Invtffion of the SltJer on Guiiteri Rii'f, 45 ^ 



fold. By the fame prejudice, probably, any new method of working by the old rule, thoush 

 iTiore expeditious and equally accurate, would be rejedled in praftice if fuch method were 

 offered to the public. But, be this as it may, I think the confideration that the probability 

 is but fmall of any particular improvement being generally adopted in practice, is not a 

 fuflicient reafon why that improvement fliould be withheld from the public eye, whilfl 

 it is confidered as fuch. There are always individuals whofe minds are unfettered by 

 prejudice*, and to whom any hinc tending to produce an improvement always proves 

 acceptable. 



The logarithmic line of numbers, known by the name of Gunter's line, is fo well un- 

 derftood by every one who is acquainted with the properties of logarithms, as to render any 

 obfervation on the conftrudlion of it unneceilary. The ufc of two fuch lines, ufually de- 

 nominated A and B, working together by means of a diredt Aider, fuperfedes the appli- 

 cation of compafles, and is taught in moft pradlical books of arithmetic. 



There is however another, and I think more commodious method of applying thf. 

 flider, than the one generally praftifed (except in working dire£t proportions), which I have 

 not feen explained, nor praftifed by any perfon j and which, therefore, I Ifiall beg the 

 favour of you to communicate to the public through the medium of your inte'relling 

 Journal, provided you deem it of fufficient iml^ortance. The method I have to communi- 

 cate lays no claim to fuperior accuracy when compared to the common method, the powers 

 of the inftrument being the fame in both ; but, befides novelty, I trull it will be found to 

 have facility to recommend it. 



The method is fimply this : Invert the flider B on any common Aiding rule, whereby 

 the numerical figures will afcend on it, and on the fixed line A, in contrary direclions : 

 now, as the diftance from unity to any multiplier, on Gunter's line, will invariably extend 

 from any multiplicand to their produ£t, it follows, that if any particular number on the in- 

 verted flider B be placed oppofite to any other given number on A, the product of thofc 

 numbers will (land on the flider B, againft unity on A ; for, in any pofition of the inverted 

 Aider, the diftance from unity to the multiplier on A, inftead of being carried forward on 

 B, as when the Aider is in a direft pofition, is brought back thereby to unity again ; fo that 

 nnity (or ten on fingle lines where the Aider is too fhort for the operation) is invariably the 

 index for the product of any two coincident numbers throughout the lines. 



In divifion, by the fame proccfs, if the dividend on B be put to the index, or unity on A, 

 the divifion and quotient will coincide on the two oppofite lines ; fo that when one is given, 

 and fought for on either line, the other is feen on its oppofite line at the fame time, 



* This prtjudicc is the effcft of habit, anJ can feldom be craJicatcd from the minds of Aich individuals as 

 confidcr the ready occurrence of a propofition as a tcft of its truth. To eft.ibli(h a new philofophical theory ha«, 

 in every inAance, required time fufficient to educate an entire generation of men. The rejeflion of the Aii- 

 floielian philofophy, the adoption of experimental refearch, the fubftitution of the doftrine of gravitation in- 

 ficad of that of vortices, and the rcjcfVion of phlo^illon by our contemporaries, are fufficientlv illuflrativc of 

 «hit alTertion. New pra£\ices are dill more difficult to be introduced. The new grammar, the new nidimcnrs 

 •f fcicnce, or the new inftrument, however fuperior to the old in fimplicity, facility, and inuh, mult be lef', 

 valuable to the ordinary teacher or artifan, whofe memory is familiarized with the precepts of the latter, and 

 VihuCc only ambiiisn ii to earn bis fubfUlence with the lead pollible exciiiun. N. 



3 M 2 . The 



