472 Prof. P. Lowell on 
perceived two bright knots on the western one. The first 
fact can, if one pleases, be explained by the proximity of 
Saturn's bright disk ; but another circumstance comes in here, 
as will be shown. The second fact demands no further 
discussion ; while for the explanation of the third Mr. Barnard 
assumes that he saw two of the inner satellites. But Mimas 
only could be in question : and it might raise difficulties to 
explain both knots by it. So the explanation needs no 
extended discussion, as it appears to me very probable that 
here another phenomenon is exhibited." 
Seeliger then goes on to attribute it to greater showing in 
the line of sight ; and he deduces from the known dimensions 
of the ring-system the places where such ansal broadening 
would cause apparent maxima, to wit : 
and 1*98 f rac ^ of Saturn from the planet's centre. 
We may here remark parenthetically that apparent agglo- 
merations or thickenings of the rings have been noticed by 
several observers since the time of Herschel, by Bond, Wray 
and Struve in especial, and agreeing more nearly than the 
above with the phenomena observed at Flagstaff ; but all the 
observers attributed them to causes other than what we shall 
now set forth. 
Taking up first the shadow phenomena seen at Flagstaff, 
calculation shows that the shadow of the whole ring-system 
including the crape ring, with the Sun as on November 9 
(1907) 1° 39 / -5 above the ring-plane, would be 0"'26 wide 
only. The position of the Earth does not sensibly change 
this. Now the shadow was nearly twice as wide as this, 
being //# 46. Such then cannot be the cause. Nor can it be 
the penumbra of the dark core, as that would be but ;/, 05 in 
width, a quantity indistinguishable in fact by the eye. The 
only explanation left is that in the black core we are looking 
at the shadow of ring A, practically plane and in the dusky 
shadow about it through particles situated above and below 
that plane lying in the other rings. In other words, that 
ring B and ring C are for the most part not flat rings but 
tores. 
Turning now to the phenomena of the rings themselves, 
the agglomerations on the Olbers- Seeliger theory of their 
showing should, as computed in the same memoir by Seeliger, 
be found at 
1*60 and 1*98 radii of Saturn from the planet's centre; 
for these are the points where the line of sight from the 
