We have measured the combination of hydrogen Lamb shifts L1S-5L2S+4L4P by comparing the frequencies of the 1S-2S and 2S-4P transitions. The measurement determines the $1S$ Lamb shift to be 8 172 827(51) kHz, the most precise value for any Lamb shift. The theoretical predictions for L1S are 8 172 802(30) and 8 172 654(40) kHz, corresponding to proton charge radius values of 0.862(12) and 0.805(11) fm, respectively.
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Berkeland et al. (1995) studied this question.
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