BAROMETRICAL TABLES. XIX 



The standard value of gravity adopted is that prevailing at latitude 

 45° and sea level. The reduction, accordingly, consists of two parts — a 

 correction for altitude and a correction for latitude. The gravity correc- 

 tion for altitude is usually combined with the reduction of the barometer 

 to sea level ; the gravity correction for latitude, which is here given, is 

 commonly called simply the "gravity correction," or the "reduction to 

 standard gravity." 



If B^ and B^^ represent the barometric heights (corrected for tem- 

 perature) at latitudes <f> and 45°, and g^, g^^ the acceleration of gravity 

 at these latitudes, we have 



^« g'i- ' 



and the correction to the observed height will be 



^ <5 45 -^ 



If the earth be an ellipsoid of revolution composed of homogeneous 

 homofocal layers arranged according to any law of density, 



in which k is ? constant depending on the ellipticity of the earth ; and 

 the correction becomes 



C = — k cos 2 <^ B^. 



The value of k adopted here is that determined by Prof. Harkness,* 



k = 0.002662. 



The correction is the same numerically for (f> = 45" + « and <f> = 45° — a. 

 It is negative for latitudes below 45° and positive for latitudes above 45? 



TABLES 12, 13. 



Table 12 {^English measures) gives the correction in thousandths of 

 an inch for every degree of latitude and for each inch of barometric pres- 

 sure from 1 9 to 30 inches. 



Table 13 {Metric measures) gives the correction in hundredths of a 

 millimetre for each 20 millimetres barometric pressure from 520 to 770 mil- 

 limetres. 

 Example : 



Barometric reading (corrected for temperature) at Dodge 



City, latitude 37° 45', = 27.434 



Gravity correction for latitude from Table 12, = — 0.018 



Barometer reduced to latitude 45°, = 27.416 



*Wm. Harkness: The solar parallax and its related constants. Washington, 

 1891, 4°, pp. 169. 



