Prof. Piazzi Smyth, commenting on this article, makes the inquiry how the sun-spot cycle and the terrestrial magnetic oscillation cycle can be considered as agreeing, the sun-spot cycle, according to Prof. Wolf, being 11·111 years, and the magnetic cycle 10·5 years according to Mr. Broun. [Sidenote: M. Faye’s remarks to a similar effect.] Another correspondent writes and quotes M. Faye, in ‘La Météorologie Cosmique,’ for the remark, “La période des taches portée à 11 ans ·1 par M. Wolf n’étant pas égale à celle des variations magnétiques (10 ans ·45), ces deux phénomènes n’ont aucun rapport entre eux.” [Sidenote: Mr. Broun’s rejoinder and explanation.] Mr. Broun, in a further letter, rejoins that if we could accept Dr. Wolf’s view we should find that the mean duration of a cycle for _both_ phenomena since 1787 would be 11·94 years, while the sun-spot results for eight cycles determined by Dr. Wolf during eighty years before 1787 give 10·23 or, if we take nine cycles, 10·43 years for the mean duration. It is by mixing these two very different means that the Zurich philosopher finds 11·1 years, a mean which Mr. Broun considers can evidently have no weight given to it. On the other hand, if Dr. Wolf is in error (as Mr. Broun believes he is) as to the existence of a maximum in 1797, the mean durations for the eighty years after and for the eighty years before 1787 agree as nearly as the accuracy of the determinations for the beginning of the eighteenth century will permit. Mr. Broun then repeats his conviction that the sun-spot maxima and minima are really synchronous with those of the magnetic diurnal observations. [Sidenote: Mr. Jenkins’s explanation of Prof. Loomis’s chart.] Mr. B. G. Jenkins, in a letter to ‘Nature,’ refers Prof. Smyth to Prof. Loomis’s chart of magnetic oscillations given in Prof. Balfour Stewart’s paper in ‘Nature’ (vol. xvi. p. 10), for the purpose of showing that there are exactly seven minimum periods from 1787 to 1871, the mean of which is twelve years, the mean of the seven corresponding maximum periods being 11·8 years. The true magnetic declination-period is, then, the mean of these, viz. 11·9 years. In exactly the same manner he finds that the mean period of sun-spots is 11·9 years. [Sidenote: Jupiter’s suspected connexion with sun-spots.] The auroral displays also have the same period. Mr. Jenkins also refers to Wolf, De La Rue, Stewart, and Loewy, as having stated their belief that Jupiter is the chief cause in the production of sun-spots, and draws attention to the period of 11·9 years as being Jupiter’s anomalistic year, or the time which elapses between two perihelion passages. [Sidenote: Infrequency of Auroræ and absence of sun-spots in 1876-78.]