OF T1IE MAGNETIC FORCE. 49 



methods of interpolation in the construction of the two tables. In the determination 

 of the numerical quantities (by application of the method of least squares) in the 

 monthly equations, due attention was paid to the relative weights of the values for 

 the even and odd hours. The coefficients are expressed in scale divisions (increasing 

 numbers denoting decrease of force), and the angle 6 counts from midnight at the 

 rate of 15 an hour. 



For January, A A = + 793 d .3 + 3 d .77 sin ( + 236 52') + 6 d .56 sin (2 9 + 96 52') 



+ 3 d .99 sin. (3 6 + 282 13') + 2 d .OO sin (49+ 91 ) 

 For February, A 4 = + 800 d .6 + 5 d .50 sin ( 9 + 218 26') + 4 d .57 sin (29 + 102 29') 



+ 3 d .27 sin (3 e + 282 40') + l d .66 sin (49 + 121 ) 

 For March, A 4 = + 805". 7 + 6 d .56 sin ( e + 243 31') + 5 d .35 sin (29+114 14') 



+ 4 d .23 sin (39 + 316 04') + l d .91 sin (49 + 113 ) 

 For April, A A = + 828 d .3 + 7 d .G5 sin ( 9 + 257 37') + 9 d .55 sin (29+ 123 06') 



+ 5 d .15 sin (39 + 306 44') + l d .18 sin (49 + 163 ) 

 For May, A* = + 832 d .2 + 2 d .24 sin ( 9 + 314 31') + 7 d .81 sin (29 + 140 53') 



+ 4". 40 sin (3 + 330 05') + l d .34 sin (49 + 214 ) 

 For June, A 4 = + 856 d .8 + 2 d .12 sin ( 9 + 356 03') + 6 d .40 sin (29 + 140 32') 



+ 4 d .48 sin (39+ 327 14') + O d .92 sin (49 + 216 ) 



For July, A A = + G7C d .3 + 3 d .42 sin ( e + 4 ll') + ll d .50 sin (2 9 + 139 14') 



+ 6 d .14 sin (3 o + 330 15') + O d .78 sin (4 9 + 210 ) 

 For August, A = + 702 d .2 + 5 d .32 sin ( 9 + 310 58') + 10 d .37 sin (29 + 153 46') 



+ 6 d .79 sin (39 + 335 55') + 2 d .88 sin (49 + 203 ) 

 For September, A 4 = + 724 d .6 + 8 d .02 sin ( + 271 57') + 9 d .59 sin (29+ 137 25') 



+ 7 d .08 sin (39 + 345 17') + l d .99 sin (49 + 215 ) 

 For October, A = + 738*.2 + 8 d .06 sin ( 9 + 237 57') + 6 d .40 sin (29+ 123 37') 



+ l d .34 sin (39 + 325 20') + 0".29 sin (49+ 174 ) 

 For November, A A = + 738 d .5 + 4 d .13 sin ( e + 237 36') + 6 d .08 sin (29 + 100 01') 



+ l d .93 sin (39 + 310 45') + O d .46 sin (49 + 211 ) 

 For December, A A = + 7C8 d . 1 + 5 d .03 sin ( o + 212 48') + 8 d .07 sin (29+ 94 14') 



+ 3".98 sin (3 o + 269 17') + l d .31 sin (49+ 88 ) 



We have also: For summer half year (April to September inclusive), for winter 

 half year (October to March inclusive), and for the whole year, the following 

 expressions for the regular solar diurnal variations: 



For summer, A 4 = + 770 d .l + 3 d . 7 9 sin ( o + 293 49') + 9".ll sin (29 + 139 10') 



+ 5 d .36 sin (3 e + 329 17') + l d .42 sin (4 e + 202 ) 



For winter, A = + 774 d .l + 5 d .36 sin ( + 231 36') + 6 d .04 sin (29 + 104 46') 



+ 2 d .88 sin (3 + 293 54') + l d .ll sin (49+ 108 ) 



For year, A A = + 772 d . 1 + 3 d .95 sin ( e + 256 19') + 7".25 sin (29 + 125 05') 



+ 3 d .96 sin (39 + 317 31') + O d .86 sin (4 9 + 165 ) 



The following expressions for January may serve as specimens of the agreement 

 of the result derived from the even and odd hours independently: 



From even hours, A = 793 d .3 + 3 d .81 sin ( 9 + 238 01') + 6 d .56 sin (2 o + 94 32') 



+ 4 d .10 sin (39 + 280 19') + 2 d .08 sin (4 9+86 ) 



From odd hours, A = 7 93 d . 4 + 3 d .71 sin ( 9 + 234 35') + 6 a .56 sin (29+ 101 32') 



+ 3 d . 7 6 sin (:i 9 + 286 00') + l d .85 sin (4 9 + 119 ) 



giving to the first equation the weight 2 and to the second the weight 1, we obtain 

 the equation as given above. 



