1187 
will again have to be found by a calculation similar to the one 
applied above in the refraction theory. 
The fundamental formula shows that the phenomenon depends on 
the width of the slit @, that is on the size of the crystals. A possible 
procedure would thus be to calculate the colour for a number of 
different values of a chosen at random and in this manner try to 
reproduce the various observations. We shall, however, confine 
ourselves to a special case in which the observations themselves give 
an indication as to the size of the crystals which were operative. 
V. The halos of May 19 1899 and of September 19 1905. 
On two occasions Hissink at Zutfen observed very interesting halos 
which are described in “Onweders etc.” as follows. 
May 19 1899. “At 10.10 a.m. the small are and the complete 
circumscribed halo became visible. For some time clouds prevented 
the observation, but when it cleared the circle became visible once 
more. At 11.52 a.m. an additional ring 0, also circular, appeared, 
principally inside the upper half of the main ring and at 12.15 p.m. 
another circle c inside the former, whereas at 12.2 p.m. a further 
one d showed itself again nearer the sun. The two rings 6 and c 
were red on the side of the sun and showed round the red a 
greenish-yellowish tint, surrounded by violet. The small circle d had 
its outer edge coloured like the former, and its red on the side of 
sun was also similar, but the space on the inside of the circle was 
dark blue with a dull-brown hue.” 
By estimation Hissink determined the radii at: d= 7°.5;¢=17°.5; 
b =19°.5 (putting the ordinary circle at 22°). 
Sept. 19. 1905. “The halo observed on this day at Zutfen was 
a very rare one. It included a the large circle, 6 the upper tangential 
are, c the small eircle, d a circle with a radius of about 19°30’, e 
a circle with a radius of about 18° and / the left parhelion. 
As regards the colour of the various parts it should be principally 
mentioned, that the large circle was comparatively brightly coloured 
and that the violet of the tangential are near the point of contact 
was particularly striking. 
The circles d and e are the most interesting, the radii being 
determined by Hissink by measuring the radius of the small circle 
with an octant, which gave 22°, and subsequently the distances 
between it and the ares d and e. The latter were found to be 2°32’ 
and 4°2', which would give 19°28’ and 17°58’ for the radii of these 
circles. Direct measurement of the radii gave 19°32’ and 18°2’ 
76 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
