59. The Scale.—The two fixed points having been determined, it is necessary to apply the scale. The thermometers in general use in the United Kingdom, the British Colonies, and North America are constructed with Fahrenheit’s scale. Fahrenheit was a philosophical instrument maker of Amsterdam, who, about the year 1724, invented the scale which has given his name to the thermometer. The freezing point is marked 32°, the boiling point 212°, so that the intermediate space is divided into 180 equal parts, called degrees. “The principle which dictated this peculiar division of the scale is as follows:—When the instrument stood at the greatest cold of Iceland, or 0 degree, it was computed to contain 11124 equal parts of quicksilver, which, when plunged in melting snow, expanded to 11156 parts; hence the intermediate space was divided into 32 equal portions, and 32 was taken as the freezing point of water: when the thermometer was plunged in boiling water, the quicksilver was expanded to 11336; and therefore 212° was marked as the boiling point of that fluid. In practice, Fahrenheit determined the divisions of his scale from two fixed points, the freezing and boiling of water. The theory of the division, if we may so speak, was derived from the lowest cold observed in Iceland, and the expansions of a given portion of mercury” (Professor Trail).
The divisions of the scale can be carried beyond the fixed points, if requisite, by equal graduations. Fahrenheit’s scale is very convenient in some respects. The meteorological observer is seldom troubled with negative signs, as the zero of the scale is much below freezing. Again, the divisions are more numerous, and consequently smaller, than on other scales in use; and the further subdivision into tenths of degrees, seems to give all the minuteness usually required.
Celcius, a Swede, in 1742, proposed zero for the freezing point, and 100 for the boiling point, all temperatures below zero being distinguishable by the sign (—) minus. This scale is known as the centigrade, and is in use in France, Sweden, and the southern part of Europe. It has the advantage of the decimal notation, with the embarrassment of the negative sign.
Reaumur, a Frenchman, proposed zero for the freezing point, and 80° for the boiling point, an arrangement inferior to the centigrade. It is, however, in use in Spain, Switzerland, and Germany.
It is merely a simple arithmetical operation to change the indications of any one of these scales into the equivalents on the others. To facilitate such conversions, tables are convenient, when a large number of observations are under discussion; and they can be easily formed or obtained.
In the absence of such tables, the following formulæ will insure accuracy of method, and save thinking, when occasional conversions are wanted to be made:—F. stands for Fahrenheit, C. for Centigrade, and R. for Reaumur.
| Given. | Required. | Solution. | ||||
| F. | C. | = | (F.-32) 5⁄9 | |||
| F. | R. | = | (F.-32) 4⁄9 | |||
| C. | F. | = | 9⁄5 | C. + 32 | ||
| C. | R. | = | 4⁄5 | C. | ||
| R. | F. | = | 9⁄5 | R. + 32 | ||
| R. | C. | = | 5⁄4 | R. | ||
Example.—Convert 25° of Fahrenheit’s scale into the corresponding temperature on the Centigrade scale.
| Here | C. = | (25 - 32) 5⁄9 | ||
| C. = - | 35 | = -3·9 | ||
| 9 | ||||
or nearly 4° below zero of the Centigrade scale. The algebraical sign must be carefully attended-to in the calculations.