Look again at the equation. The log of the indicated time is multiplied by 1.62 and added to the log of the correction at 1 second indicated time to get the log of the correction. The answer is "No".
To convert that equation to one that can be solved quickly on a TI-30 pocket calculator (cost about $20) : tm is indicated exposure time. tc is amount to be added to indicated time. tc,1 is correction to be applied to a 1 second tm. tr is exposure time adjusted for reciprocity failure. Then,
tr = tc,1*(tm^1.62) + tm
The * is what shows when you press the multiply key. The ^ means "raised to the power"
Mr. Gadget - this is cool stuff. Do you have any words of wisdom on the change in development that would ne need as the exposure time is increased to maintain a consistent contrast?
I had an old Kodak Technical document from the late 1970's that had a set of tables showing the percentage development time change needed as the exposure time increased. But I have no clue where it is and I suspect the information is way out of date for today's emulsions.
Mr. Gainer-or you could just carry the little chart that Mr. Bond so kindly published! I rather photograph than do calculations but that's why your known as Gadget Gainer!
Lee, you said "I'm curious about the method used by Bond, and the range of exposure lengths covered."
Howard's experiments covered up to 240 indicated seconds by factors of 2: 1,2,4,8 etc. He found the exposure for 400TX to be 1006 seconds at 240 indicated. This is about 1/2 stop less than I would calculate by fitting the whole range of data, but 1/2 stop is not much when you get down to it. I often find when I am metering a scene that I have to average readings with a greater spread than that, and even if I do three exposures at +/- 1/2 stop, I cannot see much difference in the final results.
If you find my article in Photo Techniques (sorry I don't remember the issue) you will see tables and graphs that illustrate what I am saying here.
My questions are simple ,as I only was able to get to grade 9 math before my teacher threw me out of class . He did not realize my mother language Moronica.
My interest is in very long exposures for some night photography as well as being able to correct very long times in the darkroom. I have been PM by someone else on this matter so I hope not lower the scope of this thread.
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If anyone is interested I could make an Excel Spreadsheet/Chart Available. I have made up a quick and dirty chart you can see here - limitations of converting Excel to HTML with GIF image. Adjustments for HP5, TMX and TMY
For convenience of interested parties, the Phototechniques web site lists:
Vol. 24, No. 5 Reciprocal Trade Agreement - Gainer
Vol. 24, No. 4 B&W Reciprocity Departure Revisited - Bond
These would be the July-Aug (No. 4) and Sept-Oct (No. 5) issues for 2003 if I'm calculating correctly.
To answer in part the questions Bob Carnie and Mike K have about adjusting development;
When you make a long exposure in the range where a film has reciprocity law failure, you'll probably have a range of a number of stops, probably a minimum of 5-7 stops or often much greater, especially in a night shot with manmade lighting and dark areas. If you took the darkest area and calculated the necessary exposure with reciprocity compensated for, then did the same with the lightest area, you'd find that the dynamic range (# of f-stops) of the scene has just expanded tremendously because of the differential in reciprocity failure between the light and dark areas. To compensate in part for this, development times are sometimes decreased to keep the contrast of the negative down, but that means marginally lower "film speed" as well. This gets out of hand rather quickly, and you often just have to accept some loss in highlights, shadows, or both. Or you can explore the stand development and other techniques used by the photographers who do cathedral interiors.
My advice is to bracket either side of your calculated exposures if the shot is important to you. I've found that bracketing with the Fibonacci series works well. That series is 1, 2, 3, 5, 8, 13, 21... each subsequent number is the sum of the previous two numbers, and I do this in either seconds or minutes. I do this because in my experience a half stop bracket is too little and a full stop is too much. It works for me in time exposures of under a minute up to a half hour or so. I started using the Fibonacci series when I was doing 2000 custom B&W prints a month using two hand-operated Omega D-V enlargers with no meter or analyzer. (Luckily I had a roller-processor for the paper.) I could eyeball the exposure and be right 95% of the time, and could always nail the second by going up or down to the next number in the sequence. It was also handy because I'd often get requests for reprints, and within the tolerance of the materials, I could always get a reasonably exact duplicate print without having written down exposures.
When you take the ratios of any two sequential numbers in the Fibonacci series, you get 1.618, which is coincidently, the golden mean ratio, and the number by which the log of the indicated exposure is multiplied in Mr. Gainer's reciprocity equation.
If you had made these plots on log-log paper, you would see straight, parallel lines.
Originally Posted by MikeK
If someone will tell me how, I will send the log charts with raw data superimposed. I have it as a jpg file of around 300 K. These are the charts that were used in my PT article.
In the Excel charting function I can only apply a log scale to the y-axis
Originally Posted by gainer
This has been a useful mental exercise for me on this wet and miserable Saturday afternoon. I have printed a little booklet from the Excel Tables and have stuck it in the back of my field notebook.