Friday, July 7, 2017

An Error in Huggins' Hydrogen Wavelengths?

  There appears to be a systematic error in the hydrogen wavelengths in Huggins' paper when one compares them with the fit for the Balmer series. Notice that there is an progressive increase in the value of the error, Δν. If one uses the first line as the reference we can set that error equal to zero and compute the relative errors Δν'.

Trying to fit a straight line to this data is a little tricky but least squares allows us to derive a formula for the best fit for a line going through the origin.

The adjusted lines give a closer estimate for the limit of the lines of the Balmer series.

It's possible that the Iceland spar prism that Huggins used was slightly nonlinear in its dispersion of light. Dispersion is dependent on frequency. This may be why rescaling gives a better result. The least squares derivation of the formula above is fairly simple. The quantities on the right of the formula are the column vectors in the second table.

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