256 Temperature of Mercury in a Siphon Barometer. 



An example may serve the purpose of illustrating the practical 

 application of the formula : — to determine the numerical co-effi- 

 cients of (10) for No. 366 Bunten's mountain barometer, I made 

 the two following sets of observations. 



a=393.575, 6=358.760, ^=-3.22 

 a''=r391.r46,5'^=355.043,r=-L 16.73. 



Here, as throughout this paper, unless the contrary is express- 

 ed, the unit in length is a millimetre, and the degrees are those of 

 the centigrade scale. The formula, however, is equally applica- 

 ble to any other denominations. The first set is the mean of ten 

 successive hourly observations, in which, during the whole time, 

 the temperature was so uniform as to vary but 1°.7. In this, as 

 in the second series, the barometer had been suspended some 

 hours before the first observation of each series was made. The 

 second set is the mean of seven hourly observations, during which 

 time the attached thermometer varied only 0.6 of a degree. To 

 remove what may seem a fallacious aspect of exactness from the 

 number of decimal places in the readings, I would observe that 

 the scale is graduated in millimetres, which are sub-divided into 

 tenths by a vernier, and these, by careful reading, may be divided 

 into halves or quarters, by the eye. The third decimal place re- 

 sults from the process of taking means, and depends for its exact- 

 ness, upon the number of observations taken. Substituting these 

 observed values of (a,) (6,) (;,) [a",) {b",) {t",) in (10,) we have 



19 950 



i'= -3.22+^'ggg (a'- 6'-34.815;) 



or, after reduction, ^'=10.576 (a'- 6' -35. 12) (10'.) 



If, for example, the upper reading is 392.35, and the lower one 

 356.63, then, according to the formula, the temperature will be 

 6.35 degrees. 



The temperatures calculated by this formula for No. 366 Bun- 

 ten's barometer I found to differ very rarely so much as one de- 

 gree from those indicated by the attached thermometer, and most 

 frequently not half that, when the observations were made with 

 suitable care in a place of comparatively uniform temperature ; 

 and the more confidence I had in the correctness of the observa- 

 tions, the closer the agreement seemed to be. 



This formula, like all others relating to the barometer, supposes 

 an exact instrument. It is desirable therefore to have the means 

 of testing its accuracy of construction, and, if faulty, of applying 

 a suitable correction. 



