2 
CAPTAIN W. DE W. ABNEY ON THE TRANSMISSION 
to criticism—one being, that if it were absolutely applicable, the light of the sky should 
probably exhibit greater polarisation in a direction perpendicular to the sun’s rays than 
it does. There is reason for believing, however, that the higher the station at which 
such observations are made the more complete is the polarisation. In any case, before 
this can be considered a valid objection, we have to know more than we do at present 
regarding the condition of the light reflected back from the earth and from the particles 
themselves. 
It must also be admitted that grosser particles exist on some days, and that for 
these the loss of light must be in the form of I' = le"'^^. They would prevent a 
certain portion of the total light from reaching the observer, whilst the smaller one 
would selectively reflect, and hence the law would not hold absolutely good, but the 
small number of gross particles, compared with the fine ones, would not appreciably 
alter the formula used except the coefficient k. 
Another objection which has been advanced by Mr. S. P. Langley in a private 
letter against the adoption of the formula is, that if the spectrum were observed with 
a large dispersion, it will be seen that as the altitude of the sun diminishes the atmo¬ 
spheric lines increase in intensity, and that these must obey the laws of ordinary 
absorption. This is an objection which at first sight may seem fatal, not to the 
correctness of the observations, but' to the adoption of the law above quoted; but it 
must be remembered that these special absorptions occupy a very limited area com¬ 
pared with the rest of the spectrum, and that they would practically disappear when 
the whole loss of light is under consideration, more especially as they would themselves 
obey the ordinary law of absorption. At any rate, the formula adopted appears to 
suit the case, and it must be borne in mind, that the results obtained by the inte¬ 
gration of the spectrum luminosities bear out the formula which has been universally 
adopted by astronomers as representing the corrections to be made in star magnitudes 
when the stars are observed at different altitudes above the horizon. 
XXIV.— The Integration of the Sjjectrum Luminosities at different Solar Altitudes 
equivalent to the Luminosity of Monochromatic Light at the same Altitudes. 
In Section XVIII. of the paper of which this is a continuation it was shown that 
the areas of the curves obtained from the formula I' = being capable of being 
represented by I' = Ie~'^-^ an important deduction could be made. 
For the area of the curve is e""" {ad'^' -f- -j- cd""'" -f- &c.). a, h, c, &c., being the 
original luminosities of the different rays, must then be represented by I = 
where A is some one ray, that is p, = kA~^ or - = A"'^ ; - is a constant and was 
K K 
found from the observations to be 105 (on the scale used for A“^), which is equivalent 
to X 5770, or a ray near the place of maximum luminosity. Hence the visual 
observations of total sunlight at different zenith distances are equivalent to observing 
the alteration in intensity of one single ray of that wave length in its spectrum,* and, 
* This, of coni’se, is only true within certain limits, bat it holds for any thickness of atmosphei’e 
through which observations were taken. 
