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



to different distances from the centre of the earth being dimi- 

 nished in the ratio of the square of those distances, its height 

 in the barometer, when counterpoising the same absolute pres- 

 sure, or such as would be indicated by a barometer at the level 

 of the sea, will be proportionally augmented. To comprehend 

 the nature of the correction (additive), we remark in the first 

 place, that as it is unnecessary to be acquainted with the speci- 

 fic gravity of the liquid of the barometers,* if alike in both, we 

 have merely to correct the observed height of the column of 

 mercury in either barometer in the inverse ratio of their specific 

 gravities. Further, as we may be suffered to express the ratio 

 of the diminution of the force of gravity at the several altitudes 

 above the level of the sea of 1, 2, 3, and 4 miles by the fractions 



12 3 4 



1978' 1978' 1978' ^"^ 1978' increasing uniformly with the altitude, 

 •and having equal differences, it is evident that whatever the 

 elevation of the lower barometer above the same levels the 

 observed height of the other, if situated a mile above it, must 



♦ This is sufficiently established by our previous demonstration that a certain number 

 of cubic feet of dry air will balance one of the liquid of the barometer, without regard to 

 its specific gravity, when the observed height is equal to a certain number of inches. 

 However, as Professor Robison asserts, in his Elements of Mechanical Philosophy, that 

 when the mercury of the barometers is not of the same specific gravity as that made use 

 of in the experiments of Sir G. Shuckburgh, calculations conformable to liis formula 

 cannot fail to be erroneous, we must so confirm our opposite statement on this important 

 subject as to leave no room for doubt. 



If we augment or diminish in the same ratio any two terms of a series of numbers in 

 geometrical progression, the differences of the corresponding terms of the arithmetical 

 will continue the same. It must, therefore, follow, that as the pressures are in geome- 

 trical, and the altitudes in arithmetical progression ; and as the heights of two columns 

 of mercury supporting the same atmospheric pressure will be constantly, during every 

 variation of the pressure, in the inverse ratio of their specific gravities, the altitudes as 

 computed from one and the same formula will be alike, without r^ard to the density of 

 die mercury. 



We have already found that when the pressures were 15-5 and 30*5 inches, the alti- 

 tude would be 17 660 feet. Supposing we had also observed the pressures with two 

 other barometers containing mercury of a density inferior in the ratio of 11 to 10, the 



1 1 -; Dill lo '3- 



heights would have been noted at 15-5 + — th, and 30-5 + -j^th, or at 17'05 and 



38*55 inches. The pressure corresponding to the mean density of the air, computed 

 precisely as before, will be found to be 24*3763 inches, and the altitude equal to 1 6-5 

 inches (the difference of the observed heights, or length of the column of mercury balanc- 



iDS that of the air) multiplied by -rr^rr-^ of 12,000 inches, or to 17,6^6 feet, the same 

 ^^ 24*37 63 , . . ,, , «. L» ?tji. 



as befiare. The pressure incumbent on the stratum of aie as indicated by the barometers 

 with the rarer liquid, would appear too great by one-tenth, and we mija^t have antici- 

 pated (the heights being reciprocally as the pressures) that the altitude Would be calcu- 

 lated proportionally in defect ; but as the length of the column of mereiiry counterpois- 

 ing the air (16-5 inches) is from its inferior specific gravity one-tenth greater than the 

 equiponderant column of mercury in the other barometers (15 inches), the two causes 

 of difference prove to be of an opposite tendency, and equal in value. 



An extremely useful alteration in the constructiim of the Englchcld barometer, 

 depending on this contested i>oint, will be proposed ^hcn \fc totnc to treat of tfie instru- 

 nient*. i -' , ' ' ■■»> ' '' •' ^- ' ' ' 



