That implies that the nameless woman has made previous visits to the tower. (It is also a somewhat dismissive phrase used for someone of a lower class.) In the mythic parallel, she is Pallas Athene disguised as Mentor disguised as an Irish milk-woman.

Mulligan is "putting on" the pious attitude and language of an Irish peasant, prompted by the announcement of the milk-woman. His attitude towards others, whether Haines or the milk-woman or Joyce himself, always involves mockery. This can be seen as the defence mechanicism of an educated Catholic of his class in Ireland - that is, the professional Catholics in a world still formally dominated by Protestants. Stephen regards his attitude as a worthless and self-defeating as compared with his own artistic intentions and believes that Mulligan fears the "rapier of [his] art".

Mulligan is frying breakfast on an open fire set in the wall of the Martello tower, a former military gun emplacement of the Napoleon period. The fire was originally designed to heat cannonballs but a grate has been inserted with a kettle-hook above it. It is very much a young man's dwelling - impractical and fantastic. In fact, Oliver St. John Gogarty - the model for Mulligan - rented it from the War Department and Joyce was only a visitor but Joyce makes Stephen claim that he 'paid for it'. The verbs Joyce uses to describe Mulligan's movements are all suited to his role as Antinous, one of Penelope's suitors. 'Hewing' and 'lunged', in particular, suggest the actions of a Homeric warrior. When Mulligan says 'the sugar is in the bag', he indicates that they should help themselves from the bag in which it was bought but also reminds us that the suitors make themselves free in Ulysses' household.

The priest's Latin blessing used in the Mass: 'In the name of the Father, the Son and the Holy Ghost'. Mulligan began the chapter with a blasphemous imitation of the eucharistic transubtantiation while shaving and throughout the book his conversation amalgamates the sacred and the profane in a spirit which he calls 'hyperborean' echoing Neitzsche's conception of the superman as one who is indifferent to conventional laws of conduct. He also plays with the idea of establishing a 'new Hellenism' at the Sandycove Tower, which he calls an 'omphalos' (or navel). That idea was formerly suggested by Oscar Wilde, whose fin-de-siècle mixture of classicism and outrageous wit is a large ingredient in Mulligan's character.

meaning: piss (urinate). Her remark and its comic rejoinder ('... in the same pot') Mrs Cahill are spoken by Mulligan in the accent of a peasant woman. Mrs. Grogan and Mrs. Cahill are two imagined persons with typical lower-class - i.e., Irish - names characters with typical names for the lower-class Irish at that period. Mulligan's comic enactment of their imaginary conversation is an example of the art of the "stage Irishman" in which the vulgarity and humour of the simple people is served up as entertainment for educated English audiences who found it convenient to regard the colonised Irish as inferior rather than different while allowing them some credit for vulgar intelligence and humour.*
  In this respect, Mulligan is hardly more than a 'court jester', as Stephen obliquely calls him, performing for Haines whom he pretends to despise. Several nineteenth-century Irish writers such as Samuel Lover and Charles Lever wrote successfully in this vein while other Irish great writers such as Shaw and Wilde can also be viewed occasionally in this light. Joyce/Stephen intends to escape the stereotype - but does he do so entirely, or does he merely raise it to a higher level?

The Roman Zeus.One of a number of expressions and figures of speech by which Haines clearly identifies himself as an upper-class Englishman with a (so-called) public school - i.e., private - education. Some commentators associate the surname Joyce gives him with French hâine ('hate') but this is probably reading too much into it. Haines is a common English name and, as such, suggests that its owner is middle-class rather than aristocratic whereas Chenevix Trench was Anglo-Irish which, in Ireland, virtually means aristocratic.
  Dermot Chenevix Trench, the actual model for Haines, wrote a pamphlet promoting the revival of the Irish language in 1907, and it Mulligan makes an anachronistic allusion to this in the chapter. In June 1909 Trench committed suicide, perhaps suggesting that his cultural engagement with the Irish-Ireland movement was fatal to his own advancement in the world - though other men like Arnold Bax who was caught up in the Irish movement was later knighted and became Master of the King's Musick in 1941.

The Roman Zeus. One of a number of expressions and figures of speech by which Haines clearly identifies himself as an upper-class Englishman with a (so-called) public school - i.e., private - education. Some commentators associate the surname Joyce gives him with French hâine ('hate') but this is probably reading too much into it. Haines is a common English name and, as such, suggests that its owner is middle-class rather than aristocratic whereas Chenevix Trench was Anglo-Irish which, in Ireland, virtually means aristocratic. Dermot Chenevix Trench, the actual model for Haines, wrote a pamphlet promoting the revival of the Irish language in 1907, and it Mulligan makes an anachronistic allusion to this in the chapter. In June 1909 Trench committed suicide, perhaps suggesting that his cultural engagement with the Irish-Ireland movement was fatal to his own advancement in the world - though other men like Arnold Bax who was caught up in the Irish movement was later knighted and became Master of the King's Musick in 1941.

i.e., folklore - of which Haines is apparently a collector. The Dun Emer Press was operated in Dundrum by W. B. Yeats's sisters who published his private editions as well as much ballad and folklore material on handprinted sheets. The 'year of the big wind' was a phrase in the colophon of his collection of that 1903, a year in which an unusually big storm occurred. (Mulligan is mocking the Yeats's adoption of peasant speech again.) The 'weird sisters' are the witches in Macbeth who likewise meet in a storm, permitting him to compare the Yeats sisters with the hags who open Shakespeare's play. The remark about text and notes is a jibe at the format of scholarly books on folklore in general rather than any produced by the Yeats sisters - though Yeats like to supply copious notes to his own poems.

The Welsh epic and the Hindu sacred text. In the period of the novel, folklorists were trying to establish the connections between all mythological traditions, together with their sources and their meaning. None of the many Irish mythological cycles are not mentioned here, and this suggests that Mulligan is staying in character as an aloof English anthropologist, hence his 'fine puzzled voice'. Stephen's answer equates Mrs. Grogan with another comic female personage who raises (his[es] up) her skirt (petticoat) and pisses. Mulligan relishes Stephen's shared irreverence for the whole folklore-collectors' outlook.

The milk-woman speaks in the pious idiom of the Irish that Mulligan has has previously imitated before her entrance. (She has had to walk up the stairs to the door of the tower.) In his mind, she is one of the 'islanders' - a term associated with the West of Ireland where Gaelic tradition was still intact and where folklorists preferred to look for their materials. Here 'islanders' is a used in a comical sense for all the people of Ireland - itself an island and sometimes thought of as a satelite of Great Britain - a description which is inherently belittling. For Stephen, by contrast, the milk-woman resembles the poetical personification of Ireland best-known from Cathleen Ni Houlihan, W. B. Yeats's patriotic play of 1901 in which she appears on stage as an old woman who has lost her "four green fields" - i.e., the provinces of Ireland. This allegorical idea is based in turn on the old Irish song Droimeann Donn Dilís ("Faithful Brown Cow") which contains the phrase shíoda na mbó - literally 'silk of the kine', meaning the best cows. In Yeats's play, young Irishmen are asked to go out and fight for the old woman, who then turns into a young queen.

Mulligan is a medical student, as was Gogarty himself - later a successful ear, nose and throat specialist working in Ireland and America. Joyce at one time planned to follow him but failed to gain admission to the Medical Faculty of Paris University in autumn 1902. His resentment against Mulligan is aggravated by the latter's rude remarks about the death of his mother reported earlier: 'It's only Stephen Dedalus whose mother is beastly dead' - and equally by his unconvincing excuse for this, based on the familiarity of death in medical circles. 
  The obsequiousness of women to men of Gogarty's profession - whom Stephen rudely calls bonesetters, in an archaic term - reminds him of their equal reverence for priests and hence rekindles his jealousy at their power over people who he thinks should respect the artist more than the priest. His anger drives him to echo the contempt for women which is built into the Catholic theology of the Fall. Here 'unclean loins' refers to menstruation and the medieval attitude towards it.
  Although the passage offers a pastiche of the prevailing clerical attitude and its associated rhetoric rather than his personal opinion, it also reveals a streak of misogyny which can be read in the context of his refusal to pray at his mother's deathbed - a refusal that triggers the feelings of guilt he experiences in the novel (cf. 'agenbite of inwit'*). Intent on preserving his intellectual freedom, Joyce himself refused to pray on the corresponding occasion in his life - a refusal which cost him the impression of seeming gratuitously cruel. Hence Mulligan tells Stephen that his (Mulligan's) aunt believes that he has 'killed his own mother' by this act of denial.

Haines has spoken some words in Irish although these are not reproduced here. Omitting them is itself a measure of Joyce's indifference to Irish language-revival in keeping with the attitude he expressed when he said that he agreed with everything in Sinn Féin policy except Irish language-revival. (Coming from a young man who learnt Norwegian to write to Ibsen in 1900, this was a stern judgement on the sentimentality of Irish cultural nationalism in the period.) The fact that a common Irishwoman - especially if she is incidentally a personification of Ireland - does not know the language seems to put Haines and the revivalists in a very odd position and her knee-jerk approval of revivalism does not strengthen his position.
  Joyce briefly attended Irish lessons given by Patrick Pearse, later the leader of the 1916 Rising. He left the classes because he could not stand Pearse's constant expression of anti-English sentiments. The Irish-language revival movement was launched by Douglas Hyde with the founding of the Gaelic League in 1893. In the following 100 years it became part of Irish educational policy and was required by law at state examinations but the actually revival never happened in any convincing way and the language remains a cultural shibboleth of the independent Irish state rather than a day-to-day language of the majority.

The milkwoman is doing the sum for a week's milk in her head using the old sterling currency of pounds, shillings and pence of the old sterling currency which was decimalised only when the UK and Ireland joined the European Union in the 1970s. There were 12 pennies in a shilling and 20 shillings in a pound. 'Over' means that 2 pennies are carried over from 14 pennies (or 'pence') after 1 shilling is reached: seven days x 1 pint @ 2p (=1s. and 2p.) + 3 days x 1 quart @ 4p (= 1s) = 1s. 2p. + 1s. The 'florin' with which Mulligan pays her - was a coin worth 2 shillings - probably named after "Florence" (English for city Firenze).