PROF. J. JOLY ON THE GENESIS OF PLEOCHROIC HALOES. 
73 
radius ; next a narrow shaded ring. Another ring sometimes succeeds. Then we 
have the somewhat variable limit of the pupil which we find developed on haloes 
darkened up within. Lastly comes the outer ring generated by the rays of ThC 2 . 
If we lay out on millimetre paper the mean readings given in the Table along a 
line and enlarge them all proportionately by the usual construction involving the 
properties of similar triangles we find that when the radius for the second ring has 
attained the radial dimension of 3'5 cm., and so comes into agreement with the 
distance of the second prominence on the curve from the axis of Y—that is, with 
the radius of a second ring supposed generated in a halo in air—then the other 
readings at foot of the Table fall into the numbered positions shown above in fig. 5. 
Examination of this figure shows that the agreement of the measurements with 
the features of the curve is very satisfactory. The outside radius of the first ling 
falls at 2'4 cm., which is just about where it might be expected. The third ring 
(numbered 3) is less definite. It seems to refer to the conspicuous prominence on the 
slope. The average pupil radius (marked 4) corresponds to the next conspicuous 
prominence. It may extend to anywhere on the lower slope leading down to the 
marked minimum of ionisation. The readings for the pupil radius, rising to 0'028 
and (R027, which are common readings in well-blackened haloes, place the outside 
limits of the pupil at 5’8 cm. from the centre (marked 5)—-that is exactly at the foot 
of the downward slope. Similarly, the average reading for the extreme radius of 
haloes (about 0h408 mm.) corresponds closely to 8’6 cm. radius of the halo in air. 
Extreme readings reach to the very foot of the curve. It is evident that the agree¬ 
ment between the measured and the theoretical features is extraordinarily close 
considering the difficulties attending the measurements. Quite possibly there is 
some chance involved in such agreement. But even if we were presented with a 
lesser degree of correspondence we would be entitled to conclude, as I think, that the 
integral curve of ionisation in a gas is certainly intimately connected with the mode 
of generation of the thorium halo. 
Assuming this, we now find that if the radial dimension of the second ring, that 
is 0'0169 mm., corresponds to 3'5 cm. in air, we get as the conversion factor 
2071. (2) 
This same conversion factor, obviously, applies to the several features of the thorium 
halo with considerable accuracy. 
The foregoing results appear to be so mutually consistent that we must, I think, 
ascribe considerable weight to the derived conversion factor. It is important to 
determine if there is any notable difference in the stopping power of this mica and 
that of the haughtonite of Ballyellen, Co. Carlow. It would seem as if there was 
but little, if, indeed, any at all. Uranium haloes, suitable for measurement, are not 
very common in the Vagnay mica. Here, however, are eight which permitted of 
correction for the nucleus and were well and clearly defined. 
