This section is from the book "Constitutional Law In The United States", by Emlin McClain. Also available from Amazon: Constitutional Law in the United States.
One becomes a citizen of the United States either by birth or naturalization. By the simple language of the Fourteenth Amendment "All persons born in the United States and subject to the jurisdiction thereof are citizens"; but interpretation has been necessary in applying this language to particular classes of cases. For instance, an Indian whose parents at the time of his birth were members and subject to the jurisdiction of his tribe, although he may have been born within the territorial limits of the United States, is not a citizen by birth and can become a citizen only by naturalization (Elk v. Wilkins); and this can be effected only under special laws relating to Indians, not under the general naturalization laws. If, however, at the time of his birth his parents, although not citizens of the United States, are not members and subject to the jurisdiction of a tribe, then he is no doubt a citizen by birth, for citizenship of parents is not essential if such parents are subject to the jurisdiction of the United States at the time when the person in question is born within the territory of the United States. Thus it has been held in United States v. Wong Kim Ark, that although the subjects of China cannot become citizens, nevertheless the children of Chinese parents having a permanent residence within the United States are citizens by birth.
A proof that the birth which confers citizenship must be not only within the actual territorial limits of the United States, but also within the jurisdiction of the United States, is the recognized rule applied to children born within the territorial limits to alien parents who are only temporarily within such limits. In such cases a right of choice is recognized; if the child remains within the limits of the United States until he reaches years of discretion he is entitled to claim citizenship by birth; while on the other hand if before years of discretion are attained he is taken by his parents to the country of their allegiance and elects to remain there he is an alien to the United States notwithstanding his birth.
As to all these matters there is some uncertainty, but by principles of international law which are recognized by the United States, as well as in all other civilized countries, children born to ambassadors and foreign ministers temporarily residing in one country as the representative of a foreign government are regarded as having been born within the jurisdiction of the government which the ambassador or minister represents and to which he owes allegiance, and not within the jurisdiction of the country in which he is thus temporarily residing. This principle is applied to children born abroad to persons who are citizens of the United States in the foreign service, and such children though not born within the actual territorial limits of the United States are by fiction said to have been born within the jurisdiction of the United States and to be citizens by birth, unless perhaps they have elected to remain permanently abroad and thus disavow the assumption of United States citizenship. In 1855 Congress enacted statutory provisions still in force by which it is declared that children born outside the limits of the United States whose fathers are citizens thereof are citizens by birth. An analogous rule is applicable, no doubt, to children born on the high seas on vessels sailing under the flag of the United States, and such persons may claim to be citizens of the United States by birth although the actual place of birth was not within the territorial limits of the United States.
The rule, in short, seems to be this, that persons born within the territorial limits of the United States are citizens by birth without regard to the citizenship of their parents at the time of birth, with the recognized exception, that if the parents are not subject to the jurisdiction of the United States by reason of being members of an Indian tribe, or foreign ambassadors or ministers, or foreign subjects on board vessels of another nationality, or perhaps foreign subjects temporarily sojourning in the United States, then the place of birth is not controlling; while on the other hand persons born outside of the territorial limits of the United States whose parents are citizens of the United States in its foreign service, or are upon United States vessels, or are subjects of the United States temporarily sojourning abroad, may claim United States citizenship on reaching the age of discretion if they so desire.
The status of persons permanently residing within the Philippine Islands and the Island of Porto Rico at the time of acquisition of such islands from Spain seems to be still in doubt; for no provision was made in the treaty with Spain, nor has any provision been made by act of Congress, respecting the acquisition of citizenship by such persons; but it will probably be decided that children born within such insular possessions of the United States subsequent to the date of their acquisition, their parents at time of birth being permanent residents of such territory, are citizens by birth irrespective of any question as to the citizenship of such parents; for, as already indicated, citizenship of the parents is not the test in determining citizenship of the children.
 
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