Logarithms. 215 



Equation f 2J is seen to. express the important truth that the 

 €0}nmon logarithm of any munber can be obtained by multiplyiuiy 

 the N^aperian logarithm of that munbei' by the modulus of the com- 

 mon system. 



36. Computation of Common Logarithms. We can now 

 compute the common logarithms of numbers. We merely need to 

 multipl}' each of the Naperian logarithms already found by the 

 modulus ,43429448 . . In this manner we find 



log 2=0.3010300 

 log 3 = 0.4771213 

 log 4=0.6020600 

 log 5 = 0.6989700 

 etc. etc. 



How can you find- log 6 ? 



37. HistoeicaIj Note. Thf; invention of logarithms is regarded as one 

 of tlie greatest discoveries in mathematical science. The honor of the inven- 

 tion as well as of the construction of the flrst logarithmic table belongs to a 

 Scotchman, John Napier (1550-1617), baron of Merchiston. His first work, 

 Mirifici logarithmorum canonis descriptio, appeared in 1614 and contained an 

 ■account of the nature of logarithms (from his standpoint) and a table of Ucitural 

 sines and their logarithms to seven or eight figures.\But Napier's logarithms 

 were not the same as those now called Naperian logarithms. The base of his 

 system was not e, although closely related to it. 



Henry Briggs, professor of geometry at Gresham College, London, was much 

 interested in Napier's invention and in Kil.") visited Napier and suggested to him 

 the advantages of a system of logarithms in which the logarithm of 1 should 

 be and the logarithm of 10 should be 1. Napier, having already thought of 

 the change, gave Briggs every encouragement to compute a system of the 

 new logarithms and made many important suggestions, among which was that 

 of keeping the mantissas of all logarithms positive by using negative char- 

 acteristics. In 1617 Briggs published the common logaiithms of the first 1000 

 numbers, the book being called Logarithmornm chilias priini. Briggs con- 

 tinued to labor at the calculation of logarithms, and in 1621 published his 

 ArHhmetica Logarithmica, which contaiiKvl the logarithms of the numbers 

 from 1 to 20000 and from 90000 to 100000 to 14 places of decimals. This gap 

 between 20000 and 90000 was filled up by Adrian Ylacq, who published in 1628 

 the logarithms of the numbers from 1 to 100000 to ten places. Vlacq's table 

 is the source from which nearly all the tables have been derived which havo 

 subsequently been published. 



