Former immigration laws prior to 1922 did not make reference to the alien husband's race.[2] However, The Cable Act of 1922 guaranteed independent female citizenship only to women who were married to "alien[s] eligible to naturalization".[3] At the time of the law's passage, Asian aliens were not considered to be racially eligible for U.S. citizenship.[4][5] As such, the Cable Act only partially reversed previous policies, allowing women to retain their U.S. citizenship after marrying a foreigner who was not Asian. Thus, even after the Cable Act become effective, any woman who married an Asian alien lost her U.S. citizenship, just as she would have under the previous law.
What does the Cable Act of 1922 have to do with children?
Prior to the Cable act, if a woman married an alien, she became his nationality and therefore her children would be ONLY of his nationality. No claim to American citizenship.
The cable act was just the first effort at allowing women to retain their own citizenship. (and therefore pass it on to their children.) The act which completed this foray into women's citizenship rights and which made it clear cut, was the citizenship act of 1934.
http://www.scribd.com/doc/43197267/1934-Citizenship-Act-73rd-Congress#scribd