Scattering of Rout gen Radiation. 239 



result; by 2ttt 2 d0, so that the final value of the excess 

 radiation becomes 



^tt^EiTN^I + cos 2 ^)^-^^!-^-^) +(F + F'){l-e- nY ) 2 ") 



-f(F + 2F / Xl-e-" Y ) 3 + ....~\0d0\ (9) 

 = ^TNn ( l4 . C0S 2 ^)(i„ g -»v) |-F + (g» v -l)Fl^ ^6>,* ) 



87r?/r 



where by excess radiation we must mean the energy scattered 

 per unit volume of the radiator per unit time in the whole 

 solid angle between and + d0, in excess of the value for 

 the same quantity calculated from the simpler formula. 



On account of our lack of knowledge of the values of many 

 of the quantities occurring in this expression, it is impossible 

 to compute the amount of this radiation. To test the theory, 

 let us therefore compare the changes of this quantity with 

 those found experimentally by Mr. Crowther for the real 

 excess radiation. 



The first of his statements, of proportionality of the excess 

 radiation to the thickness of the radiator, is obviously true of 

 the calculated value, which is a certain quantity per unit 

 volume of the radiator. 



By making the primary beam harder, keeping E 2 TN 

 •constant, the volume V is diminished at any given angle, so 

 that the excess radiation, which increases with V, is thereby 

 diminished. On the other hand, an increase of atomic weight, 

 if it means an increase of n, must increase the excess radiation. 

 The second condition is therefore satisfied. 



The agreement of the formula w r ith Mr. Crowther's third 

 statement is apparently not so good, as it seems as if, when 

 the pulses from tw r o neighbouring electrons arrived at the 

 observing point at times differing by some fraction of T, 

 the resulting radiation might not be quite so hard as the 

 primary. But it may be that this effect would be too small 

 to be detected experimentally. 



The agreement of the expression (9) with Mr. Crowther' s 

 formula for the scattered radiation depends of course on the 

 way in which V, F, and F' vary with 0; but on careful 



* Note that 



«-«? i-(i_«-»Vj 



and that 



„+»v..^ = L =lj-(l-«- y )+(l-,-»V+< 1 -«~' y )'+..., 



,+2«V_ 1^ 



--- * _(—±—\ 



(e- iiy y [i_(i_ e -»V)]* d{\-e- ny ) 



= l-h2(l-e- 7iV )+3(l-e-' lV ) 2 +4(l-e- nV ) 3 +... 



