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divifions performed by fmall divifors. Whereas, to find the na- 

 tural number — , by the application of the fradion ?_ ^ , 



a ^ ^^ q-6p+L 



or the natural number — , by the application of the fradion 



b 



'— — ?- , two divifions are fufiicient, of whatever fyftem the 



q + 6p + L ' 



logarithm may be. For 12/' being given (fince/ is the modulus 

 of the fyftem) q is found by one divifion. Another divifion will 



give the value of the fradion ^ — -?- =, all its terms beins 



q^dp-^L ^ 



known and of one dimenfion. 



Since ^- = S±^P±Il and ^ =: lll|/_±r^, we have b = 



a-V l^ ^nAa = b-l^^ 



q—6p-\-L q+6p + L 



Whence if a logarithm of any fyftem be given, to find its 

 correfponding natural number 5 find the diiFcrence of the given 

 logarithm and the neareft logarithm to it (in the fame fyftem) 

 whofe natural number is known. Call this difference L; the 



modulus of the fyftem p ; and - -^ ■ = q. Then, if the given 



Vol. VI. 3 I logarithm 



