Curious about religion-specific oath and affirmation practices circa 1804?

Thanks to Google Books and a pointer from a helpful guide, I've recently had occasion to take a look at an early nineteenth-century guide- and sourcebook for judges on inferior state courts and justices of the peace dealing with federal matters: Samuel Bayard, An abstract of those laws of the United States which relate chiefly to the duties and authority of the judges of the inferior state courts: and the justices of the peace, throughout the union; illustrated by extracts from English law books. To which is added, an appendix, containing a variety of useful precedents (1804). 

Of interest to MOJ readers may be Bayard's description of how oaths and affirmations were to be administered, which differed depending on a witness's religion (or absence thereof):

Prior to giving evidence in a cause, a witness in all cases, must be sworn or affirmed to declare "the truth, the whole truth, and nothing but the truth."

A Jew may be sworn on the books of the Old Testament; a Mahometan on the Alcoran; pagans, or infidels of any description, also persons of any religious denomination may be sworn according to the ceremonies of the religion they profess, and are admissible witnesses in any cause ....

In the courts of Great Britain, in pursuance of an express act of parliament, the affirmation of a quaker cannot be received in any criminal case; but in the United States, where the religious principles, and pure morals, of this respectable denomination of christians, are well known, and where sincere scruples of conscience are more respected; their affirmation is in all cases, regarded as equivalent to the oath of other christians. It is considered as an appeal to Heaven for the truth of what they declare, and by our laws, where taken falsely, it is punished in the same manner, as where a false oath is taken. (p.216)

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An atheist, who professes to have no belief in the existence of a God, and of course disbelieves a future state of rewards and punishments; also a person who has no idea of a God or religion, who is altogether ignorant of the obligations of an oath; ought not to be sworn. (p. 217)

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[There are also some more explicit directions later:]

NB. The witness having laid his right hand on the Bible or New Testament, then kisses the same.

If a Jew, he should be sworn on the five books of Moses, with his hat on.

If a Roman Catholic, there should be a cross on the book.

A Mahomedan must be sworn on the Alkoran, and other witnesses according to the ceremonies of their respective systems of faith (or mode of worship). (pp. 252-53)

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[The appendix also contains a "special form of an oath used by some denominations of christians."]

"I, A.B., do swear by Almighty God, the searcher of all hearts (or by the ever living God) that the evidence I will give, &c. and that, as I shall answer to God, at the great day." (p .253)