4-GS ^yi.scons^}l Academy of Sciences, Arts, and Lcllcr 

 Tlien if, instead of /'' and /" we put 



i!a)+i2)H3)ancU(l)+i(5) 



Tvo sliall liavG nineteen independcTit sources of error and find 

 tliat 



V 



^r'/v2 





Lastly by insertir.g the factor 



10-G -]^ 



we sliall obtain the probable error by v»'liicb c is afrected, as ex- 

 pressed in the following table : 



Since wF approaches infinity as m approaches zero, this form- 

 ula is eidently unsuitable for general use. 



C. The Gaussiaii equations for computing the third side c 

 furnish another exani])le. They are the following four, if we 



put 



VziA-B) =ju and i^(^+^) = v 



Viz: 



cin }^o sin ju 

 sin }^c cos JU 

 cos l<>c sin V 



cos 3^20 C03 V 



sin 3^(a— 6) cos y2,C 

 sin }2{^'\~^) siii y^O 

 cos }^{a — b) cos }^iO 

 coa}^{a-\-b) sin }^C, 



