Washington brings up the human heart a few times in his farewell address, as a way to add some emotional heft to the text. He references both his own heart and the hearts of the people. It's an effective way to try and bring people together behind a common emotion.

"You have a heart and feel things? I have a heart and feel things! We must do lunch sometime."

Bam: unity.

Washington's first mention of the heart is definitely the most poetic, when he reminds the audience how "[i]nterwoven […] is the love of liberty with every ligament of your hearts" (8.1). That's a pretty powerful image—a human heart with "liberty" just wrapped up with all the arteries and ventricles.

He also warns the audience about "the jealousies and heartburnings" (15.3) that develop when they give in to regional differences, as well as "that love of power, and proneness to abuse it, which predominates in the human heart" (26.3). Everyone can understand getting carried away with things like envy or ultimate power (who hasn't been there?), so Washington is making his arguments more relatable.

He also talks about himself in this way. One of his closing lines references "the benign influence of good laws under a free government, the ever-favorite object of my heart" (50.1). We can all understand the warm and fuzzy feelings that come with…good laws. Okay, maybe we get excited about different things, but it does humanize Washington and show the audience that he has the same kinds of feelings they do.

Although we can't speak for American citizens of 1796 and whether or not "good laws under a free government" were their favorites, too. Let's just assume they ranked pretty highly.