| a = 5·96131330259 |
| log. a1 = 0·82340688193 − 1 |
| log. b1 = −·01309734295 |
| log. a2 = 0·74110951837 |
| log. b2 = −·00212510583 |
The relation between the temperature t with reference to the centesimal thermometer, and the pressure p in millimètres of mercury at the temperature of melting ice, will then be expressed by the following formula:—
| log. p = a − a1b120 + t − a2b220 + t. (1.) |
Formulæ have, however, been proposed, which, though not applicable to the whole scale of temperatures, are more manageable in their practical application than the preceding.
For pressures less than an atmosphere, Southern proposed the following formula, where the pressure is intended to be expressed [Pg506] in pounds per square inch, and the temperature in reference to Fahrenheit's thermometer,—
| p = 0·04948 + ( | 51·3 + t | ) | 5·13 | .(2.) |
| 155·7256 | ||||
| t = 155·7256 {(p − 0·04948)1⁄5·13 − 51·3} | ||||
The following formula was proposed by Tredgold, where p expresses the pressure in inches of mercury:—
| p = ( | 100 + t | ) | 6 | . |
| 177 |
This was afterwards modified by Mellet, and represents with sufficient accuracy experiments from 1 to 4 atmospheres. Let p represent pounds per square inch, and t the temperature by Fahrenheit's thermometer,—
| p = ( | 103 + t | ) | 6 | .(3.) |
| 201·18 | ||||
| t = 201·18 p1⁄6 − 103 | ||||