My thesis advisor, Dr. William. F. Sager, outlined an approach on the blackboard. It was sketchy but it put me to work. It involved trying to design a Least Squares Calculation for an exponential equation. It is not possible to do this directly because one of the variables is in an exponent. Dr. Sager's idea was to use an assumed rate constant in the exponent and correct it with a factor in the second term in a Taylor expansion which had this correction as one of the linear constants in the equation. It would need an assumed constant that was within 5% of the real value. Fortunately this is rather easy to approximate from the apparent half-life of the reaction.
I spent two weeks over a Chrismas vacation working out the three equations and their simultaneous solution for the three constants. I had to do it three times till I got the same answer twice. Each solution took about twenty sheets of legal size lined yellow paper!
There are other supposed solutions for this curve fitting problem. I don't know the basis for them but am a bit suspicious. There are a number of methods to fit a curve but I don't believe they involve the exponential itself. I'm put in mind of the old Ptolemy/Copernicus controversy.The Ptolemaic description predicted everything very well, it just didn't relate to reality. Its calculation involved epicycles etc. to fit the observations of a moving system observed from a moving platform. No one believes that the planets and stars move in an epicyclic manner. The calculation is still accurate, just useless because it makes no valid predictions.
I am going to list here a program I wrote for this calculation many years ago. It's in the form of Basic in use at that time. Basic has been improved and now I can no longer program in it. However, I am going to learn as fast as I can and get this program updated so it can be used in True Basic. I have a System X Mac computer and True Basic can not be run on it. I have an older clamshell laptop with System 9 and I am trying to use it there. I am trying to find some local help that can shorten the learning curve for me. I still know how to program in Basic, it's the framework that has changed. Being 85 has slowed me up a little.
I am going to post here two old Basic programs, the oldest one
first. There will be five pages for the first, more compelete, program I used. The sixth page is a
sample calculated result. This was written in the day when the data was added through punched cards.
So the injection of data will have to be done differently. I expect the various data runs will be
stored in separate data banks to be called up as needed. That's another aspect where I will need
help. The writing of the results has changed as well.
The second is a more abbreviated, later version.
Please consider this program and others derived from it as copyrighted.
I must explain something that an experimental scientist will initially feel is a kind of heresy. One must totally abandon any consideration of "significant figures". There are no insignificant figures when using least squares.
Least squares is a study of residuals, errors. If one "rounds off" numbers in the calculation you destroy the study of the errors. Therefore, you will find enormous numbers quoted here.
For the purpose of least squares, the DATA beome PURE NUMBERS, as many zeroes as you need.
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Here is a re-write of the program for a different computer and three results.
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I have been trying to break through this "ceiling" for fifty years.
I cannot imagine what scurrilous lies were told Bartlett about me but Bartlett must also have
communicated them to Dr. Sager.
I wrote this letter to Dr. Sager seven years ago and have no memory
of an answer. I phoned him several times and he was cordial but I felt there was a veil between us.
Both he and Bartlett are now gone to the great research laboratory
in the sky. I am the only one left. I don't want this method lost when I am gone!
All of this has got to be put aside and the method evaluated "on its merits".
I have no fear of that.
It is a remarkable method.
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