476 



same result ; though the result for each place has been confirmed by 

 the discussion of different periods. 



In order to obtain the lunar diurnal action, it has been usual to 

 consider the magnetic declination at any time as depending on the 

 sun's and moon's hour-angles and on irregular causes. Thus, if 

 at conjunction, H be the variation due to the sun on the meridian, 

 arid A be that due to the moon on the meridian, H, the variation 

 for the sun at l h , h^ for the moon on the meridian of l h , and so on ; 

 it is supposed that we may represent the variations for a series of 

 days by the following expressions, where the nearest values of h to 

 the whole hour-angles are given : 

 1st day. H' +A' +x' H\ + h\ +J 1 ... H' 23 + ' 

 2nd day. H" + A" M +aj" W\ + h\ + a?\. . . H" 23 + A 



nth day. Hj + A? +** H* +^ +fl . . . ! + +, 



where x is due to irregular causes, and n is the number of days in a 

 lunation nearly. 



Summing these quantities we have approximately, 



SH +^ 3 A-f-S* o , SH 1 +2 2 / + S^ , . . . SH 23 + 2/+2^ 23 (A.) 



and the means are, 



H + C + , H,+ t + *fs, ... H M + I +?3s ...... (B.) 



n 



Here the hourly means are affected by the constant due to the total 

 action of the moon on all the meridians, and by variables depending 

 on disturbing causes. If, on the other hand, we arrange the series as 

 follows, 



H' +h' +ff' , H' t +A' 1 +< > . . . H" 



Summing these quantities we have, 



i 

 and for the means, 



..... (D., 



