46 



EESEARCHES ON 



II. 



The values of the radius of the circle B, the half length of the needle L, and 

 its deviation from the magnetic meridian plane, are already given by observation 

 with the quantity p, which is the distance of the middle of the needle from 

 the centre of the globe, reckoned on the vertical axis OX. Let us take, for 

 example, the case of the needle at nine-tenths of the radius, as we explained it in 

 the description of the experiment, and let the deviation be 30°. Expressing all 

 the numbers by centimeters, we have 



20.25, d = 30^ 



Remembering, also, that from § 3 we have 



m =:: L COS. d, 11 ^ L sin. d, tang, a = — , 



m 



h} =z E [p sin. a + m cos. a),(^) 



h^ = S' + m^ + if + / + 2 li\ 



.2 _ i^ 

 The calculation may be arranged as in the following example :- 



E = 22.5,i = 2,p = lE 



Specimen of Calculation of the Formula (6), the Needle being at i%t7is of the Radius, 



and d ■=. 30°. 

 Log. cos. d; = 30° . . . . = 9.9375306 



+ log. L = 



log. 



2 . . . 



= 0.3010300 



log. m 







0.2385606 



log. p = 



log. 



20.25 . 



= 1.3064250 



— log. m 







. = 0.2385606 



log. tang 



a = 



= 85° 6' 40" 



= 1.0678644 



log.p . 







. = 1.3064250 



log. sin. a 





= 9.9984172 



log. s . 







. = 1.3080078 



+ log. R 







= 1.3521825 



log. h^ 







. = 2.6601903 



h' . 







= 457.288 



2h^ . 







. = 914.576 



ih^ 







= 1829.152 



R' 







. = 506.25 



m^ + n^ 







= 4.00 



/ 





• > . . 



. = 410.0625 



2h' 





• 



= 914.576 



h^ 



. = 1834.8885 



(') After having made all the calculations, we observed, § 6, that m being = s cos. a, and p = s s-w). a, 

 we have Ji} = R {s sin.' a + s cos.' a) = Es. This shortens a little the calculationSj and the value of s 

 taken from any of those two values can be introduced. 



