This paper reports new measurements of the pressure shifts in argon of the hyperfine splitting of hydrogen and tritium. A spin-exchange optical pumping technique was used to make these measurements. The fractional pressure shift (pressure shift in cps/mm Hg at 0°C divided by the hyperfine splitting in kMc/sec for hydrogen in argon is -4.78 ± 0.03; the ratio of the fractional pressure shift for tritium to that for hydrogen is 1.007±0.012; the temperature shift at constant density of the hydrogen hyperfine splitting is 0.012±0.003 cps/°K mm Hg. This new value for the hydrogen pressure shift is then used to reanalyze the Yale data for the hyperfine splitting of muonium, under the hypothesis that the fractional pressure shift for muonium is the same as that for hydrogen. This gives for the muonium hyperfine splitting an alternative value of 4463.23(2) Mc/sec. This value of the muonium hyperfine splitting gives for the fine-structure constant α the alternative value ${\alpha }^{-1\mathrm{}}=137.0367\mathrm{}\left(10\right)\mathrm{}$. This value of $\alpha$ is compared with the values obtained from the hydrogen fine structure, hydrogen hyperfine structure, and the ac Josephson-effect determination of $\frac{2e}{h}$.

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