OF THE MAGNETIC FORCE. 



23 



The preceding mean diurnal variations were put in the following analytical form, 

 in which the angle 6 counts from midnight at the rate of 15 an hour. 



Year 1840-41 H = 223 d .5 + 5".98 sin (fl + 252 14') + 1K68 sin (28 + 121 16') + 5*.89 sin (38 + 314 42') 



" 1841^*2 H = 551.5 + 4.03 sin (fl + 244 07 ) + 6.58 sin (2 9+131 32 ) + 4.48 sin (3 fl + 312 19 ) 



" 1842-43 H = 789.9 + 4.14 sin (fl + 250 06 ) + 7.07 sin (2 fl + 132 24 ) + 3.74 sin (38 + 323 06 ) 



" 1843-44 H = 1007.4 + 2.14 sin (8 + 273 65 )+ 5.09 sin (20 + 128 58 ) + 2.35 sin (38 + 317 58 ) 



" 1844-45 H = 1191.4 + 4.40 sin (fl + 271 13 ) + 6.86 sin (2 fl + 123 25 ) + 4.11 sin (38 + 321 26 ) 



To show the degree of correspondence hi the formula when deduced from the 

 observations of the even and odd hours separately, the results for the last year have 

 been added, viz: 



Even hours II = 1191 d .3 + 4.20 sin (fl + 271 28') + 6 d .98 sin (28+ 122 36') + 4 d .ll sin (3 fl + 322 35') 

 Odd hours H = 1191.5 + 4.60 sin (fl + 270 59 ) + 6.73 sin (2 8 + 124 13 ) + 4.12 sin (38 + 320 17 ) 



The close agreement between the observed and computed values is shown gene- 

 rally in the annexed diagram. 



(A). IHBQDALITY IN THE DICKNAL VARIATION OP THE HORIZONTAL INTENSITY. 



1840-41. 



1841-42. 



1842-43. 



1843-44. 



1844-45. 



O h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24" 

 A. M. P. M. 



Philadelphia local time. 



The following table exhibits the differences for the year 1842-43, as an example 

 of the numerical correspondence. 



