Joe has an electron gun and a cloud chamber. When he fires an electron into the cloud chamber, the electron ionizes air molecules, causing water vapor to condense into little droplets. The droplets trace out the path of the electron, so that Joe can measure its position at any time.
# motion of an electron in a region which # may or may not have a significant electric field # time(microsec) position(cm) pos_uncert(cm) 0.0 0 0.5 1.0 12.3 0.5 2.0 21.1 0.6 3.0 31.9 0.5 4.0 40.6 0.7 5.0 48.7 0.9
"Hmmm," thinks Joe, "that looks like a pretty straight line. Let me make a linear fit, using a model with 2 parameters, a and b, like this:"
y = a + b*t
a = 1.54
b = 9.69
"Well, that's not bad," says Joe, "but it looks as if there might be some curvature there. Maybe I should try a quadratic fit with 3 parameters, like this:"
y = c + d*t + e*t*t
c = 0.26
d = 11.60
e = -0.382