470 NUMERICAL CALCULATION OF THE MAGNETIC FORCES 



3. Calculation of the weights of the observations for every 5th degree 

 of geographical colatitude, on the assumption that the weight of any deter- 

 mination of magnetic force is proportional to the area of the surface over 

 ivhich the observations extend. 



If p be the radius of curvature of the terrestrial meridian for the 

 geographical colatitude 6, and if N be the normal terminated by the axis 

 of revolution, we have seen that 



and that an element of the surface 



Take a as unity, then the weight of the observation for any belt 



When the observations extend over a zone of 5 in breadth, the area 

 of the zone will contain the factor 2 sin - , where w is the circular measure 



a 



n ,o T 



f 5 =36" 



The weight found by the above formula must be divided by 2 sin 



Zt 



or 01 in order to reduce it to the scale employed when observations are given 

 to every 5 of latitude. This summation will only extend to latitude 87'5. 



The area of the small circle of radius 2 '5 round the pole is very 

 approximately 



8wJHl-V) (I-OO.ZT), 



\ */ 



hence the weight for this small area 



CO 



1-C08- 



= ^(l-e 2 ) - 



(a 

 2sm- 



