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# Article: Reciprocity revisited.

1. ## Reciprocity revisited.

The equation I used to represent available experimental reciprocity data is:
T = Tm + Tc
Where:
T is the exposure time corrected for reciprocity characteristics.
Tm is the time indicated by your exposure meter's calculator.
Tc is the correction to be added to Tm.

Through much curve fitting I found that:
Tc = a*Tm^b
Where a and b are constants for a given film but vary with the film. Thus, for HP5+ film:
Tc = 0.11 * Tm ^ 1.62
Fortuitously, this equation graphs as a straight line on full log graph paper. If you cannot find full log paper, also called log-log, many pocket calculators can do the exponential function, Tm raised to the 1.62 power. Again fortuitously, the constant 1.62 is the same, within experimental error, for all films for which I have data. Only the constant "a" changes from one film to another.
Film factors:
Film Ff
400TX 0.17 (1.0 by Kodak)
400TMAX 0.07
100TMAX 0.07
HP5 Plus 0.11 (0.5 by Ilford)
100Delta 0.05 (0.5 by Ilford)
Note that we deal only with exposure time, not exposure value in the sense of the product of illumination and time. Your exposure meter finds the time for a given f-stop, which most view camera users make primary for reasons of depth of field. If you feel the need to change f-stop, use the meter's calculator to find the new measured time and the equation to find the new correction to that time.

A coefficient a = 0.5 in my equation gives a very close fit to the Ilford data for HP5+. The difference between the Ilford data and the correct exposure according to Bond, who is a very meticulous person and knows his business, as well as how to play the trumpet, can be pretty large. At 10 second indicated exposure, my equation based on Bond's data would tell you to add 4.6 seconds, while Ilford's data would have you add 21 seconds. You would wind up with twice the correct exposure. At 20 seconds indicated, the ratio is 2.47, and at 30 seconds indicated, 2.68.

2. comments from the previous article system:

By pnance - 05:48 PM, 05-25-2006 Rating: None
Is there any reason this would not be applicable to paper? The only real difference is that paper is already in the seconds range.

By JeffD - 04:17 PM, 07-29-2006 Rating: None
This is pretty interesting. I wish I had an equation as convenient that would help me determine development time, so my contrast would be *normal*, when processing film that has been exposed to account for reciprocity failure.

By jstraw - 10:00 PM, 09-15-2006 Rating: None
I love your formulas but I find I struggle to make the clear to myself. I can't be on the right track with this one.
Tri-X at 60 seconds:
.17(Ff) * 60(seconds) ^ 1.62 = 43.04 + 60(seconds) = 103.4(seconds)
My 3 charts say 480 seconds, 600 seconds and 832 seconds (this big discrepency is why I want a new handle on this problem).
Where am I losing my grip on your formula?

3. Now that this is back, I'd love to pick up this conversation again.

4. Sandy:

By chance would you happen to have the coeficients for other films? I remember when you first published your findings a number of us pubished tables which made it easier to calculate the new exposure times. I published a set of tables and a chart at http://home.pacbell.net/mkirwan/reciprocity_failure.htm

Really would like to expand to include XP-2 and Pan-F

Thanks

Mike

5. Originally Posted by Sean
comments from the previous article system:

...
By jstraw - 10:00 PM, 09-15-2006 Rating: None
I love your formulas but I find I struggle to make the clear to myself. I can't be on the right track with this one.
Tri-X at 60 seconds:
.17(Ff) * 60(seconds) ^ 1.62 = 43.04 + 60(seconds) = 103.4(seconds)
My 3 charts say 480 seconds, 600 seconds and 832 seconds (this big discrepancy is why I want a new handle on this problem).
Where am I losing my grip on your formula?
Exponentiation has higher precedence than multiplication. Using substitution, the complete formula for calculating the exposure time is as follows:

T = Tm + Tc
Tc = a * Tm^1.62
T = Tm + ( a * Tm^1.62 )

using your example above, we get the following:

T = 60 + ( 0.17 * 60^1.62 )
T = 60 + 0.17 * 759.64
T = 60 + 129.14
T = 189.14

which is more in line with the numbers you were expecting, although certainly less than the published numbers.

Here are the calculations for the four films, using the factors published above:

TXP TMX HP5+ Delta
1 1.17 1.07 1.11 1.05
2 2.52 2.22 2.34 2.15
3 4.01 3.41 3.65 3.30
4 5.61 4.66 5.04 4.47
5 7.31 5.95 6.49 5.68
6 9.10 7.28 8.00 6.91
7 10.98 8.64 9.57 8.17
8 12.94 10.03 11.19 9.45
9 14.97 11.46 12.87 10.76
10 17.09 12.92 14.59 12.08
60 189.14 113.17 143.56 97.98

The formatting is a bit hard to read, but if you import the data into a spreadsheet, it'll be readable.

6. I just made an excel sheet with calculations from 1 second up to ~72 hours at one stop intervals. Tri-X would have to be exposed for approx. 1100 days for a metered 72 hour exposure. Anyone interested in the sheet?

7. Here's the chart, I'm gonna try to make it a bit more readable during the weekend...