Final answer:
Abraham Lincoln's well-known speech after July 1863 was the Gettysburg Address, given at the dedication of the Soldiers' National Cemetery in Pennsylvania, which emphasized equality and the preservation of the Union.
Step-by-step explanation:
The specific well-known speech that President Abraham Lincoln gave after July 1863 was the Gettysburg Address. Delivered several months after the Battle of Gettysburg on the occasion of the dedication of the Soldiers' National Cemetery in Pennsylvania, this speech is renowned for its brevity and depth, emphasizing the principles of human equality and the importance of preserving the Union. Although it received a polite response at the time, it has since become one of the most famous speeches in American history.