Proposal for the Union Flag of the second United Kingdom (after the unification of Ireland and Great Britain on 1 January 1801) printed in the March 1803 Gentleman's Magazine as an illustration to an anonymous letter letter dated 20 March 1803 signed from A Stupid Fellow. (See plate III, figure 11 in volume LXXIII, part 1, pages 217 &amp; 221.) The letter is a response to one by Thomas Walters published in the February 1801 Gentleman's Magazine; unsatisfied with the official Union Flag designed by the College of Arms and approved by the king in November 1800, Walters had suggested the addition of the Irish harp and a green disc to the existing Union Flag. The anonymous correspondent did not like this suggestion but was also dissatisfied with the official result; the writer offered a suggestion which had been speculatively created before the Union took effect but which eschewed the use of an Irish harp:
Long before the alteration in the Union Jack was made known to the publick, I was amusing myself with some friends in conjecturing how the cross of St Patrick would be inserted; various plans were produced, but that which appears most correct I send you (fig. 11,) hoping you will give it a place in answer to the note in vol, LXXI p. 122. I cannot agree with Mr. Walters in introducing the harp on a flag which bears the crosses of England and Scotland, with which, for the sake of similarity, the cross of Ireland should be blended. It remains only to be considered whether the character of each cross can be presented without confusion. This is, I think, satisfactorily done in the inclosed card; and certainly meets my ideas better than the jack of Mr. Walters, or the counterchanged jack which the Heralds have produced.

F. Edward Hulme, in his The Flags of the World: Their History, Blazonry and Associations, page 54, says this suggestion is "by no means a bad one" (Hulme's fig. 89), but pointing out that it: like all the other suggestions, good, bad, and indifferent, suffered from the fatal objection that it saw the light when the whole matter was already settled and any alteration scarcely possible.

NB that the red saltire is beneath the white saltire. In the illustration in The Gentleman's Magazine, the flag is square with the proportions of the ordinaries very similar to the irregular ones shown here: here, each of the the ends of each of the saltires are offset from the corners by a distance equal to one sixth of the flag's height. The colours are as used in the 21st century British flag.
The Gentleman's Magazine, March 1803 (vol. LXXI, part 1, plate III, figure 11, volume LXXIII, part 1, pages 217 &amp; 221).
Own work based on: Flag of Great Britain (1707–1800).svg:   and Saint Patrick's Saltire.svg: