[ 4:^7 ] 



I F the logarithm of the number 7 be required it may be found 

 from that of 28. Here 2'' x 3 =: 24 = at — 2, "5^' = 25 =x — i, 



31' = zy = X + I, and 2'* ><■ "] — 2S = x + 2. Andj'= — i + 



I = 8749. If we ufe the two firfl terms of the feries as it was 

 firll laid down, we may find the logarithm to 19 places of decimals. 

 But if we ufe the two firft terms of the contraded feries, which 

 may be done with only the additional trouble arifing from dimi- 

 nifhing the fecond divifion by i, 8, we may get the logarithm 

 true to 28 places. 



I T is raanifeft that the logarithm of fome number muft be 

 found by the immediate application of the feries. If then Na- 

 pier's logarithm of li be found by this method, we thence obtain 



the logarithm of — -. The logarithm of being found in 



I 2 C 



the fame manner, and added to that of — r^, gives Napier's lo- 



64 



garithm of 2. If the logarithms be required of Briggs's form, 

 having found Napier's logarithm of 8, from his logarithm of 2, 

 by adding the logarithm of i^ as already found, we get Napier's 

 logarithm of 10 ; the reciprocal of which will be the modulus of 



3 H 2 Briggs's 



