Question

What was "the principle of which we were ashamed" in the writing of the constitution?

Answer 1

"The principle of which we were ashamed" refers to slavery.  In the writing of the US Constitution, the word slavery was omitted from Article 1, Section 2 which outlined how the states would be represented in Congress according to their population.  Each free man counted as one person, and every five slaves counted as three.  However, slaves were referred to in the document as "other persons" prompting a moral objection by John Dickinson who wrote the little-known phrase in his personal notebook during the 3/5ths debate at the Constitutional Convention in 1787.

Answer 2

Slavery--the word "slave" or "slavery" is never explicitly stated in the Constitution.

The statement referred to the three-fifths compromise regarding representation for the House of Representation. The South demanded their slaves be counted as persons but not be regarded as persons or even freed in the law. The compromise counted "other persons" as 3/5 a person when counting for representation as opposed to a whole when counting whites. Some of the Representatives from the North felt this was a moral error and one the US should be ashamed.