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logarithm found will differ from the truth by lefs than half an 

 unit in the 8th place of decimals. 



Here the number whofe logarithm is fought, being denoted by 

 the fador .v+ 7, the logarithm comes out lefs than the truth ; if 

 the number were denoted by the fador «■+ 8, we fhould get the 

 logarithm greater than the truth. The reafon of this is manifeft, 

 from the relation between the produds. 



The logarithms of numbers exceeding 300 may be found by this 

 method to 10 places of decimals. And the logarithms of numbers 

 exceeding 1300, to 14 places. 



A SIMILAR application may be made of the fadors of the 

 produds of four dimenfions, which will ferve to conftrud the 

 logarithms of numbers exceeding 20,000 to fourteen places of 

 decimals; fo that, ■ if neceffary, we may have an eafy way of 

 compleating the chiliads omitted by Briggs. E. G. Let it be 

 propofed to find the logarithm of 19997, being even fomewhat 

 lefs than, 20000. 



^=19995 



