Found this note explaining the term "half-gentlemen" as used in Emma:

Note 1: (half-gentlemen)

Half-gentleman seems to refer to someone making a living for himself, and doing well enough, and in a respectable-enough line of trade-probably with a good education-to be concidered nearly a gentleman.

Gentlemen are usually land-owners and people with independant income, as well as sons of such men. Younger sons would have to earn their living and usually would do so in either the church, the military, or in the law-they would also be concidered gentlemen. However, after a generation or two, their offspring would probably have fallen into lower social strata. It might be these men, on the way down the social ladder, as well as those who are on their way up, who are ranked as half-gentlemen.

We do know by name one person in Emma who falls into this category. At the end of Volume I Chapter 8, we learn that Mr. Perry, the apothocary, is a part of this whist club. His profession would preclude him from being a true gentleman, but he was concidered respectable enough to be able to socialize with the first class of men in the district-thus he could be regarded a half-gentleman.