The law for standard immigrants prior to this additional law was an immigrant had to declare intent with a court of law then provide proof of 5 years settlement within the United States.
In 1863 they modified the law for alien service members to be over 21 years of age, have an honorable discharge from the military and proof of 1 years settlement within the U.S..
https://books.google.com/books?id=XGZZAAAAYAAJ&pg=PA1090&dq=Naturalization+"United+states"&hl=en&sa=X&ved=0ahUKEwjJqr2Wyf7RAhWD54MKHf9lB3QQ6AEIRjAG#v=onepage&q=Naturalization%20%22United%20states%22&f=false