Thanks A.J.! The deviation from 0.5 is overall far less than your initial post #16 had indicated. I'm happy with using 0.50.
Yes, well, um.... It looks as if I was deceiving you (and myself) a bit there. It turns out after all that the factor does go up appreciably at higher pH. Here's how things look as corrected and presented in what I hope is a much clearer way:
Let's be absolutely clear about what this graph shows. It gives values for a factor by which you multiply the mmol/L bicarbonate as given on a water report to get the mmol/L CaCO3 that was dissolved by nature (or whomever) to give you the water you have in hand. Put in other words if you multiply the reported bicarbonate in mg/L by this factor and then multiply the result by (100/61) the result is the mg/L CaCO3 that was originally dissolved and, therefore, the amount of CaCO3 you would find in the residue if you evaporated a liter of the water.
Therefore, to use this factor to estimate gravimetric TDS you would
1) Add up the masses of all the ions in the report
except HCO3- and CO3--
2) Multiply the reported bicarbonate (mg/L) by (100/61) times the factor
3) Add that to the sum obtained in 1.
As the curves show the factor is 0.5 up to pH 8 and pretty close to it up to pH 9. Note that the deviation is largest when the alkalinity is smallest which is, of course, when there isn't much limestone dissolved in the water anyway and continuing to use 0.5 will cause only a small error because of that. Above pH 9 you'll have to make your own determination. Note that this is in the region where the bicarbonate = 61/50 approximation used by so many 1st Gen calculators is starting to fall apart so you don't have a good bicarbonate number to work with. A Gen II calculator never even bothers to calculate bicarbonate determining the amount of lime initially dissolved directly from the alkalinity and sample pH.
Now there is a BIG caveat that goes with this. Suppose you put 100 mg of limestone in a liter of water and added HCl to dissolve it and adjust the pH to 8.4. At that point you would have about 1 mmol of bicarbonate ions and an alkalinity of about 1 mEq/L. If you put pH = 8.4 and 1 mEq/L into the factor formula it is, as the curves show, going to give you a factor of a little over 0.5. Multiplying that by the 1 mmol/L bicarbonate would tell you that half a mmol of limestone (50 mg) were dissolved. That isn't right, of course. Thus the use of this factor is, for the moment, only applicable where the water is natural. Clearly in this simple case we can detect this situation by observing that the temporary hardness is about equal to the total hardness and there may be a work around for the more general case based on this. An area for some further thought at another time and place.
For now the function to compute the factor in natural water has been added to the Voltmeter spreadsheet (brewingfunctions.yolasite.com). I've also put a note on how to calculate it there.