Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/18

vertical rays). Then the vertical rays from the earth traverse the quantities ${\text{K}}=1$ and ${\text{W}}=1$; rays that escape under an angle of 30° with the horizon (air-mass $=2$) traverse the quantities ${\text{K}}=2$, ${\text{W}}=2$ and so forth. The different rays that emanate from a point of the earth's surface suffer, therefore, a different absorption – the greater, the more the path of the ray declines from the vertical line. It may then be asked how long a path must the total radiation make, that the absorbed fraction of it is the same as the absorbed fraction of the total mass of rays that emanate to space in different directions. For the emitted rays we will suppose that the cosine law of Lambert holds good. With the aid of Table III. we may calculate the absorbed fraction of any ray, and then sum up the total absorbed heat and determine how great a fraction it is of the total radiation. In this way we find for our example the path (air-mass) 1.61. In other words, the total absorbed part of the whole radiation is just as great as if the total radiation traversed the quantities 1.61 of aqueous vapour and of carbonic acid. This number depends upon the composition of the atmosphere, so that it becomes less the greater the quantity of aqueous vapour and carbonic acid in the air. In the following table (IV.) we find this number for different quantities of both gases.

Table IV. – Mean path of the Earth's rays.

H2O→ ↓CO2.	0.3.	0.5.	1.	2.	3.
0.67	1.69	1.68	1.64	1.57	1.53
1.00	1.66	1.65	1.61	1.55	1.51
1.50	1.62	1.61	1.57	1.51	1.47
2.00	1.58	1.57	1.52	1.46	1.43
2.50	1.56	1.54	1.50	1.45	1.41
3.00	1.52	1.51	1.47	1.40	1.43
3.50	1.48	1.48	1.45	1.42

If the absorption of the atmosphere approaches zero, this number approaches the value 2.