MAGNETIC DECLINATION AT TREVANDRUM. 753 



pened when the moon was on one of the meridians of h., 6 h., 12 h., and 18 h., 

 there would have been nothing remarkable in this result, it would have agreed 

 with previous ideas of the mean law of lunar diurnal variation ; but this is not 

 the case, the maxima and minima occurring at hour angles differing from the 

 above by three hours in some months, and changing hour with more or less 

 regularity from month to month. It could scarcely, therefore, be supposed to 

 be a coincidence dependent on the true law of variation. 



48. At least two questions present themselves in reference to this result : 

 First, How this constancy of maxima and minima for fixed hour angles of the 

 moon can agree with the fact of the change of hour shown (18) in the means 

 for each month ? We find an explanation of the apparent contradiction when 

 we examine the curves for the phases, and consider the maxima and minima 

 which do not happen at sunrise. Thus, the curve for new moon in the months 

 of January to May shows that the principal maximum gradually shifts from an 

 hour before the upper passage in January, to 3 h. before it in April and May. 

 Similarly the passage of the minimum (in the same curves) for the moon on the 

 meridian of 5 h. in January, to on the meridian of h., though not equally regu- 

 larly, is clearly shown. The change for the corresponding minimum in the third 

 quarter happening more gradually from 5^ h. in January to h. in July. 



49. The next question has reference to the mode in which the moon acts on 

 the needle, on days intermediate betwixt two of the quarters; when, for example, 

 she is on the meridian of 17 h., 16 h., 15 h., at sunrise, how does the movement 

 change from that shown in the thin curve in January (new moon), where the 

 movement is rapidly eastward after sunrise to that shown in the thin curve 

 for the first quarter, where the movement is rapidly westwards at the same solar 

 hour % Does the epoch of maximum or minimum vary at all with sunrise, or 

 does the coincidence seen in these curves hold only for the four positions of 

 the moon to which the curves strictly belong ? 



50. In order to answer these questions, the consideration of one period of 

 seven days will suffice ; for this end twelve periods from new moon to the first 

 quarter in the months of December and January, showing the greatest varia- 

 tions, were chosen. In each of these periods the sum was taken of the diurnal 

 variations for each hour in the week, having new moon in the middle ; the sums 

 of the twelve sums thus found having been formed, the means (from seventy-two 

 days) gave the mean variation corresponding to new moon. A similar calcula- 

 tion was made for the weeks having the moon, one, two, to seven days old 

 in the middle. These means are projected, Plate XXVII. 



51. It will be seen from these curves, that the sunrise seems to pass from 

 the minimum near 18 h. to the maximum near 12 h., gradually and without 

 having any marked influence on the epoch of minimum or maximum. These, 

 however, are mean results, the curve for each day being derived from three days 



