soMi: coxTH.uroh:ii<y .ii>i\ixciis /.v riiysics—ii 175 



form a single iioiiit-charnc (12 — n)e, and the remaining (12 — «) 

 electrons lie on the spherical surface, which encloses the "empty 

 space" nuMitionetl al)ove. The functions / anil /•' assume the forms 



fip) = 2 arc cot 4^^-^ (fia) 



VR'-P' 



AX.) = .Vy. cot (A,) cosec^ (i«) j-;;^.(|y^^|^. (7a) 



in which ju = \nii'-R cE\ the SNinhols ha\e tile s.inK' nu-atiingsas in ((>). 

 anil (7), with which these erjuations become identic.il if R is made 

 infinite. 



This "limite*i-field" distribution-function has some odd character- 

 istics. At very high speeds large deflections naturally are rare, hut 

 as the s[iee<l is lowered they become relatively more frequent; the 

 1,500-volt, 1,000-volt and 750-volt curves for magnesium illustrate 

 this. This tendency gains rapidly as U is decreased; at a certain 

 critical value, given by m= 1. the deflections arc uniformK- distributed 

 in all directions'; at a lower critical value, given b\- n = \, all the 

 electrons are turned through 180° and return on their tracks. As 

 the speed is still further decreased, the condition of uniformly-dis- 

 tributed deflections is again approached, and we have the extraor- 

 dinary- feature of the average deflection decreasing as the energy 

 of the electrons goes down.' In the family of curves for magnesium 

 there appears \ery clearly an intermediate velocity at which 180° 

 deflections are peculiarly frcfjuent; the curves spread outward in the 

 direction = 180° whence the primary electrons come, as the energy- 

 of the primaries rises from 24 to "o volts, and retract themselves 

 again as the energy rises beyond 100 volts. This is a particularly 

 important feature of the curves. 



To make an adequate test of the new expression for /•', it is neces- 

 sary to apply certain corrections to the curves presented, particularly 

 a correction required because the distance travelled by the deflected 

 electrons within the target metal varies with 4>, so that the percentage 

 which goes astray, owing to loss of speed or otherwise, varies simi- 

 larly. A curve exempt from this correction can, however, be ob- 



' .Meaning that the number dellectefi per unit solid angle is independent of *. 

 which means that the distribution-in-angic function is of the form const. Isin ^i. 



' It may be recalled from the last number of this Journal, page 110, that H. .A. 

 Wilson used this property as an explanation of the anomalous variations of elcctron- 

 mean-frce-paths with speed in various gases. 



