HEIGHT OF THE WORCESTERSHIRE BEACON. 397 



temperature, or diminishing that in the warmer by its g^ part for 

 every degree of difference between the two. 



3. Take the diflference of the common logarithms of the two 

 heights of the barometer (so corrected) considering the first four 

 figures as whole numbers — which will give an approximate height, 



4. Take the mean of the two detached thermometers 3 and for 

 every degree which this differs from 31° take so many times the 

 -^ part of the approximate height 5 and add them, if the mean 

 temperature be above 31° 5 but subtract them if it be below 3l» j 

 and the sum, or difference, will be the true altitude in English 

 fathoms. 



These formulae have been somewhat modified, and perhaps 

 improved by subsequent philosophers. 



The following proceeding is recommended by Mr. Daniell in his 

 Meteorological Essays, being, in fact, mainly Dr. Hutton's process, 

 with additional corrections for the elasticity and density of the air, 

 consequent upon the presence of more or less vapour, at either of 

 the observed stations. 



1. Observe the heights of the barometer at the top and bottom 

 of any elevation, and the heights of the attached thermometers. 

 Observe also the temperature of the air in the shade at the two 

 stations, by a detached thermometer : the dew point must also be 

 accurately taken at the upper and lower situation — these observa- 

 tions being made as nearly as possible at the same time. 



2. Correct the heights of the barometer observed at the top and 

 bottom of the station, for the expansion of mercury and the mean 

 dilatation of the tube (by the table) to the temperatures observed 

 by means of the attached thermometer, at these two stations. 



3. Take the difference of the common logarithms of the two 

 heights of the barometer (so corrected) considering the first four 

 figures as whole numbers — which will give an approximate height 

 in fathoms. 



4. Find the mean of the two temperatures observed by the 

 detached thermometer, in the shade, at the upper and lower 

 station — and (referring to the table) note the expansion of air due 

 to this mean temperature, and subtract it from 1.00000 which will 

 give the specific gravity of the air corrected for temperature, 



5. Note the temperature of the constituent vapour of the atmos- 

 phere, by finding the dew point at the upper and lower station. 



6. Find the expansion of air for vapour at these two observed 

 points (by the table), and subtract from each of them the increase, 

 of density which air undergoes for vapour (found by the table) at 

 the same points ; and the mean of this result, subtracted from the 

 specific gravity of air corrected for temperature (4) will give the 

 correct specific gravity of the air, — And then say — 



7. As this correct specific gravity is to 1.00000 (the standard) 

 so is the approximate height (3) to the correct height,* 



* The Tables referred to above, will be found in Daniell's " Meteorological 

 NO. VI. 3 G 



