PEOFESSOE BUNSEN AND DE. H. E. EOSCOE’S PHOTO-CHEMICAL EESEAECHES. 917 
the afternoon the calculated is about thirty minutes earlier than the observed point. 
Ihese differences are, however, satisfactorily explained by the fact, that, in the situation 
at which the observations were made, the horizon towards north, west, and east is not 
free, owing to the hills of the Neckar Valley which rise 12° above the horizon, in con- 
sequence of which a deviation in the direction observed must occur. 
We pass now to the consideration of the total chemical effect which the direct sun- 
light, varying with the time of day, produces on a unit of area lying in the plane of the 
horizon during a given time. 
As has been already shown, the formula 
0-4758 P 
Wj— COS ^ X 318’3 X 10 (15.) 
gives the chemical effect ( W j) which the sun’s rays exert on a horizontal unit of surface 
in the space of one minute. For the further calculation, it is, however, simpler to 
express W, by a series of powers of the sun’s zenith-distance, 
Wi = 0! COS^ COS'^ (p-\-C. cos'* • 
By help of formula (15.) we have calculated the value of Wj for every 10° of zenith- 
distance between 0° and 90°, and then by the method of least squares found the values 
of the coefficients a, h, and c. The calculation gives 
Wi=-31-99cos" 417-6 cos=*<p-248-7cos^?5 (16.) 
The accompanying numbers show that the differences between the values of Wj, cal- 
culated according to the two formulae (15.) and (16.), are so inconsiderable, as to fall 
within the unavoidable errors of observation. 
According to 
formula ] 5. 
According to 
formula 16. 
138*4 
o 
0 
136*9 
134*6 
10 
133*8 
123*3 
20 
124*3 
105*4 
30 
107*3 
82*2 
40 
83*3 
56*0 
50 
65*2 
30*1 
60 
29*6 
9*5 
70 
9*6 
0*5 
80 
1*0 
CO 
90 
0*0 
We will now calculate the amount of the chemical rays which fall during a given 
time and at a given situation upon a unit of surface in the plane of the horizon. 
The sun s zenith-distance is connected with the true solar time of a place by the 
equation 
cos (p—cos h cosp cos ^-j-sin ^ sin^, 
when ^ represents the sun’s declination, p the latitude of the place, and t the sun’s hour- 
angle. If, for the sake of shortness, we call sinSsin^=a, and cos§cos^=/3, and 
MDCCCLIX. g J1 
