TERRESTRIAL MAGNETISM. 209 



of the degree of uncertainty which still attaches to the funda- 

 mental members. 

 From the equations 



-/ pio fj p2o fj pao 



"-3 du ^ du ^ du '^^' 



the total number of which is double the number of the par- 

 allels, we have to obtain, by the method of least squares, (after 



d P''" 

 substituting in -t — , &c., and in P'°, &c. the corresponding nu- 

 merical values of u,) as many of the co-efficients ff^'^, g^'°, g^'^, &c. 

 as require to be taken into account. 

 In Uke manner the equations 



^ du ^ du ^ ^ du ' 



p\\ p2) p31 



L' = ffi-i 4-— + /•! 4— + /•» 4-— +, &c. 



"^ sm M sin w sm « 



m' = 2/-1 P'-i -F 3/1 P2-i -h4/-' P3-» +, &c., 



the number of which is three times as great as the number of 



parallels, serve to determine the co-efficients y*', /"', /'i, &c. 



And the following, 



du du du 



pil p2.1 psi 



-l' = ^11 4-— + A^-i 4—- -H /i^i 4— +, &c. 

 sm u sm u sm % 



i»/' = 2 ^ji-i Pii + 3 7i^-i P2-» -f- 4 ^3-1 P^-' -h, &c. 

 determine the coefficients h}'^^ /t^', h^'^, &c. Further, the equa- 

 tions 



- k" = /'^ ^ + /-^ ^ + /-^ ^' +, &c. 

 ■^ aw ^ du ^ du ^' 



p2-2 p3-2 p4.3 



£// = 2/2 4— + 2^3.9 il_ _^ 2/-^ 4— +, &c. 

 "^ sm u " sm M ^ sm w ' 



m" c= 3 /^ p2-2 + 4 /•* P3-^ + 5 /-^ P4-2 +, &c. 



determine the co-efficients g-'^, g^"^, Z'^, &c.; and we obtain the 



co-efficients of the succeeding higher numbers in a similar manner. 



24. 

 The chief advantage which this method possesses over that 



