It traverses thirty-two atmospheres when it is very nearly setting. Bougier and Forbes have calculated that the extreme thickness of the
atmosphere, traversed by its light when the sun is on the horizon, is approximately 35½ atmospheres. The absorption shown by 32 atmospheres will therefore be very close to that which would be observed at sunset on an ordinary day, and it will be seen that practically all rays have been scattered from the light, except the red, and a little bit of the orange.
As to the luminosity of the sun at these different altitudes, we can easily find it by reducing the luminosity curve of the sun at some known altitude by the factors in the table just given, for as many wave-lengths as we please, and thus construct another curve. The area of the figure thus obtained would be a measure of the total luminosity on the same scale as the area of the luminosity curve from which it was derived.
The following are the approximate luminosities of the sun when the light shines
| through | 0 | atmospheres | 1 |
| " | 1 | " | ·840 |
| " | 2 | " | ·705 |
| " | 3 | " | ·594 |
| " | 4 | " | ·496 |
| " | 5 | " | ·417 |
| " | 6 | " | ·303 |
| " | 7 | " | ·256 |
| " | 8 | " | ·215 |
| " | 32 | " | ·002 |
It will thus be seen that the sun is 420 times less bright just at sunset than it is if it were to shine directly overhead, and about 350 times brighter than it is for a winter sun in a cloudless and mistless sky at twelve o'clock, for the altitude of the sun in our latitude is about 30° at that time, and corresponds with a thickness of two atmospheres, through which the sun has to shine. We all know that to look at the sun at any time near noon in a cloudless sky dazzles the eyes, but that near sunset it may be looked at with impunity. The reduction in luminosity explains this fact.
The distribution of the scattering particles in the atmosphere is very far from regular. As we ascend, the particles get more sparse, as is shown by the less scattering that takes place of the blue rays compared with the red. Thus at an altitude of some 8000 feet the mean coefficient of scattering is about ·0003, instead of ·0017, which it is at sea-level. It must be recollected that there is only about three-fourths of the air above us at 8000 feet, and it is less dense. There will therefore be a diminution of particles not only because there is less air, but because the air itself is less capable of keeping them in suspension. Up to 3000 or 4000 feet there is no very great marked difference in the scattering of light, as observations carried on during five years have shown; but above that the scattering rapidly diminishes, and at 20,000 feet it must be very small indeed, if the diminution increases as rapidly as has been found it does at the altitude of 8000 feet.
We must repeat once more that the blue of the sky is principally if not entirely due to the presence of these particles, the rays scattered by them, which are principally the blue rays, being reflected back from them, giving the sensation of blue which we know as sky-blue. The greater the number of these fine particles that are encountered by sunlight, the greater the scattering will be, and the bluer the sky. It is more than probable that the blue sky of Italy, so proverbial for being beautiful, is due to this cause, since from its geographical position the small particles of water must be very abundant there.
Carrying this argument further, we should expect that as we mount higher the blue would become more fully mixed with the darkness of space, and this Alpine travellers will tell you is the case. At heights of 12,000 feet or more, on a clear day, the sky seems almost black, and it is no uncommon thing to see this admirably rendered in photographs of Alpine scenery when taken at a height. Many of the late Mr. Donkin's photographs show this in great perfection, as also Signor Sella's.
Before quitting this subject we may call attention not only to the colour of the sun itself at sunset, but also to the colouring of the sky which accompanies the sun as it sinks. This colouring is often different to the colour that the sun itself assumes; but we can easily show that the effects so wonderfully beautiful are entirely dependent on this scattering of light by these small intervening particles in the air. We often see a ruddy sun, and perhaps nearly in the zenith, or even further away from the sun, clouds of a beautiful crimson hue, lying on a sky which appears almost pea-green, whilst nearer to the sun the sky is a brilliant orange, which artists imitate with cadmium yellow. Let us fix our attention first on the crimson cloud. The clouds of which the colouring is so gorgeous are often not 1000 feet above us, and were we to be at that altitude we should see the sun not quite so ruddy as we see it from the earth, and the cloud would consequently be illuminated by the sun with a more orange tint; but the light reflected from the cloud to our eyes has to pass through, say 1000 feet of dense atmosphere, and thus the total atmosphere that the light traverses in the latter case is always greater than the air thickness through which the direct light from the sun has to pass; hence more orange is cut off, and the light reflected from the cloud is redder. This red, however, will not account for the brilliant crimson and purples which we so often see. It has to be remembered that not sunlight alone illumines the cloud, but also the blue light of the sky. The feebler the intensity of the red, the more will the blue of the sky be felt in the mixture of light which reaches our eyes, and consequently we may have any tint ranging from crimson to purple, since red and blue make these hues, according to the proportions in which they are mixed.