184 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



we get 



= -67xlO- 8 . 

 m 



Now the equation 



tan ka = ka ( I H Fa a J 



l\ m J 



has a root ka = 0, and if -- is small, a root given approximately by Fa 2 = f . The 



other roots make ka finite, and are of no further concern here. 

 Similarly, the equation 



tanto-fl + ^V-"' ' W 



mil m 



has a root ka = 0, and for small the other roots make ka finite. 



m 



Under these conditions the rate of radiation is given approximately by 



V J 7/3 "A 1 '* 4-1 ' 4-' 1 1 7 /< m 'V' 2 



rrom & = to ka = the expression is negative ami above ka = ( * 



\ 2 m/ \ m/ 



it is positive. We thus conclude that the particle absorbs radiation and sends it out 

 after in a conical beam for wave-lengths from infinity to a certain value, and for 

 shorter wave-lengths would emit radiation, which is the normal condition. 



It is to be understood that the exciting source is a train of plane electric waves, 

 for with a purely mechanical exciting force there is always emission, according to the 

 result in Section 10. 



With the preceding value of - - we find that the critical point, at which the change 



from absorption to emission takes place, is given by ka = 10" 4 . This corresponds to 

 light of wave-length about ten times that for sodium light. 



The value could readily be brought into the vicinity of the visible spectrum by 

 taking a particle made up of a group. 



The true mass of such a composite particle would be proportional to the number of 

 components, while the electric mass would be proportional to the square, and thus 

 m' could be increased. 



We have already referred to LAMB'S conclusion that, if the dielectric ratio is of 

 order 10 6 , the free periods come in the vicinity of the visible spectrum. We have 

 also noted the free period given by ka = jf\/8, which is necessarily in the ultra-violet, 

 and for which the agitation of the particle and, consequently, the excitation of the 

 other free vibrations must be abnormally increased. 



If the exciting period does not exactly coincide with a free period, we may use the 

 approximate equations to show that there is emission of radiation in those free 

 periods. 



