196 MR BROUN ON THE RELATION OF THE VARIATIONS OF THE 

produce two minima. Thus, if APA be the curve due to distance, NSN 
that due to declination, the curve B PC, produced by the superposition of their 
ordinates will have two minima, if the sum of the ordinates ab +a'b’ be less 
than the sum DN+AB, and a” b”+a” b’” 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 0:000455 ; for 1845, 
0000390 ; and, for the mean of both years, 0:000380. 
18. I have already mentioned (14), that, by taking 13 revolutions of the moon, 
with respect to its declination, we eliminate any effect due to the varying phase of 
the moon. Similarly, if we 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. declination, it is evi- 
dent that 6 lunations will be sufficient to eliminate the effect of declination. (See 
Curves, No. 7, Plate IV.) Ihave 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 
