MAGNETIC DECLINATION AT TREVANDRUM. 745 



Thus, if the scheme just given represents a lunation in December, the moon 

 will be farthest south in the first days of the lunation, and the night hours will 

 correspond to the lunar hour angles of 6 h. to 17 h. ; while for a lunation in June, 

 the moon will be farthest north when the night hours correspond to the same 

 lunar hours ; in the intermediate months, the position of the moon in declina- 

 tion will be different at the commencement of each lunation, and the night 

 hours will thus correspond to the same lunar hours for all the different positions 

 of the moon. 



27. It has been, however, supposed that each horizontal line represents the 

 lunar diurnal variation in the same way ; but we know that the mean position 

 of the magnetic needle varies from day to day. A separate investigation has 

 shown that the change of the daily mean is, if not wholly independent of the 

 varying positions of the moon, so nearly so that its effect on this discussion 

 may be neglected, and the other changes may be considered as irregular varia- 

 tions, the effects of which will be eliminated in the discussion of a sufficiently 

 large number of observations.* 



If, now, we obtain the means of the vertical columns for the night hours, 

 these means will correspond to all the positions of the moon (in declination, &c), 

 a similar remark holds for the means obtained from the day hours. The sums 

 having been taken for the night hours in the lunations, the whole or greater 

 part of which occurred in January in each of the eleven years, these were com- 

 bined, and the means taken ; a similar operation was performed for the day 

 hours ; and in each case this was done for each of the twelve months. The 

 conclusions from this discussion are as follows. See second half of Plate 

 XXVL, where the derived means are projected. 



28. 7th, The action of the moon on the declination needle is, in every month 

 of the year, greater during the day than during the night ; the range of the 

 oscillation in January and June, being between three and four times greater 

 during the day than during the night, the ratio being less in the intermediate 

 months. 



The following are the ranges, and the areas of the curves (from observation 

 and computation by formulae similar to those given (14) ) for day and night, 

 with their ratios for each month of the year : — 



Jan. Feb. March. April. May. June. July. Aug. Sept. Oct. Nov. Dec. 

 Range ( Day, 0'-85 0'47 0'-49 0'41 0'-24 0'-36 OHO 0'-39 0'-31 0'-23 0'41 0'-69 

 observed, I Night, 0'-24 0'-26 0'-23 0'-22 0'44 0'41 0'-22 0'48 0'21 0'-21 0'-20 0'-23 



Ratio, T^fl 3-6 18 24 1-8 1-6 3-2 1-9 24 1-5 14 21 3-0 



' Night, 



* 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. 



