94 Proceedings of the Royal Society of Edinburgh. [Sess. 
To determine yu 2 , the term ix 2 bc 0 , which has the same value for points 
of the same curve, must be eliminated from (IV). Therefore deduct from 
each equation (IV) belonging to a month the mean of its three equations 
appertaining to the zenith distances of 90°, 85°, 80°, and then proceed as 
for D r 
The values of /*, and /m. 2 are compiled below. The agreement between 
the two columns is so good that I assume their mean values, /jl, for both. 
y-i 
^2 
A 
January . 
2-30 
1-91 
2-10 
February . 
1*67 
1-58 
163 
March 
1*31 
1-34 
1-33 
April 
1-00 
1-09 
1*04 
May 
0*89 
091 
0-90 
June 
0-88 
0*87 
0-88 
July 
1*01 
0-96 
0-98 
August . 
1*11 
103 
107 
September 
1*11 
1*14 
1-12 
October . 
1'27 
1-28 
1-28 
November 
1-63 
1-63 
1-63 
December 
2-07 
1-94 
2-00 
The factors may be determined in the same way from the corresponding 
quantities for f orf. I find that in every case they differ less than five 
per cent, from the values in the table. 
I now calculate juD-fr) . . . for each month. The means of these 
monthly values are printed in section 7 in the first three columns. In 
formula (I*) the factor jul may be combined with the quantities E, F, G, 
which depend on the solar intensity. It thus appears that only part of 
the solar radiation, and not the same parts in the several months, has been 
effective. This may be explained by the variability, from month to month, 
of the average cloudiness in that region of the sky where the sun stands. 
Let c be the fraction of the sky that is clouded over, and / a constant 
during the year, then c = 1 —fl/u* In Glasgow direct observation gives the 
value 0’7 to the average cloudiness, which nearly belongs to unit value 
of /a. Hence /= 0*3, to which belongs an average cloudiness of 0‘86 in 
January, and of 0*65 in June, according to the values of p. in the 
table above. 
(6) n and the Coefficient of Transmission in the Atmosphere . — I 
employ formula (III) for the determination of n, and obtain the value 
by trial and error. I choose successively the values n = 0T0, 0T5, 0T6, 
0T7, 020, 0*25, and calculate the numerical values of G from formulae 
(5), (6), (7). Two of the unknowns, a and g, are determined in each case 
