82 Mr, Nixon on the Theory of the [Aug. 



Method of calculating Heights. 



We may now proceed to the calculation of the vertical height 

 of an object situated within the atmosphere of the earth, the 

 data being the height of the barometer at its summit and base, 

 together with the temperature of the intercepted stratum of air 

 (uniformly at 32^ F. and perfectly dry) . 



To reduce the problem to the greater siifaptioity, we remark 

 in the first place, that it is immaterial whether the instruments 

 are placed in the same vertical line or not, for every point of the 

 surface of the atmosphere of uniform temperature being at the 

 same distance from the centre of the earth,* and the pressures 

 being directly as the depths below the surface of the fluid, the 

 heights indicated by two or more barometers equidistant from 

 the earth's centre will be precisely the same without regard to 

 their horizontal distance. Secondly, as the pressure exerted by 

 fluids is uninfluenced by their figure, it is unnecessary to have 

 regard to the area of the strata of the atmosphere, increasing 

 (but not in the simple ratio of the height) as we ascend from the 

 surface of the earth.f Thirdly, as the height of the upper baro- 

 meter exhibits the value of the pressure incumbent on the inter- 

 cepted stratum of air, and thus aflbrds the datum requisite to 

 ascertain its mean density as far as regards pressure, it would 

 be superfluous even to inquire what is the fluid exerting that 

 pressure. Lastly, as the absolute pressure exerted by a fluid is 

 directly as the height multiplied by its mean specific gravity, if 

 we multiply the difference of the heights of the barometer at the 

 two stations by the ratio of the mean specific gravity of the 

 equiponderant intercepted column of air to that of the mercury, 

 we shall have the vertical height of that column ; equal to the 

 difference of level of the base and summit of the object. 



Theheights (or volumes)of equal weights of dry air being reci- 

 procally as the pressures they sustain, and as every stratum of 

 the atmosphere supports the total pressure of those above it, it 

 has been demonstrated that when the altitudes above the lowest 

 station increase in arithmetical progression, the heights of the 

 mercury in the barometer decrease in geometrical progression. 

 Such being the case, it is evident that the difference of some 

 two consecutive terms of the geometrical series will be equal to, 

 or coincide with the difference of any two consecutive terms of 

 the arithmetical one ; and that where this equality of differences 

 takes place, the density of the air there will be equal to the mean 

 density of the whole. Or, supposing the density of the column 



the height in inches of the barometer (if of the syphon construction with branches of 

 equal diameter), without regard to the specific gravity of the mercury. 



It is almost superfluous to remark, tliat at ordinary temperatures the liqiud of the 

 liarometer should not generate elastic vapours, or the height will be observed in defect ; 

 the depression increasing (unequally) with the temperature. 



• See S ^, P- ♦^S. t See § 6, p. 435. 



