DEPARTMENT OF TERRESTRIAL MAGNETISM. 277 



t rating radiation, and h the average distance which a corpuscle travels from 

 its point of origin, the corpuscular current density will be 



. qeh 



The average value of the air-eai'th current-density as obtained from several 

 stations is 6.7 X 10"'^ e. s. u. per square centimeter, so that if q be taken as 3, 

 which is about equal to the number of pairs of ions produced per cubic centi- 

 meter per second in a closed vessel as a result of the part of the penetrating 

 radiation in question, the value of h necessary to account for the above mean 

 current-density is 9 meters. This value is quite within the range of possibility, 

 .-^ince Eve has observed /3-rays, from radioactive substances, with a range of 

 7 meters. 



The corpuscular current-density, and consequently the conduction current- 

 density, will not necessarily be independent of the altitude, for the factors 

 upon which i depends, viz, the intensity and quality of the penetrating radia- 

 tion, the number of molecules per cubic centimeter available for possible 

 ionization by the radiation and the range of the corpuscles set free all change 

 with the altitude. 



Perhaps the principal difficulty confronting the above is the following: It 

 may be argued that, while there is no primary objection to assuming that cor- 

 ])uscles may be ejected from the molecules of air with a speed sufficient to 

 give them a range of 9 meters, nevertheless, if we do assume this, are we not 

 forced to expect that, during the process of their absorption by the atmosphere, 

 these corpuscles will produce many more ions? In this case, the 3 ions pro- 

 duced per cubic centimeter per second as an apparent result of the penetrating 

 radiation are really to be considered as the net outcome of a very much smaller 

 number of corpuscles originally set free by the penetrating radiation directly. 

 Quite apart from the matter of the Earth's electric charge, if we do assume that 

 each of the corpuscles originally emitted by the penetrating radiation is capa- 

 ble of producing a large number of ions, the meaning to be attached to the 

 ionization as measured in a closed vessel assumes a very indefinite form, as 

 a httle consideration will show. Yet, theory practically forces us to the con- 

 clusion that corpuscles emitted by a radiation as penetrating as the penetrating 

 radiation coming from above are emitted with speeds comparable %vith the 

 smftest jS-rays of radioactive substances. 



Experiment shows that the number of ions produced per centimeter of path 

 diminishes with increase of velocity of the corpuscle, and attains a value of 

 about 40 ions per centimeter for velocities comparable with that of light. A 

 vital feature of this diminution of ionization is the fact that as the velocity of 

 the corpuscle increases, the time during which it is in a position to act 

 effectively for ionization, during its passage by a molecule, gets shorter. Now 

 when velocities very near to that of light are attained, the concentration of the 

 corpuscles' tubes of force in the equatorial plane perpendicular to its motion 

 becomes increasingly important, although this phenomenon is of negligible 

 account for such velocities as have figured in the measurements on ionization. 

 A corpuscle moving with a velocity actually equal to that of light would exert 

 no electric force except in its equatorial plane, and there the force would be 

 infinite. Its mode of ionizing during its passage by a molecule would thus 

 be one of applying an infinitely large force for an infinitesunal time. The 

 electron to be ejected from the atom would have to suffer an enormous acceler- 

 ation in order to take advantage of the momentum offered to it, and a very 

 great amount of energy would be wasted in the acquisition of the momentum. 

 In other words, a very much larger amount of energy would have to leave the 



