h resting on a plane surface in a semi- infinite medium (see Fig. 2) we have 

 for the total amount of radioactivity M. = 4a bh C . , where C^ is the finite 

 initial concentration of radioactivity in the source. The dispersion from the 

 finite box source can be formulated from relation (4) by considering all sources 

 within the finite box at positions x' , y ' , z ' and of strength C . dx' dy' dz' 



thus : 



.= ?2i Cdx'^dy' Cexp r-(x-x')^+(y-y')^ + (z+z')^1^^/ 



' 8(uKt)3/2 J J J L 4Kt J 



-a -b -h 



(5) 



where C . is presumed uniform throu^out the box source. The integration is 

 extended over an image source below the surface in order to satisfy the boundary 

 condition of zero flux through the horizontal plane at z = , and assures the con- 

 tinuity condition that the total amount of radioactivity of isotope i above the 

 plane z = is equal to M. at all times . 



Carrying out the integrations indicated in Eq. (5) gives 



where 



m = >\|2Kt (7) 



and izi ( P ) is the probability integral defined by 



0(|3) =2^ f e"^ /^ds (8) 



o 

 and has the properties 



