DEPARTMENT OF TERRESTRIAL MAGNETISM. 329 



The above theory was worked out on the assumption that the problem may 

 be treated as equivalent to that of two infinite, oppositely charged plates 

 separated by a large distance. The lower charged plate is the surface of the 

 Earth, and the upper plate may be represented by the highly conductive layers 

 which possibly exist in the higher regions of the atmosphere. Though the 

 case where the plates are near together is of no particular cosmical interest, it 

 is important to notice that the above conclusions would not hold in this case. 

 It turns out, for instance, that if the plates were only 14 centimeters apart, 

 and the potential gradient midway between them were 100 volts per meter, 

 the potential gradient at one of the plates would be about 1.0026 times the 

 value midway between them, instead of 2.76 times that value, as in the case 

 where the plates are very far apart. Again, the variations of rii and Ui with 

 the distance from one of the plates follow different laws to those which hold 

 when the distance is very great. 



The measurement of atmospheric conductivity, together with certain remarks on the theory 

 of radioactive measurements. W. F. G. Swann.Terr. Mag., voL 19, pp. 23-37 (1914). 



The theory of the method of measuring atmospheric conductivity by noting 

 the alteration of potential of a charged stretched wire surrounded by an 

 earthed net is examined from a mathematical standpoint. The paths of the 

 ions coming to the wire are calculated, and it is shown that, for a net of the 

 size usually employed under ordinary conditions of wind velocity, a practically 

 true value of the conductivity would be obtained if there were no potential 

 gradient. The effect of the potential gradient is to cause a negative charge 

 to appear on the earthed net, however, and in the determination of the con- 

 ductivity due to the negative ions the charge on the net widens out the paths 

 of the ions, reducing the number which would otherwise enter the net, and 

 reducing consequently the conductivity. The effect becomes most pronounced 

 for small wind velocities. For a case where the component of the wind 

 velocity resolved perpendicular to the wire is as small as 20 cm. per second, 

 and the potential gradient is as high as 260 volts per meter, the measured 

 value of the conductivity would be only about 0.65 of the true value for a 

 potential difference of 200 volts between the wire and netting. 



In the second portion of the paper, the theory of the collection of active 

 material by a charged wire is considered, when the wire is exposed in the 

 atmosphere, and formulae are deduced relating the activity as measured for 

 the wire with the amount of active material per cubic centimeter of air. The 

 effect of that portion of the charge on the wire resulting from the potential 

 gradient is discussed, and it is shown that unless suitable precautions are taken 

 to allow for it, the results may be greatly in error. 



The theory of electrical dispersion into the free atmosphere, with a discussion of the theory 

 of the Gerdien conductivity apparatus, and of the theory of the collection of radio- 

 active deposits by a charged conductor. W. F. G. Swann. Terr. Mag., vol. 19, pp. 

 81-92 (1914). 



If a sphere charged with Q units of electricity is exposed to a stream of air 

 moving with uniform velocity over a cross-section, and if n is the number of 

 ions per cubic centimeter of opposite sign to Q, in the air, v the specific velocity 



of the ions, and e the electronic charge, Riecke has shown that , = 4 irQnev. 



The formula has been shown to hold also in the case of an infinitely long wire 

 charged with uniform surface density. In the present paper it is also shown 

 that the formula is quite general, and applies to a conductor of any shape, 

 even when the conductor is not the only charged body in the neighborhood, 

 provided that a certain condition, not of a very restrictive character, is satisfied. 

 The formula is, moreover, true when the air velocity varies over a cross-section. 



