1 72 Mr. Herapath on the Velocity of Sound and 



IIT. — Barometric Depression. 



Unluckily I have not a single case by me of an elevation 

 determined trigonometrically and barometrically, so that I am 

 incapable of comparing the other formula with direct experi- 

 ment. However, as Laplace's empirical formula is said to 

 agree exceedingly with observations, its co^oaparison with ours 

 will afford a tolerably good indirect test. ;ikl do' 



For the ease of calculation, we may suppose the tempera- 

 tures of the upper and lower barometer to be the same, and at 

 32° Fahr., or Cent. With these conditions, Laplace's for- 

 mula (Playfair's OutHnes, vol. i. p. 240) is in Eng. fathoms 



X = 10050 (l-^^).log|; 



C being the negative Cent. temp, of the higher station. And 

 our theorem in fathoms and logs, is 



a:=|l~ r|V| rh, or \o^x = logjl ~ TgW + 4.4164760. 



Now Laplace's formula affording us no assistance in determin- 

 ing the value of C, we have no resource but to compute it from 

 that theorem which we have shewn to agree so well with ob- 

 servation. Assuming, therefore, :C = = _— , our formula 



gives X = 298.29 fathoms, from which C = 3°, and conse- 

 quently by Laplace x = 299.3, or 1 fathom above ours. 



Putting g = 1-n = |, ours gives 780.88 and C = 8°, and 



hence, liaplace's 782.47, or 1.59 above ours. Again, when 



■^ = .^^ = 7T» we have from our theorem 1704.8 fathoms, 



and C z=i 17°. 42, and from Laplace's 1708.1, or only 3.3 more, 

 in an altitude of nearly two miles. In Gay Lussac's great 

 ascent, the temp, sunk from 30°.8 Cent, to — 9°.5 ; the baro- 

 meter from 1000 to 432 ; the density of the air from 1 to J; 

 and we are informed the height ascended, doubtless determined 

 from these data by Laplace's formula, was 7630 yards, or 

 3815 fathoms. From the barometric condition, our formula 

 gives 7600 yards, or 3800 fathoms, that is, 15 fathoms less in 



