I was merely commenting that Kodak used the same method. And, as such the data is pretty much as you have shown, but they only do it for one contrast value.
PE
If I seemed a little prickly, it's because I was having trouble getting my graph through to the screen. NOBODY had seen my data at that point, unless they remembered it from a paper in Photo Techniques a few years ago. IIRC, it was titled "Photographers Can Ride on Logs."
The graph actually is an analog of the charging of a capacitor through a fixed resistor to a fixed potential which makes it also a pretty good analog of the developing process as far as the shape of the curve goes. The charging potential is the analogy of Gmax. Gmax doesn't come with the film instructions these days, but the means of calculating it from 2 properly chosen experiments has been around a long time. I found it in Principles of Optics by Hardy & Perrin. The method of doing it by successive approximation from found data where you can't choose the developing times you'd like to have is mine, or at least I like to think so.
The solid black circles show the raw data I used to define the general equation. The two at 65 F defined the slope and Gmax, and the third at 70 F defined that line. The line showing Gmax - G at constant 5 minute development time allowed me to interpolate to make lines for other temperatures. The hollow circles show where other Kodak data fall that were not used in generating the graph. There was no least-squares curve fitting used.
The time constant of the development can be influenced considerably by agitation.
Well, then, imagine trying to generalize among tantalum capacitors, electrolytic capcitors and etc. They are all different.
BTW, I used to keep a charged 10,000 MFD capacitor on the shelf in my electronics shop most of the time to discourage idiots who visit and try to handle everything! It worked!
Well, then, imagine trying to generalize among tantalum capacitors, electrolytic capcitors and etc. They are all different.
BTW, I used to keep a charged 10,000 MFD capacitor on the shelf in my electronics shop most of the time to discourage idiots who visit and try to handle everything! It worked!
PE
Yes, but they all have leakage, inductance and internal resistance. That is what makes them differ from one another. The development process should not have the analog of leakage resistance. If it did, it would start to lose the image in the stop bath. I have yet to see the analog of inductance.
In my years at NACA-NASA we had to do our dynamic simulations using analog computers. Digital was only good for some calculations, mostly book keeping. The analog computer had 100 +,- 100 volt op amps, each with two vacuum tubes the size of wine bottles and several smaller ones as preamp. It took about 10 KW to run and had its own air conditioner. We had two crackerjack engineers maintaining the monster. Frequency response, defined by allowable phase shift, was 30 kHz.
A few days ago the French celebrated my 81st birthday. For some reason, they call it Bastille Day. I just realized I'm a little more than 1/3 the age of the United States.
Happy Birthday, PG (that's Patrick Gainer, not Propylene Glycol), and anyone else who had a birthday in the last year (or 4 years for those born on Feb 29).
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Murray
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We originally used an analog computer such as you describe at Kodak. And, the operator's name was James Kirk. (His middle initial was not "T"). In any event, hypo can bleach the silver image so it can be made to vanish during fixation.
My point being though that every capacitor has its own characteristics and you agree from what I read. This is also true of films and developers, and the variety and number of results from combinations can be staggering.
We originally used an analog computer such as you describe at Kodak. And, the operator's name was James Kirk. (His middle initial was not "T"). In any event, hypo can bleach the silver image so it can be made to vanish during fixation.
My point being though that every capacitor has its own characteristics and you agree from what I read. This is also true of films and developers, and the variety and number of results from combinations can be staggering.
PE
Exactly so. All the more reason to attempt to minimize the number of experiments needed to define a characteristic curve. When I saw that all these films plotted as straight lines as log(Gmax - G) vs time and that Gmax for a given film-developer was independent of temperature, it became apparent that 2 experimental determinations of gradient G at one temperature and one determination at another temperature would define all the data provided by Kodak for 1 film. In other words, 3 experiments provided all the information that was contained in 15 by Kodak, and more besides because the effects of times and temperatures not tested can be estimated with good accuracy from the same 3 experiments.
You understand, of course, that random experimental errors can and do occur. It is always best to have more data than the minimum that would be required if there were no experimental error. My preference is to make the 2test times as different as practical and to repeat tests at those times for averaging out errors. Obviously, making one time twice the other would eliminate the use of successive approximation to solve for Gmax.
Kodak plotted on semilog paper at one gamma, that of the aim for the film. They then went on to plot several films in one developer or one film in several developers. None of these curves were parallel and therefore none could be reduced to a single equation. Even so, none could be reduced to a linear equation.
You're missing a point. I did not plot gamma against time or temperature. I found the assymptote of the gamma-time curve by a well known equation when values of gamma at times such that t2 = 2 t1. If such data were not available from Kodak, which is most often the case since the data presented were for times to produce specific values of gamma, I used a successive approximation to calculate the gamma infinity from two available times. Now, if you plot the difference between the assymptote and any value of gamma from the curve, you will see the typical exponential decay curve on linear paper, which plots neatly on semilog paper as a straight line. The starting point for this curve is at the assymptote which we often call "gamma infinity" and 0 time of development. Temperature alone has no effect on gamma infinity, so curves for different temperatures emanate from the same point and are also straight lines. It only takes 2 points to define a straight line. After the first line has been defined, the line for any other temperature may be defined by one more experiment because the intersection of the first line with the t=0 axis defines a second point.
I'm sure you have or can access some ordinary charts of gamma vs development time that extend to or near the asymptote. The curve is generally the same shape as the time history of potential on a capacitor being charged through a resistor from a constant source potential. You will see the similarity to an upside-down exponential decay curve. If you subtract each value from the asymptotic value and plot the logs of those values on ordinary graph paper or the values themselves on semilog paper with time on the linear axis, you will see a straight line. This line contains just as much information as the original data.
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Gadget Gainer
Last edited by gainer; 07-20-2008 at 06:35 PM.
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