HEIGHT OF THE WORCESTERSHIRE BEACON. 399 



3. Temperature at the \ 64 and 53 mean 58.5 — 32 =26.5 

 two Stations. J 26.5 x 144.190 = 3821.035 

 then 3821.035 m 00244 = 9.323, &c. 



and 144.190 « 9.323 = 153.513 Fathoms 

 6 



Height in English feet, 921.078 



Proceeding in the same way with the second series of observa- 

 tions — we obtain 934.596 — and a mean of these two numbers gives 

 927.937 feet. 



The height deduced by following the method of Dr. Hutton is — 

 from the first series of observations 910.800 feet — and from the 

 second 927.882, the mean being 919.341 feet. 



The greatest reliance ought perhaps to be placed upon the 

 results obtained by following Daniell's formula, because it embraces 

 the important corrections necessary for the vapour always in a 

 greater or less degree existing in the air. Following his directions, 

 the height, by the first series of observations, is 924.01 feet ; and 

 by the second, it is 925.50 feet ; a remarkably close approximation. 

 The mean of the numbers obtained by Maskelyne's and Hutton' s 

 formulae, is 923,639. The details of Daniell's formula are sub- 

 joined, taking the second series of observations as data. 



Barometer at upper station, 29.543 



correction for the expansion of mercury > ^^jq 



at the temperature 65 « ^ Logarithm. 



29.460 — 4692327 

 Barometer at lower station, 28.550 diff. 144.945 fath. 



correction for the expansion of mercury \ 



at the temperature 58° J 0.57 x 



28.493 — 4547382 6 



Approximate height in feet, 869.670 



Lower station, temperature of air, 65.0 Dew point, 58.5 



Upper ditto, ditto, 58.0 Ditto, 52.0 



Mean, 61.5 



Expansion of air for temperature, (61) per table, .06041 

 Ditto, ditto, for vapour, 58 ditto .01633 

 Ditto, ditto, ditto 52 ditto .01336 



Mean, .01484 



Total expansion, .07525 



Then, : 1.07525 : 100000 : : 100000 : .93002 



Increase of density for vapour at 58 — .01051 

 Ditto, ditto, ditto, at 52 — .00864 



Mean .00958 



Correct sp. gravity, .93960 



Then : .93960 : 1.00000 : : 869670 : 925.5 the height in feet 



