The subject is from Book IX of the Odyssey and had been first sketched by Turner about I807 in the Wey, Guildford' sketchbook, though there is no connection in composition (T.B.XCVIII- 5). This picture is based on one of the sketches on coarse canvas almost certainly painted in Italy in 1828-9 (No.475), though the hollowed-out arches of rock, probably based on those around the Bay of Naples, are only found in another of the sketches (Tate Gallery 2959).

Ruskin, who called this 'the central picture in Turner's career', noted Turner's fidelity to Pope's translation of the text in the portrayal of the morning light, though his suggestion that the sun-god Apollo is formless because 'he is the sun' is countered by Thornbury's statement that 'thanks to sugar of lead, Phoebus has vanished' (1862, 1, p.315). John Gage has also pointed out Turner's fidelity over such things as Ulysses' ship being in 'the shallows clear' and the way in which Polyphemus almost forms part of the 'lone mountain's monstrous growth', but he suggests that Turner went further by using the mythological subject to illustrate a picture about the forces of nature (1969, pp.128-32). The smoke rising from the mountain gives it a distinctly volcanic appearance and Polyphemus' fellow Cyclops were associated with thunder and lightning, which had themselves been associated with volcanic activity in the later eighteenth century. The Nereids playing around Ulysses' ship are not mentioned by Homer and seem to have been introduced as embodying the idea of phosphorescence, as in Erasmus Darwin's The Botanic Garden of 179I. By now, Gage summarises, Turner had moved beyond the mere personifying of natural causes that he had found in Thomson and Akenside to something 'far closer to the more purely scientific mythography of Shelley' (p.145).

Gage (pp.95-6) also suggests that the heightened colouring, particularly in the sky, was partly influenced by Italian fourteenth and fifteenth-century frescoes and temperas, to which Turner seems to have paid particular attention on his second visit to Italy, perhaps reflecting the growing interest in this period of his friends Samuel Rogers, Thomas Phillips and William Young Ottley (see the 'Roman and French' notebook of 1828, T.B.CCXXXVII-38v and 39, for Turner's notes on the frescoes in the Campo Santo at Pisa). Indeed the Morning Herald for 5 May 1829 held that Turner's bright colouring, which had 'for some time been getting worse and worse': , had in this picture reached the perfection of un-natural tawdriness. In fact, it may be taken as a specimen of colouring run mad - positive vermilion - positive indigo, and all the most glaring tints of green, yellow, and purple contend for mastery of the canvas, with all the vehement contrasts of a kaleidoscope or Persian carpet'. The Literary Gazette for 9 May protested that 'Although the Grecian hero has just put out the eye of the furious Cyclops, that is really no reason why Mr. Turner should put out both the eyes of us, harmless critics. ... Justice, however, compels us to acknowledge, that although Mr Turner thus continues to delight in violating nature and defying common sense, yet that, considering this performance as a gorgeous vision of the imagination, as a splendid dream of practical fancy, it is highly captivating'. Other critics too felt that the painter's excesses were justified by his poetical feeling. Ruskin's perhaps over-subjective view was that 'The somewhat gloomy and deeply coloured tones of the lower crimson clouds, and of the stormy blue bars underneath them, are always given by Turner to skies which rise over any scene of death, or one connected with any dreadful memories', and in Modern Painters he lists the picture among works in which the sky is 'the colour of blood' (Vol.Iv, 1856, Library Edition vI, p.381).