260 
PROFESSOR FORBES ON THE EXTINCTION OF THE SOLAR RAYS 
91. A curve, nearly approaching to that of Curve XV., has been drawn through 
the points therein defined, which curve, as already stated, was drawn by the eye 
without reference to any theory whatever. Tangents were mechanically drawn to 
this curve, and the rate of loss for a given thickness was ascertained corresponding 
to equal increments of intensity, or for the parallels of 15, 20, 25, 30, 35, 40, and 45 
actinometric degrees. For convenience, the rate of loss was found corresponding to 
500 millimetres of mass of air in each case, and found to be 
l°-2 3°‘0 6°‘0 9°'5 12°'8 15°7 18°‘3, 
numbers nearly in arithmetical progression. 
92. The rate of loss in terms of the intensity is projected in Curve XVI., Plate 
XXIII., and an interpolating straight line has been passed through the points. Now, 
were the loss everywhere proportional to the intensity, which is the logarithmic law, 
the straight line would have cut the axis when the intensity = 0, whereas the rate of 
loss vanishes when the intensity = 14°‘3 nearly, which indicates the limit towards 
which the intensity is continually tending, below which it cannot fall, and which is 
consequently the position of the asymptote. The equation to this line is of the form 
x — av — b, 
where v is the intensity in actinometric degrees, and x being the rate of extinction for 
one millimetre of thickness, a = ‘001224, b = ‘0175032, whence the rate of extinction 
for 500 millimetres has been computed, in order to be compared with the graphical 
results (of which the possible errors, as in every case of drawing tangents, are very 
sensible). 
Rate of loss for 500 millimetres. 
Intensity. 
Observed. 
Calculation. 
Differences. 
o 
45 
18‘3 
1879 
+0-49 
40 
15*7 
1573 
+0‘03 
35 
12'8 
12‘67 
— 0‘13 
30 
9‘5 
9‘61 
+ 0‘11 
25 
6 0 
6‘55 
+0‘55 
20 
3‘0 
3‘49 
+ 0‘49 
15 
1*2 
0’42 
-078 
93. Assuming the form of this approximation to be satisfactory (with a slight mo- 
dification of the constants), we have for the value of the first differential coefficient 
of the equation to the Curve XV., 
dv , 
j — av — b 
dx 
, dv 
ax — — 7- 
av — b 
- ~log (av — b) + c 
-t'°s(^) + c • 
X = 
(b.) 
(c.) 
