The laws for terminating a marriage during the 1800's was particular to each state. Death rates among child-bearing couples were much higher, for one thing, and multiple marriages were not abnormal. However, other than the U.S. Federal Census records reports of "years married" and at times whether these marriages were "first" or "second," it can be difficult to determine exactly when one marriage ended, and why - especially if any of these changes took place within the 10 year period between census reports.
I have been entirely unsuccessful in locating divorce documents. For a great grandfather who married three times between 1882 and 1925, I've only found one definite indication of legal divorce. Particularly in rural areas (such as island communities off the coast of Maine) these records are even sketchier.
History tells us that divorce rates began to climb steadily, after the woman's rights movements fought for a wife's right to attach her husband's property as her own, during the dissolution of a marriage. Whether this is wholly true or not, I am not sure. There were other accompanying factors - such as women beginning to earn their own living outside the home, which would increase the ending of unhappy marriages.
At any rate, it seems true in the 1800's that sometimes "separation" for a period of time, in some places, constituted dissolution of a marriage - enough so that one or both parties could then remarry. If anyone else finds this to be true, in their own research, please let me know!