BremiJccr — Errors Affecting Logarlihmic Computations. 431 



These equations, if applied to any logarithmic commutation 

 whatsoever, show the error of the final result as a linear func-" 

 tion of the separate errors. To illustrate this, take as an ex- 

 ample the equation 



ein* \c = sin* l{n — b) -f- sin a sin b sin* 10 



which expresses the third side c of a spherical triangle in terms 

 of the given sides a and b and the included angle C. First com- 

 pute 



cot /I = sipjC^i/sin a sin b 

 sin^ {a—b) 



tHeu 



-• 1 ^ einiCt''sin « sin 6 



Bin ^ c = = — • 



cos Jil 



Then if the errors of the logarithms of the table are arranged in 



order, 



in sin ^ C the error f^ 



" sin a *' " /a 



•• sin 5 " " /s 



•' sin ^{a—h) " " /4 



♦* cot /I " ♦• /s 



«• cos JU " " /fl 



«* Bin^c " " ft 



tte error in the sum from which cot /i is determined will be 



fi "r zfz 'T -if z 7 4 



whence tHere arises an error 



in ft equal to — ^^ sin S/iC/j+A/'z-l-i/'s— A— A) 



in log cos I* " •• sin«>/(/,-^i/,-fi/8-/4-/5)+/« 

 in log sin ic •* •« /i+i/j+i/ 3-sin V(/i-f-iA+i/3-/4-/5)--/e 



= cos»//(A-fi/84-^A)+einV(/4+/5)-/, 



and in c equal to — tan ic | cos2//C/*i+i/'84-i/3)+Bin V(/4+/6) — /e — /? f 



