You've gotten a number of good answers, but maybe I can still add a
little helpful information.

The resonant length and the bandwidth of an antenna are determined by
some basic electromagnetic principles. Although simple in concept, the
exact solution for the impedance (and therefore the resonant frequency
and bandwidth) of even an elementary dipole is actually very complex.
The most common method involves solution of a triple integral equation,
which can't be done directly at all, but requires a computer to
numerically approximate the result.(*) The formulas you see in handbooks
are just a rough approximation that's more-or-less good over a limited
range of conditions. The actual resonant frequency and bandwidth are
affected by wire diameter, height above ground, and angle between the
wires, as well as just the wire length. And the relationships aren't
really simple at all.

So the bottom line is that the formulas work well enough to get you into
the ballpark, from which you've usually got to do some trimming -- just
as you did. You can't expect more than that from them.

Readily available, inexpensive or free, computer programs can do the
complex calculations from fundamental electromagnetic principles with
rather astounding accuracy, in a small fraction of a second for a simple
antenna. The computed results can still differ from reality, though, due
to differences between the model antenna and the real one, like nearby
objects or wire insulation not included in the model, wire sag,
capacitance of end insulators, common mode feedline current, and so
forth. But they'll still get you much closer than the simple handbook
formulas. However, the simple formulas and a bit of cut and try are
perfectly adequate for many simple antennas, and might easily be faster
in the long run for someone not familiar with the programs.

(*) Before the ready availability of computers, many different methods
were devised to approximate the solution, with varying degrees of
complexity and accuracy.

Roy Lewallen, W7EL

Ken Bessler wrote:
I just put up an inverted V for 30 meters.
I started out with each leg being 24'0". This
gave me a low SWR at 9.5665 mhz which
works out to 229.6 instead of the usual 234/F.

As I trimmed, I decided to keep track of how
much I trimmed and what the nnn/F number
would be. As I got closer to my goal of 10.15,
the number went down, eventually ending up
at 227.28/10.1955=22.292' Also, the 2:1 swr
bandwidth went up - it started at 567 kc and
ended up at 655 kc.

Either way, I got the antenna up and it's working
fine - I'm just curious why the formula for length
and the bandwidth changed as the antenna got
shorter.

Ken KG0WX