86 Prof. 8. P. Langley on a Possible 
that a single computation of the solar constant takes about 
one week. 
‘It is of course the third branch of the inquiry, namely, 
the calculation of total atmospheric absorption from the 
bolometric measures, which offers the chief and perhaps 
insurmountable uncertainty. The measures on the extinction 
of homogeneous rays are assumed to be expressed by a 
logarithmic formula as follows :— 
log d=m log a+ constant, 
in which d is the ordinate of the bolographic energy-curve 
corrected for instrumental absorption, m the air-mass (pro- 
portional to the secant of the zenith distance of the sun for 
moderate inclinations), and a the assumed transmission of 
the atmosphere for vertical incidence. If a@ is constant 
during the period of observation, the expression is in the 
form of the equation of a straight line, the tangent of whose 
inclination is log a. Accordingly the measures of a single 
day, for separate wave-lengths, are plotted (Pl. I.) * with 
log d as ordinates, and mas abscissee, and from these plots 
the values of a are determined. The logarithmic formula is 
itself immediately derived from the exponential formula of 
Bouguer ; which for constant barometric pressure and homo- 
geneous rays may be written :— 
eé= éya”, 
where ¢ is the energy of the ray observed at the earth’s 
surface, é) its energy outside the atmosphere. Since d, the 
corresponding ordinate of the bolographic curve, is propor- 
tional to the energy of the ray, we may write 
dl 
Pm 
where d, is the ordinate of the bolographic curve corrected 
for atmospheric transmission. 
Thus, assuming that we know a, and knowing m, we may 
immediately determine corrected ordinates representing the 
bolographic curve outside the atmosphere. The total area 
under such a curve is proportional to the total energy of all 
wave-lengths, so that the ratio of the area of the curve out- 
side the atmosphere to the area of the curve at the earth’s 
surface is the correcting factor to be applied to the solar 
radiation as observed at the surface of the earth, to give the 
value of solar radiation outside the atmosphere. 
As remarked by the writer at page 147 of the Report of 
* The plots here shown are borrowed from the “Smithsonian Mis- 
cellaneous Collections.” 
d=, Or, te od, 
0 
