750 J. A. BROUN ON THE LUNAR DIURNAL VARIATION OF 



From the means of the observations, and the quantities computed by the 

 preceding equations, we obtain the following results : — 



39. In the group October to April, the areas of the curves representing the 

 observed and computed variations are in the ratios — 



For Apogee : for Perigee : : 1 : 118 by observation ; 

 » „ : : 1 : 1*15 by computation. 



While for the group May to September the ratios are— 



For Apogee : for Perigee : : 1 : 1'31 by observation ; 

 ,, „ : : 1 : P38 by computation. 



The ratios of the ranges of the two oscillations (from the observed quan- 

 tities) are approximately 



October to April, . . A : P = 1 : 1-20 



May to September, . . A : P = 1 : 1-24 



The total ranges of the oscillations by computation are in the ratios 



October to April, . . A : P = 1 : 1-18 



May to September, . . A : P = 1 : 126 



40. The ratios appear greatest for the mean curves representing the group 

 of months May to September, but an examination of the ratios of the areas of 

 the curves for the separate months (which vary considerably, and from other 

 causes than that of distance), shows that this difference is accidental. On 

 taking the ratios of the areas of the observed curves for each month, and the 

 means of these ratios for the six months October to March, and April to Sep- 

 tember, we obtain— 



October to March, . . A : P = 1 : 1-25 

 April to September, . . A : P = 1 : 1-23 



This agreement of the ratios is probably accidental, since when the means 

 of the ratios for the six months January to June, and July to December, are 

 taken, they are found as 1 : 114, and as 1 : 1*34 respectively. But in whatever 

 way we obtain the ratios, the mean for the year is always nearly the same, or 



A : P = 1 : 1-24 nearly, 



which is probably not far from the truth. 



41. The ratio of the moon's mean distance from the earth in the half orbit 

 about apogee is to that in the half orbit about perigee nearly as 1 "07 is to 1 ; as 

 the cube of 1 07 = 1 '23 nearly, we see that the mean ranges of the curves, as 

 well as the mean areas, for the two distances are in the approximate ratios of 

 the inverse cubes of the moon's distance from the earth, as in the theory of the 

 tides. 



