One evening, while perusing MRL® Handbook-17, which I hadn't done in some time, the MRL® #39 circuit hit me between the eyes !  This circuit has some amazing similarities to, and differences from, the Australian Mystery Set. 

    The original MRL® #39 had the antenna attached to point 3. Consider points 1 through 5 on the schematic: there are 20 possible ways to attach antenna and ground to these points -- 25, if you also consider antenna alone. Using a prototype set, I looked at all 25 and found that point 5 consistently was the best ground, and points 2 and 4 gave the best Selective and Broad tuning antenna connections. That's for my particular antenna and ground, anyway -- the point here is, experiment and see.
 
 

    Very little thought or science, on my part, went into the design:  I just roughed out a primary which would match my 550 pF variable capacitor and followed the Australian design, making the secondary half that number of turns. 

C1 two-gang, 550/500 pF per gang air variable capacitor, with vernier drive dial

L1 "Mystery" type basket-wound coil: 36 turns 660/46 litz wire, wound in an 'over 2 posts / under 1 post' pattern on a 5-inch diameter, 13-point form.  Inductance 184 uH; unloaded Q = 867 at 0.7 MHz.

L2 18 turns 420/46 litz wire, inter-wound and centered with L1.  Details below. The total length of L1-L2 is about 1-7/8 in. 

D1 diode:  1N34 type, or galena

    Note on winding L2:  The winding of L2 is carefully "synchronized" with the L1 winding so as to preclude any adjacent turn segments lying side-by-side.  This reduces the L1-L2 coupling by some small amount.  Whether this offers any performance advantage, I don't know, but this is good basket-winding practice.  For the 'over 2 / under 1' pattern on a 13-point form, synchronized windings can be had by following exactly the pattern shown:
 
 

    The elegance of the Mystery Sets, the MRL®# 39, and other like sets in the Telefunken genre (untuned secondary closely coupled to tuned primary) is what they accomplish with just single-dial control.  The MRL® # 39 is the epitome:  ONE coil (albeit a special one), ONE capacitor (albeit a special one), ONE diode -- that's it !
 
 

Vernier Readout Scale
    I added a vernier readout scale to the dial to help with loggings.  Vernier scales are best made by machine.  Hand-scribing tick marks is exceedingly difficult, and results are usually so-so.  While the idea is elegant, I'm finding that eyeballing fractions of a scale division with a fine hairline pointer is entirely adequate for crystal set work.

Initial Results
   Performance is quite impressive, although -- no surprise -- it doesn't hold a candle to a double-tuned set.  Using a trap on a 690 kHz local, I can pick up the 720 kHz 5 kW station on Kauai, 116 miles away, in the daytime. [I later found it could be pulled in without the trap.]  DX conditions are way down with summer approaching, but in a few evening sessions I've heard a few of the strongest W.C. stations including KFI 640 L.A., KPNW 1120 Eugene and KXTA 1150 L.A.  The last one is by far the most reliable west-coast station here.  I'm looking forward to improved conditions in the fall.

Antenna Connections
    I find the BROAD connection has sufficient selectivity for DXing, plus the advantage of more signal.  While the SELECTIVE antenna connection might be useful for coping in the urban jungle, I was thinking of omitting it in future versions of the set, until ...

I went through a systematic test of the 20 possible antenna-ground connections with this set.  Qualitatively, behavior was similar to earlier versions:  some connections work fine, others not at all.   One surprise was, at the upper end of the band, the SELECTIVE connection was not only more selective, but it was also more sensitive than the BROAD connection.  The BROAD/SELECTIVE connections might be better labeled LOW BAND/HIGH BAND. The crossover is in the 1300 to 1400 kHz region.  Of course, all this may be specific to the particular antenna-ground system being used.

SW QRM Susceptibility
    One potential drawback: the set is susceptible to lower-end short-wave QRM.  Fortunately I only have to contend with 2.5- and 5 MHz WWVH out here. A small coil in the antenna lead may help to knock out this QRM.

Telefunken and Other Precedents
    It appears that the precedent for this set and the 'Mystery'-type sets is the classic Telefunken circuit that has been around since the year one:

    This particular circuit appears in the MRL® literature as the MRL® #4 set.  If you make the dashed line connection you have the "Mystery Plus" set from the Brisbane Sunday Mail, April 16, 1933.

    My theory has it that 'Proton' "invented" the original Mystery circuit when he screwed up the antenna and ground attachments to his Telefunken set.  Then, making further "improvements" to his newfound Mystery set, lo and behold, he arrived back at what is essentially the original Telefunken circuit !

    Per the MRL® write-up (MRL® Handbook-17), it appears it was correspondent, Mr. R.B. Richardson, who came up with the two-gang capacitor (so-called "Tuggle") in the tuning circuit.

    Dan Petersen did some interesting, closely-related work, starting with the Mystery circuit:
 http://www.worldaccessnet.com/~petersen/Mystery-article.htm

    Basically, using a two-gang capacitor in the Mystery, Dan 'discovered' the MRL® #39 set !  He came up with Broad/Selective configurations different from mine -- possibly due to our antenna-ground differences.