in the Air upon the Temperature of the Ground* 253 



vertical rays). Then the vertical rays from the earth traverse 

 the quantities K = l and W = l; rays that escape under an 

 angle of 30° with the horizon (air-mass = 2) traverse the 

 quantities K = 2, 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 Earttis rays. 



H 2 



(C0 2 



0-3. 



0-5. 



1. 



2. 



3. 



0-67 



1-69 



1-68 



1-64 



1-57 



1-53 



1 



1-66 



1-65 



1-61 



1-55 



1-51 



1-5 



1-62 



1-61 



1-57 



1-51 



1-47 



2 



1-58 



1-57 



1-52 



1-46 



1-43 



2-5 



1-56 



1-54 



1-50 



1-45 



1-41 



3 



1-52 



1-51 



1-47 



1-44 



1-40 



3-5 



1-48 



1-48 



1-45 



1-42 





If the absorption of the atmosphere approaches zero, this 

 number approaches the value 2. 



Phil. Mag. S. 5. Vol. 41. No, 251. April 1896. 



