The determination of the expansion of mercury by the absolute or hydrostatic method of balancing two vertical columns maintained at different temperatures does not appear to have been seriously attempted since the time of Regnault (‘Mém. de l’Acad. Roy. des Sci. de l’Institut de France,' tome I., Paris, 1847). His results, though doubtless as perfect as the methods and apparatus available in his time would permit, left a much greater margin of uncertainty than is admissible at the present time in many cases to which they have been applied. The order of uncertainty may be illustrated by comparing the value of the fundamental coefficient of expansion (the mean coefficient between 0° and 100°C.) given by Regnault himself, with the values since deduced from his observations by Wüllner and by Broch. They are as follows:— Regnault . . . . . . 0·00018153. Wüllner . . . . . . 0·00018253. Broch . . . . . . . 0·00018216. The discrepancy amounts to 1 in 180 even at this temperature, and would be equivalent to an uncertainty of about 4 per cent, in the expansion of a glass bulb determined with mercury by the weight thermometer method. The uncertainty of the mean coefficient is naturally greater at higher temperatures. If, in place of the mean coefficient, we take the actual coefficient at any temperature, the various reductions of Regnault’s work are still more discordant, and the rate of variation of the coefficient with temperature, which is nearly as important as the value of the mean coefficient itself in certain physical problems, becomes so uncertain that the discrepancies often exceed the value of the correction sought. It is only fair to Regnault to say that these discrepancies arise to some extent from the various assumptions made in reducing his results, and are not altogether inherent in the observations themselves.
I. On the absolute expansion of mercury