OF THE MAGNETIC DECLINATION. 15 



For January, A d = + 1'.423 sin (15 n + 225 09') + 1'.491 sin (30 n + 16 38') 



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

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



+ 0'.472 sin (45 n + 231 59') + 0'.352 sin (60 n + 60 . . ) 

 For March, A<J = + 2'.093 sin (15 n + 206 46') + 1'.827 sin (30 n + 26 34') 



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

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



-f 0'.926 sin (45 n + 223 29') + 0'.245 sin (60 n + 80 . . ) 

 For May, A<J = +2'. 746 sin (15 n + 210 38') + 2'.377 sin (30 n + 45 50') 



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

 For June, Ad = + 2'.883 sin (15 n + 204 09') + 2'.438 sin (30 n + 44 15') 



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

 For July, A d = +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, Ad = +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 n + 51 . . ) 

 For September, A<J = +2'.706 sin (15 n + 220 05') + 2'.372 sin (30 n + 55 54'> 



+ l'.126sin(45n + 261 14') + 0'.414 sin (60n + 115 .. ) 

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



+ 0'.727 sin (45 n + 230 52') + OM50 sin (60 n -f 47 . . ) 

 For November, Ad = +1'.259 sin (15 n -f 229 06') + 1'.257 sin (30 n + 39 15') 



+ 0'.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 -f 23 34') 



+ 0'.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, Ad = +2'.936 sin (15 n -f 210 36') + 2'.404 sin (30 n + 46 07') 



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



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



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



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



-f 0'.759 sin (45 n + 244 40') + 0'.198 sin (60 n + 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') + K888 sin (30 n + 38 59') 

 +0'.729 sm (45 n + 244 57') + 0'.183 sin (60 n + 83 26') 



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

 +0'.848 sin (45 n + 243 49') + 0'.242 sm (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 G v C 3 , C 3 , G 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, A<j = +2M67 sm ( -f ^3 55') -f K875 sm (2fl + 218 52') 

 +0'.759 sm (38 + 64 40') + 0'.198 sm (40 + 263 05') 



For Dublin, Ad = +3'.519 sm ( 6 + 64 18')+ 2'.127 sm (28 + 225 22') 



+0'.688 sm (38 + 70 40') + 0'.322 sm (4 + 242 27') 



This latter expression is copied from the Rev. H. Lloyd's discussion of the Dublin observations in 

 1840-'43. 



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



