1188 
respectively. The means 19°30' and 18°O' must therefore have a 
comparatively high degree of certainty”. 
Similar circles have been observed on other occasions. BurNry on 
June 9 1831 saw a ring of a radius of 20°). Hissink himself saw 
one on Sept. 5 1899 of a radius estimated at 19°. On the ordinary 
theory all such circles are explained by means of specially shaped 
crystals with refracting angles which produce a circle at the distance 
required, The following crystal-faces come into consideration’) for 
the above cases: 
Refracting 
angle D, (yellow) 
50°28' two pyramidal faces at the same end of theerystal 17°26’ 
53°50' two pyramidal faces at opposite ends of the crystal 18°56’ 
54°44’ a base face with a pyramidal face at the other end 
or a prism face with a pyramidal face exactly 
opposite. 19°20’ 
The distances of the rings for yellow are then 2°30’, 2°54’ and 
4°24' respectively. 
The first one agrees exactly with Htssink’s measurements, whereas 
the last is too large. The colours give difficulties which are not 
solved in this manner. 
Starting from the supposition, that the rings of 18° and 19°30’ 
are nothing but secondary diffraction rings, I have made a calculation 
of the colours in the following manner. 
PerNTER *) gives the positions of the maxima and minima for the 
diffraction through slit-shaped apertures in connection with the 
theory of coronae, as follows: 
position intensity 
1st maximum 0.0000 1.000000 
1st minimum 1 0 
2°¢ maximum 1.4303 0.047191 
2nd minimum 2 0 
3rd maximum 2.4590 0.016480. 
Applying these results to Hissink’s measurements in 1905, where 
nk AEN) b= 1974 eis 4) 
A=3=b = 2 20 Oa 
the angle of diffraction 9 of the first minimum is found to be 
1) PERNTER, l.c. page 266. 
2) Onweders etc. 26 p. 83. 1905. 
3) PERNTER, |. c. pag. 452. 
