1923. No. 10. DISTRIBUTION OF MATTER IN THE ATM'T^SPHERE. :^ 



Whatever may be the cause of the charged state, we must assume 

 the charge attached to the gas: Thus o may be regarded as a function 

 of o and the equation l5 al takes the form: 



1^-0 d o I \ d o\- /2 g g Q d o\ \ d o 2 g o A rr n 

 n d r^ d o\o d r) \r a a o d q) o d r a r o a 



Now we might always put: 



where a is a function of o. 



We know that in a great many cases the aurorae have the same colour 

 from the upper limit to the bottom edge. If the auroral region is electric- 

 ally charged, this would indicate that in this region a should be nearly a 

 constant quantity. We are thus led to consider the case that a is constant 

 down to a certain distance r« from the centre. 



Putting this distance equivalent to r« in equation (2), it follows that 

 above this distance the density should be determined b^- the the differential 

 equation : 



d- o ^ (d or 2 d o 2 o^ o 4 n a- o- 



—J — ^ -^ ^^ ^ = U (b) 



a r^ o \d r) r a r a r a 



Even under these simplified conditions the differential equation is a 

 rather complicated one. and up to the present I have not been able to 

 find the integral function. But at any rate we may find the variation of 

 o bv means of numerical intisrration. 



§2. 



Without entering further into the problem of sohHng the differential 

 equation, we can make some estimates as to the degree of ionisation and 

 the amount of electricity- which may be present in the higher strata of the 

 atmosphere, and draw some conclusions of importance with regard to the 

 state of the higher strata of the atmosphere. 



We know that the earth — in some way or other — maintains a 

 negative charge, and this charge will be compensated by positive electricity 

 in the atmosphere. This charging process must be continually going on, 

 and we might suppose that the positive electricity is formed by photo- 

 electrie action in the upper layer of the atmosphere. — At a certain height 

 the positive electric mass inside a sphere through the point just equals the 

 negative — and on this sphere the electric force will he zero. Below this 

 level the electric force is directed downwards, and only above it will there 

 be an upward directed electric force. 



