Since what you have posted (code from 1845) has since been changed by Constitutional amendment and statute, it has no applicability to a birth in 1961. Not to mention that it applied only to New York state, not any other state. Are you claiming 0bama was born in New York?
Please do not play dense. Here is how this works. We establish what WAS, we establish when and how it was changed, and then we establish what IS.
I will take it from your response that you concede the point that in 1845,(I will point out that Lynch v Clarke was in 1844, and the legislature of New York explicitly rebuked the court's decision with this new law.) the law (In the State of New York and others) was that a child of transient aliens was NOT a citizen, and therefore birth on the soil would NOT make someone a "natural born citizen". If my understanding of your position is correct, then let me know.
There is no point in discussing 1961 until we have solidified what was the law prior to the 14th amendment. I have shown you evidence that "birth on the soil" was not the sole requirement. (as if the proof of Indians, Slaves and diplomats wasn't enough)