PEOFESSOE BUNSEN AND DE. H. E. EOSCOE’S PHOTO-CHEMICAL EESEAECHES. 901 
Table X. 
1 
1 Zenith- 
1 distance. 
! 'p- 
j-_ — 
Clieniical 
brightness 
in light- 
units. 
w. 
Zenith- 
distance. 
Chemical 
brightness 
in light- 
units. 
w. 
Zenith- 
distance. 
0. 
Chemical 
brightness 
in light- 
imits. 
w. 
Zenith- 
distance. 
<p. 
Chemical 
brightness 
in light- 
units. 
w. 
Zenith- 
distance 
<j>. 
Chemical 
brightness 
in light- 
units. 
w. 
Zenith- 
distance. 
<p. 
Chemical 
brightness 
in light- 
units. 
w. 
j 20 
1350-0 
O 
32 
1017*2 
O 
44 
775*1 
56 
565*7 
68 
371*5 
O 
80 
184-8 
21 
1315'0 
33 
994-9 
45 
756-8 
57 
549*0 
69 
355-8 
81 
170-4 
22 
1281-9 
34 
973-0 
46 
738-7 
58 
532-5 
70 
340*1 
82 
155*0 
23 
1250-6 
35 
951-7 
47 
720-8 
59 
515*9 
71 
324-3 
83 
139*7 
24 
1220-5 
36 
930-9 
48 
703-0 
60 
499-6 
72 
308-9 
84 
125-5 
25 
1192-0 
37 
910-4 
49 
685*3 
61 
483*5 
73 
293-4 
85 
110-3 
26 
1164-4 
38 
890-1 
50 
667-8 
62 
467*2 
74 
277*7 
86 
95-0 
27 
1 137*7 
39 
870-2 
51 
650-4 
63 
451-1 
75 
262-2 
87 
79*8 
28 
1112-2 
40 
850-6 
52 
633-4 
64 
435-1 
76 
246-6 
88 
64*6 
29 
1087*4 
41 
831-5 
53 
616-3 
65 
419-2 
77 
231-1 
89 
49-5 
30 
1063*4 
42 
812-5 
54 
599*2 
66 
403*3 
78 
216-7 
90 
34-4 
31 
1039*9 
43 
793-6 
55 
582*3 
67 
387*2 
79 
201*2 
The curve (fig. 9, Plate XLV.) shows how closely the actual observations approach 
the calculated values. The simple points about the curve represent the observations 
made on July 23, 1858; the small circles denote the experiments of August 5, 1858; 
and the crosses those of October 18, 1856. As these observations were made in ditferent 
years and at different times of the day and year, we may conclude from the near approach 
of the single points to the calculated curve, that in this case, as in that of the deter- 
mination of visible illumination, alterations in the humidity and temperature of the air 
have but a \eiy slight influence upon the dispersion of light in the atmosphere when 
free from clouds or mist; and that, therefore, the chemical actions effected at equal 
hour-angles on each side of the sun’s culminatiug point, may, without risk of appreciable 
eiTor, be taken as equal. 
After this investigation we may now pass to the determination of the chemical action 
which the whole \dsible heaven effects upon a horizontal unit area of earth’s surface at 
various zenith-distances of the sun. The numbers marked I in Table VIII. give the 
relation of the light falling on a unit of area from the whole sky, visually measured, to 
that falling from a given portion of zenith-sky, also measured visually. In Table X. 
we find the chemical actions produced by the same portion of zenith-sky. Now, as we 
have formerly shown that in light from the same source the chemical is proportional 
to the visual action, we have only to multiply together the numbers in each Table 
corresponding to the same zenith-distance, in order to have the required chemical action 
of the whole heavens. The action (w,) thus obtained can be expressed in a form adapted 
for calculation, as a function of the sun’s zenith-distance, according to the following 
formula, 
w,=a-f-Jcos ^+(?cos®ip-l-...., (8.) 
in which the fourth term can be neglected. The values of the coefficients a, h, and o 
have been calculated, according to the method of the least squares, from the following 
eight values of <p and Wj : — 
MDCCCLIX. c r 
