25 
Also Am is the modulus of the atmospheric curve. The area on Aa is ob- 
tained by multiplying Am by Aa. Also the height of the column of 
homogeneous air multiplied by the density at A (that is Aa) represents the 
whole pressure at A. Thus — 
Am x Aa = whole pressure, or area. 
Height of homogeneous air x Aa _ same. 
. * . height of homogeneous atmosphere = Am = modulus. 
Sp. gr. of air : sp. gr. of Mercury : : 30 in. : height, &c. 
1 : 11121 : : 30 in. : 27863 ft. 
To transfer the atmospheric logarithms into the common logarithms 
divide the modulus of one by the modulus of the other. Thus — 
.US = 64020 
. • . 64020 (log. d i at A — log. d 3 at C) is the height of AC, 
substituting h & K for & c? g 
AC = 64020 (log. h — log. 
In practice it is convenient to reduce the constant 64020, so that it may 
correspond with a temperature of 32° instead of 55°. For this purpose 
deduct i for each degree. Then 64020 — ^ x 23 = 60637. 
435 ° 435 
Rainond gives ~ for each degree in the Pyrenees. Other authors use 
the fraction • 
450 
The specific gravity is taken by some at 55°, by others at 60° ; also the 
constant is reduced in some cases to 32°, and in other to 28°. Hence , 
arise discrepancies in the formulae. 
The modes of calculating heights as given by three authors, I have 
adjusted by using feet and Farenheit's scale, for fathoms and the centi- 
grade, and by some other changes, so as to present them in the same form., 
and thus to facilitate their comparison. 
The first correction, n, is of the upper barometric column h\ by assum- 
ing the expansion of the mercury, minus that of the scale, to be 
or ToJoo tfte commn f° r eacn degree of temperature. Glaisher's 
tables give jj-^ as nearer the truth ; n is positive or negative according 
as a is greater or less than a\ 
It will be noticed that the constants differ, as well as the corrections for 
temperature. This correction is required by the varying height of the 
uniform atmospheric column, according to temperature, that is, the length 
of Am on the diagram. The next correction is for the difference of 
gravity and centrifugal force in different latitudes. In the second formula 
this is simplified by taking advantage of the corresponding diminution of 
mean temperature and x = mmn te ™P->— s 2 m This correction is unimportant, 
and is omitted in the third formula. It will be seen that each author has 
so adjusted the corrections, that the corrected constants are very nearly 
alike, 
