Topband: Question - optimum number of radials

[James Rodenkirch]

Besides "optimim number(s)," I wonder if there is supporting analysis for the connection of the radial ends??
I have around 80 elevated radials that range from 50 foot lengths, running east and west, and 25 foot lengths running north and south (all of that a function of being geographically challenged).  I have not tied the bitter ends together....never really thought about it when I put the radial field together but seem to recall reading something about tieing the ends together and having a well bounded complete "grid" underthe antenna.
Thoughts? I tend to think it wouldn't hurt...  72, Jim Rodenkirch K9JWV