In pre-Civil war times, marriage was often seen as an institution that was subject to the invocation of Mark 10:9, to wit: "What therefore God hath joined together, let not man put asunder," and consequently divorces were not given for frivolous reasons nor were they easy to obtain by government or religious authority. This means that marriages of earlier generations were quite often until "till death do us part," unlike today's "no-fault" divorces and the more relaxed mores of modern society. However, while it may be an absolute certainty that divorces have increased substantially in America since those times, there were ways to effectively divorce in the 1800s which did not involve the trouble of necessitating official documents to reflect this fact.
For instance, in the 1800s it was far more common, even the norm, to essentially live within the bounds of your local community for your entire life, so that those that traveled far enough away from their birthplace, and that might only be 100 miles or even less, could begin their life anew in a different community, and under different circumstances than their previous livelihood. This means, that for some husbands, trapped in an unhappy marriage, or simply not wishing to remain in an undesirable situation, that the abandonment of one's wife and his attendant family responsibilities, was an option that some men took advantage of, which, in effect, accomplished the same purpose as a divorce but without any of the backlash of religious or societal condemnation.
So that when studying the statistics of divorce from generations ago and comparing them to the divorce rates of today, one must understand that there was a significantly higher degree of what was in essence the equivalent of divorce by abandonment, along with in all probability, a much higher incident of bigamy, to which one party would typically not be completely aware of undisclosed peculiar circumstances. Consider that Andrew Jackson, our seventh President of the United States, unbeknownst to himself "married" Rachel Donelson in 1791, only to discover rather inconveniently that his wife had not been legally divorced from her husband who had separated from his wife, previously, whereupon ultimately a legal divorce was finalized under the grounds of adultery, and they were legally married in 1794.
Another important fact to remember, is that the law in regards to divorce, was much more amendable to those that had the money, connections, and the time to effect changes as they might desire back in the 1800s, as compared to most people of that day that were consume with their work and family duties, so as to not have any excess monies available to pursue a divorce, even under reasonable grounds such as adultery or desertion or similar.
The no-fault divorce laws of today, makes it fairly straightforward to get a divorce from your spouse, if that is your desire, even if your spouse is adamantly opposed to it; whereas in earlier times, a divorce for the common man was often not easily achievable, and had its incumbent society ill-after taste, so that often times, it would be much more conducive to simply abandon your spousal duties and move on to another town so as to begin anew, which essentially served the purpose that you had aspire to have done in the first place, for better or for worse.