been taken. It need scarcely be said that the observations on three out of four days
have been incomplete owing to atmospheric conditions not remaining constant. Every
one of these has been tabulated, however, in the note books, and a check has thus
been introduced in estimating the relative intensities of the light at the same altitudes
of the sun above the horizon at the same observing station, for, in many instances,
two or three observations under favourable conditions were made, the remainder being
useless for the purpose of obtaining the coefficients of absorption.
Even the observations which are recorded are apparently so discordant, that it might appear difficult to arrange them in any order sufficient to get any empirical law which might connect barometric pressure with the exponential coefficient of transparency. As necessarily any approach to a law can only be an approximation, it has not been considered necessary to enter into any refinements such as the varying distance of the sun from the earth at different seasons, since any differences due to difference in atmospheric condition would more than hide any alteration due to that cause. On certain days remarks are made that the atmosphere is exceptionally clear, and when we group such days together the results are not devoid of regularity. Taking the observations at Faulhorn when the barometer was 21.5 inches, and when the day was noted as exceptionally fine, we get two values, 231 and 235 '. These are winter observations. We may take 233 as the mean exponential coefficient at this barometric height in the clearest weather.
We also have on similar days
| Bar. | μ1 | |
| At Derby | 29-6 | .437 |
| Above Zweilutchinen. | 26-6 | .356 |
| Grindelwala | 24.4 | .307 and 307 |
| 23:3 | .275 -273 | |
| Faulhorn | 21.5 | .231 -233 |
In addition to the observations given in the tables others were made at higher altitudes up to 12,000 feet at Zermatt on suitable days. It was not practicable to take a whole series of readings at these high altitudes, as it was not possible under ordinary circumstances to spend sufficient time at such elevations and that to get a difference in zenith distance sufficient to give a variation in air-thickness of such a magnitude as would give a reliable coefficient. As, however, the expeditions were made at such a time of the day as enabled a return to a station where the lapse of a few hours in the afternoon sufficed to obtained a large variation in the air-thickness, it became possible, by calculating first the coefficient of this station, and thence calculating the readings which would have been obtained at the time when the observations at the higher altitudes were made, to calculate the coefficient for the latter, assuming, of course, that no alteration in the general condition of the sky had taken
