From thomasnast.com, where the cartoon is explained:
Nast created the Republican Elephant almost five years after his first depiction of the Democratic Donkey. At the time, and for seven cartoons afterward, it represented the Republican Vote, not the Republican Party. The Elephant’s actual emergence on October 29, 1874 — six days before the mid-term election — paralleled the timing of the Tammany Tiger’s birth three years earlier.
Nast’s target in this cartoon was James Gordon Bennett, Jr., the wealthy, conceited, autocratic editor of the Herald. In June 1873, Bennett’s Herald livened up the dog days summer by accusing President Ulysses Grant of “Caesarism” — thirsting for a third term.
As mentioned in the above quote, while the first Thomas Nast Republican elephant cartoon appeared in the Harper’s Weekly issue dated November 7, 1874, that edition of the magazine appeared on the newsstands 10 days earlier – on October 29, 1874.
Like the Democratic donkey, Nast did not create the elephant as a symbol of the Republican party.
The evolution of the 1864 Republican elephant from HarpWeek:
… However, Safire and others following his lead also mention an alleged appearance of an elephant in the pro-Lincoln campaign newspaper of 1860, The Rail Splitter. Although an image of a stampeding elephant was published in the Chicago version of that partisan periodical, it was part of an advertisement for a Chicago shoe store, Willet & Co. The elephant in the ad wears boots and carries a banner in its trunk labeled “Good Boots and Shoes.
The same boot-wearing, banner-carrying pachyderm used in the 1860 Willet advertisements is shown in the September 27, 1864 issue of Father Abraham celebrating Union military victories, instead of selling shoes. Since “seeing the elephant” was slang among Civil War soldiers for engaging in combat, the symbol was a natural choice for honoring successful military campaigns.
In the featured illustration from the October 18, 1864 issue of Father Abraham, the same emblem (minus the boots) bears a banner proclaiming, “The Elephant is Coming.” The animal is surrounded by text celebrating Republican victories in state elections, which were seen as precursors of the presidential contest a few weeks later in early November. This first appearance of the Republican Elephant had transitioned smoothly and swiftly from the language and imagery of war to that of American politics.
In 1872, Harper’s Weekly published a cartoon depicting the breakaway Liberal Republicans as a sham elephant. However, in neither 1864 nor 1872 did the symbolic caricature have a lasting impact on political cartoonists or the public.
It was the popularity of Thomas Nast and his repeated use of the symbolism that permanently connected the elephant and the Republican Party. That first Nast elephant was from Harper’s Weekly dated 150 years ago today.