464 Wt^sconsiti Academy of Sciences, Arts, and Letters. 



Then we have 



/(c) = ^ tan i c |/{log sin Ic) +/"3 \ 



If next the vahie found for / (log sin % c) is substituted in 

 these eqn;idons and if every /' is change<l into the form 

 i/^ +5/^2 +y"3 5 aiid every _/' into the form — i/^ — ^/sj 

 and then if, for simplicity, f^, f^, etc., be denoted by (1), 

 (2), etc., so that we may write 



Therefore the probable error by which c is aifcctcd, if si:: place 

 logarithms are used, is 



p 



wF = 10-6 -^^/^(a2) 

 |/G 



in which it is necessary to write the coefncients of the qiiantitisc 



