I want to make some general comments and I'll use Chip Sample's
posting as a foil, though I don't wish to berate him for what I
consider to be somewhat incorrect interpretation. I will have
to do a bit of cutting and pasting to make the points.
If your uncertainty in measurement of the absolute charge on
that 8e drop was +/-5% then you could not even claim that the
number of charges was 8; it could easily have been 7 or 9!
To which Chip replied:
I tend to agree with you. (Although it looks more like 11 or
12% to me).
I think this represents an error that students often make. When
I stated an uncertainty of +/- 5% in a measurement I was using a
statistical convention which means that two thirds of the time I
expect my result to be less than 5% different from the true value
of the quantity being measured. It does not mean that it will
never be farther from the true value than that. I imply that one
time in three I expect to be farther out than 5%. Now if you
reread my original statement will you still say it "looks more
like 11 or 12%"? I wouldn't.
I make the general observation that we teachers do not pay
sufficient attention to the interpretation of the results of the
experiments our students do in undergraduate laboratories. It is
unsurprising that the students often find these exercises
pointless if we do not help them to see the meaning in their
results. Chip now agrees that the experiment was rather shallow.
Should we not let on to our students that they must measure many
more than five drops to discover what Millikan discovered?
Chip's interpretation of what his professor was thinking when he
assigned this task is this:
Just guessing here, but I'll bet that the professor knew we
could measure the charges accurately enough with the equipment
at hand to get decent results (it was not a "student" apparatus),
and because we had only slide rules to do the computations, we
probably weren't required to do anymore than the minimum to get
an answer we could compare with the accepted value.
No, Chip, that's not what he was thinking. That would imply an
uncharitable interpretation of his intelligence.
I'm just guessing here, but I guess that the professor just didn't
give much thought to the point of the exercise. He was probably
being intellectually lazy; that's certainly something I am often
guilty of in teaching laboratories. I really have much lower
expectations of my students in the laboratory than is justified by
their abilities, and lower than my expectations of them in the
examinations in lecture courses. In our university we credit and
grade laboratories separately from lecture courses. Often they are
merely a component of the lecture course in other universities,
sometimes graded in a desultory manner which indicates to students
that we, the professors, do not consider them to be particularly
important. That is an intellectual crime in my view.
I performed this experiment in a course called Physics 110C at Cal
in 1956. I did use a computer to reduce my data (that computer is
now on display in the Smithsonian Museum of American History) but
with work I could have done so on a Marchant caculator. A slide
rule would have been inappropriate to the calculation as I recall.
Finally Chip says:
With computers today, one can automate the computations and data
from more drops could have been collected and analyzed in the
same amount of time. Then students can actually do "science";
analyze data and demonstrate whether, within the uncertainty of
the results, they support or contradict a particular hypothesis.
I much prefer this to measuring things with the purpose of
comparing with an accepted value.
With or without computers, I heartily agree with your preference.