This being substituted, we may have
Finally, these being substituted in the above value of z we get
The terms of this formula are generally reduced to tabular form for practical use.
Guyot’s formula which is derived from this, reducing meters to feet and the constants depending on temperature being changed to accord with Fahrenheit’s scale, is
The three terms after the first are the corrections. The first being that for the temperature at the two stations. The second is the correction for the force of gravity depending on the latitude.
The third contains, first the correction for action of gravity on the mercury column at the elevation z, and second a correction required for decrease in density of air owing to decrease in action of gravity at the greater elevation. The factor s being the approximate difference in altitude of the stations.