"Why the devil! A horse is mortal; suppose mine had had the glanders or the farcy?

These are two very contagious and troublesome diseases of horses, quite common at the time of the story.

farcy
n.
5ME farsine < OFr farcin < ML farcina (for LL farciminum) < L farcimen, a sausage < farcire, to stuff6 a chronic form of glanders characterized by skin ulcers and swollen lymph vessels

glanders
n.pl.
5OFr glandres < L glandulae, swollen glands in the neck, pl. of glandula: see GLAND16 [with sing. v.] a contagious, chronic or acute disease of horses, mules, etc. characterized by fever, swollen lymph nodes, ulcerous nodules on the skin, inflammation of the nasal mucous membranes, etc.: it is caused by bacteria (Pseudomonas mallei) and is transmitted to certain other animals and humans: see FARCY