excerpts from a post by David Morning (dam@dcs.gla.ac.uk)

What's a Wheatstone Bridge?

This is a wheatstone bridge:

 
Battery + ------------------------------
                |                       |
                |                       |
                \                       \
                /                       /
           R1   \                    R2 \
                /                       /
                \                       \
                /                       /
                |                       |
                |-------Meter-----------|
                |                       |
                \                       \
                /                       /
                \                       \
           R3   /                    R4 /
                \                       \
                /                       /
                |                       |
                |                       |
Battery - ------------------------------ 
Balance occurs when R1*R4 = R2*R3.

Usually one of these resistors is the unknown, the person being measured, thus to obtain a balance, its complementary resistor is made variable and adjusted to give a 'null' (zero deflection) on the meter. Thus if R1 is the unknown, R4 would be a variable. Also, because there can be a wide range of body resistance dependant on weather conditions, health etc, one of the resistors R2 or R3 would have to be a variable (big rotary switch types look impressive) to keep in range.

The main problem with this type of passive Wheatstone Bridge is that it is not suitable for measuring high values of resistance as the current drawn by a simple moving coil meter would swamp the bridge, thus the bridge has to be buffered by an op-amp. Even the ancient 741 can be pressed into this use, although for better accuracy (and more dials!) any low offset op-amp could be used. Those with external offset null pots would be even more impressive.

National Semiconductor Analogue Circuit data books provide a wealth of these circuits and the cost to construct an active wheatstone bridge along the lines outlined would be minimal, although adding fancy dials may add to the cost. Actual component cost would probably be <$20. For those who like to dabble, try the following:

 
               ---\/\/\/\------
              |  _____         |
              | |      \       |
     - -\/\/\/--|-(2)   \      |
                |        \     |
                |         \    |
                |      (6) >---------Meter---0 volts
                |         /
     + -\/\/\/--|+(3)    /
              | |       /
              \ |      /  Op amp (741/TLO71)
              /  -----
              \
              |
               -------------------------------0 volts
The + and - ends are fed from the 'meter' connections on the wheatstone bridge, and the supply should be +/- 9 volts: two small 9 volts batteries should do the trick. The meter can be anything from a moving coil to a cheap digital multimeter - it should be set to measure voltage. If you wish to be more accurate, the single opamps have two pins on them marked "offset null". A small (or big if you wish to impress) pot should be connected to these and they should be used to trim the op-amp for zero volts output after shorting the + and - pins together. All resistors should be 1 Meg ohm. If you wish to impress further, replace Rf with a pot of around 2.2 megohm and label it "sensitivity".

More detail can be found in National Semiconductors' very useful data books.

[ A Scientologist writes: ]

The Wheatstone Bridge is a means of measuring an unknown resistance precisely, by way of a voltage difference across a set of 3 known resistances, plus the unknown one, set up as pair of voltage dividers. In extremely basic terms, this is a reasonable functional description of any resistance meter, but the E-meter, as does any odern instrument, actually uses active amplifiers and so transcends the analogy.
In other words, the old galvanometer type meter with a 20c differential op-amp, pretty standard stuff so far, it's still based on the good old fashioned wheatstone bridge - even the addition of an 'active amplifier' doesn't render it any more than basic bridge measurement and since the wheatstone bridge has never been bettered for resistance accuracy, it seems a fair bet that this is what the E-meter uses. Since the individual is in fact, the "unknown resistance" being measured, you would appear to be confirming the use of a wheatstone bridge.

[ The Scientologist continues: ]

... as an electronics engineer, I can assure you the E-Meter isn't even vaguely comparable to any handful of parts found at Radio Shack. Its price seems generally higher than its hardware alone would suggest, but that's the prerogative of the seller. And you can pay many times more for a half-decent stereo.
True...if you're foolish enough to believe the sales hype regarding stereos - as they say, a fool and his money...