I followed you completely. What you appear to have missed in my post is that you can only do this for one film and one developer due to the variations in thickness (difffusion related), silver coverage, and emulsion type and for the developer you have to consider developing agent(s), concentrations, ratios, pH and other addenda.
Simple substitution of Benzotriazole for bromide as antifoggant can upset this entire scheme of things. I have plots that show some developers to be nearly parallel and others to be big outliers. I think there is an earlier set of curves posted here that you may wish to look at.
So you are right for one film and one developer but you cannot use that same equation for multiple films and developers, only the methodology holds true. So, I would use your method for time/temp for PX, SXX, TX and etc in one developer (which might work) or PX in multiple developers (again which might work), but I wouldn't cross the data over. Kodak has shown data to support my position in the book I noted earler.
He is using semi log paper to plot the same generic type of data, but with a twist as he is varying contrast. The Kodak and your data and mine are based on "aim" contrast. Our data also compare a film in a developer or a group of developers. Or a group of films with a developer to show the curves you have.
If you look at your 3 films, they just don't match each other! That is the key to this. Each film and each developer is different. Patrick is just doing something different in that his example, as I said, has varying contrasts.
I followed you completely. What you appear to have missed in my post is that you can only do this for one film and one developer due to the variations in thickness (difffusion related), silver coverage, and emulsion type and for the developer you have to consider developing agent(s), concentrations, ratios, pH and other addenda.
Simple substitution of Benzotriazole for bromide as antifoggant can upset this entire scheme of things. I have plots that show some developers to be nearly parallel and others to be big outliers. I think there is an earlier set of curves posted here that you may wish to look at.
So you are right for one film and one developer but you cannot use that same equation for multiple films and developers, only the methodology holds true. So, I would use your method for time/temp for PX, SXX, TX and etc in one developer (which might work) or PX in multiple developers (again which might work), but I wouldn't cross the data over. Kodak has shown data to support my position in the book I noted earler.
PE
I don't know what you mean by "the same equation." If you mean the constants in the equation vary with each film-developer combination, you are right. I never said otherwise. If you mean that the form of the equation is different for each case, I have proved otherwise by using that form to fit every film that Kodak reported in the time-temperature tables that Kodak published soon after XTOL hit the market, which included the Ilford films and others as well as the then-current TMAX films. The same general equation fits an exponential decay function. I guess I'll have to find a way to post the whole article.
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Gadget Gainer
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If you look at some of the premises here, they present a single equation to do just that, and that is the point of the whole argument. I am agreeing with you and disagrring with them. There is even an excel spreadsheet posted here that purports to do just what you and I say is impossible.
I did not come up with the equations I used without some basis. According to Hardy & Perrin in "Principles of Optics":
G = Gmax - Gmax * e^(-kt)]
or,
Gmax - G = Gmax * e^(-kt)
where G is gamma and Gmax is gamma infinity. Taking the logarithm of both sides,
log(Gmax - G) = log(G max) - kt
Thus, a plot of log(Gmax -G) vs time of development should be a straight line with negative slope k. Likewise, a plot of Gmax-G vs time on semilog graph paper should be a straight line. The rub is that we must know the value of Gmax. If the results of two development tests at time such that one is twice the other, then:
Gmax = (G1^2)/(2*G1 - G2).
(For the uninitiated, read that "Gmax = G1 squared divided by the quantity (2 times G1 - G2).)
If any of our current films were not to follow this form, I would think it would be the Tmax type. They were among the closest to this form.
I did not say or show in any way that development time for constant G is a straight line. What I showed was that over the range of data available, the gradient is a linear function of temperature on semilog paper when development time is held constant. Look closely at the chart I provided. There is no implication or statement that I consider the same numerical relationship to be valid for any other combination of film and developer. The linear relationship between temperature and log(G) at constant time has held for all the films and developers I have tested, including those that Phil Davis printed in Photo Techniques (probably Darkroom Techniques then). If you read the times at constant log(G) from my chart, you will see that there is definitely NOT a linear relationship. What are we really arguing about?
so curves for different temperatures emanate from the same point and are also straight lines.
Gadget,
Does this chart agree with your graphing ? I'm not quite following what you're saying, and am a little confused. Well, confused.
don
The premise in the Rodinal curves is that you are trying to hold a constant gamma by adjusting time to suit temperature. My curves show the effects of time and temperature on gamma, but the "mapping" is not conventional. Each line on my plot is for a constant temperature. Each line on the Rodinal chart is for a constant gamma. I will look in more detail to see what kind of a chart I can get from the one you posted. I used to have a copy of that chart.
I used the Agfa data for 20 C, 12 m, G=0.55, 16.8 m, G=0.65, to estimate that the Gmax for APX100 is 0.834. I had to use my program for successive approximation to get it. This establishes a line on semilog paper. I used a point at 22 C, G=0.65, t=14 m to establish another line. Now I have two lines on semilog paper emanating from 0.834 at t=0, one passing through (0.834 - 0.65) at 16.8 m and the other through (0.834 - 0.65) at 14 m. G is on the log axis and t is on the linear axis.
In order to establish lines for 18 C and 24 C, I drew a vertical line across the other lines. I marked a point along this line above the 20 degree line a distance equal to the distance along the vertical line between the 20 and 22 degree lines, and another point the same distance below the 20 degree line. I now have 4 constant temperature lines emanating from the same Gmax. All of these were constructed from the 2 pairs of time-gamma values. That of course does not make them valid representations of nature, but there are data on the Rodinal chart I have not used yet. The value of G at 20 C, 18.8 minutes should be 0.75, according to Agfa's chart. I see a value of Gmax-G of about 0.1. 0.834 -.1 = 0.734 in the chart I made.
It occurred to me that some may have gotten the idea that I was trying to generalize this analysis too much. I would not have done it if I had not in fact realized that all films are different in particulars. At the same time, there are similarities that have been recognized since before the days of hurter & Driffield, Hardy & Perrin, and many other well known and respected researchers into the mysteries of photography. My premise was that I should be able to use the similarities to minimize the amount of testing needed to define the specific differences among films.
Linear Mode
