Purpose of inductor between antenna and coupling to radio

[DrMag]

My biggest beef with amateur radio is how difficult it is sometimes to understand even the most basic concepts. I'm going through the ARRL Basic Radio book, and it starts off with a very simple crystal radio design, with a strong encouragement to actually build it. All well and good--except the book doesn't explain much at all of the circuit itself. I've included an equivalent schematic drawing for reference.

Here's what I've been able to figure out: the 230 uH inductor paired with the 365 pF variable capacitor tunes the radio to roughly the AM broadcast band. I'm assuming the Q must be pretty low in this circuit because the text implies (and you actually hear when you build it) that you pick up all the radio stations available to you at once. The diode of course detects the AM signal, while the 0.01 uF capacitor paired with the hi-z headphones act as a low-pass filter. The 1 uF cap removes any DC offset for the headphones. On the other end, the 30 turn inductor couples the antenna to the receiver.

That leaves one thing I don't understand--what is the purpose of the variable inductor between the antenna and the receiver? The only guess I have is that it somehow provides a load to the coupling transformer, but why does it need to be an inductive load? Is there some frequency filtering purpose so that only a band portion is coupled to the receiver to begin with?

I've been trying for ages to figure this out--google has been of very little help, because any google search on crystal radios will give you myriad circuit examples, all of which are different. I'm hoping that if I can understand one, then I can start looking at others to try and understand what significance the different designs have compared to each other and why you might choose one over another.

[w2aew]

My simple take on this is that any wire antenna for the AM broadcast band is very likely going to be far short of a 1/4 wavelength "Marconi" antenna, simply due to the very long wavelengths in this band.  The series loading coil electrically "lengthens" the antenna.  Here's a few quick references from a simple Google search on loading coils:
https://en.wikipedia.org/wiki/Loading_coil
https://www.w8ji.com/mobile_and_loaded_antenna.htm
http://www.amateur-radio-wiki.net/index.php?title=Antenna_loading

[DrMag]

Ah, I have heard that term before! Ok, I think that makes sense.

I was able to find an online calculator to find base-loading inductance for a vertical dipole, and using that, a 500 uH loading coil would require 18.45 feet of antenna length to be centered on the AM broadcasting band, while 1500 uH would require a 5.19 feet antenna length--that seems a reasonable range for a "grab a long wire" type antenna, which would be what a design like this would be intended to use. In fact, an antenna length anywhere between 1.9 feet and 93.9 feet could be tuned to a resonance somewhere within the AM broadcast band using an inductance somewhere in the 500-1500 uH range.  (I assumed 14awg wire in these calculations, but a smaller wire wouldn't require much longer of an antenna--minimum 2.2 feet for 20awg.)

For future reference, here's where I found the calculator:
http://www.66pacific.com/calculators/coil-shortened-vertical-antenna-calculator.aspx

Thanks!