I 
1919-20.] Note on the Scattering of X-Rays. 47 
for each pair of electrons. In the real case L varies from pair to pair. 
It is easily seen that the effect of this variation will be obtained by 
adding the radii of different curves of the type shown in the diagram. 
All such curves coincide at 0= 180°, so we shall always have a well-marked 
extra-radiation there. But the oscillations shown by B and C will occur at 
different values of 0 in the different cases. Hence these oscillations will 
annul one another, and, if 2&L is large, we shall simply have the extra- 
radiation passing smoothly into the simple curve A. And, of course, 
the radii of the curve F are always n times Hie radii of the curve A. 
To show that the curves in fig. 4 are in accordance with experiment, 
we may quote from a paper by E. A. Owen : * “ The distribution on the 
incident side of the radiator in each case agrees closely with the theoretical 
distribution given by I fl = Lr/2(l + cos 2 0). In the case of the hardest rays 
the same theoretical distribution is also obtained on the emergent side 
for the positions examined (i.e. to 150°). A dissymmetry, however, appears 
when the rays become softer, and this increases with the softness of 
the rays.” And, to quote from another paper by the same author, p. 530 
in the same volume : “ The total excess radiation round the radiator 
decreases as the primary beam becomes harder and increases with the 
atomic weight of the radiator.” 
It is not possible to derive a value, or even an average value, of L 
from the observations already made on the extra-radiation. They do 
not come close enough to 180°. 
Let us now consider the numerical value of I x / 2 for the same ideal 
case of the tetrahedral atom. We have 
L -/2 
I'v2 U + 12 
sin (2 kh cos r) 
ZkL> cos \tt 
This is represented as a function of 7cL in fig. 5, the horizontal line giving 
the value for no interference. The curve starts at an ordinate four times 
as high as the straight line, decreases towards the latter, and approaches 
it in a series of diminishing oscillations. For an actual atom owing to 
L having different values for the different pairs, the oscillations take 
place at different points when plotted as a function of 7c, and hence 
annul one another. In the case of lead the value of the ordinate at the 
origin should be eighty-two times the end value. 
§ 3. We have now to consider the low value of the scattering coefficient 
for y-rays. This is a great difficulty. According to the formula given 
above, the scattering should diminish until the molecule is large compared 
* Proc. Carnb. Phil. Soc 16, 1910-12, p. 161. 
