Since 1857, there have been two schools of thought as to how Emile received his fatal dose of arsenic:

Emile killed himself

At the time of Madeleine's trial, some people felt that Emile accidentally poisoned himself, mistaking the arsenic for some form of medicine. The problem with this theory is that no arsenic (or arsenic container) was found on his body or among his possessions. Also, his name was not found in any Poison Books in the Glasgow, Stirling, or Bridge of Allan areas.

Another theory is that Emile killed himself and purposely framed Madeleine for his death. The lack of arsenic in Emile's possession applies to this theory, too, in addition to other questions:

If Emile killed himself with his own arsenic, how did he know that Madeleine was, coincidentally, buying the same poison? (Some have theorized that Emile, in order to frame Madeleine, convinced her to start buying arsenic. But there is not a single piece of documentation or evidence that shows that Emile ever had even a passing conversation about arsenic with Madeleine, let alone a direct attempt to persuade her to buy the poison. None of the letters reflect such a conversation, either -- and this theory remains highly speculative.)

If Emile killed himself with his own arsenic, what did Madeleine do with the arsenic she purchased? None of Madeleine's biographers, even those who were clearly pro-Madeleine, believe that she actually used it as a cosmetic arsenic wash, as she stated in her official Declaration.

Much of the circumstantial evidence points to this, but, there are questions with this theory, too:

If Madeleine was secretly poisoning Emile over the course of several weeks, why did she make her arsenic purchases so blatantly? She even brought an eyewitness with her to one of her purchases....

If Emile suspected that he was being poisoned by Madeleine, as several trial witnesses testified to, why did he continue to take the poisonous beverages from Madeleine?

Even with Emile dead, Madeleine knew that highly damning evidence, her letters to Emile, were still in existance and were bound to be discovered. But she made no attempt to retrieve the letters from Emile's rented room and office.