A 'fourthy' is a partial erection. One might be apt to call it a half-boner, but this would be technically incorrect as a 'fourthy' occurs when a penis is more than 1/4th of the way up...hence, a fourthy.

It should be noted that fourthies (plural form) are apt to occur at inopportune times (such as in public places) and as such are typically surpressed to prevent a complete erection.

If a complete erection does take place, it would be said that 'he has a boner', not a 'fourthy'.

In most cases fourthies are largely unsightly however exceptions are known to occur.