IN PASSING THROUGH THE ATMOSPHERE. 
251 
Section V. — Analysis of the Observations of the 25th of September, 1832. 
63. Looking first to the differential observations, or the comparative results of those 
at the two stations, we observe with respect to the solar intensities at Brientz and 
the Faulhorn as contained in Table E, and as projected in Plate XXL, — 1st, that the 
intensity at the higher station always exceeded that at the lower by a very appreciable 
quantity, varying from nearly ten to nearly two degrees of the actinometer B. 2 ; 
2nd, that this loss, compared to the intensity at the higher station, varied from 
or xjth of the total amount, to above i^yth or one-fourth of the total amount ; 3rd, 
that this relative loss appears to have varied rather irregularly, having two maxima 
nearly equal at 1 1 a.m. and \\ p.m. 
64. If (without inquiring for the moment into the cause and measure of this varia- 
tion of elfect) we simply seek to deduce a mean value for the opacity of the atmo- 
sphere for the entire day of the 25th of September, 1832, we may do so in the follow- 
ing manner : — 
65. Let the intensity of the sun’s rays at the upper station be denoted by 1, and 
let its varying value be v : then let x measure the mass of air traversed, measured by 
an equiponderant column in millimetres of mercury ; further, let m be a constant. 
On the hypothesis of uniform opacity, 
1 
A. 
II 
e 
0-) 
dv 7 
= m dx 
V 
log — m x 
o v 
(2A 
Any number of such observations being made giving corresponding values of v and 
x, by summation 
2 log = m 2 x ; 
whence 
m — 
21°g| 
2 * 5 
(3.) 
where m maybe a constant adapted to the tabular instead of hyperbolic logarithms. 
66. If the measure of opacity sought (which is that to which we shall generally 
refer) be the residual intensity of the sun’s rays, after passing vertically through a 
mass of air which balances 760 millimetres of mercury, and if this residual intensity 
be \y~], we shall have by (2.) 
2 log — 
= x ” 60 
67- If we wish to find the mean condition of the air traversed relatively to con- 
tained moisture, we evidently must not take the mean hygrometric result, but consi- 
2 k 2 
