106 



MR BROUN ON THE RELATION OF THE VARIATIONS OF THE 



]iroduce two minima, Tims, if A P A be the curve due to distance, N S N 

 that due to declination, the curve B P C, produced by the superposition of their 

 ordiuates will have two minima, if the sum of the ordinates o.h-va'h' be less 

 than the sum DN + AB, and «" h" + a"' U" be less than EN + AC. 



The fact, that in both the solar and lunar curves the maxima are nearly 

 equal, is against the supposition that both distance and declination are equally 

 concerned, as it seems rather improbable that the effect of increasing distance 

 should precisely counterbalance the effect of increasing N. declination. We have, 

 however, much more singular cases of compensation in the motions of the heavenly 

 bodies. 



17. The range of the lunar declination curve for 1844 is 0000455 ; for 1845, 

 000390 ; and, for the mean of both years, 0-000380. 



18. 1 have already mentioned (14), that, by taking 13 revolutions of the moon, 

 with respect to its dechnation, we eliminate any effect due to the varying phase of 

 the moon. Similarly, if Ave take 12 lunations, and sum the mean intensity for 

 the twelve days on which the moon was full, the twelve days on which it was one 

 day old, and so on, we eliminate the effect of varying declination, and also the 

 annual period very nearly. If, however, we may consider the intensity with 

 respect to N. declination similar to that with respect to S. dechnation, it is evi- 

 dent that 6 lunations will be sufficient to eliminate the effect of declination. (See 

 Curves, No. 7, Plate IV.) I have had the observations during the six summer 

 lunations for 1844 summed by themselves, and also those during the six winter 

 lunations ; the mean intensities for both, for each day of the moon's age, have been 

 projected, and also the mean for the year. All indicate a maximum of intensity 

 about two days after the new moon, and a minimum perhaps two days after the 

 full moon ; the summer curve has an irregularity before full moon, and its range 

 is only half that for the winter months. The minor irregularities may be ac- 

 counted for in the same way as for the declination curve. The range for the 



