NOVEMBEB 11, 1910] 



SCIENCE 



667 



subject. In consequence it appeals also to 

 those interested in the history of mathematics. 



A brief resume of the conclusions reached 

 is in place, especially because of the fact that 

 the most important result of Professor Ca- 

 jori's investigation appears in the addenda, 

 having no mention either in the preface 

 (which in every well ordered book should be 

 written after all the addenda are completed), 

 nor in the index. 



In 1620, only six years after the publication 

 of Napier's " Mirifici logarithmorum canonis 

 descriptio," Edmund Gunter, who was pro- 

 fessor of astronomy in Gresham College, Lon- 

 don, designed a logarithmic scale of numbers, 

 in which the numbers 1, 2, 3, . . . 10 (not 

 " digits," however, as Cajori has it), are 

 placed upon it in such a way that the ratio of 

 the distance from the point 1 to the point 2 

 to the distance from point 1 to any other 

 point equals the ratio of the logarithm of 2 

 to the logarithm of the number of the other 

 point, i. e., distances are taken proportional 

 to the logarithms of the corresponding num- 

 bers. Compasses were used to take off dis- 

 tances, thus serving the purpose of the slide. 

 The writer who did most in spreading infor- 

 mation about Gunter's " logarithmic line of 

 numbers '' was an English lavTyer Edmund 

 Wingate, 1593-1656, to whom the invention 

 of the slide rule has frequently been errone- 

 ously attributed, as occurs indeed in the text 

 of the work under discussion. 



Some time before 1630 William Oughtred, 

 a preacher known as the inventor of the sym- 

 bol X for multiplication and the proportion 

 symbol : : , devised two rules to be applied to 

 each other, obviating the necessity of the com- 

 passes. Oughtred further placed such log- 

 arithmic lines upon concentric circles, one 

 circle being movable. In place of the slider 

 a pair of pointing radii were used. Oughtred 

 explained his invention in 1630 to his pupil 

 William Forster, who in 1632 made it public 

 in a book entitled " The Circles of Proportion 

 and the Horizantall Instrument." In 1633 

 Forster published an addition with an ap- 

 pendix, " The Declaration of the Two Eulers 

 for Calculation." The sliding feature seems 

 to have been effected in 1657 by the surveyor 



Seth Partridge, although not explained in 

 print until 1672. The iirst runner was con- 

 structed by John Robertson (1712-76), a 

 teacher of mathematics. Robertson's work 

 was published two years after his death by 

 one William Mountaine. 



Of recent improvements noteworthy is the 

 fact brought here to the attention of Ameri- 

 can readers that the Mannheim type of slide 

 rule, now in use in America, is being sup- 

 planted in Prance by the regie des ecoles, a 

 slide rule with somewhat simpler arrangement 

 of the scales affording greater accuracy. 



Porster's account of his conversation with 

 Oughtred is worth repeating. He says: 



I wondered that he could so many yeares con- 

 eeale such useful inventions, not onely from the 

 world, but from my selfe, to whom in others parts 

 and mysteries of Art he had bin so liberall. He 

 answered. That the true way of Art is not by 

 Instruments, but by Demonstration: and that it 

 is a preposterous course of vulgar Teachers, to 

 begin with Instruments and not with the Sciences, 

 and so instead of Artists to make their Sehollers 

 only doers of tricks, and as it were Juglers: to 

 the despite of Art, losse of precious time, and 

 betraying of willing and industrious wits unto 

 ignorance, and idlenesse. 



Newton's employment of logarithmic scales 

 for the solution of cubic and biquadric equa- 

 tions is of interest. Professor Cajori ascribes 

 to Newton the first suggestion of a " runner " 

 because Newton's explanation requires that 

 straight lines be drawn across two scales. 

 Oughtred's sliding radii would seem to have 

 a better claim. 



The statement is made (p. 45) that the au- 

 thor has failed to find any references to 

 Sauveur, Camus and Clairaut in French 

 works of the eighteenth century. Bion's 

 " Traite de la Construction et des principaux 

 Usages des Instruments " refers to Sauveur 

 as the inventor of a logarithmic gauge, ex- 

 plaining the instrument and giving a cut of 

 it. Further the author remarks (p. 46) that, 

 " so far as we have observed, the early Eng- 

 lish designers of slide rules (Wingate, Ough- 

 tred, Partridge, Coggeshall, Everard) are 

 never mentioned by continental writers of the 

 eighteenth century." But Montucla ("Histoire 

 de Mathematique," Paris, 1799) mentions 



