Constant current source advice

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I obtained a schematic of the entire apparatus from the journal article's (retired) author, if anyone is interested.

circuit1.jpg
 
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He certainly used good quality parts. Are you familiar with those IC's ?

OP07 is a precision opamp.
Left hand one causes voltage selected by selector switch E1 to appear across R10. That's what sets the charging current through your capacitor C13-C14. Observe when T2 is off no current can flow through R10 so capacitor charging current is zero.

Turning on T1 discharges capacitor through whatever resistance is across E4 terminals.

Right hand OP07 is just a buffer to repeat capacitor voltage over at Vout for your meter there. That way a few milliamps of meter current won't discharge the capacitor. .

74121 is a pulse generator, colloquially called a "retriggerable one shot" or "monostable", that makes a pulse of precise duration every time the 555 gives it a "go" pulse. P2-C15 set that pulse width. Its two outputs are complementary, that is when one is high the other is low.

Have fun !