ON MATHEMATICAL TABLES. 73 



him to Briggs, was privately printed in 1839, under the title " De Arte 

 Logistica Joannis Naperi Merchistonii Baronis libri qui'supcrsuut," edited by 

 Mr. Mark Napier. An historical sketch, mainly derived from the same 

 author's ' Memoirs,' is prefixed. In 1787 was also published ' An account 

 of the Life, Writings, and Inventions of John Napier of Merchiston,' by 

 David Stewart, Earl of Buchan, and Walter Minto, LL.D. Perth, 4to. See 

 also Phil. Mag. Suppl. No., December, 1872, " On some early Logarithmic 

 Tables." Leslie (' Philosophy of Arithmetic,' 2nd edit., 1820, p. 24(3) 

 describes Napier's work as " a very small duodecimo ;" the last word should 

 be " quarto." The page is 7*7 inches by 5*7 inches. 



We may remark that Napier's name is spelt in a variety of Avays ; we 



have seen Neper, Naper, Nepair, and Nepper. He always Latinized his 



name into Neperus or Naperus, but spelt it in the vernacular several ways. 



' The family now write the name Napier; and this spelling is generally 



adopted, and with good reason. 



Napier, 1619 (' Constructio '). This work contains no table, and is there- 

 fore not properly included in this Report. We have, however, noticed it on 

 account of its being a sequel to the ' Descriptio,' and also on account of its 

 rarity (the fuU title is given in § 5). The only copy we have seen (in the 

 Cambridge University Library), which belonged to Oughtred, contains two 

 titlepages, the first running " Mirifici logarithmorum canonis descriptio. . . . 

 accesserunt opera posthuma ; primo, Mirifici ipsius canonis constructio .... 

 Edinburgi. . . . 1619," and the second being as given in § 5. From this we 

 infer that a reprint of the ' Descriptio ' (1619) was prefixed to the 

 ' Constructio,' but that it was torn out from the copy we have examined. 



On the reprints, &c. of the ' Constructio,' see under Napier, 1614. 



Ursinus, 1624—1625. A canon exactly similar to Napier's in the 

 ' Canon Mirificus,' 1614, only much enlarged. The intervals of the argu- 

 ments are 10" ; and the results are given to eight places : in Napier's canon 

 the intervals are 1', and the number of places is 7. The logarithms are strictly 

 Najplerian, and the arrangement is identical with that in the canon of 1614. 

 This is the largest Napierian canon that has been calculated. The copy we 

 have seen is in the British Museum. In 1618 Ursinus published his 

 * Cursus Mathematicus,' of which there is a copy in the Cambridge Uni- 

 versity Library. 



The only table of Napierian logarithms described in § 4 is Schulze, 1778 

 [T. v.] (sines and tangents). 



Art. 18. Logistic and Proportional Logarithms. 



What arc now called fractions or ratios used to be styled logistic numbers ; 



and logistic logarithms are logarithms of ratios : thus a table of log -, x 



[ being the argument and o a constant, would be called a table of logistic or 



proportional logarithms ; and since log - = log o — log x, it is clear that the 



tabular results only differ from those of an ordinary table of logarithms by the 

 subtraction of a constant and a change of sign. It appears that Kepler, in 

 his ' Chilias ' described below, originated tables of this kind ; but the step that 

 separates logistic from common logarithms is so small that no great interest 



attaches to their first appearance. The use of the tabulation of log - in the 



working of proportions in which the third term is a fixed quantity a is evident. 



