dwbPulseTimer.ino

long pulseCount = 0;  //a pulse counter variable

unsigned long pulseTime,lastTime, duration, totalDuration;

int samplingPeriod=2; // the number of seconds to measure 555 oscillations

int fivefivefive = 13; // the pin that powers the 555 subcircuit

void setup()
{
  Serial.begin(9600);
  
      pinMode(fivefivefive, OUTPUT);   
           
}

void loop()
{
  delay(1000); // imagine riffle is doing other stuff (like sleeping)
  
  // now make a conductivity measurement
  
  //turn on the 555 system
  digitalWrite(fivefivefive,HIGH); //turns on the 555 timer subcircuit
  
  pulseCount=0; //reset the pulse counter
  totalDuration=0;  //reset the totalDuration of all pulses measured
  
  attachInterrupt(1,onPulse,RISING); //attach an interrupt counter to interrupt pin 1 (digital pin #3) -- the only other possible pin on the 328p is interrupt pin #0 (digital pin #2)
  
  pulseTime=micros(); // start the stopwatch
  
  delay(samplingPeriod*1000); //give ourselves samplingPeriod seconds to make this measurement, during which the "onPulse" function will count up all the pulses, and sum the total time they took as 'totalDuration' 
 
  detachInterrupt(1); //we've finished sampling, so detach the interrupt function -- don't count any more pulses
  
  //turn off the 555 system
  digitalWrite(fivefivefive,LOW);
  
  if (pulseCount>0) { //use this logic in case something went wrong
  
  double durationS=totalDuration/double(pulseCount)/1000000.; //the total duration, in seconds, per pulse (note that totalDuration was in microseconds)
  
  // print out stats
  Serial.print("sampling period=");
  Serial.print(samplingPeriod);
    Serial.print(" sec; #pulses=");
  Serial.print(pulseCount);
  Serial.print("; duration per pulse (sec)=");
  Serial.println(durationS,4);
  
  }
  }
  

void onPulse()
{
  pulseCount++;
  //Serial.print("pulsecount=");
  //Serial.println(pulseCount);
  lastTime = pulseTime;
  pulseTime = micros();
  duration=pulseTime-lastTime;
  totalDuration+=duration;
  //Serial.println(totalDuration);
}

Ah, that was a fluke -- I had the UNO plugged into the circuit at the same time -- now I'm recovering the same values on the Pro Mini as I had on the UNO:

sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21455
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21466
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21462
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21451
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21466
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21463
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21453
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21466
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21463
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21453
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21468
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21452
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.21468

-- which is actually reassuring. The difference between the pulse duration theory and actual is to be expected from deviations in the resistor and capacitor from their nominal values.