1193 
outside the main circle. PerNTER mentions two observations of that 
kind *), but the data are too incomplete for a calculation to be based 
on them. In this connection the observation at Souppes (Nr 10 of 
the table) is important: in this case two concentric ares are reported, 
the wider one of which is the inferior tangential are. The other one 
may, as it seems to me, be looked upon as an external diffraction- 
ring of this-are. 
As regards the main maximum, the theory gives it as lying at 
22°0’ in complete agreement with the observations which give 21°50’ 
as the mean. | 
It is very probable, that by a calculation of the system of colours 
for other values of the width a the other observations may also be 
reproduced. In this connection the facet should be noted that in the 
various reports some combinations of colours occur repeatedly and 
will probably have to be ascribed to crystals of the same size. Some 
instances may be given here: 
“Spectral colours”: Circle of 22°: 9 and 10 
Circle of 46°: 7 and 31 
Parhelion | 14 
Red, yellow, green, violet: Circle of 22°: 3 and 6 
Upper tangential are: 175 
Red, violet: Cirele of 22°: 2 
Upper tangential are: 20 and 23 
Red, blue: Circle of 46°: 95 
Circumzenithie are: 1 and 30 
Red, green: Circle of 46°: 6a and 23 
Upper tangential arc: 21 
IN 
The case of red, yellow, blue, violet (circle of 22°, 9a and upper 
tangential are, 13) is dealt with above. 
The very lengthy calculations which would be required for the 
further testing of the theory, have not been carried out so far and 
we shall confine ourselves to some general remarks. 
1. As in the rainbow we have in the colours a means of determin- 
ing the size of the refracting particles. In order to obtain say a 
well developed violet it is necessary that the maximum intensity of 
violet coincides about with the extinction of red and green. A very 
rough approximation to the dimensions in this case is arrived at as 
follows. 
Supposing the colours B, C, D and £ to have their first minimum 
1) PERNTER, l.c. p. 260. GRESHOW’s halo, Oct. 20 1747, radius 26°; and an 
observation by WuisTon, radius 29°, 
