182 Light and Electrons. 



So at 27° C. the mean square velocity for unstimulated 

 electrons is 



m 2 = 3x 300 x 7-7 x 10 10 = 69 x 10 12 c.g.s. 



or w E =8'3xl0 6 



== 83 kilometres per second. 



Now the critical velocity at which escape occurs, from an 

 atom with the atomic number 1ST, was found above, by (3),. 

 as 2180 kilometres-per-seeond multiplied by N ; which 

 would only be attained, if at all, by an insignificant per- 

 centage of the particles without some additional stimulus ; 

 and yet the speed attained by random influences alone is not 

 hopelessly of an inferior order of magnitude, though it would 

 have to be multiplied by 26 N to reach the critical speed. 



If we now take into account the /3 2 factor, 1 — v 2 /c 2 , which 

 is effective in reducing the holding force and increasing the 

 centrifugal inertia, we shall find that the unaided gas speed 

 for ordinary temperatures makes the value of v 2 /c 2 only 

 *000000077" y (or 7*7 x 10~ 8 ), which is therefore insignificant; 

 but that the term rapidly rises in value with increase of 

 speed, however produced, until, as the critical velocity is 

 approached, by reason let us say of aid from synchronous 

 ether disturbances, it tends to become 5*3 x 10~ 5 N 2 ; which 

 is '000053 for hydrogen and *45 for uranium. 



Hence the auxiliary factor 1 — v 2 /c 2 can attain the low 

 value "55 for uranium, and is of obvious importance in 

 promoting disruption. So it is for many of the heavy 

 atoms ; even for lead this /3 2 factor can be '64. 



The value of n 2 b* (by 1) is reduced in the ratio /3 2 , while 

 nb 2 (by 2) is reduced in the ratio j3. This requires that 

 the reduction shall apply to the critical frequency n, not to 

 the critical distance b } and that the n and the v calculated 

 above are subject to a /3 reduction. 



It would seem that the liberation of electrons by light 

 should be easier, or at least prompter, at a high temperature, 

 because less energy would have to be supplied by or during 

 the synchronizing stimulus. And at a sufficiently high 

 temperature electrons ought to come away of themselves, 

 without the need for any specific radiation-stimulus. 



To find this temperature we can put 



3R E T= (2-18xl0 8 N) 2 

 whence 



T = 2xl0 5 .N 2 . 



At this temperature the average electronic-gas velocity 

 would equal the escape velocity, and the atoms of a substance 



