Flogging a dead horse (alternatively beating a dead horse, or beating a dead dog in some parts of the Anglophone world) is an idiom that means to continue a particular endeavour is a waste of time as the outcome is already decided.
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According to the Oxford English Dictionary, the first recorded use of the expression in its modern sense was by the English politician and orator John Bright, referring to the Reform Act of 1867, which called for more democratic representation in Parliament. Trying to rouse Parliament from its apathy on the issue, he said in a speech, would be like trying to flog a dead horse to make it pull a load. The Oxford English Dictionary cites The Globe, 1872, as the earliest verifiable use of flogging a dead horse, where someone is said to have "rehearsed that [. . .] lively operation known as flogging a dead horse".
However Jay Dillon has discovered an earlier instance attributed to the same John Bright thirteen years earlier: speaking in Commons 28 March 1859, Lord Elcho (Francis Charteris, 10th Earl of Wemyss) remarked that Bright had not been "satisfied with the results of his winter campaign" and that "a saying was attributed to him [Bright] that he [had] found he was 'flogging a dead horse.'"
Earlier meaning
Some scholars claim that the phrase originated in 17th-century slang, where a "dead horse" was work that was paid for in advance, e.g. "His land 'twas sold to pay his debts; All went that way, for a dead horse, as one would say." This attribution confuses "flogging a dead horse" with an entirely different phrase: "to work (for) the dead horse". This phrase was slang for "work charged before it is executed". This use of 'dead horse' to refer to pay that was issued before the work was done was an allusion to using one's money to buy a useless thing (metaphorically, "a dead horse"). Most men paid in advance apparently either wasted the money on drink or other such vices, or used it to pay outstanding debts.
In his book Old England and New Zealand published in London in 1879 the author Alfred Simmons gives detailed explanation and background of the "Flogging the Dead Horse" ceremony performed on board ship by a ship's crew at the end of the first month of their voyage (page 113).
"To slay the slain"
A comparable expression for useless labour is "thrice to slay the slain", a quotation from John Dryden, in Alexander's Feast, stanza iv. Dryden drew his inspiration from Sophocles's Antigone in which the blind seer Tiresias is led onstage by a boy, and declaims, "Nay, allow the claim of the dead; stab not the fallen; what prowess is it to slay the slain anew?" The trope was used in Latin, too: in Libanius's funeral oration for the Emperor Julian, he declares of a scoundrel, "Of the three who had enriched themselves through murders, the first had gone over the whole world, accusing people falsely, and owed ten thousand deaths to both Europe and Asia; so that all who knew the fellow were sorry that it was not possible to slay the slain, and to do so thrice over, and yet oftener." The expression was used in "literary" contexts, as when Edward Young mused:
While snarlers strive with proud but fruitless pain
To wound immortals, or to slay the slain.
In the heated atmosphere of literary journalism, the phrase was often quoted to show the writer's knowledge. In Punch for May 1861, a broad satire on the heated controversies caused by the publication of Charles Darwin's Origin of Species, which was defended by Thomas Henry Huxley, concluded as follows.
To twice slay the slain,
And so I shall bid you 'Adieu'!