And, yet that didn't stop the practice of the government having a Chaplain to guide them and lead them in prayers. The Senate begins every session by being led in prayer by their Chaplain and follows it with the pledge of allegiance to the flag with the words "under God".
http://www.senate.gov/reference/office/chaplain.htm
(excerpt:
Throughout the years, the United States Senate has honored the historic separation of Church and State, but not the separation of God and State. The first Senate, meeting in New York City on April 25, 1789, elected the Right Reverend Samuel Provost, the Episcopal Bishop of New York, as its first Chaplain.
During the past two hundred and seven years, all sessions of the Senate have been opened with prayer, strongly affirming the Senate's faith in God as Sovereign Lord of our Nation. The role of the Chaplain as spiritual advisor and counselor has expanded over the years from a part-time position to a full-time job as one of the Officers of the Senate. The Office of the Chaplain is nonpartisan, nonpolitical, and nonsectarian.
In addition to opening the Senate each day in prayer, Chaplain Blacks duties include counseling and spiritual care for the Senators, their families and their staffs, a combined constituency of six thousand people. Chaplain Blacks days are filled with meeting Senators about spiritual and moral issues, assisting Senators staffs with research on theological and biblical questions, teaching Senate Bible study groups, encouraging such groups as the weekly Senate Prayer Breakfast, and facilitating discussion and reflection small groups among Senators and staff.
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By the way, if your response to this is that just because they've been doing it for over two hundred years....doesn't make it right - - - I've already heard that and even our liberal Supreme Court has never bothered with that issue.