45887. 9400I &c. 

 42603. =/'\ 



[ 419 ] 

 Ip. 'And, ,18861. 16970. 11613. 92922. 



Let it be required to find Briggs's logarithm of 101. 



First, by Dr. Halley's method, or by the application of produdls 



of two dimenfions. 



X— I 



100 



T*:^=i 



X X ■\- \ Log. ratio of*— i. x-\-\'': x=i£--\- 



y 



^^^ ^°^ &c. which is to be added to the loga- 



X— I. x + i = 10200 rithm of the antecedent, to find that 

 2.*^T. ^T+i+l =20401=/ °f ^^^ confequent the ratio of ;< — i. 



X + 1 : «•', being one of lefler inequa- 

 lity. 

 20401) ,43429.44819.03251. 82765. 1 1289 (,00002. 12879. 01666. . 

 (74436. 68276 &c. =^ 



>e—\ = 100 Log. 2, 



a; + I = 102 2, 00860 01717 6ir)Tj 56104 89366 92 



a; — I . .V + 1 



X I. X "t" I'' 



Ratio of, «■ — I. ;<• -j- 11" : * 



4, 00860 01717 619 17 56104 89366 92 



2,00430 00858 80958 78052 446S3 46 



2 12879 01666 74436 6S276 62 true to the 14th 



decimal place. 



X = lOI Log. 2, 00432 13737 82625 52489 12960 08 fue to the I4tli 



place. 



5 G 2 



Secondly 



