O P T U E M A ( i N E T 1 C F OllCE. j<) 



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

 of the numerical quantities (by application of the method of leasl 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 counts from midnight at the 

 rale of 1 5° an hour. 



For January, a a = + 793 d .3 + 3 d .tt sin ( o + 236° 52') + 6 d .56 sin (2 o + 96° 52') 



+ 3*99 sin (3 9 + 282 ' 13') + 2 d .00 sin (49 + 117° ) 

 For February, a 4 = + 800 4 .6 + 5 d .50 sin ( o + 218° 26') + 4 d .57 sin (2o + 102° 29') 



+ 3 d .27 sin (3 9 + 282° 40') + L d .66 sin (1 9 + 121° ) 

 For March, a, = + 805''. 7 + 6 d .56 sin ( 9 + 243° 31') + 5 d .35 sin (2 9 + 114° 14') 



+ 4 d .23 sin (3 + 310° 04') + l d .91 sin (4 9 + 113° ) 

 For April, a, = + 828 d .3 + t d .65 sin ( s + 257° 37') + 9 d .55 sin (2 o + 123° 06') 



+ 5 d .15 sin (3 o + 306° 44') + l d .18 sin (4 o + 103° ) 

 For May, a,. = + 832 d .2 + 2''.24 sin ( e + 314° 31') + 7 d .81 sin (2 9 + 140° 53') 



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

 For June, a„ = + 856 d .8 + 2 d .12 sin ( 8 + 350° 03') + G d .40 sin (2 9 + 140° 32') 



+ 4 d .48 sin (3 8 + 327° 14') + 0".92 sin (4 9 + 210° ) 

 Km- July, a 4 = + 676 d .3 + 3 d .42 sin ( 0+ 4° ll') + ll d .50 sin (29 + 139° 14') 



+ 6 d . 1 t sin (3 5+ 330° 15') + d .78 sin (4 'J + 210° ) 

 Fur August, a 4 = + 702 d 2 + 5 d .32 sin ( + 310° 58')+10 d .37 sin (2o + 153° 40') 



+ 6 d .79 sin (3 o + 335° 55') + 2". 88 sin (4 9 + 203° ) 

 For September, a a = + 724 d .6 + 8 d .02 sin ( o + 271° 57') + 9 d .59 sin (2 9 + 137° 25') 



+ 7 d .08 sin (3 9 + 345° 17') + l d .99 sin (4 9 + 215° ) 

 For October, a 4 = + 738 d .2 + 8 d .06 sin ( 9 + 237° 57') + 6 d .40 sin (2 o + 123° 37') 



+ l d .34 sin (3 9 + 325° 20') + a .29 sin (4 9+ 174° ) 

 For November, a_ = + 738 d 5 + 4 d .13 sin ( 9 + 237° 3(1') + 6".08 sin (2 + 100° 01') 



+ r'.!)3 sin (3 9 + 310° 45') + d 46 sin (4 + 211° ) 

 For December, a„ = + 768 d .4 + 5 d .03 sin ( 9 + 212° 48') + 8''.07 sin (2 o + 94° 14') 



+ 3".98 sin (3 9 + 269° 17') + l l 31 sin (4 9+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: — 



Fur summer, A ft = + 770 d .l + 3'.70 sin ( 9 + 293° 4!)') + tr'.ll sin (2 o + 139° 10') 



+ 5".36 sin (3 9 + 329° 17') + l d .42 sin (4 e + 202° ) 



Fur winter, a,. = + 771'.1 + 5 d .36 sin ( 9 + 231° 30') + 6 d .04 sin (2 9 + 104° 40') 



+ 2''. 88 sin (3 9 + 293° 54') + l".ll sin (49+ 108° ) 



For year, a„ = + 772'. 1 + 3 d .95 sin ( 9 + 250° 19') + 7 d .25 sin (2 9 + 125° 05') 



+ 3 d . 96 sin (3 9 + 317° 31') + 0".8G sin (4 9 + 105° ) 



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 Lours, a, = 793 d .3 + 3 d .81 sin ( 9 + 238° 01') + 6 d .'56 sin (2 o + 94° 32') 



+ 4 a . 1 sin (3 9 + 280° 1 9') + 2".08 sin (4 9 + 86° ) 



From odd hours, a,. = 793'U + 3 d .71 sin ( 9 + 234° 35') + 6 d .56 sin (2 9+101° 32') 



+ 3''. 70 sin (3 o + 286° 00') + L d .85 sin (49 + 1 19° ) 



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

 the equation as given above. 



