4 Olif THE REDUCTION OE TfiE 



In tliis formula eacli term, after the first, is relatively siflallei? 

 than the corresponding term in (iv.) j and if — — is large, the terma 



having sensible magnitude, are alternately positive and negative. 

 Therefore the error, introduced by neglecting aU terms beyond the 

 first, is relatively less in (v.) than in (iv.) j but, since B is not 

 known until R has been determined, this formula could only be 

 employed by successive approximation, and is therefore inconvenient. 



It may be seen by inspection that, in Table XIX.', N is very 



o t 



nearly equal to — , N . That this should be so, may be proved 

 thus : — 



As already explained 



10^ 



1,T A i 10 3 



S^, ^"^lO^^l ^'^i'~WB 



.N' 



^"' '-i^ '"^(-i,), 



2 



1 1 _J_ I 



10 5 "^ 2" lO-Sl ''' 



j_ 1 XT' 



10 j8 "^ 2 ■ 10/31 "^ 



= — nearly, (vi.) 



^IT. = -^ ' 2f. nearly, as above stated. 

 JS t Jo R t 



