26(5 TABLES FOR REDUCING BAROMETRICAL OBSERVATION. 



must thus be diminished by the amount of that, of the scale, that is, by nearly y 1 ^, 

 this being the proportion between the expansion of brass and that of mercury. 



It is also the expansion of the scale which causes an apparent anomaly in the 

 Tables for the Reduction of the English and Old French Barometers. It can be 

 seen, that, though the observations are to be reduced to the freezing point, or tn 

 32 Fahrenheit and zero Reaumur, the Tables give still a correction for observa- 

 tions taken at that temperature. The reason of it is, that the normal length of the 

 English and Old French standards has not been determined at the temperature of the 

 freezing point, as is the case with the metre, but respectively at the temperatures 

 of 62 Fahrenheit and 13 Reaumur. It is thus only at these temperatures that the 

 scales graduated with these standards have their true length. Above and below, the 

 inches of the scales are longer or shorter than the inches of the standards. At the 

 freezing point, therefore, the correction for the expansion of the mercury is null, but 

 that for the expansion of the scale is not. The scale being too short, the reading 

 will be too high, and a subtractive correction must still be applied, which will be 

 gradually compensated at lower temperatures by the now additive correction of the 

 mercurial column. Thus the point of no correction will occur at 28. 5 Fahrenheit, 

 instead of 32, in the English Barometer, and at 1.5 Reaumur, instead of zero, 

 in the Old French. 



Schumacher has calculated and published in his Collection of Tables, &c., and in 

 his Jahrlmch for 1836, 1837, and 1838, extensive tables for the reduction of the Eng- 

 lish, Old French, and Metrical Barometers, using the following general formula : 

 Let h = observed height. 



" t = temperature of the attached thermometer. 



" T = temperature to which the observed height is to be reduced. 



" 77i = expansion, in volume, of mercury. 



" I = linear expansion of brass. 



44 # = normal temperature of the standard scale. 

 The reduction to the freezing point will be given by the formula, 



h m(t-T)-l(f S) 

 l+m(t-T) 



The following tables, which may be found more convenient for ordinary use, have 

 been calculated from the same formula. Table XVII., published in the Instructions 

 of the Royal Society of London, is mostly abstracted from the table of Schumacher. 

 It gives the reduction of the English Barometer, adopting the following values : 

 Let h == observed height in English inches. 



" t temperature of attached thermometer in degrees of Fahrenheit. 

 " m = expansion, in volume, of mercury for one degree Fahrenheit = 0.0001001. 

 u I = linear expansion of brass for one degree Fahrenheit = 0.0000104344. 

 The normal temperature of standard being = 62. 

 The reduction to 32 Fahrenheit will be given then by the formula, 

 H h . _(*-32)-i(-(8) . 



The elements for the other tables are found at the head of each. 

 C 62 



