One of the most important results of observations made upon the eclipse of July 29, 1878, indicates the existence of a law of sympathy, so to speak, between the solar corona and the sun-spots. The inquiry into this relation seems to me likely to lead to a very interesting series of researches, from which may possibly result an interpretation not only of the relation itself, should it be found really to exist, but of the mystery of the sun-spot period. I speak of the sun-spot period as mysterious, because even if we admit (which I think we cannot do) that the sun-spots are produced in some way by the action of the planets upon the sun, it would still remain altogether a mystery how this action operated. When all the known facts respecting the sun-spots are carefully considered, no theory yet advanced respecting them seems at all satisfactory, while no approach even has been made to an explanation of their periodic increase and diminution in number. This seems to me one of the most interesting problems which astronomers have at present to deal with; nor do I despair of seeing it satisfactorily solved within no very long interval of time. Should the recognition of a sympathy between the corona and the sun-spots be satisfactorily established, an important step in advance will have been made,--possibly even the key to the enigma will be found to have been discovered. I propose now to consider, first, whether the evidence we have on this subject is sufficient, and afterwards to discuss some of the ideas suggested by the relations which have been recognised as existing between the sun-spots, the sierra, the coloured prominences, and the zodiacal light.