The additional jackshaft reduces blade speed from about 3000 fpm down to about 200 fpm.
The autotransformer provides the low-end speed range. It varies the voltage to the AC induction motor from about 75 volts up to about 145 volts with a corresponding range of motor speeds blade speeds.
An "Autotransformer" allows you to vary the speed of your existing, AC, induction motor by varying the impressed voltage. They're basically transformers with a single winding that allow varying the voltage from zero up to (typically) about 115% of line voltage to vary angular velocity.
They're also commonly known by the trade names "Variac" and "PowerStat".
Make sure you purchase a unit with sufficient amperage capacity for motor startup current. A new, chinese 20 amp unit is about US$100 on ebay:
20 amp autotransfomer
Reviews indicate they're serviceable, but not industrial production quality as you'd find with PowerStat and Variac (General Radio) products.
Being separate from the bandsaw, they're also useful to control speeds on any other AC-powered devices you might use.
The 20-amp industrial control products are *quite* expensive when purchased new, but sometimes appear at appealing prices on ebay. Lower capacity units can also serve well enough, depending on motor size. In my case, the bandsaw draws about 10.5 amps at startup, then settles to a continuous draw of about 6.5 amps no-load current for a motor (over!)-rated as 3/4 HP. (Current draw suggests it's actually about 1/2 HP).
By contrast, the radial arm saw surges to 20 amps at startup before settling at about 5 amps no-load speed.
A tachometer *greatly* simplifies determining blade speed. Non-contact instruments transmit a light beam onto reflective tape that's been attached onto the rotating bandsaw wheel and produces a direct readout of the angular velocity in RPM. With the RPM reading and knowing the bandsaw wheel diameter makes for simple arithmetic to determine blade speed. No more bothering with motor RPM * multiple belt reduction factors * wheel diameter!
eBay search for "digital laser tachometer"
Blade speed (inches per minute) = Angular velocity (RPM) * Wheel diameter (inches) * Pi (3.14) [See Note 1]
Blade speed (feet per minute) = blade speed (inches per minute) / 12
A "DRO" (digital readout) seems like overkill...
I measured the current draw with a "vintage" Radio Shack clamp-on Ammeter, readily available on eBay for about ten bucks. If you want one, make sure it includes the "3-prong adapter" or you can't use it when "hot" and "neutral" are bundled (as on a line cord).
eBay search for "Radio Shack ammeter 22-161"
In this universe, the mathematical constant Pi has a value starting with 3.1415926 EXCEPT in Great State of Indiana, where Indiana Pi Bill #246 decrees the value of Pi as EXACTLY 3.2. Inhabitants of parallel dimensions and/or "multiverses" may also need to adjust the arithmetic.