^{page 735 note *} Trans. Royal Soc. Edin., vol. xvi. p. 143, § 19.

^{page 735 note †} The most important of these have been discussed by General Sir E. Sabine.

^{page 735 note ‡} Trans., vol. xxiv. p. 669.

^{page 736 note *} Proceedings of the Royal Society of London, vol. x. p. 475. 1861.

^{page 736 note †} Proc. Roy. Soc. Lond., vol. xvi. p. 59.

^{page 736 note ‡} Hence the mean solar diurnal variation sought, in any case, from fewer than a month's observations will be more or less in error, according as the lunar action (and the change of its law during the lunation) is more or less considerable

^{page 737 note *} I have touched on the objections to this method in a note which appeared in the Proceedings of the Royal Society, of London, vol x. p. 479. The Astronomer Royal (Trans. Roy. Soc. Lond.,vol. cliii. p. 617), and Dr Lloyd (Dublin Mag. Observ., vol. i. p. 91, foot note) have also both objected to this process.

^{page 737 note †} Proc. Roy. Soc. Lond., vol. x. p. 481.

^{page 737 note ‡} The test for determining whether a day is one of marked disturbance has been obtained in different manners. I believe that the most certain test would be one depending on the value of the mean difference obtained by comparing each hourly observation with that immediately following it; the characteristic mark of what is termed a disturbance being the irregular movement of the needle.

^{page 738 note *} With a single exception (in about 80,000 observations) in which the mean of the preceding and succeeding observations was substituted.

^{page 740 note *} The epochs for the diurnal and semi-diurnal periods are obtained directly from the values of c ₁ and c ₂ in the preceding series of formulæ; those for both terms are obtained from the formulæ by the equation

where α is the correction to an estimated epoch of the maximum or minimum. See footnote to a paper on the “ Horizontal Form of the Earth's Magnetism,” Trans. Roy. Soc. Edin., vol. xxii. p. 529.

^{page 742 note *} Trans. Roy. Soc. Edin., vol. xxiv. p. 673.

^{page 742 note †} See the projections for this lunation, Plate XLIII, Trans. Roy. Soc. Edin., vol. xxii.

^{page 742 note ‡} It is also partially due to the mode of combination—a lunation being considered in January, if fifteen days were in that month, the other fourteen being in February or December, for which months the range is considerably less than in January, and the maxima and minima occur at different times.

^{page 743 note *} See Proc. Roy. Soe. Lond., 20th June 1861. The law of lunar disturbance is that relating to the greater or lesser irregularity of the position of the needle in the diurnal variation for the moon on the different meridians.

^{page 744 note *} It will be seen in the scheme that the lunar day has been considered equal to 25 hours (it is equal to 24 h. 50 m. nearly), and consequently the lunar hour angle is equal to only 14°4. Also 0 h. is repeated in the last column. This was always done in order to find the correction due to changes of mean declination, which caused the variations to increase or diminish from the 1st to the following 0 h., especially in means derived from limited series of observations. It was found ultimately that it would be preferable to repeat 1 h., and perhaps even 2 h. in order to obtain this correction with more accuracy. Other details as to the precautions taken in these discussions will be found in the first volume of Trevandrum Observations.

^{page 745 note *} Had the method here considered, or an idea of any probable result to be derived from it, presented itself at first, differences, independent of the irregularities of the daily means, would have been obtained by reducing each of the daily means to the monthly mean, so that the sums of the plus and minus differences in each lunar day would have been equal to zero.

^{page 746 note *} Postscript.—When this was written it was intended to give the projected curves for the different positions of the moon in declination ; this the Postscript (43) and the Plate (XXVII.), with curves for the times of the moon's phases, render unnecessary; for the conclusions here drawn the curves for the phases may be consulted, approximately, as follows :—

^{page 747 note *} See curves for third quarter in February, and for full moon in March.

^{page 747 note †} See curve for new moon in June.

^{page 746 note ‡} See curve for full moon in June, Plate XXVII.

^{page 748 note *} It will be obvious that this separation cannot be perfect, since, for example, in the vertical summation of the first seven horizontal lines in the scheme (26), when the difference of day and night hours is disregarded (as in the discussions for the moon's position), the mean for the lunar hour 3 would be obtained from three observations made during the day and four during the night. In the projected results, six hours on each side of the mean midnight point are marked as night hours ; that point would correspond to the lunar hour 8½; in the means for the first week in the scheme. In this way, however, the extremes of parts marked as night hours are still affected by the greater action of the day. An examination of Plate XLIII., Trans. Roy. Soc. Edin., vol. xxiv. (differences under solar hours), will show the small lunar effect during the night hour throughout a lunation.

^{page 749 note *} The calculations are being made with reference to these components of force.

^{page 751 note *} The mean diurnal variations of the atmospheric pressure due to the sun and moon, show similar regular double maxima and minima. The consideration of a mass of observations made by me in India at different heights, induced me several years ago (Phil. Mag., August 1858) to suggest an electro-magnetical attraction as a cause of these variations (and I found an analogical phenomenon in the action of the sun on the gases of comets). The atmosphere having acquired a certain polarity, would by this attraction assume ellipsoidal forms with the longer axis directed towards the attracting luminaries (or making nearly constant angles with these directions), thus producing waves or currents as a given meridian turns round under axes of different lengths. I have in consequence of this idea sought to find some connection between the laws of terrestrial magnetism and those of atmospheric pressure, but hitherto without any conclusive result. The difference of the lunar action on the magnetic needle during the day and during the night, suggested the examination of the lunar diurnal variation of atmospheric pressure for a like difference ; but the result of this investigation was negative, no difference being perceptible ; the lunar diurnal variation in January and June was shown equally well by the observations during the night and by those during the day.

^{page 751 note †} Added by permission of the Council, June 27th 1872.

^{page 754 note *} As no observations were made on Sunday, there were twelve days' observations for new moon, and for the moon four and seven days old, eleven days for the moon six days old, ten days for the moon three days old, and only nine days for the moon one, two, and five days old.

^{page 754 note †} The time of sunrise varies at Trevandrum from 6 h. 8 m. m.t., on the 15th December, to 6 h. 20m. on the 15th January, a change due nearly altogether to the equation of time, the interval betwixt sunrise and true noon, being (refraction effect included) nearly 5 h. 48 m. during the whole month.

^{page 755 note *} It must be remembered that these curves cannot be compared with those preceding them, day by day; 1d. (under 0d. in the plate) does not correspond to new moon (but to half a day or more after it), and there are only six days hero included between the day for the moon on the meridian near noon, and the moon on the meridian at 6 h. p.m., whereas seven days were included by the other method.

^{page 756 note *} The means for 12½ a.m., are calculated for the end of each day as well as for the beginning, in order to connect in the projection the value for the end of each day with that for the beginning of the next.