These physicians were the ideal audience for a product called Pulmonary Inspirator. This is the product featured in an advertisement in The Medical Progress dated July, 1896. The product is an inhaler specifically designed for the inhalation of antiseptics.
I'm sure the product could also have been used for other solutions too, and I'm sure it must have been experimented with. Likewise, as with other inhalers of this time, the product was probably clumsy, bulky, fragile and expensive.
Medicine must have been inserted into the container with water. Heat would have warmed the water, and the patient would have inhaled the fine medicated steam. The product was patented and sold under a physician's prescription only.