39^ SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



a more general view of the equations (14) and (15) above given 

 and slightly alter them. 



We have indeed only to drop the index a that was introduced 

 to show that we are considering a definite portion of the earth or 

 atmosphere, and to add the horizontal line above in order to em- 

 phasize the fact that we are considering the boundary surface of 

 the atmosphere, thus transposing the equation into the following: 



q T = q r and q T - q T = u h - u h (17) 



but must always remember that in the present case, where Ave are 

 dealing with the whole earth, the difference il — tL which I will 

 designate by u t is always small in comparison with the quantities 

 q T and q T . 



Of course the equation (16) also holds good in this case after 

 corresponding modifications; therefore if we put 



and 



we must have 



\ ~ "*o = "r, and u h ~ u h = u r 2 



T l + T 2 — T 



U T . = - U, 



that is to say, if we divide the year into two arbitrary intervals 

 then the increase of the energy that the whole earth has gained in 

 one of these intervals is equal to the loss that it has experienced 

 in the other interval. 



If now we imagine the beginning of the year so chosen and the 

 division into intervals so devised that in one interval u is always 

 above and in the other always below the annual mean, then the 

 year falls into two halves that are in general unequal, one of which 

 Ave may call the Avarmer and the other the colder half respect- 

 ively. 



Since the insolation at different portions of the earth's surface 

 shoAvs remarkably great differences at all times of the year, being 

 indeed zero at some places and times, Avhereas the radiation out- 

 ward is always effective, and since, on the other hand, the total 

 energy of the Avhole earth is only subject to small periodic changes 

 within the year so that it £ is always small as compared with q and 

 q, therefore Ave can so subdivide the Avhole boundary of the atmos- 



