208 



Mr. C. G. Darwin 



on 



To show the character of the orbits which are not 

 spirals, I shall find those for which the fi particle describes 

 exactly one and exactly two rounds and returns towards the 

 direction from which it came. The p's for these cases will 

 be denoted by p 2 and p 2 . 



Table II. The External Orbits. 



V/c ... 



•01 



•1 



•9 -99 



Pi/Pcrit. ••• 

 Pi 



5-5 

 1-5X10" 8 



2-6 



7-2X10" 10 



1-5 1-5 



2-OxlO -11 6-OxlO -12 



Ps/Pcrik. .» 



1-16 

 3-3X10 -9 



115 



3-2xl0" 10 



Ml 111 



l'oXlO -11 4-4xl0 -12 



P 2 





5. These orbits have been calculated with a complete 

 neglect of radiation. There are, of course, very definite 

 indications that the mechanism of radiation is in some way 

 different from that given in the electromagnetic equations, 

 and our incomplete theory is certainly most at fault in the 

 parts which concern the emission of energy in radiation. 

 But in spite of this it is almost impossible that this emission 

 should help the escape of the electron. For the radiation 

 corresponds to a loss of energy, and this means a reduction 

 of velocity; and we have seen that a reduction of velocity 

 makes escape harder. Nor can the aberration of forces help 

 escape; for when two oppositely charged particles A and B 

 both revolve fast round their common centre, there will still 

 be this radiation of energy and a consequent reduction of 

 velocity. This is quite independent of the direction of the 

 force of each on the other ; but as a matter of fact it is easy 

 to show that for very high velocities the force of B on A pro- 

 duces a direct retardation quite apart from the reaction of A's 

 own acceleration on itself. 



An estimate of the influence which the radiation may have 

 can be made in the following way. Constrain the electron 

 to follow with the proper velocity the path it would take if 

 radiation were neglected. It is then possible to calculate 

 the radiation emitted under these circumstances. If this 

 amounts to any considerable fraction of the whole initial 

 energy of the electron, we may expect that it will be 

 caught. 



To make the estimate I have used Abraham's formula for 

 the radiation *. Since this is calculated for a rigid spherical 



* M. Abraham, Theorie der Elektrizitcit, vol. ii. p. 122. 



