)

What does ‘earldoms’ mean? Does it mean the fee given to earls or does it mean status of earl or something else whose meaning I don’t catch? (Could help me?)

Thanks in advance.