[young] calculation OF ATOMIC DIAMETERS 57 



dM ' = - 



H e^ Sp cos d if Sp is the area of an orbit of 



47rw type p. 



H e"- r"p cos 6 



\m 

 and has a component along the direction of the field of the amount 



H e~ r^j, cos- 6 



dM" = T^ 



4m 



Then the magnetic moment contributed by the N electronic orbits 

 per unit volume will be 



sin 6 d t vr H e- r"p cos^ t 



2 4wî 



H e'~ r\N 

 ^ ~ 12m 



This quantity is the induced diamagnetic moment per unit 

 volume and by definition is equal to the intensity of magnetisation, 

 i.e., 



dM = 



^__ Ne^r\H __ e^~ H ^, 



TTf ' 



12m 12irm 



So far, all the orbits have been supposed to be of the one type p, 

 but, as is known, all theories of atomic structure have assumed that 

 this is not the case, and in considering diamagnetic phenomena we 

 have as yet no reason for rejecting any of the electronic orbits. 



Let there be n types of orbits in the atom and vp orbits of area 

 Sp, say. Then the expression for the intensity of magnetisation given 

 above will become: 



e" H "" 

 But B = tiH = H+47rI = H- - ^vpSp 



Sm I 



Hence 1-/'.= ^^vp Sp 



or X Vp Sp= 



I e- 



where yu is the permeability per unit volume. 



To evaluate the summation term all there is to do is to find the 

 sum of the areas of the orbits of one atom of the substance and then 

 multiply b}^ the number of atoms per ccm. of the element under 

 consideration. In applying this to Bohr's model of. the atom, the 



