IN PASSING THROUGH THE ATMOSPHERE. 
261 
Whence, if the rate of loss 
d v 
di v 
be projected in terms of the thickness, as in Curve 
XVII., it ought to give the logarithmic curve, which it evidently approaches nearly. 
94. When x — 0, let v — V the intensity in actinometric degrees exterior to the 
atmosphere. 
(d.) 
When av — b, or v — — , x = oo,— is therefore the distance from the horizontal axis 
to the asymptote. 
95. Dividing both numerator and denominator in equation ( d .) by a , it becomes 
, v-i 
* = T lo s — b> 
V 
a 
which is the equation to a logarithmic curve whose general ordinate is v — — instead 
of v . This, therefore, is the form of the curve of extinction in Curve XV. 
96. For calculation, (the logarithms being hyperbolic, and s denoting the base of 
that system) by equation {d.), 
2X 
a\ — b 
av — b 
(/) 
and any corresponding ordinates v and x being given, as well as the values of a and 
b , we may deduce the initial value or V in the following terms : — 
V = ~ {b + (av -b)^} ; (g.) 
and taking Tabular Logarithms, 
log - ( V ~ 4) = lo 2 ( w “ + a x lo ^ 2 ( A 0 
97. In the construction of the Curve XV., constants a little different from those 
above found have been used as expressing the mass of the observations rather better. 
The value of-^- instead of 14 0, 3 has been assumed at 15°*2. A line is drawn parallel 
to the axis of x at that distance, and a logarithmic curve constructed upon it, with 
the value of m in equation (1.) Art. 7? which is the same as a log s of equation ( h ), 
equal to 
•00050708. 
The following ordinates have been thence computed. 
Thickness, or x in millimetres of mercury. Intensity, or v in degrees of Actinometer B. 2. 
0 
57°86 
+ 
15° 2 
= 7 3° 06 
500 
32-3 
+ 
15-2 
= 47-5 
1000 
18-0 
+ 
152 
= 33-2 
1500 
10-3 
+ 
15-2 
= 255 
2000 
56 
+ 
15-2 
= 20-8 
