The small print in the caption is a reference to the following lines from Gilbert's & Sullivan's Patience, (1881) a comic opera that also satirized the Aesthetic Movement:
A pallid and thin young man,
A haggard and lank young man,
A greenery-yallery, Grosvenor Gallery,
Foot-in-the-grave young man!
ariadne in naxos
Ariadne In Naxos; or Very Like a Wail appeared in the February 4th, 1882 issue of Punch, or the London Charivari, a British weekly magazine of humour and satire.
The cartoon was the centerpiece of a fake interview with Wilde, the purpose of which was to ridicule the Aesthetic Movement that Wilde was going to America to espouse. The image depicts the Greek goddess Ariadne who represents the grief of Aestheticism as she watches Wilde depart aboard the ship Arizona.
The theme is taken from a version of the Ariadne myth in which Dionysus appears to Theseus saying that he had chosen Ariadne as his wife, and demands that Theseus leave her on the Greek island of Naxos for him.
The treatment of the composition (as the caption to it attests) is in homage to W.B. Richmond's "Electra at the Tomb of Agamemnon", 1874 (below), a painting that Wilde had described in detail in his review  of its showing at the The Grosvenor Gallery in London.
The Grosvenor Gallery, 1877
by Oscar Wilde, reprinted in Miscellanies, 1908.
VERY LIKE A WAIL
The cartoon is alternatively entitled Very Like A Wail. The closest source  for this phrase is a poem of the same name from The Knightly Heart, and other poems, a book of light verse by James Freeman Colman (1873).
Colman's poem similarly concerns the lovelorn condition, in his case a youth faced with the fickleness of the opposite sex; these lines are typical and also have a nautical theme:
From: Very Like A Wail
James Freeman Colman, 1873
 For the Dublin University Magazine (July 1877)
 Colman's title itself is likely a punning allusion to Shakespeare's Hamlet. Act iii. Sc. 2.:
Ham. Do you see yonder cloud that’s almost in shape of a camel?
Pol. By the mass, and ’tis like a camel, indeed.
Ham. Methinks it is like a weasel.
Pol. It is backed like a weasel.
Ham. Or like a whale?
Pol. Very like a whale.
The Knightly Heart, and other poems
Oscar The Apostle
Original research © John Cooper