DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
64 
§ 25. The Heating Effects of the Upper Air Currents. 
In his second memoir (p. 185) Schuster remarked that a further consequence of 
the theory outlined for the magnetic variations would be the production of a sensible 
heating effect by the electric currents circulating in the low pressure conducting 
layer. This, it was suggested, might assist in the explanation of the isothermal 
layer of the atmosphere. The primary cause of the approximate constancy of 
temperature in the stratosphere is now well understood, and the suggested heating 
effect can have only a secondary influence on the phenomenon. For other reasons, 
however, it seems desirable to examine numerically this thermal consequence of the 
theory. The results prove to be of some interest, and may explain part of the 
difference between the solar and lunar diurnal magnetic variations. 
If the conductivity of the upper atmosphere is small during the night hours, the 
electric currents in question will flow entirely or mainly in the sunlit hemisphere. 
The heating effect is proportional to the square of the current, so that all the 
harmonics in the current function, whatever their period, contribute to the heating 
of this one hemisphere. As the earth revolves, the temperature of a given portion 
of the conducting layer will begin to increase at sunrise, and the increase will 
continue till the time of sunset. During the night hours cooling, mainly by 
radiation, must take place in order that the average state may remain steady. The 
conducting layer will thus suffer a diurnal change of temperature in which the 
24-hour term is of much greater magnitude than any sub-component. This 
variation, moreover, is purely solar diurnal, including even the part due to the 
currents which produce the lunar diurnal magnetic variations. The temperature 
variation will be confined mainly to the conducting layer so far as conduction and 
convection are concerned (the kinematic viscosity will be very high in regions of 
such low pressure). A corresponding variation of pressure and of motion, not confined 
to tire conducting layer, will result, and this may possibly account for the diurnal 
oscillation suggested by the magnetic variations. The phase should be constant 
throughout the year, though the amplitude would be expected to show a seasonal 
change. The most important question regarding these effects is that of their 
absolute magnitude, however, and we proceed to a rough numerical calculation with 
this in view. 
For simplicity the solar diurnal magnetic variations will alone be considered, 
though the lunar variations will slightly increase the heating effect, to a degree 
depending very little on lunar phase. 
The principal terms in the solar diurnal magnetic variation potential at the 
equinoxes (mean of 1905 and 1902) are as follows ( cf. Table F):— 
(84) 10°. ^ = — 38Qd cos (t + 33°) —5'0Q 3 2 cos (2t + 26°) —0‘39Q 4 3 cos (3£ + 40°). 
lb 
