A Hatter in 1845 is the profession of making hats traditionally using the skins of beaver, rabbits, and goat. [1]During this process a hatter would use mercury to make the material easier to mend, work and improve the quality of the felt. It is the usage of mercury that caused many hatters to suffer from mercury poisoning. Mercury poisoning would lead to illnesses such as Dementia and erethism (also referred to as mad hatter syndrome) and thus lead to the prevalence of the phrase “Mad as a Hatter” around 1830.  

[1]203 occupation dictionary Pg 203

https://corrosion-doctors.org/Elements-Toxic/Mercury-mad-hatter.htm