As Mulligan explains to Haines in Telemachus, the "Martello" towers that line the Irish coast at intervals north and south of Dublin (12 to the north, 16 to the south) were built in the early years of the 19th century by the British government under the leadership of "Billy Pitt" (Prime Minister William Pitt the Younger), to protect against the threat of invasion "when the French were on the sea."
The Napoleonic Wars between Britain and France, which had been brewing ever since the French Revolution, began in earnest in 1803. Fearing that French forces would invade to assist the cause of Irish revolution, as they had in the 1790s, the British constructed a series of small defensive fortifications along the coasts of England and Ireland, beginning in 1803 and ending with Pitt’s death in 1806. The tower at Sandycove, by some accounts, was the first built in Ireland, to protect the approaches to Dublin (personal communication from Robert Seidman). If true, this primacy may partly explain Mulligan’s saying that “ours is the omphalos” (i.e., the navel or source of all the others).
The British took as their model for all these fortifications
a squat round tower constructed by the Genovese at Punta
Mortella (Myrtle Point) in Corsica, which two of their
warships had tried to destroy in 1794. Their combined
firepower of 104 guns failed to disable the tower. Most
defensive fortifications enjoy the advantage of height: they
can fire down on attacking ships, while the ships’ guns must
use a good portion of their power (and risk explosive rupture
of the barrel) simply to overcome gravity. In addition,
the design of this tower was brilliant. Its roundness,
combined with a gentle slope inward from base to top,
deflected much of the power of incoming shot, and whatever
force was not deflected was absorbed by exceptionally thick
walls. Additionally, its round
artillery platform meant that it could direct fire
around an unlimited arc. After two and a half hours of close
bombardment HMS Fortitude was badly damaged by shot
from the tower’s two eighteen-pounders, and the warships were
forced to withdraw.
The tower was eventually captured by British land forces
after two days of fierce fighting, but the British were
impressed and resolved to copy the highly effective design.
After ringing England and Ireland with similar towers (called
Martellos, in a garbled recollection of Mortella), they went
on to build many more throughout the Empire during the first
two thirds of the century—about 140 in all. The towers were
finally made obsolete in
the 1860s and 1870s by the introduction of more accurate and
powerful rifled artillery on warships.
 Coincidence governs the events of Joyce's universe in
countless ways large and small, fictional and historical. In The
Ulysses Guide: Tours through Dublin, 2nd ed. (New
Island, 2015), Robert Nicholson notes an interesting fact:
"Coincidentally enough, the order for the building of this
tower, and others in the area, was dated 16 June 1804"