*270 
PROFESSOR FORBES ON THE EXTINCTION OF THE SOLAR RAYS 
109. If we compare the longest with the shortest columns on the 13th of August, 
we obtain in the notation of Art. 100., taking V = 1 , [u] — *6403, m — *000*2549. 
V in degrees of actinometer S. 1 . = 35°*22. 
And on the 14th of August, [V] = *5680, m = *0003232. 
V in degrees of actinometer S. 1. = d0°*87. 
110. These results are on the logarithmic hypothesis. If, however, we project the 
observations, as we have done those of the 25th of September, 1832, we find that 
they cannot be represented by a simple geometrical progression. An interpolating 
curve, which will satisfy them sufficiently well, is a logarithmic curve, whose asym- 
ptote is distant 7°‘25 actinometric degrees from the axis of x. The curve is repre- 
sented in Plate XXVI. Curve XXIII. The constants of the curve were derived by a 
graphical process, as in the former case, tangents having been first drawn to the 
empirical curve, whence the following velocities of extinction were deduced, which 
are compared with a formula of the same form as in Art. (93.), namely 
d v 7 
r~ ~ av — b. 
dx 
The values of a and b were deduced from the projection, Curve XXIV. in the same 
Plate, which gives 7°'25 for the intensity when the rate of extinction is zero ; and 
a — *00192 1 
b = *01396 J 
for l mm 
of thickness. 
Rate of loss for 500 millimetres. 
Intensity. 
Observed. 
Calculation. 
Difference. 
25 
16*5 
17-04 
+ 0*54 
20 
12*6 
12*24 
-0*36 
15 
8*0 
7’44 
— 0*56 
10 
2*3 
2*64 
+ 0*34 
Whence the following points of the curve have been computed from forms similar to 
those of Art. 96, ~ being here 7*25. 
Thickness, or x in millimetres of mercury. 
0 
500 
1000 
1500 
2000 
2500 
Intensity, or degrees of Actinometer S. I. 
70*74 + 7-25 = 77‘99 
25*51 + 7"25 = 32*76 
9*20 + 7‘25 = 16*45 
3*32 + 7’25 = 10*57 
1*20 -{- 7’25 = 8*45 
0*43 + 7’25 = 7’68 
111. Hence it appears that a general analogy holds with results of the 25th of Sep- 
tember 1832. It is even not improbable that the degrees of the two instruments do 
not greatly differ in value, and that the lower indications in 1841 are due solely to 
the greater opacity of the air, marked by the rapid decline of the curve, and (as 
might be anticipated) the lower value of the limiting or final intensity. 
