ing point of water, the melting point of it. But neither these corrections nor the incidental recognition by the Florentine Academicians of the invariability of the melting point of ice diminish the importance of Réaumur's discovery.
Having discovered a fixed temperature, Réaumur deduced a way of making spirit thermometers that could be compared with one another. If we plunge a glass bulb prolonged into a fine tube and filled with spirit into freezing water, and draw a line marked zero flush with the top of the liquid, then determine the volume occupied by the liquid under these conditions; if we divide the tube into portions, the interior capacity of which represents at the temperature of the freezing of water aliquot parts of that volume—hundredths, for example—and number these divisions from the line marked zero; then if, in an experiment, we see the spirit rise to the level of the division marked five, we know that the spirit in the glass has suffered an apparent dilatation of five hundredths between the freezing temperature of water and the temperature of the experiment. If we always take care to use spirit of the same quality—and Réaumur prescribed minute rules on this subject—and if we neglect the changes which the variable nature of the glass will introduce into the law of dilatation of the thermometric receptacle, we will obtain instruments of a kind that will always mark the same degree when they are equally heated or cooled.
For two instruments constructed according to the laws laid down by Réaumur to be rigorously comparable, it was essential that they be made of the same glass and filled with the same liquid. If the glass of which they are made has not exactly the same composition and tempering in both, and the alcohol has not the same degree of concentration, they will not agree. In order to diminish these variations, it is convenient to fix all thermometers, whatever they may be made of, so that they shall give the same indications for two fixed temperatures. The point reached by the liquid at the lower of these temperatures is marked on the instrument, and then it is raised to the higher temperature, and the point which it reaches then is marked. The interval is then divided into parts having the same interior volume, and the division is carried out beyond the fixed points. In such thermometers the liquid will stand at the same mark for an equal degree of heat, notwithstanding slight inequalities in the glass and the fluid.
It was some time before the two fixed temperatures at which the thermometric scale should be marked were determined upon. Dalence, in 1688, took a mixture of water and ice for the zero, and the melting point of butter as the upper point. Renaldini, in 1694, recommended a mixture of water and ice and the boiling point of
