400 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



Hence the equations of the neutral lines for any given moment 

 of the year take the form 



(+ p, X, t) = and ¥ (- /?, X, f) - 



where for definite values of / the one or the other of these equations 

 becomes useless since the line to which it refers vanishes entirely. 

 If the surface of the earth were perfectly homogenous and the 

 earth's orbit circular the following equation between the functions 

 <f> and <p would hold good 



0(-/U, 0-# 





that is to say, under this assumption the neutral line on either hemi- 

 sphere would at any given moment have exactly the same location 

 that it would occupy on the other hemisphere a half-year earlier 

 or later. Also each hemisphere would belong to its region of excess 

 of insolation for exactly the same intervals of time as the other. 



Now an interchange of heat by convection takes place between 

 the region of excess of insolation and that of excess of radiation 

 just as in the annual average. 



But the equations for this convection current are much more 

 complex for short intervals of time than for the annual average, 

 since in this latter case all quantities that refer to the storage of 

 energy fall out, whereas for shorter intervals they play an important 

 role. 



In order to understand this we do best to subdivide the energy 

 u £ in equation (18) into two portions u and u p , one of which relates 

 to the insolation region and the other to the radiation region. 



Thus that equation takes the form 



% ~ % ~ n a =<7 P - % + u t 



(19) 



where the left-hand side of the equation represents the remnant of 

 heat that remains after subtracting the radiated heat and the 

 stored-up heat from the heat received by insolation in the insolation 

 region. 



Evidently this remnant must flow as a convection current to the 

 radiation region. 



The average [thermal] intensity of this current is 



J a 



% ~ <?a 



(20) 



