Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/160

144 {{c|{{larger|VIII.}} The logarithms of the calculated values of the intervals of time exceed those of the given values by .0002416 for the first interval ($$\tau_{3}$$) and .0002365 for the second ($$\tau_{1}$$). Therefore, since the corrections for aberration have been incorporated in the data, we set for the correction of the formula (for the second hypothesis) {{MathForm2||$$\Delta \log \tau_{1} = -.0002365$${{gap}}$$\Delta \log \tau_{2} = -.0002416$$}} This gives {{MathForm2||$$\Delta \log A_{3} = .0000026$${{gap}}$$\Delta \log A_{2} = -.0000025$$ $$\Delta \log B_{1} = -.004872$${{gap}}$$\Delta \log B_{2} = -.004782$${{gap}}$$\Delta \log B_{3} = -.0004665$$}} The new values of the logarithms of $$A_{1}, A_{3}$$ are {{MathForm2||$$\log A_{1} = 9.6854923$${{gap}}$$\log A_{3} = 9.7120418$$}} Applying these corrections to equations $$\text{III}_{1}, \text{III}_{2}, \text{III}_{3}$$ we get the following: {{block center/s}} {{block center/e}}

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