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the liquid. Yet the photographs . and * suffice to show that, with 
these drops too, dark spots can be produced, winch, in contrast with 
tlTforJr case, have a bright rim on the side opposite the centre 
Some observations were made with the vessel divided into tw 
partitions by a glass plate. In J the left part contained the opUcally 
thinner medium with a local condensation, the right part thedenser 
medium with a rarefaction. Finally the image P shows both cases 
in one and the same medium: on the left two salt drops on the 
right two glycerine drops are floating in a mixture ot the two 
solutions. All these drops were lengthened in a direction near y 
perpendicular to the plane of the image. 
What 
sun-spot t 
So far our results justify the suggestion, that the darkness of sun¬ 
spots and the distribution of brightness round about them might be 
mere consequences of refraction. 
A difficulty arises. The typical sun-spot has a principal characteristic, 
which we do not observe as such in our imitations, namely: a 
penumbra, enclosing the umbra, from which, as a rule, it can be 
rather sharply distinguished. But this objection is easily removed. 
Indeed, there is an essential difference between the arrangemen 
of the gradients of optical density in a diffusing drop on the one 
hand, and round a vortex on the other hand. With the diffusing 
drop, the greatest gradients are to be found in the layei o quic es 
diffusion, that is, not far from the outside; whereas in the region 
of circulation, always surrounding a whirling mass of gas, the gradients 
increase as we approach the vortex. 
It is not so easy, of course, to realize by experiment this latter 
case with its optical consequences; but that it must resu t in e 
appearance of an umbra and a penumbra, is clearly shown by the 
scheme fig. 3, plate I. Within the cylindrical space abed the mattei 
is supposed to be circulating about the vortex W. Rays nee e 
towards the observer after emerging from the innermost parts o ia 
region (the thin vortex-thread itself may be left out ot regar ) ave 
suffered the greatest change of direction; they come from the space 
outside the photosphere, have little intensity, and produce the umbra. 
Parts of the spot, lying a little farther from the vortex, send us the 
light which left the photosphere tangentially: here we have t e 
boundary between umbra and penumbra (in a certain sense. an m\ei e 
“image” of the solar horizon). Next follow the penumbra rays; first 
those having left the photosphere at great angles with the sun s 
