678 Prof. F. A. Lindemann on the 



ions and electrons, i. e. positive and negative particles, and 

 taking account of electrostatic attraction, the free path 



1 



\ = 



\ mv z aj 



mv 



2e 2 

 o beino- the radius of the electron rf— and .- = 3/2/cT 



the equipartition energy. Putting T = 6000° this reduces to- 



9*07 . 10 18 



— , n being the number of ions per unit volume. 



Since n is small and continually decreasing as the cloud of 

 gas expands, it would seem that collisions and recombination 

 may therefore be neglected. 



The shape of the cloud will consequently only be modified 

 by the movement of the particles under their own initial 

 velocities, for there are no appreciable macroscopic electric 

 charges present and therefore the electrostatic forces are 

 small. A few electrons will probably escape from the cloud,, 

 but as soon as the potential of the cloud becomes so high 

 that the work done in escaping is of the order of the thermal 

 energy, this will cease. The resulting electrostatic forces can 

 only cause an expansion of the same order as that due to 

 the velocity of the ions. Otherwise the electrons will 

 naturally be forced to conform to the velocity of the more 

 massive hydrogen ions. One may therefore estimate the 

 rate at which the cloud expands laterally as somewhat 



greater than \/^ =5.10 5 cm, sec, if T = 6000° and A = l 



as in hydrogen. If the radial velocity of the cloud is taken 

 as 8.10 7 therefore it will expand to a radius somewhat 

 greater than 10 11 cm. by the time it reaches the earth's 

 orbit. 



The length of the cloud will be very much greater, since 

 it is not to be assumed that the radial velocities of the 

 particles in the cloud are exactly the same but rather that 

 the velocities will be distributed about the mean velocity. 

 Suppose, for instance, the velocities to vary from 6.10' 

 cm./sec. to 10. 10 7 cm./sec, the cloud would take 10 5 seconds 

 to cross the earth's orbit, as its length when the particles of 

 velocity 8. 10" cm./sec. reached the earth's orbit would be 

 7-5 . 10' 12 cm. 



Since the earth's velocity in its orbit is about 3.10 6 cm./sec, 

 it would on the average take a time of the order of 7 . 10 4 

 seconds to pass through such a cloud. Dr. Chapman's- 



