918 PEOEESSOE BUjS^SEjST AND DE. H. E. EOSCOE’S PHOTO-CHEMICAL EESEAECHES. 
develope formula (16.) in a series of powers of cos we have 
Wi = «(a"-4-2a|3 cos cos" t) 
-i-5(c4^-J-3a"j3 cos i^-}- 3a|3" cos" cos" t) 
-]-c(a'*+4a"(3 cos cos" cos" ^+/3^ cos^ t). 
The integral J Wi(Z^ has now to be determined. For this purpose we consider 
ldt=t 
JcosM^=sin^ 
c 9 j. COS it sin ^ 
j cos" tdt= 2 
Jcos"M#= ^ 
J cos' tdt^ 1 hi COS Sin ^+f f. 
For the equinox a=0 and j3=cosj} ; if the action for the whole day is required, the 
integration must be taken from 
"”2 ^””^2 ’ 
for these limits we have— 
^dt =7r 
^coBtdt =2 
Jcos"M^ =y 
J cos" tdt =1 
Jcos'^<^^=f‘r; 
also 
Jw(^^=^«cos"_p-l-f5 cos"ji-l-|^ cos'yi, 
and 
W= 12 X 60 cos"^+^ ^ cos®^j-l-f G cos'^^ i 
on substitution of the values of a, 5, and c, 
W= — 11620 cos"_p+127600 cos"yi— 67140 cos'^. 
Calculated according to this formula, the following Table (XXI.) contains the total 
amount of sunlight, expressed in degrees of light, falling diuiiig the da}' at the 'sernal 
equinox upon the horizontal unit of area at the previously mentioned places. Dhision I. 
contains the names of the places for which the calculation has been made ; dhision II. 
the latitudes of these places ; division III. the chemical degrees of light to which the 
horizontal area is illuminated by sunshine alone ; dhision IV . the degrees of light, 
already given in Table XIII. h, to which the same area is illuminated by the total 
