As a result of analyses of reciprocity correction determined by Howard Bond
through painstaking experiment, I found that the time to be added to iindicated exposure to correct for reciprocity misbehavior is expressed by the following equation.
Log(tc) = log(tc,1) + 1.62 log(tm)
where tc,1 is the correction at 1 second indicated time.
The factor 1.62 is accurate for all the films tested which were 400TX(0.169),
TMY(0.061), TMX(0.069), HP5+(0.101) and 100Delta(0.046). The numbers in
parentheses are the values of tc,1. This equation is easily plotted on Log-Log
graph paper, or calculated on most pocket calculators. On such a plot, all the
lines are parallel.
Howard found that the factors supplied by manufacturers were not accurate,
possibly because they were not updated with changes in emulsions. Due to the fact that the factor 1.62 works for these diffeent films of different manufacturers, it is my opinion that it will work for any current emulsion to acceptable accuracy. That is to say that I expect it to be within the spread among readings of indicated exposure made by a number of proficient photographers of the same scene. If this is the case, all one needs to know is the reciprocity correction to one indicated exposure to find the correction for any other indicated exposure. The graphical solution is very easy. Plot the correction time at any indicated time on log-log paper and draw a line through that point with a slope of 1.62 vertical inches for each horizontal inch. As you see, the grphical solution does not need the correction at 1 second, and if you plan to do any experimenting, it will be better to use a greater indicated time given the very small corrections required at 1 second for most current films.
Remember, there are no negative coordinates on log-log paper. Negative logs are logs of reciprocals, as log (1/10) = -log(10). If your line goes off the bottom of the graph before it gets to 1 second, just add another piece of paper to give you more cycles. You should be able to get Log-Log graph paper at a college bookstore. If you cant and want to try this approach, I can mail you some sheets. I wrote a program to print the stuff. You can make as many copies as you want without infringing on a copyright.
Pat, that's really interesting. Thanks for doing the analysis!
Have you tried it for color slide films, some of which seem to need no reciprocity correction out to 2 minutes or more (or so the manufacturers claim--I don't seem to do many exposures this long in color myself)?
This is very interesting to me as well. Is the Bond information on method and/or your analysis published anywhere? I'd love to see it.
Robert Reeves, in chapter 7 of "Wide-Field Astrophotography", (ISBN 0-943396-64-6) offers a technique for determining reciprocity law failure characteristics of film. You set up a gray card (and gray scales/color patch charts as preferred) to shoot at 1/8 second, then put on an ND 3.0 filter and shoot exposures for 128 seconds at varying apertures with the same illumination. You find the amount of failure by measuring negative density on the long exposures relative to the baseline 1/8 sec exposure. This obviously works off failure factor data much further out than 1 second, and perhaps is more applicable to pinhole shooters and astrophotographers. But the method is sound and interesting. The aim in astrophotography is to find suitable films that have the least reciprocity failure and least color shift in the very long exposures used. Spectral sensitivity is also an issue in that application.
I'm curious about the method used by Bond, and the range of exposure lengths covered.
Lee-the Howard Bond article was published in Photo-Techniques magazine. See if you can get a back issue from them. If not you can PM me and I will dig it out for you. Mr. Bond also did an article on Reciprocity several years ago on the older films; i.e. Tri-x,Tmax,Hp5 etc. His basic conclusion on the new films is that they don't increase nearly as much as the older films. They do increase as the times get longer though. See if you can find the article......if not then contact me.
Regards Peter
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13 seconds should do it. On my TX-30X calculator I did ,169*(8^1.62)+8. the .169 is the reciprocity correction for 400TX at 1 second indicated exposure and 1.62 is the same for all tested films.
Lee-the Howard Bond article was published in Photo-Techniques magazine. See if you can get a back issue from them. If not you can PM me and I will dig it out for you. Mr. Bond also did an article on Reciprocity several years ago on the older films; i.e. Tri-x,Tmax,Hp5 etc. His basic conclusion on the new films is that they don't increase nearly as much as the older films. They do increase as the times get longer though. See if you can find the article......if not then contact me.
Regards Peter
My article in Photo Techniques was in the next issue after Howards, I believe. It was called "Reciprocal Trade Disagreement". I always try to be humorous, probably because we were not allowed to at NASA.
Does this reciprocity factor hold at 1.62 for all long exposures, ie. 10 minutes equals 16.2 minutes, or 30 minutes equals 48.6???
thankyou for your insight
Reciprocity misbehavior. 
Linear Mode
