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probably an offspring of the uranium family; a side branch, as it were, in the formation of which relatively few transforming atoms took part.  On Rutherford’s theory then, actinium should always accompany uranium and radium, but in very subordinate amount.  The absence of actinium haloes clearly supports this view.  For if actinium was an independent element we would be sure to find actinium haloes.  The difference in radius should be noticeable.  If, on the other hand, actinium

was always associated with uranium and radium, then its effects would be submerged in those of the much more potent effects of the uranium series of elements.

It will have occurred to you already that if the radioactive origin of the halo is assured the shape of a halo is not really circular, but spherical.  This is so.  There is no such thing as a disc-shaped halo.  The halo is a spherical volume containing the radioactive nucleus at its centre.  The true radius of the halo may, therefore, only be measured on sections passing through the nucleus.

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In order to understand the mode of formation of a halo we may profitably study on a diagram the events which go on within the halo-sphere.  Such a diagram is seen in Fig. 15.  It shows to relatively correct scale the limiting range of all the alpha-ray producing members of the uranium and thorium families.  We know that each member of a family will exist in equilibrium amount within the nucleus possessing the parent element.  Each alpha ray leaving the nucleus will just attain its range and then cease to affect the mica.  Within the halosphere, there must be, therefore, the accumulated effects of the influences of all the rays.  Each has its own sphere of influence, and the spheres are all concentric.

The radii in biotite of the several spheres are given in the following table

URANIUM FAMILY. 
Radium C — 0.0330 mm. 
Radium A — 0.0224 mm. 
Ra Emanation — 0.0196 mm. 
Radium F — 0.0177 mm. 
Radium — 0.0156 mm. 
Ionium — 0.0141 mm. 
Uranium 1 — 0.0137 mm. 
Uranium 2 — 0.0118 mm.

THORIUM FAMILY. 
Thorium CE — 0.040 mm. 
Thorium A — 0.026 mm. 
Th Emanation — 0.023 mm. 
Thorium Ci — 0.022 mm. 
Thorium X — 0.020 mm. 
Radiothorium — 0.119 mm. 
Thorium — 0.013 mm.

In the photograph (Pl.  XXIV, lower figure), we see a uranium and a thorium halo in the same crystal of mica.  The mica is contained in a rock-section and is cut across the cleavage.  The effects of thorium Ca are clearly shown

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as a lighter border surrounding the accumulated inner darkening due to the other thorium rays.  The uranium halo (to the right) similarly shows the effects of radium C, but less distinctly.