OF THE MAGNETIC DECLINATION. 15 



Fur January, Xi = + 1'.423 sin (15 n + 225° 0!)') + F.491 sin (30 n + 16° 38') 



■+0'.579 sin (45 n + 220° 23') + 0'.548 sin (60 n + 53° . . ) 

 For February, A d = + 1'.469 sin (15 n + 211° 09') + F.456 sin (30 n + 20° 50') 



+ 0'.4T2 sin (45 n + 231° 59') -f C.352 sin (60 « + 60° . . ) 

 For March, A d = +2'.09S sin (15 « + 206° 46') + 1'.827 sin (30 n + 26° 34') 



+ 0'.693 sin (45 n + 230° 10') + 0'.413 sin (60 n + 84° . . ) 

 For April, a,* = +2'.906 sin (15 n + 213° 21') + 2'.001 sin (30 n + 34° 01') 



+ 0'.926 sin (45 « -f 223° 2'.)') + 0'.245 sin (60 /! -f 80° . . ) 

 For May, A rf = + 2'.746 sin (15 n + 210° 38') -f 2'.37Y sin (30 n + 45° 50') 



+ 0'.970 sin (45 n + 251° 57') + O'.IOO sin (60 n +161° .. ) 

 For June, a,, = +2'.883 sin (15 n + 204° 09') + 2'.438 sin (30 w + 14° 15') 



+ 0'.94l sin (45 n + 254° 03') + 0'.216 sir! (60 h +114° . . ) 

 For July, a,; = +3'.310 sin (15 n + 204° 19') + 2'.465 sin (30 n + 38° 48') 



+ 1'.047 sin (45 n + 251° 38') + 0'.092 sin (60 n +176° . . ) 

 For August, a,, = +3'. 161 sin (15 n + 211° 37') + 2'. 849 sin (30 n + 52° 16') 



+ 1'.375 sin (45 n + 265° 49') + 0'.201 sin (60 ra + 51° . . ) 

 . For September, A rf = +2'.706 sin (15 n + 220° 05') -f 2'.372 sin (30 n + 55° 54') 



+ 1M26 sin (45 n + 261° 14') + 0'.414 «i» (60n+115° .. ) 

 For October, a (( = +1'.271 sin (15 n + 226° 29') + 1'.325 sin (30n + 33° 12') 



+ 0'.727 sin (45 n + 230° 52') + 0'.150 sin (60 n + 47° . . ) 

 For November, A rf = +1'.259 sin (15 n + 229° 06') + 1'.257 sin (30 n + 39° 15') 



+ C.390 sin (45 n + 236° 30') + 0'.242 sin (60 n + 87° . . ) 

 For December, A d = +1'.212 sin (15 n + 231° 46') + 1'.321 sin (30 n + 23° 34') 



+ C.367 sin (45 n + 205° 46') + 0'.418 sin (60 n + 32° . . ) 



In like manner, we obtain for the summer half-year (from April to September 

 inclusive), for the winter half-year (from October to March inclusive), and for the 

 whole year, the following expressions for the diurnal variation: — 



For summer half-year, A d = +2'.936 sin (15 n + 210° 36') + 2'.404 sin (30 n + 46° 07') 



-f 1'.031 sin (45 n+ 253° 37') + OM78 sin (60 n + 132° 20') 



For winter half-year, A d = + 1'.420 sin (15 n + 220° 41') + F.399 sin (30 n + 26° 39') 



+ C.520 sin (45 n + 227° 26') + 0'.310 sin (60 n + 61° 17') 



For the whole year,' A<i = +2'. 167 sin (15 n + 213° 55') -f 1'.875 sin (30 n + 38° 52') 



+ 0'.759 sin (45 n + 244° 40') + 0'.198 sin (60 n -f 83° 05') 



1 For the purpose of showing the correspondence when the above equation is deduced independently, 

 from the observations at the even and odd hours, I add here the values for the two cases: — 



From even hours, Ad = +2'.170 sin (15 n + 213° 27') + l'.88S sin (30n + 38° 59') 

 +C.729 sin (45 n + 244° 57') + 0US3 sin (60 n + 83° 26') 



From odd hours, Ad = +2M59 sin (15 n + 215° 19') + 1'.835 sin (30 n -f 38° 31') 

 +C.848 sin (45 n + 243° 49') + 0'.242 sin (60 n + 82° 01') 



The relative weights of the results by the even hours and the odd hours are as 3 : 1. 



If, for the purpose of comparison with the previous results in Part I of this discussion, and with 

 other similar expressions, we change the angles C v C a , C 3 , C v by 180°, which is equivalent to an easterly 

 deviation from the mean for positive results and to a westerly deviation for negative results, we find — 



For Philadelphia, Ad = +2M67 gin ( 6 + 33° 55') + 1'.875 sin (28 + 218° 52') 



+0'.759 sin (3 8 + 64° 40') + OM98 sin (48 -f 263° 05') 



For Dublin, Ad = +3'.519 sin ( 8 + 64° 18') + 2'.127 sin (2 8 + 225° 22') 



+0'.«8S sin (3 8 + 70° 40') + C.322 sin (4 8 + 242° 27') 



This latter expression is copied from the Rev. H. Lloj'd's discussion of the Dublin observations iu 

 1840-'43. 



For a comparison of the monthly equations, the reader may also consult similar expressions obtained 



