Magnetkal Observatory of Dublin during the Years 1840-43. 



79 



year, the winter half-year, and the whole year, respectively, the mean value of A 

 at any hour will be expressed by the following equations, in which .r = « x 15" 

 « denoting the number of hours, and parts of an hour, reckoned from midnight] 



Summer Half-year. 



A„ = 4'-288 sin {x + 55° 44') + 2'-653 sin (2^' + 23r47') 

 + 0'-872 sin (3^ + 70^6') + 0'.189 sin {Ax + 253' 56'). 



Winter Half-year. 



A„ = 2'-873 sin {x + 77° 10') + 1'.647 sin {2x + 214° 56') 

 + 0'.500 sin {Zx + 72° 7') + 0'-463 sin (4^ + 237^ 47'). 



Whole Year. 



A„ = 3'.519 sin {x + 64° 18') + 2'.127 sin (2.7; + 225' 22') 

 + 0'-688 sin {ix + 70° 40') + 0'-322 sin {Ax + 242^27'). 



7. It is manifest that the coefficients of the equation of the diurnal curve 

 may be generally expressed as periodical functions of the time, reckoned from a 

 given epoch of the year. For this purpose we have only to apply to the values 

 of yl and 5, belonging to the several months of the year (Table 11.), the same 

 process which has been abeady applied to the values of A, corresponding to 

 the several hours of the day. We thus obtain the following formula, in which 

 x = nx 30°, n denotijig the number of months, and parts of a month, reckoned 

 from the 1st of January. The terms of the series which follow those here given 

 are neglected as inconsiderable. 



{x + 280° 37') + 0'.541 sin {2x + 294° 56'); 

 {x + 297' 29') + 0'-265 sin {2x + 110° 21') ; 

 {x + 96° 39') + 0'-339 sin {2x + 83° 41') ; 

 {x + 239° 56') + 0'-078 sin {2x + 210° 48'); 

 {x + 297° 5') + 0'.280 sin {2x + 281° 40') ; ' 

 {x + 119° 1') + 0'-030 sin (2a- + 20° 26'); 

 {x + 269° 36') + O'-lOO sin {2x + 147° 17') ; 

 {x + 144° 23') + 0'-150 sin {2x + 248° 50'). 



