1184 
maximum is nearer to the sun. Prerntger’), taking the mean of a 
large number of trustworthy measurements, finds 21°50’. This dif- 
ference of more than '/,° is much too large. Moreover, the refraction 
theory leads to the conclusion, that the inside of the circle would 
be red-orange, yellow, green-yellow and that blue can hardly appear 
and violet not at all. No increase of the intensity of the light can 
improve this disagreement with observation; the white always 
remains 24 times as intense as the blue; specially directed crystals 
are not capable of producing colours which are not there before. 
The colouring of the parhelia and tangential curves are not explained. 
It may also be noticed that on the underlying refraction-theory the 
size of the erystals which is determined by a cannot have an influence 
on the colour-phenomenon either, seeing that the width of the beam 
changes in the same ratio as a for all colours and that the light 
is parallel. 
The conclusion to be drawn is simply this: the refraction theory 
is not able to give a complete explanation of the halo-phenomena. 
I have not carried out a similar calculation for crystals with a 
refracting angle of 90°, but the circumstance, that the minima of 
deviation lie further apart in this case’), cannot be sufficient to 
explain the presence of differently coloured rings of 46°. 
IV. The diffraction theory. 
We may again confine ourselves to the phenomenon as occurring 
in one plane sun-crystal-eye, with the refracting edge at right angles 
to this plane. We shall also assume the special case of all crystals 
having the same size, which must be looked upon as a limiting 
case which is specially favourable to a development of colour. 
As we have seen a beam of definite width emerges from the 
erystal after refraction, but this beam will be subject to diffraction. 
A large number of erystals of the same size, irregularly distributed, 
with parallel edges, all give similar beams, which will give rise to 
interference phenomena: the light source is seen as it were through 
1) PERNTER, Le. 230. PreRNTER’s proof that a ring must be formed at 21950 
is by no means conclusive. He only shows that the yellow light has a minimum 
deviation of that magnitude (p. 313). The maximum intensity lies further out: 
about at 22°21’ (min. dev. of violet) + 16’ (sun’s radius) = 22°37’, the place 
where all the colours of the complete spectrum are fully developed, in accordance 
with what the above more elaborate calculation gives. The light circle seen against 
the dark background will appear narrower to the eyes. Thereby the difference 
between observation and calculation becomes smaller, but it is more than doubtful, 
whether this effect could cause the difference to disappear altogether. 
2) PERNTER, l.c, p. 354, 357. 
