18*25.] Barometrical Mtasuremeni of He'ig/Us. 9)i 



tiplied by their mean densities,* it follows that the heights of 

 two barometers sustaining the san)e atmospheric pressure, but 

 exposed to different temperatures, will not coincide; the column 

 of the one having the inferior temperature being shorter than 

 the other in proportion to the increase of density. The observed 

 heights will, therefore, require to be reduced to their value at 

 32° F. or simply, as the specific gravity of the mercury, if the 

 same in both instruments does not affect the calculation, the 

 length of the one column must be reduced to its height at the 

 temperature of the other. But this reduction, as it supposes 

 the scale of inches, generally of brass, to be unaffected by change 

 of temperature, is of course overrated ; were the linear dilatation 

 of the scale equal to that of mercury in volume, the heights of 

 the barometer would not in fact require a correction for differ- 

 ence of temperature. The fraction expressing the reduction 

 must consequently be equal to the expansion of mercury mhms 



that of brasSjOrtoryjTg per degree from 32° F.f if 



To construct a table enabling us to correct the altitude com* 

 puted from the observed pressures, we have but to find as a basis 

 the value in feet of the correction for a difference of temperature 

 of the barometers equal to one degree, the air being at 32°. 

 Whatever the heights of the columns, provided we reduce them 



all in the same ratio, or of (jy^ + jyj^ of 11153 =)YiTEi'i^^^ 

 heights of the columns of air at 32° F. balancing the minute 

 columns of mercury intercepted by the observed and corrected 

 heights will be sensibly equal. The 1000th part of 30 inches is 

 0-030 in. and the same proportion of 15 inches is but half the 

 quantity, yet as the former supports double the pressure of the 

 latter, its density is greater in the same ratio, and the heights, 

 inversely as the densities, are alike. Under a pressure of 

 26-208 inches, one vertical foot of air at 32° F. half saturated 



f|'lt,ij qttitt sjippriiHjup. ^o. jgewjaTki^.tlj^j^^e, i^warfased. diameter; of A^, ^lu^rajt j|^ 

 mercury from the dilatation of the glass of the tubes does not interfere with the equtK- 

 brium of pressure of the atmosphere and the mercury, and must not be regarded. - 



, ^ Expansion of mercury (in volume) 1 : I '000 100 10 



.f ^ Ditto brass (linear). ....l....'l : 1*00001044 > 



r^ee a valuable paper on the Expansion of INfetals^ "feci'by the (now) t^re'sidient hVxxst 

 ^ondou Astronomical Society, inserted in the second voltime of their Memoirsf^or ',; 



Ij: RuU To reduce the observed height to its length at 32° F. multiply it by the 



number of degrees of the^ attached thermometers above 32°, and divide ]the product by 

 1 1 1 5? ipjus the multiplier. The temperature being below the freezing point, multiply 

 by the number of degrees below 32°, and divide the product by 1 1 153 Mnus the mul- 

 tiplier. 



■■'•^•For tln^ stationary barometer, generally above 38° in these climates, we might apply 

 nvonstant divisor that would caitse the least errors between 32° and 82°. It wouldc^ 

 course exceed the ai^ithmetical mean of 111 33 and 11 203, the divisors at tliose tempCT- 

 atures, " -TT-T ' *'""^'^^ ''^' 'f- '>'^^'" *-'^'''-''' "t^J^-'^ro'r.AD ad.t ri^fmrt^I-: ..*rvU'~\ iwite 



